RAF Bulletin No. 24

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Bulletin No. 24

AIRBORNE MEASUREMENTS FOR CLOUD MICROPHYSICS

rev. 1/89

Darrel Baumgardner

  1. GENERAL

    The Research Aviation Facility (RAF) provides airborne instrumentation for acquiring data in support of various facets of cloud microphysical research. These instruments measure the amount of cloud water, particle concentration, shapes, and sizes. Instrument configurations vary according to aircraft and scientific objective, and scientists who use data from these instruments should be aware of the measurement limitations imposed by the capabilities of the instruments and by particular mounting configurations, when applicable.

    1. Cloud Particle Measurements

      The accurate measurement of cloud particles is complicated by the large range of sizes, shapes, and concentrations found in the natural cloud types and conditions. In a cloudy environment, particle diameters may be as small as 10 cM, as in the case of cloud condensation nuclei, or larger than 1 cM, which is not unusual for graupel and aggregates of ice crystals. The concentrations of these particles range from > 1000 per cM3 for the smaller sizes to < 0.1 per liter at the largest sizes. The particles may be spherical water droplets or complex dendritic ice crystals. The ability to analyze all of these types of particles, both quantitatively and qualitatively, requires more than a single instrument. The RAF presently has instrumentation capable of measuring particles over the range of 0.12 µM to > 6,400 µM in diameter by using combinations of particle probes that are manufactured by Particle Measuring Systems, Inc. (PMS, 1855 57th Street, Boulder, CO 80301). Aerosol particles ranging in size from 0.12 µM to 3.1 µM are sized and counted with the Active Scattering Aerosol Spectrometer Probe (ASASP). Water droplets from 0.5 µM to 45 µM in diameter are measured with the Forward Scattering Spectrometer Probe (FSSP). Water and/or ice particles ranging in diameter from 10 to 4,500 µM are sized and counted using one-dimensional (1D) optical array probes (OAPs). These OAPs thus overlap the FSSP in the cloud droplet range and extend to all but the largest sizes of hydrometeors usually encountered. If further differentiation between ice and water is desired, mixed-phase particles may be detected using the two-dimensional (2D) optical array probes for particles with diameters ranging from 25 to > 6,400 µM. A summary of these probes, listing their size ranges and resolutions, is given in Table 1. Figure 1 illustrates the locations on each aircraft where the instruments are usually mounted.

    2. Cloud Liquid Water Content Measurements

      The amount of liquid water for a given volume of air may be determined through mass integration of the particle distributions measured by the PMS probes. Another method of directly measuring the liquid water content is with two different types of hot-wire probes (manufactured by Cloud Technology, 606 Wellsbury Ct., Palo Alto, California 94306 and PMS, Inc.). These instruments relate the change in resistance of a heated sensing wire to the amount of cooling caused by the vaporization of cloud droplets impinging on the sensors.

      The liquid water content in supercooled clouds can also be estimated from the Rosemount icing rate detector described in the next section. Although liquid water estimates from this sensor are not as accurate as those from the hot wire probes, much lower liquid water contents can be detected. The ice probe is especially useful in mixed phase clouds where measurements from other methods of detection are affected by ice particles.

    3. Cloud Icing Measurements

      The icing rate in supercooled clouds can be estimated through the use of the previously-described instruments and their measurement of droplet size and liquid water content. As a direct measurement of icing rate, the RAF uses a Model 871 icing detector manufactured by the Rosemount Engineering Co., P.O. Box 35129, Minneapolis, Minnesota 55435. This probe produces a voltage proportional to the ice accumulated on a cylinder which is exposed to supercooled water droplets in the airstream.

    4. Particle Spatial Distribution Measurements

      Small-scale structure of cloud particle distributions are measured using the particle spacing monitor (PSM) developed at RAF. By measuring the arrival times between individual particles detected by either the FSSP or 1D OAPs, the spacing between particles is measured directly. The 2D OAPs also provide the interarrival times of particles which they image.

    5. Further Information

      Note: Separate from this Bulletin, the following hyperlinks have newer, additional information on the instruments described here.

      From Darrel Baumgardner:

      From Chris Webster:

  2. THE ACTIVE SCATTERING AEROSOL and
    FORWARD SCATTERING SPECTROMETER PROBES
    1. Operating Principles

      The ASASP and FSSP relate the amount of forward-scattered light by a spherical particle to its size according to electro-magnetic-wave scattered light by a spherical particle to its size according to electro-magnetic-wave scattering theory. The ASASP uses an aerodynamically-focused airstream to define a fixed sample volume (Figure 2.) The FSSP uses two photodetectors to define the sample volume in which the particles will be detected. One photodetector is optically masked so only the light outside the defined depth-of-field (DOF) is detected. The signal from this detector is used to discriminate particles outside the DOF (Figure 3.) The source of illumination is a He-Ne laser operating at wavelength of 6328 angstroms. All the optics and electronics are integrally packaged with the exception of the data system required to store the accumulated size and concentration information.

