A Numerical Study of Sea-Fog Formation over Cold Sea Surface Using a One-Dimensional Turbulence Model Coupled with the Weather Research and Forecasting Model

Boundary-Layer Meteorol (2012) 143:481505DOI 10.1007/s10546-012-9706-9

ARTICLE

A Numerical Study of Sea-Fog Formation over Cold SeaSurface Using a One-Dimensional Turbulence ModelCoupled with the Weather Research and ForecastingModel

Chang Ki Kim Seong Soo Yum

Received: 2 August 2011 / Accepted: 7 February 2012 / Published online: 29 February 2012 Springer Science+Business Media B.V. 2012

Abstract The formation mechanism of a cold sea-fog case observed over the Yellow Seanear the western coastal area of the Korean Peninsula is investigated using numerical simu-lation with a one-dimensional turbulence model coupled with a three-dimensional regionalmodel. The simulation was carried out using both Eulerian and Lagrangian approaches; bothapproaches produced sea fog in a manner consistent with observation. For the selected coldsea-fog case, the model results suggested the following: as warm and moist air flows over acold sea surface, the lower part of the air column is modified by the turbulent exchange ofheat and moisture and the diurnal variation in radiation. The modified boundary-layer struc-ture represents a typical stable thermally internal boundary layer. Within the stable thermallyinternal boundary layer, the air temperature is decreased by radiative cooling and turbulentheat exchange but the moisture loss due to the downward vapour flux in the lowest part of theair column is compensated by moisture advection and therefore the dewpoint temperaturedoes not decrease as rapidly as does the air temperature. Eventually water vapour saturationis achieved and the cold sea fog forms in the thermal internal boundary layer.

Keywords One-dimensional turbulence model Radiation Sea fog Thermal internal boundary layer Three-dimensional regional model Turbulence

1 Introduction

Fog, defined as a cloud of which the base is at or near the surface, is considered to be a mete-orological hazard for traffic systems when the visibility is less than about 1 km (Johnson andGraschel 1992; Leigh 1995; Croft et al. 1995). In particular, nautical navigation is hinderedby the severe visibility degradation due to sea fog; Trement (1989) reported that 80% of

C. K. Kim S. S. Yum (B)Department of Atmospheric Sciences, Yonsei University, 134 Shinchon-dong, Seodaemun-gu,Seoul 120-749, Koreae-mail: [email protected]

123

482 C. K. Kim, S. S. Yum

oceanic disasters were related to sea fog. In addition, any sea fog advected to coastal areascan result in damage to the traffic systems in these areas.

Observational fog studies date back about 200 years and have been steadily done since(e.g., Wells 1814; Willett 1928; Roach et al. 1976; Duynkerke 1991; Fu et al. 2004; Pagowskiet al. 2004). However, these studies focused either on radiation fog over land surfaces or steamfog over large lakes, due to the spatial and temporal limitations of the observations. Over thepast several decades, studies have been conducted using observations from research vessels oraircrafts. Taylor (1917) suggested that air temperature might decrease to match the dewpointtemperature by eddy mixing over a cold sea surface. Pilie et al. (1979) proposed formationmechanisms for sea fog over the California coast using meteorological observations madeon a research vessel as follows: (1) sea fog is triggered by instability and mixing over warmsea surface, (2) sea fog can develop as a result of the lowering process of stratus cloud, (3)the formation of sea fog is associated with low-level convergence, or (4) coastal radiationfog is advected to sea via nocturnal land breezes. Sea fog formed near the coast of northernScotland, haar, was characterized as typical advection fog by Findlater et al. (1989). Lewiset al. (2003) demonstrated through observational analyses that sea fog over the Californiacoast could be formed via synoptic scale forcing, leading to the subsidence of stratus cloudsdown to the surface. However, field campaigns for the investigation of sea-fog formation areoften difficult to conduct due to spatial and temporal limitations. Moreover, meteorologicaldata from weather stations in coastal regions often do not adequately represent the weatherconditions over the sea, and the routine meteorological instruments installed at buoys do notmeasure the microphysical characteristics of sea fog.

For these reasons, there have been many numerical studies on the formation, developmentand dissipation of sea fog that might compensate for the intrinsic weaknesses of observa-tional studies. Ballard et al. (1991) were the first to attempt fog prediction using a regionalmodel, and predicted the fogs off the coast of northern Scotland with marginal success, usingthe United Kingdom Meteorological Office (UKMO) numerical mesoscale model. Pagowskiet al. (2004) attempted to identify the formation mechanisms of fog over Lake Ontario usingthe fifth-generation Pennsylvania State University/NCAR mesoscale model (MM5) with ahigh spatial resolution. Using the same model, Koracin et al. (2005) demonstrated the tran-sition of stratus to sea fog off the west coast of the United States. van der Velde et al. (2010)summarized the performance of three-dimensional (3D) regional models in predicting fog,and suggested that the predictability of fog formation was critically dependent on the verti-cal resolution and the parametrization of boundary-layer turbulence in the model. However,expensive computational costs are a major concern for 3D regional model simulations withhigh spatial resolution.

An alternative approach is to use a one-dimensional (1D) turbulence model. This type ofmodel has been shown to be an appropriate tool for studying the effects of turbulence on fogevolution (e.g., Musson-Genon 1987; Bergot et al. 2007). Bergot et al. (2007) compared theperformance of six 1D turbulence models in predicting two typical radiation-fog cases. Theintercomparison revealed that these 1D turbulence models were able to reproduce several ofthe major features of the life cycle of a fog layer. However, a typical 1D turbulence modeldoes not resolve the horizontal advection or pressure gradient force and therefore is limitedto applications in radiation-fog studies. More recently, a 1D turbulence model was coupledwith a 3D model to compensate for the intrinsic limitations of the 1D turbulence model (e.g.,Holtslag et al. 1990; Bergot and Guedalia 1994; Koracin et al. 2001; Mller et al. 2007; Shiet al. 2011). Bergot and Guedalia (1994), Mller et al. (2007), and Shi et al. (2011) added thehorizontal advection of heat and moisture simulated by a 3D regional model into the tendencyequations of heat and moisture in a 1D turbulence model. Meanwhile, Holtslag et al. (1990)

123

A Numerical Study of Sea-Fog Formation over Cold Sea Surface 483

and Koracin et al. (2001) considered an air column moving along a trajectory simulated bya 3D regional model and studied atmospheric boundary-layer modification caused by thechange in surface condition.

Kim and Yum (2010) examined the statistical characteristics of sea fog that forms overthe Yellow Sea off the west coast of Korea. They classified 35 sea-fog occurrences into 26cases of cold sea fog and nine cases of warm sea fog, based on the difference, T, betweenair temperature (T ) and sea-surface temperature (SST) (T = T SST ) three hours beforethe onset of fog formation (i.e., cold sea fog for T > 0 and warm sea fog for T < 0) andlinked the occurrence statistics with relevant meteorological variables. Their study showedthat the formation of cold sea fog was related to the movement of warm and moist air massesover the cold sea surface while warm sea fogs were formed due to the cold advection ofair that leads to a large negative T . However, the formation mechanism of sea fog can-not be explained only by synoptic conditions. As an effort to further this result, Kim andYum (2011) identified the relative contributions of turbulence, advection and radiation on airtemperature and dewpoint temperature in the atmospheric boundary layer over the YellowSea. They found that, not only the turbulent cooling but also the radiative cooling before theonset of fog, crucially contributed to the decrease of air temperature over the cold sea surfaceand consequently to water vapour saturation in the stable boundary layer to form a cold seafog. However, for warm sea fog, water vapour saturation was achieved by the increase ofdewpoint temperature due to the turbulent transport of moisture from the warm sea surfaceto the convective boundary layer.

