## Abstract

An analysis of the influence of circulation patterns on temperature changes in an extended Italian Alpine area has been performed by nonlinear methods and neural network modeling. This leads to the clarification of the roles of these patterns in the various seasons and permits the development of models that are able to reconstruct in a satisfactory manner the behavior of temperature anomalies in the second half of the twentieth century in this limited region. This nonlinear analysis shows that the role of the North Atlantic Oscillation (NAO) is probably overestimated, and that European blocking and the Scandinavian pattern should be considered as prime candidates as temperature drivers in this area.

## 1. Introduction

Attribution studies aim at understanding which external—natural or anthropogenic—forcings mainly influence the mean values of some meteoclimatic variables, such as temperature *T* and precipitation, at global and continental scales. In this framework, it has been shown that the global warming of the second half of the twentieth century can be mainly attributed to anthropogenic greenhouse gases (Hegerl et al. 2007). Recently, moreover, particular attention has been paid to the study of the contribution of internal variability of the climate system to the “modulation” of the increasing global temperature trend (DelSole et al. 2011; Wu et al. 2011), and its role has been found to be relevant to the multidecadal behavior of the temperature curve.

At regional or local scales, however, one observes an enhanced interannual variability that can mask any direct link between global forcings and temperatures. Furthermore, this variability seems more linked to high-frequency changes in regional circulation patterns than to wider multidecadal oscillations in the coupled atmosphere–ocean system. A well-known example is the influence of the North Atlantic Oscillation on winter climate in Europe: see, for instance, Trigo et al. (2002). Therefore, these circulation patterns may be the key elements for performing a correct attribution of temperature behavior at these scales.

Of course, a complete attribution at the regional scale can be seen as a two-step problem, requiring the identification of the influence of external forcings on circulation patterns and their regimes (first step), and linking these patterns with the main climatic variables at this scale (second step). Here we do not deal with the first step of this problem: see Corti et al. (1999) for a pioneering study, and Straus and Molteni (2004) and Stoner et al. (2009) for more recent investigations. We study just the relevance of several circulation patterns in influencing the behavior of annual and seasonal temperatures in the second part of the twentieth century over an extended Italian Alpine region. In doing so, neural network (NN) modeling is applied as a tool to obtain fully nonlinear relationships between circulation patterns and the temperature itself.

## 2. Data

The European area that surrounds the Alps is characterized by the presence of many long time series of climatic data. Recently, a homogenized database (about 200 yr long) has been built for this so-called Greater Alpine Region (GAR) (Auer et al. 2007). Here, we consider monthly-mean temperature data for the period 1951–99 in the southwest (SW) region of this area (SW-GAR), shown in Fig. 1. These data are freely available online (http://www.zamg.ac.at/HISTALP).

To assess the influence of circulation on temperature, we consider the indices that summarize the behavior of the following patterns:

North Atlantic Oscillation (NAO)

east Atlantic pattern (EA)

Arctic Oscillation (AO)

Scandinavian pattern (SCAN)

east Atlantic/west Russia pattern (EAWR)

Euro-Atlantic blocking (EAB)

European blocking (EB)

El Niño–Southern Oscillation (ENSO)

The indices related to the first five well-known circulation patterns are freely downloadable (from http://www.cpc.noaa.gov); the EAB and EB indices were first introduced by Tibaldi and Molteni (1990) and Tibaldi et al. (1994) and their data were courteously supplied by the Agenzia Regionale Previenzione e Ambiente dell’Emilia-Romagna Servizio Meteorologico Regionale (ARPA-SMR), Bologna, Italy; data concerning ENSO [the Southern Oscillation index (SOI)] were obtained online (http://www.cru.uea.ac.uk) and then transformed into monthly anomalies.

## 3. Method

The main tool adopted here to assess the influence of circulation patterns on temperature behavior is NN modeling.

General references for the structure of our networks are Hertz et al. (1991) and Bishop (1995), while recent reviews about the application of NN modeling in atmospheric and climate sciences can be found in Krasnopolsky (2007), Haupt et al. (2009), and Hsieh (2009). More specifically, an NN tool for both diagnostic characterization and forecast in complex systems was developed some years ago by Pasini and Potestà (1995). Over the years, it has been applied to diagnostic and prognostic problems in the boundary layer (Pasini and Potestà 1995; Pasini et al. 2001; Pasini and Ameli 2003; Pasini et al. 2003), the analysis of toy models of climatic relevance (Pasini 2008; Pasini et al. 2010), climatic impacts on fauna (Pasini et al. 2009) and, finally, to the problem of attribution at global and regional scales (Pasini et al. 2006; Pasini and Langone 2010).

The kernel of our NN tool has been extensively described elsewhere (Pasini and Potestà 1995; Pasini et al. 2001; Pasini and Langone 2010). Here we will just mention that the networks considered are feed forward and are endowed with one hidden layer and a single output. Two kinds of NNs are utilized in this study: in the first network, we adopt sigmoid transfer functions, both in the hidden layer and in the output layer; and in the second network, a linear function replaces the sigmoid in the output layer. The phase in which the model learns from the data is performed through an error-backpropagation training characterized by generalized Widrow–Hoff rules (endowed with gradient descent and momentum terms) for updating connection weights.

