**The Hydrological Modeling course aims to teach to simulate the hydrological cycle at various spatial scales in order to be able to adequately manage the water resource and to prevent the risk of floods.**The importance of these two issues is widely covered by the EU 2000/60 framework directives or "Water directive" and EU 2006/60, "Flood directive". Based on the hydrological knowledge acquired in the course of Hydrology at the Bachelor of Engineering for the Environment and the Territory, the hydrological processes, analyzed as punctual phenomena are extended to the water catchment areas.

Precipitation is analyzed as a measured statistical data, both from ground stations and from remote sensing; the other processes are suitably modeled, as briefly described below.

**At the end of the course, a student must be able to independently model the flow rates, evaporation and transpiration in a river basin of various sizes, after having delineated it starting from digital terrain data.**Of course, the student will have to demonstrate that he has critically understood the concepts that underlie the hydrological modeling presented.
The knowledge acquired may be used in the River Engineering course for the design of defense works. Hydrological modeling also introduces concepts that are used in the course of Aqueducts and Sewers for the calculation of stormwater networks. The course is partly useful for the Hydraulic Protection of the Territory course.

A more condensed part of the version of the course can be found @GWS2020.

**Methods**

The

**lectures of the course will be held in English**, according to the methods already followed in the Numerical Modeling course (i.e. with summary in Italian at the beginning of the lesson, lessons in English, questions and explanations in Italian). The first part of the course, until on April 3, will be dedicated to the presentation and discussion of theoretical concepts. The lectures will be recorded and uploaded on the course's YouTube channel (or Vimeo). The lessons will cover 4 of the five hours per week. The fifth hour will be dedicated to the preparation of the data necessary for the projects to be completed in the second part of the course.
Students must take care to understand the hydrological concepts and discuss them with the lecturer. The first twenty minutes of each lesson will be devoted to the discussion of the topics covered in the previous lesson and the problems that arose in the preparation of the data (in Italian). Every group had to prepare an appropriate question or comment to which the lecturer will replay. A summary, again in Italian, of the lesson and then the actual lesson will follow.

The second part of the course will use the theoretical themes of the first part and using the tools made available by the GEOframe system (https://abouthydrology.blogspot.com/2015/03/jgrass-newage-essentials.html). Students, in groups of two or three, will have to estimate hydrological flows and quantities over a significant period of time and with an hourly time step using a time series of hydro-meteorological data in inputs for period long enough to allow adequate calibration of the models. With the help of the tutor and the reader, students will face problems of missing data, validate the models, discuss and implement an adequate configuration of the

**GEOframe**hydrological system in order to get the hydrological water balance of the basin. At the end they will also have to calculate and discuss the discharges n a closure section of the chosen basin, in the event of a rainfall stress with an assigned rainfall return time of 10, 100 and 300 years.**Part of the work is the estimation of forecast errors.**

**Used Software**

There is no engineering without using models. During the class will be used various open source softwares and resources:

- Python 3.* within Jupyterlab for scripting, and in particular the numpy, scipy, matplotlib (also here) and pandas (also here).
- Part of the GEOframe system for the various simulations.

All these resources are free, besides being open. For installations requirements, please see the GEOframe winter school material here. For understanding a little more about this material, please look at "Getting started with Docker OMS and Jupyterlab" post.

**Material of the course (other than indexed here)**

The material of the course will be uploaded usually at this OSF site.

**Exams**

At the end of the first part of the course, an intermediate test will verify the theoretical / conceptual knowledge acquired by the student through three open-ended questions. These questions will be a random selection among a group of questions presented after the classes and that students will have them available before the test. The evaluation of the second part of the course consists in the discussion and presentation of the elaborated hydrological project of which the inputs, the outputs discussed through appropriate Jupyter notebooks must be delivered, accompanied by the necessary discussions, graphs and spatial maps. The formulation of the final grade will also assess the quality of the interaction of the groups with the tutor and the students, as well as the formal quality of the papers (appropriate use of the graphics, the Italian language -though the use of English will be allowed- and setting of the papers).

