Analysis of flight test results of the Optical Ice Detector.
Cloud phase discrimination, coupled with measurements of liquid water content (LWC) and ice water content (IWC) as well as the detection and discrimination of supercooled large droplets (SLD), are of primary importance in aviation safety due to several high-profile incidents over the past two decades. The UTC Aerospace Systems Optical Ice Detector (OID) is a prototype laser sensor intended to discriminate cloud phase, to quantify LWC and IWC, and to detect SLD and differentiate SLD conditions from those of Appendix C. Phase discrimination is achieved through depolarization scattering measurements of a circularly polarized laser beam transmitted into the cloud. Optical extinction measurements indicate the liquid and ice water contents, while the differential backscatter from two distinct probe laser wavelengths implies an effective droplet size.
The OID is designed to be flush-mounted with the aircraft skin and to sample the air stream beyond the boundary layer of the aircraft. The volume of the sampled airstream is several orders of magnitude greater than that of traditional airborne cloud probes, such as the Forward Scattering Spectrometer Probe (FSSP). The OID has flown on the University of North Dakota (UND) Cessna Citation-II research aircraft in a wide variety of atmospheric conditions, which cloud probes on the aircraft have verified to corroborate the OID data. In this paper, we compare UND cloud probe measurements with those from the UTC Aerospace Systems OID to demonstrate the possibility of using the OID to meet the need for measurements of various icing parameters.
CITATION: Ray,M. and Anderson, K., "Analysis of Flight Test Results of the Optical Ice Detector," SAE Int. J. Aerosp. 8(1):2015, doi: 10.4271/2015-01-2106.
Increased awareness of the flight hazards posed by supercooled large droplets and airborne ice crystals has prompted civil aviation authorities to issue new industry standards to cover atmospheric conditions beyond those in 14 CFR 25, Appendix C. The new Appendix O includes freezing drizzle and freezing rain.  Numerous cases of engine power loss and even flameouts have been attributed to ice crystal ingestion, focusing additional attention on the need to detect high concentrations of airborne ice crystals. Airframe manufacturers must demonstrate the capability of an aircraft to comply with these new standards. One means of compliance is to sense the presence of hazardous conditions with sufficient rapidity for the crew to take appropriate action, whether that should be activating icing protection systems, increasing engine thrust, or simply exiting the hazardous region. We present the results of recent flight tests of a prototype Optical Ice Detector (OID) intended to meet the need for cognizance of hazardous flight conditions beyond those specified in Appendix C.
Previous flight tests of a prototype OID demonstrated the capability of distinguishing liquid water clouds from ice clouds. [2, 3, 4] Estimates of liquid water content (LWC) were also made with the effective droplet diameter derived from the other traditional particle sizing probes on the test aircraft. For these latest flight tests, the OID uses a two-color differential absorption technique to estimate the effective droplet diameter of the cloud, obviating the need for data from other cloud droplet-sizing probes. The cloud data in this paper are derived solely from the OID, with those from the other optical probes included only for reference and comparison.
The OID is an airborne, micro-pulse polarimetric lidar with a footprint comparable to that of current ice detectors. Unlike traditional optical cloud probes, the OID simultaneously samples all of the particles illuminated by the laser beam rather than individual droplets or crystals that pass a few at a time through a thin sample volume. The received light is a composite of the scattering from all particles (both water droplets and ice crystals) illuminated by the laser. Likewise, the polarization state of the received light is a composite of the polarization generated by all of the illuminated particles. Simultaneously sampling a large number of particles ensures that data collected are representative of the entire cloud.
With the use of pulsed near-infrared lasers, the OID is capable of correlating the temporal delay of the received light signal with distance from the sensor. Range resolution allows the exclusion of scattering generated by particles within the boundary layer of the aircraft, where the droplet and crystal distribution is likely to be dissimilar to that impinging on other parts of the aircraft. This reduces the need for aerodynamic analysis in selecting the optimal location of the detector on the particular airframe.
Cloud Sampling Volume
Appendix O regulations include typical cumulative droplet distributions for freezing rain and drizzle, with MVD greater than and less than 40 [micro]m. The largest droplet diameters, which contribute heavily to the LWC and pose the greatest icing hazard, are also the least numerous. It is vital for an optical icing sensor to sample a sufficient volume of space to ensure that these sparse, large droplets are at least illuminated by the probe laser beams.
