diff --git a/dev/postprocessing/plot_results.R b/dev/postprocessing/plot_results.R
index f9fc250..4b76253 100644
--- a/dev/postprocessing/plot_results.R
+++ b/dev/postprocessing/plot_results.R
@@ -1,3 +1,11 @@
+#!/usr/bin/env Rscript
+
+##################################################################
+#Description    : plot fields (era5, cerra, downscaled and 
+#                 difference) and PSD for individual timesteps
+#Author         : Konrad Mayer
+##################################################################
+
 library(here)
 library(lubridate)
 library(stars)
@@ -8,6 +16,31 @@ library(dplyr)
 library(patchwork)
 library(metR)
 library(stringr)
+library(radialpsd)
+
+# helpers
+truncate_to_square <- function(m) {
+    dim_m <- dim(m)
+    mindim <- min(dim_m)
+    start <- floor((dim_m - mindim) / 2)
+    end <- start + mindim
+    start <- start + 1
+    m[start[1]:end[1], start[2]:end[2]]
+}
+
+replace_na <- function(m, replacement = 0) {
+    m[is.na(m)] <- replacement
+    m
+}
+
+do_psd <- function(x) {
+    tmp <- replace_na(truncate_to_square(as.matrix(x[[1]])))
+    psd <- radial.psd(tmp, plot = FALSE, scaled = FALSE, normalized = FALSE)
+    max_dist <- sqrt(sum((ceiling(dim(tmp)/2)-1)^2))
+    mutate(psd, wavenumber = wavenumber / max_dist)
+}
+
+# main
 
 per_lead_time <- function(lead_time) {
         
@@ -20,11 +53,14 @@ per_lead_time <- function(lead_time) {
     downscaled <- read_stars(here(glue("dat/TESTING/SAMOS/postprocessed/samos-postprocessed_{lead_time}.nc"))) %>%
         setNames("samos")
 
+    era5_regridded <- era5 <- read_stars(here(glue("dat/TESTING/PREPROCESSED/ERA5_regridded/t2m_era5_{lead_time}.nc"))) %>% # only needed for PSD
+        setNames("era5")
+
     diff_field <- downscaled[0]
     diff_field[["diff_samos_cerra"]] <- downscaled[[1]] - units::drop_units(cerra[[1]])
 
     dothis <- function(eval_datetime) {
-        plts <- map2(
+        plts <- c(map2(
             list(era5, cerra, downscaled, diff_field) %>% map(~filter(.x, time == eval_datetime)),
             list(scale_fill_viridis_c, scale_fill_viridis_c, scale_fill_viridis_c, scale_fill_divergent),
             ~ggplot() +
@@ -37,10 +73,23 @@ per_lead_time <- function(lead_time) {
                     ) +
                 .y() +
                 theme_minimal()
-        )
+        ),
+        list(map(
+            list(era5_regridded, cerra, downscaled) %>% map(~filter(.x %>%.[1, 3:238,6:160], time == eval_datetime)[drop = TRUE]),
+            ~{do_psd(st_apply(.x, c("x", "y"), mean))}
+        ) %>%
+            setNames(c("era5", "cerra", "samos")) %>%
+            bind_rows(.id = "model") %>%
+            ggplot(aes(wavenumber, r_spectrum, lty = model)) +
+            geom_line() +
+                theme_minimal(20) +
+                scale_y_log10() + annotation_logticks() + scale_x_log10(sec.axis = sec_axis(trans = ~ (.^-1), name = "wavelength")) +
+                labs(y = "Power")
+        ))
+
 
-        wrap_plots(plts, ncol = 2) + plot_annotation(title = eval_datetime)
-        ggsave(here(glue("plt/SAMOS/{format(eval_datetime, '%Y%m%dT%H%M%S')}_testset.pdf")), height = 7, width = 10)
+        wrap_plots(plts[1:4], ncol = 2) | plts[[5]] + plot_annotation(title = eval_datetime)
+        ggsave(here(glue("plt/SAMOS/{format(eval_datetime, '%Y%m%dT%H%M%S')}_testset.pdf")), height = 6, width = 20)
 
