Detecting Events in Gridded Data

Two good choices: dplyr vs. plyr

When we want to make the same calculation across multiple groups of data within one dataframe we have two good options available to us. The first is to make use of the map() suite of functions found in the purrr package, and now implemented in dplyr. This is a very fast tidyverse friendly approach to splitting up tasks. The other good option is to go back in time a bit and use the ddply() function from the plyr package. This is arguably a better approach as it allows us to very easily use multiple cores to detect the MHWs. The problem with this approach is that one must never load the plyr library directly as it has some fundamental inconsistencies with the tidyverse. We will see below how to perform these two different techniques without causing ourselves any headaches.

It is a little clumsy to use multiple functions at once with the two methods so we will combine the calculations we want to make into one wrapper function.

event_only <- function(df){
  # First calculate the climatologies
  clim <- ts2clm(data = df, climatologyPeriod = c("1982-01-01", "2011-01-01"))
  # Then the events
  event <- detect_event(data = clim)
  # Return only the event metric dataframe of results
  return(event$event)
}

system.time(
# First we start by choosing the 'OISST' dataframe
MHW_dplyr <- OISST %>% 
  # Then we group the data by the 'lon' and 'lat' columns
  group_by(lon, lat) %>% 
  # Then we run our MHW detecting function on each group
  group_modify(~event_only(.x))
) # ~123 seconds

# NB: One should never use ALL available cores, save at least 1 for other essential tasks
# The computer I'm writing this vignette on has 8 cores, so I use 7 here
registerDoParallel(cores = 7)

# Detect events
system.time(
MHW_plyr <- plyr::ddply(.data = OISST, .variables = c("lon", "lat"), .fun = event_only, .parallel = TRUE)
) # 33 seconds

A harmonious third option

As one may see above, running these calculations on a very large (or even global) gridded dataset can quickly become very heavy. While running these calculations myself on the global OISST dataset I have found that the fastest option is to combine the two options above. In my workflow I have saved each longitude segment of the global OISST dataset as separate files and use the dplyr method on each individual file, while using the plyr method to be running the multiple calculations on as many files as my core limit will allow. One may not do this the other way around and use dplyr to run multiple plyr calculations at once. This will confuse your computer and likely cause a stack overflow. Which sounds more fun than it actually is… as I have had to learn.

In order to happily combine these two options into one we will need to convert the dplyr code we wrote above into it’s own wrapper function, which we will then call on a stack of files using the plyr technique. Before we do that we must first create the aforementioned stack of files.

for(i in 1:length(unique(OISST$lon))){
  OISST_sub <- OISST %>% 
    filter(lon == unique(lon)[i])
  saveRDS(object = OISST_sub, file = paste0("~/Desktop/OISST_lon_",i,".Rds"))
}

This may initially seem like an unnecessary extra step, but when one is working with time series data it is necessary to have all of the dates at a given pixel loaded at once. Unless one is working from a server/virtual machine/supercomputer this means that one will often not be able to comfortably hold an entire grid for a study area in memory at once. Having the data accessible as thin strips like this makes life easier. And as we see in the code chunk below it also (arguably) allows us to perform the most efficient calculations on our data.

# The 'dplyr' wrapper function to pass to 'plyr'
dplyr_wraper <- function(file_name){
  MHW_dplyr <- readRDS(file_name) %>% 
    group_by(lon, lat) %>% 
    group_modify(~event_only(.x))
}
# Create a vector of the files we want to use
OISST_files <- dir("~/Desktop", pattern = "OISST_lon_*", full.names = T)

# Use 'plyr' technique to run 'dplyr' technique with multiple cores
system.time(
MHW_result <- plyr::ldply(OISST_files, .fun = dplyr_wraper, .parallel = T)
) # 31 seconds

# Save for later use as desired
saveRDS(MHW_result, "~/Desktop/MHW_result.Rds")

Even though this technique is not much faster computationally, it is much lighter on our memory (RAM) as it only loads one longitude slice of our data at a time. To maximise efficiency even further I would recommend writing out this full workflow in a stand-alone script and then running it using source() directly from an R terminal. The gain in speed here appears nominal, but as one scales this up the speed boost becomes apparent.

As mentioned above, recent changes to how dplyr interacts with one’s computer has perhaps slowed down the plyr + dplyr workflow shown here. It may be now that simply using plyr by itself is the better option. It depends on the number of cores and the amount of RAM that one has available.