Generally, an NN is powerful enough to obtain a nonlinear function that reconstructs in detail the values of targets (in our case, temperatures) starting from data about inputs (indices of circulation) if every input–target pair is known to it, and a large number of neurons in the hidden layer are allowed. But in this case, NNs overfit data and no realistic regression law can be obtained. Thus, we have to exclude some input–target pairs from the training set on which the regression law is built and must consider only a small number of hidden neurons. Only if the map derived from the training set is able to describe the relation between inputs and target even on independent sets can we say that a realistic regression law has been obtained.

In the present application, the length of the time series is just half a century; therefore, we chose to maximize the extension of the training set. A specific facility of our tool, the so-called all-frame or leave-one-out cross-validation procedure, is used (it is reproduced schematically in Fig. 2). Now each target (temperature value) is estimated—we obtain an output—after the exclusion of the corresponding input–target pair from the training set used for fixing the connection weights. Referring to Fig. 2, the white squares represent the elements (input–target pairs) of our training set, while the gray square (one single element) represents the validation set. The relative composition of training and validation sets change at each step of an iterative procedure of training and validation cycles. A “hole” in the complete set represents our validation set and moves across this total set of pairs, thus permitting the estimation of all temperature values at the end of the procedure.

Here, this leave-one-out procedure is adopted for both the neural model and the multilinear control regression. In doing this, we test the reconstruction capabilities of our NN model. Adopting a more standard training–validation test approach, one could also test its predictive capabilities, but this exceeds the scope of this paper.

## 4. Preliminary bivariate nonlinear analysis

As a preliminary step, it is interesting to test which circulation patterns are the most correlated with mean temperatures. This analysis can obviously be performed by calculating the Pearson coefficient *R* between inputs and targets, but because of the nonlinear nature of the climate system, even variables that do not show high linear correlations with temperature can be influential by means of more complex and nonlinear relationships. Thus, we have also calculated values of the so-called correlation ratio *R*_{nl}, a nonlinear “analogue” of *R*, whose square can be written (Pasini et al. 2001) as

Using NN jargon, we consider the target (temperature, in our case) as the dependent variable and one input at a time (a value of one of the circulation indices) as the independent variable. Here *R*_{nl} is defined in terms of the average of the target for every specific *i*th value of the chosen input: in fact, *q _{i}* is the sample size for the

*i*th class of the input (

*i*= 1, … , N), is the average target for the

*i*th class of the input, is the average target of all the classes of the input, and is the total size of the set considered here. The whole range of input values is divided into

*N*intervals that are labeled as classes:

*N*is empirically chosen for each input as the highest number of classes that allows us to obtain a smooth histogram.

Even if *R*_{nl} does not measure all types of nonlinearities, its calculation allows us to determine if there are nonlinearities that are hidden in the relationships among the variables considered here. The results of this bivariate analysis are shown in Table 1, and the main points are briefly discussed below.

First of all, almost all indices are significantly correlated with annual temperatures and extended winter ones. On the other hand, the influence of the EA and the AO seem to be important in almost all periods.

More specifically, the well-known influence of the NAO on temperatures in extended winter is recognized, but influences of the same magnitude are also due to the EA and the EAB. The influences of the EB and the SCAN are significant in summer and those of the EAWR in winter. ENSO shows negligible correlations with temperatures in every season; however, because of a possible delayed influence of this Pacific pattern, cross correlations were tested to ascertain the influence of ENSO on temperatures in the forthcoming seasons: significant anti-cross correlations are found for the spring ENSO index with the temperatures in the next fall season and for the fall ENSO index with the next summer temperatures.

Finally, it is worthwhile to note that, sometimes indices that show low linear correlations (such as the EB and the EAB) are endowed with a quite high correlation value in terms of *R*_{nl}. This leads us to think that these patterns may exert a peculiar nonlinear influence on *T*, which cannot be recognized by investigations performed employing linear methods.

## 5. NN application and results

After this preliminary bivariate analysis, we apply NN models, fed by circulation indices as inputs. In doing so, we can evaluate once more the major influence of circulation patterns on *T* in different periods and test the ability of NNs to model temperature behavior at this regional scale.

In choosing the combinations of inputs for the nonlinear multivariate analysis via NNs, we have considered the indices whose linear correlation with *T* is significant and also indices that are not linearly significant, but which show high nonlinear correlations with *T*. Because of the limited length of the record of input–target pairs, we consider combinations of just four indices as inputs and fix the number of hidden neurons at four, thus avoiding the conditions in which overfitting occurs.

