Microphysical Characteristics of a Sea Fog Event with Precipitation Along the West Coast of the Yellow Sea in Summer

Abstract

The microphysics and visibility (Vis) of a sea fog event with precipitation were measured at the Baguan Hill Meteorological Station (BGMS) (36.07° N, 120.33° E; 86 m above sea level) from 27 June to 28 June 2022. The duration of the fog process was 880 min. The mean value of the number concentration (N_d) was 190.62 cm⁻³, and the mean value of the liquid water content (LWC) was 0.026 g m⁻³. Small droplets contributed 81% to N_d and had a greater impact on visibility attenuation, while larger droplets accounted for 58% of the total LWC. The observed droplet size distribution (DSD) was better represented by the G-exponential distribution than by the Gamma distribution. Incorporating both N_d and LWC in Vis parameterization resulted in the best prediction performance. This work enhances understanding of sea fog microphysics in the west coast of Yellow Sea in summer and highlights the need for long-term observations.

1. Introduction

Sea fog occurs in the lower atmosphere over oceans, coastlines, and islands, characterized by a significant reduction in visibility (Vis) due to the condensation of water vapor [1]. Coastal fog is considered a subtype of sea fog [2]. When the sea fog moves in, Vis drops to below 1 km, and in some cases, to just a few dozen meters. This can severely impact aviation, transportation, and human activities along the coastal areas, classifying it as a hazardous weather phenomenon [3,4,5]. Therefore, improving the accuracy of forecasts is essential to reduce economic losses and protect lives during fog events.

Fog significantly affects Vis, primarily due to its microphysical characteristics, such as number concentration (N_d), liquid water content (LWC), effective radius (r_e), mean radius (r_m), and droplet size distribution (DSD) [2,6]. Accurate prediction of Vis requires a thorough understanding of these features. However, current models often struggle to provide precise predictions, typically treating N_d as a constant or assuming a specific DSD [7,8]. To improve forecast accuracy, numerous field observation projects have been conducted worldwide to develop Vis parameterization schemes [4,9,10].

The Yellow Sea, particularly its western coast near Qingdao, is one of China’s most fog-prone regions, with frequent sea fog events occurring from April to July [11]. Despite this, recent studies on the microphysical characteristics of coastal fog near Qingdao are scarce. Wang et al. [12] documented a spring 2017 sea fog event at the Qingdao Meteorological Station (QDMS), analyzing its microphysical properties and introducing a new distribution function for fog DSD. In this study, we examined a sea fog event with precipitation from 27 to 28 June 2022, analyzing its microphysical characteristics to further understand coastal fog properties in Qingdao.

The rest of the paper is organized as follows: Section 2 describes data and methods. Section 3 presents the results of the microphysical characteristics and the suitable expression for DSD. Finally, we compare various parameterization schemes for calculating Vis of this fog process. Section 4 gives the summary and conclusions.

2. Materials and Methods

2.1. Study Location and Instrumentation

The study site is located at Baguan Hill Meteorological Station (BGMS) in the Ocean University of China, Shandong Province, China (36.07° N, 120.33° E; 86 m above sea level). BGMS is about 600 m from the sea, closer to the shore than QDMS where Wang et al. conducted their study [12] (Figure 1). Climatic data indicate that southeast winds prevail in the Qingdao area during sea fog events, transporting warm, humid air from the Yellow Sea to the coast and providing sufficient water vapor for fog formation. The absence of buildings in this direction makes it suitable for long-term sea fog observations.

For this study, we used a Droplet Measurement Technology Fog Monitor (FM-120) (Longmont, CO, USA) and an automatic meteorological station at BGMS. The FM-120 enables continuous measurement of microphysical quantities, including N_d, LWC, and particle number concentrations across different diameters. Particle diameters range from 2 to 50 μm, divided into 30 bins, with a sampling frequency of 1 Hz. The automatic meteorological station collects data on Vis, air temperature (Ta), relative humidity (RH), precipitation, surface wind, and other parameters every minute.

