A study of infrared diabatic forcing of ice clouds in the tropical atmosphere

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. D4, 4139, doi: /2002jd002146, 2003 A study of infrared diabatic forcing of ice clouds in the tropical atmosphere Tiziano Maestri and Rolando Rizzi Atmospheric Dynamics Group Bologna, Dipartimento di Fisica, Alma Mater, Università di Bologna, Bologna, Italy Received 29 January 2002; revised 30 September 2002; accepted 16 December 2002; published 26 February [1] The diabatic exchange occurring in the atmosphere and within ice cloud layers in tropical standard conditions is investigated. The crossover from the spectral region in which the cloud s layer experiences a net emission (roughly the far infrared) to the region in which it experiences net absorption (window) does not significantly depend on the ice amount, but appears strictly connected with cloud s height and atmospheric temperature structure. For a fixed atmosphere, the cloud s internal structure of radiative heating and cooling is highly dependent on cloud trasmissivity. The energy absorbed by ice crystals at the base of a cirrus is different from that absorbed by the air molecules occupying the same layer and the effects of scattering are quantified and compared to particle s emission. Simulations have been done in case of spherical and hexagonal column-shaped ice particles. Small differences are obtained in the integrated quantities due to compensating effects which appear fairly unimportant when compared to uncertainties caused by our inadequate knowledge of some of the main properties of ice clouds, such as ice amount and effective radius. Of larger magnitude are variations in layer s absorbed flux due to changes in the water vapor concentration. INDEX TERMS: 0360 Atmospheric Composition and Structure: Transmission and scattering of radiation; 1640 Global Change: Remote sensing; 1610 Global Change: Atmosphere (0315, 0325); 1655 Global Change: Water cycles (1836); 3359 Meteorology and Atmospheric Dynamics: Radiative processes Citation: Maestri, T., and R. Rizzi, A study of infrared diabatic forcing of ice clouds in the tropical atmosphere, J. Geophys. Res., 108(D4), 4139, doi: /2002jd002146, Introduction [2] A large number of feedback processes are known to occur in the Earth s climate system. The uncertainties associated with the feedback processes involving water in its different phases cause considerable concern for the predictive ability of climate models. [3] The radiative cooling of the Earth to space implies diabatic heating or cooling within the fluid itself, hence is an important term from the dynamic point of view both for large-scale dynamics and for convective motions within the cloud itself [Slingo and Slingo, 1988]. One of the most significant results in recent years has been the recognition [Clough et al., 1992; Clough and Iacono, 1995; Sihna and Harries, 1995] that the altitude of maximum cooling in clear-sky conditions is strongly wave number dependent and the humidity of the mid and upper troposphere exerts a strong influence on the outgoing long-wave radiation mostly through absorption and emission from the pure rotational band of water vapor. This cooling component in fact dominates the overall long-wave cooling by water vapor, even more so in cold and dry arctic conditions. This region clearly requires increased attention in the context of studying radiation balance [Clough et al., 1992] and it can Copyright 2003 by the American Geophysical Union /03/2002JD be said that water vapor is the most important greenhouse gas because of its absorption properties in the far infrared (FIR) region. Because of the importance of the subject, these results have undergone intense verification [Brindley and Harries, 1998; Mertens et al., 1999]. The condensed phases of water vapor are also extremely important in modulating the atmospheric emission, especially the ice phase. Cirrus clouds are believed to be important for climate [Liou, 1986], above all in the tropical regions because of their prevalence and persistence, and have been implicated as important components of feedback loops to climate forcings [Randall et al., 1989]. Bulk radiative studies of cirrus clouds show that they may cool radiatively or heat the upper atmosphere in the thermal infrared wavelengths depending upon height, thickness and microphysical size of the cirrus clouds [Slingo and Slingo, 1988; Stephens et al., 1990; Stackhouse and Stephens, 1990]. [4] Recent studies have quantified the increasing importance of the FIR part of the spectrum in top of atmosphere (TOA) fluxes with increasing cloudiness for all the six standard model atmospheres [Rizzi and Mannozzi, 2000]; the greenhouse effects of water and ice clouds have been recognized of particular intensity in the window (WIN) and in the FIR region, thus stressing the importance of the role of water vapor on tropospheric upward and downward fluxes more and more, and so heating rates [Maestri, 2000; Rizzi and Maestri, 2001]. ACL 5-1

