Radiative impacts of ASC

method, the integral over wavelength may be computed before-hand since the D are e, k fixed in time. Thus, the above integral is approximated as, N bins b , A D N Q , 14 Ž . Ž . Ý ext k k ext , k ks1 where Q , E Q D , m, l d l r E d l. 15 Ž . Ž . H H ext , k l ext e , k l D l D l Similar forms are easily derived for v and g by thin and thick averaging. For all optical Ž . properties, solutions to Eq. 15 are computed and stored as model input. During RAMS Ž . integration, Eq. 14 is used to compute the optical properties of drops and ice crystals. To test the accuracy of this method, computations were done using gamma distribu- tion functions for which accurate analytical solutions are known. Tests were then conducted by breaking a gamma distribution of a given shape, n s 6, into 25 discrete bins and then applying the above method to compute the optical properties. Fig. 6 shows the relative error associated with using the bin method to derive the optical properties Ž . for a range of distribution mean sizes 1 to 400 mm and for a particular radiation band. Note that errors in the bin method are, in general, quite small. In particular, the bin method over-estimates the optical properties by about 1 for extremely narrow distribu- Ž . tions D ; 1 . For distributions with D R 4 errors are negligible. This was also mean mean found to be true for the ice-phase parameterization.

4. Radiative impacts of ASC

In order to illustrate the flexibility of the above scheme and the importance of microphysical characterization of mixed-phase ASC as regards the radiative heat budget, we have conducted a set of studies using microphysical output from previous modeling Ž . efforts. This allows us to illustrate two things: 1 the influence of the choice of Ž . microphysical characterization and structure on the radiative heating, and 2 the influence of the ice phase on the cloud radiative properties. All of the following Ž . computations are done for solar zenith angles u F 608 and with a surface albedo of Ž . 0.65 Curry, 1986 , except where noted. The cases used in this study are the mixed-phase ASC cases described in Harrington Ž . Ž et al. 1999 . Our discussions are limited to the diabatic heatingrcooling i.e. absorption . and emission by the cloud layer and the net surface fluxes for two reasons. First of all, radiative heatingrcooling significantly influences the dynamics and, hence, the evolu- Ž . tion of ASC see Olsson et al., 1998; Harrington et al., 1999; Jiang et al., 2000 . Alterations in cloud microstructure lead to changes in the radiative heatingrcooling of Ž the cloud layer, which then alters the dynamics and thickness of the cloud layer Boers . Ž . Ž . Ž . and Mitchell, 1994 . Additionally, solar absorption A A and infrared IR cooling ´ Ž . give us some idea of how much the boundary layer BL is warming or cooling due to the radiative properties of a given cloud. Ž Second, since ASC are quite ubiquitous e.g. Herman and Goody, 1976; Utall et al., . 1999; Intrieri et al., 1999 , they have a significant influence on the Arctic surface Ž . Ž . radiation budget Curry, 1995 and, thus, the sea ice thickness Curry and Ebert, 1990 . In fact, it has been suggested that alterations in cloud microphysical properties can lead Ž . to as much as a 3-m alteration of the average sea-ice thickness Curry and Ebert, 1990 . Ž . In addition, Royer et al. 1990 have shown that alterations in sea-ice coverage can provide a feedback to the cloud coverage in either a positive or a negative fashion Ž . depending on the cloud parameterization such that the sea ice either grows or disappears. Hence, we examine how important the characterization of cloud microstruc- Ž y q . ture might be to the prediction of the surface net flux F s F y F . These net parameters, while not exhaustive, are sufficient to illustrate the potential impacts of cloud microstructure on the radiative heat budget of the cloudy BL and the surface. 