Interpretation of mean-field bias correction of radar rain rate using the concept of linear regression

In this study, the correction problem of mean-field bias of radar rain rate was investigated using the concept of linear regression. Three different relationships were reviewed for their slopes to be used as the bias correction factor: Relationship 1 (R1) is based on the conventional linear regression, relationship 2 (R2) is forced to pass the origin and relationship 3 (R3) is the line whose slope is the G/R ratio. In other words, R1 is the regression line connecting the intercept and the mass centre of measurement pairs, R2 is the regression line forced to pass the origin, and R3 is the line connecting the origin and the mass centre. The slopes of all three relationships were reviewed analytically to compare them, and thereby, the effect of zero measurements could be evaluated. Additionally, the effect of using switched independent and dependent variables on the derived slopes was also evaluated. The theoretically derived results were then verified by analysing the rainfall event on 10-11 August 2010 in Korea. Finally, the difference between the bias-corrected radar rain rate and the rain gauge rain rate was quantified by root mean square error and mean error so that it could be used as a measure for the evaluation of bias correction factors. In conclusion, the slope of R2 was found to be the best for the bias correction factor. However, when deciding the slope of this R2, the radar rain rate should be used as the independent variable in the low rain rate region, and the rain gauge rain rate in the high rain rate region above a certain threshold.