##################    CLIMATE INTERPOLATION FUSION METHOD   #######################################

############################ Merging LST and station data ##########################################

#This script interpolates tmax values using MODIS LST and GHCND station data                     #

#interpolation area. It requires the text file of stations and a shape file of the study area.   #       

#Note that the projection for both GHCND and study area is lonlat WGS84.                         #

#AUTHOR: Brian McGill                                                                            #

#DATE: 06/19/212                                                                                 #

#PROJECT: NCEAS INPLANT: Environment and Organisms --TASK#363--                                  #

###################################################################################################

###Loading R library and packages                                                      

library(gtools)                                         # loading some useful tools 

library(mgcv)                                           # GAM package by Simon Wood

library(sp)                                             # Spatial pacakge with class definition by Bivand et al.

library(spdep)                               # Spatial pacakge with methods and spatial stat. by Bivand et al.

library(rgdal)                               # GDAL wrapper for R, spatial utilities

library(gstat)                               # Kriging and co-kriging by Pebesma et al.

library(fields)                              # NCAR Spatial Interpolation methods such as kriging, splines

library(raster)                              # Hijmans et al. package for raster processing

### Parameters and argument

infile1<- "ghcn_or_tmax_covariates_06262012_OR83M.shp"             #GHCN shapefile containing variables for modeling 2010                 

infile2<-"list_10_dates_04212012.txt"                     #List of 10 dates for the regression

#infile2<-"list_365_dates_04212012.txt"

infile3<-"LST_dates_var_names.txt"                        #LST dates name

infile4<-"models_interpolation_05142012.txt"              #Interpolation model names

infile5<-"mean_day244_rescaled.rst"                       #Raster or grid for the locations of predictions

#path<-"/home/parmentier/Data/IPLANT_project/data_Oregon_stations"

path<-"M:/Data/IPLANT_project/data_Oregon_stations"   #Locations on Atlas

#Station location of the study area

stat_loc<-read.table(paste(path,"/","location_study_area_OR_0602012.txt",sep=""),sep=",", header=TRUE)

#GHCN Database for 1980-2010 for study area (OR) 

data3<-read.table(paste(path,"/","ghcn_data_TMAXy1980_2010_OR_0602012.txt",sep=""),sep=",", header=TRUE)

prop<-0.3                                                                           #Proportion of testing retained for validation   

#prop<-0.25

seed_number<- 100                                                                   #Seed number for random sampling

out_prefix<-"_07022012_10d_fusion12"                                                   #User defined output prefix

setwd(path)

############ START OF THE SCRIPT ##################

#

### Step 0/Step 6 in Brian's code...preparing year 2010 data for modeling 

#

###Reading the station data and setting up for models' comparison

filename<-sub(".shp","",infile1)             #Removing the extension from file.

ghcn<-readOGR(".", filename)                 #reading shapefile 

CRS<-proj4string(ghcn)                       #Storing projection information (ellipsoid, datum,etc.)

mean_LST<- readGDAL(infile5)                 #Reading the whole raster in memory. This provides a grid for kriging

proj4string(mean_LST)<-CRS                   #Assigning coordinate information to prediction grid.

ghcn = transform(ghcn,Northness = cos(ASPECT*pi/180)) #Adding a variable to the dataframe

#ghcn = transform(ghcn,Northness = cos(ASPECT)) #Adding a variable to the dataframe

#ghcn = transform(ghcn,Eastness = sin(ASPECT))  #adding variable to the dataframe.

ghcn = transform(ghcn,Eastness = sin(ASPECT*pi/180))  #adding variable to the dataframe.

#ghcn = transform(ghcn,Northness_w = sin(slope)*cos(ASPECT)) #Adding a variable to the dataframe

#ghcn = transform(ghcn,Eastness_w = sin(slope)*sin(ASPECT))  #adding variable to the dataframe.

ghcn = transform(ghcn,Northness_w = sin(slope*pi/180)*cos(ASPECT*pi/180)) #Adding a variable to the dataframe

ghcn = transform(ghcn,Eastness_w = sin(slope*pi/180)*sin(ASPECT*pi/180))  #adding variable to the dataframe.

