Effect of microphysical schemes on simulation of a rainfall process in the central parts of the Democratic People's Republic of Korea

Abstract

This study attempts to investigate the numerical simulations of a rainfall processes over the central region of the Democratic People’s Republic of Korea (DPRK) that occurred on 11–12 August 2009 using Advanced Research Weather Research and Forecasting model. Three simulations are preformed to study the WRF model sensitivity to cloud microphysics parameterization schemes (WDM6, Thompson, SBU-YLIN) on the rainfall prediction. The detailed comparison was made between the 45 h spatial distribution of model rainfall and observations obtained from rainfall gauges. Model results are compared in terms of probability of detection, false alarm ratio, and BIAS from 29 weather stations. Results show that the microphysics schemes significantly influenced the rainfall simulation due to differences in mixing ratios of different hydrometeors. The SBU-YLIN scheme captured the spatial distribution and cumulative amounts of rainfall in close agreement with the observations. The Thompson and WDM6 schemes predicted the rainfall event with lower intensity. Results suggest that the SBU-YLIN scheme captured the time evolution of different hydrometeors that led to produce the observed rainfall distribution spatially and temporally. The results of this study show the importance of the microphysics schemes in simulating rainfall processes, as well as the high potential of using WRF for future forecasts, especially for heavy rainfall events over the DPRK.

Appendix

1.1 Detailed description of the considered microphysical parameterization schemes

• a. WDM6 scheme

The WRF Double-Moment 6-class (WDM6) Microphysics scheme (Lim et al. 2010) has been developed by adding a double-moment treatment for the warm-rain process into the WRF Single-Moment 6-class (WSM6) Microphysics scheme. The cloud-raindrop size distributions in WDM6 scheme are assumed to the follow the normalized form and can be expressed as:

$$N(D) = N_{{0}} \frac{\alpha }{\Gamma (v)}\lambda^{\alpha v} D^{\alpha v - 1} \exp \left[ { - (\lambda D)^{\alpha } } \right],$$

(4)

where $\lambda$ is the corresponding slope parameter, $\alpha$ and $v$ are the two dispersion parameters (Lim and Hong 2010). Also, $N_{{0}}$ and $D$ represent the predicted total number concentration and diameter of drop category (rains and clouds), respectively.

The variable slope parameter is given by:

$$\lambda = \left[ {\frac{\pi }{6}\rho_{{\text{w}}} \frac{\Gamma (\nu + 3/\alpha )}{{\Gamma (\nu )}}\frac{{N_{{0}} }}{{\rho_{{\text{a}}} q}}} \right]^{1/3} ,$$

(5)

where dispersion parameters for the size distribution of rain are chosen as $\nu$ = 2 and $\alpha$ = 1, and for the cloud water size distribution are chosen as 1 and 3, respectively.

The governing equation of the number concentration for each species is given by:

$$\frac{{\partial N_{{0}} }}{\partial t} = - {\mathbf{V}} \cdot \nabla_{3} N_{{0}} - \frac{1}{{\rho_{a} }}\frac{\partial }{\partial z}\left( {\rho_{a} N_{{0}} V} \right) + S,$$

(6)

where the first and second terms in the rhs (right hand side) represent the 3-D advection and sedimentation, respectively. The term $S$ represents the source and sink of number concentration. The number-weighted-mean terminal velocity can be obtained by integrating the terminal velocity of rainwater, which is expressed as:

$\overline{V}_{{{\text{NR}}}} = \frac{{\int {V_{{\text{R}}} (D_{{\text{R}}} ){\text{d}}N_{{{\text{DR}}}} } }}{{\int {{\text{d}}N_{{{\text{DR}}}} } }} = \frac{{a_{{\text{R}}} }}{{\lambda_{{\text{R}}}^{{b_{{\text{R}}} }} }}\Gamma (2 + b_{{\text{R}}} )\left( {\frac{{\rho_{0} }}{{\rho_{{\text{R}}} }}} \right)^{1/2} ,$ (7)

where the terminal velocity $V_{{\text{R}}} (D_{{\text{R}}} )$ for a rain particle with diameter $D_{{\text{R}}}$ is expressed as:

$$V_{{\text{R}}} (D_{{\text{R}}} ) = a_{{\text{R}}} D_{{\text{R}}}^{{b_{{\text{R}}} }} \left( {\frac{{\rho_{0} }}{{\rho_{{\text{R}}} }}} \right)^{1/2} ,$$

(8)

where $a_{{\text{R}}}$, $b_{{\text{R}}}$ are the empirical formulas of $V_{{\text{R}}}$($a_{{\text{R}}}$ = 841.9 ${\text{m}}^{{1 - b_{{\text{R}}} }} \,{\text{s}}^{ - 1}$, $b_{{\text{R}}}$ = 0.8), $\rho_{0}$ is air density and $\rho_{{\text{R}}}$ is density of air at reference state.

