1. Introduction
Techniques for determining the coefficient k have been discussed by Heymsfield and Miloshevich (1989), Baumgardner and Rodi (1989), and Claffey et al. (1995). The difficulties in defining k are related to simultaneous, accurate measurements of accumulated ice ΔM and frequency changes ΔF. Heymsfield and Miloshevich (1989) suggested calibrating the Rosemount probe by using ΔM derived from Forward Scattering Spectrometer Probe (FSSP) measurements. The limitation of this method is that the FSSP is known to react to ice particles, and it is difficult to determine what fraction of the counts in supercooled clouds were caused by ice and what fraction were caused by liquid droplets. This leads to uncertainty in measurements of ΔM. Baumgardner and Rodi (1989) found that the coefficient k varies from probe to probe, and it depends also on the distribution of ice over the cylinder surface. They obtained a different k coefficient than that reported by Heymsfield and Miloshevich (1989). Claffey et al. (1995) calibrated three RICE probes using a rotating multicylinder at the Mt. Washington Observatory. They found that each ice detector was unique and should be calibrated individually before being used.
This paper presents a theoretical study of ice accretion on the surface of the cylinder in the flow of supercooled droplets. A steady-state heat balance on the surface of the icing cylinder is considered in detail. A new calibration technique for the RICE probe, based on the measurements of the rate of ice sublimation in cloud-free air, is suggested. The calibration coefficient derived using this sublimation technique is compared with that obtained using the conventional technique, that is, when ice is accreting on the cylinder.
2. Heat balance on the surface of a riming cylinder
Consider a cylinder exposed to the flow of air with velocity U, temperature Ta, pressure Pa, and containing supercooled droplets with radius r and liquid water content (LWC) W. It is assumed that the axis of the cylinder is perpendicular to the axis of the vector of the air velocity. The temperature of the droplets is considered to be the same as the temperature of the air. In the vicinity of the cylinder the trajectories of the droplets due to their inertia will deviate from the trajectories of the air. As a result the droplets will hit the cylinder within a certain band limited by polar angles −ϕ0 to ϕ0 (Fig. 1). The angle ϕ0 is a function of the droplet radius, cylinder radius, airspeed, air temperature, and pressure (Langmuir and Blodgett 1945; Mazin 1957; Borovikov et al. 1963). At angles ϕ > |ϕ0| the droplets with radii r do not impact the cylinder and they flow around the cylinder with the airflow. Thus in the case of supercooled droplets, ice would accrete on the surface of the cylinder where ϕ < |ϕ0|. In principle, the shape of the accreted ice depends on the airspeed, droplet size, LWC air temperature, and other parameters that define the thermodynamical processes on the icing surface. The shape of the accreted ice is also a function of time and can vary significantly from that shown in Fig. 1.
The shape of accreted ice on a cylindrical surface has been discussed in a number of studies (e.g., Mazin 1957;Lozowski et. al 1983a,b). The RICE probe automatically de-ices itself with an internal heater after approximately 0.5 mm of ice accumulates on its surface. This value is small compared to the RICE cylinder diameter (≈6.3 mm). Therefore, in this study it is assumed that the ice accreted on the RICE probe surface has a shape close to that of a circular cylinder. The spongy ice formation and runback icing is not considered in the frame of this study.
a. Local heat balance
The pioneering work on heat balance of an icing surface goes back to the 1950s (e.g., Hardy 1945; Ludlam 1951; Tribus 1951; Messinger 1953; Fraser et al. 1953;Hardy and Brown 1954). A detailed discussion of these papers can be found in Mazin (1957).
Consider a steady-state heat balance at a local point on the surface of the cylinder. The surface temperature is defined by several processes: dynamic heating, freezing of droplets, ice sublimation, heat exchange between the droplets, and the cylinder’s surface. These processes are schematically shown in Fig. 2. Due to axial symmetry of the cylinder, the thermal processes on the surface will be a function of the polar angle ϕ (Fig. 1).