    2. Calibration Procedures

      The ASASP and FSSP are calibrated periodically before and after each field project to check for sizing accuracy. Monodispersed glass beads are used to determine the necessary sizing information with appropriate corrections made for the index of refraction differences between glass and water. The laser beam diameter and DOF also are checked periodically to maintain an accurate record of the sample volume of the FSSP. The flow rate through the ASASP, which is a constant-volume device, also is routinely checked.

    3. Probe Limitations

      Cloud particle concentrations measured by these probes are under-estimated when particles are either coincident in the beam or pass through the sensing area of the probe during the electronic processing period of a previously-detected particle. The combination of these effects typically exceeds 10% when the natural particle concentrations are greater than 300 per cM3. The majority of these losses, however, may be recovered as described by Baumgardner, et al. (1985).

      The sizing accuracy is affected by several factors. Although the lasers used in the probes are operated in a higher-order mode to produce a semi-uniform beam intensity, there are still significant non-uniformitites which affect the amount of light that a particle scatters. This problem is compounded by the response time of the electronics that causes particles to be undersized at airspeeds greater than about 50 M/s. Corrections are applied to the data that account for this problem (Baumgardner, 1987). Mis-sizing also will occur as a result of particles coincident in the beam which will be detected as a single particle but sized somewhat larger. This type of sizing error will usually be negligible, and, at present, no attempt is made to correct the data for this event. However, special software is available from RAF that can be used when special processing is desired by the user.

      Another limitation implied in the principles of operation is that these probes cannot discriminate between water and ice particles. Ice particles pass through the sample volume of these probes in random orientation, and the measured sizes will depend upon this orientation and the shape of the crystals. Ice particles outside the nominal sample area of these probes will sometimes be sized and counted if they fall partially within the sample volume. Therefore, the sample volume for ice particles will be indeterminate. For these reasons, the FSSP or ASASP should not be used for ice crystal measurements, and measurements from these probes should be used carefully whenever they are used in known mixed-phase situations. In these conditions, the spectra usually show a characteristic flat shape in the larger size channels.

  3. THE ONE-DIMENSIONAL OPTICAL ARRAY PROBE
    1. Operating Principles

      The 1D illuminates a linear array of photodiodes with a He-Ne laser. As a particle passes through this focused beam, a shadow image is cast on the diodes (See Figure 4.) and a count of the total number of occulted diodes represents the particle's size. The diodes at each end of the array act as a mechanism for rejecting those particles which do not pass entirely within the bounds of the linear array and would be undersized otherwise. The 1D probe types are differentiated by their magnification factors according to the size range desired. The 200X sizes particles with diameters from 40 µM to 280 µM in 20 µM increments; the 200Y sizes particles from 300 µM to 4,500 µM in 300 µM increments; and the 260X sizes particles from 40 µM to 620 µM in 10 µM increments.

    2. Calibration Procedures

      The 1D probes are calibrated periodically before and after each field project. The imaging probes are quite stable in their sizing of particles, and changes occur only because of changes in optical path or exceptionally dirty optical components. The sizing calibration is done with monodispersed particles, such as glass or polystyrene beads. These particles are projected across the DOF until a statistically suitable number of counts have been accumulated. Routine maintenance is a part of RAF procedures for insuring the integrity of the measurements. Such maintenance includes checking laser alignment and cleaning dirty optical elements.

    3. Probe Limitations

      The electronic response time of the instruments imposes some limitation on the minimum detectable size. A photodiode is registered as shadowed when its output is detected to change by 50%. However, even when a particle shadows 50% of a diode, the detected change may be less than this size if the particle passes too rapidly across the array. This condition depends upon the size of the particle as well as the width of the array. The 200X and 260X have lower size limits of 40 µM at a speed of 100 M/s because of this effect.

      Although the 1D probes will detect any particles which cause the diode array to be occulted, these probes cannot differentiate shapes, types, or particle orientation. If liquid water content information is desired, some fairly loose assumptions must be made with regards to the phase, habit, and density of the particles. These assumptions can lead to non-trivial errors.