2 ACL 5-2 MAESTRI AND RIZZI: INFRARED DIABATIC FORCING OF ICE CLOUDS Table 1. Selected Properties of the Clouds Used in the Computations Reference Cloud z = km (Seven Levels) a IWP, g/m 2 IWC, g/m 3 Tr at 1000 cm 1b IWP, g/m 2 (Three Levels) High cloud z = km Low cloud z = km (Four Levels) a Cloud s top and bottom altitude and the number of levels inserted for the radiative computations. b Transmissivity of reference cirrus at 1000 cm 1. [5] The work presented in this paper builds upon this activity and specifically addresses the diabatic exchanges occurring in the atmosphere and within (ice) cloud layers in standard tropical conditions. Particular attention has been given in understanding the role, if any, of the energy transfer occurring long-wave of 16 microns because we do not have any spectral measurement in that range and we have already outlined its particular importance to describe the diabatic exchange in clear-sky conditions. In the absence of measurements, we must rely on line-by-line and multiple scattering computations, since most accurate calculations are essential to our understanding of atmospheric diabatic processes. Line-by-line techniques represent in any case the standard for more rapid and approximate methods required for climate and weather prediction models. [6] The methods used to compute radiances and fluxes in cloudy conditions are outlined in section 2, where an important limitation to the concept of cooling rate is also addressed. In section 3, the attention is focused on the energy balance of cloud layers located at various heights. The change in diabatic forcing both above and below the cloud layer, induced by the latter, is investigated in section 4, together with the role of scattering and absorption/ emission processes. The same section also discusses the role of water vapor and skin temperature in shaping the diabatic forcing in the presence of cloud layers. Finally, in section 5 a comparison is made of diabatic forcing obtained using Mie theory and a parameterization of optical properties of hexagonal cylinders. Conclusions are drawn in section Methodology [7] LBL computations of layer optical depths are done using HARTCODE. A detailed description of the code mechanics that includes the standards adopted for continuum gaseous properties is given by Rizzi et al. [2002] and R. Amorati and R. Rizzi (Simulated radiances in presence of clouds using a fast radiative transfer model and a full scattering scheme, submitted to Applied Optics, 2001, hereinafter referred to as Amorati and Rizzi, submitted manuscript, 2001). The layer total gaseous optical depth is obtained by integration of the monochromatic optical depths over intervals of width 0.05 cm 1, the latter figure also representing the sampling rate of the final product (layer optical depth). The integration of the radiative transfer equation in clear and cloudy conditions, including multiple scattering, is based on the code RT3 [Evans and Stephens, 1991]. Since our aim is the description of the long-wave heat balance we have done spectral computations in the range cm 1,at0.05cm 1 resolution. The whole simulation scheme has been recently compared to infrared interferometric measurements in clear and cloudy conditions [Rizzi et al., 2001]. Radiances and fluxes, the latter calculated using a 10-point Gaussian quadrature in each quadrant, are computed at 55 levels with TOA placed at 60 km. [8] Ice cloud layers with geometry and properties defined in Table 1 are inserted into the tropical standard atmosphere [Anderson, 1986]. These cloudy layers are actually made of a number of sublayers (for example the reference cloud is made of six layers). The method used to account for the cloud microphysics was given by Amorati and Rizzi (submitted manuscript, 2001). Although there is experimental evidence that temperature is the predominant factor controlling ice crystal size distribution and volumetric ice content (ice water content or IWC) [Liou, 1992], in our analysis we have chosen a fixed particle size distribution, the H71 Standard [Hansen, 1971; Hansen and Travis, 1974] with fixed effective radius, R eff (50 mm), and effective volume, V eff (0.3), and use IWC as the modulator of the transmissivity of the cloud. Other choices could have been, for example, changing cirrus thickness or R eff (we have studied these cases, but results are not presented here). We have not addressed the effects of density of ice crystals since Stephens [1987] states that single-scattering extinction properties of distribution of particles differ very little as a function of density. In Table 1, IWC and ice water path (IWP), used in our computations, are listed together with the transmissivity Tr Tr ¼ e kabs ziwc ; for absorption at 1000 cm 1 (k abs is the spectral absorption coefficient (m 2 /g) and z is the thickness of the cloud). Typical values of IWC are found between and 0.5 g/m 3 [Liou, 1992]. The transmissivity is used as a measure of the opacity of the reference cloud in the presence of absorption processes alone, a zero value indicating a transmissivity lower than [9] Two sets of computations are done assuming that cloud particles are spherical and hexagonal columns. In the first set, Mie theory is used to compute the extinction and scattering coefficient and the four independent terms of the scattering matrix for the distribution of spherical particles. In the second set, Fu s parameterization [Fu et al., 1997, 1998] is used. The latter parameterization is selected as the coefficients are available for broad spectral bands in the whole long-wave range and can be readily obtained from ð1þ

