Neural computation in paleoclimatology: General methodology and a case study

Neurocomputing 113 (2013) 262–268

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Letters

Neural computation in paleoclimatology: General methodology and a case study L. Carro-Calvo a, S. Salcedo-Sanz a,n, J. Luterbacher b a b

Department of Signal Processing and Communications, Universidad de Alcalá, Spain Department of Geography, University of Giessen, Germany

art ic l e i nf o

a b s t r a c t

Article history: Received 26 January 2012 Received in revised form 3 September 2012 Accepted 26 December 2012 Communicated by M.T. Manry Available online 18 March 2013

In this paper we present the general methodology and main issues related to the application of neural networks to paleoclimatic reconstruction problems. We establish the basic methodological framework, data selection, organization and their relation to neural networks' features. We also describe a skill score to compare regressors' performance and finally the paleoclimatic variable's reconstruction. We show a case study focused on winter precipitation reconstruction in the Mediterranean back to 1700, using multi-layer perceptrons, and the comparison of the obtained results to that of the existing alternative methodologies. & 2013 Elsevier B.V. All rights reserved.

Keywords: Paleoclimatology Neural networks Climate reconstruction

1. Introduction In the last few years, the study of paleoclimatology has attracted the attention of the scientific community, in an attempt to corroborate the anthropogenic origin of the global climate change detected in the second half of the twentieth century [1,2]. In this sense, temperature, pressure and precipitation are the key variables in many human ecosystems, and are the most affected ones by global change. The Mediterranean region offers an unusually rich combination of long, high-quality instrumental time series, natural archives, and documentary information across time and space, making possible sufficiently sensitive reconstructions of climate in past centuries to shed light on both changes in climate extremes and socio-economic impacts prior to the instrumental period [3]. In [3] an in-depth review of early instrumental data and high temporal resolution proxies can be found. That study supports the statistically based multi-proxy field reconstructions of winter temperature and precipitation covering the past 500 years. Temporal high resolution paleoclimatological studies mainly rely on reconstructions that cover several centuries ago, what usually require a large amount of data. There are different types of data that can help in paleoclimatic reconstructions: natural proxies (tree rings, spelethems, corals, ice cores, etc., see [1] for a recent review), instrumental records (meteorological measures taken in the past), n Correspondence to:Sancho Salcedo-Sanz. Department of Signal Processing and Communications, Universidad de Alcalá. Tel.: þ34 91 885 6731; fax: þ34 91 885 6699. E-mail address: [email protected] (S. Salcedo-Sanz).

0925-2312/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.neucom.2012.12.045

and finally documentary evidences (documents made in the past that record events related to meteorological variables [4]). Europe and the Mediterranean area are one of the few regions in the world where all these different data are available [5–9]. The general methodology of any paleoclimatic reconstruction based on measuring data is the following: the available data are divided into a calibration period and a reconstruction period. The data in the calibration period are used to calibrate the regression algorithms. Then, these algorithms are applied to the data in the reconstruction period, in order to obtain the final paleoclimatic variable reconstruction. Different algorithmic approaches have been applied to paleoclimatic reconstruction, such as classical regression approaches and Bayesian hierarchical modeling [1,10–14]. There are several studies devoted to show that neural computation approaches can also be successfully applied in paleoclimatology, specifically, paleotemperature reconstruction [15–18], studies on paleovegetation [19,20] and Antarctic paleoclimate [21]. However, none of these approaches provide a general methodology for the application of neural networks to paleoclimate problems. In this paper we present such a general methodology for the application of neural computation methods to paleoclimate reconstruction problems. The general methodology proposed takes into account the several peculiarities of the reconstruction problem, related to the existence (or not) of reconstruction variables in the data, the geographic distribution of the different data types and the reconstruction skill considered as figure of merit to measure the good performance of the neural networks considered. Finally, we show a case study in a problem of winter (December to February) precipitation reconstruction for the Mediterranean land areas back to AD 1700.

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The paper is structured as follows: the next section comprises the body of the paper, where we present the general methodology of paleoclimatic reconstruction problems involving neural networks and the case study of precipitation reconstruction in the Mediterranean. Section 3 shows some results in the case study considered, to illustrate the performance of a multi-layer perceptron in this problem. Section 4 concludes the paper by drawing some final remarks.

