The document provides an overview of hillslope hydrology and summarizes key concepts. It discusses Richards' equation, which describes water movement in unsaturated soils. Through a series of assumptions and simplifications, the equation can be used to model hydrological processes on hillslopes. It also presents the derivation of simplified forms of Richards' equation that describe saturated vertical flow and lateral flow on hillslopes.
This document summarizes geomorphological aspects of hydrological modeling from 1979 to the present. It discusses how geomorphological information has been incorporated into hydrological models over time. In the 1980s, the availability of digital elevation models allowed for isochrones and width functions to be derived from digital data. This provided a finer representation of geomorphology. In the following decades, models incorporated more geomorphological details like separating hillslope and channel flow velocities. Overall, incorporating geomorphological details improved the ability of models to predict rainfall-runoff responses and event hydrographs.
This document provides an overview of AVO (amplitude variation with offset) principles, processing, and inversion. It discusses the early theoretical work developing AVO analysis and various approximations of the Zoeppritz equations that relate seismic reflection amplitudes to rock properties. The document reviews principles of AVO analysis and describes several common approximations of the Zoeppritz equations, including those by Bortfeld, Aki-Richards-Frasier, Shuey, and Smith-Gidlow. It also discusses using AVO attributes and inversion to estimate changes in P-wave velocity, S-wave velocity, and density.
Almost the same as the talk given to Ph.D. students one year ago. It covers the problem of research reproducibility and the tools for doing it. First comes some "theoretical" arguments, then the enumeration of some tools.
This document analyzes seismic data recorded by four seismographs deployed on an Antarctic iceberg (C16) over a period of 60 days. Cross-correlating the ambient seismic noise between station pairs reveals information about the sources and propagation of signals associated with icebergs. Three main phases of noise propagation are identified: (1) flexural-gravity waves dominate at frequencies below 10 seconds, (2) hydroacoustic waves in the water column dominate above 10 Hz, and (3) faster seismic propagation is seen between 2-6 Hz. Changes in the noise correlations over time provide insights into iceberg-generated ocean noise and properties of the iceberg environment.
The Final Seminar of the Project for Assessment of Earthquake Disaster Risk for the Kathmandu Valley in Nepal was held on 14 February 2018.
The public seminar was held three times during the project.
The Final Seminar, “ Understanding Disaster Risks and Moving Towards DRR and Resilience”, presented on the activities and accomplishment of the project, construction of robust and resilient society against natural disaster risk.
Thank you all for your support and enthusiastic participation in this seminar.
Presentation: Overview of Hazard Assessment Results
This document summarizes geomorphological aspects of hydrological modeling from 1979 to the present. It discusses how geomorphological information has been incorporated into hydrological models over time. In the 1980s, the availability of digital elevation models allowed for isochrones and width functions to be derived from digital data. This provided a finer representation of geomorphology. In the following decades, models incorporated more geomorphological details like separating hillslope and channel flow velocities. Overall, incorporating geomorphological details improved the ability of models to predict rainfall-runoff responses and event hydrographs.
This document provides an overview of AVO (amplitude variation with offset) principles, processing, and inversion. It discusses the early theoretical work developing AVO analysis and various approximations of the Zoeppritz equations that relate seismic reflection amplitudes to rock properties. The document reviews principles of AVO analysis and describes several common approximations of the Zoeppritz equations, including those by Bortfeld, Aki-Richards-Frasier, Shuey, and Smith-Gidlow. It also discusses using AVO attributes and inversion to estimate changes in P-wave velocity, S-wave velocity, and density.
Almost the same as the talk given to Ph.D. students one year ago. It covers the problem of research reproducibility and the tools for doing it. First comes some "theoretical" arguments, then the enumeration of some tools.
This document analyzes seismic data recorded by four seismographs deployed on an Antarctic iceberg (C16) over a period of 60 days. Cross-correlating the ambient seismic noise between station pairs reveals information about the sources and propagation of signals associated with icebergs. Three main phases of noise propagation are identified: (1) flexural-gravity waves dominate at frequencies below 10 seconds, (2) hydroacoustic waves in the water column dominate above 10 Hz, and (3) faster seismic propagation is seen between 2-6 Hz. Changes in the noise correlations over time provide insights into iceberg-generated ocean noise and properties of the iceberg environment.
The Final Seminar of the Project for Assessment of Earthquake Disaster Risk for the Kathmandu Valley in Nepal was held on 14 February 2018.
The public seminar was held three times during the project.
The Final Seminar, “ Understanding Disaster Risks and Moving Towards DRR and Resilience”, presented on the activities and accomplishment of the project, construction of robust and resilient society against natural disaster risk.
Thank you all for your support and enthusiastic participation in this seminar.
Presentation: Overview of Hazard Assessment Results
This contains the talk given at the 2017 meeting of the SteepStream ERANET project. It is assumed to talk about the hydrological cycle of the Noce river in Val di Sole valley (Trentino, Italy). It is a preliminary view of what we are going to do in the project.
This discusses the fact that one as to solve the right equations for a problem and show some interesting cases which consist in modifications of the Richards' equation. These equations, in turns, require special methods to be solved, and the right equations are useless without the appropriate numerics. The second part of the talk discusses the how equations are not the whole picture in a research or technical environment. Several other conditions need to be met.
This chapter reviews concepts of 1D open channel hydraulics relevant to modeling sediment transport in rivers and turbidity currents. It discusses simplifying the cross-sectional shape of channels to rectangular, defines important parameters like flow depth and velocity, and reviews equations for normal flow, boundary shear stress, and resistance relations that are used to estimate properties of bankfull flow conditions based on the assumption of normal flow.
Hydraulic and Hydrologic Design ConceptYimam Alemu
This chapter discusses hydrologic concepts related to hydropower design. It defines hydrology and the hydrologic cycle, including precipitation, evaporation, transpiration, infiltration and runoff. Methods for measuring runoff include rainfall records, empirical formulas, runoff curves and tables, and stream gauges. Factors affecting runoff include rainfall amount, catchment area properties, soil/vegetation conditions, and meteorology. Hydrographs plot discharge over time and are used to understand flow rates and volumes. Flow duration curves show flow exceedance and are used to evaluate firm and secondary power potential for hydropower.
The document analyzes water eutrophication in the Sulejow Reservoir in Poland using coupled CFD and WASP models. A 3D CFD model was developed to simulate hydrodynamics, which was then verified with field measurements. The WASP model was used to simulate nutrient transport and cycling factors like phytoplankton growth, considering hydrodynamics from the CFD model. The results showed proper correlation between measured and calculated values, indicating the models realistically captured the distribution of temperatures, velocities and nutrient concentrations contributing to eutrophication in the reservoir. The methodology can be applied to other reservoir systems to analyze ecological status.
This document describes a graphical language for representing reservoir systems using time-continuous Petri nets (TCPN).
Places in the TCPN represent water storages such as volumes of groundwater or energy/momentum contents. Transitions represent fluxes between storages. The TCPN uses colors to distinguish different types of quantities (mass, energy, etc.) and storages. Connections between places and transitions represent differential equations governing the system.