Equation (15) describes the heat balance at a local point on the surface of the cylinder. The RICE probe response depends on the mass of accreted ice and its distribution on the surface of the cylinder (Baumgardner and Rodi 1989). In the following discussion it is assumed that ice is distributed uniformly along the axis of the cylinder.
b. Integral heat balance
Here Ts is the temperature averaged over the surface covered by ice, that is, over the sector limited by the angles −ϕ0 to ϕ0; Li = Li(Ts) is the latent heat of evaporation at temperature Ts; Ei = Ei(Ts) is water vapor pressure saturated over ice at temperature Ts, ɛ = ∫ ɛϕ cosϕ dϕ is the integral collision efficiency (appendix B),
These assumptions work with a reasonable accuracy, if changes of the variables along the surface are relatively small. Estimates show that if U < 180 m s−1 αϕ and Ts change by not more than ±30%. The averaged product of the above variables deviate from the product of the averaged ones by no more than 10%–15%.
3. Threshold liquid water content
Equation (21) contains only one unknown variable Ts, which can be computed using numerical methods.
Figure 3 shows the dependence of the difference Ts − Ta versus the air velocity U for different: (a) air temperatures Ta, (b) relative humidity ea/Ew, and (c) air pressure Pa. As is seen from Fig. 3, the ice sublimation results in additional cooling of the surface compared to a dry cylinder (curve Ts = TsA). The effect of cooling depends on Ta, ea/Ew, Pa, and U, and it increases with an increase of the air temperature (Fig. 3a), a decrease of relative humidity (Fig. 3b), and a decrease of pressure (Fig. 3c). At U = 100 m s−1 the effect of cooling is about 2°C (Fig. 3a at Ta = −5°C, Pa = 800 mb), while at U = 200 m s−1 the effect increases up to 9°C (Fig. 3c at Ta = −10°C, Pa = 400 mb). At low temperatures (Ta < −40°C) the cooling effect becomes insignificant (Fig. 3a). Under certain conditions [i.e., when ea > Ei(Ts)] the effect of ice sublimation may exceed the adiabatic heating and the temperature of the surface of the ice becomes lower than the temperature of the air (Fig. 3b). Such situations may occur if the air is dry. This phenomenon is similar to the cooling of a wet thermometer. The analysis of Eq. (21) shows that under certain conditions the deposition of ice on the surface of the cylinder from water vapor is possible. It is worth noting that Ts in Eq. (22) does not depend on the collection efficiency ɛ and the angle ϕ0.
Figure 4 shows the dependence of We0 on airspeed using Eq. (20), for different air pressures and humidity. Though the zero relative humidity case is unrealistic for in-cloud regions, the examples of We0 calculated for zero humidity give an idea about the behavior of We0. This may be useful for studies of icing in wind tunnels or simulated icing behind air tankers where the humidity may be significantly less 100%. For calculations of We0 the radius of the droplets was assumed to be r = 10 μm and the collision efficiency ɛ, angle ϕ0, and coefficient ξ were calculated based on this droplet size (appendixes A and B).
It is seen from Fig. 4 that We0 increases with increasing temperature and airspeed in saturated air. The characteristic values of We0 in saturated air at U = 100 m s−1 is of the order of 0.005 g m−3. At U = 200 m s−1 We0 exceeds 0.01 g m−3 at Ta > −20°C.
The value We0 is an important parameter, since it defines a theoretical lower threshold for liquid water content measurements by the RICE probe; that is, the RICE probe cannot measure liquid water content less than We0. If W = We0 the RICE probe will measure zero LWC, and if W < We0 the RICE signal will decrease, if it was not zero. Another important conclusion is that it is necessary to make corrections for the mass of sublimating ice when the LWC is of the order of 0.01 g m−3, and it becomes comparable with the amount of sublimating ice. This is important for aircraft with speeds higher than 150 m s−1.
4. Saturated liquid water content (Ludlam limit)
An increase of the LWC leads to an increase of the heat flux q4. At some LWC the heat of freezing will increase the surface temperature Ts to 0°C. Further increase in the LWC will not result in an increase in the surface temperature. In this case only a fraction of the supercooled water freezes. This fact may be taken into account by introducing the coefficient of freezing (Mazin 1957; Borovikov et al. 1963). The minimum value of the LWC W = Wcr at which Ts reaches 0°C is called the Ludlam limit (Ludlam 1951). The unfrozen fraction of liquid water may shed away with the airflow or freeze at the backside of the cylinder (runback icing), or may be partly incorporated into a spongy ice structure similar to hail growth (Greenan and List 1995). For the RICE probe an increase in the LWC above Wcr would cause a dropoff of the rate of change of the output signal, so that for LWCs W > Wcr cannot be accurately measured by the RICE probe. Baumgardner and Rodi (1989) and Cober et al. (2001) demonstrated this effect in RICE measurements when the Ludlam limit is reached. Thus, Wcr can be considered as an upper limit of supercooled LWC that can be measured by RICE probe.
