FORMATION, EVOLUTION, AND DISSIPATION OF COASTAL SEA FOG

Transcription

1 Boundary-Layer Meteorology (2005) 117: Ó Springer 2005 DOI /s FORMATION, EVOLUTION, AND DISSIPATION OF COASTAL SEA FOG DARKO KORACˇ IN 1,5, *, JOOST A. BUSINGER 2, CLIVE E. DORMAN 3 and JOHN M. LEWIS 1,4 1 Desert Research Institute, Reno, Nevada, U.S.A.; 2 University of Washington, Seattle, Washington, U.S.A.; 3 Scripps Institution of Oceanography and San Diego State University, San Diego, California, U.S.A.; 4 National Oceanic and Atmospheric Administration, Severe Storms Laboratory, Norman, Oklahoma, U.S.A.; 5 Desert Research Institute, 2215 Raggio Parkway, Reno, Nevada 89512, U.S.A. (Received in final form 3 February 2005) Abstract. Evolution of sea fog has been investigated using three-dimensional Mesoscale Model 5 (MM5) simulations. The study focused on widespread fog-cloud layers advected along the California coastal waters during April According to analysis of the simulated trajectories, the intensity of air mass modification during this advection significantly depended on whether there were clouds along the trajectories and whether the modification took place over the land or ocean. The air mass, with its trajectory endpoint in the area where the fog was observed and simulated, gradually cooled despite the gradual increase in sea-surface temperature along the trajectory. Modelling results identified cloud-top cooling as a major determinant of marine-layer cooling and turbulence generation along the trajectories. Scale analysis showed that the radiative cooling term in the thermodynamic equation overpowered surface sensible and latent heat fluxes, and entrainment terms in cases of the transformation of marine clouds along the trajectories. Transformation of air masses along the trajectories without clouds and associated cloud-top cooling led to fog-free conditions at the endpoints of the trajectories over the ocean. The final impact on cloud-fog transition was determined by the interaction of synoptic and boundary-layer processes. Dissipation of sea fog was a consequence of a complex interplay between advection, synoptic evolution, and development of local circulations. Movement of the high-pressure system over land induced weakening of the along-shore advection and synoptic-pressure gradients, and allowed development of offshore flows that facilitated fog dissipation. Keywords: Lagrangian framework, Mesoscale model 5 (MM5), Mesoscale simulations, Offshore fog, Radiative cooling, U.S. West Coast. 1. Introduction Understanding the formation and evolution of sea fog remains a research challenge primarily due to the lack of surface and upper-air observations over the ocean. Satellite data are emerging as a valuable tool providing significant * Darko.Koracin@dri.edu

2 448 DARKO KORACˇ IN ET AL. weather information over the oceans; however, there is still ambiguity and uncertainty in characterizing three-dimensional cloudiness and fog using satellite data. Due to the existence of routine land-based observations, fog over land has received considerably more attention than fog at sea. We focus on a sea-fog event along the U.S. West Coast where there is significant complexity in the ocean structure, in the marine atmospheric boundary layer, and in coastal topography. As noted by Filonczuk et al. (1995), fog along the West Coast occurs over a wide range of observed wind and temperature conditions, and the frequency of fog events is spatially and temporally variable along the coast. Although there is a range of conditions conducive to fog formation, it appears that there is no set of most favourable conditions that uniquely define the occurrence and maintenance of sea fog. As discussed in Leipper (1994), Leipper and Koračin (1998), and Lewis et al. (2004), forecasting sea fog along the California coast is a very challenging task due to the complex topography, delicate interplay of physical processes, and the scarcity of offshore observations. Nevertheless, there have been important contributions to the study of sea fog off the West Coast, notably the early work of Byers (1930), Anderson (1931), and Petterssen (1936, 1938). In the period following World War II, Leipper (1948) and the Cornell Aeronautical Laboratory (CALSPAN) team (Mack et al., 1974; Pilie et al., 1979) set the stage for numerical experiments that used one-dimensional models with turbulence parameterization and treatment of radiative heat transfer (e.g., see Oliver et al., 1978). In the spirit of the early work of G.I. Taylor (Taylor, 1917) and Oliver et al. (1978), Koračin et al. (2001) (hereafter K2001) conducted a synthesized modelling and observational study of sea fog that accounted for the path history of surface air and the turbulence-radiative processes in the marine layer. They developed a conceptual model of the formation and evolution of sea fog. Koracin et al. (2001) used a one-dimensional model with turbulence closure and radiative parameterization similar to the model used by Oliver et al. (1978); however, in contrast to Oliver et al., they emulated evolution of the air parcel in a Lagrangian frame of reference along multi-day trajectories over varying sea-surface temperatures and a strong marine inversion. In the case study (April 1999) that was central to the K2001 investigation, sea fog formed as a result of stratus lowering along multi-day, over-water trajectories. The modelling results were consistent with the observed time of fog onset and the location of fog along the coast as well as at sea, and identified cloud-top radiative cooling as the primary mechanism for fog formation. Radiative cooling at the top of the marine layer over-compensated for warming at the surface in the presence of a sea surface that was several Kelvin (K) warmer than the adjoining surface air. Net cooling led to condensation and fog. Although one-dimensional models can emulate specific advection associated with a Lagrangian path, they inherently cannot account

