A comparison of spectral bin and two-moment bulk mixed-phase cloud microphysics

Atmospheric Research 80 (2006) 46 – 66 www.elsevier.com/locate/atmos

Research Article

A comparison of spectral bin and two-moment bulk mixed-phase cloud microphysics Axel Seifert a,*, Alexander Khain b, Andrei Pokrovsky b, Klaus D. Beheng a a

Institut fu¨r Meteorologie und Klimaforschung, Universita¨t Karlsruhe/Forschungszentrum Karlsruhe, Karlsruhe, Germany b Institute of the Earth Sciences, The Hebrew University of Jerusalem, Jerusalem, Israel Received 28 February 2004; received in revised form 25 February 2005; accepted 22 June 2005

Abstract This numerical study investigates the representation of cloud microphysical processes in cloud resolving models and the effects of different characteristics of cloud condensation nuclei (CCN) on the evolution of deep convective storms. A comparison of several simulations is presented obtained by applying a spectral bin method and a two-moment bulk microphysical scheme to a deep convective cloud and a squall line. Both modeling approaches show similar results regarding the vertical structure of the clouds, updraft velocities and surface precipitation as well as the sensitivity of these parameters to changes in CCN characteristics. The simulated isolated cell reveals a strong effect to the variation of CCN concentration on the amount of surface precipitation, while the results for the squall line system depend on the specific treatment of the nucleation process. D 2005 Elsevier B.V. All rights reserved. Keywords: Cloud microphysics; Cloud parameterization; Precipitation formation

* Corresponding author. Deutscher Wetterdienst, Kaiserleistr. 42; 63067 Offenbach, Germany. Tel.: +49 69 8062 2729; fax: +49 69 8062 3721. E-mail address: [email protected] (A. Seifert). 0169-8095/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.atmosres.2005.06.009

A. Seifert et al. / Atmospheric Research 80 (2006) 46–66

47

1. Introduction One of the important factors influencing the formation of clouds and precipitation is atmospheric aerosol (Rosenfeld, 2000; Ramanathan et al., 2001), which can both increase or decrease the amount of surface precipitation depending in their concentration, composition and size distribution. One of the limitations of most atmospheric models is their inability to reproduce these aerosol effects explicitly. This is a major problem in climate modeling, e.g. studying the sensitivity of the hydrological cycle to anthropogenic pollutants, but neglecting aerosol effects can also affect the skill of quantitative precipitation forecasts (QPF). In detail, aerosol particles acting as CCN lead, due to their different characteristics (size distribution and chemical composition) to the formation of different cloud types, which can be categorized by their droplet number and mass densities as being typical continental or maritime and can, in addition, be affected by anthropogenic pollution. In this way aerosol particles influence the microphysical and dynamical evolution of individual clouds as well as larger-scale cloud system. Commonly applied parameterizations of the microphysical processes rely on the prediction of the liquid/ice contents of a limited number of hydrometeor classes (Kessler, 1969; Lin et al., 1983). Using the mass contents only, this type of parameterization can be classified as one-moment schemes. During the last decades this approach has shown substantial skill in prediction of the main features of cloud systems, but since these models carry no information about the size or number of cloud droplets they can hardly simulate aerosol-cloud effects. In addition, it is widely assumed that these schemes are not sufficient for reaching the goals of mesoscale QPF (USWRP, 2001; Fritsch and Carbone, 2004). However, two different microphysical approaches are available going beyond these simple parameterizations. First, spectral bin models which explicitly predict the spatiotemporal behavior of a number of size categories for each hydrometeor type (see review by Khain et al., 2000). Most of these models consider CCN as part of the aerosol distribution from which droplets are formed by heterogenous nucleation. By this approach a very large number of model variables has to be handled which is currently and in near future too expensive for regional climate models or operational QPF, but is a very attractive method for basic research. Second, two-moment parameterizations which use, in addition to mass variables, the number concentrations of the liquid and ice hydrometeors (Cotton et al., 1986; Murakami, 1990; Ferrier, 1994; Meyers et al., 1997; Reisner et al., 1998). At present these two-moment schemes are the most promising microphysical compromise to be used in future operational forecast models for mesoscale cloud-resolving QPF since they show a forecast skill superior to commonly used one-moment cloud microphysical schemes (Reisner et al., 1998). These schemes are computationally efficient, since the number of variables is only increased by a factor of two compared to a one-moment mixed-phase scheme. Moreover, in its most rigorous formulation the two-moment approach should be able to describe the microphysical processes including aerosol effects on a sound physical basis. Recently Seifert and Beheng (2005a) presented a new two-moment scheme which explicitly considers different types of cloud droplet spectra as they originate from different aerosols. Applying this scheme to a wide variety of atmospheric conditions they have

48

A. Seifert et al. / Atmospheric Research 80 (2006) 46–66

shown that aerosol effects expressed in form of maritime and continental cloud droplet spectra lead to a diverse development of clouds and precipitation (Seifert and Beheng, 2005b). The main purpose of the present paper is to prove that (a) the response of the twomoment scheme of Seifert and Beheng (2005a) to changes in CCN, respectively, the cloud droplet number concentration, is similar to the spectral bin microphysical model by Khain et al. (2000, 2001), and (b) that for some clouds the precipitation efficiency is highly sensitive to CCN assumptions while other clouds might be less sensitive. Several comparisons of spectral bin and bulk microphysical model results have been presented previously. Early attempts in the 70s and 80s were restricted to warm phase microphysics and based on simple one-moment bulk schemes (Silverman and Glass, 1973; Shiino, 1983). Later on more sophisticated bin and bulk models have been developed and compared including ice phase processes (Geresdi, 1998) or CCN sensitivity of warm phase processes (Feingold et al., 1998). The results of all these investigations showed more or less strong disagreements between results obtained by applying bin or bulk schemes. Amongst others it turns out that especially the Kessler formulation using a threshold value for autoconversion initiation is not adequate to achieve a reasonable agreement with a spectral bin model (Shiino, 1983; Beheng and Doms, 1986). The present study is dedicated to a comparison of results from a bin microphysics scheme with those from an advanced two-moment scheme with both covering the full mixed-phase microphysics of deep convective storms or squall lines and including CCN effects on warm as well as ice phase microphysics. The next section gives an overview of the spectral bin model as well as the two-moment scheme used in this study. In Sections 3 and 4 two different test cases are discussed in detail. Conclusions are presented in Section 5.

