Delfini Ilaria: Dynamic 3D modelling of the unconfined aquifer of the river Marecchia alluvial fan (

ALMAMATERSTUDIORUM UNIVERSITÀDIBOLOGNA

DIPARTIMENTODIINGEGNERIACIVILE,CHIMICA, AMBIENTALEEDEIMATERIALI

Secondcycledegreein CIVILENGINEERING

Degreedissertationin SUSTAINABLEDESIGNOFWATERRESOURCESSYSTEMS

DYNAMIC3DMODELLINGOFTHE UNCONFINEDAQUIFEROFTHERIVER MARECCHIAALLUVIALFAN(RIMINI)

CANDIDATE:

IlariaDelfini

Serialnumber:907090

SUPERVISOR: Chiar.moProf.AlbertoMontanari

CO-SUPERVISOR: Ing.AndreaChahoud

AcademicYear2019/2020 IIIsession

Figures

Figure 1.1. Graphical distribution of the locations of water on Earth. (By USGShttps://water.usgs.gov/edu/gallery/watercyclekids/earth-water-distribution.html - traced and redrawn from File:Earth's water distribution.gif, Public Domain, https://commons.wikimedia.org/w/index.php?curid=10396859)........................................14

Figure 1.2. Geographical location of the River Marecchia (Di OrsOrazio - based upon Image:Map of Italy (w.o. Labels).jpg, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=1528309)..........................................19

Figure 1.3. Marecchia River Alluvial fan and its different areas (Severi, Bonzi, & Ferrari, Managed aquifer recharge in the Marecchia alluvial fan (Rimini, Italy): trial and early results,2016)........................................................................................................................21

Figure 1.4. Longitudinal geological section of the River Marecchia fan with aquifers scheme and site of the Incal System recharge lake (blue rectangle). Indication of the different areas: intramountain plain (black dashed area), amalgamated fan (red dashed area), multilayer fan (downstream) and phreatic plain aquifer (green dashed area) (from ServizioGeologicod’Italia–RegioneEmilia-Romagna2005,modified)..........................22

Figure 1.5. Infiltration pond scheme. The aquifer level is typical of summer conditions (Casini,Severi,Bonzi,&Pellegrino,2018)........................................................................23

Figure 1.6. Monitoring network to verify the managed aquifer recharge efficacy (Severi, Bonzi, & Ferrari, Managed aquifer recharge in the Marecchia alluvial fan (Rimini, Italy): trialandearlyresults,2016).................................................................................................24

Figure 2.1. 3D discretization of the domain.

(https://pubs.usgs.gov/tm/2005/tm6A16/PDF/TM6A16.pdf)..............................................32

Figure 2.2. Discretized aquifer showing boundaries and cell designation.

(https://pubs.usgs.gov/tm/2005/tm6A16/PDF/TM6A16.pdf)..............................................38

Figure 2.3. Flowchart of program to simulate GWF.

(https://pubs.usgs.gov/tm/2005/tm6A16/PDF/TM6A16.pdf)..............................................40

Figure2.4. Situationrequiringacorrectiontolimit thedrawdown flowintocell(i,j,k+1) as a result of partial saturationof a cell.

(https://pubs.usgs.gov/tm/2005/tm6A16/PDF/TM6A16.pdf)..............................................47

Figure 2.5. Plot of flow from a general-head boundary source into a cell. (https://pubs.usgs.gov/tm/2005/tm6A16/PDF/TM6A16.pdf)..............................................54

Figure 2.6. Plot of flow into a drain as a function of head. (https://pubs.usgs.gov/tm/2005/tm6A16/PDF/TM6A16.pdf)..............................................59

Figure 2.7. Plot of volumetric evapotranspiration as a function of head. (https://pubs.usgs.gov/tm/2005/tm6A16/PDF/TM6A16.pdf)..............................................59

Figure3.1.GeoReferencedialogbox.................................................................................64

Figure3.2.CoordinatesandelevationsofsomepointsdefiningtheModelTop................65

Figure3.3.ImportPointsdialogboxtodefineModelTop.................................................65

Figure3.4.Gridandlayerdefinition...................................................................................66

Figure3.5.Activedomain...................................................................................................67

Figure3.6.DistributionofKx valuesoverthetoplayer......................................................68

Figure3.7.StartingHeadvalues..........................................................................................69

Figure3.8.Distributionofspecificstorageoverthetoplayer............................................70

Figure3.9.Distributionofspecificstorageoverthetoplayer............................................71

Figure3.10.MODFLOWTimesettingsforthefirststressperiods....................................74

Figure3.11.Pointobjectsrepresentingthepumpingwells.................................................76

Figure3.12.Rechargezones................................................................................................78

Figure3.13.RepresentationofIncalSystemrechargelakeinthemodel............................79

Figure3.14.MapsofnodesandarchesfortheRiverMarecchia.(Arpae)..........................82

Figure3.15.Crosssectionofthearchrepresentedinthemodel.(Arpae)...........................83

Figure3.16.ModelrepresentationofMarecchiariver........................................................84

Figure3.17.Pointsdefiningthegeneral-headboundaryconditions...................................85

Figure3.18.Pointobjectsrepresentingtheobservationwells.............................................86

Figure 4.1. Comparison between observed head values (X axis) and simulated ones (Y axis)......................................................................................................................................93

Figure 4.2. Distribution of the differences between observed head values and simulated results,asafunctionoftheobservedinputdata..................................................................93

Figure 4.3. Cumulative contributions added to the aquiferby each element interacting with it...........................................................................................................................................94

Figure 4.4. Inflow rates at each stress period given by the terms contributing to the aquifer waterbalance.......................................................................................................................94

Figure4.5.Cumulativecontributionsremovedfromtheaquiferbyeachelementinteracting withit...................................................................................................................................95

Figure 4.6. Outflow rates at each stress period given by the terms contributing to the aquiferwaterbalance...........................................................................................................95

Figure 4.7. Comparison between inflow and outflow rates caused by Head dep bounds termateachstressperiod.....................................................................................................96

Figure4.8.TotalINandOUTcumulativecontributiontotheaquiferwaterbalance.........96

Figure 4.9. Total inflow and outflow rates contributing to theaquiferwater balance at each stressperiod.........................................................................................................................97

Figure 4.10. Trend over time of the difference between volumes entering and exiting the aquifer..................................................................................................................................98

Figure 4.11. Comparison between the trends of IN-OUT difference,in terms of cumulative volumesandflowrates........................................................................................................98

Figure4.12.Discrepancytrendasafunctionoftime..........................................................99

Figure 4.13. Trend over time of the head values simulated at the upstream (17, 44, 4) and downstream (48, 15, 4) sections of the river. The coordinates represent the model cells containingthecorrespondingsectionofinterest.................................................................99

Figure 4.14. Comparison among head values at upstream and downstream sections, the difference between the two, and inflows in the aquifer due to river leakage (these multipliedby5)..................................................................................................................100

Figure 4.15. Total IN and OUT cumulative contributions of the lake to the aquifer water balance...............................................................................................................................101

Figure 4.16. Total inflow and outflow rates relative to the lake contributing to the aquifer waterbalance.....................................................................................................................101

Figure 4.17. Comparison between IN and OUT flow rates defining the lake water balance at each stress period, and the input injection rates. All the curves are represented as positivecontribution,eventhoughtheyassume differentsigns accordingto thedirectionof theflow(positivefromthelaketotheaquifer,negativefromtheaquiferto thelake).....102

Figure4.18.Variationofwatervolumeinthelakeoverthesimulationperiod................102

Figure 5.1. Variation of the cumulative IN volumes of the lake contribution to the aquifer waterbalance,expressedasafunctionoftimefordifferentvaluesofinitialwaterstage.104

Figure 5.2. Variation of the cumulative OUT volumes of the lake contribution to the aquifer water balance, expressed as a function of time for different values of initial water stage...................................................................................................................................104

Figure 5.3. Variation of the cumulative difference between of IN and OUT volumes of the lake contribution to the aquifer water balance, expressed as a function of time for different valuesofinitialwaterstage................................................................................................105

Introduction

Water is an essential resource for drinking, sanitation, food production and, in general, for the setting up of a robust, resilient societal and economic system. For example, the COVID-19 pandemic put a spotlight on the need for clean water for hygienc-sanitary reasons,exacerbatingtheimpactsofwaterinequalitiesworldwide.

Water distribution on Earth indicates that there is much more freshwater stored in the ground than there is in liquid form on the surface. Moreover, groundwater bodies usually underly extended areas and are less susceptible to annual and seasonal variability, making distribution and regulation systems easier to design and run over time. These elements makegroundwateranextremelyimportantresource.

For this reason, an exhaustive and certain knowledge about groundwater bodies would be crucial. If on the one hand monitoring is an essential tool to reach this purpose, on the other hand it is more challenging, since information about flow and transport of groundwaterissparse,andonlyavailableatwells.

Groundwater models are computer representations of underground flow systems, used to predict and simulate aquifer conditions in order to facilitate planning and management of water resources. Computations are based on groundwater flow equation, which can often besolvedonlybynumericalcodesapplyingapproximatenumericalmethods.

Around 2001, Arpae Emilia-Romagna and Regione Emilia-Romagna started a specific developmentand implementationplanforgroundwatermathematical modelling,appliedto different contexts with the purpose of ordinary and emergency management of the groundwater resources. In particular, Regione Emilia-Romagna established a technical committee to face water crises, which are particularly significant for the Romagna area: here, in fact, during the summer period the significant population growth results in a sharp increment in water demand, coupled with particularly hot and dry summers intensified by climatic changes. This situation involves problems of water supply caused mainly by superficial scarcity. For this reason, in dry periods aquifers represent the most valuable resourcetofacethewatershortage.

In this context, the committee, coordinated by the Civil Protection and constituted by relevanttechnicalbodies, inJanuary2014approvedamanagedrechargeexperimentonthe alluvial fan of the River Marecchia, which plays a strategic role in the drinking-water

supply for the whole area of Rimini. This intervention consists mainly in the injection in the fan aquifer of an additional volume, taken from the River Marecchia (the same that would feed theaquiferin natural conditions) and injected into a quarry lake, according to a technique termed as infiltration pond. Water recharges the aquifer taking advantage of the infiltration characteristics of the sides and the bottom of the lake itself. Therefore, an increment in the water volume in the lake should be translated in an increment in the piezometriclevelintheaquifer.Thiswouldimplyalargeravailabilityofgroundwater.

In 2017, by the Decision of Regional Government (Deliberazione di Giunta Regionale –DGR) ofEnvironmental Impact Assessment (VIA),the recharge projectwas approved: the water withdrawal should be 1�� /��, active in no-irrigation period (October – April) with respect for environmental flow. Among the requirements of this document, there is the implementation, by Arpae, of a mathematical flow and transport model for groundwater; the objective is the quantification of the recharge efficiency on the alluvial fan, in particulareffectsonthegroundwaterflowdynamicsanditsstorageinthesystem.

Between 2007 and 2018, a groundwater flow model representing the whole alluvial fan of theRiverMarecchiawascreatedandcalibrated,thankstotheavailabilityofmanydifferent information (geological reconstruction, piezometric and chemical data, aqueduct withdrawals,hydrodynamicparameters,hydraulicandhydrogeologicdata).

In general, extremely complex hydrological situations can affect the efficiency of a managed recharge intervention. In the specific case of Marecchia, the interaction among aquifer, lake and river can play a major role. Due to this, and to better evaluate the efficiency of the managed recharge plant, since 2016 a new detail groundwater flow and transport model has been implemented using the software MODFLOW, starting from the one simulating the whole Marecchia fan thanks to the appropriate scale variations, detail verificationsandrelativetechnologicaladaptations.

Thepurposeofthisworkistosimulatetheoutcomefrom theartificialrechargeexperiment carried out in 2014-2015, reproducing the groundwater model of the River Marecchia alluvial fanby using adifferent model interface and advanced computationaland graphical methods.

The thesis is structured according the following scheme: in the first chapter, an overview ofgroundwaterandgroundwatermodelsis provided,aswellasareportaboutthemanaged recharge project of the River Marecchia alluvial fan; the second chapter consists of a

description of the main characteristics and the operation of the software MODFLOW and the interface ModelMuse; in the third chapter the implementation of the model in ModelMuse is described; the main results in terms of water balance are presented in the fourth chapter; in Chapter 5, some additional simulations are carried out in order to evaluate the effect of the variation of some initial parameters on the lake water budget; conclusionsaredrawninChapter6.

The material necessary to implement the model is part of the database supporting the artificial recharge project and particularly aimed at the development of the mathematical model representing the recharge system, commissioned to Arpae. Such database is shared between Regione Emilia-Romagna and Arpae, that are members of the “Comitato di attuazione e monitoraggio per la realizzazione di un impianto di ricarica in condizioni controllate nella conoide alluvionale del fiume Marecchia”, instituted by means of “DeterminazionedelDirettoreGeneraleCuradelTerritorioedAmbientedellaRER”.

1. Groundwatermodels

1.1Groundwater

The importance of water for life and therefore human society is vital in several different fields: everyday life, agriculture and industry are only some examples that demonstrate the urgency of water to achieve good living conditions. The distribution of water in space and time is extremely important to secure this resource to human population, but the fluxes among water volumes stored in the Earth’s crust and the atmosphere are even more important. Figure 1.1 provides a rough quantitative distribution of water storages (flows arenotconsidered)onEarth:

Figure 1.1.

of the

of water on Earth. (By USGShttps://water.usgs.gov/edu/gallery/watercyclekids/earth-water-distribution.html - traced and redrawn from File:Earth's water distribution.gif, Public Domain, https://commons.wikimedia.org/w/index.php?curid=10396859)

Most of water in Earth’s atmosphere and crust (more than 97%) comes from the World Ocean’s saline seawater whereas only 2.5% is freshwater, which is what life needs to survive. Considering the latter only, it is almost completely locked up in ice and in the ground. Only 1.2% of all freshwater is in surface bodies, such as lakes and rivers, which serves most of life’s needs. Most of surface water is locked up in ice (69%), and another 21% of it is in lakes. Almost 0.50% of surface freshwater is in rivers: even though it seemsatinyamount,riversareactuallythemostimportantwatersourceforhumans.

Graphical distribution

locations

From these statistics, it is evident that there is much more freshwater stored in the ground than there is in liquid form on the surface. Moreover, rainfall continually seeps into the ground to recharge aquifers, while at the same time the volumes stored in the ground continually recharge rivers through seepage. All these elements make groundwater an extremelyimportantresource.

Theuseofgroundwaterwithrespecttosurfacewatertosupplythedemandischaracterized bysomeadvantagesandsomedisadvantages:

 groundwater bodies usually underly extended areas, so the need for distribution systemsislower;

 considering annual and seasonal variability of water amounts, fluctuations are usually smallerthanthoseofsurfacebodies,andregulationisingenerallessexpensive;

 the operating costs are higher, since there is a considerable expenditure of energy to liftwaterfromtheground;

 considering quality issues, groundwater is less susceptible to pollution; however, if pollutionoccurs,restorationcanbemuchslower;

 the pumping of groundwater can lead to some problems, such as land subsidence or saltwaterintrusion;

 the use of groundwater is not characterized by an economy of scale1, and a staged and gradualdevelopmentiseasiertoperform;

 information about flow and transport of groundwater is sparse, and only available at wells.

In order to assess the characteristics of any water body, monitoring is an essential tool. As highlighted by the last point of the list, collecting data about groundwater is complicated: for this reason, monitoring is more challenging, and an exhaustive and certain knowledge aboutgroundwaterbodiesishardlyachievable.

1 In microeconomics, economies of scale are the cost advantages that enterprises obtain due to their scale of operation (typically measured by the amount of output produced), with cost per unit of output decreasing withincreasingscale.

1.2Groundwatermodels

Groundwater models are computer representations of underground flow systems, used to predict and simulate aquifer conditions. Several different variants exist, but the physical principles are the conservation of mass and momentum, the same as for surface models. These can be also coupled with chemical and/or ecological models to describe water quality,thereforeallowingtodesignconservationandremediationstrategies.

This kind ofmodels isbased on the application ofthe groundwaterflow equation, which is the mathematical relationship describing the water movement through an aquifer. The transient flow of groundwater is described by a form of diffusion equation, similar to that used in heat transfer to describe the flow of heat in a solid (heat conduction). A distinguishing behaviour of groundwater flow is its reduced velocity, which makes the assumptionofsteadystateflowareasonableworkinghypothesis.Insteady stateconditions groundwater flow is described by Laplace equation (a second order partial differential equation),whichisaformofpotentialequationandhasanalogsinnumerousfields. As computations in mathematical models are based on groundwater flow equation, which canoftenbe solvedonly byapproximate methods usinganumerical analysis,thesemodels are called mathematical, numerical or computational groundwater models. The mathematical equations, based on the real physics the groundwater flow follows, are solved using numerical codes such as MODFLOW, ParFlow2, HydroGeoSphere3 , OpenGeoSys4, etc, adopting various types of numerical solutions (like the finite difference methodandthefiniteelementsmethod).