      The 1D probes are unable to resolve particles coincident in the beam; however, this type of error can usually be neglected, since concentrations of particles of the size measured by these instruments are normally quite small.

      Obtaining a statistically representative sample of the cloud particle population can also be a problem because of the relatively small sample volume of these instruments and the small concentrations of larger particles in a cloud. The sample volume of these probes is size dependent. Appendix A discusses how to calculate these sample volumes.

  4. THE TWO-DIMENSIONAL OPTICAL ARRAY PROBE
    1. Operating Principles

      The 2D OAP's optical detection system is almost identical to that of the 1D probe. Whereas the 1D probes only give information about the maximum dimension along the array width, the 2Ds also give information about the area and shape of the particle and don't reject particles that shadow end elements. As a particle passes through the 2D's DOF and occults the diodes in the array, the shadowed state of each diode is stored each time the probe moves the distance of one array width. These image slices are restored during analysis later to form a reconstructed two-dimensional image of each particle. This method of measurement allows the shape of the particle to be discerned as well its size. Some information concerning the composition of the particle may be deduced from the shape and from other information such as the temperature, liquid water content, or altitude at which the aircraft made its measurements. The 2Ds are classified as either a 2D-C (cloud particle probe), which detects particles with diameters from 50 µM to > 800 µM in 25 µM intervals, or as a 2D-P (precipitation probe), which detects particles with diameters from 200 µM to > 6,400 µM in 200 µM intervals.

      A 2D probe also sends to the data system a "Shadow-Or" count, which is generated every time a particle passes through the laser. The image data are stored by the data system asynchronously and require separate processing from the synchronous data from other sensors. However, the Shadow-Or count is accumulated at the same rate as the rest of the synchronous data and can be used to calculate estimates of particle concentrations.

    2. Calibration Procedures

      The 2D probes are calibrated and aligned with the same procedures and regularity as the 1D probes.

    3. Probe Limitations

      One limitation arises from the large quantity of information produced by the 2Ds which is necessary for the two-dimensional description of a particle. If the 2D probe is operated at its maximum sampling rate, a typical 7-inch reel of magnetic tape will be filled in about five minutes or about the same time as it would take to make a single cloud pass. The maximum rate at which the 2D probe can store image slices is 4 million slices per second. This rate will not impose airspeed limitations on the lower-resolution probes. However, for the 25 µM resolution 2D-C probe, this will mean that images will become distorted at airspeeds greater than 100 M/s. When the airspeed exceeds 100 M/s, the slice rate is maintained at the maximum rate. This causes shortened images along the direction of flight.

      The high sampling rate of the 2D probe will sometimes impose another limitation on particle measurements. The image slices are stored temporarily in buffers in the probe. After one buffer is filled with 1,024 image slices, it is transferred to the data system while a second buffer is being filled. Although the image data may be collected at a rate up to 4 million slices per second, they can only be transferred to the data system at about 30k slices per second. This poses a problem only during episodes of high ice concentration. During these periods, the second buffer can become filled before the first buffer has finished emptying to the data system. This condition is called an "overload," and simply means that the probe is unable to take data during these periods.

      The orientation of ice crystals can be affected by air distortions caused by the aircraft. Measurements at the mounting locations of the PMS proves on the King Air (See (Figure 1.) are particularly susceptible to these effects because of sheared flow in front of the probe. Crystals such as plates and dendrites have been observed to rotate into preferred orientations that will cause them to be viewed on edge if the orientation of the probes is not adjusted to account for these rotations. The 1D and 2D probes are flown in an orientation to minimize these effects; however, the image data should be viewed with discretion.

    4. Data Reduction

      During the flight, the 2D images may be displayed on a CRT, but no hard copy is currently available. After the project the 2D data are processed by programs that eliminate spurious particles, plot the images on microfilm, and print derived values of concentration and size distributions. Appendix D provides a more complete description of the criteria used for detecting and eliminating spurious particles.

      Interpretation of the 2D images is highly subjective. For this reason, the RAF does not process the image data with any automatic pattern-recognition software and leaves that option to the user.

    5. Further Information

      Additional information on the PMS-2D probes can be found at http://www.atd.ucar.edu/atd/instruments/raf/pms2d/

  5. THE PARTICLE SPACING MONITOR
    1. Operating Principles

      The particle spacing monitor (PSM) provides a measurement of the small-scale structure of cloud particle distributions by measuring the spacing between individual particles. This instrument monitors the total particle count from an FSSP or 1D probe and measures the time between successive counts. This time is encoded into one of 64 size channels and sent to the data system in the same manner as particle size data from other 1D probes. The time-to-channel relationship can be set to any desired value, depending upon the expected distribution of the cloud particles. Figure 5a is a schematic representations of the PSM. Figure 5b is an example of the type of distribution produced by this instrument.

