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Sensitivity of the Sacramento Soil Moisture Accounting Model to Space-Time Scale Precipitation Inputs from NEXRAD

Bryce D. Finnerty
Michael B. Smith
Dong-Jun Seo
Victor Koren
Glenn Moglen
Office of Hydrology
NOAA/National Weather Service
1325 East-West Hwy.
Silver Spring, Maryland 20910


The objective of the National Weather Service (NWS) distributed modeling project is to optimally utilize the spatial information contained in the high resolution 1-hour, 4x4 km2 Next Generation Weather Radar (NEXRAD) precipitation products for operational hydrologic forecasting. This analysis addresses the problem of creating biases in the volume and timing of runoff when forecasting at space-time scales different from those with which the model parameters were calibrated. Hydrologic model parameters are inherently tied to the space-time scales at which they were calibrated. The NWS calibrates rainfall runoff models using 6-hour mean areal precipitation (MAP) inputs derived from gage networks. The Sacramento Soil Moisture Accounting (SAC-SMA) model response was analyzed using 9 months of NEXRAD data to derive input MAPs. The continuous model time steps included 1, 3, and 6 hours. The spatial analysis investigated sub-basin sizes ranging from 4x4 km2 up to 256x256 km2.

Results showed that surface runoff, interflow, and supplemental baseflow runoff components of the SAC-SMA model were the most sensitive to the space-time scales of the sub-basins. Water balance components of evapotranspiration and total channel inflow were also discovered to be sensitive to sub-basin space-time scales.


The National Weather Service (NWS) distributed modeling project is analyzing the space-time hydrologic model response to high resolution precipitation estimates from Next Generation Weather Radar (NEXRAD) (Hudlow, 1988; Klazura and Imy, 1993) in order to improve operational hydrologic forecasting. The NWS primarily uses the Sacramento Soil Moisture Accounting (SAC-SMA) model to generate river forecasts on basins with a response time of greater than 12 hours. The SAC-SMA model is a conceptually based rainfall runoff model with spatially lumped parameters (Burnash, 1995; Burnash et al., 1973). It is applied to river basins ranging from 100 mi2 up to 1500 mi 2, with exceptions outside of this range. Basin sizes vary according to hydrologic region, geomorphology, forecast point requirements, and available data. The SAC-SMA model is generally run at a 6-hour time step but can run at any time step. Inputs to the SAC-SMA model are 6-hour mean areal precipitation (MAP) and 6-hour mean areal potential evapotranspiration (MAPE). The SAC-SMA model parameters are manually and automatically calibrated with the objective of making the model simulation match historical observed discharge data. Calibration is performed on 5 to 10 years of historical data providing the input time series. Therefore, the calibrated parameters are inherently tied to the space-time scale, terrain, geographic location, and gage networks from which they were calibrated.

Precipitation events have spatial characteristics which are known to be greater than the resolution of the 4x4 km2 NEXRAD data but generally smaller than the spatial resolution of the rain gage networks and the more common basin scales. River forecasters acknowledge that the space-time characteristics, and the volume of precipitation from some rain events, are not adequately captured by point gage networks. The following differences between radar and gage data should be considered when using both data types for hydrologic forecasting. First, the measurement of precipitation from radar is inherently different from rain gage devices and, therefore, produces different precipitation estimates. Second, the spatial resolution of the radar estimate is approximately a 4x4 km2 HRAP bin with complete spatial data coverage under the radar umbrella. The NWS Hydrologic Rainfall Analysis Project (HRAP) uses a polar stereographic projection grid to optimally merge rainfall data from multi-radars, rain gages, and satellites (Greene et al., 1979). Precipitation gages, however, take point measurements, and the data is then spatially distributed using various methods. Even in areas with dense rain gage networks, the space-time resolution of the gage precipitation data is poor as compared to the NEXRAD high resolution data. NEXRAD has proven to be a very beneficial tool for estimating precipitation where point gage measurements are inadequate or nonexistent.