After many NN runs on all the combinations of inputs satisfying the criteria cited above, and using the cross-validation procedure described in section 3, we obtained the results summarized in Table 2. Here both the NN and the multilinear regression performances are presented in terms of the values of *R* between targets and outputs. The “error bars” related to NN performances come from ensemble runs of the networks starting from different random initial weights, so that the single networks are able to explore widely the landscape of the cost function even in this local method of backpropagation training.

Referring to Table 2, the importance of the AO and the EA (previously recognized in the bivariate analysis) is now confirmed by the need to include these indices as inputs to obtain the best results by NN modeling. Even the SCAN and blocking indices appear to have an important role in influencing temperatures on numerous occasions within the study period, and this is an important result of our nonlinear analysis, as these patterns did not show high bivariate linear correlations with *T* in Table 1.

Vice versa, the relative importance of the NAO seems to require rescaling: the AO and other indices appear to be more relevant even in winter and extended winter. In particular, it is worthwhile to note that attempts at including the AO and the NAO as inputs in the same networks lead to poor performance, even when these indices are highly correlated with the targets. This fact is quite understandable because these two indices are strongly correlated with each other while, as is well known—see, for instance, Back and Trappenberg (2001)—NNs require input variables that are as independent of each other as possible for an optimal performance.

In all periods, except one, we were able to find an NN model that leads to a reconstruction of temperature anomalies that is significantly better than that of the multilinear regression. This result is confirmed by other performance metrics, such as mean absolute error (MAE) and mean square error (MSE), or false-alarm rate (FAR), probability of detection (POD), and Heidke skill score (HSS) (not shown here).

In this framework, it is noteworthy that, to achieve the best results, networks endowed with sigmoids in the output layer must be chosen for intermediate seasons (spring and fall), while a linear transfer function must be considered for other periods. This suggests the existence of stronger nonlinear relationships between indices and temperature in intermediate (more complex) seasons, when compared with other periods.

We should further note that sometimes the values of *R* in Table 2 are lower than the corresponding ones for single variables in Table 1. This should not be a surprise, because in the multivariate runs we adopt the leave-one-out method and this usually leads to a considerable decrease in performance when applied to short data records, as in our case.

An example of the NN performance is presented in Fig. 3, where the reconstruction of temperature anomalies for extended winter (by a single run of the NN ensemble) is shown, together with the multilinear reconstruction. This graphical example shows well that our NN model is able to reproduce the interannual behavior of *T* in this limited region, qualitatively and even quantitatively (only a few of the peak values are not precisely reconstructed by the model). In particular, in this and other cases, we can recognize the low bias in the NN reconstruction and its ability to discern better the tendencies from one year to the next, if compared with results from multilinear reconstruction, which sometimes show a more averaged behavior or countertendency derivatives.

In the past, the GAR dataset has been studied in detail in terms of multivariable analysis (Brunetti et al. 2009) and attempts at assessing the linear influence of large-scale circulation on climate variability in this region has been performed (Efthymiadis et al. 2007). Another linear analysis has been also performed on a subregion of SW-GAR: see Ciccarelli et al. (2008).

Here, for the first time, a fully nonlinear analysis of this influence problem is performed. Our study confirms some general results found in previous studies, but it allows us to obtain new relevant findings. Thus, the importance of the AO, the EA, and the NAO is recognized, but, at the same time, the relative importance of the NAO in driving winter and extended-winter temperatures needs to be revisited and our study shows that, probably, the NAO has a less prominent role than previously thought. Other indices, often endowed with a low linear correlation with *T*, show their relevance in this analysis. In particular, the SCAN and blocking indices (especially the EB) appear often to have a major influence in driving temperature in many periods. Furthermore, the delayed influence of ENSO is clearly shown by our analysis. Finally, for the first time our fully nonlinear analysis allows the construction of models that are able to reproduce well the behavior of temperature anomalies under the influence of large-scale circulation patterns.

## 6. Conclusions and prospects

In this paper, a nonlinear analysis of the influence of eight circulation patterns on temperature changes in an extended Italian Alpine region has been performed. To the best of our knowledge, it represents the first extensive study of this kind with nonlinear methods.

This analysis has led to the clarification of the roles of these patterns in various seasons and also to new insights. In particular, our results show that the role of the NAO is probably less prominent than previously thought, while European blocking and the Scandinavian pattern should be considered more seriously as prime candidates for driving temperatures in the SW-GAR area in many periods of the year. Furthermore, our nonlinear method allows us to obtain NN models that are able to reconstruct in a satisfactory manner the behavior of recent temperature anomalies in this European region.

Future studies will concern the use of more sophisticated NN models and their application to other climatic variables and/or other regions.

Finally, we would like to stress that the present investigation opens concrete prospects of performing reliable downscaling activities. In fact, the present study has shown that we are able to find a transfer function (via NNs) from circulation patterns to past temperature anomalies. Thus, if future GCMs show improved ability to simulate the behavior of these patterns, a fruitful approach can be envisaged to obtain reliable future scenarios of temperature changes at regional scales by employing NN downscaling.

## Acknowledgments

We thank ARPA-SMR for having supplied us with data about the EB and EAB indices.