    2. Limitations

      The PSM is limited only by the probe to which it is attached. For example, when attached to the FSSP, the minimum spacing between particles that the PSM can measure is slightly greater than the combined transit time of a particle through the laser and the subsequent electronic delay time. This is usually on the order of 7-8 µs, or a spacing of 0.7-0.8 mM if the aircraft is flying at 100 M/s.

  6. THE CLOUD TECHNOLOGY AND PMS/CSIRO PROBES
    1. Operating Principles

      The operating principle of these two instruments (commonly referred to as the JW and KING probes, respectively) are based upon measuring the amount of cooling of a heated sensor by the evaporation of water droplets as they impact the sensor. These devices, shown schematically in Figures 6a and 6b, differ in their methods of measuring the amount of cooling. The JW senses changes in the resistance of the heated element as it cools, and through calibration, relates it to the liquid water content. Cooling is also caused by convective heat losses, so the probe measures these losses with a second heated wire oriented to be out of the droplet stream but still in a component of the airstream. This "compensation" signal is subtracted electronically from the sensing wire signal so that the resultant measurement is only of the liquid water component of cooling. The KING probe operates as a constant-temperature probe and measures the amount of power necessary to maintain the heated element at the same temperature while it is cooled by convection and evaporation. The liquid water content can be directly related to the power consumption using the energy equation that relates the total energy supplied to the sensing element to the energy lost through convection and evaporation. Convective heat losses are determined through calibration in dry air over a range of air speeds and temperatures.

    2. Calibration Procedures

      The JW probe requires wind tunnel calibrations to establish the gain coefficients for each individual sensing head. The compensation-wire offset is adjusted during speed runs at different altitudes prior to the beginning of a field program.

      The KING probe requires no calibration for translating the power loss to liquid water content, as this is determined from the energy balance equation. (See Appendix C.) The convective heat losses must be determined, however, since they are affected by the environmental conditions, e.g., air density, viscosity, thermal conductivity, etc., and the wire dimensions and temperature. The dry air heat loss term also is explained in Appendix C.

    3. Probe Limitations

      The JW probe is sensitive to liquid water content values down to approximately 0.05 g/M3, below which the inherent noise of the instrument masks any signal. The dry air compensation wire does not adequately remove all the effects of convective heat losses. This limitation is seen when the out-of-cloud measurements vary as much as 0.1 g/M3. These drifts are removed during data processing when possible. (See Appendix C.)

      As a device for measuring relative changes in the liquid water content, the JW has proved fairly reliable under a wide range of conditions. However, its accuracy as an absolute measure of liquid water content is questionable without measuring its response in a calibrated wind tunnel. Such calibrations have proved to be the best method of determining JW probe reliability and calibration. Extensive testing has shown that the response of this probe differs with each sensing element. Without a careful calibration, the accuracy of these probes is no better than approximately ± 20%.

      Under particularly severe conditions where the liquid water content is greater than 1.0 g/M3 and the temperature is below -15C, the heaters in the JW sensing head are not sufficient to melt quickly enough any ice that has accumulated on the probe shield. Subsequently, ice builds up on the compensation wire, and erroneous data are obtained.

      When droplet diameters exceed about 30 µM, droplets begin to break up on the sensing elements of both the JW and KING probes and are removed by the airflow before they have totally evaporated. Under these circumstances, both probes will underestimate the liquid water content.

      Both the JW and KING probes respond to ice particles as well as water droplets. However, these probes are not calibrated with respect to ice, and caution should be used when interpreting data from these probes in mixed-phased environments.

      The KING probe is considered by the RAF to be the primary instrument for measuring liquid water content because of its reliability and easy calibration. The JW is flown as a redundant measurement should there be a failure of the KING probe.

    4. Data Reduction

      Processing of the data from these probes includes corrections for airspeed on the JW and dry-air heat losses on the KING probe.

  7. THE ROSEMOUNT ICING DETECTOR
    1. Operating Principles

      The Rosemount Model 871 detector, shown schematically in Figure 7, measures the amount of ice mass accumulation on a metal cylinder. The property of certain metals known as magnetostriction is employed to drive the sensing probe cylinder at its natural frequency of 40 kHz. As the ice accretes on the cylinder, the frequency of the vibration decreases. A phase-locked loop detects the change in frequency, and a voltage proportional to this change is recorded by the data system. When a preset voltage threshold is reached, the probe tip is heated for a fixed, short period of time to remove the ice, whereupon the cycle is repeated. This probe is primarily an icing detector; however, with additional information about the temperature and air speed, an ice water content can be estimated from its measurements.

    2. Calibrations

      The frequency change versus mass relationship is known through both theoretical and empirical studies. Wind tunnel tests have been conducted in which the operation of this probe was studied during typical airspeeds and icing conditions to establish the gain coefficients of the instrument. Flight data also are used to determine the calibration coefficients that are used to calculate the ice water content from these probes. The liquid water content is derived from the equations described in Appendix C.

    3. Limitations

      The ice probe is a very sensitive device and responds to very small ice water contents. Data loss occurs, however, during the deicing period and for about a five-second period after this, as the probe reaches equilibrium with the ambient temperature.

      Ice water contents derived from the icing rate measurements have an uncertainty on the order of 20% as a result of uncertainties in droplet collection efficiency and sampling volume.

  8. FURTHER INFORMATION

    Investigators interested in discussing additional aspects of cloud physical measurement should contact the Facility Manager, Jeffrey L. Stith, PhD

    email
    Phone: (303) 497-1032

    Additional information on the instrumentation discussed above may be found in the Bibliography listed at the end of this Bulletin.

 


 

APPENDIX A.

Calculation of Particle Spectrum Parameters

 

The particle distributions measured by the ASASP, FSSP, 1D, and 2D are usually characterized by the total concentration, the mean diameter, the standard deviation, and the liquid water content. An explanation and derivation of these parameters follow.

Total Concentration

Particle concentration is defined as the number of particles per unit volume. In the case of the ASASP and FSSP, the dimensions are the number of particles per cubic centimeter. Concentrations measured by the imaging probes are usually expressed in number per liter. The method of calculating the total concentration is:

(A.1)

where:
cT = total concentration
ni = number of particles accumulated in channel i (for all probes but the FSSP)
= total droplets passing through the DOF for the FSSP
m = total number of size channels
SV = sample volume

The sample volume is defined as:

SV = (TAS)(SA)(T)

(A.2)

where:
TAS = true airspeed
SA = sample area
T = sampling period

The sample volume is determined for the FSSP by:

SA = (DOF)(BD)

(A.3)

and for the imaging probes by:

SA = (DOF)(ESW)

(A.4)

where:
DOF = depth of field
BD = effective beam diameter
ESW = effective sample width

The ASASP is a constant-volume device and is set to 1.0 cM3/s. The DOF and ESW of the imaging probes are functions of the particle size and are calculated as (Knollenberg, 1970):

(A.5)

where:
R = radius of the particle (mM)
= laser wavelength = 0.6238 x 10-3 mM

which gives a DOF of

DOF = 9482 R2

(A.6)

The DOF of the instruments is limited by the distance between probe arm tips. The maximum depth of field for the 200X, 260X, and 2D-C is 61 mM, which corresponds to a particle radius of 80 µM. The 200Y and 2D-P have a maximum depth of field of 261 mM for particles 165 µM radius or larger.

The effective sample width for the 1D probe is defined as:

(A.7)

where:
D = diode diameter = 0.2 mM
M = probe magnification factor
N = number of diodes in the array
X = number of diodes shadowed by a particle

This method of determining the effective sample width is used to account for the fact that, as particles get larger, the probability increases that they will occult an end diode and be rejected. Table A.1 tabulates M, N, and sample area formulae for each of the 1D imaging probes.

TABLE A.1
PROBE TYPE Magnification
M
DIODES In ARRAY
N
SAMPLE AREA EQUATION (mM2)
200X 10 16 189.6 x (15 - X) x R2 (R <= 80 µM)
1.22 x (15 - X) (R > 80 µM)
260X 20 64 94.8 x (63 - X) x R2 (R < 95 µM)
0.86 x (63 - X) (R >= 95 µM)
200Y 0.667 24 284.30 x (23 - X) x R2 (R < 175 µM)
87.3 x (23 - X) (R >= 175 µM)

The ESW of the 2D probes is determined in a different fashion than that for the 1D probes, since particles which shadow the end diodes are not rejected and can be included in the sample statistics if the sample volume is adjusted accordingly. A particle-weighting technique is used which increases the ESW with increasing particle size. Figures A.1 and A.2 show the sampling areas for the five probes as a function of particle diameter.

