Analyzing the Improvement Effect of the k-Distribution Method on the Radiation Parameterization for WRF Model

Abstract

To address the need for the accurate parameterization of radiative absorption by gasses (for predicting atmospheric warming), Chou et al. developed a new k-distribution method. In this study, we compared the improved k-distribution method (hereinafter referred to as the NEW method) with the New Goddard radiation schemes (hereinafter referred to as the OLD method) for the WRF (the weather research and forecasting) model. The results of radiative flux calculations by the NEW and OLD methods of k-distribution using the New Goddard Radiation Scheme were compared with the results of the line-by-line (LBL) method, and the results showed that the radiative flux calculated by the NEW was accurate to within 1.00 Wm⁻² with respect to the LBL, while the OLD showed large differences at altitudes above the upper troposphere and near the surface. Therefore, in this study, we selected clear-sky and cloudy-day conditions and compared the weather elements prediction results of WRF using the NEW and OLD methods. For the clear-sky days, the downward shortwave radiation at the surface and the temperature at 2 m above the surface (hereinafter referred to as T2) over land and ocean were reversed in sign due to the highly sensitive absorption coefficients of gasses. For cloudy days, the absorption effect by gasses harmonized with the scattering effect induced by cloud droplets; the differences in the shortwave and longwave radiations and radiative heating rate between the NEW and OLD methods were obvious. Thus, it was analyzed that the proposed NEW method could lead to significant improvements in forecasting weather elements.

1. Introduction

For weather and climate prediction, several numerical forecasting models have been operated by different countries worldwide; these numerical forecasting models consist of dynamics and physical processes [1]. Numerical weather prediction (NWP) models are broadly categorized into weather prediction and climate models. Weather models developed are regional models, which are used for short-term forecasts with a limited domain; in these models, initial and boundary values are important for ensuring good performance. However, climate models are used for conducting long-term forecasts at the global scale; radiative processes are the key to long-term forecasts, in addition to dynamics and cloud physics. To improve the accuracy of weather forecasts and climate projections, various research efforts are underway to improve radiation models and NWP models. Improvements in radiation models will more accurately simulate the radiative transfer process in the atmosphere, which is critical for forecasting with NWP models. High-resolution NWP models [2,3,4] are being used to accurately predict micrometeorological phenomena such as the urban heat island effect. In addition, research is also underway to use NWP models to simulate regional and global climates in detail [5,6].

The Earth maintains its thermal equilibrium by receiving radiant energy from the sun and emitting infrared radiation back to space; in recent years, the Earth has been warming gradually due to greenhouse gasses (GHGs) that comprise the Earth’s atmosphere [7,8]. The need for and importance of studying atmospheric radiation is increasing because the GHGs contained in the Earth’s atmosphere absorb shortwave radiation and trap the infrared radiation emitted by the planet into space, causing weather/climate changes [9,10,11,12,13,14].

In the radiation wavenumber region of the Earth’s atmosphere, the ultraviolet and visible regions are absorbed by ozone and scattered by air molecules and aerosols. This study focuses on analyzing the effect of gas absorption in the infrared wavenumber region. To parameterize the absorption process of radiation by gasses in a weather/climate model, it is necessary to calculate the radiative transmission of the layers in the model atmosphere. As the radiative transmission of the layers is a function of wavenumber, the LBL (line-by-line) method should be used for accurate calculations, but the parameterization method can be used for approximate calculations.

The weather research and forecasting (WRF) model [15] is equipped with the Goddard, New Goddard, Dudhia, community atmosphere model (CAM), rapid radiative transfer (RRTMG), Fu-Liou-Gu (FLG), and Geophysical Fluid Dynamics Laboratory (GFDL) models for shortwave radiation parameterization and the Goddard, New Goddard, RRTM, CAM, FLG, and GFDL models for longwave radiation parameterization [16,17,18,19,20,21,22]. The studies on the properties and sensitivities of the radiative parameterizations included in these WRF models have been published by Zempila et al. [23] and Kong et al. [24].

With respect to the radiation parameterization methods for the WRF model described in the previous paragraph, the New Goddard scheme uses the k-distribution method, which extends the absorption coefficients of gasses for a reference pressure ($p_r$) and temperature (${\theta }_r$) to all atmospheric layers [25,26]. However, because the absorption coefficients of gasses can be changed rapidly with altitude (with the changes in the pressure and temperature), the New Goddard scheme can lead to significant errors in the calculation of the absorption coefficients at high altitudes. Therefore, Chou et al. [27,28] developed a new k-distribution method that accounts for the variations in the reference air pressure (Pr) and temperature (θr) according to the types of gasses in the atmosphere and uses the absorption coefficients calculated using the LBL model to improve the accuracy of the radiation parameterization.