#Remove NA for LC and CANHEIGHT

ghcn$LC1[is.na(ghcn$LC1)]<-0

ghcn$LC3[is.na(ghcn$LC3)]<-0

ghcn$CANHEIGHT[is.na(ghcn$CANHEIGHT)]<-0

set.seed(seed_number)                        #Using a seed number allow results based on random number to be compared...

dates <-readLines(paste(path,"/",infile2, sep=""))

LST_dates <-readLines(paste(path,"/",infile3, sep=""))

models <-readLines(paste(path,"/",infile4, sep=""))

#Model assessment: specific diagnostic/metrics for GAM

results_AIC<- matrix(1,length(dates),length(models)+3)  

results_GCV<- matrix(1,length(dates),length(models)+3)

results_DEV<- matrix(1,length(dates),length(models)+3)

results_RMSE_f<- matrix(1,length(dates),length(models)+3)

#Model assessment: general diagnostic/metrics 

results_RMSE <- matrix(1,length(dates),length(models)+4)

results_MAE <- matrix(1,length(dates),length(models)+4)

results_ME <- matrix(1,length(dates),length(models)+4)       #There are 8+1 models

results_R2 <- matrix(1,length(dates),length(models)+4)       #Coef. of determination for the validation dataset

results_RMSE_f<- matrix(1,length(dates),length(models)+4)    #RMSE fit, RMSE for the training dataset

results_RMSE_f_kr<- matrix(1,length(dates),length(models)+4)

# #Tracking relationship between LST AND LC

# cor_LST_LC1<-matrix(1,10,1)      #correlation LST-LC1

# cor_LST_LC3<-matrix(1,10,1)      #correlation LST-LC3

# cor_LST_tmax<-matrix(1,10,1)     #correlation LST-tmax

#Screening for bad values: value is tmax in this case

#ghcn$value<-as.numeric(ghcn$value)

ghcn_all<-ghcn

ghcn_test<-subset(ghcn,ghcn$value>-150 & ghcn$value<400)

ghcn_test2<-subset(ghcn_test,ghcn_test$ELEV_SRTM>0)

ghcn<-ghcn_test2

#coords<- ghcn[,c('x_OR83M','y_OR83M')]

month_var<-c("mm_01","mm_02","mm_03","mm_04","mm_05","mm_06","mm_07","mm_08","mm_09", "mm_10", "mm_11", "mm_12")

ghcn.subsets <-lapply(dates, function(d) subset(ghcn, date==d)) #this creates a list of 10 or 365 subsets dataset based on dates

#Start loop here...

## looping through the dates...this is the main part of the code

#i=1 #for debugging

#j=1 #for debugging

for(i in 1:length(dates)){            # start of the for loop #1

  date<-strptime(dates[i], "%Y%m%d")   # interpolation date being processed

  month<-strftime(date, "%m")          # current month of the date being processed

  LST_month<-paste("mm_",month,sep="") # name of LST month to be matched

  ###Regression part 1: Creating a validation dataset by creating training and testing datasets

  mod_LST <-ghcn.subsets[[i]][,match(LST_month, names(ghcn.subsets[[i]]))]  #Match interpolation date and monthly LST average

  ghcn.subsets[[i]] = transform(ghcn.subsets[[i]],LST = mod_LST)            #Add the variable LST to the subset dataset

  n<-nrow(ghcn.subsets[[i]])

  ns<-n-round(n*prop)   #Create a sample from the data frame with 70% of the rows

  nv<-n-ns              #create a sample for validation with prop of the rows

  ind.training <- sample(nrow(ghcn.subsets[[i]]), size=ns, replace=FALSE) #This selects the index position for 70% of the rows taken randomly

  ind.testing <- setdiff(1:nrow(ghcn.subsets[[i]]), ind.training)

  data_s <- ghcn.subsets[[i]][ind.training, ]   #Training dataset currently used in the modeling

  data_v <- ghcn.subsets[[i]][ind.testing, ]    #Testing/validation dataset

  #i=1

  date_proc<-dates[i]

  date_proc<-strptime(dates[i], "%Y%m%d")   # interpolation date being processed

  mo<-as.integer(strftime(date_proc, "%m"))          # current month of the date being processed

  day<-as.integer(strftime(date_proc, "%d"))

  year<-as.integer(strftime(date_proc, "%Y"))

  #setup

  #mo=9           #Commented out by Benoit on June 14

  #day=2

  #year=2010

  datelabel=format(ISOdate(year,mo,day),"%b %d, %Y")

  ###########

  #  STEP 1 - 10 year monthly averages

  ###########

  #library(raster)

  #old<-getwd()

  #setwd("c:/data/benoit/data_Oregon_stations_Brian_04242012")

  #l=list.files(pattern="mean_month.*rescaled.tif")

  l=list.files(pattern="mean_month.*rescaled.rst")

  molst<-stack(l)  #Creating a raster stack...

