Outline. Hydrologic Modeling. Bottom line: one page summary
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1 Facts are stubborn things, but statistics are pliable. Mark Twain Hydrologic Modeling June 13, 2013 Phoenix, AZ Outline Model basics Conceptual models (WoW) Modeling continuum Examples of models Model shortcomings On line modeling tools Parameter estimation (Gupta) 1 2 Bottom line: one page summary A Model is a simplified representation of a system Models are made up of various components defined in terms of parameters and states/processes Most hydrologic models include many submodels Computational effort and Convergence are two important model characteristics Empirical models are questionable in new settings Physical models have sign. computational and data requirements. What is a Model? A Model is a simplified representation of a system. Its purposes are: a) to enable reasoning within an idealized framework, and b) to enable testable predictions of what might happen under new circumstances. The representation is based on explicit simplifying assumptions (known to be false, or perhaps poorly-known, in some detail) that allow acceptably accurate simulations of the real system. 4 3 HWR 642 Hoshin Gupta
2 Purpose of Model Systems Models Critical part of science to test our understanding of complex behavior Forward Goal: basic parameters known Estimation Prediction / Planning Input Process, State or Reservoir Output Inverse/Inversion Goal: learn from model Data interpretation Flows or Flux 5 6 Feedback Model Inversion Model / Input Process or Reservoir Output parameters Model Compare RMSE? Flows or Flux Observation 7 8
3 Effective Parameters and States time invariant vs. time varying identical input input real world heterog. homog. (x eff,θ eff ) output measurement model output identical? Continuum of Model Approaches examples follow Conceptual more qualitative Lumped parameter/process Empirical Physical/Mathematical most quantitative Distributed: grid/gis based model Aggregated or classified Decision Support Simulations (DSS) Scenario Models After Grayson and Blöschl, 2000, Cambridge Univ. Press 9 10 Conceptual Models What are they? Qualitative Might be based on graphs Represent important system: components processes linkages interactions Conceptual Models When should they be used? As an initial step For hypothesis testing For mathematical model development As a framework For future monitoring, research, and management actions at a site Developed by: Hagley Updated: May 30, 2004 U5-m21a-s11 Developed by: Hagley Updated: May 30, 2004 U5-m21a-s12
4 Conceptual Models Conceptual Model Example - Ecologic How can they be used? Design field sampling and monitoring programs Guide selection of measurement Suggest likely causes of environmental problems Identify system linkages and possible cause and effect relationships Identify potential conflicts among management objectives Anticipate the range of possible system responses to management actions Including potential negative effects Algal biomass - Nutrient release due to anoxia Transparency Increased nutrient loading Primary productivity Increased ph % blue-green algae Grazing impact Sedimentation rate Hypolimnetic oxygen depletion - - Macrophytes Fish cover - Mean zooplankton size Zooplankton refuges Developed by: Hagley Updated: May 30, 2004 U5-m21a-s13 Developed by: Hagley Updated: May 30, 2004 U5-m21a-s14 Mathematical Models What are they? Mathematical equations that translate a conceptual understanding of a system or process into quantitative terms How are they used? Diagnosis E.g., What is the cause of reduced water clarity in a lake? Prediction E.g., How long will it take for lake water quality to improve, once controls are in place? Categories of Mathematical Models Type Empirical Based on data analysis Time Factor Static or steady-state Time-independent Mechanistic Based on theory Dynamic Changes with time Treatment of Data Uncertainty and Variability Deterministic Stochastic Single output Address variability/uncertainty Developed by: Hagley Updated: May 30, 2004 U5-m21a-s15 Developed by: Hagley Updated: May 30, 2004 U5-m21a-s16
5 Mathematical Models Remember! When should models not be used? If you do not understand the problem or system well enough to express it in concise, quantitative terms If the model has not been tested and verified for situations and conditions similar to your resource It is important to understand model: Structure (processes, variables, numerics) Assumptions Limitations Models do not substitute for: logical thinking problem expertise direct observation / data collection in-depth analysis Models should be no more complicated than is necessary for the task at hand Developed by: Hagley Updated: May 30, 2004 U5-m21a-s17 Developed by: Hagley Updated: May 30, 2004 U5-m21a-s18 Selecting or Developing a Model Important first steps Define the question or problem to be addressed with the model Determine appropriate spatial and temporal scales Identify important ecosystem components and processes that must be considered to answer the management questions Selecting or Developing a Model Some specific questions to ask Temporal scale Do I need to predict changes over time or are steady-state conditions adequate? If time is important, do I need to look at Short-term change (e.g., daily, seasonal) or Long-term change (e.g., trends over years)? Spatial scale Is my question best addressed: On a regional scale (e.g., compare streams in a region) or By modeling specific processes within an individual system? Developed by: Hagley Updated: May 30, 2004 U5-m21a-s19 Developed by: Hagley Updated: May 30, 2004 U5-m21a-s20
