Introduction and Overview. Summary

Transcription

1 Introduction and Overview CIVE 781: Principles of Hydrologic Modelling University of Waterloo Jun 19 24, 2017 Summary Course Objectives Assignments and Project Hydrologic Modelling Overview Different classes of models Mass and Energy balance basics Integrated models 2 1

2 Assignments Provided to all, voluntary for professional registrants 3 assignments (10% each; due August 1) 1 project (70%, due August 11th) Final day bring your own data/project 3 Assumptions about Background Coursework in basic hydrology Familiarity with water cycle Moderate mathematical competence Not completely afraid of basic programming concepts 4 2

3 Course Objectives By the conclusion of this course, students will: Understand the internal functioning of lumped and semi distributed models of surface water hydrology, (principles of mass and energy balance, means of representing storage flux relationships, algorithmic descriptions of critical hydrologic processes) Choose modelling approaches appropriate to the region being investigated, for supporting specific model goals, including water resource management decisions or scientific hypotheses Be able to intelligently apply concepts from the course to inform, build, and interpret hydrological models of watersheds. Be able to apply a number of standard and advanced software tools to manipulate and analyze hydrologic data, calibrate and evaluate models, and assess model uncertainty Have a greater appreciation of the difficulties inherent in prediction of hydrologic phenomena and the challenges specific to Canadian landscapes, their hydrological processes, and the availabiilty of data to describe them 5 Course Foci Learning key tools How to convert/map conceptual models of a watershed into mathematical models How to parameterize models How to look critically at a model Sources of model error How to maximize use of available data 6 3

4 What this course does not cover Urban Hydrology Statistical hydrology Contaminant/Sediment transport/water Quality Infinite hydrological equations and their details How to be an expert in a single modelling platform 7 Outline 8 4

5 Introductions 9 Hydrologic Simulation Models: Goals Forecasting short & long term forecasting of flows to a reservoir Design Determination of design floods (peaks and hydrographs) from design storms Assessment of potential system reliability (reservoirs, water supplies) Prediction Understanding potential impacts of land use/climate change Estimating long term nutrient loadings to a lake Understanding Attempting to understand/untangle causality in complex systems More often than not: What is the peak/total volume of/timing of/minimum outflow at a point? Wide variety of models used to these ends 10 5

6 11 Model Types: Treatment of processes Physically based Based on physical laws: conservation of mass, momentum, energy Often includes some empirical equations for some components Data intensive Empirical Model of data only (black box) E.g. regression relationship, Universal Soil Loss Equation (USLE), SCS curve numbers Conceptual A middle ground between the two above Often mixes physically based modelling concepts with (occasionally gross) simplifications 12 6

7 Model Types: Discretization Lumped Also called lumped parameter Region or watershed is considered a single unit (a blackbox ) Average inputs/parameter values predict output (state variables) of the single unit Distributed A.k.a. spatially distributed Region or watershed is subdivided into spatial units and model responses (i.e. streamflow) and state variables (i.e. soil water content) calculated for each unit Unique model inputs possible for each spatial unit Inputs assumed homogeneous over each spatial unit Complexity increases because computations repeated for each spatial unit but also because fluxes between spatial units must be computed (often leads to solution of large system of ODEs/PDEs) Continuum Extreme case of distributed 3D model represented using PDEs Properties vary from cell to cell 13 Key Discretization Concept: the HRU Hydrological response unit A fictive, but useful characteristic part of the landscape that has a unique response to hydrological forcing Often used as a computational unit in hydrological models A.K.A., GRUs (grouped response units), REWs (representative elementary watersheds), Tiles, etc., but base concept is the same 14 7

8 The modelling continuum Simple Lumped Empirical Conceptual Moderate Semi distributed Mixed Complex Continuum Purely Physics based Little Data Costs little time and effort Easy questions Fast Lots of Data Takes a lot of work Harder Questions Slow 15 The modelling continuum Physically-based Lumped Operational models Research models Distributed Unit hydrograph Conceptual 8

