Simulation models of watershed hydrology (also referred to as “rainfallrunoff models”) are calibrated to the best available streamflow data, which are typically published discharge time series at the outlet of the watershed. Even after calibration, the model generally cannot replicate the published discharges because of simplifications of the physical system embedded in the model structure and uncertainties of the input data and of the estimated model parameters, which, although optimized for the given calibration data, remain uncertain. The input data errors are caused by uncertainties in the forcing data, such as precipitation and other climatological data, and in the published discharges used for calibration. In the numerical algorithms used for calibration, the published discharges are often assumed to be without error, but they are themselves uncertain, typically having been computed using ratings, which are models fitted to uncertain discharge measurements.
In this study, uncertainty of published daily discharge data and how the discharge uncertainty is transmitted to the parameter values of the Hydrological Simulation Program–FORTRAN (HSPF) rainfallrunoff model and to the simulated discharge at both calibration and prediction locations were investigated for the Lake Michigan diversion in northeastern Illinois and northwestern Indiana. The HSPF model used in this study is used by the U.S. Army Corps of Engineers as part of quantifying the diversion of water from Lake Michigan by the State of Illinois. In this study, the model is calibrated jointly at two watersheds in the study area; the resulting model is considered the base model in this study. Seven other gaged watersheds in the study area are used for testing predictive simulations. A Bayesian rating curve estimation (BaRatin) approach, the BaRatin stageperioddischarge (SPD) method, was used to estimate the uncertainty of the published discharge from the calibration watersheds. To characterize the effect of the discharge uncertainty on parameter values, the HSPF model parameters were recalibrated to 17 nonrandomly selected pairs of discharge series from the BaRatin SPD analysis. To provide an indicator of the effect of parameter uncertainty to compare to the effect of discharge uncertainty, 1,000 parameter sets also were randomly generated from the estimated parameter covariance matrix of the base model. The recalibrated and random parameter sets were then used in HSPF simulations of discharge at the two calibration watersheds and at the seven prediction watersheds. Selected discharge summary statistics—the periodofstudy (POS, water years 1997 to 2015) mean discharge, selected flowduration curve (FDC) quantiles, and water year mean discharges—are used to characterize the variability between simulated and published discharge.
A normalized variability index (
The work described in this report provides preliminary estimates of a limited range of sources of error in predicted discharge uncertainty. Future work would be beneficial to obtain a better statistical characterization of the effect of the uncertainty of calibration discharge series and to address additional sources of uncertainty, such as from precipitation input data used in calibration and prediction and from structural (model) errors.
For more information on the USGS—the Federal source for science about the Earth, its natural and living resources, natural hazards, and the environment—visit
For an overview of USGS information products, including maps, imagery, and publications, visit
Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.
Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.
John Doherty, developer of the Model Independent Parameter Estimation (PEST) software package, graciously responded to many questions regarding the design of the methodologies used in the study. Ben Renard and Jérôme Le Coz (Institut national de recherche pour l'agriculture, l'alimentation et l'environnement, France) provided the Bayesian rating curve estimation (BaRatin) software and assisted its application. The Lake Michigan Diversion Accounting project managers Dr. TzuohYing Su (retired) and Mr. Jeff Fuller of the U.S. Army Corps of EngineersChicago District provided operational project support. Mr. Jeff Fuller also provided hourly meteorological and precipitation data used in this study.
Marvin Harris, Crystal Prater, and Ryan Beaulin of the U.S. Geological Survey (USGS) provided discharge measurement information and assisted in its interpretation. Kevin Kho and Peter Regan provided programming assistance. Amy Russell provided guidance on and facilitated workflows and participated in report organization and review.
The help of all these individuals is sincerely appreciated.
Multiply  By  To obtain 
Length  

inch (in.)  2.54  centimeter (cm) 
inch (in.)  25.4  millimeter (mm) 
foot (ft)  0.3048  meter (m) 
mile (mi)  1.609  kilometer (km) 
Area  
square mile (mi^{2})  259.0  hectare (ha) 
square mile (mi^{2})  2.590  square kilometer (km^{2}) 
Volume  
cubic foot (ft^{3})  0.02832  cubic meter (m^{3}) 
Flow rate  
cubic foot per second (ft^{3}/s)  0.02832  cubic meter per second (m^{3}/s) 
inch per hour (in/h)  0.0254  meter per hour (m/h) 
Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows: °C = (°F – 32) / 1.8.
Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).
A water year is the 12month period from October 1 through September 30 and designated by the calendar year in which it ends (for example, water year 2019 is the period beginning October 1, 2018, and ending September 30, 2019).
Bayesian rating curve estimation
Cook County Precipitation Network
confidence interval
coefficient of variation
evapotranspiration
flowduration curve
Hydrological Simulation Program–FORTRAN
Lake Michigan Diversion Accounting
North American Datum of 1983
National Land Cover Database
National Weather Service Cooperative Observer Program
ModelIndependent Parameter Estimation and Uncertainty Analysis package
period of record
period of study
stageperioddischarge
Technical Review Committee
Time Series Processor
U.S. Army Corps of Engineers
U.S. Geological Survey
normalized variability index
weirchannelflood plain
water year
With increasing needs for streamflow information but scarcity of available observations, statistical and physical models are used for predicting discharge in ungaged or sparsely gaged basins. Uncertainty in discharge predictions can be appreciable, and the International Association of Hydrological Sciences conducted a decadelong (2003–12) initiative aiming to reduce uncertainties from the hydrological data and hydrological modelling on prediction in ungaged basins (
A canal construction project in northeastern Illinois from 1892 to 1922 (
The diversion has various components; for example, the wastewater treatment plant discharges to the Chicago Sanitary and Ship Canal, originating from water supplied by pumpage for water supply from Lake Michigan (
Among the nine HSPF parameter sets, the parameter sets from the original calibration were determined from calibration of published daily discharges from four gaged watersheds adjacent to the diverted watershed in the 1960s and 1970s (for example,
The study area in northeastern Illinois and northwestern Indiana, including land use, the nine gaged watersheds used in this study, the diverted watershed where the runoff is predicted using the HSPF model, and the raingages used in the HSPF modeling, is shown in
Table 1. Background information for the U.S. Geological Survey streamgages for nine study watersheds.
[mi^{2}, square mile]
Station number 
Station name  Short name  Drainage area (mi^{2})  Impervious land^{1} (percent)  Grassland (percent)  Forest (percent)  Cumulative area above dams/drainage area above streamgage  Period of published daily discharge^{2} 
05533000  Flag Creek near Willow Springs, Illinois  Flag Creek  16.5  37.6  60.4  2.0  0.0  7/26/1951–present 
05535070  Skokie River near Highland Park, Illinois  Skokie River  21.1  31.4  55.5  13.1  0.0  8/21/1967–present 
05536255  Butterfield Creek at Flossmoor, Illinois  Butterfield Creek  23.5  29.9  62.7  7.4  0.122  5/17/1948–present 
05536340  Midlothian Creek at Oak Forest, Illinois  Midlothian Creek  12.6  36.6  53.3  10.1  1.207  10/1/1950–present 
^{3}05536500  Tinley Creek near Palos Park, Illinois  Tinley Creek  11.2  28.8  46.3  24.9  0.025  7/11/1951–present 
^{3}05537500  Long Run near Lemont, Illinois  Long Run  20.9  23.3  59.8  16.8  0.127  7/1/1951–present 
05539000  Hickory Creek at Joliet, Illinois  Hickory Creek  107.5  23.2  64.1  12.8  0.101  10/1/1944–present 
05536179  Hart Ditch at Dyer, Indiana  Hart Ditch at Dyer  37.6  7.7  69.9  22.5  0.0  9/19/1989–present 
05536190  Hart Ditch at Munster, Indiana  Hart Ditch at Munster  70.7  19.6  63.4  17.0  0.0  10/1/1942–present 
Impervious land is the hydraulically connected impervious land; the fractions were determined based on the 2011 version of the 2006 National Land Cover Database (
Present refers to year 2020.
Calibration watersheds.
Location of diverted Lake Michigan watershed and the Cook County Precipitation Network gages, U.S. Geological Survey streamgages and associated watersheds, and National Weather Service Cooperative Observer Program precipitation gages used in this study.
Figure 1. Map showing
The diverted watershed area is covered by a precipitation gage network, the 25gage Cook County Precipitation Network (CCPN;
Areal coverages for three types of land covers in the nine watersheds were determined using the 2011 version of the 2006 National Land Cover Database (NLCD;
Floodcontrol reservoirs have been built in the study area since the 1960s (
Errors in model structure, in model parameter values, and in the data used for climatic forcing and calibration contribute to uncertainty in rainfallrunoff simulations. Even with an optimized parameter set, rainfallrunoff models are not capable of reproducing all aspects and portions of the hydrograph equally well, which is a consequence of structural error (
Calibration, also known as history matching, is the process of conditioning the model parameters to historical system response data (
Through calibration, the inaccuracy of model simulations, represented as the simulationtoobservation misfits, can be reduced but not eliminated. However, the uncertainty remains because misfits may or may not stay within the same range as in the calibration when the calibrated parameter set are applied in predictions (
Researchers have attempted to identify structural and parameter errors when the model is used to make predictions (for example,
Transferring model parameterizations from gaged to ungaged watersheds generally has been implemented through regionalization efforts (
This study aims to quantify the uncertainties in the HSPFsimulated discharges at the ungaged catchments in the diverted Lake Michigan watershed used in LMDA computations. This report presents the first set of results of the study. The primary objectives of this report are to describe how uncertainty in the published discharge records used for HSPF parameter calibration is transmitted to calibrated parameter values and how the resulting parameter uncertainty affects simulated discharge volumes. The results are based on HSPF models of nine gaged watersheds in or near the diverted Lake Michigan watershed (see
All the HSPF PEST calibrations and HSPF simulations were forced by hourly climatic data, whereas the simulated discharge data were aggregated from hourly to daily time steps to compare with the published streamgage records (
The effects of the uncertainty of published discharge records and of the uncertainty of model parameters on HSPF predictions for LMDA are characterized in this study with two sets of HSPF simulations, one for each type of uncertainty, and these two sets of simulations are based on investigations of the underlying uncertainty. The models, input, and output data are available from
The simulations used to characterize the effect of uncertainty of the published discharge records are based on parameters obtained by recalibrating the base model with discharge series selected from realizations of the uncertain published discharges from the calibration watersheds to derive respective optimal parameter sets. The simulations used to characterize the parameter uncertainty are based on parameters obtained from Monte Carlo simulations of parameter sets based on the estimated covariance matrix of the basemodel parameters. The base, recalibrated, and random parameter sets are then used for HSPF simulations from the nine study watersheds (that is, the two calibration and the seven prediction watersheds). In this study, the uncertainties are analyzed using selected discharge summary statistics: the POS (WYs 1997 to 2015) mean discharge, selected flowduration curve (FDC) nonexceedance probability quantiles, and WY mean discharges.
This section has four subsections. In the first, the estimation of the uncertainty of the published discharge records at the two calibration watersheds is described. In the second, the twowatershed calibration scheme adopted with modification from
As discussed previously, the discharge series at the streamgages used in this study, particularly those at the calibration streamgages (Tinley Creek and Long Run), are computed with stagedischarge rating curves. That is, for each stage measurement
The USGS ratingcurve development process is described briefly here to provide a qualitative understanding of the uncertainty involved and to provide perspective on the applicability of the selected uncertainty estimation method. A rating curve is a curve fit to pairs of stage and discharge measurements. The curve is usually fit by the hydrographer who made the measurements and is fit by judgement, based on their knowledge of stream conditions (for example, stages corresponding to changes in hydraulic control, such as the top of the channel banks) and of the discharge measurement uncertainties, which are recorded using qualitative codes assigned at the time of the measurement (
Because of the high degree of judgement involved in the determination and adjustment of stagedischarge rating curves following the USGS development process, no quantitative method for assigning uncertainty to the rating curves or to the resulting computed discharge has been developed. Lacking such a method, the approach taken here is to apply a stateoftheart automated method for ratingcurve fitting and discharge computation with builtin uncertainty estimation and to adapt the uncertainty results to the published USGS daily discharge by a ratio technique.
The selected automated method is the stageperioddischarge (SPD) extension of the Bayesian rating curve estimation (BaRatin) method (hereafter referred to as BaRatin SPD) proposed by
The channel at the Tinley Creek streamgage (
Downstream view at the lowwater control and overbank at the Tinley Creek near Palos Park, Illinois, streamgage (U.S. Geological Survey [USGS] station 05536500) on December 2, 2003. Gage height was 2.45 feet, and discharge was 3.47 cubic feet per second. Photograph was taken by Perry Draper, USGS.
Figure 2. Photograph showing downstream view at the lowwater control and overbank at the Tinley Creek near Palos Park, Illinois, streamgage on December 2, 2003.
The Long Run streamgage (
Downstream view at the lowwater control and overbank at the Long Run near Lemont, Illinois, streamgage (U.S. Geological Survey [USGS] station 05537500) on April 22, 2008. Gage height was 1.07 feet, and discharge was 12.0 cubic feet per second. Photograph was taken by David Schrader, USGS.
Figure 3. Photograph showing downstream view at the lowwater control and overbank at the Long Run near Lemont, Illinois, streamgage on April 22, 2008.
The ratingcurve periods that cover the HSPF analysis period and the number and range of discharge measurements within each at the Tinley Creek and Long Run streamgages are given in
Table 2. Properties of U.S. Geological Survey ratingcurve periods that cover water years 1995 to 2016 at Tinley Creek near Palos Park, Illinois, and Long Run near Lemont, Illinois
[SPD, stageperioddischarge; Qms, discharge measurements; ft^{3}/s, cubic feet per second]
Ratingcurve number  BaRatin SPD period  Range of dates  Number of Qms  Range of Qms (ft^{3}/s) 
Tinley Creek  

