Hydrosoft Gridded WSI — Computation Specification

Deterministic calculation rules for the Water Security Index. Every WSI score produced by this platform follows these documented equations and decision rules, ensuring reproducibility and auditability.

1. Hierarchy

Structure

WSI = f( D₁, D₂, ..., D₈ )
Dₖ = f( I₁, I₂, ..., Iₙ ) — dimension from indicators
Iⱼ = f( P₁, P₂, ..., Pₘ ) — indicator from parameters

8 Dimensions → 65 Indicators → 96 Parameters. Each parameter is a measurable quantity with defined units and directionality (benefit or cost).

2. Normalization

Raw parameter values are normalized to [0, 1] before aggregation. Three methods are available:

2.1 Min-Max (default)

Benefit variable (higher = better)

x̂ = (x - x_min) / (x_max - x_min)

Cost variable (lower = better)

x̂ = 1 - (x - x_min) / (x_max - x_min)

Where x_min and x_max are the observed minimum and maximum across all grid cells for that parameter.

2.2 Z-Score (Sigmoid)

Standardize then sigmoid transform

z = (x - μ) / σ
x̂ = 1 / (1 + e⁻ᶻ) — maps to (0, 1)
If cost: x̂ = 1 - x̂

2.3 Rank-Based

Percentile rank

x̂ = rank(x) / (N - 1) — where N = number of cells with data
If cost: x̂ = 1 - x̂

Rule: If x_max = x_min (all values identical), the normalized score defaults to 0.5.

3. Aggregation

3.1 Parameter → Indicator

Equal weight within indicator

Iⱼ = (1/m) × Σₖ x̂ₖ — m = number of available parameters

3.2 Indicator → Dimension

Weighted aggregation (method-dependent)

Dᵢ = Aggregate( I₁w₁, I₂w₂, ..., Iₙwₙ )
Weights are renormalized: wⱼ' = wⱼ / Σwⱼ (only available indicators)

3.3 Dimension → WSI

Final composite score (0–100)

WSI = 100 × Aggregate( D₁W₁, D₂W₂, ..., D₈W₈ )
Weights renormalized for available dimensions only

3.4 Aggregation Methods

Method	Formula	Behavior
`weighted_sum`	Σ(wᵢ × sᵢ)	Linear combination. Default. Compensatory — high scores offset low scores.
`geometric`	∏(sᵢ^wᵢ)	Penalizes low scores more. Requires all dimensions to perform reasonably.
`harmonic`	1 / Σ(wᵢ/sᵢ)	Strongest penalty for low scores. Most conservative.
`min`	min(sᵢ)	Score = weakest dimension. Non-compensatory.

4. Missing Data Rules

Scenario	Rule
Parameter has no data for cell	Skip this parameter. Indicator computed from remaining parameters only.
All parameters of an indicator missing	Skip this indicator. Dimension computed from remaining indicators with renormalized weights.
All indicators of a dimension missing	Skip this dimension. WSI computed from remaining dimensions with renormalized weights.
No dimensions have data	WSI = null. Confidence = "none".

Important: Missing data causes weight redistribution. A WSI computed from 3 dimensions is not comparable to one computed from 8. The confidence score reflects this.

5. Confidence Classification

Data Completeness	Confidence	Meaning
≥ 80% of parameters	High	Result suitable for decision-making
50–79%	Medium	Indicative; some dimensions underrepresented
1–49%	Low	Preliminary only; major data gaps
0%	None	Cannot compute

6. WSI Classification Scale

Range	Category	Implication
0 – 20	Very Low	Critical water insecurity. Urgent intervention required.
20 – 40	Low	Significant vulnerabilities. Priority for investment.
40 – 60	Moderate	Functional but with material risks. Monitoring recommended.
60 – 80	High	Generally secure. Maintenance and resilience focus.
80 – 100	Very High	Excellent water security. Sustainable and resilient.

7. Numeric Precision Rules

Stage	Rule
Normalization	Full IEEE 754 double precision (no intermediate rounding)
Aggregation	Full precision throughout
Final WSI	Rounded to 2 decimal places for display
Dimension scores	Stored as [0,1], displayed as percentage (0–100)
Comparisons	Based on unrounded values; rounding applied only at display

8. Manifest Structure

Every computed WSI generates a JSON manifest for audit purposes:

Manifest schema

{
  "engine_version": "1.0.0",
  "timestamp": "ISO 8601",
  "method": { "normalization", "aggregation", "weight_preset" },
  "data_hashes": { "D1": "sha256...", ... },
  "cell_id": "c_NNNNN",
  "coordinates": { "lon", "lat" },
  "dimensions": [ { "id", "score", "weight", "indicators":[...] } ],
  "wsi": 62.45,
  "confidence": "medium",
  "completeness": { "total", "available", "pct" }
}

WSI26 · Hydrosoft Institute · Water Research Commission · Computation Specification v1.0