5 Cloud Physics Variables
5.1 Measurements of Liquid Water Content
Power, PMS/CSIRO (King) Liquid Water Content (W): PLWC, PLWC1
The power dissipated by the sensor of a PMS/CSIRO (King) liquid water probe (in watts). PLWC is the power required to maintain constant temperature in a heated element as that element is cooled by convection and evaporation of impinging liquid water. The convective heat losses are determined by calibration in dry air over a range of airspeeds and temperatures, so that the remaining power can be related to the liquid water content. The instrument is described in RAF Bulletin 24 and at this URL. See the following
description for the algorithm used to obtain liquid water content from this measurement of power.
PMS/CSIRO (King) Liquid Water Content (g/m3): PLWCC, PLWCC1
The liquid water content measured by a King probe. This is calculated by relating the power consumption required to maintain a constant temperature to the liquid water content, taking into account the effect of convective heat losses. The instrument and processing are described by King et al. (1978)34 and in a note available at this URL. Because the temperature of the sensing wire is typically well above the boiling point of water, the assumption made in processing is that the water collected on the sensing wire is vaporized at the boiling point Tb. The boiling point is represented as a function of pressure as described below.
PLWC = total power dissipated by the probe [W]
\(P_{D}\) = power dissipated
by the cooling effect of dry air alone
\(P_{W}\) = power needed to heat and vaporize the liquid water that
hits the probe element
\(L\) = length
of the probe sensitive element,
typically 0.021 m
\(d\)= diameter of the probe sensitive
element, typically 1.805\(\times10^{-3}\)m
\(T_{s}\)= sensor temperature
[\(^{\circ}\)C]
\(T_{a}\)= ambient temperature [\(^{\circ}\)C] = ATX
\(T_{b}\) =
boiling temperature of water (dependent on pressure):
with \(x=\log_{10}(p/(1\)hPa)), \(B=1^{\circ}\)C,
and {\(b_{0},\) \(b_{1}\), \(b_{2}\), \(b_{3}\)} = {0.03366503, 1.34236135,
-0.33479451, 0.0351934}:
\(T_{b}=B\times10^{(b_{0}+b_{1}x+b_{2}x^{2}+b_{3}x^{3})}\)
\(T_{m}=(T_{a}+T_{s})/2\) = mean temperature for air properties
\(L_{v}(T_{b})\) = latent heat of vaporization of water
= (2.501-0.00237\(T_{b}\))\(\times10^{6}\)J\(\,\)kg\(^{-1}\)
\(c_{w}\) =
specific heat of water = 4190 J\(\,\)kg\(^{-1}\)K\(^{-1}\) (mean value,
0–90\(^{\circ}\)C)
\(U_{a}\) = true airspeed [m/s] = TASX
\(\lambda_{c}\)
= thermal conductivity
of dry air (2.38+0.0071\(T_{m}\))\(\times10^{-2}\)J\(\,\)m\(^{-1}\)s\(^{-1}\)K\(^{-1}\)
\(\mu\)
=viscosity of air = (1.718+0.0049\(T_{m})\times10^{-5}\)
kg\(\,\)m\(^{-1}\)s\(^{-1}\)
\(\rho_{a}\) = density
of air = \(p / (R_{d}(T_{a}+T_{0}))\)
Re = Reynolds number = \(\rho_{a}U_{a}d/\mu_{a}\)
Nu = Nusselt Number relating conduction
heat loss to the total heat loss for dry air:
typically Nu=\(a_{0}\mathrm{Re}^{a_{1}}\) where
for the GV:
\(\{a_{0},\,a_{1}\}=\{1.868,\,0.343\}\) for Re<7244
and \(\{0.135,\,0.638\}\) otherwise,
except when TASX < 150 m/s;
then use \(\{0.133,\,0.382\}\).
For the C-130:
\(\{a_{0},\,a_{1}\}=\{0.118,\,0.675\}\).