**Foreseen Schedule (up to Easter)**

**I or directly written in Italian in for Italian, unspecified for English. All slides are in English**

(boldface dates are those with definitive material,

(boldface dates are those with definitive material,

**)**

Lab material here

**2020-03-03**- Syllabus - Introduction 2 Hydrological Modelling - Illustrating the catchments for the lab.

- The real start
- Prerequistes
- The Topics (from a general point of view) (Vimeo Video 2020)
- How you will be graded
- Catchments and related issues

**2020-03-05**- Discussion of previous lesson topics. Riassunto della lezione in Italiano. (This will be always done, each lesson, but for now on omitted). The rational of introducing these concepts is that catchments are spatially extended and in this course we are interested to deal with catchments hydrology. So this first part is:

- Introduction to Geomorphometry I (Storyboard 2020 della lezione, I):
- DEMs sources (from Wikipedia). Local and other sources of data:
- The basics of DEM analysis (YouTube video 2019,YouTube2020, Sintesi in Italiano 2020)
- Hydrogeomorphology: the derived quantities, drainage directions and contributing areas (YouTube video 2019,YouTube2020, Sintesi in Italiano 2020)
- On the estimation of tangential stresses in a curved topography (Whiteboard 2020)
- References for who wants to go deeper
- Peckham, R. J., and G. Jordan. 2007.
. Edited by Robert Joseph Peckham and Gyozo Jordan. New York: Springer, Berlin, Heidelberg. Lecture Notes In Geoinformation and Cartography.*Digital Terrain Modelling*: Development and Applications in a Policy Support Environment

**2020-03-10**- Introduction to Geomorphometry II (Storyboard 2020 in Italiano):

- Where do channels begin: Extracting channels and hillslope (YouTubeVideo 2020 b, Sintesi in Italiano 2020)
- Old but useful material: extracting the hillslope (YouTube Video 2019,YouTube2020)
- Topological classification of catchments elements: Horton-Strahler Ordering (Whiteboard2020); Pfafstetter (Whiteboard2020; an alternative presentation here) and other ordering schemes (Whiteboard 2020 here).
- If you want to go a little deeper: Rigon, Riccardo, Ignacio Rodriguez-Iturbe, Amos Maritan, Achille Giacometti, David G. Tarboton, and Andrea Rinaldo. 1996. “On Hack’s Law.”
*Water Resources Research*32 (11): 3367–74. - Other interesting quantities: distances to outlet; distance to channels and drainage density, angle of view; shadows.
- Catchment description in informatics
- Detecting the human landscape (please try to read and summarize the main concepts):
- Cao, Wenfang, Giulia Sofia, and Paolo Tarolli. 2020. “Geomorphometric Characterisation of Natural and Anthropogenic Land Covers.”
*Progress in Earth and Planetary Science*7 (1): 2. - Other references:
- Older classes in Italian
- Geomorphology with References
- Various information from the AboutHydrology Blog
- R.Rigon, E. Ghesla, C. Tiso and A. Cozzini, The Horton Machine, pg. viii, 136, ISBN 10:88-8443-147-6, University of Trento, 2006
- W. Abera, A. Antonello, S. Franceschi, G. Formetta, R Rigon , "The uDig Spatial Toolbox for hydro-geomorphic analysis" in Geomorphological Techniques, v. 4, n. 1 (2014), p. 1-19

**2020-03-12**- This lecture, assumed that now you have at least the concepts of what a catchment is and theoretically you know how to extract it and subdivide it in parts, now you have to deal with the data to drive its hydrology. Because catchments have a spatial distribution, then also the driving data must be distributed. We need therefore methods of interpolation. Hydrological data (Storyboard2020 in Italian)