2. Model descriptions The dynamical framework of this study is the two-dimensional Hebrew University Cloud Model (HUCM). The dynamical and thermodynamical equations solved in HUCM have been described by Khain and Sednev (1996) as well as Khain et al. (2000, 2001, 2004). The spectral bin microphysics implemented in HUCM is based on solving prognostic equations for size distributions of seven hydrometeor types: water drops, three types of ice crystals (columnar, plate-like and dendrites), snowflakes (aggregates), graupel and hail/frozen drops. To simulate the effects of atmospheric aerosols on the cloud development and precipitation formation a size distribution function for atmospheric aerosol particles, playing the role of cloud condensation nuclei (CCN), is considered. Each size distribution is represented by 33 mass doubling bins, which gives a sum of 264 prognostic variables for the microphysics. The maximum size of all hydrometeors is defined by an equivalent drop diameter of 7 mm. All relevant microphysical processes/interactions including droplet nucleation, primary and secondary ice generation, condensation/evaporation of drops, deposition/sublimation of ice particles, freezing/melting, and mutual collisions between the various hydrometeors are calculated explicitly. The dependence of the collision efficiencies on height, as well

A. Seifert et al. / Atmospheric Research 80 (2006) 46–66

49

as effects of turbulence on the rate of collisions are taken into account. To describe the effect of turbulence on the collision rate (collision efficiency) the collection kernel is multiplied with the factors given in Table 1 of Khain et al. (2004). Collisional breakup is neglected in the spectral bin model. The two-moment scheme which is used in this study is the two-moment mixed-phase scheme as described in detail by Seifert and Beheng (2005a), which was originally implemented in the 2nd generation Karlsruhe Mesoscale Model (KAMM2). For this comparison study the scheme has been incorporated in HUCM. Hence, both microphysical schemes are compared in a modeling framework with identical dynamics, numerics (e.g. advection) and physical parameterizations. Note that for the two-moment scheme novel parameterizations comprising autoconversion, accretion and self-collection of water drops have been derived by Seifert and Beheng (2001) directly from the stochastic collection equation itself, following the theoretical formulation of Beheng and Doms (1986) as well as Doms and Beheng (1986). In the Seifert and Beheng (2005a) we introduced a modified version of this warm rain scheme using slightly different coefficients based on the Pinsky et al. (2001) collection kernel and including a parameterization of collisional breakup. It should be noticed that since the two-moment scheme predicts also number concentrations it is able to describe effects of variations of cloud droplet number concentration on the efficiency of precipitation formation. In contrast to most other schemes, the new autoconversion parameterization further considers aging of the cloud droplet size distribution with time by relying on a dynamic similarity theory. Using a simple one-dimensional rain shaft model Seifert and Beheng (2001) have already shown that this scheme compares well with a spectral bin model of droplet growth (see also Seifert (2002) for the new version). Based on this warm phase parameterization, and following the previous work of Reisner et al. (1998) and others, Seifert and Beheng (2005a) developed a mixed-phase cloud scheme using number and mass concentrations as variables for the five hydrometeor classes cloud droplets, raindrops, cloud ice, snow and graupel. In previous studies, this scheme has shown its ability to simulate the development of mixed-phase multicell and supercell thunderstorms as well as aerosol effects on these cloud systems (Seifert and Beheng, 2005b; Bertram et al., 2004). Similar to the spectral bin microphysics used in HUCM the two-moment bulk scheme includes CCN effects and within this comparison study both models use the same CCN activation relations for maritime and continental CCN given by NCCN ðS Þ ¼ CCCN S j

ð1Þ

with S = supersaturation and N CCN = number of cloud condensation nuclei. The coefficients are C CCN = 1.26  103 cm 3 and j = 0.308 for continental conditions or C CCN = 1.0  102 cm 3 and j = 0.462 for maritime conditions (Khain et al., 2001). In case of maritime CCN it is assumed that at S max = 1.1% all CCN are already activated and no further activation takes place. The supersaturation is that as explicitly resolved by the model. This approach has some deficiencies, since the modeled nucleation process, especially of the bulk scheme, is known not to be independent of the chosen numerical time step. In the spectral bin scheme an aerosol budget is included, but currently no CCN sources are taken into

50

A. Seifert et al. / Atmospheric Research 80 (2006) 46–66

account. In this scheme, Eq. (1) is only applied during the model initialization while later on a prognostic equation is solved for the aerosol size distribution as described by Khain et al. (2001). This includes the calculation of the critical radius according to Ko¨hler’s theory and the activation of all CCN exceeding this particle size (droplet nucleation). CCN smaller than the critical size remain non-activated. As a result of this nucleation scheme, the concentration of CCN decreases continuously. In the two-moment scheme Eq. (1) is used in a quasi-stationary sense, thus providing always the same number of activated droplets for a given supersaturation. For specific conditions, this difference in the CCN budget assumptions can lead to a serious difference in the evolution of convective systems as will be shown below. However, for most parts of this comparison study, it is sufficient that both models treat the cloud droplet nucleation in a similar way using Eq. (1) with different coefficients for maritime or continental CCN. This results in similar spatial fields of the cloud droplet number concentrations which triggers the following microphysical development. Heterogenous ice nucleation in both models is parameterized as a function of supersaturation with respect to ice using the empirical formula given by Meyers et al. (1992). As described in Seifert and Beheng (2005a) the two-moment bulk scheme is based on the drop–drop collection kernel of Pinsky et al. (2001) with enhancement factors given by Pinsky and Khain (2002) to account for turbulence effects. Since in the HUCM version used for the current study turbulence effects are taken into account as given in Table 1 of Khain et al. (2004), the autoconversion parameter k cc is accordingly increased from k cc = 10.6  109 cm3 g 2 s 1 to a value of k cc = 15  109 cm3 g 2 s 1. The increased value for k cc applies also to the self-collection of cloud droplets. The characteristics of the particle types including fall velocities, particle densities or the parameterizations of particle conversions are different between the spectral bin and the two-moment bulk scheme. Since the formulation of these relations in the bulk scheme is based on simple power-law approximations, adapting the mass–size- or velocity–sizedependencies used in the spectral bin model is not possible. In addition, the spectral bin microphysics in HUCM distinguishes graupel from frozen drops/hail. Therefore it has been necessary to change the definition of the graupel class in the bulk scheme to a combined graupel–hail class where it is considered that particle density in that class increases with size. The relations used for the graupel–hail class are given in Table 1. More details on the both microphysical models can be found in Khain and Sednev (1996) as well as in Khain et al. (2004), and references therein and in Seifert and Beheng (2005a), respectively. Another modification refers to the exponents of the generalized gamma distributions describing the various particle spectra which have been used throughout this study (see Table 1 Parameters/relations used for the graupel–hail hydrometeor class in the two-moment bulk scheme (diameter D in m, terminal fall velocity v in m/s, drop mass x in kg) Size–mass relationship Velocity–mass relationship Min. mean mass Max. mean mass

