Issues in estimating observed change at the local scale - a case study: the recent warming over France
Ribes, Aurélien ; Corre, Lola ; Gibelin, Anne-Laure ; Dubuisson, Brigitte
In order to estimate observed warming, many studies rely on linear trends with uncertainty ranges derived using a white noise assumption on the residuals. Here, we assess the extent to which these two very rough assumptions - that the change is linear in time and that internal variability (IV) is a white noise - can be used to estimate the observed warming accurately. While such general issues have been widely discussed in statistics, this article provides a few practical recommendations for use in climate data. First, we assess the impact of different assumptions regarding the temporal shape of the change, e.g. a linear trend versus a more refined temporal pattern deduced from climate model responses to historical forcings. Secondly, we discuss how the observed warming, with its uncertainty ranges, can be estimated if IV is not assimilated to a white noise. In this respect, we compare the ordinary and generalized least square estimators; the first is much more commonly used while the latter has optimal properties. We also illustrate the impact of different assumptions on IV - either a white noise, a red noise or that deduced from long, unforced simulations by climate models - on both the best estimate and confidence intervals of observed changes. Our results suggest that non-linear estimates should be preferred and that a calibrated red noise assumption leads to an adequate estimation of uncertainty. This analysis is illustrated using a new data set of monthly homogenized temperatures across mainland France and suggests that the observed warming is now significant on the local scale throughout the country, with an overall warming of +?1.5 ± 0.5?°C over the 1959-2009 period.
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