An example TCPN represents a system of three differential equations with three storages, inputs, and both linear and nonlinear fluxes. Additional information like parameter values can be provided in tables. Adjacency matrixes describe the connections between places and transitions. TCPNs provide an algebraic framework for conceptual
These are the slides presented at EGU 2017 General Meeting, the Pico session was entlited: Monitoring and modelling flow paths, supply and quality in a changing mountain cryosphere
The document discusses different ways of representing water budgets and fluxes between reservoirs in a conceptual hydrological model. It proposes using a formalized set of symbols to represent different types of reservoirs, fluxes, inputs, outputs, and relationships in a clear and standardized way. This is aimed at building an "algebra of objects" to concisely capture the key interactions and mass balances governing a reservoir system. Examples are provided of simple reservoir models represented with this symbolic notation.
The document discusses engineering hydrology, which uses hydrologic principles to solve problems related to water resource management and development. It defines engineering hydrology as studying the hydrologic cycle and its components like precipitation, evaporation, infiltration and runoff. Engineering hydrologists work on projects for water control, utilization and management by estimating maximum floods, droughts, water supply and more using statistical and modeling techniques. The key aspects of hydrology discussed are data collection, analysis and prediction.
This dissertation examines the stability and nonlinear evolution of an idealized hurricane model. The author uses the quasi-geostrophic shallow water equations to model the hurricane as a simple axisymmetric annular vortex with a predefined potential vorticity distribution. Both single-layered and two-layered models are considered. For the single-layer case, linear stability analysis reveals barotropic and baroclinic instabilities that depend on parameters like the potential vorticity within the core and the Rossby deformation length. Nonlinear simulations then show how the annular structure breaks down in different ways depending on these parameters. For the two-layer case, linear stability is found to be identical to the single-layer case, and phase diagrams
DSD-INT 2019 Modeling vegetation controls on gravel bed river morphodynamics ...Deltares
This document summarizes a presentation on modeling vegetation controls on gravel bed river morphodynamics. It describes two modeling frameworks - one where vegetation is represented as a single biomass and another that considers the role of plant roots. The models reproduce major effects of vegetation on river morphology and show that plant root feedbacks are mediated by a balance between erosion and root resistance that determines vegetation disturbance. While the models provide insights, further development is needed to better represent uprooting mechanisms and apply the models to more complex environments.
In this paper, an analysis was done on laminar boundary layer over a flat plate. The analysis was performed by changing the Reynolds number. The Reynolds number was changed by changing horizontal distance of the flat plate. Since other quantities were fixed, the Reynolds number increased with increment of horizontal distance. Iterations were increased in scaled residuals whenever the Reynolds number was increased. Maximum value of velocity contour decreased with the increment of the Reynolds number. The value of the largest region of velocity contour decreased with the increment of the value of the Reynolds number and it also affected the appearance of contour. The value of pressure contour increased with the increment of the Reynolds number. Vertical distance versus velocity graph was not depended on the Reynolds number. In this graph, the velocity increased rapidly with the increment of vertical distance for a certain period. After that, the velocity decreased slightly with the increment of vertical distance. Finally, the velocity became around 1.05 m/s.
Analysis and Simulation of Flat Plate Laminar Boundary LayerIJMREMJournal
In this paper, an analysis was done on laminar boundary layer over a flat plate. The analysis was performed by
changing the Reynolds number. The Reynolds number was changed by changing horizontal distance of the flat
plate. Since other quantities were fixed, the Reynolds number increased with increment of horizontal distance.
Iterations were increased in scaled residuals whenever the Reynolds number was increased. Maximum value of
velocity contour decreased with the increment of the Reynolds number. The value of the largest region of velocity
contour decreased with the increment of the value of the Reynolds number and it also affected the appearance of
contour. The value of pressure contour increased with the increment of the Reynolds number. Vertical distance
versus velocity graph was not depended on the Reynolds number. In this graph, the velocity increased rapidly
with the increment of vertical distance for a certain period. After that, the velocity decreased slightly with the
increment of vertical distance. Finally, the velocity became around 1.05 m/s
Abstract. This talk is about the GEOtop and JGrass-NewAge model, their physical bases, their informatics based on older (the first) and new (the latter) programming paradigms, the lessons I learned in building them with my group of people in an academic environment, their future, and the understanding that there is no the best model, but certainly a better way to do models.
Hydrological modelling was for long time, and still is, almost a synonym of simulating rainfall-runoff. Recently, however, the scope of hydrology became wider, even among engineers. Modelling in hydrology now certainly still means modelling discharges, but also modelling snow, evapotranspiration and turbulent exchanges, and surface/subsurface interactions. With the goal of reproducing the whole picture of the terrestrial hydrological fluxes, my coworkers and I worked together in the last decade to build new models and new types of models. We started from the lesson by P. Eagleson, and we built first the process-based (grid based) GEOtop model. GEOtop is “terrain-based” (it is based on the use of digital terrain models and uses the knowledge of interaction between morphology and process) “distributed” (all the simulated variables are calculated for each pixel of the basin) model of “the water cycle” (it simulates all the components of the water cycle, accounting for both the mass budget and the energy budget, the two budget equations being coupled through the temperature of the soil, which controls evaporation, hydraulic conductivity, and accumulation of the snowpack). However, this GEOtop was intimidating many, either for the complexity of the process and its internals, and possibly not adapted to large scale modelling where faster solutions are required.
Therefore we also worked on a different, more parsimonious model, called JGrass-NewAGE. From the lesson learned by implementing and maintaining GEOtop, we also found necessary to build the new model on new informatics. This system sacrifices process details in favour of efficient calculations. It is made of components apt at returning statistical hydrological quantities, opportunely averaged in time and space. One of the goals of this implementation effort was to create the basis for a physico-statistical hydrology in which the hydrological spatially distributed dynamics are reduced into low dimensional components, when necessary surrogating the internal heterogeneities with "suitable noise" and a probabilistic description. Unlike other efforts of synthesis, JGrass-NewAge keeps the spatial description explicit, at various degrees of simplicity. This has been made possible by opportune processing of distributed information which, in this way, has become part of the model itself.
This document provides an overview of seismic exploration fundamentals and concepts related to refracted and reflected seismic waves. It discusses topics like refracted ray and angle, total time of refraction travel, apparent versus true velocity, constructing time-distance plots from single-layer models, and exercises for determining arrival times using ray-tracing concepts. Homework problems are also presented relating to Nafe-Drake curves, seismic velocities in a two-layer model, and anomalous velocities for ice. Students are directed to online resources for more information on derivations and single-layer modeling equations.
This document provides an overview of coastal engineering processes and applications. It begins with an introduction to coastal processes, including terminology, typical coastal zones, and examples of engineering projects. It then covers topics like sediment characteristics, long-term processes like sea level rise, hydrodynamics including tides, storms, and water waves. Methods for measuring and modeling coastal responses are discussed, along with techniques for modifying shorelines like beach nourishment and hard structures. The document uses diagrams and photographs of international case studies to illustrate key concepts in coastal engineering.
