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Hydrologic Modeling
ADEQ SW Short CourseJune 13, 2013Phoenix, AZ
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“Facts are stubborn things, but statistics are pliable.” Mark Twain
ADEQ SW Short Course The University of Arizona
Outline
• Model basics• Conceptual models (WoW)• Modeling continuum• Examples of models• Model shortcomings• On‐line modeling tools• Parameter estimation (Gupta)
ADEQ SW Short Course The University of Arizona 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.
ADEQ SW Short Course The University of Arizona 3HWR 642 © Hoshin Gupta
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What is a Model ?
A Model is a simplified representation of a system.
Its purposes are:a) to enable reasoning within an idealized framework,
andb) 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 simulationsof the real system.
Purpose of Model
• Critical part of science – to test our understanding of complex behavior
• Forward – Goal: basic parameters known– Estimation– Prediction / Planning
• Inverse/Inversion – Goal: learn from model– Data interpretation
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Systems Models
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Input Output
Process,State orReservoir
Flows or Flux
Feedback Model
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Input Output
Processor
Reservoir
+/‐
Flows or Flux
Inversion Model
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parametersModel
∆
Observation
CompareRMSE?
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homog.
(xeff,θeff)
input
input
output
output
identical identical?
heterog.
measurement
After Grayson and Blöschl, 2000, Cambridge Univ. Press
real world
model
Effective Parameters and Statestime invariant vs. time varying
ADEQ SW Short Course The University of Arizona
Continuum of Model Approachesexamples 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
10ADEQ SW Short Course The University of Arizona
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s11
Conceptual Models
What are they? Qualitative Might be based on graphs Represent important system:
componentsprocesses linkages interactions
www.waterontheweb.org/curricula/ws/unit_05/index.html
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s12
Conceptual Models
When should they be used? As an initial step –
For hypothesis testingFor 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-s13
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-s14
Conceptual Model Example - Ecologic
Macrophytes
Zooplankton refugesNutrient release due to anoxia
+
-
+
+
+
-
-
-Fish cover
Mean zooplankton size
Grazing impact
+Sedimentation rate
Hypolimnetic oxygen depletion
+
Algal biomass
+
+
+
Increased nutrient loading
Primary productivity
Increased pH
% blue-green algae
+
++Transparency
+
+
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s15
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?
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s16
Categories of Mathematical Models
TypeEmpirical
Based on data analysis
Mechanistic
Based on theoryTime Factor
Static or steady-state
Time-independent
Dynamic
Changes with time
Treatment of Data Uncertainty and VariabilityDeterministic
Single output
Stochastic
Address variability/uncertainty
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s17
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-s18
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
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s19
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-s20
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?
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Climate Predictions
P
E
Qs
Ss
Sg
Q
gIg
Antecedent Conditions
Hydrologic/Routing Models
Water Resources Applications
Snow Measurements
End‐to‐End Modeling of Land‐Surface Hydrology
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Evolution of Hydrologic Models
Hydrologic Models
API
QB
QR
t
q
RIA
Fi
tF Index
partitioningOverland routing
Sum upflow
components
INTERFLOWSURFACERUNOFF
INFILTRATIONTENSION
TENSION TENSION
PERCOLATION
LOWERZONE
UPPERZONE
PRIMARYFREE
SUPPLE-MENTAL
FREE
RESERVED RESERVED
FREE
EVAPOTRANSPIRATION
BASEFLOW
SUBSURFACEOUTFLOW
DIRECTRUNOFF
Precipitation
Sacramento Model
Mike SHE Model
Atm
osph
ere
Land
Mesoscale coupled land-atmosphere models
VIC Model
ADEQ SW Short Course The University of Arizona
Physical Processes
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Interception
Flows• ArrowsReservoirs• Boxes
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SURFACE
UPPERZONE
LOWERZONE
PerviousArea
ImperviousArea
SubsurfaceDischarge
Interflow
SurfaceRunoff
DirectRunoff
ChannelFlow
PrecipitationET DEMAND ET DEMAND
Streamflow
PCTIM
ADIMP
Tension WaterUZTWM
UZFWMFree Water
PrimaryLZFP
SupplementalLZFS
Free WaterTensionWaterLZTW
PercolationZPERC, REXP
1-PFREE PFREE
RSERV
PrimaryBaseflow Baseflow
Supplement.Baseflow
