**Step 1: Understand what ecosystem productivity means**
Ecosystem productivity is the rate at which energy (or biomass) is produced by the ecosystem. It is expressed as the amount of energy generated per unit area of the ecosystem over a period of time.

**Step 2: Identify the dimensions involved**
- Energy is measured in kilocalories (KCal).
- The spatial dimension is area, measured in square metres (m²).
- The temporal dimension is time, commonly expressed in years (yr) for ecological studies.

**Step 3: Combine the dimensions**
Since productivity is “energy per area per time”, the correct unit combines these three components multiplicatively:

$KCal·m-2·yr-1$

This notation means “kilocalories per square metre per year”.

**Step 4: Why the other options are incorrect**
- $KCal·m-2$ lacks the time factor, so it represents energy density, not a rate.
- $KCal·m-3$ refers to energy per unit volume, which is used for processes like heat content in a water column, not surface productivity.
- $g·m-2$ measures mass per area, useful for describing litter or nutrient deposition, but does not convey the energy‑time rate required for productivity.

**Conclusion**
The unit that correctly captures the definition of ecosystem productivity is $KCal·m-2·yr-1$, i.e., (KCal m⁻²) yr⁻¹.