1. Reference evapotranspiration, ET₀

Evapotranspiration (ET) is water lost from soil (evaporation) and through plants (transpiration). FAO Irrigation and Drainage Paper 56 (Allen et al., 1998) defines a reference rate ET₀ for a well-watered grass surface using the FAO Penman–Monteith equation. You will not need to evaluate it by hand; the idea is simply that hot, sunny, dry and windy days pull more water out of a field:

It combines energy (net radiation $R_n$, soil heat flux $G$) with the drying power of the air (wind speed $u_2$ and vapour pressure deficit $e_s-e_a$); $\Delta$ is the slope of the saturation vapour pressure curve and $\gamma$ the psychrometric constant. Units: $R_n$ and $G$ in MJ m⁻² day⁻¹, $T$ the mean air temperature at 2 m in °C, $u_2$ the wind speed at 2 m in m s⁻¹, vapour pressures in kPa, and $\Delta$, $\gamma$ in kPa °C⁻¹; the factor 0.408 converts MJ m⁻² to mm of evaporated water. In Kenya ET₀ is typically 3–6 mm per day. The lab uses typical monthly ET₀ values for each location, reduced on rainy, cloudy days.

2. Crop evapotranspiration and the crop coefficient

The crop coefficient $K_c$ changes with growth stage: low in the initial stage (mostly soil evaporation), rising through development, peaking in mid-season when the canopy is full, then falling in the late season as the crop matures and dries. Mulch reduces the soil-evaporation part, so it lowers $K_c$ most while the canopy is still open.

3. The root-zone water balance

FAO-56 tracks the root-zone depletion $D_r$: how far the soil water is below field capacity, in mm. Each day

where $P$ is rain, $RO$ runoff, $I_{\text{net}}$ the irrigation water that actually reaches the root zone, and $DP$ deep percolation: water that drains below the roots when the soil is already at field capacity ($D_r$ cannot go below 0).

4. How much water can the soil store?

Field capacity $\theta_{FC}$ is the water content after free drainage; at the wilting point $\theta_{WP}$ roots can no longer extract water. TAW is the total available water in a root zone of depth $Z_r$ (m). Only the readily available water RAW, a fraction $p$ (≈0.4–0.6) of TAW, can be used without stress. FAO-56 adjusts $p$ for the evaporative demand: $p=p_{\text{table}}+0.04\,(5-ET_c)$.

5. Water stress

In words: while the soil still holds readily available water the crop is unstressed ($K_s=1$). Once depletion passes RAW, $K_s$ falls in a straight line to 0 at the wilting point, and the crop can use only $K_s$ times the water it needs.

6. From water to yield: FAO-33

Doorenbos and Kassam (FAO Paper 33, 1979) related relative yield loss to relative ET deficit through the yield response factor $K_y$:

$K_y>1$ (maize ≈1.25) means yield falls proportionally faster than water use, so the crop is drought sensitive; $K_y<1$ (sorghum ≈0.9) means it is relatively tolerant. Stress at flowering is usually most damaging; the lab uses the seasonal $K_y$ for simplicity.

7. Runoff: the SCS curve number

A higher curve number (clay, crusted or bare soil) means more runoff. Mulch and conservation tillage improve infiltration, lowering CN.

8. Irrigation efficiency

Typical application efficiencies: furrow ≈ 60%, sprinkler ≈ 75%, drip ≈ 90%. The losses are evaporation, wind drift, runoff and deep percolation. The lab's Refill at RAW schedule irrigates when $D_r\ge RAW$ and refills to field capacity.

9. Nitrogen: diminishing returns

Yield response to nitrogen is modelled with a Mitscherlich curve: each extra kilogram adds less than the last.

$f_0$ is the relative yield without fertiliser (low on depleted soils, high for legumes that fix nitrogen). The economic optimum $N^*$ is where the value of the extra yield equals the price of nitrogen $p_N$; with water stress ($f_w<1$) the optimum is lower.

1. Beat the drought. Grow rain-fed maize (no irrigation, no pan) in a Drought year on the 15 March planting and still harvest at least 2.8 t/ha. Hint: combine climate-smart options and watch Projected yield as the season runs. (auto-checked)
2. Water productivity. Achieve a water productivity of at least 1.4 kg of maize grain per m³ of crop evapotranspiration (water actually used by the crop and soil). The season report shows your value. (auto-checked)
3. Profitable tomatoes. Make a profit of at least KES 250,000 from one acre of tomatoes. (auto-checked)
4. Stress-free in a drought. At the Machakos-like site in a Drought year, finish a season with fewer than 5 water-stress days while using less than 250 mm of gross irrigation. Hint: an efficient irrigation system alone is not enough; you also need to cut the crop's water demand and losses. (auto-checked)
5. Pest response. Spot a pest outbreak without IPM and spray within the 7-day window. (auto-checked)
6. Planting date. With maize in a normal year, compare planting on 1 March, 15 March and 15 April. Explain the yield differences from the depletion chart.
7. Furrow vs drip. Irrigate the same drought season with furrow and with drip. Compare gross water, deep percolation and profit. When is the cheaper system the better choice?
8. Sand vs clay. Why does sandy soil cause stress sooner but almost no runoff? Use TAW and the curve number in your answer.

Climate-smart agriculture (CSA)

CSA aims at three things at once: higher productivity, better resilience to climate shocks, and lower emissions where possible. The options in the lab are widely promoted in Kenya: