Abstract

A hybrid hydrologic model (lumped conceptual and distributed feature model), Distributed-Clark, is introduced to perform hydrologic simulations using spatially distributed NEXRAD quantitative precipitation estimations (QPEs). In Distributed-Clark, spatially distributed excess rainfall estimated with the Soil Conservation Service (SCS) curve number method and a GIS-based set of separated unit hydrographs are utilized to calculate a direct runoff flow hydrograph. This simple approach using few modeling parameters reduces calibration complexity relative to physically based distributed (PBD) models by only focusing on integrated flow estimation at watershed outlets. Case studies assessed the quality of NEXRAD stage IV QPEs for hydrologic simulation compared to gauge-only analyses. NEXRAD data validation against rain gauge observations and performance evaluation with model simulation result comparisons for inputs of spatially distributed stage IV and spatially averaged gauged data for four study watersheds were conducted. Results show significant differences in NEXRAD QPEs and gauged rainfall amounts, with NEXRAD data overestimated by 7.5% and 9.1% and underestimated by 15.0% and 11.4% accompanied by spatial variability. These differences affect model performance in hydrologic applications. Rainfall–runoff flow simulations using spatially distributed NEXRAD stage IV QPEs demonstrate relatively good fit [direct runoff: Nash–Sutcliffe efficiency ENS = 0.85, coefficient of determination R2 = 0.89, and percent bias (PBIAS) = 3.92%; streamflow: ENS = 0.91, R2 = 0.93, and PBIAS = 1.87%] against observed flow as well as better fit (ENS of 3.7% and R2 of 6.0% increase in direct runoff) than spatially averaged gauged rainfall for the same model calibration approach, enabling improved estimates of flow volumes and peak rates that can be underestimated in hydrologic simulations for spatially averaged rainfall.

1. Introduction

Precipitation is one of the primary inputs for hydrological modeling and related fields of work. As a grand effort to enhance precipitation estimation procedures, the National Weather Service (NWS) deployed a nationwide network of Weather Surveillance Rader-1988 Doppler (WSR-88D) radars (over 160) under the Next Generation Weather Radar (NEXRAD) program during the 1990s (Hudlow and Smith 1989; Crum and Alberty 1993; Fulton et al. 1998). In the data processing steps of Precipitation Processing System (PPS), which is one of the radar product generators, stage I generates hourly digital precipitation (HDP) [now labeled digital precipitation array (DPA)] accumulations from WSR-88D reflectivity data, performing quality control with limited gauge data incorporation. Stage II uses additional gauge and satellite data to produce individual multisensor precipitation estimates (MPEs), and the NWS River Forecast Centers (RFCs) make stage III products (regional MPEs), which are mosaicked from stage II data with additional quality control and use of additional gauge data (Shedd and Fulton 1993; Fulton et al. 1998). In late 2001, the NWS/National Centers for Environmental Prediction (NCEP) began to routinely generate “NCEP stage IV” quantitative precipitation estimation (QPE) products mosaicked from the 12 RFCs’ regional multisensor data covering the entire continental United States (CONUS; Lin and Mitchell 2005).

NEXRAD QPE products have been used by scientists and engineers for various purposes, particularly for GIS-based watershed-scale hydrologic model application improvement, because of their ability to characterize spatial variability. They can capture localized storms that completely miss rain gauges (Reed and Maidment 1999; Young et al. 2000). However, to be used in conjunction with other geospatial products, the Hydrologic Rainfall Analysis Project (HRAP) grid (which is a rectangular grid of approximately 4 km × 4 km and defined in a polar stereographic map projection using a spherical Earth datum) precipitation data have to be translated into regular grid-based data that use an appropriate map projection system (Reed and Maidment 1995, 1999). In 1995 the U.S. Army Corps of Engineers (USACE) Hydrologic Engineering Center (HEC) proposed the use of a standard hydrologic grid (SHG), whose map system is the Albers equal-area projection. Then, a series of utility programs were also developed [e.g., Hydrologic Engineering Center’s Data Storage System Visual Utility Engine (HEC-DSSVue) and Hydrologic Engineering Center’s Grid Utility program (HEC-GridUtil); USACE 2009, 2011, 2013], but are only applicable in HEC software. On the other hand, Nelson et al. (2003) developed a data browser in a GIS platform instead as a processing tool for radar rainfall data, using a cylindrical equidistant project as a map projection. Similarly, Xie et al. (2005) introduced automated NEXRAD stage III precipitation data processing approaches for GIS-based data integration and visualization with the universal transverse Mercator (UTM) coordinate system. Zhang and Srinivasan (2010) also developed GIS software for NEXRAD data (stage III; MPEs) processing, taking into account NEXRAD data’s validation and calibration using rain gauge data, and its processing automation for hydrological and ecological model applications.

With regard to applications of NEXRAD QPEs in hydrological modeling, there have been considerable works whose programs can be termed physically based distributed (PBD) models. The Cascade Two-Dimensional model (CASC2D), a physically based distributed parameter hydrologic model, was used with radar rainfall for runoff model sensitivity to radar precipitation data resolution issues (Ogden and Julien 1994) and hydrologic analyses of flash floods that are caused by intense thunderstorms moving across partial areas of a watershed (Julien et al. 1995; Ogden et al. 2000). The Gridded Surface Subsurface Hydrologic Analysis (GSSHA) model (Ogden et al. 2003), which is a physically based, distributed parameter, structured grid, hydrologic model and a significant reformulation and enhancement of CASC2D, was also utilized with NEXRAD products for their case studies of an extreme flood simulation (Sharif et al. 2010) and comparison of the model results with gauge and satellite precipitation data (Chintalapudi et al. 2012). In addition, the NWS formulated and initiated the Distributed Model Intercomparison Project (DMIP) to improve river and flash flood forecasting with distributed models that utilized information from high-resolution radar rainfall estimates and GIS datasets (Reed et al. 2004; Smith et al. 2012). In this project, the NWS provided required data for hydrologic modeling, including the use of NEXRAD QPEs. Twelve [DMIP, phase 1 (DMIP1)] and 16 [DMIP, phase 2 (DMIP2)] hydrologic models were involved and demonstrated model performance against NEXRAD data (MPEs) applications. Representative models are as follows:

