Research papersEstimation of prediction interval in ANN-based multi-GCMs downscaling of hydro-climatologic parameters
Introduction
The general circulation models (GCMs) as climate models are employed to forecast the atmospheric conditions, understand the weather and forecast climate change. There are some studies focus on the impact of the climate change on the atmospheric variables over the world (e.g. see McSweeney et al., 2015, Campozano et al., 2016, Osman and Abdellatif, 2016, Ranjbar et al., 2018, Liu et al., 2019). In addition, there are some studies assess the impact of climate change on the temperature and precipitation in Middle East countries. In Alotaibi et al., (2018) various GCMs and data-driven models were applied to study changes in temperature and precipitation of Qassim Region in Saudi Arabia. Results in this study showed that the temperature may be increased in the region and rainfall will differ over various spans of the future. In Okkan (2015) the impact of climate change on monthly precipitation of Tahtali watershed in Turkey was investigated. It was concluded that precipitation is decreased around 12.4% during the period between 2020 and 2039, 10.0% during the period between 2040 and 2059, and 18.3% during the period between 2080 and 2099 and statistically significant changes during the periods 2001–2019 and 2060–2079. Okkan and Kirdemir (2016) downscaled the monthly precipitation for Gediz basin in Turkey and used several GCMs and the obtained results showed a decrease trend for precipitation with different intensities in different scenarios.
Despite the GCMs trustworthy provision of atmospheric data, the coarse spatial resolution of GCMs causes weak application in local scale modeling. Therefore, an appropriate downscaling approach should be used to access local scale weather data from large scale GCMs (Wilby and Wigley, 1997). In order to project local climate change, it is essential to interpret the coarse-scale GCMs and reanalysis output to finer spatial scale by dynamical or statistical downscaling methods. In dynamical downscaling, a regional climate model is attained by GCM boundary conditions and solving equations of motion and thermodynamics (Danandeh Mehr and Kahya, 2016). Although these models have the ability to develop climate variables, the process consists of uncertainty in parameterization of sub‐grid‐scale processes with higher computational costs. Whereas statistical downscaling discovers relationships between local climate variable and GCMs, independent of any information about the physics of the process (Sailor and Li, 1999, Olsson et al., 2004, Harpham and Wilby, 2005, Chen and Adams, 2006, Sousa et al., 2007, Spak et al., 2007, Beecham et al., 2014). However, there are assumptions for statistical downscaling, e.g. as statistical downscaling serves black box modeling tools, so the calibrated model can’t be similarly used in other regions. Also there should be data from a regional station and for downscaling. In addition, developing a statistical downscaling model for finer time scales (such as daily or hourly) often becomes a challenging task due to high memory requirements and slow convergence associated with modeling large data sets (Şen, 2010).
Artificial neural network (ANN) is a black box model, with the ability to extract complicated relations between predictor and predictand variables and simulate the nonlinear and time-varying features of the atmospheric variables at various scales (e.g. monthly, daily, hourly) could lead to prevalent use of ANN in GCM data downscaling (e.g. see, Wilby and Wigley, 1997, Dibike and Coulibaly, 2006, Fistikoglu and Okkan, 2010, Okkan and Fistikoglu, 2014, Okkan and Inan, 2015, Okkan and Kirdemir, 2016).
Although there are intensive applications of ANN for downscaling of GCMs data, point estimation/ prediction of targets by ANN conveys no information about the sampling error, prediction accuracy and uncertainty of the model. With this regard, some studies already examined the uncertainty and reliability of ANN-based GCM downscaling procedure focusing on the confidence intervals (CIs) (e.g., Khan et al., 2006, Samadi et al., 2013).
Prediction intervals (PIs) and CIs are two prevalent measures for assessment of prediction/forecast uncertainty. CIs correspond to the accuracy of the prediction of the regression i.e., the mean of the target probability distribution whereas PIs assimilate the accuracy of the predicted values versus the measured values (Heskes, 1997, Khosravi et al., 2011b). Confidence Interval (CI) corresponds to the modeling uncertainty, which can be classified into different forms based on the variability arises from model inputs, parameters and structures which combine together contributes in producing the prediction uncertainty. PIs correspond to the accuracy of the prediction of targets instead of estimating the true model, therefore PIs are included more sources of the uncertainty and are wider than CIs and as so are more beneficial from practical aspect since the constructed upper and lower bounds of PI are capable of capturing exact observed values (Shrivastava et al., 2015). Decision makers should provide design plan to manage critical issues due to climate change. With this regard in prediction intervals by considering uncertainties, a bound is obtained that is essential in decision making, management and design. Optimistic and pessimistic decision making can be considered by prediction intervals. If we have the bounds in the case that the problem is critical so pessimistic decision making is applied and upper bound will be the bases of planning but it may not be economical; however, in the case that optimistic decision making is considered, the lower bound will be the bases of planning but with a bit high risk.