\(C_{kg2g}=1000\) = grams per kilogram
(unit conversion to conventional units for liquid water content)
\(\chi\) = liquid water
content [g/m\(^{3}\)] = PLWCC
\[\begin{equation}
\mathrm{\{PLWC\}} = P_{D}+P_{W}
\tag{5.1}
\end{equation}\]
where
\[\begin{equation}
P_{D}=\pi\mathrm{Nu}\,L\lambda_{c}(T_{s}-T_{a})
\tag{5.2}
\end{equation}\]
\[\begin{equation}
P_{W}=L\,d[L_{v}(T_{b})+c_{w}(T_{b}-T_{a})]\,U_{a}\chi
\tag{5.3}
\end{equation}\]
Result:
\[\begin{equation}
\mathrm{\{PLWCC\}}=\chi=\frac{C_{kg2g}(\mathrm{\{PLWC\}}-P_{D})}{L\,d\,U_{a}[L_{v}(T_{b})+c_{w}(T_{b}-T_{a})]}
\tag{5.4}
\end{equation}\]
PVM-100 Liquid Water Content (g/m3): PLWCG
Cloud liquid water content for cloud droplets in the approximate size range from 3–50 μm. The PVM produces a measure of the liquid water content directly, but a baseline value is sometimes subtracted by reference to another cloud droplet instrument such as an FSSP or CDP, such that when the other instrument measures a very low droplet concentration the baseline value for the PVM-100 is updated at the corresponding time and that average is then subtracted from the measurements directly produced by the PVM-100.Rosemount Icing Detector Signal (V): RICE
The voltage related to loading on the element of a Rosemount 871F ice-accretion probe. This instrument (see this URL) consists of a rod set in vibration by a piezoelectric crystal. The oscillation frequency of the probe changes with ice loading, so in supercooled cloud ice accumulates on the sensor and the change in oscillation frequency is transmitted as a DC voltage. When the rod loads to a trigger point, the probe heats the rod to remove the ice. The rate of voltage change can be converted to an estimate of the supercooled liquid water content, as described in connection with the obsolete variable SCLWC. This calculation is no longer provided routinely but can be duplicated by a user on the basis of the SCLWC algorithm (see SCLWC in Section 10 for one example; there are several other published algorithms.)5.2 Sensors Detecting Individual Hydrometeors (1-D Probes)
The RAF operates a set of hydrometeor detectors that provide single-dimension measurements (i.e., not images) of individual particle sizes. RAF Bulletin 24 contains extensive information on the operating principles and characteristics of some of the older instruments. Here the focus will be on the meanings of the variables in the archived data files.
Four- and five-character variable names shown in this section are generic. The actual names appearing in NIMBUS-generated production output data sets have appended to them an underscore (_) and three or four more characters that indicate a probe’s specific aircraft mounting location. For example, AFSSP_RPI refers to a variable from an FSSP-100 probe mounted on the inboard, right-side pod. The codes presently in use are given in the following table. For the GV, there are 12 locations available, characterized by three letters. The first is the wing ({L,R} for {port,starboard}), the second is the pylon ({I,M,O} for inboard, middle, outboard}), the third is which of the two possible canister locations at the pylon is used ({I,O} for {inboard, outboard}).
suffix | location | aircraft |
---|---|---|
OBL | Outboard Left | C-130Q |
IBL | Inboard Left | C-130Q |
OBR | Outboard Right | C-130Q |
IBR | Inboard Right | C-130Q |
LPO | Left Pod Outboard | C-130Q |
LPI | Left Pod Inboard | C-130Q |
LPC | Left Pod Center | C-130Q |
RPO | Right Pod Outboard | C-130Q |
RPI | Right Pod Inboard | C-130Q |
RPC | Right Pod Center | C-130Q |
OBL | Left Wing | Electra |
IBL | Left Pylon | Electra |
WDL | Window Left | Electra |
OBR | Right Wing | Electra |
IBR | Right Pylon | Electra |
WDR | Window Right | Electra |
{L,R}W{I,M,O}{I,O} | see discussion above | GV |
The probe type also is coded into each variable’s name, sometimes using four characters, sometimes only one: FSSP-100 (FSSP or F), FSSP-300 (F300 or 3), CDP (CDP or D), UHSAS (UHSAS or U), PCASP (PCAS or P), OAP-200X (200X or X), OAP-260X (260X or 6) and OAP-200Y (200Y or Y). Prefix letters are used to identify the type of measurement (A=accumulated particle counts per time interval per channel, C = concentration per channel, CONC = Concentration from all channels, DBAR = mean diameter, DISP = dispersion, PLWC =liquid water content, DBZ = radar reflectivity factor).