D = 0.11 x 0.3 v = 700 x 0.25 x¯min = 2.6  10- 10 x¯max = 5.0  10- 4

A. Seifert et al. / Atmospheric Research 80 (2006) 46–66

51

Table 2 Exponents of the generalized C-distribution f(x) = Ax m exp(Bx l ) with particle mass x as used for the different hydrometeor types of the two-moment scheme Cloud droplets Raindrops Cloud ice Snowflakes Graupel

m

l

1 2/3 1/3 1/2 1

1/2 1/3 1/3 1/3 1/3

Table 2). These values differ only slightly from Seifert and Beheng (2005a) resulting in a cloud droplet distribution which is skewed more towards larger droplets and the distributions for cloud ice and snow are broader. This short overview has shown that many microphysical parameters inherent in both schemes are consistently formulated and therefore it should be possible to achieve a reasonable agreement between corresponding results.

3. Case 1: single cell deep convection The first case for the comparison is the well-documented simulation of an isolated deep convective cloud based on the sounding from 13 August 1999, Midland/Texas (Khain et al., 2001). To elaborate the effects of different CCN or different cloud droplet concentrations on the warm phase coagulation and the mixed-phase microphysics, this cloud is simulated assuming continental as well as maritime aerosol. For the more realistic continental CCN this is an example of a deep convective cloud sustaining a high amount of supercooled liquid water at upper levels and most precipitation develops via ice phase processes. A more general and detailed description of the cloud and the environmental conditions is given by Rosenfeld and Woodley (2000) as well as by Khain et al. (2001). For all simulations of this case the two-dimensional domain is 64 km wide and 15 km high. The model resolution has been chosen as a 250-m grid spacing in horizontal and 125 m in vertical direction. Convection has been initiated by artificial differential heating in the boundary layer as described in Khain et al. (2004). In order to discuss the basic evolution of this cloud, two simulations are presented assuming continental CCN characteristics only. The results are presented in Figs. 1–4. Figs. 1 and 3 show composite pictures of the mass contents of cloud, rain, ice, snow and graupel particles after 30 min and 60 min after model initialization. In addition, the corresponding surface precipitation rate is depicted. Here, and in all following figures, the 3 ice particle distributions (plates, columns, and dendrites) of the spectral model are combined to dcloud iceT and in all plots, except those showing mass spectra, the hail/frozen drop category is added to dgraupelT. Figs. 2 and 4 show mass density spectra at selected grid points within the convective updraft (4 km and 10 km height) and outside the updraft where no cloud water exists. After 30 min the convective cloud is in its development stage and the cloud top has already reached a height of 12 km. Within the updraft core a mixture of all different

52

A. Seifert et al. / Atmospheric Research 80 (2006) 46–66 cloud

a) spectral bin:

b) two-moment bulk: 12

10

10

z in km

14

12

z in km

14

8 6

6 4

2

2

0

0

12

10

10

graupel 5.00 1.00 0.50 0.10 0.01

ice

8

4

4

2

2

5.00 1.00 0.50 0.10 0.01

0 5 4 3 2 1 0

0 5 4 3 2 1 0

5.00 1.00 0.50 0.10 0.01

6

R in mm/h

R in mm/h

z in km

14

12

z in km

14

8

rain 5.00 1.00 0.50 0.10 0.01

8

4

5.00 1.00 0.50 0.10 0.01

16 17 18 19 20 21 22 23 24 25 26 27 28

x in km

6

snow

16 17 18 19 20 21 22 23 24 25 26 27 28

x in km 3

Fig. 1. Hydrometeor mass densities in g m for (a) the spectral bin as well as (b) the two-moment bulk scheme after 30 min simulation time of the Texas case (blue = cloud, red = rain, yellow = cloud ice, green = snow, grey = graupel/hail). In addition, the surface precipitation rate in mm/h is shown (herein is zero).

particle types is present and ice formation becomes dominant at higher levels only. Cloud water is sustained up to 10 km height, ice nucleation at this stage is mostly heterogenous and snow is present only at the outer flanks of the cloud where the liquid water content is low. The dominant particle type is graupel formed from frozen drops as well as from rimed ice crystals. Most microphysical features show up using both cloud schemes, but some differences are obvious, e.g. the two-moment bulk scheme predicts more rainwater at mid-levels. As seen in Fig. 2 the mass density spectra of cloud droplets show a very good agreement above cloud base, i.e. the distribution simulated by the bin model is well represented by the gamma distribution of the two-moment scheme. At 10 km height both models predict cloud water co-existing with cloud ice and graupel. The spectra of all hydrometeor types calculated by both microphysical schemes are well correlated. Outside the updraft some unrimed aggregates (snow) are predicted by both microphysics schemes with a more than satisfactory agreement of the particle spectra. After 60 min (Fig. 3) a fully developed deep convective cloud has formed with a broad anvil consisting of small ice crystals, snow and graupel. The dominant source of these ice particles is homogenous freezing of cloud droplets at the top of the major updraft which still contains supercooled liquid water up to 10 km height. Again both

0:30:00.0, x = 21 km, z = 4 km

0:30:00.0, x = 21 km, z = 10 km

rain graupel

ice frozen drops / hail

1*101 0 5*10 1*100 5*10-1 1*10-1 5*10-2 1*10-2

2

cloud snow

rain graupel

1*10 5*101

ice frozen drops / hail

mass spectra in g m–3

cloud snow

mass spectra in g m–3

mass spectra in g m–3

0:30:00.0, x = 25 km, z = 9 km

2

1*10 5*101 1*101 0 5*10 1*100 5*10-1 1*10-1 5*10-2 1*10-2

0.01

0.1

D in mm

1.0

10.0

cloud snow

rain graupel

ice frozen drops / hail

1*101 0 5*10 1*100 5*10-1 1*10-1 5*10-2 1*10-2

0.01

0.1

D in mm

1.0

10.0

0.01

0.1

1.0

10.0

D in mm

Fig. 2. Mass density spectra in g m 3 at selected grid points (solid = spectral bin, dashed = two-moment bulk) at simulation time t = 30 min. For better interpretation, the abscissa values are given by the equivalent drop diameter D ranging from 2 Am to 10 mm. The largest grid point of the bin model is at 7 mm equivalent drop size (left and middle plate: grid points within the convective updraft; right plate: grid point outside the convective updraft). Note that the frozen drops/hail category is not considered in the two-moment scheme.

