Revision e81e5dff
Added by Benoit Parmentier about 10 years ago
climate/research/oregon/interpolation/contribution_of_covariates_paper_interpolation.R | ||
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4 | 4 |
#different covariates using two baselines. Accuracy methods are added in the the function script to evaluate results. |
5 | 5 |
#Figures, tables and data for the contribution of covariate paper are also produced in the script. |
6 | 6 |
#AUTHOR: Benoit Parmentier |
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#MODIFIED ON: 08/08/2014
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#MODIFIED ON: 09/03/2014
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#Version: 5 |
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#PROJECT: Environmental Layers project |
10 | 10 |
################################################################################################# |
... | ... | |
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met_stations_outfiles_obj_file<-"/data/project/layers/commons/data_workflow/output_data_365d_gam_fus_lst_test_run_07172013/met_stations_outfiles_obj_gam_fusion__365d_gam_fus_lst_test_run_07172013.RData" |
70 | 70 |
CRS_locs_WGS84<-CRS("+proj=longlat +ellps=WGS84 +datum=WGS84 +towgs84=0,0,0") #Station coords WGS84 |
71 | 71 |
y_var_name <- "dailyTmax" |
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out_prefix<-"_07182014"
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out_prefix<-"_09032014"
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out_dir<-"/home/parmentier/Data/IPLANT_project/paper_contribution_covar_analyses_tables_fig" |
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#setwd(out_dir) |
75 | 75 |
|
... | ... | |
330 | 330 |
#temp.colors <- matlab.like(no_brks) |
331 | 331 |
temp.colors <- colorRampPalette(c('blue', 'khaki', 'red')) |
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png(filename=paste("Figure_3_paper_Comparison_daily_monthly_mean_lst",out_prefix,".png",sep=""),width=960,height=480)
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png(filename=paste("Figure_3_paper_Comparison_daily_monthly_mean_lst",out_prefix,".png",sep=""),width=980,height=480)
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par(mfrow=c(1,2)) |
335 | 335 |
plot(lst_md,col=temp.colors(25),axes=F) #use axes=F to remove lat and lon or coordinates |
336 | 336 |
plot(interp_area,add=TRUE) |
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title("Mean for January 1")
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title("(a) Mean for 1 January")
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338 | 338 |
plot(lst_mm_01,col=temp.colors(25),axes=F) |
339 | 339 |
plot(interp_area,add=TRUE) |
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title("Mean for month of January") |
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title("(b) Mean for month of January") |
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dev.off() |
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png(filename=paste("Figure_3_paper_Comparison_daily_monthly_mean_lst",out_prefix,".png",sep=""),width=980,height=480) |
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par(mfrow=c(1,2)) |
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p <-levelplot(lst_md,col.regions=temp.colors(25),axes=F,margin=F,scales = list(draw = FALSE), #use list(draw=F) so as not to dispaly coordinates!!! |
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main="(a) Mean for 1 January") #use axes=F to remove lat and lon or coordinates |
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p_shp <- layer(sp.polygons(interp_area, lwd=0.8, col='black')) |
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#title("(a) Mean for 1 January") |
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p1 <- p+p_shp |
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#plot(interp_area,add=TRUE) |
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p <-levelplot(lst_mm_01,col.regions=temp.colors(25),axes=FALSE,margin=F,scales = list(draw = FALSE), |
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main="(b) Mean for month of January") #use axes=F to remove lat and lon or coordinates |
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p2 <- p+p_shp |
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#plot(lst_mm_01,col=temp.colors(25),axes=F) |