6 TENSION PRIMARY FREE RESERVED FREE TENSION SUPPLE- MENTAL FREE RESERVED End to End Modeling of Land Surface Hydrology Evolution of Hydrologic Models Precipitation Sacramento Model EVAPOTRANSPIRATION Climate Predictions Water Resources Applications API UPPER ZONE LOWER ZONE TENSION INFILTRATION SURFACE PERCOLATION INTERFLOW RUNOFF DIRECT RUNOFF Mike SHE Model F Index partitioning Overland routing i R IA t F BASEFLOW SUBSURFACE OUTFLOW P E Hydrologic/Routing Models Sum up flow components q Q R Q t B Hydrologic Models Snow Measurements S s S I g g Antecedent Conditions Q s Q g Mesoscale coupled land-atmosphere models Atmosphere VIC Model Land Physical Processes Sacramento Soil Moisture Accounting (SMA) Model ET DEMAND Precipitation ET DEMAND ET Pervious Are a Impervious Area PCTIM ADIM P Direct Runoff ET Interception Flows Arrows Reservoirs Boxes SURFACE UPPER ZONE LOWER ZONE Tension Water UZTWM 1-PFREE Tension Water LZTW Percolation ZPERC, REXP Supplemental LZFS UZFWM Free Water PFREE Free Water RSERV Primary LZFP excess UZK LZSK Surface Runoff Interflow Supplement. Baseflow Channel Flow RIVA Distribution Function Flows Arrows Processes Boxes Streamflow LZPK Primary Baseflow Baseflow ( SIDE ) Subsurface Discharge 23 24
7 Distributed vs. Lumped SCS Curve Number Model cover Water Bare Wood Open 25 number introduction.html 26 Decision Support Models DSS Submodels Shower What affects demand % households w frontloader front loader gal per use Potential Shower Savings Shower per Day last year Shower Pre 89 new houses to purchase frontloaders current year Households clotheswasher use use per day Shower Time persons-house Shower Low Flow reg gallons per use Clothes washer Households 1989 Households Shower Use 27 28
8 Scenarios Context Scenarios Development Process Scenario Development for Water Resources, Mohammed Mahmoud, 2008 also, Environmental Modeling & Software 24 (2009) Scenario Themes Scenario Dimensions Scenario Development for Water Resources, Mohammed Mahmoud, 2008 also, Environmental Modelling & Software 24 (2009) Stakeholder Scenarios 32
9 Liang, et al., J. Geophys. Res., 99(D7), 14,415 14,428., 1994 EXAMPLES OF MODELS HEC HMS HMS, Yu, Components Watershed Physical Description Meteorology Description Hydrologic Simulation Parameter Estimation Analyzing Simulations GIS Connection 35 36
10 Estimating Floods Requires data like: Topo Soils Slope Storm Rural/urban Land cover Impoundments Based on: Regional regression eqs. RQ = ax b Y c Z d Dimensionless hydrograph Flood frequency graphs Model Shortcomings The modeler s dilemma: Know everything or Make lots of approximations Discretization Challenge: How to represent something digitally Too simplistic Numerical errors Improper application Poor calibraion Edge effects Non unique solutions 39 40
11 Calibration & Validation Challenge: assessing model reliability Model Mesh or Grids Challenge: Min. nodes, Max. resolution 41 Journal of Hydrology, 341(3 4) 1 Aug 2007, p robust polygonal grids for modflow usg using visual modflow flex Nested Models Challenge: avoid edge effects Parameter Estimation Challenge: avoiding non unique solutions MSE Function Contours Parameter ZPERC Parameter REXP 43 Automatic Calibration of Conceptual Rainfall-Runoff Models: The Question of Parameter Observability and Uniqueness Sorooshian, S. and V.K. Gupta, Water Resources Research, Vol. 19, No.1, pp , 1983 ADEQ SW Uniqueness Short Course and Observability of Conceptual The Rainfall-Runoff University Arizona Model Parameters: The Percolation Process Examined 44 Gupta, V.K. and S. Sorooshian, Water Resources Research, Vol. 19, No.1, pp , 1983
12 water.epa.gov/learn/training/wacademy/index.cfm ON LINE STUDY MATERIALS wikiwatershed.org/model.php 47 48
13 The Problem of Parameter Estimation: star.mit.edu/hydro/ All RR models are (to some degree) lumped, so that the equations and parameters are effective conceptual representations of hydrologic processes aggregated in space & time. The effective nature of model parameters means they are usually not directly measurable (at the model scale) and must therefore be specified by some indirect process, such as: Theoretical considerations Lookup tables (previous studies) Calibration of model to input-output data Stages in Parameter Estimation LEVEL ZERO (Qualitative Analysis) Specify feasible ranges and nominal values based on Theoretical considerations, Regional estimates, Lookup tables, Maps & Databases, etc. LEVEL ONE (Behavioral Analysis) Estimate Parameter (ranges) by isolating & examining particular segments of the input-state-output response LEVEL TWO (Regression) Estimate Parameter (ranges) by matching model output response to observed data for some calibration period of interest Ignores parameter interactions Considers parameter interactions Level Zero Parameter Estimation Define initial parameter uncertainty by specifying feasible ranges for each parameter, using estimates from similar watersheds, look-up tables, maps & databases. SOIL TEXTURE Clayey Blue River Sandy PEDOTRANSFER FUNCTIONS LEVEL 0 INFO PEDOTRANSFER FUNCTIONS SOIL HYDRAULIC PARAMETERS KOREN EQUATIONS MODEL PARAMS % SAND θsat θfld UZTWM %CLAY Ψsat θwlt UZFWM CN Ψfld µ UZK Ds Ψwlt ZPERC b REXP Ks PFREE LZTWM LZFPM LZFSM LZPK LZSK Koren et al (2000) Yilmaz et al (2006) Boyle, Gupta & Sorooshian, 2000 Boyle, Gupta & Sorooshian, 2000