Mean Diameter and Standard Deviation

The mean diameter is the arithmetic average of all particle diameters and is calculated by:

(A.8)

The standard deviation is a measure of the deviations from the mean and is calculated by:

(A.9)

where:
= mean diameter (µM)
S = standard deviation (µM)
Ni = number of particles in channel i
di = size of which channel i represents (µM)
m = number of channels
NT = total number of particles

Liquid/Ice Water Content

The liquid or ice water content is calculated from the measured size spectrum using a summation of the individual particle masses per unit sample volume:

(A.10)

where:
= density of water
Ni = concentration of particles in size channel i
die = equivalent melted diameter (the size an ice particle would be if it were melted) in size channel i

The equivalent melted diameter is strongly dependent upon the particle habit which is measured. The method for choosing this value must be specified by the user.

Radar Reflectivity

The radar reflectivity is defined as the amount of reflectivity a measured distribution of particles would have If detected by a radar. This reflectivity is calculated with dimensions of decibels (dBZ) and is dependent upon the wavelength of the radar and the density of the particles. This reflectivity is calculated as follows:

(A.11)

where:
dB(Z) = decibels of reflectivity
Ni = concentration of particles in size channel i
die = equivalent melted diameter (the size an ice particle would be if it were melted) in size channel i

 


 

APPENDIX B.

FSSP Sample Area Calculations and Dead Time-Coincidence Corrections

 

Sample Area Calculations

The sample area of the FSSP is just its depth of field times the effective beam diameter. The effective beam diameter is some fraction of the total diameter that is dependent upon the velocity averaging mechanism of the instrument used to exclude particles passing through the edges of the beam. A running average of each particles transit time through the beam is maintained electronically. Each incoming particles transit time is compared to the average. If the particles time is less than the average, it is rejected from sizing but still included in the running average.

The ratio of accepted particles to all particles used in the average is a measure which may be employed to determine the fraction of the sample area to use in concentration calculations. Therefore, the FSSP sample area is calculated by

(B.1)

where:
DOF = depth of field
BD = beam diameter
na = velocity-accepted particles
nt = total particles passing within DOF (total strobes)

Coincidence and Deadtime Corrections

The correction for particles missed because of coincidence in the beam or because of passage through the beam during the electronic dead time involves an extensive statistical analysis beyond the scope of this bulletin. Only the end results with the necessary definitions will be given. Details of the derivations and accompanying assumptions may be found in Baumgardner et al. (1985). In short, the total number of particles passing through a scattering probe's sample volume during a given sample time can be expressed as

na = nm + nc + nd

(B.2)

where:
na = actual number of particles passing through the DOE
nm = measured number of particles passing through the DOE
nc = particles undetected because of coincidence during the sampling period
nd = particles undetected because of dead time during the sampling period

The coincident particles lost, nc, are estimated using Poisson statistics, such that

(B.3)

where:
= average transit time of a particle through the laser beam
= mean arrival rate of a particle in the beam
Pd = probability of a dead time event occurring

The average transit time is found by

(B.4)

The mean arrival rate is given as

(B.5)

where:
Na = actual particle concentration
W = beam width
v = airspeed
LD = depth of field
L1 = section of the annulus sensitive to coincidence events

The probability of a dead time event is just

(B.6)

where:
, the cumulative electronic dead time during a given sample period T, is found by

(B.7)

where:
= slow reset delay time
= fast reset delay time
no = all particles that pass outside the DOF

Then

(B.8)

To solve directly for Na requires an iterative procedure, since Na is also in the exponential term. The magnitudes of coincidence and dead time losses are shown graphically in Figure B.1, where they are plotted as a percentage of the total number of particles passing through the viewing volume.

FSSP FUNCTION VARIABLES

Several variables are typically output which give a record of the FSSP probe operation. These are used in both sample volume determination and dead time calculations. A few of these variables are listed below.


FSSP Fast Resets (cnts) - FRESET
This variable records the number of fast resets that occur during the FSSP sampling. A fast reset occurs when a particle traverses the beam outside the depth of field. When this occurs, the probe electronics must be reset. This variable is required to account for the probes total dead time. (The fast reset time is determined in the laboratory.)

FSSP Total Strobes (cnts) - FSTROB
This variable records the number of particles which traverse within the depth of field both inside and outside the "effective beam diameter". The "effective beam diameter" is that portion of the beam defined by velocity averaging circuitry contained in the FSSP. That velocity averaging circuitry is designed to reject particles passing through the outer portions of the beam in order to provide a more accurate sizing (within this "effective beam diameter"). The velocity averaging circuitry keeps track of particle transit times and rejects those which are below a certain, probe dependent threshold.

