This study gives a phenomenologically based stochastic model of space-time rainfall. Specifically, two random variables on the spatial rainfall, e.g., the cumulative rainfall within a season and the maximum cumulative rainfall per rainfall event within a season are considered. An approach is given to determine the cumulative distribution function (c.d.f.) of the cumulative rainfall per event, based on a particular random structure of space-time rainfall. Then the first two moments of the cumulative seasonal rainfall are derived based on a stochastic dependence between the cumulative rainfall per event and the number of rainfall events within a season. This stochastic dependence is important in the context of the spatial rainfall process. A theorem is then proved on the rate of convergence of the exact c.d.f. of the seasonal cumulative rainfall up to the iᵗʰ year, i ≥ 1, to its limiting c.d.f. Use of the limiting c.d.f. of the maximum cumulative rainfall per rainfall event up to the iᵗʰ year within a season is given in the context of determination of the 'design rainfall'. Such information is useful in the design of hydraulic structures. Special mathematical applications of the general theory are developed from a combination of empirical and phenomenological based assumptions. A numerical application of this approach is demonstrated on the Atterbury watershed in the Southwestern United States.

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.

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.

No description available.

"The main objective of this study is to examine the influence of global SSTAs [sea surface temperature anomalies] on rainfall over eastern Africa (Fig. 1) using Florida State University T21 Global Spectral Model (FSUT21GSM) during the southern hemisphere summer of 1982 (wet year) and 1983 (dry year) (Fig. 2)"--Leaf 3. / Typescript. / "Summer Semester, 1991." / "Submitted to the Department of Meteorology in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: T. N. Krishnamurti, Professor Directing Thesis. / Includes bibliographical references.

Wong Chun Kit. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves [132-143]). / Abstracts in English and Chinese. / List of Tables --- p.i / List of Figures --- p.iv / List of Symbols --- p.v / Chapter CHAPTER ONE: --- INTRODUCTION --- p.1 / Chapter 1.1 --- Objectives and Significance of the Study --- p.4 / Chapter 1.2 --- Physical Setting of Hong Kong --- p.5 / Chapter 1.3 --- Climate of Hong Kong --- p.9 / Chapter 1.4 --- Data Acquisition --- p.11 / Chapter 1.4.1 --- Raingauges in Hong Kong --- p.11 / Chapter 1.4.2. --- Database for the Spatial Variation Analyses --- p.14 / Chapter 1.4.2.1. --- Data Selection for the Analyses for Factors Affecting Rainfall ´ؤ Elevation and Aspect --- p.15 / Chapter 1.4.2.2. --- Data Selection for the Classification of Stations and Inter-station Correlation Analysis --- p.17 / Chapter 1.4.3 --- Database for the Temporal Variation Analyses --- p.20 / Chapter CHAPTER TWO : --- LITERATURE REVIEW --- p.22 / Chapter 2.1 --- Spatial Variation of Rainfall --- p.22 / Chapter 2.2 --- Detection of Temporal Changes in Rainfall --- p.28 / Chapter 2.3 --- Urban Influence on Rainfall --- p.29 / Chapter 2.4 --- Studies in Hong Kong --- p.33 / Chapter CHAPTER THREE : --- METHODOLOGY --- p.33 / Chapter 3.1 --- Preliminary Processing of the Data --- p.38 / Chapter 3.2 --- Data Analysis --- p.40 / Chapter 3.2.1 --- General Pattern of Rainfall Distribution --- p.40 / Chapter 3.2.2 --- Data Analyses of Spatial Variation --- p.41 / Chapter 3.2.2.1 --- Correlation between Rainfall and Elevation --- p.41 / Chapter 3.2.2.2 --- Correlation between Rainfall and Aspect --- p.42 / Chapter 3.2.2.3 --- Classification of Stations --- p.43 / Chapter 3.2.2.4 --- Inter-Station Correlation Analysis --- p.46 / Chapter 3.2.3 --- Data Analysis of Temporal Variation --- p.46 / Chapter 3.2.3.1 --- The Running Mean Method --- p.47 / Chapter 3.2.3.2 --- The 'Standard Error of the Difference' Test --- p.49 / Chapter CHAPTER FOUR: --- RESULTS AND DISCUSSION --- p.50 / Chapter 4.1 --- Graphical Representation of Spatial Rainfall Pattern --- p.50 / Chapter 4.1.1 --- Annual Rainfall Pattern --- p.50 / Chapter 4.1.2 --- Monthly Rainfall Pattern --- p.56 / Chapter 4.1.3 --- Frequency Distribution of Raindays --- p.59 / Chapter 4.1.4 --- Pentade Rainfall Pattern --- p.64 / Chapter 4.1.5 --- Diurnal Rainfall Pattern --- p.67 / Chapter 4.1.6 --- Implications of the Spatial Rainfall Pattern --- p.70 / Chapter 4.2 --- Analyses of Spatial Variation in Rainfall --- p.78 / Chapter 4.2.1 --- Relationship between Rainfall and Elevation --- p.78 / Chapter 4.2.2 --- Relationship between Rainfall and Aspect --- p.82 / Chapter 4.2.3 --- Classification of Stations --- p.85 / Chapter 4.2.3.1 --- Principal Components Interpretation --- p.87 / Chapter 4.2.3.2 --- Result of Classification --- p.90 / Chapter 4.2.4 --- Inter-Station Correlation Analysis --- p.98 / Chapter 4.2.5 --- Discussion of the Rainfall Spatial Variation --- p.103 / Chapter 4.3 --- Analyses of Temporal Variation in Rainfall --- p.107 / Chapter 4.3.1 --- Annual Rainfall --- p.107 / Chapter 4.3.2 --- Monthly Rainfall --- p.110 / Chapter 4.3.3 --- Pentade Rainfall --- p.112 / Chapter 4.3.4 --- Diurnal Rainfall --- p.117 / Chapter 4.3.5 --- Discussion of the Rainfall Temporal Variation --- p.118 / Chapter CHAPTER FIVE: --- CONCLUSIONS AND RECOMMENDATIONS --- p.126 / Chapter 5.1 --- Summary of Findings --- p.126 / Chapter 5.2 --- Limitation of this Research --- p.129 / Chapter 5.3 --- Prospects of this Research --- p.130 / Bibliography

