A Novel Hybrid Approach for Predicting Western Australia’s Seasonal Rainfall Variability

Australian rainfall has a distinct nature as coastal regions experience wetter winter while inland west encounters less rainfall at that time. Several studies around the world explored teleconnections between the climate indices with regional rainfalls (Ghamariadyan and Imteaz 2021; Calado et al. 2019). Around Australia, primarily IOD and SAM have been found as influential drivers for rainfall generation in south-eastern and western parts, Blocking Highs for southern parts, and ENSO Modoki and Madden Julian Oscillation (MJO) for north-western and northern parts (Ashok et al. 2003; Marshall and Hendon 2014; Risbey et al. 2009). Among these drivers, ENSO is found as a significant contributor to rainfall generation all over Australia (Montazerolghaem et al. 2016). Pacific Ocean SST anomalies significantly affect rainfall generation in tropical and eastern regions, whereas Indian Ocean SST anomalies influence the rainfall generation in southern and western regions (Risbey et al. 2009). Current literature suggests that most of the attempts related to seasonal rainfall forecasting in Western Australia (WA) are region-based, with a majority of them being developed for South West Western Australia (SWWA) (Evans et al. 2020; Feng et al. 2015; Islam and Imteaz 2020; Ummenhofer et al. 2008). The majority of these studies attempted to demonstrate the concurrent relationship between climate indices and SWWA rainfall as the lagged relationships were not explored in detail.

Improved rainfall forecasting techniques aimed at optimum precision are an evolving process, where both linear and non-linear techniques are widely adopted (Bagirov and Mahmood 2018; Hossain et al. 2020; Islam and Imteaz 2019). As rainfall generation is a complicated phenomenon, any linear or non-linear model with overwhelming limitations may not be able to develop an accurate forecast model by itself. Hybrid modelling can overcome those limitations and is usually performed by trialling either linear or non-linear forecasting first and then analyzing the remains (i.e., residuals) using the other technique at a later stage. Previous studies have demonstrated that the hybrid model is more successful in developing an accurate forecast model compared to the individual forecast models (Wu et al. 2021; Xu et al. 2019). A combination of Gene Expression Programming (GEP) and other model techniques such as Auto-Regressive (AR), Auto-Regressive Moving Average (ARMA), Auto-Regressive Integrated Moving Average (ARIMA), Bayesian Network (BN), Linear Regression (LR), Multiple Linear Regression (MLR), Genetic Algorithm (GA) was attempted for estimating rainfall, flood, and streamflow trends (Al-Juboori 2022, Barbulescu and Bautu 2009, Kumar and Sahay 2018, Mehdizadeh and Sales 2018, Mehr 2018, Mozaffari et al. 2022, Sharghi et al. 2019).

Mehdizadeh and Sales (2018) reported that hybrid models (GEP-AR, GEP-ARMA, BN-AR, BN-ARMA, MLR-AR, and MLR-ARMA) demonstrated more accurate prediction compared to single models (GEP, BA, AR, ARMA, and MLR) for streamflow forecasting. A study performed by Mehr (2018) used a hybrid GEP-GA model for streamflow forecasting and demonstrated the superior performance of the hybrid GEP-GA model. Similarly, Karimi et al. (2016) also proposed a hybrid Wavelet-Genetic Programming (WT-GP) model that showed better performance in both short-term and long-term streamflow prediction compared to ARIMA, Adaptive Neuro-Fuzzy Interference System (ANFIS), and Artificial Neural Network (ANN) models. Barbulescu and Bautu (2009) applied a hybrid ARIMA-GEP model for precipitation analysis, where a combination of these two techniques improved the model's accuracy. Furthermore, a study conducted by Kumar and Sahay (2018) showed that the hybrid Wavelet-GEP (WT-GEP) model successfully predicted extreme flood cases which remained undetected in AR and GP models.

This study aimed at developing a hybrid model to improve the forecasting ability for WA rainfall prediction. The influence of lagged correlation between the climate indices and seasonal autumn rainfall variability for the south coast and north coast regions of South West Division (SWD) and summer rainfall variability for the Kimberley region of North West Western Australia (NWWA) was investigated. Later, the prediction outcome of the hybrid models was compared with a time series linear ARIMAX and non-linear GEP models.

In this study, a correlation analysis was conducted between rainfall data and climate indices first. Afterwards, climate indices with high correlation were used as an input set for model development. Linear time series (ARIMAX) and non-linear (GEP) models were developed to see their capability to forecast seasonal rainfall in WA. The residuals derived from these two models were further analyzed using a different technique resulting in a hybrid model. The selection of methods was independent and aimed at describing the rainfall variability as per the inherent model structure, its capability to explain the relationship type (linear/ non-linear), and residual characteristics.

A comparative analysis of the statistical performance of different models in both calibration and validation periods has been presented in Table 6. Table 6 also presents the statistical performance parameters \(RMSE, MAE\), and refined Willmot index of agreement (\({d}_{r}\)) for the selected model sets.

For the south coast region, the DMI_Oct-Nino3_Nov model developed using the ARIMAX technique showed its capability to forecast autumn rainfall up to four months in advance with Pearson correlation \(\left(r\right)\) values ranging from 0.58 to 0.60 and 0.62 to 0.80 in the calibration and validation period, respectively. For the GEP model, the same model set showed its capability of forecasting up to four months in advance with a correlation value ranging from 0.75 to 0.79 and 0.75 to 0.82 in the calibration and validation period, respectively. In contrast, the hybrid (GEP-ARIMAX) model showed much better forecasting capability with correlation values ranging from 0.87 to 0.91 and 0.88 to 0.92 during the calibration and validation period.

