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

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

  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

  #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"))

  #Adding layer LST to the raster stack

  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"

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

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

  ###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.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)

  ###BEFORE model 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..

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

  nv<-nrow(data_v)

  ### PREDICTION/ Interpolation

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

  names(data_s)[pos]<-y_var_name

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

  names(data_v)[pos]<-y_var_name

  #if y_var_name=="dailyTmax"

  data_v$y_var<-data_v[[y_var_name]]/10  #Note that values are divided by 10 because the var is temp

  data_s$y_var<-data_s[[y_var_name]]/10

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

  formula1 <- as.formula("y_var ~1", env=.GlobalEnv)

  formula2 <- as.formula("y_var~ x_OR83M+y_OR83M", env=.GlobalEnv)

  formula3 <- as.formula("y_var~ x_OR83M+y_OR83M+ELEV_SRTM", env=.GlobalEnv)

  formula4 <- as.formula("y_var~ x_OR83M+y_OR83M+DISTOC", env=.GlobalEnv)

  formula5 <- as.formula("y_var~ x_OR83M+y_OR83M+ELEV_SRTM+DISTOC", env=.GlobalEnv)

  formula6 <- as.formula("y_var~ x_OR83M+y_OR83M+Northness+Eastness", env=.GlobalEnv)

  formula7 <- as.formula("y_var~ LST", env=.GlobalEnv)

  formula8 <- as.formula("y_var~ x_OR83M+y_OR83M+LST", env=.GlobalEnv)

  formula9 <- as.formula("y_var~ x_OR83M+y_OR83M+ELEV_SRTM+LST", env=.GlobalEnv)

  mod1<- try(autoKrige(formula1, input_data=data_s,new_data=s_sgdf,data_variogram=data_s))

  mod2<- try(autoKrige(formula2, input_data=data_s,new_data=s_sgdf,data_variogram=data_s)) 

  mod3<- try(autoKrige(formula3, input_data=data_s,new_data=s_sgdf,data_variogram=data_s))

  mod4<- try(autoKrige(formula4, input_data=data_s,new_data=s_sgdf,data_variogram=data_s))

  mod5<- try(autoKrige(formula5, input_data=data_s,new_data=s_sgdf,data_variogram=data_s))

  mod6<- try(autoKrige(formula6, input_data=data_s,new_data=s_sgdf,data_variogram=data_s))

  mod7<- try(autoKrige(formula7, input_data=data_s,new_data=s_sgdf,data_variogram=data_s))

  mod8<- try(autoKrige(formula8, input_data=data_s,new_data=s_sgdf,data_variogram=data_s))

  mod9<- try(autoKrige(formula9, input_data=data_s,new_data=s_sgdf,data_variogram=data_s))

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

  ### Model assessment

  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"

    #krmod_auto<-get(mod)

    #If mod "j" is not a model object

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

      #results_m1[1,1]<- dates[i]  #storing the interpolation dates in the first column

      results_m1[1,1]<- sampling_dat$date[i]

      results_m1[1,2]<- ns        #number of stations used in the training stage

      results_m1[1,3]<- "SSERR"

      results_m1[1,j+3]<- NA

      results_m2[1,1]<- results_m1[1,1]<-  #storing the interpolation dates in the first column

      results_m2[1,2]<- ns        #number of stations used in the training 

      results_m2[1,3]<- "GCV"

      results_m2[1,j+3]<- NA

      results_m3[1,1]<- sampling_dat$date[i] #storing the interpolation dates in the first column

      results_m3[1,2]<- ns        #number of stations used in the training stage

      results_m3[1,3]<- "DEV"

      results_m3[1,j+3]<- NA

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

      results_RMSE_f[1,2]<- ns        #number of stations used in the training stage

      results_RMSE_f[1,3]<- "RSME_f"

      results_RMSE_f[1,j+3]<- NA

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

      results_MAE_f[1,2]<- ns        #number of stations used in the training stage

      results_MAE_f[1,3]<- "MAE_f"

      results_MAE_f[1,j+3]<-NA

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

      results_RMSE[1,2]<- ns          #number of stations used in the training stage

      results_RMSE[1,3]<- "RMSE"

      results_RMSE[1,j+3]<- NA  #Storing RMSE for the model j

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

      results_MAE[1,2]<- ns           #number of stations used in the training stage

      results_MAE[1,3]<- "MAE"

      results_MAE[1,j+3]<- NA    #Storing MAE for the model j

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

      results_ME[1,2]<- ns            #number of stations used in the training stage

      results_ME[1,3]<- "ME"

      results_ME[1,j+3]<- NA      #Storing ME for the model j

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

      results_R2[1,2]<- ns            #number of stations used in the training stage

      results_R2[1,3]<- "R2"

      results_R2[1,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,"autoKrige")) {

      rpred<-mod$krige_output  #Extracting the SptialGriDataFrame from the autokrige object

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

      y_pred<-rpred$var1.pred                  #is the order the same?