3 COASTAL SEA FOG 449 for variability in the three-dimensional structure of the atmospheric boundary layer and advective processes. Another approach to investigating air parcel modification within a Lagrangian or quasi-lagrangian framework was performed by Stevens et al. (2003a, b) using aircraft observations off southern California. They followed cloud parcels by means of circular aircraft patterns and focused on the roles of cloud-top radiative cooling, entrainment, and drizzle on the evolution of nocturnal marine stratocumulus. Stevens et al. (2003a, b) analysed the aircraft data and concluded that the observed temperature and moisture discontinuities for a strong marine inversion over the U.S. West Coast definitely would lead to significant entrainment and cloud drying based on cloud-top entrainment instability (Deardorff, 1980; Randall, 1980). In contrast, the observations indicated persistent cloud layers that were even further developed during the time when entrainment instability suggested cloud dissipation. In addition, the consequent microphysical evolution led to significant formation of observed drizzle flux. Stevens et al. (2003a) indicated that the role of radiative processes in the maintenance and growth of clouds should be investigated further. In this study, we seek to complement previous studies by examining simulated air parcel trajectories and investigating the roles and interplay of advection, cloud-top radiation, surface fluxes, and entrainment on the evolution of the cloudy marine atmospheric boundary layer (MABL). To better understand air transformation along Lagrangian trajectories, we performed three-dimensional numerical simulations using Mesoscale Model 5 (MM5) (Grell et al., 1994). To support the three-dimensional modelling, we relied on a recent observational study that explored the formation, maintenance, and dissipation of sea fog for this particular case (Lewis et al., 2003). The main objective of our study is to develop a qualitative and quantitative understanding of the modification determinants relevant to the eventual formation of sea fog. Under certain conditions characterized by advection, strength of the marine inversion, and subsidence, modification of the cloudy marine layer can lead to sea-fog formation. The influence of land-driven circulation on sea-fog dissipation is analysed and elaborated on, and implications of the study findings on the operational forecasting of sea fog are discussed in the concluding remarks and epilogue. 2. Offshore Cloudiness and Fog Along the California Coast During April 1999 Extensive cloud and fog layers occurred along the California coast during April 1999 in response to a synoptic disturbance that moved on to the West Coast on 11 April (K2001; Lewis et al., 2003). Prior to fog formation, a

4 450 DARKO KORACˇ IN ET AL. Figure 1. Composite mean (0000 and 1200 UTC) sea-level pressure (hpa) for 13 April (a) and 16 April (b) Obtained from the National Oceanic and Atmospheric Administration, Climate Diagnostic Center using National Centers for Environmental Prediction and National Center for Atmospheric Research re-analysis. high pressure system over the north-eastern Pacific and a low pressure system over Arizona and California set up intense north-westerly and northerly flows along the West Coast that are characteristic of warm season dynamics in this region (Figure la). The high pressure system and associated subsidence (reaching 0.05 m s )1 ) maintained a strong marine inversion of 10 K or more (Lewis et al., 2003). As the high pressure system moved inland (Figure lb),

5 COASTAL SEA FOG 451 the pressure gradient weakened along the coast and induced offshore flows in the coastal zone. According to our analysis, this synoptic evolution had a significant impact on the evolution of offshore cloudiness and fog. The initial intense northerly and north-westerly flows were favourable to the cooling of cloudy air along over-water trajectories. Inland displacement of the high pressure system reduced horizontal pressure gradients and winds, leading to conditions favourable to the formation of sea fog. Gradual development of offshore flows at the end of the fog event, however, induced drying of the marine layer near the coast at night as well as drying and warming of this layer during daytime hours. This is further explained in the following sections. 3. Numerical Model Mesoscale Model 5 is used worldwide and was developed jointly by Pennsylvania State University and the National Center for Atmospheric Research in Boulder, Colorado. Details of the model structure are described in Grell et al. (1994). Mesoscale Model 5 has been used in a variety of research and application studies focused on atmospheric dynamics and cloudiness along the California coast (Koračin and Dorman, 2001), structure and evolution of wind stress and wind-stress curl impacting ocean dynamics (Koračin et al., 2004), and as a driver for an ocean model (e.g., Powers and Stoelinga, 1999; Beg-Paklar et al., 2001), among others. To account for synoptic processes and also to resolve characteristics of mesoscale processes, coarse and nested grids were set up to cover a large portion of the U.S. West Coast from southern Oregon to the Los Angeles region (Figure 2). The coarse grid was centred at 37.5 N, W and consisted of points with a horizontal resolution of 6 km. The nested grid (consisting of points with a horizontal resolution of 2 km) extended from the northern California coast to Point Conception (34.4 N, W) where the coastline sharply turns to the east. Most of the clouds and fog were observed in this area. Table I shows the model s vertical grid structure with average heights converted from 43 full-sigma levels (integer values). Horizontal wind components and thermodynamic variables are computed on half-sigma levels, while vertical velocity is computed on full-sigma levels (midpoint values). In order to provide high vertical resolution within the MABL, seventeen vertical levels are provided in the lowest kilometre. Topography input was extracted from the 30 -resolution global terrain and land use files. The main physics options included warm-rain microphysics; the Grell cumulus parameterization; the Gayno-Seaman second-moment, turbulence parameterization with the prognostic turbulence kinetic energy (TKE) equation (Shafran et al.,

