### Orthogonality & Concurrency

Summary

The introduction of uncertainty into a geomorphic change detection study is not just limited to data collection and errors contained within the surveyed points. When dealing with raster it is essential to practice orthogonality and concurrency to avoid blatant miscalculations involving rasters.

#### ET-AL Recommendations to IPC

For every study reach IPC uses, it is recommended that a single, conservatively large primary raster with 2 foot cell resolution extents rounded up to the nearest 100 foot is suggested. ALL subsequent data preparation and analyses should use rasters that are concurrent with this primary raster for that reach.

### Concepts

#### Orthogonality & Concurrency

Aside from surveying, there are some very basic problems that have to do with raster compatibility, which can wreak havoc in change detection analyses. A DEM of Difference is a simple subtraction operation. To do the simple math on a cell-by-cell basis, the cells must line up (i.e. their grids must be orthogonal). Here we discuss the concepts of dimensional divisibility, orthogonality, the special case of concurrency, and data extents. We also explain how problems typically arise and what you can do to avoid them.

It is crucial to adhere to the concepts of orthogonality and concurrency when differencing (or performing any calculations between) two rasters. Two rasters are defined as Orthogonal if they have the same resolution and are aligned in both easting and northing which ensures they have the exact same grid centers. Two rasters are defined as concurrent if they also share the same extents.

Although the concept is simple, it is very easy to produce non-concurrent rasters in ArcGIS unintentionally. This page explains why. To avoid the problems, Philip Bailey (North Arrow Research) has built an extremely simple spreadsheet extents calculator to help you ensure that your raster extents are orthogonal and concurrent:

`Concurrency Calculator.xlsx`

The GCD software strictly enforces concurrency and orthogonality rules and provides checks to assist in this enforcement

### Why care if GCD handles it…

Even though the GCD Software and ArcGIS will 'take care' of the problem of compatible rasters so that you can do analyses, it is better practice to excercise absolute control yourself over this. Although most of the time the fixes work, they can unnecessarily potentially introduce interpolation errors during re-sampling that you can (and should) avoid.

### Applications

#### Using ArcMap Environment Settings

To accomplish concurrency, raster extents should be in whole numbers and the width and height both evenly divisible by the cell resolution. This can be accomplished by inputting any raster into the raster calculator of GIS software and manipulating the environment settings on the raster calculator to meet the above specified criteria. There is no noticeable difference in the output of the rasters from this calculation however by applying the same concurrent and orthogonal settings to the extents of both rasters ensures that calculations between the two will apply to the same cells in each.