In this study, we applied the results of Chou et al. [27,28] to the New Goddard scheme and compared the differences in results of the radiative flux and heating (cooling) rates and the temperature predicted using the WRF model obtained using the existing (OLD) and improved (NEW) k-distribution methods. As the results of the improved k-distribution method developed by Chou et al. [27,28] portrayed significant differences compared to those obtained using the existing k-distribution method, especially at high altitudes, we set the top of the atmosphere in the WRF model to 50 hPa and 10 hPa, respectively. Furthermore, we compared the results for urban, forest, and marine areas in the same latitude region around the Korean Peninsula to analyze the differences in the surface characteristics inferred by both methods.

2. Data and Methods

2.1. Existing k-Distribution (OLD) Method

The Earth’s atmospheric radiation is divided into different wavelengths (from ultraviolet to infrared) by wavenumber; however, scattering by air molecules, aerosols, and cloud particles, which is important in the ultraviolet–visible region, is not the focus of this study. In this study, we analyzed the results of the development of the parameterization of the absorption process of gasses in the wavenumber regions of 14,290–1000 cm⁻¹ (shortwave radiation) and 3000–20 cm⁻¹ (longwave radiation). The equations used for the k-distribution method are summarized below. Notably, for a clear atmosphere with no clouds, the direct shortwave flux [F(p)] in the wavenumber region Δν, through a scaled absorber amount of gas (w), can be represented as shown below [25]:

$$F\left(w\right)=\underset{\Delta \nu }{\overset{ }{{\displaystyle \int }}}{e}^{-k_{\nu }w}{S}_{\nu }d\nu$$

(1)

where $S_{\nu }$ is the extraterrestrial shortwave flux at the wavenumber region (Δν), and $k_{\nu }$ is the absorption coefficient. Then, using Equation (1), we defined the flux-weighted mean transmission [T(w)], as shown in Equation (2).

$$T\left(w\right)=\underset{\mathsf{\Delta }\nu }{\overset{ }{{\displaystyle \int }}}{e}^{-k_{\nu }w}{S}_{\nu }d\nu /\underset{\mathsf{\Delta }\nu }{\overset{ }{{\displaystyle \int }}}{S}_{\nu }d\nu$$

(2)

For the calculation of T(w) in Equation (2), $k_{\nu }$ can be calculated using the LBL method, based on the wavenumber, and parameterized using the k-distribution method, as shown below:

$$k_{\nu }\left(p,\theta \right)=k_{\nu } \left(p_r,{\theta }_r\right){\left[\frac{p}{p_r}\right]}^{m}f\left(\theta ,{\theta }_r\right)$$

(3)

where $p_r$ and ${\theta }_r$ denote the reference pressure and temperature, respectively; m is the empirical constant (m ≤ 1), and f(θ,${\theta }_r$) is the temperature scaling function. Notably, the T(w) value shown in Equation (2) for a given wavenumber region can be calculated in a short time using the k-distribution method (see Equation (3)). However, the calculation of the radiant flux-weighted average transmittance for gasses in the atmosphere requires effort and experience, owing to its rapid changes depending on the type of gas, wavenumber, pressure, and temperature.

Similarly, for infrared radiation, we calculated the Planck-weighted flux transmittance, (p,p′), for a given wavenumber region (Δν) and pressure range (from p′ to p), using the k-distribution method shown in Equation (3) [26].

$$T\left(p,p^{\prime }\right)=\frac{{{\displaystyle \int }}_{\mathsf{\Delta }\nu }^{ }{B}_{\nu }\left({\theta }_0\right)T_{\nu }\left(p.p^{\prime }\right)d\nu }{B\left({\theta }_0\right)}$$

(4)

where $B_{\nu }$ is the Planck function, and Tν(p.p′) is the flux transmittance for isotropic radiation, expressed in terms of the μ direction (cosine of zenith angle) for a plane parallel atmosphere, which can be expressed as follows:

$$T_{\nu }\left(p.p^{\prime }\right)=2\underset{0}{\overset{1}{{\displaystyle \int }}}{e}^{-k_{\nu }\left(p,p^{\prime }\right)/\mu }\mu d\mu$$

(5)

2.2. Improved k-Distribution (NEW) Method

In the k-distribution method mentioned in Section 2.1, $p_r$ in Equation (3) was empirically set to the pressure in the upper troposphere; however, this method may cause significant errors in the simulation of the upper atmosphere, where the pressure is low. In other words, as global warming is an important concern for several countries, and radiation parameterization is important for climate analysis and prediction, as well as regional weather assessment, it is important to improve the accuracy of the existing k-distribution method. In line with this need, Chou et al. [27,28] used the following Equation (6) instead of using Equation (3).

$$k_g\left(p,\theta \right)={\omega }_g{k}_{g.lin}\left(p,\theta \right)+\left(1-{\omega }_g\right)k_{g.nonlin}\left(p,\theta \right),0<{\omega }_g<1$$