23  5  10/05/1991–11/11/1995  29  0.29–121 
24  4  11/11/1995–11/24/1999  36  0.50–2,100 
25  3  11/24/1999–10/15/2007  54  0–189 
26  2  10/15/2007–10/26/2012  31  0.057–89.9 
27  1  10/26/2012–02/14/2017  28  0.13–870 
Long Run  
27  6  10/01/1990–07/17/1996  39  0.613–315 
28  5  07/17/1996–03/09/1998  12  1.40–2,740 
29  4  03/09/1998–01/23/1999  7  1.90–35.5 
30  3  01/23/1999–10/05/2001  22  1.79–246 
31  2  10/05/2001–10/25/2010  53  1.95–648 
32  1  10/25/2010–01/24/2017  39  0.54–903 
Discharge measurements at the streamgages shown in
Two hydraulic configurations for the application of BaRatin SPD to the streamgages in the calibration watersheds were tested, and the weirchannelflood plain (WCF) configuration, which combines a rectangular weir (for low flows), a channel (for inchannel flows), and a channel with flood plain (for overbank flows) to simulate the hydraulics at both streamgages was selected. Following the notation of
is the discharge being computed;
is the discharge coefficient;
is the effective weir width perpendicular to the flow;
is the acceleration of gravity;
is the stage;
is the offset;
is an exponent that generally is taken to be 3/2 for a rectangular weir; and
is the stage factor for a weir, equal to
Also following the notation of
is the discharge being computed;
is the Strickler flow resistance coefficient;
is the effective channel width;
is the bed slope;
is the stage;
is the offset;
is an exponent that generally is taken to be 5/3 for a wide rectangular channel; and
is the stage factor for a wide rectangular channel, equal to
Assuming only the weir and channel offsets
is the estimated discharge at stage
is the stage factor for the first (lowflow) control modeled as a weir, that is,
is stage;
is the stage offset for the first control and the
is the stage exponent for the first control;
is the activation stage for the first control and the
is the activation stage for the second control and the
is the stage factor for the second (channel) control modeled as a wide rectangular channel, that is,
is the stage offset for the second control and the
is the stage exponent for the second control;
is the stage factor for the flood plain part of the third control, that is,
is the activation stage for the third control.
The values of the activation stages are deduced from continuity (
The hydraulicgeometry dimensions and prior values of the parameters to be used for Bayesian inference by BaRatin SPD were estimated from the measurement section of the most recent rating period and using prior probability distributions following guidance and examples in
Table 3. Prior information for physical parameters and their distributions used for BaRatin stageperioddischarge analysis of Tinley Creek near Palos Park, Illinois, streamgage.
[ft, foot;
Specified parameter  Definition  Prior distribution  Inferred parameter  Definition  Prior distribution 
Control 1—Lowflow weir  

Offset (ft)  
Offset, period 1 (ft)  
Weir width (ft)  
Offsets, periods 2–5 (ft)  ^{1}  
Discharge coefficient (unitless)  Stage factor for a weir, equal to 

Gravitational acceleration (ft/s^{2})        
Exponent (unitless)        
Control 2—Channel flow  
Offset (ft)  
Offset, period 1 (ft)  

Channel width (ft)  
Offsets, periods 2–5 (ft)  ^{1}  

Strickler coefficient (m^{1/3}/s)  Stage factor for the channel, equal to 


Bed slope (unitless)        
Exponent (unitless)        
Control 3—Flood plain plus channel flows  
Offset (ft)  Stage factor for the flood plain, equal to 


Floodplain width (ft)      

Strickler coefficient (m^{1/3}/s)      

Bed slope (unitless)        
Exponent (unitless)        
Incremental change in stage (2< 

Local change (ft)      
Overall change (ft)      
Structural error  
Intercept (ft^{3}/s)      
γ_{2}  Slope (unitless)       
See “Uncertainty of StageDischarge Rating Curves” section.
Table 4. Prior information for physical parameters and their distributions used for BaRatin stageperioddischarge analysis of Long Run near Lemont, Illinois, streamgage.
[ft, foot;
Specified parameter  Definition  Prior  Inferred parameter  Definition  Prior 
Control 1—Lowflow channel  

Offset (ft)  
Offset, period 1 (ft)  
Weir width (ft)  
Offsets, periods 2–6 (ft)  ^{1}  
Discharge coefficient (unitless)  Stage factor for a weir, equal to 

Gravitational acceleration (ft/s^{2})        
Exponent (unitless)        
Control 2—Channel flow  
Offset (ft)  
Offset, period 1 (ft)  

Channel width (ft)  
Offsets, periods 2–6 (ft)  ^{1}  

Strickler coefficient (m^{1/3}/s)  Stage factor for the channel, equal to 


Bed slope (unitless)        
Exponent (unitless)        
Control 3—Flood plain plus channel flows  
Offset (ft)  Stage factor for the flood plain, equal to 


Floodplain width (ft)      

Strickler coefficient (m^{1/3}/s)      

Bed slope (unitless)        
Exponent (unitless)        
Incremental change in stage (2< 

