Outline

This document outlines the steps taken in the completion of four tasks: (i) extracting, aggregating, and plotting precipitation from a reanalysis dataset; (ii) generating time series of precipitation anomalies centred over Ireland, Iceland, and Newfoundland; (iii) calculating and plotting the correlation of North Atlantic precipitation anomalies with these internal time series; and, (iv) calculating, plotting, and assessing the statistical significance of the correlation of North Atlantic precipitation anomalies with external time series of Irish precipitation and an index of the North Atlantic Oscillation (NAO).

Data

The following three datasets are used in this workshop: (i) the NCEP/NCAR Reanalysis (R1); (ii) the Island of Ireland (IoI) precipitation series; and, (iii) the Hurrell Principal Component (PC)-based NAO index.

NCEP/NCAR Reanalysis (R1)

Climate reanalysis is the consistent reprocessing of archived weather observations using a modern forecasting system (Dee et al., 2014). In reanalysis, a data assimilation routine is used to merge available observations with forecast from a numerical weather prediction (NWP) model to produce comprehensive, uniform gridded estimates for a large number of atmospheric, sea-state, and land surface parameters at regular intervals over long periods of time (Dee et al. 2014; Parker, 2016). The equations of motion and physical processes as represented in the model allow for the estimation of many parameters that are not directly observed, and also ensure that such estimates are physically consistent with observations (Dee et al., 2014). Hence, reanalysis data have been widely employed in the evaluation of climate models, the detection and attribution of climate change, and the provision of climate services (Dee et al., 2014; Parker, 2016).

The NCEP/NCAR Reanalysis (R1) is a joint project of the National Centres for Environmental Prediction (NCEP) and the National Centre for Atmospheric Research (NCAR). It was the first major reanalysis product which delivered global gridded data at sub-daily intervals for the period 1957-96 (Kalnay et al., 1996). R1 was later extended back to 1948 and provisions were made to continue to perform data assimilation into the future. It remains an ongoing project which provides reanalysis data from 1948 to the present day (Kistler et al., 2001). R1 can be distinguished from the NCEP-DOE Reanalysis (R2), a follow-up project which corrected a number of errors with and updated the parameterisation schemes of the underlying model. However, R2 should not be seen as a replacement for R1 as it only provides data from 1979 onward (Kanamitsu et al., 2002). R1 is still frequently used and where precipitation is concerned, as is the case here, the spatial patterns as represented in R1 have been shown to be more consistent with observations than those represented in R2 (Bosilovich et al., 2008).

The reanalysis data used in this workshop is R1 precipitation covering the period 1948-2014.

Island of Ireland (IoI) Precipitation Series

The Island of Ireland (IoI) precipitation series is a 305-year continuous monthly rainfall series for the Island of Ireland covering the period 1711-2016 (Murphy et al., 2018). It is a composite series in which pre-1850 data is sourced from instrumental and documentary records compiled but not published by the UK Met Office (Murphy et al., 2018) and post-1850 data is the existing quality assured Island of Ireland Precipitation (IIP) network (Noone et al., 2016).

Hurrell Principal Component (PC)-based NAO Index

The NAO represents the most prominent and recurrent pattern of interannual variability in atmospheric circulation over the middle and high latitudes of the Northern Hemisphere (Hurrell, 1995; 1996; Hurrell et al., 2003) It refers to the large-scale redistribution of atmospheric surface pressure between the Azores High and the Icelandic Low and has a notable controlling influence over the weather and climate of the North Atlantic (Hurrell et al., 2003).

Given that there is no unique way to define the spatial structure of the NAO, it follows that there is no universally accepted index to describe the temporal evolution of the phenomenon (Hurrell, 2018). Station-based indices, which typically measure the pressure differential between the Azores High and the Icelandic Low, have been widely applied but are limited in their ability to capture the seasonal, interannual, and multidecadal spatial variability of the phenomenon (Hanna and Cropper, 2017).

A popular alternative to station-based indices is the Hurrell principal component (PC)-based NAO index. This is the time series of the leading empirical orthogonal function (EOF) of SLP anomalies over the Atlantic sector (20-80°N; 90°W-40°E). It is used to measure the NAO throughout the year and tracks the seasonal movements of the Azores High and the Icelandic Low (Hurrell, 2018). PC-based indices are advantageous as they are a more optimal representation of the spatial pattern of the NAO. Additionally, although generally shorter in length, PC-based indices tend to be less noisy than station-based indices (Hurrell, 2018).