Theapplicabilityofa groundwatermodelto arealsituationdependson the accuracyof the input data and the parameters. The determination of these values requires a considerable study,likecollectionofhydrological data(rainfall,evapotranspiration,irrigation,drainage) andestimationoftheparameterscharacterizingthegroundwaterbody.

2 ParFlow is an open-source numerical model that simulates the hydrologic cycle from thebedrock to the top of the plant canopy. It integrates 3D groundwater flow with overland flow and plant processes using physically-basedequations.

3 HydroGeoSphere (HGS) is a 3D control-volume finite element simulator, designed to simulate the entire terrestrialportionof thehydrologic cycle. Itusesa globally-implicit approach to simultaneously solvethe2D diffusive-waveequationandthe3DformofRichard’sequation.

4 OpenGeoSys (OGS) is a scientific open source project for the development of numerical methods for simulationofthermo-hydro-mechanical-chemical(THMC)processesinporousandfracturedmedia.

This need for information may represent a problem since, as already mentioned, gathering information about the aquifer considered is not an easy task. Thus, the use of groundwater models for the planning and the management of water resources is the possible goal of a longandcomplexcourseofresearchandstudy.

In order to avoid a model to be an end in itself, the development process should always be opened by means of the updating and the verification of the effects of new knowledge and data.

The setting up and the following processes to be applied on a groundwater model are dividedintotwomainphases:

 Model development: it includes the construction and the calibration of the model; here the geometry and the structure of the system, the temporal and spatial discretization,theparametrizationandtheboundaryconditionsaredefined;

 Model management: it consists of data update, adjustments (Update/Verification phase) and, above all, execution of simulations and forecasts (Utilization); the updateconcerns thetime-dependent variables (boundaryhydraulic head, drains and recharges), whereas the acquisition of new time series of the hydraulic head (by meansofmonitoring)allowstocalibratethemodeltoimproveitsperformance.

In this field, the international framework provides the example oftheUSGS (UnitedStates Geological Survey), but also valid examples at European level, such as French and Danish geological services. The national scene proposes some cases limited to local realities, wheretheprocessislaunchedoratleastsetupinitsinitialphases.

Arpae Emilia-Romagna and Regione Emilia-Romagna started (the latter within the program ofits waterresources planning and management activity),around 2001, aspecific development and implementation plan for groundwater mathematical modelling, still ongoing and constantly evolving (Chahoud, et al., 2013). In particular, in Regione EmiliaRomagnathegroundwaterresourcesplanningandmanagementactivitiesarecarriedout,in consistency with the guidelines of the European Union and of the more recent Italian legislation, by the Servizio Tutela e Risanamento Acqua, Aria e Agenti fisici: it supports the regional government action about the water resources, in order to guarantee goodquality availability of it, for a sustainable future. In this context, groundwater modelling representsavalidinstrumenttobeusedatbothregionalandlocalscale.

In the last ten years, Arpae Emilia-Romagna created different flow models supporting competent authorities; they had both a planning and an ordinary or emergency managementaimconsideringthegroundwaterresources. Inparticular,two differentspatial scaleswereconsidered:

 The scale of the whole regional aquifer, applied for the Emilia-Romagna water resources protection plan (Piano di Tutela delle Acque della Regione EmiliaRomagna), on the basis of the conceptual model defined on that occasion. The first versionwasfollowedbysubsequentandrepeatedupgrades,thelatestonein2009;

 The detail scale (generally considering the individual alluvial fan), applied in situations deemed strategic for the local needs to exploit the resource, and where thenecessityemergedtodisposeofadequatesupporttools.

Inparticular,thegroundwaterflowmodelsrealizedbyArpaeEmilia-Romagnaare:

- EmiroII–Regional

- FC-RAAquifers

- RenoAlluvialFan

- MarecchiaAlluvialFan

- EmiroII–CoastalZone

All of them have in common the 3-dimensional structure. This choice, adopted from the beginning, allowed a continue updating of lithological features following the evolution of sedimentologicalandhydrostratigraphicknowledge.

1.3ManagedaquiferrechargeintheMarecchiaalluvialfan(Rimini,Italy)

The Adriatic Coast of Regione Emilia-Romagna is one of the most important touristic areas in Italy; during the summer period, the significant population growth results in a sharp increment in water demand (Casini, Severi, Bonzi, & Pellegrino, 2018). Since about 2007, climatic changes led to a series of particularly hot and dry summers; this situation involved problems of water supply caused mainly by superficial scarcity. For this reason, indryperiodsaquifersrepresentthemostvaluableresourcetofacethewatershortage.

After concertation between the various stakeholders, in January 2014 a managed recharge experiment began on the alluvial fan of the River Marecchia (Figure 1.2), which plays a strategic role in the drinking-water supply for the whole area of Rimini. This intervention

consists mainly in the injection in the fan aquifer of an additional volume, taken from the RiverMarecchia (thesame thatwouldfeedtheaquiferinnaturalconditions)(Severi, etal., 2016).

Thisprojecthasseveralpurposes:

 increase the water storage in the fan, creating a potential resource to overcome dry periods;

 enrichthebiodiversityofthesite;

 improvegroundwaterqualitythankstothereleaseofhigh-qualityvolumes;

 counter the phenomenon of subsidence, which is the sudden sinking or gradual downward settling of the ground surface with little or no horizontal motion; it may becausedbynaturalprocessesorbyhumanactivities;

 reducesaltwaterintrusion5 incoastalaquifers.

5 Saltwater intrusion isthemovement of saline water intofreshwater aquifers, which canlead to groundwater quality degradation. Saltwater intrusion can naturally occur in coastal aquifers, due to the hydraulic connection between groundwater and seawater: since saltwater is denser than freshwater, the first one can push inland beneath the second one. Certain human activities (especially groundwater pumping from coastal wells, have increased saltwater intrusion in many coastal areas. Other contributors include navigation or agricultural channels, which provide conduits for saltwater to move inland, sealevel rise and some extreme events(likehurricanestormsurges).

Figure 1.2. Geographical location of the River Marecchia (Di OrsOrazio - based upon Image:Map of Italy (w.o. Labels).jpg, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=1528309)

The formal implementation of the project was defined by a specific procedure of Environmental Impact Assessment (Valutazione di Impatto Ambientale – VIA), successfullycompletedinOctober2017. Giventhepositiveoutcome oftheexperiment andthepublicinterestin theimplementation of the intervention, the managed aquifer recharge in the Marecchia alluvial fan was inserted as a specific measure counteracting climatic changes in District Management Plans (Piani di Gestione Distrettuale) following the guideline 2000/60/CE. Groundwater qualitative and quantitative monitoring, aimed at evaluating the effects of the managed rechargeonthealluvialfan,isundertakenbyboth theGeological, SeismicandSoilSurvey andArpaeEmilia-Romagna–TechnicalDirection.DataareavailableonArpaewebsite.

1.3.1 AquiferofthealluvialfanoftheRiverMarecchia

The River Marecchia is 70���� long and has a catchment basin of about 600���� ; its average annual flow at the entrance of the alluvial fan is estimated at about 6�� /�� (Severi,Bonzi,Ferrari,&Pellegrino,2014).

Analluvial fanis an accumulation of sediments shaped like a section of a shallow cone,with its apex at a point source of sediments. Alluvial fans typically form where flow emerges from a confined channel and is free to spread out and infiltrate the surface. This reduces the velocity of the flow and thus its carrying capacity, resulting in deposition of sediments.

The Marecchia alluvial fan develops at the end of a mountain basin and is divided, from a geologicalpointofview,intothreedifferentareas(Figure 1.3):

 an intramountain plain, with a thickness of not more than 10�� and formed mostly bygraveldepositsleaningdirectlyonthemarinesubstrate;

 an amalgamated fan, comprised of prevailing gravels, for a maximum thickness up to80��abovetheseaclays;

 a multilayer fan, formed by alternating gravelly levels and mainly fine levels, for a thickness up to 250�� and more, above the coastal marine deposits of the Imola Sands.

From the hydrogeological point of view, the intramountain plain corresponds to a phreatic aquifer, as well as the amalgamated fan, although there can be local confinement conditions inside it. The amalgamated portion corresponds to the area of maximum recharge of the entire fan, which is mainly due to effective infiltration of rainwater and dispersion from the River Marecchia. The multilayer fan is formed by a system of superimposed confined and semiconfined aquifers. Above them, in direct contact with the surface,thereisaphreaticaquiferabout10��thick,mainlymadeofsandysiltdeposits.

Figure 1.3. Marecchia River Alluvial fan and its different areas (Severi, Bonzi, & Ferrari, Managed aquifer recharge in the Marecchia alluvial fan (Rimini, Italy): trial and early results, 2016).

1.3.2 Managedrechargeofthealluvialfan

In the portion of the amalgamated fan, on the right bank of the Marecchia, there are three lakes, remaining from previous quarrying activities and whose water level corresponds to thephreaticwatertable. Theselakesare located inthemaximumrecharge area,so theyare hydraulically connected with theentirealluvial fan. Thepossibility ofusing these lakesfor arechargeinterventionwasalreadyconsideredbetweenthe1990s andtheearly 2000s,and more recently it was the subject of a further detailed study designed to assess the efficacy of a managed recharge operation through a mathematical flow model, implemented by ArpaeEmilia-Romagna(2008)(Severi,etal.,2016).

Figure 1.4. Longitudinal geological section of the River Marecchia fan with aquifers scheme and site of the Incal System recharge lake (blue rectangle). Indication of the different areas: intramountain plain (black dashed area), amalgamated fan (red dashed area), multilayer fan (downstream) and phreatic plain aquifer (green dashed area) (from Servizio Geologico d’Italia –Regione Emilia-Romagna 2005, modified).

The trial, taking into account previous studies, applies a technique defined as infiltration pond(Figure 1.5) (Casini,Severi,Bonzi,&Pellegrino,2018). Itinvolves theinjectionof a certain amount of waterto thequarrylake called Incal System, which hasan areaof 16ℎ�� and is owned by the municipality of Rimini, through the Mulini Channel (whose use is leasedtotheLandReclamationConsortiumofRomagna).Thechanneltakeswaterdirectly from the river at Ponte Verucchio, and runs parallel to it for about 9���� (Severi, et al., 2016). Along the way, the stream loses part of the sediments it contains, improving its quality also thanks to the vegetations on the sides and the floor of the channel. At the end ofMuliniChannel,water could bereinjectedintheRiverMarecchiaordivertedtothe lake by a specific sluice-gates system. When water reaches the lake, it can recharge the aquifer taking advantage of the infiltration characteristics of the sides and the bottom of the lake itself.

As already mentioned, the lake lies in the recharge area of the alluvial fan, where the aquiferisamalgamated andoutcropping.Undertheseconditions,anincrement inthewater volume in the lake should be translated in an increment in the piezometric level in the aquifer.Thiswouldimplyalargeravailabilityofgroundwater. During the two-years recharge experiment, 2˙500˙000�� of water were released in the Marecchia aquifer. The total volume wasdividedinto threedistinct rechargecyclescarried out in the no-irrigation period (form October to April) and with maximum discharge equal to1�� /��.

Thetotalwatervolumereleasedinthelakefrom2014to2018is5˙803˙000�� .

Figure 1.5. Infiltration pond scheme. The aquifer level is typical of summer conditions (Casini, Severi, Bonzi, & Pellegrino, 2018).

1.3.3 Monitoring

To verify the efficacy of the recharge operation, a special monitoring network (Figure 1.6) was implemented, made up of 20 measuring points, including 5 wells specifically drilled (Severi, Bonzi, & Ferrari, 2016). In 9 of these points a data logger was installed for the continuous monitoring ofthe level, temperature and specific electric conductivity at20°��. A data logger recording only the level was also positioned in the channel through which thewaterflowstothelake.

The water release from the channel to the lake began on 25th February 2014, after about a monthofmeasuringthewatertablelevelwithout recharge;theaim wasto betterassessthe expectedriseduetotheincrementinthelakevolumes.

2016).

The two-year test was approved by Regione Emilia-Romagna in agreement with Provincia di Rimini, Comune di Rimini, Consorzio di Bonifica della Romagna and Ente di Gestione dei Parchi e della Biodiversità della Romagna (Chahoud, 2019). Later, by the Decision of Regional Government (Deliberazione di Giunta Regionale – DGR) of Environmental

Figure 1.6. Monitoring network to verify the managed aquifer recharge efficacy (Severi, Bonzi, & Ferrari, Managed aquifer recharge in the Marecchia alluvial fan (Rimini, Italy): trial and early results,

Impact Assessment (VIA) n. 1649 of 30/10/2017 (in accordance with Dm 100/20166 and D.Lgs n. 152/2006, Article 104 paragraph 4bis7), the recharge project was approved: the water withdrawal should be 1�� /��, active in no-irrigation period (October – April) with respect for environmental flow (0.903�� /�� at Ponte Verucchio). The project is also part ofthePianodiGestionedelDistrettodell’AppenninoSettentrionale2015-2021.

1.3.4 EnvironmentalImpactAssessmentrequirements

ThemainrequirementslaiddownbytheVIAcanbesummarizedasfollows:

 to conclude an agreement protocol (Protocollo di Intesa) to define the coordination of the work and the roles of the many stakeholders: Regione Emilia-Romagna, Comune di Rimini, Ente di Gestione per i Parchi e la Biodiversità della Romagna, Arpae. At the expiry of the VIA (31/12/2021), the protocol could be extended, on thebasisalsooftheeffectivenessoftheactionsundertakentoreachthegoals;

 to ensure the proper functioning of hydraulic engineering in accordance with ConsorziodiBonificadellaRomagna;

 to carry out the qualitative and quantitative monitoring of surface and ground water,continuousoratagivenintervals,consideringseveralparameters;

 tocarryouttheperiodicvisualmonitoringofwaterlevelinthelake;

 to carry out a periodic monitoring of the species of animals and of the habitats of Communityinterest;

 thecreationofamathematicalflowandtransportmodelforgroundwater. Moreover,theresearchactivitiesshouldbepromptlyinterruptedif:

 sufferingoftheecosystemisdetected,duetothelakewaterlevel;

6 «Regolamento recante criteri per il rilascio dell'autorizzazione al ravvenamento o all'accrescimento artificiale dei corpi idrici sotterranei al fine del raggiungimento dell'obiettivo di qualità, ai sensi dell'articolo 104, comma4-bis, del decreto legislativo 3 aprile 2006, n. 152.» Regione Emilia-Romagna: Misura dei Piani diGestioneDistrettuali2015-2021

7 «….. l'autorità competente, al fine del raggiungimento dell'obiettivo di qualità dei corpi idrici sotterranei, può autorizzare il ravvenamento o l'accrescimento artificiale dei corpi sotterranei, nel rispetto dei criteri stabiliti con decreto del Ministero dell'ambiente e della tutela del territorio e del mare. …….. Tali misure sono riesaminate periodicamente e aggiornate quando occorre nell'ambito del Piano di tutela e del Piano di gestione»(commaintrodottodallaleggen.97del2013)

 early warning monitoring shows a significant qualitative depletion in the withdrawalwaterbody;

 the water body suffers a global chemical and ecological depletion downstream of thewaterwithdrawal.

1.3.5 Mathematicalmodel

Among the requirements mentioned in the previous paragraph, there is the setting up, by Arpae, of a mathematical flow and transport model for groundwater; the objective is the quantification of the recharge efficiency on the alluvial fan. In particular, it would be usefulintheevaluationofthemanagedrechargeeffectsonthegroundwaterflowdynamics anditsstorageinthesystem.

Between 2007 and 2018, it was possible to develop and calibrate a groundwater flow model representing the whole alluvial fan of the River Marecchia. Its construction was possiblethankstotheavailabilityofmanydifferentinformation,amongwhich:

 detailedgeologicalreconstructionoftheground;

 piezometric and chemical data about the regional network and the Marecchia fan network;

 dataaboutaqueductwithdrawals(directlyfromHera);

 hydrodynamicparameters(fromhistoricalanddedicatedtests);

 hydraulicandhydrogeologicdata,flowratetestsontheriverMarecchia. This model, constantly updated with monthly data, has been used in different contexts, such asresourcemanagement (also considering scenario simulations) and managed aquifer recharge.

In general, extremely complex hydrological situations can affect the efficiency of a managed recharge intervention. In the specific case of Marecchia, the interaction among aquifer,lakeandrivercanplayamajorrole.Itdependson:

1. thetrendofthewaterlevelintheriverovertime;

2. theseepagefromthebottomoftheriverbed;

3. the flow in the unsaturated zone between the bottom of the riverbed and the phreaticsurfacebelow;

4. flowintheaquifersaturatedzone.

For thesereasons and to better evaluate theefficiencyof the managed rechargeplant, since 2016 a new detail groundwater flow and transport model has been implemented in MODFLOW, starting from the one simulating the whole Marecchia fan. The first covers an area of about 5���� , against the 140���� of the second one. The aim is representing more accurately the area of the lakes, where the recharge is applied, allowing a performanceimprovementwith respecttothe already-existingmodel.This will bepossible thanks to the appropriate scale variations, detail verifications and relative technological adaptations. The two models are linked by means of the boundary conditions that can be transferred from one to the other, representing the elements that are external to the simulated domain but actually affect what happens inside it (for example, upstream or downstreamparticularsituations).

