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Calibrations and Performance of the Airborne Cloud Extinction Probe [Journal of Atmospheric and Oceanic Technology](Journal of Atmospheric and Oceanic Technology Via Acquire Media NewsEdge) ABSTRACT A new airborne instrument that measures extinction coefficient ß in clouds and precipitation has been designed by Environment Canada. The cloud extinction probe (CEP) utilizes the transmissometric method, which is based on direct measurement of light attenuation between the transmitter and receiver. Transmissometers are known to be susceptible to forward scattering, which becomes increasingly significant as the particle size increases. A new technique for calibrating transmissometers was developed here in order to determine the response function of the probe. Laboratory calibrations show that CEP-derived ß may be underestimated by a factor of 2 for circular particles with diameters greater than 100 µ m. Results for spherical particles are in good agreement with theoretical predictions. For nonspherical particles, however,estimates of ß can deviate significantly from those derived for spheres that have the same projected area. For in situ observations of ice particles, CEP measurements often deviate significantly from theoretical calculations, whereas for small cloud droplets agreement is good. It is hypothesized that CEP-derived estimates of ß for ice clouds depend much on variations in the scattering phase function that arise from details in ice crystal surface roughness and fine crystal structure. This would complicate greatly the estimation of ß from transmissometers for ice-bearing clouds. (ProQuest: ... denotes formulae omitted.) 1. Introduction Extinction coefficient b is one of the fundamental microphysical parameters characterizing bulk radiative properties of clouds. Knowledge of b is of crucial im- portance for radiative transfer mu in weather prediction and climate models given that Earth's radiation budget is significantly modulated by clouds. In order for a large- scale model to properly account for the radiation budget and its perturbations, it must ultimately be able to sim- ulate cloud b well. In turn, this requires adequate and simultaneous simulation of profiles of cloud water con- tent and particle habit and size. Similarly, remote infer- ence of cloud properties requires assumptions to be made about cloud phase and associated single-scattering properties-of which b is crucial. Hence, b plays an im- portant role in both application and verification of methods for remote inference of cloud properties from data obtained from both satellite and surface sensors (e.g., Barker et al. 2008). Early attempts to use airborne extinctiometers for measuring visibility in clouds go back to aufm Kampe (1950) and Weickmann and aufm Kampe (1953). The first airborne extinctiometer utilized the transmissometric method. It consisted of an incandescent lamp, a colli- mator, and a photocell for measuring light intensity. The source of light and the photocell were mounted on the wing and separated by a few meters. Zabrodsky (1957) built an airborne double-pass transmissometers, where light traveled to a retroreflector and back where it was then measured by a photodetector. Nevzorov and Shugaev (1972, 1974) advanced the double-pass transmissometer with improved stability and higher sensitivity. This de- sign yielded a large dataset of b for different types of clouds (Kosarev et al. 1976; Korolev et al. 2001). King and Handsworth (1979) built a single-pass transmissiometer with an ultraviolet source of light generated by a ger- micidal lamp. Zmarzly and Lawson (2000) designed a multipass and multiwavelength cloud extinctiometer. Gerber et al. (2000) constructed a cloud-integrated neph- elometer, in which b was calculated from an arrangement of four Lambertian sensors, two of which had cosine masks. Gayet et al. (2002) used polar nephelometer mea- surements to estimate b from the scattering phase func- tion of an ensemble of cloud particles. In many studies b was estimated from composite particle size distributions measured by several cloud spectrometers. Earlier measurements for liquid clouds (Korolev et al. 1999) showed good agreement between b measured by a cloud transmissometer and that derived from PMS Forward Scattering Spectrometer Probe (FSSP) droplet size spectra. Calculation of b from par- ticle size distributions for ice and mixed-phase clouds, however, is subject to potentially large errors due to uncertainties related to size-to-area conversion technique, shattering issues, and limited accuracy in measurements of concentration and sizes of ice particles smaller than approximately 100 mm. Despite the importance of b for simulation of radia- tion transfer for cloudy atmospheres and Earth's climate in general, probes that are capable of inferring b from first principles have not become a part of conventional airborne microphysical instrumentation. The effort to fill this gap has been undertaken by the Cloud Physics and Severe Weather Research Section of Environment Canada (EC). The cloud extinction probe (CEP) was de- signed and built in 2006 by EC (Korolev 2008) for airborne measurement of cloud b and has operated successfully during several flight campaigns. Since the early 1950s, it was recognized that the trans- missometric method is prone to contamination by pho- tons passing through the receiving aperture that had been scattered into the near-forward direction. Hence, as long as one interprets the measured intensity of light as though it were unattenuated, b will be underestimated systematically through inversion of the Beer-Bouguer equation. Theoretical considerations (Gumprecht and Sliepevich 1953; Deepak and Box 1978a,b) showed that the effect of forward scattering on estimation of b de- pends on the angle of the receiving aperture (u) and the scattering phase function of particles. Mie scattering calculations show that forward scattering is relatively weak for small particles, and so in the case of small drop- lets underestimation of b will be small. Large particles, however, have strong forward-scattering lobes that may result in significant underestimation of b. Theoretical cal- culations showed that for large particles, the relative error in b approaches a factor of 2 (e.g., Deepak and Box 1978a,b). Until now, because of the absence of calibrating standards, experimental techniques have been incapable of estimating errors in b as a function of particle size. Gumprecht and Sliepevich (1953) attempted to utilize monodisperse glass beads suspended in water to mea- sure forward scattering. However, their ability to main- tain a constant bulk number concentration in the test cell was poor. The number concentration is also affected by the rate of sedimentation for large glass beads. In the present paper we describe a novel technique and laboratory installation for the transmissometer calibration. The main objective of this calibration is to obtain a calibration curve for instrumental