The structure of polar volumes

# Let's first download the NEXRAD polar volume files for the KHGX radar (Houston)
# for a 15 minute period in 2017:
download_pvolfiles(date_min=as.POSIXct("2017-05-04 01:25:00"), date_max=as.POSIXct("2017-05-04 01:40:00"), radar="KHGX", directory="./data_pvol")
# store the filenames in my_pvolfiles
my_pvolfiles <- list.files("./data_pvol", recursive = TRUE, full.names = TRUE, pattern="KHGX")
# print to console our files:
my_pvolfiles
# let's load the first of our downloaded files:
my_pvol <- read_pvolfile(my_pvolfiles[1])

Exercise 1: What is the minimum and maximum scan elevation contained in the volume? And which scan parameters are available? (See manual page of the read_pvolfile() function for the nomenclature of various available quantities).

Plotting radar scans

# let's extract the scan collected at 1.5 degree elevation from our polar volume:
my_scan <- get_scan(my_pvol, 0.5)
# print some information about this scan:
my_scan
# let's plot the reflectivity factor parameter of the scan in a range - azimuth coordinate system:
plot(my_scan, param = "DBZH")

Usually it is easier to visually explore radar scans as a PPI (plan position indicator), which is a projection of the scan on a Cartesian (X,Y) or (lat,lon) grid:

# before we can plot the scan, we need to project it on a Cartesian grid,
# i.e. we need to make a Plan Position Indicator (PPI)
my_ppi <- project_as_ppi(my_scan)
# print some information about this ppi:
my_ppi
# you can see we projected it on a 500 meter grid
# (check the manual of the project_as_ppi function to see how you can
# change the grid size (argument grid_size) and the maximum distance
# from the radar up to where to plot data (argument range_max))
#
# Now we are ready to plot the ppi, for example let's plot reflectivity factor DBZH:
plot(my_ppi, param = "DBZH")

Exercise 2: This case shows an incoming precipitation front, characterized by localized but intense thunderstorms, as well as biological scattering. Make also a ppi plot of the correlation coefficient (RHOHV) and radial velocity (VRADH). Verify which regions are precipitation, and the approximate direction of movement of biology and precipitation.

Exercise 3: Based on the radial velocity image, are the biological scatterers birds or insects? Why?

Overlaying radar scans on maps

# It is often informative to plot radar data on a base layer.
# First choose a base layer from the list of rosm::osm.types()
basemap = "osm"
# then overlay the PPI on the basemap, restricting the color scale from -20 to 40 dBZ:
map(my_ppi, map = basemap, param = "DBZH", zlim = c(-20, 40))

using correlation coefficient

Screening precipitation based on correlation coefficient is arguably the most simple and established approach for screening out weather in cases where dual-polarization data is available. It is based on removing data above a certain \(\rho_{/HV}\) thresholds, most commonly 0.95.

# Screen out the reflectivity areas with RHOHV < 0.95
my_ppi_clean <- calculate_param(my_ppi, DBZH = ifelse(RHOHV > 0.95, NA, DBZH))
# plot the original and cleaned up reflectivity:
map(my_ppi, map = basemap, param = "DBZH", zlim = c(-20, 40))
map(my_ppi_clean, map = basemap, param = "DBZH", zlim = c(-20, 40))

using MistNet

You can use MistNet for screening out weather when * the radar operates at S-band wavelengths * you only have single polarization data available (specifically, the three basic quantities radial velocity VRADH, reflectivity DBZH, and spectrum width WRADH).

# apply the MistNet model to the polar volume file and load it as a polar volume (pvol):
my_pvol <- apply_mistnet(my_pvolfiles[1])
# mistnet will add additional parameters to the
# elevation scans at 0.5, 1.5, 2.5, 3.5 and 4.5 degrees
# let's extract the scan closest to 0.5 degrees:
my_scan <- get_scan(my_pvol, 0.5)
# plot some summary info about the scan to the console:
my_scan

using depolarization ratio

Another quantity that has been proposed for distinguishing weather and biology is the depolarization ratio (\(D_r\)), which is defined as

\[D_r=\frac{Z_{DR}+ 1 -2 \sqrt{Z_{DR}} \ \rho_{HV}}{Z_{DR}+ 1 +2 \sqrt{Z_{DR}} \ \rho_{HV}}\] First we add the depolarization ratio (DR) as a parameter. We’ll express DR on a dB scale by transforming: \[DR=10\log_{10}(D_r) \] (see Kilambi et al. 2018, A Simple and Effective Method for Separating Meteorological from Nonmeteorological Targets Using Dual-Polarization Data for more information)