FSSP Beam Fraction - FBMFR
This is a derived variable that is the ratio of the number of velocity-accepted particles (particles that pass through the effective beam diameter) to the total number of particles detected in the depth-of-field of the beam.
FBMFR = FSSP / FSTROB

where:
FSSP = the total number of particles velocity-accepted by the FSSP
FSSP-100 Calculated Activity Fraction (none) - FACT
This is the calculated FSSP probe activity. It represents the probe dead time, the time the probe electronics are busy processing particle data. The probe activity is calculated from fast resets, total strobes, and both slow and fast reset times (determined in the laboratory).
FACT = (FSTROB) + (FRESET)

where:
= slow reset time
= fast reset time

At the request of the user, 2D data will be processed by the RAF Data Management Group on the CRAY-1 at the Scientific Computing Division. Since the images may be interpreted in a variety of ways, the user will be asked to select from a number of available options before the processing begins.

 


 

APPENDIX C.

Liquid Water Content Calculations

 

PMS/CSIRO Liquid Water Content

The electrical power required to maintain the sensor of this probe at a constant temperature must compensate for heat losses from the sensor to the passing air stream and to that absorbed by impinging droplets. This is expressed through an energy balance equation as:

P = Pd + Pw

(C.1)

where the losses to the air, Pd, are described by

Pd = pi k (Ts - Ta) Nu

(C.2)

and the losses to the droplets, Pw, are similarly expressed as

Pw = l d w v [Lv + c (Tb - Ta)]

(C.3)

where:
pi = 3.14159...
Nu = Nusselt number
k = thermal conductivity of dry air
l = length of sensor
d = diameter of sensor
Ts = temperature of sensor
Ta = temperature of air
Tb = boiling point of water
c = specific heat of water
v = airspeed
w = liquid water content

The liquid water content can be immediately obtained by measuring the power P, if the value for the Nusselt number is known. The Nusselt number can be determined as a function of the Reynolds number, Re, that takes the form of a power law

Nu = A Rex

(C.4)

where A and x are determined empirically from flight data taken at several altitudes and airspeeds.

JW Baseline Drift Removal

The compensation wire in the JW partially removes the effects of convective heat losses from the JW measurements. However, the compensation is affected by changes in temperature and pressure, and oftentimes the zero baseline of the instrument will drift by 0.2 to 0.3 g/M3 when out of cloud. This zero offset can be removed when the FSSP is present by using this probe to detect the presence of cloud. When the FSSP indicates the absence of cloud, a running average is maintained of the JW-measured LWC. During the cloud penetration, this average offset value is subtracted from the measurement.

Rosemount Ice Detector LWC Calculations

The voltage output of the Rosemount ice detector is directly proportional to the mass of ice that accretes on the sensor. When the aircraft is in cloud, the voltage increases steadily as ice builds on the sensor up to the point that a preset threshold is reached and the sensor heat is activated to remove the ice. An estimate of the LWC can be made from the voltage rate of change if several assumptions are made. The mass accumulated on the sensor is determined by:

m = Ec d l v w t

(C.5)

where:
Ec = droplet collection efficiency of the sensor
d = diameter of the sensor
l = length of the sensor
v = aircraft velocity
w = liquid water content
t = accumulation time

Thus the mass accumulation rate is:

dm/dt = k w

(C.6)

where:
k = Ec d l v

(C.7)

The voltage-to-mass calibration factor is determined either in laboratory calibrations or with in-flight comparisons with other LWC measurements. If the voltage-to-mass calibration is described by:

V = G m

(C.8)

then:

dV/dt = G dm/dt

(C.9)

and solving for the LWC, w,

w = (l dV)/(Gk t)

(C.10)

This expression for the LWC can be evaluated if the collection efficiency is known and if the diameter and length of the sensor can be assumed to be constant. These assumptions involve some uncertainty, since the collection efficiency is a function of the diameter of the sensor, the size of the water droplets, the speed of the aircraft, and the temperature and viscosity of the air. The estimated uncertainty in collection efficiency is on the order of 20%.

An additional uncertainty in the evaluation of Equation C.10 arises because of the assumption of constant diameter and length of the sensor. Wind tunnel and laboratory tests have shown that ice does not accumulate evenly on the ice probe sensor because of aerodynamic effects around the probe. Thus the value of l is variable depending upon the environmental conditions. The ice mass that builds on the sensor changes the effective cross section of the probe, so that the value of d changes as a function of time, airspeed and liquid water content. There is a 30% uncertainty in estimating the sample volume because of these factors.

Finally, the gain G, is a function of where the ice accretes to the sensor and can change as much as 30% during the accumulation period depending upon the accretion pattern.

