JOURNAL OF GEOPHYSICAL RESEARCH,VOL. 93, NO. D9, PAGES 11,051_11,058,SEPTEMBER 20, 1988

Temperature Dependenceof Cirrus Extinction: Implications for Feedback

C. M.c,RrIN R. Pr.lrrl lNo HAnsnve.RDHAN2'3

Laboratory for Atmospheres, N ASA Godilard Space Flight Center, Greenbelt, Maryland

T from previous I The measured temperature dependence of absorption in cirrus obtained extensive lidar and radiometer (LIRAD) observations of cirrus is used to investigate the sensitivities of I changes in cirrus optical properties to changes in global temperature. Values of infrared absorption and b ice water content calculated previously from observations of cirrus cloud microphysics are also used to investigate climate sensitivities. The values of calculated mean infrared absorption give a very similar temperature dependence, and thus , to the LIRAD results. Values of mean ice water content calculated from the observations of cloud microphysics are compared with the available ice water content calculated from moist adiabatic ascent through a vertical cloud depth of 300 m, and a similar temperature dependence is found in both cases.However, taking into account the observed cloud depths of cirrus, considerable dilution of ice water content below adiabatic values is obviously occurring. The temperature sensitivities of extinction (or absorption) coeffrcients (calculated from a combination of LIRAD and microphysics results) are found to be generally less than the temperature sensitivities of ice water contents, due to an increase in cloud particle mode radius with tempetature. The temperature sensitivity of cirrus extinction is found to vary from 0.033"C-1 at -22.5'C to 0.200"C-1 at -'12.5"C. Equivalent sensitivities for cirrus optical depth are influenced by observed changes in cirrus cloud depth with temperature and vary from 0.003"C-1 at -22.5"Cto O.241'C-t at -'72.5"C. As high cold cirrus are considered to cause a positive feedback with global temperature change, such a feedback is seen to become particularly strong at the lowest temperatures. A simple method of parameterization of cirrus visible and infrared optical properties in terms of clotrd temperature is presented, thus making it possible to introduce cirrus optical properties into a numerical model without requiring knowledge of the ice water content.

INtnopucrIoN scribed changes in cirrus optical properties have been found to The likelihood of an increase in trace gases in the atmo- have significant climatic effects. Such models contain nonin- sphere causing a and thereby heating up the teractive clouds [/-ioz and Gebharilt, 1982; Ramanathan et aI., atmosphere is now well accepted. However, feedback mecha- 1983; Ou and Liou, 19841 or interactive clouds lWang et al., nisms resulting from the response of the atmosphere to such a l98l; Charlock, 19821. forcing are not at all well understood, although they are Charlock was able to show that for very cold cirrus of low known to be significant. For instance, the introduction of optical depth, an increase in temperature due to an increase, into the calculation is shown, on the simple argu- say, in the solar constant, was amplified by the interactive feed- ment of increasing evaporation, to provide a positive feed- increase in cirrus, but for warmer and denser cirrus the back, the temperature increase for a given perturbation being back becamemore negative. These preliminary attempts to understand the climate ef- enhanced considerably lM iiller, 1963). fects of cirrus clouds point out the necessity of knowing the Clouds also have a marked feedback effect [e.g., Paltidge, distribution with altitude of cirrus clouds, as well as an accu- 19801,but neither the amplitude nor even the net sign of the rate specification of optical properties. effect on the temperature increase is known in detail. It is not Further progress has been hampered by our present in- even obvious that an increase in evaporation will cause an ability to form cloud in a realistic manner. If the cloud liquid increase in cloud amount lRoails, L978; Schneider et al., 1978], water content and cloud temperature could both be specified, and furthermore, high clouds have very different feedback ef- then it might be possible to predict optical properties quite fects from low clouds. High clouds can have a distinct warm- accurately le.g., Heymsfield and Platt, 1984f. However, in the ing effect lPlatt, 1981.;Stephens anil Webster, l98l; Charlock, present state of general circulation models (GCM) the predic- 19821,whereas low clouds tend always to cool. tion or parameterization of cloud liquid water content is still Some piogress in our understanding of how sensitive the in a crude state. The most that models can achieve is a diag- climate is to cirrus clouds has been made with radiative- nostic cloud, when either a layer in the atmosphere becomes I convective equilibrium climate models, in which small pre- saturated, or, aTtetnatively, the layer has a specified humidity. In the former case, when supersaturation occurs, the excess water is precipitated out; that is, some fractional cloud rPermanently at Division of Atmospheric Research,CSIRO, As- pendale,Mordialloc, Victoria, Australia. amount is assigned le.g., Slingo, 19801. Then either an extinc- 2Alsoat Department of Meteorology,University of Maryland, Col- tion coefhcient is assigned, from which cloud reflectivity and legePark. absorption can be calculated, or cloud reflectivities and ab- 3Now at Department of Earth and AtmosphericSciences, Purdue sorptivities are prescribed for some rough delineation of University,West Lafayette,Indiana. height, such as "middle," "low," and "high" lWetherald anil Copyright 1988by the AmericanGeophysical Union. Manabe, l98ol. Papernumber 7D0848. An alternative approach is to parameterize cloud optical 0 r48-o227/88 / OOTD-0848$05.00 properties according to experimental data: data which have a

