runGAMFusion <- function(i) {            # loop over dates

  date<-strptime(sampling_dat$date[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

  #Adding layer LST to the raster stack

  pos<-match("LST",layerNames(s_raster)) #Find the position of the layer with name "LST", if not present pos=NA

  s_raster<-dropLayer(s_raster,pos)      # If it exists drop layer

  pos<-match(LST_month,layerNames(s_raster)) #Find column with the current month for instance mm12

  r1<-raster(s_raster,layer=pos)             #Select layer from stack

  layerNames(r1)<-"LST"

  #Screen for extreme values" 10/30

  min_val<-(-15+273.16) #if values less than -15C then screen out (note the Kelvin units that will need to be changed later in all datasets)

  r1[r1 < (min_val)]<-NA

  s_raster<-addLayer(s_raster,r1)            #Adding current month

  ###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

  dst$LST<-dst[[LST_month]]

  #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.training<-sampling[[i]]

  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 using input sampling

  ns<-nrow(data_s)

  nv<-nrow(data_v)

  #i=1

  date_proc<-sampling_dat$date[i]

  date_proc<-strptime(sampling_dat$date[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"))

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

  ###########

  #  STEP 1 - LST 10 year monthly averages

  ###########

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

  min_val<-(-15)     #Screening for extreme values

  themolst[themolst < (min_val)]<-NA

  plot(themolst)

  ###########

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

  ###########

  modst<-dst[dst$month==mo,] #Subsetting dataset for the relevant 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..

  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)

  png(paste("LST_TMax_scatterplot_",sampling_dat$date[i],"_",sampling_dat$prop[i],"_",sampling_dat$run_samp[i], out_prefix,".png", sep=""))

  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)

  dev.off()

  #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(d)[pos]<-y_var_name

  names(x)[pos]<-y_var_name

  #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",suffixes=c("",".y2"))  #LOOSING DATA HERE!!! from 113 t0 103

  xmoday=merge(modst,x,by="id",suffixes=c("",".y2"))  #LOOSING DATA HERE!!! from 48 t0 43

  mod_pat<-glob2rx("*.y2")   

  var_pat<-grep(mod_pat,names(dmoday),value=FALSE) # using grep with "value" extracts the matching names

  dmoday<-dmoday[,-var_pat]

  mod_pat<-glob2rx("*.y2")   

  var_pat<-grep(mod_pat,names(xmoday),value=FALSE) # using grep with "value" extracts the matching names

  xmoday<-xmoday[,-var_pat] #Removing duplicate columns

  data_v<-xmoday

  ###

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

  #xmoday contains the daily tmax values for validation with TMax being the monthly station tmax mean

  png(paste("Daily_tmax_monthly_TMax_scatterplot_",sampling_dat$date[i],"_",sampling_dat$prop[i],

            "_",sampling_dat$run_samp[i],out_prefix,".png", sep=""))

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

  dev.off()

  ########

  # STEP 5 - interpolate bias

  ########

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

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

  #Adding options to use only training stations : 07/11/2012

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

  #bias_xy2=project(as.matrix(c(dmoday$lon,dmoday$lat),proj_str)

  if(bias_val==1){

    sta_bias<-dmoday$LSTD_bias

    bias_xy<-cbind(dmoday$x_OR83M,dmoday$y_OR83M)

  }

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

  #The output is a krig object using fields: modif 10/30

  #mod9a<-fitbias

  mod_krtmp1<-fitbias

  model_name<-paste("mod_kr","month",sep="_")

  assign(model_name,mod_krtmp1)

  ##########

  # 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

  #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: modif 10/30

  #mod9b<-fitdelta

  mod_krtmp2<-fitdelta

  model_name<-paste("mod_kr","day",sep="_")

  assign(model_name,mod_krtmp2)

  png(paste("Delta_surface_LST_TMax_",sampling_dat$date[i],"_",sampling_dat$prop[i],

            "_",sampling_dat$run_samp[i],out_prefix,".png", sep=""))

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

  dev.off()