# let's add depolarization ratio (DR) as a parameter (following Kilambi 2018):
my_ppi <- calculate_param(my_ppi, DR = 10 * log10((1+ ZDR - 2 * (ZDR^0.5) * RHOHV) /
  (1 + ZDR+ 2 * (ZDR^0.5) * RHOHV)))

Like correlation coefficient you can apply simple thresholds to its value to screen out precipitation. It has a good (potentially even better) ability to distinguish weather and biology:

  # plot the depolarization ratio, using a viridis color palette:
map(my_ppi, map = basemap, param = "DR", zlim=c(-25,-5), palette = viridis::viridis(100))

MistNet adds several new parameters: * WEATHER: a probability (0-1) for the weather class * BIOLOGY: a probability (0-1) for the biology class * BACKGROUND: a probability (0-1) for the background (empty space) class * CELL: the final segmentation, which is based on the WEATHER parameters of all five MistNet elevation scans. CELL also includes a fringe calculated by a region growing approach. CELL values equal 1 for the additional fringe, and 2 for the originally segmented precipitation area by MistNet.

# as before, project the scan as a ppi:
my_ppi <- project_as_ppi(my_scan)
# plot the probability for the WEATHER class
plot(my_ppi, param = 'WEATHER')
# plot the final segmentation result:
# plot the probability for the WEATHER class
plot(my_ppi, param = 'CELL')
# let's remove the identified precipitation area (and additional fringe) from the ppi, and plot it:
my_ppi_clean <- calculate_param(my_ppi, DBZH = ifelse(CELL >= 1, NA, DBZH))
map(my_ppi_clean, map=basemap, param = 'DBZH')

Exercise 4: Calculate and plot a ‘cleaned up’ PPI for the radial velocity that includes only the segmentation by MistNet and not the additional fringe.

Loading processed vertical profiles

# Usually we would load processed vertical profiles (vp files) by:
# my_vplist <- read_vpfiles("./your/directory/with/processed/profiles/goes/here")
# my_vplist contains after running the command a list of vertical profile (vp) objects
# To save time, we load these data directly from file
my_vplist <- readRDS("data_vpts/KBRO20170514.rds")
# print the length of the vplist object. It should contain 95 profiles
length(my_vplist)

Inspecting single vertical profiles

Now that you have loaded a list of vertical profiles, we can start exploring them. We will start with plotting and inspecting single vertical profiles, i.e. a single profile from the list of vp objects you have just loaded.

# let's extract a profile from the list, in this example the 41st profile:
my_vp <- my_vplist[[41]]
# print some info for this profile to the console
my_vp
# test whether this profile was collected at day time:
check_night(my_vp)
# plot the vertical profile, in terms of reflectivity factor
plot(my_vp, quantity = "dbz")
# plot the vertical profile, in terms of (linear) reflectivity
plot(my_vp, quantity = "eta")

eta and dbz are closely related, the main difference is that reflectivity factors are logarithmic, and reflectivities linear. You can convert one into the other using eta_to_dbz() and dbz_to_eta() functions, which follows this simple formula:

eta = (radar-wavelength dependent constant) * 10^(dbz/10)

The reflectivity factor dBZ is the quantity used by most meteorologist. It has the useful property that at different radar wavelengths (e.g. S-band versus C-band) the same amount of precipitation shows up at similar reflectivity factors. The same holds for insects, as well as any other target that is much smaller than the radar wavelength (S-band = 10 cm, C-band = 5 cm), the so-called Rayleigh-scattering limit.

In the case of birds we are outside the Rayleigh limit, because birds are of similar size as the radar wavelength. In this limit reflectivity eta is more similar between S-band and C-band. eta is also more directly related to the density of birds, since eta can be expressed as (bird density) x (radar cross section per bird). For these two reasons, for weather radar ornithologists reflectivity eta is the more conventional unit.