6 452 DARKO KORACˇ IN ET AL. Figure 2. Setup of MM5 modelling domains. The outer domain (D01) consists of grid points with horizontal resolution of 6 km, and the inner domain (DO2) has grid points with horizontal resolution of 2 km. 2000); a cloud-radiation algorithm; and a multi-layer soil temperature model. First guess fields and lateral boundary conditions for the coarse grid for every 12 h were obtained from the National Centers for Environmental Prediction (NCEP) Global Data Assimilation System archive. Synoptic information included virtual temperature, geopotential height, horizontal wind components, and relative humidity on a global grid (with a horizontal resolution of 2.5 in both latitudinal and longitudinal directions). These first-guess fields were horizontally interpolated onto the model grid by a two-dimensional, 16- point overlapping parabolic fit. In the second step of the preprocessing the first guess fields were refined using observations. Similarly, the first-guess seasurface temperature (SST) field was extracted from the U.S. Navy s daily values (with a horizontal resolution of 2.5 in both latitudinal and longitudinal directions), updated with buoy and coastal station data, and interpolated onto the model grid using a bilinear interpolation method. Simulations were performed for the period from 12 April 1999 at 0000 UTC to 17 April 1999 at 0000 UTC, corresponding to the widespread cloud and fog event that was described by K2001 and Lewis et al. (2003). Time steps on the coarse and nested grids were 18 and 6 s, respectively.

7 COASTAL SEA FOG 453 TABLE I Average heights (m) of full-sigma and half-sigma vertical levels of MM5 grids. Level Full-sigma level height (m) Half-sigma level height (m)

8 454 DARKO KORACˇ IN ET AL MODEL EVALUATION Comparison with Buoy and Coastal Station Data Observations from eight buoys and two coastal land stations were used for model evaluation. Table II shows buoy positions and summary statistics of the comparison between the model and observations for a five-day period (12 17 April 1999). Standard statistical parameters included the bias or mean error (ME), the mean absolute error (MAE), the population root-meansquare error (RMSE), and the root-mean-square vector error (RMSVE). These parameters have been commonly used (Koračin et al., 2004) and also are defined in Koračin and Dorman (2001). The correlation coefficient for wind speed ranged from 0.43 to 0.75, which is similar to Koracˇ in and Dorman s (2001) results for the comparison between model results and buoy data along the California coast for all of June According to standard deviations from the model results and measurements, the model shows temporal variability similar to observations. The bias expressed by the ME is relatively small and still should be reduced due to the difference in height between the model grid points and elevation of the buoy sensors. Some of the differences are likely due to differences in sampling. (i.e., buoy data are an 8-min average at every hour, while the model results represent grid- and short time-averaged values during the last timestep at each hour). As will be shown in the next sections, accurate representation of wind direction by the model is crucial to determining the origin and fate of airmass back-trajectories. Consequently, special consideration is given to the model s ability to successfully reproduce wind direction. Figure 3 shows the time series of modelled and observed wind direction at the Point Arena and San Francisco coastal land stations that are central to our analysis elaborated on in the next section. Wind speeds at the Point Arena station were higher than at San Francisco and showed persistent north-north-westerly flow in the first part of the period (fog development). In the second part of the period, both stations show variable wind direction including offshore flow from the eastern quadrant (prior to and during the fog dissipation period). The figure shows that MM5 was able to capture the main behaviour of the flows at the coastal land stations Comparison with Satellite Data In addition to the point comparison described in the previous subsection, we also compared model results with satellite data. Figure 4 shows Geostationary Operational Environmental Satellite 10 (GOES-10) visible images over the West Coast at hourly intervals from 1600 to 2300 UTC on 13 April An extensive cloud and fog layer was observed over the entire California coast at the beginning of the period, and the layer cleared from the north toward the end of the period. Figure 5 shows horizontal cross-sections

9 COASTAL SEA FOG 455 TABLE II Statistical parameters of the comparison between MM5 results and buoy and coastal land station data for the period April Buoy ID N. Lat. ( ) W. Long. ( ) Height buoy Height MM5 N Mean Std dev Corr ME (m s )1 ) (m MSL) (m MSL) MM5 OBS MM5 OBS (m s )1 ) (m s )1 ) (m s )1 ) (m s )1 ) MAE (m s )1 ) RMSE (m s )1 ) RMSVE (m s )1 ) Wind speed Santa Maria Bodega Bay Pt. Arena Pt. Arguello ) San Francisco San Martin Santa Barbara Pt. Conception Pt. Arena PTAC (land) San Fran. Airport SFO

10 456 DARKO KORACˇ IN ET AL. Table II Continued. Buoy ID N. Lat. ( ) W. Long. ( ) Height buoy Height MM5 N Mean Std dev Corr ME ( C) (m MSL) (m MSL) MM5 OBS MM5 OBS ( C) ( C) ( C) ( C) MAE ( C) RMSE ( C) Temperature Santa Maria Bodega Bay Pt. Arena Pt. Arguello San Francisco San Martin Santa Barbara Pt. Conception P. Arena (land) PTAC ) San Fran. Airport SFO RMSVE ( C)

