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A sensitivity study of WRF model microphysics and cumulus parameterization schemes for the simulation of tropical cyclones using GPM radar data

Abstract

The present study focuses on determining the best combination of microphysics (MP) and cumulus parameterization (CP) schemes for the simulation of Tropical Cyclones (TCs) in the Indian subcontinent region, using the Weather Research and Forecasting (WRF) model. From the available schemes, four CP schemes, namely Kain–Fritsch, Betts–Miller–Janjic, New Simplified Arakawa–Schubert, and Grell–Devenyi, and four MP schemes, namely WSM6, Purdue Lin, Thompson, and Morrison, are selected for the sensitivity study. Seven TCs are simulated using all combinations of the chosen physics schemes. The simulated tracks and intensities are compared against the India Meteorological Department (IMD) observations. The results show that the Kain–Fritsch scheme, in combination with all MP schemes, predicts the tracks best among all the available CP schemes, but the performance of microphysics schemes is indistinguishable. A further study is conducted using the Global Precipitation Measurement (GPM) radar data to identify the best MP scheme by comparing the reflectivities. An existing radar simulator is modified to calculate the simulated reflectivities from the WRF model output corresponding to the MP schemes. The simulated reflectivities are compared against the GPM radar reflectivities, and the results show that the Thompson scheme reproduces the reflectivities closest to observations. The performance of the best set of schemes obtained from this study is compared with a random set of schemes for cyclone Bulbul, and the best set of schemes outperformed the random schemes in every aspect.

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Acknowledgements

The authors are thankful to the international WRF community for their tremendous efforts in developing the WRF model and supporting us through providing the model. The model simulations are performed on Aqua High-Performance Computing (HPC) system at the Indian Institute of Technology Madras, Chennai, India. The figures are plotted using the python language and NCAR Command Language (NCL). The authors would like to thank the ‘Centre of Excellence (CoE) in climate change impact on coastal infrastructure and the adaptation strategies’ for their suggestions. Department of Science and Technology is funding the research grant DST/CCP/CoE/141/2018(C) for this project (CIE1819265DSTXSACI) under SPLICE – Climate Change Programme.

Author information

Affiliations

Authors

Contributions

Harish Baki and Sandeep Chinta conceptualized the study, designed the methodology, performed the formal analysis and edited the draft of the paper. Harish Baki performed the investigation and prepared the original draft. C Balaji and Balaji Srinivasan provided critical revisions for the manuscript and supervised the work.

Corresponding author

Correspondence to C Balaji.

Additional information

Communicated by Parthsarathi Mukhopadhyay

Appendix

Appendix

A1. Drop size distributions of hydrometeors in the Lin scheme

The Purdue Lin scheme adopted classical exponential drop size distribution for hydrometeors rain, snow, and graupel as:

$$\begin{aligned} n(D)=N_0e^{-\lambda D}dD \quad \text{in}\, \text{m}^{-3} .\end{aligned}$$

Here, \(n(D)\) is the drop size distribution as a function of the diameter \(D\), \(dD\) is the differential diameter, \(N_0\) is the intercept parameter, and \(\lambda \) is the slope parameter. The intercept and slope parameter values will vary for different hydrometeors.

A1.1 Rain

$$ \begin{aligned} n_R(D)&=N_{0R}e^{-\lambda D}dD \quad \text{in} \,\text{m}^{-3} \\ N_{0R}&=8\times 10^6 \quad \text{in} \,\text{m}^{-4}\\ \lambda _R&=\left( \frac{\pi \rho _RN_{0R}}{\rho _{\text {dair}} Q_R}\right) ^\frac{1}{4} \quad \text{in}\, \text{m}^{-1}\\ \rho _R&= 1000 \;\; \text{kg/m}^3. \end{aligned}$$