A. Seifert et al. / Atmospheric Research 80 (2006) 46–66

2

1*10 5*101

53

54

A. Seifert et al. / Atmospheric Research 80 (2006) 46–66 cloud

b) two-moment bulk: 14

12

12

10

10

z in km

14

8 6

4 2

0

0 14

12

12

10

10

z in km

14

8 6

4 2

0 5 4 3 2 1 0

0 5 4 3 2 1 0

10 15 20 25 30 35 40 45 50 55 60

x in km

ice 5.00 1.00 0.50 0.10 0.01

6

2

5

graupel 5.00 1.00 0.50 0.10 0.01

8

4

0

5.00 1.00 0.50 0.10 0.01

6

2

5.00 1.00 0.50 0.10 0.01

rain

8

4

R in mm/h

R in mm/h

z in km

z in km

a) spectral bin:

snow

0

5

10 15 20 25 30 35 40 45 50 55 60

5.00 1.00 0.50 0.10 0.01

x in km

Fig. 3. As Fig. 1, but at t = 60 min. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

micro-physical models agree reasonably well, but the amount of snow is much lower and located at lower level in the two-moment bulk scheme. This can be traced back to the different definitions of the class dsnowT in the spectral and the two-moment scheme: In the spectral scheme the classification depends on the mass of snowflakes whereas in the two-moment scheme on the degree of riming. The latter accounts for the more abundant snow mass in the lower levels. The spatial distribution of graupel and rain water are in good agreement, although the bulk model predicts more graupel and rain within the updraft. The surface rain rate reaches about 2 mm h 1 in both simulations. Looking at the mass density spectra depicted in Fig. 4 reveals that the spectral bin model predicts larger raindrops and frozen drops at 5 km height and a bimodal graupel distribution at 11 km height. Also the cloud ice distribution at this level show larger particles in the bin model. These differences will be further discussed below. So far, only the two simulations assuming continental CCN have been presented. We now turn to the differences occurring due to the application of different CCN characteristics. Figs. 5 and 6 show the cloud droplet number concentrations as predicted by the bin and the bulk model for the different CCN assumptions during the development stage of the cloud (20 min and 30 min). As expected, drop nucleation mainly happens at cloud base, but in addition both schemes predict significant in-cloud nucleation which can be important for the anvil structure (Pinsky and Khain, 2002;

1:00:00.0, x = 30 km, z = 5 km

rain graupel

ice frozen drops / hail

1

1*10 0 5*10 0

1*10 -1 5*10 -1

1*10 -2 5*10 -2

1*10

0.1

D in mm

1.0

10.0

cloud snow

rain graupel

ice frozen drops / hail

1

1*10 0 5*10 0

1*10 -1 5*10 -1

1*10 -2 5*10 1*10

0.01

2

1*10 1 5*10

mass spectra in g m–3

cloud snow

mass spectra in g m–3

mass spectra in g m–3

1:00:00.0, x = 30 km, z = 11 km

2

1*10 1 5*10

-2

0.1

D in mm

1.0

10.0

rain graupel

ice frozen drops / hail

1

1*10 0 5*10 0

1*10 -1 5*10 -1

1*10 -2 5*10 1*10

0.01

cloud snow

-2

0.01

0.1

1.0

10.0

D in mm

Fig. 4. As Fig. 2, but at t = 60 min (left plate: grid point below cloud base; middle plate: grid point within the convective updraft; right plate: grid point above the level of homogenous freezing). Note that the frozen drops/hail category is not considered in the two-moment scheme.

A. Seifert et al. / Atmospheric Research 80 (2006) 46–66

1:00:00.0, x = 30 km, z = 2 km 2

1*10 1 5*10

55

56

A. Seifert et al. / Atmospheric Research 80 (2006) 46–66

b) two-moment bulk: 20 min

14

14

12

12

10

10

z in km

z in km

a) spectral bin: 20 min

8 6

6

4

4

2

2 0

0 15 16 17 18 19 20 21 22 23 24 25 26 27

15 16 17 18 19 20 21 22 23 24 25 26 27

x in km

x in km

c) spectral bin: 30 min

d) two-moment bulk: 30 min

14

14

12

12

10

10

z in km

z in km

8

8 6

1000 750 500 250 100 0

6

4

4

2

2

0

Nc

8

0 15 16 17 18 19 20 21 22 23 24 25 26 27

15 16 17 18 19 20 21 22 23 24 25 26 27

x in km

x in km

Fig. 5. Cloud droplet number concentrations in cm 3 at t = 20 min (a, b) and t = 30 min (c, d) using continental CCN assumptions.