Several numerical studies on sea fog over the Yellow Sea have been carried out during thepast decade (e.g., Choi and Speer 2006; Fu et al. 2006; Gao et al. 2007). From the RegionalAtmospheric Modeling System (RAMS) and MM5 modelling studies, respectively, Fu et al.(2006) and Gao et al. (2007) showed that the characteristics of sea fog over the Yellow Seain summer were similar to those of a typical advection fog. However, the sea fogs examinedin these studies were observed near the east coast of China, and on the opposite side of theYellow Sea to the west coast of Korea, where this study focuses on. Moreover, the authors didnot explicitly state what factors led to water vapour saturation. Meanwhile, Choi and Speer(2006) demonstrated the land/sea-breeze effects on advective-radiative fog over the complexcoastal terrain in the western Korean Peninsula.

As a continuation of the studies by Kim and Yum (2010, 2011), the present study aims atbroadening our knowledge on the formation mechanisms of sea fogs off the west coast of theKorean Peninsula using numerical modelling. Here we focus only on cold sea fogs mainlybecause they are more frequent than warm sea fogs. The effects of turbulence, advectionand radiation on cold sea-fog formation are closely examined. In particular, we focus on theinfluences of the turbulent mixing of heat and moisture, and radiative cooling, using a 1Dturbulence model coupled with a 3D regional model.

Section 2 describes the case examined in this study, and the numerical models used areintroduced in Sect. 3 with Sect. 4 explaining the numerical experimental design. In Sect. 5,we show the results from the numerical experiments, and turbulent and radiative effects,the source of turbulence and limitations of the study, are discussed in Sect. 6. Finally, theconclusions are given in Sect. 7.

2 Case Description

Air temperature (T ), SST, dewpoint temperature (Td), relative humidity (RH), wind direc-tion, wind speed and mean sea-level pressure are measured every hour from a meteorological

123


Fig. 1 Surface fields at 1200 UTC, 18 April, 2006 along with the WRF domain setting and the air-columntrajectory used for the PAFOG simulation with the Lagrangian approach. The shaded colour indicates thesea-surface temperature (SST, C), and the contour line represents the mean sea-level pressure (hPa). Theasterisks in trajectory marks the location every 3 h. The map in the left bottom corner is the enlargement ofthe WRF D3 and shows the locations of IIA and the other measurement sites: the asterisk, the closed circle,the triangle, and the rectangle indicate IIA, the buoy site, the radiosonde site at Baeknyeong Island, and thelighthouse at Seonmi Island, respectively

buoy near Dukjeok Island, 40 km from Incheon International Airport (hereafter IIA, Fig. 1).Rawinsondes are launched from the weather station at Baeknyeong Island every day at 0000UTC (0900 local standard time, LST) and 1200 UTC (2100 LST).

This study selected the 18 April 2006 case among the 26 cold sea-fog cases classified byKim and Yum (2010). Figure 1 shows the surface synoptic fields at 1200 UTC, 18 April 2006.A low pressure centre is located over Chinese coastal area, and southerly winds dominateover the eastern Yellow Sea that advect a warm and moist air mass to this region. Then thepositive T over the Yellow Sea (Fig. 2a) may induce heat transfer from the atmosphere tothe sea surface. Td(= Td SST ) over the Yellow Sea is also positive (Fig. 2b), indicatingthat the water vapour flux is downward from the atmosphere to the sea surface.

123


Fig. 2 T (C) (a) and Td (C) (b) fields at 1200 UTC, 18 April, 2006

Figure 3 shows the time variation of T , SST, Td and RH measured at the buoy during thisepisode of cold sea fog, observed from 1900 UTC, 18 April to 0500 UTC, 19 April, basedon the 95% RH criterion (Sorli et al. 2002). Air temperature decreases slowly from 0000 to1700 UTC, 18 April and then decreases rapidly until the onset of sea fog (1900 UTC, 18April; see the high RH period) with the rate of 0.8C h1. The strong cooling rate duringthis period is probably due to nighttime radiative cooling that enhances the turbulent coolinginduced by positively large T . Meanwhile, dewpoint temperature rapidly increases from0000 to 0300 UTC, 18 April and then increases slowly with some variations. The SST ispractically constant during the whole period but due to the decrease in air temperature duringthe fog, T is lowest at 0200 UTC, 19 April. Some previous studies on sea fog suggestedthat radiative cooling at the fog top as a main cause of air temperature decrease during fog(e.g., Douglas 1930; Petterssen 1938; Brown and Roach 1976; Pilie et al. 1979; Koracin et al.2001). We will discuss the effect of radiative cooling at the fog top in detail later. In additionto the radiative effect, cold advection may also contribute to the decrease in air tempera-ture. The dewpoint temperature matches with air temperature and decreases in the maturestage of the fog as the vapour pressure decreases due to vapour condensation to form fogdroplets. In the dissipation stage, air temperature remains constant but dewpoint temperaturedecreases.

The time evolution of the fog-top height, estimated from MeTeorolgical SATelite-1(MTSAT-1) geostationary satellite data, is shown in Fig. 4. In the present study, the dif-ference in brightness temperatures between the 3.8-m and the 10.8-m channels in theMTSAT-1 satellite output was used to detect the fog or stratus clouds at night, followingthe algorithm suggested by Ellrod (1995) and Underwood et al. (2004). The fog-top heightwas estimated using a function of the difference between the two channels, as suggested inYamanouchi et al. (1987). In order to evaluate the accuracy of the estimation of fog heightusing the satellite data, this study compares the vertical profiles of RH measured at two rawin-sonde sites (Baeknyeong Island and Jeju Island, marked in Fig. 4d) and the satellite estimatedcloud/fog depth at the two locations. At 0000 UTC, 19 April 2006, the cloud/fog top height,based on the 95% RH criterion, was 301 m at Baeknyeong Island, which is slightly higher

123


Date/Hour (dd/hhmm, UTC)18/0000 18/0600 18/1200 18/1800 19/0000 19/0600 19/12

T (o C

)

4

8

12

16

SST

(o C)

4

8

12

16

T d(o C

)

4

8

12

16

RH (%

)

52

68

84

100

TSST TdRH

Fig. 3 Time series of air temperature (T , solid line), SST (dotted line), dewpoint temperature (Td, dashedline with closed triangle) and related humidity (RH, dashed line) measured at the buoy

than the estimated fog depth of 275 m. Similarly the cloud-top height at Jeju Island was 766m, which is again somewhat higher than the satellite-estimated cloud-top height of 650 m.However, Ellrod (1995) suggested that the satellite product from Geostationary OperationalEnvironmental Satellites (GOES) might slightly overestimate the fog depth. The differencemay be due to the difference of the satellites used for the estimation of fog depth (MTSAT-1in our study vs. GOES in Ellrod (1995)). However, this methodology is not valid during thedaytime because the brightness temperature at 3.8 m is affected by solar radiation. Instead,the fog-top pressure and the mean sea-level pressure provided by the International SatelliteCloud Climatology Project (ISCCP) were used to estimate the fog-top height during thedaytime. ISCCP was established to collect and analyze satellite radiance measurements toinfer the global distribution of clouds, their properties, and their diurnal, seasonal, and inter-annual variations. Several studies verified a good reliability of cloud product from ISCCP(e.g., Rossow et al. 1993; Weare 1994; Inoue and Kamahori 2001). There is no fog over theYellow Sea at 0300 UTC, 18 April (Fig. 4a). Fifteen hours later, sea fog is detected over thesea close to the west coast of the Korean Peninsula (Fig. 4b) and remains until 0300 UTC,19 April (Fig. 4ce). The sea fog disappears from the coastal area almost completely at 0600UTC, 19 April (Fig. 4f).

3 Model Description

3.1 WRF

This study uses the Weather Research and Forecasting (WRF) model version 3.1.1 as the3D regional model (Skamarock et al. 2008), which is a fully compressible and Euler non-hydrostatic system that is conservative with regard to scalar variables. The horizontal coor-dinates employs an Arakawa-C grid, and terrain-following vertical grid stretching is usedfor the vertical coordinate. The WRF model includes modules for microphysics, cumulusparametrization, surface physics, planetary boundary-layer physics, atmospheric radiation

123


Fig. 4 Spatial distribution of the fog-top height estimated from the MTSAT-1 satellite data during the period ofthe fog. In (d), triangle and rectangle indicate the location of Baeknyeong Island and Jeju Island, respectively

physics and a land-surface model. One-way or two-way interactive grid nesting proceduresare employed. A 3D meteorological field is required as the initial and boundary conditionsfor real case simulations.