3 MAESTRI AND RIZZI: INFRARED DIABATIC FORCING OF ICE CLOUDS ACL 5-3 Figure 1. (a) Layer energy balance (mw/m 2 cm 1 ) versus wave number (cm 1 ) for the reference cirrus; IWPs are expressed in g/m 2. (b)vertical profiles of net flux (W/m 2 ) for the reference cirrus with two ice contents (IWP is in g/m 2 ) and for clear sky. Horizontal dotted lines define the cloud layer. First panel, FIR band ( cm 1 ). Second panel, WIN band ( and cm 1 ). published literature. We compare the two sets of computations to provide a measure of the differences that can be found in largely different cloud microphysical conditions, one of which, the solid ice spherical particles, is characterized by unit tunneling effect [Baran et al., 1998]. [10] In a time interval t, the heat absorbed or emitted by a certain volume V of air mass is: Q V t ¼ F z ; where z is the vertical dimension and F is the net irradiance. Assuming (fundamental hypothesis of our model) the condition of local thermodynamic equilibrium (LTE) from this formula, it is simple get the equation: T t ¼ g C p F p ; used in the computations of heating rates (g is the Earth gravity acceleration, C p is the specific heat of air, and p is ð2þ ð3þ the atmospheric pressure). However, in the presence of cloud particles it is difficult to think of a unique heating rate for cloud droplets (or ice crystals) and gas molecules. Instead we should consider the different ways of absorbing energy, and consequently, also the interchange of heat between air and cloud particles after a temperature gradient eventually develops. In what follows, no conclusion is drawn on how energy is partitioned in a layer when we are in the presence of a cloud, the attention being focused on the energy lost or gained within the layer. 3. Energy Balance of an Ice Cloud Layer in the Tropical Atmosphere [11] First, we consider the energy balance inside the depth of the reference cloud by differentiating net fluxes at cloud base and top. In Figure 1a, the energy balance for the reference cirrus is shown for two different IWPs (26.7 g/m 2 corresponding to a transmissivity of 0.65 that we consider a

4 ACL 5-4 MAESTRI AND RIZZI: INFRARED DIABATIC FORCING OF ICE CLOUDS quite transparent tropical cirrus, and 890 g/m 2 corresponding to a zero transmissivity that is completely opaque). The spectral results are integrated over 5 cm 1 for visual purposes; positive values indicate radiation absorption. In agreement with preceding studies [Stackhouse and Stephens, 1990], we noted net absorption in the WIN ( and cm 1 ) and net emission in the FIR ( cm 1 ); spectral integration yields absorption (7.3 W/m 2 for IWP = 26.7 g/m 2 and 27.8 W/m 2 for IWP = 890 g/m 2 ) while the same layers lose energy ( 11.1 W/m 2 )in the clear-sky case. The vertical profile of net fluxes, shown in Figure 1b, shows that the cloud produces a change in the energy balance at every atmospheric level with respect to the clear-sky case. In the water vapor s pure rotational band in the FIR (Figure 1b, first panel) small net fluxes are seen at cloud base while the atmosphere above the cloud is more transparent and net fluxes have larger values. On the other hand, in the WIN (Figure 1b, second panel), the upward flux under the cirrus base is quite strong (as radiation comes from the ground and the atmospheric levels nearest to it) and greater than the downward flux of the cloud (in the limit case, IWP = 890 g/m 2, the cloud emits as a blackbody whose temperature is lower than that of the surface or lowest atmospheric levels). Therefore net fluxes below cloud base are larger than the ones above the top. Resultant is a positive value in the absorbed flux in WIN (as seen in Figure 1a). We have seen that changes of IWC strongly affect the proportion of energy absorbed and emitted by the layer, but they do not significantly shift the crossover point from absorption to emission (at around 720 cm 1 ). The same layer in clear-sky condition (not shown) reveals a net emission of radiation, mostly due to water vapor, almost in the same spectral region ( cm 1 ) as the cloud s layer; on the other hand, the clear layer absorbs very little in the WIN because of the high molecular transparency at that altitude. [12] A cloud placed at lower altitude (referred as low cloud in Table 1) is immersed in a more opaque atmosphere. The pure rotational band of water vapor has a strong impact at this altitude, producing a very small value of net flux under the cloud (Figure 2b) especially in the FIR and at the lower wave number end of WIN. The net flux at the top of the cirrus remains large in the FIR since the downward flux is still smaller compared with the upward emission due to the cloud and water vapor inside it. For these reasons, the cloud shows a strong emission in the FIR (Figure 2a). A similar reasoning can be done for the vibro-rotational band of water vapor centered at 1587 cm 1, which now clearly shows emission, even if the energy involved is much smaller. We must also consider that cirrus placed at lower altitude means a higher cloud temperature (the emission s peak of the blackbody curve is shifted toward higher wave numbers), and hence enhanced emission (Figure 2b, second panel) whose overall effect is a decrease of WIN absorption in absolute terms and a reduction of its spectral range with a changeover around 800 cm 1. Spectral integration gives a loss of energy of 30.3 W/m 2 for IWP = 32.4 g/m 2 and 31.2 W/m 2 for IWP = 1080 g/m 2 (in clear-sky condition, the loss is 27.5 W/m 2 ). The same layer, in case of clear sky, experiences a net emission in approximately the same spectral regions ( and cm 1 ) as the cloudy sky; the reason being the large changes in water vapor s optical depths from the bottom to the top of the layer. [13] With similar arguments and considerations on the atmospheric temperature and transmissivity, it is possible to explain the case in which the cirrus is placed at higher altitude (Figures 3a and 3b); the spectral region in which we have emission is narrowed, and absorption, now present also at the high wave number end in the FIR, is increased (the layer absorbs 52.9 W/m 2 for IWP = 32.1 g/m 2 and 97.0 W/m 2 for IWP = 1070 g/m 2 ). As in the previous cases, a crossover appears well defined (at about 460 cm 1 in these conditions), independent of the chosen IWP. In case of clear sky, the layer undergoes a net emission in a broader spectral region ( cm 1 ), but because of the high altitude, and consequently, the low temperature and low water vapor amount the emission of the clear layer is rather low in the whole range ( 0.6 W/m 2 ). 