Robust Decadal Hydroclimate Predictions for Northern Italy Based on a Twofold Statistical Approach
Abstract
:1. Introduction
2. Data and Methods
2.1. Data
2.2. Prediction Strategy
2.2.1. Detection of Deterministic Components of the Time Series
2.2.2. AR Method
2.2.3. NN Method
2.3. Metrics for Forecast Skill and Robustness
2.4. Drought Severity Quantification
3. Results
3.1. Po River Spectral Analysis
3.2. Hindcasts for the Last 25 Years
3.3. Forecast for the Next 25 Years
3.4. Evaluation of Drought Severity
4. Discussion
4.1. Rainfall vs. Runoff Processes
4.2. Methodological Aspects
4.3. Drought Severity and Attribution
4.4. Broader Climatic and Socioeconomic Implications
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
Singular Spectrum Analysis (SSA)
Appendix B
Autoregressive Model Method
- Selection of the best order of the AR method. The AR method turns out to be most reliable and robust when the order MAR of the autoregressive model is not too large with respect to the length N of the time series, since the variance of the AR-coefficient estimates increases with the order. For this analysis, the choice of a suitable AR order is done a posteriori using goodness-of-fit criteria [35], namely the final prediction error (FPE; [36]) and the Akaike information criterion (AIC; [37]). We perform the predictions over the test section using a wide range of values of the AR model (between 1 and 60) and calculate both AIC and FPE values. The value of MAR which minimizes these indices is selected to perform the forecasts.
- Evaluation of the AR model coefficients. The values of the MAR coefficients of model are evaluated with Burg’s algorithm [38] applied to the learning section.
- Quantification of the prediction error. In order to quantify the uncertainty associated with this method, we perform 25-year predictions over different portions of this time interval (namely the cross-validation section, Figure 2a). More specifically, we repeat the procedure of the previous point varying the length of the learning section. In this way we obtain an ensemble of 25-year-predictions translated in time. By evaluating the root-mean-square-error between the predicted and original data as a function of the lead time (RMSE(l)) we obtain the uncertainty associated with the predictions. A useful scheme describing this procedure can be found in Alessio et al. [10].
Appendix C
Neural Network Method
- Partition of the learning section. While in the AR method all the data in the learning section are used to evaluate the coefficients of the model, in this case this, section is divided into two subsections: training (82% of the data in the learning section) and validation (18%). The partition can consist of continuous blocks, as shown in Figure 2b, or also in a random division of the data into the two subsets.
- Training of the network. The training set is used to compute the error gradient and update the weights and biases according to the Levenberg–Marquardt algorithm [63,64]. The validation set serves to assess the predictive skills of the NN being trained. More specifically, the error on the validation set—namely the mean squared error between predicted and observed data—is monitored during the training process and normally decreases during the initial phase of training, as does the training set error. When the network begins to overfit the data, the error on the validation set typically begins to rise. Thus, the final network weights and biases are those yielding the minimum error on the validation set. The parameter ranges of the NN architecture, namely the length I of the input vector and the numbers H1 and H2 of neurons in the hidden layers, are specifically evaluated for each component. The transfer functions used to evaluate the neuron scalar output are the sigmoid hyperbolic-tangent function for the hidden layers and the linear function for the output one.
- Prediction and quantification of the error. Each trained network is used to forecast the component in the test section, and the corresponding RMSE is calculated between predicted and observed data. Then, among all the values of I, H1 and H2, the network architecture that best reproduces the samples in the test section is chosen. The trained network is finally used for the predictions over the forecast section. Since the training process depends upon the random choice of the initial guesses for weights and biases, the procedure described above is repeated 100 times for each component, thus yielding 100 predictions. Then, the average of all the predictions in both the test and the forecasting section is evaluated, after discarding potential anomalous scenarios. Error bands associated with the predictions correspond to one standard deviation, while the standard error of the mean is used as the uncertainty associated with the average prediction.
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r (p-Value) | CE | PI | |
---|---|---|---|
AR | 0.95 (<10−4) | 0.84 | 0.79 |
NN | 0.96 (<10−3) | 0.89 | 0.86 |
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Rubinetti, S.; Taricco, C.; Alessio, S.; Rubino, A.; Bizzarri, I.; Zanchettin, D. Robust Decadal Hydroclimate Predictions for Northern Italy Based on a Twofold Statistical Approach. Atmosphere 2020, 11, 671. https://doi.org/10.3390/atmos11060671
Rubinetti S, Taricco C, Alessio S, Rubino A, Bizzarri I, Zanchettin D. Robust Decadal Hydroclimate Predictions for Northern Italy Based on a Twofold Statistical Approach. Atmosphere. 2020; 11(6):671. https://doi.org/10.3390/atmos11060671
Chicago/Turabian StyleRubinetti, Sara, Carla Taricco, Silvia Alessio, Angelo Rubino, Ilaria Bizzarri, and Davide Zanchettin. 2020. "Robust Decadal Hydroclimate Predictions for Northern Italy Based on a Twofold Statistical Approach" Atmosphere 11, no. 6: 671. https://doi.org/10.3390/atmos11060671
APA StyleRubinetti, S., Taricco, C., Alessio, S., Rubino, A., Bizzarri, I., & Zanchettin, D. (2020). Robust Decadal Hydroclimate Predictions for Northern Italy Based on a Twofold Statistical Approach. Atmosphere, 11(6), 671. https://doi.org/10.3390/atmos11060671