Sandy loam irrigation frequency and volume

Given: water held between FC and PWP = 140 mm/m, $D_r = 0.30$ m, $CWR = 5$ mm/day, area = 60 ha, allowable depletion = 35%, $\eta_a = 40\%$.

Available moisture in the root zone

$$AM = 140\times 0.30 = 42\ \text{mm}$$

(i) Allowable depletion depth between irrigations

$$d = 0.35\times 42 = 14.7\ \text{mm}$$

(ii) Frequency of irrigation

$$f = \frac{14.7}{5} = 2.94\ \text{days}\approx 2\ \text{days}$$

(iii) Net application depth. The soil is refilled up to field capacity by the allowable depletion:

$$d_{net} = 14.7\ \text{mm}\quad\left(d_{gross} = \frac{14.7}{0.40} = 36.75\ \text{mm}\right)$$

(iv) Volume of water required per irrigation (gross, i.e. at the field inlet, for 60 ha)

$$V = \frac{36.75}{1000}\times 60\times 10^4 = 22,050\ \text{m}^3$$

(Net volume stored in the root zone = 8,820 m$^3$.)

Answer: depletion depth = 14.7 mm; frequency $\approx$ 2 days (2.94); net depth = 14.7 mm; volume = 22,050 m$^3$ per irrigation. If the interval is rounded down to exactly 2 days, only $2\times5 = 10$ mm is used between irrigations, giving gross depth 25 mm and 15,000 m$^3$ per irrigation.