OHD/HL - papers: Sensitivty of SMAM

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

ABSTRACT

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.

INTRODUCTION

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.

METHOD

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.

RESULTS

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 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.

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.

CONCLUSIONS

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

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