Thursday, February 1, 2024

Hydrological modelling 2024

Welcome to the 2024 Hydrological modelling class. To understand better what is below: 
  • A storyboard is a summary, usually in Italian, of the lecture
  • A whiteboard is an explanation of a particular topic made on the whiteboard (using Notability on the iPad)
  • Slides are commented in English (since 2021)
  • Videos are available to comment the slides. They are usually recorded during the lectures with no editing at all (which would be too much time expensive). 2024 Videos are uploaded to a Vimeo Showcase that can be found here. 
  • Additional  information (only for the brave or the curious) and references are in italics
 

2023-02-19 - I  - Syllabus - Introduction 2 Hydrological Modelling 

Here  I introduced the class. Its learning by doing philosophy (altered by the necessity due to COVID-19 times that impose to do first the all the theoretical parts and subsequently all the practical parts hoping that they can be done in presence). 
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
2024-02-22 - Geomorphometry   - Discussion of previous lesson topics. The rational of introducing these concepts  is that catchments are spatially extended and in this course we are interested to deal with catchments hydrology. 

In this first part we deal with the geometrical (differential) characteristics of the topography. Elevations, slopes, curvatures. They will be necessary later to extract the river network and the parts of a catchment.
In this class we define also what the drainage directions are and how they are computed in the case of DEMs (a topography discretized over a regular grid).  From drainage directions are determined the total contributing areas in each point of  a DEM. These two characteristics are eventually used to determine  the channels head and extract the river network. In turn, the extraction of the channel network allows for the extraction of hillslope and a first definition of  the Hydrologic Response Units (HRU). 
    2024-02-26
    Q&A - 

    2024-02-29 -  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. 

    2024-03-04 -  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.
    2024-03-06-Hydrological Models 

    For old material give a look to Hydrological Modelling 2023
    2024-03-11
    2024-03-18
     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.
    • Summarizing the previous class results at the blackboard(Vimeo2022)
    2024-03-21
     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. 
    2024-03-25
    2024-03-28
    Intermediate exam (2024-04-22)

     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. 
    2024-04-04
    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:

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    Hydrology 2024 lab

    The lab is almost half of the class. According to the motto "learning by doing" it covers at least three numerical experiments:

    • Some elaborations with time series
    • The estimation of the Intensity-Duration-Frequency curves
    • A few experiments with infiltration
    • A few experiments with evaporation and transpiration 
    Please find below
    Videos and material are  indicated singularly below.


     2023-03-04 Introduction to working with Jupyter and Notebooks
    2024-03-12
    • Counting the events and producing their empirical statistics (Vimeo2022)

    Interpolating the Gumbel distribution to annual precipitation maxima

    2024-05-06/07 - Introduction to Infiltration with WHETGEO 1D

    Below, you'll discover the resources for the second part of the lab, which encompass instructions for utilizing Object Modelling System version 3 (OMS3) models such as WHETGEO1D and GEOET. Within the OMS Projects, you'll find a directory named Jupyter_Notebook, housing sets of notebooks designed to guide you through handling both input and output data for these programs.
    A general introduction to some OMS3 concepts

    Please below find Notebooks and video related to the estimation of radiation. Theradiationin this class, will be functional to the estimation of evapotranspiration with the Priestley-Taylor and Penman-FAO models,
    2024-05-20 - Introduction to the estimation of evapotranspiration

    Addendum

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    Hydrology 2024

    The Course of Hydrology 2024 will be 90% similar to last year class with minor modifications.  Indication of tools used etc can be found at the 2023 Index (3 minutes reading). Here you'll find the material of the classes including slides, old and new videos. Hydrology is an exciting field since water is so important for life and human activities. Here a  brief introduction from a National Geographics post. 

    Companion of this post il the laboratory page on which you find material for your exercises. 
    Lab page is at this link. 