I 1,051 l,052 Pr.a.rr aNo Hensgvnnoru.N: Crnnus Crouo ergn Crrllare Fprosecx

10 cording to temperature. As shown later, the absorption coef- r Tropical ficient of cirrus at any wavelength bears a simple relationship + Summer *+ to the absorption or extinction coefficient at any other wave- 1 x Wint€r length, providing that the size distribution remains the same, T tr H-P as it is found to do approximately in a given temperature E l< interval (see later discussion). The temperature dependence of .1 absorption, and therefore also of extinction, thus provides a (u simple method of parameterizing cirrus in a GCM or climate o model by scaling the optical properties in a realistic manner .01 with temperature, thus bypassing considerations of speciflc hu- midity or cloud water content. Also, measurements of cloud microphysical quantities by Heymsfield ll977l on many cases of cirrus in the contiguous 1 10 100 United States were used by Heymsfield and Platt [1984] to T + 82.5 (oC) calculate a cloud infrared absorption coefficient in terms of temperature. When averaged over many cases,the values were Fig. 1. Plot of cirrus beam absorption coelficientaI 1l pm (o,)) versusmidcloud temperature.The "tropical," "summer,"and "winter" found to be remarkably similar to those obtained by the points representLIRAD data; the Il-P points representvalues of o, LIRAD method in Australia lPlatt, 19841. Similar systematic calculatedfrom the cirrus particle sizedistributions given by Heyms- changes in the liquid water content with temperature were field and Platt ll984l. also established, but with a different dependence on temper- ature lHeysmfield anil Platt, 19841, indicating changes in par- ticle size. consistent relationship in some way with an atmospheric vari- Figure 1 shows absorption coeflicients from both Platt et al. able, such as temperature or pressure. Thus Feigelson ll978f [1987] and Heymsfield and Platt [1984], plotted against tem- reported measured average cloud liquid water contents which perature. The line fitted by least squares to the LIRAD data showed a fairly consistent dependence with cloud temperature, represents the following equation and Someruilleand Remer [1984] employed this data for sensi- o,: B(T + T)2 (1) tivity studies in a one-dimensional model. Somerville and Remer assumed that the cloud extinction coeffrcient or optical where ao is the IR volume absorption coefficient (l0-t2 pm) depth was a linear function of the cloud liquid water content, per kilometer, B : 1.6 x 10-4, and To : 82.5'C. The an assumption which is valid in the infrared only for small "summer" and "winter" points refer to measurements at As- cloud drops (<5 pm) and which is rarely valid in the short- pendale, Victoria (38'S latitude), and the "tropical" points wave solar spectrum lStephens, 1978; Bohren, 19851.Never- refer to Darwin, northern Australia (12.4'5 latitude). Equation theless,Somerville and Remer's results showed clearly that the (1) is valid over the range of temperatures considered experi- effects on the cloud-climate sensitivity problem of a temper- mentally, that is, from -5" to -77'C. The values of absorp- ature variation of cloud liquid water content were appreciable. tion coeffrcient shown in Figure 1 represent values typically The present paper considers a similar cloud parame- averaged over about 400 observations of cloud within a given terization in terms ofthe observed optical properties ofcirrus temperature range. This averaging reduces by a factor of reported recently by Platt and Dilley [1981] and Platt et al. about 20 the uncertainties due to errors of measurement of the [1987] and the dependenceofthese optical properties on tem- cloud emittance (about 20Y" for a single measurement but perature. It is shown that the observed temperature depen- increasing to greater than 5O"/oat the lowest emittances) as dence of the cirrus absorption coefficient is consistent with the well as uncertainties due to the observed natural cloud emit- thermodynamic properties of the moist atmosphere and also tance variability of about + IOO% about the mean. The re- with the cirrus microphysical observations of Heymsfield sidual error is thus about +lOoA. In the present study we are LL977l, which were subsequently analyzed further by Heyms- concerned with the average, long-term climate effects ofcirrus, field and Platt U9841. and therefore it seems reasonable to utilize the average values The paper then demonstrates how the temperature depen- of absorption coefficient within each temperature range, as dence of cirrus optical properties can be used in climate sensi- given in Figure 1. tivity calculations to give predictions of feedback effects at The physical reasons for the apparent temperature depen- various cirrus temperatures and further points out how cirrus dencies ofboth the average cloud liquid water content and the optical properties can be parameterized, simply for use in absorption coeflicient found by Heymsfield and Platt ll984l GCM or climate models. will become evident in the discussion that follows. First, we consider from a physical standpoint whether any relationship Ts[4pnnA,ruREDnpnNpeNce or Crnnus ExlrNcrroN should exist between the absorption coefficient and liquid aNn Crnnus IcB Wa.rnn CoNrrwr water content for cirrus clouds and also between the absorp- Platt ll984l and Platt et al. lI987f have shown recently tion and extinction coeflicients at different wavelengths. from a year's extensive LIRAD (ground-based lidar and pas- Second,we consider how the thermodynamic properties of the sive radiometer) observations that, when averaged over many moist atmosphere determine the cloud liquid water content cases, the cirrus infrared absorption coefficient is a well- and its observed dependence on temperature. defined monotonic function of atmospheric temperature, at Any possible relationship between the cloud absorption (or least for nonprecipitating clouds within a temperature range extinction) coeffrcient and the liquid water content in cirrus of from -80" to -10'C. This implies that absorption in such clouds is complicated by the composition of these clouds, clouds at the wavelength of measurement can be scaled ac- which are thought to contain only ice particles at temper- Pla,tr lNo HARSHVARDHAN:Crnnus CLoUD AND Cr-rulre FEEDBAcK I 1,053