extinction efficiency Q* versus particle size D. The actual extinc- tion efficiency Q is an oscillating function that ap- proaches 2 asymptotically as D increases (e.g., van de Hulst 1981). Deepak and Box's (1978a,b) theoretical analysis suggests that, because of forward scattering of light, Q*(D) varies from 2 for small particles to 1 for large particles. Knowledge of Q*(D) would allow one to make corrections to CEP-inferred b when particle size distributions are measured simultaneously. The manuscript is arranged as follows. The CEP's principle of operation is described in section 2. Section 3 presents theoretical calculations of the dependence of Q*(D) versus D for different receiving apertures. Sec- tion 4 describes the principles of calibration techniques and presents results of laboratory calibrations using optical targets with different shape configurations. Re- sults of in situ measurements in liquid and ice clouds are presented in section 5. Section 6 discusses the effects on measured b due to shape and surface roughness of ice crystals. A summary is provided in section 7. 2. Principles of operation and description of CEP The CEP utilizes the transmissometric method. The principle of operation is based on measurement of in- tensity of visible light from a known source after it has traversed, and been attenuated by, a known volume. If the volume consists of randomly distributed cloud par- ticles, then the Beer-Bouguer-Lambert law states that ... (1) where l is wavelength, I0 is emitted light intensity, I is light intensity measured parallel to the incident beam, b(l) is the spectral volumetric extinction coefficient, and L is the geometric distance between emitter and re- ceiver. As the CEP provides, or controls, all variables in Eq. (1), save for b, its inversion yields an estimate of mean extinction coefficient b across L. The CEP consists of an optical unit that combines a transmitter and receiver as well as a retroreflector. Figure 1 shows a schematic of the optical unit. A colli- mated light beam is generated by an optical system consisting of 1) a high-power light-emitting diode (LED) at l 5 0.635 mm, 2) a diffuser, 3) a condenser, 4) a pinhole, and 5) an objective. The beam travels from the optical unit to 6) the retroreflector, where it is re- directed back to the optical unit. After passing though the objective and 7) beam splitter, its intensity is mea- sured by 8) a photodetector. 9) The optical chopper, with the help of 10) an optocouple, modulates the light beam and controls turning on and off the LED. The optical chopper consists of a sequence of holes, dark areas, and mirrors glued to its surface. During the first half of the period when the hole is opened, the LED is on and the photodetector measures the intensity of transmitted light plus the background intensity (Itot). During the second half of the open hole period, the LED is off and the photodetector measures the intensity of background light (Ibkg). During the first half of the period when the hole is closed and the LED on, light is reflected from the mirrored surface. After passing through a beam splitter, the reflected light is measured by the photodetector (Inorm). This signal characterizes the intensity of the LED and is used to normalize all other measured sig- nals. During the second half of the closed hole period, the LED is on and the beam irradiates the blackened surface of the chopper. In this case, the photodetector measures the signal (Iint) related to the light scattered inside the optical unit due to reflection from the optical surfaces and the different parts inside the probe's housing. The advantage of such a scheme is that it allows the intensities of the LED, background light, and at- tenuated light to be measured by the same photode- tector. This scheme minimizes the effects of changes in photodetector sensitivity during flight (e.g., caused by temperature drift). The back reflection from the front optics (heated glass and objective lens) was estimated from Itot, when the output aperture was covered by a weakly reflecting black cover. It was found that the effect of back reflection does not exceed 1.7% and can be accounted for, along with the background light and internal scattering, during postprocessing. The optical scheme was designed to produce a highly uniform collimated beam. Variations in light intensity across the beam do not exceed 2%. This minimizes the effect of vibration and mutual motion of the optical unit and retroreflector with respect to each other during flight. A similar approach was used by Nevzorov and Shugaev (1974). The size of the retroreflector is such that a displacement of it from the center of the beam by less than ;1 cm will not affect the output signal. The CEP was designed to operate in all weather conditions. The optics unit is heated to prevent fogging during rapid descents. The environment inside the op- tical unit is temperature controlled, so that the instru- ment can operate at air temperatures as low as 2608C. Based on flight tests, the threshold sensitivity of the probe was found to be ;0.2 km21. Conversely, the min- imum detectable signal Itot corresponds to the maximum inferred b of ;200 km21. The CEP was installed on the National Research Council (NRC) Convair 580. The optical unit was moun- ted inside the wingtip canister and the retroreflector inside a hemispherical cap at the rear side of a PMS probe canister (see Fig. 2). The distance between the optical unit and retroreflector was L 5 2.35 m. The sample area S of the probe is set by L and the diameter of the reflector (d 5 25 mm). For the Convair 580 installation, S 5 Ld ' 0.06 m2. Noting that the chopper allows for measurement of b only during one- quarter of the modulation cycle, at a typical airspeed of 100 m s21, the corresponding cloud volume sampling rate is approximately 1.5 m3 s21. Assuming adequate sensitivity, the above-mentioned sampling rate allows measurement of a reliable b for ice particles with con- centrations of a few per cubic meter. 