Previous studies identified droplet loss as a key source of uncertainty in FM-120 [13]. This issue is particularly significant in ship-based observations, where ship speed and wind speed can push or pull the sampled air, creating turbulent pulsations at the FM-120’s inlet, leading to data bias that requires correction [14]. However, recent studies showed that aligning the spectrometer inlet with the prevailing wind direction on land minimized particle loss and size discrepancies, eliminating the need for data correction [15,16]. To ensure data quality, the instrument was rigorously calibrated before use. We also aligned the spectrometer inlet with the climatological prevailing wind direction (southeast) in Qingdao’s coastal area to reduce measurement errors.

2.2. Calculation Methods

The microphysical parameters can be calculated as follows:

$${\mathrm{N}}_{\mathrm{d}}=\int \mathrm{n}\left(\mathrm{r}\right)\mathrm{d}\mathrm{r},$$

(1)

$$\mathrm{L}\mathrm{W}\mathrm{C}=\int {\displaystyle \frac{4}{3}}\mathsf{\pi }{\mathsf{\rho }}_{\mathrm{w}}\mathrm{n}\left(\mathrm{r}\right){\mathrm{r}}^3\mathrm{d}\mathrm{r},$$

(2)

$${\mathrm{r}}_{\mathrm{m}}={\displaystyle \frac{\int \mathrm{n}\left(\mathrm{r}\right)\mathrm{r}\mathrm{d}\mathrm{r}}{\int \mathrm{n}\left(\mathrm{r}\right)\mathrm{d}\mathrm{r}}},$$

(3)

$${\mathrm{r}}_{\mathrm{e}}={\displaystyle \frac{\int \mathrm{n}\left(\mathrm{r}\right){\mathrm{r}}^3\mathrm{d}\mathrm{r}}{\int \mathrm{n}\left(\mathrm{r}\right){\mathrm{r}}^2\mathrm{d}\mathrm{r}}},$$

(4)

where n(r) is the number concentration of droplets at each bin interval, r is the midpoint radius of each bin, and ρ_w is the density of water (10⁻⁶ g m⁻³).

Equations (3) and (4) reference two parameters that describe particle size: r_m, the statistical mean radius, and r_e, the effective radius, which is widely regarded as the optimal parameter for characterizing scattered light and assessing the impact of cloud droplets on cloud albedo [17,18].

According to the Koschmieder formula [19], Vis is defined as:

$$\mathrm{V}\mathrm{i}\mathrm{s}=-\mathrm{l}\mathrm{n}\left(\mathsf{\epsilon }\right)/{\mathsf{\beta }}_{\mathrm{e}\mathrm{x}\mathrm{t}},$$

(5)

where ε is the brightness contrast threshold which is assumed to be 0.02 [20,21]. Vis sensor extinction coefficient (β_ext) is the sum of the extinction coefficient of fog droplets, which can be calculated by Mie theory [22]. Then, the value of Vis is clear. The detailed calculation process can be referred to [12].

In the evaluation of the estimated model performance, the following metrics can be used:

$$\mathrm{S}\mathrm{S}\mathrm{T}=\sum _{\mathrm{i}=1}^{\mathrm{k}}{\left({\mathrm{y}}_{\mathrm{i}}-\overline{\mathrm{y}}\right)}^2,$$

(6)

$$\mathrm{S}\mathrm{S}\mathrm{E}=\sum _{\mathrm{i}=1}^{\mathrm{k}}{\left({\mathrm{y}}_{\mathrm{i}}-{\widehat{\mathrm{y}}}_{\mathrm{i}}\right)}^2,$$

(7)

$${\mathrm{R}}^2=1-{\displaystyle \frac{\mathrm{S}\mathrm{S}\mathrm{E}}{\mathrm{S}\mathrm{S}\mathrm{T}}},$$

(8)

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{\mathrm{k}}}\sum _{\mathrm{i}=1}^{\mathrm{k}}|{\mathrm{y}}_{\mathrm{i}}-{\widehat{\mathrm{y}}}_{\mathrm{i}}|,$$

(9)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{\mathrm{k}}}\sum _{\mathrm{i}=1}^{\mathrm{k}}{\left({\mathrm{y}}_{\mathrm{i}}-{\widehat{\mathrm{y}}}_{\mathrm{i}}\right)}^2},$$

(10)

where ${\mathrm{y}}_{\mathrm{i}}$ represents the observed values, ${\widehat{\mathrm{y}}}_{\mathrm{i}}$ represents the estimated values, and $\overline{\mathrm{y}}$ is the mean. SST denotes the total sum of squares, SSE represents the sum of squared errors, R² is the coefficient of determination, MAE is the mean absolute error, and RMSE is the root mean square error. Lower values of SST, SSE, MAE, and RMSE indicate a smaller discrepancy between fitted and observed values, while an R² value closer to 1 signifies a better fit [23,24].