A1.2 Snow

$$ \begin{aligned} n_S(D)&=N_{0S}e^{-\lambda D}dD \quad \text{in}\, \text{m}^{-3}\\ N_{0S}&=3\times 10^6 \quad \text{in}\, \text{m}^{-4}\\ \lambda _S&=\left( \frac{\pi \rho _SN_{0S}}{\rho _{\text {dair}} Q_S}\right) ^\frac{1}{4} \quad \text{in} \,\text{m}^{-1}\\ \rho _S&= 100 \,\, \text{kg/m}^3 .\end{aligned}$$

A1.3 Graupel

$$ \begin{aligned} n_G(D)&=N_{0G}e^{-\lambda D}dD \quad \text{in}\, \text{m}^{-3}\\ N_{0G}&=4\times 10^6 \quad \text{in} \,\text{m}^{-4}\\ \lambda _G&=\left( \frac{\pi \rho _GN_{0G}}{\rho _{{\text dair}} Q_G}\right) ^\frac{1}{4} \quad \text{in}\, \text{m}^{-1}\\ \rho _G&= 917 \,\, \text{kg/m}^3 .\end{aligned}$$

In the above equations, \(Q_R,Q_S,Q_G\) are the mixing ratios (in kg/kg) of the hydrometeors rain, snow, and graupel, \(\rho _R, \rho _S, \rho _G\) are the densities, and \(\rho _{\text {dair}}\) is the dry air density (in kg/m\(^3\)).

A2. Drop size distributions of hydrometeors in the WSM6 scheme

The drop size distributions of the hydrometeors adopted in the WSM6 scheme are based on the Lin scheme, and thus follow the same exponential distribution, with a little modification adopted for snow.

A2.1 Rain

$$ \begin{aligned} n_R(D)&=N_{0R}e^{-\lambda D}dD \quad \text{in} \,\text{m}^{-3} \\ N_{0R}&=8\times 10^6 \quad \text{in}\, \text{m}^{-4}\\ \lambda _R&=\left( \frac{\pi \rho _RN_{0R}}{\rho _{\text {dair}} Q_R}\right) ^\frac{1}{4} \quad \text{in}\, \text{m}^{-1} \\ \rho _R&= 1000 \,\, \text{kg/m}^3. \end{aligned} $$

A2.2 Snow

$$ \begin{aligned} n_S(D)&=N_{0S}e^{-\lambda D}dD \quad \text{in}\, \text{m}^{-3}\\ N_{0S}&=2\times 10^6\times e^{0.12(T-T_0)} \quad \text{in}\, \text{m}^{-4}\\ \lambda _S&=\left( \frac{\pi \rho _SN_{0S}}{\rho _{\text {dair}} Q_S}\right) ^\frac{1}{4} \quad \text{in} \,\text{m}^{-1} \\ \rho _S&= 100 \,\, \text{kg/m}^3. \end{aligned} $$

Here, \(T\) is the temperature (K) and \(T_0\) is the reference temperature (273.16 K).

A2.3 Graupel

$$ \begin{aligned} n_G(D)&=N_{0G}e^{-\lambda D}dD \quad \text{in}\, \text{m}^{-3}\\ N_{0G}&=4\times 10^6 \quad \text{in} \,\text{m}^{-4}\\ \lambda _G&=\left( \frac{\pi \rho _GN_{0G}}{\rho _{\text {dair}} Q_G}\right) ^\frac{1}{4} \quad \text{in} \,\text{m}^{-1} \\ \rho _G&= 500 \,\, \text{kg/m}^3. \end{aligned} $$

A3. Drop size distributions of hydrometeors in the Thompson scheme

The Thompson scheme assumes generalized gamma distribution for each hydrometeor (except for snow) as:

$$\begin{aligned} n(D)&= \frac{N_t}{\Gamma (\mu +1)}\lambda ^{\mu +1}D^\mu e^{-\lambda D}dD \\ \lambda&= \left[ \frac{\Gamma (1+\mu +b_m)}{\Gamma (1+\mu )}\frac{a_mN_x}{Q_x}\right] ^{1/b_m} \\ N_t&= N_x\rho _{\text {dair}}. \end{aligned} $$

