"How many panels do I need for my pump?" is the most common solar question we take, and it has no honest answer until three numbers are known. The arithmetic, once you have them, fits on a napkin.
The three numbers
Daily water volume. How many cubic metres a day the system must deliver.
Total head. Water level plus lift plus friction: the real metres the pump works against.
Peak sun hours. Your site's equivalent full-sun hours per day: roughly 4 in northern climates, 6 or more in strong sun regions.
The working
Lifting one cubic metre by 100 metres takes about 0.27 kWh of hydraulic energy. Scale by your volume and your head, then divide by pump and controller efficiency, around 50 to 60 percent combined for a good system, and you have the daily electrical demand. Divide that by peak sun hours and you have the array's required wattage.
Worked example: 20 m³ a day from 40 metres. Hydraulic energy: 20 × 0.4 × 0.27 ≈ 2.2 kWh. After efficiency, about 4 kWh of electricity per day. At 5 peak sun hours, an 800 W array; in practice, 1 kW after losses and cloudy-day margin.
The number that changes everything is head. Doubling the lift doubles the array. Which is why the first question back is never about panels: it is "how deep is the water?"