Cloud Parameterizations, Cloud Physics, and Their Connections: An Overview Y. Liu1*, P. H. Daum1, S. K. Chai2, and F. Liu3 1 Brookhaven National Laboratory, Atmospheric Sciences Division, Upton, Bldg. 815E, 75 Rutherford Drive, Upton, NY 11973-5000 2 Desert Research Institute, Atmospheric Sciences Division, Reno, NV 89512 3 Ocean University of Qingdao, P.R. China * Corresponding Author January 2002 For publication in "Recent Research Developments in Geophysics," Research Signpost, Trivandrum, India ABSTRACT paradigm shift from reductionist approaches to systems approaches. A systems theory that has This paper consists of three parts. The recently been formulated by utilizing ideas first part is concerned with the from statistical physics and information theory parameterization of cloud microphysics in is discussed, along with the major results climate models. We demonstrate the crucial derived from it. It is shown that the systems importance of spectral dispersion of the cloud formalism not only easily explains many droplet size distribution in determining puzzles that have been frustrating the radiative properties of clouds (e.g., effective mainstream theories, but also reveals such new radius), and underline the necessity of phenomena as scale-dependence of cloud specifying spectral dispersion in the droplet size distributions. The third part is parameterization of cloud microphysics. It is concerned with the potential applications of the argued that the inclusion of spectral dispersion systems theory to the specification of spectral makes the issue of cloud parameterization dispersion in terms of predictable variables and essentially equivalent to that of the droplet size scale-dependence under different fluctuating distribution function, bringing cloud environments. parameterization to the forefront of cloud physics. The second part is concerned with 1. INTRODUCTION theoretical investigations into the spectral shape of droplet size distributions in cloud Clouds have attracted great interests physics. After briefly reviewing the from humans, as implied by the poem by mainstream theories (including entrainment Vollie Cotton [1], "Clouds are pictures in the and mixing theories, and stochastic theories), sky/They stir the soul/ they please the eye/They we discuss their deficiencies and the need for a bless the thirsty earth with rain/which nurtures 2 life from cell to brain/But no! They are content and droplet concentration. We also demons, dark and dire/hurling hail, wind, argue that the same is true for cloud-resolving flood, and fire/Killing, scarring, cruel models, in which the effect of spectral shape is masters/Of destruction and disasters /Clouds often ignored in the parameterization of cloud have such diversity/Now blessed, now microphysics. The inclusion of spectral shape cursed/the best, the worst/But where would life in cloud parameterizations makes the subject without them be?" Clouds, which play a crucial of cloud parameterizations essentially role in regulating the energy cycle and water equivalent to the relatively old subject of cycle of the Earth, have been a focus of the specifying the droplet size distribution cloud physics community over the last few function. As a result, instead of being treated decades. With the increasing recognition of as separate subjects, the key to improving the importance of clouds in regulating climate cloud parameterizations becomes the core of and the growing concern over potential global cloud physics. climate change caused by human activities, In Section 3, we introduce some long- clouds have recently come to the center stage standing issues regarding the spectral shape of of climate research. Cloud effects and cloud the droplet size distribution, and then briefly feedbacks have been identified as one of the discuss the traditional mainstream theories largest uncertainties in current climate models proposed to address these issues and their [2]. Cloud processes/properties need to be deficiencies, including various entrainment and parameterized in climate models as subgrid mixing models and stochastic models. In processes because they cannot be explicitly Section 4, we focus on a systems theory that resolved by the state-of-art climate models. For has been recently formulated based on ideas of the same reason, cloud microphysics has to be statistical physics and information theory to parameterized in cloud-resolving models. avoid the difficulties of the mainstream Despite the great progress made over the theories. This theory establishes a self- last few decades, many issues regarding clouds consistent theoretical framework, offers new remain unsolved. This work is concerned with insights into the issues that have been two of them: microphysics parameterizations frustrating the mainstream theories, and reveals of warm clouds in climate models (cloud that droplet size distributions depend on the parameterizations hereafter for brevity), and scale over which the size distributions are theoretical studies of cloud droplet size