123


3.2 PAFOG

The PArameterized FOG (PAFOG) model, developed by the University of Bonn in Germany,consists of four modules: dynamic solver, microphysics, radiation physics and vegetation-soil model (Bott and Trautmann 2002). PAFOGs dynamic solver is a 1D model of theatmospheric boundary layer consisting of a set of prognostic equations for horizontal windfield, the potential temperature, and specific humidity. These equations are described indetail in Bott et al. (1990) and Siebert et al. (1992). Turbulence is treated with a 2.5-levelMellorYamada parametrization (Mellor and Yamada 1974, 1982), and the turbulent flux atthe fog top essentially describes the entrainment process and therefore it can be said that theentrainment process is explicitly calculated.

Shortwave and longwave radiation streams are calculated using the -two stream approxi-mation proposed by Zdunkowski et al. (1982), and in which the solar spectral interval (0.286m) is divided into four sub-intervals, in which the extinction occurs due to water vapour,ozone, aerosols, and cloud droplets. In the infrared spectral region (3.5100 m), the atmo-spheric window region (8.7512.25 m) is separately treated by considering the extinctionsdue to gases, aerosols, and cloud droplets. In the remaining part of the infrared spectralregion, only the absorption by gases, aerosols and cloud droplets is calculated accordingto an emissivity method. Radiation is calculated at 5-min intervals in order to reduce thecomputational burden.

The microphysical scheme in this model is based on a double-moment parametrization,as suggested in Nickerson et al. (1986) and Chaumerliac et al. (1987). In this scheme, twoprognostic equations are solved for the total number concentration of cloud droplets (Nc)and for the cloud water mixing ratio (qc). The droplet size distribution is calculated usingthe following log-normal distribution,

dNc = Nc2c D

exp[ 1

2 2cln2

(DD0

)]dD, (1)

where D is the droplet diameter, D0 is the mean value of D, and c is the dispersion parameterof the given droplet distribution (standard deviation/mean). In Chaumerliac et al. (1987), cwas chosen as a function of the particular aerosol type (maritime: c = 0.28, continental: c= 0.15), and herein we use c = 0.2.

At a given supersaturation S (in percent), the number of activated cloud droplets (Nact) isdetermined according to the Towmey relation (Pruppacher and Klett 1997),

Nact = C Sk, (2)

where the constants C and k depend on the air-mass type. The present study determinesthese constants based on measurements on the west coast of the Korean Peninsula (Yum etal. 2005) (C = 5,000 cm3, k = 0.4). The calculation of S follows the work of Sakakibara(1979). In the present version of PAFOG, the drizzle formation is not included since thismodel is aimed at simulating fog, and so cloud droplets grow only by the diffusion of watervapour.

PAFOG employs the vegetation-soil model from Siebert et al. (1992), which describesthe interaction of the land surface with the overlying atmosphere, and is used only when thePAFOG air column is over land.

123


Table 1 Summary of the WRF model simulation conditions

Domain 1 Domain 2 Domain 3

Grid spacing (km) 18 6 2Timestep (s) 108 36 12Initial, boundary conditions NCEP GDAS 1 Domain 2 DomainsPBL YSU YSU YSUShortwave radiation Dudhia Dudhia DudhiaLongwave radiation RRTM RRTM RRTMMicrophysics WSM6 WSM6 WSM6Convection KF KFNumber of vertical layers 65The lowest level 0.998 ( -level)Soil model 5-Layer soil model

4 Numerical Experiment

4.1 WRF

Figure 1 shows the domain setting for the WRF simulation, where one-way grid nestingis used for the three domains. Domain 3 (D3) with the finest horizontal resolution of 2km, which is centred on IIA, resolves the evolution of sea fog, as well as the local mete-orological characteristics off the west coast of the Korean Peninsula. Table 1 summarizesthe model configuration of WRF. The entire grid system has 65 vertical layers, with thelowest level, = 0.998 (about 7 m above ground level), in coordinates. The six-hourly data from the Global Data Assimilation System (GDAS) produced by NationalCenter for Environment Prediction (NCEP) are used as the initial and boundary condi-tions.

4.2 PAFOG

In this study, the vertical resolution of the model is set to be sufficiently high so that themodel equations are solved at 400 levels distributed between the surface and an altitude of2,500 m, using a constant resolution of 5 m for grids from the surface to 1,500 m and thence alogarithmic spacing from 1,500 m to the top of the model. A total of ten additional levels from2,500 m to the top of the atmosphere are used only for use in the radiative transfer equations.The integration time interval is 5 s. For the initial wind conditions, 10% of the wind speed atthe top of the model (from the WRF calculation) is used as a substitute for the lowest levelvalue, and the wind speeds from the lowest level to the model top are assumed to take on alogarithm profile. The lower boundary was set at the sea surface for the Eulerian approach(explained later), and therefore the vegetation-soil model is not activated. For the Lagrangianapproach, however, the vegetation-soil model is activated when the air column moves overthe land. The types of land and soil used in the vegetation-soil model were urban and sandyclay loam, respectively, based on the data from the United States Geological Survey (USGS)report.

123


4.3 Coupling of PAFOG with WRF

4.3.1 Eulerian Approach

As Mller et al. (2007) suggested, the 1D turbulence model of PAFOG can be coupled to theWRF model in the Eulerian approach. In order to consider the heat and moisture transportedto a point in an air column, the horizontal advection terms of heat and moisture are addedto the tendency equations for air temperature and dewpoint temperature, respectively. In thisstudy, the air column in PAFOG is located at the buoy site and the horizontal advection ofheat and moisture simulated by the WRF model is used and updated hourly to represent theexternal forcing terms in PAFOG. Since this study focuses on the in situ formation of fogover the cold sea surface, the advection of liquid water (i.e., the transport of fog from someother region) is not considered.

Both potential temperature and dewpoint temperature at the grid corresponding to thebuoy location from the WRF fields are used as the initial profiles for the Eulerian approach.SST values (from the WRF model) are held constant at 281 K. Even though the SST (281 K)is higher by 1 K than the observed SST (Fig. 3), the SST from the WRF model is used in orderto complete the model configuration only with the WRF fields (potential temperature ( ),dewpoint temperature, wind speed, horizontal advection). The vertical profile of potentialtemperature in Fig. 5a represents the characteristics of a stable boundary layer. Wind speedat low levels increases with height logarithmically and reaches 16.1 m s1 at 2.5 km altitude.The simulation is executed from 0000 UTC, 17 April to 1200 UTC, 19 April. Figure 6 isthe timeheight plot of the horizontal advection of air temperature and dewpoint temperatureat the buoy location, simulated by the WRF model. There is warm-air advection at loweraltitudes (below 300 m) from 0000 UTC, 17 April to 2100 UTC, 18 April (Fig. 6a) but dur-ing the fog event (2100 UTC, 18 April to 0500 UTC, 19 April) there is cold-air advection.Meanwhile moisture is advected to the buoy location below 300 m altitude from 1700 UTC,17 April to 2100 UTC, 18 April and drier air is then advected during the fog event and intothe dissipation stage of fog (Fig. 6b). This heat and moisture advection is used as externalforcing to PAFOG.

4.3.2 Lagrangian Approach

In the Lagrangian approach, the 1D turbulence model of PAFOG is simulated along a pathdetermined by the WRF model. To perform the desired simulation using this approach,PAFOG is modified to account for specified time-varying lower boundary conditions for heatand moisture availability at the surface. When the trajectory of the air column is over thesea, the vegetation-soil model is disabled but is enabled when the air column moves over theland.