# let's plot the vertical profile, in terms of bird density
plot(my_vp, quantity = "dens")
# print the currently assumed radar cross section (RCS) per bird:
rcs(my_vp)

Exercise 5: If you change your assumption on the bird’s radar cross section in the previous example, and assume the RCS is 10 times as large, what will be the effect on the bird density profile?

The assumed radar cross section can be changed as follows:

# let's change the RCS to 110 cm^2
rcs(my_vp) <- 110

Exercise 6: Verify your answers on the previous two questions, by re-plotting the vertical profiles for the bird density quantity.

Plotting vertical profile time series

We will now examine multiple vertical profiles at once that are ordered into a time series, e.g. the vertical profiles obtained from a single radar over a full day.

# convert the list of vertical profiles into a time series:
my_vpts <- bind_into_vpts(my_vplist)
# time series objects can be subsetted, just as you may be used to with vectors
# here we subset the first 50 timesteps:
my_vpts[1:50]
# here we extract a single timestep, which gives you back a vertical profile class object:
my_vpts[100]
# to plot the full time series:
plot(my_vpts)
# check the help file for the plotting function of profile time series
# Because profile timeseries are of class 'vpts', it's associated plotting function
# is called plot.vpts:
?plot.vpts

Let’s make a plot for a subselection of the time series:

# filter our vpts for night time
my_vpts_night <- filter_vpts(my_vpts, night=TRUE)
# plot this smaller time series:
plot(my_vpts_night)

Exercise 7: Interpret the wind barbs in the profile time series figure: what is the approximate speed and direction at 1500 meter at 6 UTC? In the speed barbs, each half flag represents 2.5 m/s, each full flag 5 m/s, [each pennant (triangle) 25 m/s, not occurring in this case].

Exercise 8: Extract the vertical profile at 6 UTC from the time series and plot the vertical profile of ground speed (quantity ff). Hint: use function filter_vpts() to extract the 6 UTC profile. Check whether your answer to the previous question was approximately correct.

Vertical and time integration of profiles

Often you will want to sum together all the migrants in the vertical dimension, for example if you want a single index of how many birds are migrating at a certain instant. There are at least two ways in which you can do that:

• by calculating the vertically integrated bird density (VID), which is surface density as opposed to a volume densities you have been plotting in the previous exercises: this number gives you how many migrants are aloft per square kilometer earth’s surface (unit individuals/km\(^{2}\)), obtained by a vertical integration of the volume densities (unit individuals/km\(^{3}\)).
• Note that the VID quantity doesn’t depend on the speed of the migrants. A common measure that reflects both the density and speed of the migration is migration traffic rate (MTR). This is flux measure that gives you how many migrants are passing the radar station per unit of time and per unit of distance perpendicular to the migratory direction (unit individuals/km/hour).

We will be using bioRad’s integrate_profile() function to calculate these quantities:

# Let's continue with the vpts object created in the previous example.
# The vertically integrated quantities are calculated as follows:
my_vpi <- integrate_profile(my_vpts)
# The my_vpi object you created is a vpi class object, which is an acronym for "vertical profile integrated". It has its own plot method, which by default plots migration traffic rate (MTR):
plot(my_vpi)
# you can also plot vertically integrated densities (VID):
plot(my_vpi, quantity = "vid")
# the gray and white shading indicates day and night, which is calculated
# from the date and the radar position. You can also turn this off:
plot(my_vpi, night_shade = FALSE)
# plot the cumulative number of birds passing the radar, i.e. migration traffic (mt):
plot(my_vpi, quantity = "mt")
# execute `?plot.vpi` to open the help page listing all the options.
?plot.vpi

The following questions only require pen and paper. Assume a night migration event in which the volume density of birds from 0-1 km above ground is 200 birds per cubic kilometer, and from 1-1.5 km 100 birds per cubic kilometer. Above 1500 meter there are no birds.

Exercise 9: What is in this case the bird’s vertically integrated density (VID)? Give your answer in units birds/km\(^2\).