(6)

where $k_g$(p,θ) denotes the mean absorption coefficient for a given spectral band for groups (g) separated according to the magnitude of the spectral absorption coefficient for each wavenumber at pressure (p) and temperature (θ) (the g values were divided into 3–12 spectral bands for shortwave and longwave radiations, depending on the type of gas). If the absorption coefficients of each gas are listed in the order of magnitude for a given spectral band, the part where the absorption coefficient does not change much can be divided into $k_{g.lin}\left(p,\theta \right)$, and the part where the absorption coefficient changes rapidly can be divided into $k_{g.nonlin}\left(p,\theta \right)$; each variable was empirically weighted (${\omega }_g$) to calculate the absorption coefficient differently. Notably, $k_{g.lin}\left(p,\theta \right)$ and $k_{g.nonlin}\left(p,\theta \right)$ were calculated according to the gas type, p, and θ, according to the LBL model, and then applied to the k-distribution method. Notably, in this case, the existing k-distribution method (New Goddard radiation scheme; hereinafter referred to as the “OLD” method) used the pressure in the upper troposphere as the reference air pressure ($p_r$) in Equation (3), Chou et al. [27,28] considered a combination of pressure values in the lower and middle troposphere and the stratosphere to improve the accuracy of the calculation of the absorption coefficient (known to vary rapidly with pressure).

The LBL model for the calculation of the right-hand side terms in Equation (6) was based on Chou and Kouvaris [29], and the absorption line data for gasses used for this calculation were derived from the HITRAN2012 spectroscopic database [30]. The radiation parameterizations were based on the LBL model results obtained using the absorption data for gasses, which were revised every 4 years. However, the radiative transfer models included in numerical weather models have a limitation; the entire radiative transfer process must be recalculated and analyzed to reflect the improved absorption data. Notably, the radiative transfer models of the numerical WRF model used in this study were based on the absorption data recorded prior to 2010.

2.3. WRF Model

The WRF model is a numerical forecasting model developed by the National Centers for Environmental Prediction (NCEP) and National Center for Atmospheric Research (NCAR) in the United States of America (USA) and the Air Force Weather Agency (AFWA) and Naval Research Laboratory (NRL) of the Department of Defense; the model is being continuously improved and developed and is widely used for weather analysis and prediction [1]. In this study, the domain for the numerical simulation of the WRF model was set as shown in Figure 1, i.e., centered at 36° N and 127.5° E, with a horizontal resolution of 179 × 216 grid and spatial resolution of 3 km; the vertical layer consisted of 70 sigma layers from the surface and the atmospheric top pressure was set at 10 and 50 hPa. The cloud microphysics parameterizations were derived from the Goddard 4-Ice scheme [31], the planetary boundary layer (PBL) from the Yonsei University (YSU) scheme PBL technique [32], and the surface model from the Noah Multiparameterized Land Surface Model (NOAA LSM) scheme (surface temperature 5-layer).

The New Goddard scheme based on the existing k-distribution parameterization (OLD) method [25,26] was used for analyzing the radiative physical process, and the improved k-distribution parameterization (NEW) method [27,28] was integrated into the scheme. As shown in Figure 1, with small squares (15 km × 15 km; 5 × 5 grids mean), we selected a city (Seoul), ocean (West Sea), and forest (Gangwon-do) area at the same latitude for the surface characterization of the radiation elements, and other numerical model elements considered in this study are summarized in

Table 1. Summary of the weather and forecasting (WRF) model configuration considered in this study.

Parameter	Configuration
NWP version	WRF V4.3
Horizontal grid spacing	3 km
Dimension	179 × 216 × 70
Integral time step (s)	3
Vertical layer	70 Sigma layers/10 hPa OR 50 hPa
Initial condition	ECMWF ERA5 reanalysis hourly data (0.25° × 0.25°)
Microphysics	Goddard 4-ice
Planetary boundary layer	YSU PBL
Land-surface Model	5-layer thermal diffusion
Experiment	OLD	NEW
Longwave radiation scheme	New Goddard (existing k-distribution method)	Improved k-distribution method
Shortwave radiation scheme	New Goddard (existing k-distribution method)	Improved k-distribution method

Abbreviations: Numerical weather prediction (NWP), Yonsei University scheme (YSU), planetary boundary layer (PBL), fifth generation of the European Centre for Medium-Range Weather Forecasts (ECMWF ERA5).

.

2.3.1. Reanalysis Data

One-hourly products of the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis version 5 (ERA5) [33] were used as the initial and boundary conditions for the simulations (https://cds.climate.copernicus.eu; accessed on 4 June 2024). Notably, ERA5 is a global atmospheric reanalysis data produced by the ECMWF; it uses a forecast model and data assimilation system to reanalyze archived observations. Compared with the previous generation (ERA-Interim), the ERA5 data have much higher spatiotemporal resolutions: (a) time scale: increased from six-hourly to hourly analysis, (b) horizontal resolution: increased from ~81 to ~31 km, and (c) vertical resolution: increased from 60 to 139 levels [33]. Gossart et al. [34] evaluated three reanalysis datasets over the Antarctic Ice Sheet and concluded that the ERA5 dataset captured the seasonal variations in the surface temperature effectively while portraying only minimal bias (compared with observations).

2.3.2. Case Selection

We considered two cases for the WRF simulation, clear day (11 November 2020) and cloudy day (24 June 2020) cases, for analyzing the shortwave and longwave radiation fluxes and heating rates; the ground weather maps for these cases are shown in Figure 2.