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#plot(interp_area,add=TRUE) |
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#title("(b) Mean for month of January") |
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grid.arrange(p1,p2,ncol=2) |
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341 | 363 |
dev.off() |
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343 | 365 |
## Calucate the proprotion of missing pixel for January 1 mean climatotology image |
... | ... | |
391 | 413 |
plot_dst_MAE(list_param_plot) |
392 | 414 |
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393 | 415 |
metric_name <-"mae_tb" |
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title_plot <- "MAE and distance to closest fitting station" |
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title_plot <- "(a) MAE and distance to closest fitting station"
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395 | 417 |
y_lab_text <- "MAE (°C)" |
396 | 418 |
add_CI <- c(TRUE,TRUE,TRUE) |
397 | 419 |
#Now set up plotting device |
... | ... | |
416 | 438 |
barplot(l1$n_tb$res_mod1,names.arg=limit_val, |
417 | 439 |
ylab="Number of observations", |
418 | 440 |
xlab="Distance to closest fitting station (km)") |
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title("Number of observation in term of distance bins")
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title("(b) Number of observations in term of distance bins")
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420 | 442 |
box() |
421 | 443 |
dev.off() |
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... | ... | |
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#debug(plot_prop_metrics) |
486 | 508 |
plot_prop_metrics(list_param_plot) |
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title(main="MAE for hold out and methods", |
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title(main="(a) MAE for hold out and methods",
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xlab="Hold out validation/testing proportion", |
489 | 511 |
ylab="MAE (°C)") |
490 | 512 |
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... | ... | |
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list_param_plot<-list(list_prop_obj,col_t,pch_t,legend_text,mod_name,metric_name,add_CI,CI_bar) |
494 | 516 |
names(list_param_plot)<-c("list_prop_obj","col_t","pch_t","legend_text","mod_name","metric_name","add_CI","CI_bar") |
495 | 517 |
plot_prop_metrics(list_param_plot) |
496 |
title(main="RMSE for hold out and methods", |
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title(main="(b) RMSE for hold out and methods",
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497 | 519 |
xlab="Hold out validation/testing proportion", |
498 | 520 |
ylab="RMSE (°C)") |
499 | 521 |
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... | ... | |
645 | 667 |
legend("top",legend=legend_text_data, |
646 | 668 |
cex=0.9, lty=c(1,2),bty="n") |
647 | 669 |
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title(main="Training and testing RMSE for hold out and methods", |
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title(main="(a) Training and testing RMSE for hold out and methods",
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xlab="Hold out validation/testing proportion", |
650 | 672 |
ylab="RMSE (°C)") |
651 | 673 |
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653 | 675 |
boxplot(diff_mae_data_mult[-4]) #plot differences in training and testing accuracies for three methods |
654 | 676 |
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title(main="Difference between training and testing MAE", |
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title(main="(b) Difference between training and testing MAE",
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656 | 678 |
xlab="Interpolation method", |
657 | 679 |
ylab="MAE (°C)") |
658 | 680 |
|
... | ... | |
727 | 749 |
lines(1:12,tb3_month$mae,col=c("blue"),type="b") |
728 | 750 |
lines(1:12,tb4_month$mae,col=c("black"),type="b") |
729 | 751 |
axis(1,at=1:12,labels=xlab_tick) |
730 |
title(main="Monthly average MAE") |
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title(main="(a) Monthly average MAE")
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731 | 753 |
legend("topleft",legend=legend_text, |
732 | 754 |
cex=0.9, pch=c(pch_t),col=c(col_t),lty=c(1,1,1),bty="n") |
