Tool for a moving average over a time series

[StefanieSteinbach]

Dear all,

I am looking for a tool to create a pixel-based moving average from a range of MODIS EVI tiles (from 2001 to 2013).

Is there a tool in ArcGIS to create the respective raster data sets by aggregating for example 3 time steps?

Thanks for your help,

Stefanie

[DanPatterson_Retired]

If you are talking moving average as being the time step for each spatial location, then have you seen

http://desktop.arcgis.com/en/desktop/latest/tools/spatial-analyst-toolbox/how-cell-statistics-works....

and the mean example.  It will give you the average at each location given rasters of the same extent, cell size just representing different times.

If you want a 'moving' average at one time step, then you want to look at

http://desktop.arcgis.com/en/desktop/latest/tools/spatial-analyst-toolbox/focal-statistics.htm

you could use a 3x3 window and calculate the average within the 9 cells.  Depending how the average is calculated for a window, this may yield the same results.

An example using simple mean calculations (and I had Python open...sorry)

>>> import numpy as np
>>> a = np.arange(9.).reshape((3,3))
>>> b = np.arange(5.,14.).reshape((3,3))
>>> c = np.arange(10.,19.).reshape((3,3))
>>> a_m = np.mean(a)
>>> b_m = np.mean(b)
>>> c_m = np.mean(c)
>>> cent_m = np.mean([a_m,b_m,c_m])
>>> cent_m
9.0
>>> all_data = np.array([a,b,c])
>>> all_data = all_data.flatten()
>>> all_data_mean = np.mean(all_data)
>>> all_data_mean
9.0
>>> a  # time step 1
array([[ 0.,  1.,  2.],
      [ 3.,  4.,  5.],
      [ 6.,  7.,  8.]])
>>> b  # time step 2
array([[  5.,  6.,  7.],
      [  8.,  9.,  10.],
      [ 11.,  12.,  13.]])
>>> c  # time step 3
array([[ 10.,  11.,  12.],
      [ 13.,  14.,  15.],
      [ 16.,  17.,  18.]])
>>> a_m, b_m, c_m  # means for arrays a, b, c
(4.0, 9.0, 14.0)
>>> all_data_mean  # mean of flattened array of all data,
9.0
>>>

Just some food for thought

EDIT

Oh yeah... of course you can do this within python.  You can get your ArcMap data layers into numpy array format using

http://desktop.arcgis.com/en/desktop/latest/analyze/arcpy-functions/rastertonumpyarray-function.htm

and you could simply create a multi-dimensional array from the inputs, or work with each layer one at a time.  It is trivial to setup and there are workarounds for humungous data files etc (ie netCDF support)

[StefanieSteinbach]

Hi Dan,

I am not sure if what you edited meets what I thought as I am really not familiar with Python programming and can't read the code.

Concerning the other two options - I am not looking for the averages over all time steps, nor for a moving window filter for one. What I am seeking is something that can easily calculate the mean for each cell for layer 1, 2 and 3, then one for 2, 3 and 4, the next one for 3, 4, and 5 etc. I know I could simply do it with the raster calculator, but since I have a large number of rasters, this will take ages to do manually.

[DanPatterson_Retired]

What you want is to do is code the local statistics in a moving loop... sorry to stick to code but ultimately you want something like this

>>> import numpy as np
>>>
>>> rasters = np.array([1,2,3,4,5,6,7,8,9])
>>> moving_mean = [np.mean(rasters[i-3:i]) for i in range(3,len(rasters)+1)]
>>> moving_mean
[2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0]
>>>

but using something like this totally unchecked code (money refunded if it doesn't work)

arcpy.CheckOutExtension("Spatial")
env.workspace = "C:/somepath/to_your/data"
rasters = arcpy.ListRasters("*", "GRID")
ras_name = "amazing"
for i in range(3,len(rasters)+1):
    outras = CellStatistics([rasters[i-3],rasters[i-2],rasters[i-1]], "Mean", "NODATA")
    ras_name = env.workspace + "/" +ras_name + str(I)
    ras_name.save(ras_name)

Now maybe someone with some data, or is so inclined could check this out.

Other info http://desktop.arcgis.com/en/desktop/latest/analyze/arcpy-functions/listrasters.htm

[StefanieSteinbach]

Thanks for the code, I'll try it on my data and will give you feedback!

I guess there's no way around Python when seriously working with ArcGIS..

[DanPatterson_Retired]

No...It is important to learn as many languages as possible...there isn't a code Bablefish however.