Modelling evaluations will allow to compare the ongoing situations (groundwater level, activity of the managed recharge, aquifer/river/lake interaction), in order to assess the effective contribution of the artificial water injection on the system behaviour, in terms of bothpiezometriclevelvariationsandhydrogeologicalbalance(Chahoud,2019).Modelling willalsoallowtooptimizetheplantmanagement.

In the period 2007-2018 the‘natural’ average recharge oftheaquiferhas beenestimated to be 25���� /��, of which 75% given by the river and 25% by the precipitation. The recharge given by the river is provided by an appropriate software package (SFR), which considers also the geometry of the riverbed and the lithology of surface deposits. It will be described in detail in Chapter 2 and 3. The recharge given by the precipitation is modeled with the software CRITERIA, a suite of soil water balance and crop modelling systems developed by the Agrometeorology Area and Hydrometeorological Service Territory of ArpaeEmilia-Romagna.

To assess the water balance of cultivated or fallow ground, all the contributions and losses of water along the vertical profile of soil have tobe computed. In particular, the amount of rainfall or irrigation that infiltrates into the ground depends on surface conditions (fouling, crevasses),onthehydrologicalcharacteristicsofthefirstlayerofsoilanditswatercontent. Waterthatcannotbeabsorbedfromthesoilcollectsinpondsformedbysurfaceroughness. Oncefilled,theycausesurfacerunoff.

The processes of storage and infiltration are governed by many parameters, such as the water content, the climate (temperature, precipitation), the type of soil (texture, porosity)

and the cropping system. Depending on the liquid content, for example, a layer can absorb or transfer water to the layer below. Moreover, the presenceof a crop or natural vegetation produces water loss in the root zone through transpiration, and simultaneously reduces evaporation loss in the surface layers covering the soil surface. Depending on the type of soil, its water content and the phenological stage of the crop, the water in the soil is more orlessavailabletoplants,thusaffectingitstranspirationrate.

All these phenomena constitute the soil water balance and are simulated in the CRITERIA model.

1.3.6 Costs,resultsandconclusions

The table below shows the main costs related to the various phases of the project. Costs of human resources (aquifer and surface water monitoring, ecosystem supervision, groundwaterflowandtransportmodel)arenotconsideredhere.

The volume added to the recharge lake induced an increment in the water level in the alluvial fan, together with a higher resource availability and an environmental benefit (subsidence,contrasttoseawaterintrusion).

In terms of groundwater, a general rise in the piezometric level was detected after a period of recharge (Casini, Severi, Bonzi, & Pellegrino, 2018). In particular, the increment is maximum near the lake and decreases moving away from it: this demonstrate that water flowsfromthelaketotheaquifer.ThebestresultwasobtainedintheperiodMarch–April 2014: the water level rose 2.75�� near the lake and 0.8�� at a distanceof more than 1���� fromit.

Among the benefits brought by the intervention, the release in the alluvial fan of highqualitywaterfromtheriverMarecchialedtoanimprovementofgroundwaterquality close to the recharge lake. In particular, the analysis showed that the nitrate amount in the aquiferdecreasesmovingtowardstherechargelake. As a result of thequick and considerable rise of the water levelin the lake, some protected birdspeciesofCommunityinterest settledwithin thearea(Severi,Bonzi,& Ferrari,2016). Since they need a precise environmental balance to nest and survive, an excessive water level increment could put them at risk. The aim of the next phases of the study will be the calibration of a level in the lake adequate to both the managed recharge and the maintenance of the existing ecosystem. To do so, the entrance of water in the lake was interruptedandthenrestartedwithalowerdischarge. In the near future it will also be interesting to assess the influence of the nearby well field on the trends of flow lines and the possible retrieval of water from the lake. Other aspects to consider in the continuation of the work will be the evaluation of the qualitative basic features of groundwater and the estimation of the possible clogging of the bottom of the lake.Thelastissuecouldinfactreducetheeffectivenessoftherecharge.Atalaterstage,it will be interesting to compare observed data to those obtained with the mathematical modelbyArpaeEmilia-Romagna.

2. MODFLOWandModelMuse

MODFLOW is a modular finite-difference flow model created by the U.S. Geological Survey, which is the scientific agency of the United States Government. It is a computer code that solves the groundwater flow equation, hence it is used by hydrogeologists to simulate the 3D movement of groundwater through porous media (aquifers). The source codeisfreepublicdomainsoftware,writtenprimarilyinFortran. Since its originaldevelopment in the early 1980s, the USGS has made four major releases, the latest one being MODFLOW 6. Nowadays there are several actively developed commercialandnon-commercialgraphicaluserinterfacesforMODFLOW. Inthischapter,figuresaretakenfromMODFLOWonlinedocumentation.

2.1Derivationofthefinite-differenceequation

2.1.1 Mathematicalmodelanddiscretizationconvention

The waterdensity is consideredconstant in most of thegroundwaterproblems, so it canbe omitted from all the terms (Psilovikos, 2006). The components of Darcy’s velocity in 3D aregivenwiththe2nd ordertensorofhydraulicconductivityasbelow:

Hence the governing partial differential equation used in MODFLOW to describe groundwater flow and non-equilibrium conditions in a heterogeneous and anisotropic mediumforaconfinedaquiferovertime�� is:

Where:

�� , �� and �� are the values of hydraulic conductivity along the ��, �� and �� coordinateaxes[���� ]; ℎ(��,��,��,��)isthepiezometrichead[��];

�� is a volumetric flux per unit volume [�� ] representing sources and sinks of water(��<0flowout,��>0flowin);

�� isthespecificstorageof theporousmaterial,i.e. thevolumeofwater that canbe injectedperunitvolume ofaquifermaterialperunitchangeinhead[�� ].

Coupled with the appropriate boundary conditions, this equation allows to find the head distribution in the domain as a function of time. However, analytical solutions are rarely possible,thustheapplicationofnumericalmethodsisrequired.

The continuous system described by Equation (2) is replaced by a finite set of discrete points in space and time, and the partial derivatives are replaced by terms calculated from the differences in head values at these points. The objective, in fact, is to estimate an approximated value of ℎ(��,��,��,��) by means of a system of simultaneous linear algebraic differenceequations.

The 3-dimensional domain can be discretized by an aquifer system with a mesh of orthogonal blocks called cells. These are assumed to be parallel and oriented to the major axes of the Cartesian coordinate system. Every cell contains a characteristic point, correspondingtothecenterofthatcell:herethevalueofthepiezometricheadiscomputed.

An(��,��,��)indexingsystemisused,where:

��=1,2,…,�� istherowindex;

��=1,2,…,�� isthecolumnindex;

��=1,2,…,�� isthelayerindex.

Anexampleofadiscretizeddomainisdepictedin Figure 2.1,where:

-

--- representstheaquiferboundary;

 identifytheactivecells,i.e.the‘nodes’atwhichheadistobecalculated;

 identifytheinactivecells.

The finite-difference equation developed in the following considers the block-centered formulationinwhichthenodesareatthecenterofthecells.

(https://pubs.usgs.gov/tm/2005/tm6A16/PDF/TM6A16.pdf)

2.1.2 Finitedifferenceequation

The continuity equation expresses the balance of flow; according to it, thesum ofall flows into and out of a central cell (��,��,��) must be equal to the rate of change of storage within thesamecell:

Where:

∑�� is the sum of all flows into and out of the cell (��,��,��) from the six neighbouring ones (on the four sides in the horizontal plane, above and below) [�� �� ];

�� isthespecificstorage[�� ];

∆�� isthevolumeofthecell[��];

ΔhisthechangeinheadoveratimeintervaloflengthΔt[��]

The Darcy’s law defines the relationship between specific discharge and hydraulic gradient;itsdiscretizedformulationcanbewrittenas:

Where:

Figure 2.1. 3D discretization of the domain.

���� , / , isthehydraulicconductivityalongtherowbetween��,��,�� and��,��−1,��

∆��∆�� istheareaofthecellsfacesnormaltorowdirection[�� ];

∆�� / isthedistancebetween��,��,�� and��,��−1,��[��].

Thesubscript��,��−1/2,�� isusedtoidentifytheregionbetweennodes��,��−1,�� and ��,��,��,anddoesnotindicateaspecificpointhalfwaybetweenthem.

The previous notation can be simplified by introducing a single constant term, the conductance,whichcombinesgriddimensionsandhydraulicconductivity:

Thesameprocedurecouldbeappliedintheothertwodirections. ConsideringDarcy’slawandtheaboveconventions,theflowsfromthesixadjacentcells tothecentralone(��,��,��)areobtained:

Additional terms are required to account for flows into the cell from features or processes external to the aquifer, such as streams, drains, areal recharge, evapotranspiration or wells. These flows may be dependent on the head in the receiving cell but independent of all other heads in the aquifer, or they may be entirely independent ofthe head in thereceiving cell.Theyarerepresentedbytheexpression:

Where:

istheflowfromthenth externalsourceintocell(��,��,��)[�� �� ];

, , , and��, , , areconstantquantities,[���� ]and[�� �� ]respectively.

Ifthereare�� externalsourcesorstressesaffectinga single cell (��,��,��),thecombinedflow isexpressedas:

Applyingcontinuityequationtocell(��,��,��):

Where:

, , is the finite difference approximation for the derivative of the head with respecttotime[���� ];

, , isthespecificstorageofcell(��,��,��)[�� ];

∆�� isthevolumeofcell (��,��,��)[�� ] Equation (8) canthusbewrittenas:

The hydrograph8 slope, or time derivative, is approximated using the change in head at the node over a time interval that precedes, and ends with, thetime atwhich flowis evaluated. This is termed a backward-difference approach, which is the most numerically stable methodtocomputetheslopeofhydrographattime�� .

Fromtheseconsiderations, Equation (9) canbewrittenas:

8 In general, a hydrograph is a graph showing the rate of flow (discharge) versus time past a specific point in a river, channel or conduit carrying flow. In the case of subsurface hydrology, a different variable is consideredsinceahydrographisarecordofthewaterlevel(theobservedhydraulichead).

This expression represents a system of equations containing 7 unknowns, which are the seven heads at the end of the time step; since 7 equations for each active cell in the grid canbewritten,thesystemissolvedsimultaneously.

2.1.3 Iteration

The set of finite-difference equations is reformulated at each time step, i.e. at each time step there is a new system of simultaneous equations to be solved. The heads at the end of the time step are the unknowns, whereas the heads at the beginning of the step are among the known terms in the equations; the solution process is repeated at each time step yieldinganewarrayofheadsfortheendofthestep.

Theiterationprocessisperformedasfollows:

1. atrialvalue,orestimate,fortheheadateachnodeattheendofagiventimestep,is arbitrarilyassigned;

2. these estimated values are altered by a procedure of calculation, producing a new setofheadvaluesinacloseragreementwiththesystemofequations;

3. these new, or interim, head values then take the place of the initially assumed heads;

4. thisprocedureisrepeatedsuccessivelyateachstage,producinganewsetofinterim headsthatincreasinglysatisfythesystemofequations;

5. ultimately, as the interim heads approach values that would exactly satisfy the set of equations, the changes produced by succeeding stages of calculation become verysmall.

Ideally, iteration should be stopped when the calculated heads are suitably close to the exact solution. However, since the actual solution is unknow, an indirect method must be applied. The most common approach is specifying that the changes in computed heads occurring from one iteration level to the next must be less than a certain quantity, termed as the ‘closure criterion’ or ‘convergence criterion’, defined by the user. Normally this methodisadequate.Asa rule ofthumb,thevalue ofclosurecriterionshould beanorderof magnitudesmallerthanthelevelofaccuracydesiredintheheadresults.

MODFLOW also considers a maximum permissible number of iterations per time step. If closure is not achieved within this number, then the iterative process is terminated and a correspondingmessageisprintedintheoutput.

Steady-State simulations

The flow equation (10) is developed assuming transient conditions (i.e. variables are not constantintime).Whenthestoragetermiszero,however,thesteady-stateflowequationis obtained: it specifies that the sum of all inflows (where outflow is a negative inflow) from adjacentcellsandexternalstressesmustbezeroforeachcellinthemodel.

A steady-state problem requires only a single solution of simultaneous equations, and therefore multiple solutions for multiple time steps are not needed. Moreover, differently from transient simulations (where an initial head was first required to calculate the time derivativeforthefirsttimestep),forsteady-state simulationsthereis nodirectrequirement forinitialheadsincethetimederivativeisremovedfromtheflowequation. In practice, however, initial head is required for steady-state simulations because of the assumption that iterative solution is used. Iterative solution, in fact, works by successively improving the estimated answer: therefore, an initial estimate is essential to start the iterativeprocess.

In MODFLOW, the user-specified initial head is considered as the initial estimate. The initial estimate should normally have no effect on the solution to the steady-state flow equation, but it may affect the number of iterations required to obtain an acceptable approximationofthesolution.

2.1.4 Formulationofequationsforsolution

MODFLOWincorporates several different options for iterativesolution ofthe setof finitedifference equations, but in every case it is convenient to rearrange Equation (10) as follows(alsoassumingthetimesuperscript�� unlessotherwiseshown):

The entire system of equations of the form of Equation (11), which includes one equation foreachvariable-headcellinthegrid,maybewritteninmatrixformas:

Where:

[��]isthematrixofcoefficientsofhead(leftsideof (11)),forallactivenodesinthe grid;

{ℎ}isthevectorofheadvaluesattheendoftimestep�� forallnodesinthegrid;

{��}isthevectorofconstantterms,������,forallnodesofthegrid.

MODFLOW assembles the vector {��} and the terms that comprise [��] through a series of subroutines. The vector {��} and the terms comprising [��] are then transferred to subroutinesthatsolvethematrixequationsforthevector{ℎ}

2.1.5 Typesofmodelcellsandsimulationofboundaries

The status of certain cells is specified in advance to simulate the boundary conditions of theproblem. InMODFLOW,cells usedto reproduceboundaryconditionsaregroupedinto twocategories:

 Constant-head: the head is specified for each time, and the head value does not changeasaresultofsolvingtheflowequations;

 No-flow:noflowintooroutofthecellispermitted. The remaining cells are termed as Variable-head: they are characterized by heads that are unspecifiedandfreetovarywithtime. Anexampleisrepresentedin Figure 2.2:

The default shape of the model grid is rectangular: no-flow cells can then be used to designate parts of the grid that fall outside the aquifer boundaries, allowing to represent aquiferswithirregularshapes.

In the model, constant-head, no-flow and variable-head cells are distinguished from one another through the ������������ variable. It contains one value for each cell in the grid, and theentriesindicatethetypeofcellaccordingtothefollowingconvention:

- ������������ , , <0:constant-headcell;

- ������������ , , =0:no-flowcell;

- ������������ , , >0:variable-headcell.

2.1.6 Horizontalandverticaldiscretization

MODFLOWhandlesspacediscretizationin thehorizontaldirectionby readingthenumber of rows, the number of columns, and the width of each row and column (that is, the width of the cells in the direction transverse to the row or column). Space discretization in the vertical direction is handled in the model by specifying the number of layers to be used as wellasthetopandbottomelevationsofeverycellineachlayer.

Verticaldiscretizationcanbedevisedconsideringtwoextremeviewpoints:

1. Extension of discretization: a more or less arbitrary process of dividing the flow system into segments in the vertical dimension, governed in part by the vertical resolution desired in the results; this approach leads to rigid superposition of an

Figure 2.2. Discretized aquifer showing boundaries and cell designation. (https://pubs.usgs.gov/tm/2005/tm6A16/PDF/TM6A16.pdf)

orthogonal 3D grid on the geohydrologic system; while there may be a general correspondence between geohydrologic layers and model layers, no attempt is madetomakethegridconformtostratigraphicirregularities.

2. Representation of individual aquifers or permeable zones by individual layers of the model: under this assumption, layer thickness is considered variable; this leads, in effect, to a deformed grid which better simulates the varying thickness of geohydrologicunits.

Inpractice,manydiscretizationschemesareacombinationoftheseviewpoints. The differences among these approaches arise in the way the conductances and storage terms are formulated and, in general, in the number of equations to be solved, the resolution and the accuracy of the results. Since the elevations of the individual cells in each layer can vary, MODFLOW can implement any of these approaches to vertical discretization.

2.2Designofthegroundwaterflowprocess

2.2.1 Procedures

The simulation period is brokendown into aseries of elements, termedin theMODFLOW onlineguideasstressperiods,thataretimeintervalsduringwhichspecifiedstressdata(i.e. the inputs of the model) are constant. Each stress period, in turn, is divided into a series of time steps. The system of finite-difference equations of the form of Equation (11) is formulated and solved to determine the head at each node at the end of each time step by using iterative solution methods. Thus, the program includes three nested loops: a stressperiod loop, within which there is a time-step loop, which in turn contains an iteration loop;suchsequenceisrepresentedin Figure 2.3

The order in which procedures are executed to create a program that solves the groundwaterflowequationisthefollowing:

1. Allocate and Read (AR) Procedure: it is performed before entering the stress loop; it pertains to the simulation as a whole and performs a number of setup functions, such as determination of the number of the cells in the grid, hydrologic options, solutionmethod.

