# Review on Parameterization Schemes of Visibility in Fog and Brief Discussion of Applications Performance

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

_{d}, D, LWC, the parameterization formula of visibility in fog, as well as their performance in meteorology operation, are reviewed. Moreover, the estimated ability of the visibility parameterization formulas combined with the numerical model is briefly described, and their advantages and shortcomings are pointed out.

## 1. Introduction

_{d}) and fog droplets size [4,14,51,52], which can establish a direct relationship to VIS, are widely adoptable in atmospheric numerical models [4,53,54,55,56,57,58,59,60,61]. Therefore, research on the relationship between the impact factors and VIS, and their application effects are summarized in the review.

_{d}, and LWC on VIS. Among them, the effect of the extinction coefficient on visibility provides the basis of others. The Koschmieder’s law, as we know it, laid the foundation for visibility observation [1,62]. Other parameters related to the extinction coefficient were later studied, and LWC. George [63] pointed out that the fog droplet spectrum and LWC provide two crucial parameters that characterized the microphysical characteristics of fog and that an excellent inverse relationship exists between LWC and VIS. Eldridge [64] analyzed the influence of droplet growth on the formation and dissipation of fog, and proposed an empirical relationship between VIS and LWC. Through a comparison of the observation results with the conclusions of Houghton and Radford, Eldridge [65] pointed out that it was necessary to consider the effect of N

_{d}on the relationship between VIS and LWC. There were inverse correlations between the microphysical parameters and VIS, and there were also correlations between the parameters themselves. Niu et al. [14] showed that when nucleation and condensation growth dominated, a pronounced positive correlation between N

_{d}and LWC existed. When the D increased, and N

_{d}was small, the LWC would also be smaller. Many other studies have discussed the relationship between VIS and the evolution of microphysical parameters [4,52,58]. The following sections will further categorize and explain the corresponding results and their applications in atmospheric numerical models. The characteristics of fog in a polluted environment are fairly remarkable; thus, parameterization schemes of VIS in fog that contains chemical composition or concentrations of aerosol are beyond the scope of this article.

_{d}, and fog droplets size, are introduced in this review due to the length limit. The following sections will summarize corresponding parameterization schemes of VIS in fog and their applications in meteorological operations.

## 2. Relationships between VIS and Extinction Coefficient

_{ext}) of the atmosphere is constant, and the flat sky is used as the background black body target during the day. Then the brightness contrast threshold (C) between the target and the background changes with the distance (VIS), and the relationship is as follows:

_{ext}is only applicable under very minimal conditions: the atmosphere must be illuminated homogeneously, the extinction coefficient and the scattering function are not allowed to vary with space, the object should ideally be black and viewed against the horizon, and the eye of the observer must have a constant contrast threshold. Horvath et al. [66] proposed a general formula, taking the facts above into account. Through the proper selection of the VIS markers, it is possible to use the Koschmieder’s formula to calculate the extinction coefficient from observed visibilities with an error of less than about 10 percent. Using radiative transfer theory, Lee et al. [67] point out that the Koschmieder’s model is workable only in situations where a common-sized object can be viewed tens of kilometers away, but not applicable for viewable distances of hundreds of meters when the angular dimension of an object is significantly greater than the eye resolution of the human being. Lee et al.’s research advocates for the measurement and distribution of detectability in bad weather.

_{ext}in Mie scattering theory is given as follows:

_{n}and b

_{n}are functions related to the Bessel function and Hankel function, and x is the radius of the droplet. In 1971, according to Beer’s law, Koening [69] pointed out that brightness was a function of the microphysical characteristics of the fog, which is due to the dependence of the extinction coefficient on the concentration and radius of the fog droplets. That is, β

_{ext}is related to the N

_{d}, droplet radius, visible light wavelength, etc. Kunkel [70] pointed out that if the drop-size distribution is known, then β

_{ext}can be readily determined from the following equation (Equation (4))

_{ext}is the extinction efficiency (normalized extinction cross-section), n is the N

_{d}, and r is the droplet radius. Moreover, If the drop-size distribution is unknown, then an empirical formula must be used to relate the LWC to β

_{ext}, and related content is discussed in detail in the next section.

^{5}m), which defines the maximum VIS that can be diagnosed [72], that is ${\beta}_{air}=\left(lne\right)/{10}^{5}$.

_{ext}. Koening’s research [69] shows that the scheme is determined by multiple factors, which will lead to certain errors in calculations and measurements. For example, Kunkel [70] compared the extinction coefficient β

_{c}, calculated through the droplet spectral distribution and the actually observed β

_{m}, showing that the calculated extinction coefficient β

_{c}is larger than the observed β

_{m}. The results of Vali et al. [76] also showed that there was a deviation between the calculated value of the extinction coefficient and the measured value. The correction method proposed by Kunkel [70] is as follows:

_{c}through the droplet spectrum distribution. Therefore, if the VIS is calculated by Equation (2), certain errors will inevitably occur.

_{clg}[77]:

## 3. Relationships between VIS and RH

_{RUC}= 4.2 km; moreover, approximate 95.3% of the measured VIS ≤ 1 km. If this scheme is used to calculate visibility, when RH is high, the calculated result will be significantly larger than the observed value. A more suitable VIS-RH relationship was proposed based on the Dalian ground observation data. The newly built scheme [83] had greatly enhanced the local low VIS forecasting ability and is represented in Equation (11).

## 4. Relationships between VIS and LWC

^{3}. A large number of studies have shown that the relationship between β

_{ext}and LWC satisfies the power–function relationship mentioned above. The values of empirical coefficients a and b from various regions vary greatly. The size distributions of droplets are affected by many factors such as the observation range of droplet size, experiment design, air particulates, and fog types. For example, in 1966 and 1971, Eldridge [65,90] conducted a comparative analysis of different droplet size ranges through experiments, and the obtained empirical values of a and b varied across a broad range. When the droplet size is between 0.6 and 16 μm, $\beta =163LW{C}^{0.65}$, and when the upper limit of the droplet size range increases, $\beta =91LW{C}^{0.65}$. In 1976, Tomasi and Tampieri [91] obtained empirical values of a and b for different types of fog. Under the warm and humid fog conditions $\beta =65LW{C}^{2/3}$ was obtained, while $\beta =115LW{C}^{2/3}$ was obtained under cold fog conditions. In the existing research, the empirical coefficient ranges from 65 to 178, and b ranges from 0.63 to 0.96 [58]. It can be seen that the performance of the VIS-LWC parameter scheme is analogous to that of the VIS-RH scheme, which is also affected by many other factors and has a strong regional character.