  #

  #### 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

  #### 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...

  #Saving kriged surface in raster images

  data_name<-paste("bias_LST_",sampling_dat$date[i],"_",sampling_dat$prop[i],

                   "_",sampling_dat$run_samp[i],sep="")

  raster_name<-paste("fusion_",data_name,out_prefix,".rst", sep="")

  writeRaster(bias_rast, filename=raster_name,overwrite=TRUE)  #Writing the data in a raster file format...(IDRISI)

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

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

  #Saving kriged surface in raster images

  data_name<-paste("daily_delta_",sampling_dat$date[i],"_",sampling_dat$prop[i],

                   "_",sampling_dat$run_samp[i],sep="")

  raster_name<-paste("fusion_",data_name,out_prefix,".rst", sep="")

  writeRaster(daily_delta_rast, filename=raster_name,overwrite=TRUE)  #Writing the data in a raster file format...(IDRISI)

  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")

  #Saving kriged surface in raster images

  data_name<-paste("tmax_predicted_",sampling_dat$date[i],"_",sampling_dat$prop[i],

                   "_",sampling_dat$run_samp[i],sep="")

  raster_name<-paste("fusion_",data_name,out_prefix,".rst", sep="")

  writeRaster(tmax_predicted, filename=raster_name,overwrite=TRUE)  #Writing the data in a raster file format...(IDRISI)

  ########

  # check: assessment of results: validation

  ########

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

  MAE_fun<-function(x,y) {return(mean(abs(x-y)))}

  #ME_fun<-function(x,y){return(mean(abs(y)))}

  #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)

  mae_fit=MAE_fun(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)

  mae<-MAE_fun(sta_pred,tmax)

  r2<-cor(sta_pred,tmax)^2              #R2, coef. of var

  me<-mean(sta_pred-tmax)

  png(paste("Predicted_tmax_versus_observed_scatterplot_",sampling_dat$date[i],"_",sampling_dat$prop[i],

            "_",sampling_dat$run_samp[i],out_prefix,".png", sep=""))

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

  abline(0,1)

  dev.off()

  #resid=sta_pred-dmoday$dailyTmax

  resid=sta_pred-tmax

  ###BEFORE GAM prediction the data object must be transformed to SDF

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

  coordinates(data_v)<-coords

  proj4string(data_v)<-CRS  #Need to assign coordinates...

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

  coordinates(data_s)<-coords

  proj4string(data_s)<-CRS  #Need to assign coordinates..

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

  coordinates(modst)<-coords

  proj4string(modst)<-CRS  #Need to assign coordinates..

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

  nv<-nrow(data_v)

  ###GAM PREDICTION

  if (bias_prediction==1){

    data_s$y_var<-data_s$LSTD_bias  #This shoudl be changed for any variable!!!

    data_v$y_var<-data_v$LSTD_bias

    data_month<-modst

    data_month$y_var<-modst$LSTD_bias

  }

  if (bias_prediction==0){

    data_v$y_var<-data_v[[y_var_name]]

    data_s$y_var<-data_s[[y_var_name]]

  }

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

  list_formulas<-vector("list",nmodels)

  list_formulas[[1]] <- as.formula("y_var ~ s(ELEV_SRTM)", env=.GlobalEnv)

  list_formulas[[2]] <- as.formula("y_var ~ s(LST)", env=.GlobalEnv)

  list_formulas[[3]] <- as.formula("y_var ~ s(ELEV_SRTM,LST)", env=.GlobalEnv)

  list_formulas[[4]] <- as.formula("y_var ~ s(lat) + s(lon)+ s(ELEV_SRTM)", env=.GlobalEnv)

  list_formulas[[5]] <- as.formula("y_var ~ s(lat,lon,ELEV_SRTM)", env=.GlobalEnv)

  list_formulas[[6]] <- as.formula("y_var ~ s(lat,lon) + s(ELEV_SRTM) + s(Northness_w,Eastness_w) + s(LST)", env=.GlobalEnv)

  list_formulas[[7]] <- as.formula("y_var ~ s(lat,lon) + s(ELEV_SRTM) + s(Northness_w,Eastness_w) + s(LST) + s(LC1)", env=.GlobalEnv)

  list_formulas[[8]] <- as.formula("y_var ~ s(lat,lon) + s(ELEV_SRTM) + s(Northness_w,Eastness_w) + s(LST) + s(LC3)", env=.GlobalEnv)

  list_formulas[[9]] <- as.formula("y_var ~ s(lat,lon) + s(ELEV_SRTM) + s(Northness_w,Eastness_w) + s(LST) + s(DISTOC)", env=.GlobalEnv)