The results of Wcr calculations are presented in Fig. 5. As seen in Fig. 5, Wcr increases rapidly with decreasing Ta and an increasing U. At temperatures Ta > −10°C and U > 100 m s−1 the situation when W > Wcr is quite typical for clouds and the Ludlam limit may be easily reached.
5. Calculation of Ts, We, W
The values of Ts, We, and W, can be found iteratively using Eqs. (16) and (20). For calculation of W and Ts at U = 175 m s−1, Pa = 400 mb, Ta = −20°C, and Wm < 0.1 g m−3 with accuracy δT = 1°C, and δW = 0.002 g m−3 12 iterations are required. The number of iterations increases with an increase in temperature and decrease of the air pressure.
6. RICE probe calibration
The objective of the calibration is to find the coefficient k, which relates the signal V and the mass of the accreted ice M on the RICE probe cylinder [Eq. (1)].
a. “Sublimating” technique
The conventional techniques derive the coefficient k for the cases when ice is growing on the cylinder, that is, dM/dt > 0 (Baumgardner and Rodi 1989; Heymsfield and Miloshevich 1989; Claffey et al. 1995). However, Eq. (1) does not imply any limitations on the sign of dM/dt. Therefore, there is a possibility to calibrate the RICE by measuring the rate of ice sublimation in cloud-free air. Figure 6 shows an example of the time history of the RICE probe signal during ice accretion inside clouds and sublimation in the cloud-free regions. After leaving cloud (Fig. 6c), ice retained on the RICE probe started to sublimate in cloud-free air resulting in a decrease in the RICE probe signal (Fig. 6d). The measured rate of the RICE probe signal reduction ΔV/Δt and the rate of ice sublimation calculated theoretically based on the measurements of U, Ta, Pa, ea can be used for calibration of the probe.
Figure 7 shows the rate of ice sublimation derived from Eqs. (16) and (19) for the assumption W = 0. The rate of sublimation increases rapidly with an increase of the airspeed and decrease of the humidity. For example, at Ta = −20°C and ea = Ew the rate of ice sublimation at U = 200 m s−1 is approximately 14 times larger than that at U = 100 m s−1. This illustrates how significant ice sublimation can be for high-speed airplanes. It is worth mentioning that ice may grow up on the cylinder at low airspeeds even when flying in cloud-free air. Thus, at temperature Ta = −20°C and ea = Ew the ice starts to build up at U < 60 m s−1 (Fig. 7b). It happens when the vapor pressure in the air becomes larger than the saturation pressure over ice at the surface temperature.
The advantage of this technique is that it derives the coefficient k from first principles and does not need reference measurements of liquid water content.
For calibration purposes, a flight leg should be chosen in cloud-free air where the pressure, air temperature, humidity, and airspeed stay approximately constant. Measuring the signal changes ΔV during time Δt and substituting into Eq. (26) gives the calibrating coefficient k. The vapor pressure Es is calculated using the temperature Ts, whereas the temperature Ts is calculated from Eq. (16) using in situ measurements of U, Ta, Pa, ea, and assuming W = 0.
Figure 8 presents results of calibrations of three different RICE probes mounted on three different aircraft:Convair-580, King Air, and Sabreliner. In the calculations of k in Eq. (26) it was assumed l = 2.54 cm, Rc = 0.317 cm, ξ = 1.41, ϕ0 = 1.48 rad (appendix A). The airspeed U, temperature Ta, pressure Pa, and dewpoint temperature Tdew were measured by the aircraft instrumentation. Water vapor pressure ea was calculated from the dewpoint temperature Tdew measured by an EG&G dewpoint thermometer. Figure 8a shows the results of calibration of the Meteorological Service of Canada (MSC) RICE probe mounted on the National Research Council (NRC) Convair-580. The measured parameters changed in the ranges 85 m s−1 < U < 115 m s−1, −23°C < Ta < −7°C, 0.46 mb < ea < 2.6 mb, 525 mb < Pa < 950 mb. Figure 8b shows the results for the National Center for Atmospheric Research (NCAR) RICE probe installed on the King Air. The measured parameters changed in the ranges 115 m s−1 < U < 140 m s−1, −29°C < Ta < −9°C, 0.18 mb < ea < 1.5 mb, 390 mb < Pa < 550 mb. Figure 8c shows the results for another RICE probe installed on the NCAR Sabreliner. The measured parameters changed in the ranges U = 180 m s−1, −34°C < Ta < −30°C, 0.07 mb < ea < 0.18 mb, 365 mb Pa < 375 mb.