- Which data are we interested and where can we find them ? (This one is a storyboard in English)
- Ground data and their interpolation (Zoom2020-I)
- Thiessen Polygons (Storyboard2020 in Italian)
- Inverse distance Weighting (Storyboard 2020 in Italian)
- Introduction to Kriging Theory:
- Building the system to solve (Storyboard 2020), the Kriging's equations (YouTube2019 - Slides were a little modified for 2020, YouTube2020, Zoom2020)
- Variography (Storyboard 2020, YouTube video 2019, YouTubeVideo2020, YouTube2020b)
- Catching the errors of estimates (Storyboard2020 in Italian, Zoom2020)
- Flow chart and Various types of Kriging (Storyboard in Italian 2020, Zoom2020)
- Additional material:
- References:
- Marialaura Bancheri, Francesco Serafin, Michele Bottazzi, Wuletawu Abera, Giuseppe Formetta, and Riccardo Rigon, The design, deployment, and testing of kriging models in GEOframe with SIK-0.9.8, Geosci. Model Dev., 11, 2189–2207, 2018 https://doi.org/10.5194/gmd-11-2189-2018
- Andràs Bardossy, Introduction to Geostatistics, year unknown.
- Goovaerts, P. (1997). Geostatistics for Natural Resources Evaluation (pp. 1–488). New York : Oxford University Press.
- P.K. Kitanidis, Introduction to GEOstatistics, 1997 https://doi.org/10.1017/CBO9780511626166
- Mitas, Lubos, and Helena Mitasova. 1999. “Spatial Interpolation.”
*Geographical Information Systems: Principles, Techniques, Management and Applications*1 (2). http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.224.5959&rep=rep1&type=pdf. - G. Raspa, Dispense di Geostatistica Applicata, Università di Roma 3, 2010

**Q&A - Spatial Interpolation**

**2020-03-17**- Hydrological Models. This is a class about hydrological models, so what are they ?

**2020-03-19**- We do concentrate on such hydrological models that are made up of systems of Ordinary differential equations (ODEs). We give here some examples of HDS (Storyboard2020 in Italiano)

- The linear reservoir model (Whiteboard2020, Zoom2020)
- Errata Corrige: Linear Reservoir Model
- More than one linear reservoir an the Nash model (Whiteboard2020,Zoom2020)
- Summing up: We can see the Hydrological Dynamical Systems as systems of reservoirs.
- An unexpected candid way (for naive people like me) to model Covid-19 spreading (Whiteboard2020, Zoom2020)
- But look how it is a more informed model

**2020-03-24**Other more complicated models (Storyboard2020)

- Here below we started a little series of lectures about a statistical way of seeing water movements in catchments. This view has a long history but recently had a closure with the work of Rinaldo, Botter and coworkers. Here it is presented an alternative vie to their concepts. Some passages could be of some difficulty but the gain in understanding the processes of fluxes formation at catchment scale is, in my view, of great value and deserves some effort. The way of thinking is the following: a) the overall catchments fluxes are the sum of the movements of many small water volumes (molecules); b) the water of molecules can be seen through 3 distributions: the travel time distribution, the residence time distribution and the response time distributions; c) the relationships between these distributions are revealed; d) the relation of these distributions with the the treatment of the catchments made through ordinary differential equations is obtained through the definition of age ranked distributions; e) The theory this developed is a generalizations of the unit hydrograph theory.
- The view of the catchment as the statistics of elementary water volumes moving stochastically
- Three points of view for the same quantities (This actually explain the same concepts of the lecture below in a more empirical way)
- Residence time, travel time, response time (Whiteboard2020, Whiteboard's pdf). A little of critical discussion is included.

**2020-03-26**- Continuing the mechanical-statistical view of the catchments (Storyboard2020)

- Response times (a.k.a. life expectations) (Whiteboard2020- Part I, Part II)
- Errata corrige. In the last two formulaI did not divided by the precipitation p_{t_{in}}. But this appears corrected in red in the second part.
- Summing up:
- Equivalences among distributions
- The Equivalences of the mechanico-statistical view with the Hydrological Dynamical System
- Coefficients of partition
- The good old Instantaneous Unit Hydrograph theory
- For the Lab part go here.
- Q&A - A student asks and I respond on travel times (in Italian)
**2020-03-31**- After digging in the complications of the travel times etc, we go back to Hydrological modelling by reservoirs.- Klicker session on Travel times, Residence Time, etc. (List of questions and answers by students, Zoom2020)
- Embedded Reservoirs ModelM (Zoom2020)
- Examples of Applications:

**2020-04-2**-

**Flipped Lecture**- We need radiation too. The topic is very boring (or technical?) but necessary to who want to do evapotranspiration and snow. After all radiation moves it all.

