Development & Methodology

Normalization, Aggregation, Indicator Formulae, and Benchmark Scales

1. Normalization Procedure

Because raw VWRI variables are measured in heterogeneous units (metres, litres, percentages, counts, INR, etc.), each indicator is first converted to a common 0–100 scale using min–max normalization before aggregation.

For “Positive” Indicators (higher raw value $X$ = better resilience):
$$S_i = \left[ \frac{X - X_{min}}{X_{max} - X_{min}} \right] \times 100$$
For “Negative” Indicators (lower raw value = better resilience, e.g. groundwater depth, breakdown frequency, rainfall variability):
$$S_i = \left[ \frac{X_{max} - X}{X_{max} - X_{min}} \right] \times 100$$

$X_{min}$ and $X_{max}$ are the minimum and maximum values of that indicator observed across the comparison set of villages, or fixed benchmark/standard values.

2. Realm (Pillar) Scores

Each Realm score is the weighted average of its normalized indicator scores:

Realm Score Formulation
$$\text{Realm Score} = \sum (w_i \times S_i), \quad \text{where } \sum w_i = 1 \text{ within the Realm}$$

Indicator weights ($w_i$) within each Realm are assigned equally by default, or through structured expert elicitation (e.g., Analytic Hierarchy Process or Delphi method) where differential weighting is justified.

3. Final Composite VWRI

Composite Equation
$$\text{VWRI} = 0.30 \times \text{Hydrological} + 0.20 \times \text{Infrastructure} + 0.15 \times \text{Water Quality} + 0.15 \times \text{Climate} + 0.20 \times \text{Socio-economic}$$

4. Indicators, Variables and Measurement Formulae

Table 1 sets out all 34 indicators, their suggested measurement formulae, and primary data sources, organised by Realm.

