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published_or_final_version / Electrical Engineering / Doctoral / Doctor of Philosophy

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Project Completion Report / OWRT Project No. A-027-ARIZ / Development of a mathematical model of infiltration which includes the effects of raindrop impact / Agreement No. 14-31-0001-3503 / Project Dates: July 1971-December 1972. / The purpose of this investigation was to use an existing mathematical model of infiltration to assist in determining which factors, including raindrop impaction, were responsible for infiltration characteristics of a bare semiarid watershed. The infiltration model developed by Roger Smith was selected as best suited for this investigation. Several laboratory and field rainfall simulator runs were modeled. Good correlation was found between the modeled and experimental results for both the infiltration data and the saturation profiles, for both bare and grass covered plots. For the lab and field experiments a realistic rotating disk rainfall simulator was used. In the field tests bare and grass covered plots were tested. In the lab specially constructed soil boxes were used that permitted measurement of infiltration and saturation profiles with time. Gross changes in saturated hydraulic conductivities due to crusting effects were also measured. Gamma ray attenuation techniques were used to obtain density and soil moisture profiles for the laboratory experiments. It was found that the Smith model can be used to simulate infiltration from different surface conditions as long as there is some method to calibrate the model. Carefully obtained saturated and unsaturated hydraulic properties for the soil types present in the watershed are needed in addition to infiltration data from a realistic rainfall simulator or through hydrograph analysis from unit subwatersheds.

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Distributions of amount of rain with rainfall rate and of duration with rate are determined for all rain of 1963 and for the heavy rain of 1958 to 1962. The rainfall rates are obtained from the rain chart records of the McGill Cbservatory tipping-bucket recording rain gauge. Separate distributions for winter and summer rain are evaluated. The distributions of amount with rate for both winter and summer rain are log-normal; they have logarithmic means of 2.5 mm hr⁻¹ and 12.6 mm hr⁻¹ respectively and logarithmic standard deviations of 0.4 and 0.7 respectively. A comparison of the distributions of amount with rate for winter rain and for snow shows that the two distributions are similar in form. [...]

Radar cells from the GATE experiment, from Spain and from the Montreal area were followed and measurements of their total rain flux and area were extracted. The values of the flux and area, for each one of the cells, for initial time increments T(,0) were used to evaluate various extrapolation schemes for forecasting purposes. The extrapolation procedure that gave the smallest error in forecasting the changes in flux and area, was found to be the linear one and the optimum increment T(,0) was about 30 min. However, even though these techniques have the advantage of establishing a trend in the behavior of the flux and area with time, a comparison of the forecast errors from the linear extrapolation scheme with those from the assumption of no change in cell area and rain flux shows insignificant improvements. A technique including both cell motion and internal changes in flux and area of the rain cells was developed to evaluate the accuracy of rain accumulation forecasts. Again, it was found that the errors were similar with those generated by the assumption of no change in rain flux and area from the moving cell. / The preceding results were used as a possible input into the design and evaluation of cloud seeding experiments. Based on this, a method is developed which gives the necessary number of experiments (i.e., seeded cases) in order for a seeding factor to be statistically significant at specified confidence levels. As a conclusion, it can be stated that the use of short term rain predictions (which are translated as differences of the rain flux in time) is very promising. In comparison to other techniques described in the literature this method appears to be superior, in the sense that fewer experiments are needed to detect seeding factors at specified confidence levels.

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In order to address rain attenuation scattering of millimetric waves and microwave sin Botswana, we have employed a comparison technique to determine the Ro.o1 at fourteen diverse locations in Botswana. In addition we have identified two rain climatic zones for Botswana. We note that Matzler employs Mie Scattering technique to determine the specific attenuation due to rain in Central Europe. Both Matzler and Olsen use the exponential distribution of N(D) to calculate y. In this dissertation we use the Mie scattering approach, but assume several distributions, including the log-normal distribution of N(D) as expounded by Ajayi et aI., to determine y for tropical and subtropical regions of Africa. The results show that the extinction coefficients depend more strongly on temperature at lower frequencies than at higher frequencies for lognormal distribution: at selected frequencies, we record high attenuation values at rising SHF bands: at 300 GHz, tropical showers take on values of 12, 12.5, 11.9 and 14 dB/km for Gaborone, Francistown, Kasane and Selebi-Phikwe, respectively. The absorption coefficient is significant but decreases exponentially with rain temperature at lower microwave frequencies. The application of the proposed model (Continental Thunderstorm is shown using practical results from Durban) is corroborated using practical results from Durban. Further, based on attenuation measurements, it is found that the lognormal distribution is suitable for Durban at rain rates greater than or equal to 21 mm/h. At rain rates below this, the loss-Thunderstorm is the better fit. Finally in this dissertation the results show that for rainfall intensity below about 10 mm/h for Marshall-Palmer (MP), Joss-Drizzle (JD), Joss-Thunderstorm (JT) and Law-Parson (LP) distributions, and below about 4 mm/h for Continental-Showers (CS), Tropical Showers (TS), Continental Thunderstorms (CT) and Tropical Thunderstorm (TT) distributions, the specific rain backscattering follows Rayleigh scattering law where the rain drops are small with respect to the wavelength when the frequency is 19.5 GHz. At rain rates above 10 mm/h for exponential distribution, and above 4 mm/h for lognormal distribution, the specific backscattering follows Mie scattering law. When the received echo power from rain becomes significant, it contributes to the rise in the noise floor and the radar receiver can lose its target. In addition, the result shows that Mie backscattering efficiency is highest at a raindrop diameter of 4.7mm. / Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2008.