Local change (ft)      
Overall change (ft)      
Structural error  
Intercept (ft^{3}/s)      
γ_{1}  Slope (unitless)       
See “Uncertainty of StageDischarge Rating Curves” section.
The stagedischarge measurement pairs for each rating period, along with the uncertainty of the discharge measurements inferred from the quality of the measurement noted by the hydrographers, are then used to infer the static and variable parameter values. The BaRatin SPD estimated discharge
is the function giving
is stage;
is the ratingcurve period;
is the vector of static and periodspecific ratingcurve parameters; and
represents the condition of
The parameters are inferred using uncertain stage, discharge, and period definition data. The error model for measured discharges is
is the
is the true discharge corresponding to the
is its measurement error, the collection of which (for all
In terms of the BaRatin SPD rated discharge (
is the BaRatin SPDestimated discharge corresponding to the
is a structural error term, whose values are assumed to be mutually independent and distributed as
is the function giving
is the stage corresponding to the
is the ratingcurve period corresponding to the
is the vector of ratingcurve parameters, and
represents the condition of
Combining
is the
is the function giving
is the stage corresponding to the
is the ratingcurve period corresponding to the
is the vector of ratingcurve parameters,
represents the condition of
is the measurement error of the ith discharge measurement, and
is the structural error term.
Using the characterization of the prior parameters as discussed previously and the posterior distribution developed based on
To obtain estimates of discharge uncertainty, the ratingcurve realizations simply need to be forced with appropriate stagedata time series. Before their use with the ratingcurve realizations, the stage data at the streamgages in the calibration watersheds, which were available mostly at a 15minute time step on the quarter hour, were preprocessed as follows: (1) the data were interpolated to be uniformly on the quarter hour; (2) the data were analyzed for gaps, and calendar days with data gaps longer than 12 hours or fewer than 48 stage values were set to missing; and (3) 500 realizations (1 per ratingcurve realization) of independent meanzero random Gaussian noise with a standard deviation of 0.01 ft (following USGS stage accuracy requirements [
The 500 realizations from the discharge time series, simulated at 15minute intervals that were obtained from applying the rating curves to the realizations of noisy stage data, were postprocessed following three steps: (1) the discharge data were aggregated to daily mean values using the trapezoidal rule (
The missing days and days when discharges were estimated in the published record were determined using USGS methodology of hydrographic comparison (
The final postprocessing step, rescaling, is crucial and was applied to adapt the uncertainty estimate provided in the BaRatin SPD realizations to the published discharge record, which is used as the basis for the rainfallrunoff model calibrations. BaRatin SPD realizations do not generally center on the published values, and this result is expected because these realizations were obtained using an independent, alternative ratingcurve estimation procedure. To address this discrepancy, the BaRatin SPD realizations were rescaled to enforce daybyday centering on the published daily record using the following equation:
is the
is the
is the published daily value on day
is the average over the 500 realizations on day
It can be deduced from
The twowatershed HSPF calibration scheme used in this study is based on the scheme developed by
HSPF parameters related to runoff generation from pervious lands (abbreviated explanations of pervious land parameters analyzed are included in
Several transformations are applied to the parameters before their use in the calibration process, as was done in
The measurement objective function comprises eight observation data groups organized from daily discharge records of the two calibration watersheds for WYs 1996–2015. The eight observation groups are as follows:
daily discharge,
daily quick flow derived from daily discharge by baseflow separation,
daily base flow derived from daily discharge by baseflow separation,
storm hydrographs for events with daily maxima above a selected threshold (200 cubic feet per second [ft^{3}/s] was used in the study),
monthly runoff volume,
annual runoff volume,
total runoff volume of the calibration period, and
FDC defined by 11 nonexceedance probabilities.
Magnitudes of the elements making up these groups (for example, the daily discharge values in the daily discharge group) may differ by orders of magnitudes; therefore, element weights were assigned to equalize the contribution of errors in each value to the group’s contribution to the measurement objective function. For each element of a group, its weight was set equal to the inverse of its value, except for the FDC group for which a constant weight was used for each of the nonexceedance probabilities. Also, to avoid infinite weights associated with zerovalued daily discharges, 0.01 ft^{3}/s was added to the daily discharges before the inversion. Then, in addition to the weighting of the elements of the observation groups described above, the groups themselves were weighted to equalize their effect on the objective function (using the PWTADJ1 utility;
When using regularized inversion, as was done here, two objective functions are used: a measurement objective function and a regularization objective function. The PEST optimization is constrained in seeking a userdefined target measurement objective function value subject to the constraint that the regularization objective function (departures of parameters from their default values or preferred condition) is minimized (
For PEST to start a search, a set of initial parameter values and parameter bounds are assigned. For the base model, the initial parameter values and the lower and upper bounds determined from
If linearity can be assumed for model outputs with respect to the model parameterization, the posterior probability function of parameters can be inferred from a Bayesian update of its prior probability density function using information learned from model calibration (
The posterior covariance matrix is not generated by PEST as part of the optimization process in the model described here because of the use of regularization in the optimization process. To obtain a linear approximation to the posterior parameter covariance matrix, the PEST utility function PREDUNC7 (
The discharge series realizations derived from the BaRatin SPD analysis at the two streamgages in the two calibration watersheds are independent from each other; therefore, the simplest approach to selecting datasets for recalibration would be as random selection of a large number (that is, from 100 to all 500 of them) of samples from the two sets of discharge series realizations. This approach would also be the most useful, because, being based on random sampling, the results would approximate the full probability distribution of uncertainty arising from uncertainty in published discharge and could be added to the uncertainty arising from the model parameters. However, random sampling of such a large number of these series is beyond the scope of this study because the subsequent calibration is computationally demanding and is not automatable because the stopping criterion requires expert judgement.
Instead of random sampling from the two sets of 500 BaRatin SPD discharge realizations for the calibration watersheds, a deterministic approach was developed to select pairs of realizations that cover most of the possible combinations of the range of simulated volumes at the two watersheds. According to this approach, the sets of realizations at the two watersheds were ranked according to the total runoff volume during the calibration period (WYs 1996–2015). The discharge realizations for each watershed with volumes closest to the 1percent, 10percent, 50percent, 90percent, and 99percent nonexceedance probability quantiles of volume for that watershed (thus, five realizations for each watershed) were selected. Among the 25 possible pairwise combinations of these two sets of five realizations, 17 pairs of discharge series realizations were selected (
Pairing of BaRatin stageperioddischarge series realizations for the Tinley Creek near Palos Park, Illinois (U.S. Geological Survey station 05536500) and Long Run near Lemont, Illinois (U.S. Geological Survey station 05537500) streamgages for investigating Hydrological Simulation Program–FORTRAN parameter uncertainty arising from the uncertainty in published discharge records.
Figure 4. Graph showing pairing of BaRatin stageperioddischarge series realizations for the Tinley Creek near Palos Park, Illinois and Long Run near Lemont, Illinois streamgages for investigating Hydrological Simulation Program–FORTRAN parameter uncertainty arising from the uncertainty in published discharge records.
The multiperiod stagedischarge ratingcurvebased BaRatin SPD method was applied to estimate the uncertainty of the observed discharge at the streamgages in the calibration watersheds at Tinley Creek and Long Run. The results of its application are described and discussed in this section, beginning with the rating curves and proceeding to the daily discharge time series.
Ratingcurve realizations resulting from the application of the BaRatin SPD method as described in the “Estimating Uncertainty of Published Discharge Methods” section are illustrated, for selected periods, in
The highest measurements in period 4 at the Tinley Creek streamgage and in period 5 at the Long Run streamgage reflect a record rainstorm in this region of Illinois in July 1996, during which these peakofrecord discharges were measured at these streamgages. The Tinley Creek streamgage measurement was an indirect measurement based on culvert hydraulics and, therefore, was rated “poor” in accuracy, whereas the Long Run streamgage measurement was direct (instrument measured) and rated “fair” in accuracy.
The shapes of the rating curves depend on the activation stages where the control transitions from one to the next control. For the Tinley Creek streamgage, the weir (lowflow) to channelcontrol transition (activation stage
Selected rating curves obtained from application of the BaRatin stageperioddischarge (SPD) method in this study compared to the corresponding official U.S. Geological Survey (USGS) rating curves.
Figure 5. Graphs showing selected rating curves obtained from application of the BaRatin stageperioddischarge method in this study compared to the corresponding official U.S. Geological Survey rating curves.