3. Results

3.1. Overview of the Sea Fog

Figure 2 shows the changes in Vis, Ta, RH, surface wind, and precipitation from 27 June to 28 June 2022. Starting at 1756 UTC on June 27 (LST = UTC + 8 h), RH stabilized at 100%, while the wind direction shifted from southwest to southeast, accompanied by a decrease in wind speed. Vis fluctuated from 35 km to below 1 km after 2011 UTC, and Ta decreased by 0.8 °C. After sunrise, Ta increased rapidly, and Vis experienced slight fluctuations. Ta reached its peak at 0447 UTC, with Vis sharply increasing and fluctuating, while the wind remained consistently below 5 m s⁻¹. After 0835 UTC on 28 June, Vis quickly rose above 5 km, the wind direction shifted northwards, and the fog event concluded. The entire fog process lasted for 880 min.

Vis changes revealed a pattern where Vis initially decreased at coastal stations and then at inland stations. This indicated that fog first reached the nearshore waters before advancing onto land in the early morning. Satellite imagery from the Himawari-8 satellite showed significant cloud coverage above the fog layer (Figure 3a,b) and precipitation was recorded at all stations during the event (Figure 3c). BGMS measured a cumulative rainfall of 22.9 mm, primarily occurring during two time periods: from 2000 to 2100 UTC on 27 June, and from 0300 to 0400 UTC on 28 June (Figure 2d).

3.2. Fog Droplets Microphysical Characteristics

Based on the temporal changes in microphysical characteristics (Figure 4), we divided the sea fog process into four stages: Formation, development, maturity, and dissipation. The corresponding time and microphysical parameters for each stage are outlined in

Table 1. Average, maximum, and minimum values of key characteristic parameters of the whole fog process and four stages.

Fog Stage	Time (UTC)	Vis (m)	Nd (cm−3)	LWC (g m−3)	rm (μm)	re (μm)
Whole Process	27 June 17:56−28 June 08:35	883 (147−15517)	190.62 (1.43−440.88)	0.026 (0.001−0.068)	2.84 (2.07−3.54)	3.44 (2.35−9.52)
Formation Stage (S1)	27 June 17:56−20:11	1961 (393−15517)	99.76 (1.43−259.10)	0.012 (0−0.030)	2.73 (2.46−3.04)	3.80 (2.91−9.52)
Development Stage (S2)	27 June 20:12−28 June 00:35	277 (170−929)	238.77 (75.76−381.19)	0.044 (0.007−0.067)	3.21 (2.48−3.54)	3.89 (2.93−5.07)
Maturity Stage (S3)	28 June 00:36−04:47	469 (147−2293)	248.58 (39.71−440.88)	0.031 (0.003−0.068)	2.81 (2.30−3.37)	3.33 (2.64−4.85)
Dissipation Stage (S4)	28 June 04:48−08:35	1368 (362−5758)	123.47 (10.40−256.77)	0.012 (0−0.037)	2.58 (2.07−3.01)	2.92 (2.35−4.10)

Note: The first row represents the mean values, with the parameter range indicated in parentheses (minimum−maximum).

.

The primary microphysical characteristics observed during the fog process were also presented in Table 1. The mean N_d was 190.62 cm⁻³, the mean LWC was 0.026 g m⁻³, the mean r_e was 3.44 μm, and the mean r_m was 2.84 μm. Compared to the sea fog process observed by Wang et al. [12], N_d in this event was higher, while LWC and r_m were lower, likely due to the presence of precipitation.