The Hurrell PC-based NAO index covers the period 1899 to the present day. It is calculated from the NCAR Sea Level Pressure dataset which is a gridded analysis of SLP from land station reports, quality controlled and homogenised to account for changes in instrumentation and station location.

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Setup

Preparatory code necessary for the completion of the workshop. 

# Load the required packages.
require(lattice)
require(latticeExtra)
require(ncdf4)
require(OpenStreetMap)
require(raster)
require(rasterVis)
require(RColorBrewer)
require(reshape2)
require(rgdal)
require(sp)

# Set the working directory.
setwd("C:/Users/Sean/Desktop/Assignments/GY659/Reconstructing Atlantic Precipitation/R/")

# Clear the global environment and reset the graphics device.
rm(list = ls())
graphics.off()

# Set the path to the data.
path <- file.path(getwd(), "Data")

# Read the coastline shapefile into a spatial vector object.
world.coast <- readOGR(dsn = file.path(path, "NE_110m_Coastline"), layer = "NE_110m_Coastline")

# Convert this object to the correct coordinate reference system.
world.coast <- spTransform(world.coast, CRS("+proj=longlat +datum=WGS84"))

Task 1

Plot annual average precipitation in the NCEP Reanalysis. The plot should be centred on the 0° meridian and the units should be displayed. 

# Import the NCEP Reanalysis data. The NetCDF format is widely used for geophysical data.
nc <- nc_open(file.path(path, "NetCDF/NCEP_Reanalysis_1948_2014.nc"))

# The data has three dimensions:
#   1. lat  (degrees_north)
#   2. lon  (degrees_east)
#   3. time (hours since 1-1-1 00:00:0.0)

# The data has one variable:
#   - prate (kg/m^2/s)

# Extract latitude and longitude.
lat <- ncvar_get(nc, "lat")
lon <- ncvar_get(nc, "lon")

# Extract time.
time <- ncvar_get(nc, "time")

# Time needs to be converted from hours to days.
# Subtracting the additional two days means monthly values will begin on the first of the month.
time <- (time / 24) - 2

# Retrieve units of time.
t.units <- ncatt_get(nc, "time", attname = "units")
t.ustr  <- strsplit(t.units$value, " ")

# Convert time to date format.
date <- as.character(as.Date(time, origin = unlist(t.ustr)[3]))

# Extract precipitation (prate).
# To convert from kg/m^2/s to mm/d multiply by 86400.
prate <- ncvar_get(nc, "prate") * 86400

# Remove missing values.
fillVal <- ncatt_get(nc, "prate", "_FillValue")
missVal <- ncatt_get(nc, "prate", "missing_value")

prate[prate == fillVal$value] <- NA
prate[prate == missVal$value] <- NA
prate[prate == -1000]         <- NA

# Split longitude.
# This is necessary to centre the plot on the 0° meridian.
split <- which(lon == 180)
lon   <- c(lon[(split + 1):length(lon)] - 360, lon[1:split])

# Rearrange the precipitation data accordingly.
prate <- prate[c((split + 1):length(lon), 1:split), ,]

# Calculate mean annual precipitation.
year <- format(as.Date(date, format = "%Y-%m-%d"), "%Y")

yrs <- unique(year)
nyr <- length(yrs)

aprate <- array(NA, c(length(lon), length(lat), nyr))

for(k in 1:nyr) {
  aprate[, , k] <- rowMeans(prate[, , year == yrs[k]], na.rm = F, dims = 2)
}

# Set up a grid.
grid        <- expand.grid(x = lon, y = lat)
grid$aprate <- as.vector(rowMeans(aprate, na.rm = F, dims = 2))

# Alternatively, mean annual precipitation can also be calculated using a single line of code:
#   aprate <- rowMeans(prate, na.rm = F, dims = 2)
#
# Values are then added to the grid as follows:
#   grid$aprate <- as.vector(aprate)
#
# These values differ slightly from the other method as the rowMeans() function is not applied twice. 
# However, as we are dealing with annual averages the resultant plot will be practically identical.