Indicator Suggested Measurement Formula Primary Data Source
Realm: Hydrological Resilience (Weight 0.30)
Groundwater Depth (DTW) DTW = mean pre-monsoon depth to water table (m bgl), averaged across observation wells in village CGWB piezometric network / State GWD; India-WRIS
Groundwater Level Trend (GTS) GTS = slope of linear regression of DTW (m) on time (years), over last 5–10 years CGWB long-term water-level series (India-WRIS); State GWD monitoring
Recharge Potential (RP) $\text{RP} = \left(\dfrac{\text{Annual GW Recharge (m}^3\text{/yr)}}{\text{Village Area (m}^2\text{)}}\right) \times 1000\text{ mm/yr}$ CGWB / State GWD Dynamic GW Resource Assessment (GEC-2015)
Water Source Density (WSD) $\text{WSD} = \dfrac{\text{No. of functional drinking sources}}{\text{Village area (km}^2\text{)}}$ Field inventory survey (GP asset register); village-boundary GIS
Restoration of Water Bodies (AHI) $\text{AHI} = \dfrac{\sum(W_i \times A_i)}{\sum(A_i)}$
$A_i$ = waterbody area, $W_i$ = condition weight (0–1)		 Field survey / remote-sensing inventory; expert or VWSC weighting
Source Reliability (SR) $\text{SR} = \left(\dfrac{\text{Operational supply days in year}}{365}\right) \times 100$ VWSC / GWSSB water-supply logbooks
Water Availability per Capita (PCA) $\text{PCA} = \dfrac{\text{Annual available water (m}^3\text{/yr)}}{\text{Village population}}\text{ (m}^3\text{/cap/yr)}$ CGWB / State Water Resources Dept; Census / GP population
Surface Water Availability (SWSI) $\text{SWSI} = \left(\dfrac{\text{Storage at onset of dry season (m}^3\text{)}}{\text{Full designed capacity (m}^3\text{)}}\right) \times 100$ State Water Resources / Irrigation Dept tank & pond records; satellite waterbody estimation
Realm: Infrastructure Resilience (Weight 0.20)
Household Supply Coverage (CR) $\text{CR} = \left(\dfrac{\text{Households with functional tap}}{\text{Total households}}\right) \times 100$ JJM IMIS dashboard; PHED tap-connection register
Storage Capacity per Capita (SPC) $\text{SPC} = \dfrac{\text{Total storage capacity (litres)}}{\text{Village population}}$ GP infrastructure asset register
Operational Reliability (OR) $\text{OR} = \left(\dfrac{\text{Pump/source operational days in year}}{365}\right) \times 100$ VWSC O&M logbooks
Pipeline Network Density (PND) $\text{PND} = \dfrac{\text{Total pipeline length (km)}}{\text{Village area (km}^2\text{)}}$ GIS-based pipeline network asset mapping
Breakdown Frequency (BF) $\text{BF} = \dfrac{\text{Breakdowns recorded in year}}{\text{Installed water-supply units}}$ Maintenance / complaint-register records
Backup Source Availability (BC) $\text{BC} = \left(\dfrac{\text{Habitations with backup source}}{\text{Total habitations}}\right) \times 100$ GP backup-source asset inventory
Distribution Delivery Efficiency (DE) $\text{DE} = \left(\dfrac{\text{Water delivered to consumers}}{\text{Water produced at source}}\right) \times 100$ Bulk-supply & consumer meter records (water-audit data)
Disaster Resilience (DFR) $\text{DFR} = \left(\dfrac{\text{Assets functional post-disaster}}{\text{Assets exposed to disaster}}\right) \times 100$ DDMA post-disaster functionality survey; asset-damage records
Pipe Material Quality (PMQI) $\text{PMQI} = \left(\dfrac{\text{Length of corrosion-resistant pipe}}{\text{Total pipeline length}}\right) \times 100$ GIS pipeline mapping; material-spec & as-built drawing register
Realm: Water Quality Resilience (Weight 0.15)
Composite Chemical Water Quality (CWQI) $\text{CCWQI} = \dfrac{\sum(W_i \times Q_i)}{\sum(W_i)}$
$Q_i$ = sub-index per BIS 10500		 Public Health Water Testing Laboratory multi-parameter analysis (BIS 10500:2012)
Safe Source Availability (SSR) $\text{SSR} = \left(\dfrac{\text{Sources meeting quality standards}}{\text{Total sources}}\right) \times 100$ Public Health Water Testing Laboratory records
Seasonal Quality Stability (SI) $\text{SI} = 100 - \left(\dfrac{|\text{WQI}_{\text{pre}} - \text{WQI}_{\text{post}}|}{\text{WQI}_{\max}}\right) \times 100$ State PHED pre- and post-monsoon sampling records
Composite Biological Water Quality (CBWQI) $\text{CBWQI} = \left(\dfrac{\text{Samples negative for } E.\ coli\text{ / coliform}}{\text{Total samples tested}}\right) \times 100$ Public Health lab microbiological (MPN / membrane-filtration) tests, BIS 10500:2012
Realm: Climate Resilience (Weight 0.15)
Rainfall Variability (CV) $\text{CV} = \left(\dfrac{\sigma}{\mu}\right) \times 100$
From $\ge 20$ years rainfall records		 IMD rain-gauge station records ($\ge 20$-yr series)
Mean SPI of Drought Years (MSPI) $\text{SPI} = \dfrac{X_i - \bar{X}}{\sigma}$
Rainfall fitted to gamma distribution		 IMD gridded/station rainfall; SPI per WMO / McKee et al. (1993)
Consecutive Dry Years (CDY) Count of consecutive years with annual rainfall < 75% of long-term average IMD rainfall records
Drought Frequency (FR) $\text{FR} = \left(\dfrac{\text{Drought years (SPI} \le -1.0\text{)}}{\text{Total years of record}}\right) \times 100$ IMD rainfall records / SPI-derived drought classification
Temperature Trend (TTS) TTS = slope of linear regression of annual mean temperature (°C) on time (years) IMD temperature station records
Recharge Sensitivity to Rainfall (RS) $\text{RS} = \dfrac{\Delta\% \text{ Groundwater recharge}}{\Delta\% \text{ Annual rainfall}}$ CGWB recharge estimates cross-referenced with IMD rainfall
GHG Emission Control Index (GECI) $\text{GECI} = \left[\dfrac{E_{\text{baseline}} - E_{\text{actual}}}{E_{\text{baseline}}}\right] \times 100$ Village/DISCOM energy records; CEA CO2 baseline / IPCC emission factors
Realm: Socio-economic Resilience (Weight 0.20)
Per Capita Income (IPC) $\text{IPC} = \dfrac{\text{Annual household income (INR)}}{\text{Household size}}$ Household socio-economic survey; Census / SECC
Livestock Dependency (LR) $\text{LR} = \dfrac{\text{Livestock population (SLU)}}{\text{Human population}}$ Livestock Census (Dept of Animal Husbandry & Dairying); village survey
Water-scarcity Migration Rate (MR) $\text{MR} = \left(\dfrac{\text{Households reporting water migration}}{\text{Total households}}\right) \times 100$ Household survey; GP migration records
Community Participation (CPR) $\text{CPR} = \left(\dfrac{\text{Active VWSC/Pani Samiti participants}}{\text{Total eligible adult population}}\right) \times 100$ VWSC / Pani Samiti attendance registers
Water Governance Index (CGS) CGS = Mean of 3 binary indicators: (1) functional VWSC; (2) regular meetings & O&M records; (3) water contingency plan VWSC records; key-informant interview / questionnaire
Conservation Participation (WCPR) $\text{WCPR} = 0.5 \times \text{AR} + 0.5 \times \text{CFI}$
(adoption rate + funding/contribution rate)		 Household survey; GP water-conservation asset records; VWSC O&M fund records

