Submitted:
26 February 2026
Posted:
04 March 2026
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Abstract
Keywords:
1. Introduction
2. Methodology
2.1. Study Area Definition and Ring-Based Analysis Zones
- Ωr1:r2 = annular analysis zone between inner radius r1 and outer radius r2
- x0 = Crucitas reference point (centroid)
- Buffer(x0,r) = circular buffer of radius r around x0
- r1,r2 = ring radii (e.g., 1–5 km, 5–10 km, 10–20 km)
- \setminus = set-difference operator (outer minus inner)
2.2. Context Covariates: Topography and Rasterized Hydrographic/Settlement Layers
2.3. Sentinel-2 Indices and Monthly Compositing (TIF23 Disturbance Stack; TIF22 Water-Proxy Stack)
- ρNIR is near-infrared surface reflectance (Sentinel-2 B8).
- ρRED is red surface reflectance (Sentinel-2 B4).
- ρSWIR1 is shortwave infrared 1 surface reflectance (Sentinel-2 B11).
- ρNIR is near-infrared surface reflectance (Sentinel-2 B8).
- ρBLUE is blue surface reflectance (Sentinel-2 B2).
- ρRED,ρNIR,ρSWIR1 are as defined above.
- ρGREEN is green surface reflectance (Sentinel-2 B3).
- ρRED is red surface reflectance (Sentinel-2 B4).
2.4. Hydrology and Erosion-Driver Layers (Ring-Compatible Footprint)
2.5. Integrated Impact-Driver Stack (TIF24) and Baseline-to-Recent Change Metrics
- Vbase is the baseline-window statistic (e.g., median over 2019–2020).
- Vrecent is the recent-window statistic (e.g., median over 2024–2025).
- ΔV is the signed change feature used for screening (e.g., ΔNDVI, ΔBSI, ΔVV).
2.6. Export Conventions and Reproducibility Controls
2.7. Zonal Feature Extraction over Analysis Zones
- sk,j(Ω,t) is the summary statistic j for predictor band k evaluated over analysis zone Ω at time t (or for a static composite when t is not time-indexed).
- Vk(x,t) is the raster value of the predictor band k at pixel location x and time t.
- Ω is the analysis zone used for aggregation (e.g., Ωr1:r2 as defined in Eq. (1)).
- M(x,t)∈{0,1} is the validity mask (1 for retained pixels after QA/masking; 0 otherwise).
- Rj(⋅) is the reduction operator defining statistic j (e.g., mean, median, percentiles, standard deviation, min–max, sum, count), applied to the set of valid pixels within Ω.
2.8. Pixel-Wise Temporal Feature Construction from Monthly Predictor Stacks
2.9. Model 2: Impact Scoring via Robust Normalization and Percentile Aggregation
- = grid-cell zonal mean for predictor k (computed using Eq. (7) with mean reducer)
- Gk = set of grid cells with finite (⋅) for predictor k
- MAD{}=median(|−median()|) over g′∈Gk
- 1.4826 scales MAD to be consistent with the standard deviation under normality
- pk(g)∈[0,1] = percentile rank of grid cell g for predictor k
- Fk(⋅) = empirical CDF of zk over Gk
- IG(g)∈[0,100] = group-level index for group G at grid cell g
- KG = set of predictors assigned to group G (e.g., land, water, hydrology)
- ICOMB(g)∈[0,100] = combined impact-prioritization score
- S = set of included groups (e.g., {LAND,WATER,HYDRO}
2.10. Scientific Validation and Triangulation Using Field Sediment Observations
- d(x) = distance from sampling location x to mine reference point xm (km)
- ‖·‖2 = Euclidean norm in projected coordinates (m); division by 1000 converts to km
2.11. Model 3: Field-Based Triangulation Using Multi-Scale Raster Sampling
2.11.1. Multi-Scale Feature Extraction at Field Locations
- μk,r(xi) = neighborhood mean of predictor k around site i using radius r
- Wr(xi) = set of raster pixels u within radius r of xi (in the raster’s native grid/CRS)
- mk(u)∈{0,1} = validity mask (1 if finite and not nodata; 0 otherwise)
- Ni,k,r=∑u∈Wr(xi)mk(u) = number of valid pixels in the window
- Vk(u) = raster value for predictor k at pixel u
- σk,r(xi): neighborhood standard deviation of predictor k around site i at radius r
- μk,r(xi): neighborhood mean (Eq. 13)
- Wr(xi): pixels within radius r of xi
- mk(u): validity mask (1 valid, 0 nodata/invalid)
- Ni,k,r: number of valid pixels in the window
- Vk(u): raster value at pixel u
- Ck,r1,r2(xi): contrast feature for predictor k at site i between radii r1 and r2
- μk,r1(xi), μk,r2(xi) neighborhood means at inner/outer radii (Eq. 13)
- r1<r2: inner and outer window radii (same raster grid/CRS)
2.11.2. Predictor Screening and Dimensionality Control
- Ik∈{0,1} indicates whether predictor k passes the coverage screen