  #setwd(old)

  molst=molst-273.16  #K->C

  idx <- seq(as.Date('2010-01-15'), as.Date('2010-12-15'), 'month')

  molst <- setZ(molst, idx)

  layerNames(molst) <- month.abb

  themolst<-raster(molst,mo) #current month being processed saved in a raster image

  plot(themolst)

  ###########

  # STEP 2 - Weather station means across same days: Monthly mean calculation

  ###########

  # ??? which years & what quality flags???

  #select ghcn.id, lat,lon, elev, month, avg(value/10) as "TMax", count(*) as "NumDays" from ghcn, stations where ghcn.id in (select id from stations where state=='OR') and ghcn.id==stations.id and value<>-9999 and year>=2000 and  element=='TMAX' group by stations.id, month;select ghcn.id, lat,lon, elev, month, avg(value/10) as "TMax", count(*) as "NumDays" from ghcn, stations where ghcn.id in (select id from stations where state=='OR') and ghcn.id==stations.id and value<>-9999 and year>=2000 and  element=='TMAX' group by stations.id, month;

  #below table from above SQL query

  #dst<-read.csv('/data/benoit/data_oregon_stations_brian_04242012/station_means.csv',h=T)

  ##Added by Benoit ######

  date1<-ISOdate(data3$year,data3$month,data3$day) #Creating a date object from 3 separate column

  date2<-as.POSIXlt(as.Date(date1))

  data3$date<-date2

  d<-subset(data3,year>=2000 & mflag=="0" ) #Selecting dataset 2000-2010 with good quality

  #May need some screeing??? i.e. range of temp and elevation...

  d1<-aggregate(value~station+month, data=d, mean)  #Calculate monthly mean for every station in OR

  id<-as.data.frame(unique(d1$station))     #Unique station in OR for year 2000-2010      

  dst<-merge(d1, stat_loc, by.x="station", by.y="STAT_ID")   #Inner join all columns are retained

  #This allows to change only one name of the data.frame

  pos<-match("value",names(dst)) #Find column with name "value"

  names(dst)[pos]<-c("TMax")

  dst$TMax<-dst$TMax/10                #TMax is the average max temp for months

  #dstjan=dst[dst$month==9,]  #dst contains the monthly averages for tmax for every station over 2000-2010

  ##############

  modst=dst[dst$month==mo,] #Subsetting dataset for the relevnat month of the date being processed

  ##########

  # STEP 3 - get LST at stations

  ##########

  sta_lola=modst[,c("lon","lat")] #Extracting locations of stations for the current month...

  library(rgdal)

  proj_str="+proj=lcc +lat_1=43 +lat_2=45.5 +lat_0=41.75 +lon_0=-120.5 +x_0=400000 +y_0=0 +ellps=GRS80 +units=m +no_defs";

  lookup<-function(r,lat,lon) {

    xy<-project(cbind(lon,lat),proj_str);

    cidx<-cellFromXY(r,xy);

    return(r[cidx])

  }

  sta_tmax_from_lst=lookup(themolst,sta_lola$lat,sta_lola$lon) #Extracted values of LST for the stations

  #########

  # STEP 4 - bias at stations     

  #########

  sta_bias=sta_tmax_from_lst-modst$TMax; #That is the difference between the monthly LST mean and monthly station mean

  #Added by Benoit

  modst$LSTD_bias<-sta_bias  #Adding bias to data frame modst containning the monthly average for 10 years

  bias_xy=project(as.matrix(sta_lola),proj_str)

  # windows()

  X11()

  plot(modst$TMax,sta_tmax_from_lst,xlab="Station mo Tmax",ylab="LST mo Tmax",main=paste("LST vs TMax for",datelabel,sep=" "))

  abline(0,1)

  savePlot(paste("LST_TMax_scatterplot_",dates[i],out_prefix,".png", sep=""), type="png")

  dev.off()