Some of the probes discussed in this section are primarily aerosol spectrometers but are described here rather than in Section 7 because they are similar to the hydrometeor spectrometers and so are most economically discussed here. However, see Section 7 for the processing algorithms that lead to concentrations from the UHSAS and PCASP/SPP-200. The following table and discussion includes some obsolete variables (for the 200X and 200Y) for the same reason. The table also includes some variables derived from imaging spectrometers (the 2DC and 2DP probes) to highlight that the primary variables are similar to those discussed in this sub-section. Those variables are discussed in the next sub-section. In two cases, the FSSP and PCASP, two versions are listed, an obsolete version and a current version with a revised processing package (SPP-100 for the FSSP, SPP-200 for the PCASP). Both are included for historical completeness, but algorithms in this document discuss the current versions.
The archived data files sometimes have “housekeeping” variables included that provide information on the operating state and data quality from the probes. For example, the CDP provides information on the average transit time, the voltage from the nominal 5-V source, the control board temperature, the laser block temperature, the laser current, the laser power monitor, the qualifier bandwidth, the qualifier baseline, the qualifier threshold, the sizer baseline, the wing-board temperature, an A-to-D overflow flag, and a count of particles rejected as being outside the depth of field. The netCDF variables and attributes should be consulted for this housekeeping information. The large number of housekeeping variables will not be included in this document, so appropriate manuals and the netCDF files should be consulted when interpreting this information.
Probes that produce size distributions of particles (with links to descriptions):Generic Name | Probe35 | Channels | Usable36 | Diameter Range | Bin Width | |
---|---|---|---|---|---|---|
FSSP-100 original | F | FSSP-10037 | 0–15 | 1–15 | ||
FSSP/SPP-100 | F | SPP-100 | 0–30 | 1–30 | 3 μm (typ.) | |
UHSAS | U | UHSAS | 0–99 | 1–99 | variable | |
CDP | D | CDP | 0–30 | 1—30 | variable | |
F300 | 3 | FSSP-300b | 0–30 | 1–30 | 0.3–20.0 μm | variable |
PCASP/original | P | PCASPb | 0–15 | 1–15 | 0.1–3.0 μm | variable |
PCASP/SPP-200 | P | SPP-200 | 0–30 | 1–30 | 0.1–3.0 μm | variable |
200X | X | OAP-200Xb | 0–15 | 1–15 | 40–280 μm | 10 μm |
260X | 6 | OAP-260X | 0-63 | 3–62 | 40-620 μm | 10 μm |
200Y | Y | OAP-200Yb | 0-15 | 1–15 | 300–4500 μm | 300 μm |
1DC38 | 2DCb,39 (old) | 0-32 | 1-30e | 25–800 μm | 25 μm | |
1DP | 2DPb (old) | 0-32 | 1-30 | 200–6400 μm | 200 μm | |
1DC | 2DC (fast) | 0-63 | 1-6240 | 25–1600 μm | 25 μm | |
1DP | 2DP (new) | 0-63 | 1-62 | 100–6400 μm | 100 μm |
Count Rate Per Channel: ACDP, AFSSP, AS100, AF300, AS200, APCAS, A200X, A260X, A200Y, AUHSAS
The size distribution of the number of particles detected by a 1D hydrometeor probe per unit time. These measurements have “vector” character in the NetCDF output files, with dimension equal to the number of channels in the table above and with one entry per channel. The first element in the vector is a historical remnant from a time when housekeeping information was stored here and should be ignored if data predates TI3GER (2022). For the size limits of the channels, see the netCDF attributes of the following variables for “Size Distribution”.