The RICE coefficients k are found to be noticeably different and equal to 1.40 × 10−5 ± 0.14 × 10−5 kg V−1 (MSC Fig. 8a); 2.13 × 10−5 ± 0.39 × 10−5 kg V−1 (NCAR Fig. 8b); 3.49 × 10−5 ± 0.41 × 10−5 kg V−1 (NCAR Fig. 8c). This result is consistent with the study of Baumgardner and Rodi (1989) who stated that the coefficient k may be significantly different from probe to probe. Another explanation may be related to the effect of the RICE probe installation location on the aircraft. If the cylinder is mounted too close to the fuselage or the wing surface, it may cause nonuniform deposition of ice on the cylinder due to the gradient of the airspeed in the vicinity of the airplane surface. This may result in different length l of the ice deposition along the cylinder’s axis, so that the length l may not necessarily be equal to the length of the cylinder. The errors related to changes of local temperature and, consequently, Es are relatively small and cannot explain the observed difference in k (see sections 4 and 8).
b. Retrieval of liquid water content
The adequacy of the proposed method was tested by a comparison of LWC measured from other probes (Wm) with the LWC retrieved from RICE measurements (Wr) using calibrating coefficient k derived from the “sublimation” technique.
Figure 9 shows a scatterplot of Wm versus Wr. The measurements of LWC Wm were conducted with the help of the airborne hot-wire Nevzorov probe (Korolev et al. 1998) installed in the NRC Convair-580. The accuracy of the Nevzorov probe in measurements of cloud LWC is estimated as 10%. The data were collected mainly in stratiform clouds associated with frontal systems during the Third Canadian Freezing Drizzle Experiment (Isaac et al. 1998) in December 1997–February 1998.
c. “Ice accretion” technique
Figure 10 shows the scatterplot of the rate of ice accretion dM/dt = 2RclU
The average value of the coefficient calculated for the dataset shown in Fig. 10 is k = 1.35 × 10−5 ± 0.42 × 10−5 kg V−1, and the correlation coefficient is 0.88. The value of k calculated using the ice accretion technique is rather close to that obtained using the sublimating technique 1.40 × 10−5 ± 0.14 × 10−5 kg V−1, though the dispersion is three times higher.
7. Discussion
a. Accuracy of the sublimating technique
The accuracy of the RICE probe calibration using the “sublimating” technique depends on the accuracy of measurements of U, Ta, Pa, Tdew, and assumptions about Rc, l, ɛ, ϕ0, α, and ξ. The first four measurable parameters result in random errors and are mainly responsible for the scatter in Fig. 8. The remaining parameters would result in systematic errors. The angle ϕ0 is defined by Re and Stk numbers and it increases approaching π/2 with an increase of droplet size. During sublimation, the angle ϕ0 decreases as well as the length l and the radius Rc of the iced cylinder. During aircraft measurements, it is not possible to control Rc, l, or ϕ0. For the calculations presented in Fig. 8 the following assumptions regarding Rc, l, ϕ0, ɛ, and ξ were made.
The length of ice is equal to the length of the RICE probe cylinder, that is, l = 2.54 cm.
The radius of curvature of the ice is equal to the cylinders radius Rc = 0.317 cm.
The collision efficiency ɛ was calculated based on Re and Stk numbers (appendix B). In the calculation it was assumed that r = 10 μm. For most cases ɛ was no less than 0.9.
The angle is equal to ϕ0 = 1.48 rad for ɛ = 0.9. Angle ϕ0 is a function of Re and Stk.
The coefficient ξ = 1.41 for the angle ϕ0 = 1.48 (appendix A).
During ice sublimation, ϕ0 and l decrease, whereas ξ and Ei increase. The net effect of the ice sublimation results in a decrease of the product Rclϕ0ξ(Eis − ea). For calibration purposes, the vague ΔV/Δt should be measured at the beginning of sublimation, before ϕ0, l, and Rc start to change.
