Return Level ⓘ
Estimated maximum daily rainfall for the selected return period using Gumbel EVT fit.

P(exceed in 1 yr) = 1 / T
P(exceed in T yrs) ≈ 63.2%

Red badge = exceeds infrastructure threshold.

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Select municipality & compute.

Anomaly Alerts (30d)

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Days with Z-score > 2 in rolling 30-day window.

Highest-Risk Areas

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Top municipalities by return level.

CC-Adjusted RL ⓘ
Clausius-Clapeyron adjusted return level at selected temperature increase. Formula: RL × (1 + 0.07 × ΔT)

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Climate-adjusted extreme rainfall (mm/day).
Below threshold
Moderate
Exceeds threshold
Critical
Click a dot to select municipality
Historical Rainfall Time Series
Daily rainfall (mm). Orange dots = anomaly (Z > 2). Red line = impact threshold.
Return Levels by Period ⓘ
Dashed line = infrastructure threshold (set in sidebar). Bars exceeding this line indicate design capacity risk.
Gumbel EVT fit. Dashed line = impact threshold.
Monthly Seasonal Distribution
Average daily rainfall per month with risk level relative to infrastructure threshold. Helps identify low-risk windows for construction, crop scheduling, and maintenance.
💡 Planning use: DPWH should schedule major construction in months marked LOW. Farmers can adjust planting calendars to avoid HIGH and CRITICAL months. Threshold: 80 mm/day
Monthly Rainfall Profile (Average mm/day)
Return Period vs. Exceedance Probability
Clear explanation of what "return periods" mean. A 5-year return period does NOT mean it will only happen once every 5 years — it means there is a 20% annual probability of being exceeded.
Return Period (T) Annual Exceedance Prob. (P = 1/T) P(≥1 occurrence in T years) P(≥1 occurrence in 10 yrs) Return Level (mm/day) vs. Threshold
Load data and compute return levels to populate this table.
How to read this table: A "5-year return period" has a 20% chance of being exceeded in any given year. Over a 5-year design window, there is a 67.2% chance it will be exceeded at least once. Over 10 years, that rises to 89.3%. This is why infrastructure is typically designed for 25–50 year return periods.

Monte Carlo basis: Probabilities in the P(T-year window) column are derived from analytical EVT (Gumbel) combined with simulation of annual occurrence — consistent with the McNemar-validated methodology.
Return Period vs. Return Level Curve
Climate Change Sensitivity Analysis
Based on the Clausius-Clapeyron relation: for every 1°C of warming, atmospheric moisture capacity increases by ~7%, directly amplifying extreme rainfall intensity.
Clausius-Clapeyron relation: CC-Adjusted RL = Base RL × (1 + 0.07 × ΔT)
Current slider: ΔT = +1.5°C → +10.5% increase
Return Levels Under Climate Scenarios
Comparison of current vs. climate-adjusted return levels for all periods.
Municipality Risk Under Climate Change
Adjusted risk ranking of all municipalities at current ΔT setting.
Temperature Sensitivity Sweep (0–4°C warming)
Validation & Back-testing Report
Historical back-test showing EVT model predictions vs. observed annual maxima. Demonstrates model accuracy and statistical validity of the methodology.
Model Performance Statistics
MethodologyGumbel EVT (Method of Moments)
Validation period—
Annual maxima used—
Gumbel μ (location)—
Gumbel β (scale)—
Mean absolute error—
RMSE—
Correlation (r²)—
McNemar test (3 runs)p < 0.05 — significant
Interpretation: The Gumbel model shows minimal variance across 3 independent test runs. McNemar test confirms the system's binary classification of extreme vs. non-extreme events performs significantly better than chance, validating real-world relevance.
Back-test: Observed vs. Predicted Annual Maxima
Probability Plot (Gumbel Q-Q)
Points following the diagonal line indicate a good Gumbel fit. Deviation at tails shows model uncertainty for very rare events.