The Lagrangian approach is an appropriate tool for the simulation of sea fog formed bythe cooling of the lower part of a warm and moist air column over a relatively cooler seasurface, as suggested by Kim and Yum (2010, 2011). The trajectory of the air column usedin this approach is synthesized from a 48-h back-trajectory and a 12-h forward-trajectory at10-m altitude at the grid point corresponding to the buoy from the WRF fields. The justi-fication for selecting the 10-m altitude instead of higher altitudes arises from the fact thatthe air-column trajectories at several levels (10, 150 and 500 m altitudes) were similar: thetrajectory at 500-m altitude deviates more from the other trajectories but all three originatedfrom the south (East China Sea) and passed over the cold sea surface, and therefore themeteorological conditions they experienced were similar (not shown). The initial conditions

123


Fig. 5 Initial conditions of potential temperature ( , K) and zonal wind speed (U, m s1) for the PAFOGsimulation using the Eulerian approach (a) and the Lagrangian approach (b). The dot at the surface altitudein each plot indicates the SST (K) at the initial time

for the Lagrangian approach are the vertical profiles of potential temperature and zonal windspeed at the starting point of the trajectory (Fig. 5b), while the SST value is extracted fromthe WRF fields and updated into PAFOG each hour. The PAFOG results mentioned hereafterimply PAFOG coupled with WRF. As illustrated in Fig. 1, the trajectory of the air column forthe selected case moves northward along the eastern part of the Yellow Sea and then crossesthe Korean Peninsula. The simulation is executed from 0000 UTC, 17 April to 1200 UTC,19 April in order to track the changes in the lower part of the marine boundary layer due tothe cold sea surface.

5 Results

5.1 Model Evaluation

The performance of PAFOG is first evaluated before we present the detailed investigationof the selected case. The threat score is used for the evaluation of PAFOG in the Eulerianapproach; the threshold values of the threat score for the observation and simulation are 95%for relative humidity at the buoy and 0.005 g kg1 for the cloud water mixing ratio at thelowest level of PAFOG, based on Tardif (2007), respectively. This makes sense since the aircolumn in PAFOG is assumed to be located at the buoy. To compare the predictabilities of

123


Fig. 6 Timeheight plots of the horizontal advections of air temperature (a) and dewpoint temperature (b) atthe buoy location, simulated by WRF

the WRF model and PAFOG, the cloud water mixing ratio at the lowest level of the WRFgrid corresponding to the buoy location in D3 is used as the threshold value to calculate thethreat score.

The threat score of PAFOG for the selected case is 0.92, which is much higher than thatof the WRF model (0.51) and the mean threat score for all 26 cold sea-fog cases was 0.79for PAFOG and 0.61 for WRF simulations. Figure 7 shows the timeheight plot of the cloudwater mixing ratio at the buoy location from the two models. The WRF model tends to simu-late deep fog, the depth of which is greater than 1.5 km and therefore incomparable to the fogdepth estimated from the MTSAT-1 geostationary satellite data (Fig. 7a). On the other hand,the simulated fog depth from PAFOG is consistent with the satellite-estimated fog depth,except for the maximum value (e.g., at 0300 UTC 19 April in Fig. 7b). In the Lagrangianapproach, the performance of PAFOG is also better than that of the WRF model. The fog

123


Eulerian Eulerian

17/0000 17/0600 17/1200 17/1800 18/0000 18/0600 18/1200 18/1800 19/0000 19/0600 19/1200 17/0000 17/0600 17/1200 17/1800 18/0000 18/0600 18/1200 18/1800 19/0000 19/0600 19/1200

Lagrangian Lagrangian

(c)

(a) (b)

(d)

17/0000 17/0600 17/1200 17/1800 18/0000 18/0600 18/1200 18/1800 19/0000 19/0600 19/1200 17/0000 17/0600 17/1200 17/1800 18/0000 18/0600 18/1200 18/1800 19/0000 19/0600 19/1200

Fig. 7 Timeheight plot of cloud water mixing ratio (g kg1) for WRF and PAFOG with the Eulerian approach(a, b) and with the Lagrangian approach (c, d). The dot in each plot indicates the estimated height of the fogtop from the MTSAT-1 satellite

forms 30 hours earlier and the fog depth is much higher in the WRF simulation than whencompared to observations (Fig. 7c). In contrast, the evolution of the fog depth in the PAFOGsimulation is similar to that of the satellite-estimated fog depth (Fig. 7d).

Such a large discrepancy between the two models seems to demonstrate the limitationof the WRF model as a fog prediction model. First of all, the WRF-simulated turbulence isknown to be more intense than in reality and this may cause the overestimation of the PBLheight (Steeneveld et al. 2011). In addition, there is the vertical resolution issue. Apparentlythe WRF grid spacing in our simulation was too large to resolve the boundary-layer struc-ture that was crucial to the formation of fog in this study. Tardif (2007) showed a similarresult: the simulation with low vertical resolution produced much deeper fog than observedwhile the simulation with high vertical resolution produced the fog depth that was similar tomeasurements.

In addition the performances of the two models for the air temperature and dewpointtemperature predictions are compared using a range of statistical parameters (Table 2). Thecorrelation coefficient ( ), root mean-square error (RMSE) and mean bias (MB) are calcu-lated from the air temperature and dewpoint temperature measured at the buoy and simulatedat the lowest level from 0000 UTC, 18 April to 1200 UTC, 19 April. Both PAFOG and theWRF model show a cold bias in the air-temperature prediction. Bergot et al. (2007) pointedout that numerical weather prediction with fine vertical resolution may have a cold bias overthe cooler surface. However, the performance of PAFOG is considered to be better than thatof the WRF model because of the higher correlation coefficient and smaller RMSE. Thecomparison of the performance of the two models for dewpoint temperature is somewhatcomplex: PAFOG has a slightly smaller correlation coefficient but much smaller RMSE.Overall, PAFOG with fine vertical resolution is considered as a better tool for simulating the

123


Table 2 Summary of the statistics that compare observations with PAFOG and WRF results

PAFOG WRF

RMSE (C) MB (C) RMSE (C) 1 MB (C)

Air temperature 0.92 2.5 1.2 0.76 3.8 1.4Dewpoint temperature 0.80 0.8 0.1 0.86 2.6 0.2

The meaning of the variables are explained in the text

evolution of sea fogs investigated in this study. However, this may not apply to all cases offog. For example, Shi et al. (2011) coupled PAFOG with MM5 to simulate the radiation fogin China but found that moisture advection was not well represented in their simulation andPAFOG failed to generate the vertical growth of the fog layer.

5.2 Sea-Fog Formation Mechanism

5.2.1 Eulerian Approach

Figure 8a shows the time series of air temperature, dewpoint temperature, SST, and the inte-grated liquid water path at 5 m altitude calculated from the Eulerian approach. The rapiddecrease of air temperature during the first three hours after the simulation started resultsfrom the spin-up effect (Mller et al. 2007). The fog is formed one hour later than observationand is dissipated three hours later than observed. Air temperature gradually increases from0300 UTC, 17 April to 1800 UTC, 18 April and then decreases rapidly until the onset timeof fog and during the fog event, air temperature becomes even lower than the SST (Fig. 8a).Dewpoint temperature follows a similar trend except it increases at the time of the rapiddecrease of air temperature near the onset of fog.

The PAFOG simulation captures the strong cooling prior to the onset of fog shown inFig. 3; there is warm-air advection from 1800 to 2000 UTC, 18 April (Fig. 6a) and thereforethe strong cooling (0.7C h1) is due to the radiative and turbulent cooling. Kim and Yum(2011) argued that radiative and turbulent cooling crucially contributed to the decrease in airtemperature before the formation of sea fog. The net radiative heating rate, the shortwave andlongwave components of the heating rate, and the turbulent heating rates 27 hours after thesimulation started (0300 UTC, 18 April) are illustrated in Fig. 9a; note that a negative heatingrate indicates cooling. Therefore radiative cooling occurs at altitudes below 300 m, whereasradiative heating prevails at higher altitudes (see the radiative heating rate in Fig. 12a). Radi-ative heating at higher altitudes is likely due to strong solar radiation at 0300 UTC 18 April(local noon). However, radiative cooling at lower altitudes cannot be explained only by solarradiation. Steeneveld et al. (2010) showed that the difference in emitted longwave radia-tion due to the discontinuity of air temperature near the surface could cause the decreaseof air temperature in the stable boundary layer. That is, outgoing longwave radiation fluxescan be greater than incoming solar radiation fluxes at lower altitudes even during the day.Figure 9a shows that the shortwave radiative heating below 40 m altitude is much weakerthan that of the longwave radiative cooling over the cold sea surface: the discontinuity of airtemperature near the sea surface in Fig. 5a implies a strong vertical gradient of longwaveradiative emission. This effect of radiative cooling on air temperature will be discussed morein Sect. 6. Meanwhile the turbulent cooling, which is due to the turbulent mixing of thecold air in contact with the sea surface with the air above, is limited to altitudes below 40 m.

