Bulk microphysics parametrization of ice fraction for application in climate models

Transcription

1 Q. J. R. Meteorol. Soc. (26), 32, pp doi:.256/qj.5.4 Bulk microphysics parametrization of ice fraction for application in climate models By FAISAL S. BOUDALA and GEORGE A. ISAAC 2 Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia, Canada 2 Cloud Physics and Severe Weather Research Section, Science and Technology Branch, Environment Canada, Toronto, Ontario, Canada (Received 2 January 25; revised 7 February 26) SUMMARY Using in situ aircraft measurements of cloud microphysical properties collected in extratropical stratiform clouds during several field programs, a parametrization of the iceparticle spectrum that includes small ice particles has been developed. This parametrization has been tested using a single prognostic equation developed by Tremblay et al. (996) for application in a regional model. The addition of small iceparticles significantly increases the vapour depositionrate when the natural atmosphere is assumed to be water saturated, and thus enhances the glaciation of simulated mixedphase cloud via the Bergeron Findeisen process without significantly affecting the other cloud microphysical processes such as riming and particlesedimentation rates. After the water vapour pressure in mixedphase cloud was modified, based on the scheme of Lord et al. (984), by weighting the saturation water vapour pressure with ice fraction, it was possible to simulate a more stable mixedphase cloud. It was also noted that the iceparticle concentration (maximum dimension L> μm) in mixedphase cloud is lower on average by a factor of three, and, consequently, the parametrization should be corrected for this effect. After accounting for this effect, the parametrized icefraction agreed well with observation. KEYWORDS: Glaciation Ice water content Liquid water content Mixedphase layerclouds Small iceparticles. INTRODUCTION Simulation of mixedphase clouds and estimation of their phase fraction (ice or liquid) require a reasonable representation of icecrystalsize distributions. This is because most largescale cloud models do not predict the icecrystalsize distribution, and as a result they assume a certain functional shape to represent the distribution. Icecrystalsize distributions are used to formulate a bulk microphysics parametrization to simulate cloud processes such icecrystal growth by riming and vapour deposition, and gravitational settling of ice particles. Many numerical models use such parametrization of icecrystalsize distribution in their schemes to parametrize these processes (e.g., Lin et al. 983; Levkov et al. 992; Zawadzki et al. 993; Tremblay et al. 996). In most cases small crystals (maximum dimension L<25 μm) are ignored, largely because of the uncertainty of their in situ measurements. In this paper, following a parametrization developed by Boudala et al. (22a) using aircraft measurements of particle spectra and small iceparticles, simplified methods of describing cloud processes related to ice microphysics have been formulated. Using these results, the evolution of mixedphase cloud and the sensitivity to small iceparticles and temperature were determined using a single prognostic equation developed by Tremblay et al. (996). 2. MEASUREMENTS This study includes data collected in five field projects. The Beaufort and Arctic Storms Experiment (BASE) was conducted in October 994 over the Canadian western Corresponding author: Cloud Physics and Severe Weather Research Division, Environment Canada, 495 Dufferin Street, Toronto, Ontario, M3H 5T4, Canada. faisalboudala@rogers.com c Royal Meteorological Society,