Figure 2a portrays the clear-day case, wherein the Korean Peninsula is surrounded by a high-pressure center at 1033 hPa, and the Vamco typhoon (with a center pressure of 975 hPa and maximum winds of 6 knots) is moving northward over the sea, east of the Philippines. Figure 2b portrays the cloudy-day case, wherein the Korean Peninsula is surrounded by a low-pressure zone, with precipitation on the west coast.

3. Results

3.1. Comparison of Radiative Flux and Heating (Cooling) Rates Calculated Using the OLD and NEW k-Distribution Methods

3.1.1. Shortwave Radiation

The calculation results of the shortwave radiation flux and heating rate are calculated using the k-distribution method, as shown in Equations (3) and (6), applied in the New Goddard scheme of WRF (along with the LBL model results), are shown in Figure 3 and Figure 4. The mid-latitude summer standard atmosphere [35] was used as the input data for the calculations, and the solar zenith angle (θ) was set as 60°. The data of the downward shortwave radiation ($S_{\nu }$) incident for the upper boundary of the model atmosphere were derived from the ASTM (the 2000 version of the American Society for Testing and Materials Standard Extraterrestrial Spectrum Reference E-490-00, with the solar constant being 1366.1 Wm⁻²; https://www.nrel.gov/grid/solar-resource/spectra-astm-e490.html; accessed on 4 June 2024). The downward shortwave radiations (extraterrestrial solar radiation, S) for the water-vapor wavenumber region (14,290–1000 cm⁻¹) and the carbon dioxide wavenumber region (8200–1000 cm⁻¹) in Figure 3 and Figure 4 were set as 364.44 and 143.23, 1.0 Wm⁻², respectively; for convenience, the pressure (Y axis) was plotted from 0.01 hPa to 1000 hPa.

Figure 3a portrays the vertical variations in the downward shortwave flux with water-vapor absorption, along with the three values derived using the LBL method (labeled LBL in the figure, the improved k-distribution method [28] (labeled NEW), and existing k-distribution method [25,36] (labeled OLD) were in agreement at 364.44, 364 Wm⁻² and 0.01 hPa (model atmosphere). The downward shortwave radiation decreased rapidly as it reached the upper troposphere; the results of the LBL, NEW, and OLD methods at the surface were 251.49, 251.13, and 247.78 Wm⁻², respectively. The difference between the LBL and NEW methods was accurate to 0.36 Wm⁻², while the difference between the LBL and OLD methods was 3.71 Wm⁻², as shown in Figure 3d. The downward shortwave radiations absorbed by the atmosphere (from 0.01 hPa to 1000 hPa) were 113.31 and 116.67 Wm⁻² for the NEW and OLD methods, respectively, with the value calculated using the NEW method being 3.36-Wm⁻² less than the values for the water-vapor absorption of shortwave radiation calculated using the OLD method.

As the carbon dioxide absorption effect of shortwave radiation (8200–1000 cm⁻¹) is weaker than that of water vapor, the difference in the results for carbon dioxide in the NEW and OLD methods was smaller than the results for water vapor, as shown in Figure 3b. The downward shortwave radiation at the top of the atmosphere was 143.23 Wm⁻² for the LBL, NEW, and OLD methods, but their values dropped sharply, corresponding to the lower stratosphere; the differences between the results of the NEW and OLD methods at the surface were 0.12 and 1.02 Wm⁻², respectively, as shown in Figure 3e. As shown in Figure 3c,f, the absorption effect of shortwave radiation by water vapor was larger than that of carbon dioxide, and the absorption of shortwave radiation (14,290–1000 cm⁻¹) by water vapor and carbon dioxide was 3.22 Wm⁻² smaller than that of OLD (119.91 Wm⁻²) in NEW (116.69 Wm⁻²).

Figure 4a presents the vertical profile of the radiative heating rate for water-vapor absorption, wherein the heating rates for the LBL and the NEW and OLD k-distribution methods, at 0.01 hPa, were 0.45, 0.42, and 3.17 K day⁻¹, respectively. The OLD method differed from the LBL method at altitudes above 1 hPa, and the difference increased to 0.01 hPa, while the NEW method was accurate, with the difference from the LBL results being less than 0.02 K d⁻¹. However, as shown in Figure 4d, at lower altitudes of 1000 hPa, the differences between the NEW and OLD methods for LBL results were smaller, −0.04 and 0.02 K d⁻¹, respectively. This indicated that for the upper atmosphere (above the stratosphere), the NEW method was more accurate than the OLD method, whereas, in the lower troposphere, the difference between the NEW and OLD methods was smaller or even reversed in magnitude at higher pressure and water-vapor content.

The heating effect induced by carbon dioxide (shown in Figure 4b) was smaller than that induced by water vapor, indicating that the difference in the heating rates between the NEW and OLD methods could be reversed for the conditions characteristic of the troposphere (Figure 4e). The combined effect of water vapor and carbon dioxide (Figure 4c and Figure 4f, respectively) was similar to the heating rate of water vapor (Figure 4a,d) in the troposphere and the heating rate of carbon dioxide (Figure 4b,e) in the stratosphere and above.