123


Eulerian

Lagrangian

(a)

(b)

17/0000 17/0600 17/1200 17/1800 18/0000 18/0600 18/1200 18/1800 19/0000 19/0600 19/1200

17/0000 17/0600 17/1200 17/1800 18/0000 18/0600 18/1200 18/1800 19/0000 19/0600 19/1200

17/0000 17/0600 17/1200 17/1800 18/0000 18/0600 18/1200 18/1800 19/0000 19/0600 19/1200

17/0000 17/0600 17/1200 17/1800 18/0000 18/0600 18/1200 18/1800 19/0000 19/0600 19/1200

Fig. 8 Time series of air temperature (T , solid line), dewpoint temperature (Td, dashed line), SST (dotted line)and liquid water path (LWP, dash-dotted line) with the Eulerian approach (a) and the Lagrangian approach(b). In (b) the arrow indicates the time that the air column is located at the buoy (arrow) and the triangleindicates the time that the air column moves onto the land

The contribution of radiative cooling to the decrease of air temperature calculated by PAFOGis consistent with the radiative effect on air temperature suggested by Kim and Yum (2011).

As illustrated in Fig. 9b, vertical profiles of radiative and turbulent heating rate at 42 hours(the time of a rapid decrease in air temperature; 1800 UTC, 18 April in Fig. 8a) show thatthe radiative cooling rate increases by about five times as the night falls but turbulent coolingis only slightly increased, when compared to Fig. 9a. Obviously nighttime radiative coolingenhances the cooling of the air at lower altitudes.

The water vapour flux at 42 hours is negative from the sea surface to an altitude of 40m (Fig. 9c). When the sea surface is colder than the air above, the water vapour flux canbe directed toward the sea surface. The key parameter to examine is actually the dewpointtemperature, which is a measure of water vapour amount in the air. Generally it is under-stood that the air in contact with the sea surface is just saturated at the SST. Therefore, if thedewpoint temperature of the air above is greater than the SST, this implies that the air abovehas a greater water vapour amount than the air in contact with the sea surface. Such a watervapour profile would induce a water vapour flux directed toward the sea surface. Boutle et al.(2010) showed that the water vapour flux could be negative over the ocean in mid-latitudesunder conditions where warm and moist air is advected over the relatively cold sea surface,

123


(a) (b)

(c)

Turbulent heating rate ( oC h-1) Turbulent heating rate ( oC h-1)

Radiative heating rate (oC h-1) Radiative heating rate (oC h-1)

Cloud water flux (x10-3 g kg-1 m s-1)

Water vapour flux (x10-3 g kg-1 m s-1)

Water vapourCloud water

Fig. 9 Vertical profiles of net (solid line), shortwave (dashed line) and longwave (dotted line) radiative, andturbulent heating rates (dashed-dot line) at 27 h (a) and 42 h (b), and water vapour (solid line) and cloud waterfluxes (dashed line) at 42 h (c) after the start of the PAFOG simulation in the Eulerian approach

as is the case in this study. Despite this turbulent moisture loss, the dewpoint temperatureincreased slightly from 0600 UTC, 17 April to the onset of fog (2000 UTC, 18 April, Fig. 8a)because of the moisture advection during the period (Fig. 6b).

Consequently the Eulerian approach suggests that the sea fog in this case is formed overthe cold sea surface due to the cooling of the air by radiation and turbulence, and moistureadvection in the stable boundary layer.

123


5.2.2 Lagrangian Approach

The air column is located over the warm sea surface at the start of the simulation (i.e., thestarting point of the trajectory) and moves along the trajectory (Fig. 1) with time, and there-fore the temporal variation also indicates spatial movement in the Lagrangian approach. Asshown in Fig. 8b, at the beginning of the simulation the SST is greater than the air temperatureand therefore the air is gradually heated from 0000 to 0900 UTC, 17 April. However, the airtemperature starts to decrease at 0900 UTC when the sea surface is still warmer, indicatingthat radiative cooling becomes dominant over turbulent warming after sunset (0900 UTC= 0600 local time). Eventually the SST becomes lower than the air temperature and boththe air temperature and SST decrease as the air column moves northward. With the start ofthe simulation dewpoint temperature also increases due to the turbulent mixing of moistureover the warm sea surface. Then dewpoint temperature starts to decrease as it approachesthe SST. Eventually water vapour saturation is attained due to the more rapid decrease of airtemperature when compared to the dewpoint temperature. The variations of air temperatureand dewpoint temperature before the onset of cold sea fog can be considered to be affected bythe interaction with the cold sea surface, as in the Eulerian approach. That is, the formationmechanism of the cold sea fog in this case is similar to that of typical advection fog: the warmand moist air column moves over the cold sea surface, and then the water vapour saturationis achieved by radiative and turbulent cooling over the cold sea surface.

Once the fog has been formed, the contributions of radiation and turbulence to the devel-opment of the fog layer increase. Brown and Roach (1976), Ballard et al. (1991), Duynkerke(1999), and Koracin et al. (2001) used numerical simulations to show that air temperaturedecreased due to the radiative cooling at the fog top, and that the difference between airtemperature at the top and bottom of the fog layer induced convection in the interior ofthe fog layer. Consequently, the convection promoted the vertical development of the foglayer. The radiative influence on the evolution of the fog layer has also been identified fromobservational studies (e.g., Roach et al. 1976; Pilie et al. 1979; Findlater et al. 1989).

The results from the Lagrangian approach clearly demonstrate the effect of radiative cool-ing at the fog top. Figure 10a shows the vertical profiles of the radiative heating rate andturbulent heat flux 48 hours after the simulation started (four hours after the formation offog). The radiative cooling peaks near the fog top, where the turbulent heat flux is negativedue to turbulent mixing of cold air with warm air above the top of the fog layer (Fig. 10a).The radiative heating rate at this time is 8C h1, which is similar to that calculated byKoracin et al. (2001) who found a radiative heating rate of 9.1C h1 at the fog top. Thefog droplets evaporate due to entrainment mixing of the warm and dry air from above the fogtop, and as a result, the cloud water flux is positive near the fog top (Fig. 10b). Meanwhilethe water vapour flux shows the opposite sign and is negative near the fog top, in contrast tothe entrainment-mixing process at the top of stratocumulus clouds (Stull 1988). Due to theentrained mixing of dry air from above the cloud top, not only the cloud water flux but also thewater vapour flux is typically positive near the top of stratocumulus clouds (e.g., Nicholls andLeighton 1986). The negative water vapour flux near the fog top (Fig. 13b) is thought to bedue to the mixing of the relatively moister but unsaturated air (higher dewpoint temperature)from above the fog layer. These characteristics will be discussed further in Sect. 6.

In contrast to the situation at the fog top, turbulent heat flux is positive at an altitude of5 m (Fig. 10a), since air temperature is lower than the SST at this time (see air temperatureand SST at 0000 UTC 19, April in Fig. 8b). This reversal of T from a positive to negativevalue during the course of the fog event is due to the cooling of the entire fog layer causedby the radiative cooling at the fog top, and is also shown in the Eulerian approach (Fig. 8a).

