Abstract
This study proposes a novel downscaling technique based on stacking ensemble machine learning (SEML) to predict rainfall under climate change. The SEML consists of two levels. Rainfall time series predicted by level 1 algorithms MLR, MNLR, MARS, M5, RF, LSBoost, LSSVM-GS, and a novel hybrid algorithm namely LSSVM-RUN) are used as inputs to the level 2 machine learning algorithm (MARS and LSSVM_RUN). Then, meta-algorithms of SEML predict rainfall based on eight predicted rainfall in level 1. This approach boosts prediction accuracy by utilizing the strong points of different machine learning (ML) algorithms. Results showed that MARS and LSSVM-RUN could be employed to improve the modeling results as meta-algorithms (level 2 of the SEML). Three global climate models (GCMs) in the historical period (1985–2014) and three SSP scenarios in the future period (2021–2050) were considered for downscaling and predicting rainfall at Lake Urmia and Sefidrood basins. Using meta-algorithms, the prediction results showed that rainfall in all scenarios and stations decreased between 0.02 and 0.20% (except Takab station in model CanESM5 scenarios). Hence, the proposed stacking ensemble ML has the potential for modeling and predicting precipitation with good accuracy and high reliability.
HIGHLIGHTS
Proposing a novel downscaling technique based on the stacking ensemble machine learning (SEML).
Using the SEML for rainfall prediction under climate change.
Utilization of a novel hybrid algorithm namely LSSVM-RUN for the first time.
Investigation of rainfall prediction uncertainty in climate change conditions by Bootstrapping method (BM).
The proposed technique has the potential to analyze other engineering problems.
ABBREVIATIONS
- A1
ACCESS-ESM1-5
- ANN
Artificial neural network
- BFs
Basic functions
- BM
Bootstrapping method
- C5
CanESM5
- CMIP
Coupled Model Intercomparison project
- CO2
Carbon dioxide
- COVID-19
Coronavirus disease 2019
- CS
Coefficient of skewness
- CV
Coefficient of variation
- ESQ
Enhanced solution quality
- GCMs
Global climate models
- GS
Grid search
- GP
Genetic programming
- KNN
k-nearest neighbors
- LSBoost
Least-squares boost
- LSSVM
Least-squares support vector machine
- M2
MRI-ESM2-0
- M5
M5 model tree
- MAE
Mean absolute error
- MARS
Multivariate adaptive regression splines
- MCDM
Multi-criteria decision-making
- ML
Machine learning
- MLR
Multiple linear regression
- MNLR
Multiple nonlinear regression
- MSE
Mean squared error
- NIS
Negative ideal solution
- PIS
Positive ideal solution
- R
Person correlation coefficient
- RBF
Radial basis function
- RCM
regional climate models
- RCPs
Representative concentration pathways
- RF
Random forest
- RK
Runge Kutta
- RMSE
Root mean square error
- RRMSE
Relative root mean square error
- RUN
RUNge Kutta optimizer
- SCA
Sine Cosine algorithm
- SCF
SSP245-cov-fossil
- SCM
SSP245-cov-modgreen
- SCS
SSP245-cov-strgreen
- SDR
Standard deviation reduction
- SEML
Stacking ensemble machine learning
- SSPs
Shared socioeconomic pathways
- SSVM
Smooth support vector machine
- Std
Standard deviation
- SVM
Support vector machine
- TOPSIS
Technique for order of preference by similarity to the ideal solution
INTRODUCTION
Rainfall is a major factor in the agricultural and industrial water supply, and sustainable water resource management requires predicting rainfall under various scenarios (Azari et al. 2021). Human activity is responsible for global warming by emitting tons of CO2 emissions from fossil fuels, which is one of the primary causes of climate change. In recent decades, climate change has impacted human health and ecological systems and increased extreme events (Sisco et al. 2017; Bennedsen 2021; Limaye 2021). Decreasing rainfall patterns, including those linked to global warming, significantly, have strained surface water resources (Abbas & Mayo 2021).
Predicting the future effects of climate change is done by using global climate models (GCMs). GCMs are tools that operate on a global scale. Predicting the impact of climate change in the future requires the use of GCMs converted to smaller scales. Dynamic and statistical downscaling methods are employed to obtain data that are downscaled for this reason. High-resolution RCM and physical laws are used in dynamic downscaling methods. Unlike dynamic methods, statistical downscaling methods use empirical relationships and have many advantages, including high accuracy and low computational costs, and for this reason, they are preferred over dynamic methods (Wilby et al. 1998; Langousis & Veneziano 2007; Stoll et al. 2011; Lafon et al. 2013; Huang et al. 2020). ML algorithms are among the best and newest tools for statistically downscaling data.
Recently, ML algorithms have been widely used in downscaling meteorological variables (Chen et al. 2010; Kundu et al. 2017; Sachindra et al. 2018; Vandal et al. 2018; Trinh et al. 2021). However, the accuracy of most ML was not satisfactory in rainfall downscaling. The accuracy of ML in rainfall downscaling can be improved by optimizing them using an optimization algorithm. There are some efforts in this task such as using a hybrid of ML with a whale optimization algorithm (Anaraki et al. 2020), and a hybrid of ML with a sine cosine algorithm (Farrokhi et al. 2021). Nevertheless, there is a need for more accurate methods for rainfall downscaling. Because, by increasing the accuracy of downscale and as a result of more accurate prediction of the amount of precipitation in the future, it is possibly better to manage water resources in climate change conditions.
ML algorithms have different structures that give them unique advantages. ML algorithms have many advantages in downscaling hydrological variables, but their structure has defects that impact their performance. SEML attempts to resolve these defects by combining several algorithms with various structures. Using multiple algorithms makes it possible to simultaneously use the benefits of different algorithms. For this reason, SEML can greatly help increase the precision of predicting hydrological variables. Morshed-Bozorgdel et al. (2022) modeled wind speed using SEML. The results showed that SEML increased the modeling accuracy by >43% compared to the single algorithms.
The advantages and disadvantages of previous rainfall downscaling studies are presented in Table 1. As seen, previous studies had drawbacks such as low accuracy, not using hybrid algorithms, lack of uncertainty analysis, and not using new GCMs and climate change scenarios. Moreover, some previous studies were conducted on limited case studies. Hence, the present study aims to cover these disadvantages by introducing a stacking ensemble machine learning algorithm (SEML) for rainfall downscaling. Although this study uses the machine learning (ML) algorithms, similar to previous studies, using SEML structure increases the accuracy of ML algorithms by using the advantages of different ML algorithms simultaneously. The new contributions of this study and its difference from other carried out studies are listed as follows:
In the present study, a novel modeling technique based on the stacking ensemble of regression-based, tree-based, curve-based, kernel-based, and hybrid algorithm-based has been designed for predicting rainfall under climate change in the northern basins of Iran.
The precision of rainfall modeling can be modified by the algorithms mentioned in this modeling technique at two levels.
Using a new hybrid algorithm (LSSVM_RUN) as a meta-model.
Predicting rainfall under climate change conditions (CMIP6 models and SSP-representative concentration pathways (RCP) scenarios) in the future.
The uncertainty of this modeling technique has been investigated by the Bootstrapping method (BM) as a reliable and robust uncertainty approach.
Station name . | CS . | CV . | Std . | Average . |
---|---|---|---|---|
Tabriz | 20.90 | 19.58 | 0.94 | 1.57 |
Sahand | 19.16 | 18.50 | 0.97 | 1.47 |
Urmia | 26.28 | 28.07 | 1.07 | 1.55 |
Maragheh | 25.13 | 26.84 | 1.07 | 1.30 |
Mianeh | 23.49 | 22.13 | 0.94 | 1.20 |
Mahabad | 33.61 | 34.63 | 1.03 | 1.10 |
Saqez | 38.37 | 40.96 | 1.07 | 1.68 |
Takab | 25.92 | 24.20 | 0.93 | 1.58 |
Zanjan | 32.02 | 31.15 | 0.97 | 1.68 |
Station name . | CS . | CV . | Std . | Average . |
---|---|---|---|---|
Tabriz | 20.90 | 19.58 | 0.94 | 1.57 |
Sahand | 19.16 | 18.50 | 0.97 | 1.47 |
Urmia | 26.28 | 28.07 | 1.07 | 1.55 |
Maragheh | 25.13 | 26.84 | 1.07 | 1.30 |
Mianeh | 23.49 | 22.13 | 0.94 | 1.20 |
Mahabad | 33.61 | 34.63 | 1.03 | 1.10 |
Saqez | 38.37 | 40.96 | 1.07 | 1.68 |
Takab | 25.92 | 24.20 | 0.93 | 1.58 |
Zanjan | 32.02 | 31.15 | 0.97 | 1.68 |
The proposed approach has the potential to provide highly accurate and reliable rainfall modeling and prediction. The remaining work is structured as follows:
Section 2 presents the used data and presented approach for downscaling rainfall, Section 3 presents the obtained results and discussion, and section 4 presents the conclusion.
MATERIAL AND METHODS
Study area and data
GCMs and future climate change scenarios
In this study, three COVID-19 post-pandemic recovery scenarios (SCF, SCM, and SCS) of CMIP6 are used, which assumes that the current climate change trend remains constant, resulting in a representative concentration pathway of 4.5 W/m2 by 2100 and the effects of economic growth, population changes and urbanization (Forster et al. 2020; Lamboll et al. 2021) and COVID-19.
SSP2 depicts a moderate growth route in which future socioeconomic development patterns follow existing development tendencies. Research has shown that changes in human activity due to the COVID-19 epidemic have had a significant effect on the composition of the atmospheric composition (D'Souza et al. 2021), particularly in the amount of solar radiation reaching the planet's surface and aerosol optical depth across southern and eastern Asia. We investigated rainfall for historical and future periods using three GCM outputs (A1, C5, and M2) and three SSP-RCP scenarios from the most recent CMIP6 (Jones et al. 2021). Three assumptions were used for COVID-19 post-pandemic recovery scenarios, with the SSP245 scenario as the baseline. The selected models and scenarios details are presented in Tables 2 and 3 (for more information, see (Riahi et al. 2017, Swart et al. 2019, Yukimoto et al. 2019, Oshima et al. 2020, Ziehn et al. 2020 and Kadkhodazadeh et al. 2022).
Model . | Institution . | Atmosphere resolutiona . |
---|---|---|
ACCESS-ESM1–5 | Commonwealth Scientific and Industrial Research Organization (Australia) | 250 km (N96), L38 |
CanESM5 | Canadian Centre for Climate Modelling and Analysis (Canada) | 500 km (T63), L49 |
MRI-ESM2-0 | Meteorological Research Institute (Japan) | 100 km (TL159, 1.125°), L80 |
Model . | Institution . | Atmosphere resolutiona . |
---|---|---|
ACCESS-ESM1–5 | Commonwealth Scientific and Industrial Research Organization (Australia) | 250 km (N96), L38 |
CanESM5 | Canadian Centre for Climate Modelling and Analysis (Canada) | 500 km (T63), L49 |
MRI-ESM2-0 | Meteorological Research Institute (Japan) | 100 km (TL159, 1.125°), L80 |
aShown as CMIP ‘nominal resolution’ in km, ‘L’ indicates number of vertical levels.
