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Rainfall chemistry networks inevitably report some missing data, caused by contamination or loss of samples. However, there are no universally accepted rules about how such data, particularly from samples contaminated in the field, are identified and reported, leading to uncertainties in data usage by third parties, and possible incorrect inferences based on the reported data. This paper describes how the UK rainfall chemistry network data have been analysed for contamination, and how missing values can be estimated based on cross-correlations in time and space, using data from 20 sites over 26 years. The final flagged dataset is available through the CEH Environmental Information Data Centre ( EIDC). Erroneous data values are identified through consideration of ion balance (internal consistency), and evidence of contamination by birds or windblown dust based on the reported chemical analysis. Overall data capture with the erroneous data excluded and no replacement of missing data was 86%, but with much smaller data capture at some sites in some years, to <30% in some cases. The use of estimated data to replace missing values resulted in an increase in overall data capture to 96%, with only one site having data capture <70% in an individual year, and all sites achieving a data capture of 88% or more over the full period. The implications of using the reported 'official' annual data, as opposed to the dataset with missing values replaced by estimates, are illustrated by consideration of the temporal trend in nitrate at one site, which shows twice the value in the 'official' reported annual data compared with the 'estimated' data, part of a consistent pattern across all sites. Use of the uncorrected 'raw' sample data leads to large errors. [ABSTRACT FROM AUTHOR]

Multivariate extreme value models are used to estimate joint risk in a number of applications, with a particular focus on environmental fields ranging from climatology and hydrology to oceanography and seismic hazards. The semi‐parametric conditional extreme value model of Heffernan and Tawn involving a multivariate regression provides the most suitable of current statistical models in terms of its flexibility to handle a range of extremal dependence classes. However, the standard inference for the joint distribution of the residuals of this model suffers from the curse of dimensionality because, in a d‐dimensional application, it involves a d−1‐dimensional nonparametric density estimator, which requires, for accuracy, a number points and commensurate effort that is exponential in d. Furthermore, it does not allow for any partially missing observations to be included, and a previous proposal to address this is extremely computationally intensive, making its use prohibitive if the proportion of missing data is nontrivial. We propose to replace the d−1‐dimensional nonparametric density estimator with a model‐based copula with univariate marginal densities estimated using kernel methods. This approach provides statistically and computationally efficient estimates whatever the dimension, d, or the degree of missing data. Evidence is presented to show that the benefits of this approach substantially outweigh potential misspecification errors. The methods are illustrated through the analysis of UK river flow data at a network of 46 sites and assessing the rarity of the 2015 floods in North West England. [ABSTRACT FROM AUTHOR]