  #list_formulas[[1]] <- as.formula("y_var ~ s(ELEV_SRTM)", env=.GlobalEnv)

  #list_formulas[[2]] <- as.formula("y_var ~ s(lat,lon)", env=.GlobalEnv)

  #list_formulas[[3]] <- as.formula("y_var~ s(lat,lon,ELEV_SRTM)", env=.GlobalEnv)

  #list_formulas[[4]] <- as.formula("y_var~ s(lat) + s (lon) + s (ELEV_SRTM) + s(DISTOC)", env=.GlobalEnv)

  #list_formulas[[5]] <- as.formula("y_var~ s(lat,lon,ELEV_SRTM) + s(Northness) + s (Eastness) + s(DISTOC)", env=.GlobalEnv)

  #list_formulas[[6]] <- as.formula("y_var~ s(lat,lon) +s(ELEV_SRTM) + s(Northness,Eastness) + s(DISTOC)", env=.GlobalEnv)

  if (bias_prediction==1){

    #mod1<- try(gam(formula1, data=data_month))

    #mod2<- try(gam(formula2, data=data_month)) #modified nesting....from 3 to 2

    #mod3<- try(gam(formula3, data=data_month))

    #mod4<- try(gam(formula4, data=data_month))

    #mod5<- try(gam(formula5, data=data_month))

    #mod6<- try(gam(formula6, data=data_month))

    #mod7<- try(gam(formula7, data=data_month))

    #mod8<- try(gam(formula8, data=data_month)) 

    for (j in 1:nmodels){

      formula<-list_formulas[[j]]

      mod<- try(gam(formula, data=data_month))

      model_name<-paste("mod",j,sep="")

      assign(model_name,mod) 

    }

  } else if (bias_prediction==0){      #Use daily data for direct prediction using GAM

    #mod1<- try(gam(formula1, data=data_s))

    #mod2<- try(gam(formula2, data=data_s)) #modified nesting....from 3 to 2

    #mod3<- try(gam(formula3, data=data_s))

    #mod4<- try(gam(formula4, data=data_s))

    #mod5<- try(gam(formula5, data=data_s))

    #mod6<- try(gam(formula6, data=data_s))

    #mod7<- try(gam(formula7, data=data_s))

    #mod8<- try(gam(formula8, data=data_s))

    for (j in 1:nmodels){

      formula<-list_formulas[[j]]

      mod<- try(gam(formula, data=data_s))

      model_name<-paste("mod",j,sep="")

      assign(model_name,mod) 

    }

  }

  #Added

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

  ### Added by benoit

  #Store results using TPS

  j=nmodels+1

  results_RMSE[1]<- sampling_dat$date[i]    #storing the interpolation dates in the first column

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

  results_RMSE[3]<- "RMSE"

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

  results_RMSE_f[1]<- sampling_dat$date[i]    #storing the interpolation dates in the first column

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

  results_RMSE_f[3]<- "RMSE_f"

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

  results_MAE_f[1]<- sampling_dat$date[i]    #storing the interpolation dates in the first column

  results_MAE_f[2]<- ns          #number of stations used in the training stage

  results_MAE_f[3]<- "RMSE_f"

  results_MAE_f[j+3]<- mae_fit  #Storing RMSE for the model j

  results_MAE[1]<- sampling_dat$date[i]    #storing the interpolation dates in the first column

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

  results_MAE[3]<- "MAE"

  results_MAE[j+3]<- mae  #Storing RMSE for the model j

  results_ME[1]<- sampling_dat$date[i]    #storing the interpolation dates in the first column