- Radiation (YouTube 2017).
- The Sun (YouTube 2017)
- Stefan-Boltzmann law and radiation spectrum (YouTube 2017)
- Sun to Earth (YouTube 2017)
- Coping with latitude and longitude (YouTube 2017)
- Atmospheric Absorptions (YouTube 2017)
- Clouds (YouTube 2017)
- Coping with terrain (YouTube 2017)
- Long wave radiation (YouTube 2017)
- Table of symbols
- Readings:
- Corripio, J. G. (2002). Modelling the energy balance of high altitude glacierised basins in the Central Andes. Ph.D Dissertation, 1–175.
- Corripio, J. G. (2003). Vectorial algebra algorithms for calculating terrain parameters from DEMs and solar radiation modelling in mountainous terrain. Int. J. Geographical Information Science, 17(1), 1–23.
- Formetta, G., Rigon, R., Chávez, J. L., & David O. (2013). Modeling shortwave solar radiation using the JGrass-NewAge system. Geoscientific Model Development, 6(4), 915–928. http://doi.org/10.5194/gmd-6-915-2013
- Formetta, G., Bancheri, M., David, O., & Rigon, R. (2016). Performance of site-specific parameterizations of longwave radiation. Hydrology and Earth System Sciences, 20(11), 4641–4654. http://doi.org/10.5194/hess-20-4641-2016
- Various material from the AboutHydrology blog
- Q&A - Some questions on radiation, your answers and my comments.

**2020-04-07 -**

**A little about models calibration****Snow-**Doing catchment hydrology in mountain areas without talking about snow modelling is kind of weird, even if many do it. We approach the structure of a few simplified models, after some description of the processing affecting snow metamorphisms

**2020-04-09 - Snow modelling equations and models**

- For who needs some rehearsal: Turbulent transport of vapor (and other quantities): the Dalton and Thermal Energy turbulen law (YouTube2018, YouTube 2019, Zoom2020)
- Turbulent Fluxes revisited (Vimeo2020)
- The Snow Mass Budget (Vimeo2020)
- Before looking at the next slides, maybe you give a look to this following link reminding why mass transport implies energy transport, valid for evaporation as in the general case:
- The Energy Budget for snow (Vimeo2020)
- Solving The coupled System (I left the link to the old version but use the link below)
- Simplified models
- Snow Measurements
- Advanced Material for interested people

- Resources:

**Extra material**

###
- Storyboard
- The issue of the maximum discharge in a simplified model
- General reference: The geomorphic structure of the runoff peak
- The Discharge inverse problem (The Vaia-Rotian case)

Seminars

###
- Matteo Dall'Amico (MobyGIS), La modellazione della neve in ambito professionale
- Alberto Bellin, Gli inquinanti negli acquiferi e la loro gestione (Vimeo2020)
- Marco Bezzi (BlueTentacles), La gestione dell'irrigazione nell'agricoltura del futuro (Vimeo2020)

Lab material is here

As general reference texts we recommend:

- Beven, K. - Raifall-runoff, the primer, ISBN 10: 047071459X, ISBN 13: 978047071459, Second Edition, Wiley-Blackwell, 2012
- Dingmann, L., Physical Hydrology, ISBN-13: 978-1478611189, ISBN-10: 1478611189, Third Edition, Waveland Press, 2015
- Lu, N. and Godt, J.W., Hillslope Hydrology and Stability, Cambridge University Press, ISBN-13: 978-1107021068, ISBN-10: 11070210652010, 2013
- Bonan, G., Ecological Climatology, concepts and applications, ISBN-13: 978-1107619050, ISBN-10: 110761905X, 2016

These books represent a shareable review of the phenomena and hydrological modeling but the methods they present are not necessarily those used in the course. The course, cause of time constraints, presents a selected and limited perspective of the subject that the texts cited dissect from various points of view often complementary to the one of the course.