Experiment-id . | Activity-id . | Description . |
---|---|---|
Baseline | ScenarioMIP | SSP-based RCP scenario with medium radiative forcing by the end of the century. Following approximately RCP4.5 global forcing pathway with SSP2 socioeconomic conditions. Radiative forcing reaches a level of 4.5 W/m2 in 2100 |
Two year blip | – | Data are modified for all of 2020 and 2021 in accordance with observed activity levels in the sectors of different countries. This is projected to continue at 2/3 of the activity reduction value for the latest month available for the rest of the 2-year period. Activity is interpolated, month for month, back towards baseline over 2022 and is equal to baseline thereafter |
SSP245-cov-fossila | DAMIP | Follows 2-year blip until 2023. Thereafter, the effects of additional investment in fossil fuels during recovery are included in a globally uniform way. Financial modeling produced estimated global Kyoto gas emissions totals consistent with 10% higher emissions than the path met if countries meet their nationally determined contributions (NDCs). We used the open-source package Silicone to find a linear combination of MESSAGE-GLOBIOM SSP2 scenarios that gave the same total Kyoto emissions. We use the global relative emissions level of each aerosol and precursor in this composite scenario to rescale the 2D emissions maps. The relative concentration change arising from this scenario is used to rescale global greenhouse gas concentrations |
SSP245-cov-modgreena | DAMIP | Follows 2-year blip until 2023. Thereafter, the effects of small additional investment in green technology are included in a globally uniform way. Financial considerations as to what emissions change is plausible with moderate ambition (in keeping with results in McCollum et al. (2018)) produced a Kyoto emissions total in 2030 of 35% lower than the NDCs, which we resolve into a linear combination of MESSAGE-GLOBIOM SSP2 scenarios. We then set a global net zero CO2 trajectory for 2060, and resolve this CO2 total into a linear combination of MESAGE-GLOBIOM SSP2 scenarios again using Silicone. The relative difference between this scenario and the baseline is used to rescale emissions and concentrations as in the fossil fuel case |
SSP245-cov-strgreena | DAMIP | Follows 2-year blip until 2023. Thereafter, the effects of large additional investment in green technology are assumed to push the scenario towards an IMAGE SSP1 world. In 2030, we are assumed to reach the emissions rate of SSP1-19, around 52% lower than following current NDCs, and thereafter follow a global net zero CO2 target for 2050. The other emissions are formed by a linear combination of IMAGE SSP1 scenarios that give the closest total CO2 match to this pathway (this composite pathway is always close to the SSP1-19 pathway after 2023) |
Experiment-id . | Activity-id . | Description . |
---|---|---|
Baseline | ScenarioMIP | SSP-based RCP scenario with medium radiative forcing by the end of the century. Following approximately RCP4.5 global forcing pathway with SSP2 socioeconomic conditions. Radiative forcing reaches a level of 4.5 W/m2 in 2100 |
Two year blip | – | Data are modified for all of 2020 and 2021 in accordance with observed activity levels in the sectors of different countries. This is projected to continue at 2/3 of the activity reduction value for the latest month available for the rest of the 2-year period. Activity is interpolated, month for month, back towards baseline over 2022 and is equal to baseline thereafter |
SSP245-cov-fossila | DAMIP | Follows 2-year blip until 2023. Thereafter, the effects of additional investment in fossil fuels during recovery are included in a globally uniform way. Financial modeling produced estimated global Kyoto gas emissions totals consistent with 10% higher emissions than the path met if countries meet their nationally determined contributions (NDCs). We used the open-source package Silicone to find a linear combination of MESSAGE-GLOBIOM SSP2 scenarios that gave the same total Kyoto emissions. We use the global relative emissions level of each aerosol and precursor in this composite scenario to rescale the 2D emissions maps. The relative concentration change arising from this scenario is used to rescale global greenhouse gas concentrations |
SSP245-cov-modgreena | DAMIP | Follows 2-year blip until 2023. Thereafter, the effects of small additional investment in green technology are included in a globally uniform way. Financial considerations as to what emissions change is plausible with moderate ambition (in keeping with results in McCollum et al. (2018)) produced a Kyoto emissions total in 2030 of 35% lower than the NDCs, which we resolve into a linear combination of MESSAGE-GLOBIOM SSP2 scenarios. We then set a global net zero CO2 trajectory for 2060, and resolve this CO2 total into a linear combination of MESAGE-GLOBIOM SSP2 scenarios again using Silicone. The relative difference between this scenario and the baseline is used to rescale emissions and concentrations as in the fossil fuel case |
SSP245-cov-strgreena | DAMIP | Follows 2-year blip until 2023. Thereafter, the effects of large additional investment in green technology are assumed to push the scenario towards an IMAGE SSP1 world. In 2030, we are assumed to reach the emissions rate of SSP1-19, around 52% lower than following current NDCs, and thereafter follow a global net zero CO2 target for 2050. The other emissions are formed by a linear combination of IMAGE SSP1 scenarios that give the closest total CO2 match to this pathway (this composite pathway is always close to the SSP1-19 pathway after 2023) |
aFor more details on how these were constructed, see Forster et al. (2020).
Present work steps
Downscaling large-scale rainfall data by the SEML (level 1): Downscaling large-scale rainfall data using eight ML algorithms including MLR, MNLR, MARS, M5, RF, LSBoost, LSSVM-GS, and LSSVM-RUN under three GCMs, including A1, C5, M2 is performed at Tabriz, Sahand, Urmia, Maragheh, Mianeh, Mahabad, Saqez, Takab, and Zanjan stations.
Select the best algorithms by the TOPSIS method in level 1: Since it is difficult to compare algorithms and select the best algorithm in level 1, the TOPSIS method is used to select the best algorithm. This process is as follows: (1) MAE, RMSE, RRMSE, and R are considered criteria of the TOPSIS method. (2) The algorithms are considered alternatives, and the lambda weight is the same for all assessment criteria. (3) The algorithm with the highest score is selected as the best algorithm.
Downscaling large-scale rainfall data by the SEML (level 2): After selecting the best algorithm using the TOPSIS method, level 2 of downscaling large-scale rainfall data is performed. For this purpose, the output of the base algorithms is used as the input of the meta-algorithms.
Prediction rainfall under climate change by meta-algorithms (2021–2050): Rainfall prediction for 2021–2050 under climate change in three GCMs, including A1, C5, and M2 and three SCF, SCM, and SCS scenarios by downscaled rainfall data and the meta-algorithms in the nine stations done.
Uncertainty analysis: Uncertainty analysis of models and scenarios is performed using BM in nine stations.
The descriptions for MLR, MNLR, M5, RF, LSBoost and TOPSIS are given in Supplementary material, section S.1.
Multivariate adaptive regression splines
Least-squares support vector machine-grid search
RUNge Kutta optimizer
The RUNge Kutta optimizer (RUN) algorithm, first proposed by Ahmadianfar et al. (2021) is a population-based optimization method based on mathematical principles and the Runge kutta (RK) method. This algorithm can be used to solve optimization problems in a variety of areas. The RK method slope changes are used by this algorithm to search for optimal solutions. It also uses the ESQ mechanism to increase the speed of convergence and avoid falling into the trap of local optimization. For more information, see Ahmadianfar et al. (2021).
Novel hybrid algorithm (LSSVM-RUN)
The LSSVM only runs by defining two parameters including C and σ parameters. The mentioned parameters significantly impact the performance of LSSVM. However, there is no specific method for selecting these two parameters; their range is in (0, ), which is wide. The trial and error method for determining C and σ is inaccurate and requires a high computational cost. As a result, this study used the RUN algorithm to determine the optimal value of the LSSVM parameters. The values C and σ are considered as decision variables in the hybrid algorithm. First, the data are randomly divided into training and testing data. Then, the RUN parameters and the initial population of the optimization and simulation algorithm are determined. After training LSSVM, the test data are used to evaluate the performance of the simulation algorithm.
Bootstrapping method
Although there are many factors that affect rainfall prediction uncertainty, this study focuses on the uncertainties related to prediction GCMs and scenarios. Bootstrapping method (BM) is one of the most powerful and accessible methods for uncertainty analysis. The steps of this method are as follows:
Input data are resampled several times, and new output data are predicted.
Predicting new outputs, a 95% prediction confidence interval is obtained using the values generated for each observation to quantify the prediction uncertainties.
Sort upper and lower bands of 95% confidence interval for each time series.
The upper quartile (97.5%) and the lower quartile (2.5%) of the 95% band are determined.
- The R-factor coefficient is calculated using the following formula. The lower the value of this coefficient, the less uncertainty.where is the standard deviation of the observed values, N is the number of observed data and and indicate the ith value of the upper quartile (97.5%) and the lower quartile (2.5%) of the 95% band.
Assessment criteria
RESULTS AND DISCUSSION
Downscaling large-scale rainfall data by the SEML (level 1)
The base algorithms in level 1 of the SEML downscale the large-scale rainfall in the nine stations. Table 4 and Supplementary material, Table S2 show the values of assessment criteria for base algorithms and three GCMs in the nine stations. According to this table, the accuracy of any algorithms that were investigated was not good at this level. Nevertheless, the MARS, LSBoost, and LSSVM-RUN had greater accuracy than other investigated algorithms during the testing period at different stations and three GCMs. In this condition, integrating the results of base algorithms with meta-algorithms can lead to good accuracy. The best algorithm in level 1 was used as a meta-algorithm. However, due to the differences in assessment criteria and the results obtained in different stations and algorithms, it is difficult to choose the best algorithm for use in level 2 of the SEML as a meta-algorithm. Hence, to select the best algorithm, the TOPSIS method was utilized.