     }
 
diff --git a/dev/preprocessing/regrid_era5.sh b/dev/preprocessing/regrid_era5.sh
index 6e4671c..8d5aa8d 100755
--- a/dev/preprocessing/regrid_era5.sh
+++ b/dev/preprocessing/regrid_era5.sh
@@ -23,4 +23,6 @@ for lt in "${leadtime[@]}"; do
     stdbuf -oL cdo griddes dat/TRAINING/RESIDUALS/CERRA/t2m_cerra_${lt}_residuals.nc > /tmp/targetgrid.txt
     # bilinear interpolation
     cdo remapbil,/tmp/targetgrid.txt ${projectroot}/dat/${dataset}/RESIDUALS/ERA5/t2m_era5_${lt}_residuals.nc ${projectroot}/dat/${dataset}/RESIDUALS/ERA5_regridded/t2m_era5_${lt}_residuals.nc
+    # bilinear interpolation of raw data
+    cdo remapbil,/tmp/targetgrid.txt ${projectroot}/dat/${dataset}/PREPROCESSED/ERA5/t2m_era5_${lt}.nc ${projectroot}/dat/${dataset}/PREPROCESSED/ERA5_regridded/t2m_era5_${lt}.nc
 done 
diff --git a/dev/verification/spatial_structures/compare_pds.R b/dev/verification/spatial_structures/compare_pds.R
new file mode 100644
index 0000000..b11cc66
--- /dev/null
+++ b/dev/verification/spatial_structures/compare_pds.R
@@ -0,0 +1,133 @@
+#!/usr/bin/env Rscript
+
+##################################################################
+#Description    : power spectral density analysis
+#Author         : Konrad Mayer
+##################################################################
+
+library(stars)
+library(purrr)
+library(here)
+library(glue)
+library(stringr)
+library(tidyverse)
+library(radialpsd)
+library(ggfan)
+
+# helpers ----------------------------------------------------------------------
+# pad_to_square <- function(m, pad = 0) {
+#     dim_m <- dim(m)
+#     maxdim <- max(dim_m)
+#     out <- matrix(pad, nrow = maxdim, ncol = maxdim)
+#     start <- floor((maxdim - dim_m) / 2)
+#     end <- start + dim_m
+#     start <- start + 1
+#     out[start[1]:end[1], start[2]:end[2]] <- m
+#     out
+# }
+
+truncate_to_square <- function(m) {
+    dim_m <- dim(m)
+    mindim <- min(dim_m)
+    start <- floor((dim_m - mindim) / 2)
+    end <- start + mindim
+    start <- start + 1
+    m[start[1]:end[1], start[2]:end[2]]
+}
+
+replace_na <- function(m, replacement = 0) {
+    m[is.na(m)] <- replacement
+    m
+}
+
+do_psd <- function(x) {
+    tmp <- replace_na(truncate_to_square(as.matrix(x[[1]])))
+    psd <- radial.psd(tmp, plot = FALSE, scaled = FALSE, normalized = FALSE)
+    max_dist <- sqrt(sum((ceiling(dim(tmp)/2)-1)^2))
+    mutate(psd, wavenumber = wavenumber / max_dist)
+}
+
+drop_units <- function(x) {
+    tryCatch(
+        units::drop_units(x),
+        error = function(e) {
+            return(x)
+        }
+    )
+}
+# main -------------------------------------------------------------------------
+
+dothis <- function(lead_time) {
+    lead_time <- str_pad(lead_time, 2, pad = "0")
+
+    # load datasets (crop a bit as SAMOS baseline has some values NA around)
+    datasets <- c(
+        cerra = "dat/TESTING/PREPROCESSED/CERRA/t2m_cerra_{lead_time}.nc",
+        downscaled = "dat/TESTING/SAMOS/postprocessed/samos-postprocessed_{lead_time}.nc",
+        era5 = "dat/TESTING/PREPROCESSED/ERA5_regridded/t2m_era5_{lead_time}.nc"
+    )
+    dat <- map2(datasets, names(datasets), 
+        ~setNames(drop_units(read_stars(here(glue(.x)))), .y)[1, 3:238,6:160]) # data gets truncated to get rid of NA values on two of the edges caused by CDO bilinear interpolation
+
+    timesteps <- seq_len(dim(dat[[1]])["time"])
+    
+    #overall
+
+    psd_overall <- map(dat, 
+        ~do_psd(st_apply(.x, c("x", "y"), mean))) %>%
+        bind_rows(.id = "model")
+
+    psd_overall %>%
+        ggplot(aes(wavenumber, r_spectrum, lty = model)) +
+        geom_line() +
+        theme_minimal(20) +
+        scale_y_log10() + scale_x_log10(sec.axis = sec_axis(trans = ~ (.^-1), name = "wavelength")) + annotation_logticks() +
+        labs(y = "Power")
+
+    ggsave(here(glue("plt/PSD/radialPSD_samos_leadtime{lead_time}_overall.pdf")), width = 10, height = 6)
+
+
+    # loop over timesteps and calculate mean psd
+    psd_timesteps <- map(dat, function(ds) {
+        map(timesteps, function(ts) do_psd(ds[,,,ts, drop = TRUE]))
+    })
+    # common dataframe
+    plotdat <- psd_timesteps %>%
