Outline Hydrologic Modeling - Sahraweb.sahra.arizona.edu/.../docs/ADEQ8_SWmodeling_4.pdf · Hydrologic/Routing Models Water Resources Applications Snow Measurements End‐to‐End

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


Systems Models


Input Output

Process,State orReservoir

Flows or Flux

Feedback Model


Input Output

Processor

Reservoir

+/‐

Flows or Flux

Inversion Model


parametersModel

∆

Observation

CompareRMSE?

9

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


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


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


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


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

+

+


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

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


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


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


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


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


Physical Processes

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Interception

Flows• ArrowsReservoirs• Boxes


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


Distributed vs. Lumped


Wood

Open

BareWater

cover

SCS Curve Number Model


www.professorpatel.com/curve‐number‐introduction.html


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


Scenarios ‐ Context

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Scenario Development for Water Resources, Mohammed Mahmoud, 2008also, Environmental Modeling & Software 24 (2009) 798–808


Scenarios ‐ Development Process


Scenario ‐ Themes


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

ADEQ SW Short Course The University of Arizona 33 34

www.hydro.washington.edu/Lettenmaier/Models/VIC/Liang, et al., J. Geophys. Res., 99(D7), 14,415‐14,428., 1994


HEC‐HMS

Components• Watershed Physical

Description• Meteorology

Description• Hydrologic Simulation• Parameter Estimation• Analyzing Simulations• GIS Connection

ADEQ SW Short Course The University of Arizona 35 36

HMS, Yu, www.essc.psu.edu/hms/hms/


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


DiscretizationChallenge: How to represent something digitally

40ADEQ SW Short Course The University of Arizona

Calibration & ValidationChallenge: assessing model reliability


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


Parameter EstimationChallenge: avoiding non‐unique solutions


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

ADEQ SW Short Course The University of Arizona 45 ADEQ SW Short Course The University of Arizona 46

water.epa.gov/learn/training/wacademy/index.cfm


https://www.meted.ucar.edu/index.php


wikiwatershed.org/model.php


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


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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


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Level One Parameter Estimation


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.


Level Two Parameter Estimation


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


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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


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)


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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


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.


Optimal value

Measure of closeness(objective function)

(error function)


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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


ReducedParameter

Uncertainty

InitialParameter

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.


ReducedParameter

Uncertainty

InitialParameter

Uncertainty

Reduced Prediction Uncertainty


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.


Documents

Outline Hydrologic Modeling - Sahraweb.sahra.arizona.edu/.../docs/ADEQ8_SWmodeling_4.pdf · Hydrologic/Routing Models Water Resources Applications Snow Measurements End‐to‐End