# Define a colour set for the plot.
col <- brewer.pal(10, "BrBG")
pal <- colorRampPalette(col)

# Plot mean annual precipitation.
levelplot(aprate~x*y, grid,
          at = c(0:10),
          col.regions = pal(100),
          xlab = "Longitude",
          ylab = "Latitude",
          main = "Mean Annual Precipitation (mm/d)") +
  layer(sp.lines(world.coast))

Figure 1: Mean annual precipitation values (mm/d) derived from the NCEP reanalysis data.

Figure 1 shows global mean annual precipitation in millimetres per day as derived from the NCEP reanalysis data. It is evident that mean annual precipitation is highest in a band extending through the equatorial regions. This is primarily a result of global circulation patterns, which cause the trade wind systems to come together at the Intertropical Convergence Zone (ITCZ), creating frontal lifting, and convective activity arising from constant solar heating. High precipitation in the equatorial regions is also associated with monsoon circulations which are particularly well-developed over tropical Asia (Barry and Chorley, 2010; Robinson and Henderson-Sellers, 2014). Regions of low precipitation include the subtropical deserts and the Polar Regions. In the case of the former, the lack of precipitation is associated not with an absence of moisture but rather an absence of mechanisms required to lift the air and bring it to saturation. In the case of the latter, the lack of precipitation is associated with both an absence of moisture and an absence of uplift (Barry and Chorley, 2010; Robinson and Henderson-Sellers, 2014). Average precipitation at the mid-latitudes generally falls between the subtropical maximum and the equatorial minimum. It is associated with frontal lifting and cyclonic activity caused by the convergence of polar and subtropical air masses which gives extended periods of gentle rain over a broad area (Robinson and Henderson-Sellers, 2014).

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Task 2

Part 1: Generate a time series of precipitation anomalies centred over Ireland. 

# Create a new variable to store anomaly values.
anom <- aprate

# Calculate the global mean.
gMean <- colMeans(anom, na.rm = T, dims = 2)

# Remove the global mean to calculate the precipitation anomaly.
for(k in 1:nyr) {
  anom[, , k] <- anom[, , k] - matrix(gMean[k], length(lon), length(lat))
}

# Define a set of coordinates for Ireland.
lon0 <- -6
lat0 <- 53

# Generate the time series.
anom.ts <- anom[max(which(lon <= lon0)), min(which(lat <= lat0)), ]

# Plot the time series.
plot(yrs, anom.ts,
     type = "n",
     xlab = "",
     ylab = "Anomaly (mm)",
     main = paste0("Precipitation Anomaly over Ireland (Lon = ", lon0, ", Lat = ", lat0, ")"))

abline(v = seq(1950, 2010, 10), col = "lightgrey", lty = "dotted") # Vertical grid lines.
abline(h = seq(-1, 0.5, 0.5), col = "lightgrey", lty = "dotted") # Horizontal grid lines.

lines(yrs, anom.ts, lwd = 2) # Draw the plot over the grid.

Figure 2.1: Time series of precipitation anomalies over Ireland, 1948–2014.

 

Part 2: Calculate and plot the correlation of this time series with precipitation anomalies over the North Atlantic. 

# Create a correlation matrix with three dimensions.
c.matrix <- matrix(NA, length(lon), length(lat))

# Calculate the correlation between the anomaly at each pair of lon/lat coordinates and the time series.
# This is done using a loop which runs for the length of the lon/lat variables.
# Correlation values are stored in the matrix.
for(i in 1:length(lon)) {
  for(j in 1:length(lat)) {
    c.matrix[i, j] <- cor(anom[i, j, ], anom.ts)
  }
}

# Add these correlation values to the grid.
grid$corr.ie <- as.vector(c.matrix)

# Define a new set of colours for the correlation plot.
col <- rev(brewer.pal(10, "RdBu")) # Reverse palette so blue = negative and red = positive.
pal <- colorRampPalette(col)

# Plot the correlation.
levelplot(corr.ie~x*y, grid,
          at = c(-10:10) / 10,
          col.regions = pal(100),
          xlim = c(-120, 10),
          ylim = c(0, 80),
          xlab = "Longitude",
          ylab = "Latitude",
          main = paste0("Correlation of Precipitation Anomaly with Lon = ", lon0, ", Lat = ", lat0)) +
  layer(sp.lines(world.coast))

Figure 2.2: Correlation of North Atlantic precipitation anomalies with Ireland.

