The Weather Research and Forecasting (WRF) model coupled with the Morrison microphysics scheme is used in this study. Five hydrometeor species (cloud droplets, raindrops, ice crystals, snowflakes, and graupel) are considered, and their mixing ratio and number concentration are predicted in this scheme (Morrison et al., 2005). The size distributions of hydrometeors are represented by the gamma function. In order to investigate the sensitivity of the effect of aerosol particles on orographic precipitation to autoconversion parameterization schemes, a moist flow over a two-dimensional idealized mountain is simulated without the parameterization schemes of radiation, surface processes, and the boundary layer. The simulated domain is an 800-point horizontal grid with a width of 400 km and a resolution of 0.5 km. In the vertical direction, 62 terrain-following levels are adopted with the grid spacing varying from 0.035 km at the surface to about 1.85 km at the model top. The duration of the simulation is 10 hours with a time step of 2 s. An idealized bell-shaped topography is used to produce orographic precipitation, as represented in Eq. (1):
where h(x) is the terrain height at the grid of x, h0 (= 1 km) is the peak height of the terrain, x0 (= 400) is the location of the center of the terrain, and a (= 20 km) is the half-width of the terrain (Xiao et al., 2014). According to the work of Muhlbauer and Lohmann (2008), the initial profiles of relative humidity and temperature are shown in Fig. 1. The surface temperature and surface pressure are set to 285 K and 1000 hPa, respectively. The relative humidity is set to 90% at the surface and the wind is set to 15 m s−1 below 10 km.
Figure 1. Initial profiles of temperature (solid line) and dewpoint temperature (dashed line) for simulation.
In order to explore the impact of autoconversion parameterization schemes on the change in aerosol-induced orographic precipitation, the equations in the microphysics schemes remain unchanged except for the autoconversion formula. In this study, the initial concentration of cloud droplets is changed from 100 cm−3 to 1000 cm−3 to describe the environmental conditions from clean to polluted. Seven autoconversion schemes are employed to investigate the sensitivity to the concentration of initial cloud droplets.
The Berry scheme (Berry, 1968; hereafter referred to as Be1968) states that the autoconversion rate is reduced by an increasing number concentration of cloud droplets and is increased by an increasing mass concentration of cloud water. However, there is a nonlinear relationship between the rate and number (or mass) concentration of cloud droplets:
where (∂qr/∂t)auto (units: kg m−3) is the autoconversion rate, Nc and qc are the number concentration (units: m-3) and mass concentration (units: kg m−3) of cloud droplets, C1 = 1.0 × 10−2, C2 = 0.12, and C3 = 1.0 × 10−12. The Tripoli and Cotton scheme (Tripoli and Cotton, 1980; hereafter referred to as TC1980) is similar to the Berry scheme, but contains the Heaviside step function:
where mu is dynamic viscosity; Ecr (= 0.55) is the mean collection efficiency; ρw is the density of liquid water; and H(qc − qc0) is the Heaviside step function, in which qc0 is the minimum cloud water for the conversion. The equation of the Beheng scheme (Beheng, 1994; hereafter referred to as Be1994) is:
where Nc and qc are the number concentration (units: cm−3) and mass concentration (units: g cm−3) of cloud droplets, μ is the spectral shape parameter, and C4 = 6.0 × 1028. The equation of the Khairoutdinov and Kogan scheme (Khairoutdinov and Kogan, 2000; hereafter referred to as KK2000) is:
where ρ0 is the density of air. The Seifert and Beheng scheme (Seifert and Beheng, 2001) states that the autoconversion rate is associated with the shape parameter, cloud water, and rainwater. The equation is:
where x* (= 2.6 × 10−7 g) referred to the boundary between cloud water and rainwater, kc (= 9.44 × 109 cm2 g−2 s−1) is a constant, xc is the mean mass, τ is the ratio of rainwater to the total liquid water mass, and
$\varPhi $is the function of τ. The Liu and Daum scheme (Liu and Daum, 2004; hereafter referred to as LD 2004) induces relative dispersion to describe the change in the cloud droplet spectrum. The equation is:
where κ2 (= 1.9 × 1011 cm−3) is a constant, and β6 is a function of relative dispersion (ε). As the cloud droplet size distribution is represented by the gamma function, β6 is shown to be
where the relative dispersion ε = 571.4Nc + 0.2714 (Morrison and Grabowski, 2007). According to the results of Xie et al. (2013), there is a negative relationship between the autoconversion rate and cloud droplet number concentration, especially for concentrations less than 300 cm−3.
In this study, the stochastic collection equation (SCE) is employed as a reference to describe the evolution of the drop spectrum. The time-dependent SCE for a spectrum of liquid water is (Tzivion et al., 1987)
where n(x, t) dx is the number of drops with masses between x and x + dx per unit volume at time t, and K(x, y) is the collection kernel. According to the solution of Tzivion et al. (1987), the SCE is converted to a set of two-moment equations and it is an efficient method to simulate the evolution of the drop spectrum with collision and coalescence. In order to separate the drop spectrum into cloud droplets and raindrops artificially for parameterization schemes, the separating drop radius of 40 μm is adopted (Seifert and Beheng, 2001; hereafter referred to as SB2001). The drop spectrum is divided into 36 bins with mass doubling between adjacent bins. The experiments are conducted with seven autoconversion equations and ten conditions of initial cloud droplet concentration (Table 1). In particular, the initial cloud droplet concentration (N) is increased from 100 cm−3 to 1000 cm−3 (N = 100 to 1000 cm−3) with a concentration interval of 100 cm−3.
Scheme reference Experiment name Equation Berry (1968) Be1968 (2) Tripoli and Cotton (1980) TC1980 (3) Beheng (1994) Be1994 (4) Khairoutdinov and Kogan (2000) KK2000 (5) Seifert and Beheng (2001) SB2001 (6) Liu and Daum (2004) LD2004 (7) Tzivion et al. (1987) SCE (8)
Table 1. List of experiments in this study.
The change in autoconversion rate in each scheme is shown in Fig. 2. In these autoconversion schemes, the cloud water content and droplet number concentration are considered to calculate the autoconversion rate. From the representation of equations, the sensitivities of the autoconversion rate to droplet number concentration is different from scheme to scheme (approximately as a function of Nc−1 in Be1968, Nc−1/3 in TC1980, Nc−3.3 in Be1994, Nc−1.79 in KK2000, Nc−2 in SB2001, and Nc−1 in LD 2004). Hence, the variation of the autoconversion rate with the change in cloud droplet number concentration from 10 cm−3 to 1000 cm−3 is also different. The Be1994 scheme is the most sensitive to cloud droplet number concentration besides the SCE scheme, while the TC1980 scheme is the least sensitive. In general, there is a significant difference in the autoconversion rate between schemes, even under the same values of cloud water content and number concentration. Moreover, the degree of variation of the autoconversion rate induced by cloud droplet number concentration is also different in every scheme.