THE RELATION OF RADAR TO CLOUD AREA - TIME INTEGRALS AND IMPLICATIONS FOR RAIN MEASUREMENTS FROM SPACE

In this work we determine the relationships between satellite-based and radar-measured area-time integrals (ATI) for convective storms and show how both depend upon the climatological conditional mean rain rate R(c) and the ratio of the measured cloud (or radar echo) area to the actual rain area of the storms. Arkin's GOES precipitation index (GPI) = GF(c)T (mm) where F(c) is the fraction of a 2.5-degrees box in GATE [GARP (Global Atmospheric Research Program) Atlantic Tropical Experiment] having clouds with infrared (IR) brightness temperatures less than 235 K, G = 3 mm h -1, and T is cloud duration. However, we show that G is the ratio of R(c) to [A(c)]/[A(r)] where A(c) and A(r) denote cloud and rain area, respectively. We have demonstrated that Arkin's GPI reaches a stable asymptotic value for boxes of 2.5-degrees in size because they include a sufficient number of storm cells to ensure that 1 ) the sample R(c), and thus the probability density function (PDF) of R, are representative of those in the climatological population; and 2) the ratio of the averages [A(c)]/A(r)] is similarly representative of the typical storm structure for the climatic regime. As the space-time sampling domain decreases, the correlation of GPI with cloud fraction decreases because these conditions are not met. Also, as the spatial sampling domain decreases, G decreases and the ratio [A(c)]/[A(r)] increases because the smaller areas tend to have a larger fraction of rain-free cloud. Since [A(c)]/[A(r)] must vary with storm type and climatic regime, the asymptotic (large area) GPI developed for GATE is unlikely to be valid for other regions. Smith et al. have also found a satellite cloud ATI for individual convective storms in North Dakota using a threshold IR brightness temperature of 250 K. In this case, we find that the ratio of the cloud to radar ATIs increases with the total volumetric rainfall, presumably because the more intense storms are associated with stronger updrafts and upper-level divergence, thus causing the cloud areas to exceed the rain areas by progressively larger amounts. Nevertheless, if the relationship between cloud and radar ATI is a stable one for a sufficient sample domain in each climatic regime, as is to be expected, then the cloud ATI becomes as powerful an estimator of convective rain as is the radar ATI (Rosenfeld et al. and others). One of its most valuable applications would be in conjunction with a satellite radar and/or radiometer as proposed for the Tropical Rainfall Measuring Mission (TRMM). TRMM could then serve as a global calibrating device to eliminate systematic biases. The increased sampling rate with the geosynchronous ATI would greatly improve the accuracy of the rainfall estimates, resulting in rms errors of 15%-20% of the mean in 2.5-degrees boxes and 12 h, as compared with the 10% error for monthly averages over 5-degrees boxes anticipated for TRMM. Such estimates would be useful for regional- and global-scale monitoring and forecasting.