  1. The Hydrology Laboratory Research Modeling System (HL-RMS)/Hydrology Laboratory Research Distributed Hydrologic Model (HL-RDHM; NWS’s operational model for DMIP1/DMIP2) employ the Sacramento Soil Moisture Accounting (SAC-SMA) lumped water balance model and the kinematic wave for hillslope–channel routing; it is a physically based conceptual model (Koren et al. 2004).

  2. The Hydrologic Research Center Distributed Hydrologic Model (HRCDHM) has a method similar to HL-RMS; it is a catchment-based distributed model (Carpenter et al. 2001; Carpenter and Georgakakos 2004).

  3. The Triangulated Irregular Network (TIN)-Based Real-Time Integrated Basin Simulator (tRIBS) simulates the soil moisture profile with topographically driven, lateral, element-to-element interaction as well as kinematic wave routing; it is a physically based, fully distributed model (Ivanov et al. 2004).

  4. TOPNET adopts the physically based variable contributing area for the soil moisture deficit calculation with kinematic wave routing; it is a distributed version of TOPMODEL (Beven and Kirkby 1979; Bandaragoda et al. 2004).

  5. The Hydrologic Simulation Program–Fortran (HSPF) uses soil moisture storage concepts and Muskingum channel routing; it is a conceptual semidistributed model (Ryu 2009).

In general, all models above performed well using NEXRAD QPEs, with performance that is acceptable in engineering hydrology. In the particular cases of DMIP, the lumped model (HL-RMS/HL-RDHM) outperformed distributed models in more cases (Reed et al. 2004; Smith et al. 2012), but it was not possible to determine which model had better overall performance. This was because some distributed models provided improved hydrograph simulations compared to a lumped model, whereas some uncalibrated distributed and lumped models performed better than other calibrated distributed models. However, since PBD models typically consider hydrologic processes taking place at various points in space and define the model variables as functions of the space dimensions (Chow et al. 1988), these models may require more complex and tedious procedures for input data preparation and model parameterization and computation than lumped models. Also, PBD model calibration is still largely based on approaches using a priori parameter values from field observation and previous studies with a basinwide scalar multiplication. Such cases limit potential improvement gained by calibration of internal basins when climate/physical properties and their uncertainties vary significantly (Smith et al. 2012). Thus, parameter estimation (model calibration) and uncertainty evaluation become major tasks in watershed-scale hydrological modeling (Koren et al. 2004; Vieux 2004; Smith et al. 2012). In addition, even though PBD models can calculate interior points–based flow interactions, they would not be useful for the following cases relative to their complexity: 1) the modeling target is only to provide an integrated flow at the watershed outlet and 2) few interior flow gauges exist within the watershed to calibrate simulation results. Hence, a watershed model, which is relatively simple (few parameters and straightforward computations) but that can utilize state-of-the-art information (e.g., spatially distributed, gridded data), is needed to reduce the model parametric uncertainty and to avoid time-consuming model calibration.

In this study, we introduce a simple hydrological modeling approach, a GIS-based spatially distributed Clark’s unit hydrograph method (Distributed-Clark; hybrid hydrologic model; Cho 2016) to use spatially distributed NEXRAD QPEs for storm event flow simulation in a GIS platform, including development of an automation tool for NEXRAD data processing to create regular grid-based spatiotemporally varied rainfall data, particularly using NEXRAD stage IV QPE products. Then, to assess the quality of stage IV QPEs for hydrologic simulation relative to gauge-only analyses, NEXRAD QPE data validation with available rain gauge data and model simulation performance comparisons against observed streamflow for spatially distributed NEXRAD stage IV and spatially averaged gauged data inputs are investigated.

2. Model description

a. Hybrid hydrologic model (Distributed-Clark)

Distributed-Clark, a GIS-based spatially distributed unit hydrograph method using Clark (1945), adopts a simple approach for the implementation of spatially distributed rainfall–runoff routing (flow simulation) based on the combined concept of unit hydrograph in Clark (1945) and its spatial decomposition methods (Maidment et al. 1996); it is a lumped conceptual and distributed feature model (hybrid hydrologic model; DeVantier and Feldman 1993; Cho 2016). In Distributed-Clark, the Soil Conservation Service (SCS) runoff curve number (CN) approach (USDA 2010) estimated spatially distributed excess rainfall and a GIS-derived time–area diagram (isochrones) based on a set of separated unit hydrographs (i.e., spatially distributed unit hydrograph) that are utilized to calculate a direct runoff hydrograph. The Distributed-Clark model has relatively few parameters compared with other PBD models that can also simulate spatially distributed runoff routing. Instead, it focuses on flow simulations for a watershed outlet point rather than fully considering flow interactions between specified grid cells within the watershed.

1) Spatially distributed excess rainfall

The SCS CN method is used to estimate runoff depth (excess rainfall) from rainfall. For a given rainfall event, at each time step t the cumulative excess rainfall Pe,t can be calculated by Eqs. (1)(3) (Chow et al. 1988):

 
formula
 
formula

and

 
formula

where Pe,t (mm) and Pt (mm) are the cumulative excess rainfall and rainfall depth at the end of time step t, respectively; Ia is the initial abstraction (i.e., initial precipitation loss to runoff λS, where λ is the initial abstraction coefficient varying from 0 to 1 and is one of the calibration parameters; mm); Fa,t is the cumulative abstraction (i.e., infiltration) at the end of time step t (mm); S is the potential maximum retention (mm); and CN is the SCS curve number.

