Insurance Risk Indices
Insurance Risk Indices are an ensemble of indices relevant for insurance industry. These indices are based on Expert Team on Climate Change Detection Indices (ETCCDI). There are currently 5 available indices to compute for extreme: heat (tx90p), cold (tn10p), wind (wx), drought (ccd) and flooding (rx5day). The individual indices can be combined into a single index with or without weighting for each component. This combined index is roughly analogous to the Actuaris Climate Risk Index.
Note: This vignette has been writen to process and plot the output of an ESMValTool namelist configured with a specific set of parameters. If you wish to run and plot the outputs for another set of parameters, you need to re-run the corresponding namelist with the desired parameters, interpolate the output NetCDF files to a common grid, and modify the vignette code accordingly.
The following exemple will compute the 5 different indices in the North Atlantic - European Sector [60ºW-40ºE; 30ºN-70ºN] using the CMIP5 projection for the 8.5 scenario.
1- Load dependencies
This example requires the following system libraries:
- libssl-dev
- libnecdf-dev
- cdo
You will need to install specific versions of certain R packages as follows:
library(devtools)
install_git('https://earth.bsc.es/gitlab/es/startR', branch = 'develop-hotfixes-0.0.2')Four functions should be load by running the following lines in R, until integrated into current version of s2dverification
source('https://earth.bsc.es/gitlab/es/s2dverification/raw/develop-Climdex/R/Climdex.R')
source('https://earth.bsc.es/gitlab/es/s2dverification/raw/develop-Climdex/R/Threshold.R')
source('https://earth.bsc.es/gitlab/es/s2dverification/raw/develop-Magic/vignettes/risk_index/DailyAnomaly.R')
source('https://earth.bsc.es/gitlab/es/s2dverification/raw/develop-Magic_WP6/R/WeightedMean.R')
source("https://earth.bsc.es/gitlab/es/s2dverification/raw/develop-Magic_WP6/R/CombineIndices.R")All the other R packages involved can be installed directly from CRAN and loaded as follows:
library(s2dverification)
library(startR)
library(multiApply)
library(ggplot2)
library(climdex.pcic)
library(parallel)2- Computing the Extreme Heat Index
The Extreme Heat Index (tx90p) is defined as the percentage of days when maximum temperature exceed the 90th percentile.
2.1- Extreme Heat Index Climatology
In order to evaluate the future projections, it is necessary to compute the index climatology during a reference historical period. In this example, the period 1971⨪2000 has been selected. The next steps should be followed:
- First is loaded the historical period with the function
Start(). The full description and examples of its use can be found here: https://earth.bsc.es/gitlab/es/startR. The object returned byStartwill have at least one time and two spatial dimensions.
var0 <- 'tasmax'
start_climatology <- '1971-01-01'
end_climatology <- '2000-12-31'
lat.min <- 30; lat.max <- 70
lon.min <- -60; lon.max <- 40
climatology_filenames <- paste0("/esarchive/scratch/pbretonn/cmip5-cp4cds/historical/day/tasmax/",
"tasmax_day_IPSL-CM5A-LR_historical_r1i1p1_19500101-20051231.nc")
reference_data <- Start(model = climatology_filenames, var = var0, var_var = 'var_names',
time = values(list(as.POSIXct(start_climatology), as.POSIXct(end_climatology))),
lat = values(list(lat.min, lat.max)), lon = values(list(lon.min, lon.max)),
lon_var = 'lon', lon_reorder = CircularSort(0, 360), return_vars = list(time = 'model',
lon = 'model', lat = 'model'), retrieve = TRUE)
metadata <- attributes(reference_data)> dim(reference_data)
model var time lat lon
1 1 10957 21 28 - To remove seasonality effects, the anomaly is computed with the next code lines. First, the day of the year, from 1 to 365, is identify for the 30 years period. Then, the anomaly for each day and gridpoint is computed by applying the
dailyAnofunction. Finally, the names of the dimensions are restablished.
dates <- attributes(reference_data)$Variables$dat1$time
dates <- as.PCICt(dates, cal = attributes(dates)$variables$time$calendar, format = "%Y%m%d")
jdays <- as.numeric(strftime(dates, format = "%j"))
anomaly_data <- Apply(list(reference_data), target_dims = which(names(dim(reference_data)) == "time"),
AtomicFun = "dailyAno", jdays = jdays, ncores = 4)$output1
names(dim(anomaly_data))[1] <- "time"- This data can be detrended by applying
Trendfunction. In order to remove the trend from thereference_data, the correction is calculated by substracting thedetrended_datato theanomaly_data. Again, the original dimensional information is restored.
detrended_data <- Trend(anomaly_data, posTR = which(names(dim(anomaly_data)) == "time"))
diff <- anomaly_data - detrended_data$detrended
diff <- aperm(diff, c(2,3,1,4,5))
detrended_data <- reference_data - diff
attributes(detrended_data) <- metadata- For each gridpoint and day of the year (from the 1st of January to the 31st of December), the maximum temperature on the position of the 90 percent of the series will be calculated as the threshold.
quantile <- 0.9
base_range <- as.numeric(c(substr(start_climatology, 1, 4), substr(end_climatology, 1, 4)))
thresholds <- Threshold(detrended_data, base_range = as.numeric(base_range),
qtiles = quantile, ncores = detectCores() -1)
thresholds_heat <- thresholds > dim(thresholds)
jdays model var lat lon
365 1 1 21 28 - By indicating the metric and introducing the threshold,
Climdex()function will return the extreme heat index during the reference periode.
base_index <- Climdex(data = detrended_data, metric = 'tx90p', quantiles = thresholds,
ncores = detectCores() - 1)The output of ´Climdex´ function will be a ´list()´ object. In the ´base_index$result´ label will be save the index values.