 

Part 3: Describe the correlation pattern.

Figure 2.2 shows the correlation of North Atlantic precipitation anomalies with Ireland.

A perfect positive correlation (r = 1) is observed at 53°N, 6°W. Moderate to strong positive correlations (0.3 ≤ r ≤ 1) are observed over Ireland and Britain, as well as the surrounding ocean. This is an indication that these areas are subject to a similar precipitation regime which is not unsurprising given that both Ireland and Britain are characterised by a temperate oceanic climate (Köppen-Geiger type Cfb, Peel et al., 2007). Rainfall over the British-Irish Isles is a product of both the prevailing westerly winds, which bring warm, moist air to the group of islands, and cyclonic activity associated with frontal lifting arising from the interaction between subtropical and polar air masses (Mayes and Wheeler, 2013; Sweeney, 2014). It is possible to track the path of the westerlies across the ocean by the relatively narrow band of weak to moderate positive correlations (0.1 ≤ r ≤ 0.5) stretching toward the eastern United States. As these winds move from west to east, with precipitation decreasing from the source region, the correlations here are weaker than over the British-Irish Isles. It would not be unreasonable to expect weak positive correlations to also extend into parts of Scandinavia and Continental Europe, eventually becoming negative as the winds lose most of their moisture and begin to dry up.

An important consideration is the fact that the direction and intensity of both the westerly winds and the rainfall generating mid-latitude cyclones that bring precipitation to the British-Irish Isles are heavily modulated by the NAO (Mayes and Wheeler, 2013). This may go toward explaining why positive correlations are observed over the Icelandic Low (between Iceland and Southern Greenland) and negative correlations are observed around the Azores High (off the coast of Portugal) as these pressure centres are enhanced during positive phases of the NAO which leads to more frequent rainfall over Western Europe, including Ireland and Britain, and less frequent rainfall over Southern Europe (Hurrell et al., 2003).

Other weak to moderate positive correlations include those observed over Southeast Greenland, parts of North America, and Central Africa. Weak to moderate negative correlations (-0.1 ≤ r ≤ -0.5) are observed over the Norwegian Sea, Northwest Africa, and Central North America.

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Task 3

Part 1: Generate a time series of precipitation anomalies centred over Iceland. 

# Define a set of coordinates for Iceland.
lon0 <- -19
lat0 <- 67

# Generate the time series.
anom.ts <- anom[max(which(lon <= lon0)), min(which(lat <= lat0)), ]

# Plot the time series.
plot(yrs, anom.ts,
     type = "n",
     xlab = "",
     ylab = "Anomaly (mm)",
     main = paste0("Precipitation Anomaly over Iceland (Lon = ", lon0, ", Lat = ", lat0, ")"))

abline(v = seq(1950, 2010, 10), col = "lightgrey", lty = "dotted") # Vertical grid lines.
abline(h = seq(-1.5, 0, 0.5), col = "lightgrey", lty = "dotted") # Horizontal grid lines.

lines(yrs, anom.ts, lwd = 2) # Draw the plot over the grid.

Figure 3.1: Time series of precipitation anomalies over Iceland, 1948–2014.

 

Part 2: Calculate and plot the correlation of this time series with precipitation anomalies over the North Atlantic. 

# Create a correlation matrix with three dimensions.
c.matrix <- matrix(NA, length(lon), length(lat))

# Calculate the correlation between the anomaly at each pair of lon/lat coordinates and the time series.
for(i in 1:length(lon)) {
  for(j in 1:length(lat)) {
    c.matrix[i, j] <- cor(anom[i, j, ], anom.ts)
  }
}

# Add these correlation values to the grid.
grid$corr.is <- as.vector(c.matrix)

# Plot the correlation.
levelplot(corr.is~x*y, grid,
          at = c(-10:10) / 10,
          col.regions = pal(100),
          xlim = c(-120, 10),
          ylim = c(0, 80),
          xlab = "Longitude",
          ylab = "Latitude",
          main = paste0("Correlation of Precipitation Anomaly with Lon = ", lon0, ", Lat = ", lat0)) +
  layer(sp.lines(world.coast))

Figure 3.2: Correlation of North Atlantic precipitation anomalies with Iceland.