A variation of r within 2 μm results in errors ξϕ0 within 3%–5%. The value of ξα changes no more than 5%. The relative effect of uncertainty in Rcl is estimated as 3%–5%. The air pressure P can be measured with high accuracy so that the relative errors due to P are less than 1%. The errors of 1°C in measurement of Ta and Tdew can result in relative errors in the term (Eis − ea) of 10%–20%. The relative error in measurements (Eis − ea) may increase when ea is close to saturation. The net effect of all errors may reach easily 20%–30%, which explains the scatter in diagrams in Fig. 8.
b. Accuracy of ice accretion technique
The accuracy of the RICE probe calibration using the rate of the ice growth on the cylinder depends significantly on the accuracy of the measurement of LWC by a reference probe. Usually, either the FSSP or hot-wire probes such as the King or Nevzorov probes are used as a reference. In the best case for the hot-wire probes the accuracy of the measurements of LWC is about 10%–15%. For LWC derived from FSSP measurements the errors may be up to 30% or more for liquid water clouds. For mixed clouds the FSSP measurements may be “contaminated” by ice particles and that may result in much higher errors. The net effect of uncertainties in Rc, l, and ɛ may result in errors about 20%. The measurements of true airspeed are rather accurate compared to other sources of errors and therefore they can be neglected. The resulting accuracy of the conventional RICE probe calibrating technique is estimated as 25%–30%.
However, the above estimate does not explain the scatter of the data in Figs. 9 and 10 where the retrieved and measured LWC may be different by a factor of 2. An additional source of error may be related to the changes of the airflow around the cylinder due to different aircraft maneuvers, such as changes of the angle of attack, climbs, descents, turns, etc. These may affect the local airflow around the cylinder or result in partial aerodynamic shadowing of the cylinder.
It should be noted that the RICE probe has a significant “dead” (or “delay”) time compared to other probes used for the measurements of LWC. During this time period the cylinder is heated to de-ice its surface and then it cools down to the air temperature. The heat balance on the surface of the icing cylinder cannot be considered as a steady state during the dead time, and the theoretical consideration developed above is not applicable for these conditions. Such periods must be excluded from measurements of ΔV/Δt. Dead time is a function of W, Ta, Pa, U, and it may vary from 10% to 90% of the measurement cycle. The fraction of the dead time increases with an increase in U and W and decrease of Ta. Similar results were found by Baumgardner and Rodi (1989).
c. Measurements in mixed and glaciated clouds
Though the RICE probe shows relatively large scatter in measurements of LWC (Figs. 8, 9), it can be effectively used in studies of mixed and glaciated clouds. For now it is the only known aircraft instrument used in cloud physics measurements that responds to the liquid phase and is insensitive to ice particles. It should be emphasized that the imaging probes, such as PMS OAPs or CPI, do not provide phase recognition for circular particles, since frozen droplets would appear in 2D imagery in the same way as liquid ones. At the same time the hot-wire probes like the King or Nevzorov probes may have a residual effect of ice particles on measurements (Korolev et al. 1998). The following example demonstrates the capability of the RICE probe in mixed and glaciated environment. Figure 11 shows synchronous measurements of the RICE probe signal and LWC derived from FSSP data. The measurements were conducted by NCAR Sabreliner in wave clouds in 1990 (Heymsfield and Miloshevich 1993). It is clearly seen that the RICE probe repeatedly triggers in approximately half of each cloud during the penetration through it. These triggers are caused by the portion of cloud containing some liquid. In the other parts of the clouds the RICE signal is decreasing due to ice sublimation, which indicates zero LWC and, consequently, complete glaciation of the cloud. This example also demonstrates that FSSP may give rather erroneous measurements of liquid water content in cold clouds. This would create problems in calibrating the RICE probe using the FSSP measurements of LWC.
8. Conclusions
The above study results in the following conclusions.
Theoretical examination of the rate of ice accretion on the RICE probe cylinder showed that the minimum measured liquid water is limited by the lower threshold We0 [Eq. (20)]. A liquid water less that We0 cannot be detected by the RICE probe. The value of We0 is mainly defined by Ta, and U. For high airspeeds (U > 200 m s−1) the threshold value We0 may well exceed 0.01 g m−3, which may become comparable with the measured cloud liquid water content.