The parameter distributions underlying the BaRatin SPD rating curves are illustrated for the Tinley Creek and Long Run streamgages in
The shifting of
Two exceptions to narrowing between prior and posterior distributions common to both streamgages are associated with the outofbank flows:
Overall, the rating curves and associated parameters and their uncertainties obtained from the BaRatin SPD rating curves and their parameters appear to be meaningfully related to the prior information and measurements and to the USGS rating curves. As a result, using these parameters to obtain random realizations of predicted discharge at these streamgages is reasonable.
Distributions of the prior and posterior ratingcurve parameters obtained with the BaRatin stageperioddischarge (SPD) method for this study at the Tinley Creek near Palos Park, Illinois, streamgage (U.S. Geological Survey station 05536500).
Figure 6. Boxplots showing distributions of the prior and posterior ratingcurve parameters obtained with the BaRatin stageperioddischarge method for this study at the Tinley Creek near Palos Park, Illinois, streamgage.
Prior and posterior ratingcurve parameters obtained with the BaRatin stageperioddischarge (SPD) method for this study at the Long Run near Lemont, Illinois, streamgage (U.S. Geological Survey station 05537500).
Figure 7. Boxplots showing prior and posterior ratingcurve parameters obtained with the BaRatin stageperioddischarge method for this study at the Long Run near Lemont, Illinois, streamgage.
Following the methods described above, 500 daily discharge series realizations, 1 for each of the 500 posterior rating curves obtained from application of the BaRatin SPD method, were obtained for the Tinley Creek and Long Run streamgages. These rating curves were rescaled to agree in daily mean with the published USGS daily streamgage record (
The variability and mean of the daily discharge percentiles and mean over the simulation period (WYs 1996–2015) are presented and are compared to the published values in
Table 5. Statistics describing variability of the mean and selected nonexceedance percentiles of the 500 BaRatin stageperioddischarge daily discharge realizations from water years 1996–2015 at the Tinley Creek and Long Run streamgages.
[Units are cubic feet per second, except coefficient of variation (CV), which is dimensionless; %, percent; Stdev, standard deviation]
Percentile  Tinley Creek  Long Run  
Published  2.5% quantile  97.5% quantile  Mean  Stdev  CV  Published  2.5% quantile  97.5% quantile  Mean  Stdev  CV  
1  0.18  0.13  0.20  0.168  0.019  0.111  0.78  0.47  0.93  0.70  0.12  0.165 
5  0.47  0.39  0.55  0.461  0.044  0.095  1.35  1.02  1.54  1.29  0.13  0.100 
10  0.87  0.72  0.99  0.850  0.069  0.081  1.90  1.57  2.13  1.85  0.14  0.076 
25  1.90  1.70  2.06  1.88  0.089  0.047  3.60  3.24  4.02  3.62  0.20  0.054 
50  4.57  4.26  4.80  4.55  0.14  0.031  8.60  7.99  9.27  8.60  0.32  0.037 
75  12.0  11.2  12.6  12.0  0.36  0.030  20.9  19.6  22.2  20.9  0.66  0.032 
90  31.8  29.0  34.0  31.8  1.26  0.040  53.1  49.3  58.0  53.4  2.13  0.040 
95  60.0  55.7  63.8  59.8  2.00  0.033  92.7  84.9  100.7  92.1  4.07  0.044 
99  187  174  206  190  8.06  0.043  274  244  312  277  17.6  0.063 
Mean  15.0  14.2  15.8  15.0  0.42  0.028  24.6  23.0  26.2  24.6  0.80  0.032 
Annual volumes are particularly relevant to the purpose of this report and are also of interest to show how the estimated uncertainty varies in time. Statistics of those volumes (presented as mean discharges) are shown in
Table 6. Water year mean statistics of discharge realizations generated by BaRatin stageperioddischarge at Tinley Creek near Palos Park, Illinois, streamgage.
[Units are in cubic feet per second, except coefficient of variation (CV), which is dimensionless; SPD, stageperioddischarge; USGS, U.S. Geological Survey; Stdev, standard deviation; %, percent; NA, not applicable]
Water year  BaRatin SPD period  USGS ratingcurve number(s)  Published  Mean  Stdev  CV  2.5% quantile  97.5% quantile  97.5%–2.5% quantile difference 
1996  4–5  23–24  17.30  17.30  0.88  0.0507  15.77  19.56  3.79 
1997  4  24  14.30  14.30  0.68  0.0477  13.08  15.99  2.90 
1998  4  24  15.69  15.69  0.84  0.0536  14.31  18.01  3.70 
1999  4  24  16.06  16.06  0.96  0.0595  14.58  18.78  4.19 
2000  3–4  24–25  14.03  14.03  0.61  0.0435  12.78  15.26  2.48 
2001  3  25  13.33  13.33  0.52  0.0389  12.30  14.36  2.06 
2002  3  25  14.04  14.04  0.59  0.0420  12.85  15.18  2.32 
2003  3  25  9.05  9.05  0.65  0.0717  7.86  10.35  2.49 
2004  3  25  16.52  16.52  0.74  0.0449  15.07  17.97  2.90 
2005  3  25  10.60  10.60  0.42  0.0398  9.73  11.41  1.69 
2006  3  25  12.60  12.60  0.53  0.0418  11.49  13.61  2.12 
2007  3  25  18.68  18.68  0.83  0.0444  17.09  20.32  3.23 
2008  2  26  17.28  17.28  1.14  0.0662  13.91  19.09  5.18 
2009  2  26  17.83  17.83  1.20  0.0675  14.34  19.82  5.47 
2010  2  26  15.59  15.59  0.95  0.0612  12.93  17.27  4.34 
2011  2  26  16.01  16.01  1.06  0.0659  12.97  17.88  4.91 
2012  2  26  10.77  10.77  0.59  0.0547  9.38  11.93  2.54 
2013  1  27  15.33  15.33  0.81  0.0526  13.77  17.02  3.25 
2014  1  27  21.23  21.23  1.17  0.0551  18.98  23.59  4.62 
2015  1  27  14.34  14.34  0.80  0.0556  12.76  15.93  3.17 
NA  NA  15.03  15.03  0.80  0.0529  13.30  16.67  3.37 
Table 7. Water year mean statistics of discharge realizations generated by BaRatin stageperioddischarge at Long Run near Lemont, Illinois, streamgage.
[Units are in cubic feet per second, except coefficient of variation (CV), which is dimensionless; SPD, stageperioddischarge; USGS, U.S. Geological Survey; Stdev, standard deviation; %, percent; NA, not applicable]
Water year  BaRatin SPD period  USGS ratingcurve number(s)  Published  Mean  Stdev  CV  2.5% quantile  97.5% quantile  97.5%–2.5% quantile difference 
1996  5–6  27–28  26.03  26.03  1.16  0.0444  23.49  28.10  4.60 
1997  5  28  18.83  18.83  1.42  0.0754  15.30  21.32  6.01 
1998  4–5  28–29  23.87  23.87  1.45  0.0606  20.71  26.68  5.97 
1999  3–4  29–30  25.29  25.29  0.98  0.0386  23.58  27.31  3.73 
2000  3  30  20.69  20.69  0.86  0.0417  19.14  22.52  3.38 
2001  3  30  17.71  17.71  0.76  0.0427  16.33  19.30  2.97 
2002  2  31  22.49  22.49  0.86  0.0381  20.78  24.24  3.46 
2003  2  31  12.69  12.69  0.48  0.0382  11.78  13.66  1.88 
2004  2  31  25.49  25.49  0.98  0.0384  23.55  27.52  3.97 
2005  2  31  18.40  18.40  0.70  0.0379  16.99  19.88  2.89 
2006  2  31  15.97  15.97  0.64  0.0400  14.74  17.22  2.47 
2007  2  31  39.78  39.78  1.54  0.0387  36.75  42.94  6.19 
2008  2  31  34.26  34.26  1.31  0.0381  31.67  36.88  5.21 
2009  2  31  37.21  37.21  1.49  0.0400  34.36  40.14  5.78 
2010  2  31  33.50  33.50  1.33  0.0396  30.94  36.22  5.28 
2011  1  32  32.70  32.70  1.31  0.0401  30.06  35.20  5.14 
2012  1  32  15.64  15.64  0.67  0.0431  14.35  16.90  2.55 
2013  1  32  22.20  22.20  0.91  0.0408  20.55  23.90  3.35 
2014  1  32  28.80  28.80  1.20  0.0416  26.42  31.06  4.64 
2015  1  32  21.06  21.06  0.87  0.0415  19.41  22.68  3.26 
NA  NA  24.63  24.63  1.05  0.0430  22.55  26.68  4.14 
Water year mean discharge simulated with the BaRatin stageperioddischarge (SPD) method and published discharge series, water years 1996–2015.
Figure 8. Graphs showing water year mean discharge simulated with the BaRatin stageperioddischarge method and published discharge series, water years 1996–2015.
BaRatin SPDgenerated discharge series realizations, where the total flow volumes correspond the closest to the 1percent, 10percent, 50percent, 90percent, and 99percent quantiles of total volume during the HSPF simulation period, were selected for both streamgages at the calibration watersheds and paired (
The POR percentiles and means of the selected realizations are given in
Table 8. Comparison of nonexceedance probability percentiles and means of selected BaRatin stageperioddischarge daily discharge realizations representing the 1, 10, 50, 90, and 99percent nonexceedance probability quantiles of total volume at the Tinley Creek near Palos Park, Illinois, and Long Run near Lemont, Illinois, streamgages for the period from water year (WY) 1996 to WY 2015.
[Units are in cubic feet per second; %, percent]
Percentile  Tinley Creek  Long Run  
Published  1% quantile  10% quantile  50% quantile  90% quantile  99% quantile  Published  1% quantile  10% quantile  50% quantile  90% quantile  99% quantile  
1  0.18  0.16  0.16  0.20  0.14  0.19  0.78  0.76  0.59  0.68  0.66  0.53 
5  0.47  0.45  0.43  0.50  0.40  0.53  1.35  1.32  1.13  1.31  1.25  1.06 
10  0.87  0.87  0.80  0.90  0.80  0.91  1.90  1.86  1.69  1.87  1.81  1.66 
25  1.90  1.87  1.82  1.93  1.84  1.96  3.60  3.56  3.33  3.62  3.69  3.45 
50  4.57  4.54  4.43  4.69  4.60  4.79  8.60  8.42  8.30  8.73  8.23  8.60 
75  12.0  11.6  12.0  12.1  12.1  12.7  20.9  20.0  20.4  20.8  21.3  21.8 
90  31.8  29.5  32.7  31.9  33.4  34.6  53.1  50.3  51.2  52.1  56.9  57.1 
95  60.0  56.0  61.7  59.8  62.3  64.0  92.7  84.9  88.6  89.2  97.9  99.2 
99  187.0  173.4  190.6  188.9  193.1  196.9  274.0  244.9  263.2  279.4  297.6  308.9 
15.0  14.1  15.3  15.0  15.6  16.0  24.6  22.9  23.6  24.6  25.6  26.5 
Fewer such crossings are observed in the annual flow volumes presented in
Table 9. Water year annual mean discharges at selected BaRatin stageperioddischarge realizations representing the 1, 10, 50, 90, and 99percent nonexceedance probability quantiles of total volume at the Tinley Creek near Palos Park, Illinois, streamgage.
[Units are cubic feet per second; SPD, stageperioddischarge; USGS, U.S. Geological Survey; %, percent; NA, not applicable]
Water year  BaRatin SPD period  USGS rating curve(s)  Published  1% quantile  10% quantile  50% quantile  90% quantile  99% quantile 
1996  4–5  23–24  17.30  16.62  17.18  17.48  16.39  18.45 
1997  4  24  14.30  13.73  14.20  14.63  13.53  15.30 
1998  4  24  15.69  15.03  15.64  16.02  14.99  16.43 
1999  4  24  16.06  15.41  16.09  16.18  15.27  16.87 
2000  3–4  24–25  14.03  13.05  14.42  13.97  14.19  14.45 
2001  3  25  13.33  12.61  13.74  13.28  13.49  13.70 
2002  3  25  14.04  13.05  14.51  13.91  14.21  14.42 
2003  3  25  9.05  9.20  8.78  9.07  9.38  9.31 
2004  3  25  16.52  15.42  17.14  16.50  16.73  16.87 
2005  3  25  10.60  9.97  10.96  10.55  10.79  10.94 
2006  3  25  12.60  11.90  13.05  12.55  12.77  12.97 
2007  3  25  18.68  17.43  19.24  18.47  18.95  19.17 
2008  2  26  17.28  16.20  17.74  17.21  18.74  19.33 
2009  2  26  17.83  16.54  18.30  17.49  19.27  20.06 
2010  2  26  15.59  14.74  15.77  15.42  16.62  17.34 
2011  2  26  16.01  15.02  16.40  15.73  17.07  18.10 