Fridlind et al., 2004). Although some differences between the bin and the bulk representation exist, we found that both schemes show a similar response to the change of the CCN type from continental to maritime, i.e. the cloud droplet number concentration decreases from about 750 cm 3 to values of 50 cm 3 and below. Hence, the effect of the different CCN assumptions, i.e. maritime vs. continental, is much larger than the disagreement due to the specific representation used in the two microphysical schemes. Figs. 7 and 8 show the spatial structure and mass density spectra after 30 min for the maritime case. The larger mean size of the cloud droplets leads to a rapid rain formation, and rain has already fallen below cloud base. Also the mass density spectra show a significant change compared to the continental case: the cloud droplet distribution is shifted toward larger droplets and rain has already formed at 4 km height. The spectral bin model predicts much larger raindrops, which – as a consequence – freeze faster and form dfrozen drops/hailT. This difference is also visible at higher levels where the bin model shows a broad or even bimodal distribution of graupel. One reason for the appearance of large raindrops in the bin model might be that collisional breakup is not taken into account in the HUCM spectral bin microphysics model, i.e. the coalescence efficiency is assumed to be

A. Seifert et al. / Atmospheric Research 80 (2006) 46–66

b) two-moment bulk: 20 min

14

14

12

12

10

10

z in km

z in km

a) spectral bin: 20 min

8 6

8 6

4

4

2

2 0

0 15 16 17 18 19 20 21 22 23 24 25 26 27

15 16 17 18 19 20 21 22 23 24 25 26 27

x in km

x in km

c) spectral bin: 30 min

d) two-moment bulk: 30 min

14

14

12

12

10

10

z in km

z in km

57

8 6

100 75 50 25 10 0

6

4

4

2

2

0

Nc

8

0 15 16 17 18 19 20 21 22 23 24 25 26 27

x in km

15 16 17 18 19 20 21 22 23 24 25 26 27

x in km Fig. 6. As Fig. 5, but for maritime CCN.

equal to one. This can lead to the formation of spectra containing many too large particles. A major problem of the two-moment scheme might be the missing frozen drop category since frozen drops are part of the graupel class. In addition, a two-moment scheme is – by definition – not able to predict bimodal distributions within one particle category. As suggested by an anonymous reviewer, the problem could also be related to the underestimation of the size of raindrops produced by autoconversion as discussed by Caro et al. (2004). Although all our previous results have shown that this problem does not occur in the Seifert–Beheng autoconversion scheme, we cannot exclude that similar problems apply here, too. To discuss the time evolution of surface rain intensities Hovmo¨ller diagrams are presented in Fig. 9. It is recognized that the spatio-temporal precipitation patterns are in reasonable agreement between the two microphysical schemes. In the continental case the spectral bin model results in a bi- or even trimodal time pattern caused by the various different rain formation pathways, e.g. via frozen drops, heterogenous or homogenous ice nucleation. The two-moment bulk scheme exhibits also several peaks, but rain rates and timing differ somewhat from the spectral bin scheme. Assuming maritime CCN leads to a faster and much stronger precipitation formation for both schemes. Overall the rain rates are about a factor of 10 larger in both maritime

58

A. Seifert et al. / Atmospheric Research 80 (2006) 46–66 cloud

b) two-moment bulk: 14

12

12

10

10

z in km

14

8 6

4 2

0

0 14

12

12

10

10

z in km

14

8

x in km

6

8

4

2

2

0 5 4 3 2 1 0

0 5 4 3 2 1 0

x in km

graupel 5.00 1.00 0.50 0.10 0.01

x in km

ice 5.00 1.00 0.50 0.10 0.01

6

4

16 17 18 19 20 21 22 23 24 25 26 27 28

5.00 1.00 0.50 0.10 0.01

6

2

5.00 1.00 0.50 0.10 0.01

rain

8

4

R in mm/h

R in mm/h

z in km

z in km

a) spectral bin:

snow

16 17 18 19 20 21 22 23 24 25 26 27 28

5.00 1.00 0.50 0.10 0.01

x in km Fig. 7. As Fig. 1, but for maritime CCN.

simulations compared to their continental counterparts. In the maritime case the first rain event occurring after 40–50 min caused by warm rain formation is dominant. With the strong sensitivity on CCN characteristic in mind, the agreement between the spectral bin and the two-moment bulk scheme regarding surface precipitation is quite satisfying. This is also supported by comparing time series of the maximum mass contents shown in Fig. 10. The two simulations assuming continental CCN develop a high cloud water content about 4 g m 3 in the early stage of the cloud evolution. Precipitation particles form after 25 min, with a rapid freezing of raindrops leading to a low rainwater content in the spectral bin model whereas a much higher rainwater content appears in the bulk scheme. The time evolution of the maximum ice content is very similar, while the spectral bin model retains more snow after 120 min compared to the bulk scheme. Assuming maritime CCN leads to a faster rain formation thus diminishing the maximum cloud water content considerably to about 2 g m 3. This is shown by both microphysical schemes. Again the differences in the rainwater content and the somewhat later graupel formation in the bulk scheme are most obvious. As already discussed, this is probably caused by the different sizes of raindrops predicted by the two microphysics schemes. In Fig. 11 time series of the accumulated surface precipitation and the maximum updraft velocities are shown for maritime and continental CCN. A reasonable agreement is

rain graupel

ice frozen drops / hail

1*101 5*100 1*100 5*10-1 1*10-1 5*10-2 1*10-2

0:30:00.0, x = 21 km, z = 10 km cloud snow

rain graupel

1*102 5*101

ice frozen drops / hail

mass spectra in g m–3

cloud snow

1*102 5*101

mass spectra in g m–3

mass spectra in g m–3

0:30:00.0, x = 21 km, z = 4 km

1*101 5*100 1*100 5*10-1 1*10-1 5*10-2 1*10-2

0.01

0.1

D in mm

1.0

10.0

0:30:00.0, x = 25 km, z = 9 km cloud snow

rain graupel

ice frozen drops / hail

1*101 5*100 1*100 5*10-1 1*10-1 5*10-2 1*10-2

0.01

0.1

1.0

D in mm Fig. 8. As Fig. 2, but for maritime CCN.

10.0

0.01

0.1

D in mm

1.0

10.0

A. Seifert et al. / Atmospheric Research 80 (2006) 46–66

1*102 5*101

59

60

A. Seifert et al. / Atmospheric Research 80 (2006) 46–66

b) two-moment bulk: continental CCN

2.0

2.0

1.8

1.8

1.6

1.6

1.4

1.4

1.2 1.0 R in mm/h

0.8

t in h

t in h

a) spectral bin: continental CCN

0.4 0.2

1.0 R in mm/h

0.8

5.0 3.0 2.0 1.0 0.5 0.0

0.6

1.2

5.0 3.0 2.0 1.0 0.5 0.0

0.6 0.4 0.2

0.0

0.0 0

5 10 15 20 25 30 35 40 45 50 55 60

0

x in km

x in km

d) two-moment bulk: maritime CCN

2.0

2.0

1.8

1.8

1.6

1.6

1.4

1.4

1.2 1.0 R in mm/h 50 30 20 10 5 0

0.6 0.4 0.2 0.0

t in h

t in h

c) spectral bin: maritime CCN

0.8

5 10 15 20 25 30 35 40 45 50 55 60

1.2 1.0 R in mm/h

0.8

50 30 20 10 5 0

0.6 0.4 0.2 0.0

0

5 10 15 20 25 30 35 40 45 50 55 60

x in km

0

5 10 15 20 25 30 35 40 45 50 55 60

x in km

Fig. 9. Hovmo¨ller diagrams showing surface precipitation in mm/h from the 4 Texas case simulations applying spectral bin (a, c) vs. two-moment bulk (b, d) microphysics and assuming continental (a, b) vs. maritime CCN (c, d) (note the different scales of rainrate R for continental and maritime CCN).

