For empirical approaches that consider precipitation, recharge, and other factors in determining the sustainable yield of a depleted aquifer system, here are some methods:

1. Water Balance Approach

The water balance method estimates sustainable yield by considering all inflows and outflows:

Sustainable Yield=Recharge−NaturalDischarge−Evapotranspiration−BaseflowContributionsSustainable \ Yield = Recharge - Natural Discharge - Evapotranspiration - Baseflow ContributionsSustainable Yield=Recharge−NaturalDischarge−Evapotranspiration−BaseflowContributions

Key components:

• Recharge Estimation: Measured using chloride mass balance, isotopic analysis, or lysimeters.
• Precipitation Contribution: Use empirical formulas like Budyko’s framework or water balance equations to determine infiltration.
• Discharge & Evapotranspiration: Estimated through field measurements and remote sensing.

2. Safe Yield Fraction Approach

This method assumes that only a fraction of the total recharge should be extracted to avoid depletion and ecological damage.

Sustainable Yield=α×RechargeSustainable \ Yield = \alpha \times RechargeSustainable Yield=α×Recharge

where α is an empirically determined fraction (often 20-40% in semi-arid regions, higher in humid climates).

• Example: In alluvial aquifers, a 30% rule is sometimes applied to maintain baseflow.

3. Recharge-Based Yield Estimation

Direct measurements of recharge using:

• Water Table Fluctuation Method (WTFM): Recharge=Sy×ΔhRecharge = Sy \times \Delta hRecharge=Sy×Δhwhere Sy is specific yield and Δh is the observed water table rise.
• Soil Moisture Budgeting: Uses soil moisture changes to estimate deep percolation.
• Natural Tracers: Isotope studies (e.g., Tritium, Deuterium) to determine recharge ages.

4. Empirical Recharge-Infiltration Models

Some empirical models relate recharge directly to precipitation:

• Chaturvedi Formula (for Indian subcontinent): R=P−(P/(a+bP))R = P - (P / (a + bP))R=P−(P/(a+bP))where R is recharge, P is precipitation, and a, b are region-specific coefficients.
• Maxey-Eakin Method (for arid regions): Uses precipitation bands to estimate recharge fractions.

5. Baseflow Separation Method

• Baseflow in rivers can indicate groundwater discharge.
• Methods like HYSEP, BFI+ software, or recursive digital filters help quantify groundwater contribution to streams, which can be a proxy for sustainable yield.

6. Managed Recharge-Based Sustainable Yield

• Sustainable yield can be enhanced by incorporating managed recharge (e.g., MAR, injection wells).
• Recharge coefficient adjustment: Some models adjust α in the formula Sustainable Yield=α×RechargeSustainable \ Yield = \alpha \times RechargeSustainable Yield=α×Recharge when managed recharge is present.

In the Murray Darling Basin, Australia it is done by making yield a % of recharge. The % depends on a precautionary factor which is empirically defined, or arbitrarily defined you might say. Further, in areas of intense pumping there are hotspot limitations applied where drawdown of indivvidual wells must be assessed to make sure there are not localized drawn down areas. This takes no regard to encraochment of brackish groundwater into fresh groundwater areas so is far from sustainable. Sustainable Yield then as a language concept can be very different to Sustainable Yield as a blinked or siloed concept in mathematical modelling of groundwater - modellling based on a conceptual model that deviates from real groundwater.

Dear @Gerardo Ruiz

Thank you for sharing your point of view.

On a groundwater regime scale, recharge to groundwater can be considered as a sustainable yield.