The microphysical structure changed significantly throughout the process, with Vis and microphysical parameters displaying roughly opposite trends. During the formation stage, Vis decreased notably, while N_d and LWC increased from 0, exhibiting low growth rates (Figure 4b). During the development stage, Vis remained below 1 km; the overall microphysical parameters were elevated, particularly droplet size, with r_m and r_e reaching significant values (Figure 4c). In the mature stage, microphysical characteristics fluctuated greatly, with both N_d and LWC reaching their maximum values throughout the entire process (Table 1). This increase was likely related to rising temperatures after sunrise over the coastal land. During the dissipation stage, Vis increased while all characteristic parameters decreased.

The 1 min average N_d spectrum indicated that fog droplets were primarily concentrated in sizes less than 10 μm (Figure 4d), while 1 min average LWC spectrum better represented the distribution of droplets with diameters ranging from 10 to 30 μm (Figure 4e). Over time, the droplet spectrum showed distinct changes. It broadened during the formation stage and exhibited pronounced bimodal characteristics in the development stage. In the mature stage, the intensity of the second peak reduced. Finally, the spectrum narrowed during the dissipation stage.

Table 2 presents a comparison of mean values and variability ranges for microphysical parameters in sea fog events observed at BGMS, Qingdao, and other coastal regions in China to better understand sea fog characteristics in our study area. The results reveal notable differences in microphysical characteristics across regions. Overall, Qingdao exhibited a relatively high mean N_d, second only to observations from the coastal area of Guangdong. However, the maximum N_d in both regions were similar, reaching approximately 400 cm⁻³. The mean LWC at BGMS was relatively low, significantly lower than in other regions except Guangxi. In terms of droplet size, Beilun had the largest mean r_m, followed by Qingdao.

Table 2. Comparison of sea fog microphysical characteristics between BGMS (Qingdao) and other coastal regions in China.

Observation Site and Time	Observation Instrument	Nd (cm−3)	LWC (g m−3)	rm (μm)
Qingdao, Shandong 27−28 June 2022	FM-120	190.62 (1.43−440.88)	0.026 (0.001−0.068)	2.84 (2.07−3.54)
Beilun, Zhejiang [25] 14−15 June 2021	FM-120	41.5 (0.31−212.93)	0.065 (0−0.64)	5.3 (1.75−11)
Xiamen, Fujian [26] 7 April 2019	FM-120	100 (0−468)	0.17 (0−1.35)	/
Maoming, Guangdong [27] 16−17 March 2008	FM-100	326.6 (15−422.6)	0.058 (0.010−0.64)	1.5 (1.2−2.45)
Zhanjiang, Guangdong [28] 23−24 February 2011	FM-100	248.0 (3−354)	0.102 (0.001−0.257)	2.6 (1.55−3.9)
Weizhou Island, Guangxi [29] 28 February 2021	FM-100	76.7 (10.6−454.9)	0.006 (0.001−0.03)	2.0 (1.9−2.2)

Note: “/” indicates the values are not shown in the reference.

Table 2. Comparison of sea fog microphysical characteristics between BGMS (Qingdao) and other coastal regions in China.

Observation Site and Time	Observation Instrument	Nd (cm−3)	LWC (g m−3)	rm (μm)
Qingdao, Shandong 27−28 June 2022	FM-120	190.62 (1.43−440.88)	0.026 (0.001−0.068)	2.84 (2.07−3.54)
Beilun, Zhejiang [25] 14−15 June 2021	FM-120	41.5 (0.31−212.93)	0.065 (0−0.64)	5.3 (1.75−11)
Xiamen, Fujian [26] 7 April 2019	FM-120	100 (0−468)	0.17 (0−1.35)	/
Maoming, Guangdong [27] 16−17 March 2008	FM-100	326.6 (15−422.6)	0.058 (0.010−0.64)	1.5 (1.2−2.45)
Zhanjiang, Guangdong [28] 23−24 February 2011	FM-100	248.0 (3−354)	0.102 (0.001−0.257)	2.6 (1.55−3.9)
Weizhou Island, Guangxi [29] 28 February 2021	FM-100	76.7 (10.6−454.9)	0.006 (0.001−0.03)	2.0 (1.9−2.2)

Note: “/” indicates the values are not shown in the reference.

