Outline. Hydrologic Modeling. Bottom line: one page summary. Purpose of Model. Systems Models

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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 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

2 Feedback Model Inversion Model / Input Process or Reservoir Output parameters Model Compare RMSE? Flows or Flux Observation 7 8 Effective Parameters and States time invariant vs. time varying identical input input real world heterog. homog. (x eff,θ eff ) output measurement output identical? Conceptual Models What are they? Qualitative Might be based on graphs Represent important system: components processes linkages interactions model After Grayson and Blöschl, 2000, Cambridge Univ. Press 9 Developed by: Hagley Updated: May 30, 2004 U5-m21a-s10 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 Conceptual Models 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 Developed by: Hagley Updated: May 30, 2004 U5-m21a-s11 Developed by: Hagley Updated: May 30, 2004 U5-m21a-s12

3 Conceptual Model Example - Ecologic Mathematical Models 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 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? Developed by: Hagley Updated: May 30, 2004 U5-m21a-s13 Developed by: Hagley Updated: May 30, 2004 U5-m21a-s14 Categories of Mathematical Models Type Empirical Mechanistic Based on data analysis Based on theory Time Factor Static or steady-state Dynamic Time-independent Changes with time Treatment of Data Uncertainty and Variability Deterministic Stochastic Single output Address variability/uncertainty Mathematical Models 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 Developed by: Hagley Updated: May 30, 2004 U5-m21a-s15 Developed by: Hagley Updated: May 30, 2004 U5-m21a-s16 Remember! 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 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 Developed by: Hagley Updated: May 30, 2004 U5-m21a-s17 Developed by: Hagley Updated: May 30, 2004 U5-m21a-s18

4 UPPER ZONE LOWER ZONE PERCOLATION TENSION PRIMARY FREE RESERVED EVAPOTRANSPIRATION TENSION FREE TENSION SUPPLE- MENTAL FREE RESERVED INTERFLOW INFILTRATION BASEFLOW SUBSURFACE OUTFLOW SURFACE RUNOFF DIRECT RUNOFF Selecting or Developing a Model End to End Modeling of Land Surface Hydrology 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? Climate Predictions Snow Measurements I g P S s S g Antecedent Conditions Water Resources Applications E Q s Q g Hydrologic/Routing Models Developed by: Hagley Updated: May 30, 2004 U5-m21a-s19 20 Evolution of Hydrologic Models F Index partitioning Overland routing Sum up flow components q Atmosphere Land i API R IA t Q R Q t B F Precipitation Mesoscale coupled land-atmosphere models Sacramento Model Hydrologic Models Mike SHE Model VIC Model Continuum of Model Approaches examples follow Physical/Mathematical most quantitative Distributed: grid/gis based model Aggregated or classified Conceptual more qualitative Lumped parameter/process Empirical Decision Support Simulations (DSS) Scenario Models 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 UZFWM Free Water Percolation ZPERC, REXP 1-PFREE PFREE Tension Free Water Water Supplemental Primary LZTW LZFS LZFP RSERV excess UZK LZSK Surface Runoff Interflow Supplement. Baseflow RIVA Channel Flow Distribution Function Flows Arrows Processes Boxes Streamflow LZPK Primary Baseflow Baseflow ( SIDE ) Subsurface Discharge 23 24

5 Distributed vs. Lumped SCS Curve Number Model cover Water Bare Wood Open 25 number introduction.html 26 Decision Support Models DSS Submodels What affects demand % households w frontloader Shower Potential Shower Savings Shower per Day front loader gal per use last year Shower Pre 89 new houses to purchase frontloaders current year Households reg gallons per use clotheswasher use use per day Shower Time persons-house Shower Low Flow Clothes washer Households 1989 Households Shower Use Scenarios Context Scenarios Development Process Scenario Development for Water Resources, Mohammed Mahmoud, 2008 also, Environmental Modeling & Software 24 (2009)

6 Scenario Themes Scenario Dimensions Scenario Development for Water Resources, Mohammed Mahmoud, 2008 also, Environmental Modelling & Software 24 (2009) Stakeholder Scenarios 32 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

7 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 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

8 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 water.epa.gov/learn/training/wacademy/index.cfm ON LINE STUDY MATERIALS wikiwatershed.org/model.php 47 48

9 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 PEDOTRANSFER FUNCTIONS KOREN EQUATIONS LEVEL 0 SOIL HYDRAULIC MODEL INFO PARAMETERS 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) 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 53 54

10 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 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 Quality MODEL USER Measure of Parameterization Closeness PARAMETER ESTIMATION 2. Model Structural Parameterization 3. Poorly Informative Data 4. Weak Optimization Method Measure of closeness (objective function) (error function) Optimization Method Optimal value 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