In this scheme the number of activated CCN $n_{a}$ can be expressed as the following:

$n_{{\text{a}}} = (n + N_{{\text{C}}} )\left( {\frac{{S_{{\text{w}}} }}{{S_{\max } }}} \right)^{k} ,$ (9)

where k is the parameter with a typical range from 0.3 to 1.0 (equal to 0.6 in this study); n is the total CCN number concentration, and N_C is the cloud droplets number concentration. S_W represents saturation ratio, and S_max is defined as the supersaturation needed to activate the total particle count n + N_C, and is set to 0.48%.

The production rate of the cloud water mixing ratio by the CCN activation can be expressed as:

$$P_{{{\text{cact}}}} ({\text{kg}}\,{\text{kg}}^{ - 1} \,{\text{s}}^{ - 1} ) = \frac{{4\pi \rho_{{\text{W}}} }}{{3\rho_{{\text{a}}} }}r_{{{\text{act}}}}^{3} \times N_{{{\text{cact}}}} ({\text{m}}^{ - 3} \,{\text{s}}^{ - 1} ),$$

(10)

where N_cact is the generation rate by activation of the CCN and r_act is the initial radius assumed to be the radius activated droplets, which is set as 1.5 µm. $\rho_{{\text{W}}}$ is the density of water. In addition, the complete evaporation of cloud drops is assumed to return corresponding CCN particles to the total CCN count:

During the autoconversion of cloud water into raindrops, the growth rate of the rain-mixing ratio (P_raut) represents as follows:

$$P_{{{\text{raut}}}} = \frac{L}{\tau },$$

(11)

where

$$\tau = 3.7\frac{1}{{\rho_{{\text{a}}} q_{{\text{C}}} }}(0.5 \times 10^{6} \sigma_{{\text{C}}} - 7.5)^{ - 1} = 3.7\frac{1}{{\rho_{{\text{a}}} q_{{\text{C}}} }}\left( {\frac{{0.5 \times 10^{6} }}{{\lambda_{{\text{C}}} }} - 7.5} \right)^{ - 1} .$$

(12)

$$L = 2.7 \times 10^{ - 2} \rho_{{\text{a}}} q_{{\text{C}}} (\frac{1}{16} \times 10^{20} \sigma_{{\text{C}}}^{3} D_{{\text{C}}} - 0.4) = 2.7 \times 10^{ - 2} \rho_{{\text{a}}} q_{{\text{C}}} \left( {\frac{{10^{20} }}{{16\lambda_{{\text{C}}}^{4} }} - 0.4} \right).$$

(13)

$\sigma_{{\text{C}}}$ is the standard deviation of the raindrop size distribution. The growth rate of rain mixing ratio is calculated only if $\sigma_{{\text{C}}}$ > 15 µm.

• b. Thompson scheme

The Thompson microphysical parameterization scheme assumed that snow size distribution depended on both ice water content and temperature and represented as a sum of exponential and gamma distribution (Thompson et al. 2008). The gamma size distribution of hydrometeor species (Table 1) assumed in this scheme is expressed as:

$N(D) = \frac{{N_{0} }}{\Gamma (\mu + 1)}\lambda^{\mu + 1} D^{\mu } e^{ - \lambda D} ,$ (14) where D is the particle diameter, N₀ is the total number of particles in the distribution, $\mu$ is the shape factor, and $\lambda$ is the slope parameter (Thompson et al. 2008).

The mass and diameter relationship is given by:

$$m(D) = cD^{d} ,$$

(15)

and the terminal velocity relation as follows:

$$v(D) = \left( {\frac{{\rho_{0} }}{\rho }} \right)^{1/2} \alpha D^{\beta } e^{ - fD} .$$

(16)

In Eqs. (15) and (16), the mass and terminal velocity constants for each/ice species are shown in Table 4.

Table 4 Mass and terminal constants for each liquid/ice species

In this scheme, the amount of cloud water converting to rain is given by:

$$\frac{{{\text{d}}r_{r} }}{{{\text{d}}t}} = \frac{{0.027\rho q_{{\text{c}}} (\frac{1}{16} \times 10^{20} D_{{\text{b}}}^{3} D_{{\text{f}}} - 0.4)}}{{\frac{3.72}{{\rho q_{{\text{c}}} }}\left( {\frac{1}{2} \times 10^{6} D_{{\text{b}}} - 7.5} \right)^{ - 1} }},$$

(17)

where the characteristic diameters, $D_{{\text{b}}}$ and $D_{{\text{f}}}$ are obtained as follows:

$$D_{{\text{f}}} = \left( {\frac{{6\rho q_{{\text{c}}} }}{{\pi \rho_{{\text{w}}} N{}_{{\text{c}}}}}} \right)^{1/3} ,$$

(18)

$$D_{{\text{g}}} = \frac{{\left[ {\frac{{\Gamma (\mu_{c} + 7)}}{{\Gamma (\mu_{c} + 4)}}} \right]}}{{\lambda_{{\text{c}}} }}^{1/3} ,\,D_{{\text{b}}} = (D_{{\text{f}}}^{3} D_{{\text{g}}}^{3} - D_{{\text{f}}}^{6} )^{1/6} ,$$

(19)

where $\rho$ is the moist air density.