Models . | Stations . | Algorithms . | Assessment criteria . | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Train . | Test . | |||||||||
MAE . | RMSE . | RRMSE . | R . | MAE . | RMSE . | RRMSE . | R . | |||
A1 | Tabriz | MLR | 16.19 | 22.41 | 0.66 | 0.75 | 24.75 | 30.33 | 1.11 | 0.43 |
MNLR | 11.60 | 15.38 | 0.45 | 0.89 | 35.08 | 45.52 | 1.66 | 0.32 | ||
M5 | 18.13 | 27.29 | 0.80 | 0.60 | 17.33 | 23.32 | 0.85 | 0.55 | ||
MARS | 18.28 | 27.62 | 0.81 | 0.59 | 15.88 | 20.50 | 0.75 | 0.66 | ||
RF | 9.05 | 14.28 | 0.42 | 0.94 | 16.62 | 21.70 | 0.79 | 0.61 | ||
LSBoost | 8.73 | 12.61 | 0.37 | 0.95 | 16.07 | 21.38 | 0.78 | 0.64 | ||
LSSVM-GS | 0.26 | 0.36 | 0.01 | 1.00 | 20.21 | 25.92 | 0.95 | 0.58 | ||
LSSVM-RUN | 15.27 | 23.27 | 0.68 | 0.78 | 16.61 | 21.66 | 0.79 | 0.61 | ||
Urmia | MLR | 13.14 | 18.22 | 0.70 | 0.72 | 20.59 | 25.77 | 1.11 | 0.32 | |
MNLR | 9.78 | 13.12 | 0.50 | 0.86 | 23.76 | 30.48 | 1.31 | 0.33 | ||
M5 | 15.16 | 22.08 | 0.84 | 0.53 | 17.24 | 21.66 | 0.93 | 0.39 | ||
MARS | 15.23 | 22.14 | 0.85 | 0.53 | 15.77 | 19.55 | 0.84 | 0.53 | ||
RF | 7.70 | 12.02 | 0.46 | 0.93 | 17.52 | 21.47 | 0.93 | 0.39 | ||
LSBoost | 2.76 | 6.80 | 0.26 | 0.98 | 15.71 | 20.13 | 0.87 | 0.51 | ||
LSSVM-GS | 0.20 | 0.28 | 0.01 | 1.00 | 18.59 | 22.36 | 0.96 | 0.46 | ||
LSSVM-RUN | 13.44 | 19.37 | 0.74 | 0.73 | 16.67 | 20.09 | 0.87 | 0.50 | ||
Zanjan | MLR | 9.46 | 12.33 | 0.65 | 0.75 | 12.30 | 16.17 | 0.86 | 0.53 | |
MNLR | 7.65 | 9.49 | 0.50 | 0.86 | 24.09 | 28.70 | 1.53 | 0.18 | ||
M5 | 10.86 | 14.60 | 0.78 | 0.63 | 11.45 | 15.95 | 0.85 | 0.53 | ||
MARS | 11.04 | 14.82 | 0.79 | 0.62 | 10.62 | 14.50 | 0.77 | 0.63 | ||
RF | 5.93 | 8.06 | 0.43 | 0.94 | 11.59 | 16.54 | 0.88 | 0.47 | ||
LSBoost | 8.18 | 10.38 | 0.55 | 0.87 | 11.02 | 15.67 | 0.83 | 0.55 | ||
LSSVM-GS | 0.15 | 0.20 | 0.01 | 1.00 | 12.18 | 18.14 | 0.96 | 0.47 | ||
LSSVM-RUN | 7.48 | 9.85 | 0.52 | 0.89 | 10.67 | 15.44 | 0.82 | 0.57 | ||
C5 | Tabriz | MLR | 14.38 | 18.87 | 0.55 | 0.83 | 29.50 | 37.52 | 1.37 | 0.35 |
MNLR | 0.00 | 0.00 | 0.00 | 1.00 | 107.05 | 131.80 | 4.81 | 0.18 | ||
M5 | 18.24 | 27.98 | 0.82 | 0.57 | 16.80 | 23.54 | 0.86 | 0.53 | ||
MARS | 18.60 | 27.82 | 0.81 | 0.58 | 15.73 | 20.76 | 0.76 | 0.65 | ||
RF | 9.31 | 14.41 | 0.42 | 0.94 | 18.66 | 24.77 | 0.90 | 0.45 | ||
LSBoost | 17.17 | 26.60 | 0.78 | 0.66 | 16.67 | 23.16 | 0.84 | 0.53 | ||
LSSVM-GS | 0.26 | 0.35 | 0.01 | 1.00 | 19.66 | 25.28 | 0.92 | 0.65 | ||
LSSVM-RUN | 1.77 | 2.73 | 0.08 | 1.00 | 16.33 | 21.21 | 0.77 | 0.63 | ||
Urmia | MLR | 10.55 | 13.94 | 0.53 | 0.85 | 24.35 | 32.01 | 1.38 | 0.21 | |
MNLR | 0.00 | 0.00 | 0.00 | 1.00 | 76.67 | 98.96 | 4.27 | 0.17 | ||
M5 | 15.32 | 21.82 | 0.83 | 0.55 | 17.53 | 22.20 | 0.96 | 0.36 | ||
MARS | 15.38 | 22.06 | 0.84 | 0.54 | 15.54 | 19.10 | 0.82 | 0.56 | ||
RF | 7.04 | 11.27 | 0.43 | 0.94 | 15.94 | 19.85 | 0.86 | 0.51 | ||
LSBoost | 14.43 | 20.80 | 0.79 | 0.67 | 16.39 | 20.05 | 0.86 | 0.50 | ||
LSSVM-GS | 0.20 | 0.27 | 0.01 | 1.00 | 18.26 | 21.92 | 0.94 | 0.56 | ||
LSSVM-RUN | 0.18 | 0.25 | 0.01 | 1.00 | 15.76 | 19.47 | 0.84 | 0.55 | ||
Zanjan | MLR | 8.40 | 10.37 | 0.55 | 0.83 | 19.79 | 25.50 | 1.36 | 0.15 | |
MNLR | 0.00 | 0.00 | 0.00 | 1.00 | 56.09 | 67.81 | 3.61 | 0.17 | ||
M5 | 11.20 | 15.20 | 0.81 | 0.59 | 11.12 | 15.97 | 0.85 | 0.52 | ||
MARS | 11.70 | 15.68 | 0.83 | 0.55 | 10.16 | 14.48 | 0.77 | 0.65 | ||
RF | 5.97 | 9.02 | 0.48 | 0.89 | 12.19 | 16.59 | 0.88 | 0.47 | ||
LSBoost | 0.97 | 1.58 | 0.08 | 1.00 | 10.99 | 15.17 | 0.81 | 0.59 | ||
LSSVM-GS | 0.15 | 0.19 | 0.01 | 1.00 | 11.91 | 17.77 | 0.94 | 0.57 | ||
LSSVM-RUN | 3.74 | 4.91 | 0.26 | 0.98 | 10.56 | 15.37 | 0.82 | 0.58 | ||
M2 | Tabriz | MLR | 13.89 | 18.55 | 0.54 | 0.84 | 25.43 | 32.61 | 1.19 | 0.51 |
MNLR | 1.09 | 1.37 | 0.04 | 1.00 | 162.55 | 200.33 | 7.31 | 0.16 | ||
M5 | 20.70 | 29.95 | 0.88 | 0.48 | 18.08 | 25.23 | 0.92 | 0.41 | ||
MARS | 19.85 | 28.73 | 0.84 | 0.54 | 17.40 | 24.06 | 0.88 | 0.52 | ||
RF | 9.81 | 15.12 | 0.44 | 0.95 | 17.86 | 23.61 | 0.86 | 0.50 | ||
LSBoost | 17.50 | 24.41 | 0.71 | 0.77 | 17.74 | 23.37 | 0.85 | 0.52 | ||
LSSVM-GS | 0.27 | 0.36 | 0.01 | 1.00 | 20.79 | 26.64 | 0.97 | 0.57 | ||
LSSVM-RUN | 10.35 | 15.35 | 0.45 | 0.95 | 16.25 | 21.90 | 0.80 | 0.60 | ||
Urmia | MLR | 11.21 | 14.43 | 0.55 | 0.83 | 22.54 | 28.93 | 1.25 | 0.42 | |
MNLR | 1.81 | 2.27 | 0.09 | 1.00 | 169.79 | 209.04 | 9.01 | 0.11 | ||
M5 | 17.16 | 23.34 | 0.89 | 0.45 | 17.59 | 21.58 | 0.93 | 0.38 | ||
MARS | 16.23 | 23.03 | 0.88 | 0.47 | 17.31 | 21.58 | 0.93 | 0.40 | ||
RF | 8.15 | 12.32 | 0.47 | 0.92 | 17.01 | 20.63 | 0.89 | 0.45 | ||
LSBoost | 15.17 | 21.57 | 0.82 | 0.64 | 16.51 | 20.14 | 0.87 | 0.50 | ||
LSSVM-GS | 0.20 | 0.28 | 0.01 | 1.00 | 18.83 | 22.68 | 0.98 | 0.51 | ||
LSSVM-RUN | 0.21 | 0.30 | 0.01 | 1.00 | 15.74 | 19.66 | 0.85 | 0.53 | ||
Zanjan | MLR | 7.75 | 9.63 | 0.51 | 0.86 | 18.08 | 22.12 | 1.18 | 0.39 | |
MNLR | 1.35 | 1.70 | 0.09 | 1.00 | 75.34 | 97.81 | 5.20 | 0.17 | ||
M5 | 11.28 | 14.98 | 0.79 | 0.60 | 11.57 | 16.11 | 0.86 | 0.52 | ||
MARS | 12.15 | 16.34 | 0.87 | 0.49 | 12.02 | 16.90 | 0.90 | 0.44 | ||
RF | 5.70 | 7.84 | 0.42 | 0.95 | 11.28 | 16.88 | 0.90 | 0.44 | ||
LSBoost | 1.91 | 2.38 | 0.13 | 0.99 | 11.56 | 15.88 | 0.84 | 0.53 | ||
LSSVM-GS | 0.16 | 0.20 | 0.01 | 1.00 | 12.43 | 18.42 | 0.98 | 0.46 | ||
LSSVM-RUN | 0.18 | 0.24 | 0.01 | 1.00 | 11.18 | 15.91 | 0.85 | 0.53 |
Models . | Stations . | Algorithms . | Assessment criteria . | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Train . | Test . | |||||||||
MAE . | RMSE . | RRMSE . | R . | MAE . | RMSE . | RRMSE . | R . | |||
A1 | Tabriz | MLR | 16.19 | 22.41 | 0.66 | 0.75 | 24.75 | 30.33 | 1.11 | 0.43 |
MNLR | 11.60 | 15.38 | 0.45 | 0.89 | 35.08 | 45.52 | 1.66 | 0.32 | ||
M5 | 18.13 | 27.29 | 0.80 | 0.60 | 17.33 | 23.32 | 0.85 | 0.55 | ||
MARS | 18.28 | 27.62 | 0.81 | 0.59 | 15.88 | 20.50 | 0.75 | 0.66 | ||