averaged (scale-dependence hereafter). This distributions. In Section 2, we review and scale-dependence has important implications compare the existing schemes for cloud for virtually all cloud-related issues, including parameterizations in climate models, with cloud parameterizations. Because the systems emphasis on the effect of spectral shape of the theory is relatively less known compared to droplet size distribution. We show that the mainstream models, it is a major focus of this spectral shape alone can cause substantial contribution. In Section 5, we discuss new errors in calculation of cloud radiative challenges ahead, address potential properties, indicating the need to specify the applications of the systems theory, and explore spectral shape in addition to liquid water 3 opportunities for a new theoretical framework to meet these challenges. 1/3 1/3 æö3 L æö re = b ç÷ç÷ , (1) 2. CLOUD PARAMETERIZATIONS èø4prw èøN 2.1. Effective Radius and Spectral Dispersion where re is the effective radius in µm, L is the liquid water content in gm-3, and N is the total Effective radius (defined as the ratio of droplet concentration in cm-3. The the third to the second moment of a droplet dimensionless parameter b is a function of the size distribution) is one of the key variables spectral shape, and can be universally used in calculation of the radiative properties expressed as [13, 16] of liquid water clouds [3-4]. The inclusion and parameterization of effective radius in climate 2/3 models has proven to be critical for assessing (13++ee23s ) b = global climate change. Slingo [5] studied the 2 , (2) sensitivity of the global radiation budget to (1+ e ) effective radius and found that the warming effect of doubling the CO2 concentration could where e is the spectral dispersion defined as be offset by reducing effective radius by the ratio of the standard deviation and the approximately 2 µm. Kiehl [6] found that a mean radius of the droplet size distribution, number of known biases of the early version of and s is the skewness of the droplet size CCM2 were diminished, and important distribution. changes in cloud radiative forcing, precipitation, and surface temperature resulted 2.2. Relationship between b and e if different values of effective radius were assigned to warm maritime and continental For clouds with a monodisperse droplet clouds. A high sensitivity to the method of size distribution as described by a delta parameterizing effective radius was also found function n(r)=Nd(r-re), effective radius equals in a recent study of the French Community the volume mean radius, and b = 1. This Climate model [7]. MO value of b was used by Bower and Choularton Early parameterization schemes expressed effective radius as either a linear or a [10], and Bower et al. [11] to estimate the effective radii of layer clouds and small cubic root function of the liquid water content, implicitly assuming no dependence of effective cumuli. In a study of the sensitivity of NCAR’s CCM2 to variations in r, Kiehl [6] radius upon the total droplet concentration [8, e 9]. There has been increasing evidence for used this scheme to provide support for choosing r of 5 µm and 10 µm for continental parameterizing effective radius as a "1/3" e power law of the ratio of the cloud liquid water and maritime clouds respectively. Martin et al. [13] found that there are differences in the content to the droplet concentration [10-16]. values of spectral dispersion between maritime The “1/3” power-law takes the form 4 and continental clouds, and derived estimates the WB expression, expressions for b as a of bMM = 1.08 for maritime stratocumulus, and function of e can be easily derived for the bMC = 1.14 for continental stratocumulus. By gamma [18, GM hereafter] and the lognormal assuming a negligible skewness of the droplet [19, LN hereafter) droplet size distributions. size distribution, Pontikis and Hicks [12] These expressions are summarized in Table 1. analytically derived an expression that relates b to the spectral dispersion. This expression is Table 1. The Commonly Used b-e Expressions hereafter referred to as Gaussian-like and denoted by GL, because the Gaussian MO b = 1 distribution represents a typical form of such MM b = 1.08 symmetrical distributions. MC b = 1.14 The assumption of either monodisperse 2/3 or Gaussian-like distribution is clearly GL (13+ e 2 ) b = problematic for cloud physicists, because it has (1+e 2 ) been long known in cloud physics that neither WB G2/3(3/b) of them represent droplet size distributions b =1.04b1/3 (See Section 4 observed in real clouds well (see Section 3 for G(2/b) details). These parameterizations are only for the relationship between b and e) appropriate for clouds with weak turbulent entrainment and mixing where droplet size 2/3 GM 2 distributions are rather narrow. For clouds (12+ e ) b = 1/3 exhibiting broad size distributions, the above- 1+e 2 mentioned parameterizations underestimate b ( ) and therefore effective radii, though to LN be=+(1 2 ) different degrees.