# Weighted averages: accounting for grid cell surface variation in proportion to the cosine of its latitude [closed]

Non-geographer learning GIS here. I'm using ArcGIS Desktop v. 10.2.2.

I have a 30-arc second Terrain Ruggedness Index (TRI) raster file, and I want to measure the average ruggedness within each polygon of shapefile I have (not public). The TRI data is available here.

The authors of these data point out that "it is important to take into account that the sea-level surface that corresponds to a 30 by 30 arcsecond cell varies in proportion to the cosine of its latitude." They provide a data file measuring the surface area of each cell, in square metres, which must be used to weight the TRI when averaging across polygons.

Questions:

1. Instead, can I re-project the raster data to an equal area projection and then calculate an unweighted average raster value? In other words, does an equal area projection account for this surface variation in proportion to the cosine of its latitude?
2. If the weighted average raster value route is a must, is the appropriate method to use the Times tool with the TRI raster and cell area raster, then calculate the average raster value of each polygon with Zonal Statistics?

## closed as too broad by PolyGeo♦May 24 '17 at 11:27

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• Note to others: the TRI data is in a geographic CRS (lat/lon). – mkennedy Aug 27 '15 at 17:04
• How large is your study area? If it is not that large (eg, smaller than a US state) you could reproject your DEM into a projected coordinate system and recalculate TRI. I would imagine that bias would not be that large at smaller extents. Bias based on cell distortion is something that is of great concern when you start getting to continental or global geographical extents. – Jeffrey Evans Aug 27 '15 at 17:23
• @JeffreyEvans Thanks for the follow up. Unfortunately I am working with a global geographic extent so your suggestion won't work for my needs. I have no objection to the weighting procedure, but it isn't clear to me how to do it properly. And importantly, I wish to understand why re-projecting to an equal area projection is not the same as weighting for bias introduced by cell distortion. – acd Aug 27 '15 at 17:31
• As per the Tour there should be only one question asked per question. – PolyGeo May 24 '17 at 11:27