14 Level One Parameter Estimation Reduce the size of the initial uncertainty by adjusting oneparameter-at-a-time to try and match particular segments of the input-output response. Parameter interaction is generally ignored. Level Two Parameter Estimation Parameters are further adjusted while examining the entire hydrograph, taking into account parameter interactions (a) (b) strategy to measure closeness between model simulations and observed watershed input-output response Strategy to reduce the size of the feasible parameter space measured input real world measured output y model( ) calculated output t prior info optimization Boyle, Gupta & Sorooshian, 2000 Boyle, Gupta & Sorooshian, 2000 Problems with Level Two Parameter Estimation 1. Dimensionality - Usually large number of parameters that can be adjusted (e.g. SAC-SMA has 15). 2. Interdependence - Parameters have similar or compensating (interacting) effects on different portions of the output. 3. Ambiguity - Exists no unique or un-ambiguous way to evaluate the closeness of the simulated and observed output time-series. 4. Uncertainty - Exists errors & uncertainties in input-output data, model initialization, and model conceptualization (structure). Parameter Estimation as Optimization Problem Classical parameter estimation methods are rooted in a philosophy of searching for the best parameter values (best = gives the closest match to the data). The underlying premise is that there is are correct values for the parameters -- the problem was only how to find them -- the solution was an optimization approach based in regression theory -- fitting the model to the data. Feasible parameter space Measure of closeness (objective function) (error function) Optimal value Boyle, Gupta & Sorooshian, 2000 Boyle, Gupta & Sorooshian, 2000
15 Causes of Difficulty in Finding Optimal Parameter Set Working Hypothesis: Poor model performance caused by inability to find the optimal parameters. Elements of the Calibration Puzzle Amount Possible Causes FROM Parameter Estimation as Optimization Problem Classical parameter estimation methods are rooted in a philosophy of searching for the best parameter values (best = gives the closest match to the data). The underlying premise is that there is are correct values for the parameters -- the problem was only how to find them -- the solution was an optimization approach based in regression theory -- fitting the model to the data. DATA 1. Wrong Measure of Closeness Feasible parameter space Structure MODEL Parameterization USER Quality PARAMETER ESTIMATION Measure of Closeness 2. Model Structural Parameterization 3. Poorly Informative Data 4. Weak Optimization Method Measure of closeness (objective function) (error function) Optimization Method Optimal value Boyle, Gupta & Sorooshian, 2000 TO Parameter Estimation as Progressive Uncertainty Reduction Modern parameter estimation methods are based in a philosophy of progressive parameter uncertainty reduction. The understanding is that: Model identification consists of an infinite series of steps in which the initial (large) uncertainty is progressively reduced by bringing more understanding and information to bear on the problem. The final estimated model will always have some remaining uncertainty. Parameter Est. as a Process of Progressive Uncertainty Reduction Impossible to reduce model uncertainty (structure & parameters) to zero, even if we have perfect (noise free) input-output data. The best we can achieve is some minimal (representative) set of models that closely and consistently approximates (in an uncertain way) the observed behavior of the system. Uncertainty in the model structure & parameters is progressively reduced, In a way that the model is constrained to be structurally and functionally (behaviorally) consistent Feasible parameter space Initial Parameter Uncertainty Feasible parameter space Initial Parameter Uncertainty Reduced Prediction Uncertainty with available qualitative (descriptive) & quantitative (numerical) information about the watershed Reduced Parameter Uncertainty Reduced Parameter Uncertainty 59 60
16 Bottom line: one page summary A Model is a simplified representation of a system Models are made up of various components defined in terms of parameters and states/processes Most hydrologic models include many submodels Computational effort and Convergence are two important model characteristics Empirical models are questionable in new settings Physical models have sign. computational and data requirements. 61
Outline. Hydrologic Modeling. Bottom line: one page summary. Purpose of Model. Systems Models
Facts are stubborn things, but statistics are pliable. Mark Twain Hydrologic Modeling June 13, 2013 Phoenix, AZ Outline Model basics Conceptual models (WoW) Modeling continuum Examples of models Model
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