栅格地理对象-线性趋势变化图

地理学变量，如降水、气温、污染物浓度等，我们希望计算得到多年栅格图像在空间上的变化趋势、显著水平p、R²、RMSE等等。这里基于matlab和R分别实现线性模型计算的方法和代码。

两者的计算结果一致，效率相当，可任选一种。

Matlab程序

clear;
clc;
warning off
dirpath='K:\liulei\DryNH3\geotif\2surfNH3\yr\';
images=[];
p_intercept=[];
p_slope=[];
fc=[];
fd=[];
fe=[];
p_R2=[];
fg=[];
p_RMSE=[];
p_sig=[];
for i=2008:1:2016
   filepath=strcat(dirpath,'\','surfNH3_',num2str(i),'.tif');
   img=imread(filepath);
   [rows, cols]=size(img);
   temp=reshape(img,rows*cols,1);
   images=[images temp];
end
for i=1:rows*cols   
    i
    xData=[2008:2016]';
    yData= images(i,:)';
    if(yData(1)<0)  
        p_intercept=[p_intercept; nan];
        p_slope=[p_slope; nan];
        p_R2=[p_R2; nan];
        p_RMSE=[p_RMSE; nan];         
        p_sig=[p_sig; nan];
    else

        [m,n]=size(xData);                         %计算自变量矩阵行列数
        X=[ones(m,1),xData];  
        Y=yData;    
        [B,Bint,E,Eint,Stats]=regress(Y,X); 
        [C P]=corrcoef(xData,yData);                       %计算相关系数矩阵
        R2=C(1,2)^2;
        [n aa]=size(xData);
        f=B(1)+B(2)*xData;                         
        RMSE=sqrt(sum((f-yData).^2)/n);
        
        p_intercept=[p_intercept; B(1)];
        p_slope=[p_slope; B(2)];
        p_R2=[p_R2; R2];
        p_RMSE=[p_RMSE; RMSE];
        p_sig=[p_sig; P(1,2)];
    end   
end
outpath='K:\liulei\DryNH3\geotif\2surfNH3\yr\Trend\program\matlab\res';
xlswrite([outpath '\parameter.xlsx'],{'p_intercept','p_slope','p_R2','p_RMSE','p_sig'},1,'a1');
xlswrite([outpath '\parameter.xlsx'],p_intercept,1,'a2');
xlswrite([outpath '\parameter.xlsx'],p_slope,1,'b2');
xlswrite([outpath '\parameter.xlsx'],p_R2,1,'c2');
xlswrite([outpath '\parameter.xlsx'],p_RMSE,1,'d2');
xlswrite([outpath '\parameter.xlsx'],p_sig,1,'e2');

a=reshape(p_intercept,rows, cols);
b=reshape(p_slope,rows, cols);
c=reshape(p_R2,rows, cols);
d=reshape(p_RMSE,rows, cols);
e=reshape(p_sig,rows, cols);

R = georasterref('RasterSize', [rows, cols], ...
       'RasterInterpretation', 'cells', ...
       'Latlim', [-90 90], 'Lonlim', [-180 180], ...
       'ColumnsStartFrom', 'north');
geotiffwrite('K:\liulei\DryNH3\geotif\2surfNH3\yr\Trend\program\matlab\res\p_intercept.tif',a,R);
geotiffwrite('K:\liulei\DryNH3\geotif\2surfNH3\yr\Trend\program\matlab\res\p_slope.tif',b,R);
geotiffwrite('K:\liulei\DryNH3\geotif\2surfNH3\yr\Trend\program\matlab\res\p_R2.tif',c,R);
geotiffwrite('K:\liulei\DryNH3\geotif\2surfNH3\yr\Trend\program\matlab\res\p_RMSE.tif',d,R);
geotiffwrite('K:\liulei\DryNH3\geotif\2surfNH3\yr\Trend\program\matlab\res\p_sig.tif',e,R);

 