2012  2  26  10.77  10.35  10.79  10.64  11.26  12.08 
2013  1  27  15.33  13.70  15.90  15.71  17.29  16.22 
2014  1  27  21.23  18.89  22.07  21.32  24.08  22.62 
2015  1  27  14.34  12.94  14.76  14.82  16.25  14.90 
NA  NA  15.03  14.09  15.33  15.05  15.56  15.98 
Table 10. Water year annual mean discharges at selected BaRatin stageperioddischarge realizations representing the 1, 10, 50, 90, and 99percent nonexceedance probability quantiles of total volume at the Long Run near Lemont, Illinois, streamgage.
[Units are cubic feet per second; SPD, stageperioddischarge; USGS, U.S. Geological Survey; %, percent; NA, not applicable]
Water year  BaRatin SPD period  USGS rating curve(s)  Published  1% quantile  10% quantile  50% quantile  90% quantile  99% quantile 
1996  5–6  27–28  26.03  24.38  25.36  26.56  25.81  28.41 
1997  5  28  18.83  17.93  18.73  18.83  16.87  21.58 
1998  4–5  28–29  23.87  22.01  23.95  23.60  22.86  24.65 
1999  3–4  29–30  25.29  23.58  24.61  25.17  26.56  26.27 
2000  3  30  20.69  19.44  19.84  20.33  21.52  21.65 
2001  3  30  17.71  16.78  17.35  17.56  18.54  18.22 
2002  2  31  22.49  20.76  21.60  22.55  24.09  24.66 
2003  2  31  12.69  11.76  12.07  12.81  13.42  13.89 
2004  2  31  25.49  23.45  24.28  25.62  27.35  27.91 
2005  2  31  18.40  17.01  17.64  18.34  19.60  19.92 
2006  2  31  15.97  14.80  15.20  15.77  16.66  16.97 
2007  2  31  39.78  36.33  37.70  39.46  42.68  43.23 
2008  2  31  34.26  31.49  32.55  34.59  36.58  37.39 
2009  2  31  37.21  33.89  35.47  37.45  40.15  40.89 
2010  2  31  33.50  30.48  31.94  33.40  36.04  36.85 
2011  1  32  32.70  30.54  31.10  32.72  34.03  34.98 
2012  1  32  15.64  15.07  14.70  15.77  15.77  15.88 
2013  1  32  22.20  20.91  21.09  22.68  23.04  23.41 
2014  1  32  28.80  26.85  27.18  28.60  30.02  30.63 
2015  1  32  21.06  20.12  19.96  21.08  21.37  21.81 
NA  NA  24.63  22.88  23.62  24.65  25.65  26.46 
The two sets of HSPF simulations in this study are based on two corresponding HSPF parameter sets, one that characterizes the effects of the uncertainty of published discharge records and the other that characterizes the uncertainty of model parameters. These parameter sets are obtained as described in the sections “Model Recalibration with Uncertain Published Discharge Time Series” and “Estimating Uncertainty of BaseModel Parameters,” respectively. The first set was obtained by recalibration to 17 discharge series pairs that characterize the uncertainty of the published discharge record. The second was obtained by Monte Carlo simulation of parameter sets based on the estimated basemodel parameter covariance matrix. In this section, the uncertainty of these two sets of parameters are discussed in terms of statistics describing their distributions.
The resulting parameters after recalibration with the 17 selected pairs of discharge realizations from the discharge uncertainty analysis showed changes in grassland and forest parameters, but not all adjustable parameters responded substantially to the differences in the calibration discharge series (
Table 11. Hydrological Simulation Program–FORTRAN parameter values resulting from calibration with published discharge records and statistics of 17 parameter sets from recalibration with discharge realizations characterizing the uncertainty of the published discharge records at the Tinley Creek near Palos Park, Illinois, and Long Run near Lemont, Illinois, streamgages.
[Base model refers to calibration with published discharge records; CV, coefficient of variation]
Parameter name^{1}  Grassland  Forest  
Base model  Mean, recalibrations  CV, recalibrations  Range, recalibrations  Base model  Mean, recalibrations  CV, recalibrations  Range, recalibrations  
FOREST  0.2  0.2  1.34E06  1.99999–0.2  0.30003  0.30005  0.00034  0.299999–0.300419 
LZSN  6.681  6.679  4.26E04  6.673–6.684  6.604  6.632  0.014  6.398–6.788 
INFILT  0.032  0.032  0.004  0.031–0.032  0.033  0.033  0.017  0.031–0.033 
LSUR  50.2  400.8  0.004  398.1–405.9  400.8  50  0  50–50.1 
SLSUR  0.0085  0.0085  0.003  0.00841–0.00852  0.0085  0.0085  0.001  0.00849–0.00853 
KVARY  1.378  1.241  0.002  1.24–1.251  1.241  1.377  0.001  1.377–1.384 
AGWRC  0.968  0.968  3.07E05  0.9679–0.9681  0.966  0.966  3.36E05  0.9663–0.9664 
PETMAX  44.9  44.5  0.012  43.286–45  45  44.8  0.007  44.111–45 
PETMIN  34.7  34.4  0.028  31.28–35  35  34.6  0.019  32.29–35 
DEEPFR  0.05013  0.05017  0.00153  0.05009–0.05035  0.04947  0.04952  0.00029  0.04949–0.04955 
AGWETP  0.0399  0.04  0.0011  0.0399–0.0401  0.0399  0.0402  0.0123  0.0399–0.0419 
CEPSC  0.08479  0.08484  0.00151  0.0847–0.0853  0.12679  0.13318  0.02955  0.1272–0.1463 
UZSN  1.019  1.022  0.008  1.015–1.052  1.019  1.191  0.127  1.021–1.754 
NSUR  0.25  0.25  0.0007  0.2492–0.25  0.4  0.3998  0.0019  0.3968–0.4 
INTFW  2.506  2.503  0.003  2.482–2.529  2.506  2.479  0.037  2.124–2.529 
IRC  0.62  0.53  0.002  0.526–0.531  0.529  0.62  0.001  0.619–0.621 
LZETP  0.138  0.139  0.003  0.1379–0.1399  0.208  0.214  0.068  0.2069–0.2678 
See
[Base model refers to calibration with published discharge records. 1/in, inverse of an inch; ET, evapotranspiration; PET, potential evapotranspiration]
Parameter^{1}  Explanation  Unit  Range (lower bound–upper bound) of parameter values  Initial parameter values for calibrating the base model  
Grassland  Forest  Grassland  Forest  
FOREST  Fraction of land that covered in (for example, conifer) forest that can transpire when there is snowpack  None  0.05–0.2  0.2–0.5  0.2  0.3 
LZSN  Lower zone nominal soils moisture storage  Inches  2.0–15.0  1.4–19.5  6.6808  6.6808 
INFILT  Index of infiltration capacity  Inches per hour  0.001–0.10  0.001–0.105  0.032  0.033 
LSUR  Length of overland flow plane  Feet  50–500  50–500  50.0  400.0 
SLSUR  Average slope of assumed overland flow plane  Feet per feet  0.0051–0.02  0.001–0.02  0.0085  0.0085 
KVARY  A constant describes the nonlinear groundwater recession  1/in  0.00001–3.0  0.00001–3.0  1.377  1.240 
AGWRC  A constant describes the base groundwater recession rate  none  0.917–0.98  0.913–0.982  0.968  0.966 
PETMAX  Temperature below which ET is reduced to 50 percent of that in the input time series. Active only when snow processes are being simulated  Degrees Fahrenheit  35–45  35–45  45.0  45.0 
PETMIN  Temperature below which ET is zero. Active only when snow processes are being simulated  Degrees Fahrenheit  30–35  30–35  35.0  35.0 
INFEXP  Exponent in infiltration equation that determines how much a deviation from nominal lower zone storage affects the infiltration rate  None  2.0  2.0  2.0  2.0 
INFILD  Ratio of maximum/mean soil infiltration capacities  None  2.0  2.0  2.0  2.0 
DEEPFR  Fraction of infiltrating water lost to inactive groundwater (deep percolation)  None  0.001–0.20  0.001–0.20  0.0501  0.0495 
BASETP  ET (specifies as fraction of PET) lost to riparian vegetation as active groundwater enters streambed  None  0.0  0.0  0.0  0.0 
AGWETP  Fraction of PERLND subject to direct evaporation from groundwater storage  None  0.0001–0.1  0.0001–0.105  0.0399  0.0399 
CEPSC  Interception storage capacity by vegetation  Inches  0.03–0.20  0.03–0.50  0.0848  0.1329 
UZSN  Nominal upper zone soil moisture storage  Inches  0.05–1.2  0.05–2.4  1.017  1.130 
NSUR  Manning’s roughness for overland flows  None  0.15–0.25  0.25–0.40  0.25  0.40 
INTFW  Determines interflow  None  1.0–5.0  0.75–1.0  2.500  2.500 
IRC  Interflow recession parameter  None  0.5−0.7  0.5−0.85  0.649  0.531 
LZETP  Parameter determines lower zone ET  None  0.1–0.9  0.15–3.24  0.138  0.208 
Parameters INFEXP, INFILD, and BASETP are not varied in the Lake Michigan Diversion Accounting Hydrological Simulation Program—FORTRAN analysis.
Having been recalibrated with the same climatic forcing data but different calibration discharges, the parameters that changed are primarily those pertinent to model evapotranspiration (ET) and losses to deep recharge (that is, processes to maintain water balance). PETMAX and PETMIN affect ET when snow processes are being simulated. With snow parameters not being calibrated, the large changes in PETMAX and PETMIN possibly reflect their taking surrogate roles for other parameters that also simulate ET but whose values are fixed throughout the year. FOREST is another parameter that affects ET when there is snowpack. In contrast to PETMAX and PETMIN, the FOREST values are sitespecific data, and, therefore, there is not much information in the discharge data for calibrating its values. Snowpack has a larger effect on winter flows, but ET is a primary component of the water balance at all times. The PETMAX and PETMIN parameters showed large variations but their effects on predicted annual discharge may be small. Other parameters affecting ET volumes include LZETP, BASETP, AGWETP, and those parameters related to soil moisture storages (for example, UZSN, LZSN, and CEPSC). These parameters also changed after recalibration, except for BASETP, which was not among the adjustable parameters considered in this study.
Among the parameters that did not vary appreciably in the recalibration process, INTFW, IRC, and AGWRC are, however, parameters that are commonly selected for calibration. These parameters, along with NSUR, LSUR, SLSUR, and KVARY varied by only a small amount (see CV values in
Hydrological Simulation Program–FORTRAN grassland and forest parameter values resulting from calibration using the published discharge records (baseQ) and from recalibration with the 17 pairs of discharge series realizations characterizing the uncertainty of the published discharge record. See
Figure 9. Graphs showing Hydrological Simulation Program–FORTRAN grassland and forest parameter values resulting from calibration using the published discharge records (baseQ) and from recalibration with the 17 pairs of discharge series realizations characterizing the uncertainty of the published discharge record.
HSPF basemodel parameter uncertainties, expressed by physical lower and upper bounds (determined based on expert knowledge) before the calibration, by their standard deviations obtained from the posterior covariance matrix estimated with the PEST PREDUNC7 utility, and by the standard deviations of the parameters sampled using the RANDPAR utility from the estimated posterior covariance matrix are presented in
Table 12. Prior and posterior statistics of adjustable parameters of the base Hydrological Simulation Program–FORTRAN model and those of the 1,000 simulated parameter sets.
[stdev, standard deviation; CV, coefficient of variation]
^{1}Parameters  Information for basemodel parameters before calibration  Posterior parameter uncertainty estimation using PREDUNC7  Random parameter set: RANDPAR samples (1,000 simulations)  
