Stochastic Hydrology Course, with focus on Geostatistics University of Querétaro
E. Leblois (Irstea Lyon) – Second version : June, 22 -27 , 2015 General structure Assumption : a course running along 2 month, with, for students, about 15 h personal work (0,5 day a week during weeks 1 to 4) 36 h course with practical exercices (1,5 day a week during weeks 1 to 4) 36 h mini project (6 days spread weeks 4 to 7) 6 h presentation (1 day in week 8) Total for students : 90 h Teacher in attendance 4 days a week along the 8 weeks ; to assist on a one-to-one basis, preferably on appointment, for the rest working on other hydrology research topics both of personal interest and relevant to UAQ. Course is designed for Master students, but attendance of PhD, Post-doc, professional and colleagues is welcomed, according to interest and as a basis for later exchanges of experience and techniques. Personal work refer to student reading lecture notes prior to tuition (pdf lecture notes will be delivered two weeks in advance, so that students have time to read them through before the course, to have a preliminary impression of the contents and some questions ready). Course will mostly stress on main points, show examples, and answer questions. Practical exercises will demonstrate and train the techniques taught, based on ad-hoc sample data sets. Mini-projects are practical studies to be either proposed by the teacher or submitted by students wishing to work on personal research topics or on full size, complex personal data set. Topic proposed by students are subject to agreement and must be submitted not later than week 3 for review of their suitability. Each student must work personally on a different topic or on clearly different data set. Validation of the module will be based on the written report to the mini project : formal presentation of the report, explicit exposure of goals pursued, relevance of the techniques chosen in handling the data, correctness of the implementation, quality of the discussion and fair assessment of results gained are considered for appraisal. The report (about 10 pages text, plus tables, figures, annexes) must be written in English with a two pages “executive and scientific summary” in Spanish added, or viceversa. Guidelines and/or template will be given. Reports are due at the end of the first day in week 8. All students will be kindly requested to make a short oral presentation of their work. Extra time may be allocated in case of works that best contribute to illustrate and extent the course. A teaching evaluation sheet will be distributed that must be filled and handed out to the coordination of the maestria, that will summarize (hiding identities). For practical exercises and mini-projects either access to a university computer or a personal laptop is requested, one per student, with installed software R to be installed before the start of the practical exercise (R is free software, see : http://www.r-project.org/ ). Additional software will be used during the course, they do not request administrator rights. All software mentioned can be kept for personal use.
Outline 0/ probability concepts (a) distribution (of a real value), joint distribution (of several real values) a. Gaussian, Log-Normal, … b. Gumbel, GEV, … c. Exponential, GPD, … d. Others : Gamma, inverse Gaussian, Kappa (b) samples, descriptors a. POT and AM samples (for extremes) b. Moments ; L-moments (c) fitting a law a. pdf, cdf b. moment or L-moment based ; likelihood based ; plots c. tests ; confidence interval ; bootstrapping techniques (d) connections within physics and statistics a. reasons why a phenomenon should follow a given distribution b. determinism, chaos, uncertainty, … c. homogeneity as a decision d. responsibility in the choice of descriptors 1/ statistical analysis of time series of hydrological interest (a) sampling and usual laws for individual series (b) regional analysis : the Hosking-Wallis approach 2/ geostatistics : principles and basic applications in hydrology (a) description : variograms etc. (b) point interpolation a. kriging techniques b. cokriging (c) simulation (d) support effects 3/ geostatistics : advanced applications in hydrology (a) interpolation of basin-related variables (b) join estimation of water balance estimates (c) simulation of input variables to a basin (d) support effects, for both conceptual and physically based models 4/ models, parameters, uncertainty (a) parametrization issues, mostly for conceptual models (b) strategies for filtering possible solutions and keep reasonable ones (c) entropy as a mesure of uncertainty (d) the derived distribution approach (e) towards Bayesian hydrology, systemic hydrology, data-physics based model a. assimilation b. derived distribution approach c. parametrization of subgrid processes 5/ not enough or to much data ? (a) a trend in hydrology : scarce relevant data complemented by indirect but possibly irrelevant “big data” (b) data mining approach : summarizing data via linear (ex : PCA) or non linear (ex : clusterization) techniques ; importance of prior knowledge in the reduction.