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The Global Historical Climatology Network-Daily database contains, amongother variables, daily maximum and minimum temperatures from weather stationsaround the globe. It is long known that climatological summary statistics basedon daily temperature minima and maxima will not be accurate, if the bias due tothe time at which the observations were collected is not accounted for. Despitesome previous work, to our knowledge, there does not exist a satisfactorysolution to this important problem. In this paper, we carefully detail theproblem and develop a novel approach to address it. Our idea is to impute thehourly temperatures at the location of the measurements by borrowinginformation from the nearby stations that record hourly temperatures, whichthen can be used to create accurate summaries of temperature extremes. The keydifficulty is that these imputations of the temperature curves must satisfy theconstraint of falling between the observed daily minima and maxima, andattaining those values at least once in a twenty-four hour period. We develop aspatiotemporal Gaussian process model for imputing the hourly measurements fromthe nearby stations, and then develop a novel and easy to implement MarkovChain Monte Carlo technique to sample from the posterior distributionsatisfying the above constraints. We validate our imputation model using hourlytemperature data from four meteorological stations in Iowa, of which one ishidden and the data replaced with daily minima and maxima, and show that theimputed temperatures recover the hidden temperatures well. We also demonstratethat our model can exploit information contained in the data to infer the timeof daily measurements.

Bias correction in daily maximum and minimum temperature measurements through Gaussian process modeling