Transposed precipitation can be adjusted using a bias correction grid. The following is an example of the bias correction calculations.
Bias Grid
The data below represents the bias correction grid. Assume the lower left corner of the raster is at location 0, 0, and the size of each grid cell is 1 unit by 1 unit.
1 | 1 | 1 | 4 | 4 | 4 |
1 | 1 | 1 | 4 | 4 | 4 |
1 | 1 | 3 | 2 | 4 | 4 |
2 | 2 | 4 | 1 | 3 | 3 |
2 | 2 | 2 | 3 | 3 | 3 |
2 | 2 | 2 | 3 | 3 | 3 |
Precipitation Grid
The data below represents a single precipitation grid, in the sequence of precipitation grids. Assume the lower left corner of the raster is at location 0, 0, and the size of each grid cell is 1 unit by 1 unit.
Bias Correction
Now, assume the lower left corner of the precipitation grid is transposed from location 0, 0 to location 3, 3.
Each ordinate of the precipitation grid is divided by the value of the bias correction grid in-situ (the original 0, 0 location).
1 ÷ 2 = 0.5 | 1 ÷ 2 = 0.5 | 1 ÷ 4 = 0.25 |
2 ÷ 2 = 1 | 2 ÷ 2 = 1 | 1 ÷ 2 = 0.5 |
2 ÷ 2 = 1 | 2 ÷ 2 = 1 | 1 ÷ 2 = 0.5 |
Next, each ordinate of the in-situ-adjusted grid is multiplied by the value of the bias correction grid in the transposed location. Recall the location of the lower left corner in the transposed location is 3, 3.
0.5 x 4 = 2 | 0.5 x 4 = 2 | 0.25 x 4 = 1 |
1 x 4 = 4 | 1 x 4 = 4 | 0.5 x 4 = 2 |
1 x 2 = 2 | 1 x 4 = 4 | 0.5 x 4 = 2 |
The resultant values represent the bias corrected grid.
Summary
To summarize, the precipitation grid was transposed from location 0, 0 to 3, 3.
The values of the grid in the original location are:
The bias-corrected values of the grid in the transposed location are:
This bias correction is performed for every grid in the gridded precipitation time-series record.