    Classes and related material

    You can find:
    • Storyboards is a summary, usually in Italian, of the lecture
    • Whiteboard is an explanation of a particular topic made on the whiteboard (using Notability on the iPad)
    • Slides are commented in English
    • Videos are available to comment the slides. They are usually recorded during the lectures with no editing at all (which would be too much time expensive). 2024 Videos are uploaded to a Vimeo Showcase that can be found here. 
    • Additional  information (only for the brave or the curious) and references are in italics

    19 Febbraio 2024 - - Introduction to the course and to hydrology
    Complementary References
    2023-02-20 - Ground based Precipitations and their statistics Separation snow-rainfall - measure of precipitation

    In this part of the class we describe where it rains and how much it rains using statistical concept. One important objective is to understand what are the extreme precipitations for their importance in engineering. 
    2024-02-26 - 2024-02-27  - Statistics of extreme precipitations

     Some reviews on statistics - Return Period
    Extreme precipitations  (Storyboard2020)
    Distributions Storyboard2020

    Determination of Gumbel's parameters
    Extreme precipitations  II
    2024-03-05 -Beyond Gumbel
    A summary about the extreme precipitation estimations (Whiteboard)

    Water in soil and aquifers 
     (Storyboard2020)
    Once precipitations arrive to the ground surface they either infiltrate or generate runoff. We first state how they infiltrate and, actually how water behave in the soil and in the ground. We talk about the complexity of the Earth surface that contains life and call it, the Critical Zone. To study infiltration we introduce the Darcy and Richards equations of which we explain the characteristics.

     - The Richardson-Richards equation  (Storyboard 2020)
    2024-04-15

     Runoff Generation and propagation (Summary 2020)

    Once the rainfall gains the terrain, it can infiltrate or producing runoff. In the next we discuss the main mechanisms that produce runoff.
    Q&A - Runoff - Runoff 2022

    2024-04-22

    Runoff moves on the surface of the terrain according to the de Saint-Venant equation. In the following the equation is derived in the 1D case.

    Evaporation generalities (Storyboard2020)

    A consistent part of root zone and surface water evaporates and returns to the atmosphere to eventually form clouds and precipitation again. The process follows quite complicate routes and is different when happening from liquid surfaces, soil or vegetation (and BTW animals).  In this group of lectures we try to figure out the physical mechanisms that act in the process and give some hint on methods to estimate evaporation and transpiration with physically based models. 
    2024-04-23
      Evaporation and Transpiration Formulas
    2024-04-29
     2024-04-30  - After all radiation moves it all 
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    Wednesday, January 31, 2024

    A little on reviews of Land Surface Models

     Please improve: A nicely comprehensive review of Land-Surface-Models LSM is given in Blyth et al., 2020 being possibly completed by a reading to Fisher, 2020 for a different perspective on processes. The pioneering models were more what we nowadays call Process Based/Mechanistic models which, however contains a lot of parameters and parameterizations that have to ne calibrated, assimilated or characterized. This calibration is essentially a statistical step that in practice transform LSMs in a mix of PDEs, ODEs solver endowed with various techniques derived from statistics or, more recently, from machine learning (ML) (Pal et al., 2021). In some cases, statistical learning pretends to entirely substitute PB model which sometimes happens for some processes but is more rare in LSM as a whole.

    With Prof. Prentice we share the quest for rei-inventing LSMs
    It is apparent from the reading of the reviews above that the scope of LSM has been greatly expanded over the years above five main modelling domains: surface and canopy exchanges, soil and snow physics, water bodies, biogeochemistry and plant physiology and vegetation dynamics.
    Some models have emerged as reference in literature. They include:


    References

    Blyth, Eleanor M., Vivek K. Arora, Douglas B. Clark, Simon J. Dadson, Martin G. De Kauwe, David M. Lawrence, Joe R. Melton, et al. 2021. “Advances in Land Surface Modelling.” Current Climate Change Reports 7 (2): 45–71. https://doi.org/10.1007/s40641-021-00171-5.

    Fisher, Rosie A., and Charles D. Koven. 2020. “Perspectives on the Future of Land Surface Models and the Challenges of Representing Complex Terrestrial Systems.” Journal of Advances in Modeling Earth Systems 12 (4). https://doi.org/10.1029/2018ms001453.

    Pal, Sujan, and Prateek Sharma. 2021. “A Review of Machine Learning Applications in Land Surface Modeling.” Earth 2 (1): 174–90. https://doi.org/10.3390/earth2010011.
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    Tuesday, January 23, 2024

    Mapping and Modeling Flowing Network Dynamics in Temporary Streams (by Gianluca Botter and Nicola Durighetto

     Gianluca Botter and colleagues (among which a notable mention is needed to Nicola Durighetto) recent work in the ERC project Dynet is remarkable (as well as the older one) and a little of it is in this presentation they kindly prepared for the AboutHydrology blog.The first slides (you find them by clicking on the Figure below) are choreographic (slide 1 only a photo, slide 2 a photographic example of network dynamics).