• c. SBU-YLIN scheme

The new State University of New York at Stony Brook bulk microphysical parameterization scheme (SBU-YLIN) is presented that includes a diagnosed riming intensity and its impact on ice characteristics (Lin and Colle 2011). This scheme represents a continuous spectrum from pristine ice particles to heavily rimed particles and graupel using one prognostic variable (precipitating ice) than two separate variables (snow and graupel). The SBU-YLIN scheme uses a generalized gamma distribution to describe the size distribution of cloud water droplets:

$$N(D) = N_{0} D^{\mu } e^{ - \lambda D} ,$$

(20)

where N₀ is the intercept, μ is the shape parameter, and λ is the slope. The total number concentration of cloud droplets generally depends on the ambient aerosol distribution and properties. In the SBU-YLIN scheme, the most representative numbers is used for maritime (100 cm⁻³) and continental air mass (250 cm⁻³).

The new method in the SBU-YLIN scheme is in the treatment of precipitating ice particles, which have a variety of riming intensities. Power laws have been widely used to describe the mass–diameter (M–D), area–diameter (A–D), and fall velocity–diameter (V–D) relationships for ice particles:

$$M = a_{{\text{m}}} D^{{b_{{\text{m}}} }} ,$$

(21)

$$A = a_{{\text{a}}} D^{{b_{{\text{a}}} }} ,$$

(22)

$$V = a_{{\text{v}}} D^{{b_{{\text{v}}} }} ,$$

(23)

where coefficients ($a_{{\text{m}}}$, $b_{{\text{m}}}$, $a_{{\text{a}}}$, $b_{{\text{a}}}$, $a_{{\text{v}}}$, and $b_{{\text{v}}}$) are calculated as follows:

$$a_{{\text{m}}} = c_{0} + c_{1} T + c_{2} {\text{Ri,}}$$

(24)

$$b_{{\text{m}}} = c_{0} + c_{1} T + c_{2} {\text{Ri}},$$

(25)

$$a_{{\text{a}}} = d_{0} + d_{1} T + d_{2} {\text{Ri}},$$

(26)

$$b_{{\text{a}}} = D_{0} + D_{1} T + D_{2} {\text{Ri}},$$

(27)

$$a_{{\text{v}}} = av\left( {\frac{{2ga_{{\text{m}}} }}{{\rho_{{\text{a}}} v^{2} a_{{\text{a}}} }}} \right)^{b} ,$$

(28)

$$b_{{\text{v}}} = b(b_{{\text{m}}} - b_{{\text{a}}} + 2) - 1.$$

(29)

In Eqs. (24–29), c₀ (0.004), c₁(6 $\times$ 10^–5), c₂ (0.15), C₀ (1.85), C₁ (0.003), and C₂ (1.25), d₀ (1.28), d₁ (− 0.012), d₂ (− 0.6), D₀ (1.5), D₁ (0.0075), and D₂ (0.5) are parameters used in the M–D and A–D relationships, and g is the gravitational acceleration constant, $\rho_{{\text{a}}}$ is the air density, v is the kinematic viscosity of the air, a is 1.08, and b is 0.499 (Lin and Colle 2011).

The riming intensity (Ri) can be approximated by the ratio between riming growth rate and the sum of riming and ice depositional growth rate, assuming steady state and saturation with respect to water as riming occurs (Lin and Colle 2011):

$${\text{Ri}} = \frac{{P_{{{\text{rim}}}} }}{{P_{{{\text{rim}}}} + P_{{{\text{dep}}}} }} = \frac{1}{{1 + \frac{F(T)}{{{\text{LWC}}({\text{IWC}})^{0.17} }}}} \approx \frac{1}{{1 + \frac{{6 \times 10^{ - 5} }}{{{\text{LWC}}({\text{IWC}})^{0.17} }}}},$$

(30)

where LWC and IWC refer to liquid water content and ice water content. Riming depends on LWC, IWC, temperature, ice habit, vertical motion, ice particle size, and droplet size.

The parameterization of autoconversion of cloud water to rain is:

$$P_{{{\text{wau}}}} = \left( {\frac{3\rho }{{4\pi \rho_{{\text{w}}} }}} \right)^{2} \kappa_{2} \beta_{6}^{6} N^{ - 1} q_{{\text{c}}}^{3} H(R_{6} - R_{{{\text{6c}}}} ),$$

(31)

$$\beta_{6}^{6} = \frac{{(1 + 3\varepsilon^{2} )(1 + 4\varepsilon^{2} )(1 + 5\varepsilon^{2} )}}{{(1 + \varepsilon^{2} )(1 + 2\varepsilon^{2} )}},$$

(32)

$$R_{6c} = \beta_{6} R_{3c} ,R_{6} = \beta_{6} R_{3} ,$$

(33)

where the coefficient $\kappa_{2}$ $\approx$ 1.9 $\times$ 10¹¹ is in cm⁻³ s⁻¹, N is the cloud droplet number concentration, $\varepsilon$ is the relative dispersion, and H is the Heaviside function to consider the threshold process such that the autoconversion rate is negligibly small when R₆ < R_6c; also, R₃ is the mean volume radius and R_3c is the threshold mean volume radius (Lin and Colle 2011).