Self-organising map (SOM) analysis

Introduction

This markdown file will contain the code used to perform the self-organising map (SOM) analysis on the prepared variable data as seen in the Variable preparation vignette and on the prepared vectors seen in the Vector preparation 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))

Possible mechanisms

“Finally, Shearman and Lentz (2010) showed that century-long ocean warming trends observed along the entire northeast U.S. coast are not related to local atmospheric forcing but driven by atmospheric warming of source waters in the Labrador Sea and the Arctic, which are advected into the region.” (Richaud et al., 2016)

Downwelling

Net heatflux (OAFlux) doesn’t line up perfectly with seasonal SST signal, but is very close, with heat flux tending to lead SST by 2 – 3 months.s (Richaud et al., 2016). It is therefore likely one of the primary drivers of SST and should therefore be strongly considered when constructing SOMs.

There is almost no seasonal cycle for slope waters in any of the regions (Richaud et al., 2016).

More ideas

It would be interesting to see if the SOM outputs differ in any meaningful ways when only data from the first half of the study time period are used compared against the second half.

The output of the SOMs could likely be more meaningfully conveyed from the point of view of the regions. What I mean by this is to take the summary of the nodes, convey them into a table, and then use that table to inform a series of information bits that is focused around each region. Some sort of interactive visual may be useful for this. Showing the percentage that each region has in each node would be a good start. This would allow for a more meaningful further explanation for which drivers affect which regions during which seasons and over which years.

Once this summary is worked out it would then follow that the same analysis be run 1, 2, 3 etc. months in the past and see what the same information format provides w.r.t. a sort of predictive capacity. All of this can then be used to check other data products with a more focused lens in order to maximise the utility of the output.

Tailored data packets

In this last stage before running our SOM analyses we want to create equally weighted and quality controlled data packets that can be fed directly into the SOM algorithm. At the moment we will just create a packet for a few choice anomaly variables. This is because not only has using all of the anomaly variables at once proven to be too large a task, it also wouldn’t be appropriate because not all of this information should be considered at the same time. The creation of these packets will be split into four steps below.

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

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

# Load the synoptic vector states data packet
system.time(
synoptic_vec_states <- readRDS("data/synoptic_vec_states.Rda")
) # 10 seconds

# Unnest the synoptic vector data
system.time(
synoptic_vec_states_unnest <- synoptic_vec_states %>% 
  select(region, sub_region, event_no, synoptic) %>% 
  unnest()
) # 27 seconds

# NB: The range of values for mixed layer depth anomalies is muuuuch greater
# in the Labrador sea than elsewhere in the study area.
# So we scale it here first before feeding it into the SOM to be scaled again
system.time(
synoptic_states_anom_fix <- synoptic_states_unnest %>% 
  select(region:lat, sst_anom, taum_anom, qt_anom, mldr10_1_anom) %>% 
  filter(lon >= NWA_corners_sub[1], lon <= NWA_corners_sub[2],
         lat >= NWA_corners_sub[3], lat <= NWA_corners_sub[4]) %>% 
  group_by(lon, lat) %>% 
  mutate(mldr10_1_anom = mldr10_1_anom/max(abs(mldr10_1_anom), na.rm = T)) %>% 
  # na.omit() %>% 
  ungroup()
) # 3 seconds

# NB: There is an issue downstream with one or more of the vector pixels always having a value of 0
  # This needs to be accounted for here before joining the data further
system.time(
synoptic_vec_states_anom_fix <- synoptic_vec_states_unnest %>% 
  select(region:lat, uoce_anom:voce_anom) %>% 
  filter(lon >= NWA_corners_sub[1], lon <= NWA_corners_sub[2],
         lat >= NWA_corners_sub[3], lat <= NWA_corners_sub[4]) %>% 
  group_by(lon, lat) %>% 
  mutate(uoce_anom = case_when(min(uoce_anom, na.rm = T) != 0 & max(uoce_anom, na.rm = T) != 0 ~ uoce_anom),
         voce_anom = case_when(min(voce_anom, na.rm = T) != 0 & max(voce_anom, na.rm = T) != 0 ~ voce_anom)) %>% 
  # na.omit() %>% 
  ungroup()
) # 8 seconds

# Constrain variables
system.time(
synoptic_states_anom_cartesian <- synoptic_states_anom_fix %>% 
  # First create means based on the nearest NAPA pixel to OISST pixel
  left_join(lon_lat_NAPA_OISST, by = c("lon", "lat")) %>% 
  dplyr::select(-lon, -lat) %>% 
  dplyr::rename(lon = lon_O, lat = lat_O) %>% 
  group_by(region, sub_region, event_no, lon, lat) %>% 
  summarise_all(.funs = "mean", na.rm = T) #%>% 
  # Then interpolate the few pixels that aren't filled
    # NB: After spending a day working on interpolation techniques 
    # I decided to leave it as this creates more artefacts than it removes
  # group_by(region, sub_region, event_no)
) # 34 seconds

# Constrain vectors
system.time(
synoptic_vec_states_anom_cartesian <- synoptic_vec_states_anom_fix %>% 
  # First create means based on the nearest NAPA pixel to OISST pixel
  left_join(lon_lat_NAPA_OISST, by = c("lon", "lat")) %>% 
  dplyr::select(-lon, -lat) %>% 
  dplyr::rename(lon = lon_O, lat = lat_O) %>% 
  group_by(region, sub_region, event_no, lon, lat) %>% 
  summarise_all(.funs = "mean", na.rm = T)
) # 32 seconds