3. Theoretical calculations of the effect of forward scattering In an attempt to better comprehend the nature of the observations, we constructed a numerical model of the extinctiometer. Rather than attempt to build an an- alytic approximation, it was decided that a Monte Carlo photon-transfer-based solution would better serve our purposes in light of the complicated character of ice scattering phase functions and multiple scattering (in- cluding backscatter). This subsection describes briefly the Monte Carlo technique. To begin, 0.635-mm wavelength photon packets are emitted uniformly from the source lens and travel par- allel to the lens axis toward the retroreflector. Distance to the first scattering event is computed as ... (2) where R is a uniform random number between 0 and 1. The scattering angle us is determined by first solving ... (3) where R is a new random number and p0 (u) is the azi- muthally averaged scattering phase function in which ... (4) This defines the deflection angle us away from the in- cident ray. Then one solves for the azimuthal scattering angle us as ... (5) where R is again a new random number and p(us, u)is the full phase function given us. If phase functions are azimuthally constant, as they are for spherical water droplets, then Eq. (5) simplifies to ... (6) For this version of the model, aerosols and Rayleigh scatter are neglected. Moreover, it is assumed that par- ticles can be represented as point scatterers and that p(u, u) and p0 (u) can be represented by far-field solu- tions (e.g., Mie theory for homogeneous spherical par- ticles). This is a valid assumption given that cloud particles are generally expected to be small compared to most distances between scattering events and re- ceiver (Mishchenko et al. 2006). The possible fates of a photon are shown in Fig. 3. If a scattered photon strays outside the emitted column of light by more than 5 times the radius of the lens d, then it is considered to have exited the experiment. This arbitrary condition was arrived at after injecting many millions of photons and receiving none in apertures narrower than ;18 that had strayed more than 5d out- side the collimated beam. Note that detectable photons are not limited simply to those that get transmitted di- rectly or undergo just a single forward-scattering event (e.g., Deepak and Box 1978a,b). Photons that undergo multiple scattering events, including backscatter, are detected too. These are, however, generally minor contri- butions for values of b within the extinctiometer's reliable operating range. Hence, to a very good approximation, the extinctiometer is effectively a single-pass device with a separate source and receiver. Nevertheless, this Monte Carlo routine is fast, provides useful benchmarks, and, importantly, like most Monte Carlo treatments, can ac- commodate arbitrarily complicated, nonanalytic scatter- ing phase functions. Let NT and NR(u*) be the numbers of photons emitted out and received at the lens of diameter d, respectively. In order for a photon to be received (i.e., detected), its angle of incidence relative to normal on the receiver's aperture has to be less than u*. For the experiments performed here, transmittance along the path from the source to the retroreflector, whose radius is r, and back is defined as ... (7) Assuming Beer-Bouguer-Lambert's law for a colli- mated beam of light, and particles distributed entirely at random, the transmitted fraction of unattenuated pho- tons is given by ... (8) However, because the receiver cannot discriminate scattered from completely unattenuated photons, if one tries to force Eq. (7) onto Eq. (8), then the implication is that ... (9) which underestimates true b, primarily because of single forward-scattering events. Hence, by defining ... (10) where f(u*) represents all contributions other than the unattenuated direct beam, the problem comes down to finding ... (11) In general, f(u*) will also depend on particle size D and type. If one assumes that single scattering prevails and that the portion of the phase function that leads to scattered photons being detected does not depend on the location of the scattering event (i.e., small u*), and that backscattered photons are of no consequence, then a very good approximation is obtained by ... (12) If these conditions are violated, or if scattering proper- ties depend much on particle orientation, then Eq. (12) could lead to untenable errors relative to the Monte Carlo. Figure 4 shows, however, that for water spheres at small u* (i.e., small pinhole apertures) and D less than about 500 mm, Eq. (12) is a very good approximation. 4. Laboratory calibrations a. Principle of transmissometers' calibrations The essence of calibrating transmissometers consists of transmitting the probe's beam through a media with a known particle dispersion and extinction coefficient, and then performing subsequent comparisons between the measured and known extinction coefficients. This technique is, however, hindered by the absence of calibrating standards. The main challenge is controlling particle size distribution and extinction coefficient. Until now there has not been a procedure for calibrating trans- missometers and obtaining the dependence of measured extinction versus particle size. To fill this gap, Environment Canada developed a technique for laboratory calibrations of transmissometers. The essence of this technique consists of passing a beam through a flat attenuator that consists of attenuating elements with known sizes D and shapes and having predetermined area coverage (or area ratio) S/S0, where S is the total area of opaque elements covering the il- luminated area S0. Extinction coefficient b of the at- tenuators calculated from S/S0 is then compared to that inferred from the measured light attenuation and related to the characteristic sizes of the attenuating elements. For calibration purposes, several types of attenuators were used. The first type consisted of a set of glass plates coated with repeating patterns of identical opaque dots (Fig. 5a), and six-ended stars (Fig. 5b); the latter was meant to simulate stellar ice crystals. The second type of attenuators consisted of monodisperse glass beads spread randomly over the surface of a glass substrate. The third type consisted of particles with random shapes, sizes, and placements, such as scatterings of crystals of sugar or broken glass. Values of S/S0 for the second and third types were deduced from micropho- tographs. Results for all types of attenuators are de- scribed in sections 4d-g. b. Calculation of instrumental scattering efficiency The differential form of the Beer-Bouguer-Lambert law for a medium consisting of monodisperse particles with concentration n and thickness dz is ... (13) where dI 5 I1 2 I0, s 5 Qs is the scattering cross section of one particle, s is the geometric cross section of the particle, and Q is the extinction efficiency for a particle of diameter D. Particle concentration is n 5 N /V 5 N /S0 dz, where N is the number of particles in volume V. Substituting n and s in Eq. (13) yields ... (14) in which S 5 Ns is the total geometrical area of particles. For the double-pass scheme (Fig. 6a), light passes twice through the attenuating array. Hence, after the second pass the intensities of incident and transmitted light are related as ... (15) Combining Eqs. (14) and (15) and excluding I1 gives ... (16) When two spatially separated identical attenuators are aligned, as shown in Fig. 6b, it can be shown that I/I0 and S/S0 are related as ... (17) When k such arrays are used, this generalizes to ... (18) Equation (16) considers an ideal case assuming that the substrate is absolutely transparent and does not at- tenuate light. In actuality, the substrate reflects light in the backward direction and can also absorb light. If not accounted, then this will bias estimates of b. This effect was taken into consideration by performing separate experiments with blank plates. Figures 6c,d provides an explanation for the calculations of the effect of