On the other hand, for the climate change, used GCMs contain various sources of uncertainty which are associated with GCMs data, scenarios and physical rules of GCMs and these uncertainties affect the predictions for future. In climate change studies while using GCMs by applying point prediction for future, designing can be uneconomical or may be critical conditions won’t be considered. In this study these uncertainties have been handled using multi GCMs and also estimating the prediction intervals instead of point prediction which can represent such uncertainties. Therefore, in climate studies, when applying GCMs, while having PI there will be more alternatives for designing.
Some classic techniques are usually used to construct the PIs for ANN methods such as delta, Bayesian, mean-variance estimation, and Bootstrap techniques. The delta technique employs the standard asymptotic theory for constructing the PIs (Chryssolouris et al., 1996, Hwang and Ding, 1997). In this technique, the intervals are constructed under the assumption that the noise is homogeneous and normally distributed which is the main limitation of this technique. The Bayesian technique is on the basis of the Bayesian statistics to express the uncertainty of the network weights in terms of probability distributions and integrates them to obtain the probability distribution of the target conditions. The Bayesian approach requires time-consuming Monte-Carlo integration overweight space in multi-dimensional real-world applications (Mackay, 1992). The mean-variance estimation-based method also assumes that errors are normally distributed around the true mean of targets. Therefore, PIs can easily be constructed if the parameters of this distribution (mean and variance) are known. The dependence of the target variance on the set of inputs is the basic assumption and of course the main limitation of this method (Nix and Weigend, 1994). On the other hand, the Bootstrap technique neither requires the complex computations of derivatives and Hessian-matrix inversion involved in the delta-method nor the Montre Carlo solutions of the integrals involved in the Bayesian approach (Dybowski and Roberts, 2001). Therefore, this simple method has been widely used in several hydro-climatologic studies (e.g., Dibike et al., 2008, Samadi et al., 2013).
In this study, Lower Upper Bound Estimation (LUBE) method which was firstly introduced by Khosravi et al. (2010) and is a novel PIs construction method in hydro-climatologic issues, is applied to construct PIs for ANN-based downscaling of monthly precipitation and temperature parameters at Tabriz and Ardabil stations (located in northwest of Iran). In the LUBE method, an ANN with two output neurons (representing upper and lower bounds of the estimation) is trained. The coverage probability of LUBE is better than other methods and it can effectively establish trade-off between the correctness and informativeness of PIs (Khosravi et al., 2011a). Moreover, the required time for PIs construction is remarkably smaller than other methods (Quan et al., 2014).
In this way, three GCMs and their ensemble are used and the obtained results by LUBE are compared with those obtained by the Bootstrap method. Although in some studies different methods have been already used to construct PIs of ANN methods in hydrological modeling (e.g., Srivastav et al., 2007, Kasiviswanathan et al., 2013, Kasiviswanathan and Sudheer, 2016, Kumar et al., 2015), to the best of authors’ knowledge, as a novel application of LUBE method in the hydro-climatic issues, this is the first study to model PIs of ANN-based GCM data downscaling.
Section snippets
Proposed methodology
In the proposed modeling, dominant atmospheric parameters related to the precipitation and temperature of both stations were distinguished using the MI measure. Thereafter point predictions by ANN method and then PIs of ANN-based downscaling were constructed and evaluated by both LUBE and Bootstrap methods using available data. Finally, point and interval predictions for future (2020–2055) values of precipitation and temperature were estimated for both stations under RCP8.5 climate change
Results and discussion
For evaluating the capability of the LUBE method to construct PIs of downscaled precipitation and temperature values, the dominant inputs from GCMs were selected by MI measure and then classic ANN with one output was trained to find point predictions. Then an ANN with two output neurons (considering of observed values as the initial guess for upper and lower bounds) was trained to initialize the weights of the network. The perturbed values of initialized weights were used to create networks
Conclusions
Although ANN-based downscaling GCM has been broadly used in prediction of climate variables, point predictions by ANN convey no information about prediction uncertainty. In this content, PI is an essential indicator for quantifying the reliability of ANN-based downscaling of climate parameters using GCMs data.
In this paper, ANN-based downscaling of temperature and precipitation variables was performed using three different GCMs and ensemble-GCMs using the data from1950 to 2012, and from 1975 to
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
The resarch was conducted under a finincial grant form University of Tabriz, Research Affairs.
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