The upper limit of the measured LWC by the RICE probe is determined by the Ludlam limit Wcr [Eq. (22)]. The value of Wcr depends on P, Ta, and U. For typical aircraft speeds (80 m s−1 < U < 200 m s−1) in the temperature range −5°C < Ta < −15°C the Ludlam limit for the RICE probe ranges from 0 to 0.8 g m−3 (Fig. 5) and such conditions can be easily met in clouds. If the liquid water content exceeds Wcr the RICE probe cannot be used for accurate measurements of LWC.
A new technique for the calibration of the RICE probe based on the measurements of the rate of ice sublimation in cloud-free air is proposed. The advantage of the method is that it derives the calibration coefficient from first principles and it does not require reference measurement of LWC by other probes. The conventional RICE probe calibration technique is based on the measurement of the rate of ice growth and it needs in addition measurements of LWC. The comparative analysis in section 7c showed that the accuracy of the sublimating calibration technique is better compared to the conventional ice accretion technique.
The range of possible supercooled LWCs measured by the RICE probe is limited by We0 and Wcr. Since We0 increases and Wcr decreases with an increase of the airspeed U, the range of measured LWC decreases with the increase of U. Therefore, the use of the RICE probe for measurements of supercooled LWC from slow moving platforms would be more effective compared to high-speed ones. For example at U > 200 m s−1, Ta > −10°C, and P > 800 mb the RICE probe cannot be used for proper measurements of LWC since Wcr = 0 (Fig. 5). Though the RICE probe will trigger under these conditions due to partial freezing of water on the upwind surface of the cylinder and runback icing. The use of the RICE at low airspeeds is also preferable because of a smaller fraction of the dead time compared to high speed under the same conditions.
Low accuracy, large dead times, and complex data postprocessing may significantly limit the capability of RICE probe for measurements of supercooled cloud liquid water. That is why in aircraft cloud microphysics studies the RICE probe is mainly used as a detector of supercooled liquid water. This is one of the most advantageous properties of the RICE probe, since the phase discriminating capability of hot-wire probes are limited due to the residual effect of ice particles (Korolev et al. 1998) and FSSP does not provide reliable LWC measurements in mixed-phase conditions. Nevertheless the RICE probe could be used as a useful additional tool for estimation of LWC values.
Acknowledgments
The authors would like to thank the financial support of the Canadian National Search and Rescue Secretariat and Transport Canada. In addition, we are grateful for the support from colleagues at the National Research Council of Canada and others at the Meteorological Service of Canada. Special thanks for Dave Rogers and two anonymous reviewers for valuable comments that certainly helped to improve the manuscript.
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APPENDIX A
Heat Transfer Coefficient
The coefficient ξ can be obtained by integrating the curve in Fig. A1 for the angle range 0 to ϕ. For ϕ = 1.48 rad the integrating results in ξ = 1.41.
APPENDIX B
Collision Efficiency
The ratio of the distance between glancing droplet trajectories hitting the cylinder in undisturbed air to the cross-section of a body is called the total collision efficiency ɛ. The collision efficiency for cylinder is a function of Stokes Stk = (2Ur2)/(9μRc)ρw and Reynolds Re = (2Ur)/υ numbers, where Rc is the radius of cylinder;μ and υ are the dynamic and kinematic viscosity, respectively; and ρw is the water density. Figure B1a shows the diagram of ɛ isolines in the Re–Stk coordinates calculated from Langmuir and Blodgett (1945), based on solution of equation of droplet motion in the air flowing around the circular cylinder (Mazin 1957). The polar angle ϕ defines the sector within which the droplets impact with the cylinder. At angles larger |ϕ| droplets do not hit the surface of the cylinder and flow away with the air. The angle ϕ is a function of Re and Stk numbers. Figure B1b show the isolines of ϕ in the Re–Stk coordinates (Mazin 1957). The diagrams in Fig. B1 were used for calculation ϕ and ɛ. For example, for U = 100 m s−1, r = 7 μm, Ta = −20°C, Pa = 600 mb, we find Stk ≅ 21, Re ≅ 72, ɛ ≅ 0.84, ϕ = 82°. For U = 100 m s−1, r3 = 10 μmta = −10° C, Pa = 800 mb, and Stk ≅ 42, Re ≅ 130, ɛ ≅ 0.88, and ϕ0 = 84°.