To calculate the spatially distributed rainfall excess, runoff depth for each cell of the CN map is calculated using Eqs. (1)(3), and then an average of all cells within an area of interest such as a NEXRAD grid cell is computed to get the average excess rainfall. Figure 1 shows the process of spatially distributed excess rainfall estimation using graphic representations.

Fig. 1.

Graphical representations of the spatially distributed excess rainfall estimates.

Fig. 1.

Graphical representations of the spatially distributed excess rainfall estimates.

2) Spatially distributed unit hydrograph

A GIS-derived time–area diagram (isochrones) and instantaneous unit excess rainfall adopted flow translation and attenuation are needed to develop the spatially distributed unit hydrograph (a set of separated unit hydrographs). Distributed-Clark creates a time–area diagram by dividing a cumulative flow travel time map for each cell to the watershed outlet with 1-h interval isochrones. In cases of flow velocity and travel time calculation for two types of grid cells within a defined flow network, the method from McCuen (2005) was used for overland flow [Eqs. (4) and (5)] and the approaches by Muzik (1996) and Melesse and Graham (2004) were used for channel flow [Eqs. (6) and (7), respectively] with some modifications:

 
formula
 
formula

where Vo is the overland flow velocity (m s−1), i is the vertical net incoming flux (mm h−1), L is the length of overland flow (m), S is the slope (m m−1), n is the Manning’s roughness coefficient, and To is the overland flow travel time (min):

 
formula
 
formula

where Vc and Tc are the channel flow velocity (m s−1) and travel time (min), respectively; Ac is the upstream drainage area (m2); P is the wetted perimeter (m); and the other variables are the same as above.

Figure 2 shows a conceptual model of the Distributed-Clark approach, which includes the instantaneous unit excess rainfall applied time–area diagram translation and its linear reservoir attenuation, particularly for obtaining NEXRAD gridcell-based separated unit hydrographs. In this method, the ordinates of the separated unit hydrograph Si,j can be obtained by Eq. (8), and their summation results in the spatially distributed unit hydrograph:

 
formula

where Si,j, Ii,j, and IUHi,j are the jth subarea’s separated unit hydrograph, translation hydrograph, instantaneous unit hydrograph at the end of ith interval [(L2 T−1) where L is the dimension of length and T is the dimension of time], respectively; Δt is the computation time interval (i.e., T), and R is the storage coefficient (i.e., T).

Fig. 2.

Distributed-Clark conceptual model.

Fig. 2.

Distributed-Clark conceptual model.

3) Direct runoff hydrograph

A direct runoff hydrograph can be calculated by Eq. (9) using a previously developed series of spatially distributed excess rainfall and separated unit hydrographs. A set of distributed direct runoff hydrographs for the watershed outlet point can be calculated, and then the sum of all distributed direct runoff hydrographs can be used to create a direct runoff hydrograph:

 
formula

where Qn is the direct runoff hydrograph at the end of nth time interval (L3 T−1), Pi,j is the average excess rainfall in the jth subarea for time interval i (i.e., L), and Si,j is the jth subarea’s separated unit hydrograph at the end of the ith interval (L2 T−1).

4) Model parameters and development

In Distributed-Clark, all three parameters of the vertical net incoming flux (i.e., i), storage coefficient (i.e., R), and initial abstraction coefficient (i.e., λ) are used to calibrate the model simulation results. The first two parameters affect the shape of the spatially distributed unit hydrograph; they are utilized for flow travel time calculation and time–discharge diagram attenuation, respectively (i.e., they are used to shift and attenuate the unit hydrograph), and the last one is used for adjusting the amount of spatially distributed excess rainfall. Model development including watershed preprocessing (i.e., watershed and stream network definition; Manning’s n and SCS CN map creation), spatially distributed excess rainfall estimation, spatially distributed unit hydrograph derivation, and direct runoff hydrograph convolution were implemented in a GIS environment using Python script tools. Figure 3 represents the overall procedures of Distributed-Clark development.

Fig. 3.

Overall procedures of Distributed-Clark development.

Fig. 3.

Overall procedures of Distributed-Clark development.

b. NEXRAD data processing tool

NEXRAD QPEs can be interpreted and processed in a GIS environment. In this study, a GIS-based tool was developed for automation of required NEXRAD data processing, particularly for stage IV composite products [Gridded Binary (GRIB) format] to generate spatiotemporally varied rainfall data for hydrological modeling. Python script tools that were developed in a GIS platform (i.e., ArcGIS 10.1; ESRI 2012) were utilized for three steps of NEXRAD data processing for map projection transformation (from HRAP to Albers equal-area conic regular grid), modeling extent and NEXRAD grid subsetting, and raster and time series data generation. The processed raster data can represent each time step’s spatial distribution of precipitation amounts, and the time series data, which are directly utilized for the Distributed-Clark model input to compute spatially distributed rainfall–runoff flow, can provide each NEXRAD grid cell’s temporally distributed rainfall amounts. General details of the NEXRAD data map system (HRAP grid), projection parameters, and transformation process can be found in related references (Reed and Maidment 1995, 1999; Cho 2016).

