Lime Assist

Soil: starting pH, soil texture (sand/loam/clay), organic carbon (OC), soil depth.
Target & timing: target pH, time horizon (years), application mode (fast vs slow).
Lime supply: supplier (neutralising value/NV %, moisture %, limestone vs dolomite), price, freight distance & rate, application/incorporation costs, VRA cost.
Production system:
- Cropping: crop types/rotation, water-limited yield, grain prices, harvest costs.
- Pasture: pasture type/system, baseline stocking rate (DSE/ha), gross margin per DSE, extra livestock costs.
Finance: discount rate, inflation (if applicable).

Soil texture and OC are converted to a pH buffering capacity (how hard it is to shift soil pH).
Higher clay/OC → higher buffering → more lime required per unit pH change.

Required pH lift = target pH − starting pH (bounded by configured limits).
Pure CaCO₃ need ≈ pH lift × buffering capacity (per zone).
Convert to product rate using supplier properties:
- Adjust for NV (purity): divide by NV fraction.
- Adjust for moisture: divide by (1 − moisture fraction) to get as-applied tonnes.
Application mode:
- Fast – apply full calculated rate so pH approaches target quickly (1–2 years).
- Slow – if target pH exceeds a threshold, apply a reduced first-year effect using configured slow_lime_rate_multiplier so pH rises more gradually.

Simulate pH each year with two scenarios: with lime and no lime.
With lime: add lime effect (fast/slow schedule) and subtract system acidification.
No lime: apply system acidification only.

For each year & crop, calculate predicted yield in t/ha from the simulated pH.
Use the water-limited yield as the base, then apply a pH response function to adjust it.
Yields are calculated separately for with-lime and no-lime pH trajectories
Value the difference at the net grain price, adjusting for harvest costs if configured.

Crop	Yield index gamma	Yield index delta	pH change	Predicted yield
Wheat	5.87	3.89	ΔpH = pH_t − 3.89	Y_predicted = (1 − e^{−5.87 × max(0, ΔpH)}) × Y_WL
Canola	3.91	3.82	ΔpH = pH_t − 3.82	Y_predicted = (1 − e^{−3.91 × max(0, ΔpH)}) × Y_WL
Barley	4.4	3.95	ΔpH = pH_t − 3.95	Y_predicted = (1 − e^{−4.4 × max(0, ΔpH)}) × Y_WL
Faba bean	2.78	3.94	ΔpH = pH_t − 3.94	Y_predicted = (1 − e^{−2.78 × max(0, ΔpH)}) × Y_WL

For each year & pasture type, calculate a yield index (unitless) from pH using a response curve defined by yield_index_gamma (steepness) and yield_index_delta (midpoint).
Base index is scaled to represent current production; the pH change produces a % gain from the base index.
Convert % gain to DSE/ha change, then to new stocking rate for lime vs no-lime scenarios.
When the total stocking rate is greater than the previous stocking rate, it is assumed additional stock are purchased using the per/head cost.
Value the extra DSE at the gross margin per DSE, subtracting any extra livestock costs.

Pasture	Yield index γ	Yield index δ	pH change (ΔpH_t)	Percent of maximum yield
Tolerant	3.75	3.63	pH_eff(t) = pH_t + r_acid·t ΔpH_t = max(0, pH_eff(t) − 3.63)	Y%_t = [1 − e^{−3.75·ΔpH_t}] × 100%
Sensitive	2.7	3.7	pH_eff(t) = pH_t + r_acid·t ΔpH_t = max(0, pH_eff(t) − 3.7)	Y%_t = [1 − e^{−2.7·ΔpH_t}] × 100%
Very sensitive	1.9	3.93	pH_eff(t) = pH_t + r_acid·t ΔpH_t = max(0, pH_eff(t) − 3.93)	Y%_t = [1 − e^{−1.9·ΔpH_t}] × 100%

Costs: lime product + freight (distance × rate) + application/incorporation (+ VRA if used) + soil mapping/testing.
CO₂ from lime (Scope 1, IPCC 2006):
- Use dry product mass and NV (purity).
- Emission factor (C basis): Limestone 0.12; Dolomite 0.13.
- Formula: E (t CO2e) = M_dry × NV × EF_C × 3.67.

Compute per-year gross margin with lime and gross margin without lime (cropping: yield-based; pasture: DSE-based).
Net benefit (year t) = (GM_with − GM_without) − (lime/testing/application costs in year t).
Discount across the horizon → NPV (and MIRR if configured). Report break-even year where cumulative discounted net benefit ≥ 0.

pH response is governed by buffering capacity and system acidification; other constraints are outside the scope beyond water-limited yield inputs.
Gamma/Delta produce a non-linear pH→production response (steepness & midpoint are configurable).
Fast vs slow changes the speed of pH improvement, not the long-run target.
Economic KPI is always the difference in paddock gross margin with lime vs without lime.