On the sampling errors from raingauges and microwave attenuation measurements

The sampling error formalism by North and Nakamoto (1989) has been widely referenced in research papers on sampling using space-borne sensors or ground-borne sensors. However, their formalism is found to not only underestimate the sampling error, especially for the raingauge network case, but also not be applicable for the cases of using a line of raingauges or microwave attenuation measurements. In this paper, the sampling error formalism has been revised and applied to the same sampling design and the same rainrate model 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 than that by North and Nakamoto (1989). For the case of using a line of raingauges we found that the sampling error converges to a certain value, not zero as in North and Nakamoto formalism, as the number of gauges increases. The microwave attenuation measurements case, which is the same as the case of using a line of infinite raingauges, also gives non-zero sampling errors. Finally, the combined sampling using both satellite and ground-borne sensors (e.g., raingauge network, a line of raingauges, or microwave attenuation measurements) was reviewed to check their design orthogonality and estimated the sampling errors for the combination of satellite and raingauge network case to see its behavior depending on various settings of these two different measurements.