2.1 Atmospheric Water Balance Studies

A number of researchers have used the atmospheric water balance to estimate hydrologic fluxes. Among these researchers, Rasmusson, 1967, Brubaker et al., 1994, and Oki et al., 1995, describe atmospheric water balance studies at river basin, continental, and global scales. Rasmusson, 1967, analyzes the characteristics of total water vapor flux fields over North America and the Central American Sea. A noteworthy observation made by Rasmusson is that a large diurnal wind system covering the central United States, part of Mexico, and the Central American Sea produces significant diurnal variations in the transport of water vapor. By decomposing the vertically integrated vapor flux term into mean motion and transient eddy terms, where the mean motion term is at a time scale of one month and the transient eddy term describes motion at a time scale of less than one month, Brubaker et. al. also observe important vapor flux transport at sub-monthly time scales. Brubaker et. al. note that poleward eddy flux transport from the Gulf of Mexico is significant, particularly during the winter months. From these observations, Brubaker et. al. surmise that the use of monthly-averaged or sparse data may significantly underestimate the eddy flux component of vapor transport. These observations are relevant to the interpretation of our results, as discussed in Section 3.3. Brubaker et al. also note that the accuracy of runoff estimates made using atmospheric data increases with the size of the study area and cite a recommendation by Rasmusson, 1977, that a minimum area of 10⁶ km² should be used . The area of Texas is about 0.7 x 10⁶ km². Improvements in observational networks and general circulation models may justify runoff estimation on smaller areas in the future.

If the annual change in atmospheric water storage and surface water storage are both negligible, runoff estimates can be obtained from the vertically integrated vapor flux convergence (). Using four years of data from the European Centre for Medium-Range Weather Forecasts (1985-1988), Oki et al. compared convergence values with the observed annual runoff for 70 river basins throughout the world. Differences between vapor flux convergence and measured runoff varied widely, although larger river basins tended to show smaller differences. On average, the vapor flux convergence was about 2/3 of the measured runoff. Oki et al. also made a more detailed study of the Chao Phraya River basin in Thailand which drains 178,000 km². Oki et al. estimated annual runoff, monthly evaporation, and monthly storage for the Chao Phraya from 1985 to 1988. The evaporation and river basin storage values were estimated by augmenting atmospheric data with precipitation and runoff data. In the Chao Phraya basin, the vapor flux convergence was consistently higher than observed runoff; however, the temporal variations of vapor flux convergence and runoff were comparable. This was illustrated by applying a reduction factor to the convergence values.

Significant uncertainties in runoff estimation using atmospheric data still exist even at the continental scale. Both Brubaker et al. and Oki et. al. compare their continental runoff estimates with those given by Baumgartner and Reichel, 1975, for river runoff. For North America, Brubaker et. al. estimate annual runoff as 84.6 mm/year while Oki et. al. estimate 263 mm/year and Baumgartner and Reichel give 223 mm/year. Both Brubaker et al. and Oki et al. make note of the fact that poorly defined continental or basin boundaries may contribute to inaccuracies in runoff estimation. This problem is solved in the current study of Texas by using a geographic information system in which any arbitrarily defined boundary can be used to compute the water balance, although the problem remains that atmospheric soundings are sparse.

2.2 Soil Water Balance Studies

Where detailed data about soil layers, depth to groundwater, and vegetation are not available, hydrologists have often resorted to simple bucket models and budgeting schemes to model near-surface hydrology. Despite numerous uncertainties associated with the simple soil-water budget model like the one used in this study, many researchers have applied this type of model to problems ranging from catchment scale studies to the global water balance and climate change scenarios (Thornthwaite, 1948; Shiklomanov, 1983; Manabe, 1969; Mather, 1978; Alley, 1984; Willmott et al., 1985; Mintz and Walker, 1993; Mintz and Serafini, 1992). This approach is attractive because of its simplicity. The simple "bucket" model used here requires minimal input data: precipitation, potential evapotranspiration, and soil-water holding capacity. The studies by Willmott et al., Mintz and Walker, and Mintz and Serafini, are climatological studies that present the global distributions of precipitation, evapotranspiration, and soil moisture. Mintz and Serafini compare their evapotranspiration estimates for sixteen major river basins throughout the world with those derived from river runoff analysis made by Baumgartner and Reichel, 1975, and the values show reasonable agreement.