_{d}from the fog droplet spectral observation and VIS from AWS during 2016–2017 in TianJin [16] were used to validate VIS parameter formulas from literatures and to fit the local formula. The observation VIS and LWC ranged from 0 to 8.2 km and 0 to 0.25 g/m

^{3}, respectively. The VIS_K84 [70] and VIS_Gultepe schemes [58] were verified in Figure 2 with a logarithmic plot. It should be pointed out that only data for VIS that were less than 1 km were adopted in Figure 2a, while the full range of observation data was adopted in Figure 2b.

## 5. Relationships between VIS, N_{d}, and Fog Droplets Size

_{MH}≤ 1 km) and the thin mist (VIS

_{ML}> 1–2 km), are obtained, respectively, as follows

_{d}, which is given in PCS m

^{−3}, both equations can be applied to the droplet with a diameter of larger than 0.5 μm. Meyer’s observational experiments also showed that the average droplet size essentially remains constant in thin fog, while VIS decreased with increasing droplet size in thick fog, and the formula under the condition of visibility in 1–2 km was $VIS=1.46\times {10}^{-4}{\left({D}_{e}^{2}\right)}^{-0.49}$, where D

_{e}was the effective diameter of the droplet. Assuming that the scattering coefficient is a constant in the spectrum, the N

_{d}·D

_{e}is proportional to the extinction coefficient. Combined with the relationship between VIS and extinction coefficient,

_{0}and λ as prognostic parameters while maintaining the shape parameter α constant. Milbrandt et al. [99] analyzed the influence of shape parameter α on sedimentation and microphysical growth rate using different schemes. The results show that α plays an important role in determining the rate of size sorting. Kunkel [70] analyzed more than 1400 droplet size samples in 1983, finding a good correlation between the droplet terminal velocity and c (LWC

^{2}/N

_{d})

^{d}(parameter c and d are both fitting coefficients). Under the condition of a fixed LWC value, air pollutants interact with water vapor to form a mass of liquid drops, which increase the N

_{d}. At the same time, a smaller droplet radius decreases the droplet terminal velocity, which results in the deposition rate of liquid water being reduced.

_{d}is considered as one of the impact factors of VIS.

_{d}relationship of the ice fog and liquid fog. The fog was classified into either ice fog (T < −1 °C) or liquid fog (T ≥ −1 °C) on the basis of temperature threshold. Approximate formulas between the VIS, ice fog number concentration (N

_{i}) and liquid fog number concentration (N

_{d}) were obtained through observational analysis and the relationships are as follows:

_{i}is PCS L

^{−1}, and the unit of N

_{d}is PCS cm

^{−3}, and PCS is the abbreviation of pieces. Gultepe [82] also noted that the results for VIS > 50 km were invalid due to uncertainties in the observation of small droplet by existing instruments. Moreover, on account of the properties of logarithmic relationships, the VIS

_{Ni}, which should be treated cautiously, varied greatly for a given N

_{i}. Based on the observational data from the forward-Scattering Spectrometer in the same year, a new relationship between VIS and N

_{d}was developed by Gultepe [58] as follows:

_{d}should be treated as an independent variable in parameterization schemes of VIS. Furthermore, in order to establish a more rational parameterization scheme, the accurate monitoring of the number concentration is required.

_{d}in Tianjin was obtained as the fitting formula: $VIS=0.2522{N}_{d}^{-0.121}$ (Figure 3). The constants and exponents parameter of local formula for VIS-N

_{d}relationship is largely different to others. Although a generally decreasing power relationship exists between VIS and N

_{d}, there is still large uncertainty in various regions.

_{d}is usually given a constant value. Fu G. [6] discussed the performance of the parameterization scheme when N

_{d}= 300 PCS cm

^{−3}, and showed that the obtained results are significantly smaller than those that do not considering the number concentration.

## 6. Relationships between VIS, LWC and N_{d}

_{d}are considered as the impact factors of VIS; moreover, there is no simple one-to-one relationship between the two factors. For example, the N

_{d}varies over a wide range for a certain LWC, resulting in great differences in VIS. Moreover, the two factors are related to each other. Considering these two main factors at the same time can better reflect the changes of VIS than considering one of them alone [70]. In 2006, based on the previous studies, a new parameterization scheme was established by Gultepe [58], combining the LWC and N

_{d}, t expressed as Equation (27)

^{−3}< LWC< 0.5 gm

^{−3}and 1 cm

^{−3}< N

_{d}< 400 cm

^{−3}. Additionally, a new definition of the fog index (FI) was formulated FI = 1/(LWC*N

_{d}), Compared with Kunkel’s studies [70], Gultepe [58] established a quantitative relational equation, and applied the new scheme to the mesoscale non-hydrostatic model of NOAA. By comparing the results with schemes of K84 and Meyer [98], the results show Equation (27), in which LWC and N

_{d}were taken into account, was more accurate in predicting VIS.

_{d}formula was fitted as VIS = 0.1418$F{I}^{0.065}$. The local relationship is far lower than in Equation (27), while it has no ability to express some larger VIS. That is to say, even though Equation (27) had done well compared to schemes of K84 and Meyer [98], there is still some work required to promote a parameterized VIS-LWC & Nd relationship in the future.

_{d}parameterization scheme proposed by Gultepe et al. [82]. The LWC was calculated from the physical quantity qcloud output by the WRF model, and the N

_{d}was solved using a historical experience statistical method. The N

_{d}was obtained according to the inversion formula of VIS:${N}_{d}={\mathrm{e}}^{Tmp}$, where $Tmp=\frac{1}{0.6437}\mathrm{ln}\left(\frac{1.002}{VI{S}_{obs}}\right)\mathrm{ln}\left(LW{C}_{obs}\right)$, in which VIS

_{obs}and LWC

_{obs}were the VIS and LWC of similar cases, respectively. The VIS forecast value can be obtained by substituting the obtained LWC and N

_{d}values into the parameterized scheme, which improves the fog forecast accuracy from 61% to 73%, compared with the Stoelinga-Warner scheme [77]. There is also a correlation between LWC and N

_{d}. Gultepe et al. [58] observed that LWC increased with increasing N

_{d}, while the range of N

_{d}changes was very large for a given LWC value. Huang et al. [101] observed and analyzed the microphysical characteristics of sea fog using a droplet spectrometer, finding that an increasing number of droplets with a diameter of more than 10 μm is the main reason for the increase of LWC, while the increase of LWC is the main reason for the decrease of atmospheric VIS under the same N

_{d}interval.