Numerical Study of Forced Convection in a Rectangular Channel
Original Research Article
Journal of Chemistry and Materials Research Vol. 1 (1), 2014, 7–11
Salim Gareh
This is a short introduction to understand just a little how hydrological models and some hydraulics works. Much relies on the oral presentation. Unfortunately this is is Italian
A short introduction to some hydrological extreme phenomenaRiccardo Rigon
For high School teachers. Kept at MUSE on October 20th 2017. It covers the typology of some phenomena giving a little of explanation of the diverse dynamics. Is a product of LIFE FRANCA EU project
This contains the talk given at the 2017 meeting of the SteepStream ERANET project. It is assumed to talk about the hydrological cycle of the Noce river in Val di Sole valley (Trentino, Italy). It is a preliminary view of what we are going to do in the project.
This discusses the fact that one as to solve the right equations for a problem and show some interesting cases which consist in modifications of the Richards' equation. These equations, in turns, require special methods to be solved, and the right equations are useless without the appropriate numerics. The second part of the talk discusses the how equations are not the whole picture in a research or technical environment. Several other conditions need to be met.
This chapter reviews concepts of 1D open channel hydraulics relevant to modeling sediment transport in rivers and turbidity currents. It discusses simplifying the cross-sectional shape of channels to rectangular, defines important parameters like flow depth and velocity, and reviews equations for normal flow, boundary shear stress, and resistance relations that are used to estimate properties of bankfull flow conditions based on the assumption of normal flow.
Hydraulic and Hydrologic Design ConceptYimam Alemu
This chapter discusses hydrologic concepts related to hydropower design. It defines hydrology and the hydrologic cycle, including precipitation, evaporation, transpiration, infiltration and runoff. Methods for measuring runoff include rainfall records, empirical formulas, runoff curves and tables, and stream gauges. Factors affecting runoff include rainfall amount, catchment area properties, soil/vegetation conditions, and meteorology. Hydrographs plot discharge over time and are used to understand flow rates and volumes. Flow duration curves show flow exceedance and are used to evaluate firm and secondary power potential for hydropower.
The document analyzes water eutrophication in the Sulejow Reservoir in Poland using coupled CFD and WASP models. A 3D CFD model was developed to simulate hydrodynamics, which was then verified with field measurements. The WASP model was used to simulate nutrient transport and cycling factors like phytoplankton growth, considering hydrodynamics from the CFD model. The results showed proper correlation between measured and calculated values, indicating the models realistically captured the distribution of temperatures, velocities and nutrient concentrations contributing to eutrophication in the reservoir. The methodology can be applied to other reservoir systems to analyze ecological status.
This document describes a graphical language for representing reservoir systems using time-continuous Petri nets (TCPN).
Places in the TCPN represent water storages such as volumes of groundwater or energy/momentum contents. Transitions represent fluxes between storages. The TCPN uses colors to distinguish different types of quantities (mass, energy, etc.) and storages. Connections between places and transitions represent differential equations governing the system.
An example TCPN represents a system of three differential equations with three storages, inputs, and both linear and nonlinear fluxes. Additional information like parameter values can be provided in tables. Adjacency matrixes describe the connections between places and transitions. TCPNs provide an algebraic framework for conceptual
These are the slides presented at EGU 2017 General Meeting, the Pico session was entlited: Monitoring and modelling flow paths, supply and quality in a changing mountain cryosphere
The document discusses different ways of representing water budgets and fluxes between reservoirs in a conceptual hydrological model. It proposes using a formalized set of symbols to represent different types of reservoirs, fluxes, inputs, outputs, and relationships in a clear and standardized way. This is aimed at building an "algebra of objects" to concisely capture the key interactions and mass balances governing a reservoir system. Examples are provided of simple reservoir models represented with this symbolic notation.
The document discusses engineering hydrology, which uses hydrologic principles to solve problems related to water resource management and development. It defines engineering hydrology as studying the hydrologic cycle and its components like precipitation, evaporation, infiltration and runoff. Engineering hydrologists work on projects for water control, utilization and management by estimating maximum floods, droughts, water supply and more using statistical and modeling techniques. The key aspects of hydrology discussed are data collection, analysis and prediction.
This dissertation examines the stability and nonlinear evolution of an idealized hurricane model. The author uses the quasi-geostrophic shallow water equations to model the hurricane as a simple axisymmetric annular vortex with a predefined potential vorticity distribution. Both single-layered and two-layered models are considered. For the single-layer case, linear stability analysis reveals barotropic and baroclinic instabilities that depend on parameters like the potential vorticity within the core and the Rossby deformation length. Nonlinear simulations then show how the annular structure breaks down in different ways depending on these parameters. For the two-layer case, linear stability is found to be identical to the single-layer case, and phase diagrams
DSD-INT 2019 Modeling vegetation controls on gravel bed river morphodynamics ...Deltares
This document summarizes a presentation on modeling vegetation controls on gravel bed river morphodynamics. It describes two modeling frameworks - one where vegetation is represented as a single biomass and another that considers the role of plant roots. The models reproduce major effects of vegetation on river morphology and show that plant root feedbacks are mediated by a balance between erosion and root resistance that determines vegetation disturbance. While the models provide insights, further development is needed to better represent uprooting mechanisms and apply the models to more complex environments.
In this paper, an analysis was done on laminar boundary layer over a flat plate. The analysis was performed by changing the Reynolds number. The Reynolds number was changed by changing horizontal distance of the flat plate. Since other quantities were fixed, the Reynolds number increased with increment of horizontal distance. Iterations were increased in scaled residuals whenever the Reynolds number was increased. Maximum value of velocity contour decreased with the increment of the Reynolds number. The value of the largest region of velocity contour decreased with the increment of the value of the Reynolds number and it also affected the appearance of contour. The value of pressure contour increased with the increment of the Reynolds number. Vertical distance versus velocity graph was not depended on the Reynolds number. In this graph, the velocity increased rapidly with the increment of vertical distance for a certain period. After that, the velocity decreased slightly with the increment of vertical distance. Finally, the velocity became around 1.05 m/s.
Analysis and Simulation of Flat Plate Laminar Boundary LayerIJMREMJournal
In this paper, an analysis was done on laminar boundary layer over a flat plate. The analysis was performed by
changing the Reynolds number. The Reynolds number was changed by changing horizontal distance of the flat
plate. Since other quantities were fixed, the Reynolds number increased with increment of horizontal distance.
Iterations were increased in scaled residuals whenever the Reynolds number was increased. Maximum value of
velocity contour decreased with the increment of the Reynolds number. The value of the largest region of velocity
contour decreased with the increment of the value of the Reynolds number and it also affected the appearance of
contour. The value of pressure contour increased with the increment of the Reynolds number. Vertical distance
versus velocity graph was not depended on the Reynolds number. In this graph, the velocity increased rapidly
with the increment of vertical distance for a certain period. After that, the velocity decreased slightly with the
increment of vertical distance. Finally, the velocity became around 1.05 m/s
Abstract. This talk is about the GEOtop and JGrass-NewAge model, their physical bases, their informatics based on older (the first) and new (the latter) programming paradigms, the lessons I learned in building them with my group of people in an academic environment, their future, and the understanding that there is no the best model, but certainly a better way to do models.