9 The modelling continuum Physically-based HGS CRHM Modflow Lumped HSPF SWAT/HEC-HMS MESH HBV UBCWM Research models Distributed GR4J SCS Unit hydrograph Operational models Conceptual Engineering Forecast Models forecasting, prediction get r done Land Surface schemes feedback to weather/climate models boundary condition Integrated models complex water resource management problems Systems hydrology models 18 9

10 Choosing a Hydrological Model AnnAGNPs Brook90 CLASS CRHM DHSVM GAWSER GWLF HBV HEC HMS HSPF HyMOD MESH Mike SHE PRMS SAC SMA SWAT SWMM TOPMODEL UBC WM VIC Each hydrological model has a considerable number of builtin assumptions Representation of key hydrological relationships Process algorithms TYPICALLY System segmentation & Landscape discretization HARD CODED Forcing function interpolation & correction Process detail Hydraulic routing These vary substantially from model to model Must be careful to ensure critical processes in your watershed can be represented using chosen model 19 Why choose one model over another? Answer: What is the Goal? What data do you have? 20 10

11 Hydrological modelling in a nutshell Step 0: Define Purpose of Model Important to quantify modeling purpose and goals at start of project Assume we are modeling streamflow at a single location Purpose of modeling could be to: Learn more about the physical processes impacting streamflow To predict a design flow under the 100 year 24hr rainfall To evaluate what if future watershed scenarios > land use management, climate change, forest fire, pine beetle Purpose or modeling goals are needed to help select appropriate model 21 Hydrological modelling in a nutshell Step 1: Discretize Watershed 22 11

12 Hydrological modelling in a nutshell Step 2: Identify and describe key processes that exchange water/mass/energy From mnr.gov.on.ca 23 Hydrological modelling in a nutshell Step 3: Describe processes in algorithmic form 24 12

13 Hydrological modelling in a nutshell Step 4: Parameterize Model Soil type Land use Vegetation Terrain Stream geometry Conductivity Field capacity Infiltration capacity Snowmelt coefficients Reservoir constants Evaporation efficiencies LAI 25 Hydrological modelling in a nutshell Step 5: Apply forcing terms and execute model Rainfall Model Secondary Diagnostic Variables Recharge Soil Moisture Net Evapotranspiration Streamflow 26 13

14 Hydrological modelling in a nutshell Step 6: Calibrate model to match data history i.e., tweak parameters 27 Hydrological modelling in a nutshell Step 7: Apply calibrated model to answer questions How much recharge reaches the groundwater under drought/wet conditions? What is the influence of canopy cover on snow ablation? What will happen to streamflow/net evaporation/carbon release under the impact of climate/land use change? Shouldn t be done unless we trust the model 28 14

15 Discretize Watershed Identify Processes At each step along the way, there are decisions (and mistakes) to be made Describe Processes Parameterize model Execute the Model Calibrate the Model 29 The devil is in the details How to subdivide the world? How to algorithmically describe processes? At what scale are these descriptions valid? How to parameterize the model? How simple/complex should the model be? How to know whether our model is working? How to know whether our model is useful? All of these details must ideally be attended to if we wish to use model output for forecasts/prediction 30 15