123


(b)(a)

Turbulent heat flux (x10 -1 K m s-1)

Radiative heating rate (oC h-1)

Cloud water flux (x10-1 g kg-1 m s-1)

Water vapour flux (x10-1 g kg-1 m s-1)

Water vapourCloud water

Fig. 10 Vertical profiles of radiative heating rate (solid line) and turbulent heat flux (dashed line) (a), andwater vapour (solid line) and cloud water (dashed line) fluxes (b) at 48 h after the start of the PAFOG simulationin the Lagrangian approach. Shaded area indicates the fog layer

The vertical variation of turbulent heat flux shows the typical characteristics of a convectiveboundary layer. In addition, the water vapour flux is positive and the cloud water flux isnegative below 50 m altitude (Fig. 10b). This opposing structure results from the decrease ofwater vapour with altitude due to fog droplet condensation in the interior of the fog layer. Thepeak values of the two fluxes occur at 30 m altitude: although the vertical gradients of watervapour and cloud water mixing ratio are a maximum at the fog top, the exchange coefficientis largest at an altitude of 30 m (not shown).

The evolution of sea fog after the flow moves over the land depends on the land-surfacecharacteristics, such as ground temperature, soil temperature and soil moisture (Ryznar 1977).Duynkerke (1991) and Siebert et al. (1992) performed sensitivity experiments on the evolu-tion of radiation fog with regard to ground temperature and soil moisture. In their studies,the lifetime of radiation fog increased as the soil moisture content increased, and the fogtransformed into a stratus cloud when the ground temperature was very high. Similarly tothese studies, in our simulation surface temperature increases after the air column movesover the land during the day (see the arrowhead at 0300 UTC 19, April in Fig. 8b). Thenthe fog base is lifted to transform into a shallow stratus cloud and eventually is dissipatedaway as the cloud depth decreases (see the shallow stratus cloud at 0600 UTC 19, April inFig. 7d).

123


Fig. 11 Vertical profiles of the potential temperature (K) (a) and the water vapour mixing ratio (g kg1) (b)at 12 h intervals during the simulation in the Lagrangian approach

6 Discussion

6.1 Turbulence and Radiation Within the Thermal Internal Boundary Layer

The air that is modified by flow over a different surface is referred to as an internal boundarylayer, because it forms within an existing boundary layer. When the surface heat flux changesacross the border between two surfaces, the modified air is referred to as a thermal internalboundary layer (TIBL) (Garratt 1987). Figure 11 shows the vertical profiles of potential tem-perature and water vapour mixing ratio at 12-h intervals during the Lagrangian simulation.The boundary layer warms for the first 12 hours due to the solar heating during the day andthe warm sea surface but as the air column traverses the cold sea surface a stable TIBL isformed within the convective boundary layer (Fig. 11a). As the TIBL grows, the convectiveboundary layer above the TIBL becomes shallower: the top altitude reduces from 800 m atthe start to 500 m at 48 hours. The characteristics of the TIBL are analogous to those of atypical stable boundary layer. However, at 48 hours (in the middle of the fog period; Fig. 8b)a well-mixed layer is clearly formed in the lowest 50 m altitude. The radiative cooling at thefog top destabilizes the fog layer (see the turbulent heat flux in Fig. 10a), leading to buoyancydriven mixing and neutral stratification in the lowest 50 m altitude.

In the Lagrangian approach, the water vapour mixing ratio increases due to the watervapour supply from the warm sea surface during the first 24 hours (Fig. 11b). The turbulentexchange of water vapour reverses by 36 hours. As stated above, turbulence over the coldsea surface does reduce water vapour mixing ratio at the lowest altitudes (


During the fog event, water vapour mixing ratio reduces as water vapour is consumed toform fog droplets in the interior of fog layer (below 40 m altitude). Consequently, the watervapour mixing ratio above the fog top becomes greater than that in the fog, resulting inwater vapour transport from above the fog top into the fog through the entrainment mixingprocess (Fig. 10b). The ascent of the fog top (Fig. 7d) may be related to the buoyancy-driventurbulence that enhances the entrainment mixing of the relatively humid air from above thefog top.

Longwave radiative cooling also significantly influences the time variation of air tem-perature within the stable TIBL even before the formation of sea fog. Figure 12a shows thetimeheight plot of the radiative heating rate simulated by PAFOG. The air below 300 maltitude experiences radiative cooling due to the presence of the cold sea surface even duringthe daytime (00000600 UTC, 18 April, 09001500 local time). This radiative cooling isenhanced at night with the absence of solar radiation and leads to the formation of fog at 2000UTC, 18 April. Then strong radiative cooling occurs at the fog top, which is accompaniedby strong radiative heating in the interior of the vertically growing fog layer that results fromthe upward longwave emission from the warmer sea surface due to the reversal of T duringthe fog.

In nine of the 26 cold sea-fog cases classified by Kim and Yum (2010), the onset of fogformation occurred during the daytime. Fog formation on 10 March 2006 is one of suchcases and is depicted in Fig. 12b. On this day, radiative cooling is so strong even during theday because of the relatively large T (5.7C; compared to 3.3C for the 18 April 2006case) that the depth of the cooling layer is extended to 900 m altitude during the daytime(00000600 UTC, 10 March) (Fig. 12b). It is apparent that this strong radiative cooling nearthe sea surface contributes crucially to the onset of fog in the daytime (0600 UTC, 10 March,1500 LST; see the fog boundary in Fig. 12b).

6.2 Source of Turbulence

The vertical profiles of the buoyancy and wind-shear production terms in the turbulent kineticenergy (TKE) equation show the contrast between the two (Fig. 13). Before the onset of fog,buoyancy consumes TKE, whereas wind shear produces TKE (Fig. 13a), implying that thesource of turbulence is identified as wind shear, which leads to turbulent cooling of the airabove the cold sea surface (not shown). At 48 hours after the simulation started (four hoursafter the formation of fog), the sign of the buoyancy production term changes to positive andits magnitude increases by 100 times. Buoyancy now produces TKE in the interior of the foglayer, which is caused by radiative cooling at the fog top (Fig. 13b). Meanwhile, the effectof wind shear is negligible, compared to the buoyancy term.

6.3 Limitations

There is a discrepancy between observations and the model results in this study. In the PA-FOG model results it is shown that the air becomes colder than the sea surface during thefog both in the Eulerian and Lagrangian approaches (T < 0C; Fig. 8), while observa-tion shows that an SST lower than the air temperature is maintained during the fog (Fig. 3).This suggests that the radiative cooling during the fog is overestimated in the model, whichcould be due to the fine vertical resolution used in the PAFOG model that was shown toproduce a cold bias (Bergot et al. 2007). Nevertheless the PAFOG simulation of the cold sea-fog case that we choose for detailed analysis indeed reveals the main characteristics of the

123


2006. 4. 18 CASE

2006. 3. 10 CASE

(a)

(b)

17/0000 17/0600 17/1200 17/1800 18/0000 18/0600 18/1200 18/1800 19/0000 19/0600 19/1200

10/0000 10/06000 10/12000 10/18000 11/0000 11/0600

Fig. 12 Timeheight plot of the radiative heating rate (101 C h1) for the cold sea fog cases on 18 April,2006 (a) and 10 March, 2006 (b) simulated by PAFOG in the Eulerian approach. The black solid line indicatesthe fog top

sea-fog formation mechanisms very well. Since observational data are lacking for many cases,however, this type of analysis cannot be done for all 26 cold sea-fog cases indentified by Kimand Yum (2010).

As a way of evaluating the model, this study employs a threat score and the threshold val-ues for the RH measured at the buoy and those for the simulated cloud water mixing ratio inthe Eulerian approach. However, this evaluation method has problems. The threat score doesnot take into account the quantitative variation of the cloud water mixing ratio. Furthermore,the vertical distribution of the cloud water mixing ratio is ignored.