3. Model application and evaluation

a. Study area

Four river basins were selected as study areas in this research: the Illinois River near Tahlequah, Oklahoma; the Elk River near Tiff City, Missouri; Silver Creek near Sellersburg, Indiana; and the Muscatatuck River near Deputy, Indiana. The first two are located near the border of Oklahoma, Arkansas, and Missouri, and the last two are located in southern Indiana. These watersheds have a data-rich environment (the first two were test basins of DMIP; Smith et al. 2004), as well as limited complications such as upstream diversions, dam operations, snow, or tile drainage (Fig. 4, Table 1).

Fig. 4.

Location of study areas (watersheds).

Fig. 4.

Location of study areas (watersheds).

Table 1.

Basic topographic and hydrologic characteristics of study areas. In the column headers, A indicates drainage area, H indicates outlet elevation [above National Geodetic Vertical Datum of 1929 (NGVD 29)], L indicates max flow length, S indicates average slope of watershed, and P indicates average annual precipitation near outlet city (from www.noaa.gov; over 30-yr period).

Basic topographic and hydrologic characteristics of study areas. In the column headers, A indicates drainage area, H indicates outlet elevation [above National Geodetic Vertical Datum of 1929 (NGVD 29)], L indicates max flow length, S indicates average slope of watershed, and P indicates average annual precipitation near outlet city (from www.noaa.gov; over 30-yr period).
Basic topographic and hydrologic characteristics of study areas. In the column headers, A indicates drainage area, H indicates outlet elevation [above National Geodetic Vertical Datum of 1929 (NGVD 29)], L indicates max flow length, S indicates average slope of watershed, and P indicates average annual precipitation near outlet city (from www.noaa.gov; over 30-yr period).

The topography of the Illinois River and Elk River watersheds can be characterized as gently rolling to hilly (Smith et al. 2004), while the Silver Creek and Muscatatuck River watersheds are relatively flat (Wilkerson and Merwade 2010). In the Illinois River basin, which contains two subcatchments, the elevation above sea level varies from approximately 202 m at the USGS stream gauge to 600 m at the basin edge, while the Elk River basin varies in elevation from 229 m to around 537 m above sea level. The Silver Creek and Muscatatuck River basins rise from elevations of 131 and 165 m to 314 and 309 m, respectively, representing smaller variances of elevation than the first two basins. Basic topographic and hydrologic characteristics for these watersheds and nested subcatchments are summarized in Table 1, and Table 2 shows the general information of land use and soil features in the study area basins. Most watersheds predominantly include forest (37.4%–55.8%), followed by agricultural land (33.3%–48.2%), developed land (up to 14.1%), and water (up to 0.8%). In particular, the Silver Creek watershed is occupied by about 56% forest. Hydrologic soil groups B and C are dominant in most areas, except in the Illinois River watershed, which has a relatively even distribution, and the Muscatatuck River, which contains a higher percentage (about 75%) of soil group C than other areas (Fig. 5).

Table 2.

Land use and hydrologic soil groups of study areas. In the land-use column headers, W indicates water, U indicates urban or built up, F indicates forest, and Ag indicates agricultural land. In the hydrologic soil group column headers, A indicates deep sand, deep loess, and aggregated silts; B indicates shallow loess and sandy loam; C indicates clay loams, shallow sandy loam, soils low in organic content, and soils usually high in clay; and D indicates soils that swell significantly when wet, heavy plastic clays, and certain saline soils.

Land use and hydrologic soil groups of study areas. In the land-use column headers, W indicates water, U indicates urban or built up, F indicates forest, and Ag indicates agricultural land. In the hydrologic soil group column headers, A indicates deep sand, deep loess, and aggregated silts; B indicates shallow loess and sandy loam; C indicates clay loams, shallow sandy loam, soils low in organic content, and soils usually high in clay; and D indicates soils that swell significantly when wet, heavy plastic clays, and certain saline soils.
Land use and hydrologic soil groups of study areas. In the land-use column headers, W indicates water, U indicates urban or built up, F indicates forest, and Ag indicates agricultural land. In the hydrologic soil group column headers, A indicates deep sand, deep loess, and aggregated silts; B indicates shallow loess and sandy loam; C indicates clay loams, shallow sandy loam, soils low in organic content, and soils usually high in clay; and D indicates soils that swell significantly when wet, heavy plastic clays, and certain saline soils.
Fig. 5.

Land use (NLCD) and hydrologic soil group (SSURGO) of study areas.

Fig. 5.

Land use (NLCD) and hydrologic soil group (SSURGO) of study areas.

b. Land surface data

The data used in this study include 1) 1 arc-s (spatial resolution around 30 m) digital elevation model (DEM), National Land Cover Database (NLCD) 2011, and National Hydrography Dataset (NHD) from the USGS National Map; 2) Soil Survey Geographic (SSURGO) database from the USDA Web Soil Survey; and 3) precipitation frequency (PF) estimates from the NOAA/Hydrometeorological Design Studies Center. DEM and NHD data were used for watershed delineation and stream network definition, whereas land use, PF estimates, and soil data were used to create flow travel time and runoff curve number map.

The time series (hourly) data and gauge information, precipitation (gauged rainfall) from NOAA/National Climatic Data Center, and streamflow from USGS National Water Information System were used to evaluate the performance of simulation results for spatially distributed NEXRAD QPEs and spatially averaged gauged data. Also, for retrieving direct runoff hydrographs from streamflow, the straight line and recursive digital filter baseflow separation methods (Eckhardt 2005) were applied.

c. NEXRAD data

NEXRAD data, NCEP stage IV QPE products, which are mosaicked from the 12 RFCs’ regional hourly/6-h multisensor precipitation estimates or estimator (stage III products or MPEs; manual quality-controlled data) in CONUS by NCEP (Lin and Mitchell 2005), are available through the NOAA Advanced Hydrologic Prediction Service (AHPS) and National Center for Atmospheric Research (NCAR) web-accessible archives. In this study, the hourly NEXRAD stage IV QPEs (GRIB format) were used as model (Distributed-Clark) input of spatiotemporally varied rainfall with data processing to subset and generate required datasets, appropriately matching its extent with study areas. Figure 6 shows the locations of individual NEXRAD radar sites and their coverage (umbrella radius; 230 km) for study watersheds. All study areas are well inside at least one radar umbrella. Since the CONUS NEXRAD stage IV data are produced based on the coordinated universal time (UTC) zone, time difference with other observed data (gauged rainfall, streamflow, etc.) must be considered. In this study, all other observed data in the watershed used local time [e.g., eastern daylight time (EDT), eastern standard time (EST), central daylight time (CDT), and central standard time (CST); 4–6 h later than UTC].