Hydrological modelling was for long time, and still is, almost a synonym of simulating rainfall-runoff. Recently, however, the scope of hydrology became wider, even among engineers. Modelling in hydrology now certainly still means modelling discharges, but also modelling snow, evapotranspiration and turbulent exchanges, and surface/subsurface interactions. With the goal of reproducing the whole picture of the terrestrial hydrological fluxes, my coworkers and I worked together in the last decade to build new models and new types of models. We started from the lesson by P. Eagleson, and we built first the process-based (grid based) GEOtop model. GEOtop is “terrain-based” (it is based on the use of digital terrain models and uses the knowledge of interaction between morphology and process) “distributed” (all the simulated variables are calculated for each pixel of the basin) model of “the water cycle” (it simulates all the components of the water cycle, accounting for both the mass budget and the energy budget, the two budget equations being coupled through the temperature of the soil, which controls evaporation, hydraulic conductivity, and accumulation of the snowpack). However, this GEOtop was intimidating many, either for the complexity of the process and its internals, and possibly not adapted to large scale modelling where faster solutions are required.
Therefore we also worked on a different, more parsimonious model, called JGrass-NewAGE. From the lesson learned by implementing and maintaining GEOtop, we also found necessary to build the new model on new informatics. This system sacrifices process details in favour of efficient calculations. It is made of components apt at returning statistical hydrological quantities, opportunely averaged in time and space. One of the goals of this implementation effort was to create the basis for a physico-statistical hydrology in which the hydrological spatially distributed dynamics are reduced into low dimensional components, when necessary surrogating the internal heterogeneities with "suitable noise" and a probabilistic description. Unlike other efforts of synthesis, JGrass-NewAge keeps the spatial description explicit, at various degrees of simplicity. This has been made possible by opportune processing of distributed information which, in this way, has become part of the model itself.
This document provides an overview of seismic exploration fundamentals and concepts related to refracted and reflected seismic waves. It discusses topics like refracted ray and angle, total time of refraction travel, apparent versus true velocity, constructing time-distance plots from single-layer models, and exercises for determining arrival times using ray-tracing concepts. Homework problems are also presented relating to Nafe-Drake curves, seismic velocities in a two-layer model, and anomalous velocities for ice. Students are directed to online resources for more information on derivations and single-layer modeling equations.
This document provides an overview of coastal engineering processes and applications. It begins with an introduction to coastal processes, including terminology, typical coastal zones, and examples of engineering projects. It then covers topics like sediment characteristics, long-term processes like sea level rise, hydrodynamics including tides, storms, and water waves. Methods for measuring and modeling coastal responses are discussed, along with techniques for modifying shorelines like beach nourishment and hard structures. The document uses diagrams and photographs of international case studies to illustrate key concepts in coastal engineering.
Numerical Study of Forced Convection in a Rectangular Channel
Original Research Article
Journal of Chemistry and Materials Research Vol. 1 (1), 2014, 7–11
Salim Gareh
This is a short introduction to understand just a little how hydrological models and some hydraulics works. Much relies on the oral presentation. Unfortunately this is is Italian
A short introduction to some hydrological extreme phenomenaRiccardo Rigon
For high School teachers. Kept at MUSE on October 20th 2017. It covers the typology of some phenomena giving a little of explanation of the diverse dynamics. Is a product of LIFE FRANCA EU project
This is the presentation given for the admission to his second year of Ph.D. studies by Michele Bottazzi. Besides sumamrizing the work done during the first year, Michele traces his pathways into the second year with an abrupt change of direction towards simulating and discussion transpiration from plants.
This is the presentation for his admission to the third year of his Ph.D.. It talks about the several direction his work had taken and look forward to the conclusion of some task in form of code release and published papers.
This contains a summary of the data available for torrente Meledrio. We are using it for the project SteepsStreams, and we want to estimate its water and sediment budgets.
This contains some hints and discussions about how to implement Grids in a Object Oriented language. Specifically the discussion is made with Java in mind, but obviosly, not limited to it.
How to implement unstructured grids in Java (or BTW in another OO language). First start from understanding what grids are and how they are described in algebraic topology. Mathematics first, can be a good idea. No explicit implementation here, but concept and literature to study and start from..
Virtual water refers to the water used in the production of agricultural and industrial products. Large amounts of water are required to produce many goods - for example, 1kg of beef requires 16,000kg of water. Countries import virtual water when they import water-intensive goods produced elsewhere. This is important for water-stressed countries. For example, in Southern Africa the average annual runoff in South Africa is 45.2km3/year, while Lesotho contributes an additional 5.2km3/year through water transfers. Several countries in the region are already experiencing water stress according to common definitions. The document provides statistics on water availability and usage in several Southern African countries.
John Dalton established quantitative hydrology in 1799 by creating a water balance for England and Wales using rainfall and river flow data. He attributed the origin of springs to rainfall, rejecting long-held myths and laying the foundation for the modern understanding of the hydrological cycle. Recent work has focused on understanding soil evaporation dynamics at the pore scale, finding that as the soil surface dries, the spacing between pores increases, leading to higher evaporative flux per pore that can maintain an overall constant evaporation rate despite a decreasing surface area. This pore-scale model provides insights into evaporation rates, surface resistance, and energy partitioning during drying.
Projecting Climate Change Impacts on Water Resources in Regions of Complex To...Riccardo Rigon
The title describes it all. Jeremy Pal's student Brianna Pagàn and coworkers put an impressive set of tools to estimate the impacts of land use and climate change on water resources of south California.
The document discusses modern approaches to flood forecasting. It begins by noting the importance of data collection and organization for hydrological modeling and forecasting. Key tools mentioned for hydrological modeling include HEC-HMS, SWAT, and SWMM. The document also discusses the importance of using multiple linked models to account for hydrological and hydraulic processes. Examples provided include systems used by ARPAE in Italy and the state of Iowa in the US. These contemporary approaches are characterized as using high-resolution data, multi-objective multi-process models, and cyberinfrastructure to run complex distributed hydrological models. However, the document notes that while such sophisticated systems provide valuable information, there are still open questions around verification at small scales
Hydrological Extremes and Human societies Riccardo Rigon
This is the talk given by Giuliano di Baldassarre at the Summer School on Hydrological Modeling kept in Cagliari this here. The topic is very up-to-date and important. He presented an analysis of a few case studies and suggested some literature.
The Science of Water Transport and Floods from Theory to Relevant Application...Riccardo Rigon
This is the presentation given by Ricardo Mantilla at University of Iowa in 2017. It talks about the system implemented in Iowa for flood forecasting in real time
Freezing Soil for the class of Environmental ModellingRiccardo Rigon
This is similar to the lecture Niccolò gave in Ottawa during his staying in Carleton University. This also contains further results from his Ph.D. thesis
Master thesis presentation by Niccolò TubiniRiccardo Rigon
The student Niccolò Tubini is developing a new interpretation of modeling freezing soils in his master's thesis. He aims to model coupled heat and water flow during freezing-thawing processes using a rigid soil scheme. The model considers unsaturated soil properties, freezing point depression due to capillary effects and solutes, and mass and energy conservation equations accounting for phase changes between water and ice. The apparent heat capacity is defined to account for heat effects during phase changes in the energy equation.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
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How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
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Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...Diana Rendina
Librarians are leading the way in creating future-ready citizens – now we need to update our spaces to match. In this session, attendees will get inspiration for transforming their library spaces. You’ll learn how to survey students and patrons, create a focus group, and use design thinking to brainstorm ideas for your space. We’ll discuss budget friendly ways to change your space as well as how to find funding. No matter where you’re at, you’ll find ideas for reimagining your space in this session.