4.1. Selected cases Model output archived during the simulated evolution of mixed-phase ASC described Ž . in Harrington et al. 1999 is used selectively in this study. Particular time periods in the Ž . cloud evolution have been chosen, which have: 1 thick liquid cloud structure with Ž . Ž . some ice precipitation, 2 thin liquid cloud with a large amount of ice, and 3 thin cloud composed almost equally of ice and liquid. Since these runs were done with the Ž . bin-resolving microphysics of Reisin et al. 1996 , detailed liquid and ice crystal distributions are available at each grid-point. The model output for each of these cases contains 61 columns of microphysical information. Since each model column is treated independently by the radiation model, the radiative analysis covers a broad range of Ž y2 . Ž y2 . liquid water paths LWP ; 6–120 g m and ice water paths IWP ; 6–80 g m . Ž These ranges of LWP and IWP cover those observed in Arctic Stratus Curry et al., . 1996; Hobbs and Rangno, 1998 , and the simulated clouds compare well with observa- Ž . tions Harrington et al., 1999 . Thus, this information forms a surrogate data set suitable Ž . for radiative analysis this procedure is similar to the approach of Duda et al., 1996 . Ž . Ž . Fig. 7a–d shows the liquid water content LWC , drop concentration N , ice water c Ž . Ž . content IWC , and ice concentration N for hour 6 of the control case described in i Ž . Harrington et al. 1999 . This case, which we will call the thick liquid ASC or TLA, has Ž . a significant amount of LWC for the arctic environment spread through approximately Ž y3 . a 300-m depth. Drop concentrations are fairly small Q 14 cm due to the Bergeron– Ž Findeisen process that causes many of the small drops to evaporate Harrington et al., . 1999 . The simulated cloud produced weak ice precipitation from the liquid layer as the Ž y1 . Ž y1 . ice concentrations at these temperatures T ; y8 l are small N Q 0.18 l . This i field is a characteristic snapshot of the evolution of this mixed-phase cloud layer, which continually precipitated small amounts of ice. Such cloud evolution is similar to Ž . previously observed cases e.g. Pinto, 1998; Hobbs and Rangno, 1998 and to observed Ž . arctic clouds over the SHEBA site Intrieri et al., 1999; Curry et al., 2000 . The second and third cases used are shown in Fig. 8. The first is a thick ice ASC Ž . TIA, Fig. 8a and b and is characterized by a very thin upper liquid cloud with a Ž . Ž . y3 Ž . y3 Ž . y3 Ž . Fig. 7. Case 5CTRL at 6 h TLA . Panels: a LWC in g m , b N in cm , c IWC in g m , and d N c i in l y1 . relatively large amount of ice below. This case is from a period of rapid glaciation Ž . described in Harrington et al. 1999 . Liquid water contents are never greater than 0.07 g m y3 ; however, IWCs become as large as 0.15 g m y3 . While this IWC may seem somewhat large for the arctic, mixed-phase clouds with IWC values as high, and greater, Ž have been observed during the transition seasons e.g. Curry et al., 2000; Olsson and . Harrington, 2000 . Ž . The third case is a thin ASC TA, Fig. 8c and d and is characterized by a very thin Ž y3 . upper liquid layer LWC F 0.045 g m and a deep, but optically thin lower ice layer Ž y3 . IWC FF 0.028 g m . Such thin layers occurred in our numerical simulations between periods of glaciation. This tenuous ice layer is similar to the clear-sky ice Ž . crystal precipitation cases frequently observed in the Arctic see Curry et al., 1996 , Ž . though the temperature T ; y148C is warmer here. Some cases from SHEBA exhibit Ž . such a structure Curry et al., 2000 . These three cases, summarized for convenience in Table 1, are used in the systematic radiative computations discussed below. First, we examine the radiative properties of the Ž . Ž . Ž . y3 Ž . Fig. 8. Thick mixed-phase TIA and thin mixed-phase TA clouds. Panels: a LWC in g m , b IWC in g y3 Ž . y3 Ž . y3 m , c LWC in g m , and d IWC in g m . selected cases, using optical properties that correspond exactly to what is predicted by the microphysical model. Second, sensitivity studies are conducted to determine how Ž . important ice crystal habit and ice effective