733 | 755 |
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734 | 756 |
#Second plot |
735 | 757 |
ylab_text<-"MAE (°C)" |
736 | 758 |
xlab_text<-"Month" |
737 |
boxplot(mae~month,data=month_data_list$gam,main="Monthly MAE boxplot", xlab=xlab_text,ylab=ylab_text,outline=FALSE) |
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boxplot(mae~month,data=month_data_list$gam,main="(b) Monthly MAE boxplot", xlab=xlab_text,ylab=ylab_text,outline=FALSE)
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738 | 760 |
dev.off() |
739 | 761 |
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740 | 762 |
#Now generate table 5 |
... | ... | |
888 | 910 |
par.main.text=list(font=2,cex=2),strip.background=list(col="white")),par.strip.text=list(font=2,cex=1.5), |
889 | 911 |
strip=strip.custom(factor.levels=names_layers), |
890 | 912 |
xlab=list(label="Spatial lag neighbor", cex=2,font=2), |
891 |
ylab=list(label="Moran's I", cex=2, font=2)) |
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ylab=list(label="Moran's I", cex=2, font=2), |
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as.table=TRUE) #as.table controls the order of the pannels!! |
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892 | 915 |
print(p) |
893 | 916 |
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894 | 917 |
dev.off() |
... | ... | |
933 | 956 |
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934 | 957 |
png(paste("Figure_8a_spatial_pattern_tmax_prediction_models_gam_levelplot_",date_selected,out_prefix,".png", sep=""), |
935 | 958 |
height=480*layout_m[1],width=480*layout_m[2]) |
959 |
#X11(height=7*layout_m[1],width=7*layout_m[2]) |
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936 | 960 |
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937 |
p<-levelplot(pred_temp_s,main="Interpolated Surfaces Model Comparison", ylab=NULL,xlab=NULL, |
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names_layers <-c("mod1 = s(lat,long)+s(elev)","mod4 = s(lat,long)+s(LST)") |
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p<-levelplot(pred_temp_s,main="(a) Interpolated Surfaces Model Comparison", ylab=NULL,xlab=NULL, |
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938 | 964 |
par.settings = list(axis.text = list(font = 2, cex = 1.3),layout=layout_m, |
939 | 965 |
par.main.text=list(font=2,cex=2),strip.background=list(col="white")),par.strip.text=list(font=2,cex=1.5), |
940 | 966 |
names.attr=names_layers,col.regions=temp.colors,at=seq(max_val,min_val,by=0.01)) |
941 | 967 |
#col.regions=temp.colors(25)) |
942 | 968 |
print(p) |
969 |
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#savePlot(paste("Figure_8a_spatial_pattern_tmax_prediction_models_gam_levelplot_",date_selected,out_prefix,".png", sep=""), |
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# type="png") |
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972 |
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943 | 973 |
#col.regions=temp.colors(25)) |
944 | 974 |
dev.off() |
945 | 975 |
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946 | 976 |
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947 | 977 |
diff<-raster(lf1$mod1)-raster(lf1$mod4) |
948 |
names_layers <- c("difference=mod1-mod4") |
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names_layers <- c("mod1-mod4") |
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979 |
diff<-stack(diff) |
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949 | 980 |
names(diff) <- names_layers |
950 | 981 |
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951 | 982 |
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952 | 983 |
png(paste("Figure_8b_spatial_pattern_tmax_prediction_models_gam_levelplot_",date_selected,out_prefix,".png", sep=""), |
953 |
height=480*layout_m[1],width=480*layout_m[2])
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height=530*1,width=534*1)
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954 | 985 |
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plot(diff,col=temp.colors(100),main=names_layers) |
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#levelplot(diff,main="Interpolated Surfaces Model Comparison", ylab=NULL,xlab=NULL, |
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# par.settings = list(axis.text = list(font = 2, cex = 1.3),layout=c(1,1), |
