Self-organising map (SOM) analysis

Introduction

This vignette contains the code used to perform the self-organising map (SOM) analysis on the mean synoptic states created in the Variable preparation vignette. We’ll start by creating custom packets that meet certain experimental criteria before then feeding them into a SOM. We will finish up by creating some cursory visuals of the results. The full summary of the results may be seen in the Node summary vignette.

# Insatll from GitHub
# .libPaths(c("~/R-packages", .libPaths()))
# devtools::install_github("fabrice-rossi/yasomi")

# Packages used in this vignette
library(jsonlite, lib.loc = "../R-packages/")
library(tidyverse) # Base suite of functions
library(ncdf4) # For opening and working with NetCDF files
library(lubridate) # For convenient date manipulation
# library(scales) # For scaling data before running SOM
library(yasomi, lib.loc = "../R-packages/") # The SOM package of choice due to PCI compliance
library(data.table) # For working with massive dataframes

# Set number of cores
doMC::registerDoMC(cores = 50)

# Disable scientific notation for numeric values
  # I just find it annoying
options(scipen = 999)

# Set number of cores
doMC::registerDoMC(cores = 50)

# Disable scientific notation for numeric values
  # I just find it annoying
options(scipen = 999)

# Individual regions
NWA_coords <- readRDS("data/NWA_coords_cabot.Rda")

# The NAPA variables
NAPA_vars <- readRDS("data/NAPA_vars.Rda")

# Corners of the study area
NWA_corners <- readRDS("data/NWA_corners.Rda")

# Create smaller corners to use less RAM
  # This also better matches the previous South African work
  # The Tasmania work had corners of roughly 2 degrees greater than the study area
# NWA_corners_sub <- c(NWA_corners[1]+8, NWA_corners[2]-8, NWA_corners[3]+8, NWA_corners[4]-8)

# The base map
map_base <- ggplot2::fortify(maps::map(fill = TRUE, col = "grey80", plot = FALSE)) %>%
  dplyr::rename(lon = long) %>%
  mutate(group = ifelse(lon > 180, group+9999, group),
         lon = ifelse(lon > 180, lon-360, lon)) %>% 
  select(-region, -subregion)

# The grid that will convert the tri-polar coordinates to cartesian
  # NB: This file was created in the 'tikoraluk' project
# load("data/lon_lat_NAPA_OISST.Rdata")

# Change to fit with this project
# lon_lat_NAPA_OISST <- lon_lat_NAPA_OISST %>% 
#   dplyr::select(-lon, -lat, -dist, -nav_lon_corrected) %>% 
#   dplyr::rename(lon = nav_lon, lat = nav_lat) %>% 
#   mutate(lon = round(lon, 4),
#          lat = round(lat, 4)) %>% 
#   mutate(lon_O = ifelse(lon_O > 180, lon_O-360, lon_O))

Tailored data packets

In this last stage before running our SOM analyses we will create data packets that can be fed directly into the SOM algorithm. These data packets will vary based on the exclusion of certain regions in the study area. In the first run of this analysis on the NAPA model data it was found that the inclusion of the Labrador Sea complicated the results quite a bit. It is also unclear whether or not the Gulf of St Lawrence region should be included in the analysis. While creating whatever packets we desire we will also be converting them into the super-wide matrix format that the SOM model desires.

# Load the synoptic states data packet
system.time(
synoptic_states <- readRDS("data/synoptic_states.Rda")
) # 3 seconds

# Unnest the synoptic data
system.time(
synoptic_states_unnest <- synoptic_states %>% 
  select(region, event_no, synoptic) %>% 
  unnest()
) # 8 seconds

# The study area size when the Labrador region is excluded
NWA_coords_nolab <- NWA_coords %>% 
  filter(region != "ls")

# The study area size when the Labrador and GSL regions are excluded
NWA_coords_nolabgsl <- NWA_coords %>% 
  filter(!region %in% c("ls", "gsl"))

# Test visuals of reduced study areas
synoptic_states[1,] %>% 
  unnest() %>% 
  filter(lat <= round(max(NWA_coords_nolabgsl$lat))+0.5) %>% 
  ggplot(aes(x = lon, y = lat)) +
  geom_raster(aes(fill = sst_anom)) +
  geom_polygon(data = NWA_coords_nolabgsl, aes(colour = region), fill = NA)

# Function for casting wide the custom packets
create_packet <- function(df){
  # Cast the data to a single row
  res <- data.table::data.table(df) %>% 
    reshape2::melt(id = c("region", "event_no", "lon", "lat"),
                   measure = c(colnames(.)[-c(1:4)]), 
                   variable.name = "var", value.name = "val") %>% 
    dplyr::arrange(var, lon, lat) %>%
    unite(coords, c(lon, lat, var), sep = "BBB") %>%
    unite(event_ID, c(region, event_no), sep = "BBB") %>%
    reshape2::dcast(event_ID ~ coords, value.var = "val")
  # Remove columns (pixels) with missing data
  res_fix <- res[,colSums(is.na(res))<1]
  return(res_fix)
}