- μk,r0(xi): extracted point-support value for predictor k at site i (Eq. 13 with radius r0)
- r0 = point-support (pixel-scale) extraction radius
- n = number of field sites with valid target measurements
- nmin = minimum required number of valid extractions across sites
- I(⋅): indicator function (1 if condition holds, 0 otherwise)
- P = set of screened predictors after Eq. (16)
- K⋆ = selected subset of predictors
- K0: target subset size (number of predictors retained)
- Xp = feature vector for predictor p across sampled points (from Eqs. 13–15)
- y: calibration target (e.g., log10(Hg) and/or ContamIndex)
- corr(⋅,⋅) = Pearson correlation computed on pairwise-complete observations
2.11.3. Cross-Validated Calibration and Significance Screening
- : LOOCV prediction for site i
- xi: feature vector at site i (constructed from Eqs. 13–15)
- f(−i)(⋅): model fit using all sites except i (with fold-internal preprocessing)
- n: number of field sites used in calibration
- p: permutation-test p-value for predictive skill
- Robs2: observed LOOCV R2 using the true targets
- Rb2: LOOCV R2 from permutation b (targets shuffled)
- B: number of permutations
- I(⋅): indicator function (1 if condition holds, 0 otherwise)
2.12. Model 4: Phase-Timed Financial Costing and Present-Value Screening
- phase(i) = assigned implementation phase for cell i
- πi = normalized descending rank of si (e.g., Nπi=rank↓(si)/N, with N evaluated cells)
- τp =cumulative phase thresholds (top 30%, top 60%, all cells)
- DF(t) = discount factor at t years from the reference year
- r = real annual discount rate
- CAPEXiPV = PV of one-time costs for cell i
- qi,m = quantity of measure m applied in cell i (e.g., derived from cell area/length and package rules)
- cm = unit cost of measure m
- TCiPV = total PV cost for cell i
- NCiPV = net PV cost for cell i after credits (bounded below by zero via max(0,·))
- OPEXiPV = PV of recurring costs (phase-activated; e.g., monitoring and water-related operations where applicable)
- CRiPV = PV of eligible credits applied to cell i
2.13. Model 5: Sensitivity Analysis, Monte Carlo Uncertainty, Exceedance Risk, and 2060 Projections
- a= annual cost rate (USD·y−1)
- t0= start year of the active phase (years from the reference year)
- Y= number of active years in the phase
- r= real annual discount rate
- k = year index within the active period (1,…,Y)
- = sampled unit cost for item m in draw b
- = low, central (mode), and high parameters
- B= number of Monte Carlo draws
- = simulated total net present-value (PV) cost (USD) in Monte Carlo draw b.
- = simulated gross PV cost (before credits) for grid cell i in draw b.
- i=1,…,N indexes grid cells
- c(b) = vector of sampled unit costs in draw b
- , are the central (Model 4) PV CAPEX and PV OPEX for cell i, computed under Model 4 timing (OPEX discounted via Eq. (24)).
- CRiPV = PV credits for cell i (held fixed when credits are already phase-timed in Model 4)
- ,) = draw-specific unit-cost multipliers (ratios relative to central unit-cost values) applied to CAPEX and OPEX PV components.
- max(0,⋅)=enforces non-negative net liabilities at the grid-cell level (no negative net PV costs).
- = estimated probability that portfolio net PV exceeds T
- T= threshold (USD, PV terms)
- I(⋅) = indicator function (1 if true; 0 otherwise)
- NC2026 = selected summary metric expressed in 2026 USD terms
- NC2060(γ) = corresponding indexation projection to 2060
- γ = assumed annual indexation rate (dimensionless)
2.14. Limitations
3. Results
3.1. Model 1 — Baseline Conditions and Recent-Change Signals
3.2. Model 2 — Impact Scoring and Prioritization Surfaces
3.3. Model 3 — Field-Anchored Screening Performance for Mercury and a Composite Contamination Index
3.4. Model 4 — Deterministic Financial Assurance Costs by Phase and Remediation Package (Baseline Portfolio)
3.5. Model 4 — Policy-Pathway Effects (Deterministic Overlays)
3.6. Model 5 — 2060 Projections and Policy Ranking Summary
4. Discussion
5. Conclusions
Supplementary Materials
Data availability
Author contributions (CRediT)
Ethics statement
Declaration of generative AI and AI-assisted technologies in the manuscript preparation process
Competing interests
References
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