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2. Paleoclimatic reconstruction with neural networks In this section we present the general methodology for paleoclimatic reconstruction problems using neural networks, and also the specific case of study is tackled in this paper.

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2.1. General methodology

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Let G be a N  M grid that represents the area where a given meteorological variable V will be reconstructed (Fig. 1). Each point of the grid Gij has associated a measure of V, V ij ðτÞ, τ∈P, where P represents the period where the measure V exists. The objective of the problem is to obtain a reconstruction of the variable V, let us call V^ , in a larger period of study P′, from a set of constructive variables. Let rp be the set of constructive variables which are proxies, ri the constructive variables which are instrumental and finally rd the constructive variables which are documentary indexes (Fig. 2). Each of these variables may be defined in different time domains in the period P′, i.e., all the constructive variables may exist in a given time period τ′∈P′ and do not exist in a different time period τn ∈P′. With these starting data, a set of regressors (neural networks in this case) is used in each point Gij, in order to reconstruct the variable V. Each neural network (k) is defined by a set of constructive variables, Rk ¼ fr kp ,r ki ,r kd g, where r kp ⊂r p , r ki ⊂r i and r kd ⊂r d . Note that not all the constructive variables in the grid are available for all the points, but only the variables that are close enough to the point in the grid are under study. In fact, depending on the point of the grid, there will be more or less constructive variables available. The selection of these variables is carried out by applying a proximity criterium, where we set circles of increasing radius around the grid point under study (Fig. 3). The neural network must have at least four variables as inputs, so in the first circle if there are not four constructive variables available, the information in the next circle is taken into account. Note finally that there are as many neural networks as the number of different time domains in which these constructive variables are defined. Then, the period P in which there exist measures of the variable under study V, is divided into a training set P o (formed by two subsets: train—for carrying out the network training and validation—for stopping the training when error starts growing in this set, in order to prevent overfitting), and test P t subperiods, in order to train the different neural networks in the grid. Once each neural network is trained, we can reconstruct the variable V back to the period P′, by using the different constructive variables available for each grid point and neural network. Fig. 5 shows an example of the neural network structure we propose for this problem, where the input variables depend on the grid point considered and also on the reconstruction time. The reconstruction performance is measured by using the reconstruction skill, Re in the test set (see [22]), that is defined as Re ¼ 1−

∑i∈P t ðV i −V^ i Þ2 ∑i∈P t ðV i −V i Þ2

ð1Þ

where V i stands for the observe (measured) values in the test set, V i are the reconstructed values over the same period and V is the

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Fig. 1. Study region (a) and associated grid for land areas (0.51 x 0.51 resolution, (b)).

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Fig. 2. Input data considered: asterisks mark natural proxies (corals and tree ring chronologies), points stand for instrumental data and circles mark documentary data.

mean in the calibration period (P o ). Note that this reconstruction skill compares the performance of a proposed regressor against a very simple one, often used in paleoclimatology: the mean over the training set. The closer Re is to 1, the better is a proposed method over the mean (reference) regressor. 2.2. Case study: winter precipitation reconstruction in the Mediterranean back to 1700 In this paper we show an example of a paleoclimatic reconstruction: winter precipitation (in millimeters1) in the Mediterranean basis, back to 1700. Precipitation reconstruction is a very important topic that has attracted the attention of many researchers in the last decades [24–32]. Specifically, in this work we consider a grid G, which covers the Mediterranean land areas, about 451N to 301N and 201W to 401E [3,5]. Fig. 1(a) shows the zone under the study and Fig. 1(b) its associated grid, with 2253 points. The variable considered, V, winter precipitation in this case, has measurement data from 1900 to 1983 (when the majority of the proxies end up). The information used in each point of the grid [23] to carry out the precipitation reconstruction is divided into three data types: proxies, instrumental and documentary indexes, taken in different points (even out of the defined grid), as shown in Fig. 2. The winter 1

Note that 1 mm of precipitation is equivalent to 1 liter per square meter.

