The Log-Linearity of Vertically Integrated Moisture Quantities and Rain Rate

Abstract:

We use radar-derived rain rates as well as radiosonde moisture data collected on Gan Island during DYNAMO to examine the relationship between CRH, a two-layered model of atmospheric moisture, vertically integrated humidity, and a unique humidity weighting method and rainfall rate. Our study compares the performance of each of metrics by evaluating the statistical relationships between our column-integrated moisture variables and rainfall rate. Additionally, the relative strengths and weaknesses uncovered for each integrated moisture variable hint at the underlying physics of rainfall over tropical oceans. We find that the relationship between CRH and rainfall rate is log-linear across the entire range of sampled CRH, and the same applies to our two-layer model. The correlation coefficient between CRH and the natural log of rainfall rate is 0.75. The two-layer model performs as well overall as CRH, but slightly better at low humidity. Using LP spaces to weight integrated relative humidity performs worse. The high R-value between CRH and log rain rate confirms that CRH is a reasonable statistical determinate of rainfall rate and encapsulates most of the relationship between atmospheric moisture and precipitation in the tropics. The two-layer model performs slightly better in low-moisture scenarios, suggesting that moisture distribution is meaningful in a way CRH fails to fully capture. The log-linearity of the relationship between all integrated moisture variables and rain rate shows that mean precipitation does not exhibit a “pickup.” Instead, the relationship between precipitation and atmospheric moisture in common, light-rain cases can be extrapolated to predict behavior for extremely high levels of atmospheric moisture.