2. Stress (ST) Procedure: it advances to a new stress period.

3. Read and Prepare (RP) Procedure: it reads and processesalldatathatpertaintoastressperiod,such aspumpingratesandarealrecharge.

4. Advance (AD) Procedure: the length of the time step is calculated and the heads for the start of the time step are initialized; other processing, needed at everytimestep,isalsoperformed.

5. Formulate (FM) Procedure: it determines the conductances and coefficients for each node as required by Equation (11); it is called prior to each solver iteration so that the conductances and coefficients in the flow equation can be changed basedonthelatestapproximateheadsolution.

6. Approximate (AP) Procedure: it approximates a solutiontothesystemoflinearequationsforhead.

7. Output Control (OC) Procedure: it is performed at the end of each iteration loop, and it determines which computed information, such as heads, budget terms,andcell-by-cellflowterms,willbeoutput.

(https://pubs.usgs.gov/tm/2005/ tm6A16/PDF/TM6A16.pdf)

8. Water Budget (BD) Procedure: budget entries are calculated, and cell-by-cell flow termsareprintedorrecorded.

9. Output(OT)Procedure:thespecifiedcomputedinformationisprintedorrecorded.

10.Deallocate (DA) Procedure: after all time steps are completed for all stress periods, thisprocedurereleasesallocatedmemory.

Figure 2.3. Flowchart of program to simulate GWF.

2.2.2 Packages

The various parts of the code that deal with defining the groundwater flow equation are divided into packages, called hydrologic packages: they calculate the coefficients of the finite-differenceequationforeachcell.

Therearetwotypesofhydrologicpackages:

 Internalflowpackages:theysimulateflowbetweenadjacentcells;

 Stress packages: they reproduce an individual kind of stress, such as rivers, wells, recharge,etc.

The solver packages are those that implement algorithms for solution of the systems of finite-differenceequations.

The only package that does not fit into the hydrologic or solver categories is the Basic Package,whichaddressesavarietyoftasksinsupportoftheentireprocess.

In Table 2.1 themainpackagesarelisted:

The structure of the groundwater flow process has been designed in such a way that packages are as independent as possible, allowing and facilitating additions and modifications.

2.2.3 PrimarySubroutines

A program can be constructed following the flow chart represented in Figure 2.3, where a sequence of procedures is defined to solve the groundwater flow equation. To do so, each procedure could be implemented as a single subroutine. From a programming perspective, this would be the most direct way to construct the program; however, the subroutines would be quite large, and there is benefit from further subdividing the work into smaller subroutines.

The approach used for MODFLOW is to divide the code into pieces that can be combined into both procedures and packages. Accordingly, a primary subroutine is defined as the code within a procedure for one package. A procedure can be constructed by grouping all the primary subroutines that comprise the procedure. A package can be constructed by groupingalltheprimarysubroutinesthatcomprisethepackage. Using this approach, the MAIN Program becomes an organized sequence of call statements to the primary subroutines. The MAIN Program does not itself do the work of simulation, but simply calls the various primary subroutines in the proper sequence to performthatwork.

The primary subroutines are named following a convention according to which the subsequent characters indicate the process, the process version number, the package and the procedure to which they belong. When primary subroutines become so large that they aredifficulttounderstand,theyarebrokeninto smallersecondarysubroutines,allofwhich startingwiththeletterS.

2.3Internalflowpackages

There are two packages simulating internal flow in MODFLOW: Block-Centered Flow (BCF) and Layer-Property Flow (LPF). Only one internal flow package can be used in a given simulation. BCF and LPF are based on identical conceptualizations, but they differ inthetypeofinputdataspecifiedbytheuserandinthedetailsofimplementation. An internal flow package calculates the ����, ���� and ���� conductance coefficients and the ground-waterstoragetermsinthefinite-differenceflow,considering Equation (11).

2.3.1 Basichydraulicconductanceequations

Hydraulic conductance is a combination of several parameters used in Darcy’s law, which definesone-dimensionalflowinaprismofporousmaterialas:

Where:

�� isthevolumetricflow[���� ];

�� isthehydraulicconductivityofthematerialinthedirectionoftheflow[���� ]

��isthecross-sectionalareaperpendiculartotheflow[��];

ℎ −ℎ istheheaddifferenceacrosstheprismparallelto flow[��];

�� isthelengthoftheprismparalleltotheflowpath[��]

Sinceconductance�� isdefinedas��= ,Darcy’slawcanbewrittenas:

Conductance can also be written as ��= , where ��[���� ] is the transmissivity (�� timesthicknessoftheprism)inthedirectionofflowand��[��]isthewidthoftheprism.

Conductance is defined for a particular prism of material and for a particular direction of flow. In an anisotropic medium that is characterized by three principal directions of hydraulic conductivity, the conductances of a prism in these three principal directions will generallydiffer.

If a prism of porous material consists of two or more subprisms in series, and the conductance of each subprism is known, an equivalent conductance representing the entire prismcanbecomputed:

Assumingcontinuityofheadacrosseachsubprismgives:

SubstitutingforheadchangeacrosseachsubprismusingDarcy’slaw:

Where:

�� istheflowacrossthesubprism[�� �� ];

�� istheconductanceofsubprism��[�� �� ].

Because flow is one dimensional, assuming no accumulation or depletion in storage, each �� isequaltothetotalflow��.Therefore:

Thus, for a set of conductances arranged in series, the inverse of the equivalent conductance equals the sum of the inverses of the individual conductances. For example, whenonlytwosubprismsexist,theequivalentconductancereducesto��=

2.3.2 Horizontalconductance

The horizontal conductance terms, ���� and ����, are calculated between adjacent horizontal nodes. ���� terms are oriented along rows and thus establish conductance between two nodes in the same row. Similarly, ���� terms specify conductance between two nodes in the same column. An important consideration, already mentioned, is that the subscript ½ denotesconductancebetweennodes,asopposedtoconductancewithinacell.

An internal flow package reads data defining the horizontal hydraulic conductivity for individual cells and computes conductance between nodes. Four methods of calculating these conductances are supported, which differ in the assumptions about the way the groundwatersystemvariesfromcelltocell.

Uniform transmissivity within a cell

This method assumes that transmissivity is uniform within a cell, whereas there can be a discrete change in transmissivity at the boundary between two of them. Due to this, the conductancebetweennodesinseriesis:

�������� isthegridwidthofcolumn��[��]; �������� isthegridwidthofrow��[��]. Thesameprocesscanbeappliedtocalculate���� / , , :

Where���� , , isthetransmissivityinthecolumndirectionatcell(��,��,��)[��

Alternative approaches

There are three alternative approaches for calculating horizontal branch conductances. These alternative approaches are each based on different assumptions about the flow system:

1. Transmissivityvarieslinearlybetweennodes:

2. Unconfinedhomogeneousaquiferwithaflatbottom:

3. Unconfined aquifer with a flat bottom and with hydraulic conductivity varying linearlybetweennodes:

Where

representshydraulicconductivity.

2.3.3 Verticalconductance

Vertical conductance is calculated assuming that nodes are in the center of cells and that discrete changes can occur in vertical hydraulic conductivity at layer boundaries. Under these assumptions, the vertical conductance between two nodes will be the equivalent conductanceoftwohalfcellsinseries.

Where:

���� , , isverticalhydraulicconductivityofcell(��,��,��);

∆�� , , isthesaturatedthicknessofcell(��,��,��)

The Quasi-3D approach allows to describe a particular situation: a semiconfining unit is present which makes no measurable contribution to the horizontal conductance or to the storage capacity of either model layer. The only effect of the confining bed is to restrict vertical flow between the cells. In this case, three intervals must be represented in the summation of conductance between the nodes: the lower half of the upper aquifer, the semiconfiningunitandtheupperhalfoftheloweraquifer.Theequationresultstobe:

Where �������� , , is the hydraulic conductivity of the semiconfining unit between cells (��,��,��)and(��,��,��+1),and∆�� isthethicknessofthesemiconfiningunit.

2.3.4 Verticalflowcorrectionunderdewateredconditions

Vertical flow correction can be activated in both the BCF and LPF packages; in this case, the vertical flow calculation is modified if a cell is unconfined (head is below its top elevation)whilethecell directlyaboveisfullyorpartiallysaturated.

In some particular situations, part of a confined aquifer may become unsaturated, for example when drawdown due to pumpage causes water levels to fall below the top of an aquifer. This condition is most likely to occur when an aquifer is overlain by a lower conductivitylayer,asrepresentedin Figure 2.4.

Pumpingfromthelowerlayerhasloweredthewaterlevelincell(��,��,��+1)belowthetop elevation, while cell (��,��,��) remains fully saturated. In the upper cell, head is ℎ , , . Just below, however, unsaturated condition prevails, so that the pressure sensed on the lower surface of the confining unit is atmospheric, i.e. zero in the model formulation. Thus, the head at the bottom of the upper cell is the elevation at that point, i.e. the elevation of the topofthelowercell.

If this elevation is designated ������ , , , then the actual flow through the confining bed is obtainedbysubstituting������ , , forℎ , , in:

The flow will be downward, from cell (��,��,��) to cell (��,��,��+1), but under this condition theflowwillnolongerbedependentonthewaterlevelinthelowercell(ℎ , , ).

In reality, this method generates problems in the solution process, since the matrix of coefficients of the entire system of finite-difference equations becomes asymmetric. An alternative approach is then used, which determines a correction term �� as the difference betweenthecomputedflowintocell��,��,�� andthe‘actual’flowintocell (��,��,��):

This term should be added to the right side of Equation (10), but still there is a problem of matrix asymmetry because Equation (26) contains ℎ , , . To circumvent this difficulty, �� iscomputedusingthevalueofℎ , , fromtheprecedingiteration:

Figure 2.4. Situation requiring a correction to limit the drawdown flow into cell (i,j,k+1) as a result of partial saturationof a cell. (https://pubs.usgs.gov/tm/2005/tm6A16/PDF/TM6A16.pdf)

Acorrectionmustalsobeappliedinformulatingtheequationsfordewateredcell:to computethiscorrection,cell��,��,�� isconsideredtobethedewateredcell,andweconsider flowinto��,��,�� fromtheoverlyingcell(��,��,��−1). �� =���� , , ������ , , ℎ , , (29)

Thistermiscomputedonthebasisoftheheadfromthepreviousiteration,andthis correctionisaddedto������in Equation (11)

2.3.5 Conversionfromdrycelltowetcell

When saturated thickness is zero, as defined by head being less than the bottom elevation of a cell, a variable-head (wet) cell should convert to dry. Unfortunately, there is not a straight-forwardwaytoknowwhenthisprocesswouldhappen.

A dry cell converts to wet based upon the head in an adjacent cell compared to a wetting threshold,������������,forthecell itself.Iftheheadin theadjacentcellequalsorexceedsthe threshold at the beginning of a solution iteration, the dry cell is converted to wet. To determine when a dry cell becomes wet, an option is to consider any of the four cells directly adjacent horizontally or the cell directly below. Another option is to consider only the cell below: this can be a better wetting indicator than the previous option when the head variations between adjacent horizontal cells are larger than the vertical head variations,whichisfrequentlythecase.

When a cell converts to wet, the initial estimate of head is established according to one of thefollowingtwoequations:

ℎ , , =������ , , +������������ ℎ ������ , ,

ℎ , , =������ , , +������������ ������������ , , (30)

Where:

������������ isauser-specifiedconstant,usuallybetween0and1;

ℎ istheheadattheneighbouringcellthatcausescell(��,��,��)toconverttowet;

������ istheelevationofthebottomofcell(��,��,��)[��].

2.3.6 Storageformulation

InMODFLOW,adistinctionismadebetween:

(a) Confined layers in which storage terms remain constant: in this case, the rate of accumulationofwateris:

Where:

�� , , isthespecificstorageofthematerial[�� ];

�������� isthewidthofcellsincolumn��[��];

�������� isthewidthofcellsinrow��[��];

∆�� , , isthecellthickness[��];

ℎ , , ,ℎ , , arethevaluesofheadincell (��,��,��) attheendofthetimesteps

�� and��−1,respectively[��];

�� , �� are the values of time at the end of time steps �� and ��−1, respectively[��];

����1isthestoragecapacityorprimarystoragecapacity.

(b) Layers in which the storage terms may convert from a confined value to a watertableone,orvice-versa:inthiscase,therateofaccumulationofwateris:

Where�� [−]isthespecificyieldand����2isasecondarystoragecapacity. Duringanytimestep,fourstorageconditionsarepossibleforeachcell:

 thecellisconfinedfortheentiretimestep;

 thecellisunconfinedfortheentiretimestep;

 thecellconvertsfromconfinedtoconfined;

 thecellconvertsfromunconfinedtoconfined.

In order to handle all the possibilities, the following expression for rate of accumulationinstorageincell(��,��,��)isused:

Where:

������ istheelevationofthetopofthemodelcell;

������ is the storage capacity in effect in cell (��,��,��) at the beginning of the timestep;

������ is the ‘current’ storage capacity, i.e. the storage capacity in effect duringthecurrentiteration.

The computed rate of release of water from storage in the time step has two components:

 Fromconfinedorcompressivestorage: , , , , , ,

 Fromwater-tablestorage: , , , , , ,

In case of steady-state simulations, no storage effects exist; thus, nothing is added to RHS andHCOFcoefficients.Astressperiodcanbespecifiedassteadystateinthediscretization file.Normally,asteady-statestressperiodwillhaveasingletimestep.

2.3.7 Block-CenteredFlowpackage

This package uses layer-type code (LAYCON) to classify layers according to which of the head-dependentformulationsareapplied.

 Layer-type 0 – Confined

The transmissivity is assumed to be unchanged in all cells throughout the simulation. This layer type is normally employed to reproduce confined conditions, but it could also simulate a layer in which unconfined conditions will always prevail, provided drawdowns are expected to be a small fraction of layer thickness and the vertical flow correction is not needed. If used to simulate an unconfined layer, specific yield should be entered in place of the confined storage coefficient.

 Layer-type 1 – Unconfined

This layer type is exclusively employed in a single-layer model or in the uppermost layer ofa model, and only whenunconfinedconditions are expected to persistinthelayerthroughouttheentireperiodofsimulation.

 Layer-type 2 – Limited convertible

This layer type is employed when heads may alternate between confined and unconfined conditions, so that the storage term conversion and limitation of flow fromabove,underdewateredconditions,arebothdesirable.

 Layer-type 3 – Fully convertible

This layer type incorporates all the Block-Centered Flow options associated with water-table conditions. Transmissivities are recalculated at each iteration using hydraulic conductivity and layer top and bottomelevations, and both storage term conversionandverticalflowcorrectionareimplemented.

2.3.8 Layer-PropertyFlowPackage

LPFPackagesupportstwotypesoflayer:

 Confined: transmissivity is constant throughout the simulation, and it is computed from hydraulic conductivity and cell elevations. In transient simulations, the storageflowiscomputed from specificstorage;thecelldrying,wettingand vertical flowcorrectioncapabilitiesarenotactive.

 Convertible: transmissivity varies based on the headthroughout thesimulation, and it is computed during each iteration based on cell thickness. The computation of transmissivity includes the possibility for a cell converting to No-flow; the vertical flow correction capability is active, and the cell wetting capability can be applied if desired.

The storage contribution to the flow equation is determined from confined and/or unconfinedstorage,dependingontheheadcomparedtothetopelevationofcells. The computations for vertical conductance can cause numerical instabilities, since thechangeinconductancecanbequitelargebetweensuccessivesolveriterations. In both confined and convertible situations, vertical conductance is computed using Equation (24) or Equation (25), depending on the presence of the confining bed. In order to allow the computation of vertical conductance, vertical conductivity is required for all cells: the input data could be the vertical hydraulic conductivity itself, or the ratio of horizontaltoverticalhydraulicconductivity.

2.4Conceptualizationofstresspackages

The stress packages add terms to the flow equation representing inflows and outflows in order to simulate hydrologic stresses to a groundwater system: mathematically, these are boundary conditions. Equation (11) is formulated so thatinflows are added to the left side, with outflows represented as negative inflows. Stresses are incorporated to the flow equation by adding terms to �������� and ������. A stress term that is a coefficient of head, ℎ , , , is added to HCOF, whereas a stress term that is constant is subtracted from ������ (thisterm,infact,hasbeenmovedtotherightsideoftheflowequation). In the following, the main stress packages will be described as well as those that will be usedinthenextchaptersfortheimplementationofthemodel.

2.4.1 WellPackage(WEL)

The Well package simulates features, such as wells, withdrawing water from or adding water to the aquifer,at a constant rate during a stress period. The flow rate fora well, ��, is independent of both the cell area and its head; it is specified by the user as a fluid volume per unit time at which water is added to the aquifer (negative values indicate pumping discharge, positiveones indicate recharging wells).For eachwell, thedata required are the row, the column and layer number of cells in which the well is located, and the recharge rate(��).

