A method for regional climate change detection using smooth temporal patterns

Abstract

This paper introduces an original method for climate change detection, called temporal optimal detection method. The method consists in searching for a smooth temporal pattern in the observations. This pattern can be either the response of the climate system to a specific forcing or to a combination of forcings. Many characteristics of this new method are different from those of the classical “optimal fingerprint” method. It allows to infer the spatial distribution of the detected signal, without providing any spatial guess pattern. The spatial properties of the internal climate variability doesn’t need to be estimated either. The estimation of such quantities being very challenging at regional scale, the proposed method is particularly well-suited for such scale. The efficiency of the method is illustrated by applying it on real homogenized datasets of temperatures and precipitation over France. A multimodel detection is performed in both cases, using an ensemble of atmosphere-ocean general circulation models for estimating the temporal patterns. Regarding temperatures, new results are highlighted, especially by showing that a change is detected even after removing the uniform part of the warming. The sensitivity of the method is discussed in this case, relatively to the computation of the temporal patterns and to the choice of the model. The method also allows to detect a climate change signal in precipitation. This change impacts the spatial distribution of the precipitation more than the mean over the domain. The ability of the method to provide an estimate of the spatial distribution of the change following the prescribed temporal patterns is also illustrated.

Appendix: Hotelling test

Denoting $\widetilde{\psi}_t = {(\widetilde{\psi}_{s,t})}_{1 \leq s \leq S}$ and $\widetilde{\phi}_t = {(\widetilde{\phi}_{s,t})}_{1 \leq s \leq S},$ model (11) can be written as a multivariate regression model:

$$ \widetilde{\psi}_t = m + g \widetilde{\mu}_t + \widetilde{\phi}_t, \quad t=2,\ldots,T, $$

(15)

where the $\widetilde{\phi}_t$ are independent and N(0, C ^(S)) distributed random vectors, and where m denotes the mean (1 − α) ψ⁰.

Within this framework, the Hotelling test is the multivariate generalization of the student test to this problem. As in the univariate case, the test is optimal and based on euclidean projections. Set

$$ X = \left[ {\mathbb{1}},\widetilde{\mu} \right], $$

(16)

one can estimate m,  g,  ϕ, respectively by $\widehat{m},\; \widehat{g},\; \widehat{\phi},$ using a least square method. The univariate estimate of the standard deviation is then replaced by the random matrix $\widehat{C^{(S)}}$ that estimates C ^(S):

$$ \widehat{C^{(S)}} = \frac{\widehat{\phi}^{\prime} \widehat{\phi}}{T-3}, $$

(17)

where A′ denotes the transpose of A. This random matrix follows a Wishart distribution $W \left( T-3,\frac{C^{(S)}}{T-3} \right).$ Finally, the Hotelling test is based on the variable v:

$$ v = \widehat{g}^{\prime} {\widehat{C^{(S)}}}^{-1} \widehat{g}, $$

(18)

that follows a Fisher distribution F(S, T − S − 2).