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proxies considered are shown in Table 3. Regarding instrumental precipitation series, we use a few long series [6] that have been applied before in other studies in the literature, described in Tables 4 and 5. Finally, documentary evidences include all noninstrumental, man-made data on past weather and climate, described in Tables 1 and 2, respectively. Documentary sources include reports from chronicles, daily weather reports, travel diaries, ships logbooks, etc. Note that we have used the same features as in [6] in order to carry out a fair comparison with the Principal Component Regression (PCR) technique described in [6]. An example of the different radius circles to select the closest constructive variables is shown in Fig. 3. Note that we have considered five different radii for the circles: 2.51, 5.01, 10.01, 15.01 and 20.01. Fig. 4 shows the availability of the different constructive variables during the reconstruction period P′, which in this case is 1700–1983. We have divided the measurement data (1901–1983) into a calibration period (P o : 1901–1956), formed by a training set (1901–1935) and validation set (1936–1956), and finally a test set (P t : 1957–1983), where we will test the performance of the neural networks. In this work we have applied a set of multi-layer perceptrons (MLP) as regressors in each point of the grid G. The structure of this neural network is given in Fig. 5. Each MLP has been trained using the Levenberg–Marquardt algorithm [33], using the data in the calibration period (P o : 1901–1956), and with a number of features that vary depending on the point of the grid to study, and the period to be reconstructed, as stated before. The number of neurons in the hidden layer of a given MLP network k, has been set to be jRk j þ1, where jRk j stands for the number of inputs in the network. In order to show an example of the MLP configuration and circles used to select the constructive variables in each MLP, Fig. 6(b) shows,

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for a point of the grid displayed in Fig. 6(a), the different MLP networks used along the time, depending on the available constructive variables. Note that to ensure the reconstruction of the complete period back to 1700, we need 25 MLP networks in this case. Fig. 7 shows the different constructive variables of the 25 MLPs, and the different circles needed to include at least four input constructive variables in each MLP (as shown in Fig. 4, not all the constructive variables are available for all the time period under study). Table 6 shows the number of constructive input for each one of the 25 MLPs needed to reconstruct the complete period back to 1700 in this point of the grid. In the next section, we compare the results obtained with those obtained in [6], where a PCR algorithm has been applied to the same data.

3. Results Fig. 8 shows a first experiment using the train and validation sets established above. In each of these sets we have obtained the average over the time of the Re obtained by the MLP (in fact, in each point, several MLPs are trained depending on the information available). The results show that the MLPs are well trained (in average) in the majority of points, but in those where the available information is very sparse. The comparison of the train and validation figures gives an idea of the mean MLP performance in terms of generalization capability of the MLP. The results obtained by the MLP in the reconstruction period are shown in Fig. 9. This figure shows the results obtained by the MLPs in terms of reconstruction skill Re. Specifically, this figure shows the points of the region under study where a positive value of the score skill (Re > 0 in green) is obtained in the test period (P t : 1957–1983), for different reconstruction periods P′, i.e. different features as input in the MLPs. Four reconstruction periods have been selected in order to calculate the average of the Re, 1700– 1750, 1750–1800, 1800–1850 and 1850–1900. Recall that positive values of Re (positive score skill) denote that the MLP performs better than the simple mean regressor in a given region and for a given period.

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Fig. 3. Example of constructive variables selection for the neural network, at a given point of the area under study, based on a structure of concentric circles. The first circle considered around a given point does not contain any input data (constructive variables), the second circle only contain three sources of data (instrumental data), and finally, the third circle contains five sources of instrumental data.

Table 1 Discontinuous documentary indices for winter precipitation reconstructions in the Mediterranean basis, see [6] for references. Location

Country

Longitude [1E]

Latitude [1N]

Start year

Barcelona Madrid Seville Murcia Lisbon Athens

Spain Spain Spain Spain Portugal Greece

2.1 −3.7 −5.9 −1.2 −9.0 23.7

41.3 40.4 37.4 37.9 38.7 38.0

1675 1675 1675 1675 1675 1675

Table 3 Proxies used for winter precipitation reconstruction in the Mediterranean basis, see [6] for references. Type of proxy

Proxy location

Country

Longitude [1E]