  ########

  # STEP 5 - interpolate bias

  ########

  # ?? include covariates like elev, distance to coast, cloud frequency, tree height

  #library(fields)

  #windows()

  quilt.plot(sta_lola,sta_bias,main="Bias at stations",asp=1)

  US(add=T,col="magenta",lwd=2)

  #fitbias<-Tps(bias_xy,sta_bias) #use TPS or krige

  fitbias<-Krig(bias_xy,sta_bias,theta=1e5) #use TPS or krige 

                                            #The output is a krig object using fields

  # Creating plot of bias surface and saving it

  X11()

  datelabel2=format(ISOdate(year,mo,day),"%B ") #added by Benoit, label

  surface(fitbias,col=rev(terrain.colors(100)),asp=1,main=paste("Interpolated bias for",datelabel2,sep=" "))

  savePlot(paste("Bias_surface_LST_TMax_",dates[i],out_prefix,".png", sep=""), type="png")

  dev.off()

  #US(add=T,col="magenta",lwd=2)

  ##########

  # STEP 6 - return to daily station data & calcualate delta=daily T-monthly T from stations

  ##########

  #Commmented out by Benoit 06/14

  # library(RSQLite)

  # m<-dbDriver("SQLite")

  # con<-dbConnect(m,dbname='c:/data/ghcn_tmintmax.db')

  # querystr=paste("select ghcn.id, value as 'dailyTmax' from ghcn where ghcn.id in (select id from stations where state=='OR') and value<>-9999",

  #    "and year==",year,"and month==",mo,"and day==",day,

  #                "and element=='TMAX' ")

  # rs<-dbSendQuery(con,querystr)

  # d<-fetch(rs,n=-1)

  # dbClearResult(rs)

  # dbDisconnect(con)

  # 

  # d$dailyTmax=d$dailyTmax/10 #stored as 1/10 degree C to allow integer storage

  # dmoday=merge(modst,d,by="id")

  ##########################Commented out by Benoit

  #added by Benoit 

  #x<-ghcn.subsets[[i]]  #Holds both training and testing for instance 161 rows for Jan 1

  x<-data_v

  d<-data_s

  pos<-match("value",names(d)) #Find column with name "value"

  names(d)[pos]<-c("dailyTmax")

  names(x)[pos]<-c("dailyTmax")

  d$dailyTmax=(as.numeric(d$dailyTmax))/10 #stored as 1/10 degree C to allow integer storage

  x$dailyTmax=(as.numeric(x$dailyTmax))/10 #stored as 1/10 degree C to allow integer storage

  pos<-match("station",names(d)) #Find column with name "value"

  names(d)[pos]<-c("id")

  names(x)[pos]<-c("id")

  names(modst)[1]<-c("id")       #modst contains the average tmax per month for every stations...

  dmoday=merge(modst,d,by="id")  #LOOSING DATA HERE!!! from 113 t0 103

  xmoday=merge(modst,x,by="id")  #LOOSING DATA HERE!!! from 48 t0 43

  names(dmoday)[4]<-c("lat")

  names(dmoday)[5]<-c("lon")     #dmoday contains all the the information: BIAS, monn

  names(xmoday)[4]<-c("lat")

  names(xmoday)[5]<-c("lon")     #dmoday contains all the the information: BIAS, monn

  data_v<-xmoday

  ###

  #dmoday contains the daily tmax values with TMax being the monthly station tmax mean

  #dmoday contains the daily tmax values with TMax being the monthly station tmax mean

  # windows()

  X11()

  plot(dailyTmax~TMax,data=dmoday,xlab="Mo Tmax",ylab=paste("Daily for",datelabel),main="across stations in OR")

  savePlot(paste("Daily_tmax_monthly_TMax_scatterplot_",dates[i],out_prefix,".png", sep=""), type="png")

  dev.off()

  ##########

  # STEP 7 - interpolate delta across space

  ##########

  daily_sta_lola=dmoday[,c("lon","lat")] #could be same as before but why assume merge does this - assume not

  daily_sta_xy=project(as.matrix(daily_sta_lola),proj_str)

  daily_delta=dmoday$dailyTmax-dmoday$TMax

  #windows()

  quilt.plot(daily_sta_lola,daily_delta,asp=1,main="Station delta for Jan 15")

