Advances in Meteorology

Volume 2016 (2016), Article ID 5070154, 11 pages

http://dx.doi.org/10.1155/2016/5070154

## Coupling WRF Double-Moment 6-Class Microphysics Schemes to RRTMG Radiation Scheme in Weather Research Forecasting Model

^{1}Korea Institute of Atmospheric Prediction Systems (KIAPS), 35 Boramae-ro 5-gil, Dongjak-gu, Seoul 70770, Republic of Korea^{2}Atmospheric Sciences and Global Change Division, Pacific Northwest National Laboratory, Richland, WA 99354, USA

Received 22 December 2015; Revised 5 April 2016; Accepted 13 April 2016

Academic Editor: Mario M. Miglietta

Copyright © 2016 Soo Ya Bae et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A method to explicitly calculate the effective radius of hydrometeors in the Weather Research Forecasting (WRF) double-moment 6-class (WDM6) microphysics scheme is designed to tackle the physical inconsistency in cloud properties between the microphysics and radiation processes. At each model time step, the calculated effective radii of hydrometeors from the WDM6 scheme are linked to the Rapid Radiative Transfer Model for GCMs (RRTMG) scheme to consider the cloud effects in radiative flux calculation. This coupling effect of cloud properties between the WDM6 and RRTMG algorithms is examined for a heavy rainfall event in Korea during 25–27 July 2011, and it is compared to the results from the control simulation in which the effective radius is prescribed as a constant value. It is found that the derived radii of hydrometeors in the WDM6 scheme are generally larger than the prescribed values in the RRTMG scheme. Consequently, shortwave fluxes reaching the ground (SWDOWN) are increased over less cloudy regions, showing a better agreement with a satellite image. The overall distribution of the 24-hour accumulated rainfall is not affected but its amount is changed. A spurious rainfall peak over the Yellow Sea is alleviated, whereas the local maximum in the central part of the peninsula is increased.

#### 1. Introduction

Clouds exert a significant influence on weather and climate by absorbing or reflecting solar radiation [1]. For example, cirrus clouds allow most of the sunlight to reach the surface, whereas thicker cumulus clouds reflect much of the sunlight back into space. Thus, the cloud effects on radiative fluxes are very sensitive to cloud type, which is characterized by the amount, phase, and size of hydrometeors [2]. In particular, the size of hydrometeors comprising clouds is one of the important factors determining cloud optical depths, but it is typically assumed to be a function of temperature and surface type, or it is roughly estimated with a radiation scheme in most models. Recently, researchers tried to study proper coupling of water substances in microphysics and radiation processes. For example, explicit coupling between the Thompson microphysics scheme and the Rapid Radiative Transfer Model for GCMs (RRTMG) radiation scheme for the purpose of calculating cloud optical properties is available in Weather Research Forecasting (WRF) (v3.5.1 and higher) [3]. Thompson et al. [3] showed that radiation fluxes reaching ground with the revised approach are better matched with observations.

An RRTMG radiation scheme [4] is broadly used in weather forecasting models, and it specifies the size of hydrometeors regardless of cloud type or amount for radiation calculations. This scheme utilizes the correlated- approach to calculate fluxes and the heating rate efficiently and accurately [5], and it includes the Monte-Carlo Independent Column Approximation (McICA) technique [6, 7] for representing subgrid cloud variability. The effective radii of cloud droplets are, however, implicitly calculated as a function of temperature, snow depth, and sea ice fraction. For ice particles, a lookup table is used to calculate their radii as a function of atmospheric temperature for the range of 180–274 K over which the radii vary in the range of 5.928–250.6 m with the maximum of 140 m for computing the cloud optical depth with ice particles. The effective radius of the snow is assumed to be constant at 10 m.

Calculating the effective radii of hydrometeors consisting of a cloud requires their number and mass concentrations. For this, double-moment bulk microphysical schemes, such as Thompson [8], WRF double-moment 6-class (WDM6) [9], and Morrison [10] schemes, are needed, and they are implemented in the WRF model. For example, the Thompson microphysics scheme predicts the mass mixing ratio and number concentration of cloud ice and rain drops. Snow is unique in this scheme, because its density varies inversely with its diameter. The double-moment method is applied for warm rain microphysics in the WDM6 scheme, which predicts the number concentration of cloud drops and rain drops [9]. The Morrison scheme predicts the mass and number concentration of five hydrometeors: rain, ice, snow, graupel, and hail. There is a user-set switch for the rimed ice category to have properties of graupel or hail consistently [11]. The comparison studies of cloud microphysics schemes showed that the WDM6 simulation resulted in consistent structures and extents of simulated precipitation with observations relative to those of other schemes [12–14]. However, the WDM6 scheme does not yet include the computation process for the effective radii of hydrometeors.