3.3. Comparison of the Effect of Large and Small Droplets

Based on the average r_e in this case, we defined an empirical threshold of 3.5 μm to classify fog droplets as “small” or “large”. The N_d of small (blue) and large (red) droplets were calculated at 1 min intervals and plotted against the total N_d (Figure 5a). The regression lines were y = 0.81x + 11.22 (R² = 0.95) for small droplets and y = 0.19x − 11.22 (R² = 0.53) for large droplets, indicating that approximately 81% of the droplets were small.

Similarly, the 1 min average LWC (Figure 5b) and β_ext (Figure 5c) were calculated for both size categories. The results showed that large droplets accounted for 58% of the total LWC, while small droplets contributed 60% of the total β_ext. This indicated that small droplets dominated N_d and played a critical role in visibility attenuation, whereas large droplets had a more significant influence on LWC.

3.4. Analytical Expression for Fog DSD

Figure 6 shows fog DSD characteristics at each stage of the fog process, specifically where the observed visibility was below 1 km. Consistent with the changes shown in Figure 4, the average spectrum first rose and then declined over time. During the development stage, there was a marked increase in the number of droplets across all sizes, leading to the widest droplet spectrum.

The average DSD of the whole fog process can be fitted using the Gamma function:

$$\mathrm{n}\left(\mathrm{r}\right)=9.12·{\mathrm{r}}^{26.68}·{\mathrm{e}}^{-9.07\mathrm{r}},$$

(11)

where r and n(r) represent the radius and the corresponding N_d at that radius, respectively.

To describe the fog DSD more accurately, Wang et al. [12] proposed a new function, the G-exponential function:

$$\mathrm{n}(\mathrm{r})={\mathrm{a}}_1{\mathrm{e}}^{-{({\displaystyle \frac{\mathrm{r}-{\mathrm{b}}_1}{{\mathrm{c}}_1}})}^2}+{\mathrm{a}}_2{\mathrm{e}}^{-{({\displaystyle \frac{\mathrm{r}-{\mathrm{b}}_2}{{\mathrm{c}}_2}})}^2},$$

(12)

where a₁, b₁, c₁, a₂, b₂, and c₂ are the parameters, and r and n(r) are defined as stated in the previous equation.

The average spectrum can be described as:

$$\mathrm{n}(\mathrm{r})=142.34{\mathrm{e}}^{-{({\displaystyle \frac{\mathrm{r}-3.04}{0.19}})}^2}+45.96{\mathrm{e}}^{-{({\displaystyle \frac{\mathrm{r}-2.80}{1.06}})}^2},$$

(13)

A comparison of the G-exponential function and the Gamma function reveals their effects during different stages of the fog event (

Table 3. Fit quality comparison between two DSD functions.

Function Type	Accuracy Metrics	Whole Process	Formation Stage	Development Stage	Maturity Stage	Dissipation Stage
Gamma	RMSE (km)	5.34	8.91	7.66	6.28	8.12
	R2	0.926	0.49	0.87	0.91	0.62
G-exponential	RMSE (km)	0.94	8.22	5.42	3.34	7.45
	R2	0.998	0.57	0.93	0.97	0.68

). The G-exponential function is more suitable for the droplet spectrum distribution in this case, corroborating the results of Wang et al. [13]. The fitting performance exhibits significant variability across different stages, but it remains robust during periods with Vis below 1 km, with R² values exceeding 90%.

3.5. Comparison of the Calculated Vis with Different Methods

When a LWC is specified in a fog model, n(r) can be computed using Equations (11) and (13). This enables the calculation of Vis based on Equation (5), with the results denoted as Vis_Gam and Vis_Gex. Additionally, visibility parameterization schemes can be established based on the power–law relationships of microphysical characteristics (

Table 4. The fitting effect of different parameterization schemes.