> str(base_index)
List of 2
$ result: num [1:30, 1, 1, 1:21, 1:28] 8.22 12.33 4.38 8.49 9.59 ...
$ years : chr [1:30] "1971" "1972" "1973" "1974" ...
> dim(base_index$result)
year model var lat lon
30 1 1 21 28- Finally, the index will standarized, by substracting the mean and dividing by the standard deviation, in order to facilitate the comparison with the future projection. Notice that, by definition, the mean of the percentage of the number of days exceeding the 90th percentile is 10. Only standard deviation is computed.
base_sd <- Apply(list(base_index$result), target_dims = list(c(1)), AtomicFun = "sd")$output1
base_heat_sd <- base_sd2.2- Extreme Heat Index Climate Projection
The Extreme Heat Index is computing for the period 2020⨪2040 by following the next steps:
- Loading data by using
Start()function.
start_model <- '2020-01-01'
end_model <- '2040-12-31'
model_filenames <- paste0("/esarchive/scratch/pbretonn/cmip5-cp4cds/rcp85/day/tasmax/",
"tasmax_day_IPSL-CM5A-LR_rcp85_r1i1p1_20060101-22051231.nc")
rcp_data <- Start(model = model_filenames, var = var0, var_var = 'var_names',
time = values(list(as.POSIXct(start_model), as.POSIXct(end_model))),
lat = values(list(lat.min, lat.max)), lon = values(list(lon.min, lon.max)),
lon_var = 'lon', lon_reorder = CircularSort(0, 360),
return_vars = list(time = 'model', lon = 'model', lat = 'model'),
retrieve = TRUE)The object returned by Start() contains the requested daily maximum temperature data for each gridpoint. summary() function allows to check their content.
> dim(rcp_data)
model var time lat lon
1 1 7671 21 28
> summary(rcp_data)
Min. 1st Qu. Median Mean 3rd Qu. Max.
221.6 276.7 283.6 283.4 291.2 321.1 - Now the index can be computed by considering the threshold obtain for the reference period.
projection_index <- Climdex(data = rcp_data, metric = 'tx90p', quantiles = thresholds,
ncores = detectCores() - 1)- Its normalized with mean 10 and the standard deviation of the reference period.
base_mean <- 10
base_sd <- InsertDim(base_sd, 1, dim(projection_index$result)[1])
HeatExtremeIndex <- (projection_index$result - base_mean) / base_sd2.3- Visualitzation of Extreme Heat Index
A Map of the mean index values during the examined period 2020-2040 is obtained and save in PNG format in the working directory with the name: “tx90p_IPSL-CMIP5_85rpc_2020-01-01_2040-12-31.png”
lat <- attr(rcp_data, "Variables")$dat1$lat
lon <- attr(rcp_data, "Variables")$dat1$lon
title <- paste0("Index for tx90p ", substr(start_model, 1, 4), "-",
substr(end_model, 1, 4), " 85rcp CMIP5-IPSL")
breaks <- -8 : 8
PlotEquiMap(Mean1Dim(HeatExtremeIndex, which(names(dim(HeatExtremeIndex)) == "year")), lon = lon,
lat = lat, filled.continents = FALSE, toptitle = title, brks=breaks,
fileout = paste0('tx90p_IPSL-CMIP5_85rpc_', start_model, "_", end_model, ".png"))
The inland average of the Extreme Heat Index can be computed to plot its time evolution using WeigthedMean function. Smoothing() returns the smoothed time series for a 3 years moving window which can be modify using runmeanlen parameter.
masc <- Start(model = '/esarchive/exp/ipsl-cm5a-lr/cmip5-rcp85_i1p1/constant/r0i0p0/fx/sftlf/sftlf.nc',
var = 'sftlf', var_var = 'var_names', lat = values(list(lat.min, lat.max)),
lon = values(list(lon.min, lon.max)), lon_reorder = CircularSort(0,360),
return_vars = list(lon = 'model', lat = 'model'), retrieve = TRUE)
temporal <- WeightedMean(HeatExtremeIndex, lon = lon, lat = lat, mask = drop(masc))
temporal_3ysmooth <- Smoothing(temporal, runmeanlen = 3, numdimt = 1)The next code should be runned to plot and save the original average and the 3 year smoothed data.
png("Temporal_Inland_ExtremeHeatIndex_IPSL-CMIP5_85rcp_2020-2040.png", width = 8, height = 5, units = 'in',
res = 100, type = "cairo")
plot(substr(start_model, 1, 4):substr(end_model, 1, 4), temporal, type = "l", lty = 5, lwd = 2, bty = 'n',
xlab = "Time (years)", ylab = "Extreme Heat Index", main = "Inland average Extreme Heat Index")
lines(substr(start_model, 1, 4):substr(end_model, 1, 4), temporal_3ysmooth, col = "darkgreen", lwd = 2)
legend('bottomright', c('Anual', '3 years smooth'), col = c(1, 'darkgreen'), lty = c(5, 1), lwd = 2, bty = 'n')
dev.off()
3- Extreme Cold Index
The Extreme Cold Index (tn10p) is defined as the percentage of days when minimum temperature falls behind the 10th percentile. The procedure will be equivalent at the previous Extreme Heat Index example.
