The crop period is divided into four stages — initial, grand growth, mid-season, and late-season — with each stage spanning 25 days. The crop coefficient varies linearly from 0.4 at the initial stage to 1.2 at the mid-season stage. The reference crop evapotranspiration on the 40ᵗʰ day is 8 mm. The corresponding actual crop evapotranspiration (in mm) is ________ (Rounded off to two decimal places)
Official Answer Key:
6.80 to 7.10
Step-by-Step Solution & Explanation
Step 1 — locate day 40 in the crop calendar.
Initial: days 1–25 | Grand growth (development): days 26–50 | Mid-season: days 51–75 | Late-season: days 76–100
Day 40 lies in the grand growth (development) stage — the stage across which Kc rises linearly.
Step 2 — linear interpolation of Kc. Kc = 0.4 at the end of the initial stage (day 25) and rises linearly to Kc = 1.2 at the start of mid-season (day 50), i.e. over 25 days:
Kc(40) = 0.4 + (1.2 − 0.4) × (40 − 25)/(50 − 25)
= 0.4 + 0.8 × (15/25)
= 0.4 + 0.48 = 0.88
Step 3 — actual crop evapotranspiration:
ETc = Kc × ETo = 0.88 × 8 = 7.04 mm
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