+        map(~bind_rows(setNames(.x, timesteps), .id = "timesteps")) %>%
+        bind_rows(.id = "dataset")
+        
+    # plot
+    plotdat %>%
+        ggplot(aes(x = wavenumber, y = r_spectrum, color = dataset, group = dataset)) + 
+        geom_interval() +
+        theme_minimal(20) +
+        scale_y_log10() + scale_x_log10(sec.axis = sec_axis(trans = ~ (.^-1), name = "wavelength")) + annotation_logticks() +
+        labs(y = "Power")
+
+    ggsave(here(glue("plt/PSD/radialPSD_samos_leadtime{lead_time}_distribution.pdf")), width = 10, height = 6)
+
+    # aggregate to seasons and calculate PSD per season
+    seasons <- list(DJF = c(12, 1, 2), MAM = 3:5, JJA = 6:8, SON = 9:11) 
+
+    per_season <- function(months) {
+        map(dat, ~do_psd(st_apply(.x %>% filter(lubridate::month(time) %in% months), c("x", "y"), mean))) %>%
+           bind_rows(.id = "model")
+    }
+
+    psd_season <- map(seasons, per_season)
+
+    psd_season %>%
+        bind_rows(.id =  "season") %>%
+        ggplot(aes(wavenumber, r_spectrum, color = season, lty = model)) +
+        geom_line() +
+        theme_minimal(20) +
+        scale_y_log10() + scale_x_log10(sec.axis = sec_axis(trans = ~ (.^-1), name = "wavelength")) + annotation_logticks() +
+        labs(y = "Power")
+
+    ggsave(here(glue("plt/PSD/radialPSD_samos_leadtime{lead_time}_season.pdf")), width = 10, height = 6)
+}
+
+lead_times <- seq(0, 21, by = 3)
+walk(lead_times, dothis)
+
+# TODO: PSD needs to be done on projected data, otherwise distance is not valid
\ No newline at end of file
diff --git a/dev/verification/spatial_structures/compare_variogram.R b/dev/verification/spatial_structures/compare_variogram.R
new file mode 100644
index 0000000..26ae994
--- /dev/null
+++ b/dev/verification/spatial_structures/compare_variogram.R
@@ -0,0 +1,55 @@
+library(tidyverse)
+library(stringr)
+library(here)
+library(stars)
+library(glue)
+library(geoR)
+
+dothis <- function(lead_time) {
+    lead_time = 12# for testing
+    lead_time <- str_pad(lead_time, 2, pad = "0")
+
+    # load datasets (crop a bit as SAMOS baseline has some values NA around)
+    cerra <- read_stars(here(glue("dat/TESTING/PREPROCESSED/CERRA/t2m_cerra_{lead_time}.nc"))) %>%
+        setNames("cerra") %>%
+        .[1, 3:238,6:160]
+    downscaled <- read_stars(here(glue("dat/TESTING/SAMOS/postprocessed/samos-postprocessed_{lead_time}.nc"))) %>%
+        setNames("samos") %>%
+        .[1, 3:238,6:160]
+ 
+
+
+#  cerra_tibble <- as_tibble(cerra[,,,10]) # how to deal with timesteps? including more results in too big ram use
+#  downscaled_tibble <- as_tibble(downscaled[,,,10])
+#  variog_cerra = variog(data = cerra_tibble[,4], coords = as.matrix(cerra_tibble[1:2]))
+#  variog_downscaled = variog(data = downscaled_tibble[,4], coords = as.matrix(downscaled_tibble[1:2]))
+
+#  plot(variog_cerra)
+#  points(variog_downscaled$u, variog_downscaled$v, col = "red")
+
+#  plot(variog_cerra)
+#  points(variog_downscaled$u, variog_downscaled$v, col = "red")
+
+ seasons <- list(DJF = c(12, 1, 2), MAM = 3:5, JJA = 6:8, SON = 9:11) 
+
+
+ # TODO: variogram needs to be done on projected data, otherwise distance is not valid
+ per_season <- function(months) {
+    cerra_tibble <- as_tibble(st_apply(cerra %>% filter(lubridate::month(time) %in% months), c("x", "y"), mean)) 
+    downscaled_tibble <- as_tibble(st_apply(downscaled %>% filter(lubridate::month(time) %in% months), c("x", "y"), mean))
+    variog_cerra = variog(data = cerra_tibble[,3], coords = as.matrix(cerra_tibble[1:2]))
+    variog_downscaled = variog(data = downscaled_tibble[,3], coords = as.matrix(downscaled_tibble[1:2]))
+    tibble(distance = variog_cerra$u, semivar_cerra = variog_cerra$v, semivar_downscaled = variog_downscaled$v)
+ }
+
+ variog_seasons <- purrr::map(seasons, per_season) %>% setNames(names(seasons))
+
+ variog_seasons %>%
+    bind_rows(.id = "season") %>%
+    pivot_longer(-c(1:2), names_to = "model") %>%
+    ggplot(aes(distance, value, lty = model, color = season)) +
+        geom_line() + 
+        theme_minimal()
+ ggsave(here(glue("plt/seasonal_variogram_samos_leadtime{lead_time}.pdf")))
+}
+