Mediterranean drought fluctuation during the last 500 years based on tree-ring data

Abstract

A 2.5 × 2.5° gridded summer (April–September) drought reconstruction over the larger Mediterranean land area (32.5°/47.5°N, 10°W/50°E; 152 grid points) is described, based on a network of 165 tree-ring series. The drought index used is the self-calibrated Palmer Drought Severity Index, and the period considered is 1500–2000. The reconstruction technique combines an analogue technique for the estimation of missing tree-ring data with an artificial neural network for optimal non-linear calibration, including a bootstrap error assessment. Tests were carried out on the various sources of error in the reconstructions. Errors related to the temporal variations of the number of proxies were tested by comparing four reconstructions calibrated with four different sized regressor datasets, representing the decrease in the number of available proxies over time. Errors related to the heterogeneous spatial density of predictors were tested using pseudo-proxies, provided by the global climate model ECHO-G. Finally the errors related to the imperfect climate signal recorded by tree-ring series were tested by adding white noise to the pseudo-proxies. Reconstructions pass standard cross-validation tests. Nevertheless tests using pseudo-proxies show that the reconstructions are less good in areas where proxies are rare, but that the average reconstruction curve is robust. Finally, the noise added to proxies, which is by definition a high frequency component, has a major effect on the low frequency signal, but not on the medium frequencies. The comparison of the low frequency trends of our mean reconstruction and the GCM simulation indicates that the detrending method used is able to preserve the long-term variations of reconstructed PDSI. The results also highlight similar multi-decadal PDSI variations in the central and western parts of the Mediterranean basin and less clear low frequency changes in the east. The sixteenth and the first part of the seventeenth centuries are characterized by marked dry episodes in the west similar to those observed in the end of the twentieth century. In contrast, the eighteenth and nineteenth centuries (Little Ice Age) are characterized by dominant wet periods. In the eastern part of the Mediterranean basin the observed strong drought period of the end of the twentieth century seems to be the strongest of the last 500 years.

Appendix: the reconstruction method

Compared to the majority of palaeoclimatological proxies, dendroclimatology has an advantage in having annual time-series for calibrating the relationships between climate and proxies. The relatively low time resolution of other proxies means that variability in time must be replaced by variability in space and a training set must be collected from a wide variety of locations. For these proxies, the modern analogue technique (MAT) has become the leading approach after Hutson (1980), Prell (1985) and Guiot et al (1985), because the method avoids spurious extrapolations and does not affect significantly the reconstructed variance. This is crucial when we are interested in large climatic changes such as glacial-interglacial fluctuations.

For a given past assemblage, the MAT is based on a search for the most similar assemblages among a collection of modern samples. An appropriate distance measure is required in order to evaluate the degree of analogy between past and modern samples. When the method is applied to tree-ring data (Guiot et al. 2005), the assemblages are replaced by annual vectors of proxies, and the objective is to fill missing data in the proxy matrix by using the most similar vectors containing sufficient data. It is possible to use a variety of distance measures, but the Euclidian distance is certainly the most practical here:

$$ {\mathop {d^{2}_{{ts}} }\nolimits_{} } = \frac{1} {{m_{{ts}} }}{\sum\limits_{k = 1}^{m_{{ts}} } {{\left( {p_{{tk}} - p_{{sk}} } \right)}^{2} } } $$

(3)

where m _ts is the number of proxies simultaneously available for year t (with missing data) and potentially analogue year s, p _tk (resp. p _sk ) is the value of proxy k for year t (resp. year s), d _ij ² is the mean squared Euclidian distance between years t and s. Each proxy series is first standardized so that it ranges between 0 and 1.

The smaller the distance, the greater is the degree of analogy between the two years. Thus, for each proxy series k and year t, we look for analogue years in the other proxy series. A subset of these years is then selected; corresponding to a small number of samples with existing data for proxy series k and the estimated value $\hat{p}_{{tk}}$ is then obtained as a weighted average of the same proxy series at the analogous years. As the estimate is an average of a subset from the same statistical population, there is a slight bias in the estimation of its variance. This non-linear approach can be compared to the expectation maximization algorithm proposed by Schneider (2001).

After infilling of the missing proxies, the relationship between instrumental climate series and proxies is calibrated by a non-linear technique (the artificial neural network, ANN) for the period for which climatic data are available. This technique has been largely applied in dendroclimatology (Guiot and Tessier 1997; Woodhouse 1999; D’odorico et al. 2000; Carrer and Urbinati 2001; Ni et al. 2002). We used the feedforward network trained with the backpropagation learning algorithm and validated by a bootstrap technique (Guiot et al. 2005). ANN does not give systematically better results than linear regression, but, when it is carefully applied (avoiding overfitting), it is never worse (Racca et al. 2001). It is better when there are strong non-linearities in the relationship.