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I'm using ArcMap 10.3. I'm a student working on a research problem where I'm taking Landsat imagery (at 30-meters resolution) and regressing it against other datasets captured at different scales (up to about 1 km^2). I am then resampling everything down to 30 square meters prior to running the regression.

My ultimate goal is to understand vegetation dynamics, which is why I wanted to bring the whole analysis down to Landsat's 30 square meters. Or is this thinking incorrect, ie, should I run the analysis at the scale of the coarsest dataset, being 1 km^2?

From what I've read- in particular, Hengl 2006 "Finding the right pixel size", there is no "ideal" grid resolution and it is dependent on the question. Another paper I read, Tarnavsky 2007 "Multiscale geostatistical analysis of AVHRR, SPOT-VGT, and MODIS global NDVI products" recommended choosing a pixel size to minimize the spatial variability between sensors. Yet other papers suggest statistical corrections in order to use multiscale data.

I can do the regression. My question is whether there are any standards for how to approach an analysis where all the input data is at a different scale, in my case, ranging from 30 square meters up to 1 km^2.

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Unfortunately there is no standard. Primarily driven by the fact that different applications have different requirements. If the key element of your study is to look at field level information, then using the coarse resolution may not be a good idea, however, if you are looking at regional trends, then the low resolution may not be that much of an issue. However, that opens up a new angle to your project - investigating how the results differ when taking different approaches.

Another option would be to look into things like StarFM for spatial unmixing of coarse resolution data, using correlated high resolution data. However, this is not particularly easy.

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