# Packet for entire study region
system.time(
  packet_all <- create_packet(synoptic_states_unnest)
) # xxx seconds
saveRDS(packet_all, "data/packet_all.Rda")

# Exclude Labrador region
system.time(
  packet_nolab <- synoptic_states_unnest %>% 
    filter(region != "ls",
           lat <= round(max(NWA_coords_nolab$lat))+0.5) %>% 
    create_packet()
) # 128 seconds
saveRDS(packet_nolab, "data/packet_nolab.Rda")

# Exclude Labrador and Gulf of St Lawrence regions
system.time(
  packet_nolabgsl <- synoptic_states_unnest %>% 
    filter(!region %in% c("ls", "gsl"),
           lat <= round(max(NWA_coords_nolabgsl$lat))+0.5) %>% 
    create_packet()
) # xxx seconds
saveRDS(packet_nolabgsl, "data/packet_nolabgsl.Rda")

Run SOM models

Now that we have our data packets to feed the SOM, we need a function that will ingest them and produce results for us.

# Function for calculating SOMs using PCI
  # NB: 4x4 produced one empty cell and one cell with only one event
  # So the default size has been reduced to 4x3
som_model_PCI <- function(data_packet, xdim = 4, ydim = 3){
  # Create a scaled matrix for the SOM
  # Cancel out first column as this is the reference ID of the event per row
  data_packet_matrix <- as.matrix(scale(data_packet[,-1]))

  # Create the grid that the SOM will use to determine the number of nodes
  som_grid <- somgrid(xdim = xdim, ydim = ydim, topo = "hexagonal")

  # Run the SOM with PCI
  som_model <- batchsom(data_packet_matrix,
                        somgrid = som_grid,
                        init = "pca",
                        max.iter = 100)
  return(som_model)
}

With the function sorted, we now feed the data.

# The SOM on the entire study area
   # NB: Not running for some reason...
    # Possibly due to a column with no range in values
    # Not too worried about it as this one isn't being used
# packet_all <- readRDS("data/packet_all.Rda")
# system.time(som_all <- som_model_PCI(packet_all)) # 201 seconds
# saveRDS(som_all, file = "data/som_all.Rda")

# The SOM excluding the Labrador Sea region
packet_nolab <- readRDS("data/packet_nolab.Rda")
system.time(som_nolab <- som_model_PCI(packet_nolab)) # 78 seconds
saveRDS(som_nolab, file = "data/som_nolab.Rda")

# The SOM excluding the Labrador Sea and Gulf of St Lawrence regions
packet_nolabgsl <- readRDS("data/packet_nolabgsl.Rda")
system.time(som_nolabgsl <- som_model_PCI(packet_nolabgsl)) # 75 seconds
saveRDS(som_nolabgsl, file = "data/som_nolabgsl.Rda")

# A 9 node SOM

# A 16 node SOM
system.time(som_nolab <- som_model_PCI(packet_nolab)) # 78 seconds
saveRDS(som_nolab, file = "data/som_nolab.Rda")

# A SOM without moderate events

Unpack SOM results

We will create two functions below that will be useful for unpacking the SOM results.

# Function for determining node indexes
# testers...
# data_packet <- all_anom; som_output <- som_all_anom
event_node_index <- function(data_packet, som_output){
  
  # Count the number of events per node
  node_count <- as.data.frame(table(som_output$classif)) %>% 
    dplyr::rename(node = Var1,
                  count = Freq) %>% 
    mutate(node = as.numeric(as.character(node)))
  
  # Create a more complete data.frame of info
  event_node <- data.frame(event_ID = data_packet[,"event_ID"],
                           node = som_output$classif) %>% 
    separate(event_ID, into = c("region", "event_no"), sep = "BBB") %>% 
    left_join(node_count, by = "node")
  
  # NB: This is potentially where the season of the event would be inserted
  
  return(event_node)
}

# Function for unpacking som results and creating 
# mean results from initial data frame based on node clustering
# testers...
# data_packet <- packet_nolab; som_output <- som_nolab
som_unpack_mean <- function(data_packet, som_output){
  
  # Determine which event goes in which node and melt
  data_packet_long <- data.frame(event_ID = data_packet[,"event_ID"],
                           node = som_output$classif) %>% 
    separate(event_ID, into = c("region", "event_no"), sep = "BBB") %>% 
    cbind(data_packet[,-1]) %>% 
    data.table() %>% 
    reshape2::melt(id = c("region", "event_no", "node"),
                   measure = c(colnames(.)[-c(1:3)]), 
                   variable.name = "variable", value.name = "value")
  