achieved for accumulated precipitation, since timing as well as the amount of precipitation is captured by the two-moment bulk scheme. Although the difference in total accumulated precipitation of about 50% is quite large, a better agreement can hardly be expected, since we are dealing with a small scale, highly sensitive system. An overall good agreement is further affirmed by the comparison of the maximum updraft velocities. An almost perfect agreement is found in the early stage of cloud development. Later on the differences between maritime and continental CCN assumptions are larger than the disagreement between the spectral bin and the two-moment bulk scheme. Both microphysical models show a longer lifetime of the updraft core in the continental case. In summary, this case shows that the problems of the two-moment bulk scheme – compared the HUCM spectral bin model – are the underestimation of the size of raindrops and the inability to predict bimodal distributions. However, for many important predicted parameters a good agreement has been found and especially the effects of different CCN on the cloud microphysics and precipitation formation are, at least in this case, much larger than the differences between the spectral bin and the two-moment bulk scheme. Therefore this comparison indicates that the two-moment bulk scheme is able to simulate the different evolution of maritime and continental

A. Seifert et al. / Atmospheric Research 80 (2006) 46–66

a) spectral bin: continental CCN

b) two-moment bulk: continental CCN 5

5 ice

rain graupel

cloud snow

4

4

3

3

L in g/m3

L in g/m3

cloud snow

2

rain graupel

ice

2

1

1

0

0 0

60

120

0

60

t in min

120

t in min

c) spectral bin: maritime CCN

d) two-moment bulk: maritime CCN

8

8 cloud snow

rain graupel

ice

cloud snow

6

rain graupel

ice

6

L in g/m3

L in g/m3

61

4

2

4

2

0

0 60

0

0

120

t in min

60

120

t in min

Fig. 10. Time series of maximum values of hydrometeor mass densities in g m 3 from the 4 Texas case simulations applying spectral bin (a, c) vs. two-moment bulk (b, d) micro-physics and assuming continental (a, b) vs. maritime CCN (c, d) (note the different scales of Y-axis for continental and maritime CCN).

a) accumulated precipitation

b) maximum vertical velocities

5.0 spectral bin - continental two-moment bulk - continental

40

spectral bin - maritime two-moment bulk - maritime

spectral bin - maritime two-moment bulk - maritime

30

w in m/s

N in mm

1.0

spectral bin - continental two-moment bulk - continental

0.5

0.1 0.05

20

10

0.01

0 0

60

t in min

120

0

60

120

t in min

Fig. 11. Time series of grid averaged accumulated surface precipitation in mm (a) and maximum vertical velocity in m s 1 (b) from the 4 Texas case simulations applying spectral bin vs. two-moment bulk microphysics and assuming continental vs. maritime CCN as indicated.

62

A. Seifert et al. / Atmospheric Research 80 (2006) 46–66

clouds due to CCN effects. Finally, it should not be overlooked that in the 2D dynamical framework applied here some effects might be exaggerated as emphasized by Caro et al. (2004).

4. Case 2: formation of a squall line The second case is the formation of a typical maritime convective system using profiles from the 1200 UTC sounding aboard the Canadian ship Quadra on day 261 of the GATE field experiment. This sounding has been used in many previous modeling studies devoted to maritime convection (Turpeinen and Yau, 1981; Simpson et al., 1982; Ferrier and Houze, 1989). In contrast to the Texas cloud, this convective system is to a large extent dominated by warm phase processes. To study the sensitivity of the microphysical models for that case the maritime as well as continental CCN relations are applied. The twodimensional slab symmetric model domain is 128 km wide and has a height of 15 km with a resolution of 250 m in the horizontal direction and 125 m in the vertical. Fig. 12 shows the spatio-temporal evolution of the surface precipitation from the 4 model runs using spectral bin vs. two-moment bulk microphysics and maritime as well as continental CCN. In all cases a first precipitation event occurs after about 30 min with

b) two-moment bulk: continental CCN

3.0

3.0

2.5

2.5

2.0

2.0

1.5 R in mm/h 1.0

t in h

t in h

a) spectral bin: continental CCN

R in mm/h 1.0

100 80 60 40 20 0

0.5

1.5 100 80 60 40 20 0

0.5 0.0

0.0 0

20

40

60

80

100

120

0

20

40

x in km

c) spectral bin: maritime CCN

80

100

120

d) two-moment bulk: maritime CCN

3.0

3.0

2.5

2.5

2.0

2.0

1.5 R in mm/h 1.0

100 80 60 40 20 0

0.5 0.0

t in h

t in h

60

x in km

1.5 R in mm/h 1.0

100 80 60 40 20 0

0.5 0.0

0

20

40

60

80

x in km

100

120

0

20

40

60

80

100

120

x in km

Fig. 12. Hovmo¨ller diagrams showing the surface precipitation in mm h 1 from the 4 GATE case simulations applying spectral bin (a, c) vs. two-moment bulk (b, d) microphysics and assuming continental (a, b) vs. maritime CCN (c, d).