# Test visuals
# test <- synoptic_states_anom_cartesian %>%
#   filter(region == "cbs", sub_region == "(0,50]", event_no == 1)
# ggplot(test, aes(x = lon, y = lat)) +
#   geom_raster(aes(fill = sst_anom)) +
#   scale_fill_gradient2(low = "blue", high = "red") +
#   coord_cartesian(xlim = NWA_corners_sub[1:2],
#                   ylim = NWA_corners_sub[3:4])

# Packet for all synoptic anomaly data for all regions etc.
system.time(
packet_all_anom <- left_join(synoptic_states_anom_fix, 
                             synoptic_vec_states_anom_fix,
                             by = c("region", "sub_region", "event_no", "lon", "lat")) %>% 
  data.table::data.table() %>% 
  reshape2::melt(id = c("region", "sub_region", "event_no", "lon", "lat"),
                 measure = c(colnames(.)[-c(1:5)]), 
                 variable.name = "var", value.name = "val") %>% 
  dplyr::arrange(var, lon, lat) %>%
  unite(coords, c(lon, lat, var), sep = "BBB") %>%
  unite(event_ID, c(region, sub_region, event_no), sep = "BBB") %>%
  reshape2::dcast(event_ID ~ coords, value.var = "val")
) # 312 seconds

# Remove columns (pixels) with missing data and save
packet_all_anom_fix <- packet_all_anom[,colSums(is.na(packet_all_anom))<1]
# saveRDS(packet_all_anom_fix, "data/packet_all_anom.Rda")

Run SOM models

Now that we have our anomaly data packet 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.

all_anom <- readRDS("data/packet_all_anom.Rda")
system.time(som_all_anom <- som_model_PCI(all_anom)) # 201 seconds
saveRDS(som_all_anom, file = "data/som_all_anom.Rda")

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", "sub_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)
}

# Functions for unpacking som results
  # Create mean results from initial data frame based on node clustering
# testers...
# data_packet <- all_anom; som_output <- som_all_anom
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", "sub_region", "event_no"), sep = "BBB") %>% 
    cbind(data_packet[,-1]) %>% 
    data.table() %>% 
    reshape2::melt(id = c("region", "sub_region", "event_no", "node"),
                   measure = c(colnames(.)[-c(1:4)]), 
                   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 packet
all_anom <- readRDS("data/packet_all_anom.Rda")

# Load SOM packet for anomaly data
som_all_anom <- readRDS("data/som_all_anom.Rda")

# Determine node index
node_index_all_anom <- event_node_index(all_anom, som_all_anom)

# Create and save mean synoptic states per node
node_mean_all_anom <- som_unpack_mean(all_anom, som_all_anom)
# saveRDS(node_mean_all_anom, "data/node_mean_all_anom.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", viridis_option = "D"){
  
  # Subset data
  node_mean_all_anom_sub <- node_mean_all_anom %>% 
    filter(var == sub_var) %>% 
    mutate(lon = plyr::round_any(lon, 0.25),
           lat = plyr::round_any(lat, 0.25)) %>% 
    group_by(node, lon, lat, var) %>% 
    summarise(val = mean(val, na.rm = T))

  # Create plot
  som_panel_plot <- ggplot(node_mean_all_anom_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_all_anom, 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 = NWA_corners_sub[1:2],
                    ylim = NWA_corners_sub[3:4], 
                    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
plot_sst_anom <- som_node_visualise("sst_anom")
# plot_sst_anom
ggsave(plot_sst_anom, filename = "output/som_plot_sst_anom.pdf", height = 12, width = 13)
ggsave(plot_sst_anom, filename = "output/som_plot_sst_anom.png", height = 12, width = 13)

# Net downward heat flux (qt)
plot_qt_anom <- som_node_visualise("qt_anom")
# plot_qt_anom
ggsave(plot_qt_anom, filename = "output/som_plot_qt_anom.pdf", height = 12, width = 13)

# Mixed Layer Depth (mldr10_1)
plot_mldr10_1_anom <- som_node_visualise("mldr10_1_anom")
# plot_mldr10_1_anom
ggsave(plot_mldr10_1_anom, filename = "output/som_plot_mldr10_1_anom.pdf", height = 12, width = 13)

# Wind stress (taum)
plot_taum_anom <- som_node_visualise("taum_anom")
# plot_taum_anom
ggsave(plot_taum_anom, filename = "output/som_plot_taum_anom.pdf", height = 12, width = 13)

# Ocean current; U (uoce)
plot_uoce_anom <- som_node_visualise("uoce_anom")
# plot_uoce_anom
ggsave(plot_uoce_anom, filename = "output/som_plot_uoce_anom.pdf", height = 12, width = 13)

# Ocean current; U (uoce)
plot_voce_anom <- som_node_visualise("voce_anom")
# plot_voce_anom
ggsave(plot_voce_anom, filename = "output/som_plot_voce_anom.pdf", height = 12, width = 13)

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 Figures vignette we will show the results in more depth.

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