At a smaller scale, Mather, 1978, (Chapter 4) describes the application of a soil-water budget model to several watersheds in the coastal plains of Delaware, Maryland, and Virginia. Comparisons between measured and computed runoff values are rather poor for monthly data, but better for annual data, although Mather suggests further refinement of the method even for annual values. In its simplest form, the soil-water budget model does not account for situations where the precipitation rate is greater than the infiltration capacity of the soil. Mather describes one approach to remedy this problem, that is, to first use the SCS method to estimate direct overland runoff and subtract this amount from the precipitation before it is allowed to enter the soil "bucket." This approach appears to yield better results (Mather, Chapter 4). A similar approach of taking an initial rainfall abstraction before allowing precipitation to enter the soil column for climatological budgeting was used in a study of the Niger Basin described by Maidment et al., 1996 (further description available at http://www.ce.utexas.edu/prof/maidment/gishydro/africa/africa.htm). In the Niger Basin study, the surplus from the soil-water budget is passed to a surface and groundwater routing model which is in turn calibrated with observed runoff.

2.3 Surface Water Balance Studies

2.3.1 Water Balances of Texas

The surface water balance, a commonly used method in hydrologic studies, relies on the fact that with the exception of coastal areas, the landscape can often be divided into watershed units from which there is only one surface water outflow point. Provided that the average watershed precipitation and runoff can be measured with reasonable accuracy, the annual evaporative losses from a watershed can be estimated. Of course this assumes that change in storage is negligible and that there are no significant inter-watershed transfers via groundwater or man-made conveyance structures. Empirical relationships are often used to estimate mean annual or mean monthly flows in ungaged areas; this approach is used in this study.

Two water balance studies that are particularly relevant to Texas are those by Ward, 1993, and the Texas Board of Water Engineers, 1961. Ward presents a water balance similar to that described here in which he estimates precipitation, evapotranspiration, runoff, recharge, and water demands for four different hydroclimatological regions in Texas and for the State as a whole. To estimate annual runoff, Ward uses an empirical relationship between rainfall and runoff. A similar approach is used in this study, although the rainfall-runoff relationship derived here is used in conjunction with a large database of measured values to develop spatially distributed maps of runoff. The Texas Board of Water Engineers (TBWE; now Texas Water Development Board) Bulletin 6001 is a study of surface runoff (1940-1956) from the major basins and sub-basins in Texas that uses measured flow data. To estimate runoff in ungaged watersheds or watersheds with insufficient streamflow records, the authors of Bulletin 6001 used a proportion of the observed runoff in a watershed with similar characteristics and an additional factor to account for the difference in precipitation if necessary. One product of Bulletin 6001 is a map of Texas sub-basins with printed values of runoff. Improvements in computer technology since 1961 allow for more detailed electronic maps to be generated in this study, although the idea of mapping runoff values is similar.

2.3.2 Runoff Mapping

Three recently published articles by Arnell, 1995; Lullwitz and Helbig, 1995; and Church et al., 1995, describe studies of runoff mapping. All three use a geographic information system (GIS) to manage spatial data at a regional or continental scale. The paper by Arnell summarizes five approaches for deriving gridded runoff maps at a 0.5 grid resolution including (1) simply averaging the runoff from all stations within each grid cell, (2) statistically interpolating runoff between gages, (3) using an empirical relationship that relates runoff to precipitation, potential evaporation, and temperature, (4) using a soil-water balance type model, and (5) overlaying grid cells onto catchment runoff maps to derive area-weighted runoff estimates. Arnell evaluates all but method (4) by mapping runoff onto 0.5 grid cells over a large portion of western Europe, and then intersecting the results with seven gaged river basins to validate the results. The results show that method (5) produces the most reasonable estimates. In a study similar to that of Arnell, Lullwitz and Helbig created 0.5 runoff maps for the Weser River in Germany. Both Arnell and Lullwitz and Helbig note that 0.5 runoff maps can be useful for validating general circulation models (GCM's). Church et. al. present maps of evapotranspiration (ET) and runoff/precipitation (R/P) ratios for the northeastern United States. Church et. al. use an interpolation method to create runoff maps. Church et al. found their results to be useful in assessing the effects of acidic deposition.

The approach used for runoff mapping in this study is different than any of the methods described above, although it is most similar to Arnell's method 5. The approach taken here combines an empirical rainfall-runoff relationship and watershed runoff balancing.