    Slide 2 shows that stream intermittency is a pervasive phenomenon in many riverscapes. All river networks, in fact, continuously expand and contract in response to time-varying climatic conditions. Consequently, the same reach can experience flowing water, ponding or no-water at all depending on the survey time, as shown by the examples reported in this slide.
    Slides 3 movie (here) represents the simulated network dynamics in the Rio Valfredda, 5 km2 (BELLUNO, Dolomites). The movie has been built combining empirical observations and a hierarchical modeling framework. Network dynamics are very complex, with wet reaches that propagate upstream in response to rainfall events, but also active channels that extend in the downstream direction as the catchment wets up. Multiple disconnections are generated and removed as the network expands and contracts.
    Slide 4 summarizes the conceptual model used to identify the timing and the duration of surface flow within a given location along the geomorphic network. According to the model, the presence of surface flow is produced by the imbalance between the local inflow Qin, which is made up by the sum of a surface and a subsurface component, and the maximum discharge capacity of the subsurface of that point, Q*. Consequently in this framework, the surface flow presence condition can be written as Q_in > Q*.
    In slide 5 (movie) it is shown that surface flow presence is driven by the imbalance between the local inflow Q_in and the maximum subsurface discharge capacity in the hyporheic region, Q*. One important point of this formulation is that Q_in changes in time as a function of the catchment wetness, but also in space, with larger values of inflows that are associated to downstream sites with a larger contributing area. Instead, the maximum outflow Q* is typically constant in time, and does not necessarily exhibit significant scaling effects as it might depend on local features such as the slope or the subsurface transmissivity. As the catchment gets wet, the local Q_in increases along the network non-uniformly and activate larger and larger portions of the network, as shown in the upper movie of this slide. The same process can be also seen looking at the corresponding “specific” quantities, dividing both sides of the surface flow presence equation by the contributing area A. The advantage is that now the specific inflow (small q_in) can be assumed as nearly uniform along the network, while the max specific outflow, rho*, decreases downstream as the contributing area increases. From this new perspective, when the catchment wets up the local specific inflow increases almost uniformly everywhere in the network, and more and more sites experience surface flow starting from the most downstream nodes for which the max specific max outflow rho* is lower.
    From a phenomenological view point (slide 6), this mechanistic formulation originates a hiearchical behaviour: during wetting, nodes are activated sequentially from from the most to the least persistent, thereby originating … a sequence of network configurations in which less and less persistent nodes activate as the network expands
    Slides 7 shows that during drying, nodes dry out with an order that is the inverse of the one experienced during the wetting… Thus, more and more persistent nodes are progressively switched off as the network retracts. The hierarchical behaviour is observed also in case of dynamically fragmented networks, as in this example.
    The hierachical structuring of channel network dynamics, shown in slide 8, has been the object of several past studies, in which the hierarchy was mathematically defined using graph theories, and the validity of the hierarchical scheme has been proved using empirical data from tens of catchments spread al lover the world. The hierarchical structuring proved to be a powerful tool to extrapolate in space incomplete empirical information on surface flow presence.
    Slides 9 shows data about local persistency as derived from field surveys in different catchments belong to a broad range of geomorphoclimatic features, from humid settings (on the left) to a dry mediterranian catchment (shown on the right). As you can see there is a general tendency for the persistency to increase moving downstream along the network (indicated by blue-like colors), in line with the expected decrease of rho* for larger contributing areas. However, the observed patterns of local persistency are much more complex than expected in most cases, owing to spatial heterogeneity of hydromorphological features, such as slope and river bed permeability.
    Activelength vs discharge plots in slide 10 are valuable to estimate the changes in the flowing length associated to changes in the catchment wetness. Different catchments show a vary different behaviour though…
    Slide 11 (movie here) shows an example simulation derived using a stochastic model for simulating the spatio-temporal dynamics of temporary streams. The model takes advantage of few, widely available climatic and morphologic parameters to generate synthetic timeseries of rainfall, streamflow and active length. Furthermore, the approach allows the reconstruction of the time-varying configuration of the active network. Thanks to its simplicity and limited computational requirements, the model can be easily coupled with ecologic models to simulate specific in-stream processes taking place on temporary streams.
    In slide 12 (movie here) the Authors combined synthetic dynamic networks with a metapopulation model. The model stochastically simulates the occupancy of a temporary stream by a target species, which is shown in dark blue in the lower plot. The available habitat for the focus species varies with time and is greatly reduced during droughts. Our results indicate that, when compared to a static network, temporary streams result in a lower average occupancy and a higher extinction probability.
    To better understand the importance of network dynamics, slide 13 compares the simulated behavior of a fish species in two different conditions: a dynamic network, shown in the bottom panel, and a static network, shown at the top panel.
    Even though the average length of the active network is the same in the two cases, the time variability of the available habitat inherent of the dynamic network results in a lower average occupancy and a higher time variability of the network length occupied by the metapopulation. Consequently, in the dynamic scenario there is also an increase in the probability of complete extinction of the target species within the network.
    The results in slide 14 suggest that the presence of disconnections along the network lowers the mean occupancy and increases extinction probability. In fact, the target species always goes extinct in less than 1 year in the scenario characterized by the largest number of disconnections (upper panel), while it can survive in the other cases. Therefore, temporary disconnections produced by stream network dynamics are crucial to the ecological functioning of rivers.
    This is an important result also in the frame of climate change, which is globally increasing stream intermittency.