the substrate. To estimate the effect of the substrate, the target plate was considered to consist of sep- arated attenuating elements and the glass substrate (Fig. 6c). The intensities of light transmitted through this system can be described by the following system of equations: ... (19) ... (20) ... (21) ... (22) The effect of a substrate (Fig. 6d) can be written as ... (23) ... (24) Solving the system of Eqs. (19)-(24) yields ... (25) Equation (25) differs from Eq. (16) in that I0 in Eq. (16) is replaced by Iglass. The values of I, Iglass, and S /S 0 can be obtained from measurements thus yielding estimates of Q from Eq. (25). The physical meaning of Q calculated from Eq. (25) should be interpreted as "instrumental'' extinction effi- ciency, which is denoted hereinafter as Q* so as to dis- tinguish it from actual extinction efficiency Q. As shown in section 3, Q* depends on the size of particles and the receiving aperture of the transmissometer. In sections 4f and 4g, it will be shown that Q* also depends on particle shape. c. Laboratory installation The main objectives of the laboratory studies de- scribed below are to determine Q*(D) and to estimate the feasibility of corrections depending on the type of cloud particles (ice or liquid) and their dispersion. To achieve these objectives, the following installation was designed and built. A vertically oriented frame housed the CEP optical unit mounted on one end and the ret- roreflector on the other. The CEP and the retroreflector were separated by 2.3 m to mimic the NRC Convair 580's configuration. The attenuating plates were installed on a horizontal platform that was mounted on a set of rails, thereby enabling the plates to be positioned anywhere between the CEP and retroreflector. Microphotography of the attenuators was facilitated by a high-resolution charge-coupled device (CCD) camera (Lumenera X32) attached to a microscope. The CCD matrix of the camera has 1216 3 1616 elements but built-in microshifting technology allowed for images with 4864 3 6464 pixels. The microscope used in these calibrations has a long working distance, varying from 13 to 89 mm depending on the optical magnification. A set of high-quality changeable Mitutoyo optics and zoom options provided high-resolution imagery of micro objects ranging in size from a few microns to a few millimeters. The microscope was mounted on a three-positioning stage, which al- lowed it to be moved in and out of the CEP beam. Thus, it was possible to microphotograph the attenuating el- ements and to measure light attenuation by the CEP without touching the plates. This is important when working with glass beads, as minor vibrations can easily shift them across the substrate surface. To attain high-quality microscope imagery, it is es- sential that there be proper illumination. A rectangular 10 cm 3 10 cm green LED array backlight (CCS Inc.) provided highly uniform diffuse illumination of the at- tenuators. The backlight illuminator was mounted on a rail with a slider lock, which could be positioned verti- cally to optimize the quality of particle imagery depending on microscope optics and magnification. The backlight illuminator holder design allowed the illuminator to be moved in and out of the CEP beam in order to take microphotographs of the optical targets and measure- ments of the light intensity without any significant re- arrangement of the installation. d. Calibrations by dot arrays Custom-made dot arrays were manufactured (Ap- plied Optics Inc.) for the CEP calibrations. They consist of 1-mm-thick glass plates coated with equally spaced blue chrome opaque dots of diameter D (Fig. 5a). The glass plates have an antiglare coating to mitigate re- flection and increase transmittance. Distances between the centers of the dots in the x and y directions are equal to 2D. Figure 5a shows that the area coverage of the dot arrays is S/S0 5 p/16 ' 0.196. The calibrating set of dot arrays consists of eight plates with the following dot diameters: 15, 31, 62, 125, 250, 500, 1000, and 2000 mm. Figure 7a shows the microphotography of the dot arrays with D 5 1000 mm. It should be noted that dot arrays form a regular spatial structure and therefore light scattered by them may interact with the incident light as a diffraction grating. The grating effect was checked with the help of the out-of-focus microphotography. Dot arrays were il- luminated by the CEP beam and observed through the microscope in the transmitted light. It was found that the grating effect is negligible for dots with D $ 15 mm. However, periodic patterns in transmitted light were found for dots with D 5 3 and 7 mm, and so they were excluded from the calibrations. The results of calibrations by the dot arrays are shown in Fig. 7b. Note that Q(D) / 1 for D . 500 mm, whereas for small dots Q(D) / 2. Such behavior is in good agreement with the theoretical predictions described in section 3. CEP calibrations were also performed with a double-plate scheme, as shown in Fig. 6b, with values of Q(D) agreeing nicely with those obtained for the single-plate scheme (Fig. 6a). The best-fit curve Q(D) for the dot arrays lies between the theoretical values calculated for the aperture angles u5 0.58 and0.98.Deviationfrom theoreticalpredictions may be related to optical misalignments, such as the center of pinhole 4 in Fig. 1 not being precisely centered on the optical axis. Another explanation might be that scattering phase functions of the opaque flat discs and transparent water spheres differ slightly. Nevertheless, results shown in Fig. 7b justify the dot array approach used for calibrating transmissometers. e. Calibrations by glass beads Calibrations by opaque flat circular patterns coated on glass substrates raise a question about whether these results are applicable to three-dimensional cloud drop- lets. The forward scattering by transparent spheres may be quite different in comparison to opaque flat discs. Therefore, opaque discs and transparent spheres with the same linear sizes may have different Q*(D). To ad- dress this question, the CEP was calibrated using mono- dispersions of glass beads (Thermo Inc.) having nominal diameters-30, 60, 70, 120, 230, 480, and 1000 mm- with standard deviations varying between 1% and 2%. Figure 8a shows a microphotograph of beads with D 5 480 mm inside the 2-cm diaphragm. Microscope magnification was selected so that bead images covered no fewer than 30 pixels in diameter. Lower magnification would result in low image resolu- tion and large errors in estimation of the area covered by the beads. For small glass beads, the microscope was set to a high magnification, resulting in a small field of view (FOV). At high magnification the microscope's FOV was reduced, thereby resulting in multiple picture frames (up to 35) in order to cover the entire diaphragm. Despite the seeming simplicity, processing of micro- photography and calculation of S/S0 had several chal- lenges related to nonuniform background illumination, determining the threshold intensity level