Need help with slope algorithms for my internship

[MattGray]

I am currently doing a GIS internship with the NRCS soil department. They have been using the default ArcMap slope algorithm for their soil maps. I have been tasked with researching the various slope algorithms out there, and to determine which how they all work and which one is most accurate.  I have found a few papers around the web that mention various slope algorithms. One in particular mentions using excel to run these various algorithms to produce various outputs based off a made up DEM. Is there a way to program the slope tool in SA to use different algorithms? I have read up on ESRI Help about the default algorithm and mostly understand the math behind it. I want to produce a slope map for each algorithm using ArcMap on a DEM that they will then go out and make field measurements with. If anyone can at least point me in the right direction, anything helps right now.

[MattGray]

I would like to thank you for your reply. I was also tasked with figuring out what was the best algorithm to use when resampling a raster to a coarser resolution. I think they have been using nearest neighbor. What in your opinion would be best in this situation to use and why?

[MattGray]

I have been reading about the algorithm that spatial analyst uses here using the maximum average algorithm. I most understand the math behind it. Can someone elaborate more on the rise/run part of the equation where it does this: �?? ( [dz/dx]2 + [dz/dy]2 )? What is going on mathematically?How is it combining the rate of change in the x  and the  rate of change in the y into one final slope? My dad thought it had something to do with vector addition but do not know. Also if anyone can elaborate on the slope algorithms found here

[MattGray]

Thank you so much for your time.

[MattGray]

In your first reply, you say

The ArcGIS slope function is not reprogrammable. However, most slope estimators can be computed as combinations of focal sums.

What do you mean by slope estimator if it is not the SA slope tool? What are various slope examples of slope estimators that can be applied in ArcMap? You also talk about testing these slope estimators by starting

with the most accurate, high-resolution DEM you have. Resample or aggregate it to a series of coarser resolutions. Apply slope estimators to the coarsened DEM and compare their results to the original DEM. In effect, the original DEM already contains the data you planned to collect in the field.

When you apply the slope estimators to the resampled coarser resolution DEMs, what are you looking for when you compare it to the original DEM to test its accuracy? The example DEM I have been using is derived from 1 meter resolution Lidar data. I have been on this project for quite some time now, and I would like to finally be able to show them something so they can validate and have faith in their data. You replies have really helped so far in helping to begin to understand this whole subject. I just graduated  so this is still fairly complex to me, and there is no one in this office that really understands GIS other than  running basic processes and analysis.

[MattGray]

So I need to resample a 1 meter LIDAR DEM to 3 meter and 5 meter. I am trying to figure out what resampling algorithm to use. I heard something about a roughness factor or roughness scale that plays a part in this decision. Any ideas?

[MattGray]

From what was said about resampling above and what I read on ESRI desktop help, I decided that bilinear interpolation is the best for resampling elevation data. Does anyone have a link to a good paper about resampling DEMs that I could cite?