Model parameters were calibrated from 11 years of historical observed river discharge and gage precipitation data from 1975 to 1985. The calibration was performed on the 307 mi2 (795 km 2) headwater basin of the Barron Fork of the Illinois River at Eldon, Oklahoma. The calibrated basin is approximately 8x8 HRAP bins and those parameters were then distributed spatially to synthetic square sub-basins of smaller

Sub-basin Scale Dimensions and Units
HRAP Bins Kilometers Kilometers2 Miles2 Approx.Miles
1 x 1 4 x 4 16 6.2 2.5 x 2.5
2 x 2 8 x 8 64 24.7 5 x 5
4 x 4 16 x 16 256 98.8 10 x 10
8 x 8 32 x 32 1,024 395.4 20 x 20
16 x 16 64 x 64 4,096 1,581.5 40 x 40
32 x 32 128 x 128 16,384 6,325.9 80 x 80
64 x 64 256 x 256 65,636 25,303.5 160 x 160

and larger sizes. The synthetic sub-basins range in size from 1x1 HRAP bin up to 64x64 HRAP bins, as shown in Table 1. MAP inputs for the sub-basins were calculated from a 64x64 HRAP bin, 1-hour, NEXRAD precipitation data set that encompasses the real calibrated basin at Eldon, Oklahoma. The calibrated parameters were assumed to be reasonable for the entire 64x64 HRAP bin area, and the area was assumed to have similar rainfall runoff processes throughout. The NEXRAD data set covers the eastern portion of the Tulsa, Oklahoma, river forecasting region and spans a 9-month period from May 7, 1993, through January 31, 1994. This time period records the very wet summer which resulted in the "Great Flood of 93" in the Midwest.

The SAC-SMA model was run in a continuous mode for the entire 9-month period using model time steps of 1, 3, and 6 hours. Soil moisture accounting was performed over the entire 64x64 HRAP bin area and was maintained independently for every sub-basin space-time scale. The precipitation inputs for the 3-hour and 6-hour time scale analysis were derived from summing up the 1-hour data. The NEXRAD data used was the Stage III product which estimates precipitation by merging the radar data with satellite and ground truth gage data (Shedd and Smith, 1991). The analysis assumed that the 6-hour Stage III MAPs were equal to the historical 6-hour gage MAPs because gage data was used by the Stage III post-processors. In addition, the calibrated SAC-SMA model parameters were assumed to be applicable to input MAPs estimated from Stage III data as well as gage network data.

The model components analyzed included: precipitation depth, impervious runoff, direct runoff, surface runoff, interflow, percolation, total evapotranspiration, supplemental baseflow, primary baseflow, total channel inflow, water balance errors, and evapotranspiration demand. The naming of the various model components are specific to the conceptual formulation of the SAC-SMA model and are not general terms of hydrologic science. Output summary statistics were calculated over the 9-month period for all 13 model components and all sub-basin scales analyzed. Statistics include mean, variance, maximum, minimum, and cumulative depth values at all sub-basin scales.

Within this framework, the space-time scale sensitivities of the SAC-SMA model runoff components to NEXRAD precipitation inputs were analyzed. Routing of runoff components through a unit hydrograph or channel network was not performed in this analysis because of the nature of the square synthetic sub-basins, and the desire was to examine the sensitivities of the SAC-SMA model to different space-time scale precipitation inputs only.


Spatial Analysis

Figure 1 shows the relative change in the SAC-SMA model runoff component volume versus the sub-basin scale for the 1-hour model time step. The runoff components have been scaled relative to their value generated at the 1x1 sub-basin spatial scale. Surface runoff was the most spatially sensitive component of the SAC-SMA model, and decreased to zero as the spatial scale increased to 64x64 HRAP bins. Interflow and supplemental baseflow were also found to be quite sensitive to spatial scale and they both decreased as the sub-basin scale increased. However, they did not show much scale dependency below the 16x16 sub-basin size. The figure shows how the reduction of surface runoff, interflow, and supplemental baseflow contribute to the overall reduction of total channel inflow with increased sub-basin scale. Percolation, direct runoff, and primary baseflow also exhibited a decrease in runoff volume as the spatial scale increased.

Evapotranspiration increased as the sub-basin scale increased, as shown in Figure 1. The long-term water balance was maintained in the SAC-SMA model because the increased total channel inflow, produced at the finer scales, resulted in less soil water available for evapotranspiration during the drying periods. The model behavior displayed in Figure 1 was primarily attributed to the spatial averaging of high intensity precipitation events that produced significant runoff. Increasing sub-basin scale averaged the precipitation over too large an area to satisfy the SAC-SMA upper zone tension and free water storages, which decreased the frequency of runoff generating events. This increased the volume of precipitation going to tension water storage where evapotranspiration took place and reduced total channel inflow.

The analysis indicates that parameters derived from the 6-hour MAP inputs at a given spatial scale cannot be distributed to sub-basins of different spatial scales and a 1-hour model time step, without introducing significant biases in the volume, timing, and distribution of SAC-SMA model runoff components. All results must be viewed according to the fundamental assumptions and limitations of the space-time analysis and may only be relevant to the geographic location of the study.