For the OID, two detection volumes must be considered. The first is the volume sampled by a single laser pulse. Each laser beam forms an oblate, conical sampling volume with the short axis of the cone base parallel to the flight vector. The sampling volume extends laterally into the airstream as far as the degradation of the signal-to-noise ratio permits. Depending on the cloud attenuation, the maximum detection range is ten to twenty meters. The beam divergence of the lasers is ~ 4 mrad x 1 mrad, with a beam waist of 12 mm diameter at the window. Light traverses the distance from the OID to particles at the maximum detectable range and back to the sensor in only 150 ns. Even at 500 knots (250 m/s) airspeed, the forward translation of the aircraft during the elapsed sampling time is less than 0.1 mm. The OID laser acts like a strobe lamp, rendering the sampled air stream virtually stationary during the sampling period. When the maximum detection range is ten meters, the sampled volume of cloud for a single laser pulse is 4.5 liters.
The other detection volume is the one created by the forward motion of the aircraft. The laser pulse repetition rate is 20 kHz. At 500 knots (250 m/s) airspeed, the aircraft moves 12 mm between consecutive laser pulses, a distance equal to the laser beam waist at the OID window. Contiguous laser pulses generate sampling volumes which almost completely overlap one another, as if the lasers were operating in a continuous-wave mode; the composite volume is the lateral cross-section of the diverging beams multiplied by the distance through which the aircraft motion sweeps the beams through the cloud. The volume is (300 x [v.sub.aircraft]) liters/s, where [v.sub.aircraft] is the forward velocity of the aircraft in m/s.
This is a large sampling volume, even over a short detection time. Optical atmospheric research probes such as the Forward Scattering Spectrometer Probe (FSSP) sample at most 40 to 50 ml/s.  Table 1 lists the total number of drizzle droplets larger than 100 [micro]m diameter and rain drops greater than 500 [micro]m that are sampled by the OID both in one laser pulse and in one second. The figures assume an aircraft traveling at 250 knots (125 m/s) through each of the four drizzle/rain conditions outlined in Appendix O, when the LWC is 0.18 g/[m.sup.3], which is the upper limit LWC for the case of freezing drizzle with MVD > 40 urn at -25 C over 17.4 nautical miles horizontal extent. (The upper limits of LWC for drizzle with MVD < 40 [micro]m and rain all lie above 0.18 g/[m.sup.3].) Every laser pulse illuminates at least one large droplet that is characteristic of drizzle or rain. The influence of these large droplets on the composite lidar signal generated by the entire distribution is considered later in this paper. However, their presence in the thousands to more than one million during one second of sampling suggests the efficacy of the OID for sensing icing conditions beyond those of Appendix C.
Table 1. Sampled large droplet counts for Appendix O freezing drizzle and freezing rain droplet size distributions (with MVD < 40 [micro]m and MVD > 40 [micro]m). The upper figure is for a single laser pulse, while the lower is for one second of signal integration. The aircraft speed is 125 m/s, and the liquid water content is 0.18 g/[m.sup.3].
With the introduction of a second laser wavelength, the Optical Ice Detector combines into one sensor three cloud lidar detection methods used by researchers for both earthbound and airborne instruments. The methods are: cloud optical extinction and backscatter measurements, differential absorption lidar for the determination of LWC and SLD conditions, and circular polarimetry for cloud phase discrimination. These three techniques provide complementary data that together form a more complete description of the icing conditions than would be possible with only a single measurement mode.
Extinction and Backscatter Lidar
Like other cloud lidars, the Optical Ice Detector directly measures the optical extinction and backscatter of the cloud that it probes. The cloud particles create a single composite echo P(r), where r is the distance that the leading edge of the laser pulse has penetrated into the cloud. (The range r is proportional to the elapsed time T after the emission of the laser pulse from the OID.)
P(r) = [beta]G(r)[e.sup.-2[alpha]r] (1)
[beta] is the backscatter coefficient (in units of [m.sup.-1] [ster.sup.-1]), and [alpha] is the extinction coefficient (in units of [m.sup.-1]). It is assumed that the cloud is homogenous over the short working range of the OID so that [alpha] and [beta] are constants. The function G(r) is a light collection efficiency function that depends on the intensity, divergence, and temporal shape of the laser pulses, as well as the configuration and efficiency of the receiver optics. This function is determined empirically by measuring the laser echoes from a hard target of known reflectance placed at various distances from the OID over its entire working range.