published_or_final_version / Civil Engineering / Master / Master of Philosophy

published_or_final_version / Statistics / Master / Master of Social Sciences

Project Completion Report, OWRT Project No. A-086-ARIZ / Agreement No. 14-34-0001-8003, Project Dates: 10/01/77-9/30/78 / Acknowledgement: The work upon which this report is based was supported by funds provided by the State of Arizona and the United States Department of Interior, Office of Water Research and Technology as authorized under the Water Resources Act of 1964. / From the Introduction: "The research work under this contract has been conducted by graduate student David B. Dunbar and summarized in his M.S. thesis entitled "Analysis of a Parameter Estimation Technique for Linear Hydrologic Systems Using Monte Carlo Simulation" submitted to the Department of Hydrology and Water Resources, University of Arizona, Tucson, in 1981. The present report is a brief summary of Mr. Dunbar's thesis." David Dunbar's thesis is available at: http://arizona.openrepository.com/arizona/handle/10150/191728 / The primary accomplishment of this research has been demonstrating the power of the deconvolution technique developed by Neuman and de Marsily (1976) in dealing with noisy rainfall- runoff records of short duration. Such records are encountered in arid environments where rainfall often occurs in short isolated bursts and the data are measured with a considerable margin of error. Our research work consisted of superimposing known noise on synthetic rainfall- runoff data and examining the ability of the Neuman -de Marsily deconvolution method to estimate the correct impulse response of the system when the data include only a single storm event. Approximately 50 Monte Carlo simulation runs were performed for each of three different noise models considered in our work. The results clearly demonstrated that the deconvolution model leads to reliable estimates and can be used with confidence in the presence of realistic noise levels. In addition to the Monte Carlo simulation tests and their analysis, certain improvements were introduced into the original deconvolution technique. In particular, the original version of the technique required that the hydrologist exercise subjective judgement in choosing the "best" solution for the deconvolution problem from a large number of admissible solutions. Our new method of selecting the "best" result is based on a comparative analysis of residuals and is more reliable than the earlier subjective approach. The improved method has been applied to real as well as synthetic rainfall -runoff data.

The sertao of northeast Brazil is a semiarid region characterized by recurring droughts. The vastness of the area (650,000 km$ sp2)$ poses a challenge to the effective monitoring of the impacts of drought at a scale that would be useful to the inhabitants of the sertao. Remote sensing data provide a viable way of assessing the extent and nature of drought across the landscape. / The work present a more effective algorithm to estimate rainfall from both the cold and warm cloud types present. Using a decision-tree methodology, the analysis yields rainfall estimates over the 0-21 mm range. Because seasonal variations in rainfall produce differences in vegetation, soils and hydrologic responses, Principal Components Analysis was used to examine these land surface responses. Individual components and component pairings were useful in identifying variations in vegetation density, geobotanical differences and drainage characteristics. The presence of cloud cover was found to dampen the land surface information that could be extracted. Landsat Thematic Mapper (TM) imagery was then used to produce a moisture index which characterizes surface wetness in relation to other features present in a scene. The multispectral combination of TM bands 1, 4 and 6 allowed for the separation of the surface types present, in locational space. This space was defined by an open-ended triange made up of a vertical "water line", a horizontal line of equal vegetation density; and a negatively-slopping iso-moisture line. The stability of the moisture index was influenced by varying scale and seasonal conditions. / In the drought conditions that prevailed in 1991-1992, these methods provide important additions to existing drought monitoring approaches in the Brazilian northeast. Further calibration is required in order to extend their applicability to other geographical regions and time frames.