atures below -40"C but which may also contain supercooled can be replaced by the extinction or absorption coelficient o at water drops at higher temperatures. Furthermore, many differ- any other wavelength, simply by inserting the correct value for ent ice crystal habits are observed in cirrus clouds, which are the ratio between the Q(r)s. dependent on both temperature and supersaturation in the In the case of cirrus clouds, the particle diameters are nor- clouds. On the other hand, the Mie theory of extinction and mally larger than the visible or infrared wavelengths con- scattering has been solved in detail only for spheres and cylin- sidered, particularly in visible wavelengths. For wavelengths in ders. As many observed ice crystal habits, such as hexagonal the solar spectrum, the extinction efficioncy Q(r) 12 for all columns, bullets, and needles, approximate ice cylinders in values ofr; hence in that case,(4) becomes shape, it is assumed in this study, following Heymsfield and o"fW : 4(/npr" (8) t Platt 119841,that ice crystals can be considered as cylinders of length L and diameter D, related by D: O.057Lo'786(both I, where o" is the approximate extinction coeffrcient for solar I and D arc in meters), and the effects ofany supercooled drops wavelengths. L are ignored. An equivalent approximation occurs for absorption, al- For simplicity the clouds will be allowed to have some though in that case, Q"(r)+ 1 for particle sizes much greater number size distribution, but with a constant relationship be- than the wavelength, and thus tween L and D, as given earlier. :2(lnpr. We consider flrst the cloud absorption coefficient o, (70-L2 o,fw (9) pm) and its relation to the ice water content. We then consider and, furthermore, o"foo: 2, independent of wavelength. How how, for a given cloud particle size distribution, oo is related well (8) holds for cirrus is not well known, although Heyms- to the absorption or extinction coellicients at other wave- field and Platt ll984f have shown that particularly for temper- lengths. The absorption coeffrcient oo for a model cloud of ice atures less than about -50'C, cloud particles in cirrus less cylinders can be written as than 2O pm in diameter are an important factor in cirrus absorption. In that case,Q(r) < 1, and o"/oo22le.g., Platt, ( 2Q"@)n(r)rLdr (2) 1e791. "": | JO The dependence of o" oh W in (8), or ao on W in (9), is seen where r : D/2, Q.(r) is the absorption efficiency (which de- to be independent or only weakly dependent on Q(r), but in- pends only on r for long cylinders), n(r) is the crystal number versely dependent on r". Only if the size distribution remains density, and ( is a factor which describes the orientation of the constant and W varies with total particle number will o be ice cylinders to the radiation flow. linearly proportional to V7. Now Heymsfield and Platt ll984l The ice water content I;I/ is given by found that the calculated increase in liquid water content with temperature in cirrus clouds was due in large part to a system- w : pf- nn14r2Ldr (3) atic increase in the cloud particle mode radius with temper- JO ature. From the same data, Platt [1984] found an equivalent where p is the density of ice. decreasein K with temperature, indicating an increase in r, of -55" -25"C. The relationship between oo and I7 is complicated by the about a factor of 6 between and At the same time, the value of oo still increased with temperature, signify- presence of Q.(r) and by the integration over size distribution. However, some insight cdn be obtained by dividing (2) bV (3), ing a stronger relationship between W and T than between r" which yields andT. The detailed physical reasons for the temperature increase o"fW :2(Q,(r)lnpr.: K (4) of rn are fairly complex, but on a simplified picture, cirrus particles can grow to larger sizes at the higher temperatures where K is the mass absorption coefficient, Q"@) is an "ef- because not only does the saturation vapor pressure water fective absorption effrciency," given by of increase, but also the difference between the saturation vapor pressure over water and that over ice also increases, with a 0,?)= e"{,)n,),"a, ,{i,r a, (5)maximum difference occurring at about - 15"C. fo* f l"- Although in reality, cirrus crystals are not cylindrical in shape, the only quantity which will vary with crystal shape is and similarly, the "effective radius" r" is given by the effective efficiency 9(r). Thus the previously mentioned basic conclusions are unaffected by crystal shape. ,.: n{,),'rar ntVza, (6) f In summary, it can be stated that the extinction (or absorp- fo* [o* tion) coefficient of cirrus increases with temperature but ap- ! It can be seen from (4) that the ratio between oo and W parently at a slower rate than does the ice water content, \ depends generally on two parameters of the particle size distri- because the particle mode radius also increases with temper- bution, Q,@) and r". ature. The resultant functional dependence of oo on W will be If we consider now the extinction (or absorption) coef- discussedfurther in the next section. ficients o, and 02 at two wavelengths ),, and Ar, and for the Having explored the relationships between the os at various same particle size distribution, we obtain wavelengths and between o and W at one wavelength, we now investigate from thermodynamic considerations what values otloz:0r|)/Qr(r) (7) W are likely to have at various temperatures and if such from (4), as W and rn remain constant. Thus the ratio of the values bear any resemblance to ice water contents calculated two coefficients at any two wavelengths depends only on the from the data of Heymsfield and Platt [1984] at various tem- effective efficiencies and is therefore a constant value for any peratures. cloud volume. This implies that the absorption coefficient oo The condensed ice or water content in a cloud will, in gen- 11,054 Pr-.e.lr:rexo HlnsnvanorreN: Cnnus Cr,out .+No Curuern Frepnecr