RF | 9.05 | 14.28 | 0.42 | 0.94 | 16.62 | 21.70 | 0.79 | 0.61 | ||
LSBoost | 8.73 | 12.61 | 0.37 | 0.95 | 16.07 | 21.38 | 0.78 | 0.64 | ||
LSSVM-GS | 0.26 | 0.36 | 0.01 | 1.00 | 20.21 | 25.92 | 0.95 | 0.58 | ||
LSSVM-RUN | 15.27 | 23.27 | 0.68 | 0.78 | 16.61 | 21.66 | 0.79 | 0.61 | ||
Urmia | MLR | 13.14 | 18.22 | 0.70 | 0.72 | 20.59 | 25.77 | 1.11 | 0.32 | |
MNLR | 9.78 | 13.12 | 0.50 | 0.86 | 23.76 | 30.48 | 1.31 | 0.33 | ||
M5 | 15.16 | 22.08 | 0.84 | 0.53 | 17.24 | 21.66 | 0.93 | 0.39 | ||
MARS | 15.23 | 22.14 | 0.85 | 0.53 | 15.77 | 19.55 | 0.84 | 0.53 | ||
RF | 7.70 | 12.02 | 0.46 | 0.93 | 17.52 | 21.47 | 0.93 | 0.39 | ||
LSBoost | 2.76 | 6.80 | 0.26 | 0.98 | 15.71 | 20.13 | 0.87 | 0.51 | ||
LSSVM-GS | 0.20 | 0.28 | 0.01 | 1.00 | 18.59 | 22.36 | 0.96 | 0.46 | ||
LSSVM-RUN | 13.44 | 19.37 | 0.74 | 0.73 | 16.67 | 20.09 | 0.87 | 0.50 | ||
Zanjan | MLR | 9.46 | 12.33 | 0.65 | 0.75 | 12.30 | 16.17 | 0.86 | 0.53 | |
MNLR | 7.65 | 9.49 | 0.50 | 0.86 | 24.09 | 28.70 | 1.53 | 0.18 | ||
M5 | 10.86 | 14.60 | 0.78 | 0.63 | 11.45 | 15.95 | 0.85 | 0.53 | ||
MARS | 11.04 | 14.82 | 0.79 | 0.62 | 10.62 | 14.50 | 0.77 | 0.63 | ||
RF | 5.93 | 8.06 | 0.43 | 0.94 | 11.59 | 16.54 | 0.88 | 0.47 | ||
LSBoost | 8.18 | 10.38 | 0.55 | 0.87 | 11.02 | 15.67 | 0.83 | 0.55 | ||
LSSVM-GS | 0.15 | 0.20 | 0.01 | 1.00 | 12.18 | 18.14 | 0.96 | 0.47 | ||
LSSVM-RUN | 7.48 | 9.85 | 0.52 | 0.89 | 10.67 | 15.44 | 0.82 | 0.57 | ||
C5 | Tabriz | MLR | 14.38 | 18.87 | 0.55 | 0.83 | 29.50 | 37.52 | 1.37 | 0.35 |
MNLR | 0.00 | 0.00 | 0.00 | 1.00 | 107.05 | 131.80 | 4.81 | 0.18 | ||
M5 | 18.24 | 27.98 | 0.82 | 0.57 | 16.80 | 23.54 | 0.86 | 0.53 | ||
MARS | 18.60 | 27.82 | 0.81 | 0.58 | 15.73 | 20.76 | 0.76 | 0.65 | ||
RF | 9.31 | 14.41 | 0.42 | 0.94 | 18.66 | 24.77 | 0.90 | 0.45 | ||
LSBoost | 17.17 | 26.60 | 0.78 | 0.66 | 16.67 | 23.16 | 0.84 | 0.53 | ||
LSSVM-GS | 0.26 | 0.35 | 0.01 | 1.00 | 19.66 | 25.28 | 0.92 | 0.65 | ||
LSSVM-RUN | 1.77 | 2.73 | 0.08 | 1.00 | 16.33 | 21.21 | 0.77 | 0.63 | ||
Urmia | MLR | 10.55 | 13.94 | 0.53 | 0.85 | 24.35 | 32.01 | 1.38 | 0.21 | |
MNLR | 0.00 | 0.00 | 0.00 | 1.00 | 76.67 | 98.96 | 4.27 | 0.17 | ||
M5 | 15.32 | 21.82 | 0.83 | 0.55 | 17.53 | 22.20 | 0.96 | 0.36 | ||
MARS | 15.38 | 22.06 | 0.84 | 0.54 | 15.54 | 19.10 | 0.82 | 0.56 | ||
RF | 7.04 | 11.27 | 0.43 | 0.94 | 15.94 | 19.85 | 0.86 | 0.51 | ||
LSBoost | 14.43 | 20.80 | 0.79 | 0.67 | 16.39 | 20.05 | 0.86 | 0.50 | ||
LSSVM-GS | 0.20 | 0.27 | 0.01 | 1.00 | 18.26 | 21.92 | 0.94 | 0.56 | ||
LSSVM-RUN | 0.18 | 0.25 | 0.01 | 1.00 | 15.76 | 19.47 | 0.84 | 0.55 | ||
Zanjan | MLR | 8.40 | 10.37 | 0.55 | 0.83 | 19.79 | 25.50 | 1.36 | 0.15 | |
MNLR | 0.00 | 0.00 | 0.00 | 1.00 | 56.09 | 67.81 | 3.61 | 0.17 | ||
M5 | 11.20 | 15.20 | 0.81 | 0.59 | 11.12 | 15.97 | 0.85 | 0.52 | ||
MARS | 11.70 | 15.68 | 0.83 | 0.55 | 10.16 | 14.48 | 0.77 | 0.65 | ||
RF | 5.97 | 9.02 | 0.48 | 0.89 | 12.19 | 16.59 | 0.88 | 0.47 | ||
LSBoost | 0.97 | 1.58 | 0.08 | 1.00 | 10.99 | 15.17 | 0.81 | 0.59 | ||
LSSVM-GS | 0.15 | 0.19 | 0.01 | 1.00 | 11.91 | 17.77 | 0.94 | 0.57 | ||
LSSVM-RUN | 3.74 | 4.91 | 0.26 | 0.98 | 10.56 | 15.37 | 0.82 | 0.58 | ||
M2 | Tabriz | MLR | 13.89 | 18.55 | 0.54 | 0.84 | 25.43 | 32.61 | 1.19 | 0.51 |
MNLR | 1.09 | 1.37 | 0.04 | 1.00 | 162.55 | 200.33 | 7.31 | 0.16 | ||
M5 | 20.70 | 29.95 | 0.88 | 0.48 | 18.08 | 25.23 | 0.92 | 0.41 | ||
MARS | 19.85 | 28.73 | 0.84 | 0.54 | 17.40 | 24.06 | 0.88 | 0.52 | ||
RF | 9.81 | 15.12 | 0.44 | 0.95 | 17.86 | 23.61 | 0.86 | 0.50 | ||
LSBoost | 17.50 | 24.41 | 0.71 | 0.77 | 17.74 | 23.37 | 0.85 | 0.52 | ||
LSSVM-GS | 0.27 | 0.36 | 0.01 | 1.00 | 20.79 | 26.64 | 0.97 | 0.57 | ||
LSSVM-RUN | 10.35 | 15.35 | 0.45 | 0.95 | 16.25 | 21.90 | 0.80 | 0.60 | ||
Urmia | MLR | 11.21 | 14.43 | 0.55 | 0.83 | 22.54 | 28.93 | 1.25 | 0.42 | |
MNLR | 1.81 | 2.27 | 0.09 | 1.00 | 169.79 | 209.04 | 9.01 | 0.11 | ||
M5 | 17.16 | 23.34 | 0.89 | 0.45 | 17.59 | 21.58 | 0.93 | 0.38 | ||
MARS | 16.23 | 23.03 | 0.88 | 0.47 | 17.31 | 21.58 | 0.93 | 0.40 | ||
RF | 8.15 | 12.32 | 0.47 | 0.92 | 17.01 | 20.63 | 0.89 | 0.45 | ||
LSBoost | 15.17 | 21.57 | 0.82 | 0.64 | 16.51 | 20.14 | 0.87 | 0.50 | ||
LSSVM-GS | 0.20 | 0.28 | 0.01 | 1.00 | 18.83 | 22.68 | 0.98 | 0.51 | ||
LSSVM-RUN | 0.21 | 0.30 | 0.01 | 1.00 | 15.74 | 19.66 | 0.85 | 0.53 | ||
Zanjan | MLR | 7.75 | 9.63 | 0.51 | 0.86 | 18.08 | 22.12 | 1.18 | 0.39 | |
MNLR | 1.35 | 1.70 | 0.09 | 1.00 | 75.34 | 97.81 | 5.20 | 0.17 | ||
M5 | 11.28 | 14.98 | 0.79 | 0.60 | 11.57 | 16.11 | 0.86 | 0.52 | ||
MARS | 12.15 | 16.34 | 0.87 | 0.49 | 12.02 | 16.90 | 0.90 | 0.44 | ||
RF | 5.70 | 7.84 | 0.42 | 0.95 | 11.28 | 16.88 | 0.90 | 0.44 | ||
LSBoost | 1.91 | 2.38 | 0.13 | 0.99 | 11.56 | 15.88 | 0.84 | 0.53 | ||
LSSVM-GS | 0.16 | 0.20 | 0.01 | 1.00 | 12.43 | 18.42 | 0.98 | 0.46 | ||
LSSVM-RUN | 0.18 | 0.24 | 0.01 | 1.00 | 11.18 | 15.91 | 0.85 | 0.53 |
Select the best algorithms by the TOPSIS method in the level 1
According to the values of the assessment criteria in Table 4 and Supplementary material, Table S1 and the weights assigned to each assessment criteria, each algorithm's score in different stations and algorithms was calculated. The assessment criteria have a lambda weight of 0.25, and the sum of all assessment criteria must be equal to one. In general, algorithms with the highest scores tend to have higher rankings. In Table 5, the results in different stations and algorithms showed that the two MARS and LSSVM-RUN algorithms with a mean score of 0.99 had better performance than other algorithms. The MARS is a nonlinear and non-parametric method that was highly effective in solving high-dimensional nonlinear problems and improving modeling accuracy with rapid convergence. Moreover, the RUN optimization algorithm worked well to find the optimal C and σ in the LSSVM, which makes the new hybrid LSSVM-RUN algorithm very precise.
