Surface-water quality and flow Modeling Interest Group
Bias in Runoff Parameter Estimation Induced by Rainfall Data
by Timothy D. Straub1
and Ronald J. Bednar2
1 Hydrologist
2 Student Trainee
USGS, Water Resources Division
221 North Broadway Avenue
Urbana, IL 61801
Internet:
tdstraub@usgs.gov
Phone: (217) 344-0037 x3024
FAX: (217) 344-0082
Editor's note:
This paper has been submitted to JAWRA,
the Journal of the American Water Resources
Association.
This version of the article has all of the figures converted to thumbnails
with links to the larger images. A version with all of the figures
inline is also available; the download
time may be longer, but the inline figures may be more convenient for viewing
and printing.
Table of Contents
Studies in Du Page County, Illinois found that a rainfall-runoff parameter
set calibrated on the basis of the National Oceanic and Atmospheric
Administration (NOAA) precipitation-gage network (non-recording and weighing
bucket gages) could not be applied with data collected from a U.S. Geological
Survey (USGS) tipping-bucket rain-gage network. The average yearly, average
monthly, and average storm-event periods simulated based on USGS rainfall
data in the hydrologic simulation model calibrated with NOAA rainfall data
was consistently low compared to simulation results based on the NOAA data
and recorded flows. Multiplying the hourly USGS rainfall data by a factor
within the hydrologic simulation model aligned USGS simulated results with
simulated results using the NOAA data for all periods. Other than applying
a constant correction factor, there is no evidence that seasonal or wind
induced corrections are needed for the USGS rainfall data used in model
simulation to better match the simulated results based on NOAA data.
Hydrologic models often are calibrated using rainfall and streamflow data
to facilitate simulation of the amount of runoff that will result from
a watershed. A consistent record of rainfall data is vital to the accuracy
of model simulation. Troutman (1983) has shown that the calibration process
transfers errors and uncertainties in the data to the model parameters in
the form of bias in the parameter values (i.e. deviation from true values).
However, because of the curve-fitting properties of the calibration process,
estimation performance of the model based on erroneous data and biased
parameters is not greatly different from that using true data and parameter
values in the range of the data. Therefore, accurate simulations can be
obtained as long as the errors and uncertainties in the input data are
similar to (consistent with) the errors and uncertainties in the data used
to calibrate the model. This technical note provides a clear illustration
of the magnitude of the simulation problems that can result when a model
calibrated to one data set is applied using a different data set. Also,
results indicate that it may be possible to develop a simple correction
factor for the non-calibration data set to yield accurate simulation
results. Previous studies in Du Page County found that a rainfall-runoff
parameter set calibrated on the basis of the NOAA precipitation-gage network
(weighing bucket and non-recording gages) could not be applied with data
collected from the USGS tipping-bucket rain-gage network (Tom Price,
Northeastern Illinois Planning Commission (NIPC), written commun., 1997).
A statistically significant difference was found between rainfall totals
collected from USGS and NOAA precipitation-gage networks in and near Du
Page County, Illinois (Straub and Parmar, 1998).
Ten tipping-bucket rain gages from the USGS rain-gage network were used in
this study. Hourly rainfall totals from April 1990 to October 1993 were
used as model input for the analysis of simulated runoff. The reciprocal
distance squared method was used to estimate periods of missing record
(U.S. Department of Commerce, 1972). Thiessen polygons were drawn to
determine the area of influence of each of the 10 rain gages. Unheated
tipping-bucket rain gages do not accurately record snowfall. For this
reason, data from each USGS tipping-bucket rain gage were replaced with
data from the nearest NOAA precipitation gage (U.S. Department of Commerce,
1990-1993) during periods of snowfall. Snowfall was determined using NOAA
precipitation data published by the National Climatic Data Center (NCDC)
(U.S. Department of Commerce, 1990-1993).
NOAA meteorological data were obtained from the NCDC and compiled for model
input by NIPC. A summary of the meteorological data used in the model is
presented by Price (1994b).
Streamflow data from seven stream gages were used to compare simulated
rainfall-runoff results with the measured streamflow. Hourly streamflow data
from April 1990 to October 1993 were used in the analysis. Land-cover data
for the seven simulated watersheds were obtained from the Du Page County
Department of Environmental Concerns.