radius r might be to the radiative heat e,i budget of the cloud layer and surface. Table 1 Summary of bin model simulations used as surrogate data for the radiative computations Simulation Acronym Description y3 Ž Thick liquid ASC TLA 300-m-thick liquid cloud, small amount of ice LWC Q 0.25 g m , y3 . IWC Q 0.06 g m y3 Ž Thick ice ASC TIA Thick ice layer topped with very thin liquid cloud LWC Q 0.07 g m , y3 . IWC Q 0.15 g m Thin ASC TA Optically thin liquid layer overlying deep, but optically thin ice layer y3 y3 Ž . LWC Q 0.045 g m , IWC Q 0.028 g m 4.2. RadiatiÕe properties of the selected cases In this section, we present radiative calculations using bin-microphysical output from RAMS in conjunction with the bin optical properties scheme discussed above. Our intent Ž . here is to illustrate the potential influence of various mixed-phase liquid-ice combina- tions on the radiative budget. Since the model simulations assumed plate crystals, these are also assumed in the optical properties. Calculations presented below are for a solar Ž . zenith angle u of 608. The influence of u variation is discussed in later sections. Ž . Ž . Fig. 9 shows the solar absorption A A and the total IR cooling of the cloud ´ , along Ž . Ž . with the net surface solar F and infrared F fluxes spanning the range of net,sw net,lw Ž . simulated water paths WP s LWP q IWP for all three cases. The case of the mostly Ž . liquid TLA cloud shows logarithmic behavior of A A with WP, which is well-known Ž . see Stephens, 1978 . As might be expected, A A is significantly reduced in TIA as compared to TLA since IWC dominates the WP and ice particle concentrations are much smaller than the drop concentrations in TLA. Such an effect has also been shown Ž . Ž . Ž . Ž . Fig. 9. Solar absorption A A , IR cooling ´ , net surface solar F and infrared F fluxes for the net,sw net,lw three mixed-phase ASC cases. Symbols are labeled in the panels. Ž . by Sun and Shine 1994 . Additionally A A does not vary much with WP and is, in fact, fairly constant. There are two reasons for this behavior. First, ice concentrations are low Ž y1 . in these clouds typically Q 10 l allowing for high transmission. Second, as IWP increases, N generally decreases due the process of ice aggregation. Because N is i i decreasing with IWP, A A is not as large as might be expected when conserving WP alone. Note also that for TIA a few of the points tend toward the solutions for the predominantly liquid cloud. This is due to the fact that these model columns have a significant amount of liquid, and little ice. Ž . Ž . The total IR cooling of the cloud ´ is fairly constant in the liquid case TLA as y2 Ž long as WP R 30 g m , which is consistent with earlier work e.g. Stephens, 1978; . Curry and Herman, 1985 . However, ´ varies little with WP in TIA for the same reasons as discussed in the preceding paragraph. This variation of ´ with WP is especially important because ASC, which persist over the ice pack, have few sources of surface-generated buoyancy. Cloud dynamics in these cases are driven largely by Ž . cloud-top radiative cooling e.g. Pinto, 1998; Harrington et al., 1999 , which is characterized by ´. Additionally, our simulations are showing that the temperature Ž structure of the arctic BL can, at times, be strongly dependent on ´ Harrington et al., . 1999; Harrington and Olsson, 1999; Olsson and Harrington, 2000 . Since the transmission of solar radiation varies little with WP for TIA, so does F net,sw Ž . Ž . Fig. 9c . However, for cases where liquid dominates the WP TLA , F decreases net,sw logarithmically with WP, as expected. A preponderance of ice clouds can, therefore, cause a significant increase in surface absorption. Details of this depends on the state of Ž y2 . the ice pack up to about 30 W m as compared to liquid clouds. Of course, ice cloud Ž predominance begins to occur most readily during the fall transition season Curry et al., . 