Models . | Stations . | Algorithms score . | |||||||
---|---|---|---|---|---|---|---|---|---|
MLR . | MNLR . | M5 . | MARS . | RF . | LSBoost . | LSSVM-GS . | LSSVM-RUN . | ||
A1 | Tabriz | 0.58 | 0.00 | 0.90 | 1.00 | 0.96 | 0.98 | 0.78 | 0.96 |
Sahand | 0.61 | 0.00 | 0.88 | 1.00 | 0.95 | 0.95 | 0.78 | 0.99 | |
Urmia | 0.41 | 0.00 | 0.80 | 1.00 | 0.80 | 0.97 | 0.70 | 0.92 | |
Maragheh | 0.71 | 0.00 | 0.91 | 1.00 | 0.95 | 0.96 | 0.78 | 0.97 | |
Mianeh | 0.83 | 0.00 | 0.84 | 1.00 | 0.86 | 0.96 | 0.76 | 0.93 | |
Mahabad | 0.60 | 0.00 | 0.89 | 0.99 | 0.96 | 0.99 | 0.84 | 0.99 | |
Saqez | 0.83 | 0.00 | 0.92 | 0.93 | 0.94 | 1.00 | 0.88 | 0.99 | |
Takab | 0.83 | 0.00 | 0.80 | 0.98 | 0.83 | 1.00 | 0.78 | 0.93 | |
Zanjan | 0.88 | 0.00 | 0.91 | 1.00 | 0.89 | 0.94 | 0.81 | 0.96 | |
C5 | Tabriz | 0.85 | 0.00 | 0.98 | 1.00 | 0.96 | 0.98 | 0.96 | 0.99 |
Sahand | 0.85 | 0.00 | 0.99 | 0.98 | 0.98 | 0.98 | 0.96 | 1.00 | |
Urmia | 0.84 | 0.00 | 0.96 | 1.00 | 0.99 | 0.99 | 0.96 | 1.00 | |
Maragheh | 0.88 | 0.00 | 0.95 | 0.99 | 0.97 | 0.98 | 0.94 | 1.00 | |
Mianeh | 0.85 | 0.00 | 0.96 | 1.00 | 0.98 | 0.98 | 0.95 | 1.00 | |
Mahabad | 0.86 | 0.00 | 0.98 | 1.00 | 0.98 | 0.99 | 0.97 | 1.00 | |
Saqez | 0.82 | 0.00 | 0.95 | 0.97 | 0.95 | 0.99 | 0.96 | 1.00 | |
Takab | 0.80 | 0.00 | 0.96 | 0.96 | 0.98 | 1.00 | 0.95 | 1.00 | |
Zanjan | 0.79 | 0.00 | 0.97 | 1.00 | 0.96 | 0.98 | 0.95 | 0.99 | |
M2 | Tabriz | 0.94 | 0.00 | 0.98 | 0.99 | 0.99 | 0.99 | 0.97 | 1.00 |
Sahand | 0.95 | 0.00 | 0.99 | 0.99 | 0.99 | 0.99 | 0.97 | 1.00 | |
Urmia | 0.95 | 0.00 | 0.99 | 0.99 | 0.99 | 1.00 | 0.98 | 1.00 | |
Maragheh | 0.96 | 0.00 | 0.98 | 0.99 | 0.99 | 0.99 | 0.97 | 1.00 | |
Mianeh | 0.96 | 0.00 | 0.99 | 0.99 | 0.99 | 0.99 | 0.97 | 1.00 | |
Mahabad | 0.96 | 0.00 | 0.99 | 1.00 | 0.98 | 1.00 | 0.98 | 1.00 | |
Saqez | 0.93 | 0.00 | 0.98 | 0.99 | 0.98 | 1.00 | 0.98 | 1.00 | |
Takab | 0.94 | 0.00 | 1.00 | 0.99 | 1.00 | 1.00 | 0.98 | 1.00 | |
Zanjan | 0.91 | 0.00 | 1.00 | 0.99 | 0.99 | 1.00 | 0.97 | 1.00 | |
Mean score | 0.83 | 0.00 | 0.94 | 0.99 | 0.95 | 0.98 | 0.91 | 0.99 |
Models . | Stations . | Algorithms score . | |||||||
---|---|---|---|---|---|---|---|---|---|
MLR . | MNLR . | M5 . | MARS . | RF . | LSBoost . | LSSVM-GS . | LSSVM-RUN . | ||
A1 | Tabriz | 0.58 | 0.00 | 0.90 | 1.00 | 0.96 | 0.98 | 0.78 | 0.96 |
Sahand | 0.61 | 0.00 | 0.88 | 1.00 | 0.95 | 0.95 | 0.78 | 0.99 | |
Urmia | 0.41 | 0.00 | 0.80 | 1.00 | 0.80 | 0.97 | 0.70 | 0.92 | |
Maragheh | 0.71 | 0.00 | 0.91 | 1.00 | 0.95 | 0.96 | 0.78 | 0.97 | |
Mianeh | 0.83 | 0.00 | 0.84 | 1.00 | 0.86 | 0.96 | 0.76 | 0.93 | |
Mahabad | 0.60 | 0.00 | 0.89 | 0.99 | 0.96 | 0.99 | 0.84 | 0.99 | |
Saqez | 0.83 | 0.00 | 0.92 | 0.93 | 0.94 | 1.00 | 0.88 | 0.99 | |
Takab | 0.83 | 0.00 | 0.80 | 0.98 | 0.83 | 1.00 | 0.78 | 0.93 | |
Zanjan | 0.88 | 0.00 | 0.91 | 1.00 | 0.89 | 0.94 | 0.81 | 0.96 | |
C5 | Tabriz | 0.85 | 0.00 | 0.98 | 1.00 | 0.96 | 0.98 | 0.96 | 0.99 |
Sahand | 0.85 | 0.00 | 0.99 | 0.98 | 0.98 | 0.98 | 0.96 | 1.00 | |
Urmia | 0.84 | 0.00 | 0.96 | 1.00 | 0.99 | 0.99 | 0.96 | 1.00 | |
Maragheh | 0.88 | 0.00 | 0.95 | 0.99 | 0.97 | 0.98 | 0.94 | 1.00 | |
Mianeh | 0.85 | 0.00 | 0.96 | 1.00 | 0.98 | 0.98 | 0.95 | 1.00 | |
Mahabad | 0.86 | 0.00 | 0.98 | 1.00 | 0.98 | 0.99 | 0.97 | 1.00 | |
Saqez | 0.82 | 0.00 | 0.95 | 0.97 | 0.95 | 0.99 | 0.96 | 1.00 | |
Takab | 0.80 | 0.00 | 0.96 | 0.96 | 0.98 | 1.00 | 0.95 | 1.00 | |
Zanjan | 0.79 | 0.00 | 0.97 | 1.00 | 0.96 | 0.98 | 0.95 | 0.99 | |
M2 | Tabriz | 0.94 | 0.00 | 0.98 | 0.99 | 0.99 | 0.99 | 0.97 | 1.00 |
Sahand | 0.95 | 0.00 | 0.99 | 0.99 | 0.99 | 0.99 | 0.97 | 1.00 | |
Urmia | 0.95 | 0.00 | 0.99 | 0.99 | 0.99 | 1.00 | 0.98 | 1.00 | |
Maragheh | 0.96 | 0.00 | 0.98 | 0.99 | 0.99 | 0.99 | 0.97 | 1.00 | |
Mianeh | 0.96 | 0.00 | 0.99 | 0.99 | 0.99 | 0.99 | 0.97 | 1.00 | |
Mahabad | 0.96 | 0.00 | 0.99 | 1.00 | 0.98 | 1.00 | 0.98 | 1.00 | |
Saqez | 0.93 | 0.00 | 0.98 | 0.99 | 0.98 | 1.00 | 0.98 | 1.00 | |
Takab | 0.94 | 0.00 | 1.00 | 0.99 | 1.00 | 1.00 | 0.98 | 1.00 | |
Zanjan | 0.91 | 0.00 | 1.00 | 0.99 | 0.99 | 1.00 | 0.97 | 1.00 | |
Mean score | 0.83 | 0.00 | 0.94 | 0.99 | 0.95 | 0.98 | 0.91 | 0.99 |
Downscaling large-scale rainfall data by the SEML (level 2)
After selecting the best algorithms using the TOPSIS method, the two MARS and LSSVM-RUN algorithms were used in the level 2 SEML to modify the downscale large-scale rainfall data of three GCMs in the nine stations. To this end, as meta-algorithms, the MARS and LSSVM-RUN algorithms integrate the results of eight Level 1 algorithms to produce high-precision outputs. According to Table 6, the outputs of the base algorithms were applied as inputs to the MARS and LSSVM-RUN algorithms. The results of the two algorithms during the historical period were compared, and MARS performed slightly better than the LSSVM-RUN algorithm. In addition, taking into account the MAE, RMSE, RRMSE and R values, downscaled rainfall, in both algorithms, the C5 model showed a higher accuracy than the A1 and M2 models. This is due to the higher resolution of the C5 compared to other models.
Algorithms . | Models . | Stations . | Assessment criteria . | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Train . | Test . | |||||||||
MAE . | RMSE . | RRMSE . | R . | MAE . | RMSE . | RRMSE . | R . | |||
MARS | A1 | Tabriz | 6.76 | 10.38 | 0.33 | 0.94 | 8.48 | 12.01 | 0.35 | 0.94 |
Sahand | 9.04 | 15.13 | 0.37 | 0.93 | 10.27 | 15.64 | 0.39 | 0.92 | ||
Urmia | 6.49 | 11.20 | 0.41 | 0.91 | 6.74 | 10.65 | 0.53 | 0.85 | ||
Maragheh | 7.54 | 12.54 | 0.36 | 0.93 | 11.00 | 17.25 | 0.55 | 0.84 | ||
Mianeh | 7.36 | 12.24 | 0.46 | 0.89 | 6.51 | 10.03 | 0.41 | 0.91 | ||
Mahabad | 5.95 | 10.12 | 0.44 | 0.90 | 4.79 | 7.60 | 0.34 | 0.94 | ||
Saqez | 9.07 | 13.97 | 0.49 | 0.87 | 9.83 | 16.18 | 0.62 | 0.79 | ||
Takab | 4.67 | 7.43 | 0.40 | 0.92 | 4.37 | 6.20 | 0.40 | 0.92 | ||
Zanjan | 4.74 | 7.56 | 0.41 | 0.91 | 4.11 | 7.28 | 0.37 | 0.93 | ||
C5 | Tabriz | 6.26 | 11.56 | 0.37 | 0.93 | 7.20 | 12.38 | 0.35 | 0.94 | |
Sahand | 9.36 | 14.68 | 0.37 | 0.93 | 11.58 | 18.45 | 0.42 | 0.91 | ||
Urmia | 6.36 | 10.44 | 0.42 | 0.91 | 7.27 | 11.96 | 0.46 | 0.89 | ||
Maragheh | 8.77 | 14.23 | 0.41 | 0.91 | 10.72 | 17.16 | 0.53 | 0.84 | ||
Mianeh | 6.51 | 11.36 | 0.41 | 0.91 | 4.53 | 6.87 | 0.31 | 0.96 | ||
Mahabad | 5.27 | 8.47 | 0.39 | 0.92 | 6.50 | 11.89 | 0.47 | 0.88 | ||
Saqez | 8.56 | 14.45 | 0.53 | 0.85 | 8.86 | 15.45 | 0.54 | 0.85 | ||
Takab | 3.86 | 6.73 | 0.38 | 0.92 | 3.16 | 6.37 | 0.36 | 0.93 | ||
Zanjan | 4.44 | 7.27 | 0.36 | 0.93 | 4.91 | 8.15 | 0.52 | 0.85 | ||
M2 | Tabriz | 6.22 | 9.73 | 0.31 | 0.95 | 8.12 | 12.92 | 0.37 | 0.93 | |
Sahand | 9.76 | 16.07 | 0.38 | 0.93 | 7.96 | 12.71 | 0.35 | 0.94 | ||
Urmia | 6.45 | 10.77 | 0.44 | 0.90 | 6.25 | 9.73 | 0.36 | 0.93 | ||
Maragheh | 7.23 | 12.95 | 0.37 | 0.93 | 9.66 | 15.86 | 0.48 | 0.88 | ||
Mianeh | 6.54 | 11.54 | 0.44 | 0.90 | 7.38 | 13.78 | 0.53 | 0.85 | ||
Mahabad | 4.70 | 8.00 | 0.37 | 0.93 | 6.44 | 11.83 | 0.47 | 0.88 | ||
Saqez | 8.58 | 14.45 | 0.51 | 0.86 | 7.94 | 12.28 | 0.48 | 0.88 | ||
Takab | 4.48 | 6.87 | 0.39 | 0.92 | 5.27 | 9.58 | 0.52 | 0.87 | ||
Zanjan | 4.53 | 7.72 | 0.40 | 0.92 | 5.09 | 9.00 | 0.52 | 0.86 | ||
LSSVM-RUN | A1 | Tabriz | 1.40 | 2.32 | 0.07 | 1.00 | 8.75 | 15.03 | 0.47 | 0.88 |
