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To compare the two approaches, testing data were collected from all the runs. RMSE, mean absolute error (MAE) and correlation coefficient (r) are statistical techniques used to compare results of forecasts. These statistical techniques have been deployed in water forecasting (Shukla et al. 2011). RMSE measures the difference between the forecast rainfall and observed rainfall quantitatively (Abbot & Marohasy 2015b). RMSE values are positive, where the closer the number is to zero, the more skilful the forecasts are. To achieve precise comparison, a deconstruction of data was performed. Deconstruction is used to divide the 10% of testing data in the first approach (all month optimization) into 12 datasets where each set contains the values of a specific month across all the years used in testing. MEA, RMSE, and r values were calculated for each month for two sites, Bingera (Table 2) and Mossman (Table 3) using the two approaches.

Table 2

MAE, RMSE and r values for Bingera monthly rainfall forecasts between October 2004 and September 2014, seasonal and annual forecasts using all months optimization and one single month optimization

Type
Seasonal (Lead 3)
Annual (Lead 12)
Approach
All-months
One-month
All-months
One-month
MonthMAE (mm)RMSE (mm)rMAE (mm)RMSE (mm)rMAE (mm)RMSE (mm)rMAE (mm)RMSE (mm)r
January 75.43 94.18 0.883 27.37 38.67 0.980 81.60 127.64 0.886 17.39 22.57 0.995 
February 66.67 83.26 0.806 20.36 27.47 0.977 88.05 109.55 0.508 35.65 44.40 0.961 
March 74.22 85.49 0.771 37.65 56.88 0.925 65.95 83.23 0.824 43.23 49.16 0.959 
April 31.96 41.73 0.113 7.69 9.31 0.977 27.96 41.11 − 0.077 16.46 23.07 0.974 
May 31.92 37.13 0.376 14.23 20.95 0.856 30.99 37.89 0.232 7.02 13.81 0.934 
June 43.17 62.42 0.385 9.88 13.96 0.973 46.89 65.01 0.458 29.26 38.24 0.932 
July 29.34 35.59 0.503 12.16 14.78 0.946 32.85 40.67 0.201 16.51 19.69 0.986 
August 31.72 45.23 0.487 20.60 28.44 0.906 34.83 55.25 − 0.240 10.94 12.53 0.964 
September 28.38 46.38 0.439 9.39 16.10 0.990 23.84 31.85 0.803 9.14 14.33 0.996 
October 46.99 54.14 0.120 23.31 28.33 0.984 28.31 34.59 0.356 18.14 22.40 0.810 
November 35.40 46.58 0.355 6.41 8.27 0.985 28.17 35.71 − 0.165 22.58 23.73 0.975 
December 50.94 73.23 0.938 57.80 105.34 0.988 74.83 124.07 0.842 62.41 110.62 0.997 
Average 45.51 58.78 0.51 20.57 30.71 0.96 47.02 65.55 0.39 24.06 32.88 0.96 
Type
Seasonal (Lead 3)
Annual (Lead 12)
Approach
All-months
One-month
All-months
One-month
MonthMAE (mm)RMSE (mm)rMAE (mm)RMSE (mm)rMAE (mm)RMSE (mm)rMAE (mm)RMSE (mm)r
January 75.43 94.18 0.883 27.37 38.67 0.980 81.60 127.64 0.886 17.39 22.57 0.995 
February 66.67 83.26 0.806 20.36 27.47 0.977 88.05 109.55 0.508 35.65 44.40 0.961 
March 74.22 85.49 0.771 37.65 56.88 0.925 65.95 83.23 0.824 43.23 49.16 0.959 
April 31.96 41.73 0.113 7.69 9.31 0.977 27.96 41.11 − 0.077 16.46 23.07 0.974 
May 31.92 37.13 0.376 14.23 20.95 0.856 30.99 37.89 0.232 7.02 13.81 0.934 
June 43.17 62.42 0.385 9.88 13.96 0.973 46.89 65.01 0.458 29.26 38.24 0.932 
July 29.34 35.59 0.503 12.16 14.78 0.946 32.85 40.67 0.201 16.51 19.69 0.986 
August 31.72 45.23 0.487 20.60 28.44 0.906 34.83 55.25 − 0.240 10.94 12.53 0.964 
September 28.38 46.38 0.439 9.39 16.10 0.990 23.84 31.85 0.803 9.14 14.33 0.996 
October 46.99 54.14 0.120 23.31 28.33 0.984 28.31 34.59 0.356 18.14 22.40 0.810 
November 35.40 46.58 0.355 6.41 8.27 0.985 28.17 35.71 − 0.165 22.58 23.73 0.975 
December 50.94 73.23 0.938 57.80 105.34 0.988 74.83 124.07 0.842 62.41 110.62 0.997 
Average 45.51 58.78 0.51 20.57 30.71 0.96 47.02 65.55 0.39 24.06 32.88 0.96 
Table 3