3.1- Extreme Cold Index Climatology
- To load the historical simulations:
var0 <- 'tasmin'
climatology_filenames <- paste0("/esarchive/scratch/pbretonn/cmip5-cp4cds/historical/day/tasmin/",
"tasmin_day_IPSL-CM5A-LR_historical_r1i1p1_19500101-20051231.nc")
reference_data <- Start(model = climatology_filenames, var = var0, var_var = 'var_names',
time = values(list(as.POSIXct(start_climatology), as.POSIXct(end_climatology))),
lat = values(list(lat.min, lat.max)), lon = values(list(lon.min, lon.max)),
lon_var = 'lon', lon_reorder = CircularSort(0, 360),
return_vars = list(time = 'model', lon = 'model', lat = 'model'), retrieve = TRUE)
metadata <- attributes(reference_data)- To compute anomalies:
dates <- attributes(reference_data)$Variables$dat1$time
dates <- as.PCICt(dates, cal = attributes(dates)$variables$time$calendar, format = "%Y%m%d")
jdays <- as.numeric(strftime(dates, format = "%j"))
anomaly_data <- Apply(list(reference_data), target_dims = which(names(dim(reference_data)) == "time"),
AtomicFun = "dailyAno", jdays = jdays, ncores = 4)$output1
names(dim(anomaly_data))[1] <- "time"- To detrend the data:
detrended_data <- Trend(anomaly_data, posTR = which(names(dim(anomaly_data)) == "time"))
diff <- anomaly_data - detrended_data$detrended
diff <- aperm(diff, c(2,3,1,4,5))
detrended_data <- reference_data - diff
attributes(detrended_data) <- metadata- To obtain the thresholds (the minimum temperature on the position of the 10 percent of the series):
quantile <- 0.1
base_range <- as.numeric(c(substr(start_climatology, 1, 4), substr(end_climatology, 1, 4)))
thresholds <- Threshold(detrended_data, base_range = as.numeric(base_range), qtiles = quantile,
ncores = detectCores() -1)- To compute the Extreme Cold Index during the reference period and its standar deviation:
base_index <- Climdex(data = detrended_data, metric = 'tx10p', quantiles = thresholds,
ncores = detectCores() - 1)
base_sd <- Apply(list(base_index$result), target_dims = list(c(1)), AtomicFun = "sd")$output13.2- Extreme Cold Index Climate Projection
The Extreme Cold Index is computing for the period 2020⨪2040 by following the next steps:
- Loading data by using
Start()function.
model_filenames <- paste0("/esarchive/scratch/pbretonn/cmip5-cp4cds/rcp85/day/tasmin/",
"tasmin_day_IPSL-CM5A-LR_rcp85_r1i1p1_20060101-22051231.nc")
rcp_data <- Start(model = model_filenames, var = var0, var_var = 'var_names',
time = values(list(as.POSIXct(start_model), as.POSIXct(end_model))),
lat = values(list(lat.min, lat.max)), lon = values(list(lon.min, lon.max)),
lon_var = 'lon', lon_reorder = CircularSort(0, 360), return_vars = list(time = 'model',
lon = 'model', lat = 'model'), retrieve = TRUE)- To compute the index an standardize it:
projection_index <- Climdex(data = rcp_data, metric = 'tx10p', quantiles = thresholds,
ncores = detectCores() - 1)
base_mean <- 10
base_sd <- InsertDim(base_sd, 1, dim(projection_index$result)[1])
ColdExtremIndex <- (projection_index$result - base_mean) / base_sd3.3- Visualitzation of Extreme Cold Index
- Map of the mean index values during the examined period 2020-2040:
title <- paste0("Index for tn10p ", substr(start_model, 1, 4), "-", substr(end_model, 1, 4),
" 85rcp CMIP5-IPSL")
breaks <- -8 : 8
PlotEquiMap(Mean1Dim(ColdExtremeIndex, which(names(dim(ColdExtremeIndex)) == "year")), lon = lon, lat = lat,
filled.continents = FALSE, toptitle = title, brks=breaks,
fileout = paste0('tn10p_IPSL-CMIP5_85rpc_', start_model, "_", end_model, ".png"))
- Evolution of inland average of the Extreme Cold Index:
temporal <- WeightedMean(ColdExtremeIndex, lon = lon, lat = lat, mask = drop(masc))
temporal_3ysmooth <- Smoothing(temporal, runmeanlen = 3, numdimt = 1)
png("Temporal_Inland_ExtremeColdIndex_IPSL-CMIP5_85rcp_2020-2040.png", width = 8, height = 5, units= 'in',
res = 100, type = "cairo")
plot(substr(start_model, 1, 4):substr(end_model, 1, 4), temporal, type = "l", lty = 5, lwd = 2, bty = 'n',
xlab = "Time (years)", ylab = "Extreme Cold Index", main = "Inland average Extreme Cold Index")
lines(substr(start_model, 1, 4):substr(end_model, 1, 4), temporal_3ysmooth, col = "darkgreen",lwd = 2)
legend('bottomleft', c('Anual', '3 years smooth'), col= c(1, 'darkgreen'), lty = c(5, 1), lwd = 2,
bty = 'n')
dev.off()
4- Extreme Wind Power Index
The Extreme Wind Power Index (Wx) is defined as the percentage of days when wind power exceeds the 90th percentile being wind power proportional to the third power of wind speed. Then, the procedure will be equivalent at the previous examples.
