Some statistical characteristics of concentration and wet deposition in relation to rainfall amount for sulfate and nitrate in rain water

Abstract Some statistical characteristics of concentration ( C ) and wet deposition ( D ) for sulfate and nitres in rain water per rain event are described in relation to rainfall amount ( R ), using the data obtained at Shobara in Japan. The lognormal distributions may be appropriate for C of sulfate and nitrate, and R . In addition, log C of these two compositions has significant correlations with log R . Consequently, the bivariate distribution of C and R is assumed, then, the regression model of log C on log R and that of log D on log R are presented. It is shown that the expectation of log C , given R = r , corresponding to the regression function of log C on log R , is linear to log R , whereas its variance does not depend on r . Similarly, the regression function of log D on log R is linear to log r and its variance is also the same as that of log C on log R . Based on these results, the relationship: β ′ = β + 1 ( ϱ ≠ 0) is obtained, where β′, β and ϱ are the coefficient of slope of log D on log R , that of log C on log R , and population correlation coefficient between log C and log R , respectively. The values of β are −0.476 for sulfate and −0.479 for nitrate. From this result, concentrations of sulfate and nitrate are approximately predicted from rainfall amount by the inverse half-power relationships.