The pressure and temperature below cloud base were calcu- lated from the equation for a standard atmosphere, with sur- face pressure and temperature being 1000 mbar and 283 K, respectively,and the lapse rate being 0.0065"Cm- 1. AIso shown in Figure 2 are the mean ice water contents and standard deviations calculated by Heymsfield and Platt ll984l from the nonprecipitating cirrus cloud particle size distri- butions measured by Heymsfield ll977f, assuming that the (o crystals are ice cylinders with the length-width relationships I E discussed previously. There is no implication here that the average vertical distance of ascent in cirrus clouds is always ; z about 300 m, but Figure 2 rather serves to demonstrate that ul F the measured liquid water contents do decrease at approxi- z mately the same rapid rate as the maximum available liquid o .vl water content, assuming some constant depth of pseudo- E. [r adiabatic ascent. The large standard deviations in W arc dve to natural spatial and temporal variations in the measured particle sizedistribution. Now, the actual geometrical depths of cirrus clouds have been found by Platt et aI. U9871to be in the range of from 1 to 4 km, with some dependence on cloud temperature. But Figure 2 indicates that the calculated adiabatic depth is gener- ally less than 300 m and is closer to 100 m at the lowei temperatures. Thus there appears to be a large dilution pro- cessacting in cirrus clouds. By varying Az in the calculation of adiabatic liquid water content and using observed cirrus cloud depths, an average dilution factor was found to be -70 -60 ,50 -40 -30 -20 -10 0 10 20 30 0.062 + 2oo/o for the ice line and 0.048 + 25Vo fot the wdter line, where the dilution factor is defined as that depth ofcloud TEMPERATURE(OC} which will give the avetage measured ice water content from Fig.2. Plot of the cirrus cloud ice and liquid water contents, adiabatic uplift divided by the average measured cloud depth calculatedby assumingmoist adiabatic ascent through 30Om. The at that temperature. These dilution factors are singlepoints representthe meanic€ water contentsover temperatures considerably of 5'C, calculatedfrom the cirrus particle size distributions given by less than those found for boundary layer stratus clouds [e.g., Heymsfieldand Plart [1984], and the bars indicate the standarddevi- Slingo et al., 1982f and for deep water clouds such as cumulus, ations in singlevalues of the ice water contentsdue to natural varia- which exhibited dilution values in the range of from about 0.2 bility in the clouds. to 0.4 fWarner,l970l. Apart from turbulent entrainment, a process which is thought to cause most of the dilution in boundary layer clouds, the appreciable found for eral, be a function of several factors, such as water vapor dilution cirrus can be at- factors ice mixing ratio, cloud depth, particle fall velocity, uplift velocity, tributed to such as the survival of crystals, and sometimes further subsequent growth, and turbulence and entrainment, However, a simple model of through fall distances which can be much greater than ascent of a parcel of saturated air along the moist adiabat the original depth of uplift and Pruppacher, 1976f. Heyrnsfield found servesto illustrate how liquid or ice condensatefor a constant lHall ll977l also that liquid water content was dependent on vertical lifting distance is strongly variable with temperature. The air veloci- It liquid water I,I/ condensed during a small vertical ascent Az is ty. seems that a certain vertical velocity is required before given by the particles can be lifted through the requisite altitude to attain a certain adiabatic liquid water content. It is clear from (dW/ dz)Lz: (dW/ dD@TI dz)Lz (10) Figure 2 that the variances of single observations of cirrus liquid water content are considerable, with maximum values where T is atmospheric temperature. The change A,W for a of about 2-4 times the average values occutring regularly. given change in the specific humidity, A4, is given by Similarly, the cloud depths vary considerably from one cloud