  # Create the mean values that serve as the unscaled results from the SOM
  var_unscaled <- data_packet_long[, .(val = mean(value, na.rm = TRUE)),
                                   by = .(node, variable)] %>% 
    separate(variable, into = c("lon", "lat", "var"), sep = "BBB") %>%
    dplyr::arrange(node, var, lon, lat) %>% 
    mutate(lon = as.numeric(lon),
           lat = as.numeric(lat))
  return(var_unscaled)
}

And now we unpack the SOM results.

# Load data packets
# packet_all <- readRDS("data/packet_all.Rda")
packet_nolab <- readRDS("data/packet_nolab.Rda")
packet_nolabgsl <- readRDS("data/packet_nolabgsl.Rda")

# Load SOM packets
# som_all <- readRDS("data/som_all.Rda")
som_nolab <- readRDS("data/som_nolab.Rda")
som_nolabgsl <- readRDS("data/som_nolabgsl.Rda")

# Determine node index
# node_index_all <- event_node_index(packet_all, som_all)
node_index_nolab <- event_node_index(packet_nolab, som_nolab)
node_index_nolabgsl <- event_node_index(packet_nolabgsl, som_nolabgsl)

## Create and save mean synoptic states per node
# All
# node_mean_all <- som_unpack_mean(packet_all, som_all)
# saveRDS(node_mean_all, "data/node_mean_all.Rda")
# No Labrador Sea
node_mean_nolab <- som_unpack_mean(packet_nolab, som_nolab)
# saveRDS(node_mean_nolab, "data/node_mean_nolab.Rda")
# No Labrador Sea or Gulf of St Lawrence
node_mean_nolabgsl <- som_unpack_mean(packet_nolabgsl, som_nolabgsl)
# saveRDS(node_mean_nolabgsl, "data/node_mean_nolabgsl.Rda")

Visualise SOM results

First up the functions for visualising the unpacked results.

# Ease of life function
som_node_visualise <- function(sub_var = "sst_anom",
                               node_data = node_mean_nolab, 
                               node_index = node_index_nolab){
  
  # Subset data
  node_data_sub <- node_data %>% 
    filter(var == sub_var)

  # Create plot
  som_panel_plot <- ggplot(node_data_sub, aes(x = lon, y = lat)) +
    # geom_point(aes(colour = val)) +
    geom_raster(aes(fill = val)) +
    geom_polygon(data = map_base, aes(group = group), show.legend = F) +
    geom_label(data = node_index, aes(x = -60, y = 35, label = paste0("n = ",count))) +
    # geom_polygon(data = NWA_coords, aes(group = region, fill = region, colour = region), alpha = 0.1) +
    coord_cartesian(xlim = c(max(node_data$lon), min(node_data$lon)),
                    ylim = c(max(node_data$lat), min(node_data$lat)), 
                    expand = F) +
    scale_fill_gradient2(low = "blue", high = "red") +
    # scale_colour_viridis_c(option = viridis_option) +
    labs(x = NULL, y = NULL, fill = sub_var) +
    facet_wrap(~node, ncol = 4) +
    theme(legend.position = "bottom")
  return(som_panel_plot)
}

And now we create a PDF for each of the 12 nodes for each variable individually.

# SST
  # NB: Comparing the SST anomaly results from the two restricted study areas
plot_sst_anom <- som_node_visualise()
plot_sst_anom_nogsl <- som_node_visualise(node_data = node_mean_nolabgsl,
                                          node_index = node_index_nolabgsl)
# plot_sst_anom
# plot_sst_anom_nogsl
ggsave(plot_sst_anom, filename = "output/som_plot_sst_anom.pdf", height = 9, width = 13)
ggsave(plot_sst_anom, filename = "output/som_plot_sst_anom.png", height = 9, width = 13)
ggsave(plot_sst_anom_nogsl, filename = "output/som_plot_sst_anom_nogsl.pdf", height = 9, width = 13)

# Air temperature (t2m)
plot_t2m_anom <- som_node_visualise("t2m_anom")
# plot_t2m_anom
ggsave(plot_t2m_anom, filename = "output/som_plot_t2m_anom.pdf", height = 9, width = 13)

# Net downward heat flux (qnet)
plot_qnet_anom <- som_node_visualise("qnet_anom")
# plot_qnet_anom
ggsave(plot_qnet_anom, filename = "output/som_plot_qnet_anom.pdf", height = 9, width = 13)