A simple inversion of the lidar signal P(r) yields the backscatter and extinction. When the range-resolved echo intensity is normalized by G(r) and plotted against r on a semi-log plot, the slope is -2[alpha] and the y-intercept is ln([beta]).
ln ([[p(r)]/[G(r)]]) = in ([beta]) - 2[alpha]r (2)
Both a and [beta] depend on the density of water droplets and ice crystals as well as their size distributions. The ratio of [alpha] to [beta] (known as the lidar ratio) is an indication of the typical droplet or crystal size. Clouds with small droplet sizes generate lidar ratios ~ 19 sr; smaller droplet sizes are associated with larger lidar ratios, and vice versa.
Calculation of LWC requires an additional parameter, the effective droplet diameter [D.sub.eff]
[D.sub.eff] = [[<[D.sup.3]>]/[<[D.sup.2]>]], (3)
which is the ratio of the third moment of the droplet diameter distribution to its second moment. The liquid water content is then
LWC = 1/3 [rho][alpha] [D.sub.eff], (4)
where [rho] is the density of water.
The correlation of lidar ratio with droplet size can provide an estimate of the effective droplet diameter.  However, measuring the backscatter [beta] requires calibration of the OID response to a cloud of known backscatter. This can be difficult to perform in the lab. (The OID is not sensitive enough to measure molecular scattering that is commonly used to calibrate cloud lidar.) Furthermore, if the flush-mounted window of the OID becomes soiled or crazed during operation, the calibration is compromised. The calculation of [alpha] requires only knowledge of the rate at which the signal is sampled and a measurement of the relative signal decay over time. The sampling rate is easily controlled and maintained, and the decay rate is independent of changes in the transmission of the window. As much as possible, the OID relies on relative measurements to avoid sensor calibrations that are difficult to perform and to maintain over the life of the sensor.
An alternative method of measuring an effective droplet diameter is to incorporate an additional wavelength, or "color", into the Optical Ice Detector. This differential absorptive two-color technique is described by Westbrook et al.  for the estimation of drizzle droplet sizes from a ground level cloud lidar. Two beams of laser light, each with a distinct near-infrared wavelength, probe the cloud. The wavelength of one beam is 905 nm, for which there is little absorption of the light by either water droplets or ice crystals. The wavelength of the additional laser beam is 1550 nm, which lies near a peak in the absorption spectra of water and ice. For droplets with diameters greater than ~20 urn, the scattering efficiency is virtually identical at both wavelengths, but the backscatter is lower at the absorbing wavelength than at the non-absorbing wavelength. The log of the ratio of the backscatter at 905 nm to that at 1550 nm is defined as the two-color ratio (TCR):
TCR = 10 x [log.sub.10] ([[[beta].sub.905]/[[beta.sub.1550]]]). (5)
Like the determination of the extinction coefficient, the two-color ratio is a relative measurement. Provided that the output of each laser is monitored and the sensitivity of each photodetector is maintained, only the relative magnitudes of [beta] are necessary. No absolute calibration of the OID sensor with regard to [beta] is required.
For a particular droplet size distribution, the two-color ratio scales with the effective droplet diameter. Westbrook et al. assume a gamma distribution of droplet sizes:
n(D) = [N.sub.0] [([[D]/[[D.sub.0]]]).sup.[micro]] exp (-(3.67 + [micro])[[D]/[[D.sub.0]]]), (6)
where n(D) is droplet number density for diameterD, [D.sub.0] is the MVD, and [mu] is a dimensionless size parameter that controls the shape of the distribution, particularly for the small droplets. The case of [mu]=0 is a simple inverse exponential. For other values of [mu], the distribution has a single mode, with the modal droplet diameter shifting toward larger values as [mu] increases. A plot of TCR vs. [D.sub.eff] (shown in Figure 3 for [mu] ranging from two to ten by increments of two) forms a look-up table for [D.sub.eff] when the two-color ratio is known. In the absence of knowledge of the shape parameter, Westbrook et al. assume [mu]=2. Using a two-color ratio curve (shown as the black dashed line) that is an average of the two extremes [mu]=2 and [mu]=10 yields a droplet sizing error that is at most 25% at [D.sub.eff]= 500 [micro]m. The MVD is readily derived from [D.sub.eff] given the distribution n(D).