  US(add=T,col="magenta",lwd=2)

  #fitdelta<-Tps(daily_sta_xy,daily_delta) #use TPS or krige

  fitdelta<-Krig(daily_sta_xy,daily_delta,theta=1e5) #use TPS or krige

                                                     #Kriging using fields package

  # Creating plot of bias surface and saving it

  X11()

  surface(fitdelta,col=rev(terrain.colors(100)),asp=1,main=paste("Interpolated delta for",datelabel,sep=" "))

  savePlot(paste("Delta_surface_LST_TMax_",dates[i],out_prefix,".png", sep=""), type="png")

  dev.off()

  #US(add=T,col="magenta",lwd=2)

  #

  #### Added by Benoit on 06/19

  data_s<-dmoday #put the 

  data_s$daily_delta<-daily_delta

  #data_s$y_var<-daily_delta  #y_var is the variable currently being modeled, may be better with BIAS!!

  data_s$y_var<-data_s$LSTD_bias

  #data_s$y_var<-(data_s$dailyTmax)*10

  #Model and response variable can be changed without affecting the script

  mod1<- gam(y_var~ s(lat) + s (lon) + s (ELEV_SRTM), data=data_s)

  mod2<- gam(y_var~ s(lat,lon)+ s(ELEV_SRTM), data=data_s) #modified nesting....from 3 to 2

  mod3<- gam(y_var~ s(lat) + s (lon) + s (ELEV_SRTM) +  s (Northness)+ s (Eastness) + s(DISTOC), data=data_s)

  mod4<- gam(y_var~ s(lat) + s (lon) + s(ELEV_SRTM) + s(Northness) + s (Eastness) + s(DISTOC) + s(LST), data=data_s)

  mod5<- gam(y_var~ s(lat,lon) +s(ELEV_SRTM) + s(Northness,Eastness) + s(DISTOC) + s(LST), data=data_s)

  mod6<- gam(y_var~ s(lat,lon) +s(ELEV_SRTM) + s(Northness,Eastness) + s(DISTOC) + s(LST)+s(LC1), data=data_s)

  mod7<- gam(y_var~ s(lat,lon) +s(ELEV_SRTM) + s(Northness,Eastness) + s(DISTOC) + s(LST)+s(LC3), data=data_s)

  mod8<- gam(y_var~ s(lat,lon) +s(ELEV_SRTM) + s(Northness,Eastness) + s(DISTOC) + s(LST) + s(LC1), data=data_s)

  #Added

  #tmax_predicted=themolst+daily_delta_rast-bias_rast #Final surface?? but daily_rst

  #### Added by Benoit ends

  #########

  # STEP 8 - assemble final answer - T=LST+Bias(interpolated)+delta(interpolated)

  #########

  bias_rast=interpolate(themolst,fitbias) #interpolation using function from raster package

                                          #themolst is raster layer, fitbias is "Krig" object from bias surface

  plot(bias_rast,main="Raster bias") #This not displaying...

  daily_delta_rast=interpolate(themolst,fitdelta) #Interpolation of the bias surface...

  plot(daily_delta_rast,main="Raster Daily Delta")

  tmax_predicted=themolst+daily_delta_rast-bias_rast #Final surface  as a raster layer...

  #tmax_predicted=themolst+daily_delta_rast+bias_rast #Added by Benoit, why is it -bias_rast

  plot(tmax_predicted,main="Predicted daily")

  ########

  # check: assessment of results: validation

  ########

  RMSE<-function(x,y) {return(mean((x-y)^2)^0.5)}

  #FIT ASSESSMENT

  sta_pred_data_s=lookup(tmax_predicted,data_s$lat,data_s$lon)

  rmse_fit=RMSE(sta_pred_data_s,data_s$dailyTmax)

  sta_pred=lookup(tmax_predicted,data_v$lat,data_v$lon)

  #sta_pred=lookup(tmax_predicted,daily_sta_lola$lat,daily_sta_lola$lon)

  #rmse=RMSE(sta_pred,dmoday$dailyTmax)

  #pos<-match("value",names(data_v)) #Find column with name "value"