_{d}parameterization scheme has certain advantages and a rather high accuracy rate, since both the LWC and N

_{d}are considered, and the microphysical interpretation is relatively more realistic. Similar to the VIS-N

_{d}scheme, it suffers from the same problem of using empirical statistical methods to estimate the concentration of droplets. In addition, the scheme still has a high degree of uncertainty. The research of Gultepe [58] showed that the uncertainty of the scheme for the calculation of VIS in various types of fog still reached 27%. In their study of the characteristics of the fog-droplet spectrum during heavy fog in Tianjin, Liu et al. [52] found that the effects of LWC and N

_{d}on VIS are not the same, and that there was a pronounced negative correlation between VIS and N

_{d}while not so obvious for LWC. Therefore, to better apply the VIS-LWC & N

_{d}relationship obtained by Gultepe et al. [58], the scheme also needs to be improved according to the actual situation in various regions. Song [102] developed a new visibility parameterization by further taking De into the VIS-LWC & N

_{d}relationship consideration at a mountain site in Korea, and indicated that this new parameterization showed better performance than the original VIS-LWC & N

_{d}relationship obtained by Gultepe et al. [58] in visibility value prediction when De was larger than 10 μm, while no obvious improvement was observed when De was less than 10 μm.

^{−1}as the critical lower limit of LWC, Bao et al. [103] simulated cluster fog along the Shanghai-Nanjing Expressway, and used Equation (27) to calculate the value of visibility, and when N

_{d}= 0 or LWC = 0, Equation (27) is found to be no longer applicable, so the VIS-RH scheme is replaced. The results show that in the early stage of heavy fog, the simulated value is lower than the observed value, but the trend of the simulated value and the observed value is consistent during the maintenance and dissipation of the fog. Long et al. [104] determined a combination scheme of VIS-LWC and VIS-RH for the North Coast of Bohai Bay; the results show that if only one scheme is adopted, the simulated VIS value and the measured VIS value will deviate significantly when LWC = 0.03 g/kg. However, the combination scheme behaves well in this condition.

## 7. Conclusions and Discussion

_{d}, have been summarized. It can be seen that the fitted parameters, with precise physical meanings, allow for the calculation of VIS by interfacing with numerical forecast products. Therefore, many models are directly interfaced with the corresponding parameterization schemes while postprocessing VIS.