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...
Hillslope hydrologyandrichards
1. An Overview Hillslope Hydrology
Mirò-BlueII
Riccardo Rigon
2nd International Summer School on
Water Research, Praia a Mare, July 2013
Monday, July 8, 13
2. Goals
• Say what a hillslope is
• Talking about Richards equation
• Say what Hydrology on hillslope is concerned about
• Simplifying Richards’ equation
1
2
• Some reflections
• And Beyond ...
Welcome
R. Rigon
Monday, July 8, 13
15. 15
Keep in mind the complexity
Courtesy of Enzo Farabegoli - Duron catchment
R. Rigon
The complexity of geology (and of gelogists)
Monday, July 8, 13
17. 17
How water moves in hillslopes ?
Turbulent flows - Laminar flows
Both are described by the Navier-Stokes equations
R. Rigon
Fundamentals
Monday, July 8, 13
18. 18
2D - de Saint Venant equations
with some smart subgrid parameterization
(e.g. Casulli, 2009)
1D - Kinematic equation
So many to cite here but ... Liu and
Todini, 2002
R. Rigon
Less is more
Navier-Stokes equations are actually never used to do
hillslope hydrology
For a synthesis see: abouthydrology.blogspot.com
R. Rigon
Monday, July 8, 13
19. 19
How water moves in hillslopes ?
Turbulent flows - Laminar flows
Darcy flows
R. Rigon
Fundamentals
Monday, July 8, 13
20. 20
Darcy equations are OK
for saturated flow
They can be obtained from Navier-Stokes Equation
by*:
•introducing a resistance term
•assuming creep flow (neglecting kinetic terms)
•integrating over the Darcy scale
*Whitaker, 1966; Bear, 1988; Narsilio et al., 2009
R. Rigon
Fundamentals
Monday, July 8, 13
22. 22
One idea is
that we can use Richards’ equation
So, on the earth what is
Richards’ equation ?
R. Rigon
Fundamentals
Monday, July 8, 13
23. 23
Richards’ equation core
is that what it is true is this
Mass conservation (no nuclear reactions) !
but actually true if the continuum (a.k.a. Darcy) hypothesis is valid
Process based models
R. RigonR. Rigon
Monday, July 8, 13
24. Not necessarily this:
24
Se = [1 + ( ⇥)m
)]
n
Se :=
w r
⇥s r
C(⇥)
⇤⇥
⇤t
= ⇥ · K( w) ⇥ (z + ⇥)
⇥
K( w) = Ks
⇧
Se
⇤
1 (1 Se)1/m
⇥m⌅2
SWRC +
Darcy-Buckingham
(1907)
Parametric
Mualem (1976)
Parametric
van Genuchten
(1981)
C(⇥) :=
⇤ w()
⇤⇥
Process based models
R. Rigon
Monday, July 8, 13
25. 25
To obtain the last slide
One has to assume the validity of the Darcy-Buckingham law:
Darcy-Buckingham Law
Volumetric flow
through the surface
of the infinitesimal
volume
Buckingham,1907,Richards,1931
~Jv = K(✓w)~r h
Fundamentals
Monday, July 8, 13
26. 25
To obtain the last slide
One has to assume the validity of the Darcy-Buckingham law:
Darcy-Buckingham Law
Volumetric flow
through the surface
of the infinitesimal
volume
Buckingham,1907,Richards,1931
~Jv = K(✓w)~r h
Fundamentals
Monday, July 8, 13
27. 25
To obtain the last slide
One has to assume the validity of the Darcy-Buckingham law:
Darcy-Buckingham Law
Volumetric flow
through the surface
of the infinitesimal
volume
Buckingham,1907,Richards,1931
~Jv = K(✓w)~r h
Fundamentals
Monday, July 8, 13
28. 25
To obtain the last slide
One has to assume the validity of the Darcy-Buckingham law:
Darcy-Buckingham Law
Volumetric flow
through the surface
of the infinitesimal
volume
Hydraulic conductivity times
gradient of the hydraulic head
Buckingham,1907,Richards,1931
~Jv = K(✓w)~r h
Fundamentals
Monday, July 8, 13
29. 26
Ignore soil hysteresis
and think of the SWRC as a function that relates water content to matric
pressure
⇤ (⇥)
⇤t
=
⇤ (⇥)
⇤⇥
⇤⇥
⇤t
C(⇥)
⇤⇥
⇤t
Hydraulic capacity of
the soil
R. Rigon
Fundamentals
Monday, July 8, 13
30. 27
Assume a parametric form
of soil water retention curves
Se :=
w r
⇥s r
Parametric
van Genuchten
(1981)
C(⇥) :=
⇤ w()
⇤⇥
Se = [1 + ( ⇥)m
)]
n
But other forms are possible ...
R. Rigon
Fundamentals
Monday, July 8, 13
31. 28
A theory for getting hydraulic conductivity
from soil water retention curves
K( w) = Ks
⇧
Se
⇤
1 (1 Se)1/m
⇥m⌅2
Parametric
Mualem (1976)
But other forms are possible also here...
R. Rigon
Fundamentals
Monday, July 8, 13
32. 29
The last representation of mass conservation
is just matter of convenience
habits, and ignorance of some phenomena
•variable and changing temperature
•soil freezing
•transition to saturation
•preferential flow
Process based models
R. RigonR. Rigon
Monday, July 8, 13
33. An example of top down derivation
from Richards’ equation
ChimpanzeeCongopainting
Monday, July 8, 13
38. 35
Depth from surface
Terrain Slope
Water table position
A lot of tricks here !
