**1.) THIESSEN POLYGONS METHOD FOR PRECIPITATION
**

Mapping point data usually involves some sort of interpolation. There are many point-interpolation methods out there (contours, IDW, TIN, tension spline, kriging, trend surface, etc.) as well as non-interpolation methods for displaying point values (proportionally-sized circles). The Thiessen Polygon method is an interpolation method commonly used for precipitation, but can be used on other point datasets.

Thiessen Polygons are Voronoi Cells, a geometric means of dividing up an area given a set of known values at a relatively small number of points. This interpolation method was first applied to weather station data by A.H. Thiessen (1872-1956), an American meteorologist for the Weather Bureau, now called NOAA National Weather Service (NWS). The Thiessen polygon method is one of 5 different ways station precip measurements are extrapolated. The others are Arithmetic Mean, Isohyetal, Distance-Weighted Grid, and MapX grid.

By the way, “Theissen” is pronounced **THEE-sun **(surname has Norman roots).

**LESSON**

The goal in this lesson is to find the area-weighted precipitation for a set of Watersheds given a set of point measurements (precipitation measurements at a set of stations).

**Instructors:** If you are setting up your own lesson, you will need a.) a shapefile containing a set of numbered station points with precip values and b.) a shapefile of named watershed polygons. Stations should be distributed both inside and outside watershed polygons (see Fig. 2). There should be more watersheds than station points. Provide only one precip measurement per station to keep things simple. An eexaggerated range of precip values makes it easier to find errors in calculations. Students should report the area-weighted precip for each Watershed. I usually have students report values at 3 scales: Watershed, Watershed Zone (sets of adjacent watersheds; add a ZONE field to the attribute table -> A,B,C,D), and for the entire Basin (all watersheds). Discuss results with respect to scale and measurement density.

– Start with Watershed polygons and Weather_Station points (shapefiles). Each station should have a unique precip value in the attribute table.

– Add labels to Weather_Station points using the **Precip** field.

File Naming Terminology

Watershed polygons = **WS_polys**

Thiessen polygons = **T_polys**

Intersected polygons = **Int_polys**

– Construct Thiessen polys from the station points layer (Analysis tools > Proximity > Create Thiessen polygons). Once created, the station precip point value is now distributed everywhere throughout the **T_poly**.

– Calculate the area of each of the **WS_polys**. Do this in the attribute table. Create a New Field called **WSArea_km** (FLOAT format) and Calculate Geometry in km2 units.

*** Note: Make sure your coordinate system and display units are correct (Data Frame Properties > General tab and Coordinate System tab).*

– Intersect **WS_polys** with **T_polys** (Analysis tools > Overlay > Intersect). This gives you **Int_polys**.

– Add a New Field to **Int_polys** layer called **IntPolyID** (Short Integer). Use **Field Calculator** to duplicate FID in this new field. See Fig 4. The reason for doing this simply for visualization. We want to symbolize by **Int_poly** ID number. But because FID field (or ObjectID field) is unavailable in the Symbology > Categories choices, we have to duplicate the values in a new field so we can use it to color each intersect poly uniquely (next step).

– Symbolize **Int_polys** on this new field (IntPolyID) by Categories > Unique Values, so that all intersected polygons have their own color.

– Calculate areas of each **Int_poly** layer in the attribute table just like you did for the watersheds layer (New Field called **IntArea_km**, FLOAT, Calculate Geometry, km2). OK any warning pop ups.

– Examine the attribute table for **Int_polys**:

**FID** = ID for Int polygons.

**Precip_1** = Precip value for the intersect polygons.

**WSArea_km** = Area of each Watershed.

**IntArea_km** = Area of each intersect polygon.

– Create a new field called **PropArea** (FLOAT) and use **Field Calculator** to find the proportion of the watershed each intersect poly represents.

Formula example: **[IntArea_km] / [WSArea_km]**

– Create another new field called **Weighted** (FLOAT) and use **Field Calculator** to find the proportion of the watershed each intersect poly represents. This gives you the weighted precip for each **Int_poly**.

Formula example: **([IntArea_km] / [WSArea_km]) * [Precip_1)**

– If you want to pretty up the table for printing, export the **Int_polys** attrribute table (select all/copy/paste or export as .txt or .dbf) for use in Excel. Do not add the new table to the map; open it in Excel and work with it there.

*** Note: How to Open .txt files Exported from ArcGIS in Excel 8:*

*File > Open > navigate to the file –> Make sure you change file type to show “All Files”*

*Original Data Type = Delimited*

*Delimiters =*

**Comma***Column Data Format =*

**General**– Save your Excel spreadsheet as a Workbook.

– Since several **Int_polys** comprise each Watershed, sum the weighted precip values generated in the previous step for each Watershed. This is easily done in Excel. This is your weighted average precip by Watershed via the Thiessen method.

– If you need to report weighted precip by **Zone** (groups of Watersheds), you will need the area for each Zone polygon. Substitute **Zone_Are**a for **WSArea_km** in the proportion calculation (PropArea) and weight calculation (Weighted).

– If you need to report for entire **Basin** (all Watersheds), you will need total area for all Watersheds (or Zones). Substitute **BAre**a**_km** for **WSArea_km** in the proportion calculation (PropArea) and weight calculation (Weighted).

Refs for Thiessen Method:

NWS Overview: Arithmetic Mean, Thiessen, Isohyetal & MapX methods LINK

A Review of Spatial Interpolation Methods for Environmental Scientists PDF

Fiedler (2003) LINK

NOAA LINK

Lejbak at UCalgary LINK

Mair & Fares (2010) PDF

Thiessen, A.H. (1911) Precip averages for large areas. Monthly Weather Review 39 LINK

Weather Bureau historical note on Major Thiessen LINK

UT Dallas LINK

**2.) ISOHYETAL METHOD FOR PRECIPITATION
**

**Iso** = single, as in a single value, the value along a contour line

**Hyetal** = pertaining to rain and rainfall distribution

Isohyetal maps are just contour maps of precipitation. Each isohyet (each contour line) represents equal precip along its length. Often one map will represent a snapshot of precip in time. In this example, we find the average precip for a watershed at one snapshot in time given station measurements. You could substitute your study area boundary (or limit of contouring) for the watershed boundary.

**Refs for Isohyetal Method:**

NWS Overview: Arithmetic Mean, Thiessen, Isohyetal & MapX methods LINK

Fiedler (2003) LINK

Pierce College Weather LINK

ESRI Forums LINK1, LINK2

StackExchange LINK

NOAA LINK

Lejbak Lab at UCalgary LINK

most.gov.mm (see pg. 15) LINK

Western Oregon University LINK

Mair & Fares (2010) PDF