2 2378 F. S. BOUDALA and G. A. ISAAC Arctic (Gultepe et al. 2). The FIRE Arctic Cloud Experiment (FIRE ACE) project began in April 998 and ended in July 998, with the Convair58 aircraft measurements being made in April (Curry et al. 2). The First Canadian Freezing Drizzle Experiment (CFDE I) was conducted in March 995 over Newfoundland and the Atlantic Ocean. The Third Canadian Freezing Drizzle (CFDE III) started in December 997 and ended in February 998. During CFDE III, the aircraft flew over Southern Ontario and Quebec, Lake Ontario and Lake Erie (Isaac et al. 2a). The first Alliance Icing Research Study (AIRS I) was conducted between 29 November 999 and 9 February 2 (Isaac et al. 2b). The instruments used for this work are the Nevzorov liquidwatercontent meter (LWC) and totalwatercontent meter (TWC), the PMS FSSP, which is designed to measure clouddroplet numberconcentration and size, the PMS 2DC and 2DP probes, which measure overall size (L, usually the maximum dimension), shape and concentration of hydrometeors in the size ranges 25 8 μm and 2 64 μm respectively, and the Rosemount icing detector. More descriptions of the instrumentation used in these projects have been described in Isaac et al. (2a,b). The small iceparticles are included following the method of Boudala et al. (22a). This assumes that the FSSP instrument overcounts ice particles but still has an accuracy which, on average, gives concentrations correct to within a factor of two (Field et al. 23), that spectra from the FSSP and 2DC instruments give the same concentrations with L = 25 μm, and that the FSSP particle spectrum can be described by a gammadistribution function. The identification of ice clouds follows the scheme of Cober et al. (2). Based on this scheme, the stratiform iceclouds are characterized by FSSP concentration <5 cm 3, Rosemount icing detector <2mVs, and Nevzorov LWC/TWC ratio <5. The temperature has been measured with a Rosemount temperatureprobe and the minimum temperature measured was near 4 C. 3. MODELLING APPROACH The model approach is based on a single prognostic equation proposed by Tremblay et al. (996) (henceforth TGYB96) given as f t = D i + R Sf F Lf + F i( f), () W T W T W T W T where f is the ice fraction, D i is the ice deposition rate, R is the riming rate, F i is the ice massflux, F L is the liquid massflux, W T is the totalwater content (TWC) and S is the source term. Following TGYB96, several assumptions are made in order to simplify Eq. (). The source term is approximated as S = wg(t, p) where w is the mean upward airvelocity and G(T, p) is defined as a vertical gradient of the saturation mixing ratio ( ρ a (r sw )/ z). Assuming that r sw 22e sw /p a (p a = pressure of dry air) and using the Clausius Clapeyron equation (de sw /dt = l v e sw /R v T 2 ), G(T, p) can be given as ). (2) G(T, p) 22ρ a r sw ( lv Ɣ w R v T 2 g R d T The symbol Ɣ w is the wet adiabatic lapse rate, l v is the latent heat of vaporization, R v and R d are the gas constants for water vapour and dry air respectively, T is the ambient temperature, r sw is the saturation mixing ratio with respect to liquid water, ρ a is the air

3 ICE FRACTION IN CLOUDS IN CLIMATE MODELS 2379 density, and g is the gravitational acceleration. An approximate expression for Ɣ w for a saturated condition is given by Iribarne and Godson (989) as Ɣ w + l vr sw R d T + 4r swl 2 v c p R d T 2 Ɣ d, (3) where c p is the specific heat capacity of dry air, Ɣ d is the dry adiabatic lapse rate, and all other expressions are as given before. The expression wg(t, p) physically represents the production of water vapour excess above saturation as result of cooling at a wet adiabatic lapse rate (Kessler 969; Tremblay et al. 996). In the TGYB96 model, a dimensionless sedimentation parameter ζ is defined as ζ = ff L ( f)f i f( f)wg. (4) The meanings of the symbols given in Eq. (4) have been defined earlier. The parameter ζ describes the net effect of mixedphase sedimentation (see TGYB96 for more details). 4. THE DETERMINATION OF D i AND R The vapourdeposition rate can be given as L=L max D i = 4uπS i (T, p) CN(L), (5) L=L min where S i (T, p) = e/e si (T ) is the supersaturation with respect to ice, e is the ambient vapour pressure, e si (T ) is the saturation vapour pressure with respect to ice, L is the particle size, N is the iceparticle concentration at size L, L min and L max are measured minimum and maximum sizes of ice particles respectively, C is the capacitance given here as C = L/π assuming an hexagonal plate, u is given by the relation ( l 2 u = s k v R v T 2 + R ) vt, (6) e s D v where l s is the latent heat of sublimation, k v is the coefficient of thermal conductivity of air, D v is the vapour diffusion coefficient. The riming rate is calculated as L=L max R = π 4 E sclwc L 2 V(L)N(L), (7) L=L min where E sc is the collection efficiency (assumed to be unity), LWC is the liquid water content and V is the terminal velocity which is related to particle dimension as V = (ρ /ρ) /2 al b where a and b are 47 cm ( b) s and 7 respectively (Locatelli and Hobbs 974). For the large iceparticle mode, L min is not allowed to be lower than four pixels or 25 μm since the first four channels of the 2DC probe measurements are unreliable. The small iceparticles (L<25 μm) are treated as spheres with density of.78 g cm 3 (Boudala et al. 22a). Equations (5) and (7) show that both D i and R