11 COASTAL SEA FOG 457 (a) Wind direction ( ) Sim Meas Day of April 1999 (b) Wind direction ( ) Sim Meas Day of April 1999 Figure 3. Time series of measured and simulated wind direction at the Point Arena (a) and San Francisco (b) coastal land stations from 12 to 17 April of the colour-filled, simulated total-cloud liquid water mixing ratio at 90 m near the beginning of the period (1200 UTC on 13 April), near the middle of the period (1800 UTC on 13 April), and at the end of the period (0000 UTC on 14 April). These periods correspond to the times shown in the satellite image (Figure 4). The simulations accurately reproduced advection of the cloud-fog edge from north-west to south-east along the coast. Figure 5 and results of the statistical comparison between the model and measurements show that the model was able to predict the general behaviour of cloud and fog-layer evolution. Consequently, model results can be used for investigating the formation, maintenance, and dissipation of sea fog as discussed in the following sections. 4. Modification of the Marine air Along Trajectories Using buoy data from along the West Coast, K2001 inferred that coastal fog in the southern part of the domain occurred in the early hours of 14 April Analysis of the one-dimensional modelling and a limited set of

12 458 DARKO KORACˇ IN ET AL. Figure 4. GOES-10 visible images in hourly intervals from 1601 to 2301 UTC on 13 April Figure 5. Horizontal, colour-filled cross-sections of the simulated liquid water mixing ratio (kg kg )1 ) at 90 m on 13 April at 1200 UTC (a), on 13 April at 1800 UTC (b), and on 14 April 1999 at 0000 UTC (c).

13 COASTAL SEA FOG 459 Figure 6. Colour-filled, sea-surface temperature contours ( C) off the southern Oregon and California coasts at the time of sea-fog formation over southern California coastal waters on 14 April 1999 at 0200 UTC. Contour interval is 0.5 K. observations described in K2001 led to the development of and conceptual model for conditions of north-westerly advection of the cloudy marine air that defined modification of the MABL. Since the SST was lower off the southern Oregon and northern California coasts and higher off the central and southern California coasts (Figure 6), surface sensible and latent heat fluxes were increasing southward and consequently warming and moistening the marine layer. Figure 6 confirms this characteristic SST structure at the time of sea-fog formation. At the same time, cloud-top cooling caused

14 460 DARKO KORACˇ IN ET AL. buoyant instability and overall cooling of the MABL, which propagated downward. As shown by K2001, cloud-top cooling can overpower warming from the surface and, together with increased moisture, can lead to fog under conditions of strong subsidence and marine inversion. Spatial and temporal variations of advection, however, strongly modify the temperature and humidity properties of marine air. In particular, it is extremely important to determine whether trajectories at different levels originate over the land or ocean, as well as whether a trajectory originally over the ocean passes over the land and undergoes air mass transformation (mainly warming and drying). 4.1 BACK-TRAJECTORIES WITH END POINTS IN FOG-COVERED AND CLEAR-SKY AREAS To better understand how marine air is modified while being advected along the coast, we constructed a series of backward trajectories computed from MM5-simulated wind fields and examined the simultaneous effects of cloudtop cooling, surface heating, and moistening along these trajectories. It should be noted that the specified height of a backward trajectory refers to the height at its end point. While tracing a trajectory backward in time, the height of the trajectory will vary in time as a consequence of vertical motions. We focus on two regions: one at which fog occurrence was inferred from buoy measurements (Point Arguello, hereafter PA), and one at which fog was absent according to the analysis of buoy observations (San Francisco, hereafter SF). The effects of cloud-top cooling can be inferred by tracing simulation results of air temperature at various levels and differences with respect to the SST. Trends in dew-point temperature as well as surface sensible and latent heat fluxes can be used to infer effects of the ocean surface on modification of the MABL as it is advected along the coast. Analysis of the simulations indicated fog formation upwind of PA in the early hours of 14 April At 0300 UTC on 14 April, model results show fog formation at the Point Arguello buoy location and no-fog conditions at the SF buoy location predictions in agreement with saturation conditions at the buoys. Figure 7 shows back-trajectories from these two sites at 10 m (near the surface), 90 m (the lower part of the marine layer), 270 m (the upper part of the marine layer), and 1000 m (above the marine layer) with an ending time of 0300 UTC on 14 April. The typical depth of the marine layer ( m) is indicated in the observational (e.g., Rogers et al., 1998) and modelling studies (e.g., Koracˇ in and Dorman, 2001). The surface back-trajectory from PA (Figure 7a) was significantly offshore, while the back-trajectory at 270 m was originally located closer to the coast, approached the coastline south of the Monterey Bay area for a short time, and then turned offshore afterwards.

