A New Parameter to Assess Impact of Rain Gauge Density on Uncertainty in the Estimate of Monthly Rainfall over India

Abstract

Abstract Rain gauges are considered the most accurate method to estimate rainfall and are used as the “ground truth” for a wide variety of applications. The spatial density of rain gauges varies substantially and hence influences the accuracy of gridded gauge-based rainfall products. The temporal changes in rain gauge density over a region introduce considerable biases in the historical trends in mean rainfall and its extremes. An estimate of uncertainty in gauge-based rainfall estimates associated with the nonuniform layout and placement pattern of the rain gauge network is vital for national decisions and policy planning in India, which considers a rather tight threshold of rainfall anomaly. This study examines uncertainty in the estimation of monthly mean monsoon rainfall due to variations in gauge density across India. Since not all rain gauges provide measurements perpetually, we consider the ensemble uncertainty in spatial average estimation owing to randomly leaving out rain gauges from the estimate. A recently developed theoretical model shows that the uncertainty in the spatially averaged rainfall is directly proportional to the spatial standard deviation and inversely proportional to the square root of the total number of available gauges. On this basis, a new parameter called the “averaging error factor” has been proposed that identifies the regions with large ensemble uncertainties. Comparison of the theoretical model with Monte Carlo simulations at a monthly time scale using rain gauge observations shows good agreement with each other at all-India and subregional scales. The uncertainty in monthly mean rainfall estimates due to omission of rain gauges is largest for northeast India (~4% uncertainty for omission of 10% gauges) and smallest for central India. Estimates of spatial average rainfall should always be accompanied by a measure of uncertainty, and this paper provides such a measure for gauge-based monthly rainfall estimates. This study can be further extended to determine the minimum number of rain gauges necessary for any given region to estimate rainfall at a certain level of uncertainty.