4 238 F. S. BOUDALA and G. A. ISAAC TABLE. C OEFFICIENTS M (n) = α n IWC βn AND THE MASSDIMENSIONAL RELATIONSHIP USED Moments M () M (b+2) α n IWC βn α (mm m 3( β) g β ) β α 2+b (mm 2+b m 3(β2+b) g β 2+b ) β 2+b ( ) (.74) ( ) (.) Heymsfield c d (23) M = cl d (cgs unit) Values in the lower half of the top half of the Table are for cloud with small iceparticles (upper line) and without them (values in lower line, between brackets). depend on a term represented here by M (n) with moment n given as L=L max M (n) = L n N(L)dL. (8) L=L min In this case n is 2 + b and for the riming and vapour deposition rate respectively. Using Eqs. (2) to (8), and noting that LWC = ( f)w T, Eq. () can be written as f t = 4uS im () ( ) /2 ρ π + a W T ρ 4 E SC( f)m (2+b) wgf ζf ( f)wg. (9) W T W T The solution of Eq. (9) depends highly on the characterization of the moments of the iceparticlesize distribution M () and M (2+b). In the original TGYB96 scheme, these moments were parametrized as a function of the third moment (M (3) ) following Zawadzki et al. (993), which implies that the ice particles are spherical in shape which is not generally true. In this scheme, the specification of the ice density is required and thus it is assumed to be. g cm 3, and the small iceparticles were not considered. In order to avoid these discrepancies, a new approach for derivation and parametrization of M () and M (2+b) is needed. Using the PMS 2DC and 2DP probe measurements for large icecrystals and the approach of Boudala et al. (22a) for small iceparticles (L<25 μm), M () and M (2+b) are derived with and without small iceparticles. Values of water content in the form of ice ( ice water content IWC) have been derived using all the observation data described in section 2, based on particlemass to particledimension relationships (Cunningham 978; Heymsfield 23); small iceparticles were included, as described by Boudala et al. (22a). The coefficients of Heymsfield (23) are given in Table and Cunningham s were described by Boudala et al. (22a). The agreement between the two methods is excellent, as shown in Fig.. Each data point represents a 3 s average (approximately 3 km of flight path) and about 228 observation points are included. Figure 2 shows M () (panel (a)) and M (2+b) (panel (b)), with and without small particles, plotted against IWC. The addition of small iceparticles increases M () by an order of magnitude and this can impact the vapour deposition term significantly. However, it has no effect on M (2+b), which implies that the riming rate is unaffected by the addition of small iceparticles. Since M () and M (2+b) are well correlated with IWC, powerlaw relationships in the form M () = α IWC β and M (2+b) = α 2+b IWC β 2+b were derived and the coefficients are given in Table. This approach has the advantage of avoiding the problem of specifying the ice density in the parametrization. Noting that we can write IWC = fw T, and inserting these expressions in Eq. (), the evolution of

5 ICE FRACTION IN CLOUDS IN CLIMATE MODELS r 2 =.996 IWC H3 (gm 3 ) IWC C78 (gm 3 ) Figure. Values of water content in the form of ice ( ice water content IWC) (g m 3 ) derived using the coefficients of Cunningham (978) (IWC C78 ) and Heymsfield et al. (23) (IWC H3 ). Figure 2. Moments of the iceparticlesize distributions used in Eq. (9) and Table, each with and without small iceparticles: (a) M () (b) M (2+b).