Name	Function	MAE (km)	RMSE (km)
VisGam	/	0.16	0.24
VisGex	/	0.15	0.23
VisGN	44.989(Nd) −1.1592 [30]	0.33	0.39
VisEdg	0.024(LWC) −0.65 [31]	0.17	0.23
Visk84	0.027(LWC) −0.88 [32]	0.26	0.36
VisGNL	1.002(Nd·LWC) −0.6743 [30]	0.13	0.27
VisFRAM	0.8771(Nd·LWC) −0.49034 [4]	0.10	0.18

). An evaluation of visibility prediction results from different methods shows that the visibility parameterization scheme using both N_d and LWC results in a smaller MRE than those using either N_d or LWC alone.

Figure 7 presents the temporal evolutions of Vis_Gex, Vis_GN, Vis_k84, Vis_FRAM, and the observed Vis, indicating that Vis_FRAM has the lowest MAE and RMSE, in turn demonstrating the best Vis prediction performance, followed by Vis_Gex.

4. Discussion

The most notable characteristic of this sea fog event is the accompanying precipitation. This precipitation maintained RH at 100% throughout the process and coincided with rising temperatures (Figure 2). The precipitation provided ample moisture to the lower layer, maintaining a high water vapor content and supporting the extended duration of the fog. In contrast, observations by Wang et al. [12] during a spring sea fog event also showed high RH, yet indicated a significant temperature drop of nearly 2 °C, which differs from the rising temperatures observed in our case.

During this sea fog event, the main periods of precipitation occurred from 2000 to 2100 UTC on 27 June and from 0300 to 0400 UTC on 28 June (Figure 2d). The changes in LWC spectrum distribution (Figure 4e) clearly show that after 21:00 UTC on 27 June, there was a significant increase in large droplet formation, resulting in a relatively strong bimodal structure. A similar phenomenon was observed after 0420 UTC on 28 June; however, due to the rise in temperature after sunrise, the fog process entered a dissipation stage, leading to a reduction in the width of the droplet spectrum and a less pronounced bimodal distribution compared to the first stage. Additionally, compared to the microphysical characteristics observed by Wang et al. [12], N_d was higher, while LWC and r_m were lower. These differences in microphysical characteristics may also be influenced by the precipitation present during this summer sea fog event, but a deeper understanding requires additional observational data.

5. Conclusions

The microphysical characteristics of a summer sea fog event with precipitation along the west coast of the Yellow Sea were observed at BGMS from 27 June to 28 June 2022. Combined with meteorological data, the microphysics of this event were analyzed, yielding the following conclusions:

• The fog event lasted 880 min, beginning at 1756 UTC on 27 June and dissipating by 0835 UTC on June 28 (LST = UTC + 8 h). Significant precipitation occurred during two periods: 2100–2200 UTC on June 27 and 0300–0400 UTC on 28 June. Although the precipitation caused fluctuations in visibility, it did not disrupt the formation or persistence of the fog.
• The observed microphysical parameters included an average N_d of 190.62 cm⁻³, LWC of 0.026 g m⁻³, r_m of 2.84 μm, and r_e of 3.44 μm. Using the average r_e as a threshold, droplets were classified as “small” or “large”. Small droplets dominated N_d (81%) and contributed significantly to visibility attenuation (60% of β_ext), while large droplets, though fewer in number, accounted for 58% of LWC.
• The fog DSD throughout the fog event was better represented by a G-exponential distribution than by a Gamma distribution. The fog process was divided into four stages: formation, development, maturity, and dissipation. During formation, droplet sizes increased. The development stage exhibited a pronounced bimodal spectrum, with the second peak weakening in maturity. By dissipation, droplet quantities decreased, narrowing the spectrum.
• A comparison of visibility parameterization methods reveals that incorporating both N_d and LWC yields a smaller MRE compared to using either parameter alone. Among the evaluated methods, Vis_FRAM demonstrates the lowest MAE and RMSE, indicating superior visibility prediction performance, followed by Vis_Gex.

This study investigates the microphysical characteristics of a precipitation-associated sea fog event along the west coast of the Yellow Sea and provides detailed parameterization for Vis estimation. While the findings are based on a single on-site fog event, potential variability may exist. Additionally, factors such as aerosol influence on N_d and LWC were not addressed. The specific impact of precipitation on sea fog microphysics requires further investigation. To address these limitations, long-term field observations at BGMS and more comprehensive instrumentation will be employed in future studies.