15 COASTAL SEA FOG 461 (a) (b) Figure 7. Horizontal projection of simulated back-trajectories at 10 m (black), 90 m (blue), 270 m (red), and 1000 m (green) with endpoints at the Point Arguello (a) and San Francisco (b) buoys on 14 April at 0300 UTC. Cloud and fog conditions at the Point Arguello buoy and cloud and fog-free conditions at the San Francisco buoy were inferred from buoy and coastal station measurements. The flow above the marine layer was fully offshore. Back-trajectories with the endpoint at the SF buoy location (Figure 7b) were offshore while approaching the buoy, but the time history indicated an origin over land where the back-trajectories encountered warming and drying. Figure 7 indicates that the origin and modification of the marine layer through warming and drying over land can be a significant determinant of cloud-free and fog-free conditions. 4.2 MODIFICATION OF AIR ALONG BACK-TRAJECTORIES RELEVANT TO FOG OCCURRENCE In order to examine simulated atmospheric conditions along back-trajectories, we constructed time series of air temperature, dew-point temperature, SST, and cloud occurrence in terms of the vertically integrated liquid water path (ILWP) (Stull, 1988) as well as surface sensible and latent heat fluxes. Figure 8 shows a time series of these parameters simulated along a surface back-trajectory with the end point at PA where fog was inferred from measurements. The SST gradually increased by about 2.5 K along the path during the first 12 h, and sensible and latent heat fluxes increased by about

16 462 DARKO KORACˇ IN ET AL. 12 pa surface t(b o) td(g x) sst(r ) Temperature (C) Integrated liquid water path (g m 2 ) Hour after simulation start pa lwp (b o) Hour after simulation start pa shflx (b o) & lhflx (g x) 80 Heat flux (W m 2 ) Hour after simulation start Figure 8. Time series of simulated air temperature (solid line with circles), sea-surface temperature (dashed line), and dew-point temperature (solid line with x) (a); integrated liquid water path (b); and surface heat (solid line with circles) and latent heat (solid with x) fluxes (c) along the surface back-trajectory at 10 m with the end point at the Point Arguello buoy location on 14 April at 0300 UTC.

17 COASTAL SEA FOG W m )2. Despite this significant increase in the SST, as well as in the surface sensible and latent heat fluxes, the air temperature gradually decreased about 4 K during the same time. Since the surface back-trajectory position was entirely offshore, we infer that the cooling mechanism originated from cloud-top and fog-top cooling. The importance of cloud- and fogtop cooling on the evolution of the MABL has been emphasized in both observational (Nicholls, 1984) and modelling studies (Koračin and Rogers, 1990; Rogers and Koračin, 1992; K2001). The mechanism and main determinants for cooling of the air as it is advected offshore are discussed further in the next section. Examination of the present simulation results (Figure 8) shows that fog formed at the beginning of the surface back-trajectory period and was maintained throughout the travel to PA, except for a brief break-up and lifting into the low-level cloud between hours 18 and 21 from the backtrajectory start. It should be noted that the main increase in temperature occurred after a significant drop in the ILWP (after hour 13). Air temperature was increasing and recovering toward the SST and, consequently, surface fluxes were reduced. After hour 20, the gradual decrease in the SST and increase in the ILWP led to a decrease in air temperature and saturation near the surface while approaching PA. Since the back-trajectory was gradually approaching the coast, the simulated boundary-layer height was greater in the starting area (about 500 m) than in the end-point area (about 300 m). Consequently, even the presence of relatively high air temperatures did not prevent fog formation and maintenance due to the moisture confined in the shallow marine layer and low surface fluxes. Figure 9 shows a time series of simulated atmospheric conditions along the back-trajectory ending at the SF buoy location where fog was not present. Evolution of the simulated atmospheric conditions was significantly different from conditions simulated along the back-trajectory ending at PA. Near-surface air temperature for the SF back-trajectory gradually increased (for the most part) due to the increase in the SST. There was a brief occurrence of fog in the far upwind side in the beginning period (first four hours) during which the air temperature initially dropped significantly and then kept relatively steady during the occurrence of fog. After the fog cleared, the air temperature adjusted toward the SST, reducing the humidity. Sensible heat flux decreased as the air temperature converged toward the SST, while the latent heat flux increased somewhat due to decreasing humidity of the nearsurface air. Since there were no significant clouds and associated cloud-top cooling present, these conditions led to a fog-free state as the flow approached SF. Another determinant for the occurrence or absence of fog is vertical structure and turbulent mixing within the boundary layer. As discussed earlier and shown in Figure 7, the back-trajectories at various vertical levels

18 464 DARKO KORACˇ IN ET AL. 12 sf surface t(b o) td(g x) sst(r ) Temperature (C) Integrated liquid water path (g m 2 ) Hour after simulation start sf lwp (b o) Hour after simulation start sf shflx (b o) & lhflx (g x) 20 Heat flux (W m 2 ) Hour after simulation start Figure 9. Same as Figure 8, except with the end point at the San Francisco buoy location. have different pathways and origins. Figure 8 shows that the air temperature along the PA back-trajectory gradually decreased within the first 10 h or so and then gradually increased in approximately the middle of its duration