6 2382 F. S. BOUDALA and G. A. ISAAC the ice fraction can be given as f t = 4uS iα W β T f β + a wgζf ( f) W T ( ρ ρ ) /2 π 4 E sc( f)f β 2+b α 2+b W β 2+b T wgf W T. () The first term in Eq. () represents the ice deposition rate, the second term is the riming rate and the last two terms represent the rates of sedimentation of the total ice content and of vapour production in the largescale slow ascent of air, respectively. Based on the formulation given by TGYB96, the sedimentation parameter ζ varies between and +. Setting ζ to implies that, on average, more liquid particles are falling out of the cloud than ice particles; setting it to zero implies no net sedimentation of ice, and setting it to + implies that many more ice particles are falling out of the cloud than liquid drops. However, in agreement with TGYB96, our analysis also confirms that the solution of Eq. () is not very sensitive to ζ, although, as will be discussed later, setting ζ =+ gave solutions which compared well with observations. 5. NUMERICAL CALCULATION OF ICE FRACTION Generally the integration of Eq. () requires a knowledge of tendencies for T, p, TWC,andw. However, as suggested by TGYB96, the ice fraction is determined by a fast microphysical process, whereas the atmospheric parameters T, p, TWCand w are determined by relatively slow largescale atmospheric processes. Consequently, for synopticscale motions, Eq. () may be integrated numerically, assuming these atmospheric quantities to be approximately constant (a good assumption for a layer of mixedphase cloud having some thickness). Indeed, this assumption appears to be consistent with observations; examples are given in Figs. 3(a) and 3(b). The data in Fig. 3(a) were collected during the First Freezing Drizzle Experiment (CFDE I) and represent about 96 s of aircraft flight time or approximately 96 km of flight path. Each point represents 3 s of averaged data. The ice fraction (IWC/TWC) is calculated using Nevzorov probe measurements. On 22 March 995 (Fig. 3(a)), the aircraft flew at a constant pressure (p) of 775 mb for about 39 s (about 39 km): during this time, the temperature (T ) and TWC remained relatively unchanged whereas the ice fraction varied considerably between all liquid and all ice. The same was true on 26 January 998 (Fig. 3(b)), flown at p 75 mb. This time the particles encountered twice changed from being almost all ice to almost all water, yet the temperature remained unchanged at about 3 C and the TWC remained between. and.3 g m 3. Figure 4 shows the numerically simulated evolution of ice fraction in a layer of cloud situated at p = 8 mb and assumed to have a fixed TWC =.3gm 3 in a water saturated atmosphere. The vapour supplyrate from the base of the cloud is varied, based on w and T as indicated in the figure. The cloud glaciates rapidly within a few minutes. Compare this with Fig. 5, which assumes no small iceparticles. In this case, the cloud approaches equilibrium. Complete glaciation does not occur if w is greater than. m s, particularly at the least cold temperature of 5 C (Figs. 4(a) and 5(a)). Equation () helps us interpret the rapid glaciation of mixedphase cloud in the presence of small icecrystals, particularly when the overall ascent of air is slow. Increasing the vertical velocity increases the vapoursupplyrate, which tends to enhance supercooled liquid water (SLW) for a fixed TWC within the cloud layer. However, adding small iceparticles increases M () significantly due to an increase in the ice

7 ice fraction ICE FRACTION IN CLOUDS IN CLIMATE MODELS 2383 A CFDE I: 22 March, P (mb) gm IWC LWC TWC T ( o C) Time (hr) Figure 3. Time series of measured pressure (p), temperature (T), ice water content (IWC), liquid water content (LWC), total water content (TWC) and deduced ice fraction (f ): (a) on 22 March 995 during the CFDE I project and (b) on 26 January 998 during the CFDE III project. TWC and LWC were measured using the Nevzorov TWC/LWC probe. Each point represents 3 s of averaged data along a 3 km flight path. concentrations without significantly affecting the riming and sedimentation parameter ξ. This increase in particle concentration translates into an increase in the growthrate term (first term) that cannot be compensated by an increase in SLW. Such a rapid glaciation of mixedphase clouds in the presence of high concentrations of ice crystals is consistent with the modelling results reported by Korolev and Isaac (23). However, they also argue, based on their box model, that an equilibrium solution is not possible for f< for significant ranges of iceparticle concentrations and rates of mean ascent of the air in clouds. Their model and the TGYB96 scheme use different assumptions. However, it is not possible comparison results directly since the model results shown in their paper are valid only for a rising adiabatic air parcel initially at 5 C. For temperatures below 5 C, the original iceparticlesize distribution used by TGYB96 would predict the ice fraction close to + for the values of vertical velocity and TWC considered in their paper. Nonetheless, modelling mixedphase cloud is still very complex and even more sophisticated cloud models have difficulty capturing the natural conditions. A modelling study by Morrison et al. (23), with detailed microphysics, also indicated that the proportion of liquid water in the simulated mixedphase cloud has