    References
    • N. Durighetto, F. Vingiani, et al. (2020). Intraseasonal Drainage Network Dynamics in a Headwater Catchment of the Italian Alps. Water Resources Research. https://doi.org/10.1029/2019WR025563
    • G. Botter, N. Durighetto (2020). The Stream Length Duration Curve: A Tool for Characterizing the Time Variability of the Flowing Stream Length. Water Resources Research. https://doi.org/10.1029/2020WR027282
    • G. Botter, F. Vingiani, et al. (2021). Hierarchical climate-driven dynamics of the active channel length in temporary streams. Scientific Reports. https://doi.org/10.1038/s41598-021-00922-2
    • N. Durighetto, G. Botter (2021). Time‐lapse visualization of spatial and temporal patterns of stream network dynamics. Hydrological Processes. https://doi.org/10.1002%2Fhyp.14053
    • F. Zanetti, N. Durighetto, et al. (2022). Technical note: Analyzing river network dynamics and the active length–discharge relationship using water presence sensors. Hydrology and Earth System Sciences. https://doi.org/10.5194/hess-26-3497-2022
    • N. Durighetto, V. Mariotto, et al. (2022). Probabilistic Description of Streamflow and Active Length Regimes in Rivers. Water Resources Research. https://doi.org/10.1029/2021WR031344
    • N. Durighetto, G. Botter (2022). On the Relation Between Active Network Length and Catchment Discharge. Geophysical Research Letters. https://doi.org/10.1029/2022GL099500
    • N. Durighetto, L. Bertassello, G. Botter (2022). Eco-hydrological modelling of channel network dynamics—part 1: stochastic simulation of active stream expansion and retraction. Royal Society Open Science. https://doi.org/10.1098/rsos.220944
    • L. Bertassello, N. Durighetto, G. Botter (2022). Eco-hydrological modelling of channel network dynamics—part 2: application to metapopulation dynamics. Royal Society Open Science. https://doi.org/10.1098/rsos.220945
    • N. Durighetto, S. Noto, et al. (2023). Integrating spatially-and temporally-heterogeneous data on river network dynamics using graph theory. I-Science. https://doi.org/10.1016/j.isci.2023.107417
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    Between Hydrology and Geology: digital twins for preventing the hydrological and geological hazards

     Invited to talk to remember Fabio Rossi I chose to take a little detour describing the perceptual model of small catchments floods dynamics in the interplay between geology, geomorphology,  and hydrology. Not much technical information though, which you can find in the cited papers, but more the vision of what can be done with physically based models. 


    The presentation ends with claiming that such approaches that could be seen as overwhelming can instead be pursued in the framework of DARTHs and within a cooperative, participatory action. Enjoy the presentation by vlivking on the figure above. 

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