Ley de transparencia y acceso a la información pública

Before closing this chapter, it appears prudent to discuss the reverse problem of the above, namely the decay of clouds due to an increase inqsbrought about, e.g., by subsiding motion.

In the cloud scheme originally proposed by Tiedtke (1993), it is assumed that the cloud condensate is homogeneous inside the cloudy area and that the change inqs (i.e., the vertical

motion and diabatic heating) are evenly distributed in the grid box. Those two assumptions automatically imply that processes that increaseqs change the cloud condensate in the same

way at each point in the cloud, and therefore do not change the cloud fraction, until the entire cloud condensate has evaporated and the cloud disappears altogether. In other words, the processes mentioned lead to a thinning out of the cloud until its complete decay.

The issue of cloud inhomogeneity, i.e., the uneven distribution of condensate inside clouds, has received much attention recently, in particular by the radiation community (e.g., Caha- lan, 1994; Barker, 1996; Barker et al., 1996; Tiedtke, 1996). This is so because the eects of those inhomogeneities on the radiative uxes, in particular in the shortwave part of the spectrum, can be substantial. It needs to be pointed out here that if some form of distribu- tion of cloud condensate was to be used in the radiative treatment of the model clouds, the assumptions made by Tiedtke (1993) about cloud dissipation can not hold anymore.

A simple example will be used here to illustrate the procedure that needs to be followed to derive sink terms for both cloud cover and cloud condensate in the presence of an inhomoge- neous distribution of cloud condensate in the cloud. It is not surprising that this procedure is an almost exact copy of that for the cloud source terms used above. Again the simplest

5.3. The generation of non-convective clouds 89 q_w f(q_w) q_{s q} s+2lc q_s+l_c ∆q_s a 2l_c

Figure5.7: Probability distribution function of total water in the cloudy area of the grid box for a uniform

distribution of cloud condensate.

distribution will be chosen to illustrate the method with minimum mathematical complexity. An extension to more complex distribution functions is straightforward. It is assumed that inside the cloud the cloud condensate is uniformly distributed between 0 and 2lct (Figure

5.7), where lct is again the in-cloud value for the condensate , i.e., lct =lt=at. For the total

water distribution, f(qw), this implies a uniform distribution of qw inside the cloud between

q_ts and q_ts+2lct. Furthermore it is assumed that there is a homogeneous increase in qs in the

entire grid box. It is evident from Figure 5.7 that at₌Z qts

+2lct

qts f(qw)dqw: (5.51)

Since f(qw) =const: (5.51) can be used to evaluate f(qw) as

f(qw) = ₂a_lt

ct: (5.52)

Furthermore from Figure 5.7 it can be seen that at+1 =

Z qts +2lct

qt+1

90 5. The parametrization of cloud generation Subtracting (5.51) from (5.53) and substituting (5.52) gives the change in cloud fraction as a function of the change in qs as

a=Z qts qt+1 s at 2lctdqw =; at 2lctqs; (5.54) with qs =qt+1

s ;qts >0, which constitutes a sink term for cloud fraction given the above

assumptions.

The derivation of the sink term for grid-mean condensate is slightly more complex. At time t the grid-mean condensate is dened by

lt₌Z qts +2lct

qts (qw;qts)f(qw)dqw; (5.55)

which by using (5.52) reduces simply tolt _=at_lct_{. The denition ofl at timet+ 1 can also}

be deduced from Figure 5.7 and is lt+1 = Z qts +2lct qt+1 s (qw;q t+1 s )f(qw)dqw; (5.56)

which when solved for the given f(qw) is simplied to

lt+1 =atl ct;a t_qs ; 1 2aqs: (5.57)

The change in grid-mean condensate then becomes l=lt+1 ;l t₌ ;a t_qs ; 1 2aqs: (5.58)

Note that (5.58) is exactly equivalent to the production term for grid-mean condensate de- rived in section 5.3.2. This does not come as a surprise, since exactly the same distributions for total water, qw, have been used in the two derivations. The example shown here demon-

strates that given a distribution function for condensate inside clouds, it is possible to derive consistent sink terms for cloud fraction and condensate. It is desirable that if such a distri- bution is assumed in certain parts of the model, such as in representing the radiative eects of clouds, it is also used in the source and sink derivation for the cloud equations, which can be more or less complex depending on the exact formulation of the distribution function itself.