For [D.sub.eff] less than 20 [micro]m, the TCR curves exhibit fluctuations that depend on the shape parameter. Very small droplets dominate the distributions, and for these small droplets the differences in scattering efficiencies for wavelengths of 905 nm and 1550 nm affect the backscatter more than the differences in absorption. The TCR can even become negative. In such cases, the maximum droplet diameter is less than 100 [micro]m, and the MVD is less than 40 [micro]m. These conditions, which are neither freezing drizzle nor rain, are not the SLD conditions that are the focus of Appendix O. A worst case estimate of 20 [micro]m for [D.sub.eff] permits an LWC calculation that errs on the side of caution for icing conditions.
Lidar ratio and two-color ratio have an inverse relationship with regard to effective droplet diameter. The lidar ratio curves for the various shape parameters [mu], if plotted against [D.sub.eff], are more closely spaced than those for the two-color ratio, but their dynamic ranges are lower. The two-color ratios vary by more than two orders of magnitude while the lidar ratios change by only a factor of four over the same droplet size range. Even if the lidar ratio were measured, the two-color ratio provides an additional degree of droplet size discrimination.
In addition to measuring the cloud backscatter, the 905 nm laser beam performs a depolarization measurement that indicates the cloud phase. The beam is right-hand circularly (RHC) polarized. As it enters the cloud, a small portion of the light scattered by the airborne droplets and crystals travels backward along the path of the laser beam and is collected by the receiver, though most of the scattered light moves in the same forward direction as the propagating laser beam. Unlike the forward component, the backscatter contains polarization information characteristic of the scattering particle, information that indicates cloud phase. Due to the smooth, spherical shape of small water droplets, laser light reflected back on itself by a liquid water cloud retains its initial polarization state, although the sense of the circular polarization state of the light is reversed due to the reversal in propagation direction. A purely liquid water cloud will generate a predominantly LHC polarization state as sensed by the OID. Ice crystals, with their more complex and faceted structures, alter the polarization state of the reflected light such that the backscatter is predominantly RHC. Mixed phase clouds will produce circular polarization states that are intermediate between those of purely liquid water and completely glaciated clouds.
Within the receiver of the OID, polarization-sensitive optical elements separate the received light into two orthogonal, circularly polarized RHC and LHC states. Photodetectors register the intensity of light in each of the states as [P(r).sub.RHC] and [P(r).sub.LHC]. The difference of these signals divided by their sum is known as the fourth Stokes parameter (V).
V = [P(r).sub.RHC]-[P(r).sub.LHC]/[P(r).sub.RHC]+[P(r).sub.LHC] (7)
Ultimately, all of the received light (whether circularly polarized or not) enters either the LHC or RHC channel. If the received light is linearly polarized or unpolarized, it has no propensity to enter one circular polarization channel rather than the other; half of it will pass into the LHC detector, and the remaining half will pass into the RHC detector. Hence, if the received light contains no circularly polarized components, V is, equal to zero. If the light is purely RHC, with no other components, V is+1. If the light is purely LHC, then Vis -1. Mxed states of circular, linear, and unpolarized light generate fourth Stokes parameters between -1 and +1.
For water clouds, V is nearly -1, while for glaciated clouds, V varies from 0 to 0.3, depending on the crystal shapes. The density of a cloud can degrade the polarization purity of the backscattered light. The stronger forward-scattered component of the beam continues propagating through the cloud, where it may undergo more forward scattering and eventually scatter backward towards the optical receiver. Rather than simply penetrating longitudinally into the cloud, the transmitted light begins to propagate transversely, creating an annular glow around the direct backscatter from the water droplets. These small-angle forward scattering events accompanied by a single backscatter no longer maintain the original polarization state of the probe laser beam. Instead, they produce depolarization that makes V more positive.
Consequently, the measured Stokes parameter for a liquid water cloud depends on the extinction coefficient. The effect has been observed in previous flight tests of the OID.  For an ice cloud, the value of V varies little with the extinction coefficient. Regardless of cloud density, V remains negative for a water cloud and positive for an ice cloud. This is the primary advantage of using circular rather than linear polarization. Glaciation of a cloud produces a distinct change in the sign of the fourth Stokes parameter.