Size Distribution:
Size Distribution (cm − 3channel − 1): CFSSP, CS100, CF300, CS200, CPCAS, CCDP, CUHSAS
Size Distribution (L − 1channel − 1): C200X, C260X, C200Y
5.2.1 Concentration (cm − 3): CONCD, CONCF, CONC3, CONCP, CONCU;
(L − 1): CONCX, CONC6, CONCY {#concentration .unnumbered}
The particle concentrations summed over all channels to give the total concentration in the size range of the probe. For example, {CONCF} = ∑i{CFSSP}i. For additional details, see RAF Bulletin 24.Mean Diameter (μm): DBARD, DBARF, DBAR3, DBAR6, DBARP, DBARX, DBARY, DBARU
The arithmetic average of all measured particle diameters from a particular probe. This mean is calculated as follows:
{Cy\(_{i}\)} = concentration
from probe y in channel i
(e.g., y=FSSP to calculate DBARF)
i1 = lowest usable channel for the probe
i2 = highest usable channel for the probe
\(d_{i}\)
= diameter of particles in channel i for this probe (\(\mu m\))
(calculated as the average of the lower and upper
size limits for the channel)
\[\begin{equation} \mathrm{\{DBARx\}}=\frac{{\textstyle \sum_{i=i1}^{i2}}{\displaystyle {\displaystyle \left\{ \mathrm{Cy}_{i}\right\} d_{i}}}}{\sum_{i=i1}^{i2}\left\{ \mathrm{Cy}_{i}\right\} } \tag{5.5} \end{equation}\]
Dispersion (dimensionless): DISPD, DISPF, DISP3, DISP6, DISPP, DISPX, DISPY, DISPU
The ratio of the standard deviation of particle diameters to the mean particle diameter.
{DBARx} = mean particle diameter [\(\mu m\)]
{Cy\(_{i}\)}, i1, i2, \(d_{i}\) as for mean diameter above
\[\begin{equation} \mathrm{\{DISPx\}}==\frac{1}{\{\mathrm{DBARx}\}}\,\left\{ \frac{{\textstyle \sum_{i=i1}^{i2}}{\displaystyle {\displaystyle \left\{ \mathrm{Cy}_{i}\right\} d_{i}^{2}}}}{\sum_{i=i1}^{i2}\left\{ \mathrm{Cy}_{i}\right\} }-\{\mathrm{DBARx}\}^{2}\right\} ^{1/2} \tag{5.6} \end{equation}\]
Liquid Water Content (g m − 3): PLWCD, PLWCF, PLWCX, PLWC6, PLWCY
The density of liquid water represented by the size distribution measured by a hydrometeor probe. These variables are calculated from the measured concentration (CONCx) and the third moment of the particle diameter, with the assumption that the particle is a water drop. The following box describes the calculation in terms of an equivalent droplet diameter, the diameter that represents the mass in the detected particle. The equivalent droplet diameter is normally the measured diameter for liquid hydrometeors, but some processing has used other assumptions and this is a choice that can be made based on project needs. Using this definition allows for the approximate estimation of ice water content in cases where it is known that all hydrometeors are ice.
\(d_{e,i}\) = equivalent melted diameter for channel \(i\) of probe x
{Cy\(_{i}\)}, i1, i2 as for mean diameter above
\(\varrho_{w}\)
= density of water [\(10^{3}kg/m^{3}\)]
\[\begin{equation} \mathrm{\{PLWCx\}}=\frac{\pi\varrho_{w}}{6}{\textstyle \sum_{i=i1}^{i2}}{\displaystyle {\displaystyle \left\{ \mathrm{Cy}_{i}\right\} d_{e,i}^{3}}} \tag{5.7} \end{equation}\] (units and a scale factor are selected so that the output variable is in units of g\(\,\)m\(^{-3}\))
Radar Reflectivity Factor (dbZ): DBZF, DBZX, DBZ6, DBZY, DBZD
The radar reflectivity factor calculated from the measured size distribution from a hydrometeor probe. This is calculated from the measured concentration and the sixth moment of the size distribution, with the assumption that the particles are water drops. An equivalent radar reflectivity factor can be calculated from the hydrometeor size distribution if another assumption is made about composition of the particles, but this variable is not part of normal data files. The radar reflectivity factor is a characteristic only of the hydrometeor size distribution; it is not a measure of radar reflectivity, because the latter also depends on wavelength, dielectric constant, and other characteristics of the hydrometeors. The normally used radar reflectivity factor is measured on a logarithmic scale that depends on a particular choice of units, so (although it is not conventional) an appropriate scale factor Zr is included in the following equation to satisfy the convention that arguments of logarithms should be dimensionless.