^{2}Initial value  ^{2}Lower bound  ^{2}Upper bound  ^{3,4}Input (prior) stdev  ^{3}Output (posterior) stdev  ^{2}Output CV  ^{2}Base model parameters (simulation input mean)  ^{3}Mean of simulated values  ^{3}Stdev of simulated values  
FORESTgrass  0.20  0.05  0.20  0.151  0.145  0.580  0.200  −0.758  0.084 
FORESTforest  0.30  0.20  0.50  0.099  0.098  0.465  0.300  −0.524  0.094 
LZSNgrass  6.681  2  15  0.219  0.044  0.304  6.681  0.823  0.045 
LZSNRforest  1.00  0.7  1.3  0.067  0.057  0.347  0.988  −0.004  0.057 
INFILTgrass  0.032  0.001  0.1  0.500  0.033  0.262  0.032  −1.499  0.033 
INFILTRforest  1.036  1  1.05  0.005  0.005  0.103  1.050  0.019  0.003 
LSURforest  400  50  500  0.250  0.116  0.511  401  2.588  0.097 
LSURgrass  50  50  500  0.250  0.090  0.443  50  1.736  0.053 
SLSURforest  0.0085  0.001  0.02  0.325  0.141  0.570  0.008  −2.070  0.133 
SLSURgrass  0.0085  0.0051  0.02  0.148  0.158  0.610  0.008  −2.079  0.151 
KVARYforest  1.240  0  3  1.369  0.266  0.839  1.241  0.076  0.248 
KVARYgrass  1.377  0  3  1.369  0.187  0.674  1.378  0.135  0.184 
AGWRCTRgrass  30.30  11  50  0.164  0.065  0.374  30.279  1.481  0.067 
AGWRCTRRforest  0.95  0.95  1.1  0.016  0.016  0.180  0.950  −0.016  0.009 
PETMAXgrass  45  35  45  0.027  0.014  0.170  44.9  1.647  0.009 
PETMAXforest  45  35  45  0.027  0.022  0.213  45.0  1.645  0.013 
PETMINgrass  35  30  35  0.017  0.010  0.144  34.7  1.537  0.007 
PETMINforest  35  30  35  0.017  0.013  0.162  35.0  1.539  0.008 
DEEPFRforest  0.0495  0.001  0.2  0.575  0.376  1.058  0.049  −1.299  0.357 
DEEPFRgrass  0.0501  0.001  0.2  0.575  0.263  0.831  0.050  −1.295  0.251 
AGWETPgrass  0.04  0.0001  0.1  0.750  0.044  0.303  0.040  −1.399  0.043 
AGWETPRforest  1.00  1  1.05  0.005  0.005  0.103  1.000  0.002  0.003 
CEPSCgrass  0.085  0.03  0.2  0.206  0.052  0.330  0.085  −1.074  0.050 
CEPSCRforest  1.567  1  2.5  0.099  0.084  0.427  1.495  0.179  0.081 
UZSNgrass  1.017  0.05  1.2  0.345  0.013  0.165  1.019  0.008  0.013 
UZSNRforest  1.130  1  2  0.075  0.033  0.260  1.000  0.013  0.019 
NSURforest  0.25  0.15  0.25  0.055  0.049  0.322  0.400  −0.417  0.028 
NSURgrass  0.40  0.25  0.4  0.051  0.045  0.306  0.250  −0.621  0.027 
INTFWgrass  2.50  1  5  0.175  0.026  0.231  2.506  0.400  0.026 
INTFWRforest  1.00  0.75  1  0.031  0.028  0.240  1.000  −0.010  0.015 
IRCTRforest  1.130  1  2.33  0.092  0.064  0.368  1.124  0.055  0.050 
IRCTRgrass  1.637  1  2.33  0.092  0.052  0.332  1.629  0.216  0.052 
LZETPgrass  0.138  0.1  0.9  0.239  0.027  0.238  0.138  −0.860  0.027 
LZETPRforest  1.5  1.5  3.6  0.095  0.050  0.326  1.500  0.196  0.030 
A suffix “R” to a parameter in forest land cover type means the parameter is a ratio of the grassland value. See
Computed from untransformed values.
Computed from log_{10}transformed values.
The PREDUNC7 input stdev was computed as log_{10}(Upper bound)/(Lower bound))/4.
In comparing the parameter standard deviations before and after calibration as calculated by PREDUNC7 (
The standard deviations of the sampled random parameters provide a check on the accuracy of the sampling process. The values are about the same or up to about 30 percent smaller than the standard deviations of the posterior parameters. The reduction in the sampled standard deviations likely results because of trimming as the sampling is performed on the assumption of a multivariate Gaussian distribution applied to the log_{10}transformed parameter values. After backtransforming to real space, the values outside the parameter bounds are trimmed to the bounds.
As described previously, the underlying parameter uncertainties as estimated using PREDUNC7 are characterized by covariance matrices from which the standard deviations that are presented were abstracted. The offdiagonal terms of these matrices (not shown) include some significant correlations that are of interest for understanding the modelparameter interactions. A detailed analysis of these is beyond the scope of this study, but to summarize, the most common significant correlations are those on the order of −0.5, which are common but not universal among forestgrassland parameter pairs such as KVARYforest and KVARYgrass. These correlations indicate that when the value for one landuse type goes up, the other goes down, indicating difficulty in identifying which land use to associate with some aspect of the calibration data, which is expected given that both calibration watersheds are mixtures of landuse types. A few parameters have significant correlations of at least 0.45 in absolute value beyond their landuse type pairing; most prominent among these is INFILTgrass, the primary infiltration parameter, which is negatively correlated with INTFWgrass and UZSNgrass, which parameterize interflow and the upper zone soil storage, which are processes closely connected with infiltration. INFILTgrass is also positively correlated with DEEPFRgrass and AGWETPgrass, which are the fraction of water lost to inactive groundwater and the fraction of land segment subject to direct evaporation from groundwater storage. All these processes are connected through the soilwater balance, so these correlations would be expected; however, they are not typically present for other parameters. For example, the parameter corresponding forest infiltration parameter INFILTRforest does not have such correlations.
To investigate how the simulated discharge could vary because of possible variations in published discharge records through the use of LMDA HSPF modeling, two sources of uncertainty are considered: (1) the effect of the uncertainty of the published discharge that is characterized by 17 HSPF simulations each based on a parameter set obtained from recalibration to a random realization that characterizes the uncertainty of the published discharge, and (2) uncertainty of the basemodel calibration parameter set characterized by 1,000 simulations from parameters sampled from its estimated covariance matrix. For a flow statistic
The central tendency and the range of variability of statistics of the simulations can be expressed dimensionlessly by considering them as fractions of their corresponding observed values. Using the median as the measure of the central tendency, these dimensionless statistics are
is the median of the vector of simulation flow statistics; and
is the observed value of the statistic.
The conditions
To assess how large the simulation range, which characterizes magnitude of the uncertainty of associated error source, is relative to the error in the simulation, the two error indices,
is the range of simulated values of
is the median of the vector of simulation flow statistics; and
is the observed value of the statistic.
The range
Typically, simulationtoobservation errors have multiple sources, and if the range of variability of
The relative variability of the two sets of simulations as measured by
In this section, the HSPF discharge simulations based on the parameters recalibrated to the 17 pairs of uncertain published discharge and the 1,000 simulations based on sampling the uncertainty of the basemodel parameters are compared to the published discharge, and to a lesser extent, the basemodel discharge at the calibration watersheds. The discussion of the results considers the POS mean discharge, selected FDC quantiles, and WY mean discharge flow statistics, focusing on the comparison of the medians of the two sets of simulations with the observed values and on the resulting
The POS mean discharges of the HSPF simulations using parameters recalibrated to the 17 pairs of discharge series characterizing the published discharge uncertainty (recalibratedQs), and the HSPF simulations using the 1,000 randomly generated parameter sets characterizing the uncertainty of the basemodel parameters (randomQs) from the Tinley Creek and Long Run watersheds are plotted (
Table 13. Statistics of the means of daily discharge of the period of study obtained from published discharge records, and Hydrological Simulation Program–FORTRAN simulated discharge series with basemodel parameters, with recalibrated parameters that characterize uncertainty of published discharge, and with random parameters that characterize the uncertainty of the basemodel parameters for the Tinley Creek and Long Run watersheds.
[Units are in cubic feet per second except Median / obsQ, Relative median error, and
Watershed  ObsQ mean  BaseQ mean  RecalibratedQs  RandomQs  
Min  Max  Median  Median / obsQ  Relative median error  2.5%  97.5%  Median  Median / obsQ  Relative median error  
Tinley Creek  14.9  14.6  13.9  14.6  14.5  0.97  0.028  0.787  14.4  14.6  14.5  0.97  0.026  0.335 
Long Run  24.6  26.1  24.8  25.9  25.8  1.05  0.049  0.443  25.6  26.1  25.9  1.05  0.054  0.191 
For the recalibratedQs, one consideration is if the simulated POS mean discharges reflect the mean discharges of the pairs of BaRatin SPD realizations used for recalibration (
It is of interest that the range of observed discharges being used for the recalibrations (14.1–16.0 ft^{3}/s at Tinley Creek streamgage and 22.9–26.5 ft^{3}/s at Long Run streamgage; bottom row of
The POS mean discharges of the 1,000 randomQs from the Tinley Creek watershed plotted with the means from the Long Run watershed (
Relations between period of study (water years 1997–2015) daily discharges at Tinley Creek and Long Run watersheds simulated by Hydrological Simulation Program–FORTRAN.
Figure 10. Graphs showing relations between period of study (water years 1997–2015) daily discharges at Tinley Creek and Long Run watersheds simulated by Hydrological Simulation Program–FORTRAN.
Considering the POS mean discharges of the two sets of simulations as collections of values characterizing the two sources of uncertainty, statistics of these collections and their relation to the observed mean discharge are presented in
Another flow characteristic commonly used to assess model fit is the FDCs of daily discharge, which can be viewed as the disaggregation of the POS mean discharge into daily magnitude bins and their associated frequencies. Summary statistics of selected FDC nonexceedance probability percentiles computed from obsQ, recalibratedQs, and randomQs daily discharges are presented in
Table 14. Statistics of selected nonexceedance probability percentiles of flowduration curves derived from published discharge records and Hydrological Simulation Program–FORTRAN simulated discharge at Tinley Creek watershed.
[ObsQ, published discharge records; ft^{3}/s, cubic feet per second;
Percentile  ObsQ (ft^{3}/s)  RecalibratedQs  RandomQs  
Median / obsQ  Relative median error  Median / obsQ  Relative median error  