Ithresh for the particle image sizing and accounting for optical aberrations. The first two issues turned out to have the largest contribution to the accuracy of calculation of S/S0. The sequence of applying corrections on distortion, non- uniform background, particle sizing, and other aspects of image processing are described in the appendix. The developed procedure enabled determining S/S0 with an accuracy varying between 5% and 10% depending on bead size and microscope magnification. Figure 8b shows the results of the CEP calibrations for different sizes of glass beads. As seen from Fig. 8b, the instrumental extinction efficiencies obtained for the glass beads are in good agreement with Q*(D) obtained for the dot arrays. This justifies the use of the arrays with regularly spaced dots for transmissometer calibration. f. Calibrations by stellar arrays The previous two sections show the importance of the dispersion of attenuating particles to measured b. This raises questions about the role of characteristic sizes of elements composing a particle on light attenuation. For example, if a 1-mm size ice particle consists of an as- semblage of 100-mm ice crystals, does it attenuate light as an ensemble of 100 mm or as a single 1-mm particle? Also, what dominates forward scattering, the elements or the entire particle? These questions are important for understanding what characteristic size of nonspherical particle should be used when applying corrections to measured extinction efficiencies. To address these questions, a set of custom-made ar- rays consisting of regularly spaced six-ended stars were used. A six-pronged stellar shape was chosen because it is one of the common habits of ice crystals. Figure 5b shows the pattern of the stellar attenuators. The width of the stellar branches is 0.1L, where L is branch length. Distance between star centers is 1.25L,soS/S0 5 0.1772. Three stellar arrays with sizes L 5 500, 1000, and 2000 mm were used for the CEP calibrations. Figure 9a shows a microphotograph of 2000-mm stars. Figure 9b shows Q* for the stellar habits. As the size of a nonsphetical particle can be defined several ways, Q* were plotted in Fig. 9b for four size definitions: 1) maximum stellar dimenffiffisffiffiiffioffiffiffinffiffi Dmax 5 L, 2) effective circular diameter Deff 5 4S/p, 3) minimal size Dmin 5 0.1L (in this case, stellar branch width), and 4) the size that fits the CEP calibrating curve for spherical particles Dfit 5 2Dmin 5 0.2L. Utilizing Dmax and Deff leads to overestimation of Q*,whereasDmin leads to under- estimation (see Fig. 12). However, Q*(D) obtained for dots would agree with that for stellar shapes defined by Dfit 5 0.2L. This implies that, in terms of attenuation measured by the CEP, a stellar particle with size L 5 500 mm behaves like an opaque disc with D 5 100 mm. These experiments demonstrate that Q*(D) and measured b depend not only on the area and size of a particle but also on its shape. g. Calibrations by irregular shaped particles Calibrations for stellar arrays has shown that for non- spherical particles (noncircular projected area) Q*(D) may be quite different from that obtained for spherical particles. The reasons for these differences are related to the ambiguity in the definition of particle size for irregular- shaped particles and the difference in scattering functions of nonspherical and spherical particles. The following set of experiments attempts to establish the feasibility of finding the size of the nonspherical particle that would be universal for different habits for use in Q*(D) and thus used for corrections to b. Broken glass particles and sugar crystals were used as optical targets in order to simulate attenuation by cloud ice particles. Figures 10a,b show examples of micro- photographs of glass and sugar particles scattered over the glass substrate. Both glass and sugar particles have transparent sections that are reminiscent of many types of ice crystals. Because of the transparent sections, the effective size Deff of the broken glass particles is smaller than Dx and Dy. However, for sugar particles all three distributions for Dx, Dy, and Deff were found to be in relatively good agreement. It should be noted that the transparent sections of the particles were not included in calculations of S/S0 and Deff. Figure 10c shows that for sugar crystals, Q*(D) are well grouped and in a good agreement with the results for dot arrays. For broken glass particles, however, Q*(D) increases with particle size. Such behavior of Q*(D) appears to be opposite of that for glass beads and dot arrays. For example, the scattering efficiency of 2-3-mm glass particles would be the same as that for approxi- mately 30-mm glass beads or dots. A reasonable expla- nation of this may be related to the transparent sections in the broken glass imagery, since this is the only distinct difference with the previous targets. This may result in a flatter forward-scattering lobe and an increase of the instrumental scattering efficiency. 5. CEP in situ measurements The extinction coefficient measured by the CEP was calculated based on the Beer-Bouguer-Lambert law as ... (26) Here I and I0 are the output signals that characterize the intensities transmitted in clouds and clear-sky, respec- tively. The intensity of the attenuated signal was calcu- lated as I 5 Itot 2 Ibkg 2 Iint, where signals Itot, Ibkg, and Iint were normalized by the current values of Inorm; I0 was determined in the same way as I but in a cloud-free atmosphere. a. Calculations of b from FSSP and CDP measurements In liquid clouds, the extinction coefficient was calcu- lated from PMS FSSP and Droplet Measurement Tech- nologies (DMT) cloud droplet probe (CDP) droplet size distributions, measured in 15 and 30 size bins, respec- tively, as ... (27) where Qj, ni, and Di are the actual extinction efficiency, concentration, and diameter of droplets in the jth size bin, respectively. For FSSP jmax 5 15 and for CDP jmax 5 30. Since the sizes of droplets measured by the FSSP and CDP are much larger than l, Q ' 2 is a good approximation. b. Calculations of b from imaging probes Extinction coefficient for ice clouds was calculated from optical array probe (OAP) particle images. OAPs provide shadowgraphs of cloud particles that pass though the sample area of the probe (see Fig. 11). In general, the OAP can be considered to be an extinctiometer, but in- stead of measuring attenuation of light integrated over the whole beam, it measures local attenuation associ- ated with the discrete binary images with shadow areas Aj (see Fig. 11b). Therefore, b can be calculated via direct integration over the area shadowed by all parti- cles ^ Aj as ... (28) where L is distance between the OAP arms (Fig. 11b) and A0 is the total area covered by the probe's laser beam having width W and moving at speed U during time Dt-that is, A0 5 WUDt. Substituting this expression into Eq. (28) yields ... (29) The direct area calculation (DAC) technique for es- timating the extinction coefficient [Eq. (29)] is based on the following assumptions regarding OAP imagery: 1) the depth of field, and the sample area width does not depend on particle size-that is, the sample area of the probe remains constant for all particles; 2) the shadow images represent geometrical shadows of cloud particles and so diffraction effects are neglected; and 3) small ice particles not seen by the probe do not produce any sig- nificant contribution in the extinction coefficient. Assumption 1 is satisfied for particles with D $ 150 mm for OAP-2DC and for particles with D $ 400 mmfor OAP-2DP, that is, when the depth of field for these particles is larger than the distance between the arms. Korolev et al. (1998, their Fig. 13b) showed that due to the diffraction effect, the image area experiences several oscillations as the particle distance from the object plane increases. The image area of particles with D , 150 mm can be overestimated no more than 40% when it passes through the maximum of the oscillations. However, the overall overestimation of the image area for these par- ticles does not exceed 20%. The effect of overestimation of the image area due to the diffraction effect decreases as the particle size increases. In other words, the DAC technique is expected to work better as particles in- crease in size. It should be mentioned that the calculation of b from OAP-2DC and OAP-2DP imagery for clouds with large concentrations of small ice particles (D , 150 mm) may result in significant underestimation of b. The DAC method gives more accurate estimation of b compared to the alternative method based on the size-to- area conversion (STAC) (e.g., Mitchell 1996), which uses ... (30) Sources of inaccuracy for the STAC method are related to uncertainty in the coefficients a and b for different particle habits. Moreover, the STAC method cannot be applied to partial images, and this seriously limits its use for particles with D . W. c. Comparisons of the CEP and particle probe data in liquid clouds Figure 12 shows time series of b for a low-level stratiform deck sampled on flight 30 of the Indirect and Semi-Direct Aerosol Campaign (ISDAC) project (McFarquhar et al. 2011). The high frequency of cycling of the Rosemount ice detector (RICE) signal indicates the presence of supercooled liquid water. Figure 12a shows that b measured by the CEP and calculated from the FSSP and CDP varied from approximately 0 to 60 km21. While this cloud layer also contained some ice particles, estimations from the OAP-2DC/2DP imagery suggest that for most of the cloud b associated with ice was less than 0.5 km21-much smaller than that for liquid regions. Therefore, this cloud layer can be con- sidered as conditionally liquid and the effect of ice par- ticles on b measured by the CEP, FSSP, and CDP can be neglected. Figures 12c,d shows scatter diagrams between CEP, FSSP, and CDP measurements of b. For liquid clouds b measured by the CEP and particle probes FSSP and CDP are in fair agreement. Differences are generally less than 15%. Such agreement is expected since, as seen from Fig. 13a, the main contribution to b arises from droplets with D , 15 mm. The CEP instrumental extinc- tion efficiency for such droplets is close to 2 (Fig. 13b). Thus, results from in situ measurements in liquid clouds provide good closure with laboratory experiments (see also Korolev et al. 1999). d. Comparisons of the CEP and particle probe data in ice Figure 14a shows spatial variations of b measured by CEP, OAP-2DC, and OAP-2DP during a flight through altostratus-nimbostratus clouds. The measurements were obtained during the Canadian CloudSat-Cloud- Aerosol Lidar and Infrared Pathfinder Satellite Observa- tions (CALIPSO) Validation Project (C3VP) conducted in southern Ontario and Quebec, Canada, during the cold season of 2006/07 (Barker et al. 2008). Extinction coefficients deduced from the 2D probes were cal- culated using the DAC technique [Eq. (29)]. Small variations of the RICE signal indicate the absence of liquid along the flight line (Mazin et al. 2001). This helps identify this cloud as glaciated. Images measured by the OAP-2DC and OAP-2DP shown in Figs. 14e,f suggest that most ice particles had irregular shapes with maxi- mum sizes extending up to 8-10 mm. The scatter diagrams in Figs. 14c,d show good agree- ment between b measured by the CEP and that derived from both OAP-2DC and OAP-2DP. Figure 15a shows the distribution of b versus particle size averaged over the time period in Fig. 14a. The extinction distribution in Fig. 15a was calculated based on the STAC method [Eq. (30)] applied to measured particle size distribu- tions. The distribution in Fig. 15a indicates that b stems largely from particles larger than ;300 mm. Laboratory calibration by opaque dots and glass beads suggest that Q*(D) in this size range should be close to 1 as shown in Fig. 15b. In this regard, it is anticipated that b measured by the CEP should be approximately half that calculated from the imaging probes. However, the comparisons between CEP, OAP-2DC, and OAP-2DP values in Figs. 14a,c,d indicate that b measured by these two different techniques are in quite good agreement. 6. Discussion The laboratory calibrations described in section 4 suggest that for spherical particles, CEP-derived Q*(D) is a unique function of D. This enables introduction of corrections to the measured extinction coefficient for liquid clouds if the droplet size distributions are known. Numerous prior measurements have shown that most liquid clouds consist of droplets with D ; 10 mm. The contribution to b by droplets with larger D is expected to be small for the majority of liquid clouds. For droplets D , 10 m m, Q is close to 2 and so CEP inferences of b do not require corrections. However, for cases with larger droplets and precipitation, errors due to forward scat- tering may reach a factor of 2 and thus will require correction. It turned out that the agreement between b measured by the CEP and that deduced from the imaging probes is observed for the majority of sampled ice clouds. In most of these cases, ice particles with D . 300 mm were the main contributors to b (see Figs. 15a). In the calculation of b from the imaging probe data in Eq. (29), it was assumed that Q 5 2. However, laboratory calibrations by the dot arrays and glass beads suggest that for D . 