\(d_{i}\) = diameter for channel \(i\) of probe x
{Cy\(_{i}\)}, i1, and i2 as for mean diameter above
\(Z_{r}\) = reference factor for units = 1 mm\(^{6}\)m\(^{-3}\)
\[\begin{equation} \mathrm{\{DBZx\}}=10\log_{10}\left({\textstyle \frac{1}{Z_{r}}\sum_{i=i1}^{i2}}{\displaystyle {\displaystyle \left\{ \mathrm{Cy}_{i}\right\} d_{i}^{6}}}\right) \tag{5.8} \end{equation}\]
Effective Radius (μm): REFFD, REFFF
One-half the ratio of the third moment of the diameter measurements to the second moment. This variable is useful in some calculations that relate the liquid water content of a cloud layer to its optical properties.
\(d_{i}\) = diameter for channel \(i\) of probe x
{Cy\(_{i}\)}, i1, and i2 as for mean diameter above
\[\begin{equation} \mathrm{\{REFFx\}}=\frac{1}{2}\frac{\sum{\displaystyle {\displaystyle \left\{ \mathrm{Cy}_{i}\right\} d_{i}^{3}}}}{\sum{\displaystyle {\displaystyle \left\{ \mathrm{Cy}_{i}\right\} d_{i}^{2}}}} \tag{5.9} \end{equation}\]
FSSP-100 Range (dimensionless): FRNG, FRANGE
The size range in use for the FSSP-100 probe.Range | Nominal Size Range | Nominal Bin Width |
---|---|---|
0 | 2–47 μm | 3 μm |
1 | 2–32 μm | 2 μm |
2 | 1–15 μm | 1 μm |
3 | 0.5–7.5 μm | 0.5 μm |
In recent NETCDF data files, the actual bin boundaries used for processing are recorded in the header. That header should be consulted because processing sometimes uses non-standard sizes selected to adjust for Mie scattering, which causes departures from the nominal linear bins. Recent projects have all used range 0, but other choices have been made in some older projects and other ranges are still available to future projects.
5.3 Hydrometeor Imaging Probes
Instruments used to obtain hydrometeor images include the two-dimensional imaging probes (2DC and 2DP) and some others that require special processing and separate data records. The former are described in this subsection. The latter include a three-view cloud particle imager (3V-CPI), a small ice detector (SID-2H), and a holographic imager (HOLODEC). For information regarding use of data from the latter set of instruments, consult EOL/RAF data management via this email address.
In addition to the standard processing that produces the variables in this subsection, an alternate processor is available that provides some additional options and capabilities, including the production of two sets of variables that include either all particles or all particles that pass a roundness test. Additional options include different ways of defining the particle size (including circle fitting or sizing based on the dimension along the direction of flight. Corrections to sizing are made to account for diffraction, and a shattering correction can be applied based on interarrival times. Some categories of spurious images (e.g., “streakers”) can be recognized and rejected. This processing is described in this document and at this web page and is made available by special arrangement.
Measurements based on the two 2D probes will be discussed together in this section because the 2DC and 2DP probes function similarly, differing primarily in the size resolution (typically 25 μm or less for the 2DC and 100 or 200 μm for the 2DP). The following variables have names like CONC1DC or CONC1DP to designate the two types of hydrometeor imagers. In addition, variables normally have location designations like ’_LWIO’ as described at the beginning of section ; see page . In the following ’y’ is sometimes used to designate either ’C’ or ’P’.
For the images from the 2D probes, separate data files need to be used. RAF provides a routine “XPMS2D” that can be used to view the images and calculate various properties of the hydrometeor population based on these separate files.
Special 1D Nomenclature
Despite the ’1D’ nomenclature, the following variables are measured by 2D instruments; the ’1D’ designation is used to indicate that this is the dimension that would be sized by an equivalent 1D probe using a test that requires unshadowed end diodes so that the full dimension of the particle can be determined. As a consequence, the effective sample volume becomes smaller as the measured dimension increases.
