Browsing Hydrology and Water Resources in Arizona and the Southwest, Volume 02 (1972) by Subjects
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Collective Utility of Exchanging Treated Sewage Effluent for Irrigation and Mining WaterThe concept of collective utility is applied to a case study of alternative water resource utilization by providing a basis for comparing alternative uses of resources from the viewpoint of aggregate welfare. The exchange of sewage effluent for groundwater used by irrigation farmers, and the exchange of sewage effluent for groundwater used by processing and milling miners in Tucson, Arizona, are given as examples. Reviewed are collective utility concepts, case problems, definitions of problems, formulation of the model, and marginal change of collective utility. The first case has a collective utility of $800,500g, where g represents unquantifiable factors, such as the reduction in quality of living due to the odor if solid waste exchanges. The second case has a collective utility of $175,000. Since it is likely that g will be on the order of $1 million per year, the first exchange is preferable to the second.

The Construction of a Probability Distribution for Rainfall on a Watershed by SimulationA raingage reading is a sample from the point rainfall population of an area. The actual average rainfall on the area (watershed) is a conditional probability distribution. For the case of thunderstorm rainfall this distribution is simulated by looking at all storms that could have produced the raingage reading. The likelihood of each storm is a function of its center depth. The amount of rain dumped on the watershed by each storm is weighted by the likelihood of its occurence and the totality of such calculations is used to produce a probability distribution of rainfall on the watershed. Examples are given to illustrate the versatility of the program and its possible use in decision analysis.

Objective and Subjective Analysis of Transition Probabilities of Monthly Flow on an Ephemeral StreamA critique of statistical properties of monthly flows on an ephemeral stream in Arizona is given. A subjective procedure, justified for managerial purposes not concerned with the variability of flow within the month, is proposed for sequential generation of monthly flow data. Ephemeral flows should be modeled by starting with at least historical daily flows for more meaningful monthly flow models. Stochastic properties of monthly streamflows and state transition probabilities are reviewed with regard to ephemeral streams. A flow chart for a streamflow model geared to digital computers, with a simulation of streamflow subroutine, is developed. Meaningful monthly flow models could serve as a check on alternative models (subjective matrix, lagone auto regressive, harmonic, bivariate normal, bivariate lognormal models). Rules and guidelines are presented in developing meaningful probability matrices.

A Proposed Model for Flood Routing in Abstracting Ephemeral ChannelsAlmost all runoff from semiarid rangeland watersheds in southern Arizona results from intense highly variable thunderstorm rainfall. Abstractions, or transmission losses, are important in diminishing streamflow, supporting riparian vegetation and providing natural groundwater recharge. A flood routing procedure is developed using data from the walnut gulch experimental watershed, where flood movement and transmission losses are represented by a system using storage in the channel reach as a state variable which determines loss rates. Abstractions are computed as a cascade of general components in linear form. Wide variation in the parameters of this linear model with increasing inflow indicates that a linear relation between losses and storage is probably incorrect for ephemeral channels.

Role of Modern Methods of Data Analysis for Interpretation of Hydrologic Data in ArizonaMathematical 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 treering analyses, streamflow gaging stations, and digital modeling of small watersheds and the Tucson aquifers.

Transmissivity Distribution in the Tucson Basin AquiferThe distribution of transmissivity within the Tucson basin aquifer, as determined by pumping tests and reviewed in the construction of a digital model of the aquifer, was not totally random in space. Data tended to be distributed normally or lognormally for biased samples of developed wells. A frequency distribution of transmissivity derived from a calibrated digital model is more nearly representative of the real world because the aquifer sample is without bias as the sample constitutes the entire aquifer. Geohydrologic setting, electric analog, and digital models of the basin are discussed. The theory of transmissivity distribution in an arid land alluvial aquifer is developed from Horton's laws of exponential relationship between stream order and drainage network parameters. It is hypothesized that there is an exponential relationship between transmissivity of an alluvial aquifer. A statistical study was made of values derived from the digital model to test the probability density function hypothesized for transmissivity. The mean value is a function of climate and drainage area. These hypotheses require further validation.