19 COASTAL SEA FOG 465 while approaching the coastline under intermittent clear-sky conditions. After hour 17, however, the back-trajectory turned offshore and under cloudy-fog conditions cooled down almost 4 K and significantly increased in humidity while approaching PA. In contrast to the PA back-trajectory, the temperature along the SF back-trajectory near the surface (Figure 9) gradually increased, with low humidity throughout the travel time. These high temperatures and low humidities at higher levels, in conjunction with increasing surface temperature and relatively low near-surface humidity (Figure 9), led to an absence of fog at the SF location. Our present threedimensional simulations confirm the results from the one-dimensional simulations of K2001, that there was noticeable TKE generated by surface fluxes and longwave cooling at the cloud top. Simulated mean TKE along the PA trajectories was 0.26 and 0.13 m 2 s )2 at the surface and 270 m, respectively, and was less along the SF trajectories (0.17 and 0.02 m 2 s )2 at the surface and 270 m, respectively) without significant cloud-fog top cooling. Reduced TKE in the latter case was a consequence of small surface fluxes and the absence of cloud-generated turbulence, mainly through cloud-top cooling, as shown in previous studies such as Koračin and Rogers (1990), Koracˇ in and Tjernstro m (1992), and Tjernstro m and Koracˇ in (1995). 5. Fog Formation in Response to the Interplay of Surface Forcing, Cloud-Top Cooling and Entrainment On the basis of our modelling results, we investigated the roles of the main components of heat transfer that can lead to net cooling or heating of the MABL. As a first step towards understanding the importance of the major components, we performed a scale analysis of the simplified thermodynamic equation from a mixed-layer model (Stage and Businger, 198la,b): dh dt ¼ w0 h 0 e þ R c R b þ w edh e : ð1þ z b z b z b The term on the left-hand side represents the total change of the potential temperature due to the following terms on the right-hand side: divergence of sensible heat flux, divergence of net radiative flux, and entrainment processes. In this equation, w 0 h 0 e is the surface kinematic heat flux; z b is the height of the MABL (equal to the height of the inversion base); R c, and R b are the normalized net radiative fluxes at the cloud top and base, respectively; w e is the entrainment rate velocity; and Dh e is the jump in equivalent potential temperature within the inversion.

20 466 DARKO KORACˇ IN ET AL SCALE ANALYSIS OF THE TERMS IN THE EQUATION FOR POTENTIAL TEMPERATURE Simulated surface fluxes were computed based on the similarity theory described by Grell et al. (1994) and Beg-Paklar et al. (2001), while the height of the MABL was estimated by jointly examining vertical gradients of the potential temperature and TKE, as well as the top of the cloud layer. Heating and cooling rates due to radiative heat transfer were simulated for each level using the parameterization by Dudhia (1989). Entrainment velocity (w e ) was computed using the simplified prognostic equation for evolution of the MABL height (z b ): dz b dt ¼ w e þ w m ð2þ where w m is the mean model vertical velocity at the top of the MABL. From the model results we computed the change of the boundary-layer height (lefthand side of Equation (2)). Then we computed w e from Equation (3) using these w m and dz b dt estimates. Since modelled radiation tendency is a computed value for each grid point, we converted radiation tendency from a particular point into the associated effect for the entire MABL. Radiation tendency for each point is assumed to be representative of the half-grid vertical interval above and below the considered point. The magnitude of the radiation tendency was 1.5 Potential temperature tendency (10 3 K s 1 ) Hour after simulation start Figure 10. Time series of simulated terms on the right-hand side of Equation (1) contributing to the MABL heating and cooling processes: surface heat flux (dashed), radiation tendency (solid), and entrainment (dashed-dotted line with circles) for back-trajectory with endpoint at the Point Arguello buoy location on 14 April at 0300 UTC.

21 COASTAL SEA FOG 467 then multiplied by the ratio of this vertical separation to the MABL depth; then these values for each layer are summed up to the top of the MABL. In our specific case, we performed this procedure for the vertical profile for every hour at the point where the trajectory was at that hour. By following this process, we were able to extrapolate the value of the radiation tendency derived for each particular point and its corresponding z into its particular contribution to heating or cooling of the entire MABL. As discussed in the previous section, turbulence was sufficient to provide mixing and redistribution of this heating and cooling. Figure 10 shows a time series of the main components contributing to the potential temperature tendency. Use of the simplified thermodynamic equation (Equation (1)) imposes a residual with respect to the simulated total change of the potential temperature that includes treatment of full threedimensional processes. The average difference between the left-hand side of Equation (1) and the simulated total change of the potential temperature is 26%. Relative magnitudes among the components shown in Figure 10, however, remain the same as the initial estimate of individual importance. Figure 10 clearly indicates that longwave cooling is the main contributor to the cooling of the MABL in the first part of the period when the overall cooling of the marine layer was simulated along the back-trajectory with the end point at Point Arguello (Figure 8). Cloud and fog-induced cooling is counteracted by heating due to the surface heat flux and entrainment. According to this scale analysis, cloud- and fog-top cooling is definitely a process that can dominate surface forcing and entrainment and, in conjunction with increased moisture, can lead to condensation. The effect was prominent during the first 7 h and at the final stage of the trajectory when the surface heat flux was low. Note that the moisture flux increased during the period of increased heat flux and that apparent cooling of the air along the trajectory during the last several hours prior to fog formation was sufficient to produce fog. 6. Dissipation of Sea Fog In accordance with the observations in K2001, the sea fog analysed in the previous section dissipated in the area north of Point Conception after 1600 UTC on 15 April. In order to examine the effect of advection and surface fluxes on fog dissipation, we constructed back-trajectories with the end point in the PA area at the time after fog clearing (0000 UTC on 16 April) and extending 18 h backward in time, while the trajectories were in the domain. Figure 11 shows the position of the back-trajectories at the surface, 90 m, 270 m, and 1000 m. In contrast to Figure 7, which shows the offshore origin of the back-trajectories, Figure 11 clearly indicates that trajectories both