At each iteration, as the matrix equations are formulated, the value of �� for each well is subtracted from the ������ value for the cell containing the well. If more than one well falls withinasingle cell,thecalculationisrepeatedforeachwellasthe������termforthatcellis assembled (thus, it is like the values of recharge within the cell are summed up to obtain a ‘total’recharge).

The WEL Package does not allow to directly reproduce wells that are open to more than one layer of the model; in this case, the well can be represented as a group of single-cell wells, each open to one of the layers tapped by the multilayer well, and each having an individual �� term specified for each stress period. If this approach is used, the recharge (negative for discharge) of the multilayer well must be divided (or apportioned in some way) among the individual layers, externally to the model program. A common method of doingsoisinproportiontothelayertransmissivities:

Where:

�� is the recharge/discharge from layer �� to a particular well in a given stress period[�� �� ];

�� isthetotalrechargeforthewellinthatstressperiod[�� �� ];

�� isthetransmissivityoflayer��[�� �� ];

∑��isthesumofthetransmissivitiesofalllayerspenetratedbythewell[�� �� ]

2.4.2 RechargePackage(RCH)

RCH Package simulates areally distributed recharge to the groundwater system. The areal recharge defined by this package is not the same as precipitation, but includes only that portion of precipitation that actually percolates in the soil and reaches the aquifer. Evapotranspiration from the unsaturated zone is not included, whereas flows from streams orriversintogroundwatercouldbeincluded,ifnotconsideredinotherways. Therechargeappliedtothemodelisdefinedas:

����, =�� , ���������������� (35)

Where:

����, is the recharge flow rate applied to the model at horizontal cell location (��,��) [�� �� ];

�� , is the recharge flux applicable to the map area of the cell (���������������� ) [���� ].

Valuesof�� , arespecifiedbytheuserateachstressperiod. Sincenaturalrechargeentersthegroundwatersystematthetop,theRCHPackagedoesnot allow for recharge to occur simultaneously at multiple depths in the same vertical column. The vertical position of the top of the system may vary with horizontal location, and with time as the water table rises and falls. Within each vertical column, the recharge could be added either (i) to the cell belonging to the uppermost layer, (ii) to any cell specified by layer number or (iii) to the uppermost variable-head cell, provided that no constant-head cell is above the variable-head one in the column. Under the first two options, if the cell designatedto receivethe rechargeisnofloworconstant-head,thennorechargeis addedto

it. In the same way, under the third option, if a constant-head cell has no variable-head ones above, then no recharge is applied: any recharge, in fact, would be intercepted by the constant-headsource.

In the formation of the matrix equations, the recharge flow rate, ����, , associated to a given horizontal cell location (��,��) and vertical location �� that is determined by the recharge option is subtracted from the value of ������ , , . This is done at each iteration for all cells that receive recharge. Since recharge is independent of aquifer head, nothing is addedtothecoefficientofhead,�������� , ,

The RCH Package could also be employed to reproduce other varieties of recharge, for exampleanartificialone.Moreover,dischargescanbesimulatedbynegativeflowvalues.

2.4.3 GeneralheadboundaryPackage(GHB)

GHB Package simulates flow into or out of a cell (��,��,��) from an external source proportionally to the difference between the head in the cell and the head assigned to the external source. The constant of proportionality is called the boundary conductance. The relationbetweenflowintothecellandtheheadinitislinear:

���� =���� ���� ℎ , , (36)

Where:

�� isaboundarynumber;

���� is the flow into cell (��,��,��) from the boundary[���� ];

���� is the boundary conductance

[�� �� ];

���� is the head assigned to the external source[��];

ℎ , , istheheadincell (��,��,��)[��]

As shown in Figure 2.5, GHB Package does not provide any limiting value of flow to bound the linear function in either direction; and as the

(https://pubs.usgs.gov/tm/2005/tm6A16/PD

F/TM6A16.pdf)

Figure 2.5. Plot of flow from a generalhead boundary source into a cell.

difference between the head in the cell containing the boundary and the source head increases, flow into or out of the cell continues to increase without limit. For this reason, unrealisticflowsduringthesimulationshouldbeidentifiedandavoided.

The term ���� is added to �������� , , and the term ���� ���� is subtracted from ������ , , as thematrixequationsareassembled.

2.4.4 RiverPackage(RIV)

RIV Package reproduces the effects of flow between surface water features and groundwatersystems.Itdoesnotsimulatewaterflowintheriver,butonlytheriver-aquifer seepage,independentlyforeachriverreach.

Measurable head losses between the river and the aquifer are assumed to be limited to those across the riverbed layer itself (i.e. no substantial head loss occurs between the bottom of the riverbed layer and the point represented by the underlying model node). Moreover,theunderlyingmodelcellisconsideredtoremainfullysaturated.Thus,theflow betweentheriverandthegroundwatersystemforreach�� isgivenby:

�������� =�������� �������� ℎ , , (37) Where:

�������� istheflowbetweentheriverand theaquifer (>0ifdirected intotheaquifer) [�� �� ];

�������� isthewaterlevel(stage)intheriver[��];

�������� isthehydraulicconductanceoftheriver-aquiferinterconnection[���� ];

ℎ , , istheheadatthenodeinthecellunderlyingtheriverreach[��].

2.4.5 Streamflow-RoutingPackage(SFR)

The Streamflow-Routing package is used to simulate streams in a model. The flow in a streamiseitherroutedinstantaneouslytodownstreamstreamsorlakes(definedintheLake package), or routed using a kinematic wave equation. Unsaturated flow beneath streams can be simulated. This package is best suited for modeling long-term simulations (months to hundreds of years) of groundwater flow and solute concentrations using averaged flows in streams. Streamflow routing is based on the continuity equation and assumption of

piecewise steady, uniform and constant-density streamflow, such that during all time periodsvolumetric inflowand outflowrates areequal(i.e. nowaterisaddedtoor removed fromstorageinthesurfacechannels).

Theprogramisdesigned toroutestreamflow throughanetworkofchannels,fixedin space during the simulation, whicharedividedinto reaches and segments. A reachis asection of a stream that is associated to a particular cell, whereas a segment is a group of reaches having uniform rates of overland flow, precipitation and evapotranspiration, uniform or linearlychangingproperties,tributaryflowsorspecifiedinfloworoutflowanddiversions. SFR package also allows to specify a particular shape for the river cross section. This configuration is used to compute depth, width and wetted perimeter for a stream segment. There are five options for simulating stream depth: (i) a specified value, Manning’s equation using a (ii) wide rectangular channel or (iii) an eight-point cross section, (iv) a power equation or (v) a table of values that relate flow to depth and width. Each stream segment can be assigned one of these options, and outflow from lakes can be computed in the same way. The stream depth is computed at the midpoint of each reach, allowing to considereventualwatersuppliesanddiversionswithinthereachitself.

Flow between streams and aquifers in the groundwater model is computed using Darcy’s Law and assuming uniform flow between a given section of stream and the corresponding volumeofaquifer. Inthis formulation,transientleakageacrossthestreambedcouldchange dependingonboththestreamheadandtheaquiferheadduringthetimestep.

The conductance term is calculated from hydraulic conductivity, stream length, streambed thickness (read in the data input) and stream width (either read in the data input or computed on the basis of streamflow),so it is no longer computed externally wheneverthe area of streambed changes as a function of flow. Differently from the River package, also the hydraulic head is not a direct input data, since it is computed from the riverbed flow rate.

The concentration of a solute in a stream reach is based on a mass-balance approach and accountsforexchangeswithgroundwatersystems.

A stream water budget for every reach, as well as the leakage rate between a stream reach and corresponding model cell, is computed each iteration of a time step and at the end of each time step, independently of the groundwater model budget. Flow out of the last reach

of a segment is saved and used as inflow to the next downstream segment, or it is allowed totheleavethemodeledareaifthelastsegmentreachexitsthesimulatedboundary. The program allowsseveralsourcesof inflow to a reach: a specified inflow and thesum of tributary flow from eventual upstream segments (these two only for the first reach of a segment), direct overland runoff, precipitation and groundwater leakage. Losses from a reach include: streamflow out of the reach, specified diversions from the last reach in a segment,evapotranspirationandleakage to theunderlyingaquifer.For eachreach,the sum inflowsisequaltothesumoutflows. Any number of inlet streams can discharge into a lake (or series of lakes). In this case, outflow from the last reach of a stream segment is used as inflow to the lake. On the contrary, to model streams that emanate from lakes, when outflow from a lake is unknown or varies asa function of waterstage,the outflow from thelake and therefore inflow to the streamis computedbyusingthelakestage asthe headatthebeginningof thefirstreachof thestreamsegment.

2.4.6 LakePackage(LAK)

The Lake package is meant to reproduce lakes where the head can rise and fall due to interactionwith groundwaterorwithstreams simulatedwith the SFR package. Ittakesinto account the water volume within the lake, its morphology and eventual water supply and withdrawal. The water stage in the lake is computed on the basis of the stored volume and ofthebathymetryofthelake.

The Lake package represents a lake using a set of inactive cells: this method allows the lake to interact with lower layers and it allows lateral inflow to the lake. The lake is also assumed to have lakebed sediments which affects the flow between the aquifer and the lake. The effect of these elements is represented with a lakebed leakance term, which includes the thickness and the hydraulic conductivity. The flow from the aquifer into the lake is a function of both the lakebed leakance and the conductance of aquifer cells adjacenttothelake.

TheLakepackage alsoincludesanoptionforsimulating‘sublakes’:suchoptionallowsthe laketopartitionintosmaller,separatelakesasthelakestagedrops.

2.4.7 HeadObservationPackage(HOB)

The Head-Observation input file is employed to specify observations of head to be used in the Observation process, which has the capability to compare model-calculated flow and heads with observed values. Thelocation of head observationsis defined by means of the row,thecolumnandlayernumberofcellsinwhichtheobservationisdetected. The simulated heads are computed by interpolating from the nearest cell centers to the position of the observation. Head observations can extend over several model layers, in which case cells from all the layers that are part of the observation will be used in calculatingthesimulatedhead.

ThedatathatcanbespecifiedfortheHeadObservationpackageinclude:

 theobservedheads andtheircorresponding times,ifmorethanoneheadwasobserved ataparticularlocation;theobservedtimeforsteady-statestressperiods;

 the observation type: the input values can be all heads or, in alternative, the first value can be a head whereas the remaining ones can be drawdowns to be subtracted at each observationtime;

 for multilayer head observations, the data on how the simulated head should be calculated: in fact, in this case the simulated head is calculated using a weighted average of the heads in all the layers; the user can specify the weights applied in the calculationinsuchawaythattheysumupto1.

If one or more of the cells used to calculate the simulated head goes dry, the simulated headcannotbedetermined.

The MODFLOW Listing file will contain a list of the observed values and the simulated equivalents.

2.4.8 Otherpackages

Drain Package (DRN)

DRN Package simulates the effects of features, such as agricultural drains, which remove water from the aquifer at a rate proportional to the difference between the head in the aquifer and some fixed head or elevation, called the drain elevation; this occurs as long as the head in the aquifer is above that elevation, otherwise the drain has no effect on the aquifer.Theconstantofproportionalityiscalledthedrainconductance.

(https://pubs.usgs.gov/tm/2005/tm6A16/PDF/TM6A16.pdf)

Evapotranspiration Package (ET)

ET Package reproduces the effects of plant transpiration and direct evaporation in removing water from the saturated groundwater regime. Evapotranspiration is conceptualized as an areal phenomenon, like the recharge simulated by RCH Package, and the samethree options areavailable for the evapotranspiration withdrawal within avertical column.

(https://pubs.usgs.gov/tm/2005/tm6A16/PDF/TM6A16.pdf)

Figure 2.6 showsagraphofflowfromadrainasafunctionofheadinthecell.

Figure 2.6. Plot of flow into a drain as a function of head.

Figure 2.7 showsagraphofevapotranspirationlossfromacellandheadin it.

Figure 2.7. Plot of volumetric evapotranspiration as a function of head.

2.5ModelMuse

ModelMuse is an open graphical user interface (GUI) for MODFLOW and PHAST9. It allows the user to locate the spatial input for the models by drawing points, lines or polygons on top, front and side views of the domain. These objects can have up to two associated formulas that define their extent perpendicular to the view plane, allowing the objects to be 3-dimensional. Formulas are also employed to specify the values of spatial data(termedas ‘data sets’)both globally and forindividual objects. Objects can be used to establish the values of data sets independent of the spatial and temporal discretization of the model. Thus, the grid and simulation periods for the model can be changed without respecifying spatial information pertaining to the hydrogeologic framework and boundary conditions. Points, lines, and polygons can assign data set properties at locations that are enclosed or intersected by them or by interpolation among objects: to this purpose, several interpolation algorithms are available. Data for the model can be imported from a variety ofsourcesandtheresultscanbeviewedinModelMuse.

ModelMuse stores all its data in a single file. Several file formats are supported; of these, the most common are text files with the extension .gpt and compressed binary files with theextension .mmZLib.

2.5.1 Thegrid

MODFLOW uses finite-difference techniques for spatial and temporal discretization; for thefirstone,agridisrequired. The grid can be rotated at an angle to the global coordinate system. The coordinate system for the grid is aligned with the grid lines but has the same origin as the global one. The coordinates of apoint in the globalcoordinatesystemarereferred to as ��,��,��, whereas its coordinates in the grid system are referred to as ��′,��′,�� (the grid is never rotated away from thehorizontalplane).Bydefault thelayersareflat,but itispossibleto setthetopand thebottomofeachcelland,doingso,togivespecificshapestothelayerthickness.

9A computer program by USGS for simulating groundwater flow, solute transport and multicomponent geochemical reactions; PHAST stands for PHREEQC And HST3D: the first one is the geochemical model that simulates the geochemical reaction, whereas the second one is a computer code for simulation of heat andsolutetransportin3Dgroundwaterflowsystems.

In MODFLOW, the grid considers block-centered nodes: the locations at which calculations are made are at the centers of blocks. The grid is numbered with 1,1,1 in the furthestupperleftcorner.

2.5.2 Datasets

Datasets areused inModelMusetodefinespatiallydistributedinformationfor each cellin MODFLOW.Each data set represents a2D or 3D array ofvalues: 3D data sets are defined forthe entire extent ofthemodeldomain, whereas2Ddatasets aredefinedfor atop, front, or side projection of it. If the number of rows, columns, or layers in the grid changes, the sizes of the data sets are also changed. In MODFLOW, data sets will always have a value foreachcell.

2.5.3 Formulas

Formulas areaimed atdescribing the distribution of valuesin data sets. Each data set hasa ‘default formula’ that is meant to assign a value to each cell, node, or element when such valuesarenotexpressedbytheuserinsomeotherway.

In certain MODFLOW packages, such as the Layer Property Flow package, it is possible to define ‘parameters’ that are used in combination with ‘multiplier arrays’ and ‘zone arrays’ to describe the spatial variability of some input data such as the hydraulic conductance (given by the hydraulic conductivity of the river bed materials divided by its verticalthicknessandmultipliedbytheareaoftheriverinthecell).

2.5.4 Objects

Objects are collections of points, polylines (a series of connected line segments), and polygons drawn in the main window of ModelMuse or imported from external files. Objectscanhaveoneormoresections,eachconstitutedbyapoint,polylineorpolygon.

Objects are meant to modify the default values of data sets and to apply boundary conditions;toachievethefirstofthesepurposes,theycanbeusedinthreeways:

1) in2-dimensionaldatasets,valuescanbeinterpolatedamongobjects;

2) values can be imposed for elements or cells whose centers or nodes are enclosed insidetheobject;

3) valuescanbeimposedforelementsorcellsintersectedbytheobject.

2.5.5 Assigningvaluestodatasets

Since values for data sets are specified using formulas and objects, the data for a given model are independent of the spatial discretization. In MODFLOW models, ModelMuse assignsvaluestodatasetsatcellsusingthefollowingprocedure:

1) a default value is allocated at every node or element by using either the selected interpolationmethodorthedefaultformulaforthedataset;

2) each object affecting the data set is processed, and nodes or elements that are intersected or enclosed by them are assigned values by using the object’s formula for the data set; doing so, each object replaces values assigned previously by the defaultformulaorbyapreviousobject.

2.5.6 Modelfeatures

Model Features are data that are only defined at certain locations. They are specified only with objects (points, lines, and polygons) and most of them also vary with time. They are treated similarly to data sets except that there are no default formulas for them. In most cases, Model Features are employed to describe the boundary conditions of the model, whosespecificationisindependentofthetimediscretizationestablishedbytheuser.

3. Calibration of ModelMuse to the alluvial fan of the River Marecchia

The work of the thesis consists in the development of the model described in Paragraph 1.3.5 with ModelMuse, the graphical user interface for MODFLOW. The latter is used in its version MODFLOW-2005 1.12, whereas the version of ModelMuse is 4.2.0.0 (released on25th February2020).

As a graphical user interface, ModelMuse allows a direct manipulation of the graphical elements, with the purpose of enhance the efficiency and ease of use for the underlying logical design of a storedprogram (MODFLOW in this case). In this way, the modelling process is simplified, and the modeler can focus more on conceptual issues rather than on the‘formal’implementation.