  #names(data_v)[pos]<-c("dailyTmax")

  tmax<-data_v$dailyTmax

  #data_v$dailyTmax<-tmax

  rmse=RMSE(sta_pred,tmax)

  #plot(sta_pred~dmoday$dailyTmax,xlab=paste("Actual daily for",datelabel),ylab="Pred daily",main=paste("RMSE=",rmse))

  X11()

  plot(sta_pred~tmax,xlab=paste("Actual daily for",datelabel),ylab="Pred daily",main=paste("RMSE=",rmse))

  abline(0,1)

  savePlot(paste("Predicted_tmax_versus_observed_scatterplot_",dates[i],out_prefix,".png", sep=""), type="png")

  dev.off()

  #resid=sta_pred-dmoday$dailyTmax

  resid=sta_pred-tmax

  quilt.plot(daily_sta_lola,resid)

  ### END OF BRIAN's code

  ### Added by benoit

  #Store results using TPS

  j=9

  results_RMSE[i,1]<- dates[i]    #storing the interpolation dates in the first column

  results_RMSE[i,2]<- ns          #number of stations used in the training stage

  results_RMSE[i,3]<- "RMSE"

  results_RMSE[i,j+3]<- rmse  #Storing RMSE for the model j

  results_RMSE_f[i,1]<- dates[i]    #storing the interpolation dates in the first column

  results_RMSE_f[i,2]<- ns          #number of stations used in the training stage

  results_RMSE_f[i,3]<- "RMSE"

  results_RMSE_f[i,j+3]<- rmse_fit  #Storing RMSE for the model j

  ns<-nrow(data_s) #This is added to because some loss of data might have happened because of the averaging...

  nv<-nrow(data_v)         

  for (j in 1:length(models)){

    ##Model assessment: specific diagnostic/metrics for GAM

    name<-paste("mod",j,sep="")  #modj is the name of The "j" model (mod1 if j=1) 

    mod<-get(name)               #accessing GAM model ojbect "j"

    results_AIC[i,1]<- dates[i]  #storing the interpolation dates in the first column

    results_AIC[i,2]<- ns        #number of stations used in the training stage

    results_AIC[i,3]<- "AIC"

    results_AIC[i,j+3]<- AIC (mod)

    results_GCV[i,1]<- dates[i]  #storing the interpolation dates in the first column

    results_GCV[i,2]<- ns        #number of stations used in the training 

    results_GCV[i,3]<- "GCV"

    results_GCV[i,j+3]<- mod$gcv.ubre

    results_DEV[i,1]<- dates[i]  #storing the interpolation dates in the first column

    results_DEV[i,2]<- ns        #number of stations used in the training stage

    results_DEV[i,3]<- "DEV"

    results_DEV[i,j+3]<- mod$deviance

    sta_LST_s=lookup(themolst,data_s$lat,data_s$lon)

    sta_delta_s=lookup(daily_delta_rast,data_s$lat,data_s$lon) #delta surface has been calculated before!!

    sta_bias_s= mod$fit

    #Need to extract values from the kriged delta surface...

    #sta_delta= lookup(delta_surface,data_v$lat,data_v$lon)

    #tmax_predicted=sta_LST+sta_bias-y_mod$fit

    tmax_predicted_s= sta_LST_s-sta_bias_s+sta_delta_s

    results_RMSE_f[i,1]<- dates[i]  #storing the interpolation dates in the first column

    results_RMSE_f[i,2]<- ns        #number of stations used in the training stage

    results_RMSE_f[i,3]<- "RSME"

    results_RMSE_f[i,j+3]<- sqrt(sum((tmax_predicted_s-data_s$dailyTmax)^2)/ns)

    ##Model assessment: general diagnostic/metrics

    ##validation: using the testing data

    #This was modified on 06192012

    #data_v$y_var<-data_v$LSTD_bias

    #data_v$y_var<-tmax

    y_mod<- predict(mod, newdata=data_v, se.fit = TRUE) #Using the coeff to predict new values.

    ####ADDED ON JULY 5th

    sta_LST_v=lookup(themolst,data_v$lat,data_v$lon)

    sta_delta_v=lookup(daily_delta_rast,data_v$lat,data_v$lon) #delta surface has been calculated before!!

    sta_bias_v= y_mod$fit

    #Need to extract values from the kriged delta surface...