In the Eulerian approach, the horizontal advection of air temperature and dewpoint tem-perature calculated in the WRF model is interpolated to resolve the difference in the vertical

123


Fig. 13 Vertical profiles of TKE production by wind shear (solid line) and buoyancy (dashed line) at 36 h(a) and 48 h (b) after the start of the PAFOG simulation in the Lagrangian approach. In (b), the shadingindicates the fog layer

resolution between PAFOG and the WRF model. In order to eliminate the numerical wavesthat may occur in the interpolation, data assimilation should be performed. For example,for operational predictions Thoma et al. (2010) carried out data assimilation between thePAFOG model output and the vertical sounding from the rawinsonde at 6-h intervals, andobtained improved results. However, the rawinsonde site (Baeknyeoung Island; Fig. 1) is toofar (approximately 200 km) from the location of the air column in the PAFOG model (buoy;Fig. 1) and therefore data assimilation is not performed in this study.

In the Lagrangian approach, the air-column trajectory was synthesized according to theback- and forward-trajectories at the buoy. In this process, the vertical movement of the aircolumn is neglected, assuming that the characteristics of the air column within the marineboundary layer remain constant.

Lastly the depth of the fog layer was estimated using the data from MTSAT-1 satellite;however, it is not easy to distinguish between fog and stratus clouds using this type of data(e.g., Ellrod 1995; Underwood et al. 2004; Bendix et al. 2006). To understand the verticalgrowth of a fog layer, a continuously operated microwave radiometer profiler or any otherinstrument that can detect the fog depth should be installed near the study area.

7 Summary and Conclusions

This study investigated the formation mechanism of a cold sea-fog case observed over theYellow Sea near the western coastal area of the Korean Peninsula using numerical simu-lations from a 1D turbulence model, PAFOG, coupled with a 3D regional model, WRF.The simulation was carried out with two approaches, Eulerian and Lagrangian: the PAFOGair column was assumed to remain at a fixed location for the former and the air column

123


followed the trajectory derived in the WRF model for the latter. The performance evaluationof the Eulerian approach showed that PAFOG coupled with the WRF model gave much betteragreement with the observed characteristics than did the WRF model alone.

For the selected cold sea-fog case, the model results suggested the following. As warmand moist air that originates over the warm sea surface moves northward, the lower part of theair column is modified by the turbulent exchange of heat and moisture over the cold sea sur-face and the diurnal variation of radiation. The modified boundary-layer structure representsa typical stable TIBL. Within the stable TIBL, air temperature decreases through radiativecooling and turbulent heat exchange but the moisture loss due to the downward vapour fluxin the lowest part of the air column is compensated by moisture advection and therefore thedewpoint temperature does not decrease as rapidly as does the air temperature. Eventuallywater vapour saturation is achieved and cold sea fog forms in the TIBL.

Before the formation of fog, the source of turbulence was identified to be wind shear thatdrives turbulent heat and moisture exchange near the surface. Once the fog has formed, thebuoyancy flux induced by the radiative cooling at the fog top destabilizes the fog layer andmixing within the fog layer produces a neutrally stratified layer. Unlike the usual positivewater vapour flux at the top of the stratocumulus-topped marine boundary layer (Stull 1988),the present study showed a negative water vapour flux at the fog top. This is probably due tothe mixing of the relatively moister but unsaturated air (higher dewpoint temperature) fromabove the fog top with the relatively drier but saturated air (lower dewpoint temperature) inthe fog layer.

Using the PAFOG model coupled with the WRF model, this study demonstrated thatthe formation of a cold sea fog off the west coast of the Korean Peninsula is dependent oncomplex interactions of turbulence, radiation and the advection of air. However, there werelimitations as discussed above. Notably the PAFOG model overestimated the radiative cool-ing during the fog, possibly due to the fine vertical resolution. Another serious limitationwas the unavailability of the appropriate observational data that could be used to verify themodel results. For a thorough investigation of the sea-fog formation mechanism, comprehen-sive observations of meteorological fields and the thermodynamic soundings in the fog areaare required, for example, using a research vessel. A double-moment microphysical schemeis employed in PAFOG and therefore if in-situ measurements of aerosols and fog dropletmicrophysics are available, the impact of aerosols on sea-fog formation and microphysicaland radiative properties of fog droplets can also be investigated, which has a great implica-tion in relation to aerosol indirect effects on climate. This study focused on the cold sea-fogformation. The formation mechanism of warm sea fog is expected to be different (Kim andYum 2011) and will be the subject of a later study using the PAFOG model.

Acknowledgment This work was funded by the Korea Meteorological Administration Research and Devel-opment Program under Grant RACS_2010-5001.

References

Ballard SP, Golding BW, Smith RNB (1991) Mesoscale model experimental forecasts of the haar of northeastScotland. Mon Wea Rev 119(9):21072123

Bendix J, Thies B, Nau T, Cermak J (2006) A feasibility study of daytime fog and low stratus detection withTERRA/AQUA-MODIS over land, vol 13. Wiley, New York. doi:10.1017/s1350482706002180

Bergot T, Guedalia D (1994) Numerical forecasting of radiation fog. Part I: Numerical model and sensitivitytests. Mon Wea Rev 122(6):12181230

123


Bergot T, Terradellas E, Cuxart J, Mira A, Liechti O, Mueller M, Nielsen NW (2007) Intercomparison of single-column numerical models for the prediction of radiation fog. J Appl Meteorol Climatol 46(4):504521

Bott A, Trautmann T (2002) PAFOGa new efficient forecast model of radiation fog and low-level stratiformclouds. Atmos Res 64(14):191203

Bott A, Sievers U, Zdunkowski W (1990) A radiation fog model with a detailed treatment of the interactionbetween radiative transfer and fog microphysics. J Atmos Sci 47(18):21532166

Boutle I, Beare R, Belcher S, Brown A, Plant R (2010) The moist boundary layer under a mid-latitude weathersystem. Boundary-Layer Meteorol 134(3):367386

Brown R, Roach WT (1976) The physics of radiation fog: IIa numerical study. Q J Roy Meteorol Soc102(432):335354

Chaumerliac N, Richard E, Pinty JP, Nickerson EC (1987) Sulfur scavenging in a mesoscale model withquasi-spectral microphysics: two-dimensional results for continental and maritime clouds. J GeophysRes 92(D3):31143126. doi:10.1029/JD092iD03p03114

Choi H, Speer MS (2006) The influence of synoptic-mesoscale winds and sea surface temperature distributionon fog formation near the Korean western peninsula. Meteorol Appl 13(4):347360

Croft PJ, Darbe DL, Garmon JF (1995) Forecasting significant fog in southern Alabama. Natl Wea Dig19(4):1016

Douglas C (1930) Cold fogs over the sea. Meteorol Mag 65:133135Duynkerke PG (1991) Radiation fog: a comparison of model simulation with detailed observations. Mon Wea

Rev 119(2):324341Duynkerke PG (1999) Turbulence, radiation and fog in Dutch stable boundary layers. Boundary-Layer Mete-

orol 90(3):447477Ellrod GP (1995) Advances in the detection and analysis of fog at night using GOES multispectral infrared

imagery. Wea Forecast 10(3):606619Findlater J, Roach WT, McHugh BC (1989) The haar of north-east Scotland. Q J Roy Meteorol Soc

115(487):581608Fu G, Zhang M, Duan Y, Zhang T, Wang J (2004) Characteristics of sea fog over the Yellow Sea and the East

China Sea. Kaiyo Mon 38:99107Fu G, Guo JT, Xie SP, Duane YH, Zhang MG (2006) Analysis and high-resolution modeling of a dense sea

fog event over the Yellow Sea. Atmos Res 81(4):293303Gao SH, Lin H, Shen B, Fu G (2007) A heavy sea fog event over the Yellow Sea in March 2005: analysis and

numerical modeling. Adv Atmos Sci 24(1):6581Garratt JR (1987) The stably stratified internal boundary layer for steady and diurnally varying offshore flow.