 

Part 3: Generate a time series of precipitation anomalies centred over Newfoundland. 

# Define a set of coordinates for Newfoundland.
lon0 <- -56
lat0 <- 49

# Generate the time series.
anom.ts <- anom[max(which(lon <= lon0)), min(which(lat <= lat0)), ]

# Plot the time series.
plot(yrs, anom.ts,
     type = "n",
     xlab = "",
     ylab = "Anomaly (mm)",
     main = paste0("Precipitation Anomaly over Newfoundland (Lon = ", lon0, ", Lat = ", lat0, ")"))

abline(v = seq(1950, 2010, 10), col = "lightgrey", lty = "dotted") # Vertical grid lines.
abline(h = seq(-1, 1, 0.5), col = "lightgrey", lty = "dotted") # Horizontal grid lines.

lines(yrs, anom.ts, lwd = 2) # Draw the plot over the grid.

Figure 3.3: Time series of precipitation anomalies over Newfoundland, 1948–2014.

 

Part 4: Calculate and plot the correlation of this time series with precipitation anomalies over the North Atlantic. 

# Create a correlation matrix with three dimensions.
c.matrix <- matrix(NA, length(lon), length(lat))

# Calculate the correlation between the anomaly at each pair of lon/lat coordinates and the time series.
for(i in 1:length(lon)) {
  for(j in 1:length(lat)) {
    c.matrix[i, j] <- cor(anom[i, j, ], anom.ts)
  }
}

# Add these correlation values to the grid.
grid$corr.nf <- as.vector(c.matrix)

# Plot the correlation.
levelplot(corr.nf~x*y, grid,
          at = c(-10:10) / 10,
          col.regions = pal(100),
          xlim = c(-120, 10),
          ylim = c(0, 80),
          xlab = "Longitude",
          ylab = "Latitude",
          main = paste0("Correlation of Precipitation Anomaly with Lon = ", lon0, ", Lat = ", lat0)) +
  layer(sp.lines(world.coast))

Figure 3.4: Correlation of North Atlantic precipitation anomalies with Newfoundland.

 

Part 5: Describe and compare the correlation patterns.

Figure 3.2 shows the correlation of North Atlantic precipitation anomalies with Iceland. A perfect positive correlation (r = 1) is observed at 67°N, 19°W. Moderate to strong positive correlations (0.3 ≤ r ≤ 1) are observed in much of the surrounding area, including the Norwegian Sea and Southeast Greenland. Weak to moderate positive correlations (0.1 ≤ r ≤ 0.5) can be seen over much of North America, including Newfoundland. Weak to moderate negative correlations (-0.1 ≤ r ≤ -0.5) are observed over the Caribbean, as well as the Azores High and Central Africa. There is little evidence of correlation between precipitation anomalies over Iceland and precipitation anomalies over the British-Irish Isles, with observed values being extremely weak. As in Figure 2.2, the positive correlations observed over the Icelandic Low and the negative correlations observed over the Azores High may be explained by the NAO and the dominant influence it exerts on North Atlantic climate variability.

Figure 3.4 shows the correlation of North Atlantic precipitation anomalies with Newfoundland. A perfect positive correlation (r = 1) is observed at 49°N, 56°W. The correlation pattern in Figure 3.4 is very similar to that in Figure 3.2. Moderate to strong positive correlations (0.3 ≤ r ≤ 1) are observed in a large area surrounding Iceland whilst weak to moderate positive correlations (0.1 ≤ r ≤ 0.5) are observed over much of North America and Southeast Greenland. Figure 3.4 differs slightly in that correlations over the British-Irish Isles are positive and stronger than in Figure 3.2. The band of positive correlations stretching from Newfoundland toward the British-Irish Isles may in part by explained by the NAO as positive phases tend to lead to a north-eastward shift in Atlantic storm activity, resulting in increased activity from Newfoundland to Northern Europe and thus more precipitation (Hurrell and Deser, 2009). Unlike Figure 3.2, correlations over the Norwegian Sea are negative rather than positive. As in Figure 3.2, negative correlations persist over the Caribbean and Central Africa though are generally stronger, being classified as moderate to strong (-0.5 ≤ r ≤ -1) rather than weak to moderate. The weak to moderate negative correlations (-0.1 ≤ r ≤ -0.5) around the Azores High also remain.