4.1- Extreme Wind Power Index Climatology
- To load the historical simulations for the daily mean wind speed and convert them to wind power:
var0 <- 'sfcWind'
climatology_filenames <- paste0("/esarchive/scratch/pbretonn/cmip5-cp4cds/historical/day/sfcWind/",
"sfcWind_day_IPSL-CM5A-LR_historical_r1i1p1_19500101-20051231.nc")
reference_data <- Start(model = climatology_filenames, var = var0, var_var = 'var_names',
time = values(list(as.POSIXct(start_climatology), as.POSIXct(end_climatology))),
lat = values(list(lat.min, lat.max)), lon = values(list(lon.min, lon.max)),
lon_var = 'lon', lon_reorder = CircularSort(0, 360),
return_vars = list(time = 'model', lon = 'model', lat = 'model'), retrieve = TRUE)
metadata <- attributes(reference_data)
reference_data <- 0.5 * 1.23 * (reference_data ** 3) - To compute anomalies:
dates <- attributes(reference_data)$Variables$dat1$time
dates <- as.PCICt(dates, cal = attributes(dates)$variables$time$calendar, format = "%Y%m%d")
jdays <- as.numeric(strftime(dates, format = "%j"))
anomaly_data <- Apply(list(reference_data), target_dims = which(names(dim(reference_data)) == "time"),
AtomicFun = "dailyAno", jdays = jdays, ncores = 4)$output1
names(dim(anomaly_data))[1] <- "time"- To detrend the data:
detrended_data <- Trend(anomaly_data, posTR = which(names(dim(anomaly_data)) == "time"))
diff <- anomaly_data - detrended_data$detrended
diff <- aperm(diff, c(2,3,1,4,5))
detrended_data <- reference_data - diff
attributes(detrended_data) <- metadata- To obtain the thresholds (the wind power value on the position of the 90 percent of the series):
quantile <- 0.9
base_range <- as.numeric(c(substr(start_climatology, 1, 4), substr(end_climatology, 1, 4)))
thresholds <- Threshold(detrended_data, base_range = as.numeric(base_range), qtiles = quantile,
ncores = detectCores() -1)- To compute the Extreme Wind Power Index during the reference period and its standar deviation:
base_index <- Climdex(data = detrended_data, metric = 'Wx', quantiles = thresholds,
ncores = detectCores() - 1)
base_sd <- Apply(list(base_index$result), target_dims = list(c(1)), AtomicFun = "sd")$output14.2- Extreme Wind Power Index Climate Projection
The Extreme Cold Index is computing for the period 2020⨪2040 by following the next steps:
- Loading wind speed daily mean data and convert to wind power
model_filenames <- paste0("/esarchive/scratch/pbretonn/cmip5-cp4cds/rcp85/day/sfcWind/",
"sfcWind_day_IPSL-CM5A-LR_rcp85_r1i1p1_20060101-22051231.nc")
rcp_data <- Start(model = model_filenames, var = var0, var_var = 'var_names',
time = values(list(as.POSIXct(start_model), as.POSIXct(end_model))),
lat = values(list(lat.min, lat.max)), lon = values(list(lon.min, lon.max)),
lon_var = 'lon', lon_reorder = CircularSort(0, 360), return_vars = list(time = 'model',
lon = 'model', lat = 'model'), retrieve = TRUE)
rcp_data <- 0.5 * 1.23 * (rcp_data ** 3) - To compute the index and standardize it:
projection_index <- Climdex(data = rcp_data, metric = 'Wx', quantiles = thresholds,
ncores = detectCores() - 1)
base_mean <- 10
base_sd <- InsertDim(base_sd, 1, dim(projection_index$result)[1])
WindPowerExtremeIndex <- (projection_index$result - base_mean) / base_sd4.3- Visualitzation of Extreme Wind Power Index
- Map of the mean index values during the examined period 2020-2040:
title <- paste0("Index for Wx ", substr(start_model, 1, 4), "-", substr(end_model, 1, 4),
" 85rcp CMIP5-IPSL")
breaks <- -8 : 8
PlotEquiMap(Mean1Dim(WindPowerExtremeIndex, which(names(dim(WindPowerExtremeIndex)) == "year")), lon = lon,
lat = lat, filled.continents = FALSE, toptitle = title, brks=breaks,
fileout = paste0('wx_IPSL-CMIP5_85rpc_', start_model, "_", end_model, ".png"))<img src="wx_IPSL-CMIP5_85rpc_2020-01-01_2040-12-31.png"/>
- Evolution of inland average of the Extreme Cold Index:
temporal <- WeightedMean(WindPowerExtremeIndex, lon = lon, lat = lat, mask = drop(masc))
temporal_3ysmooth <- Smoothing(temporal, runmeanlen = 3, numdimt = 1)
png("Temporal_Inland_ExtremeWindPowerIndex_IPSL-CMIP5_85rcp_2020-2040.png", width = 8, height = 5,
units= 'in', res = 100, type = "cairo")
plot(substr(start_model, 1, 4):substr(end_model, 1, 4), temporal, type = "l", lty = 5, lwd = 2, bty = 'n',
xlab = "Time (years)", ylab = "Extreme Wind Power Index",
main = "Inland average Extreme Wind Power Index")
lines(substr(start_model, 1, 4):substr(end_model, 1, 4), temporal_3ysmooth, col = "darkgreen",lwd = 2)
legend('bottomleft', c('Anual', '3 years smooth'), col= c(1, 'darkgreen'), lty = c(5, 1), lwd = 2,
bty = 'n')
dev.off()img src=“Temporal_Inland_ExtremeWindPowerIndex_IPSL-CMIP5_85rcp_2020-2040.png” /
5- Extreme Drought Index
The Extreme Drought Index (cdd), which measures the maximum length of dry spell, is defined as the maximum number of consecutive days with daily precipitation amount lower than 1 mm. Then, the procedure will be equivalent at the previous examples.