300 mm, the CEP Q*(D) ;1. Therefore, b measured by the CEP is expected to be roughly half those calculated from the imaging probes. Thus, the CEP in situ mea- surements of b in ice clouds and its comparisons with the imaging probes appear to contradict the laboratory calibrations. Rather, the agreement between CEP and OAPs in ice clouds suggests that Q*(D) ;2forice particles. Potential explanations of the agreement between b measured by the CEP and imaging probes may be re- lated to 1) underestimation of particle areas by the im- aging probes, 2) difference in b measured in the horizontal direction by the CEP and the vertical direction by the OAP stemming from differences in particle orientation, and 3) ice crystals scatter light in the forward direction in wider angles as compared to that for opaque discs and glass beads with the same linear dimensions. Korolev et al. (1998) showed that imaging probes with coherent illumination (OAP-2DC/2DP, etc.) are sus- ceptible to overestimation of the measured particle size and area. Therefore, the imaging probe measurements are likely to result in overestimation, rather than under- estimation, of b. Thus, explanation 1 does not seem a likely reason for the agreement in b measurements. The extinction coefficient for ice clouds may be an- isotropic due to the preferential orientation of ice par- ticles. During free fall ice particles are oriented such that the plane of their maximum projection is perpendicular to the direction of gravity. Therefore, b in the vertical direction is anticipated to be higher than in the hori- zontal. Hence, OAP extinction will be larger than that measured by the CEP. This excludes explanation 2 as a potential cause of the agreement between OAP and CEP extinction coefficients. Figure 16 shows images of cloud ice particles with different habits. Many of these particles have trans- parent areas. The images of the particles clearly indicate that the dimensions of the distinct components forming an ice particle (internal inhomogeneities visible in transmitted light, features forming particle edges, etc.) are, in some cases, much smaller than the linear di- mensions of the entire particle. Therefore, it would be reasonable to hypothesize that the forward scattering by such particles may be significantly affected by these small-scale features, thereby resulting in broadening of the forward-scattering lobe. This effect would result in the enhancement of Q*(D) eventually approaching 2. This consideration is supported by laboratory mea- surements of broken glass particles (section 4g). Large glass particles with transparent parts had Q*(D . 1) (Figs. 10c). This hypothesis is in line with the findings of Ulanowski et al. (2010, 2012), who showed that as ice crystal surfaces roughen, their asymmetry parameter g decreases. It is, however, the nature of the very forward- scattered radiation that is of concern to the CEP, and this might not change much despite reductions in g. The above-mentioned consideration, suggests that explanation 3 could be one of the likely reasons for the agreement between the CEP and imaging probes in ice clouds. This consideration raises a series of important ques- tions. First, do ice particles scatter light like a conglom- eration of small particles (Fig. 17b) or like an opaque solid (Fig. 17c)? Second, what is the effect of particle transparency on b? Third, how should the transparent parts be accounted for in calculations of b derived from imaging probe data? It may be possible that the transparent parts in the images of ice particles appear only when the ice crystal is viewed through the imaging optics with the object plane close to the ice particle. Because of inhomogeneities of ice particle facets, the light rays transmitted through the transparent ice crystal sections may become nonparallel to the incident beam. In this case the transparent parts appear only in the near field. In calculations of b at in- finite distance, however, the transparent parts should be ignored and the area inside the circumference of the ice crystal image treated as opaque. Laboratory experiments described in section 4, along with the frequently observed agreement between b measured by CEP and imaging probes obtained from in situ measurements, suggest that for ice particles Q*(D) is an ambiguous function of D. In other words, in- formation just about linear size D of an ice particle is insufficient to determine Q*. Ideally, a scattering func- tion for ice particles would uniquely address this ques- tion. A potentially attractive approach seems to be that ice particle habit along with particle size may provide a link to the scattering function and Q* . However, the infinite variety of particle shapes significantly hinders this approach, and even makes it impossible, if one re- quires arbitrarily high accuracies. 7. Summary The following outcomes have been obtained in this work: 1) Laboratory calibrations of the CEP by dot arrays and glass beads showed that Q*(D) can be considered as a unique function of D for the case of spherical par- ticles. This finding confirms that corrections of b measured for liquid clouds are feasible. The corrections of b can be made based on droplet size distributions measured by particle probes (e.g., FSSP, CDP) and the function Q*(D) obtained from laboratory calibrations. 2) For most measurements in liquid, nonprecipitating clouds, the contribution to b by droplets with D . 15 mm was relatively small and does not exceed 10%- 15%. Therefore, most CEP measurements do not require corrections due to forward scattering and can be used as reported. For the case of precipitation size droplets, the error in measurements of b may reach a factor of 2 with corrections on b becoming mandatory. 3) It appears that for the case of ice particles, Q* is a nonunique function of particle linear size. It was also found that for nonspherical particles, Q* also depends on particle shape. At this stage, corrections to b measured for ice clouds do not seem feasible. Additional studies are required in this regard. The cloud extinction probe is a new instrument that lacks analogs among existing airborne instruments that attempt to measurement b. The set of experiments de- scribed in this work is a first attempt to characterize instrumental scattering efficiency from laboratory mea- surements. The set of tests and calibrations described here shows problems relevant to the transmissometric tech- nique. The results of this work, and the developed meth- odology, can be used as a starting point for further improvements to existing airborne transmissometers. The outcomes of this study bring up a series of im- portant questions, which should be addressed in future studies: 1) How should scattering by ice particles be described: as conglomerations of small particles (Fig. 17b) or as opaque solids (Fig. 17c)? 2) How do the transparent portions and surface rough- ness of crystals impact b? 3) How should the transparent parts of crystals be treated in calculations of b from imaging probe data? Acknowledgments. The authors appreciate Darrel Baumgardner and two anonymous reviewers for their thoughtful comments, which helped to improve the man- uscript. This work was funded by Environment Canada, Transport Canada, and the U.S. Department of Energy under DOE/SC-ARM-TR-105, Contract 143648. REFERENCES aufm Kampe, H. J., 1950: Visibility and liquid water in clouds and in the free atmosphere. J. Atmos. Sci., 7, 54-57. Barker, H. W., A. V. Korolev, D. R. Hudak, J. W. Strapp, K. B. Strawbridge, and M. Wolde, 2008: A comparison between CloudSat and aircraft data for a multilayer, mixed phase cloud system during the Canadian CloudSat-CALIPSO Vali- dation Project. J. Geophys. Res., 113, D00A16, doi:10.1029/ 2008JD009971. Deepak, A., and M. A. Box, 1978a: Forward scattering corrections for optical extinction measurements in aerosol media. 