8 2384 F. S. BOUDALA and G. A. ISAAC ice fraction B.5 CFDE III: 26 January, P (mb) gm IWC LWC TWC T ( o C) Time (hr) Figure 3. Continued. been less than that observed in nature. They also attribute this discrepancy to the unrealistically rapid growth of ice crystals via vapour deposition at the expense of evaporating liquid drops. Tremblay et al. (23) used a power law (Heymsfield and Platt 984) and gamma icecrystalsize distributions to include small icecrystals in their model. Comparisons of their model simulation with aircraft observations also show that the model under estimates supercooled water and this cannot be improved by better model resolution. On average, average upward velocities in stratiform clouds are believed to be a few tens of cm s, which is consistent with values predicted from low level convergence of synopticscale flows (see Rogers and Yau (989)). However, although stratiform clouds are characterized by weak vertical velocities and appear to be horizontally homogeneous, there may be smallscale inhomogeneity as a result of some embedded convection with strong vertical velocities in the cloud structure. These clouds may contain supercooled droplets at low temperatures and may last for several hours (Pruppacher and Klett 997). In Figs. 4 and 5, when the mean w is near. m s, a value appropriate to stratiform clouds, only if small iceparticles are initially entirely absent can one expect the cloud to remain entirely liquid after 2 25 minutes. Given this sensitivity to even very small concentrations of small icecrystals (and other quantities such as saturation vapour pressure), and the complexity of microphysical processes in mixedphase clouds,

9 ICE FRACTION IN CLOUDS IN CLIMATE MODELS A 5 o C P=8 mb, TWC=.3 gm 3, = B.8 o C Time (min).8 C 5 o C 5 5 Time (min) 5 5 Time (min).8 D 2 o C w =. m s w = m s w =.3 m s w = m s 5 5 Time (min) Figure 4. The calculated evolution of ice fraction (f ) at four different temperatures for four rates of largescale ascent of the cloudy air (calculated using coefficients in Table that include small iceparticles): (a) 5 C; (b) C; (c) 5 C, and (d) 2 C. we must recognize that such microphysical quantities, and processes, are not handled well in existing models. There is also some evidence, based on observations, that the concentrations of large icecrystals (L> μm) in mixedphase clouds are smaller than those in ice clouds on average by about a factor of three. Figure 6 shows temperatureaveraged iceparticle concentrations plotted against temperature. The iceparticle concentrations and temperature were measured in stratiform clouds in extra tropical regions during the CFDE I, CFDE III, FIRE.ACE, and AIRS projects. For all cloud phases, about 83 3second averaged data points were analysed. This represents approximately km of aircraft flight. The iceparticle concentrations are not very sensitive to temperature in any of the cloud phases. Using a similar dataset, Gultepe et al. (2) have shown the same trend for glaciated clouds. A similar behaviour may exist for the concentration of small iceparticles in a mixedphase as compared to an ice cloud, but this cannot be supported by observation, since it is hard to measure concentration sof small iceparticles in mixedphase clouds. However, in the present dataset, the mean value of measured IWC is also three times larger in ice clouds than in mixedphase clouds. This suggests that the application of a parametrization based on iceparticle spectra measured in ice clouds for mixedphase clouds may overestimate the ice mass. Nevertheless, a difference as great as three times in the ice mass may not fully explain the rapid glaciation of the simulated mixedphase cloud, even when the small iceparticles are ignored.