Another advantage of circular polarization is its sensitivity to mixed phase conditions. In a 2008 Applied Optics paper, Gimmestad  explores the relationship between the intrinsic depolarization parameter [delta] of a cloud and the effect of [delta] on both linearly and circularly polarized lidar. Complete depolarization of light by a cloud (for which [delta] = 1) creates equal signals in the orthogonal polarization detectors of a linear polarimetric lidar, but for a circular polarimetric lidar, the signal passes fully from one polarization state detector to its counterpart. Circular polarization measurements are, in principal, twice as sensitive to the depolarization parameter [delta] as those from linear polarization. The "parameter space" spanned by the transition of a cloud from liquid to mixed phase to fully glaciated is larger for a circularly rather than linearly polarized lidar.
This fact is borne out in the work of Del Guasta et al. , which uses a ground level polarimetric lidar capable of probing the same cloud in both linear and circular polarization modes. For an ice-precipitating altocumulus cloud, the range-resolved circular polarization measurements show the same transition from ice virga at the cloud base to a dense, liquid state at the cloud top as do those for linear polarization. However, the degree of variation in polarization and the clarity of subtle variations over height are greater for circular polarization. The same enhanced sensitivity is incorporated into the OID.
All of the flight tests of the Optical Ice Detector occurred on the University of North Dakota Cessna Citation-II research aircraft. The aircraft is equipped with a suite of atmospheric monitoring instruments. A Cloud Droplet Probe (CDP) from Droplet Measurement Technologies and a Two-Dimensional array probe (2D-C) together measure the size distribution of water droplets and ice crystals. A Nevzorov probe measures the liquid water content and the total water content and then computes ice water content from the difference of the two.
The droplet diameter size range for the CDP is 2 to 50 [micro]m, while that of the 2D-C is 15 [micro]m to 3.6 mm. The size distributions from both probes are spliced together to form a single distribution with an update rate of 1 Hz. A Mie scattering code, such as that of Wolf and Voshchinnikov , computes optical parameters such as extinction and backscatter at the relevant wavelengths by using the measured droplet size distribution. Other parameters derived from the droplet distribution (such as TCR, LWC, MVD, [D.sub.eff] and [D.sub.max]) all have the same 1 Hz update rate.
The housing of the prototype OID is not yet certified for flush mounting with the aircraft skin. During flight tests, the OID resides within the aircraft cabin and samples the airstream through an optical-grade window mounted into the fuselage. The window is approximately one meter to the fore of the leading edge of the wing. This window is not heated, as it will be on the fully-developed OID. Instead, a fan in the cabin passes air across the inner surface of the window to prevent fogging and icing on the inside surface. No icing was observed on the outside surface of the window during these flight tests.
Previous tests of the OID in a wind tunnel and on the Cessna Citation II demonstrated the distinction of water clouds from ice clouds using the computed fourth Stokes parameter. In some cases, V lay between the extremes of liquid and ice, suggesting mixed phase clouds. In this test, the Citation II flew through a stratocumulus cloud with an outside air temperature at a few degrees below freezing. A simple model of the relationship between V and the fraction of ice present is applied to the data from a flight:
Fraction Ice (t) = [[V(t,[alpha](t))-[V.sub.water]([alpha](t))]/[[V.sub.ice]([alpha](t))-[V.sub.water]([alpha](t))]], (8)
where V(t, [alpha](t)) is the fourth Stokes parameter at time t, and a(t) is the measured cloud extinction at time t. [V.sub.jce]([alpha](t)) and [V.sub.water]([alpha](t)) are the extrema of V characteristic of purely glaciated and purely liquid clouds for cloud extinction [alpha](t).
The functions [V.sub.ice] ([alpha]) and [V.sub.water]([alpha]) are derived empirically from previous flight tests of the OID, as shown in Figure 4. [V.sub.ice]([alpha]) is zero, since it has been observed that a fourth Stokes parameter that is positive indicates pure glaciation, regardless of the cloud extinction. [V.sub.water]([alpha]) is linear with an upward slope. The minimum Stokes parameter of -0.85, rather than -1, is due partly to the limited polarization purity of the transmitted laser beam but mainly to the limited polarization discrimination of the receiver optics. The LHC channel receives most of the light from backscatter of the laser by a liquid water cloud, but the beamsplitter cube passes some residual light into the RHC channel. The "cross-talk" fraction is approximately 1:14 for LHC light entering the receiver so that the lowest value for V will be ~ -0.85. (There is also cross-talk into the LHC channel for RHC light that ice crystals generate, but the similar limit on positive V is well above the maximum observed in glaciated clouds.)