Latitude [1N]

Start year

Tree ring-widths

Afraskou Afechtal AmmiHsain Boulzane Col du Zad Ich Ramouz Jaffar Ta Adlount Tissouka Tounfite Dana Reserve

Morocco Morocco Morocco Morocco Morocco Morocco Morocco Morocco Morocco Morocco Jordan

−5.0 −3.2 −4.5 −4.6 −4.9 −3.8 −3.1 −4.4 −4.9 −4.7 35.5

32.3 32.3 32.5 32.5 33.0 33.8 32.5 32.4 35.1 32.4 30.6

1500 1500 1500 1500 1500 1500 1500 1728 1748 1500 1500

Corals δ18 O

Ras Umm Sidd

Egypt

34.3

27.9

1751

Table 2 Continuous documentary indices for winter precipitation reconstructions in the Mediterranean basis, see [6] for references. Location

Country

Longitude [1E]

Latitude [1N]

Start year

Swiss plain Southern Germany Ancient Hungary Southern Spain

Switzerland Germany Hungary Spain

7.3 11.4 19.0 −5.4

46.5 ∼48 47.5 36.2

1500 1500 1500 (gap 1780 1840) 1501

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Table 4 Instrumental data used for winter precipitation reconstructions in the Mediterranean basis (I), see [6] for references.

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Longitude [1E]

Latitude [1N]

Start year

1800

Ajaccio Athens Bad Gastein Bad Gleichenberg Bad Ischl Basel Beirut Bern Bistrita Bologna Bordeaux Bregenz Bucharest Budapest Chateau d'Oex Chaumong Coimbra Constantine Dijon Dareibeida Evora Engelberg Geneva Grand St.-Bernhard Graz Hvar Innsbruck Jerusalem

France Greece Austria Austria Austria Switzerland Lebanon Switzerland Romania Italy France Austria Romania Hungary Switzerland Switzerland Portugal Algeria France Algeria Portugal Switzerland Switzerland Switzerland Austria Croatia Austria Israel

8.8 23.7 13.1 15.9 13.6 7.6 35.5 7.2 24.5 11.7 −0.7 9.73 26.1 19.0 7.1 7.0 −8.4 6.6 5.1 3.3 −7.9 8.2 6.2 7.1 15.4 16.3 11.4 35.2

41.9 38.0 47.1 46.9 47.7 47.6 31.8 46.6 47.1 44.5 44.8 47.5 44.4 47.5 46.3 47.0 40.2 36.3 47.3 36.7 38.6 46.5 46.2 45.5 47.1 43.1 47.3 31.8

1856 1871 1859 1880 1859 1864 1888 1760 1853 1813 1842 1875 1865 1841 1879 1864 1866 1838 1831 1859 1870 1864 1826 1874 1865 1864 1866 1846

1850 1900 documentary

Proxies

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90

Fig. 4. Availability of the different types of inputs data within the reconstruction time back to 1700. The figure represents all the available data in the different years considering all the points in the grid where data are available.

r1 Proxies

rNp r1 Instrumental

rNi r1 Documentary

rNd

Table 5 Instrumental data used for winter precipitation reconstructions in the Mediterranean basis(II). Country

Longitude [1E]

Latitude [1N]

Start year

Klagenfurt Kremsmunster Lisbon Lugano Luqa Lyon Madrid Marseille Milan Nantes Munchen Odessa Perpignan Ponta Delgada Porto Salzburg San Fernando Seckau Severin Sibiu Sils Maria Sion Sulina Tbilisi Timisoara Tolouse Trieste Tripoli Vienna Zurich

Austria Austria Portugal Switzerland Malta France Spain France Italy France Germany Ukraine France Portugal Portugal Austria Spain Austria Romania Romania Switzerland Switzerland Romania Georgia Romania France Italy Libya Austria Switzerland

14.3 14.1 −9.0 9.0 14.5 4.8 −3.7 5.4 9.2 −1.6 11.5 30.6 2.9 −25.7 −8.7 13.5 −5.7 14.8 22.6 24.1 9.7 7.3 29.7 44.9 21.3 1.4 13.8 13.1 21.8 8.6