The total uncertainty in estimating the LWC from Equation C.10 is approximately 50% if the theoretical derivation of w is used along with the estimates of collection efficiency, sample volume, and voltage-to-mass calibration. However, the value of the product Gk can be determined empirically without having to assume specific values for the components that go into the derivation of these variables. If Gk is determined by comparisons with the LWC from the hot-wire probes, the resulting accuracy in the derived LWC is decreased to approximately 20%.

 


 

APPENDIX D.

Spurious Image Rejection Techniques in the Processing of Data from the 2D Probe

 

The 2D probes capture the image of particles in the shape of shadows that pass across the linear array of diodes. Some of these images are not truly representative of real particles but are the result of splashing or breakup of ice or water on the probe arm tips. In especially heavy concentrations of raindrops, liquid water content, or graupel, the rate at which these spurious images are generated can be high and will seriously bias the derived concentrations and size distributions. The remainder of this appendix describes each type of spurious image, its cause, and the pattern recognition technique used to identify and reject it.

Short Arrival Time Rejection

When a particle strikes the arm tip of the probe, the result is a cloud of secondary particles that stream through the probe's sample volume. (See Figure D.1.) The distance between these particles will be quite small, and the measured particle interarrival times also will be very short. On the average, cloud particles are distributed homogeneously and the spacing between them is random and determined by the average concentration, C. Although some of the distances between particles can be short, on average, the spacing is:

la = (1/C)1/3

(D.1)

Thus, when particles in the size range of the 2D probes are even in modest concentrations of 1 to 10 per liter, the average spacing is on the order of 5 to 10 cM.

A 2D probe measures the distance between particles along with the particle image. The majority of spurious particles generated by collisions with the probe tips will be rejected if a threshold is specified that is much smaller than the average expected spacing between particles. This threshold will eliminate some legitimate particles, of course, since there is a finite probability that the spacing between some particles is very short. The fraction of particles erroneously eliminated can be calculated if the particles are assumed to be distributed randomly in space with an exponential probability distribution function:

P(l < lt) = 1 - e-lt/la

(D.2)

where:
l = distance between particles
lt = threshold distance

Hollow and Gapped Particle Rejection

Another characteristic of particles created spuriously by arm tip collision is that they will be so close together that the probe cannot recognize the end of one particle and the start of another, and the result is an image that looks like a number of distinct particles in the same image frame. This condition is detected in the analysis in two different ways. Sometimes several blank image slices will occur within the image. (See Figure D.2.) When this condition is detected, the particle is rejected. The other method is to measure the ratio of the area of the shadow image to the area of the rectangle that would enclose the image and reject the image if this ratio is less than a preset threshold. This fraction (shown graphically in Figure D.3) is determined by:

f = A/(XY)

(D.3)

where A is the image area expressed in number of diodes shadowed and X and Y are the lengths of the sides of the rectangle that circumscribe the image. These lengths are also expressed in terms of the number of diodes.

The threshold is usually set to 0.4, a value that has been determined empirically after visually examining a large number of spurious 2D images and calculating the average fraction, f, from Equation D.3.

Water Streamer Rejection

Under conditions of heavy liquid water content, pools of water will build on the splashguards of the probe and eventually be discharged across the opening in the arm tip and will appear as an elongated image. (See Figure D.4.) These images are rejected by comparing the length of the particle along the direction of flight to its width along the diode array. If the length is greater than six times the width, the particle is assumed to be a "streaker" and is rejected. This criterion will also sometimes reject larger particle or particles only partially in the sample volume. To minimize rejecting too many of these types of particle, extra constraints are imposed on the rejection criterion. When the width of the particle is greater than three-quarters of the array width, or if any of the diode array end elements are shadowed, then the rejection criterion is not imposed.

Blank Image Rejection

The 2D probe will often register the occurrence of a particle, but the resulting image frame will be blank. The "zero area" images are usually the result of particles whose size is of the same order as the resolution of the probe. When a particle enters the beam, the 2D probe is placed in a ready state and waits until the occurrence of the next cycle of the timing clock (which is called the "true air speed clock," since the frequency is proportional to the aircraft velocity). If the particle is small, it will have passed completely across the array by the time the next clock cycle occurs. In these cases, the shadow state of the diodes is not captured in time, yet the event is still recorded by the probe by the appropriate time word in the data buffer.

Most of these zero-area events are caused by legitimate particles and could be used to calculate the total concentration; however, it is left to the discretion of the investigator whether or not to reject these events and exclude them from the analysis of the data.

 


 

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