R. Rigon
Richardsoniana
Monday, July 8, 13
39. and one equation for
Iverson,2000;CordanoeRigon,2008
36
So Richards equation is
divided into one equation for
Richardsoniana
R. Rigon
Monday, July 8, 13
40. 37
Interestingly
Water table was not present in the original Richards
equation
Hydrostatic hypothesis
R. Rigon
Richardsoniana
Monday, July 8, 13
44. 41
In turn
“Short term
solution” Taylor’s
expansion
Water table
equation Taylor’s
expansion
Slope normal flow
time scale Lateral flow
time scaleSee also. D’Odorico et al., 2003
Richardsoniana
R. Rigon
Monday, July 8, 13
45. 42
Pay attention to this
Slope normal flow
time scale Lateral flow
time scale
Richardsoniana
R. Rigon
Hydraulic diffusivityD( ) :=
K( )
C( )
Monday, July 8, 13
46. 43
Details
that can be found in Cordano and Rigon, 2008
in words
•Take the dimensionless Richards equation
•Substitute in it the solution structure (asymptotic plus fast part)
•Here you obtain two coupled equations
•Further expand the solution structure in Taylor series
•Consider the terms which have the same expansion exponent in
•Solve each equation
R. Rigon
Richardsoniana - Iversoniana
Monday, July 8, 13
47. 44
Neglecting those details
that can be found in Cordano and Rigon, 2008
Zeroth perturbation order
R. Rigon
Richardsoniana - Iversoniana
Monday, July 8, 13
48. 45
Neglecting those details
that can be found in Cordano and Rigon, 2008
Zeroth perturbation order
R. Rigon
1D-Richards equation A source term
(exchange with water table)
Richardsoniana - Iversoniana
Monday, July 8, 13
49. 46
Neglecting those details
that can be found in Cordano and Rigon, 2008
Water Table equation
R. Rigon
Richardsoniana - Iversoniana
Monday, July 8, 13
50. 47
Neglecting those details
that can be found in Cordano and Rigon, 2008
Zeroth perturbation order
First perturbation order
+ analogous for d*
R. Rigon
Richardsoniana - Iversoniana
Monday, July 8, 13
51. 48
Integrating zeroth order solution in the column
Making a long story short
R. Rigon
Richardsoniana - Iversoniana
Monday, July 8, 13
53. 50
Integrating zeroth order solution in the column
Making a long story short
Topkapi* model
Liu and Todini, 2002
R. Rigon
*With some interpretation
Richardsoniana - Iversoniana
Monday, July 8, 13
54. 51
Integrating first order solution slope-parallel
Making a long story short - II
Boussinesq equation
(e.g. Cordano and Rigon, 2013)
R. Rigon
: dimensionless transmissivities
: drainable porosity
Richardsoniana - Iversoniana - and beyond
Monday, July 8, 13
55. 52
Making a long story short - III
R. Rigon
Figure represents a map of a small catchment, river network and a hillslope (hollow type, in gray). The distance of
any point (P in the figure) in the hillslope to the channel head (C in the figure) is evaluated along the path drawn
following the steepest descent (the dashed line). The characteristic length of the hillslope L (the length of x axis in
Figure) is the mean of hillslope to channel distance for any point in the hillslope. The x axis used in the paper is
downward parallel to mean topographic gradient, the axis y is normal to x (parallel to contour lines in a planar
hillslope) and the z axis orthogonal to the x and y axes downward.
Integrating again over the lateral dimension
from Boussinesq
Richardsoniana - Iversoniana - and beyond
Monday, July 8, 13
56. 53
Integrating Boussinesq
Making a long story short - III
HsB
Troch et al. 2003
R. Rigon
: is the so called width function
Richardsoniana - Iversoniana - and beyond
Monday, July 8, 13
58. 55
Simplifying HsB assuming stationarity of fluxes
and neglecting diffusive terms
Making a long story short - IV and V
Topog
O’Loughlin, 1986
R. Rigon
Richardsoniana - Iversoniana - and beyond
Monday, July 8, 13
59. 56
Simplifying HsB assuming stationarity of fluxes
and neglecting diffusive terms
Making a long story short - IV and V
assuming an exponential decay of vertical hydraulic
conductivity
Topmodel
Beven and Kirkby, 1979
R. Rigon
Richardsoniana - Iversoniana - and beyond
Monday, July 8, 13
60. 57
Take home message
We can use Richards equation at various degree of simplification:
•1D (if we think that just slope-normal infiltration counts
•1D + 2D Boussinesq (Beq) if we want to account for lateral flow
* On this I will come back later
R. Rigon
Richardsoniana - Iversoniana - and beyond
Monday, July 8, 13
61. 58
Take home message
We can use various simplification of either 1D and 2D Beq together:
• 1D Complete + 2D asymptotic- stationary
• 1D linearized + 2D asymptotic- stationary
• 1D bulk* + 2D asymptotic- stationary
• 1D Complete + 2D full Beq
• 1D linearized + 2D full Beq
• 1D bulk* + 2D full Beq
* On this I will come back later
R. Rigon
Richardsoniana - Iversoniana - and beyond beyond
Monday, July 8, 13
62. 59
Take home message
We can also try a kinematic approximation of the Boussinesq equation, and
therefore:
• 1D Complete + 2D Kinematic
• 1D linearized + 2D Kinematic
• 1D bulk* + 2D Kinematic
* On this I will come back later
R. Rigon
Richardsoniana - Iversoniana - and beyond beyond
Monday, July 8, 13
63. 1D linear + 2D asymptotic
a.k.a D’Odorico et al., 2005
Mirò.The-nightingale-s-song-at-midnight-and-the-morning-rain
Monday, July 8, 13
64. C(⇥)
⇤⇥
⇤t
=
⇤
⇤z
⇤
Kz
⇤⇥
⇤z
cos
⇥⌅
+ Sr
In literature related to the determination of slope stability this equation
assumes a very important role because fieldwork, as well as theory, teaches
that the most intense variations in pressure are caused by vertical infiltrations.
This subject has been studied by, among others, Iverson, 2000, and D’Odorico
et al., 2003, who linearised the equations.
61
The Richards Equation!
R. Rigon
Linearize it !
Monday, July 8, 13
65. The analytical solution methods for the advection-dispersion equation
(even non-linear), that results from the Richards equation, can be found
in literature relating to heat diffusion (the linearised equation is the
same), for example Carslaw and Jager, 1959, pg 357.
Usually, the solution strategies are 4 and they are based on:
- variable separation methods
- use of the Fourier transform
- use of the Laplace transform
- geometric methods based on the symmetry of the equation (e.g.
Kevorkian, 1993)
All methods aim to reduce the partial differential equation to a system
of ordinary differential equations
62
TheRichardsEquation1-D
R. Rigon
Linearize it !
Monday, July 8, 13
66. ⇥ ⇥ (z d cos )(q/Kz) + ⇥s
Iverson,2000;D’Odoricoetal.,2003,
CordanoandRigon,2008
63
s
The Richards equation on a plane hillslope
R. Rigon
Linearize it !
Monday, July 8, 13
67. Assuming K ~ constant and neglecting the source terms
⇤⇥
⇤t
= D0 cos2 ⇤2
⇥
⇤t2
64
The Richards Equation 1-D
C( )
@
@t
= Kz 0
@2
@z2
D0 :=
Kz 0
C( )
D’Odoricoetal.,2003
R. Rigon
Linearize it !
Monday, July 8, 13
68. The equation becomes LINEAR and, having found a solution
with an instantaneous unit impulse at the boundary, the
solution for a variable precipitation depends on the
convolution of this solution and the precipitation.
65
The Richards Equation 1-D
D’Odoricoetal.,2003
R. Rigon
Linearize it !
Monday, July 8, 13
70. For a precipitation impulse of constant intensity, the solution can be
written:
⇥0 = (z d) cos2
D’Odoricoetal.,2003
67
= 0 + s
s =
8
<
:
q
Kz
[R(t/TD)] 0 t T
q
Kz
[R(t/TD) R(t/TD T/TD)] t > T
The Richards Equation 1-D
R. Rigon
Linearize it !
Monday, July 8, 13
71. In this case the equation admits an analytical solution
D’Odoricoetal.,2003
68
R(t/TD) :=
⇤
t/( TD)e TD/t
erfc
⇤
TD/t
⇥
s =
8
<
:
q
Kz
[R(t/TD)] 0 t T
q
Kz
[R(t/TD) R(t/TD T/TD)] t > T
TD :=
z2
D0
The Richards Equation 1-D
R. Rigon
Linearize it !