For this study, shortwave radiation was categorized into ultraviolet (57,140–25,000 cm⁻¹), visible (25,000–14,280 cm⁻¹), and infrared (14,280–1000 cm⁻¹) radiation; the absorption and scattering processes by ozone were dominant in the ultraviolet and visible regions, which were not the focus of this study. In the infrared wavenumber region of shortwave radiation (14,280–1000 cm⁻¹), wherein the absorption of water vapor and carbon dioxide is important, the difference between the shortwave radiation flux and heating rate in the lower troposphere and upper stratosphere was obvious in the NEW method. Thus, compared to the results of the OLD method, those of the NEW method can portray significant differences at high altitudes above the troposphere and stratosphere. These differences can be significant, especially if the WRF’s top-of-model atmosphere is extended to altitudes above the troposphere (for climate analysis).

3.1.2. Longwave Radiation

With respect to infrared radiation (20–3000 cm⁻¹), the difference in the radiative flux and radiative cooling rate between the NEW and OLD methods for LBL is shown in Figure 5 and Figure 6, using standardized mid-latitude summer atmosphere data.

With respect to shortwave radiation (57,140–1000 cm⁻¹), ultraviolet and visible light were absorbed by ozone; however, ozone absorption was not considered in this study because ozone absorption coefficients in these wavenumber regions vary weakly with pressure and temperature, rendering the k-distribution method ineffective. However, the infrared radiation emitted by the Earth and its atmosphere is absorbed by not only water vapor and carbon dioxide but also ozone. Minor gasses, such as ${\mathrm{N}}_2\mathrm{O} {\mathrm{and} \mathrm{CH}}_4$, are also important infrared radiation absorbers; the calculation results for the flux and radiative cooling rate for these minor gasses in this infrared wavenumber region were introduced in the study conducted by Chou et al. [27]. In our study, the results for the radiation flux and cooling rate calculations for water vapor (20–3000 cm⁻¹) and carbon dioxide (540–1100 and 1900–3000 cm⁻¹), known to be an important absorber of infrared as well as shortwave radiation, are shown in Figure 5 and Figure 6, respectively. All the gasses in these figures mean not only water vapor and carbon dioxide but also ozone (980–1100 cm⁻¹) and minor gasses, such as ${\mathrm{N}}_2\mathrm{O}$ and ${\mathrm{CH}}_4$.

As shown in Figure 5a, the net longwave radiation results estimated using the LBL method for the water-vapor wavenumber region (20–3000 cm⁻¹) at the upper limit of the model atmosphere pressure (0.00 hPa) and the surface pressure (1013 hPa, surface temperature = 294 K) were −335.19 and −150.95 Wm⁻² (the “−“ sign denotes the upward direction), respectively; the infrared radiation emitted from the atmosphere to space was estimated to be −184.24 Wm⁻². The infrared radiation fluxes estimated using the NEW and OLD methods at the upper limit and surface of the model atmosphere were −335.10 and −150.31 Wm⁻² and −335.92 and −155.46 Wm⁻², respectively. Compared to the LBL method, the NEW (−335.10−(−150.31) = −184.79 Wm⁻²) method portrayed a larger infrared radiation emitted to the space (0.55 Wm⁻²), while the OLD (−335.92-(−155.46) = −180.46 Wm⁻²) method portrayed a smaller infrared radiation emission (3.78 Wm⁻²). The difference in the net infrared radiation with altitude between the NEW and OLD methods, compared to that estimated by the LBL method, portrayed an increasing trend toward the surface, as shown in Figure 5d.

In the case of carbon dioxide (Figure 5b,e), the flux difference between the LBL and NEW methods was not greater than 2.00 Wm⁻², whereas that between the LBL and OLD methods was greater than 5.00 Wm⁻² at all altitudes of the model atmosphere (except at the surface level). The results for all gasses, including water vapor, carbon dioxide, and minor gasses (Figure 5c,f), were similar to the estimation for water vapor; however, the flux difference between the NEW and OLD methods compared to the LBL method varied with altitude, as shown in Figure 5f. The longwave radiation emitted from the atmosphere to space, as estimated using the NEW and OLD methods, was −175.76 Wm⁻² and −172.71 Wm⁻², respectively; compared to the LBL method (−176.41 Wm⁻²), the NEW method was more accurate than the OLD method, portraying a difference of 0.65 Wm⁻² compared to the difference of 3.70 Wm⁻² noted for the OLD method.

As shown in Figure 6a,d, for the infrared radiative cooling rate due to water vapor, the results of the LBL and NEW methods were in agreement, within 0.500 Kday⁻¹, for the entire model atmosphere, whereas the results of the OLD method differed significantly from those of the LBL for altitudes above the upper troposphere. The difference noted between the LBL and OLD methods for water vapor was similar to that for carbon dioxide, shown in Figure b,e. A large difference in the infrared radiation cooling rate was noted, beginning from the altitude of 1.00 hPa to the upper limit of the model atmosphere (see Figure 6c,f); the results for water vapor and carbon dioxide portrayed similar characteristics.