The graph in Figure 5 overlays the results of our model with the fraction of ice computed from the Nevzorov probe. The update rate of both sensors is 1 Hz. Both curves exhibit the same large scale patterns, with the OID indicating periods of complete glaciation lasting ten to fifteen seconds, or one to one and a half kilometers in spatial extent. Within the macro structure, both probes exhibit fluctuations on the same time scale. Neither probe appears to lag in its response behind the other, at least for the time scales over which the ice contents of the clouds vary. During several periods, each lasting a few seconds, the OID reports an ice fraction nearly three times lower than that from the Nevzorov probe. However, at 21:19:02 UTC, the Nevzorov reports no ice while the OID indicates approximately 20% ice.
The more obvious discrepancy between the probes occurs for completely glaciated clouds, as indicated by the OID. The Nevzorov probe measures 80% to 90% ice fraction during these periods. Previous flight tests have confirmed the ability of the OID to detect pure ice clouds reliably. The discrepancy is likely due to the response of the Nevzorov hot-wire LWC detector to ice crystals, even when no liquid water is present. This response has been observed in completely glaciated clouds at true airspeeds of 100 m/s.  The typical measurement of the hot-wire detector is 19% of the IWC, even though the LWC is zero. Hence, an ice fraction from 80% to 90% reported by the Nevzorov is expected for a cloud composed entirely of ice crystals.
Liquid Water Content
The liquid water content, as shown in Equation 4, is a product of the optical extinction and the effective droplet diameter. In previous work , the OID measured the extinction while the droplet size measurements from the probes on the aircraft supplied the effective diameter. For these latest flight tests, the goal has been to estimate [D.sub.eff] from the OID alone.
As an initial confirmation of the process, the two-color ratio derived from the measured droplet size distribution and that reported by the OID appear in Figure 6. Once every 200 ms, the OID generates a range-resolved laser echo signal that is an average of the individual signals for each laser pulse in that period. The two-color ratios from these reported echoes are averaged in groups of five to generate a series of TCR values at 1 Hz update rate, each data point having an error bar computed from the standard deviation of the five averaged measurements. Like the fractional glaciation curves from the OID and Nevzorov probe, the TCR from the OID and the droplet size data follow similar large scale patterns.
When the two-color ratio from the OID lies between 0 and 5 dB, it agrees to within two standard deviations with the two-color ratio derived from the UND droplet sizing instruments. Both curves occasionally dip below zero, suggesting the presence of small droplets for which differential scattering rather than differential absorption dominates the TCR. At certain times in the flight, the two-color ratio from the OID becomes more negative than the computed TCR. At a time when the computed TCR is absent due to a lack of data from the UND cloud sizing probes, the TCR reported by the OID drops to -3 dB.
One possible explanation is that the OID is sensitive to droplets smaller than the lower size limit of the CDP probe. The CDP does not report droplets smaller than 2 [micro]m in diameter, but droplets below this limit lie near the maximum scattering efficiency of both near-infrared wavelengths of the OID. As the plot in Figure 3 shows, the two-color ratio can be negative for small effective droplet diameters. The lowest [D.sub.eff] on the plot is 4 [micro]m; a ratio of -3 dB, as seen in Figure 6, is conceivable for [D.sub.eff] less than 2 [micro]m.
Above 5 dB, the TCR measured by the OID falls well below the values calculated by the Mie scattering code operating on the reported droplet distributions. An examination of both the liquid water content and the droplet parameters provides some insight into the cause. From 17:11:46 to 17:14:00 UTC, the LWC computed from Equation 4 agrees quite well with the LWC derived from droplet size measurements. This is the purpose of introducing the two-color method into the OID-to enable droplet size estimation and thus eliminate the need for other instruments to assist the OID in the measurement of LWC.
However, beyond 17:14:00, the agreement between the two LWC curves is poor, despite the fact that for three brief periods the measured and computed two-color ratios actually coincide. The liquid water content during this period is high, indicating the presence of rain drops. The plot of [D.sub.eff] MVD, and [D.sub.max] in Figure 8 confirms this. [D.sub.max] rises to and remains at more than 2 mm, beyond the 500 [micro]m lower limit of [D.sub.max] for rain.
During this time period, the droplet size distributions show two types of character. Sometimes [D.sub.eff] and MVD nearly coincide. At other times, [D.sub.eff] lies far below MVD. The first condition indicates a cloud with a single droplet size distribution mode, while the second suggests a cloud with a distribution that is bimodal. For a bimodal size distribution, rain drops exist within a cloud of smaller droplets, which have formed through condensation rather than coalescence.