5.1- Extreme Drought Index Climatology
- To load the historical simulations for the daily precipitation amount variable and convert units to mm from kg·m-2·s-1:
var0 <- 'pr'
climatology_filenames <- paste0("/esarchive/scratch/pbretonn/cmip5-cp4cds/historical/day/pr/",
"pr_day_IPSL-CM5A-LR_historical_r1i1p1_19500101-20051231.nc")
reference_data <- Start(model = climatology_filenames, var = var0, var_var = 'var_names',
time = values(list(as.POSIXct(start_climatology), as.POSIXct(end_climatology))),
lat = values(list(lat.min, lat.max)), lon = values(list(lon.min, lon.max)),
lon_var = 'lon', lon_reorder = CircularSort(0, 360),
return_vars = list(time = 'model', lon = 'model', lat = 'model'), retrieve = TRUE)
metadata <- attributes(reference_data)
reference_data <- reference_data * 60 * 60 * 24- To compute anomalies:
dates <- attributes(reference_data)$Variables$dat1$time
dates <- as.PCICt(dates, cal = attributes(dates)$variables$time$calendar, format = "%Y%m%d")
jdays <- as.numeric(strftime(dates, format = "%j"))
anomaly_data <- Apply(list(reference_data), target_dims = which(names(dim(reference_data)) == "time"),
AtomicFun = "dailyAno", jdays = jdays, ncores = 4)$output1
names(dim(anomaly_data))[1] <- "time"- To detrend the data:
detrended_data <- Trend(anomaly_data, posTR = which(names(dim(anomaly_data)) == "time"))
diff <- anomaly_data - detrended_data$detrended
diff <- aperm(diff, c(2,3,1,4,5))
detrended_data <- reference_data - diff
attributes(detrended_data) <- metadata- To compute the Extreme Drought Index during the reference period and its standar deviation and mean:
Note: This index doesn’t require to compute a threshold as Climdex function integrates the threshold of precipitation amount lower than 1 mm internally. However, this case requires the calculation of the mean.
base_index <- Climdex(data = detrended_data, metric = 'cdd', ncores = detectCores() - 1)
base_mean <- Apply(list(base_index$result), target_dims = list(c(1)), AtomicFun = "mean")$output1
base_sd <- Apply(list(base_index$result), target_dims = list(c(1)), AtomicFun = "sd")$output15.2- Extreme Drought Index Climate Projection
The Extreme Drought Index is computing for the period 2020⨪2040 by following the next steps.
- Loading data by using
Start()function and converting to mm:
model_filenames <- paste0("/esarchive/scratch/pbretonn/cmip5-cp4cds/rcp85/day/pr/",
"pr_day_IPSL-CM5A-LR_rcp85_r1i1p1_20060101-22051231.nc")
rcp_data <- Start(model = model_filenames, var = var0, var_var = 'var_names',
time = values(list(as.POSIXct(start_model), as.POSIXct(end_model))),
lat = values(list(lat.min, lat.max)), lon = values(list(lon.min, lon.max)),
lon_var = 'lon', lon_reorder = CircularSort(0, 360),
return_vars = list(time = 'model', lon = 'model', lat = 'model'),
retrieve = TRUE)
rcp_data <- rcp_data * 60 * 60 * 24- To compute the index and standardize it:
projection_index <- Climdex(data = rcp_data, metric = 'cdd', ncores = detectCores() - 1)
base_mean <- InsertDim(base_mean, 1, dim(projection_index$result)[1])
base_sd <- InsertDim(base_sd, 1, dim(projection_index$result)[1])
DroughtExtremeIndex <- (projection_index$result - base_mean) / base_sd5.3- Visualitzation of Extreme Drought Index
- Map of the mean index values during the examined period 2020-2040:
title <- paste0("Index for cdd ", substr(start_model, 1, 4), "-", substr(end_model, 1, 4),
" 85rcp CMIP5-IPSL")
breaks <- -8 : 8
PlotEquiMap(Mean1Dim(DroughtExtremeIndex, which(names(dim(DroughtExtremeIndex)) = "year")), lon = lon,
lat = lat, filled.continents = FALSE, toptitle = title, brks=breaks,
fileout = paste0('cdd_IPSL-CMIP5_85rpc_', start_model, "_", end_model, ".png"))<img src="cdd_IPSL-CMIP5_85rpc_2020-01-01_2040-12-31.png"/>
- Evolution of inland average of the Extreme Drought Index:
temporal <- WeightedMean(DroughtExtremeIndex, lon = lon, lat = lat, mask = drop(masc))
temporal_3ysmooth <- Smoothing(temporal, runmeanlen = 3, numdimt = 1)
png("Temporal_Inland_ExtremeDroughtIndex_IPSL-CMIP5_85rcp_2020-2040.png", width = 8, height = 5, units= 'in', res = 100, type = "cairo")
plot(substr(start_model, 1, 4):substr(end_model, 1, 4), temporal, type = "l", lty = 5, lwd = 2, bty = 'n',
xlab = "Time (years)", ylab = "Extreme Drought Index", main = "Inland average Extreme Drought Index")
lines(substr(start_model, 1, 4):substr(end_model, 1, 4), temporal_3ysmooth, col = "darkgreen",lwd = 2)
legend('bottomleft', c('Anual', '3 years smooth'), col= c(1, 'darkgreen'), lty = c(5, 1), lwd = 2,
bty = 'n')
dev.off()<img src="Temporal_Inland_ExtremeDroughtIndex_IPSL-CMIP5_85rcp_2020-2040.png" />
6- Extreme Flooding Index
The Extreme Flooding Index (rx5day) is defined as the maximum precipitation amount in 5 consecutive days.