The objective of this study is to develop a method for explicitly calculating the size of hydrometeors with the WDM6 microphysics scheme and to achieve physical consistency between the WDM6 microphysics and the RRTMG radiation schemes by using the calculated effective radii of hydrometeors for a radiative flux calculation. We formulate equations for calculating the effective radii of hydrometeors based on their characteristics, and we implement them in the WDM6 scheme to test the effect of this development on the simulation of radiative fluxes and precipitation for short-term weather forecasting.

#### 2. Method for Calculating Effective Radii of Hydrometeors

The WDM6 scheme includes prognostic calculations of cloud droplets, rain, cloud ice, snow, and graupel by accounting for the aerosol effects on cloud properties and the precipitation processes, and it produces cloud condensation nuclei (CCN), cloud water, and rain drop number concentrations [9, 15]. An ice process follows the WRF single-moment 6-class (WSM6) microphysics scheme [16] that the number concentration of ice particles is diagnosed with the mixing ratio of ice based on the equation derived from the ice’s terminal velocity and mass-diameter relationship. A snow size distribution is assumed to be exponential with the intercept of snow () as a function of temperature such that increases as the temperature decreases, and vice versa. The slope parameter for the size distribution of snow varies with the temperature and the mixing ratio of snow [17, 18].

Coupling the microphysics scheme to the RRTMG radiation scheme requires a calculation of hydrometeors’ effective radii, which is performed using the equations below. The effective radius of cloud water () is calculated with the following equation:where and are the radius and size distribution of the cloud droplet, respectively. The size distribution is a normalized form, and it can be expressed aswhere is the number concentration of cloud droplets and and are dispersion parameters for the size distribution with values of and . is a slope parameter [9], and it is defined as follows: where and are water and air density in kg m^{−3}, respectively. is the mixing ratio of cloud water in kg kg^{−1}. By substituting (2) into (1), the effective radius of cloud water can be obtained as

The number concentration () and the maximum dimension of cloud ice () can be expressed as a function of the mass concentration of the cloud ice () [19]. The shape of the cloud ice is assumed to be a single bullet. Mitchell et al. [20] showed an equation for the effective radius of cloud ice as a function of the maximum dimension. That equation slightly changes with the shape of the cloud ice. The effective radius of the ice () applied in this study is

For snow, several assumptions are applied to calculate the effective radius. The shape of the snow is a hexagonal plate, the ratio of the height to the diameter of the snow is 0.1 , and the diameter of the hexagonal snow is the same as the mean-volume diameter of snow calculated in the single-moment scheme . The size distribution of snow is assumed to be exponential with the slope parameter (), which is given byHere, is the density of the snow, and is the mixing ratio of the snow. The intercept value of the snow size distribution depends on the temperature as shown in Hong and Lim [16]. The effective radius of snow is the ratio of the volume to the cross section. The equations for the geometric cross section () and volume () are shown in Liou et al. [21] as follows: Applying the assumptions above to (7), we obtain the effective radius of snow () as follows:

The effective radius of cloud water for the single-moment scheme (WSM3, WSM5, and WSM6) uses a different equation from that for the double-moment scheme. The cloud size distribution is assumed to be the same as that of the rain, which is the exponential form. used in this study is 300 cm^{−3} [22]. The effective radius of cloud water for the single-moment scheme is obtained simply as . The effective radii of ice and snow for the single-moment scheme are the same as those for the WDM6 scheme.

#### 3. Numerical Experimental Setup

A significant amount of rainfall was recorded over the mid-western region of the Korean Peninsula from 26 to 28 July 2011 with a local maximum of approximately 587.5 mm. Most rainfall occurred during the 24-hour period from 1200 UTC 26 July to 1200 UTC 27 July, with a local maximum of about 449.5 mm day^{−1} [23]. At 1200 UTC 26 July 2011, typical synoptic scale features for a heavy rainfall development were observed. Low-level jets between the western Pacific subtropical high and the low-pressure system over central China brought warm and moist air from the Yellow Sea to the Korean Peninsula. The low-level jet with moist, warm air and a low-pressure trough in north China with dry and cold air rapidly developed a heavy rain cloud in the middle region of the Korean Peninsula [23, 24]. A more detailed synoptic overview of this heavy rainfall event was described in Jang and Hong [24].

The model used in this study is the Advanced Research WRF (ARW) version 3.6 [25] released in April 2014, which is constructed based on a fully compressible and nonhydrostatic dynamic core. The model uses a terrain-following hydrostatic pressure coordinate, and horizontal resolutions of the models are 27, 9, and 3 km for one-way nesting. The 3 km model covers the Korean Peninsula (Domain 3, 355 352) which is surrounded by the 9 km grid model (Domain 2, 259 223). Domain 2 is nested inside the 27 km grid model in turn (Domain 1, 178 150) (Figure 1). The number of vertical layers is 51 from the surface to 50 hPa. The simulation period is from 1200 UTC 25 July to 1200 UTC 27 July 2011. Initial and boundary conditions are from the NCEP Final (FNL) operational global analysis data on 1.0° 1.0° resolutions, and the boundary conditions are forced every 6 h.