3.2. Sensitivity of the WRF Model

The NEW method calculated the radiation flux and heating rate (cooling rate) more accurately than the OLD model. In this section, we compare the variations in the radiative components and temperature (2 m above the surface) predicted using both the k-distribution methods (NEW and OLD) for WRF (using the New Goddard scheme), for clear and cloudy cases around the Korean Peninsula.

3.2.1. Clear Day

Shortwave Radiation

To analyze the difference between the NEW and OLD methods for radiation parameterization (New Goddard scheme), the numerical simulation for the WRF model for the clear-day case (11 November 2020) was set as per Figure 2 and Table 1, and the upper limit of the model atmosphere was set to 10 hPa (Figure 7).

Figure 7 portrays the spatial distribution of downward shortwave radiation at the surface (SSWDN) and upward shortwave radiation at the top of the atmosphere (TSWUP), based on the result of numerical experiments with the WRF model for 03UTC 11 November 2020 (note that the extreme left and right values in these plots are due to light cloud cover, which we did not consider in this study). The SSWDN was higher at low latitudes, as shown in Figure 7a,b, while the TSWUP passed through the atmosphere, as shown in Figure 3 and Figure 4d, due to the variations in the shortwave radiation transmittance with the amount of water vapor and pressure near the land surface. Notably, the flux difference between the NEW and OLD method simulations over land and ocean portrayed a reverse sign, as shown in Figure 7c. However, the estimation of the TSWUP at the top of the atmosphere (Figure 7d–f) was larger in the NEW method than that estimated by the OLD method due to the estimated large water-vapor absorption in the OLD method (at the top of the atmosphere) (as shown in Figure 3d).

Longwave Radiation

The differences between the NEW and OLD methods for longwave radiation are shown in Figure 8. The differences between the land and ocean area for shortwave radiation fluxes and heating rates were clear, as shown in Figure 7, but the differences for longwave radiation were not obvious. As shown in Figure 8a, the SLWDN estimated using the NEW method was greater than that estimated using the OLD method (at the surface), and the difference in longwave radiation was greater than that of shortwave radiation, as shown in Figure 7c. Moreover, at high altitudes above the stratosphere, as shown in Figure 6a,c, the absorption of longwave radiation by gasses estimated using the OLD method was small; therefore, the emission of longwave radiation in the direction of the surface was also small. In the lower troposphere (at 1000 hPa), the estimated downward longwave radiation was greater (10.00 ± 5.00 Wm⁻²) in the NEW method than that in the OLD method, as shown in Figure 8a. As shown in Figure 6a,c, the simulation conducted using the OLD method indicated less absorption of the longwave radiation emitted by the surface and atmosphere; therefore, the upward longwave radiation reflected to the space from the top of the atmosphere (TLWUP) was greater than 3.00 ± 2.00 Wm⁻² in the OLD method, as shown in Figure 8b.

Air Temperature at An Altitude of 2 m from the Surface

Figure 9 portrays the spatial distribution of the temperature 2 m above the surface (denoted as T2 in Figure 9) with respect to the numerical simulation for the clear-day case (11 November 2020) in Figure 2. Figure 9a portrays the predicted results at T2 at 03UTC (12LST) predicted using the OLD method, wherein the maximum temperature in the ocean was around 290 K, and the land temperature was assumed to be lower than the ocean temperature. Figure 9b portrays the difference in the temperature estimations between the NEW and OLD methods, which varied from ±4 to 5 K depending on the region, and the temperature estimated using the NEW method was higher than that estimated using the OLD method over land; the opposite trend was observed over the ocean, due to the variations in the absorption coefficients of gasses depending on the atmospheric pressure and temperature.

The temperature values at the height of 2 m numerically simulated using the WRF for two land areas (Seoul and Gangwon-do) and the sea (West Sea) at the same latitude are shown in

Table 2. Mean temperatures (T2) in the Seoul, West Sea, and Gangwon-do regions were simulated using the weather research and forecasting (WRF) model at 03UTC on 11 November 2020 (Units: K).

	WRF Top Level	OLD	NEW	NEW-OLD
Seoul	10 hPa	285.29 ± 0.70	285.63 ± 0.75	0.34
	50 hPa	285.37 ± 0.72	285.67 ± 0.76	0.29
West Sea	10 hPa	285.57 ± 0.13	285.56 ± 0.11	−0.01
	50 hPa	285.64 ± 0.11	285.60 ± 0.09	−0.04
Gangwon-do	10 hPa	281.75 ± 0.53	281.86 ± 0.52	0.11
	50 hPa	281.78 ± 0.53	281.88 ± 0.53	0.10

. Seoul and Gangwon-do are land areas; the temperature estimated using the NEW method was higher than that estimated using the OLD method, as shown in Figure 9b, while the opposite was true for the sea area. In addition, the temperature when the upper limit of the model atmosphere was set to 50 hPa was higher by 0.10 K or less in all three regions, as the amount of radiation reaching the surface increased because less radiation was absorbed by the atmosphere when the upper limit was set to 50.