      #y_prederr<-rpred$var1.var

      raster_pred<-r1

      layerNames(raster_pred)<-"y_pred"

      clearValues(raster_pred)        #Clear values in memory, just in case...

      values(raster_pred)<-as.numeric(y_pred)  #Assign values to every pixels 

      #data_name<-paste("predicted_mod",j,"_",dates[[i]],sep="")

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

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

      raster_name<-paste("Kriging_",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)

      #Save png plot here...

      #data_name<-paste("predicted_mod",j,"_",dates[[i]],sep="")

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

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

      png_name<-paste("Kriging_plot_",data_name,out_prefix,".png", sep="")

      png(png_name) #Create file to write a plot

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

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

      #datelabel2=format(ISOdate(year,mo,day),"%B ") #Plot label

      plot(mod) #Plot to file the autokrige object

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

      dev.off()  #Release the hold to the file

      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 kriged surface tmax and the location of weather stations

      rpred_val_v <- overlay(pred_sgdf,data_v)             #This overlays the kriged 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 - data_s[[pred_mod]]           #Residuals from kriging training

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

      ####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

      R2_mod_f<- cor(data_s$y_var,data_s[[pred_mod]], use="complete")^2

      RMSE_mod_f<- sqrt(mean(res_mod_s^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_f<- mean(abs(res_mod_s), na.rm=TRUE)

      results_m1[1,1]<- sampling_dat$date[i]  #storing the interpolation dates in the first column

      results_m1[1,2]<- ns        #number of stations used in the training stage

      results_m1[1,3]<- "SSERR"

      results_m1[1,j+3]<- mod$sserr

      results_m2[1,1]<- sampling_dat$date[i]  #storing the interpolation dates in the first column

      results_m2[1,2]<- ns        #number of stations used in the training 

      results_m2[1,3]<- "GCV"

      results_m2[1,j+3]<- NA

      results_m3[1,1]<- sampling_dat$date[i]  #storing the interpolation dates in the first column

      results_m3[1,2]<- ns        #number of stations used in the training stage

      results_m3[1,3]<- "DEV"

      results_m3[1,j+3]<- NA

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

      results_RMSE_f[1,2]<- ns        #number of stations used in the training stage

      results_RMSE_f[1,3]<- "RSME_f"

      results_RMSE_f[1,j+3]<-RMSE_mod_f

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

      results_MAE_f[1,2]<- ns        #number of stations used in the training stage

      results_MAE_f[1,3]<- "MAE_f"

      results_MAE_f[1,j+3]<-MAE_mod_f

      results_R2_f[1,1]<- sampling_dat$date[i]      #storing the interpolation dates in the first column

      results_R2_f[1,2]<- ns            #number of stations used in the training stage

      results_R2_f[1,3]<- "R2_f"

      results_R2_f[1,j+3]<- R2_mod_f      #Storing R2 for the model j

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

      results_RMSE[1,2]<- ns          #number of stations used in the training stage

      results_RMSE[1,3]<- "RMSE"

      results_RMSE[1,j+3]<- RMSE_mod  #Storing RMSE for the model j

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

      results_MAE[1,2]<- ns           #number of stations used in the training stage

      results_MAE[1,3]<- "MAE"

      results_MAE[1,j+3]<- MAE_mod    #Storing MAE for the model j

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

      results_ME[1,2]<- ns            #number of stations used in the training stage

      results_ME[1,3]<- "ME"

      results_ME[1,j+3]<- ME_mod      #Storing ME for the model j

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

      results_R2[1,2]<- ns            #number of stations used in the training stage

      results_R2[1,3]<- "R2"

      results_R2[1,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_R2_f<-as.data.frame(results_R2_f)

  results_table_m1<-as.data.frame(results_m1)

  results_table_m2<-as.data.frame(results_m2)

  results_table_m3<-as.data.frame(results_m3)

  tb_metrics1<-rbind(results_table_RMSE,results_table_MAE, results_table_ME, 

                     results_table_R2,results_table_RMSE_f,results_table_MAE_f,results_table_R2_f)   #

  tb_metrics2<-rbind(results_table_m1,results_table_m2, results_table_m3)

  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","mod9")

  colnames(tb_metrics2)<-cname

  #colnames(results_table_RMSE)<-cname

  #colnames(results_table_RMSE_f)<-cname

  #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=",")

  #}  

  #print(paste(date_proc,"processed"))

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

  # Kriging object may need to be modified...because it contains the full image of prediction!!

  ##loop through model objects data frame and set field to zero...

  mod_obj<-list(mod1,mod2,mod3,mod4,mod5,mod6,mod7,mod8,mod9)

  names(mod_obj)<-c("mod1","mod2","mod3","mod4","mod5","mod6","mod7","mod8","mod9") #generate names automatically??

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

  #save(mod_obj,file= paste(path,"/","results_list_mod_objects_",dates[i],out_prefix,".RData",sep=""))

  for (j in 1:nmodels){

    if (inherits(mod_obj[[j]],"autoKrige")){

      mod_obj[[j]]$krige_output<-NULL

    }

  }

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

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

  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=""))

  return(results_list)

  #return(tb_diagnostic1)

}