Fig. 6.

Location of NEXRAD radar sites and coverage for study area.

Fig. 6.

Location of NEXRAD radar sites and coverage for study area.

d. Storm event selection

Storm events for the four study areas were selected to compare and evaluate the performance of simulation results for spatially distributed NEXRAD QPEs and spatially averaged gauged data in the Distributed-Clark model. For this application, an independent (isolated) single storm event was considered because the SCS CN method for runoff depth estimation does not account for infiltration recovery during intervals of no rain; otherwise, overestimated runoff outcomes will result (Woodward et al. 2002). Hence, isolated single events of NEXRAD QPEs were chosen for each study area to conduct validation against gauged data and model (Distributed-Clark) calibration and validation. In this case, because of the data availability (hourly) of the NEXRAD stage IV QPE products (generated from January 1997), rain gauge observations (many missing or erroneous records), and streamflow (until September 2007), a total of 24 events (six events for each watershed) from 1998 to 2007 were selected (Table 3).

Table 3.

Storm events for study areas. Precipitation total is only considered the amount of independent event rainfall (for model simulation period) from the total storm event duration. Columns G1–G4 are rain gauge number for areal average precipitation (Thiessen polygon weighted). Asterisks indicate that nearest gauged data were used.

Storm events for study areas. Precipitation total is only considered the amount of independent event rainfall (for model simulation period) from the total storm event duration. Columns G1–G4 are rain gauge number for areal average precipitation (Thiessen polygon weighted). Asterisks indicate that nearest gauged data were used.
Storm events for study areas. Precipitation total is only considered the amount of independent event rainfall (for model simulation period) from the total storm event duration. Columns G1–G4 are rain gauge number for areal average precipitation (Thiessen polygon weighted). Asterisks indicate that nearest gauged data were used.

e. Model evaluation criteria

The model performance in calibration and validation phases was evaluated using three indicators: Nash–Sutcliffe efficiency ENS, from −∞ to 1.0 (perfect fit; Nash and Sutcliffe 1970); coefficient of determination R2, from 0 (no correlation) to ±1.0 (perfect linear relationship); and percent bias (PBIAS), from 0% (optimal value) to ±100% (volume difference tendency against observed counterparts; Moriasi et al. 2007) from Eqs. (10) to (12). For all cases of model simulation performance evaluation, the statistics computed for comparisons of observed and simulated streamflow are for the periods of model simulation (for direct runoff), not the total storm event duration:

 
formula
 
formula
 
formula

where Oi and Si are the observed and simulated streamflow, respectively, and and are the averages of observed and simulated streamflow, respectively.

f. Model comparison

Model simulation results for spatially distributed NEXRAD stage IV and spatially averaged gauged data were compared. To investigate model performances for NEXRAD data’s spatial variability as well, model outputs from the areal average of NEXRAD QPEs are also presented. The rainfall inputs, unit hydrographs, and SCS CN values applied to each model are summarized in Table 4. For reference, model output from use of rainfall for each NEXRAD gridcell interpolation is designated D1, the areal average using NEXRAD grid cell is designated D1a, and the areal average of gauge observation based on the Thiessen method is designated D2.

Table 4.

Model input data (rainfall and CN) and unit hydrograph. Gridded CN is a histogram of CN values corresponding to subarea of interest.

Model input data (rainfall and CN) and unit hydrograph. Gridded CN is a histogram of CN values corresponding to subarea of interest.
Model input data (rainfall and CN) and unit hydrograph. Gridded CN is a histogram of CN values corresponding to subarea of interest.

4. Results and discussion

a. NEXRAD data

1) Validation

All selected storm event data, hourly NEXRAD stage IV QPEs, for model application were validated against rain gauge–only observations. In this validation, the average value of NEXRAD QPEs for each study area’s extent was compared with watershed areal average rainfall from gauges (by Thiessen method) due to most available rain gauges being located outside watershed boundaries (Fig. 4). Thus, gridcell values of NEXRAD data could not be directly compared with rain gauge point values. As shown in scatterplots (Fig. 7), both hourly precipitation estimates have significant correlations for amounts. This is because NEXRAD reflectivity-based QPE values, which are indirectly produced by precipitation processing algorithms, are quality controlled using rain gauge observations; they are not independent. However, since there can be possible errors in gauge-only rainfall, the validation results of NEXRAD QPEs with gauge data do not always show a good relationship (Xie et al. 2006; Wang et al. 2008). Efforts to enhance the quality of polarimetric radar-based QPEs with new algorithms and multisensor data continue (Ryzhkov et al. 2005; Giangrande and Ryzhkov 2008; Zhang et al. 2016). In this study, the data for the Muscatatuck River basin show the highest correlation (R2 = 0.69) in contrast to relatively low correlation results for other watersheds (R2 = 0.56–0.57). Underestimation trends also can be seen for larger values of NEXRAD stage IV QPEs. The total NEXRAD rainfall amounts are overestimated by 7.5% and 9.1% in the Illinois and Elk Rivers, respectively, while underestimated by 15.0% and 11.4% in Silver Creek and Muscatatuck River, respectively. Total precipitation plots of storm events comparing these two datasets are also presented in Fig. 8.