Monday, July 8, 13
73. 70
Second message
Why using other simplifying assumptions (like
Horton’s or Green-Ampt), if we have this ?
R. Rigon
Forget them!
Monday, July 8, 13
75. 72
Did you care about hypotheses ?
Is it for any occasion realistic ? Look at the following sandy-loam:
Hypotheses counts
R. Rigon
Monday, July 8, 13
76. 72
Did you care about hypotheses ?
Is it for any occasion realistic ? Look at the following sandy-loam:
Hypotheses counts
R. Rigon
Monday, July 8, 13
77. constant diffusivity
73
The Decomposition of the Richards equation
is possible under the assumption that:
Time scale of infiltration
soil depth
time scale of lateral flow
hillslope length
reference conductivity
reference hydraulic capacity
Iverson,2000;CordanoandRigon,2008
Hypotheses counts
R. Rigon
Monday, July 8, 13
79. 75
For the sandy-loam soil
assuming the water table at one meter depth
we have a vertical variation of hydraulic conductivity of one order of magnitude !
Hypotheses counts
R. Rigon
Monday, July 8, 13
80. 76
D which characterizes the time scales of flow is varying
with depth
Hypotheses counts
R. Rigon
So a D0 reference cannot be significant
Monday, July 8, 13
81. 77
Therefore
at surface
so, lateral flow at the water table level
has the same time scale vertical flow at
the surface (at least if we believe to
Richards’ equation)
Hypotheses counts
R. Rigon
Monday, July 8, 13
82. 78
igure 2: Experimental set-up. (a) The infinite hillslope schematization. (b) The initial suction head pr
il-pixel hillslope numeration system (the case of parallel shape is shown here). Moving from 0 to 900
sponds to moving from the crest to the toe of the hillslope
The OpenBook hillslope in a 3D
simulation
Comparing with 3D
R. Rigon
LanniandRigon,unpublished
Monday, July 8, 13
83. 79
- 54 LANNI ET AL.: HYDROLOGICAL ASPECTS IN THE TRIGGERING OF SHALLOW LANDSLIDES
(a) DRY-Low (b) DRY-Med
Simulations result
Comparing with 3D
R. Rigon
LanniandRigon,unpublished
Monday, July 8, 13
84. 80
At the beginning the pressure is constant
along the whole transect (except for
phenomena at the divide’s edge
Comparing with 3D
R. Rigon
Monday, July 8, 13
85. 81
After a certain amount of time (25h in this
simulation) pressures along the slope
differentiate. With a little of analysis we
c a n d i s t i n g u i s h t w o r e g i o n s o f
differentiation. One controlled by the
boundary conditions at the bottom.
The second generated by lateral water
flow accumulation.
Comparing with 3D
R. Rigon
Monday, July 8, 13
86. 82
(a) (b)
Figure 6: Temporal evolution of the vertical profile of hydraulic conductivity (a) and hydraulic conductivity at the soil-bedrock interface
Hidraulic conductivity is varying by three order of magnitude
at the bedrock interface.
The key to understand this phenomenology
Lannietal.,2012
Comparing with 3D
R. Rigon
Monday, July 8, 13
87. 83
56 LANNI ET AL.: HYDROLOGICAL ASPECTS IN THE TRIGGERING OF SHALLOW LANDSLIDES
(a) (b)
(a)
(c)
Figure 7: Transient pore pressure profiles related to points No. 300, 450
(c) cases, and soil hydraulic conductivity function inferred using the Mu
position of the water table at different timing
D R A F T September 24, 2
Another view
R. Rigon
Comparing with 3D
Monday, July 8, 13
88. 84
When simulating is understanding
courtesyofE.Cordano
T’L can be very small indeed .....
Interpretations
R. Rigon
Monday, July 8, 13
89. 85
Understanding from simulations
At the beginning of the infiltration process the situation in surface is
marked by the blue line, the situation at the bedrock is marked by the
red line
courtesyofE.Cordano
R. Rigon
Interpretations
Monday, July 8, 13
90. 86
When lateral flow start we are in the following situation
courtesyofE.Cordano
Understanding from simulations
R. Rigon
Interpretations
Monday, July 8, 13
91. 87
At the beginning
The condition of the perturbative derivation are verified
courtesyofE.Cordano
R. Rigon
Interpretations
Monday, July 8, 13
92. 88
At the end
courtesyofE.Cordano
Conditions for lateral flow are dominating. Actually the same
phenomenology deducted by the perturbation theory! But obtained for a
different reason.
R. Rigon
Interpretations
Monday, July 8, 13
93. 89
Take home message:
Never fully believe on the magic of simplifications
Detailed physics in models can help
R. Rigon
Magic ad Mermeids do not exist (Sponge Bob)
Monday, July 8, 13
94. 90
Lateral Flow
•Can be fast, ... very fast, much faster than what happens in vadose
conditions
•In fact, to have the effects just described, we have to believe to the form
that Soil Water retention Curves have.
•Other soils behave differently
•If macropores or cracks are present, vertical infiltration can still remain
faster
R. Rigon
Interpretations
Monday, July 8, 13
97. 93
CAPITOLO 5. IL BACINO DI PANOLA
Figura 5.2: Rappresentazione della profondit`a del suolo del pendio di Panola.
costante su un campione prelevato a 10 cm di profondit`a, risulta pari a 64 [cm/h]; per ci`o che concerne
il valore della conducibilit`a idraulica a saturazione del bedrock, non esistono misure dirette e↵ettuate
su campioni prelevati in sito; tuttavia si stima che il suo valore sia 2-3 ordini di grandezza inferiore
rispetto a quella del terreno soprastante. Entrambi i valori di conducibilit`a idraulica satura (del bedrock
e del terreno) saranno comunque oggetto di calibrazione numerica all’atto delle simulazioni svolte con
GEOtop, utilizzando come valori di partenza quelli qui citati.
Panola’s hillslope
R. Rigon
Richards equation is still valid here ?
Monday, July 8, 13
98. 94
Terrain surface Bedrock surface Soil depth varies
Depression
Soil (sandy loam) Bedrock
Ksat = 10-4 m/s Ksat = 10-7 m/s
Panola’s hillslope
R. Rigon
Richards equation is still valid here ?
Monday, July 8, 13
100. 96
t=6h t=9ht=7h t=14h
Lannietal.,2011
With a rainfall of 6.5 mm/h and a duration of 9 hours
Tromp Van Meerveld et al., 2006 call it filling and spilling
R. Rigon
Richards equation is still valid here ?
Monday, July 8, 13
102. 98
1D
3D
No role played by hillslope
gradient
First Slope Normal infiltration works
Then Lateral flow start
Infiltration front propagate
Drainage is controlled by the bedrock form
As in the open book case
Lannietal.,2011
R. Rigon
Richards equation is still valid here ?
Monday, July 8, 13
103. 99
Now we want a model that can run 100 times faster
In which we obviously use all the machinery of the
Richards’ equation, i.e. hydraulic conductivity and soil
water retention curves
R. Rigon
Richards equation is still valid here ?