In summary, it is evident from both Figure 3.2 and Figure 3.4 that precipitation anomalies over Iceland and Newfoundland are positively correlated with one another and similarly correlated with precipitation anomalies across the North Atlantic, with these correlations being slightly stronger in the case of Newfoundland.

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Task 4

Part 1: Load the Noone et al. (2016) time series and trim to the same time range as the reanalysis precipitation. Calculate the correlation pattern in the NCEP dataset associated with this external time series. How do we assess the confidence or significance of the correlation values? Overlay this information on your figure (hatches, stippling, or blank out areas). 

# Import the IoI series.
ioi <- read.csv(file.path(path, "CSV/IOI_1711_SERIES.csv"))

# Aggregate to yearly data.
ioi <- aggregate(ioi$Median, by = list(ioi$Year), FUN = mean, na.rm = T)

# Rename the columns.
colnames(ioi) <- c("Year", "Precipitation")

# Trim the series to the same length as the NCEP Reanalysis (1948-2014)
ioi <- ioi[238:304, ]

# Create a correlation matrix with three dimensions.
c.matrix <- matrix(NA, length(lon), length(lat))

# Create an additional matrix to store associated p-values.
t.matrix <- matrix(NA, length(lon), length(lat))

# Calculate the correlation between the anomaly at each pair of lon/lat coordinates and the time series.
# The significance of each correlation is tested using cor.test().
# For each correlation, the results of cor.test() are stored as a variable (p.vals).
# The p-values are then extracted and stored in t.matrix.
for(i in 1:length(lon)) {
  for(j in 1:length(lat)) {
    c.matrix[i, j] <- cor(anom[i, j, ], ioi$Precipitation)
    p.vals <- cor.test(anom[i, j, ], ioi$Precipitation)
    t.matrix[i, j] <- p.vals$p.value
  }
}

# Add these values to the grid.
grid$corr.ioi <- as.vector(c.matrix)
grid$pval.ioi <- as.vector(t.matrix)

# Stippling can be used to highlight significant correlations.
# Assuming a 5% significance level, subset the grid data where pval.ioi < 0.05.
# Convert this subset to a spatial points data frame.
# It can then be overlayed on the plot in a manner similar to world.coast.
ioi.sig <- subset(grid[, c(1, 2, 7, 8)], pval.ioi < 0.05) # 1 = lat, 2 = lon, 7 = corr.ioi, 8 = pval.ioi.
ioi.sig <- SpatialPointsDataFrame(coords = ioi.sig[, c(1, 2)], data = ioi.sig)

# Plot the correlation.
levelplot(corr.ioi~x*y, grid,
          at = c(-10:10) / 10,
          col.regions = pal(100),
          xlim = c(-120, 10),
          ylim = c(0, 80),
          xlab = "Longitude",
          ylab = "Latitude",
          main = "Correlation of Precipitation Anomaly with IoI Series") +
  layer(sp.lines(world.coast)) +
  layer(sp.points(ioi.sig, pch = 20, cex = 0.55, col = "black"))

Figure 4.1: Correlation of North Atlantic precipitation anomalies with the Island of Ireland precipitation series. Stippling indicates correlations which are statistically significant (p < 0.05).

 

Part 2: Load the NAO index time series and trim to the same time range as the reanalysis precipitation. Calculate the correlation pattern in the NCEP dataset associated with this external time series. How do we assess the confidence or significance of the correlation values? Overlay this information on your figure (hatches, stippling, or blank out areas). 