    #sta_delta= lookup(delta_surface,data_v$lat,data_v$lon)

    #tmax_predicted=sta_LST+sta_bias-y_mod$fit

    tmax_predicted_v= sta_LST_v-sta_bias_v+sta_delta_v

    #data_v$tmax<-(data_v$tmax)/10

    res_mod<- data_v$dailyTmax - tmax_predicted_v              #Residuals for the model for fusion

    #res_mod<- data_v$y_var - y_mod$fit                  #Residuals for the model

    RMSE_mod <- sqrt(sum(res_mod^2)/nv)                 #RMSE FOR REGRESSION STEP 1: GAM     

    MAE_mod<- sum(abs(res_mod))/nv                     #MAE, Mean abs. Error FOR REGRESSION STEP 1: GAM   

    ME_mod<- sum(res_mod)/nv                            #ME, Mean Error or bias FOR REGRESSION STEP 1: GAM

    R2_mod<- cor(data_v$dailyTmax,tmax_predicted_v)^2              #R2, coef. of var FOR REGRESSION STEP 1: GAM

    results_RMSE[i,1]<- dates[i]    #storing the interpolation dates in the first column

    results_RMSE[i,2]<- ns          #number of stations used in the training stage

    results_RMSE[i,3]<- "RMSE"

    results_RMSE[i,j+3]<- RMSE_mod  #Storing RMSE for the model j

    results_MAE[i,1]<- dates[i]     #storing the interpolation dates in the first column

    results_MAE[i,2]<- ns           #number of stations used in the training stage

    results_MAE[i,3]<- "MAE"

    results_MAE[i,j+3]<- MAE_mod    #Storing MAE for the model j

    results_ME[i,1]<- dates[i]      #storing the interpolation dates in the first column

    results_ME[i,2]<- ns            #number of stations used in the training stage

    results_ME[i,3]<- "ME"

    results_ME[i,j+3]<- ME_mod      #Storing ME for the model j

    results_R2[i,1]<- dates[i]      #storing the interpolation dates in the first column

    results_R2[i,2]<- ns            #number of stations used in the training stage

    results_R2[i,3]<- "R2"

    results_R2[i,j+3]<- R2_mod      #Storing R2 for the model j

    #Saving residuals and prediction in the dataframes: tmax predicted from GAM

    pred<-paste("pred_mod",j,sep="")

    #data_v[[pred]]<-as.numeric(y_mod$fit)

    data_v[[pred]]<-as.numeric(tmax_predicted_v)

    data_s[[pred]]<-as.numeric(tmax_predicted_s) #Storing model fit values (predicted on training sample)

    #data_s[[pred]]<-as.numeric(mod$fit) #Storing model fit values (predicted on training sample)

    name2<-paste("res_mod",j,sep="")

    data_v[[name2]]<-as.numeric(res_mod)

    temp<-tmax_predicted_s-data_s$dailyTmax

    data_s[[name2]]<-as.numeric(temp)

    #end of loop calculating RMSE

  }

  # end of the for loop1

}

## Plotting and saving diagnostic measures

#Specific diagnostic measures related to the testing datasets

results_table_RMSE<-as.data.frame(results_RMSE)

results_table_MAE<-as.data.frame(results_MAE)

results_table_ME<-as.data.frame(results_ME)

results_table_R2<-as.data.frame(results_R2)

results_table_RMSE_f<-as.data.frame(results_RMSE_f)

cname<-c("dates","ns","metric","mod1", "mod2","mod3", "mod4", "mod5", "mod6", "mod7","mod8","mod9")

colnames(results_table_RMSE)<-cname

colnames(results_table_RMSE_f)<-cname

#tb_diagnostic1<-rbind(results_table_RMSE,results_table_MAE, results_table_ME, results_table_R2)   #

tb_diagnostic1<-results_table_RMSE      #measures of validation

tb_diagnostic2<-results_table_RMSE_f    #measures of fit

write.table(tb_diagnostic1, file= paste(path,"/","results_fusion_Assessment_measure1",out_prefix,".txt",sep=""), sep=",")

write.table(tb_diagnostic2, file= paste(path,"/","results_fusion_Assessment_measure2",out_prefix,".txt",sep=""), sep=",")

#### END OF SCRIPT