5. Raw-Value Rating Scale (Benchmark Reference)

Each indicator is also rated on a 5-tier scale (Very Low → Very High) applied directly to its raw measured value, before normalization. Boundaries are anchored to recognised standards (CGWB, BIS 10500:2012, Jal Jeevan Mission, Falkenmark Index, IMD/WMO climate classifications, IPCC, NSSO/Census) where available, or to the empirical range typical of semi-arid Gujarat villages, divided into five approximately equal classes.

Note: For “Negative” indicators, the Very Low–Very High labels still denote resilience, so the numeric direction of the band is reversed relative to “Positive” indicators.

Hydrological Resilience

Indicator (unit) Very Low Low Moderate High Very High
DTW (m)> 4020–4010–205–10≤ 5
GTS (m/yr)> 0.200.05–0.20−0.05 to 0.05−0.20 to −0.05< −0.20
RP (mm/yr)≤ 5050–100100–200200–350> 350
WSD (src/km²)≤ 0.50.5–1.51.5–3.03.0–5.0> 5.0
AHI (0–1)0–0.20.2–0.40.4–0.60.6–0.80.8–1.0
SR (%)≤ 40%40–60%60–75%75–90%> 90%
PCA (m³/cap/yr)≤ 500500–1,0001,000–1,7001,700–2,500> 2,500
SWSI (%)≤ 20%20–40%40–60%60–80%> 80%

Infrastructure Resilience

Indicator (unit) Very Low Low Moderate High Very High
CR (%)≤ 20%20–40%40–55%55–90%> 90%
SPC (L/cap)≤ 2525–5050–7070–100> 100
OR (%)≤ 40%40–60%60–75%75–90%> 90%
PND (km/km²)≤ 0.50.5–1.51.5–3.03.0–5.0> 5.0
BF (/unit/yr)> 42–41–20.5–1≤ 0.5
BC (%)≤ 20%20–40%40–60%60–80%> 80%
DE (%)≤ 50%50–65%65–80%80–90%> 90%
DFR (%)≤ 20%20–40%40–60%60–80%> 80%
PMQI (%)≤ 20%20–40%40–60%60–80%> 80%

Water Quality Resilience

Indicator (unit) Very Low Low Moderate High Very High
CWQI (0–100)≤ 4040–5555–7070–85> 85
SSR (%)≤ 40%40–60%60–75%75–90%> 90%
SI (0–100)≤ 6060–7575–8585–95> 95
CBWQI (%)≤ 50%50–70%70–85%85–95%> 95%

Climate Resilience

Indicator (unit) Very Low Low Moderate High Very High
CV (%)> 45%35–45%25–35%15–25%≤ 15%
MSPI≤ −2.0−2.0 to −1.5−1.5 to −1.0−1.0 to −0.5> −0.5
CDY (yrs)> 43–42–31–2< 1
FR (%)> 40%30–40%20–30%10–20%≤ 10%
TTS (°C/yr)> 0.050.03–0.050.02–0.030.01–0.02≤ 0.01
RS (elasticity)> 2.01.5–2.01.0–1.50.5–1.0≤ 0.5
GECI (%)≤ 20%20–40%40–60%60–80%> 80%

Socio-economic Resilience

Indicator (unit) Very Low Low Moderate High Very High
IPC (₹/yr)≤ 40,00040k–70k70k–1,00k1,00k–1,50k> 1,50,000
LR (SLU/cap)> 1.51.0–1.50.6–1.00.3–0.6≤ 0.3
MR (%)> 20%10–20%5–10%1–5%≤ 1%
CPR (%)≤ 10%10–25%25–40%40–60%> 60%
CGS (0–1)= 00–0.330.33–0.670.67–1 (partial)= 1
WCPR (%)≤ 20%20–40%40–60%60–80%> 80%