L,W: Aqp,/R\ (11) to another at the same temperature. h where p, and T, represent pressure and temperature, respec- { tively, at cloud top. Cnnus Oprrcer. Deptn CneNces AND CLTMATE Values of LWI:(LWlLz)(A,zl2)l are shown plotted in SBNsrrrvrty Figure 2. These results were obtained by assuming that dWldz was linear over a height Az of 300 m, the moist pseudo- The strong variation of cirrus absorption coefficient with adiabat being calculated from a formula given in the Smithson- temperature, as illustrated in Figure 1, indicates that any ian Meteorological Tables lList, l97ll and the saturated change in global temperature due to a climate perturbation vapor pressure being calculated from the exponential form of could lead to significant changes in cirrus optical properties. the Clausius-Clapeyron equation, with the variation in the Following Someruilleand Remer U984], these changescan be latent heat of ice being modified empirically to constrain the identified using a climate sensitivity factor which describes the values of vapor pressureto agree with the Smithsonian tables. temperature coeffrcient ofchange in optical depth. Prarr aNo Hnssvlnosax: Crmus Crouo lNo Crrrrrlrn FEEDBAcK I1,055

TABLE 1. CalculatedValues of SensitivityFactors /(o) and Differentiating (1) and dividing by o" yields f(h) and Derived Values of ./(6) f(o) : f(o : 2/(T + 82.5) (r7) Temperature,'C ' ' "C ' ") f(o),"C f(t),"C "f(6), A factor f(W) can similarly be calculated, either from the -22.5 -0.030 0.033 0.003 adiabatic curve in Figure 2 V(W)"1, or from the individual -27.5 0.036 -0.026 0.010 data points in the latter case,f(W)# was -32.5 0.040 0.016 0.056 U(W)#l; calculated -37.5 0.044 0.017 0.061 from two separate straight lines fitted to the four lowest and -42.5 0.050 0.018 0.068 four highest data points, respectively,on a longJog plot. _ia < 0.057 0.020 0.077 The factor f (h) can be estimated using average cirrus cloud -52.5 0.067 0.023 0.090 depths measured by the LIRAD method et aI., 19871. -5'7.5 0.080 lPlatt 0.026 0.106 For mid-latitude -62.5 0.100 0.029 0.129 clouds the cloud depths tended to increase -70" -35"C -67.5 0.133 0.034 0.167 between temperatures of to but to decreaseat *72.5 0.200 0.041 0.241 higher temperatures. Thus two empirical linear equations were derived for the two ranges: ft(km):0.0456i"+4.7 (-72.s"C< T < -35"C) (18)

Thus a temperature coeflicient of absorption/(o,) (or sensi- h(km) : -0.06sT + 0.72s (-3s"C < T < -15"C) (19) tivity factor) can be defined as Values ofl(o),f(h), andf(d) are shown in Table 1,/(6) being obtained as the sum of the other two terms, as shown in (13). f(o,\ : (l/o,)(do,ldT) (r2) Yatues of f (W)*, f (W)#, and f (K) are shown in Table 2. The Now, for a fixed cloud particle size distribution it has been /(K) was calculated from (16),using values of f (o) andf (W)#. shown earlier that the extinction (or absorption) coefficient at It is recalled that values of oo were calculated from the data of any wavelength can be related linearly to that at any other Heymsfield and Platt [1984] and that the results fitted well wavelength. This implies that as the quantity oo appears in with the LIRAD values, as shown in Figure 1. Values of both the numerator and denominator of the sensitivity factor f(W)# were calculated from the same data, so that they f(o"), this factor will be independent of wavelength at any would be consistent with the values of/(o,) or f (o). The ratio given temperature and will apply equally to extinction, scat- f (o)lf W)# is also included in Table 2. The ratio compares tering, or absorption. Thus /(o"):/(o), where a is at any the sensitivity factor f (o) with that which would be obtained arbitrary wavelength, and can apply equally to solar or infra- (i.e.,f (W)#) if o was a linear function of W, as assumed by red wavelengths. Someruilleand Remer [1984]. Similarly, an optical depth sensitivity factor/(d) can be de- It is pertinent at this point to consider the uncertainties fined for any wavelength as inherent in the various climate sensitivity factors. First, re- sidual uncertainties in (1) and (17) due to scatter about the (6) : (r o)(do ttT\ (r (1 f / / + / h)(dhldr) 3) regression line should be considered. By assigning realistic where maximum and minimum gradients to the points in Figure 1, the uncertainty inf (o) is estimated to be about +2oo/o. By a 5: oh (14) similar calculation the uncertainties in f (h) from (18) and (19) are found to be considerably greater and to be in the region of and h is the cloud depth. It is convenient also to investigate +30-50%. Furthermore, values of/(ft) for tropical cirrus tend the relationships between o, W, and the mass absorption coef- to be rather different. Thus the ficient K. such that values of/(ft), and therefore /(6), should not be taken too seriously. They are included to o:WK (15) illustrate that changes in cloud depth as well as cloud extinc- tion are likely to be significant. The factorf (W)* is theoretical and therefore and is simply a factor of the adiabatic depth considered. The f (o): (tlw)(dwldr) + (r/K)(dKldr) (16) factor f (W)#, from the experimental points, is obviously sub-