_{d}, etc. Gultepe et al. [8] point out that further modifications in microphysical observations and parametrizations are needed to promote the fog predictability of numerical-weather-prediction models.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- WMO. WMO Guide to Meteorological Instruments and Methods of Observation; Secretariat of the WMO: Geneva, Switzerland, 2006; p. 569. [Google Scholar]
- Wu, B.G.; Xie, Y.Y.; Wu, D.Z.; Wang, Y.N.; Wang, D.S. Poor visibility on Jingjintang Expressway in autumn/ winter and relevant measures. J. Nat. Disaster
**2009**, 18, 12–17. (In Chinese) [Google Scholar] - Lewis, J.M.; Koracin, D.; Redmond, K.T. Sea Fog Research in the United Kingdom and United States: A Historical Essay Including Outlook. Bull. Am. Meteorol. Soc.
**2004**, 85, 395–408. [Google Scholar] [CrossRef][Green Version] - Niu, S.J.; Lu, C.S.; Lü, J.J.; Xu, F.; Zhao, L.J.; Liu, D.Y.; Yue, Y.Y.; Zhou, Y.; Yu, H.Y.; Wang, T.S. Advances in fog research in China. Adv. Meteor. Sci. Technol.
**2016**, 6, 6–19. [Google Scholar] - Koračin, D.; Dorman, C.; Lewis, J.M.; Hudson, J.G.; Wilcox, E.; Torregrosa, A. Marine fog: A review. Atmos. Res.
**2014**, 143, 142–175. [Google Scholar] [CrossRef] - Fu, G.; Li, X.L.; Wei, N. Review on the atmospheric visibility research. Period. Ocean. Univ. China
**2009**, 39, 855–862. (In Chinese) [Google Scholar] - Niu, S.; Lu, C.; Yu, H.; Zhao, L.; Lü, J. Fog research in China: An overview. Adv. Atmos. Sci.
**2010**, 27, 639–662. [Google Scholar] [CrossRef] - Gultepe, I.; Heymsfield, A.J.; Fernando, H.J.S.; Pardyjak, E.; Dorman, C.E.; Wang, Q.; Creegan, E.; Hoch, S.W.; Flagg, D.D.; Yamaguchi, R.; et al. A Review of Coastal Fog Microphysics during C-FOG. Boundary-Layer Meteorol.
**2021**, 181, 1–39. [Google Scholar] [CrossRef] - Gultepe, I. Fog and Boundary Layer Clouds: Introduction. Pure Appl. Geophys.
**2007**, 164, 1115–1116. [Google Scholar] [CrossRef] - Laj, P.; Fuzzi, S.; Lazzari, A. The Size Dependent Composition of Fog Droplets. Contrib. Atmos. Phys.
**1998**, 71, 115–130. [Google Scholar] - Frank, G.; Martinsson, B.G.; Cederfelt, S.I. Droplet Formation and Growth in Polluted Fogs. Contrib. Atmos. Phys.
**1998**, 71, 65–85. [Google Scholar] - García-García, F.; Virafuentes, U.; Montero-Martínez, G. Fine-scale measurements of fog-droplet concentrations: A preliminary assessment. Atmos. Res.
**2002**, 64, 179–189. [Google Scholar] [CrossRef] - Hsieh, W.C.; Jonsson, H.; Wang, L.; Buzorius, G.; Flagan, R.C.; Seinfeld, J.H.; Nenes, A. On the representation of droplet coalescence and autoconversion: Evaluation using ambient cloud droplet size distributions. J. Geophys. Res. Atmos.
**2009**, 114, D07201. [Google Scholar] [CrossRef][Green Version] - Niu, S.; Lu, C.; Liu, Y.; Zhao, L.; Lu, J.; Yang, J. Analysis of the microphysical structure of heavy fog using a droplet spectrometer: A case study. Adv. Atmos. Sci.
**2010**, 27, 1259–1275. [Google Scholar] [CrossRef] - Wang, T.; Niu, S.; Lü, J.; Zhou, Y. Observational Study on the Supercooled Fog Droplet Spectrum Distribution and Icing Accumulation Mechanism in Lushan, Southeast China. Adv. Atmos. Sci.
**2019**, 36, 29–40. [Google Scholar] [CrossRef] - Liu, Q.; Wang, Z.-Y.; Wu, B.-G.; Liu, J.-L.; Nie, H.-H.; Chen, D.-H.; Gultepe, I. Microphysics of fog bursting in polluted urban air. Atmos. Environ.
**2021**, 253, 1–11. [Google Scholar] [CrossRef] - Fuzzi, S.; Facchini, M.C.; Orsi, G.; Bonforte, G.; Martinotti, W.; Ziliani, G.; Mazzalit, P.; Rossi, P.; Natale, P.; Grosa, M.M.; et al. The NEVALPA project: A regional network for fog chemical climatology over the PO Valley basin. Atmos. Environ.
**1996**, 30, 201–213. [Google Scholar] [CrossRef] - Ma, C.-J.; Kasahara, M.; Tohno, S.; Sakai, T. A replication technique for the collection of individual fog droplets and their chemical analysis using micro-PIXE. Atmos. Environ.
**2003**, 37, 4679–4686. [Google Scholar] [CrossRef] - Mancinelli, V.; Decesari, S.; Emblico, L.; Tozzi, R.; Mangani, F.; Fuzzi, S.; Facchini, M.C. Extractable iron and organic matter in the suspended insoluble material of fog droplets. Water Air Soil Pollut.
**2006**, 174, 303–320. [Google Scholar] [CrossRef] - Raja, S.; Raghunathan, R.; Yu, X.-Y.; Lee, T.; Chen, J.; Kommalapati, R.R.; Murugesan, K.; Shen, X.; Qingzhong, Y.; Valsaraj, K.T.; et al. Fog chemistry in the Texas–Louisiana Gulf Coast corridor. Atmos. Environ.
**2008**, 42, 2048–2061. [Google Scholar] [CrossRef] - Li, Z.; Liu, D.; Yan, W.; Wang, H.; Zhu, C.; Zhu, Y.; Zu, F. Dense fog burst reinforcement over Eastern China: A review. Atmos. Res.
**2019**, 230, 104639. [Google Scholar] [CrossRef] - Roach, W.T. Effective of Radiative Exchange on Growth by Consideration of a Cloud or Fog Droplet. Q. J. R. Meteorol. Soc.
**1976**, 102, 361–372. [Google Scholar] [CrossRef] - Guo, L.; Guo, X.; Fang, C.; Zhu, S. Observation analysis on characteristics of formation, evolution and transition of a long-lasting severe fog and haze episode in North China. Sci. China Earth Sci.
**2015**, 58, 329–344. [Google Scholar] [CrossRef] - Oliver, D.A.; Lewellen, W.S.; Williamson, G.G. The interaction between turbulent and radiative transport in the development of fog and low level stratus. J. Atmos. Sci.
**1978**, 35, 301–316. [Google Scholar] - Wu, B.G.; Zhang, H.S.; Zhang, C.C.; Zhu, H.; Wang, Z.Y.; Xie, Y.Y. Characteristics of turbulent transfer and its temporal evolution during an advection fog period in North China. Chin. J. Atmos. Sci.
**2010**, 34, 440–448. (In Chinese) [Google Scholar] - Ye, X.; Wu, B.; Zhang, H. The turbulent structure and transport in fog layers observed over the Tianjin area. Atmos. Res.
**2015**, 153, 217–234. [Google Scholar] [CrossRef] - Wu, B.; Li, Z.; Ju, T.; Zhang, H. Characteristics of Low-level jets during 2015–2016 and the effect on fog in Tianjin. Atmos. Res.
**2020**, 245, 105102. [Google Scholar] [CrossRef] - Kim, C.K.; Yum, S.S. A study on the transition mechanism of a stratus cloud into a warm sea fog using a single column model PAFOG coupled with WRF. Asia-Pacific J. Atmos. Sci.