10 2386 F. S. BOUDALA and G. A. ISAAC.8 A 5 o C P=8 mb, TWC=.3 gm 3, = B o C C 5 o C Time (min) D.8 2 o C w =. ms w = ms w =.3 ms w = ms Time (min) Figure 5. As Fig. 4, but with no small iceparticles. The calculated evolution of ice fraction (f)at four different temperatures for four rates of largescale ascent of the cloudy air (calculated using coefficients in Table that do not include small iceparticles): (a) 5 C; (b) C; (c) 5 C, and (d) 2 C all phase (83) Ice phase (2344) Mixedphase (4695) L> m Concentarion (L ) Temperature ( o C) Figure 6. Observed concentrations (l ), over a wide range of temperature, of icecrystals whose maximum dimension exceeded μm, for mixedphase, glaciated, liquid, and all forms of layer cloud. The numbers of 3secondaveraged datapoints used for temperatureaveraging for each cloud phase are shown in the box top right.

11 ICE FRACTION IN CLOUDS IN CLIMATE MODELS 2387 It should also be noted that these numerical calculations were based on the assumption that the atmosphere is saturated with respect to water (e = e sw ). Such a supersaturation with respect to ice is, of course, the whole basis of the Bergeron Findeisen process. As a result, a mixedphase cloud becomes unstable unless there is a sustained supply of moisture from below to increase the ambient watersaturation. Some modelling studies (e.g., Korolev and Mazin 23) have suggested that mixedphase clouds are saturated with respect to water since the production of vapour via droplet evaporation is faster than the removal via ice deposition. This modelling is based on the assumption that cloud particles are well mixed and uniformly distributed in space, and also neglects other processes such as removal of cloud droplets by riming and turbulence. However, ice crystals and cloud particles are not necessarily well mixed in natural clouds, they may exist in patches (e.g., Field et al. 24). Recent aircraft observations within mixedphase clouds also seem to indicate ambient relative humidities, at scales of m (Fu and Hollars 24), % below water saturation. By contrast, in the temperature range from 5 Cto 35 C on the same spatial scale, Korolev and Isaac (personal communication 26) found relative humidities in mixedphase clouds close to water saturation. It is worth mentioning, however, that relative humidity measurements by present instruments are quite sensitive to measurement errors, particularly near saturation points; consequently, it is difficult to ascertain whether mixedphase clouds are saturated with respect to water or not. In a largescale situation, the characterization of mixedphase cloud is even more ambiguous as data must be averaged over some length of flight path which incorporates subsaturated air. The description of such clouds in a model is very difficult and certain assumptions have to be made. One way to account for the mixedphase condition in cloud, especially for large scale models, is to modify the ambient water vapour pressure in a form e mix = ( f)e sw + fe si, () where e sw and e si are the saturation vapour pressures over water and ice respectively, and f the ice fraction (Lord et al. 984; Fu and Hollars 24). Note that to use Eq. () is to assume that a mixedphase cloud remains close to water or ice saturation depending onf. On the assumption that air at the surface of an ice crystal is always saturated with respect to ice, it was Eq. () which was substituted into G, S i and u to give the water vapour mixing ratio of the environment. Figure 7 shows the evolution of the mixedphase cloud after modification using Eq. (9). In this case, the mixedphase cloud approaches equilibrium within a few minutes and may last for several hours if the condition is right. If ζ is assumed to be negligible or positive, for a given TWC, then the last term in Eq. () always tends to increase the liquid fraction. However, since the humidity is not allowed to increase above water saturation, the liquid drops evaporate and the ice crystals grow at their expense, but the growth rate of the ice crystals is reduced (slows down the Bergeron Findeisen process) as a result of the new parametrization of saturation vapour pressure. These processes are assumed to take place instantaneously and it is analogous to the saturation adjustment scheme adapted by Lord et al. (984). In their scheme, they assume that all vapour which produces supersaturation with respect to water condenses or deposits depending on the ambient air temperature. In the present scheme, vapour is partitioned between condensation and deposition depending on supersaturation relative to water or ice as appropriate to each type of particle. This controls the growth rate of both droplets and crystals. However, at low rates of ascent and temperatures below 5 C, the cloud is still dominated by ice (Figs. 7(b), (c) and (d)).