2D Count Rate Per Channel (count per time interval): A1DC, A1DP
The number of particles counted by a 2D probe in each of 62 size bins in a specified time interval, usually 1 s. These are used to calculate the derived variables like CONC1DC, C1DC, and others that follow, but are provided to allow re-calculation if a user wants to use different sample volumes or sizing assumptions.
2D Size Distribution (L − 1channel − 1): C1DC, C1DP
The concentration of particles measured by a 2D probe in each of 62 bins in a specified time interval, usually 1 s. These are calculated from A1DC by application of an assumed size-dependent sample volume based on probe characteristics and the flight speed. These are provided in a 64-element array for historical convention; the first element should be ignored if data predates TI3GER (2022), and the technique requires that the end elements be unshadowed and so precludes any measurement with width of 63 bins, so the 64-element vector has valid information only in bins 1–63. The cell boundaries are specified in the netCDF header as an attribute of C1DC or C1DP, and they specify the end points of the bin; e.g,, in the 64-element array of provided cell boundaries, the first element is the lower size limit of the first data cell which is the second element in C1DC. For a typical 2DC with 25-μm size resolution, the cell sizes increase by 25 μm per bin for each of the C1DC bins. Also included as attributes with the netCDF variable C1DC or C1DP are the size-dependent depth of field (mm) and effective sample area41
(mm), the latter having values of zero for the first and last elements in the 64-value vector.
2D Concentration (L − 1): CONC1DC, CONC1DC100, CONC1DC150, CONC1DP
The total concentration of all particles detected by a 2D hydrometeor imager, or in the case of CONC1DC100 or CONC1DC150, the concentration of all particles sized to be at least xxx μm in the dimension perpendicular to the direction of flight, where xxx may be 100 150. These concentrations are the sum of the particle size distribution given below (C1DC or C1DP), with appropriate channels excluded for CONC1DC100 and CONC1DC150.
2D Dead Time (ms): DT1DC
The time in the sample interval during which the data rate exceeded the recording capability of a 2DC probe. This is used as a correction factor when concentrations like CONC1DC or C1DC are calculated. The variable does not apply to measurements from a 2DP probe.
2D Mean Diameter (μm): DBAR1DC, DBAR1DP
The mean diameter calculated from the measured size distribution. In this calculation, the bin sizes are taken to be the averages of the lower and upper limits of the size bins. The calculation is as described by (5.5).
2D Dispersion (dimensionless): DISP1DC, DISP1DP
The standard deviation in particle diameter divided by the mean diameter. The formula used is given by (5.6).
2D Liquid Water Content (g m − 3): PLWC1DC, PLWC1DP
The liquid water content (mass per volume) calculated from C1DC or C1DP. The calculation is as described by (5.7). To conform to common usage, the liquid water content is expressed in non-MKS units of g m − 3.
2D Radar Reflectivity Factor (dBZ): DBZ1DC, DBZ1DP
The radar reflectivity factor calculated from the measured size distribution under the assumption that all particles are spherical water drops. The calculation is as described by (5.8).
2D Effective Radius (μm): REFF2DC, REFF2DP
One-half the ratio of the third moment of the particle diameter to the second moment. The formula used is given by (5.9).King, W. D., D. A. Parkin and R. J. Handsworth, 1978: A hot-wire liquid water device having fully calculable response characteristics. J. Appl. Meteorol., 17, 1809–1813. See also Bradley, S. G., and W. D. King, 1979 Frequency response of the CSIRO Liquid Water Probe. J. Appl. Meteorol., 18, 361–366.↩︎
Channels may be unusable because the first channel is a historical carry-over and should be ignored if data predates TI3GER (2022), or because in the case of 2D probes the entire-in sizing technique reduces the number of bins where particles can be sized. Also, when some channels have been considered unreliable the netCDF header may specify that the usable bins are smaller than indicated here.↩︎
Now obsolete but present in many archived data sets.↩︎
Measurements from this and the next three 2D probes are discussed in Section 5.3.↩︎
Some of the lowest channels are often considered unreliable and excluded in processing.↩︎
commonly called “EffectiveAreaWidth” in the netCDF files↩︎