**2013**, 49, 245–257. [Google Scholar] [CrossRef] - Hu, H.; Sun, J.; Zhang, Q. Assessing the Impact of Surface and Wind Profiler Data on Fog Forecasting Using WRF 3DVAR: An OSSE Study on a Dense Fog Event over North China. J. Appl. Meteorol. Clim.
**2017**, 56, 1059–1081. [Google Scholar] [CrossRef][Green Version] - Gilson, G.F.; Jiskoot, H.; Cassano, J.J.; Gultepe, I.; James, T.D. The Thermodynamic Structure of Arctic Coastal Fog Occurring During the Melt Season over East Greenland. Boundary-Layer Meteorol.
**2018**, 168, 443–467. [Google Scholar] [CrossRef] - Ju, T.; Wu, B.; Zhang, H.; Liu, J. Characteristics of turbulence and dissipation mechanism in a polluted radiation–advection fog life cycle in Tianjin. Meteorol. Atmos. Phys.
**2020**, 133, 515–531. [Google Scholar] [CrossRef] - Shi, C.; Roth, M.; Zhang, H.; Li, Z. Impacts of urbanization on long-term fog variation in Anhui Province, China. Atmos. Environ.
**2008**, 42, 8484–8492. [Google Scholar] [CrossRef] - Tian, M.; Wu, B.G.; Huang, H.; Wang, Z.W.; Zhang, W.Y. The synoptic condition and boundary layer characteristics of coastal fog around the Bohai Sea. Climatic Environ. Res.
**2020**, 25, 199–210. (In Chinese) [Google Scholar] - Li, Q.; Wub, B.; Liu, J.; Zhang, H.; Cai, X.; Song, Y. Characteristics of the atmospheric boundary layer and its relation with PM2:5 during haze episodes in winter in the North China Plain. Atmos. Environ.
**2020**, 223, 1–10. [Google Scholar] [CrossRef] - Huang, H.; Liu, H.; Huang, J.; Mao, W.; Bi, X. Atmospheric Boundary Layer Structure and Turbulence during Sea Fog on the Southern China Coast. Mon. Weather. Rev.
**2015**, 143, 1907–1923. [Google Scholar] [CrossRef] - Bergot, T.; Escobar, J.; Masson, V. Effect of small-scale surface heterogeneities and buildings on radiation fog: Large-eddy simulation study at Paris-Charles de Gaulle airport. Q. J. R. Meteorol. Soc.
**2015**, 141, 285–298. [Google Scholar] [CrossRef] - Gultepe, I. Fog and Boundary Layer Clouds: Fog Visibility and Forecasting; Birkhäuser Verlag AG: Basel, Switzerland, 2008. [Google Scholar]
- Roquelaure, S.; Bergot, T. A Local Ensemble Prediction System for Fog and Low Clouds: Construction, Bayesian Model Averaging Calibration, and Validation. J. Appl. Meteorol. Clim.
**2008**, 47, 3072–3088. [Google Scholar] [CrossRef] - Ryerson, W.R.; Hacker, J.P. The Potential for Mesoscale Visibility Predictions with a Multimodel Ensemble. Weather. Forecast.
**2014**, 29, 543–562. [Google Scholar] [CrossRef] - Lin, J.C.-H.; Tai, J.-H.; Feng, C.-H.; Lin, D.-E. Towards Improving Visibility Forecasts in Taiwan: A Statistical Approach. Terr. Atmos. Ocean. Sci.
**2010**, 21, 359–374. [Google Scholar] [CrossRef][Green Version] - Leyton, S.M.; Fritsch, J.M. Short-Term Probabilistic Forecasts of Ceiling and Visibility Utilizing High-Density Surface Weather Observations. Weather. Forecast.
**2003**, 18, 891–902. [Google Scholar] [CrossRef] - Ryerson, W.R.; Hacker, J.P. A Nonparametric Ensemble Postprocessing Approach for Short-Range Visibility Predictions in Data-Sparse Areas. Weather. Forecast.
**2018**, 33, 835–855. [Google Scholar] [CrossRef] - Pasini, A.; Pelino, V.; Potestà, S. A neural network model for visibility nowcasting from surface observations: Results and sensitivity to physical input variables. J. Geophys. Res. Space Phys.
**2001**, 106, 14951–14959. [Google Scholar] [CrossRef] - Roquelaure, S.; Tardif, R.; Remy, S.; Bergot, T. Skill of a Ceiling and Visibility Local Ensemble Prediction System (LEPS) according to Fog-Type Prediction at Paris-Charles de Gaulle Airport. Weather. Forecast.
**2009**, 24, 1511–1523. [Google Scholar] [CrossRef][Green Version] - Zhou, B.; Du, J. Fog Prediction from a Multimodel Mesoscale Ensemble Prediction System. Weather. Forecast.
**2010**, 25, 303–322. [Google Scholar] [CrossRef] - Hansen, B. A Fuzzy Logic–Based Analog Forecasting System for Ceiling and Visibility. Weather. Forecast.
**2007**, 22, 1319–1330. [Google Scholar] [CrossRef] - Zhou, B.; Ferrier, B.S. Asymptotic Analysis of Equilibrium in Radiation Fog. J. Appl. Meteorol. Clim.
**2008**, 47, 1704–1722. [Google Scholar] [CrossRef] - Sohoni, V.V.; Paranjpe, M.M. Fog and relative humidity in India. Q. J. R. Meteorol. Soc.
**1934**, 60, 15–22. [Google Scholar] [CrossRef] - Francis, K.E. Study of ice fog particles in alaska. Bull. Am. Meteorol. Soc.
**1962**, 43, 139. [Google Scholar] - Li, X.N.; Huang, J.A.; Shen, S.H.; Liu, S.D.; Lu, W.H. Evolution of Liquid Water Content in a Sea Fog Controlled by a High-Pressure Pattern. J. Trop. Meteorol.
**2010**, 16, 409–416. [Google Scholar] [CrossRef] - Liu, D.Y.; Pu, M.J.; Yang, J.; Zhang, G.Z.; Yan, W.L.; Li, Z.H. Microphysical Structure and Evolution of a Four-Day Persistent Fog Event in Nanjing in December 2006. Acta Meteorol. Sin.
**2009**, 24, 104–115. [Google Scholar] - Liu, Q.; Wu, B.; Wang, Z.; Hao, T. Fog Droplet Size Distribution and the Interaction between Fog Droplets and Fine Particles during Dense Fog in Tianjin, China. Atmosphere
**2020**, 11, 258. [Google Scholar] [CrossRef][Green Version] - Steeneveld, G.J.; Ronda, R.J.; Holtslag, A.A.M. The Challenge of Forecasting the Onset and Development of Radiation Fog Using Mesoscale Atmospheric Models. Boundary-Layer Meteorol.
**2015**, 154, 265–289. [Google Scholar] [CrossRef] - Singh, A.; George, J.P.; Iyengar, G.R. Prediction of fog/visibility over India using NWP Model. J. Earth Syst. Sci.
**2018**, 127, 26. [Google Scholar] [CrossRef][Green Version] - Philip, A.; Bergot, T.; Bouteloup, Y.; Bouyssel, F. The Impact of Vertical Resolution on Fog Forecasting in the Kilometric-Scale Model AROME: A Case Study and Statistics. Weather. Forecast.
**2016**, 31, 1655–1671. [Google Scholar] [CrossRef] - Tian, M.; Wu, B.; Huang, H.; Zhang, H.; Zhang, W.; Wang, Z. Impact of water vapor transfer on a Circum-Bohai-Sea heavy fog: Observation and numerical simulation. Atmos. Res.
**2019**, 229, 1–22. [Google Scholar] [CrossRef] - Price, J.D.; Lane, S.; Boutle, I.; Smith, D.K.E.; Bergot, T.; Lac, C.; Duconge, L.; McGregor, J.; Kerr-Munslow, A.; Pickering, M.; et al. LANFEX: A Field and Modeling Study to Improve Our Understanding and Forecasting of Radiation Fog. Bull. Am. Meteorol. Soc.
