Numerical Errors in Ice Microphysics Parameterizations and their Effects on Simulated Regional Climate

Abstract

The major characteristics of ice microphysics in Weather Research and Forecasting (WRF) Double-Moment 6-class (WDM6) bulk-type cloud microphysics originate from the diagnosed ice number concentration, which is a function of the cloud-ice mixing ratio. In this study, we correct numerical errors in ice microphysics processes of the WDM6, in which the cloud-ice shape is assumed as single bullets and examine the impact on regional climate simulations. By rederiving the relationships between cloud microphysics characteristics, including the one linking the cloud-ice mixing ratio and number concentration, we remove numerical errors intrinsic to the description of cloud-ice characteristics in the original WDM6 microphysics scheme. The revised WDM6 is tested using a WRF framework for regional climate simulations over the East Asian region. We find that our correction to the WDM6 improves the model’s performance in capturing the observed distribution of the monsoon rain band. A reduction in cloud ice is significant in the revised WDM6, which strengthens the Western North Pacific High. By conducting the additional sensitivity experiment in which the characteristics of cloud-ice shape are revised as the one for the column type, our study also finds out that the impacts of the existing numerical errors on the simulated monsoon is as large as the ones of the changes in cloud-ice shape.

Appendices

Appendix A. Equations of Cloud Microphysics Processes Affected by Numerical Errors

The microphysics processes of hydrometeor (a) mixing ratio and (b) number concentration, affected by the numerical errors present in Hong et al. (2004), are shown in the following.

• a Production Terms for Mixing Ratio of Cloud Ice

  $$\begin{array}{l}\mathrm{Pgaci}\left[\mathrm{kg}\;\mathrm{kg}^{-1}\mathrm s^{-1}\right]={\frac\pi4E_{GI}q_IN}_{0G}\left|{\overline {V_G}}-\overline{V_I}\right|\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\times\left[\frac{\Gamma(3+\mu_G)}{\lambda_G^{3+\mu_G}}+2D_I\times\frac{\Gamma(2+\mu_G)}{\lambda_G^{2+\mu_G}}+D_I^2\times\frac{\Gamma(1+\mu_G)}{\lambda_G^{1+\mu_G}}\right]\end{array}$$
  $$\mathrm{Piacr}\left[\mathrm{kg}\;\mathrm{kg}^{-1}\mathrm s^{-1}\right]=\frac\pi{4\rho_a}a_Rc_RE_{RI}N_IN_{0R}\left(\frac{\rho_0}{\rho_a}\right)^\frac12\left[\frac{\Gamma(b_R+d_R+\mu_R+3)}{\left(f_R+\lambda_R\right)^{b_R+d_R+\mu_R+3}}\right]$$
  $$\mathrm{Pidep}\left[\mathrm{kg}\;\mathrm{kg}^{-1}\mathrm s^{-1}\right]=\frac{4D_I\left(S_I-1\right)N_I}{A_I+B_I}$$
  $$\mathrm{Pigen}\left[\mathrm{kg}\;\mathrm{kg}^{-1}\mathrm s^{-1}\right]=\min\left[\frac{\left(q_{I0}-q_I\right)}{\Delta t},\frac{\left(q-q_{SI}\right)}{\Delta t}\right]$$
  $$\begin{array}{l}\mathrm{Praci}\left[\mathrm{kg}\;\mathrm{kg}^{-1}\mathrm s^{-1}\right]={\frac\pi4E_{RI}q_IN}_{0R}\left|{\overline {V_R}}-\overline{V_I}\right|\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\times\left[\frac{\Gamma\left(3+\mu_R\right)}{\lambda_R^{3+\mu_R}}+2D_I\times\frac{\Gamma\left(2+\mu_R\right)}{\lambda_R^{2+\mu_R}}+D_I^2\times\frac{\Gamma\left(1+\mu_R\right)}{\lambda_R^{1+\mu_R}}\right]\end{array}$$
  $$\begin{array}{l}\mathrm{Psaci}\left[\mathrm{kg}\;\mathrm{kg}^{-1}\mathrm s^{-1}\right]={\frac\pi4E_{SI}q_IN}_{0S}\left|\overline{V_S}-\overline{V_I}\right|\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\times\left[\frac{\Gamma(3+\mu_S)}{\lambda_S^{3+\mu_S}}+2D_I\times\frac{\Gamma(2+\mu_S)}{\lambda_S^{2+\mu_S}}+D_I^2\times\frac{\Gamma(1+\mu_S)}{\lambda_S^{1+\mu_S}}\right]\end{array}$$
  $$\mathrm{Psaut}\left[\mathrm{kg}\;\mathrm{kg}^{-1}\mathrm s^{-1}\right]=a_1\frac{\left(q_I-q_{Icrit}\right)}{\Delta t}$$

  By removing the numerical errors of the ice microphysics processes in Hong et al. (2004), Psaut can be enhanced with the decreased ${q}_{Icrit}$ (Table 2) if other meteorological conditions except cloud ice are unchanged. Moreover, Pidep can be enhanced with the increased ${D}_{I}$ and ${N}_{I}$ under the saturated environment over cloud ice (Fig. 1a and c). Pigen and Piacr can be decreased towing to the decreased ${q}_{I0}$ and increased ${N}_{I}$, respectively (Fig. 1a and b). Praci, Psaci, and Pgaci can either decrease or increase because these processes are affected by both ${V}_{I}$ and ${D}_{I}$.

• b Production terms for number concentration of cloud ice

Niacr $\left[{\mathrm{m}}^{-3} {\mathrm{s}}^{-1}\right]=\frac{\pi }{4}{a}_{R}{E}_{RI}{N}_{0R}{N}_{I}{\left(\frac{{\rho }_{0}}{{\rho }_{a}}\right)}^\frac{1}{2}\left[\frac{\Gamma (3+{b}_{R}+{\mu }_{R})}{{({\lambda }_{R}+{f}_{R})}^{3+{b}_{R}+{\mu }_{R}}}\right]$

Nimlt $\left[{\mathrm{m}}^{-3} {\mathrm{s}}^{-1}\right]=\frac{{N}_{I}}{{q}_{I}}$

Niacr and Nimlt can be enhanced with the increased ${N}_{I}$ (Fig. 1a).

Appendix B

Table 6 List of symbols