Using Regression Models and the Climatic Water Budget
              to Predict Water Temperatures and Water Heights
                for Application in Climate/Dengue Analysis

                              Shouquan Cheng
                              Paula Fornwalt
                               Scott Greene
                           Laurence S. Kalkstein

                       Center for Climatic Research
                          Department of Geography
                          University of Delaware
                             Newark, DE 19716

Goal: To predict maximum and minimum water temperatures using regression models and to predict water heights using the climatic water budget for different containers in the different sites.

Water temperature:

The procedure used in this study is the stepwise regression for maximum and minimum water temperatures. The independent variables in the regression are maximum and minimum air temperatures, maximum and minimum dew point temperatures, daytime (7:00 AM to 6:00 PM) and nighttime (7:00 PM to 6:00 AM) mean total cloud cover, and a parameter utilized to compensate the loss of long-wave radiation from water for covered sites, which is called "shelter" in the equations. For the maximum water temperature, one additional variable used in the regression is "sun exposure". The values of shelter and sun exposure for different sites are the best combination based upon our tests.

Maximum and minimum water temperatures (oC) for any site and container can be predicted by the following equations:

WaterTempmax = -0.751 + 0.171*MaxT + 0.096*MinT + 0.088*MinDpt - 0.183*DayCC + 9.819*SunExp + 11.464*Shelter

WaterTempmin = -14.849 + 0.079*MaxT + 0.254*MinT + 0.102*MaxDpt + 0.070*MinDpt + 9.211*Shelter,

where MaxT and MinT are maximum and minimum air temperatures (oF), MaxDpt and MinDpt are maximum and minimum dew point temperatures (oF), DayCC is day mean cloud cover (10th), Sunexp is sun exposure. The model coefficient determinations (R2) are 0.7673 and 0.8086 for maximum and minimum water temperatures respectively. These imply that 76.73% and 80.86% of the variation in maximum and minimum water temperatures is accounted for by the models. In addition, both models have a significance level of 0.0001.

These new regression equations appear to be a better predictor of minimum and maximum water temperatures than the original regression equations (Focks 1993; see attached graphs labeled "Dengue Modelled" for site 2). For our regression equation, the factor "shelter" seems to be especially important in determining the minimum water temperature because it accounts for the reradiation of heat trapped by the site. Also, because minimum water temperature values are recorded at night, we determined that sun exposure is not a relevant factor in predicting the minimum water temperature.

Water heights:

Water heights for three different containers were modeled using the Thomthwaite/Mather climatic water budget. A water budget is an account for daily or monthly moisture gains, losses, and storages for a particular place. Using a water budget, quantitative values of water storage, surplus, runoff, and deficit can be obtained by comparing precipitation and potential evapotransipiration. We possess user-friendly software to compute daily and monthly water budgets.

The daily temperature, precipitation, and initial water volume of the container are used in the water budget model. Some parameters should be initialized for the model. We can send the software of the model to you, and tell you how to modify the parameters and run the programs.

For some particular sites, such as under a tree or roof, the daily temperature and precipitation were modified. By adjusting these variables, we can account for temperature and precipitation changes caused by a protective roof. However, precipitation increased under the tree, probably because of trunk flow.

Because site 1 is uncovered, the temperature and precipitation did not need to be modified. On the other hand, site 4 (under roof, no walls) was not adjusted because of inconsistencies in the water height observations. Water height for the five gallon container never increased, as would be expected for a site under a roof. However, both the tire and the one gallon container appeared to accumulate precipitation. In addition, the temperature and precipitation could not be adjusted because a correction for one part of the data would worsen the other part (see attached graphs of site 4).

The climatic water budget appears to be a better estimator of water height than the original model (Focks 1993; see attached figures labeled "Dengue Modelled" for five gallon container, all sites). Because it is more physically and meteorologically based, values obtained from the water budget are comparable to the observed values.