Sahand | 7.36 | 12.85 | 0.31 | 0.95 | 9.86 | 17.15 | 0.44 | 0.90 | ||
Urmia | 5.64 | 9.26 | 0.39 | 0.92 | 6.51 | 10.93 | 0.39 | 0.92 | ||
Maragheh | 3.63 | 6.02 | 0.17 | 0.99 | 7.76 | 12.96 | 0.41 | 0.91 | ||
Mianeh | 5.94 | 10.40 | 0.39 | 0.92 | 7.89 | 12.90 | 0.53 | 0.85 | ||
Mahabad | 5.36 | 8.92 | 0.39 | 0.92 | 5.34 | 9.82 | 0.43 | 0.90 | ||
Saqez | 5.46 | 10.08 | 0.36 | 0.93 | 8.19 | 15.58 | 0.55 | 0.83 | ||
Takab | 3.91 | 6.07 | 0.34 | 0.94 | 4.90 | 7.95 | 0.46 | 0.89 | ||
Zanjan | 4.64 | 7.41 | 0.37 | 0.93 | 6.64 | 10.28 | 0.65 | 0.78 | ||
C5 | Tabriz | 2.14 | 4.03 | 0.13 | 0.99 | 7.72 | 15.95 | 0.45 | 0.89 | |
Sahand | 6.52 | 10.95 | 0.27 | 0.96 | 9.12 | 16.01 | 0.38 | 0.93 | ||
Urmia | 5.50 | 9.44 | 0.35 | 0.94 | 8.40 | 14.19 | 0.67 | 0.74 | ||
Maragheh | 6.30 | 11.35 | 0.33 | 0.94 | 8.34 | 15.64 | 0.45 | 0.89 | ||
Mianeh | 3.33 | 6.03 | 0.24 | 0.97 | 6.49 | 13.06 | 0.46 | 0.88 | ||
Mahabad | 2.38 | 4.26 | 0.18 | 0.98 | 5.36 | 8.30 | 0.39 | 0.92 | ||
Saqez | 4.75 | 9.14 | 0.34 | 0.94 | 8.17 | 14.43 | 0.48 | 0.88 | ||
Takab | 2.02 | 3.87 | 0.21 | 0.98 | 3.46 | 6.20 | 0.37 | 0.93 | ||
Zanjan | 1.79 | 3.46 | 0.18 | 0.98 | 3.83 | 7.23 | 0.41 | 0.91 | ||
M2 | Tabriz | 6.51 | 11.43 | 0.36 | 0.94 | 8.59 | 13.71 | 0.42 | 0.91 | |
Sahand | 8.21 | 13.73 | 0.33 | 0.95 | 9.13 | 16.65 | 0.41 | 0.92 | ||
Urmia | 5.53 | 9.44 | 0.37 | 0.93 | 7.15 | 12.07 | 0.50 | 0.87 | ||
Maragheh | 7.32 | 12.87 | 0.37 | 0.93 | 8.25 | 14.58 | 0.46 | 0.89 | ||
Mianeh | 6.49 | 11.57 | 0.43 | 0.91 | 6.58 | 10.62 | 0.44 | 0.90 | ||
Mahabad | 5.09 | 8.54 | 0.36 | 0.93 | 5.02 | 7.81 | 0.38 | 0.93 | ||
Saqez | 6.08 | 10.96 | 0.38 | 0.93 | 7.50 | 13.02 | 0.52 | 0.86 | ||
Takab | 3.19 | 5.52 | 0.30 | 0.96 | 4.71 | 7.26 | 0.48 | 0.88 | ||
Zanjan | 3.10 | 5.43 | 0.30 | 0.96 | 5.86 | 12.21 | 0.60 | 0.81 |
Algorithms . | Models . | Stations . | Assessment criteria . | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Train . | Test . | |||||||||
MAE . | RMSE . | RRMSE . | R . | MAE . | RMSE . | RRMSE . | R . | |||
MARS | A1 | Tabriz | 6.76 | 10.38 | 0.33 | 0.94 | 8.48 | 12.01 | 0.35 | 0.94 |
Sahand | 9.04 | 15.13 | 0.37 | 0.93 | 10.27 | 15.64 | 0.39 | 0.92 | ||
Urmia | 6.49 | 11.20 | 0.41 | 0.91 | 6.74 | 10.65 | 0.53 | 0.85 | ||
Maragheh | 7.54 | 12.54 | 0.36 | 0.93 | 11.00 | 17.25 | 0.55 | 0.84 | ||
Mianeh | 7.36 | 12.24 | 0.46 | 0.89 | 6.51 | 10.03 | 0.41 | 0.91 | ||
Mahabad | 5.95 | 10.12 | 0.44 | 0.90 | 4.79 | 7.60 | 0.34 | 0.94 | ||
Saqez | 9.07 | 13.97 | 0.49 | 0.87 | 9.83 | 16.18 | 0.62 | 0.79 | ||
Takab | 4.67 | 7.43 | 0.40 | 0.92 | 4.37 | 6.20 | 0.40 | 0.92 | ||
Zanjan | 4.74 | 7.56 | 0.41 | 0.91 | 4.11 | 7.28 | 0.37 | 0.93 | ||
C5 | Tabriz | 6.26 | 11.56 | 0.37 | 0.93 | 7.20 | 12.38 | 0.35 | 0.94 | |
Sahand | 9.36 | 14.68 | 0.37 | 0.93 | 11.58 | 18.45 | 0.42 | 0.91 | ||
Urmia | 6.36 | 10.44 | 0.42 | 0.91 | 7.27 | 11.96 | 0.46 | 0.89 | ||
Maragheh | 8.77 | 14.23 | 0.41 | 0.91 | 10.72 | 17.16 | 0.53 | 0.84 | ||
Mianeh | 6.51 | 11.36 | 0.41 | 0.91 | 4.53 | 6.87 | 0.31 | 0.96 | ||
Mahabad | 5.27 | 8.47 | 0.39 | 0.92 | 6.50 | 11.89 | 0.47 | 0.88 | ||
Saqez | 8.56 | 14.45 | 0.53 | 0.85 | 8.86 | 15.45 | 0.54 | 0.85 | ||
Takab | 3.86 | 6.73 | 0.38 | 0.92 | 3.16 | 6.37 | 0.36 | 0.93 | ||
Zanjan | 4.44 | 7.27 | 0.36 | 0.93 | 4.91 | 8.15 | 0.52 | 0.85 | ||
M2 | Tabriz | 6.22 | 9.73 | 0.31 | 0.95 | 8.12 | 12.92 | 0.37 | 0.93 | |
Sahand | 9.76 | 16.07 | 0.38 | 0.93 | 7.96 | 12.71 | 0.35 | 0.94 | ||
Urmia | 6.45 | 10.77 | 0.44 | 0.90 | 6.25 | 9.73 | 0.36 | 0.93 | ||
Maragheh | 7.23 | 12.95 | 0.37 | 0.93 | 9.66 | 15.86 | 0.48 | 0.88 | ||
Mianeh | 6.54 | 11.54 | 0.44 | 0.90 | 7.38 | 13.78 | 0.53 | 0.85 | ||
Mahabad | 4.70 | 8.00 | 0.37 | 0.93 | 6.44 | 11.83 | 0.47 | 0.88 | ||
Saqez | 8.58 | 14.45 | 0.51 | 0.86 | 7.94 | 12.28 | 0.48 | 0.88 | ||
Takab | 4.48 | 6.87 | 0.39 | 0.92 | 5.27 | 9.58 | 0.52 | 0.87 | ||
Zanjan | 4.53 | 7.72 | 0.40 | 0.92 | 5.09 | 9.00 | 0.52 | 0.86 | ||
LSSVM-RUN | A1 | Tabriz | 1.40 | 2.32 | 0.07 | 1.00 | 8.75 | 15.03 | 0.47 | 0.88 |
Sahand | 7.36 | 12.85 | 0.31 | 0.95 | 9.86 | 17.15 | 0.44 | 0.90 | ||
Urmia | 5.64 | 9.26 | 0.39 | 0.92 | 6.51 | 10.93 | 0.39 | 0.92 | ||
Maragheh | 3.63 | 6.02 | 0.17 | 0.99 | 7.76 | 12.96 | 0.41 | 0.91 | ||
Mianeh | 5.94 | 10.40 | 0.39 | 0.92 | 7.89 | 12.90 | 0.53 | 0.85 | ||
Mahabad | 5.36 | 8.92 | 0.39 | 0.92 | 5.34 | 9.82 | 0.43 | 0.90 | ||
Saqez | 5.46 | 10.08 | 0.36 | 0.93 | 8.19 | 15.58 | 0.55 | 0.83 | ||
Takab | 3.91 | 6.07 | 0.34 | 0.94 | 4.90 | 7.95 | 0.46 | 0.89 | ||
Zanjan | 4.64 | 7.41 | 0.37 | 0.93 | 6.64 | 10.28 | 0.65 | 0.78 | ||
C5 | Tabriz | 2.14 | 4.03 | 0.13 | 0.99 | 7.72 | 15.95 | 0.45 | 0.89 | |
Sahand | 6.52 | 10.95 | 0.27 | 0.96 | 9.12 | 16.01 | 0.38 | 0.93 | ||
Urmia | 5.50 | 9.44 | 0.35 | 0.94 | 8.40 | 14.19 | 0.67 | 0.74 | ||
Maragheh | 6.30 | 11.35 | 0.33 | 0.94 | 8.34 | 15.64 | 0.45 | 0.89 | ||
Mianeh | 3.33 | 6.03 | 0.24 | 0.97 | 6.49 | 13.06 | 0.46 | 0.88 | ||
Mahabad | 2.38 | 4.26 | 0.18 | 0.98 | 5.36 | 8.30 | 0.39 | 0.92 | ||
Saqez | 4.75 | 9.14 | 0.34 | 0.94 | 8.17 | 14.43 | 0.48 | 0.88 | ||
Takab | 2.02 | 3.87 | 0.21 | 0.98 | 3.46 | 6.20 | 0.37 | 0.93 | ||
Zanjan | 1.79 | 3.46 | 0.18 | 0.98 | 3.83 | 7.23 | 0.41 | 0.91 | ||
M2 | Tabriz | 6.51 | 11.43 | 0.36 | 0.94 | 8.59 | 13.71 | 0.42 | 0.91 | |
Sahand | 8.21 | 13.73 | 0.33 | 0.95 | 9.13 | 16.65 | 0.41 | 0.92 | ||
Urmia | 5.53 | 9.44 | 0.37 | 0.93 | 7.15 | 12.07 | 0.50 | 0.87 | ||
Maragheh | 7.32 | 12.87 | 0.37 | 0.93 | 8.25 | 14.58 | 0.46 | 0.89 | ||
Mianeh | 6.49 | 11.57 | 0.43 | 0.91 | 6.58 | 10.62 | 0.44 | 0.90 | ||
Mahabad | 5.09 | 8.54 | 0.36 | 0.93 | 5.02 | 7.81 | 0.38 | 0.93 | ||
Saqez | 6.08 | 10.96 | 0.38 | 0.93 | 7.50 | 13.02 | 0.52 | 0.86 | ||
Takab | 3.19 | 5.52 | 0.30 | 0.96 | 4.71 | 7.26 | 0.48 | 0.88 | ||
Zanjan | 3.10 | 5.43 | 0.30 | 0.96 | 5.86 | 12.21 | 0.60 | 0.81 |
In the Supplementary material, Figures S1 and S2 display both the observed rainfall time series and the downscaled rainfall time series of meta-algorithms during training and testing periods. As can be seen in Supplementary material, Figures S1 and S2, the difference between the values estimated by the MARS and LSSVM-RUN algorithms and the observed values was very small in most cases. The high R-value indicates the excellent performance of algorithms in downscaling rainfall data. The accuracy of the algorithms was significantly improved by applying the output of the base algorithms as inputs to the meta-algorithm, as shown in Supplementary material, Figures S1 and S2. According to the results, the SEML's downscaling accuracy was increased by over 45% because of the simultaneous use of the advantages of different algorithms in the SEML. The LSSVM-RUN performed well, as evidenced by the results. The proximity of the observed and downscaled values means that the RUN algorithm had a positive effect on improving the performance of LSSVM. According to the downscaling results with the MARS algorithm and C5 model, the highest downscaling accuracy was obtained in the Mianeh (MAE = 4.53, RMSE = 6.87, RRMSE = 0.31, R = 0.96), and Takab (MAE = 3.16, RMSE = 6.37, RRMSE = 0.36, R = 0.93) stations. The accuracy of downscaling using the LSSVM-RUN and C5 model in the Takab station was the highest among stations (MAE = 3.46, RMSE = 6.20, RRMSE = 0.37, R = 0.93).