A. Seifert et al. / Atmospheric Research 80 (2006) 46–66

63

instantaneous rain rates exceeding 100 mm h 1. After this first event the surface precipitation rate decreases while the region of weak precipitation expands in up- and down-wind direction. The simulation using spectral bin microphysics and the continental CCN relation (shown in Fig. 12a) develops some minor secondary events until, after 90 min, an intense, quasi-stationary squall line system is formed which again produces very high rain rates up to 180 mm h 1. The corresponding simulation with the two-moment bulk scheme depicted in Fig. 12b shows a similar structure, but the squall line is weaker, less stable and decays after about one hour. Later on, smaller convection cells are produced by this simulation. Assuming maritime CCN in the spectral bin microphysics (Fig. 12c) leads to a complete suppression of secondary deep convection and no squall line develops, instead only weak precipitation occurs dying out after about two hours simulation time. In that case the two-moment bulk scheme (Fig. 12d) results in a remarkably different evolution since secondary deep convection is simulated, but less intense than for the corresponding continental CCN case. The reason for this difference is that the spectral bin model predicts a strong decrease of CCN in the maritime case leading to very low cloud droplet number concentrations (below 10 cm 3) in the secondary cells, which are shallow clouds only. In comparison, the nucleation treatment in the two-moment bulk scheme implies a constant background of CCN, so that the cloud droplet number concentrations for the secondary cells are as high as for the primary convection (~100 cm 3). To demonstrate this effect of the different nucleation schemes a 5th simulation has been performed changing the nucleation treatment of the spectral bin microphysics to an simple diagnostic dbulk CCNT scheme as it is used in the bulk model. The results are depicted in Fig. 13 showing secondary convection similar to the maritime two-moment bulk case. This effect can be seen even more clearly in the time series of the accumulated surface precipitation depicted in Fig. 14. This diagram reveals that the GATE case simulation is to a large extent a dynamically forced system, since four of the five simulations show a very similar rain accumulation. Only the spectral bin model assuming maritime CCN with its strong decrease of available CCN, which leads to the suppression of any secondary deep convection, changes the evolution of the total precipitation. Nevertheless, as seen in Figs. 12 and 13 different CCN

spectral bin: maritime bulk CCN 3.0 2.5

t in h

2.0 1.5 R in mm/h 1.0

100 80 60 40 20 0

0.5 0.0 0

20

40

60

80

100

120

x in km Fig. 13. As Fig. 12c, but applying a bulk CCN scheme.

64

A. Seifert et al. / Atmospheric Research 80 (2006) 46–66 6 spectral bin - continental CCN spectral bin - maritime CCN two-moment bulk - continental CCN two-moment bulk - maritime CCN spectral bin - maritime bulk CCN

5

N in mm

4 3 2 1 0

0

60

120

180

t in min Fig. 14. Time series of grid averaged accumulated surface precipitation in mm from the 5 GATE case simulations.

assumptions can result in a different temporal and spatial distribution of precipitation. And, as in the Texas case, both microphysical models have a similar sensitivity to CCN variations, but in the GATE case the main effect is that the more continental CCN leads to higher rain rates and stronger secondary convection.

5. Summary and conclusions The comparison of results obtained from a sophisticated spectral bin model and a twomoment bulk microphysical scheme has shown that both approaches predict a similar evolution of the important microphysical and dynamical variables, e.g. surface precipitation and maximum updraft velocities, when applied to cloud resolving simulations of mixed-phase deep convection. Both approaches also reveal that the studied isolated deep convective cloud is very sensitive to the CCN characteristics. In this case the assumption of maritime CCN leads to about 10 times more surface precipitation compared to continental CCN characteristics. The simulated squall line is less sensitive, but is essentially influenced by the treatment of the CCN budget resulting in a different evolution of secondary convection. Maybe the most important ingredient to achieve a good agreement of the bulk scheme with the spectral bin method is an accurate representation of the warm phase autoconversion process, here parameterized using the scheme derived by Seifert and Beheng (2001). Hence, in addition, some modifications of certain parameters of the twomoment bulk scheme have been performed in this study and were necessary to obtain comparable simulations. This was mainly done by adjusting the parameters of the various size distributions. Note that only one set of constant parameters has been used for all simulations. This shows that the exact shape of the spectra is maybe of minor importance and that the evolution of the particle spectra is dominated by number and mass concentration. From this study it is concluded that a two-moment bulk scheme might be sufficient to investigate the effects of different CCN on the formation of precipitation and the dynamics

A. Seifert et al. / Atmospheric Research 80 (2006) 46–66

65

of cloud systems. Therefore two-moment bulk schemes which include the cloud droplet number concentration are a very attractive method for regional climate studies and quantitative precipitation forecasts. Especially since the two-moment scheme is at least a factor of 30 less expensive compared to the computer resources necessary for the spectral bin method. But, since nucleation and activation processes are very difficult to be reliably represented in a bulk scheme and due to some other weaknesses, the bulk approach has obviously its limitations and the interpretation of the results has to be done very carefully. If possible, the results should be verified using spectral bin microphysics. Therefore, we suggest to build model systems which include efficient one- and two-moment bulk schemes as well as expensive spectral bin microphysics where the latter can serve as a benchmark.

Acknowledgments We acknowledge the helpful comments by two anonymous reviewers. Parts of this work have been funded by BMBF grants 02WT0249, WT/1722 and WT403, respectively (German–Israeli cooperation in water technology).

References Beheng, K.D., Doms, G., 1986. A general formulation of collection rates of cloud and raindrops using the kinetic equation and comparison with parameterizations. Contrib. Atmos. Phys. 59, 66 – 84. Bertram, I., Seifert, A., Beheng, K.D., 2004. The evolution of liquid/ice content of a mid-latitude convective storm derived from radar data and results from a cloud-resolving model. Meteorol. Z. 13, 221 – 232. Caro, D., Wobrock, W., Flossmann, A.I., Chaumerliac, N., 2004. A two-moment parameterization of aerosol nucleation and impaction scavenging for a warm cloud microphysics: description and results from a twodimensional simulation. Atmos. Res. 70, 171 – 208. Cotton, W.R., Tripoli, G.J., Rauber, R.M., Mulvihill, E.A., 1986. Numerical simulation of the effects of varying ice crystal nucleation rates and aggregation processes on orographic snowfall. J. Clim. Appl. Meteorol. 25, 1658 – 1680. Doms, G., Beheng, K.D., 1986. Mathematical formulation of self-collection, auto-conversion and accretion rates of cloud and raindrops. Meteorol. Rundsch. 39, 98 – 102. Feingold, G., Walko, R.L., Stevens, B., Cotton, W.R., 1998. Simulations of marine stratocumulus using a new microphysical parameterization scheme. Atmos. Res. 47–48, 505 – 528. Ferrier, B.S., 1994. A double-moment multiple-phase four-class bulk ice scheme: Part I. Description. J. Atmos. Sci. 51, 249 – 280. Ferrier, B.S., Houze, R.A., 1989. One-dimensional time-dependent modeling of GATE cumulonimbus convection. J. Atmos. Sci. 46, 330 – 352. Fridlind, A.M., Ackerman, A.S., Jensen, E.J., Heymsfield, A.J., Poellot, M.R., Stevens, D.E., Wang, D., Miloshevich, L.M., Baumgardner, D., Lawson, R.P., Wilson, J.C., Flagan, R.C., Seinfeld, J.H., Jonsson, H.H., VanReken, T.M., Varutbangkul, V., Rissman, T.A., 2004. Evidence for the predominance of mid-tropospheric aerosols as subtropical anvil cloud nuclei. Science 304, 718 – 722. Fritsch, J., Carbone, R., 2004. Improving quantitative precipitation forecasts in the warm season. Bull. Am. Meteorol. Soc. 85, 955 – 965. Geresdi, I., 1998. Idealized simulation of the Colorado hailstorm case: comparison of bulk and detailed microphysics. Atmos. Res. 45, 237 – 252.