The DMI-Nino3 model set showed its ability to forecast autumn rainfall up to four months in advance with different lagged months for different rainfall stations in the north coast region. For Northampton, the DMI_Jan-Nino3_Nov model set developed using ARIMAX showed its capability to forecast autumn rainfall up to two months in advance with a Pearson correlation \(\left(r\right)\) value of 0.82 and 0.70 in the calibration and validation period, respectively. The same model set developed using the GEP technique showed its capability of forecasting autumn rainfall with a correlation value of 0.82 and 0.84 in the calibration and validation period. However, the DMI_Jan-Nino3_Nov model developed using the hybrid (GEP-ARIMAX) technique outperformed both ARIMAX and GEP models and showed better forecasting capability with a significant correlation of 0.92 and 0.96 in the calibration and validation period respectively.

For the Kimberley region, the WTIO-SOI model set showed its ability to forecast summer rainfall with different lagged months for different rainfall stations. For Anna Plains, the WTIO_Aug-SOI_Mar model set developed using the ARIMAX technique showed its capability of forecasting up to four months in advance with a correlation of 0.83 and 0.65 in the calibration and validation period, respectively. The WTIO_Aug-SOI_Mar model developed using the GEP technique showed similar forecasting capability to ARIMAX (i.e., four months in advance), with a significant correlation value of 0.82 during the calibration and validation period. The same model set (i.e., the WTIO_Aug-SOI_Mar) developed using the hybrid (GEP-ARIMAX) technique showed much better forecasting capability than ARIMAX and GEP. A significantly high correlation value ranging from 0.94 and 0.89 in both the calibration and validation period was obtained. For Bidyadanga, the WTIO_Aug-SOI_May model set developed using the ARIMAX, and GEP techniques showed promising performance, as the ARIMAX model returned a correlation value of 0.68 and 0.77, wherein for the GEP model, the correlation values obtained were as high as 0.85 and 0.87 for the calibration and validation period, respectively. Both the model sets demonstrated their prediction capability up to four months in advance. On the other hand, the developed hybrid (GEP-ARIMAX) model resulted in a significantly high correlation of 0.94 in both the calibration and validation period. While Pearson correlation \((r)\) values are compared, a Pearson correlation \((r)\) value of more than 0.5 is considered a significant effect (Field 2013).

The refined Willmot index of agreement (\({d}_{r}\)) value is an indicator of the model fitness, where a relatively high positive value indicates a good fit (Willmott et al. 2012). For the developed hybrid model, \({d}_{r}\) value in the calibration and validation period were ranging from 0.72 to 0.82 and 0.69 to 0.84 respectively. Also, the developed hybrid model returned relatively low \(RMSE\) and \(MAE\) values in both the calibration and validation periods than the ARIMAX and GEP models. An observed vs. predicted plots for ARIMAX, GEP, and hybrid models are presented in Fig. 3 for Albany, Mingenew, and Bidyadanga. From observed vs. predicted plots, it is apparent that the hybrid (GEP-ARIMAX) model’s prediction performance demonstrated a similar pattern to the naturally occurring rainfall events. It is also notable that the developed hybrid model can predict all the severe rainfall cases; however, it could not predict some drought cases.

The findings of this study demonstrated that for WA’s south and north coast regions, a combined effect of DMI and Nino3 has a noticeable impact on seasonal autumn rainfall, whereas a different climate index set, namely WTIO-SOI, showed a significant contribution to the Kimberley region’s seasonal summer rainfall. To develop the rainfall forecast models for these regions, both linear (ARIMAX) and non-linear (GEP) relationships were evaluated. Even though the GEP model’s capability to predict seasonal autumn and summer rainfall for the selected regions is comparatively higher than ARIMAX models, residuals from the GEP models were fed into ARIMAX models, and the developed hybrid model showed improved forecasting for all the regions.

For the south coast region, the maximum correlation obtained in the ARIMAX models was reported as 0.64 for Grassmere, which is relatively lower than the minimum correlation found in the GEP models (0.75 for Grassmere) and hybrid models (0.87 for Albany). For the north coast region, the maximum correlation obtained in both the ARIMAX and GEP models was 0.82 for Northampton, which is relatively lower than the maximum correlation obtained for hybrid models (0.95 for Ogilvie). Similarly, the hybrid models developed for the Kimberley region stations showed correlation values as high as 0.94 for Anna Plains and Bidyadanga, whereas, relatively low correlations were achieved in ARIMAX and GEP, in particular for Gogo Station and Quanbun Downs. A comparatively high positive Willmott index of agreement (\({d}_{r}\)) values for all selected stations were also evident.

An overview of the error measurement for the developed models indicates that comparatively low RMSE and MAE values were obtained for hybrid models for all selected stations. From the observed vs predicted plots, many peaks and troughs were also well captured by the hybrid model if compared to ARIMAX and GEP. All these developed models have also shown robust prediction capability, as forecasting the rainfall as early as 1 month in advance is possible for the south coast (Nabawa and Ogilvie) and Kimberley (Quanbun Downs) regions. This is expected to offer greater flexibility in economic decision-making principles and better management of the agricultural and water resources. Furthermore, the developed models are expected to assist in disaster risk management and abnegating associated costly remediation, hence, creating robust disaster recovery and economic preparedness plans for Western Australia.