R程序

library(maptools) 
library(ncdf4)
library(raster)
library(rasterVis)
library(RColorBrewer)
library(zoo)
library('stringr')
library('latex2exp')
library(marmap)
library(sf)
library(greenbrown)
library('reticulate')

ncfname2 <- paste("/home/lei/R/data/GC/surfNH3sate/",  paste('surfNH3_', c(2008:2016),".tif", sep="") , sep="")
ConvNH4=stack(ncfname2)
#ConvNH4=projectRaster(ConvNH4,crs="+proj=longlat +datum=WGS84")

ConvNH4v2=as.array(ConvNH4)
xyz=dim(ConvNH4v2)
ConvNH4v2=array_reshape(ConvNH4v2, c(xyz[1]*xyz[2],xyz[3]))

parasFit=c(0)

for (index in 1:(xyz[1]*xyz[2]))
{
index
NH3layer=c(0)
NH3layer=ConvNH4v2[index,]
Height=c(1:9)

if(any(is.na(NH3layer))){
parasFit=rbind(parasFit,c(NA,NA,NA,NA))
}else{
fit <- lm(NH3layer~Height) 
yfitted=predict(fit, data.frame(x=Height))
yfitted=as.numeric(as.character(yfitted))
NH3layerv2=NH3layer
R2 <- summary(fit)$r.squared
pVal <- anova(fit)$'Pr(>F)'[1]
parasFit=rbind(parasFit,c(array(coef(fit)),R2,pVal))
}
}
#write.csv(parasFit[2:dim(parasFit)[1],],paste('/home/lei/R/data/GC/surface/yr/Guassian',j,'.csv',sep=''))

R2layer=array_reshape(parasFit[2:dim(parasFit)[1],3], c(xyz[1],xyz[2]))
R2layer <-raster(R2layer)
extent(R2layer) <-extent(ConvNH4)
crs(R2layer ) <- CRS("+proj=longlat +datum=WGS84") 
writeRaster(R2layer,paste('/home/lei/R/data/GC/surfNH3sate/Trend/Wet_R2_v3','.tif',sep=""),options=c('TFW=YES'), overwrite=TRUE)
print(c(cellStats(R2layer,stat='min'), cellStats(R2layer,stat='max')))

Alayer=array_reshape(parasFit[2:dim(parasFit)[1],1], c(xyz[1],xyz[2]))
Alayer <-raster(Alayer)
extent(Alayer) <-extent(ConvNH4)
crs(Alayer) <- CRS("+proj=longlat +datum=WGS84") 
writeRaster(Alayer,paste('/home/lei/R/data/GC/surfNH3sate/Trend/Wet_A_v3','.tif',sep=""),options=c('TFW=YES'), overwrite=TRUE)
print(c(cellStats(Alayer,stat='min'), cellStats(Alayer,stat='max')))

Blayer=array_reshape(parasFit[2:dim(parasFit)[1],2], c(xyz[1],xyz[2]))  
Blayer<-raster(Blayer)
extent(Blayer) <-extent(ConvNH4)
crs(Blayer) <- CRS("+proj=longlat +datum=WGS84") 
writeRaster(Blayer,paste('/home/lei/R/data/GC/surfNH3sate/Trend/Wet_B_v3','.tif',sep=""),options=c('TFW=YES'), overwrite=TRUE)
print(c(cellStats(Blayer,stat='min'), cellStats(Blayer,stat='max')))

player=array_reshape(parasFit[2:dim(parasFit)[1],4], c(xyz[1],xyz[2]))  
player <-raster(player)
extent(player) <-extent(ConvNH4)
crs(player) <- CRS("+proj=longlat +datum=WGS84") 
writeRaster(player,paste('/home/lei/R/data/GC/surfNH3sate/Trend/Wet_p_v3','.tif',sep=""),options=c('TFW=YES'), overwrite=TRUE)
print(c(cellStats(player,stat='min'), cellStats(player,stat='max')))