AN APPLICATION OF RANK-ORDER STATISTICS TO THE JOINT SPATIAL AND TEMPORAL VARIATIONS OF METEOROLOGICAL ELEMENTS

PAUL R. JULIAN Laboratory of Atmospheric Sciences, National Center for Atmospheric Research, * Boulder, Colo.

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Abstract

Principal components or empirical orthogonal functions are virtually the sole statistical tool used to date for investigations of space-time variability of meteorological elements. Maximum statistical efficiency and possible physical interpretation of empirical orthogonal functions derives from the assumptions of stationarity and homoscedasticity of the scalar variables in space and time. In this study, a rank table technique is given in which temporal data from a number of stations is ranked time-wise, and rank sums for each time obtained by summing ranks over the total number of stations. The technique offers some advantages for investigations of joint space-time variability. First, it is nonparametric; second, analysis of variance schemes are simplified; and third, a test of homoscedasticity can easily be performed. Networks of streamflow and precipitation data over the conterminous 48 States are used to illustrate the use of the technique. As a result, streamflow and precipitation data are shown to be spatially heteroscedastic—dry periods are better correlated spatially than wet periods. A runs test on the temporally varying rank sums suggests that while precipitation is not temporally heteroscedastic (dry and wet periods are both essential randomly distributed), streamflow data might be. Apparently, years of deficient streamflow tend to be persistent while years of excessive streamflow are essentially randomly distributed in time.

Abstract

Principal components or empirical orthogonal functions are virtually the sole statistical tool used to date for investigations of space-time variability of meteorological elements. Maximum statistical efficiency and possible physical interpretation of empirical orthogonal functions derives from the assumptions of stationarity and homoscedasticity of the scalar variables in space and time. In this study, a rank table technique is given in which temporal data from a number of stations is ranked time-wise, and rank sums for each time obtained by summing ranks over the total number of stations. The technique offers some advantages for investigations of joint space-time variability. First, it is nonparametric; second, analysis of variance schemes are simplified; and third, a test of homoscedasticity can easily be performed. Networks of streamflow and precipitation data over the conterminous 48 States are used to illustrate the use of the technique. As a result, streamflow and precipitation data are shown to be spatially heteroscedastic—dry periods are better correlated spatially than wet periods. A runs test on the temporally varying rank sums suggests that while precipitation is not temporally heteroscedastic (dry and wet periods are both essential randomly distributed), streamflow data might be. Apparently, years of deficient streamflow tend to be persistent while years of excessive streamflow are essentially randomly distributed in time.

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