4. Tropospheric Diabatic Forcing Induced by an Ice Cloud [14] Figure 4a shows the results of calculations of spectral flux convergence P v, expressed in mw/(m 2 km cm 1 ), P v ¼ F n ð4þ z for the tropical atmosphere in the altitude range 0 60 km using the reference cirrus with IWP = 26.7 g/m 2. Positive values of P v indicate that the incoming flux in the layer is larger than the exiting one and the layer experiences heating. Differences with the clear-sky case are shown in Figure 4b. Spectral flux convergences are very small across the vibro-rotational band of H 2 O as a consequence of the relatively small fluxes and net fluxes involved. In analyzing Figure 4b, we also see that a cloud emits and scatters radiation, enhancing the downward fluxes below its base and that part of atmosphere is heated if there is a gas capable of absorbing this additive energy. This is the case of water vapor, in particular, in the rotational band. The reduction in the upward flux due to the cloud means less energy is reaching stratospheric levels which brings, for instance,to a reduction to ozone heating. A more opaque cloud, for example, the limit case IWP = 890 g/m 2 represented in Figure 4c, produces larger absorption at cloud base and larger emission at the top, both occurring all over the spectrum but with different intensity, while in the inner part of the cloud we have an almost perfect blackbody behavior. However, as shown in the previous section and in Figure 1a, when discussing the energy balance of the entire cloud depth, a substantial part of the energy absorbed at WIN is still counterbalanced by that lost at FIR (with a peak around 300 cm 1 ), even when the cloud has quite a large optical depth. [15] Spectrally integrated flux convergence, P, for the low, reference, and high clouds is plotted in Figure 5, for different IWP values. In the first panel, we consider tenuous clouds (transmissivity is between 0.84 and 0.87 at 1000 cm 1 ) and we compare their effect to that of clear sky. The low cirrus reveals a net infrared cooling at all levels even if cooling is less intense than in clear-sky conditions in the bottom cloud layers. Since the low cirrus is placed at altitudes where the atmosphere is quite opaque, the upwell-

5 MAESTRI AND RIZZI: INFRARED DIABATIC FORCING OF ICE CLOUDS ACL 5-5 Figure 2. (a) Same as Figure 1a, but for the low cloud. (b) Same as Figure 1b, but for the low cloud. ing radiation is relatively small, and so is the absorption, while the cloud radiates to space from all its levels without receiving great amounts of energy from the transparent layers above. The net effect is the negative convergence at all levels. For the high cirrus we obtain a net heating in the whole cloud body in accordance with the results of Platt et al. [1984] and Ackerman et al. [1988]. In this case, the radiation coming from the lowest atmospheric levels is absorbed throughout the entire vertical extent of the cloud which emits at very low temperature. The reference cirrus presents an intermediate behavior with an attenuation of clear-sky cooling at the bottom levels and a reinforcement at the top. In the second panel of Figure 5, the three cloud types are considered but with larger values of IWP (transmissivity is reduced with respect to the first panel but is still quite high, from 0.60 to 0.65 at 1000 cm 1 for the three cases). Cooling in the top layer and heating at the base is now well evident for the reference cirrus. A similar behavior is obtained for the low cirrus even if cooling predominates. Again, in the case of high cirrus we have heating at all levels. In fact cooling at the top is obtained only with more opaque clouds (not shown). [16] It is important to establish the quantity of energy gained or lost at every cloud level in determining the

6 ACL 5-6 MAESTRI AND RIZZI: INFRARED DIABATIC FORCING OF ICE CLOUDS Figure 3. (a) Same as Figure 1a, but for the high cloud. (b) Same as Figure 1b, but for the high cloud. radiative destabilization that induces convective mixing and in defining the conditions of the ice microphysical processes; arguments that are particularly important in the climatological debate. [17] If we consider a cloud with even higher value of optical depth we get larger positive values of P at its base (128 mw/m 3 for IWP = 89 g/m 2 for the reference cirrus), due to positive contribution of all bands while strong heat loss is seen in the highest levels. We have also made computations in the case of the completely opaque reference cirrus (IWP = 890 g/m 2 ), obtaining extremely high values of heating at cloud base (458 mw/m 3 ) and cooling at the cloud top ( 1.39 W/m 3 ). [18] If we focus our attention on the change of flux convergence profile below the cloud we notice that the lower is the altitude of the cirrus, larger is the decrease in the infrared cooling of the lowest tropospheric levels (and so the surface). As in a work by Slingo and Slingo [1988], the surface infrared warming is greater for low clouds. The comparison of first and second panels of Figure 5 also shows a reduction in the energy lost below the cloud with respect to the clear-sky case, which depends on ice content.

