将地理加权回归模型参数应用于更精细的空间尺度

Question

我有两个光栅层，一个粗分辨率和一个精细分辨率。我的目标是提取GWR的系数(拦截和斜率)，并将它们应用到我的精细分辨率光栅中。

当我执行简单的线性回归时，我可以很容易地做到这一点。例如：

library(terra)
library(sp)

# focal terra
tirs = rast("path/tirs.tif") # fine res raster
ntl = rast("path/ntl.tif") # coarse res raster
    
# fill null values
tirs = focal(tirs, 
             w = 9, 
             fun = mean, 
             na.policy = "only", 
             na.rm = TRUE)
  
gf <- focalMat(tirs, 0.10*400, "Gauss", 11)
r_gf <- focal(tirs, w = gf, na.rm = TRUE)
  
r_gf = resample(r_gf, ntl, method = "bilinear")

s = c(ntl, r_gf)
names(s) = c('ntl', 'r_gf')

model <- lm(formula = ntl ~ tirs, data = s)

# apply the lm coefficients to the fine res raster
lm_pred = model$coefficients[1] + model$coefficients[2] * tirs

但是当我运行GWR时，斜率和截距不仅仅是两个数字(就像线性模型中的那样)，而是一个范围。例如，下面是GWR的结果

GWR系数估计综述：

                Min.     1st Qu.      Median     3rd Qu.     Max.

Intercept -1632.61196   -55.79680   -15.99683    15.01596 1133.299

tirs20      -42.43020     0.43446     1.80026     3.75802   70.987

我的问题是如何提取GWR模型参数(拦截和斜率)并将它们应用到我的精细分辨率光栅中？最后，我想做和线性模型一样的事情，即GWR_intercept + GWR_slope *精细分辨率光栅。

这是GWR的代码

library(GWmodel)
library(raster)

block.data = read.csv(file = "path/block.data00.csv")

#create mararate df for the x & y coords
x = as.data.frame(block.data$x)
y = as.data.frame(block.data$y)
sint = as.matrix(cbind(x, y))

#convert the data to spatialPointsdf and then to spatialPixelsdf
coordinates(block.data) = c("x", "y")
#gridded(block.data) <- TRUE

# specify a model equation
eq1 <- ntl ~ tirs

dist = GWmodel::gw.dist(dp.locat = sint, focus = 0, longlat = FALSE)

abw = bw.gwr(eq1, 
       data = block.data, 
       approach = "AIC", 
       kernel = "tricube",
       adaptive = TRUE, 
       p = 2, 
       longlat = F, 
       dMat = dist,
       parallel.method = "omp",
       parallel.arg = "omp")

ab_gwr = gwr.basic(eq1, 
          data = block.data, 
          bw = abw, 
          kernel = "tricube",
          adaptive = TRUE, 
          p = 2,
          longlat = FALSE, 
          dMat = dist,
          F123.test = FALSE,
          cv = FALSE,
          parallel.method = "omp",
          parallel.arg = "omp")

ab_gwr

您可以从csv下载这里。我用的光栅：

ntl = rast(ncols=101, nrows=85, nlyrs=1, xmin=509634.6325, xmax=550034.6325, ymin=161598.158, ymax=195598.158, names=c('ntl'), crs='EPSG:27700')

tirs = rast(ncols=407, nrows=342, nlyrs=1, xmin=509600, xmax=550300, ymin=161800, ymax=196000, names=c('tirs'), crs='EPSG:27700')

Answer 1

这就是如何进行全局回归和预测到更高的分辨率(降级)。

library(terra)
r <- rast(system.file("ex/logo.tif", package="terra"))
a <- aggregate(r, 10, mean)

model <- lm(formula = red ~ green, data=a)
p <- predict(r, model)

和

d <- as.data.frame(a[[1:2]], xy=TRUE)

也许这有助于在你的问题中写出一个更好的例子。