16 Hydrological Models in a Nutshell Precipitation Temperature Radiation Humidity known forcing functions Distribution Generation Correction Algorithms Process representation Hydrographs Physical Process System segmentation Descriptions Landscape discretization Soil Moisture Numerical Solvers Physical Discretization Hydrological Model Water Balance Distributed ET Distributed Recharge Model Output Soil Type Physical Parameters Granularity Land Use (e.g., Conductivity) Resolution Vegetation Cover Parameter mapping Empirical Coefficients Parameter generation (e.g., for power laws) Physiography Model Parameters classifications Used for (1) Hypothesis Testing (2) Forecasting (3) Simulation 31 Questioning our Models How best to populate unknown forcing functions? How does Precipitation interpolation choice impact model output? Temperature Radiation Humidity known forcing functions Physical Process Descriptions Am I using the most appropriate representation of the physical process? Numerical Solvers Are threshold constraints impacting the numerics? Physical Discretization Hydrographs Soil Moisture Water Balance Distributed ET How sensitive are our results Model Distributed to our choice Recharge of model? When can we simplify? When should we simplify? What are the impacts of uncertainty Model of Output model structure? Soil Type How should land classifications map to parameters? Physical Parameters What level of detail Land Use is required in our scheme? (e.g., Conductivity) How do we best determine/specify these Used parameters? for How does classification resolution impact model results? How should parameters be spatially (1) distributed? Hypothesis Testing Vegetation Cover Empirical Coefficients (2) Forecasting (e.g., for power law) (3) Simulation Physiography The output signal we used Model to try Parameters and answer these questions with Aquifer has Structure filtered through a complex web of interrelated decisions; how classifications do we untangle the web? 32 16

17 One of the goals of this class is to get you to critically think about each one of these steps While you may have to go back and do it by the book or be constrained by what your required software can do, you can at least know what you might be doing wrong 33 With the overview out of the way, we will now get to the fundamentals: Some basic definitions Mass/energy balance ODEs/PDEs 34 17

18 Basic Definitions State variables (OUTPUT) The variables being solved for by the model Typically include water storage and temperature, but may also include (e.g.,) snowpack density Auxilliary Variable (OUTPUT) A variable which changes in known relation to state variable, but is not a model degree of freedom. Snow depth can be calculated from snow SWE and snow density (S.V.) Parameter (INPUT) A property of the watershed/soil/vegetation that describes the relationships between state variables and water/energy fluxes. Usually incompletely known Forcing (INPUT) The external sources of mass and energy that control the response of the watershed Rainfall, snowfall, short/longwave radiation 35 Laws of Physics Conservation of Mass Conservation of Energy Conservation of Momentum Fundamental ingredients of any watershed model At very least, model will conserve and track water mass May track changes in temperature (energy) Usually mass=volume in watershed models 36 18

19 Mass Balance Once defined, we can monitor the movement and storage of water within the watershed using a simple mass balance: where is the storage in the watershed basin (typically in mm) is the rate of inflow (mm/d) is the rate of outflow (mm/d) / is the rate of accumulation of water (mm/d) The continuity equation can also be expressed in finite difference form: Δ Δ where Δ can be any time increment 37 Volumetric Flow Units Hydrologists deal with volumetric flows using two units: mm/d a flux volumetric flow per sq. m. of land surface (i.e., mm m 2 /d/m 2 ) rainfall, evaporation, infiltration,... m 3 /s stream discharge To convert between the two, (A in km 2 )

20 Watershed Mass Balance For a watershed, change in mass storage = mass gain mass loss: Divide by, Influx: Mean precipitation [mm/d] wshed area [m 2 ] Outflux: exiting streamflow [m 3 /d] Groundwater losses [mm/d] Actual Evapotranspiration [mm/d] 39 Compartment Mass Balance We can write out a mass balance on any individual system component Inflows: I Infiltration[mm/d] C Capillary fluxes [mm/d] Here, soil storage is treated as mm of water in the shallow subsurface Outflows: L lateral flow [mm/d] G Groundwater fluxes [mm/d] E Evaporation [mm/d] T Transpiration [mm/d] Again, all terms should be considered spatial averages Note individual terms themselves depend on storage An ODE! 40 20

21 Continuum Mass balance A special case where we assume the soil/snow/canopy is a vertical continuum: Divide by Δ lim Δ AΔ 1 volumetric moisture content [m 3 /m 3 ] internal sink/source term [m 3 /m 3 d] vertical flux [m 3 /m 2 /d]=[m/d] A PDE! Requires constitutive law, Δ 41 Mass Balance Note that all of these expressions result in ODEs or PDEs for water storage in the landscape Compartment ODEs Continuum PDEs The same will be true for application of energy balance laws: It is also true that, generally speaking, the fluxes are themselves often functions of storage in the system e.g.,, These are often referred to as constitutive relations, and are typically phenomenological rather than derived from physics Many of these relationships are actually unknown The sum of all of these constitutes a numerical model More compartments, more complex 42 21