6.1- Extreme Flooding Index Climatology
- To load the historical simulations for the daily precipitation amount variable and convert units to mm from kg·m-2·s-1:
var0 <- 'pr'
climatology_filenames <- paste0("/esarchive/scratch/pbretonn/cmip5-cp4cds/historical/day/pr/",
"pr_day_IPSL-CM5A-LR_historical_r1i1p1_19500101-20051231.nc")
reference_data <- Start(model = climatology_filenames, var = var0, var_var = 'var_names',
time = values(list(as.POSIXct(start_climatology), as.POSIXct(end_climatology))),
lat = values(list(lat.min, lat.max)), lon = values(list(lon.min, lon.max)),
lon_var = 'lon', lon_reorder = CircularSort(0, 360),
return_vars = list(time = 'model', lon = 'model',
lat = 'model'), retrieve = TRUE)
metadata <- attributes(reference_data)
reference_data <- reference_data * 60 * 60 * 24- To compute anomalies:
dates <- attributes(reference_data)$Variables$dat1$time
dates <- as.PCICt(dates, cal = attributes(dates)$variables$time$calendar, format = "%Y%m%d")
jdays <- as.numeric(strftime(dates, format = "%j"))
anomaly_data <- Apply(list(reference_data), target_dims = which(names(dim(reference_data)) == "time"),
AtomicFun = "dailyAno", jdays = jdays, ncores = 4)$output1
names(dim(anomaly_data))[1] <- "time"- To detrend the data:
detrended_data <- Trend(anomaly_data, posTR = which(names(dim(anomaly_data)) == "time"))
diff <- anomaly_data - detrended_data$detrended
diff <- aperm(diff, c(2,3,1,4,5))
detrended_data <- reference_data - diff
attributes(detrended_data) <- metadata- To compute the Extreme Flooding Index during the reference period and its standar deviation and mean:
base_index <- Climdex(data = detrended_data, metric = 'rx5day', ncores = detectCores() - 1)
base_mean <- Apply(list(base_index$result), target_dims = list(c(1)), AtomicFun = "mean")$output1
base_sd <- Apply(list(base_index$result), target_dims = list(c(1)), AtomicFun = "sd")$output16.2- Extreme Flooding Index Climate Projection
The Extreme Flooding Index is computing for the period 2020-2040 by following the next steps.
- Loading data by using
Start()function and converting to mm:
model_filenames <- paste0("/esarchive/scratch/pbretonn/cmip5-cp4cds/rcp85/day/pr/",
"pr_day_IPSL-CM5A-LR_rcp85_r1i1p1_20060101-22051231.nc")
rcp_data <- Start(model = model_filenames, var = var0, var_var = 'var_names',
time = values(list(as.POSIXct(start_model), as.POSIXct(end_model))),
lat = values(list(lat.min, lat.max)), lon = values(list(lon.min, lon.max)),
lon_var = 'lon', lon_reorder = CircularSort(0, 360),
return_vars = list(time = 'model', lon = 'model', lat = 'model'), retrieve = TRUE)
rcp_data <- rcp_data * 60 * 60 * 24- To compute the index and standardize it:
projection_index <- Climdex(data = rcp_data, metric = 'rx5day', ncores = detectCores() - 1)
base_mean <- InsertDim(base_mean, 1, dim(projection_index$result)[1])
base_sd <- InsertDim(base_sd, 1, dim(projection_index$result)[1])
FloodingExtremeIndex <- (projection_index$result - base_mean) / base_sd6.3- Visualitzation of Extreme Flooding Index
- Map of the mean index values during the examined period 2020-2040:
title <- paste0("Index for rx5day ", substr(start_model, 1, 4), "-", substr(end_model, 1, 4),
" 85rcp CMIP5-IPSL")
breaks <- -8 : 8
PlotEquiMap(Mean1Dim(FloodingExtremeIndex, which(names(dim(FloodingExtremeIndex)) == "year")), lon = lon,
lat = lat, filled.continents = FALSE, toptitle = title, brks=breaks,
fileout = paste0('rx5day_IPSL-CMIP5_85rpc_', start_model, "_", end_model, ".png"))<img src="rx5day_IPSL-CMIP5_85rpc_2020-01-01_2040-12-31.png"/>
- Evolution of inland average of the Extreme Flooding Index:
temporal <- WeightedMean(FloodingExtremeIndex, lon = lon, lat = lat, mask = drop(masc))
temporal_3ysmooth <- Smoothing(temporal, runmeanlen = 3, numdimt = 1)
png("Temporal_Inland_ExtremeFloodingIndex_IPSL-CMIP5_85rcp_2020-2040.png", width = 8, height = 5,
units= 'in', res = 100, type = "cairo")
plot(substr(start_model, 1, 4):substr(end_model, 1, 4), temporal, type = "l", lty = 5, lwd = 2, bty = 'n',
xlab = "Time (years)", ylab = "Extreme Flooding Index",
main = "Inland average Extreme Flooding Index")
lines(substr(start_model, 1, 4):substr(end_model, 1, 4), temporal_3ysmooth, col = "darkgreen",lwd = 2)
legend('bottomleft', c('Anual', '3 years smooth'), col= c(1, 'darkgreen'), lty = c(5, 1), lwd = 2,
bty = 'n')
dev.off()<img src="Temporal_Inland_ExtremeFloodingIndex_IPSL-CMIP5_85rcp_2020-2040.png" />
7- Combining Indices
HeatExtremeIndex = array(1:(234), dim=c(2,3,4)) ColdExtremeIndex = array(100:(100+234), dim=c(2,3,4)) WindPowerExtremeIndex = array(1000:(1000+234), dim=c(2,3,4)) DroughtExtremeIndex = array(10000:(10000+234), dim=c(2,3,4)) FloodingExtremeIndex = array(100000:(100000+234), dim=c(2,3,4))
Extreme Indices should be saved in the same list object.