1: Monodispersions. Appl. 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Lawson, 2000: An optical extinctiometer for cloud radiation measurements and planetary explora- tion. Final Rep. Submitted to NASA Goddard Space Flight Center in Fulfillment of Contract NAS5-98032, 131 pp. [Available online at www.specinc.com/sites/default/files/ software_and_manuals/Reports_Extinctiometer%20Final% 20Report_revFinal_20000201.pdf.] ALEXEI KOROLEV,ALEX SHASHKOV, AND HOWARD BARKER Cloud Physics and Severe Weather Research Section, Environment Canada, Toronto, Ontario, Canada (Manuscript received 21 January 2013, in final form 10 September 2013) Corresponding author address: Alexei Korolev, Environment Canada, 4905 Dufferin Street, Toronto ON M3H5T4, Canada. E-mail: [email protected] DOI: 10.1175/JTECH-D-13-00020.1 APPENDIX Calibration by Glass Beads The calibrations were done with monodispersions of glass beads (Thermo Inc.) having nominal diameters- 30, 60, 70, 120, 230, 480, and 1000 mm-with relative standard deviations, as declared by the manufacturer, of 1%-2%. Calibration using glass beads consisted of the follow- ing sequence of operations: 1) Obtain CEP measurements of the intensity Iglass of the beam transmitted through a glass substrate in- stalled in the center of the beam. 2) Position glass beads, at random, on the surface of the glass substrate. The surface of the substrate was located inside a 2-cm-diameter circular diaphragm. Figure 8a shows a microphotograph of beads with D 5 480 m m inside the 2-cm diaphragm. 3) Obtain CEP measurements of the intensity I of beam attenuated by the glass beads. 4) Position the microscope with the help of the 3D po- sitioning stage and take several microphotographs of the beads. Then, move the microscope out of the beam. 5) Remove beads from the substrate and measure Iglass again. Microscope magnification was selected according to bead size so that bead images were no less than 30 pixels in diameter. Lower magnification would result in both low image resolution and large errors in estimated area covered by the beads. For small glass beads the micro- scope was set to a high magnification, resulting in a small field of view. This resulted in the need to take multiple pictures so as to cover the entire area of the 2-cm di- aphragm. Thus, for glass beads with diameters ranging from 30 to 200 mm, the selected microscope magnifica- tion (1000 pixels mm21) required 35 frames in order to cover the entire area. For glass beads with diameters larger than 200 mm, the microscope magnification was set low (200 pixels mm21), so that one image frame cov- ered the entire diaphragm area. Despite its seeming simplicity, processing of micro- photography and calculation of S/S0 had several signif- icant challenges. First, image size is sensitive to the Ithresh selected for particle image sizing. This means that the size of the image increases with increasing Ithresh. The effect of Ithresh in the measured image size is shown in Fig. A1a. A special calibration procedure was applied to identify Ithresh for each microphotograph. Second, the background illumination varied over the microscope's field of view with the intensity decreasing toward the outer edges. The nonuniform background intensity affects particle image size depending on its position in the microscope's field of view. As such, if constant Ithresh is used for the entire image frame, then after conversion of the grayscale image into a black-and- white image, the size of the monodisperse particles near the center will be smaller than those near the periphery. The effect of the inhomogeneity of the background in- tensity is explained with the help of a schematic diagram in Fig. A1b. Third, microscope images are prone to different op- tical aberrations; the most significant one contributing to errors in S/S0 is distortion aberration. Distortion aber- rations result in deformation of images of beads from the center to the periphery of the microscope's view field (Fig. A1c) and consequently influence the estimation of bead image areas. To account for these effects, the following procedures were applied during image processing: 1) The processing of microphotographs begins with accounting for the effect of nonuniform illumination. The background of the original image frame popu- lated with glass beads was normalized by the background intensity obtained from the image without beads. 2) The term Ithresh was calculated during the second step and used for conversion of the original grayscale (8 bits) microphotograph into a black-and-white (binary) image; Ithresh was determined as a middle point between the maxima of intensity distributions of all pixels in the grayscale image frame. Figure A2a shows an example of two distributions of pixel intensities calculated for the image frames in Figs. A2b,c. The maximum with the higher intensity corre- sponds to the background intensity, whereas the maximum with the lower intensity is associated with the particle images. The vertical dashed lines indicate cutoff Ithresh for particle sizing. Analysis of the micro- photographs of the dot arrays yielded that a 50% threshold intensity level provides the best agreement between the measured diameters of the dots and their nominal diameters. 3) The grayscale image was then converted into a binary image. Because of refraction by the glass spheres, bead images may include bright spots near their centers. These spots were identified and eliminated during image processing. 4) The effect of distortion aberration was accounted for with the help of the retrieval matrices C obtained from the microphotographs of the images of dot arrays. Corrections were applied with the help of the MATLAB function imtransform(Im, C) from the Im- age Processing Toolbox. This function performs spatial transformations of the image Im with the rule estab- lished in accordance with the correction matrix C. The final tuning corrections described above were accomplished with the help of the microphotographs of dot arrays. The ratio S/S0 was calculated from the binary image as a ratio of occluded pixels to all pixels within the diaphragm. Figure A3 shows the influence of the effects men- tioned above on the sizing of dot images obtained from microphotograph analysis of the 125-mm dot array. For this study, nonuniform intensity background turned out to have a significant effect on image sizing (Fig. A3a). Figure A3b also shows high sensitivity of image sizing to the intensity cutoff level Ithresh. The effect of distortion aberration was found to be small relative to the first two effects. After applying the corrections, the accuracy in de- termining S/S0 is estimated as varying between 5% and 10% depending on bead size and microscope magnifi- cation. If the corrections are not applied, then system- atic errors in calculations of S/S0 may exceed 30%. (c) 2014 American Meteorological Society |