7 MAESTRI AND RIZZI: INFRARED DIABATIC FORCING OF ICE CLOUDS ACL 5-7 Figure 4. Spectral flux convergence P dv (mw/(m 2 km cm 1 )) plotted as function of wave number (cm 1 ) and altitude (km). (a) P dv for the reference cirrus with IWP = 26.7 g/m 2. (b) Differences between the case in Figure 4a and the clear-sky case. (c) P dv for the reference cirrus with IWP = 890 g/m 2.(d)P dv differences for the reference cirrus with IWP = 26.7 g/m 2 in Mie and Fu cases. See color version of this figure at back of this issue. The values of P above cirrus clouds appear only slightly reduced with respect to clear sky even if the change in TOA net flux can be very intense. For example, in case of the presence of rather transmissive clouds the clear sky net infrared flux is reduced by 102, 72, and 58 W/m 2 by the presence of high (IWP = 32.1 g/m 2 ), reference (IWP = 26.7 g/m 2 ), and low (32.4 g/m 2 ) clouds, respectively. [19] We have previously underlined the difficulties in defining the heating rate at levels where a cloud is present, since two different heating rates are required, one for the air molecules and one for the ice (or water) particles. In doing so, we must differentiate the amount of energy absorbed by the ice crystals from that absorbed by the molecules, taking into account the fact that scattering by cloud particles increases the optical paths with respect to pure absorption cases (clear sky with molecular scattering neglected and cloud absorption only considered). We have therefore run simulations for four different cases: clear sky (indicated as C), absorbing cloud only (A), scattering cloud only (S), and the full solution with absorption and scattering (F). Gaseous absorption is included in all cases and scattering means multiple scattering. Results for the reference cirrus with IWP = 26.7 g/m 2 are shown in Figure 6. As expected, scattering processes imply longer mean geometrical and optical paths and more heating at the base and more cooling at the top of the cloud. A decrease in energy lost to space, with respect to the clear-sky case, is evident in layers under the cloud (for example P increases by 1 mw/m 3 from C to S case), due to increased downward fluxes by backscattering. However, the major contributor is the cloud s downward emission as the A and F solutions clearly indicate. Outside the cloud layer the differences S-C and F-A provide two measures of scattering. In evaluating the difference S-C we are just quantifying the redistribution of energy with respect to the clear case due to the presence of ideal ice scatterers in a layer of atmosphere; it is an evaluation of the pure geometrical effect of multiple scattering on the radiative transfer. In the case F-A, the multiple scattering effect is quantified also in presence of ice absorption (this means that we take into account the attenuation and the spectral

8 ACL 5-8 MAESTRI AND RIZZI: INFRARED DIABATIC FORCING OF ICE CLOUDS Figure 5. Total flux convergence (mw/m 3 ) as a function of altitude. The low, reference, and high clouds are used for different IWPs and compared to clear sky divergence. Note that the abscissa scales are different for the two panels. The horizontal lines define the three cloud layers. dependence of the reemitted radiation). The different values in the two differences (S-C and F-A) confirm the nonlinear effect of multiple scattering. [20] As a first approximation, the energy absorbed by cloud particles could be computed by the difference between the F and S solutions (optical paths are the same). If we add the rough assumption that ice crystals do not interchange heat with air molecules and we are in a stationary case, it is possible to evaluate the time employed by particles close to cloud s base to melt. In fact the energy required by ice in the time interval t to reach the temperature of fusion T fusion and to change phase (L is latent heat of fusion) is: Pðice part: Þt ¼ " T Zfusion # IWCC p ice ðtþdt þ L IWC ; ð5þ T ice where the dependence from temperature of specific heat at constant pressure of ice (C p_ice ) is taken into account [Pruppacher and Klett, 1997]. For IWP = 26.7 g/m 2 we have estimated a time of 176 s for near-cloud base ice crystals to melt. This estimate serves the only scope to show the magnitude of the effect of radiative fluxes on cloud particles. If we evaluate t through the difference between the A and the C solution, the result is 181 s with an overestimation with respect to the F-S case that in first approximation can be attributed to reduced mean geometrical and optical paths and so absorbed energy by the ice crystals. We are considering small differences in ray paths as our attention concentrates at cloud base and light has traveled just a few meters into the cloud s body. This explains the relatively small difference in the two results. [21] Taking the flux convergence difference of the F-S case as the energy absorbed by the ice crystals, then the energy absorbed by the molecules inside the cloud is described by the flux convergence for the S case. Again, taking into account the cloud base level, it is found that while in few seconds the ice temperature would increase by more than 40, the air exhibits a very slow but opposite behavior of 3 mk (we are always neglecting the icemolecule interchange of heat). This sudden breaking of equilibrium suggests that transport of sensible heat (by conduction) from ice to air molecules is very important in