1  0.20  0.002  0.998  0.00059  0.003  0.997  0.0401 
5  0.50  0.604  0.396  0.121  0.585  0.415  0.266 
10  0.80  0.803  0.197  0.227  0.771  0.229  0.303 
20  1.50  0.871  0.129  0.229  0.838  0.162  0.328 
25  1.90  0.895  0.105  0.341  0.864  0.136  0.347 
50  4.50  0.932  0.068  0.431  0.907  0.093  0.322 
75  12  0.956  0.044  0.508  0.939  0.061  0.308 
80  15  1.009  0.009  2.193  0.995  0.005  4.784 
90  32  1.028  0.028  0.599  1.034  0.034  0.238 
95  60  1.004  0.004  4.618  1.013  0.013  0.682 
99  186  0.890  0.110  0.308  0.898  0.102  0.129 
NA  NA  NA  0.341  NA  NA  0.308 
Table 15. Statistics of selected nonexceedance probability percentiles of flowduration curves derived from published discharge records and Hydrological Simulation Program–FORTRAN simulated discharge at Long Run watershed.
[ObsQ, published discharge records; ft^{3}/s, cubic feet per second;
Percentile  ObsQ (ft^{3}/s)  RecalibratedQs  RandomQs  
Median / obsQ  Relative median error  Median / obsQ  Relative median error  
1  0.80  0.036  0.964  0.00161  0.033  0.967  0.0385 
5  1.30  0.619  0.381  0.077  0.585  0.415  0.197 
10  1.90  0.846  0.154  0.215  0.810  0.190  0.286 
20  3.00  0.973  0.027  0.753  0.938  0.062  0.660 
25  3.60  1.012  0.012  2.461  0.966  0.034  1.376 
50  8.80  0.962  0.038  0.688  0.925  0.075  0.431 
75  21  1.028  0.028  0.738  1.006  0.006  4.259 
80  27  1.045  0.045  0.603  1.021  0.021  1.061 
90  54  1.066  0.066  0.329  1.061  0.061  0.203 
95  93  1.115  0.115  0.180  1.121  0.121  0.099 
99  275  1.023  0.023  1.277  1.059  0.059  0.333 
NA  NA  NA  0.603  NA  NA  0.333 
The relative median error is very high, nearly 100 percent, for the 1st percentile, but then drops quickly for both parameter sets and for both watersheds. At the Tinley Creek streamgage, the lowest relative median error is 0.4 percent for the recalibratedQs and 1.3 percent for the randomQs; the highest relative median error excluding the 1st percentile is 39.6 percent for the recalibratedQs and 41.5 percent for the randomQs (
The normalized variability index (
The WY mean discharges can be viewed as the disaggregation of the POS mean discharge to annual time steps. These discharges for the obsQs, baseQs, recalibratedQs, and randomQs for the Tinley Creek and Long Run watersheds are presented in
Table 16. Water year (WY) mean discharge of published discharge records and statistics of WY mean discharge of simulated discharge based on recalibrated and random parameters at the Tinley Creek watershed.
[WY, water year; USGS, U.S. Geological Survey; no., number; ObsQ, published daily discharge records; ft^{3}/s, cubic feet per second; RecalibratedQs, discharge series simulated with the recalibrated parameters; RandomQs, discharge series simulated with random parameters;
WY  USGS rating curve no.  ObsQ (ft^{3}/s)  RecalibratedQs  RandomQs  
Median / obsQ  Relative median error  Median / obsQ  Relative median error  
1997  24  14.31  1.084  0.08  0.221  1.085  0.08  0.117 
1998  24  15.69  0.974  0.03  0.847  0.976  0.02  0.404 
1999  24  16.06  0.870  0.13  0.137  0.872  0.13  0.060 
2000  24,25  14.03  0.910  0.09  0.276  0.915  0.09  0.115 
2001  25  13.33  0.958  0.04  0.538  0.959  0.04  0.222 
2002  25  14.04  0.810  0.19  0.093  0.810  0.19  0.043 
2003  25  9.05  0.869  0.13  0.206  0.871  0.13  0.083 
2004  25  16.51  0.868  0.13  0.158  0.870  0.13  0.068 
2005  25  10.60  1.043  0.04  0.559  1.039  0.04  0.278 
2006  25  12.59  1.016  0.02  1.883  1.018  0.02  0.698 
2007  25  18.66  0.998  0.00  8.384  0.998  0.00  5.815 
2008  25,26  17.28  1.158  0.16  0.168  1.160  0.16  0.063 
2009  26  17.81  1.138  0.14  0.114  1.138  0.14  0.067 
2010  26  15.58  1.337  0.34  0.077  1.341  0.34  0.032 
2011  26  16.01  1.067  0.07  0.367  1.071  0.07  0.127 
2012  26  10.78  0.904  0.10  0.260  0.904  0.10  0.105 
2013  26,27  15.33  0.895  0.11  0.246  0.895  0.10  0.084 
2014  27  21.24  0.778  0.22  0.091  0.781  0.22  0.031 
2015  27  14.33  0.756  0.24  0.072  0.758  0.24  0.031 
NA  NA  NA  NA  0.233  NA  NA  0.094 
Table 17. Water year (WY) mean discharge of published discharge records and statistics of WY mean discharge of simulated discharge based on recalibrated and random parameters at Long Run watershed.
[WY, water year; USGS, U.S. Geological Survey; no., number; ObsQ, published discharge records; ft^{3}/s, cubic feet per second; RecalibratedQs, discharge series simulated with the recalibrated parameters; RandomQs, discharge series simulated with random parameters;
WY  USGS rating curve no.  ObsQ (ft^{3}/s)  RecalibratedQs  RandomQs  
Median / obsQ  Relative median error  Median / obsQ  Relative median error  
1997  28  18.83  1.613  0.61  0.037  1.617  0.62  0.026 
1998  28,29  23.88  1.195  0.19  0.130  1.201  0.20  0.063 
1999  29  25.29  1.023  0.02  0.799  1.029  0.03  0.343 
2000  29  20.69  1.016  0.02  1.421  1.024  0.02  0.548 
2001  29,30  17.71  1.279  0.28  0.117  1.284  0.28  0.048 
2002  30,31  22.48  0.980  0.02  0.936  0.982  0.02  0.576 
2003  31  12.68  1.344  0.34  0.115  1.354  0.35  0.046 
2004  31  25.51  1.113  0.11  0.212  1.120  0.12  0.095 
2005  31  18.42  1.095  0.09  0.240  1.092  0.09  0.140 
2006  31  15.97  1.323  0.32  0.112  1.331  0.33  0.055 
2007  31  39.79  0.823  0.18  0.076  0.825  0.18  0.047 
2008  31  34.27  1.043  0.04  0.497  1.048  0.05  0.202 
2009  31  37.22  0.902  0.10  0.117  0.905  0.10  0.087 
2010  31  33.48  1.109  0.11  0.177  1.114  0.11  0.088 
2011  31,32  32.70  0.957  0.04  0.489  0.964  0.04  0.249 
2012  32  15.66  1.030  0.03  0.933  1.034  0.03  0.383 
2013  32  22.18  1.029  0.03  1.023  1.033  0.03  0.342 
2014  32  28.81  0.891  0.11  0.190  0.898  0.10  0.087 
2015  32  21.06  0.823  0.18  0.107  0.828  0.17  0.054 
NA  NA  NA  NA  0.201  NA  NA  0.092 
At Tinley Creek, the range of the recalibratedQ WY mean discharges encloses the obsQ WY mean for 3 years, overestimates the obsQ mean for 5 years, and underestimates the obsQ mean for 11 years (
The
Water year (WY) mean discharges from Hydrological Simulation Program–FORTRAN simulations and published daily discharges for WYs 1997–2015.
Figure 11. Water year (WY) mean discharges from Hydrological Simulation Program–FORTRAN simulations and published daily discharges for WYs 1997–2015.
Applying the recalibrated and random parameter sets to the seven prediction watersheds provides an opportunity to evaluate the transferability of regional parameters at noncalibration locations where the characteristics of climatic forcing, watershed properties, and measured discharge are different from those used in calibration. Thus, this application gives an indication of the fraction of the prediction error that the processes considered in this report, calibration discharge uncertainty and parameter uncertainty, can explain at ungaged sites. In addition to the inherent differences between calibration and prediction sites (that is, that the parameters of the model had been adjusted to account for the various model and input errors at the calibration watersheds but not the prediction watersheds), there are a few special considerations regarding why the prediction errors may increase at the prediction sites used in this study:
The sites are located on the border of or outside the CCPN coverage; therefore, precipitation inputs were supplemented with the use of disaggregated data from NWS–COOP daily stations (see “Watersheds and ModelInput Data” section).
Although the prediction watersheds have published discharge computed using the same basic approach as the calibration watersheds (that is, using a stagedischarge rating), and therefore may be expected to have a similar errors, the Hart Ditch at Munster streamgage (
The Flag Creek, Hickory Creek, Hart Ditch at Dyer, and Hart Ditch at Munster streamgages have effluent discharges added to their simulated values. The hourly effluent discharges were approximated from their reported monthly data using a uniform distribution and therefore are less accurate (
The Midlothian Creek, Hickory Creek, and Butterfield Creek watersheds have reservoirs that were not explicitly simulated (as does Long Run) (
As discussed in the “Uncertainty of Simulated Discharge at Calibration Watersheds” section, the discussion of the results at the prediction watersheds will focus on the
The presentation of the results on uncertainty of simulated discharge begins with the POS mean discharge. The published POS mean discharge (obsQ), median/obsQ ratio, relative median error, and
Table 18. Published period of study (POS) mean discharge and statistics of POS mean discharge simulated with Hydrological Simulation Program–FORTRAN using the recalibrated and random parameters at the seven prediction watersheds.
[Units are in cubic feet per second, except Median / ObsQ, Relative median error, and
Watershed  ObsQ (ft^{3}/s)  RecalibratedQs  RandomQs  
Min  Max  Median  Median / obsQ  Relative median error  2.5%  97.5%  Median  Median / obsQ  Relative median error  
Butterfield Creek  22.6  30.0  30.8  30.7  1.358  0.36  0.052  30.5  31.0  30.9  1.365  0.36  0.035 
Hart Ditch at Dyer  41.4  31.4  33.5  33.3  0.805  0.20  0.133  32.9  33.9  33.5  0.810  0.19  0.060 
Flag Creek  32.3  38.8  39.2  39.1  1.209  0.21  0.029  39.0  39.3  39.2  1.212  0.21  0.026 
Hickory Creek  125.4  137.7  142.5  141.9  1.132  0.13  0.144  140.9  143.5  142.6  1.138  0.14  0.075 
Midlothian Creek  16.9  17.5  17.9  17.9  1.056  0.06  0.248  17.8  18.0  17.9  1.060  0.06  0.131 
Hart Ditch at Munster  97.8  85.8  89.3  88.9  0.908  0.09  0.191  88.2  89.8  89.3  0.913  0.09  0.094 
Skokie River  24.8  29.2  30.1  30.0  1.211  0.21  0.089  29.8  30.3  30.1  1.216  0.22  0.046 
Tinley Creek^{1}  14.9  13.9  14.6  14.5  0.972  0.03  0.787  14.4  14.6  14.5  0.974  0.03  0.335 
Long Run^{1}  24.6  24.8  25.9  25.8  1.049  0.05  0.443  25.6  26.1  25.9  1.054  0.05  0.191 
Calibration watershed.
Regarding the FDC results at the prediction watersheds, to focus the discussion on explaining the predictive errors, only the
Table 19. Normalized variability index of discharge magnitudes at selected nonexceedance probability percentiles of the flowduration curves at the seven prediction watersheds for water years 1997 to 2015 based on Hydrological Simulation Program–FORTRAN simulations.
[Watershed locations shown in
Percentile  RecalibratedQs  RandomQs  
Butterfield Creek  Hart Ditch at Dyer  Flag Creek  Hickory Creek  Midlothian Creek  Hart Ditch at Munster  Skokie River  Butterfield Creek  Hart Ditch at Dyer  Flag Creek  Hickory Creek  Midlothian Creek  Hart Ditch at Munster  Skokie River  
1  0.197  0.003  0.000  0.124  3.73E−05  0.016  0.010  15.436  0.015  0.011  0.433  0.007  0.108  0.173 
5  0.023  0.008  0.011  0.104  0.028  0.297  0.235  0.270  0.038  0.034  0.274  0.165  1.646  2.001 