The Hydrological Simulation Program - Fortran (HSPF) continuous hydrologic
simulation model (Bicknell and others, 1993) was calibrated to data
collected at four streamflow gages in Du Page County (Price, 1994a).
The calibrated model was then verified with data from 10 streamflow gages
in Du Page County (Price, 1994b). The results of the verification and
calibration have been updated, but not formally published at the time
of this study. Rainfall data from five NOAA precipitation gages (four
non-recording and one weighing-bucket gage) and one weighing-bucket gage at
Argonne National Laboratory were used as input data in the model for both
the model calibration and verification. The updated verification results
were obtained from Tom Price, NIPC, for comparison with simulation results
based on USGS rainfall data.
The calibrated HSPF model for DuPage County, updated by NIPC, was used
as the hydrologic simulation model. The rainfall data input was the only
difference between the USGS simulation and the NIPC simulation. The USGS
simulation was based on data collected from the 10 USGS tipping-bucket
rain gages in and near Du Page County. Both the type of rain gages and
the rain-gage network densities (10 USGS gages and 6 NOAA gages) differed.
The simulated time period was from April 1, 1990, to September 30, 1993.
Antecedent conditions for April 1, 1990, were computed using NOAA rainfall
data from October 1, 1988, to March 31, 1990, as input to the model.
Simulation results from April 1, 1990, to September 30, 1990, were not
used in the analysis so that the effect of the initial conditions using
the NOAA rainfall data would be minimized.
The magnitude of the difference between simulated and recorded flow was
compared simply by calculating the simulated to recorded ratio (S/R)
((calculated as averageSi/averageRi) for all stream gages "i") for per
unit-area values ((m3/s)-day/km2) of annual, monthly,
and event runoff.
The S/R value for average annual flow from October 1, 1990, to September
30, 1993 using USGS rainfall data in the hydrologic simulation model
calibrated with NOAA rainfall data was 0.84 (table 1). Multiplying the
hourly USGS rainfall data by 1.14 within the hydrologic simulation model
improved the S/R for average annual flow to 1.00 (table 1). A factor
of 1.14 was chosen based on the results of Straub and Parmar (1998).
The adjusted USGS rainfall data produce simulated results comparable to
the simulated results using NOAA rainfall data, which yield an S/R value
of 0.97 for average annual flow (table 1).
Table 1. Average annual flow comparisons for seven watersheds in
Du Page County, Illinois.
The S/R values for average monthly flow for each month using USGS rainfall
data in the hydrologic simulation model calibrated with NOAA rainfall data
is shown in table 2. The S/R values for average monthly flow obtained by
multiplying the hourly USGS rainfall data by 1.14 within the hydrologic
simulation model also is shown in table 2. The adjusted USGS rainfall data
produce simulated results comparable to the simulated results using NOAA
rainfall data for S/R values for average monthly flow (table 2-columns 6
and 8).
Table 2. Average monthly flow comparisons (water years 1990-93)
for seven watersheds in Du Page County, Illinois. [The water year starts
October 1 and ends September 30 and is designated by the calendar year in
which it ends.]
Multiple-day storm events (41 events for the 7 watersheds (4 to 9 events
per watershed)), selected by NIPC, throughout water years 1990-93 were
extracted from the NIPC and USGS simulation results. The S/R results for
these events are shown in table 3. The S/R value for average event flow
using USGS rainfall data in the hydrologic simulation model calibrated
with NOAA rainfall data was 0.76 (table 3). Multiplying the hourly USGS
rainfall data by 1.14 within the hydrologic simulation model improves the
S/R for average event flow to 1.00 (table 3). The adjusted USGS rainfall
data produce simulated results comparable to the simulated results using
NOAA rainfall data, which yield an S/R value of 0.99 for average event flow
(table 3).
Table 3. Average event flow comparisons for seven watersheds in Du
Page County, Illinois.
Seasonal variations in simulated flow were analyzed to determine if
seasonal adjustment factors would be more appropriate in model simulation
than applying one factor for the entire year. No difference is apparent
between the NOAA S/R variation and the USGS S/R variation throughout the
year (figs. 1 and 2). The primary difference between the NOAA S/R and
USGS S/R variation is the consistently lower USGS S/R.
Figure 1. Monthly S/R for each stream gage using USGS rainfall data.
