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Mixed Station Method and Program <br />Alley and Burns (1981) developed the Mixed Station Method (MSM) for filling missing time <br />series data by linear regression. The name refers to its capability to fill several series in rapid <br />succession, using data from all available stations. Stations are labeled dependent or independent, <br />according to whether they are being filled, or regressed against (used to fill), at any given time <br />step. There is only one dependent series at a time. As soon as that series has been filled in, it <br />becomes an independent station and another becomes the dependent. Many independent stations <br />can be used to fill one time series, but only one station is used to fill each individual missing <br />value. Estimated missing values are never used to fill other missing data, and zero values, <br />although kept as actual gaged data, are not used in calculating correlation coefficients between <br />the gages. <br />The filling procedure is by selection of maximum correlation, using all eligible independent <br />gages to predict one missing value. The value that corresponds to the least standard error of <br />prediction (SEP) is kept. Eligible gages must have correlations that satisfy a selected confidence <br />interval (95% is default)with the dependent gage, and contain auser-defined minimum number <br />of concurrent values with the dependent series. Missing values can be predicted using monthly <br />and/or annual correlations; this maybe user-defined or also dependent on the least SEP. For <br />more information on this process, see the article by Alley and Burns (1981) referenced at the end <br />of this report. <br />The original United States Geological Society (USGS) Prime version of the MSM program was <br />rewritten to run on a PC in 1989 (Denver USGS). It was obtained for this project through the <br />Montana Department of Natural Resources and Conservation. The program performs the Mixed <br />Station Method, allowing the user to define: (1) the type of regression, (2) the type of <br />correlation, (3) the dependent and independent stations, (4) the first year of the extended record, <br />and (5) the minimum number of concurrent values between dependent and independent series. <br />These options are discussed in the following paragraphs. <br />Originally, there were four types of regression available in the MSM program: (1) simple linear <br />regression, (2) Maintenance of Variance (MOVE) I, (3) MOVE II, and (4) Regression Plus Noise <br />(RPN). Only the first three options were converted to PC language. The user should be aware <br />that simple linear regression tends to underestimate sample variance, and MOVE II and I tend to <br />overestimate it. Depending on the ultimate use of the filled data series, the user should chose the <br />method of regression accordingly. For more information on these methods see Hirsch (1982). <br />There are three correlation options in the Mixed Station program: cyclic (monthly), non-cyclic <br />(annual), or SEP dependent. As previously explained, the third option allows the program to try <br />both monthly and annual correlations in filling the missing data. The filled value that <br />corresponds to the least SEP will be preserved. <br />Next, the user is allowed to define which stations are independent, and which are dependent. <br />The dependent stations with missing data will be filled in, and the independent stations will be <br />used in the filling process. Thus, it is possible to define all stations as independent and <br />dependent, meaning they will all be filled, and they will all be used as potential predictor gages <br />for one another. <br />Appendix E E-111 <br />