Trend detection

With our MHW detected we will now look at how to fit some GLMs to the results in order to determine long-term trends in MHW occurrence.

Up first we see how to calculate the number of events that occurred per pixel.

# summarise the number of unique longitude, latitude and year combination:
OISST_n <- MHW_result %>% 
  mutate(year = lubridate::year(date_start)) %>% 
  group_by(lon, lat, year) %>% 
  summarise(n = n(), .groups = "drop") %>% 
  group_by(lon, lat) %>%
  tidyr::complete(year = c(1982:2019)) %>% # Note that these dates may differ
  mutate(n = ifelse(is.na(n), 0, n))
head(OISST_n)

Then we specify the particulars of the GLM we are going to use.

lin_fun <- function(ev) {
  mod1 <- glm(n ~ year, family = poisson(link = "log"), data = ev)
  # extract slope coefficient and its p-value
  tr <- data.frame(slope = summary(mod1)$coefficients[2,1],
                   p = summary(mod1)$coefficients[2,4])
  return(tr)
}

Lastly we make the calculations.

OISST_nTrend <- plyr::ddply(OISST_n, c("lon", "lat"), lin_fun, .parallel = T)
OISST_nTrend$pval <- cut(OISST_nTrend$p, breaks = c(0, 0.001, 0.01, 0.05, 1))
head(OISST_nTrend)

Visualising the results

Let’s finish this vignette by visualising the long-term trends in the annual occurrence of MHWs per pixel in the chosen study area. First we will grab the base global map from the maps package.

# The base map
map_base <- ggplot2::fortify(maps::map(fill = TRUE, plot = FALSE)) %>% 
  dplyr::rename(lon = long)

Then we will create two maps that we will stick together using ggpubr. The first map will show the slope of the count of events detected per year over time as shades of red, and the second map will show the significance (p-value) of these trends in shades of grey.

map_slope <- ggplot(OISST_nTrend, aes(x = lon, y = lat)) +
  geom_rect(size = 0.2, fill = NA,
       aes(xmin = lon - 0.1, xmax = lon + 0.1, ymin = lat - 0.1, ymax = lat + 0.1,
           colour = pval)) +
  geom_raster(aes(fill = slope), interpolate = FALSE, alpha = 0.9) +
  scale_fill_gradient2(name = "count/year (slope)", high = "red", mid = "white",
                       low = "darkblue", midpoint = 0,
                       guide = guide_colourbar(direction = "horizontal",
                                               title.position = "top")) +
  scale_colour_manual(breaks = c("(0,0.001]", "(0.001,0.01]", "(0.01,0.05]", "(0.05,1]"),
                      values = c("firebrick1", "firebrick2", "firebrick3", "white"),
                      name = "p-value", guide = FALSE) +
  geom_polygon(data = map_base, aes(group = group), 
               colour = NA, fill = "grey80") +
  coord_fixed(ratio = 1, xlim = c(13.0, 23.0), ylim = c(-33, -42), expand = TRUE) +
  labs(x = "", y = "") +
  theme_bw() +
  theme(legend.position = "bottom")

map_p <- ggplot(OISST_nTrend, aes(x = lon, y = lat)) +
  geom_raster(aes(fill = pval), interpolate = FALSE) +
  scale_fill_manual(breaks = c("(0,0.001]", "(0.001,0.01]", "(0.01,0.05]",
                               "(0.05,0.1]", "(0.1,0.5]", "(0.5,1]"),
                    values = c("black", "grey20", "grey40",
                               "grey80", "grey90", "white"),
                    name = "p-value",
                    guide = guide_legend(direction = "horizontal",
                                               title.position = "top")) +
  geom_polygon(data = map_base, aes(group = group), 
               colour = NA, fill = "grey80") +
  coord_fixed(ratio = 1, xlim = c(13.0, 23.0), ylim = c(-33, -42), expand = TRUE) +
  labs(x = "", y = "") +
  theme_bw() +
  theme(legend.position = "bottom")

map_both <- ggpubr::ggarrange(map_slope, map_p, align = "hv")
map_both

From the figure above we may see that the entire study area shows significant (p<= 0.05) increases in the count of MHWs per year. This is generally the case for the entire globe. Not shown here is the significant increase in the intensity of MHWs as well.