Time Scale Analysis

The time scale analysis was performed to investigate the effects of changing from the 6-hour model time step, most commonly used for current operational forecasting, to the 1-hour time step of the Stage III precipitation data. Modeling at finer time steps is desirable for increasing forecast lead times and increasing forecasting accuracy in fast response basins. The temporal analysis revealed significant hydrological problems facing river forecasting centers when applying 1-hour NEXRAD products. This analysis assumed the 6-hour MAP from the Stage III products were similar to the 6-hour MAPs derived from gage data. This assumption was reasonable because Stage III products were verified against, and merged with, "ground truth" gage data during post processing.

Figure 1: Relative changes in SAC-SMA model runoff component volumes vs. size of sub-basins using 9 months of 1-hour NEXRAD data. Runoff volumes were scaled to the values produced at the finest spatial scale (1x1) and 1-hour temporal scale. Surface runoff is the most sensitive runoff component, followed by interflow and supplemental baseflow. These changes in runoff components cause the rusultant reduction of total channel inflow as spatial scale increases.

Figure 2 displays the percent change in SAC-SMA model runoff component volumes when changing from a 6-hour time scale to a 1-hour time scale while holding the model parameters constant. The figure shows that surface runoff was the most sensitive model component at finer sub-basin scales. Surface runoff at the 8x8 spatial scale increased by over 21 percent when changing to the shorter 1-hour time scale. Interflow at the 8x8 spatial scale was shown to increase by 20 percent when changing from the 6-hour to the 1-hour time scale, but was not as sensitive as surface runoff at the finer spatial scales. Supplemental baseflow decreased with decreasing time scale and was more sensitive at the finer spatial scales analyzed. Total channel inflow also increased at the 1-hour time scale and was more sensitive at the finer spatial scales.

Figure 2: Percent change in SAC-SMA model runoff component volumes resulting from changing from a 6-hour time scale to a 1-hour time scale. At the 8x8 HRAP bin spatial scale, surface runoff increases 21%, interflow increases 20%, supplemental baseflow decreases 9%, and total channel inflow (tci) increases 3%.

The results shown in Figure 2 are primarily attributed to the temporal averaging of high-intensity, short-duration precipitation events which tend to produce surface runoff. This indicates that the hydrologic processes in the region are operating at a finer time scale than 6 hours, and that the 1-hour Stage III products can be used to improve hydrologic forecasting. The temporal analysis also indicates the parameters calibrated at the 6-hour time step cannot be applied at the 1-hour time step without introducing the volume biases shown in Figure 2. These runoff volume biases are particularly important because they were most significant in the fast response runoff components. Changing the model time scale redistributes runoff between the rising limb (surface) and the falling limb (interflow) of the runoff hydrograph, as well as between near surface and groundwater runoff components.


The SAC-SMA model runoff components were found to be sensitive to both space and time scales of the NEXRAD precipitation inputs. The analysis revealed a general increase in surface runoff, interflow, supplemental baseflow, and total channel inflow when moving to finer spatial scales. Evapotranspiration decreased as spatial scale decreased which offset the increase in total runoff in the long-term water balance. Changing the time scale of the model from 6 hours to 1 hour, while holding the spatial scale constant, resulted in a significant increase in surface runoff, interflow, and total channel inflow. Decreasing the time scale caused a decrease in the supplemental and primary baseflows. These space-time scale effects on the SAC-SMA hydrologic model response are attributed to the space-time averaging of high intensity, short duration, runoff generating precipitation events. The finer space-time scales appeared to more accurately model the physical attributes of the rainfall runoff processes in the study area.

The results presented highlight the need for a greater understanding of the space-time distribution of SAC-SMA model parameters. The analysis indicated that parameters derived at a given space-time scale cannot be applied at different scales without introducing significant runoff volume biases. These biases were displayed in the redistribution of runoff volume between fast and slow response components, as well as between near surface and groundwater response.


Future research will focus on methods for space-time distribution of SAC-SMA model parameters that do not introduce significant runoff volume and timing errors. Work has begun on a potential method to adjust existing model parameters for their application across different space-time scales. Research is also underway at the NWS on reformulating the SAC-SMA model to account for the spatial variability in NEXRAD precipitation fields. Once calibrated, the reformulated SAC-SMA model and its parameters are expected to be less sensitive to spatial scale than the current model version. Alternative models, with parameters derived from existing and new physiographic data sets, should also be investigated. Research will also be focused on deriving synthetic unit hydrographs and developing channel routing procedures for ungaged areas. All model developments will be verified on real basins and evaluated based on their contribution to operational river forecasting accuracy.


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