9 MAESTRI AND RIZZI: INFRARED DIABATIC FORCING OF ICE CLOUDS ACL 5-9 Figure 6. Clear-sky (C) total flux convergences (mw/m 3 ) as a function of height are compared with the same computed in presence of the reference cirrus IWP = 26.7 g/m 2 accounting for scattering only (S), absorption only (A), and the complete multiple scattering solution (F). The plot focuses on the layers just below the cloud. The two horizontal (gray) lines define the cloud layer. the heat balance inside the cloud [Stephens, 1983]. If the whole energy absorbed by the cloud (a decrease in the net flux of about 8 W/m 2 from cloud bottom to top) were to be used to increase the particles temperature in the whole cloud, we would have the complete fusion of ice in about 25 min; a result that is consistent with that of others authors [Platt et al., 1984]. In the case of the more opaque cirrus (IWP = 890 g/m 2 ) this time becomes larger (around 6 hours and 30 min) since, even if the flux convergence increases (around 28 W/m 2 the difference between bottom and top net flux), the predominant factor is now the large ice content (IWC = 0.5 g/m 3 ). [22] We have also computed the cloud energy budget when the reference cloud is placed in a tropical atmosphere with a water vapor concentration increased/decreased by 20% (case P/M) with respect to the standard model (case S). The energy balance differences between case P and M against S are shown in Figure 7. It is clear that a cloud absorbs more energy when placed in a more transparent atmosphere. In case M the cloud traps more radiation at WIN as more radiation arrives from below, and produces a lesser emission in the cm 1 region. The reduction in the water vapor concentration makes the atmosphere above the cirrus in the cm 1 region less opaque which means more emission in that spectral region. Case P reveals a nearly opposite behavior even if the two cases are not perfectly symmetric, as is evident from the dotted line which is the difference between the absolute values of the (M-S) and the (P-S) cases. An increase in the differences is obtained with increasing IWP. The reference cirrus absorbs 2.7 W/m 2 in the M case more than in the S one with IWP = 26.7 g/m 2 and the difference becomes 4.6 W/m 2 with IWP = 890 g/m 2. We note (not shown) that the crossover wave number, defining the cloud layer passage from emission to absorption, does not undergo a noticable shift for changes of the 20% in the atmospheric water vapor concentration. All these suggest the atmospheric temperature profile as the main factor controlling the crossover point.

10 ACL 5-10 MAESTRI AND RIZZI: INFRARED DIABATIC FORCING OF ICE CLOUDS Figure 7. Three different concentrations of water vapor (S, standard; P, +20%; M, 20%) are used to plot the spectral differences (M S, P S, and abs (M S)-abs (P S)) in the spectral layer energy balance (mw/m 2 cm 1 ) for the reference cirrus (IWP) = 26.7 g/m 2 ) as a function of the wave number (cm 1 ). [23] We have already discussed the role of the temperature profile in the energy balance of cloud layers. In Figure 8, we consider the effect of a change in surface skin temperature. A higher surface temperature increases the energy absorbed by the cloud layer in all transparent spectral regions. From the plot we also note an increase of the absorption with decreasing water vapor optical thickness. The increase in absorbed energy (with respect to the standard skin temperature) is 0.52 W/m 2 for the M case and 0.30 W/m 2 for the P case. In section 5, we will see that these values are comparable with those found if we change the cloud particles microphysics. 5. Comparison Between Mie and Fu Parameterization [24] The use of Mie theory to specify the cloud properties raises serious issues [Baran et al., 1998; Fu et al., 1998]. The latter authors developed a composite method to determine single-scattering properties of hexagonal ice crystals in the whole infrared domain by comparing results from Mie, anomalous diffraction theory, geometrical optics method, and finite difference time domain method. The derived parameterization has been used to compute the absorption and single-scattering coefficient of our reference cirrus cloud. A generalized effective size (D ge )of77mmhas been obtained from our effective spherical particle radius (50 mm) using the method described by Fu [1996]. Singlescattering and absorption optical depths, for a cloud of depth of 1 km, derived from Mie and Fu are shown in Figure 9. In the whole spectral range, except from 700 to 900 cm 1, the Fu solution implies lower absorption. In the range cm 1 the mean reduction in optical depth is about 5.7% and in the cm 1 the mean reduction is 1.2% with a maximum of 5.4% at 990 cm 1. In the range cm 1 the mean increase is of 2.8% with a maximum of 4.2% at 820 cm 1. [25] In Figure 4d, the differences between the spectral flux convergences obtained using Mie theory (M) and Fu parameterization (F) are presented for the reference cloud with IWP = 26.7 g/m 2 Fu results are subtracted with their sign from Mie ones. Computations are done in the spectral range from 100 to 2500 cm 1 and in the altitude range 0 60 km. [26] Assuming that Mie and Fu data agree in sign (which is true except in very limited parts of the domain) it is possible to distinguish four different cases: 1. (M+) (F+) = positive, then we have more heating in M case; 2. (M ) (F ) = positive, then we have less cooling in M case; Figure 8. Spectral differences (mw/m 2 cm 1 ) in layer energy balance for the reference cirrus (IWP = 26.7 g/m 2 ) due to a change in the surface temperature (+1 K) as a function of the wave number (cm 1 ). The results for two different water vapor concentrations are reported in order to connect surface temperature to atmospheric transmissivity.