**2018**, 99, 2061–2077. [Google Scholar] [CrossRef] - Gultepe, I.; Müller, M.D.; Boybeyi, Z. A New Visibility Parameterization for Warm-Fog Applications in Numerical Weather Prediction Models. J. Appl. Meteorol. Clim.
**2006**, 45, 1469–1480. [Google Scholar] [CrossRef] - Porson, A.; Price, J.; Lock, A.; Clark, P. Radiation Fog. Part II: Large-Eddy Simulations in Very Stable Conditions. Boundary-Layer Meteorol.
**2011**, 139, 193–224. [Google Scholar] [CrossRef] - Kim, C.K.; Stuefer, M.; Schmitt, C.G.; Heymsfield, A.; Thompson, G. Numerical Modeling of Ice Fog in Interior Alaska Using the Weather Research and Forecasting Model. Pure Appl. Geophys.
**2014**, 171, 1963–1982. [Google Scholar] [CrossRef] - Koračin, D. Modeling and Forecasting Marine Fog. In Marine Fog: Challenges and Advancements in Observations, Modeling, and Forecasting; Koračin, D., Dorman, C.E., Eds.; Springer International Publishing: Cham, Switzerland, 2017; pp. 425–475. [Google Scholar]
- Koschmieder, H. Theorie der horizontalen Sichtweite. Beitr. Phys. Fr. Atmos.
**1924**, 12, 33–53. [Google Scholar] - Malone, T. Compendium of Meteorology; American Meteorological Society: Boston, MA, USA, 1951. [Google Scholar]
- Houghton, H.G.; Radford, W.H. On the measurement of drop size and liquid water content in fogs and clouds. Phys. Oceanogr. Meteorol.
**1938**, 6, 1–31. [Google Scholar] [CrossRef][Green Version] - Eldridge, R.G. The Relationship Between Visibility and Liquid Water Content in Fog. Atmos. Sci.
**1971**, 8, 1183–1186. [Google Scholar] [CrossRef][Green Version] - Horvath, H. On the applicability of the koschmieder visibility formula. Atmos. Environ. 1967
**1971**, 5, 177–184. [Google Scholar] [CrossRef] - Lee, Z.; Shang, S. Visibility: How applicable is the century-old Koschmieder model? J. Atmos. Sci.
**2016**, 73, 4573–4581. [Google Scholar] [CrossRef] - Mie, V.G. Consideraciones sobre la óptica de los medios turbios, especialmente soluciones coloidales. Por Gustav Mie Ann. Der Phys.
**1908**, 25, 377–445. [Google Scholar] [CrossRef] - Koenig, L.R. Numerical experiments pertaining to warm-fog clearing. Mon. Weather. Rev.
**1971**, 99, 227–241. [Google Scholar] [CrossRef][Green Version] - Kunkel, B.A. Parameterization of Droplet Terminal Velocity and Extinction Coefficient in Fog Models. J. Clim. Appl. Meteorol.
**1984**, 23, 34–41. [Google Scholar] [CrossRef][Green Version] - ECWMF. IFS DOCUMENTATION–Cy47r3, Operational Implementation. PART IV: PHYSICAL PROCESSES; European Centre for Medium-Range Weather Forecasts: Shinfield Park, Reading, RG2 9AX, UK. 12 October 2021. Available online: https://www.ecmwf.int/sites/default/files/elibrary/2021/20198-ifs-documentation-cy47r3-part-vi-physical-processes.pdf (accessed on 8 December 2021).
- Clark, P.A.; Harcourt, S.A.; Macpherson, B.; Mathison, C.T.; Cusack, S.; Naylor, M. Prediction of visibility and aerosol within the operational Met Office Unified Model. I: Model formulation and variational assimilation. Q. J. R. Meteorol. Soc.
**2008**, 134, 1801–1816. [Google Scholar] [CrossRef][Green Version] - Gao, S.; Lin, H.; Shen, B.; Fu, G. A heavy sea fog event over the Yellow Sea in March 2005: Analysis and numerical modeling. Adv. Atmos. Sci.
**2007**, 24, 65–81. [Google Scholar] [CrossRef] - Fu, G.; Guo, J.; Pendergrass, A.; Li, P. An analysis and modeling study of a sea fog event over the Yellow and Bohai Seas. J. Ocean Univ. China
**2008**, 7, 27–34. [Google Scholar] [CrossRef] - Fu, G.; Guo, J.; Xie, S.-P.; Duan, Y.; Zhang, M. Analysis and high-resolution modeling of a dense sea fog event over the Yellow Sea. Atmos. Res.
**2006**, 81, 293–303. [Google Scholar] [CrossRef] - Vali, G.; Politovich, M.K.; Baumgardner, D.G. Conduct of Cloud Spectra Measurements; Air Force Geophysics Laboratory, Wright-Patterson AFB: Fairborn, OH, USA, 1979; pp. 1–61. [Google Scholar]
- Stoelinga, M.T.; Warner, T.T. Nonhydrostatic, Mesobeta-Scale Model Simulations of Cloud Ceiling and Visibility for an East Coast Winter Precipitation Event. J. Atmos. Sci.
**1999**, 38, 385–404. [Google Scholar] [CrossRef] - Elias, T.; Haeffelin, M.; Drobinski, P.; Gomes, L.; Rangognio, J.; Bergot, T.; Chazette, P.; Raut, J.-C.; Colomb, M. Particulate contribution to extinction of visible radiation: Pollution, haze, and fog. Atmos. Res.
**2009**, 92, 443–454. [Google Scholar] [CrossRef] - van Oldenborgh, G.J.; Yiou, P.; Vautard, R. On the roles of circulation and aerosols in the decline of mist and dense fog in Europe over the last 30 years. Atmos. Chem. Phys. Discuss.
**2010**, 10, 4597–4609. [Google Scholar] [CrossRef][Green Version] - Hänel, G. The Properties of Atmospheric Aerosol Particles as Functions of the Relative Humidity at Thermodynamic Equilibrium with the Surrounding Moist Air. Adv. Geophys.
**1976**, 19, 73–188. [Google Scholar] [CrossRef] - Smirnova, T.G.; Benjamin, S.G.; Brown, J.M. Case study verification of RUC/ MAPS fog and visibility forecasts. In Preprints, 9th Conference on Aviation, Range, and Aerospace Meteorology; AMS: Orlando, FL, USA, 2000; pp. 31–36. [Google Scholar]
- Gultepe, I.; Isaac, G.A. Visibility Versus Precipitation Rate and Relative Humidity. In Proceedings of the Wisconsin: Meteor. Soc., 2006; P2.55. 12th Cloud Physics Conf. Madison, Amer. 12 July 2006. Available online: http://ams.confex.com/ams/Madison2006/techprogram/paper_113177.htm (accessed on 8 December 2021).
- Cao, X.C.; Shao, L.M.; Li, X.D. Research on parameterization scheme of visibility in Fog Model. In Proceedings of the 31st Annual Meeting of the Chinese Meteorological Society, Beijing, China, 3 November 2014; 2014; pp. 1–5. [Google Scholar]
- Gültepe, I.; Milbrandt, J.A. Probabilistic Parameterizations of Visibility Using Observations of Rain Precipitation Rate, Relative Humidity, and Visibility. J. Appl. Meteorol.