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958 |
# par.main.text=list(font=2,cex=2),strip.background=list(col="white")),par.strip.text=list(font=2,cex=1.5), |
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# names.attr=names_layers,col.regions=temp.colors) |
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960 |
dev.off |
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986 |
#plot(diff,col=temp.colors(100),main=names_layers) |
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levelplot(diff,main="(b) Difference between models", ylab=NULL,xlab=NULL, |
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margin=F, |
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par.settings = list(axis.text = list(font = 2, cex = 1.3),layout=c(1,1), |
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990 |
par.main.text=list(font=2,cex=2),strip.background=list(col="white")),par.strip.text=list(font=2,cex=1.5), |
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names.attr=names_layers,col.regions=temp.colors) |
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992 |
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993 |
dev.off() |
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961 | 994 |
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962 | 995 |
############################### |
963 | 996 |
########## Prepare table 6 |
... | ... | |
1075 | 1108 |
plot(tb_sig_p_val_rec2) |
1076 | 1109 |
#Now prepare |
1077 | 1110 |
s_table_LST_mod4 <- subset(s.table_term_tb,mod_name=="mod4" & term_name=="s(LST)") |
1078 |
tb_mod4_LST_rec3 <- aggregate(s_table_LST_mod4$p_val_rec3~s_table_term_mod4$month,FUN=mean) |
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1111 |
#tb_mod4_LST_rec3 <- aggregate(s_table_LST_mod4$p_val_rec3~s_table_term_mod4$month,FUN=mean) |
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1112 |
tb_mod4_LST_rec3 <- aggregate(s_table_LST_mod4$p_val_rec3~s_table_LST_mod4$month,FUN=mean) |
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1113 |
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1079 | 1114 |
plot(tb_mod4_LST_rec3,type="l",ylim=c(0.2,1)) |
1080 | 1115 |
s_table_elev_mod4 <- subset(s.table_term_tb,mod_name=="mod4" & term_name=="s(elev_s)") |
1081 | 1116 |
#tb_mod4_elev_rec3 <- aggregate(tb_mod4_elev_rec3$p_val_rec2 ~ tb_mod4_elev_rec3$month,FUN=mean) |
1117 |
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1082 | 1118 |
plot(tb_mod4_elev_rec3) |
1083 | 1119 |
lines(tb_mod4_elev_rec3) |
1084 | 1120 |
test1 <- subset(s.table_term_tb,mod_name=="mod1" & term_name=="s(elev_s)") |
... | ... | |
1139 | 1175 |
type="b", |
1140 | 1176 |
ylab=list(label="\u0394RMSE between mod1 and mod4",cex=1.5), |
1141 | 1177 |
xlab=list(label="Month",cex=1.5), |
1142 |
main=list(label="Proportion of significant LST term in mod4",cex=1.8)) |
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1178 |
main=list(label="(a) Proportion of significant LST term in mod4",cex=1.8))
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1143 | 1179 |
p_prop <- update(p_prop,par.settings = list(axis.text = list(font = 2, cex = 1.3), |
1144 | 1180 |
par.main.text=list(font=2,cex=2),strip.background=list(col="white")),par.strip.text=list(font=2,cex=1.5)) |
1145 | 1181 |
|
... | ... | |
1148 | 1184 |
type="b", |
1149 | 1185 |
ylab=list(label="\u0394RMSE between mod1 and mod4",cex=1.5), |
1150 | 1186 |
xlab=list(label="Month",cex=1.5), |
1151 |
main=list(label="Monthly \u0394RMSE betwen mod1 and mod4",cex=1.8), |
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1187 |
main=list(label="(b) Monthly \u0394RMSE betwen mod1 and mod4",cex=1.8),
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1152 | 1188 |
par.settings = list(axis.text = list(font = 2, cex = 1.3), |
1153 | 1189 |
par.main.text=list(font=2,cex=2),strip.background=list(col="white")),par.strip.text=list(font=2,cex=1.5)) |
1154 | 1190 |
p_dif <- update(p_dif, panel = function(...) { |
... | ... | |
1166 | 1202 |
ylim=c(-1,1), |
1167 | 1203 |
ylab=list(label="Pearson Correlation",cex=1.5), |
1168 | 1204 |
xlab=list(label="Month",cex=1.5), |
1169 |
main=list(label="Pearson Correlation",cex=1.8), |
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main=list(label="(c) Pearson Correlation",cex=1.8),
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1170 | 1206 |
auto.key = list("topright", corner = c(0,1),# col=c("black","red"), |