22 468 DARKO KORACˇ IN ET AL. Figure 11. Horizontal projection of simulated back-trajectories at 10 m (black), 90 m (blue), 270 m (red), and 1000 m (green) that are relevant to fog dissipation. The back-trajectories have their end point at the Point Arguello buoy location on 16 April at 0000 UTC. within and above the MABL originated over land and entered the coastal waters mainly as an easterly flow. Figure 12 shows a time series of the temperature, dew-point temperature, ILWP, and surface sensible and latent heat fluxes along the surface back-trajectory shown in Figure 11. In contrast to the properties of the air mass along the back-trajectory relevant to fog formation (Figure 8), the air mass at the origin of the trajectory over land was warm and dry and encountered cooling and moistening while mixing with coastal air over the ocean. The air temperature gradually decreased, approaching the SST, as shown by the reduction in sensible heat flux. The main temperature decrease was from hour 6 to 11 when the air mass encountered thin cloud, as indicated in Figure 12. ILWP was more than 10 times lower in this case than in the case of the offshore trajectory relevant to cloud and fog formation (Figure 8). During the short-term cooling from hours 6 to 11, surface fluxes were small and did not contribute to vertical moisture transport. In spite of the gradual increase in the dew-point tem-

23 COASTAL SEA FOG 469 (a) 20 Temperature (C) Hour after backtrajectory start (b) Integrated liquid water path (g m ) Hour after backtrajectory start (c) 50 Heat flux (W m 2 ) Hour after backtrajectory start Figure 12. Time series of simulated air temperature (solid line with circles), sea-surface temperature (dashed line), and dew-point temperature (dashed dotted line with x) (a); integrated liquid water path (b); and surface heat (solid line with circles) and latent heat (dashed line with x) fluxes (c) along the surface back-trajectory that are relevant to fog dissipation. The end point of the back-trajectory is at the Point Arguello buoy location on 16 April 1999 at 0000 UTC.

24 470 DARKO KORACˇ IN ET AL. perature until the last few hours of the back-trajectory, there was no significant cooling of the surface air when the trajectory was approaching PA. All these processes led to clear-sky conditions at the end of the considered back-trajectory. Another complexity in the formation and dissipation of sea fog is the interaction of synoptic processes and locally induced coastal circulations (Lewis et al., 2003). A process of gradual cooling of the cloudy marine air occurred along the offshore advection path with sufficient moisture, turbulence, and saturation. In the case of synoptic pressure centre displacements and weakening of the synoptic pressure gradients, land-breeze flows develop during nighttime and, by mixing with alongshore marine flows, induce general drying of the MABL. During daytime, sea breezes develop and in the return flow, they bring warm and dry air that originated over land. Drying and warming are enhanced by daytime shortwave radiational heating of the cloud and fog layers (Nicholls, 1984; Koracˇ in and Rogers, 1990). All these effects promote fog dissipation. The effects of radiative processes on the diurnal evolution of coastal clouds are discussed by Betts (1990) and Koračin and Dorman (2001). Figure 13a shows surface vector winds at the time (0200 UTC on 14 April) when fog onset was simulated in the PA area. This area was under the (a) (b) MAXIMUM VECTOR: 13.9 m s -1 MAXIMUM VECTOR: 21.6 m s -1 Figure 13. Simulated vector winds and wind speed contours on 14 April at 0200 UTC (13 April at 1800 LST) during fog formation, at the surface (a) and at 500 m (b). Contour interval for the wind speed is 2 m s )1. For clarity, wind vectors are plotted at every tenth grid point.

25 COASTAL SEA FOG 471 influence of alongshore marine flows with strong winds near San Francisco and Monterey Bay that weakened south of Monterey Bay. We simulated similar flow characteristics, although with greater wind speeds, at 500 m (Figure 13b). Simulated vector winds at the surface and at 500 m (prior to fog dissipation) are shown in Figure 14a, b, respectively. As indicated in Figure 1 and explained further in this section (see Figures 15 and 16), the high pressure system moved inland and synoptic pressure gradients were substantially weaker. This produced a significant decrease in winds within the marine layer and allowed for the development of offshore flows. Offshore flows were simulated throughout the marine layer, as shown by the vector winds at the surface and 500 m (Figure 14a, b). The main impact of the offshore flows was to warm and dry the MABL near the coast. This is clearly seen in Figure 15, which shows colour-filled, surface-temperature contours during fog formation (Figure 15a) and 48 h later (Figure 15b). The figure shows gradual warming and a decrease of the pressure gradients over the ocean in the southern and south-western regions of the domain. Gradual heating of the air over land associated with the high pressure system also can be seen in Figure 15. Another important feature of the offshore flows is the consequent drying of the MABL near the coast. Figure 16 shows gradual (a) (b) MAXIMUM VECTOR: 13.5 m s -1 MAXIMUM VECTOR: 17.8 m s -1 Figure 14. Simulated vector winds and wind speed contours on 15 April at 1300 UTC (0500 LST) prior to fog dissipation, at the surface (a) and at 500 m (b). Contour interval for the wind speed is 2 m s )1. For clarity, wind vectors are plotted at every tenth grid point.