indices <- list()
indices[[1]] <- HeatExtremeIndex
indices[[2]] <- ColdExtremeIndex
indices[[3]] <- WindPowerExtremeIndex
indices[[4]] <- DroughtExtremeIndex
indices[[5]] <- FloodingExtremeIndex
names(dim(Indices))[1] <- 'index' ; names(dim(Indices))[-1] <- c('lon','lat','time')If weights parameter is defined as NULL, all indices will be equally weighted if operation parameter is set as mean (by default). To define other weights a vector of length equal to the number of considered indices (5 in this example) and with total sum equal to 1. To consider other settings visit: LINK????
aci <- CombineIndices(indices, weights = c(0.1,0,0.4,0,0.5))A spatial visulitzation can be performs by executing:
title <- paste0("Combine Indices ", substr(start_model, 1, 4), "-", substr(end_model, 1, 4),
" 85rcp CMIP5-IPSL")
breaks <- -8 : 8
PlotEquiMap(Mean1Dim(FloodingExtremeIndex, which(names(dim(FloodingExtremeIndex)) == "year")), lon = lon,
lat = lat, filled.continents = FALSE, toptitle = title, brks=breaks,
fileout = paste0('rx5day_IPSL-CMIP5_85rpc_', start_model, "_", end_model, ".png"))<img src="rx5day_IPSL-CMIP5_85rpc_2020-01-01_2040-12-31.png"/>
library(reshape) data_frame <- data.frame(aci = combined_area_average, cdd = area_mean[[1]], rx5day = area_mean[[2]], tx90p = area_mean[[3]], tx10p = area_mean[[4]], wx = area_mean[[5]], years = years)
xymelt <- melt(data_frame, id.vars = “years”)
years = as.numeric(start_model) : as.numeric(end_model) g <- ggplot(xymelt, aes(x = years, y = value, color = variable, linetype = variable, size = variable)) + theme_bw() + geom_line(aes(size = variable)) + ylab(“Component”) + xlab(“Year”) + theme(text=element_text(size = font_size),legend.text=element_text(size = font_size), axis.title=element_text(size = font_size)) + #scale_colour_manual(values=c(“red”, “black”, “black”, “black”, “black”, “black”)) + scale_size_manual(values = c(1, 0.5, 0.5, 0.5, 0.5, 0.5)) + ggtitle(paste0(“ACI components (”, model_name, " " ,rcp_scenario, " “, paste(weight_name, collapse = ‘’), “)”)) ggsave(filename = paste0(“aci”, “area_mean”,model_name,““, rcp_scenario,””, startdate, ““, enddate,””, paste(weight_name, collapse =’’),”.png“), g, device = NULL)
8- Projection Comparison
The next exemple compares the Extreme Heat Index for two different projections 8.5 and 2.6 scenarios for summer.
It’s necessary to reload the maximum temperature daily data during for historical simulations to select summer season:
Notice that other seasons can be selected by modifying the parameter seasons in SeasonSelect() function to boreal winter ('DJF'), spring ('MMA') and autumn ('SON').