1171 | 1207 |
border = FALSE, lines = TRUE,cex=1.2)) |
1172 | 1208 |
p_cor <- update(p_cor, panel = function(...) { |
... | ... | |
1223 | 1259 |
p1<-plot(raster_prediction_obj_3$method_mod_obj[[1]]$mod[[1]]$exp_var,raster_prediction_obj_3$method_mod_obj[[1]]$mod[[1]]$var_model, |
1224 | 1260 |
ylim=c(0,9), |
1225 | 1261 |
ylab=list(label="Semivariance",cex=1.5), |
1226 |
xlab=list(label="Distance (meter)",cex=1.5),
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1227 |
main=list(label="Mod1 January 1, 2010",cex=1.8),
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1262 |
xlab=list(label="Distance (m)",cex=1.5), |
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1263 |
main=list(label="(a) Mod1 1 January 2010",cex=1.8),
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1228 | 1264 |
par.settings = list(axis.text = list(font = 2, cex = 1.3), #control the font size!! |
1229 | 1265 |
par.main.text=list(font=2,cex=2),strip.background=list(col="white")), |
1230 | 1266 |
par.strip.text=list(font=2,cex=1.5) |
... | ... | |
1233 | 1269 |
p241<-plot(raster_prediction_obj_3$method_mod_obj[[241]]$mod[[1]]$exp_var,raster_prediction_obj_3$method_mod_obj[[241]]$mod[[1]]$var_model, |
1234 | 1270 |
ylim=c(0,9), |
1235 | 1271 |
ylab=list(label="Semivariance",cex=1.5), |
1236 |
xlab=list(label="Distance (meter)",cex=1.5),
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1237 |
main=list(label="Mod1 September 1, 2010",cex=1.8),
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1272 |
xlab=list(label="Distance (m)",cex=1.5), |
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1273 |
main=list(label="(b) Mod1 1 September 2010",cex=1.8),
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1238 | 1274 |
par.settings = list(axis.text = list(font = 2, cex = 1.3), |
1239 | 1275 |
par.main.text=list(font=2,cex=2),strip.background=list(col="white")), |
1240 | 1276 |
par.strip.text=list(font=2,cex=1.5) |
... | ... | |
1271 | 1307 |
col=c("grey"), |
1272 | 1308 |
ylab=list(label="Percent of total",cex=1.5), |
1273 | 1309 |
xlab=list(label="Variogram model",cex=1.5), |
1274 |
main=list(label="Variogram model type",cex=1.8)) |
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1310 |
main=list(label="(a) Variogram model type",cex=1.8))
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1275 | 1311 |
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1276 | 1312 |
p_bw1<- bwplot(tb_variogram$range~tb_variogram$month,do.out=F,ylim=c(0,250000), |
1277 | 1313 |
ylab=list(label="Range of variograms",cex=1.5), |
1278 | 1314 |
xlab=list(label="Month",cex=1.5), |
1279 |
main=list(label="Mod1 range",cex=1.8)) |
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1315 |
main=list(label="(b) Mod1 range",cex=1.8))
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1280 | 1316 |
p_bw2<-bwplot(tb_variogram$Nug~tb_variogram$month,do.out=F,ylim=c(0,12), |
1281 | 1317 |
ylab=list(label="Nugget of variograms",cex=1.5), |
1282 | 1318 |
xlab=list(label="Month",cex=1.5), |
1283 |
main=list(label="Mod1 Nugget",cex=1.8)) |
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1319 |
main=list(label="(c) Mod1 Nugget",cex=1.8))
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1284 | 1320 |
p_bw3<-bwplot(tb_variogram$psill~tb_variogram$month,do.out=F,ylim=c(0,30), |
1285 | 1321 |
ylab=list(label="Sill of variograms",cex=1.5), |
1286 | 1322 |
xlab=list(label="Month",cex=1.5), |
1287 |
main=list(label="Mod1 sill",cex=1.8)) |
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1323 |
main=list(label="(d) Mod1 sill",cex=1.8))
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1288 | 1324 |
#grid.arrange(p1,p2,p3,ncol=1) |
1289 | 1325 |
grid.arrange(p_hist,p_bw1,p_bw2,p_bw3,ncol=2) |
1290 | 1326 |
|
... | ... | |
1306 | 1342 |
day<-as.integer(strftime(date_proc, "%d")) |
1307 | 1343 |
year<-as.integer(strftime(date_proc, "%Y")) |
1308 | 1344 |
datelabel=format(ISOdate(year,mo,day),"%b %d, %Y") |
1309 |
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1345 |
datelabel <- format(ISOdate(year,mo,day),"%d-%m-%Y") |
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1310 | 1346 |
#height=480*6,width=480*4) |
1311 | 1347 |
list_p <- vector("list", length(names_mod)) |
1312 | 1348 |
for (k in 1:length(names_mod)){ |
... | ... | |
1379 | 1415 |
grid.arrange(list_p[[10]], |
1380 | 1416 |
ncol=3) |
1381 | 1417 |
dev.off() |
1418 |
