How Much Water Does a Crop Actually Need? ET0, Kc and Sizing the Solar Pump Backwards

The short answer: the crop asks in millimetres per day, the pump catalogue answers in cubic metres per hour, and the only honest bridge between them is a two-line formula — ETc = ET0 x Kc. Weather gives the reference demand ET0; the crop multiplies it by its coefficient Kc; the irrigation system then wastes a known fraction of everything the pump lifts. Size a solar pump from habit or from the neighbour’s hardware and you will almost always get the same result: a system oversized for most of the season and undersized for the one week that decides the yield — the mid-season peak. This guide runs the conversion the other way round, from the crop backwards to the model number, with every figure sourced and every pump verified against the live catalogue.

The unit mismatch is the whole problem. Agronomy speaks in millimetres — a nice, area-independent unit: 1 mm over 1 hectare is exactly 10 cubic metres. Pump engineering speaks in cubic metres per hour at a given total head. Nothing on a pump datasheet mentions millimetres, and nothing in a crop table mentions metres of head, so the two halves of the project are usually bought separately and hope to meet in the field. They meet far too often at the error: the grower who installed for the average July and met the extreme August; the furrow block that quietly demanded fifty percent more water than the drip design it replaced.

ET0: what the sky demands

Reference evapotranspiration ET0 is the water use of a standard short grass surface under the local weather — computed by the FAO-56 Penman-Monteith method from temperature, humidity, wind and sunshine. It is the sky’s thirst, before any crop is planted. Typical daily values by climate:

Local values come from agricultural meteorological services and irrigation districts, which publish daily ET0 in most irrigated regions; where no station is near, satellite-derived monthly estimates (NASA POWER among them) cover any coordinate on Earth. The sizing number is the peak-month value, not the annual average — the same worst-month discipline our Africa guide applies to sunshine applies double to crop water, because both the sky’s demand and the sun’s supply swing together across the season.

Kc: the crop’s multiplier, and why its shape matters

Each crop scales ET0 by a crop coefficient Kc that follows its growth stages — initial, development, mid-season, late season. The standard FAO single-coefficient values for well-managed conditions:

Total growing periods span wide ranges — wheat 120–150 days, maize 125–180, tomato 135–180, onion 150–210, cotton 180–195 — and the mid-season stage lands in the hottest weeks for a spring-planted crop, which is exactly the trap: the Kc peak multiplies the ET0 peak. A tomato crop in a hot arid valley mid-season: 7.0 x 1.15 = 8.05 mm/day — and that single product is the pump’s true design number.

The shape matters as much as the peak. A full-season ledger for that same hectare of tomato (spring planting, arid climate, 135 days):

The season drinks about 7,900 cubic metres per hectare in total — but the pump was sized for the 8.05 mm/day week. The initial and late stages run at less than half the peak rate, which is the quiet opportunity hidden in the ledger: one pump can serve two blocks whose mid-seasons do not collide (a spring wheat crop and a summer vegetable block, say), at the size of neither peak alone.

From millimetres to a pump duty: the five-step conversion

1. Crop demand. ETc = ET0 (peak month) x Kc (mid-season). Tomato in the hot valley: 7.0 x 1.15 = 8.05 mm/day.
2. Net volume. 1 mm over 1 hectare = 10 m³. One hectare: 8.05 x 10 = 80.5 m³/day net.
3. Gross volume. Divide by the application efficiency of the system (next section). Drip at 90 percent: 80.5 / 0.90 = 89.4 m³/day the pump must actually lift.
4. Pump flow. Divide by the effective pumping hours — our design convention is a 5.5-hour solar day: 89.4 / 5.5 = 16.3 m³/h per hectare.
5. Model and array. Put that flow against the total dynamic head on a real pump curve; size the array at 1.3 times pump power or better (the arithmetic of that rule lives in our watts guide).

Every step is small; the chain is the discipline. Skip step 3 and you have bought a pump for water the system will waste; skip step 4 and you have assumed a pump that works a 24-hour day, which no solar pump does.

Application efficiency: three water bills for one crop

The FAO’s indicative field application efficiencies are stable across its irrigation manuals: about 60 percent for surface (furrow and border) irrigation, 75 percent for sprinkler, 90 percent for drip, for reasonably well-designed and managed systems. The same tomato hectare therefore has three water bills:

Furrow pays fifty percent more than drip for the same crop — and that difference is not paid at the water counter, it is paid at the pump counter, the array counter and the borehole counter. Converting a block from surface to drip is, among other things, a pump-downsizing decision; the full design logic lives in our drip irrigation guide. (The FAO ranges are honest: a poorly managed furrow scheme does worse than 60 percent, and a well-managed one beats it — which is why the ledger uses the standard values and the commissioning test measures the real ones.)

