### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Data
- 3. Method
- 4. NN application and results
- 5. Conclusions
- References

**At the regional scale, enhanced climatic variability masks the role of external forcings. It has been shown that a consistent attribution of regional temperature behaviour can be achieved just by considering circulation patterns as driving elements. Here we address this question: is the role of external forcings completely hidden in the changes of circulation patterns (eventually induced by them), or is there evidence of a more direct role for these forcings? Performing a fully nonlinear analysis shows that a direct role for anthropogenic forcings can be detected also at this regional scale, while natural forcings do not seem to influence temperature behaviour**.

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. Data
- 3. Method
- 4. NN application and results
- 5. Conclusions
- References

Attribution studies at the global scale aim at understanding which external forcings mainly influence the mean values of some climatic variables, such as temperature and precipitation. At a smaller scale, however, several researches (see, for instance, Efthymiadis *et al.* (2007) and Ciccarelli *et al.* (2008) for bivariate linear analyses, and Pasini and Langone (2010, 2012) for multivariate fully nonlinear models) show that the enhanced interannual variability can be fully caught just by considering circulation patterns as the main driving elements.

Some years ago, a pioneering paper (Corti *et al.*, 1999) discussed the hypothesis that anthropogenic forcings mainly act as drivers of changes in the frequency of occurrence of atmospheric circulation regimes, more than as factors that directly force changes in climatic variables. If this hypothesis is correct, the attribution problem at regional or local scales could be split into a two-step process: (1) find the influence of external forcings on circulation patterns and their regimes, (2) identify the link between these patterns and the main climatic variables at these scales. Furthermore, considering circulation patterns should be sufficient to correctly reconstruct the characteristic features (trend, variability and so on) of a variable such as temperature.

In this framework, here we do not aim at modelling the relationship between external forcings and circulation patterns (see Stoner *et al.* (2009) for a recent investigation of this kind), but analyse the previous hypothesis and the roles of both circulation patterns and external forcings in driving temperature behaviour. In particular, a case study is performed with a neural network (NN) model on annual temperature data in the second part of 20th century over an extended Alpine region.

### 2. Data

- Top of page
- Abstract
- 1. Introduction
- 2. Data
- 3. Method
- 4. NN application and results
- 5. Conclusions
- References

In Europe, the Alpine region has been extensively analysed from a climatological point of view. At present, a homogenized database (about 200-year long) is available online at http://www.zamg.ac.at/HISTALP (Auer *et al.*, 2007). Here, we consider annual mean temperature data on the southwest area of the so-called Greater Alpine Region (GAR)—see Figure 1—for the period 1950–1999, as in Pasini and Langone (2012).

To assess the influence of circulation on temperature, the indices that summarize the behaviour of the following patterns are taken into account:

- east Atlantic pattern (EA);
- Arctic Oscillation (AO);
- European blocking (EB);
- El Niño Southern Oscillation (ENSO).

The time series of indices related to EA and AO are freely downloadable from http://www.cpc.noaa.gov. The EB index was firstly introduced by Tibaldi and Molteni (1990) and Tibaldi *et al.* (1994) and its data were courteously supplied by the Agenzia Regionale Prevenzione e Ambiente dell'Emilia-Romagna Servizio Meteorologico Regionale (ARPA-SMR), Bologna, Italy. Finally, data about the Southern Oscillation Index (SOI), related to ENSO, have been downloaded from http://www.cru.uea.ac.uk and then transformed into monthly anomalies.

As far as the external forcings are concerned, we consider the following variables and related time series:

Here, we consider TSI and SAOT as natural forcings, GHG-total (CO_{2} + CH_{4} + N_{2}O + CFCs) RF (hereafter GHG-RF) and GSE as anthropogenic forcings.

### 3. Method

- Top of page
- Abstract
- 1. Introduction
- 2. Data
- 3. Method
- 4. NN application and results
- 5. Conclusions
- References

NN modelling is the main tool adopted here to assess the influence of circulation patterns and external forcings on temperature. The application of NN modelling in atmospheric and climate sciences is quite recent: reviews can be found in Krasnopolsky (2007), Haupt *et al.* (2009), and Hsieh (2009).

Our networks are simple feed-forward ones with one hidden layer and a single output (see Hertz *et al.* (1991) and Bishop (1995) as general references for this kind of networks). More specifically, here we adopt an NN tool developed some years ago by Pasini and Potestà (1995) for both diagnostic characterization and forecast in complex systems. Over the years, it has been applied to several problems in the atmospheric boundary layer (Pasini and Potestà, 1995; Pasini *et al.*, 2001; Pasini and Ameli, 2003; Pasini *et al.*, 2003), to the analysis of toy models of climatic relevance (Pasini, 2008; Pasini *et al.*, 2010), to 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, 2012).

