Uncertainty of Areal Rainfall Estimation Using Point Measurements

Abstract:

The spatial variability of precipitation has a great influence on the quantity and quality of runoff water generated from hydrological processes. In practice, point rainfall measurements (e.g., rain gauges) are often used to represent areal rainfall in catchments. The spatial rainfall variability is difficult to be precisely captured even with many rain gauges. Thus the rainfall uncertainty due to spatial variability should be taken into account in order to provide reliable rainfall-driven process modelling results. This study investigates the uncertainty of areal rainfall estimation due to rainfall spatial variability if point measurements are applied.

The areal rainfall is usually estimated as a weighted sum of data from available point measurements. The expected error of areal rainfall estimates is 0 if the estimation is an unbiased one. The variance of the error between the real and estimated areal rainfall is evaluated to indicate the uncertainty of areal rainfall estimates. This error variance can be expressed as a function of variograms, which was originally applied in geostatistics to characterize a spatial variable. The variogram can be evaluated using measurements from a dense rain gauge network.

The areal rainfall errors are evaluated in two areas with distinct climate regimes and rainfall patterns: Greater Lyon area in France and Melbourne area in Australia. The variograms of the two areas are derived based on 6-minute rainfall time series data from 2010 to 2013 and are then used to estimate uncertainties of areal rainfall represented by different numbers of point measurements in synthetic catchments of various sizes. The error variance of areal rainfall using one point measurement in the centre of a 1-km² catchment is 0.22 (mm/h)² in Lyon. When the point measurement is placed at one corner of the same-size catchment, the error variance becomes 0.82 (mm/h)² also in Lyon. Results for Melbourne were similar but presented larger uncertainty. Results indicated that the errors of areal rainfall intensities become more significant as the size of the catchment increases and can be decreased with more rain gauges placed in a catchment. The quantified areal rainfall uncertainty benefits further uncertainty analysis in rainfall-driven process modelling.