Monday, July 8, 13
104. 100
Introducing the concept of concentration time
in subsurface flow
we have the distances from the channels
R. Rigon
Variations
Monday, July 8, 13
105. 101
If we assume that water just move laterally in saturated
conditions, we can use Darcy law for getting the
velocities
possibly in its more traditional form:
R. Rigon
Variations
Monday, July 8, 13
106. 102
If we assume that water just move laterally in saturated
conditions, we can use Darcy law for getting the
velocities
And assuming Dupuit approximation, i.e. hydrostatic
distribution of pressures
R. Rigon
Variations
Monday, July 8, 13
107. 103
Then:
Time = Lengths/velocity
And, for any point:
is the max residence time*
R. Rigon
Variations
*The operator means that we are looking for the maximum of T choosing it from all the possible path
that we can define upstream of the point i
Monday, July 8, 13
108. 104
The largest time
is the concentration time
Up to concentration time
The area contributing to the discharge is not the
TOTAL upslope area
R. Rigon
Variations
Monday, July 8, 13
109. 105
The area contributing to the discharge is not the
TOTAL upslope area
Lannietal.,2012a
R. Rigon
!(Steady state)
Monday, July 8, 13
110. 106
Actually there is a second issue
Water table cannot “exist” everywhere
Fig. 1. A flow chart depicting the coupled saturated/unsaturated hydrological model developed in this study.
1
2
3
4
Figure 2. The concept of hydrological connectivity. Lateral subsurface flow occurs at point5
(x,y) when this becomes hydrologically connected with its own upslope contributing area6
A(x,y).7
8
Fig. 2. The concept of hydrological connectivity. Lateral subsurface
flow occurs at point (x,y) when this becomes hydrologically con-
nected with its own upslope contributing area A(x,y).
storage of soil moisture needed to produce a perched water
table (i.e. zero-pressure head) at the soil–bedrock interface
(Fig. 3); and I [LT 1] is the rainfall intensity assumed to be
uniform in space and time. Computation of V0 and Vwt re-
quire the use of a relationship between soil moisture content
✓ [ ] and suction head [L], and a relationship between
1
2
3
4
Figure 3. i(z) and i(z) are, respectively, the in5
head vertical profiles. wt(z) and wt(z) represe6
head vertical profiles associated with zero-suction7
8
Fig. 3. ✓i(z) and i(z) are, respecti
and the initial suction head vertical p
resents the linear water content and
associated with zero-suction head at
the relation between [L] and
equilibrium:
= (z = 0) + z = b + z,
Lannietal.,2012b
R. Rigon
!(Steady state)
Monday, July 8, 13
111. 107
Ii.e. time to water table
development
Twt(x,y):= [Vwt(x,y)-V0(x,y)]/I
Initial conditions
(hydrostatic slope normal)
boundary conditions
(including rainfall, I)
t> Twt(x,y)
YES
NO
Lannietal.,2012
Slope Normal
unsaturated flow
A heuristic model
for each
time
step
Faster is better
R. Rigon
Monday, July 8, 13
114. 110
* Is not completely true.
I question also of personal attitude:
I understand (fluid) mechanics through
equations and I try to interpret observations
through equations.
Someone else (i.e. many of my students)
simply did not have the training for that and
prefer to rebuilt the physics of the problem by
small pieces.
This has a certain appealing to many (especially
to natural scientists and geologists), and can
indeed be useful to see thing from different
perspectives.
Doodley,Muttley,andtheirflyingmachines
R. Rigon
Attitudes
Monday, July 8, 13
115. 111
3968 C. Lanni et al.: Modelling shallow landslide susceptibility
1
2
3
Figure 7. Patterns of Return period TR (years) of the critical rainfalls for shallow landslide4
triggering (i.e., FS≤1) and associated levels of landslide susceptibility obtained by means 5
of QDSLaM.6
7
Fig. 7. Patterns of return period TR (years) of the critical rainfalls for shallow landslide triggering (i.e. FS 1) and associated levels of
landslide susceptibility obtained by means of QDSLaM.
Table 3. Percentages of catchment area (C) and observed landslide area (L) in each range of critical rainfall frequency (i.e. return period TR)
for QDSLaM.
Susceptibility
Pizzano Fraviano Cortina
TR level Ca Lb Ca Lb Ca Lb
Years Category % % % % % %
Uncond Unstable 9.9 60.2 7.7 77.7 8.5 56.8
0–10 Very high 20.3 26.9 16.1 18.5 13.5 39.2
10–30 High 7.8 0.0 5.6 1.5 5.8 4.0
Lannietal.,2012
However, it works
R. Rigon
Faster is better if it works (Klemes fogive me!)
Monday, July 8, 13
117. 113
CAPITOLO 5. IL BACINO DI PANOLA
Figura 5.4: Immagine tratta da Tromp-van Meerveld e McDonnell, (2006a) [24]; (a) deflusso sub-
superficiale totale per i segmenti in cui `e stata suddivisa la trincea e (b) numero di eventi meteorici che
producono deflussi misurabili.
5.2.1 Il ruolo dei macropori
TrompVanMeerveldetal.,2006
And finally macropores
R. Rigon
Macropores
Monday, July 8, 13
118. 114
Macropore Flow
Initiation
Water supply to the
macropores
Interaction
Water transfer between
macropores and the
surrounding soil matrix
M.Weiler,fromMochaproject
Macropores!
R. Rigon
Macropores
Monday, July 8, 13
119. 115
0.00
date (dd/mm) 2002
01/01 11/01 21/01 31/01 10/02 20/02 02/03 12/03 22/03 01/04 11/04 21/04 01/05 11/05 21/05
Figura 5.16: Confronto tra flussi misurati e computati attraverso la Simulazione 0 presso la trincea
alla base del pendio.
0.000.020.040.060.080.10
Simulazione 0 - evento 6 febbraio
date (dd/mm) 2002
portate[l/s]
05/02 06/02 07/02 08/02 09/02 10/02 11/02 12/02
Flussi misurati
Simulazione 0
0.000.020.040.060.080.10
Simulazione 0 - evento 30 marzo
date (dd/mm) 2002
portate[l/s]
29/03 30/03 31/03 01/04 02/04 03/04 04/04 05/04 06/04 07/04
Flussi misurati
Simulazione 0
Figura 5.17: Confronto tra flussi misurati e computati attraverso la Simulazione 0 presso la trincea
alla base del pendio: a sinistra si riporta l’evento del 6 febbraio 2002, a destra quello del 31 marzo.
pu`o essere causata da diversi fattori, quali un’errata assegnazione delle caratteristiche del suolo o del
bedrock, oppure un errore nello stabilire la condizione iniziale circa la quota della falda.
Un aspetto decisamente importante da considerare, tanto in questi risultati quanto in quelli presentati
successivamente, `e che nella creazione della geometria di calcolo 3D utilizzata da GEOtop non `e
DaPrà,2013
Certainly the volumes of water cannot be
simulated with the only Richards equation
No way!
R. Rigon
Macropores
Monday, July 8, 13
120. Thank you for your attention
116
G.Ulrici-
R. Rigon
Slides on http://abouthydrology.blogspot.com
Monday, July 8, 13