1. Introduction

1. Grid Cell Energy and Moisture Fluxes Grid Cell Vegetation Coverage 2 ... N 1 N+1 RS L RL Variable Infiltration Curve Ec Et S τG E R Infiltration capacity Canopy Layer 0 Layer 1 Fraction of area Baseflow Curve B Layer 2 Baseflow, B Layer 2 soil moisture H12A-0919: SENSITIVITY OF SURFACE HYDROLOGIC FLUXES PREDICTED BY A MACROSCALE HYDROLOGIC MODEL TO ENERGY BALANCE CLOSURE ASSUMPTIONS Ingjerd Haddeland, Niklas Christensen, and Dennis P. Lettenmaier 1. Introduction The Variable Infiltration Capacity (VIC) macroscale hydrology model can be run in two modes: energy or water balance. In energy balance mode, the model iterates on an effective surface temperature that closes the energy balance, whereas in water balance mode, the effective surface temperature is assumed to equal air temperature. The water balance mode is much more computationally efficient than is the energy balance mode, whereas energy balance mode reflects more closely the use of the model in fully coupled land-atmosphere applications. For parameter estimation purposes, it is desirable to do parameter searches in water balance mode, but understanding the implications of model performance for a given set of parameters in energy balance mode is clearly important. Furthermore, the energy balance mode often requires shorter time steps to avoid numerical and conceptual problems associated with diurnal variations of radiative forcings, for instance. The objective of this study was to establish relationships between model performance in the different modes and temporal resolutions at which the VIC model is run. 2. The VIC model The VIC macroscale hydrologic model Liang et al., 1994] solves the water and energy balance equations at the land surface. Land cover variability is represented through partitioning each grid cell into multiple vegetation types and bare soil, and the soil column is divided into multiple (typically three) soil layers. The saturation excess mechanism, which produces direct runoff, is parameterized through a variable infiltration curve. Release of baseflow from the lowest soil layer is controlled through a non-linear recession curve. See also Figure 1. 3. Study areas Two study areas, including a wide range of climatic and land cover characteristics, were selected for analyses, see Figure 2. Area 1 is a transect of 201 one-eighth degree cells from the Rocky Mountains in the west to the Appalachians in the east. The majority of the 145 cells in Area 2 is within the Columbia River basin. • 4. Model analyses • Three model configurations were analyzed; • Daily water balance (24WB) • 3 hourly water balance (3WB) • 3 hourly energy balance (3FE) • The basic meteorological input data were daily total precipitation (uniformly apportioned • within the day for subdaily time steps), and temperature maxima and minima, from which • VIC estimates the diurnal cycle of temperature and radiative forcings. Snow • accumulation and ablation processes are solved via an energy balance approach at 3 • hourly time steps in both water balance and energy balance mode. For each analysis, the • model was run for five years (1988-1992). Figure 2: Location of the study areas Figure 1: Schematic representation of the VIC model 5. Results Figure 3 shows mean monthly values (in mm averaged over each study area), at daily and 3 hourly time steps, of a) runoff, and b) evapotranspiration. Runoff ratios for the three simulations in both study areas are shown in Figure 4. In general, evapotranspiration decreases and total runoff increases when the model's temporal resolution is decreased, and also when going from water balance to energy balance mode. The difference in time step accounted for 38 percent of the difference in total runoff for Area 1, while the difference in time step causes negligible changes in runoff in the snowmelt dominated Area 2. Mean annual moisture fluxes for each cell within the two study areas at daily time steps (water balance mode), compared to mean annual moisture fluxes at 3 hourly time step (water balance mode and energy balance mode), are shown in Figure 5. The results from Figures 3-6 were used in an attempt to find a relationship between runoff production in daily water balance mode and 3 hourly energy balance mode. For calibration purposes, it is preferable to establish this relationship on a monthly basis. Figure 7 shows monthly simulated (A) and calculated (B) runoff values for each cell in Area 1, based on the following equation: where Q is runoff, PET is ‘potential’ transpiration, and RNET is net radiation (see Figure 6). In Figure 8, calculated runoff values averaged over Area 1, are compared to the simulated runoff values presented in Figure 3. The above equation overestimates runoff somewhat in the summer, which is expected given that PET is transpiration given no soil moisture stress. Figure 5: Mean annual moisture fluxes in each cell at daily time steps, compared to 3 hourly time steps Figure 3: Mean monthly moisture fluxes • Figure 6 shows mean monthly values of • transpiration given no soil moisture limitation (‘potential’ transpiration), and • net radiation. • The differences in transpiration values in • Figure 6 a) indicates that the diurnal • variation in temperature and vapor • pressure deficit results in lower • transpiration values, given that soil • moisture does not limit transpiration. The • iterated surface temperatures in energy • balance mode results in lower outgoing • longwave radiation, which is reflected in • the difference in net radiation shown in • Figure 6 b). Figure 7: Mean monthly simulated and calculated runoff for each cell, Area 1. Figure 4: Runoff ratios Figure 6: Mean monthly values of transpiration given no soil moisture limitation (‘potential’ transpiration), and net radiation Figure 8: Mean monthly simulated and calculated runoff, Area 1. • 6. Conclusions • Daily average temperature and vapor pressure deficits favor transpiration, as compared with temporally disaggregated values. • In energy balance mode, the iterated surface temperatures are generally higher than the air temperatures, leading to increased outgoing longwave radiation and decreased net radiation. • If snow is present, the difference between total runoff values in daily water balance mode and energy balance mode is smaller than if no snow is present. • A simple equation, based on simulated daily water balance variables and variables that can be calculated off-line, is a first step towards a relationship between simulated runoff at daily water balance mode and 3 hourly energy balance mode. 7. References Liang, X., D. P. Lettenmaier, E. F. Wood, and S. J. Burges, A simple hydrologically based model of land surface water and energy fluxes for general circulation models, Journal of Geophysical Research, 99(D7), 14,415-14,428, 1994. Contacts: Ingjerd Haddeland (ingjerd@geofysikk.uio.no) Norwegian Water Resources and Energy Directorate P.O. Box 3091 Majorstua N-0301 Oslo Niklas Christensen (niklas@hydro.washington.edu) Dennis P. Lettenmaier (dennisl@u.washington.edu) University of Washington Department of Civil and Environmental Engineering Box 352700 Seattle, WA 98175-2700