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 trialand-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, Ksat
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 trialand-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.