Thursday, February 6, 2025

The Hydrological Modeling 2025 class

 Welcome to the 2025 Hydrological Modeling Class!

To better understand the materials provided:

  • Storyboards – Summaries of the lectures, usually in Italian.
  • Whiteboards – Explanations of specific topics, presented on a whiteboard using Notability on an iPad.
  • Slides – Commented in English (available since 2021).
  • Videos – Recorded during lectures to complement the slides, with no editing (as post-production would be too time-consuming).
    • 2025 videos are available on a [Vimeo Showcase] (link here).
  • Additional information & references – Marked in italics, for the curious and the brave who want to explore further.

📅 24 February 2025 – Part I

Syllabus & Introduction to Hydrological Modeling

In this session, I introduced the course and its learning-by-doing philosophy. We cover all theoretical concepts first, followed by the practical applications (with Professor Giuseppe Formetta).

The real start 

To begin is also worth to have a little (philosophical) analysis of what a model is. This is what done in the following parte of the lecture

📅 25 February 2025 – Geomorphometry

This session begins with a discussion of previous lesson topics and the rationale behind introducing geomorphometric concepts. Since catchments are spatially extended, understanding their geometry is essential for studying catchment hydrology.

In the first part, we focus on the geometrical and differential characteristics of topography, including:

  • Elevation
  • Slope
  • Curvature

These parameters are fundamental for extracting the river network and identifying different parts of a catchment.

We then define drainage directions and explore how they are computed using Digital Elevation Models (DEMs)—where topography is discretized on a regular grid. From these drainage directions, we determine the total contributing area at each point of a DEM.

These two key characteristics allow us to:

  1. Identify channel heads and extract the river network.
  2. Define hillslopes and establish an initial framework for Hydrologic Response Units (HRUs).

    📅 3 March 2025 

    Q&A - 

    Interpolations 
    This lecture, assuming 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, deals with the data to feed catchments hydrology models. Because catchments have a spatial distribution, then also the driving data must be distributed. We need therefore methods of interpolation. 

    Installations of the software can be found here, at this link.

    📅 10 March 2025 

     Interpolations part II
    In this class we try to understand how to estimate the errors over the estimates. Besides we introduce a method (the Normal Score) to avoid to obtain negative values when positive interpolated values are required.
    Q&A - 
    Spatial Interpolation (Vimeo2023)

    Hydrological Models. This is a class about hydrological models, so what are they ?

    The title is self-explanatory. A theoretical approach to modelling is necessary because we have to frame properly our action when we jump from the laws of physics to the laws of  hydrology. Making hydrology we do not have to forget physics but for getting usable models we have to do appropriate simplifications and distorsions. The type of model we will use in the course are those in the tradition are called lumped models. Here we also introduce a graphical tool to represent these models.

    📅 17 March 2025 

    Hydrological Models 

    For old material give a look to Hydrological Modelling 2023

    📅 25 March 2025 

     Linear Models for HRUs

    Once we have grasped the main general (and generic) ideas, we try to draw the simplest systems. They turn out to be analytically solvable, and we derive their solutions carefully. From the group of linear systems springs out the Nash model, whose derivation is performed.  Obviously, it remains the problem to understand how much the models can describe "reality". However, this an issue we leave for future investigations.
    A little more on the IUH and looking at the variety of HDSys models

    We introduced previously without very much digging into it the concept of Instantaneous Unit Hydrograph. Here we explain more deeply its properties, Then we observe that there are issues related to the partition of fluxes and we discuss some simple models for obtaining them. Not rocket science here. The concept that we need those tools is more important than the tools themselves. We also observe that linearity is not satisfactory and we give a reference to many non linear models. Finally we discuss an implementation of some of the discussed concepts in the System GEOframe. 

    📅 31 March 2025 

      📅 7 April 2025 

      • Additional material
      Digressions I - A Glimpse on distributed process-based models
       Travel Time, Residence Time and Response Time
      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. 

      📅 14 April 2025 

      Some References (advanced)
      Additional material

      Digressions I - A Glimpse on distributed process-based models
      Digressions II - Radiation -  After all radiation moves it all.
      Digressions III 
      Equations for disease spreading (Out of schedule)
      Digressions IV

    • Examples of Applications:
      • Intermedia
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