TABLE 2. Values of /(o) andf(W) and Derived Values of /(K) andf(o)lf(W# 'C I oc-t 1 Temperature, f(o), "C f(W*,a f(w)#, "c-t f(K), "c f(o)lf(w)#b fr -22.5 0.033 0.074 0.042 -0.009 0.79 -27.5 -0.010 I 0.036 0.080 0.046 0.78 -32.5 0.040 0.086 0.051 -0.01I 0.78 I -37.5 0.044 0.092 0.057 -0.013 0.77 *42.5 0.050 0.098 0.080 -0.030 0.62 -47.5 0.057 0.103 0.092 -0.035 0.62 -52.s 0.067 0.r09 0.t09 -0.042 0.61 -57.5 0.080 0.il5 0.133 -0.053 0.60 -62.5 0.100 0.121 -67.5 0.133 0.127 -72.5 0.200 0.133

"From the adiabaticice line. bFrom a fit to the experimentalice water contentpoints. Pr-lrr axo HnnssveRpseN: Crnnus Croup nNp Cr.ruere FBBosecx

ject to some considerable uncertainty, as indicated in Figure 2, with an estimated error of + 4O%. Thus the values ofl(K) and theratio f (o)lf (W)# are subject to uncertainties of over 507o. With the caveats of the previously mentioned error analysis, -€= 1-exp(-07S6,) several significant points rise out of these results. First, the factor f (6) ranges from values close to zero at -225"C to very -72.5"C. 8oo high values at As a comparison, Someruille anil u-l Remer used cn ll984l values between 0.04 and 0.05, which they J obtained from the airuaft dala of Feigelson [1978] for a tem- -, 03 -20"C. I perature range of +5" to The effect of the factor f (h\ is to enhance the values off(o) at the lower temperatures but z with an opposite effect at high temperatures. Thus the effect of 10, cloud depth change is obviously important in climate sensitiv- ity calculations, although the estimated uncertainties in f (h) call for caution in interpretation. Stephensand Webster ll98ll and Charlock [1982] have shown that any increase in cirrus optical depth (or cloud amount) will lead to a climate- warming tendency, at least for low optical depths, which are 0 0.1 02 03 0.4 0.5 0.6 0.7 0B 0.9 1.O typical for high, low-density cirrus Platt et aI., 1987f. [e.g., FLUXEMITTANCE Thus the large sensitivity factors at low temperatures indicat- ed in Table 1 would lead to strong positive feedbacks with any Fig. 3. Plot of planar albedo against broadband flux emittance for global temperature change. two values ofp(:ges 0), 0 being the solar zenith angle. Second, the factor f(W)* obtained from thermodynamic considerations is seento increasesteadily with decreasingtem- then it is just a matter of relating solar albedo a and a broad- perature. The values extend those obtained by Betts and band infrared flux emittance e to the measured beam absorp- Harshuardhan [I987] for water clouds, where values are con- tion emittance e". Such a parameterization has been used in siderably smaller. However, values of f(W)# tend to be lower the past by Platt [1981] and Stephensand Webster U9811. thanf (W)*, except at the lowest temperatures. Figure 3 shows two rather similar parameterizations. The Third, the values of /(K) are negative and significant at the first is based on the work of Platt ll983l and Platt et al. lower temperatures, thus depressingvalues of/(o) well below [1980]. The albedo a is first obtained in terms of visible opti- values of f(W)#. Thus the use of f(W)# as the extinction cal depth 6, from theoretical computations by Liou 119737, coefficient sensitivity factor will tend to give values which are who computed a for a model cloud of ice cylinders with an too high. Bohren U9851, by assuming that mean particle asymmetry patameter of 0.735. radius would increasein a consistent manner with water con- The optical depth d, is then related to the infrared optical (and tent thus with temperature), derived a value of f(o)l depth 6, at ll pm through a linear factor B (:d,/d,), which f(W)# equal to 0.67 (he assumed that the cloud depth re- for ice "cylinders" of the size found in cirrus has a valte of 2 mained constant). Now, as discussed previously in this afiicle, fPlatt,1983f. the particle size distributions given by Heymsfielil anil Platt The optical depth d, is then related to the beam absorption [1984] indicate that the particle size mode radius does indeed emittance eothrough the equation increase with temperature in the case of cirrus clouds, and - therefore it is not surprising that the quantities shown in the eo:7 exp (-6") (20) final column of Table 2 are lower than unity and, in fact, not which neglects the effects of scattering. The beam emittance e" too far removed from Bohren's value of 0.67. is related to the broadband flux emittance in two steps.First, Fourth, the finite values ofl(K) indicate that K is changing eois related to the flux (diffuse) emittance t' at ll pm by a with temperature and, in fact, is decreasing with increasing relation given by Platt and StephensU9801. Values of e for temperature. This is a function of the mode radius rn (see ' various values of e, are shown in Table 3. The ll-prm flux equation (4)),which is known to decreasewith decreasingtem- emittance is then related to the broadband flux emittance e by perat[re fPlatt, 1984f. These changes in the mass absorption a linear factor of 0.97 lPlatt and Stephens, 19801. Values of e coefficient K should be taken into account when relating the are also shown in Table 3. For large values ofeo, e approaches cirrus extinction (absorption) coeffrcient to the ice water con- or exceedsunity, as a result of infrared reflection. It is shown tent.