Much of the water content is contained in the large droplets that are sparse compared to the numerous small drops present in condensation clouds. The OID lidar signal is an average of the backscatter contribution of all droplets, small and large, sampled by the laser beam. But the finite volume in the beam, coupled with the scarcity of large droplets, causes the contribution of large droplets to appear as intense, sporadic flashes in a temporally smooth background of scattered light generated by the small droplets.
Two different effects result from the large droplets, depending on the character of the droplet distribution. If the distribution has a single-mode, the scintillations from large droplets form most of the lidar signal and can begin to drive the photodetector into saturation, even if the time-averaged signal appears to exhibit no clipping. The effect is worse for the 905 nm channel since the light is not absorbed by the large droplets as much as it is for 1550 nm. Consequently, in rain with a single-mode drop size distribution, the two-color ratio is anomalously low.
If the distribution is bimodal, the large droplets are fewer in number for a given LWC than if the distribution were single-mode. Averaging the signal over many laser pulses causes the large droplet scintillation to reduce in significance compared to the overall signal while reinforcing the steady background from small droplets. The measured two-color ratio will agree with the computed ratio, but the ratio alone will not indicate the presence of the large droplets.
Both of these effects appear to occur at times beyond 17:14:00 when one compares Figures 6, 7, and 8. Bi-modal large droplet distributions (i.e. distributions for which [D.sub.efff] << MVD) generate accurate two-color ratios, while single mode large droplet distributions produce anomalously low two-color ratios. However, both types of distributions lead to an underestimate of the LWC. The large droplets, which contain much of the LWC of the cloud, are not fully sensed with the current signal averaging technique that has proven adequate for clouds with single mode small droplet distributions. Our approach to resolving both effects will be to monitor the large droplet scintillation on a pulse-by-pulse basis, ensuring there is never signal saturation and detecting the presence of large droplets in clouds with effective diameters below 100 [micro]m. 
Recent flight tests of the Optical Ice Detector have demonstrated its ability to differentiate cloud phase and estimate the fraction of ice water content within a cloud. With the recent addition of a second laser wavelength, the OID is capable of estimating the characteristic droplet size of the cloud and computing its liquid water content without data from other aircraft sensors. The LWC measurements compare favorably with those of the other aircraft sensors for conditions within the realm of Appendix C. Future work will focus on the extension of this capability into the icing conditions of Appendix O.
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[3.] Halama, G., Ray, M., Anderson, K., and Nesnidal, M., "Optical Ice Detection: Test Results from the NASA Glenn Icing Research Tunnel," Paper AIAA 2010-7532 presented at the 2nd AIAA Atmospheric and Space Environments Conference, Toronto, ON, August 2-5, 2010.
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[9.] Del Guasta, M., Vallar, E., Riviere, O., Castagnoli, F. et al., "Use of polarimetric lidar for the study of oriented ice plates in clouds," Applied Optics, 45, 4878-4887, 2006.
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The authors gratefully acknowledge the assistance of David Socha, Marvin Onken, Brian Snyder, Christopher Sanden, Darren Jackson, Mchael Nesnidal, Magdi Essawy, and Mark Miller (all of United Technologies Aerospace Systems), as well as David Delene and Jonathan Sepulveda (both of the University of North Dakota School of Aerospace Sciences) in the development and testing of the Optical Ice Detector and in the preparation of this manuscript. This technology is Patent Pending and is the subject of patent applications filed 2008 through 2014 in the US Patent & Trademark Office.
This paper does not contain technical data as defined in the ITAR or EAR.
2D-C - Two-Dimensional Cloud array probe
CDP - Cloud Droplet Probe
FSSP - Forward Scattering Spectrometer Probe
LHC - Left-hand circular (polarization)
LR - Lidar ratio
LWC - Liquid water content
MVD - Median volume diameter
OID - Optical Ice Detector
RHC - Right-hand circular (polarization)
SLD - Supercooled large droplets
sr - steradian
TCR - Two-color ratio
UND - University of North Dakota
UTC - United Technologies Corporation, Universal Time Coordinated
Mark Ray and Kaare Anderson UTC Aerospace Systems
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|Author:||Ray, Mark; Anderson, Kaare|
|Publication:||SAE International Journal of Aerospace|
|Date:||Sep 1, 2015|
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