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The Global ETD Search service is a free service for researchers
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Showing 1 to 6 of 6 (0.065 seconds)Spelling suggestions: "subject:"amathematical studies"" "subject:"dmathematical studies""
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Uncertainties in Digital-Computer Modeling of Ground-Water BasinsGates, Joseph S., | Kisiel, Chester C. 23 April 1971 (has links)
From the Proceedings of the 1971 Meetings of the Arizona Section - American Water Resources Assn. and the Hydrology Section - Arizona Academy of Science - April 22-23, 1971, Tempe, Arizona / Much future computer modeling of the responses of groundwater to water development stresses may be poorly done if the errors and limitations of digital models are not fully appreciated by groundwater hydrologists. Two digital models were constructed of the Tucson basin, one with 1,890 nodes of 1/4 square mile area each and one with 509 nodes of 1 square mile each. The starting point for the digital model was the 2-dimensional, linear, parabolic, time-and space-invariant differential equation of incompressible flow through porous media. An explicit finite-difference equivalent was determined, and a set of 1,890 equations were put in implicit form and solved on a computer in less than 20 seconds at a cost of 2.00 dollars. The errors associated with the model are discussed. In deciding what new data collected in the Tucson basin would give the most improvement in the digital model, a statistical decision theory approach was utilized in which expected opportunity loss and expected worth of sample were calculated for 5 variables. The data was computed using about 110 seconds of computer time, costing about 13.00 dollars. This technique has the advantage of including basin dynamics in estimating worth of additional data by means of using the digital model to compute all values of predicted and 'true' water levels included in the loss function.
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Conditional Streamflow ProbabilitiesRoefs, T. G., Clainos, D. M. 23 April 1971 (has links)
From the Proceedings of the 1971 Meetings of the Arizona Section - American Water Resources Assn. and the Hydrology Section - Arizona Academy of Science - April 22-23, 1971, Tempe, Arizona / Streamflows of monthly or shorter time periods, are, in most parts of the world, conditionally dependent. In studies of planning, commitment and operation decisions concerning reservoirs, it is probably most computationally efficient to use simulation routines for decisions of low dimensions, as planning and commitment, and optimization routines for the highly dimensional operation rule decisions. This presents the major problem of combining the 2 routines, since streamflow dependencies in simulation routines are continuous while the direct stochastic optimization routines are discrete. A stochastic streamflow synthesis routine is described consisting of 2 parts: streamflow probability distribution and dependency analysis and a streamflow generation using the relationships developed. A discrete dependency matrix between streamflow amounts was then sought. Setting as the limits of interest the class 400-500 thousand acre ft in January and 500-600 thousand acre ft in February, and using the transforms specified, the appropriate normal deviates were determined. The next serious problem was calculating the conditional dependency based on the bivariate normal distribution. In order to calculate the joint probability exactly, double integrations would be required and these use too much computer time. For the problem addressed, therefore, the use of 1-dimensional conditional probabilities based on the flow interval midpoint is an adequate and effective procedure.
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Augmenting Annual Runoff Records Using Tree-Ring DataStockton, Charles W., Fritts, Harold C. 23 April 1971 (has links)
From the Proceedings of the 1971 Meetings of the Arizona Section - American Water Resources Assn. and the Hydrology Section - Arizona Academy of Science - April 22-23, 1971, Tempe, Arizona / Statistical analyses of existing hydrologic records suffer from the problem that such records are of relatively short duration, and therefore may not necessarily be random samples of the infinite population of events. On the hypothesis that tree-ring series and runoff series respond to a common climatic signal or signals that permit prediction of annual runoff from annual ring-width index, tree-ring data are used to extend available runoff records backwards in time to permit more accurate estimates of the 3 most common statistics used in hydrology: the mean, the variance and the 1st order correlation. It is assumed that both series are generated by the climatic parameters of precipitation, temperature, evapotranspiration, seasonal regime and spatial distribution. Of major concern in the reconstruction of annual runoff series from tree-ring records was the difference in persistence within each of the 2 series. A matrix of the tree-ring data was constructed, lagged up to 3 times and principal components were extracted. The covariation in this matrix was then decomposed by extracting the Eigen-vectors, and multiple regression was then used to weight the respective series and the differences in persistence were determined. This method was applied to watersheds of diverse characteristics and improved estimates of the mean and variance were obtained.
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Input Specifications to a Stochastic Decision ModelClainos, D. M., Duckstein, L., Roefs, T. G. 06 May 1972 (has links)
From the Proceedings of the 1972 Meetings of the Arizona Section - American Water Resources Assn. and the Hydrology Section - Arizona Academy of Science - May 5-6, 1972, Prescott, Arizona / The use of discrete conditional dependency matrices as input to stochastic decision models is examined. Some of the problems and initial assumptions involved with the construction of the above mentioned matrices are discussed. Covered in considerable detail is the transform used to relate the gamma space with the normal space. A new transform is introduced that should produce reasonable results when the record of streamflow (data) has a highly skewed distribution. Finally, the possibility of using the matrices to provide realistic inputs to a stochastic dynamic program is discussed.
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Role of Modern Methods of Data Analysis for Interpretation of Hydrologic Data in ArizonaKisiel, Chester C., Duckstein, Lucien, Fogel, Martin M. 06 May 1972 (has links)
From the Proceedings of the 1972 Meetings of the Arizona Section - American Water Resources Assn. and the Hydrology Section - Arizona Academy of Science - May 5-6, 1972, Prescott, Arizona / Mathematical models, requiring substantial data, of hydrologic and water resources systems are under intensive investigation. The processes of data analysis and model building are interrelated so that models may be used to forecast for scientific reasons or decision making. Examples are drawn from research on modeling aquifers, watersheds, streamflow and precipitation in Arizona. Classes of problems include model choice, parameter estimates, initial condition, input identification, forecasting, valuation, control, presence of multiple objectives, and uncertainty. Classes of data analysis include correlation methods, system identification, stationarity, independence or randomness, seasonality, event based approach, fitting of probability distributions, and analysis for runs, range and crossing levels. Time series, event based and regression methods are reviewed. The issues discussed are applied to tree-ring analyses, streamflow gaging stations, and digital modeling of small watersheds and the Tucson aquifers.
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Effects of Brush to Grass Conversion on the Hydrology and Erosion of a Semiarid Southwestern Rangeland WatershedSimanton, J. R., Osborn, H. B., Renard, K. G. 16 April 1977 (has links)
From the Proceedings of the 1977 Meetings of the Arizona Section - American Water Resources Assn. and the Hydrology Section - Arizona Academy of Science - April 15-16, 1977, Las Vegas, Nevada / Increased nutritional and economic demands for agricultural products have dictated the need for greater and more efficient use of western grass forage. Vegetation manipulation is the quickest and most economical means of increasing forage. However , the hydrologic effects must be taken into consideration before embarking on a large scale vegetation manipulated program. This study discusses the hydrologic and erosion changes measured from a 110-acre semiarid watershed which was converted from brush to grass by root plowing and seeding. Significant changes were observed in rainfall-runoff relationships as average summer runoff was considerably in excess of predictions. Sediment yield also varied, and both of these results were tied to the change in vegetative cover and post conversion rainfall conditions.
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