Missing Rainfall Data Estimator
Continuous Time-Series Patching
Batch Results Viewer
Viewing Target:
Total Arith. Mean
Uniform regions ($N$ within 10%)
0.0 mm
Total Normal Ratio
Varying regions ($N$ diff > 10%)
0.0 mm
Total IDW
Spatial interpolation ($1/d^2$)
0.0 mm
Spatial Distribution Map
Target
Index
Static Weights Matrix
| Index Station | Variance in N | Norm Ratio (Nx / Ni) |
Dist (d) (km) |
IDW Weight (1/d2) / ∑ |
|---|
Reconstructed Hyetograph (Target Station)
Recommended Fit Results (mm)
Best of Arithmetic/Normal Ratio
IDW Spatial Alternative Results (mm)
Inverse Distance Weighting
Theoretical Background & Method Selection
When a rain gauge breaks or misses a storm event, its data can be synthetically patched using the recorded values from nearby "Index Stations." The methodology used depends strictly on the variation in long-term Normal Annual Precipitation ($N$) between the stations.
1. Arithmetic Mean Method
Used when the Normal Annual Precipitation ($N_i$) of every index station is within 10% of the target station's Normal ($N_x$).
$$P_{x,t} = \frac{1}{M} \sum_{i=1}^{M} P_{i,t}$$
2. Normal Ratio Method
Mandatory when the Normal Annual Precipitation of any index station differs from the target station by more than 10%.
$$P_{x,t} = \frac{N_x}{M} \sum_{i=1}^{M} \frac{P_{i,t}}{N_i}$$
3. Inverse Distance Weighting (IDW)
A spatial interpolation method that does not rely on long-term normals.
$$P_{x,t} = \frac{\sum_{i=1}^{M} \left( \frac{P_{i,t}}{d_i^2} \right)}{\sum_{i=1}^{M} \left( \frac{1}{d_i^2} \right)}$$
References & Sources
- Chow, V. T., Maidment, D. R., & Mays, L. W. (1988). Applied Hydrology. McGraw-Hill.
- Subramanya, K. (2013). Engineering Hydrology (4th ed.). Tata McGraw-Hill Education.
- Paulhus, J. L. H., & Kohler, M. A. (1952). Interpolation of Missing Precipitation Records. Monthly Weather Review.
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