66

A. Seifert et al. / Atmospheric Research 80 (2006) 46–66

Kessler, E., 1969. On the Distribution and Continuity of Water Substance in Atmospheric Circulations, Meteor. Monogr., vol. 32. Amer. Meteor. Soc, Boston. Khain, A.P., Sednev, I.L., 1996. Simulation of precipitation formation in the Eastern Mediterranean coastal zone using a spectral microphysics cloud ensemble model. Atmos. Res. 43, 77 – 110. Khain, A., Ovtchinnikov, M., Pinsky, M., Pokrovsky, A., Krugliak, H., 2000. Notes on the state-of-the-art numerical modeling of cloud microphysics. Atmos. Res. 55, 159 – 224. Khain, A.P., Rosenfeld, D., Pokrovsky, A., 2001. Simulating convective clouds with sustained supercooled liquid water down to 37.5 8C using a spectral microphysics model. Geophys. Res. Lett. 28, 3887 – 3890. Khain, A., Pokrovsky, A., Pinsky, M., Seifert, A., Phillips, V., 2004. Simulation of effects of atmospheric aerosols on deep turbulent convective clouds using a spectral microphysics mixed-phase cumulus cloud model: Part I. Model description and possible applications. J. Atmos. Sci. 61, 2963 – 2982. Lin, Y.-L., Farley, R.D., Orville, H., 1983. Bulk parameterization of the snow field in a cloud model. J. Clim. Appl. Meteorol. 22, 1065 – 1092. Meyers, M.P., Cotton, W.R., 1992. New primary ice-nucleation parameterizations in an explicit cloud model. J. Appl. Meteorol. 31, 708 – 721. Meyers, M.P., Walko, R.L., Harrington, J.Y., Cotton, W.R., 1997. New RAMS cloud microphysics parameterization: Part II. The two-moment scheme. Atmos. Res. 45, 3 – 39. Murakami, M., 1990. Numerical modeling of dynamical and microphysical evolution of an isolated convective cloud — the 19 July 1981 CCOPE cloud. J. Meteorol. Soc. Jpn. 68, 107 – 128. Pinsky, M., Khain, A., 2002. Effects of in-cloud nucleation and turbulence on droplet spectrum formation in cumulus clouds. Q. J. Royal Meteorol. Soc. 128, 501 – 533. Pinsky, M., Khain, A., Shapiro, M., 2001. Collision efficiency of drops in a wide range of Reynolds numbers: effect of pressure on spectrum evolution. J. Atmos. Sci. 58, 742 – 764. Ramanathan, V., Crutzen, P., Kiehl, J., Rosenfeld, D., 2001. Aerosols, climate and the hydrological cycle. Science 294, 2119 – 2124. Reisner, J., Rasmussen, R.M., Bruintjes, R.T., 1998. Explicit forecasting of supercooled liquid water in winter storms using the MM5 mesoscale model. Q. J. Royal Meteorol. Soc. 124, 1071 – 1107. Rosenfeld, D., 2000. Suppression of rain and snow by urban and industrial air pollution. Science 287, 1793 – 1796. Rosenfeld, D., Woodley, W.L., 2000. Deep convective clouds with sustained super-cooled liquid water down to 37.5 8C. Nature 405, 440 – 442. Seifert, A., 2002. Parametrisierung wolkenmikrophysikalischer Prozesse und Simulation konvektiver Mischwolken. PhD thesis, Institut fu¨r Meteorologie und Klimaforschung, Universita¨t Karlsruhe/Forschungszentrum Karlsruhe, Karlsruhe (in German). Seifert, A., Beheng, K.D., 2001. A double-moment parameterization for simulating autoconversion, accretion and selfcollection. Atmos. Res. 59–60, 265 – 281. Seifert, A., Beheng, K.D., 2005a. A two-moment cloud microphysics parameterization for mixed-phase clouds: Part I. Model description. Meteorol. Atmos. Phys. doi:10.1007/S00703-005-0112-4. Seifert, A., Beheng, K.D., 2005b. A two-moment cloud microphysics parameterization for mixed-phase clouds: Part II. Deep convective storms. Meteorol. Atmos. Phys. doi:10.1007/S00703-005-0113-3. Shiino, J.-I., 1983. Evolution of raindrops in an axisymmetric cumulus model: Part I. Comparison of the parameterized with non-parameterized microphysics. J. Meteorol. Soc. Jpn. 61, 629 – 655. Silverman, B.A., Glass, M., 1973. A numerical simulation of warm cumulus clouds: Part I. Parameterized vs nonparameterized microphysics. J. Atmos. Sci. 30, 1620 – 1637. Simpson, J., Helvoirt, G.V., 1982. Three-dimensional simulations for cumulus congestus clouds on GATE day 261. J. Atmos. Sci. 39, 126 – 145. Turpeinen, O., Yau, M.K., 1981. Comparison of results from a three-dimensional cloud model with statistics of radar echoes on day 261 of GATE. Mon. Weather Rev. 109, 1495 – 1511. USWRP, 2001. An implementation plan for research in quantitative precipitation forecasting and data assimilation. (available from the USWRP web site http://uswrp.mmm.ucar.edu/uswrp).