# Import the NAO series.
NAO <- read.csv(file.path(path, "CSV/NAO_PC_MONTHLY.csv"))

# Trim to the same length as the NCEP Reanalysis (1948-2014).
NAO <- NAO[50:116, ]

# Aggregate to yearly data.
NAO <- data.frame(Year = NAO$Year, NAOi = rowMeans(NAO[, 2:13], na.rm = T))

# Create a correlation matrix with three dimensions.
c.matrix <- matrix(NA, length(lon), length(lat))

# Create an additional matrix to store associated p-values.
t.matrix <- matrix(NA, length(lon), length(lat))

# Calculate the correlation between the anomaly at each pair of lon/lat coordinates and the time series.
# Use cor.test() to calculate the significance of each of these values.
for(i in 1:length(lon)) {
  for(j in 1:length(lat)) {
    c.matrix[i, j] <- cor(anom[i, j, ], NAO$NAOi)
    p.vals <- cor.test(anom[i, j, ], NAO$NAOi)
    t.matrix[i, j] <- p.vals$p.value
  }
}

# Add these values to the grid.
grid$corr.nao <- as.vector(c.matrix)
grid$pval.nao <- as.vector(t.matrix)

# Assuming a 5% significance level, subset the grid data where pval.nao < 0.05.
# Convert this subset to a spatial points data frame.
nao.sig <- subset(grid[, c(1, 2, 9, 10)], pval.nao < 0.05) # 1 = lat, 2 = lon, 9 = corr.nao, 10 = pval.nao.
nao.sig <- SpatialPointsDataFrame(coords = nao.sig[, c(1, 2)], data = nao.sig)

# Plot the correlation.
levelplot(corr.nao~x*y, grid,
          at = c(-10:10) / 10,
          col.regions = pal(100),
          xlim = c(-120, 10),
          ylim = c(0, 80),
          xlab = "Longitude",
          ylab = "Latitude",
          main = "Correlation of Precipitation Anomaly with NAO Index") +
  layer(sp.lines(world.coast)) +
  layer(sp.points(nao.sig, pch = 20, cex = 0.55, col = "black"))

Figure 4.2: Correlation of North Atlantic precipitation anomalies with the Hurrell PC-based NAO index. Stippling indicates correlations which are statistically significant (p < 0.05).

 

Part 3: Describe and compare the correlation patterns.

Figure 4.1 shows the correlation of North Atlantic precipitation anomalies with the IoI precipitation series. A strong, statistically significant (p < 0.5) positive correlation (0.5 ≤ r ≤ 1) is observed over Ireland whilst moderate to strong statistically significant positive correlations (0.3 ≤ r ≤ 1) are observed over the surrounding area. Weak to moderate statistically significant negative correlations (-0.1 ≤ r ≤ -0.5) are observed over the Norwegian Sea, as well as parts of South Greenland. The pattern in Figure 4.1 is very similar to that in Figure 2.2 and in general the strong, statistically significant positive correlation over Ireland is indicative of the quality and accuracy of the IoI precipitation series. As in Figure 2.2, the path taken by the prevailing westerlies across the ocean can be tracked by the band of weak to moderate positive correlations (0.1 ≤ r ≤ 0.5) stretching toward the eastern United States, though these correlations are not statistically significant.

Figure 4.2 is markedly different to Figure 4.1 as it shows the correlation of North Atlantic precipitation anomalies with the Hurrell PC-based NAO index, which describes the state of a natural mode of climate variability. Moderate to strong, statistically significant (p < 0.5) positive correlations (0.5 ≤ r ≤ 1) are observed over Iceland and the surrounding area whilst moderate to strong, statistically significant negative correlations (-0.5 ≤ r ≤ -1) are observed over the Azores and the surrounding area. These correlations correspond with the two centres of pressure that comprise the NAO, the Icelandic Low and the Azores High. Given the upward trend in the NAO index since the 1960s, the observed patterns reflect the fact that a stronger (positive) NAO index is associated with higher precipitation over Western Europe and Northern Scandinavia (positive correlation) and lower precipitation over Southern Europe (negative correlation) due to changes in the transport and convergence of atmospheric moisture arising from shifts in circulation and storminess (Hurrell et al., 2003; Hurrell and Deser, 2009). Other statistically significant positive correlations are observed around the Eastern United States, extending into Canada, and other statistically significant negative correlations are observed over Central Africa and the Caribbean. It is worth noting that the pattern present in Figure 4.2 is not dissimilar to those in Figure 3.2 and Figure 3.4, reinforcing the role played by the NAO in influencing precipitation over Iceland and Newfoundland.

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References

Barry, R. G. & Chorley, R. J. (2010). Atmosphere, Weather and Climate. 9th edition. New York: Routledge

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