Three water balance methods - an atmospheric water balance, a soil-water balance, and a surface water balance - have been used in an attempt to gain an improved understanding of the stocks of water in different components of the hydrologic cycle and the fluxes between these components. Long term average values indicate that the air flowing over Texas carries 7800 mm year^-1 of moisture, of which 720 mm year^-1 becomes precipitation, from which 78 mm year^-1 becomes surface runoff, all of these quantities being spatially averaged over the State. The runoff estimate of 78 mm year^-1 comes from the surface water balance which has the least uncertainty and highest spatial resolution of the three methods. Comparing mean annual runoff estimates from the other two methods to this figure is one way to assess the accuracy of these methods.

Given adequate data, the atmospheric water balance is a promising method for estimating regional evaporation, runoff, and changes in basin storage; however, data used in this study were not at a high enough resolution to make accurate calculations for Texas. Estimates of mean annual divergence over the State were made using both observed rawinsonde data and the output data from a general circulation model. Both methods show that there is significant uncertainty associated with atmospheric water balance calculations at the scale of Texas, yielding runoff estimates of 1206 mm year^-1 and 379 mm year^-1 which are about 15 times and 5 times greater than the observed runoff, respectively. A review of literature indicates that the magnitude of the errors found in these calculations are not unheard of, although results for some regions have proven much more accurate, particularly when the water balance is assessed over larger areas. Assuming that monthly changes in atmospheric storage are negligible, estimates of monthly evaporation were made for 1992 using the relation (). The 1992 evaporation estimates based on the observed data are not physically realistic while the estimates generated using the general circulation model output show reasonable monthly trends except in January, February, and March. Several sources of error were identified including the sparseness of observations, errors associated with taking the difference between two large numbers, and using monthly average flux values when a significant amount of mass transport can occur at smaller time scales. The contributions of the first and third sources of error mentioned here may be reduced as better data sets become available and if more detailed calculations are made.

The soil-water balance is a climatological approach which is instructive, but also contains substantial uncertainties. The main reasons for the uncertainties in the soil-water balance are a simplified representation of land surface hydrology, the use of monthly average rainfall data, and the fact that there is no calibration with observed data of either soil moisture or runoff. Because of these assumptions, the soil-water balance model predicts zero runoff over large areas of the State where surface runoff actually does occur. The soil-water balance does provide qualitative information about the space and time variability of soil moisture and evapotranspiration that are not revealed by the annual surface water balance, but a way to confirm these results has not been worked out.

Use of the soil-water balance requires an estimate of potential evapotranspiration. One approach taken to estimating potential evapotranspiration was to use the Priestley-Taylor method because a net radiation data set described by Darnell et al., 1995, was available. The other approach was to use gross reservoir evaporation estimates (TWDB, 1995) derived using pan coefficients. As expected, the Priestley-Taylor method was not appropriate for arid areas in West Texas and it is seen that net radiation may be a better surrogate for actual evapotranspiration rather than potential evapotranspiration.

To facilitate the surface water balance, 166 USGS gaging stations were selected for analysis, and a 500 m digital elevation model was used to delineate the drainage areas for each gage. A 5 km grid of mean annual precipitation and mean annual runoff values compiled for each gage (both time averaged from 1961-1990) were used to derive a relationship between mean annual precipitation (mm) and the mean annual surface runoff (mm). This relationship is given in Equation 5.2 and applies in areas without unusually large groundwater recharge, springflow, urbanization, or reservoir impoundment. Applying this relationship to the precipitation grid, a grid of expected runoff was derived. While the precipitation in Texas ranges from about 200 mm year^-1 in West Texas to 1483 mm year^-1 in East Texas, the expected runoff varies from near 0 in West Texas to 417 mm year^-1 in the wettest parts of East Texas.

In locations where information about observed flows was used, the differences between expected runoff and observed runoff could be determined, and Figure 5.14 is a map showing where deviations from expected runoff occur. On this map, areas where observed runoff is much higher than the expected runoff correspond to watersheds where inter-watershed transfers are received or urbanization has caused high runoff coefficients, while the areas where observed runoff is much lower than expected correspond to watersheds from which recharge is transferred to other watersheds or the impacts of agriculture are significant. Adding the grid of deviations from expected runoff to the grid of expected runoff yielded a grid of actual runoff for the State (Figure 5.15). Accumulated flow maps were also created, using these runoff maps and a 500 m digital elevation model to define the drainage network. Using various line colors and line thicknesses to represent accumulated flow, these maps reveal statewide spatial trends such as the increased density of stream networks in East Texas, while also capturing localized phenomena such as large springflows. The runoff grids developed in this study have several potential uses. The grid of observed runoff may be useful in estimating non-point source pollution loads in a manner similar to that described by Saunders and Maidment, 1996. Use of the expected runoff grid or a similar grid may be helpful in assessing the amount of water available for human use. Accumulated flow maps may be useful in attributing digitized stream networks with flow data.

A grid of mean annual expected evaporation was estimated by subtracting the grid of expected runoff from the precipitation grid. The values of expected evaporation range from 200 mm year^-1 in West Texas to 1066 mm year^-1 in East Texas. Using the evaporation grid, the net radiation grid, and a temperature grid, a map of mean annual Bowen ratios for the State was created. These Bowen ratio values vary from 4.6 in West Texas (sensible heating of air dominates evaporation in a dry area) to 0.24 in East Texas (latent heat absorbed by evaporation dominates over sensible heating of air in a wet area).

As spatial data sets from remote sensing continue to improve along with tools like a GIS for manipulating spatial data, hydrologists can think in terms of water maps both in the atmosphere and on the land surface rather than thinking just in terms of point measurements. Working with a GIS allows for the computation of water balances on arbitrary control volumes and simplifies the use of complex spatial data. A large amount of data for the state of Texas has been compiled during this study, and his data will be useful to others in the future. A CD-ROM is available from the Center for Research in Water Resources (CRWR), University of Texas at Austin, that contains the data and programs used to make the computations described in this report. A description of the contents of this CD-ROM is provided in the Appendix to this report. Data used to plot the figures presented in this report are included on this CD-ROM and these data files are indexed in Part C of the Appendix.