MAE, RMSE and r values for Mossman monthly rainfall forecasts between October 2004 and September 2014, seasonal and annual forecasts using all months optimization and one single month optimization

Type
Seasonal (Lead 3)
Annual (Lead 12)
Approach
All-months
One-month
All-months
One-month
MonthMAE (mm)RMSE (mm)rMAE (mm)RMSE (mm)rMAE (mm)RMSE (mm)RMAE (mm)RMSE (mm)r
January 153.16 198.33 0.738 196.27 212.38 0.931 117.22 158.22 0.691 76.86 99.28 0.925 
February 182.64 221.22 0.884 116.42 174.66 0.878 199.88 279.86 0.522 202.63 241.85 0.904 
March 169.72 193.28 0.670 72.06 80.21 0.963 123.37 154.09 0.798 76.26 93.29 0.935 
April 174.53 245.61 − 0.189 39.63 63.06 0.963 99.64 120.61 0.841 57.52 88.35 0.984 
May 65.56 118.57 − 0.042 35.56 59.77 0.986 75.14 125.18 − 0.164 14.17 21.33 0.998 
June 43.93 53.71 0.016 21.78 34.82 0.859 48.88 63.06 − 0.173 11.56 21.16 0.926 
July 21.92 25.77 0.041 9.62 11.67 0.962 29.85 35.83 − 0.076 3.39 4.49 0.989 
August 29.90 32.07 − 0.058 9.35 12.05 0.963 19.72 26.30 0.605 1.70 2.10 0.998 
September 32.42 48.95 0.371 8.98 11.61 0.982 29.29 49.85 0.317 13.05 15.65 0.965 
October 54.12 82.50 0.180 15.04 19.22 0.976 72.22 99.51 0.000 13.90 18.20 0.992 
November 100.53 123.78 − 0.309 52.35 63.23 0.965 84.78 118.53 0.099 39.67 52.48 0.969 
December 91.40 107.58 0.583 76.06 93.78 0.867 72.65 93.42 0.706 44.61 48.76 0.958 
Average 93.32 120.95 0.24 54.43 69.71 0.94 81.05 110.37 0.35 46.28 58.91 0.96 
Type
Seasonal (Lead 3)
Annual (Lead 12)
Approach
All-months
One-month
All-months
One-month
MonthMAE (mm)RMSE (mm)rMAE (mm)RMSE (mm)rMAE (mm)RMSE (mm)RMAE (mm)RMSE (mm)r
January 153.16 198.33 0.738 196.27 212.38 0.931 117.22 158.22 0.691 76.86 99.28 0.925 
February 182.64 221.22 0.884 116.42 174.66 0.878 199.88 279.86 0.522 202.63 241.85 0.904 
March 169.72 193.28 0.670 72.06 80.21 0.963 123.37 154.09 0.798 76.26 93.29 0.935 
April 174.53 245.61 − 0.189 39.63 63.06 0.963 99.64 120.61 0.841 57.52 88.35 0.984 
May 65.56 118.57 − 0.042 35.56 59.77 0.986 75.14 125.18 − 0.164 14.17 21.33 0.998 
June 43.93 53.71 0.016 21.78 34.82 0.859 48.88 63.06 − 0.173 11.56 21.16 0.926 
July 21.92 25.77 0.041 9.62 11.67 0.962 29.85 35.83 − 0.076 3.39 4.49 0.989 
August 29.90 32.07 − 0.058 9.35 12.05 0.963 19.72 26.30 0.605 1.70 2.10 0.998 
September 32.42 48.95 0.371 8.98 11.61 0.982 29.29 49.85 0.317 13.05 15.65 0.965 
October 54.12 82.50 0.180 15.04 19.22 0.976 72.22 99.51 0.000 13.90 18.20 0.992 
November 100.53 123.78 − 0.309 52.35 63.23 0.965 84.78 118.53 0.099 39.67 52.48 0.969 
December 91.40 107.58 0.583 76.06 93.78 0.867 72.65 93.42 0.706 44.61 48.76 0.958 
Average 93.32 120.95 0.24 54.43 69.71 0.94 81.05 110.37 0.35 46.28 58.91 0.96 

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