var0 <- 'tasmax'
climatology_filenames <- paste0("/esarchive/scratch/pbretonn/cmip5-cp4cds/historical/day/tasmax/",
"tasmax_day_IPSL-CM5A-LR_historical_r1i1p1_19500101-20051231.nc")
reference_data <- Start(model = climatology_filenames, var = var0, var_var = 'var_names',
time = values(list(as.POSIXct(start_climatology), as.POSIXct(end_climatology))),
lat = values(list(lat.min, lat.max)), lon = values(list(lon.min, lon.max)),
lon_var = 'lon', lon_reorder = CircularSort(0, 360),
return_vars = list(time = 'model', lon = 'model', lat = 'model'), retrieve = TRUE)
reference_data <- SeasonSelect(reference_data, seasons='JJA')
metadata <- attributes(reference_data)To obtain the thresholds values and the standard deviation of the model during the reference period the same code as in paragraph 2.1 should be performed:
dates <- attributes(reference_data)$Variables$dat1$time
dates <- as.PCICt(dates, cal = attributes(dates)$variables$time$calendar, format = "%Y%m%d")
jdays <- as.numeric(strftime(dates, format = "%j"))
anomaly_data <- Apply(list(reference_data), target_dims = which(names(dim(reference_data)) == "time"),
AtomicFun = "dailyAno", jdays = jdays, ncores = 4)$output1
names(dim(anomaly_data))[1] <- "time"
detrended_data <- Trend(anomaly_data, posTR = which(names(dim(anomaly_data)) == "time"))
diff <- anomaly_data - detrended_data$detrended
diff <- aperm(diff, c(2,3,1,4,5))
detrended_data <- reference_data - diff
attributes(detrended_data) <- metadata
quantile <- 0.9
base_range <- as.numeric(c(substr(start_climatology, 1, 4), substr(end_climatology, 1, 4)))
thresholds <- Threshold(detrended_data, base_range = as.numeric(base_range),
qtiles = quantile, ncores = detectCores() -1)
base_index <- Climdex(data = detrended_data, metric = 'tx90p', quantiles = thresholds,
ncores = detectCores() - 1)
base_sd <- Apply(list(base_index$result), target_dims = list(c(1)), AtomicFun = "sd")$output1
base_heat_sd <- base_sdThe two projections are loaded by running:
model_filenames <- paste0("/esarchive/scratch/pbretonn/cmip5-cp4cds/",
c("rcp85/day/tasmax/tasmax_day_IPSL-CM5A-LR_rcp85_r1i1p1_20060101-22051231.nc",
"rcp26/day/tasmax/tasmax_day_IPSL-CM5A-LR_rcp26_r1i1p1_20060101-22051231.nc"))
rcp_data <- Start(model = model_filenames, var = var0, var_var = 'var_names',
time = values(list(as.POSIXct(start_model), as.POSIXct(end_model))),
lat = values(list(lat.min, lat.max)), lon = values(list(lon.min, lon.max)),
lon_var = 'lon', lon_reorder = CircularSort(0, 360),
return_vars = list(time = 'model', lon = 'model', lat = 'model'),
retrieve = TRUE)The object returned by Start() contains two models:
> dim(rcp_data)
model var time lat lon
2 1 7671 21 28 - Now the index can be computed by considering the threshold obtain for the reference period.
projection_index <- Climdex(data = rcp_data, metric = 'tx90p', quantiles = thresholds,
ncores = detectCores() - 1)- Its normalized with mean 10 and the standard deviation of the reference period.
base_mean <- 10
base_sd <- InsertDim(base_sd, 1, dim(projection_index$result)[1])
HeatExtremeIndex <- (projection_index$result - base_mean) / base_sd2.3 Visualitzation of Extreme Heat Index
A Map of the mean index values during the examined period 2020-2040 is obtained and save in PNG format in the working directory with the name: “tx90p_IPSL-CMIP5_85rpc_2020-01-01_2040-12-31.png”
lat <- attr(rcp_data, "Variables")$dat1$lat
lon <- attr(rcp_data, "Variables")$dat1$lon
title <- paste0("Index for tx90p ", substr(start_model, 1, 4), "-",
substr(end_model, 1, 4), " 85rcp CMIP5-IPSL")
breaks <- -8 : 8
PlotEquiMap(Mean1Dim(HeatExtremeIndex, which(names(dim(HeatExtremeIndex)) == "year")), lon = lon,
lat = lat, filled.continents = FALSE, toptitle = title, brks=breaks,
fileout = paste0('tx90p_IPSL-CMIP5_85rpc_', start_model, "_", end_model, ".png"))
The inland average of the Extreme Heat Index can be computed to plot its time evolution using WeigthedMean function. Smoothing() returns the smoothed time series for a 3 years moving window which can be modify using runmeanlen parameter.
masc <- Start(model = '/esarchive/exp/ipsl-cm5a-lr/cmip5-rcp85_i1p1/constant/r0i0p0/fx/sftlf/sftlf.nc',
var = 'sftlf', var_var = 'var_names', lat = values(list(lat.min, lat.max)),
lon = values(list(lon.min, lon.max)), lon_reorder = CircularSort(0,360),
return_vars = list(lon = 'model', lat = 'model'), retrieve = TRUE)
temporal <- WeightedMean(HeatExtremeIndex, lon = lon, lat = lat, mask = drop(masc))
temporal_3ysmooth <- Smoothing(temporal, runmeanlen = 3, numdimt = 1)The next code should be runned to plot and save the original average and the 3 year smoothed data.
png("Temporal_Inland_ExtremeHeatIndex_IPSL-CMIP5_85rcp_2020-2040.png", width = 8, height = 5, units = 'in',
res = 100, type = "cairo")
plot(substr(start_model, 1, 4):substr(end_model, 1, 4), temporal, type = "l", lty = 5, lwd = 2, bty = 'n',
xlab = "Time (years)", ylab = "Extreme Heat Index", main = "Inland average Extreme Heat Index")
lines(substr(start_model, 1, 4):substr(end_model, 1, 4), temporal_3ysmooth, col = "darkgreen", lwd = 2)
legend('bottomright', c('Anual', '3 years smooth'), col = c(1, 'darkgreen'), lty = c(5, 1), lwd = 2, bty = 'n')
dev.off()