46.5 48.0 38.7 46.0 35.8 45.7 40.4 43.3 45.5 47.3 48.1 46.5 42.7 37.7 41.2 47.8 36.4 47.3 44.6 45.8 46.7 46.2 45.2 41.7 45.8 43.6 45.7 32.7 48.2 47.4

1814 1820 1835 1861 1841 1841 1860 1749 1764 1835 1848 1847 1850 1865 1863 1865 1806 1892 1883 1851 1864 1864 1869 1844 1873 1835 1841 1879 1841 1708

Fig. 5. Structure of the neural network used in this study of reconstruction of winter precipitation in the Mediterranean.

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In order to obtain an indication of the real performance of the MLPs in this problem, we have compared the results to that of an existing algorithm, the PCR applied in [6]. Fig. 10 shows a comparison of the performance of both algorithms, in terms of

Fig. 6. MLPs used along the time and circle that contains the input variables for precipitation reconstruction in a given point. Different colors stand for the different MLPs used in the reconstruction process. (a) Location of grid point; and (b) MLP used. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

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Fig. 7. Different reconstructive variables used by each MLP in Fig. 6 (25 MLPs are needed for the reconstruction of the period under study), displayed together with the circles needed for the variables' selection.

Table 6 Number of input variables for each MLP in the example considered in Fig. 6. MLP identifier

No. of input variables

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

5 4 4 4 5 6 7 8 9 8 9 10 12 13 4 5 4 4 5 5 5 4 13 14 14

differences ReMLP −RePCR , so the closer a given point is to 1, the better the performance of the MLP compared to the PCR, and the closer it is to −1, the better is the PCR. Note that again, the compared performance depends on the reconstruction period, but we can observe that the largest differences between the two methods are obtained consistently in central Italy and northern central Africa. In general the MLP obtains better results than the PCR in points of the grid far away from information source (proxies, documentary indices or instrumental data). As a final example, Fig. 11(a) shows the reconstruction of the winter precipitation during the complete P′, for the point shown in

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Fig. 8. Score skill values (Re) obtained in the area considered, using the MLP in the train and validation sets; (a) Re in the train set; and (b) Re in the validation set.

Fig. 11(b). Fig. 11(a) also shows in gray color the maximum error margin (the real signal is within the gray zone with a probability of 95%) in the reconstruction of the signal. In order to calculate this, we consider Gaussian noise with a variance calculated in the test period P t . Each period has different data inputs, that produce different uncertainties in the objective variable's reconstruction. Note that the reconstruction in the initial period 1700–1750 is the one with the largest reconstruction error (large error margin), as expected. The rightmost part of the figure shows the reconstruction in periods P o and P t . Specially important is the reconstruction in the test period P t , where the reconstructed signal can be compared with the measured variable. Note that the reconstruction is quite good obtaining the peaks of precipitation, even if it is able to capture a large precipitation peak in the winter of 1960. However, note also that the proposed neural network tends to over-estimate the lack of precipitation, as can be seen in the figure.

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Fig. 10. Comparison of the improvement in score skill (ReMLP −RePCR ), obtained by the neural network performance against the PCA regression in the region under study.

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Fig. 9. Points of the region under study where a positive score skill (Re > 0 in green) result is obtained using the proposed MLP approach. Different time periods of winter precipitation reconstruction are shown. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

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The results shown in this paper reveal that neural networks, an MLP in this case, are interesting algorithms to solve Paleoclimatology reconstruction problems, with results that can be better than the best existing approach in the literature. This paper opens new research possibilities, for example on improving the neural network performance, and on comparing the performance of different regressors based on neural computation in this and related paleoclimatic reconstruction problems.

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4. Conclusions The study of paleoclimatology has gained relevance in the last 20 years in the context of global climate change studies. In this paper we have presented a basic methodological framework for applying neural networks to paleoclimatic variable reconstruction. We have presented the main issues related to the application of neural networks, such as the different numbers of features depending on the point and reconstruction time under study. We have also considered other problem's characteristics such as the different data needed in this application and the performance measure, based on a skill score which allows a direct comparison between different approaches. We have presented a case study where neural networks are able to successfully reconstruct winter precipitation in the Mediterranean, back to 1700.

