I am working with weather forecasters and have access to historical climatology data. Given current weather conditions in an area of interest (i.e. the current "map"), we want to try to find the most similar "map" from the past data. The idea is to try and make a weather forecast by finding the best analog from past data.
The data is represented as a regular X by Y grid (i.e. a matrix) of points, where X is the horizontal location and Y is the vertical location, and the (X,Y)th value in the matrix represents the response variable Z at that location. In addition, the grid points are evenly spaced out. As an example, Z can be a measure of surface temperature, which is measured at each of the grid points.
We take care of seasonal effects by restricting the search in the past data to a window of +/- 15 days of the test date. For example, if we want to find the best analog for a map from 2013-06-19, we would only consider maps from 2012-06-19 +/- 15 days, 2011-06-19 +/- 15 days, etc. We also restrict the search to observations taken at the same time as the test date. For example, if the test data is an observation taken at noon, then we will only look at the past data taken from the same time.
I have two questions.
(1) Given two grids (or "maps" or matrices) of data, how can I best calculate the similarity between them? Are there methods that take into account the spatial nature of the data? For example, point (1,1) will be highly correlated with the nearby point (1,2), etc.
I am currently using a very simple distance metric, where I just take the difference of the two maps and find the Frobenius norm. The map from the past that yields the smallest value is the 'closest' map to the test conditions.
(2) I am new to spatial statistics and I am looking for literature that relates to what I am trying to do. What should I read to become familiar with working with grid data? What resources are there to learn about pattern recognition in spatial or spatio-temporal data?
(I want to mention that I am working in R, so I would welcome package recommendations as well!)