Prediction rainfall under climate change by meta-algorithms (2021–2050)
After training and testing the SEML for downscaling the rainfall in the historical period, the rainfall in nine stations was predicted under three scenarios SCF, SCM, and SCS of different GCMs, including A1, C5, and M2. Tables 7 and Supplementary material, Table A3 show the results of predicting rainfall in investigated scenarios and stations using the MARS algorithm as a meta-algorithm of the SEML. In this table, the mean (Mean), minimum (Min), and maximum (Max) of observed and predicted rainfall values were compared. According to Tables 7 and Supplementary material, Table A3, by comparing the observed and predicted values in different GCMs and scenarios, in Tabriz station, the highest rate of rainfall changes (−0.13%) was related to the C5 and SCM, and the lowest rate (−0.06%) was for A1 and the SCF. In Sahand station, the most predicted change was −0.12% by A1 and SCS. However, the lowest rainfall change (−0.08%) was related to the C5 and the SCS. At Urmia station, the most change was predicted to be −0.06% by C5 and its three scenarios and the lowest rate was −0.05% by A1 and M2 and their three scenarios. A1 predicted the highest rainfall reduction (−0.16%) at Maragheh station under SCM and SCS. However, the smallest change (−0.05%) was in C5 in all scenarios. At the Mianeh station, the highest rainfall change was projected to be −0.09% by C5 and SCS, and the lowest rate (−0.07%) was related to M2 and its three scenarios. At Mahabad station, the C5 and SCM predicted a rainfall change rate of −0.10%, while M2 and its three scenarios predicted a rainfall change rate of −0.03%. At Saqez station, the highest rainfall change (−0.12%) was predicted by M2 under SCF and SCM scenarios. Also, the lowest change rate of rainfall (−0.04%) was predicted by model A1 and SCM scenarios. Takab station was the only station where the rainfall will increase in the future (0.06%). This increase was related to C5 under its three scenarios. In Zanjan station, the A1 predicted a rainfall change rate of −0.06% in all three scenarios. However, the lowest rate (−0.02%) was related to the C5 and its three scenarios.
. | A1 SCF . | A1 SCM . | A1 SCS . | C5 SCF . | C5 SCM . | C5 SCS . | M2 SCF . | M2 SCM . | M2 SCS . |
---|---|---|---|---|---|---|---|---|---|
Tabriz | |||||||||
Mean-Obs | 31.88 | 31.88 | 31.88 | 31.88 | 31.88 | 31.88 | 31.88 | 31.88 | 31.88 |
Mean-Pred | 29.53 | 29.51 | 29.12 | 27.91 | 27.85 | 27.88 | 29.24 | 29.21 | 29.13 |
Min-Obs | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
Min-Pred | 2.56 | 5.07 | 16.12 | 14.14 | 15.56 | 15.58 | 3.75 | 0.02 | 2.80 |
Max-Obs | 214.90 | 214.90 | 214.90 | 214.90 | 214.90 | 214.90 | 214.90 | 214.90 | 214.90 |
Max-Pred | 73.24 | 63.12 | 43.39 | 41.13 | 44.26 | 42.23 | 70.78 | 68.92 | 64.14 |
Change mean (%) | −0.06 | −0.07 | −0.09 | −0.12 | −0.13 | −0.12 | −0.08 | −0.08 | −0.09 |
Urmia | |||||||||
Mean-Obs | 26.02 | 26.02 | 26.02 | 26.02 | 26.02 | 26.02 | 26.02 | 26.02 | 26.02 |
Mean-Pred | 24.68 | 24.68 | 24.67 | 24.43 | 24.42 | 24.42 | 24.63 | 24.63 | 24.62 |
Min-Obs | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
Min-Pred | 8.04 | 8.98 | 7.39 | 6.29 | 2.75 | 4.67 | 0.00 | 2.81 | 0.00 |
Max-Obs | 165.72 | 165.72 | 165.72 | 165.72 | 165.72 | 165.72 | 165.72 | 165.72 | 165.72 |
Max-Pred | 41.56 | 41.18 | 40.19 | 50.55 | 43.82 | 41.94 | 56.36 | 74.66 | 52.74 |
Change mean (%) | −0.05 | −0.05 | −0.05 | −0.06 | −0.06 | −0.06 | −0.05 | −0.05 | −0.05 |
Zanjan | |||||||||
Mean-Obs | 20.52 | 20.52 | 20.52 | 20.52 | 20.52 | 20.52 | 20.52 | 20.52 | 20.52 |
Mean-Pred | 19.35 | 19.29 | 19.28 | 20.08 | 20.08 | 20.08 | 19.87 | 19.90 | 19.88 |
Min-Obs | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
Min-Pred | 5.30 | 4.19 | 5.10 | 5.01 | 4.81 | 7.46 | 4.28 | 3.78 | 1.66 |
Max-Obs | 114.84 | 114.84 | 114.84 | 114.84 | 114.84 | 114.84 | 114.84 | 114.84 | 114.84 |
Max-Pred | 51.31 | 60.46 | 66.41 | 39.73 | 35.81 | 38.89 | 34.24 | 35.27 | 42.28 |
Change mean (%) | −0.06 | −0.06 | −0.06 | −0.02 | −0.02 | −0.02 | −0.03 | −0.03 | −0.03 |
. | A1 SCF . | A1 SCM . | A1 SCS . | C5 SCF . | C5 SCM . | C5 SCS . | M2 SCF . | M2 SCM . | M2 SCS . |
---|---|---|---|---|---|---|---|---|---|
Tabriz | |||||||||
Mean-Obs | 31.88 | 31.88 | 31.88 | 31.88 | 31.88 | 31.88 | 31.88 | 31.88 | 31.88 |
Mean-Pred | 29.53 | 29.51 | 29.12 | 27.91 | 27.85 | 27.88 | 29.24 | 29.21 | 29.13 |
Min-Obs | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
Min-Pred | 2.56 | 5.07 | 16.12 | 14.14 | 15.56 | 15.58 | 3.75 | 0.02 | 2.80 |
Max-Obs | 214.90 | 214.90 | 214.90 | 214.90 | 214.90 | 214.90 | 214.90 | 214.90 | 214.90 |
Max-Pred | 73.24 | 63.12 | 43.39 | 41.13 | 44.26 | 42.23 | 70.78 | 68.92 | 64.14 |
Change mean (%) | −0.06 | −0.07 | −0.09 | −0.12 | −0.13 | −0.12 | −0.08 | −0.08 | −0.09 |
Urmia | |||||||||
Mean-Obs | 26.02 | 26.02 | 26.02 | 26.02 | 26.02 | 26.02 | 26.02 | 26.02 | 26.02 |
Mean-Pred | 24.68 | 24.68 | 24.67 | 24.43 | 24.42 | 24.42 | 24.63 | 24.63 | 24.62 |
Min-Obs | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
Min-Pred | 8.04 | 8.98 | 7.39 | 6.29 | 2.75 | 4.67 | 0.00 | 2.81 | 0.00 |
Max-Obs | 165.72 | 165.72 | 165.72 | 165.72 | 165.72 | 165.72 | 165.72 | 165.72 | 165.72 |
Max-Pred | 41.56 | 41.18 | 40.19 | 50.55 | 43.82 | 41.94 | 56.36 | 74.66 | 52.74 |
Change mean (%) | −0.05 | −0.05 | −0.05 | −0.06 | −0.06 | −0.06 | −0.05 | −0.05 | −0.05 |
Zanjan | |||||||||
Mean-Obs | 20.52 | 20.52 | 20.52 | 20.52 | 20.52 | 20.52 | 20.52 | 20.52 | 20.52 |
Mean-Pred | 19.35 | 19.29 | 19.28 | 20.08 | 20.08 | 20.08 | 19.87 | 19.90 | 19.88 |
Min-Obs | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
Min-Pred | 5.30 | 4.19 | 5.10 | 5.01 | 4.81 | 7.46 | 4.28 | 3.78 | 1.66 |
Max-Obs | 114.84 | 114.84 | 114.84 | 114.84 | 114.84 | 114.84 | 114.84 | 114.84 | 114.84 |
Max-Pred | 51.31 | 60.46 | 66.41 | 39.73 | 35.81 | 38.89 | 34.24 | 35.27 | 42.28 |
Change mean (%) | −0.06 | −0.06 | −0.06 | −0.02 | −0.02 | −0.02 | −0.03 | −0.03 | −0.03 |
Table 8 and Supplementary material, Table S4 show the results of rainfall prediction in investigated scenarios and stations by the LSSVM-RUN. According to these tables, in Tabriz and Sahand stations, the highest rainfall changes (−0.17 and −0.20%) were related to A1 and SCS. Also, the lowest rate of rainfall changes was predicted to be −0.08% by C5 and SCS in Tabriz and −0.6% by M2 and its two scenarios (SCM and SCS). At Urmia station, the highest rainfall change was predicted (−0.05%) by M2 and its three scenarios, and the lowest rate (−0.03%) was related to A1 and its three scenarios. At Maragheh station, the most changes (−0.20%) in rainfall were in the A1 and its three scenarios. Also, the lowest rate (−0.05%) was related to C5 and its three scenarios. At Mianeh station, the highest rate of rainfall changes was predicted to be −0.09% to the C5 and SCF, and the lowest rate (−0.05%) was related to A1 and SCM. At the Mahabad station, the highest changes (−0.11%) were in the A1 model and the SCM. Also, the lowest rainfall changes were predicted to be −0.06% by C5 (SCF) and M2 (SCM and SCS). In Saqez stations, the highest rate of rainfall changes (−0.15%) was predicted by M2 and SCM, and, the lowest rate was predicted to be −0.04% by A1 (SCS) and C5 in its three scenarios. Takab station is the only station where rainfall will increase in the future. The highest rate of rainfall changes was predicted to be 0.03% by the C5 and SCF. Also, the lowest rate (−0.03%) was related to A1 (SCF) and M2 (SCF). At Zanjan station, the highest rate of rainfall changes (−0.05%) was predicted by the M2 and its three scenarios, and, the lowest rate (−0.01%) was related to C5 and its three scenarios. Similar to the prediction with the MARS algorithm, the highest increase of rainfall prediction with MARS and LSSVM-RUN algorithms in the Takab station was predicted at 0.06 and 0.03%, respectively. Also, the lowest rate of rainfall changes was related to the Zanjan station by −0.02 and −0.01%, respectively. In most scenarios, the rate of rainfall changes will decrease by −0.04% in most stations.