3.2.2. Cloudy Day

Shortwave and Longwave Radiations

For the cloudy-day case (24 June 2020) shown in Figure 2, the results of the same analysis as in Figure 7 were shown in Figure 10. On a clear day in Figure 7c, the difference in the downward short wave flux between the NEW and OLD methods at surface was 5.00 Wm⁻², but when thick clouds were moving from the northwest (as shown in Figure 10a), the combination of radiation absorption and emission by a large amount of water vapor and scattering by cloud droplets caused the difference between the NEW and OLD to be more than 400.00 Wm⁻² (as shown in Figure 10b). The TSWUP reflected back to space from the top of the atmosphere (as shown in Figure 10c) also portrayed regions where the difference between the estimations of the NEW and OLD methods was greater than 500.00 Wm⁻² in cloudy areas (as shown in Figure 10d). This suggested that the difference in the radiative fluxes and heating rates between the NEW and OLD methods in cloudy situations (compared to the clear-day case) can have a significant impact on the prediction of meteorological elements, including precipitation.

Figure 10e,f portray the vertical profiles of the shortwave radiation heating rate for Seoul for the same cloudy case; when the OLD method was used, and the upper limit of the model atmosphere was set to 10 hPa, the heating rate was 24.24 K d⁻¹ at a cloud height of 500 hPa, portraying a difference of ±10.00 K d⁻¹ compared to the estimations of the NEW method.

Figure 11 portrays the same results for longwave radiation as in Figure 10; for the results of the OLD method shown in Figure 11a, the downward longwave radiation at the surface was above 400.00 Wm⁻², depending on the cloud distribution. The difference between the downward longwave radiation estimated using the NEW and OLD methods was ± 20.00 Wm⁻², depending on the cloud distribution, as shown in Figure 11b, which was much smaller than the estimations of shortwave radiation shown in Figure 10b. In addition, the TLWUP reflected space ranged from −100.00 to −300.00 Wm⁻² in the OLD method, depending on the distribution of clouds, as shown in Figure 11c, while the difference between the NEW and OLD methods was mostly ±100.00 Wm⁻² or less, as shown in Figure 11d. The cooling rate (Figure 11e,f) of longwave radiation for the Seoul region was maximized to 18.91 K d⁻¹ at a height of about 400 hPa for the OLD method when the upper limit of the model atmosphere was 10 hPa, and the difference with the NEW method was somewhat larger than that shown in Figure 10e,f.

Air Temperature at An Altitude of 2 m

Figure 12a portrays T2 predicted using the OLD method for the summer case (24 June 2020), portraying a variation from 290 K to 300 K depending on the cloud fraction, and the difference between the NEW and OLD methods was similar to the results for the clear-day case shown in Figure 9b. However, as shown in Figure 12c, depending on the cloud distribution and time, the difference in the temperature (T2) between the NEW and OLD methods was up to 4.00 K or more in the SEOUL region, but this difference was very small, less than 1.00 K, in the West Sea region. This indicates that over land, the accuracy of calculating radiative absorption by gasses can be emphasized because the combination of albedo and multiple scattering between clouds and the surface can result in large temperature (T2) changes.

Precipitation

For the case of a cloudy day (24 June 2020), a precipitation distribution (using OLD method) of 10.00 ± 5.00 mm/h was predicted, moving from the western coast of the Korean Peninsula to the eastern land, as shown in Figure 13a, and the difference between the NEW and OLD method was about ±5.00 mm/h, as shown in Figure 13b. In Seoul and West Sea, the hourly precipitation difference between the NEW and OLD methods was about ±2.00 mm/h, as shown in Figure 13c,d, and the difference between the NEW and OLD methods was up to ±2.00 mm/h or more (10:00 h on 24 June in Seoul), when the upper limit of the model atmosphere was set to 10 hPa and 50 hPa.

3.3. Validation

In this study, the correlation coefficient between the meteorological elements (shortwave radiation, temperature, and precipitation) predicted using the numerical WRF and the data of the Korea Meteorological Administration’s ground observation network (AWS: Automated Synoptic Observing System, ASOS: Automated Synoptic Observing System; number of stations: more than 600, but only 55 shortwave radiation stations) was calculated, as shown in Figure 14. In this figure, for SSWDN, only the clear data (11 November 2020) was used due to the instability of pyranometer observations during cloud cover and precipitation; for temperature (at 2 m height), both clear and cloudy data (24 June 2020) were used; for precipitation, only data from rainy areas were used. The WRF numerical experiments set the upper limit of the model atmosphere to 10 hPa, and the radiation parameterization used the improved k-distribution method (NEW).