1997 , and during this time solar forcing is quite weak. However, as Fig. 9d shows, the transition to ice-laden clouds is expected to have a significant influence on the IR surface budget. Ž . Fig. 9d illustrates that for the case of mostly liquid clouds TLA , the surface can be warmed in the IR by the existence of overlying stratus if WP R 30 g m y2 . Additionally, it should be noted that our case contains a strong surface inversion typical of this Ž . y2 environment e.g. Curry, 1986; Pinto, 1998 , and this is the reason for the ; 20 W m warming of the surface by the overlying, mostly liquid, ASC. In the case of ice clouds Ž . TIA, TA , the cloud layer is quite transmissive in the IR because of the very low ice crystal concentrations. This leads to nearly a 60 W m y2 cooling of the surface, for all WPs, as compared to liquid clouds. Thus, the transition from the predominantly liquid clouds of summer to largely ice clouds in fall and winter should have a significant impact on the surface IR budget. 4.3. SensitiÕity: impact of ice habit Of necessity, the computation of ice crystal optical properties requires some specifi- cation of ice habit. However, it is not obvious whether habit plays a significant role in the computation of heatingrcooling of the cloud and surface. In this section we revisit the three mixed-phase cases and estimate the impact of ice habit on cloud radiative properties. Ž Fig. 10 shows the impact that two of the habits, columns and rosettes Mitchell et al., . 1996 , have on cloud and surface IR radiative properties. These habits were chosen because they have the largest differences in their optical properties. For comparison purposes, computations using the traditional equivalent volume sphere approximation are also included. Ž . Ž Fig. 10. Total IR cooling ´ and F for the three cases using various ice crystal habits labeled in the net,lw . panels . Ž . The thick, largely liquid ASC TLA reveals only a slight dependency of radiative heatingrcooling to changes in ice habit. This is to be expected as liquid dominates the Ž . WP. A weak impact due to habit is also found for the thin clouds TA in the 5–15 g y2 Ž . m WP range. However, once ASC contain greater than 50 ice mass as in TIA , and IWP R 25 g m y2 , ice crystal habit begins to have a significant effect on the IR heat y2 Ž budget of the cloud and surface. As Fig. 10 shows, ´ can be 5–20 W m smaller i.e. . more cloud cooling if rosette rather than columnar crystals dominate. Additionally, the Ž . net IR surface cooling F is reduced by a similar amount when rosette crystals are net,lw assumed. This results because rosettes have a larger total extinction cross-section due to Ž . their branched structure Mitchell and Arnott, 1994 . Note also that equivalent volume spheres tend to have a radiative impact similar to that of rosette crystals. In Fig. 11 differences between calculations using columns and equivalent volume spheres are shown, illustrating the influence of ice habit on the solar radiative properties Ž . of mixed-phase ASC. As Fig. 11a shows, clouds which are mostly ice IWPrWP R 0.5 absorb 4–15 W m y2 less solar radiation if columns are assumed instead of spheres. Rosette crystals also absorb more than columns; however, the difference is only between y2 Ž . 0.5 and 1 W m not shown . This results from the high degree of sensitivity of A A to Ž . the relative difference in d between the crystal habits Fig. 2 . e Clouds that consist mostly of ice show a weaker sensitivity of F than A A to net,sw changes in ice habit. Fig. 11b shows that F is 3–8 W m y2 greater for columns than net,sw for equivalent volume spheres. This result holds for a large range of m . Similar results are produced if spheres are replaced by rosette crystals. Overall, the total impact is not large and, therefore, ice habit may not be particularly important for computations of F . Still, ice habit may be important for computing the amount of solar energy net,sw deposited in the cloudy BL. 4.4. SensitiÕity: ice effectiÕe radius In this section we explore the sensitivity of the cloud and surface radiative budgets to the choice of r in bulk microphysical models. This is accomplished by using