Exercise 10: Let’s assume that in the lower layer birds fly at 50 km/hour, and in the upper layer at 100 km/hour. What is in this case the migration traffic rate across a transect perpendicular to the direction of movement? Give your answer in units birds/km/hour.

Exercise 11:Let’s assume migration continued for exactly three hours after sunset, and then halted abruptly. How many birds have passed a 10 km transect perpendicular to the direction of movement in this night? Give your answer in terms of migration traffic (mt) in units birds/km.

Both MTR, VID and MT depend on the assumed radar cross section (RCS) per bird. If you are unwilling/unable to specify RCS, alternatively you can use two closely related quantities that make no assumptions RCS:

# instead of vertically integrated density (VID), you can use vertically integrated reflectivity (VIR):
plot(my_vpi, quantity = "vir")
# instead of migration traffic rate (MTR), you can use the reflectivity traffic rate (RTR):
plot(my_vpi, quantity = "rtr")
# instead of migration traffic (MT), you can use the reflectivity traffic (RT):
plot(my_vpi, quantity = "rt")

VIR gives you the total cross-sectional area of air-borne targets per square kilometer of ground surface, whereas RTR gives you the total cross-sectional area of targets flying across a one kilometer line perpendicular to the migratory flow per hour.

Inspecting precipitation signals in profiles

Precipitation is known to have a major influence on the timing and intensity of migration, therefore it is a useful skill to be able to inspect profiles for presence of precipitation.

Also, although automated bird quantification algorithms become more and more reliable, distinguishing precipitation from birds remains challenging for algorithms in specific cases. It is therefore important to have the skills to inspect suspicious profiles. That may help you to identify potential errors of the automated methods, and prevent your from overinterpreting the data.

An easy way of doing that is plotting the vertical profile of total reflectivity (quantity DBZH), which includes everything: birds, insects and precipitation. Precipitation often has higher reflectivities than birds, and also extends to much higher altitudes.

# load a time series for the KBGM radar in Binghamton, NY
my_vpts <- readRDS("data_vpts/KBGM20170527-20170602.rds")
# print the loaded vpts time series for this radar:
my_vpts
# plot the bird density over time:
plot(my_vpts, quantity = "dens")

Exercise 12: Compare the above plot for bird density (quantity dens) with a profile plot for total reflectivity (quantity DBZH, showing birds and precipitation combined). Compare the two plots to visually identify periods and altitude layers with precipitation.

Processing a polar volume into a profile

# download a polar volume for the KBRO radar in Brownsville, TX
download_pvolfiles(date_min=as.POSIXct("2017-05-14 05:50:00"), date_max=as.POSIXct("2017-05-14 06:00:00"), radar="KBRO", directory="./data_pvol")
# Load all the polar volume filenames downloaded so far for the KBRO radar:
my_pvolfiles <- list.files("./data_pvol", recursive = TRUE, full.names = TRUE, pattern="KBRO")
# we will process the first one into a vp:
my_pvolfile <- my_pvolfiles[1]
# calculate the profile, using MistNet to remove precipitation:
# we calculate 60 layers of 50 meter width, so up to 30*100=3000 m.
my_vp <- calculate_vp(my_pvolfile, n_layer=60, h_layer=50, sd_vvp_threshold = 1)

Exercise 13: Plot the bird density in the vertical profile you just estimated and compare it with the plots above of the beam height and width of the lowest radar beam. At which approximate range do you expect the radar will no longer be able to resolve the altitude distribution of the migratory birds. And at which range will the radar start to overshoot the migration layer entirely?

To correct for the decreasing ability of the radar to resolve the altitude distributions of birds with range, we will make one important (and likely imperfect!) assumption:

We assume that all birds within the image are distributed vertically according to the same relative vertical profile.