Figure 2. Monthly S/R for each stream gage using NOAA rainfall data.
Wind blowing on certain orifice types and at different heights can reduce
the amount of catch in a rain gage (Sevruk, 1996). Because the USGS rain
gages used in the study have a different orifice type and are, on average,
installed approximately 1.2 m higher than the NOAA precipitation gages, wind
effect was analyzed for the event simulations. The wind effect was used to
determine a correlation between wind and the difference between simulations
based on the USGS and NOAA rain-gage networks (fig. 3). Hourly wind data
from O'Hare International Airport in Chicago were averaged for each event
only during the time when it was raining. No apparent correlation was
found between the O'Hare wind data and the simulated differences between
the use of USGS and NOAA rainfall data for each storm event.
Figure 3. NOAA and USGS simulation differences compared with average
wind speed at O'Hare International Airport during the storm event and
percent difference between NOAA and USGS event simulation.
The S/R for average yearly, average monthly, and average event periods
simulated using USGS rainfall data in the hydrologic simulation model
calibrated with NOAA rainfall data is consistently below 1. The use of
different input data (USGS) resulted in underestimation of annual flow by
about 13 percent, of monthly flow between 6 and 21 percent, and in storm
runoff of about 23 percent relative to the use of the NOAA input data,
which are consistent with the calibration data set. In this case, the bias
in the simulation results could be removed by applying a simple correction
factor to the different input data (USGS). Multiplying the hourly USGS
rainfall data by 1.14 within the hydrologic simulation model improves the
S/R and aligns simulated results with simulated results obtained using NOAA
rainfall data for annual, monthly, and storm-event data. No difference is
apparent between the NOAA S/R variation throughout the year and the USGS S/R
variation. Therefore, there is no evidence that a season-dependent factor
is needed to better align USGS simulated results with the simulated results
based on NOAA data. No correlation is apparent between the O'Hare wind
data and the USGS and NOAA simulation differences for each storm event,
indicating that no wind-dependent correction factor is needed to better
match USGS simulated results with the simulated results based on NOAA data.
Bicknell, B.R., Johanson, R.C., Imhoff J.C., Kittle J.L., and Donigian
A.S. Jr., 1993, Hydrological simulation program - fortran (HSPF): users
manual for release 10. 1993. Athens, Ga., Environmental Protection Agency
Research Laboratory, 660 p.
Price, T.H., 1994a, Hydrologic calibration of HSPF model for Du Page
County: West Branch Dupage River at West Chicago, West Branch Dupage River
at Warrenville, East Branch Dupage River at Maple Avenue, Salt Creek at
Western Springs. Northeastern Illinois Planning Commission, NIPC. Chicago,
Illinois.
Price, T.H., 1994b, Meteorologic database extension and hydrologic
verification of HSPF model for Dupage County: West Branch Dupage River
at West Chicago, West Branch Dupage River at Warrenville, West Branch
Dupage River at Naperville, East Branch Dupage River at Downers Grove, East
Branch Dupage River at Bolingbrook, Salt Creek at Elmhurst, Salt Creek at
Western Springs, Sawmill Creek near Lemont, St. Joseph Creek at Route 34,
Kress Creek at West Chicago. Northeastern Illinois Planning Commission,
NIPC. Chicago, Illinois.
Sevruk, B., 1996, Adjustment of tipping-bucket precipitation gauge
measurements, Atmospheric Research, 42, 237-246.
Straub, T.D. and Parmar, P.S., 1998, Comparison of rainfall records
collected by different rain-gage networks, in Proceedings of the
First Federal Interagency Hydrologic Modeling Conference, Las Vegas,
Nevada, p. 7-25 - 7-32.
Troutman, B.M., 1983, Runoff prediction errors and bias in parameter
estimation induced by spatial variability of precipitation, Water
Resources Research, 19(3), 791-810.
U.S. Department of Commerce, National Oceanic and Atmospheric Administration,
1972, National Weather Service river forecast system forecast procedures,
Technical memorandum NWS HYDRO-14, National Weather Service, Washington,
D.C.
U.S. Department of Commerce, National Oceanic and Atmospheric Administration,
1990-1993, Climatological data, Illinois: Asheville, N.C., Environmental
Data and Information Service. (published monthly).
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