Boundary-Layer Meteorol 38:369394Holtslag AAM, De Bruijn EIF, Pan H-L (1990) A high resolution air mass transformation model for short-

range weather forecasting. Mon Wea Rev 118(8):15611575Inoue T, Kamahori H (2001) Statistical relationship between ISCCP cloud type and vertical relative humidity

profile. J Meteorol Soc Jpn 79(6):12431256Johnson GA, Graschel J (1992) Sea fog and stratus: a major aviation and marine hazard in the northern

Gulf of Mexico. In: Symposium on weather forecasting, Atlanta, GA. American Meteorological Society,pp 5560

Kim CK, Yum SS (2010) Local meteorological and synoptic characteristics of fogs formed over Incheoninternational airport in the west coast of Korea. Adv Atmos Sci 27(4):761776

Kim CK, Yum SS (2011) Marine boundary layer structure for the sea fog formation off the west coast of theKorean Peninsula. Pure Appl Geophys. doi:10.1007/s00024-011-0325-z

Koracin D, Lewis J, Thompson WT, Dorman CE, Businger JA (2001) Transition of stratus into fog along theCalifornia coast: observations and modeling. J Atmos Sci 58(13):17141731

Koracin D, Businger J, Dorman C, Lewis J (2005) Formation, evolution, and dissipation of coastal sea fog.Boundary-Layer Meteorol 117(3):447478

Leigh RJ (1995) Economic benefits of terminal aerodrome forecasts (TAFs) for Sydney airport, Australia, vol2. Wiley, New York. doi:10.1002/met.5060020307

Lewis J, Koracin D, Rabin R, Businger J (2003) Sea fog off the California coast: viewed in the context oftransient weather systems. J Geophy Res 108(D15). doi:10.1029/2002jd002833|issn0747-7309

Mellor GL, Yamada T (1974) A hierarchy of turbulence closure models for planetary boundary layers. J AtmosSci 31(7):17911806

Mellor GL, Yamada T (1982) Development of a turbulence closure model for geophysical fluid problems. RevGeophys 20(4):851875

Mller MD, Schmutz C, Parlow E (2007) A one-dimensional ensemble forecast and assimilation system forfog prediction. Pure Appl Geophys 164(6):12411264

123


Musson-Genon L (1987) Numerical simulation of a fog event with a one-dimensional boundary layer model.Mon Wea Rev 115(2):592607

Nicholls S, Leighton J (1986) An observational study of the structure of stratiform cloud sheets: part I. Struc-ture. Q J Roy Meteorol Soc 112(472):431460

Nickerson EC, Richard E, Rosset R, Smith DR (1986) The numerical simulation of clouds, rains and airflowover the Vosges and Black forest mountains: a meso- model with parameterized microphysics. MonWea Rev 114(2):398414

Pagowski M, Gultepe I, King P (2004) Analysis and modeling of an extremely dense fog event in southernOntario. J Appl Meteorol 43(1):316

Petterssen S (1938) On the causes and the forecasting of the California fog. Bull Am Meteorol Soc 19(2):4955Pilie RJ, Mack EJ, Rogers CW, Katz U, Kocmond WC (1979) The formation of marine fog and the develop-

ment of fog-stratus systems along the California coast. J Appl Meteorol 18(10):12751286Pruppacher H, Klett J (1997) Microphysics of cloud and precipitation. Kluwer, Dordrecht, 955 ppRoach WT, Brown R, Caughey SJ, Garland JA, Readings CJ (1976) The physics of radiation fog: Ia field

study. Q J Roy Meteorol Soc 102(432):313333Rossow WB, Walker AW, Garder LC (1993) Comparison of ISCCP and other cloud amounts. J Clim

6(12):23942418Ryznar E (1977) Advection-radiation fog near lake Michigan. Atmos Environ 11(5):427430Sakakibara H (1979) A scheme for stable numerical computation of the condensation process with large time

steps. J Meteorol Soc Jpn 57:349353Shi C, Wang L, Zhang H, Zhang S, Deng X, Li Y, Qiu M (2011) Fog simulations based on multi-model system:

a feasibility study. Pure Appl Geophys. doi:10.1007/s00024-011-0340-0Siebert J, Sievers U, Zdunkowski W (1992) A one-dimensional simulation of the interaction between land

surface processes and the atmosphere. Boundary-Layer Meteorol 59(1):134Skamarock WC et al (2008) A description of the advanced research WRF version 3. NCAR Tech Note

NCAR/TN-475+STR, 113 ppSorli B, Pascal-Delannoy F, Giani A, Foucaran A, Boyer A (2002) Fast humidity sensor for high range 8095%

RH. Sens Actuators A 100(1):2431Steeneveld GJ, Wokke MJJ, Groot Zwaaftink CD, Pijlman S, Heusinkveld BG, Jacobs AFG, Holtslag

AAM (2010) Observations of the radiation divergence in the surface layer and its implication for itsparameterization in numerical weather prediction models. J Geophys Res 115(D6):D06107. doi:10.1029/2009jd013074

Steeneveld GJ, Tolk LF, Moene AF, Hartogensis OK, Peters W, Holtslag AAM (2011) Confronting the WRFand RAMS mesoscale models with innovative observations in the Netherlands: evaluating the boundarylayer heat budget. J Geophys Res 16:D23114. doi:10.1029/2011JD016303

Stull RB (1988) An introduction to boundary layer meteorology. Kluwer, Dordrecht, 666 ppTardif R (2007) The impact of vertical resolution in the explicit numerical forecasting of radiation fog: a case

study. Pure Appl Geophys 164(6):12211240Taylor GI (1917) The formation of fog and mist. Q J Roy Meteorol Soc 43(183):241268Thoma C, Schneider W, Rohn M, Rohner P, Beckmann B-R, Masbou M, Bott A (2010) Development of

the one dimensional fog model PAFOG for operational use at Munich airport. In: The 5th internationalconference on fog, fog collection and dew, Munster, Germany. European Meteorological Society, p 34

Trement M (1989) The forecasting of sea fog. Meteorol Mag 118:6975Underwood SJ, Ellrod GP, Kuhnert AL (2004) A multiple-case analysis of nocturnal radiation-fog devel-

opment in the central valley of California utilizing the GOES nighttime fog product. J Appl Meteorol43(2):297311

van der Velde IR, Steeneveld GJ, Wichers Schreur BGJ, Holtslag AAM (2010) Modeling and forecasting theonset and duration of severe radiation fog under frost conditions. Mon Wea Rev 138(11):42374253

Weare BC (1994) Interrelationships between cloud properties and sea surface temperatures on seasonal andinterannual time scales. J Clim 7(2):248260

Wells WC (1814) Essay on dew, and several appearance connected with it. Taylor and Hessey, LondonWillett HC (1928) Fog and haze, their causes, distribution, and forecasting. Mon Wea Rev 56(11):435468Yamanouchi T, Suzuki K, Kawaguchi S (1987) Detection of clouds in Antarctica from infrared multispectral

data of AVHRR. J Meteorol Soc Jpn 65:949962Yum SS, Hudson JG, Song KY, Choi BC (2005) Springtime cloud condensation nuclei concentrations on the

west coast of Korea. Geophy Res Lett 32(9). doi:10.1029/2005gl022641Zdunkowski W, Panhans W-G, Welch RM, Korb GJ (1982) A radiation scheme for circulation and climate

models. Contrib Atmos Phys 55:215238

123

A Numerical Study of Sea-Fog Formation over Cold Sea Surface Using a One-Dimensional Turbulence Model Coupled with the Weather Research and Forecasting ModelAbstract1 Introduction2 Case Description3 Model Description3.1 WRF3.2 PAFOG

4 Numerical Experiment4.1 WRF4.2 PAFOG4.3 Coupling of PAFOG with WRF4.3.1 Eulerian Approach4.3.2 Lagrangian Approach

5 Results5.1 Model Evaluation5.2 Sea-Fog Formation Mechanism5.2.1 Eulerian Approach5.2.2 Lagrangian Approach

6 Discussion6.1 Turbulence and Radiation Within the Thermal Internal Boundary Layer6.2 Source of Turbulence6.3 Limitations

7 Summary and ConclusionsAcknowledgmentReferences

Documents

A Numerical Study of Sea-Fog Formation over Cold Sea Surface Using a One-Dimensional Turbulence Model Coupled with the Weather Research and Forecasting Model