Uncertainty of estimates of monthly areal rainfall for temporally sparse remote observations

The uncertainty of monthly areal mean rainfall estimates, caused by a finite sampling time resolution, is investigated making extensive use of data collected by tipping-bucket rain gauge networks at Darwin, Australia, and Melbourne, Florida. Using a subsampling methodology, the uncertainty is studied for complete area-covering observations occurring at regular time intervals. The analysis indicates that the sampling uncertainty is constrained by the rainfall depth, the sampling frequency, and the domain size. Taking into account that a rain gauge network does not truly reflect the sampling uncertainty one would encounter using complete area- covering observations, such as provided by radar or satellite, a rule of thumb is established for estimating the average sampling uncertainty as a function of the above factors. The estimated root mean square error E, expressed as a percentage of the monthly rainfall amount R(s), is found to be inversely proportional to the rain amount and the domain size A but proportional to the sampling time interval AT and can be approximated by E = 8.5 x 10³ X R(s)/^-0.6 A^-0.5 ΔT. Within this framework the various results reported in the literature from studies based on using other data and different spatial scales are found to be consistent with our results and among each other. The scaling of our results to timescales other than a month is indicated.