**2009**, 49, 36–46. [Google Scholar] [CrossRef] - Lin, Y.; Wang, M.S.; Lin, L.G. Numerical simulation of a winter fog in Sichuan and parameterization of visibility. J. Nanjing Univ. Inf. Sci. Technol. Nat. Sci. Ed.
**2013**, 5, 222–228. [Google Scholar] - Roquelaure, S.; Bergot, T. Contributions from a Local Ensemble Prediction System (LEPS) for Improving Fog and Low Cloud Forecasts at Airports. Weather. Forecast.
**2009**, 24, 39–52. [Google Scholar] [CrossRef][Green Version] - Lin, Y.; Yang, J.; Bao, Y.S.; Wang, Z.J.; Dai, Y.X. The numerical simulation of visibility during the fog in Shanxi province in winter. J. Nanjing Univ. Inf. Sci. Technol. Nat. Sci. Ed.
**2010**, 2, 436–444. [Google Scholar] - Bari, D. A Preliminary Impact Study of Wind on Assimilation and Forecast Systems into the One-Dimensional Fog Forecasting Model COBEL-ISBA over Morocco. Atmosphere
**2019**, 10, 615. [Google Scholar] [CrossRef][Green Version] - Martinet, P.; Cimini, D.; Burnet, F.; Ménétrier, B.; Michel, Y.; Unger, V. Improvement of numerical weather prediction model analysis during fog conditions through the assimilation of ground-based microwave radiometer observations: A 1D-Var study. Atmos. Meas. Tech.
**2020**, 13, 6593–6611. [Google Scholar] [CrossRef] - Eldridge, R.G. Haze and Fog Aerosol Distributions. J. Atmos. Sci.
**1966**, 23, 605–613. [Google Scholar] [CrossRef][Green Version] - Tomasi, C.; Tampieri, F. Features of the proportionality coefficient in the relationship between visibility and liquid water content in haze and fog. Atmosphere
**1976**, 14, 61–76. [Google Scholar] [CrossRef][Green Version] - Pinnick, R.G.; Hoihjelle, D.L.; Fernandez, G.; Stenmark, E.B.; Lindberg, J.D.; Hoidale, G.B.; Jennings, S.G. Vertical Structure in Atmospheric Fog and Haze and Its Effects on Visible and Infrared Extinction. J. Atmos. Sci.
**1978**, 35, 2020–2032. [Google Scholar] [CrossRef][Green Version] - Musson-Genon, L. Numerical Simulation of a Fog Event with a One-Dimensional Boundary Layer Model. Mon. Weather. Rev.
**1987**, 115, 592–607. [Google Scholar] [CrossRef] - Wang, Q.; Zhang, S.-P.; Wang, Q.; Meng, Z.-X.; Koračin, D.; Gao, S.-H. A Fog Event off the Coast of the Hangzhou Bay during Meiyu Period in June 2013. Aerosol Air Qual. Res.
**2018**, 18, 91–102. [Google Scholar] [CrossRef][Green Version] - Singh, A.; Dey, S. Influence of aerosol composition on visibility in megacity Delhi. Atmos. Environ.
**2012**, 62, 367–373. [Google Scholar] [CrossRef] - Shen, X.J.; Sun, J.Y.; Zhang, X.Y.; Zhang, Y.M.; Zhang, L.; Che, H.C.; Ma, Q.L.; Yu, X.M.; Yue, Y.; Zhang, Y.W. Characterization of submicron aerosols and effect on visibility during a severe haze-fog episode in Yangtze River Delta, China. Atmos. Environ.
**2015**, 120, 307–316. [Google Scholar] [CrossRef][Green Version] - Gonser, S.G.; Klemm, O.; Griessbaum, F.; Chang, S.-C.; Chu, H.-S.; Hsia, Y.-J. The Relation Between Humidity and Liquid Water Content in Fog: An Experimental Approach. Pure Appl. Geophys.
**2011**, 169, 821–833. [Google Scholar] [CrossRef] - Meyer, M.B.; Jiusto, J.E.; Lala, G.G. Measurements of Visual Range and Radiation-Fog (Haze) Microphysics. J. Atmos. Sci.
**1980**, 37, 622–629. [Google Scholar] [CrossRef][Green Version] - Milbrandt, J.A.; Yau, M.K. A Multimoment Bulk Microphysics Parameterization. Part I: Analysis of the Role of the Spectral Shape Parameter. J. Atmos. Sci.
**2005**, 62, 3051–3064. [Google Scholar] [CrossRef][Green Version] - Hu, B.; Du, H.L.; Hao, S.F.; Yu, L.M.; Teng, L.N. A forecast method of coastal sea fog based on the combination of statistic technique and dynamical interpretation. Marin. Forec.
**2014**, 31, 82–86. (In Chinese) [Google Scholar] - Huang, H.J.; Huang, J.; Mao, W.K.; Liao, F.; Li, X.N.; Lü, W.H.; Yang, Y.Q. Characteristics of liquid water content of sea fog in Maoming area and its relationship with atmospheric horizontal visibility. Acta Oceanol. Sin.
**2010**, 32, 40–52. (In Chinese) [Google Scholar] - Song, J.I.; Yum, S.S.; Gultepe, I.; Chang, K.-H.; Kim, B.-G. Development of a new visibility parameterization based on the measurement of fog microphysics at a mountain site in Korea. Atmos. Res.
**2019**, 229, 115–126. [Google Scholar] [CrossRef] - Bao, Y.X.; Ding, Q.J.; Yuan, C.S.; Yan, M.L. Numerical simulations of a highly complex fog event on Shanghai-Nanjing Expressway. Chin. J. Atmos. Sci.
**2013**, 37, 124–136. (In Chinese) [Google Scholar] - Long, Q.; Wang, F.; Mi, X.Y.; Wang, C.; Liu, Y. Research on the Formation Mechanism and Forecast Technology of Sea Fog on the North Coast of Bohai Bay. In Proceedings of the 2020 National Marine Ecological Environmental Protection and Monitoring Technology Symposium, Shenzhen, China, 18 December 2020; pp. 238–246. [Google Scholar]
- Haeffelin, M.; Bergot, T.; Elias, T.; Tardif, R.; Carrer, D.; Chazette, P.; Colomb, M.; Drobinski, P.; Dupont, E.; Dupont, J.-C.; et al. Parisfog Shedding New Light on Fog Physical Processes. Bull. Am. Meteorol. Soc.
**2010**, 91, 767–783. [Google Scholar] [CrossRef][Green Version] - Li, Z.H.; Peng, Z.G. Physical and chemical characteristic of the Chongqing winter fog. Acta. Meteorol. Sin.
**1994**, 16, 46–54. (In Chinese) [Google Scholar] - Sun, J.; Huang, H.; Zhang, S.; Mao, W. How Sea Fog Influences Inland Visibility on the Southern China Coast. Atmosphere
**2018**, 9, 344. [Google Scholar] [CrossRef][Green Version] - Marzban, C.; Leyton, S.; Colman, B. Ceiling and Visibility Forecasts via Neural Networks. Weather. Forecast.
**2007**, 22, 466–479. [Google Scholar] [CrossRef][Green Version] - Gilleland, E.; Fowler, T.L. Network design for verification of ceiling and visibility forecasts. Environmetrics
**2006**, 17, 575–589. [Google Scholar] [CrossRef] - Fabbian, D.; de Dear, R.; Lellyett, S. Application of artificial neural network forecasts to predict fog at Canberra International Airport. Weather. Forecast.
**2007**, 22, 372–381. [Google Scholar] [CrossRef] - Bari, D.; Ouagabi, A. Machine-learning regression applied to diagnose horizontal visibility from mesoscale NWP model forecasts. SN Appl. Sci.
**2020**, 2, 1–13. [Google Scholar] [CrossRef][Green Version] - Bingui, W.; Jianchun, Z.; Yinghua, L.; Yanan, W.; Mei, X.; Jing, C.; Xuelian, W.; un, G.X.; Xiaobin, Q. Research on Numerical Interpretative Forecast for Low-Visibility at Tianjin Port in Autumn and Wint. Meteorol. Mon.
**2017**, 43, 8630871. [Google Scholar]