t A PeneuerenrzATroN oF CTRRUS TABLE 3. Valuesof Flux Emittancee,, and BroadbandFlux In order to examine the effects of changing properties of Emittancee for Various Values of Beam AbsorptionEmittance e,, 1 at ll ilm cirrus on the climate, some simple way of introducing cirrus {

optical properties into a is required. As dis- Elt cussed earlier, in the present crude state of cloud parame- terization in climate models, it seems to make sense to bypass 0.1 0.25 0.24 0.2 0.40 0.39 considerations of cloud liquid water content and to appeal 0.3 0.53 0.51 directly to experimental data, such as that obtained in the o.4 0.64 0.62 LIRAD measurementsof Platt et al. lL987l, where the cloud 0.5 0.'76 0.74 infrared emittance, like the absorption coeflicient, has been 0.6 0.85 0.82 found to be a monotonic function of cloud temperature. Thus 0.8 0.9'7 0.94 0.9 -1.00 -.-1.00 if the cloud temperature is specified in a numerical model, PLaTr aun HlnsnvnnornN: Ctnnus Crouo euo Clrlrere Fnrnsecr I 1,057

by Platt and Dilley [1981] that average cirrus beam emit- dence of cloud absorption (or extinction) on ice water content tances do not exceed 0.7, so that emittances greater than this using an ice cylinder model is rather weakly related to an value are not relevant to this discussion. effective absorption (or extinction) efficiency and inversely These relations between e, err, and edwere computed theo- proportional to the mode radius. retically, as described by Stephens[1980], who used realistic Ice water contents calculated from a model of uplift and tropical and mid-latitude atmospheres to calculate the infra- condensation, or sublimation, along the moist adiabat for a red transmittance and reflectance properties of cirrvs. Platt constant cloud depth indicate arapid decreasein liquid water and Stephens [1980] used these results to construct relation- content with temperature. The adiabatic cloud depth used ships between broadband flux emittances and narrow-beam (300 m) gives average water contents, which are somewhat absorption emittances, which iocluded the effects of the atmo- greater t than those which were calculated by Heymsfield and spheresconsidered. Stephens [1980] showed that the flux emit- Platt ll984f from cirrus cloud microphysics data. Bearing in taflces were not independent of the atmospheres because of mind that actual measured cirrus cloud depths are from 1 to 4 i finite reflection of the cirrus, particularly for high, il cold tropi- km, it is evident that there is a considerabtedilution process cal cirrus situated over a hot tropical ground surface. The acting in cirrus. This can be accounted for, among other effects were also dependent on particle size and gave vari- things, by the survival of cirrus ice crystals falling in subsatu- ations in flux emittance of about 20% of the mean for tropical rated air through large vertical depths. cirrus but less than 10o/ofor midJatitude cirrus. The vari- The implications of the rapid increase of cirrus absorption ations between the upward and downward flux emittances coefflrcient (and optical depth) with temperature for climate were of the same order. feedback processesare investigated with the use of a temper- The parameteization here represents the next step in com- ature coeffrcient of the optical depth sensitivity factor. This plexity, the previously mentioned effects due to particle size factor is found to increase sharply with decreasing temper- are neglected, and only broadband flux emittances averaged ature, with the highest values occufring at the lowest temper- over the upward and downward directions are used. Such atures, where cirrus clouds have low optical depths. Such values for the effective flux emittances are shown in Tabte 3. clouds are known to cause a positive feedback to climate The second parameterization is somewhat simpler, being warming, so that the large sensitivity factor has significant intended for numerical models. The albedo a is calculated in implications for the theory of climate feedback. terms of optical depth d,, using the delta-Eddington approxi- The LIRAD observations also indicated a significant mation and a value of the asymmetry parameter of 0.85. The change in cloud depth with temperature, which has the effect d, is then related to e through the expression of enhancing the sensitivity factors at low temperatures,but it has the opposite effect at high temperaturesbecause the cloud e:1-exp(-0.756,) (21) depth decreaseswith increasing temperature above -35"C. This expression is arrived at using the value 0 (:2) used These results indicate the importance of distinguishing be- previously and a diffusivity factor of 1.5, which is tuned to tween cloud amount, cloud depth, and cloud absorption (or allow reasonable agreement with the flrst parameterization, extinction) coefficient.If, say, cloud amount increased as well describedearlier. as absorption coefficient and cloud depth, then sensitivity fac- The albedo a of cirrus clouds is reasonably independent of tors would be enhanced above the values reported here. The wavelength (except in the known gaseous absorption bands) ice water sensitivity factor also increaseswith decreasingtem- so that the previously described