Fig. 7.

Scatterplots comparing hourly NEXRAD stage IV QPEs and gauge data (areal average).

Fig. 7.

Scatterplots comparing hourly NEXRAD stage IV QPEs and gauge data (areal average).

Fig. 8.

Total precipitation plots of storm events comparing NEXRAD stage IV QPEs and gauge data (areal average).

Fig. 8.

Total precipitation plots of storm events comparing NEXRAD stage IV QPEs and gauge data (areal average).

2) Spatial variability

For each watershed’s selected storm events, the spatial variability of cumulative precipitation depth was examined. Figure 9 shows the 2 km × 2 km regular grid-based NEXRAD stage IV QPEs, which were resampled from the original approximately 4 km × 4 km HRAP grid. They adopt the Albers equal-area conic map projection system. The spatial distributions can be seen with each event’s gridded rainfall amounts. For instance, differences of 782% (13.3–117.2 mm) occurred in event 6 for the Elk River (second-largest basin) with a skewness value of 1.01 (in Table 3), whereas differences were 85% (33.7–62.3 mm, skewness −0.10) in event 3 for the Silver Creek basin. These spatially distributed NEXRAD stage IV QPEs can be used as model (Distributed-Clark) inputs for excess runoff depth estimation to convolute a direct runoff flow hydrograph with a set of separated unit hydrographs.

Fig. 9.

Spatial variability of cumulative precipitation depth (mm) of selected storm events for four study areas, as obtained by NCEP stage IV QPE products.

Fig. 9.

Spatial variability of cumulative precipitation depth (mm) of selected storm events for four study areas, as obtained by NCEP stage IV QPE products.

b. Model development

The model development results of the flow travel time map, time–area diagram (isochrones), and spatially distributed unit hydrograph (summation of separated unit hydrographs) for each study watershed are represented in Figs. 10 and 11. In the time–area diagram and unit hydrograph (Fig. 11), each selected NEXRAD grid cells’ (S1 and S2) results, which represent the portion of 1-h interval incremental area contributions of flow to the outlet (Fig. 11, left) and its separated unit hydrographs (Fig. 11, right), can be identified. Hence, these gridcell separated unit hydrographs can be convoluted with NEXRAD QPEs based on spatially distributed excess rainfall, which are estimated using the SCS curve number approach (gridded CN), to obtain a watershed outlet’s direct runoff flow hydrograph.

Fig. 10.

Flow travel time map (from calibrated i; Table 5) for time–area diagram development.

Fig. 10.

Flow travel time map (from calibrated i; Table 5) for time–area diagram development.

Fig. 11.

(left) Time–area diagram (from calibrated i; Table 5) and (right) spatially distributed unit hydrograph (from default R; 2 h); S1 and S2 show the portion of incremental area contributions of flow to outlet (left) and their separated unit hydrographs (right).

Fig. 11.

(left) Time–area diagram (from calibrated i; Table 5) and (right) spatially distributed unit hydrograph (from default R; 2 h); S1 and S2 show the portion of incremental area contributions of flow to outlet (left) and their separated unit hydrographs (right).

c. Model performance

1) Calibration and validation

Model calibration and validation to improve fit of simulation hydrographs against observed streamflow were conducted for all four study watersheds using six storm events for each area (total of 24). The default Distributed-Clark model using parameter values of the average intensity of 2-yr, 24-h rainfall for i; 2 h for R; and 0.20 for λ were calibrated using rainfall inputs for spatially distributed NEXRAD stage IV QPEs and spatially averaged gauged data. Model validation was also performed for three out of six events (randomly selected before calibration). The estimated parameter values following calibration are shown in Table 5. While the estimated parameter values of i and R are the same in each watershed, the initial abstraction coefficient, λ values, which are used to adjust for antecedent runoff conditions in watersheds for each storm event, differed since the model calibration and validation were made to match the total volume of observed flow data.

Table 5.

Parameter values of model calibration and validation results for spatially distributed and averaged rainfall data simulations. Parameter i represents vertical net incoming flux (mm h−1), R represents storage coefficient (h), and λ represents initial abstraction coefficient. ARC number I represents dry, II represents average, and III indicates wet. Averaged data simulation (D2) has the same i and R values with distributed data simulation (D1, D1a).

Parameter values of model calibration and validation results for spatially distributed and averaged rainfall data simulations. Parameter i represents vertical net incoming flux (mm h−1), R represents storage coefficient (h), and λ represents initial abstraction coefficient. ARC number I represents dry, II represents average, and III indicates wet. Averaged data simulation (D2) has the same i and R values with distributed data simulation (D1, D1a).
Parameter values of model calibration and validation results for spatially distributed and averaged rainfall data simulations. Parameter i represents vertical net incoming flux (mm h−1), R represents storage coefficient (h), and λ represents initial abstraction coefficient. ARC number I represents dry, II represents average, and III indicates wet. Averaged data simulation (D2) has the same i and R values with distributed data simulation (D1, D1a).