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

  results_ME[3]<- "ME"

  results_ME[j+3]<- me  #Storing RMSE for the model j

  results_R2[1]<- sampling_dat$date[i]    #storing the interpolation dates in the first column

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

  results_R2[3]<- "R2"

  results_R2[j+3]<- r2  #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)

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

  #Adding the results back into the original dataframes.

  data_s[[pred_mod]]<-sta_pred_data_s

  data_v[[pred_mod]]<-sta_pred 

  #Model assessment: RMSE and then krig the residuals....!

  res_mod_s<- data_s$dailyTmax - data_s[[pred_mod]]           #Residuals from kriging training

  res_mod_v<- data_v$dailyTmax - data_v[[pred_mod]]           #Residuals from kriging validation

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

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

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

  mod_obj<-vector("list",nmodels+2)  #This will contain the model objects fitting: 10/30

  mod_obj[[nmodels+1]]<-mod_kr_month  #Storing climatology object

  mod_obj[[nmodels+2]]<-mod_kr_day  #Storing delta object

  for (j in 1:nmodels){

    ##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"

    mod_obj[[j]]<-mod  #storing current model object

    #If mod "j" is not a model object

    if (inherits(mod,"try-error")) {

      results_AIC[1]<- sampling_dat$date[i]  #storing the interpolation dates in the first column

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

      results_AIC[3]<- "AIC"

      results_AIC[j+3]<- NA

      results_GCV[1]<- sampling_dat$date[i]  #storing the interpolation dates in the first column

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

      results_GCV[3]<- "GCV"

      results_GCV[j+3]<- NA

      results_DEV[1]<- sampling_dat$date[i]  #storing the interpolation dates in the first column

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

      results_DEV[3]<- "DEV"

      results_DEV[j+3]<- NA

      results_RMSE_f[1]<- sampling_dat$date[i]  #storing the interpolation dates in the first column

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

      results_RMSE_f[3]<- "RSME_f"

      results_RMSE_f[j+3]<- NA

      results_MAE_f[1]<- sampling_dat$date[i]  #storing the interpolation dates in the first column

      results_MAE_f[2]<- ns        #number of stations used in the training stage

      results_MAE_f[3]<- "MAE_f"

      results_MAE_f[j+3]<-NA

      results_RMSE[1]<- sampling_dat$date[i]    #storing the interpolation dates in the first column

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

      results_RMSE[3]<- "RMSE"

      results_RMSE[j+3]<- NA  #Storing RMSE for the model j

      results_MAE[1]<- sampling_dat$date[i]     #storing the interpolation dates in the first column

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

      results_MAE[3]<- "MAE"

      results_MAE[j+3]<- NA    #Storing MAE for the model j

      results_ME[1]<- sampling_dat$date[i]      #storing the interpolation dates in the first column

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

      results_ME[3]<- "ME"

      results_ME[j+3]<- NA      #Storing ME for the model j

      results_R2[1]<- sampling_dat$date[i]      #storing the interpolation dates in the first column

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

      results_R2[3]<- "R2"

      results_R2[j+3]<- NA      #Storing R2 for the model j

    }

    #If mod is a modelobject

    #If mod "j" is not a model object

    if (inherits(mod,"gam")) {

      results_AIC[1]<- sampling_dat$date[i]  #storing the interpolation dates in the first column

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

      results_AIC[3]<- "AIC"

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

      results_GCV[1]<- sampling_dat$date[i]  #storing the interpolation dates in the first column

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

      results_GCV[3]<- "GCV"

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

      results_DEV[1]<- sampling_dat$date[i]  #storing the interpolation dates in the first column

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

      results_DEV[3]<- "DEV"

      results_DEV[j+3]<- mod$deviance

      y_var_fit= mod$fit

      results_RMSE_f[1]<- sampling_dat$date[i]  #storing the interpolation dates in the first column

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

      results_RMSE_f[3]<- "RSME_f"

      #results_RMSE_f[j+3]<- sqrt(sum((y_var_fit-data_s$y_var)^2)/ns)

      results_RMSE_f[j+3]<-sqrt(mean(mod$residuals^2,na.rm=TRUE))

      results_MAE_f[1]<- sampling_dat$date[i]  #storing the interpolation sampling_dat$date in the first column

      results_MAE_f[2]<- ns        #number of stations used in the training stage

      results_MAE_f[3]<- "MAE_f"