Chapter 6

Cloud fraction and microphysics

6.1 Introduction

The development of cloud parametrizations that explicitly predict the amount of cloud con- densate necessitates an increased sophistication in the description of microphysical processes. In diagnostic descriptions of clouds (e.g., Manabe et al., 1965) the generation of precipitation was simply achieved by precipitating out all condensate formed when removing supersatu- ration at the grid scale. The desire to \leave some condensate behind" as cloud demands at least a simple description of the manifold conversion processes from cloud to precipitation size particles, normally referred to as cloud microphysics. Many attempts to improve the description of these processes in GCMs have been reported on in the recent literature (e.g., Ghan and Easter, 1992; Bechthold et al., 1993; Fowler et al., 1996; Lohmann and Roeckner, 1996; Rotstayn, 1997).

One inherent diculty in the description of cloud microphysics is that the processes take place on scales that are signicantly smaller than GCM grid boxes. For many of the processes it is the local environment that determines parameters such as evaporation rates etc. An additional complication arises from the fact that most GCMs predict the occurrence of clouds over only part of their grid box using a cloud fraction parametrization of some form (e.g., Slingo, 1987; Sundqvist, 1988; Smith, 1990; Tiedtke, 1993; Rasch and Kristjansson, 1998). Cloud fraction parametrizations of this kind represent in a simple way the complex structure of cloud elds both in the horizontal and in the vertical. Figure 6.1 is a schematic of a distribution of clouds frequently encountered in tropical convective situations (e.g., Houze and Betts, 1981) where penetrating convective towers with their associated anvils and outow cirrus coexist with shallow or medium convective clouds. One may ask if a cloud parametrization scheme should be able to resolve some of the variability shown in

92 6. Cloud fraction and microphysics Figure 6.1 by producing vertically varying cloud fraction and condensate.

Figure6.1: Schematic of a possible cloud distribution in the Tropics.

Vertical variations in cloud fraction and optical thickness inuence the distribution of the radiative uxes in the atmosphere. Radiation parametrization schemes account for this vari- ability by introducing overlap assumptions (e.g., Geleyn and Hollingsworth, 1979; Morcrette and Fouquart, 1986), which determine the horizontal position of a 'cloud' at each model level relative to the clouds at other model levels. Yu et al. (1996) have used these overlap assumptions to divide model grid boxes into sub-columns when comparing model clouds to satellite observations. Stubenrauch et al. (1997) recently proposed an overlap scheme which creates blocks of cloud spanning several model levels in the vertical and then distributes the blocks in the horizontal following some overlap rules.

The eects of vertical variations of cloud fraction on the parametrization of microphysical processes have received far less attention than their radiative eects. For instance, if ice from a cirrus anvil falls into a cloud with supercooled liquid (as depicted in the leftmost low cloud in Figure 6.1), then the liquid may be converted to ice through the Bergeron process (e.g., Baker, 1997). Whether or not this occurs depends on whether the anvil ice falls into the lower cloud. Similarly evaporation of precipitation can only occur when precipitation falls into clear air. GCMs have shown a large sensitivity to the treatment of precipitation evaporation (e.g., Gregory, 1995) and it therefore appears to be desirable to treat the subgrid-scale nature of the evaporation process more carefully. Few studies have tried to account for such eects by determining a precipitation fraction (Rotstayn, 1997) or by adjusting microphysical parameters such as autoconversion rates and accretion rates in cases of vertically varying

6.2. Cloud and precipitation overlap - The problem 93