ModelMuse was chosen as possible choice, different from the interfaces used in the previous applications of MODFLOW to the River Marecchia, for its ability to import data from a variety of sources; moreover, the output results can be handled by several postprocessing software, setting up a single, wider environment for the implementation of the model.

In the following, figures showing portions of ModelMuse interface are taken directly from thefilecontainingtheimplementationofthemodel.

3.1Gridandlayerdefinition

First of all, it is necessary to recreate, starting from a series of point data, the physical structure of the model, based on a grid with 55 rows, 57 columns and subdivided into 15 layers. The coordinates in the horizontal plane of the origin of the local reference system and the rotation angle of the grid (−38.5°) are available, as well as an Excel file containing,foreachcell:

- indication about the position of the cell in the model with respect to the indexing system of rows (��), columns (��) and layers (��), starting from the origin of the local referencesystem;

Calibration of ModelMuse to the alluvial fan of the River Marecchia

- coordinates X and Y in the global reference system, which define the position of thecellinthehorizontalplane;

- topandbottomelevation;

- indicationaboutthestatusofthecell(active/inactive).

All the (X,Y) coordinates are expressed in the UTM ED50 reference system (European Datum 1950),a geodetic datum which was defined afterWorld War IIfor theinternational connection of geodetic networks. This information is recorded in the Geo Reference dialog box(Figure 3.1):

Length unit and Time unit are those that will be used in the model for all input and output; inthiscasetheyaresettometersandseconds,respectively.

Dataarespecifiedevery50�� inthedirectiondefinedbyrows(thedirectioninwhichthe�� index varies), and every 49.3�� in the perpendicular one (the direction in which the �� index varies). To respect this distribution, the width of the rows is 50�� and the width of thecolumnsis49.3��

Each layer has a variable thickness, so it is necessary to specify the top and the bottom elevation of each cell. To do so, 16 objects are created, one referred to the Model Top and the others to the bottom of the further layers. For each of them a series of points is imported, characterized by coordinate X, coordinate Y and elevation (Figure 3.2). When importing point information, they are assigned to the data set Layer Definition of the consideredlayer(Figure 3.3).

Figure 3.1. Geo Reference dialog box.

Calibration of ModelMuse to the alluvial fan of the River Marecchia

The result is an object made of several point values which, interpolated, allow to shape the profile of the layers. Interpolation methods are used to determine how values should be interpolated among a group of objects. Eight algorithms are available in ModelMuse: Nearest, Point Average, Nearest Point, Inv. Dist. Sq. (Inverse Distance Squared), Triangle Interp. (Triangle Interpolation), Fitted Surface, Point Inv. Dist. Sq. (Point Inverse Distance Squared), and Natural Neighbor. Each of them has different characteristics, and the most suitable one should be chosen according to the specific kinds of objects involved and the desired outcomes. In this case, the Nearest Point interpolation method is used: it determines the object that is closer to the location where the data set in question is being evaluated,thentheformulaforthatobjectisappliedandthatlocation. The result is shown in Figure 3.4. In this figure and in the following ones the vertical exaggeration is set to 5: this option is used to change the ratio of the horizontal to the vertical scale, thus affecting how the model is displayed on the screen (front, side, and 3D views).

Figure 3.2. Coordinates and elevations of some points defining the Model Top.

Figure 3.3. Import Points dialog box to define Model Top.

Itis evidentthatsome unrealisticvalues arepresent, forexampleinthetop-rightportionof the grid. However, they fall outside the simulated domain and therefore this situation will notbeaproblem,asitwillbebetterspecifiedin Paragraph 3.2.1.

3.2InputDatasets

In the following, the other data sets specified in the implementation of the model will be presented.

Coordinates of active cells and values of initial heads are imported following the same procedure applied for layers elevations (Paragraph 3.1): series of point data are created, one for each layer, and they are assigned to the data set of interest; this process ends up with the creation of 15 objects perdata set. Fortheremaining data sets, a slightly different approach is used. For each of them, a single points object is created, whose vertices coincides with all the cells (in all the layers) of the active domain: they are then assigned thecorrespondingvaluesofthedatasetofinterest. Finally, the magnitude of horizontal anisotropy is 1 everywhere, so its default formula is setto1inordertoinvolveallthemodelcells.

Figure 3.4. Grid and layer definition.

3.2.1 Definitionofthesimulateddomain

As already mentioned in Chapter 2, MODFLOW is able to work with rectangular grids only. The representationof irregular-shaped simulation domains can be achievedby means of the implementation of the data set Active, specifying, for each cell, whether it is active or not. The simulated domain is constituted by active cells only, whereas inactive ones representthepartsofthegridwhichfalloutsidetheaquiferboundaries. Datasets(Paragraph 2.5.2)shouldbespecifiedforeverycell,activeorinactive.Therefore their default formulas are always stated, and applied in absence of any further indications of the user. However, only active cells are simulated when the model is run, and this allows to have some unrealistic or meaningless data sets values in the inactive parts of the grid, as occurs for the layer elevations in this case (Paragraph 3.1). In fact, this would not be relevant, provided that the definition of the cells to be considered active in the simulation is performed correctly. To do so, the default formula in the data set Active is changed to False, in order to make all the cells inactive in the absence of explicit indications. Then, following the same process applied to characterize the elevations (Paragraph 3.1), it is necessary to import the coordinates and the elevations of the cells to be made active, and to assign themto thedata set Active. Finally, for each of these objects, in the Object Properties dialog box, in the Active data set the formula is switched to True, inordertoturnallthecellsintersectedbytheobjectactive.

Figure 3.5 depictstheactivemodeldomain.

Figure 3.5. Active domain.

Calibration of ModelMuse to the alluvial fan of the River Marecchia

3.2.2 Hydraulicconductivity(Kx,Ky,Kz)andHorizontalanisotropy

The horizontal anisotropy is defined as the ratio of hydraulic conductivity along columns to hydraulic conductivity along rows, where Kx is the hydraulic conductivity along rows. Thus, the hydraulic conductivity along columns, Ky, is the product of the values in Kx and Horizontal_Anisotropy data sets. In this case, since horizontal anisotropy is 1 everywhere, Ky valueswillalwaysbeequaltoKx ones(Figure 3.6).

3.2.3 Startinghead

The data set Modflow_Initial_Head defines the initial head considered in the model. In steady-state conditions it represents the first trial distribution of hydraulic head, which allowstheiterativesimulationprocesstostart.Onthecontrary,intransientcondition(asin this case) it is an indication of the amount of water contained in the system at the beginningofthesimulation.

Figure 3.6. Distribution of Kx values over the top layer.

Calibration of ModelMuse to the alluvial fan of the River Marecchia

Theinitialheaddistributionconsideredinthepresentcaseisrepresentedin Figure 3.7.

3.2.4 Specificstorage

Specific_Storage data set, as well as Specific_Yield, has to be defined when the LPF, BCF6, or UPW package is active and the model contains at least one transient stress period. As already mentioned in Paragraph 2.1.1, the specific storage is the amount of water that a portion of an unconfined aquifer releases from storage, per unit mass or volume of the aquifer itself, per unit change in hydraulic head, while remaining fully saturated.Itisanaquiferproperty,anditisexpressedas:

Where:

- �� isthespecificweightofwater[���� �� ];

- �� is the porosity of the material, i.e. the ratio of the volume of voids over the total volume(dimensionlessnumberbetween0and1);

Figure 3.7. Starting Head values.

Calibration of ModelMuse to the alluvial fan of the River Marecchia

- �� isthecompressibilityofthebulkaquifermaterial[���� �� ];

- �� isthecompressibilityofwater[���� �� ]

Specificstoragevaluesadoptedinthemodelarerepresentedin Figure 3.8.

3.2.5 Specificyield

Specific yield, also known as the drainable porosity, is a ratio, less than or equal to the effective porosity, indicating the volumetric fraction of the bulk aquifer volume that a given aquifer will yield when all the water is allowed to drain out of it under the forces of gravity.

Where:

- �� isthevolumeofdrainedwater;

- �� isthetotalmaterialvolume.

Itisprimarilyusedforunconfinedaquifers,andcanbeclosetoeffectiveporosity.

Figure 3.8. Distribution of specific storage over the top layer.

Calibration of ModelMuse to the alluvial fan of the River Marecchia

3.2.6 Cellswettingoptions

In MODFLOW, as described in Paragraph 2.3.5, if the head in a convertible layer falls belowthebottomofthecorrespondingcell,thatcellturnsinactiveanditis ‘removed’from the model. However, an option exists which, if activated, makes dry cells active again in case neighbouring ones have heads higher than the base of the dry cell. This is termed as Rewetting option: with it, models could simulate the aquifer in a more realistic way, but at thesametimetheycouldbecomelessstable.

ModelMusedefinesthreedatasetsrelatedtotherewettingoption:

 Wet_Dry_Flag

If Wet_Dry_Flag > 0,anycelladjacenttothedrycell,excepttheoneaboveit,can cause the dry cell to convert to active. If Wet_Dry_Flag = 0, the dry cell cannot

Thedistributionofspecificyieldvaluesimportedinthemodelisshownin Figure 3.9.

Figure 3.9. Distribution of specific storage over the top layer.

Calibration of ModelMuse to the alluvial fan of the River Marecchia

convert to active again. If Wet_Dry_Flag < 0, only the cell below the dry one can turnittoactive.

 Wet_Dry_Threshold

It is the wetting threshold. Before the dry cell can convert to active, the head in neighbouring cells must exceed the sum of the elevation of the bottom of the dry cellandthewettingthreshold.

 WetDry

It is the product of Wet_Dry_Flag and Wet_Dry_Threshold. In it, the wetting threshold(������������)isspecified.

In the current model, Wet_Dry_Flag is set to −1 in all active cells, Wet_Dry_Threshold correspondsto1/10ofthelayerheight,and WetDry isequalto−0.01inallactivecells.

3.3Solverpackagesettings

The solver package (Paragraph 2.2.2) adopted is the Preconditioned Conjugate-Gradient (PCG), whichis usedto solve thefinite difference equations in eachstep of aMODFLOW stress period. The values of the several variables that have to be specified (Table 3.1) were providedasoperationalguidelinesbyArpae:

Itisthemaximumnumberofouteriterations,i.e.callstothe solutionroutine.ForalinearproblemMXITERshouldbe1, whereasifmorethan50inneriterationsarerequired MXITERcouldbeaslargeas10.Alargernumber(generally lessthan100)isrequiredforanonlinearproblem.

ITER1

NPCOND

Itisthenumberofinneriterations.Fornonlinearproblems, ITER1usuallyrangesfrom10to30;avalueof30willbe sufficientformostlinearproblems. 300

Itistheflagusedtoselectthematrixconditioningmethod:

- 1forModifiedIncompleteCholesky(foruseon scalarcomputers)

10 (1)

10 Inlinearalgebra,theCholesky decompositionorCholeskyfactorization isadecompositionof aHermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions. An incomplete Cholesky factorization of a symmetric positive definitematrixisasparseapproximationoftheCholeskyfactorization.

IHCOFADD

Calibration of ModelMuse to the alluvial fan of the River Marecchia

- 2forPolynomial(foruseonvectorcomputersorto conservecomputermemory)

Itisaflagthatdetermineswhathappenstoanactivecell surroundedbydrycells:ifitis0,thecellconvertstodry regardlessofHCOF(Equation (11))value(defaultoption);if itisnot0,thecellconvertstodryonlyifHCOFis0(i.e.no head-dependentstressesorstorageterms).Thisvariableis usedwithMODFLOW-2005andMODFLOW-NWTonly.

Convertactivecells todrywhen surroundedbydry cells(0)

HCLOSE

Itistheheadchangecriterionforconvergence,inunitsof length;whenthemaximumabsolutevalueofheadchange fromallnodesduringaniterationislessthanorequalto HCLOSE,andthecriterionforRCLOSEisalsosatisfied, iterationstops.

0.01 RCLOSE

Itistheresidualcriterionforconvergence,inunitsofcubic lengthpertime.Whenthemaximumabsolutevalueofthe residualatallnodesduringaniterationislessthanorequal toRCLOSE,andthecriterionforHCLOSEisalsosatisfied, iterationstops.

Fornonlinearproblems,convergenceisachievedwhenthe convergencecriteriaaresatisfiedforthefirstinneriteration.

0.01

RELAX

ItistherelaxationparameterusedonlywithNPCOND=1. Usually,RELAX=1.0,butforsomeproblemsavalueof0.99, 0.98,or0.97willreducethenumberofiterationsrequired forconvergence.

IPRPCG

MUTPCG

ItistheprintoutintervalforPCG.IfIPRPCGisequaltozero, itischangedto999.Themaximumheadchange(positiveor negative)andresidualchangeareprintedforeachiteration ofatimestepwheneverthetimestepisanevenmultipleof IPRPCG.Thisprintoutalsooccursattheendofeachstress periodregardlessofthevalueofIPRPCG.

Itisaflagthatcontrolsprintingofconvergenceinformation fromthesolver:0isforprintingtablesofmaximumhead changeandresidualateachiteration;1isforprintingonly thetotalnumberofiterations;2isfornoprinting;3isfor printingonlyifconvergencefails.

0

DAMPPCG

Itisthedampingfactor,aparameterthatcharacterizes thefrequencyresponseofasecond-orderordinary differentialequation.Itistypicallysetequaltoone,which indicatesnodamping.Avaluelessthan1andgreaterthan0 causesdamping.

>0:appliestobothsteady-stateandtransientstressperiods. <0:appliesonlytosteady-statestressperiods.Theabsolute valueisusedasthedampingfactor.

0

DAMPPCGT

Itisthedampingfactorfortransientstressperiods. DAMPPCGTisanoptionalvariablethatonlyisrequiredwhen DAMPPCGisspecifiedasanegativevalue.IfDAMPPCGTis notread,thenthesingledampingfactor,DAMPPCG,isused forbothtransientandsteady-statestressperiods.

Table

0

Noprinting(2)

3.1. PCG Package adopted variables.

Calibration of ModelMuse to the alluvial fan of the River Marecchia

3.4Internalflowpackage settings

As mentioned in Paragraph 2.2.2, internal flow packages simulate flow between adjacent cells. In the current model, Layer Flow Property (LPF) package is adopted. The following optionsareselected:

 Use vertical conductance correction (inverse of NOCVCORRECTION): NOCVCORRECTIONindicatesthatverticalconductanceisnot correctedwhenthe vertical flow correction is applied (the NOCVCORRECTION option is used when thecheckboxisnotchecked);

 Use vertical flow correction under dewatered conditions (inverse of NOVFC): NOVFC option turns off the vertical flow calculation described in Paragraph 2.3.4 and a vertical conductance correction, since its computation for convertible layers can cause numerical instabilities; these can be caused by possible large change in conductance between successive solver iterations; the NOVFC option is used when thecheckboxisnotchecked.

3.5Definitionofthe simulationperiods

The simulation covers a time span corresponding to the years 2014 and 2015. These are divided in 24 stress periods, represented by the months between January 2014 and December2015.So,thelengthofeachstressperiodcorresponds totheduration(expressed in seconds) of each month. Every stress period is subdivided into 25 time steps, and the simulationisin Transient conditions.

Figure 3.10. MODFLOW Time settings for the first stress periods.

Calibration of ModelMuse to the alluvial fan of the River Marecchia

Theunitsofmeasurement consideredfortheexpressionofanyinputdataandoftheresults are meters and seconds in the whole model (Figure 3.1). For this reason, also the starting and the ending time of each stress period should not be specified in conventional date format: on the contrary, they should be converted into seconds considering 01/01/2014 at 00:00astheinitialmoment.Followingthisconvention,forexample,the day01/02/2014at 00:00 will correspond to a value of 2678400��, given by 31��∙24ℎ/��∙60������/ℎ∙ 60��/������, where 31�� are the days in January (i.e., the time preceding the beginning of February).

Table 3.2 reports the definition of the 24 stress periods, comparing the two described formats.

Table 3.2. Starting and Ending time of the 24 stress periods.

Calibration of ModelMuse to the alluvial fan of the River Marecchia

3.6Definitionofthe wells

In the model fourwells arepresent: Pozzo 35, Linaro, Bornaccino and Ceccarino. For each ofthem,somefeaturesareavailable:

- XandYcoordinates;

- theelevationofthegroundlevelwherethewellislocated;

- thedepth;

- thepositionandthelengthofthefilters;

- the average discharge value for each stress period of the simulation, expressed in �� /��.

To represent the wells, four point objects are created (Figure 3.11). Each of them is assigned its coordinates in the horizontal plane (X and Y) and the top and the bottom elevation, identified respectively by the upper and lower elevations of the filter expressed inmetersabovesealevel.

Finally,whentheWELpackageisactivated,thevaluesrelativetoeachstressperiod(listed in Table 3.3) are imported for each well. As described in Paragraph 2.4.1, negative values representwaterwithdrawal.

Figure 3.11. Point objects representing the pumping wells.