11 MAESTRI AND RIZZI: INFRARED DIABATIC FORCING OF ICE CLOUDS ACL 5-11 Figure 9. Extinction (first panel) and absorption (second panel) optical depths as function of wave number (cm 1 ), for a 1-km deep cloud, for the Mie (R eff =50mm, V eff = 30 called M50 and R eff =45mm, V eff = 30 called M45) and Fu parameterization (D ge =77mm called F77). 3. (M+) (F+) = negative, then we have less heating in M case; and 4. (M ) (F ) = negative, then we have more cooling in M case. Combined examination of Figures 9 and 4d clearly shows that radiative properties of cirrus clouds in the infrared are dominated by absorption, in agreement with Fu et al. [1998]. [27] In the cm 1 spectral interval M induces more cooling in the upper cloud layers (case 4) as absorption and emittance are higher. In the lower cloud layers, larger M emission produces smaller net fluxes, and consequently, smaller cooling (case 2). [28] Larger heating at cloud base (case 1) is found in the and cm 1 spectral interval. Lesser cooling is observed in the troposphere under the cloud. [29] At wave numbers between 700 and 900 cm 1 we have less heating at cloud base (case 3) and more energy reaching the cloud top and producing larger heating (case 1). Larger cooling is seen near the surface layer due to lesser downward fluxes for the M solution. [30] The spectral difference in the layer s energy balance (reference cloud with IWP = 25.7 g/m 2 ) for the M and F case, shown in Figure 10 (first panel), follows the absorption coefficient s behavior which brings a greater loss of radiation in the FIR and a greater absorption in the WIN for Mie case (the integrated difference in the absorbed fluxes in the cm 1 interval is positive). The cloud layer in the Mie case absorbs a total of 7.5 W/m 2 ;the Fu parameterization lowers this value by 0.49 W/m 2.We have previously seen that a 1 K change in the skin surface temperature brings comparable values in the cloud layer s energy balance. The percentage difference (Mie Fu)/ ABS(Mie)100 (Figure 10, second panel) shows that the difference is confined to ±5% except for isolated peaks where Mie values are close to zero. Results obtained with the reference cloud but with different opacities are not shown as they are spectrally very similar. [31] The upward flux at TOA in the range cm 1 is equal to W/m 2 (M) and (F) W/m 2 (0.25%). The main differences are revealed in the FIR with W/m 2 (M) and W/m 2 (F). Results with different IWPs (listed in Table 1 for the reference cloud) show largest differences in flux at TOA (0.72 W m 2, corresponding to 0.4% of the outgoing flux) for IWP = 53.4 g/m 2 corresponding to a transmissivity of We have focused our

12 ACL 5-12 MAESTRI AND RIZZI: INFRARED DIABATIC FORCING OF ICE CLOUDS Figure 10. First panel: Spectral differences (mw/m 2 cm 1 ) in the layer energy balance for the reference cirrus (IWP = 26.7 g/m 2 ) when Mie and Fu parameterization are used as function of wave number (cm 1 ). Original data is averaged over 5 cm 1. Second panel: Percentage error (with sign) of the previous differences: (Mie-Fe)/abs(Mie)100. attention on the IWP = 26.7 g/m 2 case as scattering effects are more important. [32] A question arises as to whether these differences are significant. Since clouds are extremely important in modulating the transfer of radiation within the atmosphere, the interaction must be accounted for as accurately as possible in medium-term numerical weather prediction and climate models. Therefore the differences between the M and F results must be weighted against the differences that are produced by our inadequate knowledge of cloud properties, especially of high clouds. Current estimates of model uncertainties in the cloud variables are summarized in a statement of the Third Assessment Report of Intergovernmental Panel on Climate Change (IPCC) [2001] which states that probably the greatest uncertainty in future projections of climate arises from clouds and their interactions with radiation. Some quantitative assessment is given in an European Space Agency Report [2001] which provides data taken from the Atmospheric Model Inter-comparison Programme (AMIP). A plot of the zonal average of vertically integrated total cloud water path for 14 different climate models for June, July, and August is provided in Figure 2.2 of the ESA Report. The comparison clearly shows that although the models are able to produce similar TOA mean upwelling radiative fluxes, they have mean values of vertically integrated IWP which vary by over an order of magnitude from one model to another, and consequently, very different heating profiles, which also likely result in different weather patterns. [33] Another parameter of great relevance for radiation computations in the presence of clouds is the effective radius of a distribution, a simplified methodology to account for the cloud s droplet size distribution. The Mie spectral optical depth for the reference cloud but with R eff = 45 mm, V eff = 0.3 is also shown in Figure 9. It is seen that the mean difference in spectral optical depth, in range cm 1, between the two Mie cases (11%) is larger than the mean difference between Mie (R eff =50mm and V eff = 0.3) and Fu case ( 2%). Therefore we tend to consider that the differences obtained using the alternate Mie and Fu simulations are fairly unimportant when compared to uncertainties caused by our inadequate knowledge of some of the