      #results_MAE_f[j+3]<-sum(abs(y_var_fit-data_s$y_var))/ns

      results_MAE_f[j+3]<-mean(abs(mod$residuals),na.rm=TRUE)

      ##Model assessment: general diagnostic/metrics

      ##validation: using the testing data

      if (predval==1) {

        ##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"

        s_sgdf<-as(s_raster,"SpatialGridDataFrame") #Conversion to spatial grid data frame

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

        y_pred<-rpred$fit #rpred is a list with fit being and array

        raster_pred<-r1

        layerNames(raster_pred)<-"y_pred"

        values(raster_pred)<-as.numeric(y_pred)

        if (bias_prediction==1){

          data_name<-paste("predicted_mod",j,"_",sampling_dat$date[i],"_",sampling_dat$prop[i],

                           "_",sampling_dat$run_samp[i],sep="")

          raster_name<-paste("GAM_bias_",data_name,out_prefix,".rst", sep="")

          writeRaster(raster_pred, filename=raster_name,overwrite=TRUE)  #Writing the data in a raster file format...(IDRISI)

          bias_rast<-raster_pred

          raster_pred=themolst+daily_delta_rast-bias_rast #Final surface  as a raster layer...wiht daily surface calculated earlier...

          layerNames(raster_pred)<-"y_pred"

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

          data_name<-paste("predicted_mod",j,"_",sampling_dat$date[i],"_",sampling_dat$prop[i],

                           "_",sampling_dat$run_samp[i],sep="")

          raster_name<-paste("GAM_bias_tmax_",data_name,out_prefix,".rst", sep="")

          writeRaster(raster_pred, filename=raster_name,overwrite=TRUE)  #Writing the data in a raster file format...(IDRISI)

        }

        if (bias_prediction==0){

          data_name<-paste("predicted_mod",j,"_",sampling_dat$date[i],"_",sampling_dat$prop[i],

                           "_",sampling_dat$run_samp[i],sep="")

          raster_name<-paste("GAM_",data_name,out_prefix,".rst", sep="")

          writeRaster(raster_pred, filename=raster_name,overwrite=TRUE)  #Writing the data in a raster file format...(IDRISI)

          #writeRaster(r2, filename=raster_name,overwrite=TRUE)  #Writing the data in a raster file format...(IDRISI)

        }

        pred_sgdf<-as(raster_pred,"SpatialGridDataFrame") #Conversion to spatial grid data frame

        #rpred_val_s <- overlay(raster_pred,data_s)             #This overlays the kriged surface tmax and the location of weather stations

        rpred_val_s <- overlay(pred_sgdf,data_s)             #This overlays the interpolated surface tmax and the location of weather stations

        rpred_val_v <- overlay(pred_sgdf,data_v)             #This overlays the interpolated surface tmax and the location of weather stations

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

        #Adding the results back into the original dataframes.

        data_s[[pred_mod]]<-rpred_val_s$y_pred

        data_v[[pred_mod]]<-rpred_val_v$y_pred  

        #Model assessment: RMSE and then krig the residuals....!

        res_mod_s<-data_s[[y_var_name]] - data_s[[pred_mod]] #residuals from modeling training

        res_mod_v<-data_v[[y_var_name]] - data_v[[pred_mod]] #residuals from modeling validation

      }

      if (predval==0) {

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

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

        #Adding the results back into the original dataframes.

        data_s[[pred_mod]]<-as.numeric(mod$fit)

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

        #Model assessment: RMSE and then krig the residuals....!