12 2388 F. S. BOUDALA and G. A. ISAAC.8 P=8 mb, TWC=.3 gm 3, = A B.8 5 o C o C C 5 o C Time (min) D 2 o C w=. ms w= ms w =.3 m s w= ms Time (min) Figure 7. As Fig. 4, the calculated evolution of ice fraction (f) at four different temperatures for four rates of largescale ascent of ambient cloudy air which includes small iceparticles, but calculated using coefficients in Table, after correction for water vapour pressure using the approach of Lord et al. (984): (a) 5 C; (b) C; (c) 5 C, and (d) 2 C. As discussed earlier, derived values of M () and M (2+b) (see Table ) were obtained from measurements in glaciated clouds. The appropriate values of values of α and α 2+b should be divided by three to correct for a mixedphase condition. For mixedphase clouds with small iceparticles, the appropriate values should be 8 4 mm m 3( β) g β and mm 2+b m 3( β2+b) g β2+b respectively. So far, we have used constant TWC in our numerical calculations, but in natural clouds, the total water content varies with temperature. Using Eq. (), keeping everything else constant, increasing the total water content enhances the glaciation process. It is, however, more appropriate to use observations to test the parametrization. Figure 8 shows numerical estimates based on the corrected coefficients, 3secondaveraged measured TWC, temperature (T ) and pressure in extratropical stratiform clouds (Boudala et al. 22b) plotted against time for various assumed rates of ascent in the range. + m s. For descent or zero vertical velocity, glaciation occurs within 2 4 min for all the observed atmospheric conditions (see Figs. 8(a) (f)), indicating that a continuous supply of vapour is required in order to maintain mixedphase clouds. For the mean atmospheric conditions presented here, equilibrium can be attained within a few minutes as long as the vertical velocity is maintained close to +. m s even at lower temperatures. It is interesting to note that the ice fraction has a maximum near 5 C (Fig. 8(c)). This is clearer in Fig. 9(a) where the ice fractions from Fig. 8 are plotted for w =+. ms for each of the six air temperatures. Note that this maximum occurs at a temperature where the ice growthrate maximum is also observed (e.g., Fukuta

13 ICE FRACTION IN CLOUDS IN CLIMATE MODELS 2389 Figure 8. The calculated evolution of ice fraction (f) at six measured temperatures and their corresponding values of total water content (TWC), but calculated using α = 8 4 mm m 3( β) g β and α 2+b = mm 2+b m 3( β2+b) g β2+b, for four different largescale vertical velocities of the ambient cloudy air. and Takahashi 999). The equilibrium values of ice fractions in Fig. 9(a) observed in stratiform clouds (Boudala et al. 24) (dashed line) are also shown in Fig. 9(b), for comparison with the numerical estimates (continuous line). Note, too, that the simulated values of the ice fractions are similar to the observed ones. Figures 8 and 9 suggest that for time scales of near 4 8 min, the ice fraction in stratiform clouds may attain equilibrium as long as the moisture supply is maintained, and, as suggested by TGYB96, to diagnose cloudphase segregation, Eq. () may be set to zero. 6. SUMMARY AND CONCLUSION Using a large dataset of in situ aircraft observations collected in mid and highlatitudes, a parametrization of the icecrystalsize distribution has been developed that can be used to simulate cloud microphysical processes, such as icecrystal growth by riming and vapour deposition, and removal of ice particles by sedimentation.