Calibration of ModelMuse to the alluvial fan of the River Marecchia

3.7Definitionofthe arealrecharge

As already mentioned, RCH Package simulates areally distributed recharge to the groundwater system. The active domain of the model is subdivided into 7 zones (Figure 3.12), on the basis of the results obtained by means of the software CRITERIA. Each zone isrepresentedasapolygon,forwhichthefollowingfeaturesareknown:

- XandYcoordinatesofthevertices;

- thedischargesenteringthemodelperunitsurfaceforeverystressperiod.

Table 3.3. Pumping well discharges.

Calibration of ModelMuse to the alluvial fan of the River Marecchia

For each of the 24 stress periods of the simulation, average monthly values are considered which are computed from the soil water balance (model CRITERIA by ARPAE-SIMC). They are listed in Table 3.4, together with colors to identify the corresponding zones in Figure 3.12

Recharge values should be assigned to the top active layer, since the model is made of severallayersandthefirstonecouldrundry.

Figure 3.12. Recharge zones.

Calibration of ModelMuse to the alluvial fan of the River Marecchia

3.8Definitionofthelake

To simulate the Incal System recharge lake, the LAK Package (Paragraph 2.4.6) is used. The cells occupied by thelake extend from theModel Top to the bottom of the third layer, andtheircoordinatesareknown(Figure 3.13).

Table 3.4. Recharge values for each zone.

Figure 3.13. Representation of Incal System recharge lake in the model.

Calibration of ModelMuse to the alluvial fan of the River Marecchia

For every stress period, the water fluxes entering and exiting the lake should be specified. They areexpressedas volumetricrates, and they could be dueto precipitation, evaporation and overland runoff; eventual other categories, such as artificial supply or withdrawal for human water use, are listed under the column Withdrawal. Negative values are used to indicateaugmentationofthewatervolumeinthelake,asinthiscase.

Theaverageflowsconsideredateachstressperiodofthesimulationarelistedin Table 3.5.

Precipitation, evaporation, and overland runoff are null at every stress period. Other variables that should be specified are the minimum and the maximum water stage in the lake (26.2m and 31.3m, respectively), and the initial stage at the beginning of the first stressperiod(29.8m).Thefirsttwovaluesareonlyused forsteady-statestressperiodsbut mustbedefinedforallstressperiods.

Table 3.5. Volumetric rates injected in the lake at every stress period.

Calibration of ModelMuse to the alluvial fan of the River Marecchia

Thepresenceoflakebed sediments, whichaffecttheflowbetweentheaquiferandthelake, is also simulated by means of a lakebed leakance term including the thickness and the hydraulic conductivity. The flow from the aquifer to the lake depends on both the lakebed leakance and the conductance aquifer cells adjacent to the lake. In this case the lakebed leakance,specifiedbymeansofaspecificdataset,is10 s . Another parameter that should be specified for the LAK Package is Theta: it is the weighting parameter factor for computing lake stage during transient MODFLOW time steps. In particular, Theta determines whether the solution for the lake package is solved implicitly (Theta = 1) or semi-implicitly (0.5  Theta  1). Theta is automatically set to 1 forallsteady-statestressperiods.

Inthiscaseitissetto0,whichinvolvestheexplicitmethodforthecomputationofthelake stage:infact,ateverystressperiodthewaterlevelinthelakeisdetermined,anditdepends onboththein-outwaterbalanceandontheshapeofthelake.

3.9Definitionoftheriver

As already mentioned, Streamflow Routing Package is applied to simulate streams; in the caseoftheconsideredgroundwatermodel,itisusedtorepresenttheRiverMarecchia.SFR package requires the subdivision of the stream in homogeneous branches (arches), separated by nodes. Such nodes represent chosen points along the river, and each of them is associated to a minimum elevation of the riverbed: the specification of this feature is connected to the availability of a topographical section detected from the riverbed morphology.

For the River Marecchia, the choice of nodes and arches in the area of the alluvial fan has beenmadefollowingthreemaincriteria:

 the differentiation between the zones covering the unconfined aquifer and those coveringthesuperiorconfinedaquifer;

 the attention given to the specific discontinuities along the topographic profile of theriverbedminimumelevations,andtothegeometryofthecrosssections;

 giving priority to the most recent observations and reliefs of the topographical sections, where many exist over the years; this is due to the fact that the riverbed

Calibration of ModelMuse to the alluvial fan of the River Marecchia

morphology is subject to sediment deposition, and so it continually evolves over time.

Riverbed elevations are determined by linear interpolation of the minimum elevations at nodes, considering constant slope between the upstream and the downstream one of every arch.

Hence each of the arches composing the River Marecchia is identified by an upstream and a downstream node, and is characterized by a riverbed cross section which is constant alongeachstretch(Figure 3.14).

The choice of the sections is performed taking into account the average and most representative features of the arch. Once these characteristic sections are identified, they are schematized by means of the 8 most relevant points; among them, 4 define the wet perimeter of the riverbed, whereas the other 4 (2 on the left and 2 on the right) complete the side banks of the section. Conventionally, the first point is the one to the uppermost hydrographic left, and the others are characterized by a progressive distance from it. Moreover,allpointsareidentifiedbytheelevationwithrespecttotheriverbed.

Figure 3.14. Maps of nodes and arches for the River Marecchia. (Arpae)

Calibration of ModelMuse to the alluvial fan of the River Marecchia

The possibility to specify the cross section of the river allows to determine the correct length of the wet perimeter as a function of the streamflow into the river. This information is very useful, sinceit is a way to characterizemore in detail the areawhere the interaction river-aquiferactuallyoccurs,anditsrelativefluctuationsduringthesimulation. In the implementation of the current model, the considered arch lies between two nodes defining (upstream and downstream, respectively) the Appennine edge and the boundary between unconfined-confined aquifer (blue area in Figure 3.14). The representative cross section considered is schematized in Figure 3.15, where the coordinates of the 8 representativepointsareknown.

Thefollowinginputdataarealsoknown:

 averagemonthlydischargevalues,computedbasedondailyones;

 Manning’sroughnesscoefficient11 for thechanneland the overbank areas in all reachesinthissegment,bothequalto0.045��/�� / foreverystressperiod.

11 The Manning formula is an empirical formula estimating the average velocity of a liquid flowing in an open channel as a function of the hydraulic radius of the stream, its slope and the Gauckler-Manning’s

Figure 3.15. Cross section of the arch represented in the model. (Arpae)

3.10 Definitionofboundaryconditions

The General-Head Boundary package is used to simulate head-dependent flux boundaries; the flux is always proportional to the difference in head. This boundary condition should be imposed to all the cell delimiting the simulated domain. From the practical point of view, an object is created made by points (Figure 3.17) characterized by the ��,��,�� coordinatesoftheinterestcells.Foreachofthem,twotypesofdatashouldbespecified:

 avalueofheadforeverystressperiodcomposingthesimulation;

 a value of conductance for the regulation of the exchange flow; such data are expressedin�� /�� anditaresupposedtobeconstantintime.

Input data are applied uniformly to all layers in the model, setting the upper and lower elevations of imported points. The analysis of the piezometric trends recorded for the monitoring boundary wells allow to derive such data by means of interpolations and adjustments.

coefficient. The latter, often denoted as n [TL-1/3], is an empirically derived coefficient, representing the roughness of the conduit where the fluid flows. It depends on many factors, including surface roughness and sinuosity, and it is inversely proportional to the fluid velocity. In natural streams, n valuesvary greatly along a reach, and also vary in a given reach of channel with different stages of flow. Most research shows that n willdecreasewithstage,atleastuptobank-full.

Figure 3.16. Model representation of Marecchia river.

3.11 Definitionofthe observedpiezometriclevels

This package is used to simulate wells and piezometers whose water level records will be used to calibrate the model. The devices considered are those belonging to the managed recharge project network for which piezometric observations are available in the time span covered by the simulation, i.e. the two-year period 2014-2015. For each device, the followingdataareknown:

- XandYcoordinates;

- thegroundelevation;

- thedepth;

- the observed piezometric values (recorded both in continuous and manually) and thecorrespondingdates.

The points of the network are represented by a series of point objects (Figure 3.18), to which the (X, Y) coordinates of the wells and the piezometers are assigned. Differently from WEL package, in this case the objects identifying the observation wells are monodimensional, their elevation being indicated by the difference between the ground elevation and the depth of the well. Moreover, points are attributed to the HOB package, and for each of them the measured piezometric levels are imported with the corresponding dates, the latter converted into seconds following the same procedure described in

Figure 3.17. Points defining the general-head boundary conditions.

Calibration of ModelMuse to the alluvial fan of the River Marecchia

Paragraph 3.5 for the stress periods. Observations are considered to be recorded at 00:00 oftheindicatedday.

3.12 Modeldevelopment

3.12.1 Implementationoftheriver

After the implementation of all the elements as described above, a first attempt to run the model was performed. As a result, the simulation stopped before completing all the 24 stress periods. The output file showed a list of the reaches with altitude error: it reported the coordinates of thecells representing theriver, their bottom elevation and the streambed elevation at that location. The resulting error was “Model stopping due to reach altitude error”, occurring in all the cells representing the river. This kind of control on the code execution is not reported in the online documentation, therefore a trial-and-error approach wasrequiredtoresolvetheproblem.

Tounderstandtheorigin oftheerror,atthebeginningthemodelrunwasrepeatedbyusing earlier versions of MODFLOW 2005 and MODFLOW 2000. Comparing the results with those obtained with version 1.12 of MODFLOW 2005, it was concluded that in this version MODFLOW developers added a check module that was not in the old versions.

Figure 3.18. Point objects representing the observation wells.

Such check module causes the altitude error, and apparently it has been implemented over theconsecutiveversionsofMODFLOW2005.

In Packages and Programs, activating the option Print flows in .sfr_out file available for the SFR package, it is possible to collect in a separate file all the elements of the water budgetrelatedtothecellswhichtheSFRconditionisattributedto. In this file it is possible to evaluate the variation of the river flowing discharge over the simulated arch, water volumes exchanged between the river and the aquifer, and other parameters characterizing the considered phenomenon. In particular, by subtracting the values listed in the column STREAM DEPTH from those in the column STREAM HEAD, thestreambedelevationsassumedbyMODFLOWcanbecalculated. Comparing the .sfr_out file with the outcome provided by MODFLOW 2005 with the altitudeerror,itwaspossibletoinfertwoconsiderations:

a) With respect to MODFLOW 2000, MODFLOW 2005 introduces a check on the streambed elevations, that should be higher than the bottom elevation of the corresponding cell (for all the cells where the SFR boundary condition is applied). The actual streambed elevation is given by the input upstream and downstream elevations (variable along the arch from 34�� to 22��) lowered by the streambed thickness (2��). This verification is performed at every iteration of the simulation and,ifnotsatisfied,itleadstotheerrorandthestoppingofthemodelrun.

b) The previous point does not imply that the SFR condition should be limited to Layer1: in fact, if cell (��,��) in the uppermost layer was inactive(dry, for example), the code would apply the SFR condition to the first active (��,��) cell, along the vertical direction, in layer k. However, this evidence does not allow to overcome theproblemhighlightedatpoint a)

Giventhatriverbedelevationsarefixed,inorderto simulaterealconditions,andtakeninto account the two previous considerations, two possible solutions have been identified to overcomethealtitudeerror:

1) to intervene on the cells containing the SFR boundary condition, lowering their bottom elevation such that it contains the bottom of the riverbed, including the streambedthickness;

2) to intervene on the IBOUND of the uppermost layers, making the cells defining the river inactive: in this way, the boundary condition would be directly applied to the underlyinglayer,overcomingthealtitudeerror. The second method entails some approximation with respect to real conditions. In particular, the water balance would not take into account the cells containing the river anymore, and this would lead to a slight variation on the stored volumes. However, such variation is acceptable, since the thickness of the first three layers (1��) is much thinner than the thickness of Layer 4, and therefore the ‘lost’ aquifer volume would amount to 1‰ofthetotalvolume.

In this way, the river-aquifer interaction would occur in Layer 4. The latest could in any case assume a water level higher than its top elevation, resulting in being fully saturated. For this reason and for the one mentioned above, the second solution method has been adopted.

Actually, this solution is not conclusive: in fact, even though the SFR cells are inactive, as thesimulationgoesonthesamecellsarere-activatedbytherewettingoption,dueto which dry cells can become active again if neighboring cells have heads higher than the base of the dry cell (Paragraph 3.2.6). As a result, the control generating the altitude error is performedagain,causingthesimulationtostop. This problem canbe solved deactivating the rewetting option. The resulting approximation can be considered acceptable, since it leads to slight variation in the river-aquifer interaction only. On the contrary, other effects are not relevant: without the rewetting option, in fact, the cells of the uppermost layers would run dry, but their thickness is negligible compared to the one of the underlying layers and the water balance will be only partially affected. Moreover, the water stage observations are linked to deeper elevations, andthereforearenotinfluencedbythestatusofthetopcells.

3.12.2 Observedvalueslocationandmodelstability

Another verification that should be performed is that observation points should not be locatedinverythinlayer.Infact,inthemodeltherecanbeinaccuraciesinthedefinitionof the ground level due to the interpolation of point data. Since the location of the observed

values is defined as a depth from the ground level, these inaccuracies may affect which layertheybelongto.

For this reason, to increase the model stability it is preferable that observation points fall into layer of significant thickness. The depth of the observation that did not fulfill this condition (RM5 and RM7) has been slightly reduced, in order for them to fall into a larger layer(Layer4).

4. Resultsandpostprocessing

The results obtained by means of the implemented model are in line with those deriving from already-existing models. In general, the process of model calibration and validation requires many steps. However, ModelMuse potential forthe representation of the results is limited. In order to increase the opportunities to perform the post-processing of the output data, two USGS application software were identified that, together with ModelMuse interface, constitute a single environment for the implementation of the model. These softwareareGW_ChartandListingAnalyst.

4.1GW_Chart

GW_Chart isaprogramforcreatingspecializedgraphsusedingroundwaterstudies,which can also convert some of the binary files produced by MODFLOW to text files. It incorporatesthefunctionalityoftwopreviousUSGSprograms(BudgeteerandHydrograph Extractor, both aimed at reading the output files from MODFLOW, plotting the results, and saving the data in forms that can be readily imported into spreadsheet and graphics programs) and adds additional new features. The program is designed to provide rapid analysis of budget data and a method of exporting them in a form that other programs can readilyutilize.

SevenmajortypesofplotscanbeshapedwithGW_Chart:

 Calibration Plots: graphs representing observed and simulated data of interest, pointingoutthedifferencesandhenceevaluatingtheefficiencyofthemodel;

 Water Budget Plots: results can be plot of either a single zone in a single time step or for all the time steps of a single zone; if the user chooses to plot a single time step, the data will be displayed as a bar graph, otherwise, a line graph will be plotted; it is also possibleto select which budget items will beshown, and atwhich timestep;

 Hydrographs,i.e.theplotsrepresentingtheflowingdischargeasafunctionoftime;

 Lake and Gage Plots: data relating to the LAK package, SFR package, or UZF (Unsaturated-Zone Flow) package can be plotted from the MODFLOW (or other sources)listingfile;

 Piper Diagrams, which are graphical representations of thechemistryof awatersampleorsamples;

 Cell Water Budgets or Zeta: GW_Chart can plot the water budget flow terms for individual cells in MODFLOW models using the information in the budget file createdbyMODFLOWorforZetafilescreatedbytheSeawaterIntrusionpackage;

 Farm Budgets: they consider the input file of the Farm Process, which estimates dynamically integrated supply-and-demand components of irrigated agriculture as partofthesimulationofsurface-waterandground-waterflow

4.2ListingAnalyst

The implementation over time of more and more powerful computers allowed to simulate groundwater models in a more exhaustive way. This finer scale of detail causes models to havelargeroutputfiles,whoseanalysiscanpresentachallengetothemodeler. ListingAnalyst is a public-domain MODFLOW utility program intended to facilitate analysis oflisting files forMODFLOWmodels. To facilitate navigation through thelisting file,theprogramautomaticallysearchesforheadingsinthelistingfileanddisplaysthemin a tree-view control when a file is first opened. The program also searches for error and warning messages, and lists them separately. Headings, errors and warnings are also identifiedthroughexaminationofthesourcecode. When ListingAnalyst opens a MODFLOW listing file, instead of loading the entire file in memory, it only shows a user-specified number of lines. The user can choose which lines to display by specifying a starting line or using a scroll bar. Since only a small part of the file is displayed at a time, the amount of employed memory is manageable. The program hasasearchfunctiontoallowtheusertosearchtheentirefile foranytextofinterest.

4.3Results

In the following,themainresultsobtainedin termsofwater balancewill bepresented. Not only the global amounts of water entering and exiting the aquifer system will be considered, but also the ‘partial’ contributions of the main elements such as the river and thelake.

A general consideration to be pointed out is thatthe water budgetis referred to the aquifer; therefore, entering (IN) terms add water to the aquifer, whereas exiting (OUT) terms indicate water flowing out of the aquifer. Moreover, two categories are distinguished within the water budget: Cumulative and Rates. The former takes into account all water volumes (expressed as [��]) as sums of volumes added to or removed from the aquifer since the simulation starting time; the latter (expressed as [���� ]), on the contrary, is representativeofthewaterflows.