        #res_mod_s<- data_s$y_var - data_s[[pred_mod]]           #Residuals from modeling training

        #res_mod_v<- data_v$y_var - data_v[[pred_mod]]           #Residuals from modeling validation

        res_mod_s<-data_s[[y_var_name]] - data_s[[pred_mod]]

        res_mod_v<-data_v[[y_var_name]] - data_v[[pred_mod]]

      }

      ####ADDED ON JULY 20th

      res_mod<-res_mod_v

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

      RMSE_mod<- sqrt(mean(res_mod^2,na.rm=TRUE))

      #MAE_mod<- sum(abs(res_mod),na.rm=TRUE)/(nv-sum(is.na(res_mod)))        #MAE from kriged surface validation

      MAE_mod<- mean(abs(res_mod), na.rm=TRUE)

      #ME_mod<- sum(res_mod,na.rm=TRUE)/(nv-sum(is.na(res_mod)))                    #ME, Mean Error or bias FOR REGRESSION STEP 1: GAM

      ME_mod<- mean(res_mod,na.rm=TRUE)                            #ME, Mean Error or bias FOR REGRESSION STEP 1: GAM

      #R2_mod<- cor(data_v$y_var,data_v[[pred_mod]])^2              #R2, coef. of var FOR REGRESSION STEP 1: GAM

      R2_mod<- cor(data_v$y_var,data_v[[pred_mod]], use="complete")^2

      results_RMSE[1]<- sampling_dat$date[i]    #storing the interpolation sampling_dat$date in the first column

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

      results_RMSE[3]<- "RMSE"

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

      results_MAE[1]<- sampling_dat$date[i]     #storing the interpolation dates in the first column

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

      results_MAE[3]<- "MAE"

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

      results_ME[1]<- sampling_dat$date[i]      #storing the interpolation dates in the first column

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

      results_ME[3]<- "ME"

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

      results_R2[1]<- sampling_dat$date[i]      #storing the interpolation dates in the first column

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

      results_R2[3]<- "R2"

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

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

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

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

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

      #end of loop calculating RMSE

    }

  }

  #if (i==length(dates)){

  #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)

  results_table_MAE_f<-as.data.frame(results_MAE_f)

  results_table_AIC<-as.data.frame(results_AIC)

  results_table_GCV<-as.data.frame(results_GCV)

  results_table_DEV<-as.data.frame(results_DEV)

  tb_metrics1<-rbind(results_table_RMSE,results_table_MAE, results_table_ME, results_table_R2,results_table_RMSE_f,results_table_MAE_f)   #

  tb_metrics2<-rbind(results_table_AIC,results_table_GCV, results_table_DEV)

  #Preparing labels 10/30

  mod_labels<-rep("mod",nmodels+1)

  index<-as.character(1:(nmodels+1))

  mod_labels<-paste(mod_labels,index,sep="")

  cname<-c("dates","ns","metric", mod_labels)

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

  colnames(tb_metrics1)<-cname

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

  #colnames(tb_metrics2)<-cname

  colnames(tb_metrics2)<-cname[1:(nmodels+3)]

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

  #}  

  print(paste(sampling_dat$date[i],"processed"))

  # end of the for loop1

  #mod_obj<-list(mod1,mod2,mod3,mod4,mod5,mod6,mod7,mod8,mod9a,mod9b)

  #names(mod_obj)<-c("mod1","mod2","mod3","mod4","mod5","mod6","mod7","mod8","mod9a","mod9b")

  mod_labels_kr<-c("mod_kr_month", "mod_kr_day")

  names(mod_obj)<-c(mod_labels[1:nmodels],mod_labels_kr)

  results_list<-list(data_s,data_v,tb_metrics1,tb_metrics2,mod_obj,data_month,list_formulas)

  names(results_list)<-c("data_s","data_v","tb_metrics1","tb_metrics2","mod_obj","data_month","formulas")

  #results_list<-list(data_s,data_v,tb_metrics1,tb_metrics2)

  #results_list<-list(data_s,data_v,tb_metrics1,tb_metrics2,mod_obj,sampling_dat[i,],data_month)

  #names(results_list)<-c("data_s","data_v","tb_metrics1","tb_metrics2","mod_obj","sampling_dat","data_month")

  save(results_list,file= paste(path,"/","results_list_metrics_objects_",sampling_dat$date[i],"_",sampling_dat$prop[i],

                                "_",sampling_dat$run_samp[i],out_prefix,".RData",sep=""))