13 MAESTRI AND RIZZI: INFRARED DIABATIC FORCING OF ICE CLOUDS ACL 5-13 main properties of clouds, such as ice amount and effective radius. 6. Conclusions [34] Previous studies on the role of far infrared (FIR) Earth s emission in clear conditions are extended to the analysis of some cloudy conditions by inserting ice cloud layers, at various heights into the Tropical standard model. As expected these cloud layers induce strong changes on spectral fluxes, especially in FIR and window (WIN) regions. [35] The vertical profile of flux convergence within the cloud reveals an internal vertical structure strongly dependent on its optical depth; when the cloud is quite transparent, cooling is seen for small wave numbers and heating for larger ones, while when the cloud approaches total opacity cooling at the top layer and heating at the base is seen at all wave numbers. Flux convergence integrated in the whole cloud depth, again reveals two well-defined spectral regions: the FIR in which we have a net emission of radiation and the WIN in which we have net absorption. Large changes in ice water path (IWP) do not significantly shift the wave number which separates the two regions. Thus the balance between radiative cooling in the FIR and radiative heating in the midinfrared is critical for determining the radiative effects of these clouds in the atmosphere. A lower cloud induces a stronger emission in the FIR and a decrease in the WIN s absorption associated with a shift of the separation wave number toward larger wave numbers. These results are explained with the immersion of the lower cirrus in more opaque atmospheric layers and above all with the increase in cloud temperature due to the lower height. Cloud s IWC strongly affects the proportion of energy absorbed and emitted by the layer. But once a cloud level and atmospheric profile are predefined, the crossover point is well defined, quite independent of cloud transmissivity. The atmospheric temperature profile is recognized as the main factor in defining the crossover point from cloud net absorption to emission. [36] The profile of flux convergence outside the cloud shows a reduction, proportional to IWP, in the energy lost below the cloud with respect to the clear-sky case. Flux convergence is strongly connected with cloud altitude. Tenuous ice clouds experience infrared heating at all cloud levels when placed at high altitude and cooling when they occupy lower layers. The crossing point from cooling at all levels to heating is related to cloud optical depth and altitude. The values of flux convergence above the cloud are only slightly reduced with respect to clear sky, but great differences are revealed in the exiting flux with varying the cloud altitude or its IWC. [37] The contribution of scattering to flux convergence, hence cooling, is more important outside than within the cloud. For the reference cloud, it is about 7.4% in the layers immediately below the cloud bottom, and decreases in relative terms at lower altitudes since the absolute flux convergence increases in the latter. [38] Atmospheric concentration of water vapor has an important impact in the cloud s energy balance since a decrease in concentration by 20% (with respect to the tropical standard atmosphere) produces an increase of about 39% in the energy absorbed by the layer (reference cirrus with a transmittance of 0.65 at 1000 cm 1 ) and of 17% when the cloud is completely opaque. The more transparent the atmosphere below the cirrus is, the more the cloud absorbs energy. [39] The results obtained with the Mie theory are compared with simulations using the Fu parameterization. The differences in the energy balance of the cloud obtained with the two methods are comparable to those obtained with a change of 1 K in the skin surface temperature. The spectral differences in flux convergences are easily related to the differences in the absorption coefficients using Mie and Fu, while the effects produced by the different scattering coefficients and phase functions are much smaller. Differences in fluxes at the top of the atmosphere are also evaluated. It is argued that all these differences are fairly unimportant when compared to uncertainties caused by our inadequate knowledge of some of the main properties of clouds, such as ice amount and effective radius. [40] Difficulties arise in defining the heating rate at levels where a cloud is present, since two different heating rates are required, one for the air molecules and one for the ice (or water) particles. A rough estimate of distribution of energy between ice particles and molecules is given, which implies an intense transport of heat via conduction between the ice particles and surrounding molecules. [41] The launch of Atmospheric Infrared Sounder (AIRS) has greatly increased the amount of spectral information measured from space. It is expected that improved estimates of cirrus parameters will be possible based on new data and experience gained with current radiometers [Stone et al., 1990]. However, all the computations shown in the present study indicate clearly that the FIR region provides a very important energy contribution within the clear atmosphere, within high cloud layers, and at the top of the atmosphere both with and without clouds. Despite this role, there is almost total absence of spectral measurements from space in the FIR. Notation Tr transmissivity of the cloud layer. k abs absorption coefficient, m 2 /g. z height, m. IWC ice water content, g/m 3 t time, s. Q heat, J. V volume, m 3. F net irradiance, W/m 2. g gravity acceleration, m/s 2. T temperature, K. C p specific heat of dry air, J/K g. C p-ice specific heat of ice at constant pressure, J/K g. P v spectral flux convergence, W/m 3 cm 1. p pressure, Pa. L latent heat of fusion, J/g. R eff effective radius, micron. V eff effective variance. generalized effective size, micron. D ge [42] Acknowledgments. We wish to acknowledge the invaluable support of Alessandro Passerini and Enrico Rossi with the upgrading and maintenance of the Linux based computing system of ADGB and of Matteo Rizzi for the help in the results database generation.

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