Scheme of ice growth on a nonrotating cylinder
Citation: Journal of Atmospheric and Oceanic Technology 18, 4; 10.1175/1520-0426(2001)018<0543:TOICFM>2.0.CO;2
Scheme of the heat fluxes to the circular icing cylinder (see text)
Citation: Journal of Atmospheric and Oceanic Technology 18, 4; 10.1175/1520-0426(2001)018<0543:TOICFM>2.0.CO;2
Deviation of the ice surface temperature from the adiabatic value ΔTs = Ts − Ta vs airspeed U at different pressure Pa, air temperature Ta, and relative humidity RH in the atmosphere with respect to water. The calculations were made for the cylinder having RICE probe radius 3.15 mm
Citation: Journal of Atmospheric and Oceanic Technology 18, 4; 10.1175/1520-0426(2001)018<0543:TOICFM>2.0.CO;2
Liquid water content We0 that compensates the ice sublimation from the surface of RICE probe cylinder vs airspeed U at different pressure Pa, temperature Ta, and relative humidity RH
Citation: Journal of Atmospheric and Oceanic Technology 18, 4; 10.1175/1520-0426(2001)018<0543:TOICFM>2.0.CO;2
The Ludlam limit Wcr (critical LWC at which the surface temperature rises to 0°C) vs airspeed U for different pressure Pa, temperature Ta
Citation: Journal of Atmospheric and Oceanic Technology 18, 4; 10.1175/1520-0426(2001)018<0543:TOICFM>2.0.CO;2
In situ measurements of (a) air temperature Ta and dewpoint temperature Tdew, (b) airspeed U, (c) liquid water content, and (d) RICE signal. The measurements were conducted during Canadian Freezing Drizzle Experiment 3 from NRC Convair-580
Citation: Journal of Atmospheric and Oceanic Technology 18, 4; 10.1175/1520-0426(2001)018<0543:TOICFM>2.0.CO;2
The rate of ice sublimation from the RICE sensor dM/dt vs airspeed U for different pressure Pa, temperature Ta, and relative humidity RH
Citation: Journal of Atmospheric and Oceanic Technology 18, 4; 10.1175/1520-0426(2001)018<0543:TOICFM>2.0.CO;2
Calibration of three different RICE probes using the sublimating method: (a) MSC, Convair-580, k = 1.40 × 10−5 ± 0.14 × 10−5 kg V−1; (b) NCAR, King Air, k = 2.13 × 10−5 ± 0.39 × 10−5 kg V−1; (c) NCAR, Sabreliner, k = 3.49 × 10−5 ± 0.41 × 10−5 kg V−1
Citation: Journal of Atmospheric and Oceanic Technology 18, 4; 10.1175/1520-0426(2001)018<0543:TOICFM>2.0.CO;2
LWC retrieved from RICE measurements (Wr) vs measured LWC (Wm): Wr was retrieved using the coefficient k derived from the sublimating technique, and Wm was measured by the hot-wire Nevzorov probe (see text)
Citation: Journal of Atmospheric and Oceanic Technology 18, 4; 10.1175/1520-0426(2001)018<0543:TOICFM>2.0.CO;2
Calibration of the MSC RICE probe using the ice accretion technique. Here dM/dt was measured by the Nevzorov probe, dV/dt was derived from the RICE probe measurements, and k = 1.35 × 10−5 ± 0.42 × 10−5 kg V−1
Citation: Journal of Atmospheric and Oceanic Technology 18, 4; 10.1175/1520-0426(2001)018<0543:TOICFM>2.0.CO;2
Time history of (a) air and dewpoint temperature, (b) LWC calculated from FSSP measurements, and (c) RICE signal. The measurements were conducted by the NCAR King Air in 1990 in wave clouds
Citation: Journal of Atmospheric and Oceanic Technology 18, 4; 10.1175/1520-0426(2001)018<0543:TOICFM>2.0.CO;2
Fig. A1. Relative heat transfer coefficient for a circular cylinder αϕ/
Citation: Journal of Atmospheric and Oceanic Technology 18, 4; 10.1175/1520-0426(2001)018<0543:TOICFM>2.0.CO;2
Fig. B1. Dependence of (a) collision efficiency ɛ and (b) polar angle ϕ for circular cylinder vs Re and Stk numbers
Citation: Journal of Atmospheric and Oceanic Technology 18, 4; 10.1175/1520-0426(2001)018<0543:TOICFM>2.0.CO;2