As shown in Figure 14a, the average correlation coefficient between the downward shortwave radiation at the surface simulated by the WRF and the data observed by the Korea Meteorological Administration (KMA) was 0.93. In the island areas to the west and south of the Korean Peninsula, the correlation coefficient was below 0.90 due to the variations in the water-vapor content (associated with westerly winds), but the correlation coefficient increased toward the interior of the Korean Peninsula, reaching a maximum of 0.97. However, as shown in Figure 14b, the correlation coefficient of T2 between the WRF numerical simulations and KMA observations was higher in the flat western part of the Korean Peninsula, compared to that in the mountainous eastern part of the Peninsula, portraying an average value of 0.88 (maximum of 0.98). For precipitation, the correlation coefficient was not high, as shown in Figure 14c, due to the mismatch between the numerical model results and observations, but the average across the Korean Peninsula was 0.47.

The KMA station, which produces the data used to verify the improvement of the gas absorption process in the radiation parameterization of the WRF, is not part of the international baseline surface radiation network (BSRN) site, but the pyranometers installed there are state-of-the-art instruments from KIPP$ZONEN (the Netherlands) and EKO (Japan), calibrated at the World Radiation Center in Davos (Switzerland) and Regional Radiation Center of Japan. Because the temperature and precipitation sensors were calibrated with the KMA’s own superior technology, the quality of the KMA’s observations is at par with international standards. However, the differences in the SWDN, T2, and precipitation at the surface, with respect to the NEW and OLD methods, were within the observation error range; therefore, the improvement of the k-distribution method was not clearly reflected by the observation data. Nevertheless, as shown in Figure 14a,b, the simulated SWDN and T2 were in relatively good agreement with the observations, and further analysis of these data can serve as a validation of the radiation parameterization method. However, further research will be required because the precipitation data were still far from the results of the theoretical numerical model.

4. Conclusions

The existing k-distribution method [25,36] is widely used to calculate gas-specific absorption coefficients in radiation parameterization models; this method was improved by Chou et al. [27,28]. The results of the NEW method were compared with the LBL model results and coupled with the WRF numerical model to analyze the prediction results of different meteorological elements.

The upward shortwave radiation flux and upward net longwave radiation flux calculated using the WRF model and input data of standard MLS atmosphere, were compared with the results of the LBL model. With respect to the shortwave radiation region (14,290–1000 cm⁻¹), the NEW method was accurate to within 1.00 Wm⁻² of the downward shortwave radiation flux estimated using the LBL model, while the OLD method portrayed a difference of up to 3.78 Wm⁻² from the LBL model (for the lower troposphere). The atmospheric absorption of shortwave radiation (364.44 Wm⁻²) incident on the model atmosphere was 3.22 Wm⁻² smaller for NEW (116.69 Wm⁻²) than for OLD (119.91 Wm⁻²).

The net longwave radiation (20–3000 cm⁻¹) emitted to space from the Earth’s surface and atmosphere (−176.41 Wm⁻²), compared to that estimated using the LBL model (−175.76 Wm⁻²) was also accurate, portraying a difference of 0.65 Wm⁻² for the NEW (−175.76 Wm⁻²) model. The estimation conducted using the OLD method (−172.71 Wm⁻²) portrayed a lower value than that estimated using the NEW method. The NEW method portrayed less absorption (by 3.22 Wm⁻²) of the shortwave radiation and higher emittance (3.05 Wm⁻²) of the longwave radiation than the OLD method; the NEW to cool the atmosphere by 6.27 Wm⁻² compared to the OLD, and this difference can have a significant impact on the prediction of various weather/climate elements, especially in the stratosphere above the troposphere and near the surface. In particular, the accurate prediction of radiant energy at the Earth's surface using this research will be important for the development of renewable energy and agricultural/fisheries applications.

The differences in the radiation, T2, and precipitation between the OLD and NEW methods for the clear and cloudy cases over the Korean Peninsula were compared. For the clear day case, the difference in the flux between the NEW and OLD methods was reversed for land and ocean due to the sensitive absorption coefficient of gasses near the surface of the Earth, which varied depending on the amount of water vapor and pressure. However, the difference between estimations over the land and ocean was not obvious for the downward longwave radiation, with the estimation conducted using the OLD method being greater than that using the NEW method for the upward longwave radiation reflected from the top of the atmosphere to the space. Additionally, T2 estimations using the NEW and OLD methods were reversed in sign over land and ocean due to the variations in the absorption coefficient of gasses. The complexity of the absorption by gasses and the scattering by cloud droplets on cloudy days suggests that the differences in the shortwave and longwave radiation and radiative heating (cooling) rates between the NEW and OLD methods can have a significant impact on the prediction of meteorological elements, including temperature and precipitation.

In this study, the improved k-distribution method (NEW) was applied to the New Goddard radiation scheme for both clear and cloudy day cases, and the WRF numerical simulation results were compared with the observations from the KMA. The downward shortwave radiation at the surface and the T2 predicted using the WRF model agreed relatively well with the observations, suggesting the possibility that the observations of the K MA can validate the simulated radiation parameterization by correcting for differences in the location, environment, and equipment of the stations.