How often and how much: root depth sets the interval

Between irrigations, the crop lives off water stored in its root zone. Two FAO-56 numbers fix the calendar: the maximum rooting depth and the depletion fraction p (the share of available water the crop can spend before stress begins):

The interval arithmetic, for the tomato hectare on a loam (about 150 mm of plant-available water per metre of soil): take the effective root depth as 0.8 m, so total available water is about 120 mm; the crop may spend 40 percent of it without stress, so the readily available share is about 48 mm; at 8.05 mm/day the longest safe interval is six days — and a competent design irrigates every four days, applying about 32 mm (320 m³ per hectare) with a margin. A maize crop on the same soil, with nearly double the rooted depth and a p of 0.55, carries roughly 100 mm of readily available water and can wait a week or more.

This table is why shallow-rooted crops — onion above all — are hard on small systems: they need frequent small doses, which makes the tank, the manifold and the float logic as important as the pump itself. Our storage-tank guide covers the buffering; the sizing consequence appears again in the designs below.

The model ladder, read as hectares of drip tomatoes

The same ladder that runs through every guide on this site, read here through the scheduling lens — drip tomatoes at moderate lift, roughly 16 m³/h needed per hectare at the mid-season peak:

Read the column with the efficiency section in mind: the same model serves more hectares of drip than furrow, more hectares of deep-rooted maize than shallow-rooted onion — and more hectares still when two crops share it with staggered peaks.

Two complete designs

A quarter hectare of tomatoes off a shallow borehole. Hot arid valley, 2,500 m² of drip tomatoes, dynamic water level 24 m, tank on a 5 m stand, friction 3 m, drip operating pressure 9 m: TDH 41 m. Demand at the peak: 8.05 mm/day x 2,500 m² = 20.1 m³/day net; drip at 90 percent lifts it to 22.4 m³/day gross; over a 5.5-hour day that is 4.1 m³/h at 41 m. The 4DSC9.5-90-110-1500 (1,500 W, 110 V) delivers roughly 6.4 m³/h at that head — deliberately more than the duty, because the surplus is the schedule: the pump finishes the block by early afternoon and tops a 20 m³ balancing tank with the rest, and on cloudy days it slides down its curve and still covers the block. The array is four 550 W modules (2,200 W against the 1,950 W floor). The four-day interval needs 80 m³ per event — about three and a half pump-hours of a full day’s production — so in the peak month the system runs nearly continuously, and in the shoulder weeks it idles every second day. The budget variant is the 750 W 3DSC6-60-48-750 with a larger tank and a slower afternoon; the arithmetic above is what tells you exactly what that trade costs in stress risk.

Two hectares in the same valley. Same sky, same crop, eight times the area: 161 m³/day net, 179 m³/day gross, 32.5 m³/h at a 40 m head (dynamic level 22 m, stand 5 m, friction 4 m, drip 9 m). Hydraulic power at the duty point is about 3,500 W, which at a realistic half-system efficiency is a 7 kW input — the 6DSC65-85-380/520-7500-A/D (7,500 W, rated 65 m³/h at 85 m maximum) runs the duty comfortably on the strong middle of its curve. Twenty 550 W modules give 11,000 W against the 9,750 W floor, holding full speed through hazy afternoons. Water goes to a 400 m³ reservoir (just over two peak days of buffer) and to the manifold directly during the solar hours; the four-day event is 640 m³. And here the A/D suffix earns its keep: for the two or three true peak weeks, evening hours from grid or generator top the reservoir without touching the array — redundancy priced per hour instead of per season. Scaling beyond this to eight or ten low-lift hectares is the 8DSC150 class, the cooperative tier of the ladder.

Five ways the ledger gets fudged

1. Sizing on the seasonal average instead of the mid-season peak. The average hides the very week the crop dies in. Average rates are for the annual water account; peak rates are for the pump.
2. Skipping the efficiency step. Net demand is the crop’s; gross demand is the pump’s. On furrow, confusing the two undersizes the system by forty percent.
3. Taking Kc from the wrong stage. The initial-stage coefficient (0.3 to 0.7) applied all season understates the peak by half. The neighbour’s crop in March is not your crop in July.
4. Ignoring the interval. A pump sized without the root-depth rule drowns the block after a long dry gap and starves it before the next — the classic onion failure, and the reason the tank is part of the pump decision.
5. Forgetting that the sky swings. ET0 in the worst month can run far above the annual average in arid climates — the same worst-month discipline our Africa and tilt-angle guides apply to sunshine must be applied to thirst, and it lands on the same pump.

The buying checklist, in order

1. Get the peak-month ET0 for your location from the met service, the irrigation district, or a satellite dataset. One number.
2. Get the mid-season Kc for the crop from the FAO table above. Multiply: that is the design demand in millimetres per day.
3. Choose the application system — drip, sprinkler or surface — and divide by its efficiency. That is the gross daily volume.
4. Divide by the solar day (design on 5.5 effective hours) to get the duty flow in m³/h.
5. Add the interval arithmetic: root depth, depletion fraction, tank size. Fix how many days an event spans and how the water is buffered.
6. Place the duty flow against the total dynamic head on a real pump curve — the model ladder above is ordered to make the shortlist obvious.
7. Size the array at 1.3 times pump power or better, and verify the controller voltage window against the string (our array design guide carries that arithmetic).
8. Write the schedule down: the interval, the event volume, the shifts, and the peak-week contingency — because the schedule is the thing the pump was actually bought to keep.