# Sequential rasters - when did point x change

Using ArcGIS 10.1 with Spatial and 3D Analysts, and Python 2.7

I have a series of reclassified rasters in which every cell is either one or zero. I need to programmatically create a single raster which shows when each cell first had a value of one. The rasters contain the date in the filename, as well as in a date field in the raster. (More detailed description of the data below)

I am completely stymied. I've tried using the Plus function in Spatial Analyst, but I lose the date. I have very little experience working with rasters, so I'm hoping that the problem is my unfamiliarity with the terminology, and that someone can point me in the right direction.

If I can figure out how to do it ‘by hand’ in ArcMap, I’m confident I can create the scripts to automate the process. Of course, a ready to go script would be very nice :^)

The data is 35 years of sea-ice concentration shapefiles from the Canadian Ice Service. Clipped tifs were generated and reclassified so that each cell in the raster has a value of either one, if the ice concentration is below 50% (break-up), or zero if it is not (i.e. concentration greater than 50% or land). I then added the date, parsed from the filename, using Create and CalculateField_management. The objective is to create annual maps showing the progression of the ice break-up to use in biological analyses.

• Mostly thinking aloud here, you'll need to somehow encode your dates to an int or float. Reclassify all the rasters such that 1 = date. Then iterate through from first to last using Con - ie, if R1=0 then R2 to produce C1; if C1=0 then R3; if C2=0 then R4; etc. May 6, 2015 at 17:20
• why not create a new band for each step? What stops you from having a raster with n bands? May 6, 2015 at 18:17
• The Spatial Analyst "Local" Toolset is your friend for such operations. For instance, if ones never revert back to zeros, a single command will do the job. May 6, 2015 at 18:44
• Thanks! Three approaches to try; I'll report back with what worked. May 6, 2015 at 18:50
• @Chris You got it right. If they do revert--or perhaps regardless--then use Highest Position. Assuming the rasters are listed in chronological order, it will report the position of the first raster in which the highest value (a one) is encountered--and that's exactly what is needed, because the resulting positions can readily be reclassified into the raster dates. As you might guess, I'm trying to avoid solutions that require pre-processing each raster in any way: that's a lot of work. May 6, 2015 at 20:25

Because this analysis is local--the result in any cell depends only on the stack of values in that cell--we might look first to the Local Toolset for inspiration. It is best when such tools can be applied without any preliminary transformation of the data, because that avoids a potentially time-consuming loop over all the rasters.

Perhaps the most general solution available in this form uses Highest Position. This calculation applies to a sequence of rasters, which ought to be perfectly aligned and registered (so there is no complication entailing from resampling the values). It returns the index 1, 2, 3, ..., etc., of the first raster at which the maximum value in the sequence is encountered. Thus, when the sequence is purely binary and there is a one, the position of its first occurrence is returned--and that's exactly what is needed.

When there is one raster per time unit (such as year), with no gaps, adding the year preceding the start year will convert this result into the raster date. Otherwise, reclassify the result to obtain the corresponding years.

Two cautions are in order.

First, if any of the input rasters has NoData in a cell, the output for that cell will be NoData. If that's a problem, the rasters will have to be pre-processed to replace the NoData values by suitable codes. Some constant negative value might work well. Use a conditional operator to make the replacements.

Second, if all of a cell's values are zeros, then `HighestPosition` will return the index of the first of those zeros--namely, 1. That is indistinguishable from the result of a cell where all values are ones. Although some conditional post-processing can be used to discriminate these two situations, a simple, elegant way to avoid this problem is to create a raster of zeros at the outset and list it first in the calculation. Now a 1 will be returned for any all-zero cell and a 2 will be returned for any all-one cell.

• Absolutely brilliant, especially the all zeroes raster. This is precisely what I was looking for. Fixed my reclassification problem (0.3 was getting treated as no data) and the output is exactly what I expected. Thanks so much May 6, 2015 at 21:17