The simulated and observed flow hydrographs for total streamflow and direct runoff are represented in Figs. 12 and 13 to show the graphical goodness-of-fit of each model’s calibration and validation. For total streamflow hydrographs, the separated base flow was added to create simulation outputs. In most cases, the calibrated model generated similar hydrographs with observed flows, but some cases produced gaps, particularly for the time to peak from observed direct runoff hydrographs (storm events 3 and 4 for the Illinois River and event 5 for Silver Creek). This indicates the imperfection of using just one representative calibrated i and R parameter value to create outputs for various storm events, since average rainfall intensity and watershed storage conditions can differ from those of the calibrated unit hydrograph. Nevertheless, the overall statistical results of the Distributed-Clark model for both spatially distributed and averaged rainfall data simulations demonstrate relatively good performance (direct runoff: ENS = 0.84, R2 = 0.86, and PBIAS = 2.39%; streamflow: ENS = 0.91, R2 = 0.92, and PBIAS = 0.33%) compared with observed data for all four study watersheds as shown in Table 6. Thus, this simple model using few parameters (Distributed-Clark) to perform storm-event-based hydrologic simulations for various types of rainfall products could provide benefits relative to PBD models if the modeling goal is only to obtain integrated flow at a watershed outlet.

Fig. 12.

Graphical results [(left) total streamflow and (right) direct runoff] for model calibration and validation at (a) Illinois River and (b) Elk River.

Fig. 12.

Graphical results [(left) total streamflow and (right) direct runoff] for model calibration and validation at (a) Illinois River and (b) Elk River.

Fig. 13.

Graphical results [(left) total streamflow and (right) direct runoff] for model calibration and validation at (a) Silver Creek and (b) Muscatatuck River.

Fig. 13.

Graphical results [(left) total streamflow and (right) direct runoff] for model calibration and validation at (a) Silver Creek and (b) Muscatatuck River.

Table 6.

Statistical results (average) of model calibration and validation for study areas. Values of ENS and R2 represent an arithmetic mean; values of PBIAS represent an arithmetic mean of absolute value.

Statistical results (average) of model calibration and validation for study areas. Values of ENS and R2 represent an arithmetic mean; values of PBIAS represent an arithmetic mean of absolute value.
Statistical results (average) of model calibration and validation for study areas. Values of ENS and R2 represent an arithmetic mean; values of PBIAS represent an arithmetic mean of absolute value.

2) Model comparison

To assess NEXRAD stage IV QPE product quality for hydrologic simulation relative to gauge-only analyses, Table 6 compares average results of model simulations for spatially distributed and spatially averaged rainfall inputs. Overall, the use of NEXRAD QPE products in Distributed-Clark (D1) did not result in large differences from outputs of rain gauge data application (D2). It shows slightly better fit with improved statistical values for ENS of 3.7% (0.82–0.85) and R2 of 6.0% (0.84–0.89) in direct runoff compared to results from spatially averaged rainfall input simulations.

However, the individual storm event simulation comparison results for two models (D1 and D2) that are represented in Figs. 1214 show some significant differences. For instance, simulation results of storm event 2 for the Illinois River, event 6 for the Elk River, and event 6 for the Muscatatuck River watershed present differences in both graphical and statistical results. In these cases, better statistical values occurred for spatially distributed rainfall data simulations. Variable ENS increases of 7.5%, 13.0%, and 10.1% and R2 increases of 8.5%, 11.4%, and 6.5% occurred in direct runoff results, respectively (Fig. 14). These differences are largely due to the amount of input rainfall and the rainfall spatial variability. Relatively larger skewness values of NEXRAD precipitation amount, −0.46, 1.01, and −0.84, are found in these storm events (Fig. 9). Thus, these rainfall inputs and each dominant area’s (NEXRAD grid cell) separated unit hydrographs enabled the model to create different outputs from gauged average rainfall simulation results. Better fit results for spatially distributed rainfall simulation can also be seen in most other individual comparisons. This may indicate the model results from NEXRAD QPE data inputs are more appropriate to simulate rainfall–runoff flows than gauged data for the same model calibration approach.

Fig. 14.

Statistical results comparison of model calibration and validation for spatially distributed (D1) and averaged (D2) rainfall data simulation.

Fig. 14.

Statistical results comparison of model calibration and validation for spatially distributed (D1) and averaged (D2) rainfall data simulation.

Nonetheless, since data quality issues can exist with NEXRAD QPE products, simulation results may not always provide good fits. In this study, the 30.6% (15.4 mm; event 1) and 36.2% (25.2 mm; event 3) underestimated stage IV QPEs for the Muscatatuck River cases affected the model performance in hydrologic simulations. Despite using potential maximum parameter values for their runoff depth [λ value of 0 for wet Antecedent Runoff Conditions (ARC III)], the model output hydrographs for storm events 1 and 3 did not match with observed flows. Thus, these results are poor compared with other cases (Fig. 14), and only the Muscatatuck River watershed’s spatially distributed stage IV QPE product simulations have poorer performance than gauged data simulations for averaged ENS and PBIAS values (Table 6).

Another case of Distributed-Clark model (D1 and D1a) results comparison to examine model performances for the spatial variability of NEXRAD stage IV QPEs was also investigated. In this case, since the intention of this comparison was only to distinguish volume changes between distributed and averaged NEXRAD QPE data simulation results, the D1a model that used the areal average of NEXRAD stage IV QPEs as input data was not calibrated from the D1 model that used the same NEXRAD products for spatially distributed data simulation. The simulated runoff obtained by spatially averaged NEXRAD QPE data inputs showed decreased volumes compared to those obtained with distributed NEXRAD data for most model simulation cases. This is possibly because the amounts of excess rainfall for each NEXRAD grid cell are reduced when estimated with spatially averaged input rainfall values compared to spatially distributed rainfall values. Typically, the CN method estimates larger depths of rainfall excess for larger input depths of rainfall (Chow et al. 1988). In other words, the averaged values of precipitation in grid cells, which were previously larger amounts, resulted in a smaller depth of excess rainfall than their possible excess rainfall depth for distributed data simulations. Hence, these reduced runoff amounts led to the overall decreased volumes of simulated flow. The flow volume differences for spatially distributed and averaged NEXRAD stage IV QPE data simulation in each study watershed are different by 1.8 (6.0%), 1.4 (10.9%), 1.7 (7.2%), and 0.8 (6.8%) for the Illinois River, Elk River, Silver Creek, and Muscatatuck River, respectively. These are not substantial amounts as identified in Figs. 12 and 13, but they changed the rate and time for peak flow of streamflow hydrographs up to 115.8 (2), 126.7 (1), 5.6 (2), and 7.6 m3 s−1 (1 h) for each watershed. Thus, the possible differences in model simulation results according to the type of rainfall inputs should not be disregarded when estimating storm event flows using hydrologic models because the results can be underestimated or overestimated based on data type.