4.3.1 Comparisonbetweenobservedandsimulatedheadvalues

Before starting with the evaluation of the various processes involved in the model, goodness of fit testing is assessed. The plot in Figure 4.1 reports on the X axis the observed head values (i.e. those imported as input data by means of the HOB package), and on the Y axis the values at the same time and location computed by the model. The straight line represents the equality of observed and simulated data, which outlines perfect model performances. The dispersion of points around this ideal configuration can be considered as a criterion to assess the efficiency of the model in representing the real situation.

The plot in Figure 4.2 provides a conceptually similarrepresentation, with theverticalaxis reporting the difference (residual) between observed and simulated values. The general trend shows a good agreement between the two series of measures; observing the two plots, it can be stated that for lower head values simulated results exceeds observed data, whereasforhigherheadvaluestheoppositesituationprevails.

4.3.2 Globalwaterbudget

Thetermsconsideredinthewaterbudgetare:

- Storage:inatransient simulation,thestoragecomponentcomesfromporousmedia storing and releasing water, because of specific storage (confined aquifers) or specific yield (unconfined aquifers); it should be remarked that flow into storage is anoutflow,whereasflowoutfromstorageisaninflow;

- Head dep bounds: it considers the contribution deriving from head-dependent flux boundarypackages(inthiscase,theconditiondefinedbyGHBpackage);

Figure 4.1. Comparison between observed head values (X axis) and simulated ones (Y axis).

Figure 4.2. Distribution of the differences between observed head values and simulated results, as a function of the observed input data.

- Recharge:it representstheamountof water duetothespecifiedareal rechargerate; totalfluxenteringeachcellwillbetheratetimesthehorizontalareaofthecell;

- Stream leakage:inflowsandoutflowsresultingfromtheriver-aquiferinteraction;

- Lake seepage:inflowsandoutflowsresultingfromthelake-aquiferinteraction;

- Wells: it represents the water volume added to or removed from the aquifer by artificial injection or withdrawal; in this case, wells only remove water from the system.

Figure 4.3 below presents the cumulative volumes entering the aquifer (Y axis) over the time span covered by the simulation (X axis). It is evident that Stream Leakage and Head dep bounds termsplay amajorroleinthe water budget.Thistrendcanbefoundalsointhe representation of each time step (Figure 4.4), where the inflow rates (Y axis) are shown as afunctionofthecorrespondingstressperiod(Xaxis).

The largest volume increment due to stream leakage occurs at the beginning of the 22nd stressperiod,i.e.October2015.Comparingthisevidencewith theinputstreamflowdata,it is possible to see that there is no correspondence between the maximum value of stream leakage and the maximum value of stream discharge (this one occurring at the 2nd stress period,i.e.February2014).So,thereisnotadirectrelationshipbetweenthetwoquantities.

Figure 4.3. Cumulative contributions added to the aquifer by each element interacting with it.

Figure 4.4. Inflow rates at each stress period given by the terms contributing to the aquifer water balance.

In Figure 4.5 and Figure 4.6, the exiting contributions are represented both in terms of cumulative volumes and in terms of flow rates, respectively. In both cases, the main contribution is given by Head dep bounds term. The largest volume decrement occurs at thesametimeasthelargestincrement,i.e.inOctober2015. Forboth cumulativeinflowsandoutflows, the curvesof all contributionsare almostlinear: thismeansthattherearenotsuddenchanges.

Since Head dep bounds results to be one of the main contributors for both inflows and outflows,itstrendhasbeenhighlightedin Figure 4.7,wherewaterflowsarerepresentedas afunctionoftime.Theoutflowratesaregreaterthantheinflowratesateverystressperiod, so this boundary condition mainly results in reducing the water amount stored into the aquifer.

It can be noticed that the trend is not regular, but there are sudden variations at the beginning of the stress periods. After some time, these peak values stabilize at an almost constantratevalue,whichprevailsuptotheendofeachstressperiod.

Figure 4.5. Cumulative contributions removed from the aquifer by each element interacting with it.

Figure 4.6. Outflow rates at each stress period given by the terms contributing to the aquifer water balance.

IN and OUT rates have an opposite trend: when inflows grow, outflows decline and vice versa.Moreover,outflowsvariationsarelargerthaninflowsones.

4.3.3 TotalINvolumesandtotalOUTvolumes

In this paragraph, the total amounts of water entering and exiting the aquifer will be considered,intermsofbothcumulativewaterbalance(Figure 4.8)andratesateverystress period (Figure 4.9). Comparing the two plots, it is possible to see that the difference between IN and OUT contributions is very small. This fact will be shown in Paragraph 4.3.4

,dealingwiththediscrepancytrendovertime.

From Figure 4.9 it can benoticed thatthere are peaks in the variation ofboth IN and OUT volumes at the beginning of each stress period, meaning that the changes in input data and boundary conditions cause sudden increments in the global aquifer water balance. These increments stabilize after some time, reaching an almost constant value before the end of eachstressperiod.

Figure 4.7. Comparison between inflow and outflow rates caused by Headdepbounds term at each stress period.

Figure 4.8. Total IN and OUT cumulative contribution to the aquifer water balance.

In order to better compare total IN and OUT volumes, the difference between the two has been represented as a function of time both as a cumulative volume (Figure 4.10) and as a rate (Figure 4.11) for every stress period. Cumulative volumes are reported with their actual value in Figure 4.10, whereas in Figure 4.11 they have been divided by 50 to make themcomparablewiththeseriesdescribingtheratesofvariation.

In Figure 4.11 the moving average of the rates series has been added. Accordingly, the value recorded at time �� is substituted by the average value computed on the interval between ��−�� and ��+�� ; in this case, �� =�� =12��. The aim is to smooth the variability of a time series, by reducing the irregularities and highlighting the underlying trend. Results at the series extremes are less reliable, since the interval on which the averageiscomputedcontainsfewervalues. When all these time series assume positive values, IN volumes are larger than OUT volumes;onthecontrary,whenthey assume negativevalues,OUTvolumesarelargerthan IN volumes. Considering the curve representing inflow and outflow rates, it can be assessed that IN quantities exceeds OUT quantities in 10 stress periods, coinciding approximatelytotheperiodswhentherechargeis applied. The cumulative series is positive only over two stress periods (March – April 2014): this means that globally outflows exceeds inflows, even though the volumes at stake are small comparedtothetotalamounts.

Figure 4.9. Total inflow and outflow rates contributing to the aquifer water balance at each stress period.

4.3.4 Percentdiscrepancy

In the volumetric budget reported in the listing file, values of percent discrepancy for each stressperiodarelisted.Theacceptablevalueofdiscrepancyisnotanabsolutecriterion,but it depends on models and their intended purposes. Therefore, there may be situations where a discrepancy of 0.05% is acceptable, whereas in other contexts the same value wouldnotbesufficientlyaccurate.

The absolute value of percent discrepancy should not be greater than 1% at any time step. However, at earlier time steps there can be a larger imbalance if boundary conditions are slightly different from real conditions; this would not be a matter of concern if the discrepancyassumesreasonablevaluesatsubsequenttimesteps.

In the current case, the values of percent discrepancy (Figure 4.12) cover an interval comprisedbetween−0.06%and0.06%,thusarealwaysinferiortothelimitvalueof1%.

Figure 4.10. Trend over time of the difference between volumes entering and exiting the aquifer.

Figure 4.11. Comparison between the trends of IN-OUT difference, in terms of cumulative volumes and flow rates.

4.3.5 Riverwaterbudget

In Figure 4.13 the heads over time at the upstream and the downstream sections of the river are represented. They have both the same trends even though the magnitudes are slightlydifferent:thisresultinthatbotharesubjecttoadecrease,butitismorerelevantfor theupstreamnode.

Figure 4.14 reports a comparison among head

upstream

downstream sections, the difference between the two, and inflows in the aquifer due to river leakage; the values of the latest series are multiplied by 5 in order to amplify their magnitude and more easily detect their trend over time. All these curves behave approximately in the same way, with some differences in the variation magnitude. Due to this, it can be stated that the contribution of the river leakage to the water amount added to the aquifer ateach time step isdirectlyproportionaltothestreamflowhead.

Figure 4.12. Discrepancy trend as a function of time.

Figure 4.13. Trend over time of the head values simulated at the upstream (17, 44, 4) and downstream (48, 15, 4) sections of the river. The coordinates represent the model cells containing the corresponding section of interest.

at

and

4.3.6 Lakewaterbudget

This paragraph will be hinged on the analysis of the contributions to the aquifer water balance given by the lake. Differently from what occurred for Head dep bounds terms, in the case of the lake seepage inflows always exceeds outflows considering cumulative volumes (Figure 4.15), and for the majority of the stress periods considering flow rates (Figure 4.16). From this observation, it is possible to infer that, even though the volumes moved by head-dependent fluxes are larger than those determined by lake seepage, the latest contribution is the most relevant in terms of increase of water volume accumulation intheaquifer.

It can also be observed that a high variability characterizes flows both from the lake to the aquifer and from the aquifer to the lake. This can be read as a signal of an active interactionbetweenthetwoelements.

Figure 4.14. Comparison among head values at upstream and downstream sections, the difference between the two, and inflows in the aquifer due to river leakage (these multiplied by 5).

In Figure 4.17, IN and OUT flow rates defining the water balance related to the lake are represented for each stress period together with the injection rates. Two considerations can bedrawn:

 an increment of IN rates is simulated when there is an increment of the injection rate; the delay between the two is very small, meaning that the effects of the artificial recharge are almost immediately detected in terms of water flow into the aquifer;

 when there is no artificial recharge, there is an increment in the outflows from the lake.

Figure 4.15. Total IN and OUT cumulative contributions of the lake to the aquifer water balance.

Figure 4.16. Total inflow and outflow rates relative to the lake contributing to the aquifer water balance.

Theplotin Figure 4.18 representsthevariationofthewatervolumepresentinthelakeasa function of time over the simulation period. The largest increment is recorded at the beginning of the second stress period (i.e. February 2014), and it is nearly equal to 14˙700�� . On the contrary, the largest decrement is recorded at the beginning of the 19th stressperiod(i.e.July2015),anditisapproximatelyequalto−18˙900�� .

Figure 4.17. Comparison between IN and OUT flow rates defining the lake water balance at each stress period, and the input injection rates. All the curves are represented as positive contribution, even though they assume different signs according to the direction of the flow (positive from the lake to the aquifer, negative from the aquifer to the lake).

Figure 4.18. Variation of water volume in the lake over the simulation period.

5. Evaluation of model sensitivity to different recharge configurations

As already mentioned in Paragraph 1.3, the purposes of the artificial recharge project of the River Marecchia alluvial fan are manifold, and primarily concern the increment of water availability within the aquifer and the improvement from a qualitative point of view. The current work did not account for any qualitative analysis, therefore only the quantitativeaspectswillbeconsidered.

The simulations that have been carried out show what is the relative contribution of the different sources of recharge. In particular, it has been shown that the total contribution from the river over the past two-years period is 39.5million �� and reaches the aquifer with a short delay. Conversely, the IN contribution from the lake is 5.6million �� . These results are not in disagreement with the observed outcomes from the recharge experiment of2014-2015,andthereforeconfirmthat:

- Thebenefitsattainablewiththerechargearesignificantintermsofstoredvolume;

- Recharge operated by theriver is much morerelevant in volume with respect to the rechargebythelake.

Some additional simulations were carried out by raising the level of the lake up to 30.3��, 30.8�� and lowering it to29.3�� and28.8��. Results were comparedin terms ofvolumes entering and exiting the aquifer over the simulation time span. Attention is given to the differenceovertimebetweenINandOUTcontributionsofthelake.

From Figure 5.1 it can be noticed that, although all the curves have the same trend over time, there is not a linear relationship between the initial water stage (and therefore, the initial volume present in the lake) and the volume of water entering the aquifer. On the contrary, the largest income to the lake occurs when the initial water stage corresponds to 29.8��

Similarconclusionscanbederivedfrom Figure 5.2,representingthecumulativeamountof water leaving the aquifer. In this case, the simulation having the initial stage equal to 29.8��producesthelowestwaterlossfromthelake.

These evidences result in the fact that an initial starting head in the lake equal to 29.8�� leads to the highest values of the difference between entering and exiting water volumes. This means that in general IN volumes are larger than OUT volumes, and in this case the differenceismorepronounced.

In Figure 5.3, all the curves representing the IN – OUT difference have the same trend; at the beginning of the simulation, however, these trends leads to a different behaviour in terms of water balance. For initial water stages in the lake higher than 29.8��, in fact, the curves always lie in the positive semi-plan: this means that IN volumes are always larger than OUT volumes, and the lake contributes to increase the water volume stored in the aquifer. On the contrary, for initial water stages smaller than or equal to 29.8��, the first partofthecurvesliesinthenegativesemi-plan,meaningthatOUTvolumesarelargerthan

Figure 5.1. Variation of the cumulative IN volumes of the lake contribution to the aquifer water balance, expressed as a function of time for different values of initial water stage.

Figure 5.2. Variation of the cumulative OUT volumes of the lake contribution to the aquifer water balance, expressed as a function of time for different values of initial water stage.

IN volumes and the aquifer ‘looses’ water because of the lake. Moreover, it can be noticed that these parts are larger as the initial water stage decreases, and therefore it can be stated that the water loss from the aquifer is larger as the initial water stage in the lake decreases andtheamountofwaterstoredinthelakebeginstoincreaseafteralongertime.

Figure 5.3. Variation of the cumulative difference between of IN and OUT volumes of the lake contribution to the aquifer water balance, expressed as a function of time for different values of initial water stage.

6. Conclusions

The work presented here confirms the potential benefits that can be provided by a groundwater simulation model for optimizing water resources management. Aquifers play a relevant role in the mitigation of the risk due to the occurrence of drought events in the Emilia-Romagnaregion. In fact, their capability to store relevant volumes of water and the long time span between meteorological and groundwater droughts make aquifers an essential resource during dry periods. On the other hand, the physical behaviours of aquifers are poorly known and therefore to plan the optimal use of groundwater is still a challenging task. Some aquifers in the Emilia-Romagna region have a long recharge time and their water has been proved to be long aged and therefore sustainability of the current waterusesisarelevantconcern.

Several international experiences on the management of aquifers for civil and agricultural water supply have shown the value of the information that can be derived by running groundwater simulation models. In particular, MODFLOW, an open access groundwater simulationmodeldevelopedbytheUnitedStatesGeologicalSurvey,iswidelyapplied. Thepurpose ofthis work isto applyMODFLOW tostudysolutionsformanagingartificial recharge in the Marecchia River Alluvial Fan. In particular, a previous application of MODFLOW proposed by the Regional Agency for Environmental Protection (ARPAE) has been repeated by using a different model interface.The purposeof the work is to study additionalrechargesolutions. Modelcalibrationhas confirmedthecapabilityofthemodeltoprovidereliablesimulations of the dynamics of the aquifer by using the parameters determined for the whole considered fan. The value assumed by the model parameters are physically plausible. However, the calibration procedure highlighted that other parameter sets may lead to comparable model performances, therefore highlighting that further calibration attempts may be needed for more specific and targeted applications. The application confirmed that recharge may be very successful in this particular case for mitigating the impact of water withdrawalintermsofstoredwatervolume.

In a more general context, the work presented here confirms the value of mathematical modelingofenvironmentalprocesses,whichmayprovidevaluabletechnicalguidance.

References

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Acknowledgements

A conclusione di questo lavoro di tesi, mi sento di ringraziare tutte le persone che finora hanno incrociato la loro vita con la mia, aiutandomi a crescere dal punto di vista professionaleeumanoelasciandomiqualcosadibello.Traloro,unpensierospecialeva:

al prof. Alberto Montanari, che in questi mesi mi ha seguito e ha avuto fiducia in me,stimolandol’interessepergliargomentitrattati;

all’Ing. Andrea Chahoud, sempre disponibile a consigliarmi e aiutarmi durante lo svolgimentodellatesi;

alla mia famiglia, in particolare ai miei genitori e a mio fratello Pietro, che mi hannosempresostenuto,consigliandomieappoggiandoognimiascelta;

a Luca,la (ri)scopertamiglioreche potessifare, chegiornodopogiorno misostiene emispronaadareilmegliodimestessa;

a tutte le compagne della mia squadra di pallavolo, in particolare a Claudia, Elisabetta, Ilenia, Letizia, Maria, Martina, Melissa e Silvia:ognunadiloro,amodo proprio, grazie alle esperienze che abbiamo condiviso negli anni dentro e fuori la palestra,èarrivataagiocareunruolofondamentalenellamiavita;

a Chiara, Marco e Riccardo, che in questi anni hanno condiviso con me gioie e fatichedella vita non solo universitaria:grazie a loro questo percorso ha avuto tutto unaltrosapore;

a Federico, che negli anni è stato una presenza costante e sicura su cui poter fare affidamento;

alle amiche e agli amici del gruppo Sentinelle Del Mattino, con cui è sempre una gioiacondividereilCamminoanchequando‘lasalitanonva’.