The calculator sizes compensatory restoration by setting the discounted ecological-service loss of an injury (the debit) against the discounted service gain a restoration project delivers (the credit), then solving for the restoration scale. This follows NOAA's equivalency-analysis practice in US natural resource damage assessment under CERCLA and the Oil Pollution Act. HEA scales against habitat service; REA against a specific resource service (for example fisheries yield or recreational use). They are kept distinct because the choice of method is itself part of the expert argument.
Let r = discount rate as a fraction, areas in hectares, service levels a fraction of baseline (0..1). Time t = 0 is the start of the injury, and everything is discounted back to it, so restoration_lag counts years from the start of the injury, not from the decision to restore.
Debit (discounted service-hectare-years lost):
debit = injured_area x [ sum_{t=0}^{injury_years-1} (baseline - injured) / (1+r)^t
+ sum_{k=0}^{recovery_years-1} (baseline - injured)(1 - (k+1)/recovery_years) / (1+r)^(injury_years+k) ]
The site sits at the injured service level through the injury years, then recovers linearly to baseline over the recovery years.
Credit (discounted service-hectare-years delivered by one hectare of restoration):
credit_per_ha = sum_{k=0}^{restoration_years-1} restoration_gain / (1+r)^(restoration_lag + k)
Restoration scale:
area_needed = debit / credit_per_ha
scaling_ratio = area_needed / injured_area
estimated_cost = area_needed x restoration_unit_cost (unit cost is an expert input; optional)
If the credit is zero or negative the calculator throws rather than report an infinite area. It also refuses inputs that fail injury-params.schema.json, or an injured service level above baseline.
Sensitivity: each input moves by sensitivity_pct (default 20%) one at a time: the service-loss fraction, discount rate, restoration gain, restoration years, recovery years, injury years and restoration lag. Whole-year inputs move by at least one year. range reports the lowest and highest area, and cost if a unit cost is given.
Injured 10 ha, baseline 1.0, injured 0.5, injury 2 yr, recovery 2 yr; restoration gain 0.5, 5 yr, no lag.
- debit = 12.5, credit_per_ha = 2.5, area_needed = 5 ha, scaling_ratio = 0.5.
This is asserted exactly in .claude/scripts/tests/hea-rea.test.mjs.
- Linear recovery and a constant restoration gain are simplifications; real trajectories vary. A restored site delivering its full gain from year one will tend to understate the area needed.
- Each year's loss is counted at the end of that year, so the last recovery year counts as zero. For recovery alone this reads about 10% below the continuous figure over 10 years.
- The tool always reports a sensitivity range, which must never be reduced to a single figure. It moves one input at a time, so it is not a worst case: inputs moving together can fall outside it.
- The service-loss fraction (
baseline - injured) is the most contested input and a matter of expert judgement, not a lookup. - The discount rate is a policy and economic choice; state it and test alternatives.
- The calculator sizes restoration to offset injury; it is not a route to a damages windfall.
REA/HEA has no documented NGT or Indian precedent. It is offered as persuasive comparative methodology to quantify the restoration the NGT may already order under NGT Act s.15(1)(c) (restitution of the environment), s.17, and Schedule II, whose heads (g) and (k) both cover restoration, applying the polluter pays principle (s.20). Every result is methodology_status: novel_persuasive and validation_status: pending_expert_review until a named ecological expert validates the inputs. The output is expert-witness input material, never a final compensation figure, and never legal advice.
US NRDA under CERCLA and the Oil Pollution Act; NOAA habitat and resource equivalency guidance. See the hea and rea entries in catalog/provisions.json for sources.