22 Example: Soil Fluxes empirically approximated,, Fluxes explicitly generated (with approximate char. Curves) 43 Common Approach Land surface schemes and semi distributed engineering hydrology models typically have a separate mass/energy balance problem posed for each HRU The runoff/baseflow released from each HRU is sent to a surface water network to be routed downstream by solving a 1 D mass/momentum balance in the stream 44 22

23 45 Mathematical Formalization Both modularity and numerical robustness benefit from a function matrix representation in each HRU Generic representation of change in state variable j due to k processes that move mass/energy to state variable(s) i Enables: Flexibility in global numerical method Truly Independent development of individual process algorithms (Flexibility in local numerical method) Built in checks and balances for threshold and mass balance considerations 46 23

24 Mathematical Formalization For mass balance 47 Initial and Boundary Conditions Because our models are ODEs and PDEs which are 1 st order in time, they require initial conditions All storage compartments require an initial storage at the start of the model Since these are usually wrong, we typically need some kind of spinup period at the start of our model to avoid artefacts of poor initial conditions The PDE components of the models require boundary conditions Flux, saturation, or pressure conditions at the end boundaries of the continuum Typically, we force fluxes (e.g., no flow at bedrock) or have freedrainage conditions Specific to problem formulation Model + Initial/Boundary Conditions + Parameters = Unique output 48 24

25 Integrated Approach: The Freeze Harlan Blueprint (1969) Instead of the compartmental model feeding into a stream network model, model the world as one big continuum Richards equation in the subsurface Navier Stokes for overland flow Diffusive vapor exchange in lower atmosphere Energy balance in snowpack This is our best conceptualization of the world at a point with fully known system properties 49 Integrated Models Richards equation in subsurface Diffusive wave approximation of overland flow Canopy, Snow EB/WB (usually 1D):

26 HYDROGEOSPHERE MODEL SLIDE 51 Integrated Models Some problems with the purely physically based paradigm: when parameters are poorly known and the continuum is too coarsely gridded, the physics become fiction Richards equation is effectively empirical at larger spatial scales (e.g., Beven and Germann, 2013) Doing it right is often computationally infeasible This approach assumes you already understand the system and the model will just give you your answer. By having so many complicated interactions, it is harder to actually understand what is happening. It looks deceptively like reality. Should be saved for data intensive sites where there is lots of time and manpower to throw at the model 52 26

27 Practical considerations The concept of a water budget/energy budget is relatively easy to understand The practical application of these water budget equations is not straightforward Unknown characteristics of subsurface Heterogeneity Uncertain forcings/climate/human intervention Unclear the best means of representing these at a reasonable scale We fundamentally can only measure a small percentage of the water balance Closure (using measurement) at the watershed scale is impossible! Approximation is pretty much mandatory. 53 Some Course Philosophies Getting a model prediction correct and correct for the right reasons are fundamentally different we will be teaching how to do both, lean towards the latter, and discriminate between the two. Getting things right for the right reasons is not easy. We will stressing the pitfalls and issues people will run into as they try to follow the basic steps. While students will be learning a bit of Raven, CRHM, R, Ostrich, and Whitebox, the stress is on the methods and thought processes over the specific tools. While less so than models, data is often wrong and we have to understand how it might be wrong and when it is most likely to be wrong as we build our model to respect it. Every watershed and every model is a different beast, so we will be talking about what is shared between all models rather than getting into the details of one 54 27

28 Take home points The process of hydrologic modelling is general The means are extremely variable Mass / Energy / Momentum balances rule Constitutive equations poorly known and hard to parameterize We will spend the rest of the course Scrutinizing input data choices Evaluating model structure choices Critically evaluating model output Finding means by which to address (or at least acknowledge) the many sources of uncertainty in a modeled system Learning a few useful tools along the way! 55 28