# Surface wind U (u10)
plot_u10_anom <- som_node_visualise("u10_anom")
# plot_u10_anom
ggsave(plot_u10_anom, filename = "output/som_plot_u10_anom.pdf", height = 9, width = 13)

# Surface wind V (v10)
plot_v10_anom <- som_node_visualise("v10_anom")
# plot_v10_anom
ggsave(plot_v10_anom, filename = "output/som_plot_v10_anom.pdf", height = 9, width = 13)

# Ocean current U (u)
plot_u_anom <- som_node_visualise("u_anom")
# plot_uoce_anom
ggsave(plot_u_anom, filename = "output/som_plot_u_anom.pdf", height = 9, width = 13)

# Ocean current V (v)
plot_v_anom <- som_node_visualise("v_anom")
# plot_v_anom
ggsave(plot_v_anom, filename = "output/som_plot_v_anom.pdf", height = 9, width = 13)

# Mixed Layer Depth (mld)
plot_mld_anom <- som_node_visualise("mld_anom")
# plot_mld_anom
ggsave(plot_mld_anom, filename = "output/som_plot_mld_anom.pdf", height = 9, width = 13)

Juggling back and forth between the SST anomaly photos with and without the Gulf of St Lawrence it first appears that they are very different, but this is mostly due to the top and bottom rows of nodes being flipped. The actual differences are much more muted and the patterns tend to hold. The patterns appear more crisp in the larger study extent (no Labrador). This is likely because the inclusion of the shallow GSL gives more power. to the atmospheric variables to compete with the Gulf Stream. For this reason we are going to proceed with the inclusion of the Gulf of St Lawrence.

See the files in the output/ folder in the GitHub repo for this project. They aren’t all shown here because they take a bit too long to render. But the following shows what the SST anomaly nodes look like.

plot_sst_anom <- som_node_visualise("sst_anom")
plot_sst_anom

Up next in the Node summary vignette we will show the results in more depth. The code used to create the summary figures may be found in the Figures vignette.

Musings

References

Session information

sessionInfo()

R version 3.6.1 (2019-07-05)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 16.04.5 LTS

Matrix products: default
BLAS:   /usr/lib/openblas-base/libblas.so.3
LAPACK: /usr/lib/libopenblasp-r0.2.18.so

locale:
 [1] LC_CTYPE=en_CA.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_CA.UTF-8        LC_COLLATE=en_CA.UTF-8    
 [5] LC_MONETARY=en_CA.UTF-8    LC_MESSAGES=en_CA.UTF-8   
 [7] LC_PAPER=en_CA.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_CA.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] bindrcpp_0.2.2    data.table_1.11.6 yasomi_0.3       
 [4] proxy_0.4-22      e1071_1.7-0       lubridate_1.7.4  
 [7] ncdf4_1.16        forcats_0.3.0     stringr_1.3.1    
[10] dplyr_0.7.6       purrr_0.2.5       readr_1.1.1      
[13] tidyr_0.8.1       tibble_1.4.2      ggplot2_3.0.0    
[16] tidyverse_1.2.1   jsonlite_1.6     

loaded via a namespace (and not attached):
 [1] tidyselect_0.2.4  reshape2_1.4.3    haven_1.1.2      
 [4] lattice_0.20-35   colorspace_1.3-2  htmltools_0.3.6  
 [7] yaml_2.2.0        rlang_0.2.2       R.oo_1.22.0      
[10] pillar_1.3.0      glue_1.3.0        withr_2.1.2      
[13] R.utils_2.7.0     doMC_1.3.5        modelr_0.1.2     
[16] readxl_1.1.0      foreach_1.4.4     bindr_0.1.1      
[19] plyr_1.8.4        munsell_0.5.0     gtable_0.2.0     
[22] workflowr_1.1.1   cellranger_1.1.0  rvest_0.3.2      
[25] R.methodsS3_1.7.1 codetools_0.2-15  evaluate_0.11    
[28] labeling_0.3      knitr_1.20        parallel_3.6.1   
[31] class_7.3-14      broom_0.5.0       Rcpp_0.12.18     
[34] backports_1.1.2   scales_1.0.0      hms_0.4.2        
[37] digest_0.6.16     stringi_1.2.4     grid_3.6.1       
[40] rprojroot_1.3-2   cli_1.0.0         tools_3.6.1      
[43] maps_3.3.0        magrittr_1.5      lazyeval_0.2.1   
[46] crayon_1.3.4      whisker_0.3-2     pkgconfig_2.0.2  
[49] xml2_1.2.0        iterators_1.0.10  assertthat_0.2.0 
[52] rmarkdown_1.10    httr_1.3.1        rstudioapi_0.7   
[55] R6_2.2.2          nlme_3.1-137      git2r_0.23.0     
[58] compiler_3.6.1