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.

111444
111444
113244
224133
222333
222333

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.

111
221
221

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 = 0.51 ÷ 2 = 0.51 ÷ 4 = 0.25
2 ÷ 2 = 12 ÷ 2 = 11 ÷ 2 = 0.5
2 ÷ 2 = 12 ÷ 2 = 11 ÷ 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 = 20.5 x 4 = 20.25 x 4 = 1
1 x 4 = 41 x 4 = 40.5 x 4 = 2
1 x 2 = 21 x 4 = 40.5 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:

111
221
221

The bias-corrected values of the grid in the transposed location are:

221
442
242

This bias correction is performed for every grid in the gridded precipitation time-series record.