parameteization can be used perature, although values calculated from the microphysical to obtain the total solar scattering albedo, with some correc- measurements are generally lower than those calculated from tion for gaseousabsorption. the adiabatic ascent. The mass absorption coefficient K, which To summarize, the steps in a parameterization could be as is the ratio between absorption coefficientand the liquid water follows. Given a cloud temperature T, the beam absorption content, has a sensitivity factor which is always negative.This coefficient can be found from (1). Multiplying by a cloud indicates that K is changing with temperature and that it depth given by (18) or (19) then gives an infrared optical depth actually increaseswith decreasingtemperature. The reason for d", from which an infrared beam emittance can be determined this is that the particle size distribution mode radius increases from (2). A flux emittance e can then be obtained by using the with increasing temperature. For numerical models which gen- numbers in Table 3, from which an albedo a can be deter- erate liquid water content and therefore use a mass absorption mined from curves, such as those shown in Figure 3. Alter- (or extinction) coefficient to calculate an optical depth, these natively, one can obtain a visible optical depth d, from the variations in K should be taken into account. value of d"and thus a value ofe from (21). The change in mass absorption coefficient with temperature This parameterization does not treat solar absorption in actually depresses the optical depth sensitivity coefficients clouds. This factor is not known to any great accuracy for below values which are obtained when it is assumed that opti- cirrus. However, the measurements of Paltridge and Platt cal depth scales with ice water content. [1981] suggest a possible parameterization in terms of beam In order to use the measured temperature sensitivity of ab- emittance eo. sorption in numerical models, it is necessary to relate the infrared beam absorption to the flux value and also to the solar albedo. It is demonstrated in this study that such meth- CoNcr-usroNs ods are availabie and can be made quite simple for numerical The strong dependence of cirrus cloud absorption on tem- models. For instance, the infrared broadband ffux emittance perature revealed both in ground-based LIRAD results lPldtr can be related by a simple equation to the visible optical et al., t9871 and in values calculated from cloud microphysics depth, and the broadband flux emittance can similarly be re- is shown to be due to both the dependenceof cloud absorp- lated to the beam absorption emittance measured within a tion on ice water content and to the rapid change in available narrow spectral intefval. adiabatic ice water with temperature. The calculated depen- The results given in this paper can thus be used to relate Pr,ltt lNr HlnsgvlnonlN: Crnnus CLoUD AND Cr-rultE Frnoslcr cirrus optical properties to cloud temperature. As numerical Platt, C. M, R., On the bispectral method for cloud parameter deter- models can at present only predict whether a cloud is present mination from satellite VISSR data: Separating broken cloud and semitransparent cloud, J. Clim. Appl. M eteorol., 22, 429439, 1983. or not, and at what temperature, but have difficulty predicting Platt, C. M. R., Extinction in clouds, in 1RS.'84: Current Problems in a cloud liquid water content, a parameterization which relates Atmospheric Radidtion, Proceedings of the International Ratliation cloud optical properties directly to cloud temperature would Symposium, Perugia, pp. 163-166, A. Deepak Publishing, Hampton, seem the appropriate way to proceed. Va.. 1984. Platt, C. M. R., and A. C. Dilley, Remote sounding of high clouds, IV, Acknowledgmenrs.This work was done while C. M. R. Platt held Observed temperature variations in cirrus optical properties, J. a National ResearchCouncil Associateshipat the Laboratory for Atmos. Sci.,J8, 1069-1082,1981. Atmospheres,NASA Goddard Space Flight Center. Harshvardhan Platt, C. M. R., and G. L. Stephens, The interpretation of remotely sensed high cloud emittances, J. Atmos. Sci., 37,2314-2322, 1980. acknowledgesthe support of the National Aeronautics and Space ? Administration through grant NAG5-783 to the University of Mary- Platt, C. M. R., D. W. Reynolds, and N. L. Abshire, Satellite and lidar land. observations of the albedo, emittance and optical depth of cirrus compared to model calculations, Mon. Weather Reu., 108, 195-204, 1980. (1 RBrnnewcns Platt, C. M. R., J. C. Scott, and A. C. Dilley, Remote sounding of high Betts, A. K., and Harshvardhan, Thermodynamic constraint on the clouds, VI, Optical properties of midlatitude and tropical cirrus, J. cloud liquid water feedback in climate models, J. Geophys. Res.,92, Armos. Sci.,44, 729-7 47, 1987. 8483-8485. 1987. Ramanathan, V., E. J. Pitcher, R. C. Malone, and M. L. Blackmon, Bohren, C. F., Comment on "Cloud optical thickness feedback in the The response of a general circulation model to refinements in radi- CO, climate problem," by Richard Somerville and L. A. Remer, J. ative processes,J. Atmos. 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