This assumptions simplifies the problem, and allows us to estimate the spatial distribution of the birds, as we will explore in the next paragraph:

Range bias correction and vertical integration on a map

# We will use the piping operator %>% of magrittr package to
# execute multiple operations in one statement:
library(magrittr)
# first, load the polar volume:
my_pvolfile %>% read_pvolfile() -> my_pvol
# Next, let's calculate a PPI for the 1.5 degree elevation scan
# Finally, we calculated the vertically integrated PPI
my_ppi_integrated <- integrate_to_ppi(pvol=my_pvol,vp=my_vp, res=1000)

Exercise 14: Visually compare the PPI for the 1.0 degree sweep and the vertically integrated PPI, and explain the difference in spatial pattern. (For the clearest comparison, make plots of comparable parameters that are either linear or logarithmic in bird density).

Accessing radar data

• US NEXRAD polar volume data can be accessed in the Amazon cloud. Use function download_pvolfiles() for local downloads
• European radar data can be accessed at https://aloftdata.eu. These are processed vertical profiles, the full polar volume data are not openly available for most countries. Use function download_vpfiles() for local downloads.

The names of the radars in the networks can be found here:

• US: NEXRAD network
• Europe: OPERA database

Useful sites for inspecting pre-made movies of the US composite are https://birdcast.info/migration-tools/live-migration-maps/ and https://www.pauljhurtado.com/US_Composite_Radar/.

Processing multiple polar volumes

This section contains an example for processing a directory of polar volumes into profiles:

First we download more files, and prepare an output directory for storing the processed profiles:

# First we download more data, for a total of one additional hour for the same radar:
download_pvolfiles(date_min=as.POSIXct("2017-05-04 01:40:00"), date_max=as.POSIXct("2017-05-04 02:40:00"), radar="KHGX", directory="./data_pvol")
# We will process all the polar volume files downloaded so far:
my_pvolfiles <- list.files("./data_pvol", recursive = TRUE, full.names = TRUE, pattern="KHGX")
my_pvolfiles
# create output directory for processed profiles
outputdir <- "./data_vp"
dir.create(outputdir)

We will use the following custom settings for processing: * We will use MistNet to screen out precipitation * we will calculate profile layers of 50 meter width * we will calculate 60 profile layers, so up to 50*60=3000 meter altitude

Note that we enclose the calculate_vp() function in tryCatch() to keep going after errors with specific files

Having generated the profiles, we can read them into R:

# we assume outputdir contains the path to the directory with processed profiles
my_vpfiles <- list.files(outputdir, full.names = TRUE, pattern="KHGX")
# print them
my_vpfiles
# read them
my_vplist <- read_vpfiles(my_vpfiles)

You can now continue with visualizing and post-processing as we did earlier:

# make a time series of profiles:
my_vpts <- bind_into_vpts(my_vplist)
# plot them between 0 - 3 km altitude:
plot(my_vpts, ylim = c(0, 3000))
# because of the rain moving in, our ability to estimate bird profiles slowly drops:
# let's visualize rain by plotting all aerial reflectivity:
plot(my_vpts, ylim = c(0, 3000), quantity="DBZH")

Note that we enclose the calculate_vp() function in tryCatch() to keep going after errors with specific files

Parallel processing

We may use one of the parallelization packages in R to further speed up our processing. We will use mclapply() from package parallel. First we wrap up the processing statements in a function, so we can make a single call to a single file. We will disable MistNet, as this deep-learning model does not parallelize well on a cpu machine.

process_file <- function(file_in){
  # construct output filename from input filename
  file_out <- paste(outputdir, "/", basename(file_in), "_vp.h5", sep = "")
  # run calculate_vp()
  vp <- tryCatch(calculate_vp(file_in, file_out, mistnet = FALSE, h_layer=50, n_layer=60), error = function(e) NULL)
  if(is.vp(vp)){
    # return TRUE if we calculated a profile
    return(TRUE)
  } else{
    # return FALSE if we did not
    return(FALSE)
  }
}

# To process a file, we can now run
process_file(my_pvolfiles[1])

Next, we use mclapply() to do the parallel processing for all files:

# load the parallel library
library(parallel)
# detect how many cores we can use. We will keep 2 cores for other tasks and use the rest for processing.
number_of_cores = detectCores() - 2
# Available cores:
number_of_cores
# let's loop over the files and generate profiles
start=Sys.time()
mclapply(my_pvolfiles, process_file, mc.cores = number_of_cores)
end=Sys.time()
# calculate the processing time that has passed:
end-start