On the sampling errors from raingauges and microwave attenuation measurements

The sampling error formalism by North and Nakamoto (1989) has been widely r eferenced in research papers on sampling using space-borne sensors or groun d-borne sensors. However, their formalism is found to not only underestimat e the sampling error, especially for the raingauge network case, bur also n ot be applicable for the cases of using a line of raingauges or microwave a ttenuation measurements. In this payer, the sampling error formalism has be en revised and applied to the same sampling design and the same rainrate mo del as in North and Nakamoto (1989) for the comparison. The sampling error estimated using the revised formula was found to be more than 50% higher th an that by North and Nakamoto (1989). For the case of using a line of raing auges we found that the sampling error converges to a certain value, not ze ro as in North and Nakamoto formalism, as the number of gauges increases. T he microwave attenuation measurements case, which is the same as the case o f using a line of infinite raingauges, also gives non-zero sampling errors. Finally, the combined sampling using both satellite and ground-borne senso rs (e.g., raingauge network, a line of raingauges, or microwave attenuation measurements) was reviewed to check their design orthogonality and estimat ed the sampling errors for the combination of satellite and raingauge netwo rk case to see its behavior depending on various settings of these two diff erent measurements.