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 just stress that a sigmoid transfer function in the hidden layer and a linear one at the output neuron are adopted. Furthermore, learning from 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, NNs are able 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 and external forcings) if every input–target pair is known to them, 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 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 on independent sets can we say that a realistic regression law has been obtained.

In past applications with small data sets we chose to maximize the extension of the training set by a specific facility of our tool, the so-called all-frame or leave-one-out cross validation procedure: see Pasini *et al.* (2006), Pasini and Langone (2010, 2012). Here we extend this procedure as follows (see Figure 2 for a sketch of it). Now each target (annual temperature value) is estimated—we obtain an output—after the exclusion of the corresponding input–target pair from the training and validation sets used to determine the connection weights. Referring to Figure 2, the white squares represent the elements (input–target pairs) of our training set, the black squares represent the elements of the validation set and the grey square (one single element) represents the test set. The relative composition of training, validation and test sets change at each step of an iterative procedure of training, validation and test cycles. A ‘hole’ in the complete set represents our test set and moves across this total set of pairs, thus permitting the estimation of all temperature values at the end of the procedure. Furthermore, the validation set is randomly chosen at every step of our procedure and the training stops when an increase in the mean square error (MSE) in the validation set appears. This new procedure allows us to definitely avoid any overfitting on data we want to reconstruct by NNs.

Obviously, the results of this extended leave-one-out procedure critically depend on the random choices regarding the initial weights and the elements of the validation set. For taking this fact into account and obtaining more robust results, we perform ensemble runs of our NNs, by repeating 20 times every estimation shown in Figure 2 with new random choices for both the weights and the elements of the validation set.

Finally, after many empirical proofs, four neurons were chosen for insertion in the hidden layer and 10 elements were considered for the validation set.

### 4. NN application and results

- Top of page
- Abstract
- 1. Introduction
- 2. Data
- 3. Method
- 4. NN application and results
- 5. Conclusions
- References

In a previous article (Pasini and Langone, 2012), it has been shown that the fully nonlinear influence of circulation patterns on temperatures in the SW-GAR can be analysed by NN modelling. This led both to identify the most influent patterns which drive temperature behaviour seasonally and annually, and to build models that are able to reconstruct well temperature variability at these temporal scales.

Here, by including natural and anthropogenic forcings in our analysis, we investigate their role in driving temperature at the regional scale. Is their role completely hidden within the changes in circulation patterns induced by them, as suggested by Corti *et al.* (1999)? Or do they play a more direct role in driving temperature behaviour?

By limiting our analyses to annual data, we first apply the extended leave-one-out procedure to networks forced by EA, AO, EB and ENSO as inputs, which led to the best reconstruction in Pasini and Langone (2012). Consistent results are obtained: for instance, the mean correlation coefficient , which is the mean of the *R*s calculated between each of the 20 NN ensemble reconstructions and the observed annual values of T, is now 0.729, while it was 0.750 in the previous analysis. This little decrease in can be attributable to the smaller number of patterns in the training set and to the fact that the ensemble variability is now slightly stronger than before: this is quite understandable if we consider that now it is due to changes in both weights and validation patterns. Furthermore, the increasing observed trend in T (= 7.35 × 10^{−3} °K year^{−1}) is underestimated in these runs.

The results of this article are summarized in Table 1, where some indices of performance are presented. In particular, a full NN ensemble approach is followed, resembling the use of ensemble runs in Global Climate Models (GCMs), where the ensemble mean has been shown to be more successful and robust than single runs for achieving satisfying climate reconstructions. Thus, the reconstruction performance of the ensemble mean curve is tested versus observed T, by the correlation coefficient *R*, the mean square error MSE and the linear trend.