Here, \(N_t\) is the total number concentration, \(N_x\) is the prognostic number concentration (in 1/kg) of hydrometeor \(x\), \(Q_x\) is the mixing ratio of hydrometeor \(x\), \(a_m \;{\text and}\;b_m\) are the constant and exponents of mass-size relationship, \(\Gamma \) is the gamma function, and \(\mu \) is the shape parameter. When \(\mu =0\), the distribution becomes the classical exponential distribution. In the Thompson scheme, along with the mixing ratios, the number concentrations of rain and ice particles are also simulated. Thus, the scheme is known to be a double-moment scheme. Further information can be found at Oue et al. (2019).

A3.1 Rain

For rain particles, the shape parameter is 0. Thus, the drop size distributions becomes classical exponential distribution. The scheme uses the model simulated prognostic rain number concentration in the distribution.

$$ \begin{aligned} n_R(D)&=N_{t}e^{-\lambda D}dD \quad \text{in}\, \,\text{m}^{-3} \\ \lambda _R&= \left[ \frac{\Gamma (1+b_m)}{\Gamma (1)}\frac{a_mN_R}{Q_R}\right] ^{1/b_m} \quad \text{in}\,\, \text{m}^{-1} \\ \text{with} \quad a_m&= \frac{\pi \rho _R}{6}, \quad b_m = 3, \; \text{ the } \text{ distribution } \text{ reduces } \end{aligned} $$

to

$$ \begin{aligned} \lambda _R&=\left( \frac{\pi \rho _RN_{R}}{ Q_R}\right) ^\frac{1}{3} \quad \text{in} \,\text{m}^{-1} \\ N_t&= N_R\rho _{\text {dair}} \\ \rho _R&= 1000 \, \text{kg/m}^3. \end{aligned} $$

Here, \(N_R\) is the number concentration (in 1/kg).

A3.2 Snow

The Thompson scheme specially build for snow. Unlike the exponential or generalized gamma distribution, it follows the combination of both.

$$ \begin{aligned} n_S(D)&=\frac{{\mathcal {M}}_2^4}{{\mathcal {M}}_3^3}\left[ K_0e^{-\frac{{\mathcal {M}}_2}{{\mathcal {M}}_3}^{\bigwedge _0D}}+K_1\left( \frac{{\mathcal {M}}_2}{{\mathcal {M}}_3}D\right) ^{\mu _s}e^{-\frac{{\mathcal {M}}_2}{{\mathcal {M}}_3}^{\bigwedge _1D}}\right] \quad \text{ in } \text{ m}^{-3}\\ {\mathcal {M}}_n&= \int {D^nN(D)dD} \quad \text{ is } \text{ the } {n}{th} \text{ moment } \text{ size } \text{ distribution }\\ {\mathcal {M}}_n&= a(n,T_c){\mathcal {M}}_2^{b(n,T_c)} \\ {{\text {log}}}(a,T_c)&= 5.065339-0.062659T_c-3.032362n+0.029469T_cn-0.000285T_c^2+0.312550n^2+0.000204T_c^2n \\& \quad +0.003199T_cn^2+0.000000T_c^3-0.015952n^3 \\ b(n,T_c)& = 0.476221-0.015896T_c+0.165977n+0.007468T_cn-0.000141T_c^2+0.060366n^2+0.000079T_c^2n\\& \quad +0.000594T_cn^2+0.000000T_c^3-0.003577n^3 \\ \end{aligned}$$

where \(K_0 = 490.6, K_1 = 17.56, \wedge _0 = 20.78, \wedge _1 = 3.29, \mu _s = 0.6357, \text{ and } \, T_c \) is the air temperature in °C, \(\rho _S = 100\,\text{kg/m}^3. \)

