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Table 4

Statistical parameters of the hybrid GPR models for three datasets

ModelValidation
Testing
Validation
Testing
RDCRMSERDCRMSERDCRMSERDCRMSE
SPI 1 Ground-based data PERSIANN-CDR data 
 EEMD–GPR 0.757 0.623 0.657 0.706 0.618 0.673 0.788 0.695 0.564 0.716 0.607 0.581 
 PE–EEMD–GPR 0.902 0.752 0.398 0.877 0.725 0.412 0.939 0.887 0.316 0.890 0.775 0.422 
 VMD–GPR 0.856 0.666 0.578 0.797 0.641 0.592 0.891 0.785 0.496 0.810 0.686 0.511 
 PE–VMD–GPR 0.952 0.873 0.376 0.927 0.841 0.389 0.948 0.887 0.299 0.940 0.823 0.393 
 CMAP data       
 EEMD–GPR 0.658 0.580 0.687 0.628 0.548 0.694       
 PE–EEMD–GPR 0.783 0.740 0.444 0.780 0.700 0.449       
 VMD–GPR 0.743 0.655 0.624 0.709 0.620 0.629       
 PE–VMD–GPR 0.833 0.859 0.419 0.830 0.812 0.424       
SPI 9 Ground-based data PERSIANN-CDR data 
 EEMD–GPR 0.870 0.881 0.561 0.850 0.839 0.597 0.914 0.921 0.308 0.862 0.836 0.384 
 PE–EEMD–GPR 0.928 0.939 0.314 0.906 0.894 0.345 0.975 0.962 0.223 0.919 0.891 0.318 
 VMD–GPR 0.897 0.907 0.494 0.875 0.864 0.525 0.942 0.949 0.293 0.888 0.861 0.374 
 PE–VMD–GPR 0.948 0.944 0.296 0.926 0.902 0.326 0.985 0.971 0.211 0.939 0.896 0.314 
 CMAP data       
 EEMD–GPR 0.866 0.863 0.584 0.926 0.826 0.606       
 PE–EEMD–GPR 0.924 0.919 0.334 0.968 0.880 0.354       
 VMD–GPR 0.892 0.888 0.514 0.953 0.850 0.534       
 PE–VMD–GPR 0.944 0.924 0.315 0.970 0.885 0.334       
SPI 24 Ground-based data PERSIANN-CDR data 
 EEMD–GPR 0.968 0.937 0.415 0.920 0.897 0.428 0.973 0.938 0.301 0.950 0.915 0.304 
 PE–EEMD–GPR 0.979 0.973 0.285 0.941 0.931 0.296 0.985 0.974 0.215 0.971 0.949 0.291 
 VMD–GPR 0.969 0.940 0.365 0.931 0.899 0.376 0.975 0.941 0.295 0.961 0.917 0.315 
 PE–VMD–GPR 0.980 0.978 0.269 0.946 0.936 0.280 0.990 0.979 0.203 0.976 0.954 0.283 
 CMAP data       
 EEMD–GPR 0.970 0.935 0.418 0.918 0.920 0.450       
 PE–EEMD–GPR 0.981 0.951 0.288 0.939 0.937 0.316       
 VMD–GPR 0.971 0.937 0.368 0.929 0.923 0.396       
 PE–VMD–GPR 0.986 0.956 0.272 0.944 0.941 0.298       
ModelValidation
Testing
Validation
Testing
RDCRMSERDCRMSERDCRMSERDCRMSE
SPI 1 Ground-based data PERSIANN-CDR data 
 EEMD–GPR 0.757 0.623 0.657 0.706 0.618 0.673 0.788 0.695 0.564 0.716 0.607 0.581 
 PE–EEMD–GPR 0.902 0.752 0.398 0.877 0.725 0.412 0.939 0.887 0.316 0.890 0.775 0.422 
 VMD–GPR 0.856 0.666 0.578 0.797 0.641 0.592 0.891 0.785 0.496 0.810 0.686 0.511 
 PE–VMD–GPR 0.952 0.873 0.376 0.927 0.841 0.389 0.948 0.887 0.299 0.940 0.823 0.393 
 CMAP data       
 EEMD–GPR 0.658 0.580 0.687 0.628 0.548 0.694       
 PE–EEMD–GPR 0.783 0.740 0.444 0.780 0.700 0.449       
 VMD–GPR 0.743 0.655 0.624 0.709 0.620 0.629       
 PE–VMD–GPR 0.833 0.859 0.419 0.830 0.812 0.424       
SPI 9 Ground-based data PERSIANN-CDR data 
 EEMD–GPR 0.870 0.881 0.561 0.850 0.839 0.597 0.914 0.921 0.308 0.862 0.836 0.384 
 PE–EEMD–GPR 0.928 0.939 0.314 0.906 0.894 0.345 0.975 0.962 0.223 0.919 0.891 0.318 
 VMD–GPR 0.897 0.907 0.494 0.875 0.864 0.525 0.942 0.949 0.293 0.888 0.861 0.374 
 PE–VMD–GPR 0.948 0.944 0.296 0.926 0.902 0.326 0.985 0.971 0.211 0.939 0.896 0.314 
 CMAP data       
 EEMD–GPR 0.866 0.863 0.584 0.926 0.826 0.606       
 PE–EEMD–GPR 0.924 0.919 0.334 0.968 0.880 0.354       
 VMD–GPR 0.892 0.888 0.514 0.953 0.850 0.534       
 PE–VMD–GPR 0.944 0.924 0.315 0.970 0.885 0.334       
SPI 24 Ground-based data PERSIANN-CDR data 
 EEMD–GPR 0.968 0.937 0.415 0.920 0.897 0.428 0.973 0.938 0.301 0.950 0.915 0.304 
 PE–EEMD–GPR 0.979 0.973 0.285 0.941 0.931 0.296 0.985 0.974 0.215 0.971 0.949 0.291 
 VMD–GPR 0.969 0.940 0.365 0.931 0.899 0.376 0.975 0.941 0.295 0.961 0.917 0.315 
 PE–VMD–GPR 0.980 0.978 0.269 0.946 0.936 0.280 0.990 0.979 0.203 0.976 0.954 0.283 
 CMAP data       
 EEMD–GPR 0.970 0.935 0.418 0.918 0.920 0.450       
 PE–EEMD–GPR 0.981 0.951 0.288 0.939 0.937 0.316       
 VMD–GPR 0.971 0.937 0.368 0.929 0.923 0.396       
 PE–VMD–GPR 0.986 0.956 0.272 0.944 0.941 0.298       
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