# Methodology Reference All indicators must be calculated for the **same season, spatial grid, and reference climatology** (default: 1991–2020, configurable — for the live Ethiopia project this is 1993–2025, see `project-context.md`). Dry day: rainfall < 1 mm/day (configurable). Wet day: rainfall ≥ 1 mm/day (configurable). > **Update note:** The drought-hazard formula below is unchanged from the original > spec. The excess-wetness formula, the standardization equations, and the > hazard-combination rule have since been refined (Rx1day/Rx5day promoted from > "add later" to primary wetness indicators) — see "Excess-wetness hazard (H_wet) > — updated formula" and the two new sections after it. Use the updated versions > for new code; the original wetness formula is kept below only for history. ## Core climate indicators - Seasonal rainfall total - Standardized Precipitation Index (SPI-3 initially) - Consecutive Dry Days (CDD) - Consecutive Wet Days (CWD) Designed to be extended later with Rx1day, Rx5day, soil moisture, runoff, and river discharge — add these as new indicator modules, not by modifying the core four. ## Drought hazard (H_drought) Normalize each indicator to a 0–1 drought score: - Low rainfall percentile → increases drought hazard - Negative SPI → increases drought hazard - High CDD percentile → increases drought hazard - Low CWD percentile → increases drought hazard ``` H_drought = 0.20 × rainfall_deficit_score + 0.35 × SPI_drought_score + 0.30 × CDD_drought_score + 0.15 × CWD_drought_score ``` ## Excess-wetness hazard (H_wet) — original formula (superseded, kept for history) Normalize each indicator to a 0–1 wetness score: - High rainfall percentile → increases wetness hazard - Positive SPI → increases wetness hazard - High CWD percentile → increases wetness hazard - Low CDD percentile → supporting evidence only, low weight ``` H_wet = 0.25 × high_rainfall_score + 0.30 × positive_SPI_score + 0.35 × CWD_wetness_score + 0.10 × low_CDD_score ``` Normalize rainfall total, CDD, and CWD using **percentile-based normalization** (not map-specific min-max) so results are comparable across years and forecast initializations. ## Excess-wetness hazard (H_wet) — updated formula (use this one) CWD measures persistence but not intensity — it won't catch a flood-producing short, intense burst of rain. Rx1day (max 1-day rainfall) and Rx5day (max consecutive 5-day rainfall) are now primary indicators instead of a later extension. CDD is dropped from the wetness formula (a low CDD isn't strong independent evidence of wetness once CWD, SPI, and rainfall percentile are already included — keeping it risked padding the score with a redundant signal). ``` H_wet = 0.20 × SPI_wet_score + 0.20 × rainfall_percentile_wet_score + 0.20 × CWD_wet_score + 0.15 × Rx1day_wet_score + 0.25 × Rx5day_wet_score ``` Weights sum to 1.00. Rx5day gets the largest single weight because accumulated multi-day rainfall is particularly relevant to soil saturation and waterlogging. Rx1day and Rx5day should **not** be used for drought (a low value there isn't meaningful evidence of dryness) — keep them wetness-only. ## Drought hazard (H_dry) — same formula, just renamed for consistency The project now refers to this as `H_dry` (equivalent to `H_drought` above) to pair naturally with `H_wet`. The formula and weights are unchanged: ``` H_dry = 0.35 × SPI_dry_score + 0.20 × rainfall_percentile_dry_score + 0.30 × CDD_dry_score + 0.15 × CWD_dry_score ``` Do **not** add Rx1day/Rx5day to the drought formula — a low value in either isn't meaningful evidence of dryness, so they stay wetness-only. ## Standardization formulas Use **local, calendar-period-specific** historical distributions — June 2026 compares against historical Junes, JJAS 2026 against historical JJAS seasons, etc. Never mix calendar periods when computing a percentile rank. **Rainfall percentile** (`P` = rainfall percentile, 0–100, at that grid cell for that calendar period): ``` S_rain_dry = clip((50 − P) / 40, 0, 1) # 10th percentile or below → max drought score S_rain_wet = clip((P − 50) / 40, 0, 1) # 90th percentile or above → max wetness score ``` Near the 50th percentile, both scores are ~0 (no hazard contribution). **SPI** (standardized value, roughly −3 to +3): ``` S_SPI_dry = clip(−SPI / 2, 0, 1) S_SPI_wet = clip(SPI / 2, 0, 1) ``` Reference points: SPI = −2.0 → dry score 1.00; SPI = −1.0 → dry score 0.50; SPI = +1.0 → wet score 0.50; SPI = +2.0 → wet score 1.00. **CDD, CWD, Rx1day, Rx5day** — use each index's own historical percentile rank `p` at that grid cell for that calendar period (not the raw value, not map-wide min-max): ``` S_CDD_dry = clip((p_CDD − 50) / 40, 0, 1) # high CDD percentile → dry S_CWD_dry = clip((50 − p_CWD) / 40, 0, 1) # low CWD percentile → dry S_CWD_wet = clip((p_CWD − 50) / 40, 0, 1) # high CWD percentile → wet S_Rx1day_wet = clip((p_Rx1day − 50) / 40, 0, 1) S_Rx5day_wet = clip((p_Rx5day − 50) / 40, 0, 1) ``` ## Combining drought and wetness into overall hazard — use max, not average Never average `H_dry` and `H_wet` — opposite hazard signals would cancel each other and mask a real hazard. Instead: ``` H_overall = max(H_dry, H_wet) ``` Dominant-hazard categorical layer `T` (same codes as the `R_dominant` categorical layer used later in the risk step — keep them consistent): ``` T = 0 if neither H_dry nor H_wet is substantial (below the high-hazard threshold) T = 1 if H_dry > H_wet (drought-dominated) T = 2 if H_wet > H_dry (wetness-dominated) T = 3 if both hazards are substantial (mixed/compound) ``` ## Hazard probability Input data has either `year × lat × lon` (historical) or `ensemble_member × lat × lon` (forecast) dimensions. High-hazard threshold: configurable, default 0.60. ``` P_drought = count(H_drought ≥ 0.60) / total_valid_realizations P_wet = count(H_wet ≥ 0.60) / total_valid_realizations P_any = count(H_drought ≥ 0.60 OR H_wet ≥ 0.60) / total_valid_realizations ``` With a 25-member ensemble (this project's default), probability moves in increments of 1/25 = 0.04 = 4% — don't report finer precision than that implies. **Caveat:** don't confuse a pre-existing "SPI drought probability" or "SPI wet probability" product (P(SPI ≤ −1.0) or P(SPI ≥ +1.0), computed from SPI alone) with the full composite `P_dry`/`P_wet` defined here. The composite probability must be computed from the member-level `H_dry`/`H_wet` hazard scores (which blend SPI with rainfall percentile, CDD/CWD, and Rx1day/Rx5day), not from SPI in isolation. If an existing GeoTIFF is named like a probability product, check what it was actually computed from before wiring it into `P_dry`/`P_wet`. Also calculate the probability of joint drought+wetness events within the selected assessment period when both can occur, and conditional severity: ``` S_drought = mean(H_drought among realizations classified as drought events) S_wet = mean(H_wet among realizations classified as wetness events) ``` ## Exposure Separate maps for: population, rainfed cropland, irrigated cropland, crop production, livestock, roads, health facilities, water infrastructure, settlements, economic assets. Maintain both: - **Absolute exposure** (people, hectares, livestock head, etc.) - **Normalized exposure index** (0–1), using robust 5th/95th-percentile normalization Do not combine incompatible physical units into one index unless a clearly documented composite exposure index is explicitly requested by the user. ## Drought vulnerability (V_drought) **Sensitivity indicators:** rainfed-agriculture dependence, drought-sensitive crop area, historical yield variability, low soil water-holding capacity, land degradation, water scarcity, poverty, food insecurity, livestock dependence. **Adaptive-capacity indicators:** irrigation access, water storage, functional water points, climate-information access, agricultural extension access, drought-tolerant seed access, credit, insurance, livelihood diversification, market access, social protection. Normalize all to 0–1; reverse beneficial indicators so higher = more vulnerable. ``` V_drought = 0.60 × drought_sensitivity + 0.40 × adaptive_capacity_deficit ``` ## Excess-wetness vulnerability (V_wet) **Sensitivity indicators:** poorly drained soils, low-lying terrain, topographic wetness, proximity to rivers, waterlogging-sensitive crops, historical wetness losses, erosion susceptibility, landslide susceptibility, poor housing, unpaved-road dependence, weak sanitation. **Adaptive-capacity indicators:** agricultural drainage, urban drainage, flood-protection structures, all-weather roads, improved storage, short-range forecast access, emergency-response capacity, health-service access, crop insurance, disease surveillance. ``` V_wet = 0.60 × wetness_sensitivity + 0.40 × adaptive_capacity_deficit ``` ## Risk calculation ``` R_drought = 100 × P_drought × S_drought × E_drought × V_drought R_wet = 100 × P_wet × S_wet × E_wet × V_wet ``` These are relative 0–100 risk scores, **not** probability percentages. ``` R_dominant = max(R_drought, R_wet) ``` Categorical dominant-risk layer: - 0 = insignificant / no identified risk - 1 = drought-dominated risk - 2 = excess-wetness-dominated risk - 3 = mixed / compound risk (where applicable) ### Member-wise (ensemble) risk When ensemble data are available: ``` member_drought_risk = drought_event × drought_severity × drought_exposure × drought_vulnerability member_wetness_risk = wetness_event × wetness_severity × wetness_exposure × wetness_vulnerability ``` Per member, overall risk = `max(member_drought_risk, member_wetness_risk)` unless cumulative impacts are explicitly requested. Average the member-wise overall risk across all members for the final ensemble risk map. ## Risk classes (configurable) | Range | Class | |-----------|------------| | 0–19.9 | Very low | | 20–39.9 | Low | | 40–59.9 | Moderate | | 60–79.9 | High | | 80–100 | Very high | The architecture must support later calibration against observed crop losses, livestock mortality, water shortages, waterlogging, and infrastructure-damage records — keep calibration as a pluggable step, not baked into the risk formula.