. | A1 SCF . | A1 SCM . | A1 SCS . | C5 SCF . | C5 SCM . | C5 SCS . | M2 SCF . | M2 SCM . | M2 SCS . |
---|---|---|---|---|---|---|---|---|---|
Tabriz | |||||||||
Mean-Obs | 31.88 | 31.88 | 31.88 | 31.88 | 31.88 | 31.88 | 31.88 | 31.88 | 31.88 |
Mean-Pred | 28.43 | 28.22 | 26.52 | 28.91 | 28.84 | 28.88 | 28.78 | 28.89 | 28.81 |
Min-Obs | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
Min-Pred | 5.11 | 7.48 | 15.04 | 15.25 | 16.64 | 16.61 | 4.50 | 0.12 | 2.73 |
Max-Obs | 214.90 | 214.90 | 214.90 | 214.90 | 214.90 | 214.90 | 214.90 | 214.90 | 214.90 |
Max-Pred | 73.51 | 63.55 | 42.19 | 43.46 | 46.41 | 44.84 | 65.84 | 65.20 | 67.79 |
Change mean (%) | −0.11 | −0.11 | −0.17 | −0.09 | −0.10 | −0.08 | −0.10 | −0.09 | −0.10 |
Urmia | |||||||||
Mean-Obs | 26.02 | 26.02 | 26.02 | 26.02 | 26.02 | 26.02 | 26.02 | 26.02 | 26.02 |
Mean-Pred | 25.16 | 25.20 | 25.21 | 24.86 | 24.87 | 24.88 | 24.74 | 24.66 | 24.65 |
Min-Obs | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
Min-Pred | 6.37 | 7.36 | 5.22 | 5.68 | 2.76 | 3.91 | 0.00 | 3.12 | 0.00 |
Max-Obs | 165.72 | 165.72 | 165.72 | 165.72 | 165.72 | 165.72 | 165.72 | 165.72 | 165.72 |
Max-Pred | 43.02 | 42.47 | 41.60 | 51.76 | 45.43 | 44.80 | 61.01 | 74.24 | 54.84 |
Change mean (%) | −0.03 | −0.03 | −0.03 | −0.04 | −0.04 | −0.04 | −0.05 | −0.05 | −0.05 |
Zanjan | |||||||||
Mean-Obs | 20.52 | 20.52 | 20.52 | 20.52 | 20.52 | 20.52 | 20.52 | 20.52 | 20.52 |
Mean-Pred | 19.74 | 19.71 | 19.77 | 20.26 | 20.23 | 20.23 | 19.53 | 19.55 | 19.54 |
Min-Obs | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
Min-Pred | 5.63 | 4.14 | 5.74 | 4.03 | 4.21 | 6.65 | 4.02 | 3.22 | 1.63 |
Max-Obs | 114.84 | 114.84 | 114.84 | 114.84 | 114.84 | 114.84 | 114.84 | 114.84 | 114.84 |
Max-Pred | 50.32 | 68.18 | 72.84 | 38.97 | 36.42 | 38.22 | 34.97 | 35.58 | 41.99 |
Change mean (%) | −0.04 | −0.04 | −0.04 | −0.01 | −0.01 | −0.01 | −0.05 | −0.05 | −0.05 |
. | A1 SCF . | A1 SCM . | A1 SCS . | C5 SCF . | C5 SCM . | C5 SCS . | M2 SCF . | M2 SCM . | M2 SCS . |
---|---|---|---|---|---|---|---|---|---|
Tabriz | |||||||||
Mean-Obs | 31.88 | 31.88 | 31.88 | 31.88 | 31.88 | 31.88 | 31.88 | 31.88 | 31.88 |
Mean-Pred | 28.43 | 28.22 | 26.52 | 28.91 | 28.84 | 28.88 | 28.78 | 28.89 | 28.81 |
Min-Obs | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
Min-Pred | 5.11 | 7.48 | 15.04 | 15.25 | 16.64 | 16.61 | 4.50 | 0.12 | 2.73 |
Max-Obs | 214.90 | 214.90 | 214.90 | 214.90 | 214.90 | 214.90 | 214.90 | 214.90 | 214.90 |
Max-Pred | 73.51 | 63.55 | 42.19 | 43.46 | 46.41 | 44.84 | 65.84 | 65.20 | 67.79 |
Change mean (%) | −0.11 | −0.11 | −0.17 | −0.09 | −0.10 | −0.08 | −0.10 | −0.09 | −0.10 |
Urmia | |||||||||
Mean-Obs | 26.02 | 26.02 | 26.02 | 26.02 | 26.02 | 26.02 | 26.02 | 26.02 | 26.02 |
Mean-Pred | 25.16 | 25.20 | 25.21 | 24.86 | 24.87 | 24.88 | 24.74 | 24.66 | 24.65 |
Min-Obs | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
Min-Pred | 6.37 | 7.36 | 5.22 | 5.68 | 2.76 | 3.91 | 0.00 | 3.12 | 0.00 |
Max-Obs | 165.72 | 165.72 | 165.72 | 165.72 | 165.72 | 165.72 | 165.72 | 165.72 | 165.72 |
Max-Pred | 43.02 | 42.47 | 41.60 | 51.76 | 45.43 | 44.80 | 61.01 | 74.24 | 54.84 |
Change mean (%) | −0.03 | −0.03 | −0.03 | −0.04 | −0.04 | −0.04 | −0.05 | −0.05 | −0.05 |
Zanjan | |||||||||
Mean-Obs | 20.52 | 20.52 | 20.52 | 20.52 | 20.52 | 20.52 | 20.52 | 20.52 | 20.52 |
Mean-Pred | 19.74 | 19.71 | 19.77 | 20.26 | 20.23 | 20.23 | 19.53 | 19.55 | 19.54 |
Min-Obs | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
Min-Pred | 5.63 | 4.14 | 5.74 | 4.03 | 4.21 | 6.65 | 4.02 | 3.22 | 1.63 |
Max-Obs | 114.84 | 114.84 | 114.84 | 114.84 | 114.84 | 114.84 | 114.84 | 114.84 | 114.84 |
Max-Pred | 50.32 | 68.18 | 72.84 | 38.97 | 36.42 | 38.22 | 34.97 | 35.58 | 41.99 |
Change mean (%) | −0.04 | −0.04 | −0.04 | −0.01 | −0.01 | −0.01 | −0.05 | −0.05 | −0.05 |
The results of rainfall prediction in 2021–2050 by meta-algorithms showed that rainfall would decrease in all scenarios and stations (except Takab station). Decreased rainfall can have several causes: (1) increasing temperature and global warming due to population growth and excessive energy consumption, (2) increased air pollution and dust that prevents the accumulation of fine vapor particles and the formation of raindrops, (3) reduce soil moisture and vegetation and reduce vertical air movement, (4) increase in greenhouse gases. Decreasing rainfall can cause major water scarcity and drought, reduced soil moisture, increased air pollution, and plant destruction.
Uncertainty analysis
R-factor = 0.63; in Takab station, A1 and SCF from LSSVM-RUN had less uncertainty (for this model and scenario the amount of rainfall decreased by −0.03%, which had more certainty than other models and scenarios).
R-factor = 0.66; in Mianeh station, M2 and SCS from MARS had less uncertainty (for this model and scenario the amount of rainfall decreased by −0.09%, which had more certainty than other models and scenarios).
R-factor = 0.67; At Zanjan station, M2 and SCF from LSSVM-RUN had less uncertainty (for this model and scenario the amount of rainfall decreased by −0.01%, which had more certainty than other models and scenarios).
CONCLUSIONS
Predicting rainfall in climate change conditions is crucial for water resource planning and management. However, rainfall modeling and prediction under the influence of climate change are often associated with bias and uncertainty. One of the most important approaches to investigate rainfall changes from the mentioned conditions is the use of stacking ensemble ML algorithms. Hence, in the present study, the novel modeling technique (using SEML) for downscaling the rainfall in Lake Urmia and Sefidrood basins was introduced. This downscaling method used MLR, MNLR, MARS, M5, RF, LSBoost, LSSVM-GS, and the novel hybrid algorithm (LSSVM-RUN) for modeling and predicting rainfall (as base and meta-algorithms); also, the TOPSIS method was used for selecting meta-algorithms. The results were examined for the date (1985–2014) and future (2021–2050). The main results of this research are as follows:
The accuracy of the base algorithms at level 1 of the SEML was low. The TOPSIS method's results revealed that MARS and LSSVM-RUN (score 0.99) were the best algorithms and were chosen as meta-algorithms.
In the second level of the SEML, the accuracy of rainfall modeling became very good. The highest modeling accuracy was obtained by MARS in the Mianeh (MAE = 4.53, RMSE = 6.87, RRMSE = 0.31, R = 0.96), and Takab (MAE = 3.16, RMSE = 6.37, RRMSE = 0.36, R = 0.93) stations in model C5. Also, in modeling using the LSSVM-RUN of the Takab station (MAE = 3.46, RMSE = 6.20, RRMSE = 0.37, R = 0.93) in the C5 model, it had the highest accuracy among the stations. The reason for this was the combination of the results of the base algorithms in level 2. In addition, at this level, thanks to the combination of the advantages of all the algorithms, the accuracy of the meta-algorithms became very high, which showed the power of SEML.
According to the prediction results, the mean rainfall in all stations (except Takab station in C5 model scenarios) decreased in all models and scenarios. The Maragheh station (0.20%) had the highest decrease, while the Takab station (0.06%) had the highest increase.
GCMs and CMIP6 scenarios were highly uncertain. However, the results obtained thanks to the new hybrid algorithm were less uncertain. Among the GCMs and scenarios considered, the A1 model and the SCF scenario in the Takab stations (R-factor = 0.63) had the least uncertainty.
The employed approach for reasonable performance needs to have sufficient lengths of data. Also predicting future meteorological and hydrological components requires large-scale data in the future.
The findings of this study (values of rainfall in the future) can assist water resource management decision-makers in managing the investigated basin in the future. For example, the obtained rainfall in future periods can be used to reduce the damages of climate change and drought, planning to define cropping patterns in the near future horizon, and optimal operation of reservoirs.
Furthermore, the technique that was introduced can be extended to other new GCMs and emission scenarios from CMIP6. Also, this technique can be used to predict other meteorological parameters in other basins to encourage locals about their climate change and severe weather concerns, as warned in Bruine de Bruin & Dugan (2022) article.
AUTHOR CONTRIBUTIONS
S.F. conceptualized the whole article; M.V.A., M.K. and A.M.-B. rendered support in data curation; M.V.A., M.K., A.M.-B. and S.F. rendered support in formal analysis; M.V.A., M.K. and S.F. investigated the data; M.V.A., M.K., A.M.-B. and S.F. developed the methodology; S.F. administered the project; M.V.A., M.K. and A.M.-B. brought the resources; M.V.A., M.K. and A.M.-B. worked on preparing the software; S.F. supervised the work; M.V.A., M.K. and A.M.-B. validated the data; M.V.A., M.K. and A.M.-B. visualized the project; M.K. and A.M.-B. wrote the original draft; S.F. and M.V.A. wrote the review and edited the article. All authors have seen and approved the final manuscript.
CONSENT TO PUBLISH
The authors have agreed to publish the study in Environment, Development and Sustainability.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.