Global high resolution versus Limited Area Model climate change projections over Europe: quantifying confidence level from PRUDENCE results

Abstract

Four high resolution atmospheric general circulation models (GCMs) have been integrated with the standard forcings of the PRUDENCE experiment: IPCC-SRES A2 radiative forcing and Hadley Centre sea surface temperature and sea-ice extent. The response over Europe, calculated as the difference between the 2071–2100 and the 1961–1990 means is compared with the same diagnostic obtained with nine Regional Climate Models (RCM) all driven by the Hadley Centre atmospheric GCM. The seasonal mean response for 2m temperature and precipitation is investigated. For temperature, GCMs and RCMs behave similarly, except that GCMs exhibit a larger spread. However, during summer, the spread of the RCMs—in particular in terms of precipitation—is larger than that of the GCMs. This indicates that the European summer climate is strongly controlled by parameterized physics and/or high-resolution processes. The temperature response is larger than the systematic error. The situation is different for precipitation. The model bias is twice as large as the climate response. The confidence in PRUDENCE results comes from the fact that the models have a similar response to the IPCC-SRES A2 forcing, whereas their systematic errors are more spread. In addition, GCM precipitation response is slightly but significantly different from that of the RCMs.

Appendix

1.1 Multidimensional scaling

The aim of this method is to plot onto one (or a few) plane(s) several points which belong to a high-dimensional vector space, so that the distances in the projection plane are as close as possible to the actual distances between the points. A simple to understand application of this technique is to represent the main European cities on a map on which the distance in cm between the cities is not proportional to the actual distance in km, as in a typical road map, but to the shortest travel time by train. In the present study, it is applied to graphically synthesize a series of numerical model fields over Europe.

Let X(i,x) be the value of field X (e.g. 2 m temperature in DJF) for model i (i=1,..., n) at location x (x representing here the latitude longitude pair). Let s(x) be the surface of the mesh corresponding to x. The mean field (centroid) is:

$${\overline{X}}(x)=\frac {1} {n}{\sum\limits_{i=1}^{n}}X(i,x)$$

(3)

and the matrix to be diagonalized is:

$$V_{ij}=\sum\limits_{x}s(x)(X(i,x)-{\overline X}(x))(X(j,x)-{\overline X}(x))$$

(4)

Let ν _k (i) be the kth eigenvector (with norm 1) associated to the eigenvalue λ _k (the eigenvalues being sorted in decreasing order. Then the kth axis for the projection is:

$$A_{k}(x)=\sum\limits_{i=1}^{n}\nu_{k}(i)(X(i,x)-{\overline X}(x))$$

(5)

The point representing model i is $({\sqrt{\lambda_{1}}}\nu_{1}(i),{\sqrt{\lambda_{2}}}\nu_{2}(i))$ and the coordinates of the point representing a new field Y(x) (k=1 or 2):

$$y_{k}=\frac {1}{{\sqrt{\lambda_{k}}}}\sum_{x}s(x)A_{k}(x)(Y(x)-{\overline X}(x))$$

(6)

In the case of a non-euclidean distance, Eqs. 3, 4, 5, 6 are no more valid since we use the array d _ij of the distances between the models, which is no more a quadratic combination of the array X(i,x). Equation 4 is replaced by

$$V_{ij}=\frac{1}{2}\left(\frac{1}{n}\sum\limits_{h}d^{2}_{hj}+\frac{1}{n}\sum\limits_{k}d^{2}_{ik}-d^{2}_{ij}-\frac{1} {n^{2}}\sum\limits_{hk}d^{2}_{hk}\right)$$

(7)

and the eigenvectors of $V_{ij}$ scaled by the square root of the (sorted) eigenvalues provide the coordinates of the representative points. In this paper, we use only euclidean distances.