LZSK
LZPK
RIVA
UZK
( SIDE )
DistributionFunction
excess
ET ET
Sacramento Soil Moisture Accounting (SMA) Model
Flows• ArrowsProcesses• Boxes
ADEQ SW Short Course The University of Arizona
Distributed vs. Lumped
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Wood
Open
BareWater
cover
SCS Curve Number Model
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www.professorpatel.com/curve‐number‐introduction.html
ADEQ SW Short Course The University of Arizona
Decision Support Models
Whataffectsdemand
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DSS Submodels
clotheswasher use
reg gallons per use
front loader gal peruse
Households
% households wfrontloader
use per day
current year
last year
new houses topurchase
frontloaders
Clothes washerShower Use
Shower Pre 89
Households 1989
Shower Low Flow
Shower per Day
Shower Time
persons-house
Potential ShowerSavings
Households
Shower
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Scenarios ‐ Context
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Scenario Development for Water Resources, Mohammed Mahmoud, 2008also, Environmental Modeling & Software 24 (2009) 798–808
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Scenarios ‐ Development Process
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Scenario ‐ Themes
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Scenario Development for Water Resources, Mohammed Mahmoud, 2008also, Environmental Modelling & Software 24 (2009) 798–808
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Scenario Dimensions
Stakeholder ScenariosADEQ SW Short Course The University of Arizona
EXAMPLES OF MODELS
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www.hydro.washington.edu/Lettenmaier/Models/VIC/Liang, et al., J. Geophys. Res., 99(D7), 14,415‐14,428., 1994
ADEQ SW Short Course The University of Arizona
HEC‐HMS
Components• Watershed Physical
Description• Meteorology
Description• Hydrologic Simulation• Parameter Estimation• Analyzing Simulations• GIS Connection
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HMS, Yu, www.essc.psu.edu/hms/hms/
ADEQ SW Short Course The University of Arizona
Estimating Floods
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Requires data like:• Topo• Soils• Slope• Storm• Rural/urban• Land cover• Impoundments
Based on:• Regional regression eqs.
• RQ = aXbYcZd• Dimensionless hydrograph• Flood frequency graphs
ADEQ SW Short Course The University of Arizona 38ADEQ SW Short Course The University of Arizona
Model Shortcomings
The modeler’s dilemma:Know everything or Make lots of approximations
• Too simplistic• Numerical errors• Improper application• Poor calibraion• Edge effects• Non‐unique solutions
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DiscretizationChallenge: How to represent something digitally
40ADEQ SW Short Course The University of Arizona
Calibration & ValidationChallenge: assessing model reliability
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Journal of Hydrology, 341(3–4) 1 Aug 2007, p.196–206
Model Mesh or GridsChallenge: Min. nodes, Max. resolution
42www.swstechnology.com/blog/generating‐robust‐polygonal‐grids‐for‐modflow‐usg‐using‐visual‐modflow‐flexADEQ SW Short Course The University of Arizona
Nested ModelsChallenge: avoid edge effects
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Parameter EstimationChallenge: avoiding non‐unique solutions
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Automatic Calibration of Conceptual Rainfall-Runoff Models: The Question of Parameter Observability and UniquenessSorooshian, S. and V.K. Gupta, Water Resources Research, Vol. 19, No.1, pp. 260-268, 1983
Uniqueness and Observability of Conceptual Rainfall-Runoff Model Parameters: The Percolation Process ExaminedGupta, V.K. and S. Sorooshian, Water Resources Research, Vol. 19, No.1, pp. 269-276, 1983
Para
met
er Z
PERC
Parameter REXP
MSE Function Contours
ON‐LINE STUDY MATERIALS
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water.epa.gov/learn/training/wacademy/index.cfm
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https://www.meted.ucar.edu/index.php
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wikiwatershed.org/model.php
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star.mit.edu/hydro/
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The Problem of Parameter Estimation:
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
ADEQ SW Short Course The University of Arizona
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Considersparameterinteractions
Ignoresparameterinteractions
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
Stages in Parameter Estimation
Boyle, Gupta & Sorooshian, 2000ADEQ SW Short Course The University of Arizona 52
Level Zero Parameter Estimation
Boyle, Gupta & Sorooshian, 2000
Define initial parameter uncertainty by specifying feasible ranges for each parameter, using estimates from similar watersheds, look-up tables, maps & databases.
