Information transfer with censored data: Some large‐sample results

This paper presents some new results for the transfer and extension of information at sites with short hydrological records. The results refer particularly to the transfer and extension of annual flood data. The methods described make use of incomplete or “censored” data such as may be supplied by people living near a river or from records collected for nonhydrological purposes, and they constitute extensions to methods already described in the literature. For two specific censoring configurations, the gain in information is assessed analytically; it is shown that, under certain conditions, the gain in information can be substantial, but in general the gain is small, particularly where scale parameters are estimated. For other configurations of censored data, an analytical formulation is not possible, and integrals are given from which information gain may be assessed by numerical calculation. Another result extends the use of flood peaks exceeding some threshold value (“peaks over a threshold,” POTs); probabilistic models of flood frequency using POTs are, in effect, fitted using censored data. The value of the results presented in the paper is likely to be restricted by assumptions about the probabilistic structure of flood sequences: in one case that their distribution (at different sites) is bivariate lognormal, and, for the POT model, that floods occur as a Poisson process with POTs exponentially distributed. The results show, in strictly qualitative terms, the circumstances in which information might be gained by the use of censored data at two sites, and how large (or small) the gains might be.