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1382 | 1419 |
########################################### |
1383 | 1420 |
### Figure 12: map of MAE by stations over 365 days to summarize residuals information |
1384 | 1421 |
|
... | ... | |
1439 | 1476 |
elev <- subset(s_raster,"elev_s") |
1440 | 1477 |
list_p_mae <- vector("list", 3) |
1441 | 1478 |
names_var <- c("mod1","mod2","mod5") |
1479 |
plot_nb <- c("(a)","(b)","(c)") |
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1442 | 1480 |
for (k in 1:length(names_var)){ |
1443 | 1481 |
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1444 | 1482 |
model_name <- names_var[k] |
1483 |
nb_p <- plot_nb[k] |
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1445 | 1484 |
res_model_name <- paste("res",model_name,sep="_") |
1485 |
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1446 | 1486 |
#res_model_name <- "res_mod1" |
1447 | 1487 |
p1 <- levelplot(elev,scales = list(draw = FALSE), colorkey = FALSE,par.settings = GrTheme) |
1448 | 1488 |
#tt <- na.omit(data_v_mae) |
1449 | 1489 |
#df_tmp=subset(data_v_mae,data_v_mae$res_mod1!="NaN") |
1450 | 1490 |
df_tmp=subset(data_v_mae,data_v_mae[[res_model_name]]!="NaN") |
1451 | 1491 |
|
1452 |
p2 <- bubble(df_tmp,res_model_name, main=paste("Average MAE per station for ",model_name,sep=""),
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|
1492 |
p2 <- bubble(df_tmp,res_model_name, main=paste(nb_p," Average MAE per station for ",model_name,sep=""),
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1453 | 1493 |
col=matlab.like(5),na.rm=TRUE) |
1454 | 1494 |
p3 <- p2 + p1 + p2 #to force legend... |
1455 | 1495 |
#print(p3) |
... | ... | |
1459 | 1499 |
} |
1460 | 1500 |
|
1461 | 1501 |
layout_m<-c(1,3) # works if set to this?? ok set the resolution... |
1462 |
png(paste("Figure12_paper_","average_MAE_",date_selected,"_",out_prefix,".png", sep=""),
|
|
1502 |
png(paste("Figure12_paper_","average_MAE_","_",out_prefix,".png", sep=""), |
|
1463 | 1503 |
height=480*layout_m[1],width=480*layout_m[2]) |
1504 |
X11(height=7*layout_m[1],width=7*layout_m[2]) |
|
1464 | 1505 |
|
1465 | 1506 |
grid.arrange(list_p_mae[[1]],list_p_mae[[2]],list_p_mae[[3]],ncol=3) |
1507 |
savePlot(paste("Figure12_paper_","average_MAE_","_",out_prefix,".png", sep=""), |
|
1508 |
type="png") |
|
1466 | 1509 |
|
1467 | 1510 |
dev.off() |
1468 | 1511 |
|
... | ... | |
1494 | 1537 |
p_bw1<-bwplot(data_v_ag$res_mod1~elev_rcstat,do.out=F,ylim=c(-15,15), |
1495 | 1538 |
ylab=list(label="Residuals (deg C)",cex=1.5), |
1496 | 1539 |
xlab=list(label="Elevation classes (meter)",cex=1.5), |
1497 |
main=list(label="Residuals vs elev for mod1=lat*lon",cex=1.8), |
|
1540 |
main=list(label="(a) Residuals vs elev for mod1=lat*lon",cex=1.8),
|
|
1498 | 1541 |
scales = list(x = list(at = c(1, 2, 3, 4), #provide tick location and labels |
1499 | 1542 |
labels = c("0-500","500-1000","1000-1500","1500-2000"))), |
1500 | 1543 |
par.settings = list(axis.text = list(font = 2, cex = 1.3), #control the font size!! |
... | ... | |
1505 | 1548 |
p_bw2 <- bwplot(data_v_ag$res_mod5~elev_rcstat,do.out=F,ylim=c(-15,15), |
1506 | 1549 |
ylab=list(label="Residuals (deg C)",cex=1.5), |
1507 | 1550 |
xlab=list(label="Elevation classes (meter)",cex=1.5), |
1508 |
main=list(label="Residuals vs elev for mod5=lat*lon+LST",cex=1.8), |
|
1551 |
main=list(label="(b) Residuals vs elev for mod5=lat*lon+LST",cex=1.8),
|
|
1509 | 1552 |
scales = list(x = list(at = c(1, 2, 3, 4), |
1510 | 1553 |
labels = c("0-500","500-1000","1000-1500","1500-2000"))), |
1511 | 1554 |
par.settings = list(axis.text = list(font = 2, cex = 1.3), #control the font size!! |
... | ... | |
1516 | 1559 |
p_bw3 <- bwplot(data_v_ag$res_mod2~elev_rcstat,do.out=F,ylim=c(-15,15), |
1517 | 1560 |
ylab=list(label="Residuals (deg C)",cex=1.5), |
1518 | 1561 |
xlab=list(label="Elevation classes (meter)",cex=1.5), |
1519 |
main=list(label="Residuals vs elev for mod2=lat*lon+elev",cex=1.8), |
|
1562 |
main=list(label="(c) Residuals vs elev for mod2=lat*lon+elev",cex=1.8),
|
|
1520 | 1563 |
scales = list(x = list(at = c(1, 2, 3, 4), |
1521 | 1564 |
labels = c("0-500","500-1000","1000-1500","1500-2000"))), |
1522 | 1565 |
par.settings = list(axis.text = list(font = 2, cex = 1.3), #control the font size!! |
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proof paper RS contribution of covar, modification to figures