Sandy
Clayey
Blue River
SOIL TEXTUREPEDOTRANSFER
FUNCTIONSPEDOTRANSFER
FUNCTIONSKOREN
EQUATIONS
Koren et al (2000)Yilmaz et al (2006)
LEVEL “0”INFO
SOIL HYDRAULIC PARAMETERS
MODEL PARAMS
% SAND θsat θfld UZTWM%CLAY Ψsat θwlt UZFWM
CN Ψfld µ UZKDs Ψwlt ZPERC
b REXPKs PFREE
LZTWMLZFPMLZFSMLZPKLZSK
ADEQ SW Short Course The University of Arizona
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Level One Parameter Estimation
Boyle, Gupta & Sorooshian, 2000
Reduce the size of the initial uncertainty by adjusting one-parameter-at-a-time to try and match particular segments of the input-output response. Parameter interaction is generally ignored.
ADEQ SW Short Course The University of Arizona 54
Level Two Parameter Estimation
Boyle, Gupta & Sorooshian, 2000
Parameters are further adjusted while examining the entire hydrograph, taking into account parameter interactions
(a) strategy to measure closeness between model simulations and observed watershed input-output response
(b) Strategy to reduce the size of the feasible parameter space
real world
model()
measuredinput
priorinfo
measuredoutput
calculatedoutput
y
t
optimization
ADEQ SW Short Course The University of Arizona
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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).
Boyle, Gupta & Sorooshian, 2000ADEQ SW Short Course The University of Arizona 56
Parameter Estimation as Optimization Problem
Boyle, Gupta & Sorooshian, 2000
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
Optimal value
Measure of closeness(objective function)
(error function)
ADEQ SW Short Course The University of Arizona
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Working Hypothesis:Poor model performance caused by inability to find
the optimal parameters.
Causes of Difficulty in Finding Optimal Parameter Set
Elements of the Calibration Puzzle
MODEL
DATA
PARAMETERESTIMATION
USERMeasure ofCloseness
OptimizationMethod
Amount
QualityStructure
Parameterization
1. Wrong Measure of Closeness
2. Model Structural Parameterization
3. Poorly Informative Data
4. Weak Optimization Method
Possible Causes
ADEQ SW Short Course The University of Arizona 58
FROM ‐‐ Parameter Estimation as Optimization Problem
Boyle, Gupta & Sorooshian, 2000
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
Optimal value
Measure of closeness(objective function)
(error function)
ADEQ SW Short Course The University of Arizona
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TO ‐‐ Parameter Estimation as Progressive Uncertainty ReductionModern 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.
Uncertainty in the model structure & parameters is progressively reduced,
In a way that the model is constrainedto be structurally and functionally (behaviorally) consistent …
… with available qualitative (descriptive) & quantitative (numerical) informationabout the watershed
Feasible parameter space
ReducedParameter
Uncertainty
InitialParameter
Uncertainty
ADEQ SW Short Course The University of Arizona 60
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.
Feasible parameter space
ReducedParameter
Uncertainty
InitialParameter
Uncertainty
Reduced Prediction Uncertainty
ADEQ SW Short Course The University of Arizona
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.
ADEQ SW Short Course The University of Arizona 61