A3.3 Graupel

For graupel also, the shape parameter is 0.

$$\begin{aligned} n_G(D)&=N_{0G}e^{-\lambda D}dD \quad \text{in}\, \text{m}^{-3}\\ N_{0G}&=\text{ max }\left[ 10^4,\text{ min }\left( \frac{200}{Q_g},5\times 10^6\right) \right] \quad \text{in}\, \text{m}^{-4}\\ \lambda _G&=\left( \frac{\pi \rho _GN_{0G}}{\rho Q_G}\right) ^\frac{1}{4} \quad \text{in} \,\text{m}^{-1} \\ \rho _G&= 500 \, \text{kg/m}^3. \end{aligned}$$

A4. Drop size distributions of hydrometeors in the Morrison double moment scheme

The Morrison scheme also adopted generalized gamma distribution for every hydrometeor. The scheme simulated number concentrations for all the hydrometeors, except cloud water. The shape parameter \(\mu \) is considered zero for rain, snow, and graupel. Thus, the generalized gamma distribution simplified to an exponential distribution, with \(N_t\lambda \) being considered as intercept. In addition, the constant and exponents of mass-diameter parameters are \(a_m = \frac{\pi \rho _x}{6}\) and \(b_m = 3\).

A4.1 Rain

$$ \begin{aligned} n_R(D)&=N_{0R}e^{-\lambda D}dD \quad \text{in}\, \text{m}^{-3} \\ N_{0R}&=N_t\lambda = N_R\rho _{\text {dair}}\lambda \quad \text{in}\, \text{m}^{-4}\\ \lambda _R&= \left[ \frac{\Gamma (1+b_m)}{\Gamma (1)}\frac{a_mN_R}{Q_R}\right] ^{1/b_m} \quad \text{in}\, \text{m}^{-1} \\ \lambda _R&=\left( \frac{\pi \rho _RN_R}{Q_R}\right) ^\frac{1}{3} \quad \text{in} \,\text{m}^{-1} \\ \rho _R&= 997 \,\, \text{kg/m}^3. \end{aligned} $$

A4.2 Snow

$$\begin{aligned} n_S(D)&=N_{0S}e^{-\lambda D}dD \quad \text{in} \,\text{m}^{-3} \\ N_{0S}&=N_S\rho _{\text {dair}}\lambda \quad \text{in}\, \text{m}^{-4}\\ \lambda _S&=\left( \frac{\pi \rho _S N_S}{Q_S}\right) ^\frac{1}{3} \quad \text{in} \,\text m^{-1} \\ \rho _S&= 100 \, \text{kg/m}^3. \end{aligned} $$

A4.3 Graupel

$$ \begin{aligned} n_G(D)&=N_{0S}e^{-\lambda D}dD \quad \text{in}\, \text{m}^{-3} \\ N_{0S}&=N_S\rho _{{\bar{\text {dair}}}}\lambda \quad \text{in}\, \text{m}^{-4}\\ \lambda _S&=\left( \frac{\pi \rho _G N_S}{Q_S}\right) ^\frac{1}{3} \quad \text{in}\, \text{m}^{-1} \\ \rho _G&= 400 \,\, \text{kg/m}^3. \end{aligned} $$

In the above equations, \(N_R, N_S, N_G\) are the number concentrations (in 1/kg) for rain, snow, and graupel, respectively.

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Baki, H., Chinta, S., Balaji, C. et al. A sensitivity study of WRF model microphysics and cumulus parameterization schemes for the simulation of tropical cyclones using GPM radar data. J Earth Syst Sci 130, 190 (2021). https://doi.org/10.1007/s12040-021-01682-3

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Keywords

  • Weather Research and Forecasting (WRF) model
  • microphysics schemes
  • cumulus physics schemes
  • GPM radar data
  • forward radar operator
  • cloud resolving model
  • radar simulator (CR-SIM)