如何通过点之间的插值绘制不规则空间数据？

Question

我有一个包含 3 列的数据框：x、y 和 z。在此数据集中，x 和 y 表示坐标位置，z 表示感兴趣的响应变量。然而，数据是不规则的；它代表了一块三面被水包围的陆地。我们只对陆地上的数据感兴趣，因此当我制作图像图时，我希望将水表示为空白。

我目前正在使用 ggplot2 中的以下代码。这会生成如下图块图。

ggplot(data=df, aes(x, y, height=0.005, width=0.005)) +
  geom_tile(aes(fill = z)) +
  scale_fill_gradientn(colours = tim.colors(7)) + 
  theme_classic()

我想用点之间的插值来绘制它。然而，我不希望插值超出陆地范围。有什么方法可以做到这一点吗？

数据子集的代码：

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Answer 1

有几种方法可以实现这一目标。您可以通过

interp

包执行线性插值：

library(interp)

df2 <- interp(df$x, df$y, df$z, nx = 500, ny = 500) |> 
  interp2xyz() |> 
  as.data.frame()

或者使用

gam

进行样条平滑（我们从

interp

方法复制 NA 值以保留形状的轮廓）

library(mgcv)

df2$z2 <- mgcv::gam(z ~ s(y) + s(x), gamma = -1, data = df) |>
          predict(newdata = df2)
df2$z2[is.na(df2$z)] <- NA

我们可以看到这些方法与原始数据的比较：

library(ggplot2)
library(patchwork)

p1 <- ggplot(data = df, aes(x, y, height = 0.005, width = 0.005)) +
  geom_tile(aes(fill = z)) +
  scale_fill_distiller(palette = "Spectral", na.value = NA) +
  theme_classic() +
  ggtitle("Raw data")

p2 <- ggplot(data = df2, aes(x, y)) +
  geom_raster(aes(fill = z)) +
  scale_fill_distiller(palette = "Spectral", na.value = NA) + 
  theme_classic() +
  ggtitle("Linear interpolation")

p3 <- ggplot(data = df2, aes(x, y)) +
  geom_raster(aes(fill = z2)) +
  scale_fill_distiller(palette = "Spectral", na.value = NA) + 
  theme_classic() +
  ggtitle("Smoothing via GAM")

p1 + p2 + p3