26 472 DARKO KORACˇ IN ET AL. (a) (b) MAXIMUM VECTOR: 13.9 m s -1 MAXIMUM VECTOR: 13.9 m s -1 Figure 15. Colour-filled, simulated surface air temperature ( C) overlaid with sea-level pressure (hpa) and surface winds (knots) at 0200 UTC at a 48-h interval: 14 April 1999 (a) and 16 April 1999 (b). Contour interval for the sea-level pressure is 0.5 hpa. For clarity, wind vectors are plotted at every tenth grid point. drying of the surface air in colour-filled, surface relative humidity contours for the same time intervals shown in Figure 15. During the fog period, humidity was high over the whole offshore region (Figure 16a), with drying propagating from the north-west to the south-east as the offshore flows developed (Figure 16b). The combined effect of the MABL warming and drying led to dissipation of clouds and fog. 7. Summary and Conclusions Using MM5, we simulated a case of widespread offshore cloud and fog layers along the California coast during April Our main objective was to investigate and quantify the effects of advection, radiation, surface fluxes, and entrainment relevant to the formation, evolution, and dissipation of sea fog. Areas where fog was observed (PA) and where fog was not present (SF) were considered for analysis using buoy and land station observations. Our results emphasize that it is crucial to investigate the formation, evolution, and eventual dissipation of sea fog in a Lagrangian framework (i.e., along long over-water trajectories and tra-

27 COASTAL SEA FOG 473 (a) (b) MAXIMUM VECTOR: 13.9 m s -1 MAXIMUM VECTOR: 8.4 m s -1 Figure 16. Colour-filled, simulated surface relative humidity (%) overlaid with sea-level pressure (hpa) and surface vector winds at 0200 UTC at a 48-h interval: 14 April 1999 (a) and 16 April 1999 (b). Contour interval for the sea-level pressure is 0.5 hpa. For clarity, wind vectors are plotted at every tenth grid point. jectories that originate over land). The study also shows that modification of the MABL is significantly dependent on advection processes over the land and ocean and whether clouds are present during the transformation. During the time when the fog formed, a fog layer and cloud layer were present with significant ILWP ( kg m )2 ). Cloud-top cooling generated net cooling of the marine layer by about 4 K despite the gradual increase in the SST by 2 3 K along the trajectory. Within 12 h this triggered an increase of the surface heat and latent heat fluxes of about W m )2 along the trajectory. This surface heating counteracted cloud-top cooling but not sufficiently to overcome the effect of cloudgenerated cooling and fog formation that was simulated at the end of the back-trajectories. Scale analysis of the major factors (radiative cloud-top cooling, surface fluxes, and entrainment) determining the evolution and fate of sea fog showed that in this case cloud-top cooling was a dominant process creating net cooling of the MABL, and leading to the formation and maintenance of the cloud and fog layers. When the cloud and fog layers were absent with a greater increase of the SST along the trajectory, surface fluxes continuously increased air and dew-point temperatures.

28 474 DARKO KORACˇ IN ET AL. Consequently, these conditions did not yield fog conditions at the end points of the trajectories. Our model results show that dissipation of sea fog along the West Coast is significantly influenced by the development of land-driven circulations. Dissipation of sea fog is governed by the complex interplay between advection, synoptic evolution, and development of local circulations. Displacement and weakening of horizontal synoptic pressure gradients and the consequent decrease in marine winds allows for development of offshore flows. These offshore flows merge with weak marine flows and cause drying of the MABL. During daytime, the offshore flows can induce warming and consequent fog dissipation. In conclusion, we would like to emphasize that we have provided a theoretical background for the formation, evolution, and dissipation of sea fog and indicated the major components determining sea-fog characteristics. This methodology should be applied to other cases and types of sea fog and further evaluated using observations from future field programs to be conducted in Lagrangian and Eulerian frameworks of reference over the ocean. 8. Epilogue on Sea-Fog Research and Implications for Operational Forecasting In addition to the summary and conclusions section, we believe that it is important to provide a general picture of sea-fog research, its challenges, and associated implications for operational forecasting. We have completed a suite of observational and modelling studies related to coastal sea fog (K2001; Lewis et al., 2003, 2004; and the current contribution). The observational studies of the sea-fog event of April 1999 (part of K2001 and Lewis et al., 2003) and the view of sea fog in the context of synoptic processes over the West Coast (Lewis et al., 2003) showed that widespread sea fog is controlled by large- and regional-scale processes: subsidence, long over-water trajectories and land-based trajectories, and the consequent structure of the marine layer. It appears that cooling of the marine layer in the presence of a warm ocean is due to radiative cooling associated with stratus. The value of these precise simulations of radiative fluxes stems from the model s very fine vertical resolution (approximately 10 m, K2001). Our three-dimensional modelling results indicate that delineation of fog and fog-free areas can be ascertained through careful analysis of trajectories within and above the MABL. These modelling results also provide reasonable values of the liquid water content of the fog layer. Further, results indicate that the dissipation of fog is linked to changes in the mesoscale wind field. Radiative cloud-top cooling generates turbulence that can induce fog maintenance and