the IWC e,i from the bin microphysics and then assuming some value of r . According to Curry e,i Ž . and Ebert 1992 , r ; 40 mm is typical for winter-time arctic low-level clouds. e,i Ž However, the data from Beaufort Arctic Storms Experiment BASE, Pinto, 1998; Jiang . et al., 2000 , shows that mixed-phase ASC can have values up to about 300 mm. Thus, we use these two r values in our computations as estimates of two possible extremes e,i in mixed-phase ASC. Fig. 12a–d compares ´ and F for TLA and TIA using both the bin and bulk net,lw optical properties from RAMS simulations with r s 40 and 300 mm. The accurate bin e,i optical properties are used to illustrate the potential problems one could encounter by using a single value of to represent ice clouds in numerical models. Note that for both Ž . Ž . the thick liquid TLA and thick ice TIA cases, r s 300 compares best with the bin e,i computations. This might be expected since mixed-phase clouds produce large ice Ž . crystals and broad ice size spectra see Pinto, 1998; Harrington et al., 1999 , which results from the large ice supersaturations. Note the significant impact of the assumed Ž r on the radiative heat budget. For mixed-phase ASC that are mostly liquid such as e,i Ž . Fig. 11. Contour plots of differences between column and sphere solar radiative properties. Panel a shows A A Ž . Ž . Ž . Ž . Ž . columns – A A spheres while b shows F columns – F spheres . net,sw net,sw . y2 TLA , the impact of the choice of r is not especially significant. For WP R 40 g m , e,i both ´ and F differ by as much as 5 W m y2 depending on the choice of r . net,lw e,i Ž . As one might expect, however, for the ice cloud TIA , the influence of r is much e,i more substantial. As Fig. 12c and d shows, both ´ and F and can vary by 30 to 70 net,lw W m y2 for the chosen range of r and WP. In this particular case, a choice of r of 40 e,i e,i Ž . Ž . Ž . Fig. 12. Total cloud IR emission ´ and F for the thick liquid ASC TLA and thick ice ASC TIA net,lw Ž . Ž . Ž . Ž . cases. Panels a and b show the impact of various r for TLA while panels c and d show the same for e,i TIA. mm would produce 40 W m y2 too much IR cloud cooling and 70 W m y2 too little surface cooling, as compared to the calculation using the bin information. In fact, as Fig. 12d illustrates, for r of 40 mm F is positiÕe rather than negatiÕe, indicating a e,i net,lw warming instead of cooling for most WPs. These differences are significant even for Ž . thinner clouds. For the case of the thin ASC TA, not shown , in which WP ; 6–14 g m y2 , the choice of r produces differences of up to 20 W m y2 in both ´ and F . In e,i net,lw fact, these large differences begin to appear for IWP as small as 8 W m y2 . This illustrates the importance of correctly predicting not only IWP in numerical models, but also r if one wishes to produce a consistent and accurate radiative response and energy e,i balance. Fig. 13a and b shows the differences between bin computations and bulk computa- tions with r s 40 mm for A A and F . Differences between the bin and bulk model e,i net,sw with r s 300 mm are small and therefore not shown. As Fig. 13a shows, for m R 0.25 e,i and IWPrWP R 0.5, solar absorption is 5 and 20 W m y2 larger for r of 40 mm as e,i compared to the bin results. Additionally, for this range of m and IWPrWP, the solar Ž . Ž . Fig. 13. Contours are of differences between bin and bulk model computations. Panel a shows A A bin – A A Ž . Ž . Ž . Ž . bulk, r s 40 mm and panel b shows F bin – F bulk, r s 40 mm . e,i net,sw net,sw e,i surface net flux is 10–30 W m y2 smaller for of 40 mm. As in the case of the IR impacts, these effects occur consistently over a broad range of IWP and are important for IWP as small as R 8 g m y2 . These results point to the fact that correct microphysical characterization of ice clouds in the Arctic is of the utmost importance if accurate BL and surface energy budgets are to be computed. This is especially true for clouds composed mostly of ice, where disparities are the greatest.

5. Concluding remarks