14 239 F. S. BOUDALA and G. A. ISAAC Figure 9. The ice fraction (f) for a rate of largescale ascent of ambient cloudy air (w) of+. m s : (a) evolution over minutes (extracted from Fig. 8) and (b) variation with temperature at t = 8 min (continuous line) (extracted from Fig. 8(a)), and observed mean liquidfraction (dashed line), as reported by Boudala et al. (24). This parametrization includes small iceparticles, and its validity has been tested based on independent measurements (Boudala et al. 22a). Using a single prognostic equation developed by Tremblay et al. (996) and the new parametrization of ice particles, it was shown that the addition of small icecrystals significantly increases the vapour deposition rate which makes the cloud unstable in an atmosphere which is saturated with respect to liquid water. It has been found that there are at least two reasons for this. Since the concentration of ice particles in ice clouds is often three times that of droplets in water clouds, studies of mixedphase clouds must take into account the way small crystals enhance a cloud s glaciation rate. It has also been found that when the atmosphere is assumed to be saturated with respect to water, the glaciation rate was also enhanced. It has been suggested that the ambient vapour pressure should be parametrized as a function of ice fraction in order to simulate physically meaningful stable mixedphase clouds, especially on the large scale. After including these effects in the parametrization, it was shown that the simulated mixedphase cloud exhibits a maximum in ice fraction at 5 C, which is consistent with the in situ observations reported by Boudala et al. (24).

15 ICE FRACTION IN CLOUDS IN CLIMATE MODELS 239 A number of assumptions were made in this paper regarding the icecrystal concentrations in mixedphase clouds, the supersaturation within mixedphase clouds for climatemodel scales, and updraught velocities in extratropical stratiform clouds. The effects of radiative heating and turbulent mixing in the development and stability of mixedphase clouds were not included. These assumptions need to be tested further. It is recognized that the conclusions in this paper may not hold for cloud types other than stratiform ones. ACKNOWLEDGEMENTS This work was partially funded by the National Search and Rescue Secretariat, Transport Canada, the Panel on Energy Research and Development, the Meteorological Service of Canada, the National Research Council of Canada as well as Boeing, NASA and the FAA. Faisal Boudala also received support from NSERC, the Climate Action Fund, and the Canadian Foundation for Climate and Atmospheric Sciences (CFCAS). The data were collected using the Canadian National Research Council Convair58 and the authors are grateful to their NRC colleagues for their assistance. The authors also would like to thank Dr. Andre Tremblay of the Meteorological Service of Canada for reading this manuscript and his valuable comments. Boudala, F. S., Isaac, G. A., Fu, Q. and Cober, S. G. Boudala, F. S., Isaac, G. A., Cober, S. G., Fu, Q. and Korolev, A. V. REFERENCES 22a Parametrization of effective ice particle sizes for highlatitude clouds. Int. J. Climatol., 22, b Parametrization of liquid fraction in terms of temperature and cloud water content in stratiform mixedphase clouds. In proceedings of th AMS Conference on Cloud Physics, 3 7 June 22, Ogden, UT, USA. Available as CDROM from Am. Meteorol. Soc., 45 Beacon St, Boston, MA, USA 24 Liquid fraction in stratiform mixedphase clouds from in situ observations. Q. J. R. Meteorol. Soc., 3, Assessing cloud phase conditions. J. Appl. Meteorol., 4, Boudala, F. S., Isaac, G. A., Cober, S. G. and Fu, Q. Cober, S. G., Isaac, G. A., Korolev, A. V. and Strapp, J. W. Cunningham, M. R. 978 Analysis of particle spectral data from optical array (PMS) D and 2D sensors. Pp in proceedings of Am. Meteorol. Soc., Fourth Symposium. Meteorological Observation Instruments, Denver, CO, USA, 4 April 978. Available from Am. Meteorol. Soc., 45 Beacon St, Boston, MA, USA Curry, J. A., Hobbs, P. V., King, M. D., Randall, D. A., Minnis, P., Isaac, G. A., Pinto, J. O., Uttal, T., Bucholtz, A., Cripe, D. G., Gerber, H., Fairall, C. W., Garrett, T. J., Hudson J., Intrieri, J. M., Jakob, C., Jensen, T., Lawson, P., Marcotte, D. L., Nguyen, L., Pilewskie, P., Rangno, A., Rogers, D., Strawbridge, K. B., Valero, F. P. J., Williams, A. G. and Wylie, D. Field, P. R., Wood, R., Brown, P. R. A., Kaye, P., Hirst, E., Greenaway, R. and Smith, J. A. 2 FIRE Arctic clouds experiment. Bull. Am. Meteorol. Soc., 8, Ice particle interarrival times measured with a fast FSSP. J. Atmos. Oceanic Technol., 2,

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