Mean Areal Precipitation

Mean Areal Precipitation Tool

Multi-Method Spatial Averaging

1. Analysis Methodology

2. Catchment Perimeter

Invalid KML KML

Format: $Lat, Lon$ per line. Points must be sequential (CW or CCW) around the boundary.

11.8322, 104.0932 11.8545, 104.1354 11.8721, 104.1788 11.8654, 104.2155 11.8412, 104.2488 11.8105, 104.2721 11.7755, 104.2688 11.7421, 104.2412 11.7255, 104.2055 11.7188, 104.1622 11.7322, 104.1255 11.7588, 104.0988 11.7955, 104.0855

3. Gauge Locations

Invalid KML KML

Order must match the data columns in Section 4.

4. Rainfall Input

Error CSV

Step Type: Date Hours Minutes Days

Active MAP Method

Thiessen Result

0.00 mm

Arithmetic Avg

0.0 mm

Catchment Area

0.0 km²

Steps Processed

0 Rows

Interactive Spatial Distribution

Gauge Basin Centroid

Mean Areal Precipitation (MAP) Hyetograph Method: Thiessen

MAP Processed Time-Series $P_{avg} = \sum_{i=1}^{n} (P_i \cdot w_i)$

Theoretical Background

The Mean Areal Precipitation (MAP) Principle

Rainfall is rarely uniform across a watershed. Gauges provide point-based measurements that must be mathematically translated into a watershed-wide average ($P_{avg}$) at every time step $t$ using a spatially-weighted linear combination:

$$P_{avg}(t) = \sum_{i=1}^{n} w_i P_i(t)$$

Where $w_i$ is the static spatial weight of gauge $i$ and $P_i(t)$ is the rain depth recorded at that gauge at time $t$.

A. Thiessen Weighted

Uses Voronoi tessellation to assign influence based on proximity. Each station "owns" the area of the basin closest to it. Standard for non-uniform networks.

$$w_i = \frac{A_{clipped, i}}{A_{total}}$$

B. Inverse Distance (IDW)

Assumes the gauge's influence decays with distance from the center of the watershed (Centroid). Using a power factor of 2, the weight is assigned based on the inverse square of the distance $d$.

$$w_i = \frac{1/d_i^2}{\sum_{j=1}^{n} (1/d_j^2)}$$

C. Arithmetic Mean

The simplest baseline. Every gauge is treated equally regardless of spatial distribution. Best for small, flat areas with many gauges.

$$w_i = \frac{1}{n}$$

References & Sources

• Chow, V. T., Maidment, D. R., & Mays, L. W. (1988). Applied Hydrology. McGraw-Hill. [Source]
• Thiessen, A. H. (1911). Precipitation averages for large areas. Monthly Weather Review. [Original Paper]
• Shepard, D. (1968). A two-dimensional interpolation function for irregularly-spaced data. ACM National Conference. (Basis for IDW weighting). [Source]

Version 1.0

CivilSheets by Sothearith Seak