Table 1. Results of NN ensemble-mean reconstructions in terms of *R*, MSE and linear Trend (Tr) | Inputs | *R* | MSE (×10^{−2}) | Tr (×10^{−3}) |
---|

1 | TSI, SAOT, GSE, GHG-RF | 0.576 | 2.33 | 7.18 |

2 | EA, AO, ENSO | 0.695 | 1.78 | 5.20 |

3 | EA, AO | 0.679 | 1.86 | 4.79 |

4 | EA, AO, ENSO, EB | 0.732 | 1.67 | 5.37 |

5 | EA, AO, ENSO, TSI | 0.666 | 1.91 | 4.69 |

6 | EA, AO, ENSO, SAOT | 0.678 | 1.86 | 4.53 |

7 | EA, AO, ENSO, GSE | 0.752 | 1.50 | 4.33 |

8 | EA, AO, ENSO, GHG-RF | 0.794 | 1.27 | 7.18 |

9 | EA, AO, TSI, SAOT | 0.649 | 2.00 | 4.63 |

10 | EA, AO, TSI, GSE | 0.738 | 1.57 | 4.39 |

11 | EA, AO, TSI, GHG-RF | 0.777 | 1.36 | 7.32 |

12 | EA, AO, SAOT, GSE | 0.747 | 1.52 | 4.07 |

13 | EA, AO, SAOT, GHG-RF | 0.661 | 1.94 | 4.91 |

14 | EA, AO, GSE, GHG-RF | 0.823 | 1.11 | 7.32 |

First of all, ensemble runs including the four external forcings (TSI, SAOT, GHG-RF and GSE) as inputs show that their performances are poor and, in particular, inter-annual variability is completely lost (see Figure 3, where one can appreciate that also the single runs short term variability does not resemble observations). Nevertheless, the multi-year increasing trend is well represented by this model.

In this framework, where it is clear that a consistent regional attribution of T with its enhanced variability can be obtained only if certain circulation patterns are considered, it is worthwhile to investigate which additional value (if any) is brought by external forcings. Owing to the short time series available, in order to avoid large networks and enhanced possibilities of overfitting, we choose to take the number of inputs to four. Thus, preliminarly, we build networks with all the possible combinations of three and two indices as inputs, so that the most significant circulation patterns for temperature reconstruction can be chosen (in Table 1 just the networks with best results in *R*, MSE and trend are shown). Then we consider all the possible combinations of external forcings with the best performing indices.

Referring to Table 1 and Figure 4(a) and (b) the results coming from the best combinations of three and two circulation indices (rows 2 and 3 in Table 1) clearly show that the inter-annual variability is caught much better than in the case when just external forcings are considered as inputs (refer to Figure 3). The further insertion of the fourth index EB (row 4 in Table 1) leads just to a little increase in performance. However, the increasing trend shown by the time series of temperature is substantially underestimated by these runs.

If now we add just natural external forcings as inputs to the latter networks (rows 5, 6 and 9 in Table 1), performances do not change very much. It seems that natural forcings do not help to increase the quality of reconstruction of regional temperature, at least in this case study. Their driving role on T, if any, could be not direct, but mediated through their possible influence on circulation patterns.

Conversely, if we add just anthropogenic external forcings to circulation indices as inputs (rows 7, 8 and 14 in Table 1), the situation is very different. Performances increase in all cases if compared with the runs previously analysed. In particular, while the insertion of GSE alone leads to a better reconstruction till 1980 but does not allow us to catch the increasing values after that date, when GHG-RF is considered this trend is very well recognised and reconstructed. The jointed insertion of GHG-RF and GSE (to the networks endowed with EA and AO as other inputs) leads to the best results (Figure 4(c)). As a further remark, we would like to stress that in the latter case the standard deviation of the single runs—members of the ensemble—is so limited that, in terms of *R*, at least the 90% of these runs perform better than the ensemble means of the NN models fed by circulation patterns only (cases 2, 3 and 4 in Table 1).

All this is clear evidence that anthropogenic forcings act on regional temperatures not only through their role of drivers of the circulation patterns' behaviour, but also as a direct driving force.

The other ensemble runs shown in Table 1 (rows 10–13) presents intermediate results. In particular, it is worthwhile to note that the substitution of ENSO with a natural forcing leads to a general small decrease of performance.

A further look at Figure 4 allows us to achieve a deeper insight. In fact, from this figure it is quite clear that the reconstructions performed by NN models driven by circulation indices only show a small increasing linear trend at a relatively constant rate: they substantially overestimate the period 1962–1980 characterized by low temperatures and underestimate the higher temperatures after 1980. Conversely, the insertion of information in input about both greenhouse gases and sulphates allows the networks to follow more closely the observed temperatures: in particular, the cold period (when sulphates show high values and GHG-RF relatively low values) is better reconstructed and the rapidly increasing trend after 1980 (characterized by a diminished value of sulphates and a steep increase of GHGs) is very well caught by the networks.