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A stochastic model is developed to simulate flows for three seasons (September through February, March and April, May through August) at Overton, Odessa, and Grand Island, Nebraska on the Platte River. The model preserves the first and second order moment properties of the historical flow series, including significant autocorrelations within each station and cross-correlations between the stations. Higher order moments are preserved by a transformation technique that allows the residuals from the model to be approximately normal. An algorithm is given for easy simulation of combined-station flows, and some simulations are carried out to determine the likelihood of specified flow shortages that could be detrimental to the wildlife habitat in the reach of the Platte River between Overton and Grand Island, Nebraska. INTRODUCTION Two primary characteristics that make a riverine habitat suitable for use by migratory waterfowl, especially sandhill cranes and whooping cranes, are a wide, open river channel and a wet meadow environment. A wide river channel containing only sparse vegetation affords roosting birds some degree of protection from predators, while wet meadow environment enhances the capability of the birds to locate and feed on invertebrates that are critical to their dietary needs. 1 To maintain desirable river channel characteristics, sufficient streamflow must be available during the seed-falling period of May through August to prevent germination on the channel bars. Similarly, river stages must be high enough during the months of March and April to raise ground-water levels in the wet meadows sufficiently so that the birds can locate invertebrates within several inches of the land surface. Probabilities of flow events involving these two periods are of great interest to wildlife managers for planning habitat-management alternatives in the event of flow shortages. Therefore, in this report a calendar year is divided into three seasons as they affect these processes. They are: (1) March and April, when river stage influences ground-water levels; (2) May through August, when streamflow may inhibit seedling germination and establishment; and (3) September through February, which is generally the low-flow period. PURPOSE AND SCOPE OF STUDY This report: (1) Describes the development of a 3-season flow-series model for Overton, Odessa, and Grand Island, Nebraska (fig. 1); (2) demonstrates how this model can be used for simulation and evaluation of certain probabilities of interest; and (3) gives results of some simulation studies. The 3-season flow series for a particular station is derived by aggregating monthly average-flow series over three predetermined seasons. A precise description of the series will be given in the next section. Seasonal sums instead of averages are used for computational convenience; however, both series (sums or averages) contain the same information. The model is designed to maintain cross correlations between stations so that simulation of simultaneous three-station series can be made. However, to -_.43NEBRASKA 96° 102° EXPLANATION A06770500 STREAMFLOW GAGING STATION AND NUMBER 0 SO 100 III 200 KILOMETERS Figure 1. Map of Nebraska showing location of streamflow gaging stations. allow single-station simulations, individual models for each station remain autonomous. For example, the individual flow series for Odessa can be simulated without the Grand Island or Overton series. The correlation structure between stations is maintained by allowing residuals from single-station models to be correlated. The individual models in this report are periodic autoregression models (Pagano, 1978). A modified Box-Cox transformation technique (Box and Cox, 1964) is used to determine a transformation that results in residuals from the fitted models approximately following a normal distribution. The primary means of checking model adequacy will be to compare the statistical properties of the historical series to the properties of model simulations, as well as to check that the model assumptions are satisfied within a reasonable degree of accuracy. ACKNOWLEDGMENTS The author wishes to express his gratitude to the following for their valuable assistance: Duane Boes, M. R. Karlinger, R. F. Hadley, and C. F. Nordin, Jr. STATISTICAL PROPERTIES OF HISTORICAL-FLOW SERIES The 3-season flow series for each station are determined by aggregating 3 the monthly flow series. This monthly series consists of average ft /s (cubic feet per second) from October, 1942 to August, 1979 (water years 1943-1979) plus September, 1942, and can be obtained from Petsch and others, (1980). Season-one flows consist of the sum of the monthly series from September to February; season-two, the sum of March and April; and season-three the sum of May through August. Sums are used instead of means because the sums are more convenient. The year of season one will be designated by the year in which it ends (that is, season one of 1943 consists of September, 1942 to February,

A stochastic streamflow model of the Platte River at Overton, Odessa, and Grand Island, Nebraska