Determining Crop Growth Stages and Kc Variation
The crop growth period is divided into four stages, each lasting 25 days:
- Initial Stage: Days 1 - 25
- Grand Growth Stage: Days 26 - 50
- Mid-Season Stage: Days 51 - 75
- Late-Season Stage: Days 76 - 100
The question asks for the actual crop evapotranspiration (ETa) on the 40th day. This day falls within the grand growth stage.
The crop coefficient (Kc) varies linearly from $0.4$ at the initial stage to $1.2$ at the mid-season stage. Based on the provided answer range, the linear variation is assumed to occur between the end of the initial stage and the beginning of the mid-season stage.
- Kc at the end of the initial stage (Day 25) = $0.4$.
- Kc at the beginning of the mid-season stage (Day 51) = $1.2$.
Calculating Kc on the 40th Day
The period of linear variation is from Day 25 to Day 51. The total duration for this variation is $51 - 25 = 26$ days.
The 40th day is $40 - 25 = 15$ days after the start of this linear variation period (Day 25).
We use linear interpolation to find Kc on the 40th day:
$ \text{Kc}_{\text{40th day}} = \text{Kc}_{\text{Day 25}} + \left( \frac{\text{Days elapsed}}{\text{Total duration}} \right) \times (\text{Kc}_{\text{Day 51}} - \text{Kc}_{\text{Day 25}}) $
$ \text{Kc}_{\text{40th day}} = 0.4 + \left( \frac{15}{26} \right) \times (1.2 - 0.4) $
$ \text{Kc}_{\text{40th day}} = 0.4 + \left( \frac{15}{26} \right) \times 0.8 $
$ \text{Kc}_{\text{40th day}} \approx 0.4 + 0.576923 \times 0.8 $
$ \text{Kc}_{\text{40th day}} \approx 0.4 + 0.461538 $
$ \text{Kc}_{\text{40th day}} \approx 0.8615 $
Calculating Actual Evapotranspiration (ETa)
The reference crop evapotranspiration (ETr) on the 40th day is given as $8\text{ mm}$.
The formula for actual crop evapotranspiration is:
$ \text{ETa} = \text{Kc} \times \text{ETr} $
Substituting the values:
$ \text{ETa}_{\text{40th day}} = 0.8615 \times 8\text{ mm} $
$ \text{ETa}_{\text{40th day}} = 6.892\text{ mm} $
Rounding off to two decimal places, the actual crop evapotranspiration is $6.89\text{ mm}$.
Important Questions from Evapotranspiration
A Class-A pan was setup adjacent to a lake for measuring evaporation losses in the lake. The depth of water in the pan at the beginning of a certain week was $250 \text{ mm}$. In that week, there was a rainfall event with $10 \text{ mm}$ depth. Water depth in the pan at the end of the week was $240 \text{ mm}$. The pan coefficient is $0.8$.
The estimated lake evaporation during the week was _________ mm (an integer value).- Three geometrically identical Lysimeters (A, B and C) installed in a paddy field have uniform initial ponding depths of 12 cm. After a week, the recorded water depths in A, B and C are 10.4 cm, 8.6 cm, and 7.0 cm, respectively. Rainfall received during this week is 15 mm, and the crop coefficient of paddy is 0.94. Lysimeter 'A' has a closed bottom with no plant. Lysimeter 'B' has an open bottom with no plant. Lysimeter 'C' has an open bottom with paddy plants. Neglecting the boundary effects and groundwater contribution in the Lysimeters, the weekly potential evapotranspiration will be ________ cm.
- Lysimeter is an instrument used to measure the following process(es):