10  0.045  0.038  0.010  0.053  0.106  0.388  0.570  0.179  0.082  0.046  0.140  0.203  1.744  4.702 
20  0.045  0.172  0.016  0.056  0.232  4.009  0.201  0.142  0.229  0.055  0.127  0.411  0.925  0.404 
25  0.041  0.230  0.013  0.076  0.331  17.640  0.244  0.121  0.260  0.046  0.136  0.454  1.155  0.357 
50  0.065  1.280  0.017  0.054  0.149  0.606  0.082  0.164  2.316  0.044  0.108  0.198  0.441  0.135 
75  0.057  0.325  0.028  0.153  0.216  0.596  0.175  0.120  0.226  0.066  0.201  0.249  1.076  0.242 
80  0.042  0.275  0.039  0.168  0.164  0.541  0.126  0.061  0.178  0.076  0.183  0.121  0.920  0.119 
90  0.041  0.095  0.019  0.152  0.096  0.175  0.056  0.033  0.048  0.032  0.095  0.078  0.096  0.034 
95  0.042  0.061  0.019  0.194  0.088  0.091  0.034  0.028  0.033  0.040  0.117  0.050  0.070  0.022 
99  0.168  0.221  0.058  0.675  0.061  0.065  0.230  0.110  0.125  0.056  0.365  0.039  0.053  0.067 
0.045  0.172  0.017  0.124  0.106  0.388  0.175  0.121  0.125  0.046  0.140  0.165  0.920  0.173 
An indication of the temporal structure of the variability and accuracy of the two simulation sets for the prediction watersheds can be obtained from examining the annual mean discharges. WY mean discharges from WY 1997 to 2015 based on the published discharge records and simulated discharge from recalibratedQs and randomQs are presented in
The
Table 20. Normalized variability index values of water year (WY) mean discharges from WY 1997 to 2015 at the seven prediction watersheds based on Hydrological Simulation Program–FORTRAN simulations.
[Watershed locations shown in
WY  RecalibratedQs  RandomQs  
Butterfield Creek  Hart Ditch at Dyer  Flag Creek  Hickory Creek  Midlothian Creek  Hart Ditch at Munster  Skokie River  Butterfield Creek  Hart Ditch at Dyer  Flag Creek  Hickory Creek  Midlothian Creek  Hart Ditch at Munster  Skokie River  
1997  0.029  0.937  0.017  0.038  0.096  0.207  0.027  0.026  0.435  0.022  0.026  0.076  0.138  0.019 
1998  0.043  0.211  0.022  0.095  0.654  0.070  0.962  0.034  0.096  0.021  0.058  0.367  0.036  0.703 
1999  0.045  0.030  0.044  0.075  0.170  0.023  3.437  0.032  0.013  0.040  0.042  0.091  0.011  0.785 
2000  0.032  0.088  0.032  0.055  0.371  7.721  0.380  0.026  0.072  0.038  0.035  0.196  6.509  0.188 
2001  0.044  0.171  0.030  0.080  0.275  0.142  0.168  0.028  0.080  0.024  0.042  0.148  0.062  0.087 
2002  0.080  0.079  0.030  0.048  0.172  0.063  0.098  0.065  0.047  0.032  0.030  0.118  0.041  0.053 
2003  0.039  0.252  0.031  0.379  0.346  0.129  1.706  0.028  0.104  0.023  0.214  0.208  0.056  1.365 
2004  0.045  0.136  0.029  0.417  0.170  0.229  0.094  0.028  0.074  0.025  0.201  0.089  0.121  0.051 
2005  0.046  0.035  0.026  0.141  0.138  0.021  0.060  0.033  0.023  0.025  0.086  0.092  0.012  0.036 
2006  0.043  0.126  0.025  0.081  0.076  0.368  0.263  0.031  0.062  0.024  0.045  0.044  0.166  0.157 
2007  0.980  0.025  0.029  0.284  0.067  0.053  0.060  0.706  0.009  0.033  0.215  0.051  0.028  0.040 
2008  0.060  0.057  0.020  0.128  0.241  0.148  0.039  0.039  0.028  0.020  0.065  0.126  0.071  0.020 
2009  0.069  0.078  0.022  0.236  0.152  0.113  0.081  0.057  0.043  0.028  0.158  0.113  0.070  0.053 
2010  0.041  0.484  0.024  0.089  0.061  0.178  0.104  0.032  0.261  0.028  0.055  0.040  0.085  0.057 
2011  0.062  0.838  0.019  0.363  2.532  0.313  0.044  0.042  0.464  0.018  0.163  0.682  0.135  0.023 
2012  0.054  0.114  0.031  0.196  0.174  1.244  0.085  0.039  0.053  0.025  0.109  0.095  0.511  0.043 
2013  0.071  0.174  0.088  0.253  0.496  0.075  0.096  0.037  0.062  0.057  0.098  0.195  0.029  0.042 
2014  0.057  0.155  0.056  0.177  0.244  0.079  0.145  0.036  0.065  0.044  0.081  0.130  0.036  0.071 
2015  0.117  0.062  0.127  0.125  0.048  0.168  0.351  0.075  0.031  0.098  0.066  0.031  0.092  0.135 
0.046  0.126  0.029  0.128  0.172  0.142  0.098  0.034  0.062  0.025  0.066  0.113  0.070  0.053 
The
Water year (WY) mean discharges from Hydrological Simulation Program–FORTRAN simulations and from published daily discharges for WYs 19972015, computed with the base model and 17 recalibrated parameters that characterize uncertainty of published discharge (left column) and with 1,000 randomly sampled parameter sets that characterize the uncertainty of the basemodel parameters (right column).
Figure 12. Graphs showing water year (WY) mean discharges from Hydrological Simulation Program–FORTRAN simulations and from published daily discharges for WYs 1997–2015, computed with the base model and 17 recalibrated parameters that characterize uncertainty of published discharge and with 1,000 randomly sampled parameter sets that characterize the uncertainty of the basemodel parameters.
A Lake Michigan Diversion Accounting (LMDA) system for estimating the volume of water diverted annually from Lake Michigan by the State of Illinois has been developed by U.S. Army Corps of EngineersChicago District. Discharge from the diverted Lake Michigan watershed in northeastern Illinois and northwestern Indiana, approximately 673 square miles (mi^{2}), has been estimated with the Hydrological Simulation Program–FORTRAN (HSPF) because most catchments in the diverted watershed are ungaged. This report presents a study of two components of the overall uncertainty of prediction in the ungaged watersheds. One component is the effect of the uncertainty of the published discharge records used for calibrating the HSPF parameters. The other component is the uncertainty of simulated discharge resulting from the uncertainty of the parameters. A twowatershed calibration scheme developed previously is used to determine parameters that minimize an objective function that is computed using discharge records from two calibration watersheds. The Parameter ESTimation and uncertainty analysis (PEST) package is applied for optimizing the parameters. The uncertainty components are investigated at nine gaged watersheds in or near the diverted watershed. Tinley Creek and Long Run in Illinois are the calibration watersheds, and Flag Creek, Skokie River, Butterfield Creek, Midlothian Creek, and Hickory Creek, all in Illinois, and Hart Ditch at Dyer and Hart Ditch at Munster in Indiana are used as prediction watersheds.
In the HSPF calibration, only the parameters used for simulating runoff from the pervious areas of the watersheds were adjusted in this study. The pervious areas were assigned two landcover types, forest and grassland. Each is modeled with a set of 17 adjustable parameters. The resulting set of 34 parameters were calibrated jointly at the two calibration watersheds.
The uncertainty of published daily discharge originates from the rating curves used for converting measured stages to discharges at a streamgage. At the calibration watershed streamgages, the uncertainty is computed by adapting the Bayesian rating curve estimation (BaRatin) method with a StagePeriodDischarge (SPD) extension, which provides rating curves, their uncertainties, and the uncertainties of computed discharges given a sequence of known rating curve periods. The BaRatin SPD analysis provided a set of 500 equally likely discharge realizations, from which uncertainty statistics were computed. As a ratio of standard deviation to the mean, that is, as the coefficient of variation (CV), the published daily discharge uncertainty of the mean discharge of the period used in applying the technique, water years (WYs) 1995–2016, was estimated to be about 3 percent at both streamgages.
To characterize the effects of the uncertainty of published daily discharge records on the pervious land parameters, 17 pairs of BaRatin SPD discharge series realizations, which span the 1percent to 99percent quantiles of mean discharge for the two calibration watersheds during the period used in HSPF simulations, WYs 1996–2015, were selected to use for recalibration. These few realizations were selected because the calibration technique is computationally intensive and dependent on expert judgement.
Uncertainty of the HSPF model parameters was also estimated by a Bayesian technique, applying a utility program provided with PEST to the pre and postoptimization parameters of the base model, which is the model whose calibration discharges are the published daily discharge records at the two calibration streamgages. The result was an estimated parameter covariance matrix, from which 1,000 parameter sets were sampled and used for simulation, to estimate the effects of the parameter uncertainty on simulated discharge.
As a result of the different Bayesian techniques applied in the uncertainty analyses, in particular the nonrandom sampling of the uncertain discharge realizations, the uncertainties predicted by the two sets of simulations could not be added but instead were analyzed separately using a common normalized variability index (
At the calibration watersheds, for both sets of simulations, the median simulation POS mean discharges had opposite errors because of the twowatershed calibration scheme balancing errors between the watersheds: the Long Run watershed had a higher simulated mean than observed and the Tinley Creek watershed had a lower simulated mean than observed. The results for the other flow statistics considered, FDCs and WY mean discharges, were consistent with the overall bias, but the bias was not uniform. At the Tinley Creek streamgage, the FDC quantiles of the simulations were biased low at all but the lowest quantiles, although slightly high at the highest. At the Long Run streamgage the results were similar but the quantiles where these biases occurred were shifted upward. For the WY mean discharges at each watershed, high bias was noted for a group of years, and low bias was noted for another group of years, but these groups of years were not the same between the two watersheds. The Tinley Creek watershed, consistent with its longterm low discharge bias, had more undersimulated years and the Long Run watershed had more oversimulated years.
At the calibration watersheds for both sets of simulations, the
At the seven prediction watersheds for both sets of simulations, it was observed that the relative median errors in POS mean discharges at these watersheds, ranging from 6 to 36 percent, were larger than those at the calibration watersheds, being 3 and 5 percent at Tinley Creek and Long Run watersheds, respectively. In agreement with their larger median errors, the corresponding
The ranking of the
The
For more information about this publication, contact:
Director, USGS Central Midwest Water Science Center
405 North Goodwin
Urbana, IL 61801
217–328–8747
For additional information, visit:
Publishing support provided by the
Rolla Publishing Service Center