DES 606 : Watershed Modeling with HEC-HMS Module 13 Theodore G. Cleveland, Ph.D., P.E 30 Sep 11

Parameter Estimation Parameter estimation in HEC-HMS refers to the specification of various values in different hydrologic elements. Methods of practical value are trial- and-error (using external initial estimates) and optimization-type techniques.

Parameter Estimation This module focuses on automated methods (Chapter 13) in HEC-HMS Estimating certain parameters does not make sense –Area, Length: Usually quite measurable Other parameters will need some estimation –Time of concentration, K sat

Calibration Model calibration is an estimation process –Observed responses are compared to model output. Parameters are adjusted to make the model output agree with the observed responses. Requires that observations exist! Calibration/Estimation is a “process”

Estimation Process Consider a HEC-HMS model. –It could have dozens of sub-basins, multiple routing elements, etc. –Each of these elements has multiple descriptive and process parameters. –These need to be estimated. Initial Estimates –Whether using the automated tools or trial- and-error initial values are needed.

Initial Estimates Make the initial estimates using various hydrology and hydraulic tools already presented. Rules-of-thumb are appropriate for making initial estimates. Then the calibration process refines these estimates.

Merit Function HEC-HMS calls this the objective function. It measures “distance” between the observed and simulated response. –Sum of Squared Errors (a common error function) –Sum of Absolute Errors (also common) –HEC-HMS has several other merit functions. For trial-and-error adjustments, a graph of simulated and observed results is probably adequate.

Illustrative Example To get an idea of the concepts involved, a single sub-basin with a reservoir is examined. –This is the EX4 case. To create the example HEC-HMS was opened and a new project was created. Then the simulation from EX4 was imported into the new project, and the data localized. Then the new project is saved – this project will be the one we use for automated parameter adjustments.

Automated Parameter Estimation Here is the initial situation. We will intentionally change the lag time to produce a poor “fit” then explore using the automated parameter estimation tool to recover the estimate.

Initial Estimates Suppose the figure to the right represents our “best” estimates by conventional means. –Table look-up, equations to estimate Tc, etc. We have observations as indicated by the black-dots.

Building an Optimization Trial Automatic parameter adjustment is called an optimization trial. We will create a trial, then specify how it is to function.

Create Optimization Trial Select “create optimization trial” Prompted to name the trial Use the default this example (Trial 1)

Which Base Simulation? Select a simulation (that contains observations) In this example only get one choice, but if one had several open projects would need to choose.

Select Observation Location Next select where the observations are available. In this example we have two choices, but the observation set is at the inlet to the reservoir, in our case the outlet of the sub-basin.

Optimization Trials Icon Notice the icon “change” that indicates we are starting optimization trials.

Compute “Trials” Next we switch to the “compute” tab in the upper left pane of the GUI. Select optimization and Trial 1

Optimization Specifications Optimization Trial specifications: –Description –RunID –Minimization Method Gradient Simplex (Nelder-Mead) –Tolerance and iteration count.

Add Parameters Next we “right-click” the Trial 1 to select parameters to add to the automated adjustments.

Set Parameter Initial Values Parameter 1 selected –Choose element to adjust (in this case Sub-Basin1) –Choose what to adjust (in this case Lag) –Can specify initial values (default is values in originating simulation)

Run the Optimization Trial Run the Trial in the same way as a regular simulation. –Trials are run independently, the original simulation is unchanged

Examine the Results Results tab, then select various summaries.

Flow Comparison Result Especially useful result is the flow comparison chart. –Perfect 1:1 agreement (like shown) is indicative of fabricated observations (which is indeed true in the example).

Automated Adjustment – Multiple Parameters The real help with automated adjustments comes when there are multiple parameters to adjust. To continue with the example, suppose both the timing value and Ksat are initially poor.

Multiple Parameters Now we will instruct the optimization trial to consider two parameters at the same time. Need to add a second parameter, and select its initial value. –Certainly improved from the original model

Accepting the Results The automated adjustments are kept separate from the base model until the analyst actually changes the base model inputs. HEC-HMS does not automatically change the base model – protects against unanticipated values creeping into the base simulation. Suggest that once values are accepted as the “calibrated” model – a duplicate model be created called “Calibrated Model of …” and the original base model be kept in a separate project as documentation of the process.

Summary Discussed automated parameter adjustments to calibrate a model. Demonstrated with a simple case. Suggested that once adjusted parameters are “accepted” a separate model be built to preserve the initial thinking and to document that an optimization process occurred.