## 3 Environmental Applications of the Tool and Results
### Predictions in Future Scenarios  
Once we have found a general transfer function from the inputs to the target and fixed the network weights, we have seen in attribution studies how we can simulate the  
Figure 4: Attribution experiment for solar influence. Black line = observed T, red lines = results of ensemble runs, blue line = ensemble mean. We mimicked stationary solar forcing by using RFSOLSTAT as an input for the validated NN models (from [6]).  
behaviour of the target variable for different values of the inputs, e.g., by placing a constant or stationary input together with the others with observed values.  
At this point, however, nobody forbids exploiting the 'law' found through the neural model to simulate the behaviour of the target variable in very different situations, in'scenarios' in which all input variables change their values. In particular, it is interesting to do this when one can hypothesise future changes in the trends of the input variables and wants to analyse what will happen to the values of the target variable.  
This approach was recently followed in a climate application [8]. We will therefore refer to this example to briefly illustrate the potential of this method.  
In addition to the finding that recent climate changes are largely driven by human influences, the climate also has an its own internal variability, due to natural cycles and oscillations. We are aware of many such examples of natural variability, and even the so-called Atlantic multidecadal oscillation (AMO) has long been considered a manifestation of natural variability. Recently, however, studies have shown how AMO may have been strongly influenced by certain anthropogenic forcings, such as sulphate aerosols.  
These studies were always carried out using GCMs. In a recent study [6], however, we carried out an attribution analysis of AMO using our neural tool. This paper significantly contributed to the current debate on the natural or anthropogenic origin of AMO. The results showed how the AMO's behaviour from 1866 to the present has been strongly influenced by anthropogenic forcings, with a particular emphasis on the radiative forcing of human-origin sulphate aerosols.  
Now, as is well known, there are future scenarios for anthropogenic forcings, such as the SSP scenarios of the Coupled Model Intercomparison Phase 6 (CMIP6). We used the scenarios from one of these models [23] to make future predictions of the AMO's behaviour by feeding these data into the networks that had best reconstructed the AMO's historical oscillations. Future data of natural forcings were statistically extrapolated, with a couple of different options for solar radiative forcing; see [8].  
The key finding of this study revealed that in all future scenarios, the AMO is expected to lose its cyclical pattern (see Figure 5). It could only be preserved in a scenario with highly unrealistic values for sulphate aerosols.  
This study showed how, by incorporating future scenarios for inputs, one can predict the behaviour of the target variable and come to very important conclusions. If these scenarios then depend on our actions, we can act to avoid the most damaging scenarios  
Figure 5: NN ensemble mean projections of the future behaviour of the AMO index under four SSP scenarios (SSP1-2, blue line; SSP2-4.5, yellow line; SSP3-7.0, brown line; SSP5-8.5, red line) in the case of high-power solar radiation hypothesised for the future (from [8]). Black line represents the historical behaviour of the AMO index.  
(in the context of climate, think of the so-called 'business as usual' scenarios for future global warming).