Three relations here, and they stack: rain reduces what you owe, efficiency inflates what you pump, and uniformity caps how good efficiency can ever be.

The net requirement. $IR_n = ET_c - P_e$ — I-R-n equals E-T-c minus P-e. $IR_n$ is the depth irrigation must supply over a period in mm, $ET_c$ the crop's total use over that same period in mm, and $P_e$ the effective rainfall. The word doing all the work is effective: rain that ran off the headland, or drained past the root zone within the day, never reached the crop and does not belong in this equation. A 40 mm thunderstorm on a dry crusted field can be worth 12 mm of effective rain, and the other 28 went to the ditch.

Application efficiency. $E_a = \dfrac{W_s}{W_d}$ — E-a equals W-s over W-d, where $W_s$ is the depth stored in the root zone and $W_d$ the depth delivered to the field, both in mm, and $E_a$ is a bare fraction. Rearranged, it is the calculation you actually do: $W_d = \dfrac{W_s}{E_a}$. Dividing by a decimal makes the number bigger, and that is the house trap of this lesson — losses can only ever make you apply MORE. Furrow irrigation historically ran 50 to 70%; sprinkler and drip reach 75 to 90%.

Distribution uniformity. $DU = \dfrac{\bar{d}_{lq}}{\bar{d}}$ — D-U equals d-bar-l-q over d-bar. Set out catch cans on a grid, run a set, measure every can. $\bar{d}$ is the mean depth over all of them; $\bar{d}_{lq}$ is the mean of the driest quarter once they are sorted. $DU$ is bare, and it can never exceed 1, because the low quarter is part of the average it is being divided by.

Here is why uniformity comes last and matters most. Uniformity sets a ceiling on efficiency that no amount of careful scheduling can lift. Irrigate long enough to satisfy the driest quarter and you have overwatered everything else by the same proportion; irrigate to the average and a quarter of the field is short. A well-designed sprinkler system reaches 75 to 85% and drip 90% — and below about 70%, no scheduling decision you make is the thing holding the field back.