**Figure 1.**Performance of VIS-RH schemes in Tianjin (VIS_Eq.7… VIS_Eq.16 denote Equation (7) to (16), and the black dashed line denotes the localized fitting curve of VIS-RH).

**Figure 2.**VIS-LWC scheme verified and the local fitting formula and the VIS less than 1 km (

**a**) and the wide-range VIS data (

**b**) (VIS_obs, VIS_K84, VIS_Gultepe, fitting curve of VIS represent the observed VIS, simulated VIS with Equation (19), Equation (20) and the local fitting, respectively).

**Figure 3.**VIS-N

_{d}scheme performance evaluation (VIS_Meyer (light fog) /VIS_Meyer (dense fog), VIS_Gultepe_N

_{d}, VIS_Gultepe represent simulated VIS from Equation (22), (21), (26), and (25), respectively. The black dashed line denotes the localized fitting curve of VIS-N

_{d}from local VIS_obs).

**Figure 4.**VIS-fog index (FI = 1/N

_{d}*LWC) scheme calculation (The black dashed line denotes the fitting curve of VIS_obs, VIS_Gultepe denotes denotes Equation (27), respectively).

Equation No | Relationship | Conditions | Reference |
---|---|---|---|

(7) | $VIS=67.7{\left(1-RH\right)}^{0.67}$ | RH in decimal form For 58% < RH < 97% | Hanel [80] |

(8) | $VI{S}_{RUC}=60\mathrm{exp}\left[-2.5\left(RH-15\right)/80\right]$ | For 30% ≤ RH ≤ 100% Set to 5 km at RH ≥ 95% | Smirnova et al. [81] |

(9) | $VI{S}_{FRAM-C}=-41.5\mathrm{ln}\left(RH\right)+192.30$ | For RH > 30% | Gultepe et al. [82] |

(10) | $VI{S}_{AIRS}=-0.0177R{H}^{2}+1.46RH+30.80$ | For RH > 30% | Gultepe et al. [82] |

(11) | $VI{S}_{MX11}=-0.00003272R{H}^{3}+0.00238R{H}^{2}-0.1165RH+21.2$ | For 30% ≤ RH ≤ 100% | Cao et al. [83] |

(12) | $VI{S}_{FRAM-L\left(5\%\right)}=-0.000114R{H}^{2.7}+27.45$ | For RH > 30% | Gultepe et al. [84] |

(13) | $VI{S}_{FRAM-L\left(50\%\right)}=-5.19\times {10}^{-10}R{H}^{5.44}+40.10$ | For RH > 30% | Gultepe et al. [84] |

(14) | $VI{S}_{FRAM-L\left(95\%\right)}=-9.68\times {10}^{-14}R{H}^{7.19}+52.20$ | For RH > 30% | Gultepe et al. [84] |

(15) | $VI{S}_{Fit}=63.19-13.04\mathrm{ln}\left(RH+11.31\right)$ | For 20% < RH < 100% | Lin et al. [85] |

(16) | $VI{S}_{Fit-5\%}=21.38-4.938\ast \mathrm{ln}\left(RH-24.53\right)$ | For 25% < RH < 100% | Lin et al. [85] |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Long, Q.; Wu, B.; Mi, X.; Liu, S.; Fei, X.; Ju, T.
Review on Parameterization Schemes of Visibility in Fog and Brief Discussion of Applications Performance. *Atmosphere* **2021**, *12*, 1666.
https://doi.org/10.3390/atmos12121666

**AMA Style**

Long Q, Wu B, Mi X, Liu S, Fei X, Ju T.
Review on Parameterization Schemes of Visibility in Fog and Brief Discussion of Applications Performance. *Atmosphere*. 2021; 12(12):1666.
https://doi.org/10.3390/atmos12121666

**Chicago/Turabian Style**

Long, Qiang, Bingui Wu, Xinyue Mi, Shuang Liu, Xiaochen Fei, and Tingting Ju.
2021. "Review on Parameterization Schemes of Visibility in Fog and Brief Discussion of Applications Performance" *Atmosphere* 12, no. 12: 1666.
https://doi.org/10.3390/atmos12121666