In addition, these simulation results were also affected by the skewness of NEXRAD QPE data amount distributions. More specifically, storm event cases of NEXRAD data that have high skewness values or wide ranges (Table 3, Fig. 9) resulted in more gaps in model flow simulations. As such cases, storm events 2 (skewness −0.46; range 131.4 mm) and 6 (−1.09; 45.8 mm) for the Illinois River, events 3 (0.31; 90.9 mm) and 6 (1.01; 103.9 mm) for the Elk River, event 2 (3.25; 44.8 mm) for the Silver Creek, and event 4 (−0.76; 59.3 mm) for the Muscatatuck River watershed show larger flow volume or peak flow differences than other events (Figs. 12, 13). However, since these gaps for compared models (D1 and D1a) can result from other modeling components that are associated with the number of NEXRAD grid cells (e.g., the shape of separated unit hydrographs and CN values for each NEXRAD grid cell) as well, it is hard to generalize the above trends from NEXRAD QPE data distributions as the main explanation for the model simulation result differences. For reference, the numbers of NEXRAD grid cells that are defined for this study’s four watersheds are 717, 624, 159, and 239, respectively.

5. Summary and conclusions

In this study, a simple hydrologic model, Distributed-Clark, was introduced to conduct hydrologic simulations using various types of rainfall data, particularly for spatially distributed NEXRAD QPEs (NCEP stage IV products). This lumped conceptual and distributed feature model (hybrid hydrologic model) can convolute a direct runoff hydrograph utilizing spatially distributed excess rainfall obtained from NEXRAD data with the SCS CN approach and a set of separated unit hydrographs that are derived using a GIS-based time–area diagram (isochrones). The Distributed-Clark model has relatively few (three) parameters compared with other PBD hydrologic models. Thus, there is a possible advantage in using it for obtaining hydrographs at watershed outlets compared to PBD models that require intensive calibration with multiple parameters and their corresponding uncertainty. Also, although the Distributed-Clark model is simple, it can utilize state-of-the-art spatially distributed data (e.g., topography, land cover, soil, and rainfall), which PBD models typically use, for extracting physical factor characteristics (flow network, Manning’s n, slope, and curve number, etc.) and NEXRAD data processing to implement rainfall–runoff flow simulation in a GIS environment.

The validation results of NEXRAD stage IV QPEs with gauged rainfall data show significant correlations (0.56–0.69) and underestimation trends for larger values in NEXRAD QPEs, and substantial differences between the precipitation amounts of both data for four study watersheds were also found (NEXRAD data are 7.5% and 9.1% overestimated in two watersheds; 15.0% and 11.4% underestimated in two watersheds). These differences and spatial variability (skewness ranges from −1.02 to 3.25 for total of 24 storm events) of NEXRAD stage IV QPEs affected model performance for single storm event flow simulation. Based on model application comparison for two cases, we identified the following performances of Distributed-Clark in rainfall–runoff flow estimations for the use of spatially distributed NEXRAD stage IV QPE products.

  1. The comparison of model simulation results with input of spatially averaged gauged rainfall showed slightly improved outputs in most NEXRAD QPE data simulations. Overall, ENS of 3.7% and R2 of 6.0% increase occurred in direct runoff for evaluations with observed flow. This suggests that spatially distributed NEXRAD QPE product application is more appropriate to compute storm event runoff flows than gauged rainfall. However, NEXRAD QPE data quality issues may result in poor model performance. In this study, two cases of inadequate simulation results for flow volumes compared with observed flows were caused because of significantly underestimated precipitation amounts.

  2. The second case compared model simulation results from the same stage IV QPE data, but the outputs of the NEXRAD gridcell-based areal average rainfall input model were utilized as comparison targets. The results identified differences in flow volume amount and peak flow rate for these different types of rainfall input simulations. The cases of spatially distributed rainfall input model showed increased flow volumes and peak rates than spatially averaged cases, and more simulation gaps occurred for the storm events having significant spatial variability with high skewness values. Thus, it can be noted that the hydrologic model simulation using spatially averaged precipitation may produce underestimated results compared to spatially distributed cases under the same calibration approach and parameter values.

These results indicate that spatially distributed NEXRAD QPEs provided better results in hydrologic application of rainfall–runoff flow simulations than spatially averaged gauge rainfall, enabling improved estimates of flow volumes and peak rates that can be disregarded in hydrologic simulations for spatially averaged rainfall.

Since many gridded types of QPEs have been developing in the research fields of Earth and space science with intensive quality control [e.g., GPM satellite-based QPEs (Hou et al. 2014) and Multi-Radar Multi-Sensor (MRMS) QPEs (Zhang et al. 2016)], these types of gridded precipitation may be more reliable data for hydrological modeling. Therefore, we expect that this study’s simple modeling approaches would support the implementation of hydrologic simulation with the use of spatially distributed QPEs.

Acknowledgments

Support for this study (part of Ph.D. studies) from Korea Water Resources Corporation (K-water) is gratefully acknowledged.

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