Year Fig. 11. Winter (December to February sum) precipitation reconstruction for one selected grid point; (a) location of grid point; (b) complete winter precipitation reconstruction back to AD 1700, including the calibration period from 1901 to 1956. The uncertainties are given in grey.

Acknowledgments Carro-Calvo is supported in part by the European Science Foundation through a Medclivar Exchange grant, number 2902, and by Fundación Iberdrola through a research Fellowship of the program “Becas de Energía y Medio Ambiente, 2011”. This work has been partially supported by Spanish Ministry of Science and Innovation, under project number ECO2010-22065-C03-02. Jürg

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Luterbacher was supported by the EU/FP6 project CIRCE (#036961), the EU/FP7 project ACQWA (#212250). Professor Luterbacher also acknowledges support by the Deutsche Forschungsgemeinschaft project PRIME within the Priority Programme “INTERDYNAMIK” and the project “Historical climatology of the Middle East based on Arabic sources back to AD 800”. References [1] P.D. Jones, K.R. Briffa, T.J. Osborn, J.M. Lough, T.D. van Ommen, B.M. Vinther, et al., High-resolution palaeoclimatology of the last millennium: a review of current status and future prospects, Holocene 19 (1) (2009) 3–49. [2] G.R. North, et al., Surface Temperature Reconstructions for the Last 2000 years, Committee on Surface Temperature Reconstruction for the Last 2000 years, National Research Council of the National Academies, National Academy Press, Washington DC, 2006. [3] J. Luterbacher, et al., Mediterranean climate variability over the last centuries: a review, in: P. Lionello, P. Malanotte-Rizzoli, R. 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Leo Carro-Calvo was born in Guadalajara, Spain, in 1984. He received the B.S. and M.S. degrees in telecommunication engineering in 2009 and 2010, respectively, from Universidad de Alcalá, Madrid, Spain, where he is currently pursuing the Ph.D. degree. He has published 10 journal papers and several conference articles in the areas of neural networks and softcomputing algorithms. He is currently a Research Fellow with the Department of Signal Processing and Communications, Universidad de Alcalá. His main research interests include evolutionary and neural network computation applied to regression and classification problems.

Sancho Salcedo-Sanz was born in Madrid, Spain, in 1974. He received the B.S degree in Physics from the Universidad Complutense de Madrid, Spain, in 1998, and the Ph.D. degree in Telecommunications Engineering from the Universidad Carlos III de Madrid, Spain, in 2002. He spent 1 year in the School of Computer Science, The University of Birmingham, U.K, as a postdoctoral Research Fellow. Currently, he is an associate professor at the department of Signal Processing and Communications, Universidad de Alcalá, Spain. He has co-authored more than 150 international journals and conference papers in the field of machine learning and soft-computing. Dr. Salcedo-Sanz has received different research awards in his career, such as the Universidad de Alcalá's Best Young Researcher award in 2009, the 3M Innovation award in 2010 and the Price of the Social Council of University of Alcalá award to technology transfer in 2011. His current interests deal with soft-computing techniques, hybrid algorithms and neural networks in different applications of Science and Engineering.

Jürg Luterbacher is Chair for Climatology, Climate Dynamics and Climate Change at the Department of Geography, Justus-Liebig University Giessen. He studied physical geography, climatology and meteorology at the University of Bern (M.A.) and achieved his Diploma in Geography in 1995. In 1999, he finished his Ph.D. degree, which was awarded by the Faculty of Sciences at the University of Bern, followed by the completion of his Habilitation (postdoctoral lecture qualification) in 2005. From 2008, he has been the Head Regional to the Continental Climate Dynamics group within the Oeschger Centre of Climate Change Research (OCCR) and work package leader at Paleoclimatology NCCR Climate, University of Bern. From 2001 to 2007 he was the Deputy Head of the Climatology and Meteorology group at the Institute of Geography, University of Bern as well as a researcher within the two EU projects SOAP and EMULATE. He has been the PI of different German Science Foundation projects. He is lead author of the paleo chapter of the 5th IPCC assessment report. He has published more than 110 peer reviewed papers.