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  • View in gallery

    CESAR site in the Netherlands. The insets show (top left) the location, (top right) the cloud radar with the construction to insert a reflector plate to convert to fog mode operation, and (middle right) the visibility sensor.

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    (a) The potential temperature and (b) relative humidity cross sections, (c) longwave downward radiation at the BSRN station, (d) the SMPS particle concentrations, and (e) the wind speed cross section for 23 Mar 2011.

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    Radar reflectivity time–height cross section for the first 10 h on 23 Mar 2011. Data are filtered to remove noise and clutter. However, some clutter still remains near the 140-m level. The lower two gates show some distortion in signal strength, possibly due to receiver saturation.

  • View in gallery

    Visibility observations at 2, 10, and 20 m for 23 Mar 2011.

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    Radar reflectivity vs visibility (20 m) for 23 Mar 2011.

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    Observed temperature and dewpoint temperature at 40 m, and their modeled counterparts, which were used to constrain the droplet activation model, for 23 Mar 2011.

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    Modeled-activated droplet concentration for three values of the hygroscopicity parameter for 23 Mar 2011.

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    A comparison of the observed visibility at the 20-m tower level with modeled visibility for three values of the hygroscopicity factor for 23 Mar 2011.

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    Modeled relationships between visibility and radar reflectivity (black, red, and blue) superimposed on the measured relationship (purple), for 23 Mar 2011.

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    Droplet concentration, extinction coefficients, and radar reflectivity at four different times during the evolution of the fog layer for 23 March 2011. Each panel under (a)–(d) consists of three subfigures. The first of the three subfigures indicates in black the original aerosol size distribution and in blue (left) the size distribution of aerosols and (right) the aerosol particles activated to fog droplets. The second subfigure represents the contribution of the inactivated and activated aerosol particles to the extinction coefficient. The third subfigure represents the contributions of the inactivated and activated aerosol particles to the radar reflectivity.

  • View in gallery

    Color plot of the time–height cross section of visibility as derived by radar reflectivity converted to visibility by means of the relationship established from Fig. 9 for 23 Mar 2011.

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Ground-Based Observations and Modeling of the Visibility and Radar Reflectivity in a Radiation Fog Layer

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  • 1 KNMI, De Bilt, Netherlands
  • 2 TNO, Utrecht, Netherlands
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Abstract

The development of a radiation fog layer at the Cabauw Experimental Site for Atmospheric Research (51.97°N, 4.93°E) on 23 March 2011 was observed with ground-based in situ and remote sensing observations to investigate the relationship between visibility and radar reflectivity. The fog layer thickness was less than 200 m. Radar reflectivity values did not exceed −25 dBZ even with visibilities less than 100 m. The onset and evaporation of fog produce different radar reflectivity–visibility relationships. The evolution of the fog layer was modeled with a droplet activation model that used the aerosol size distribution observed at the 60-m altitude tower level as input. Radar reflectivity and visibility were calculated from model drop size spectra using Mie scattering theory. Since radiative cooling rates are small in comparison with cooling rates due to adiabatic lift of aerosol-laden air, the modeled supersaturation remains low so that few aerosol particles are activated to cloud droplets. The modeling results suggest that the different radar reflectivity–visibility relationships are the result of differences in the interplay between water vapor and cloud droplets during formation and evaporation of the fog. During droplet activation, only a few large cloud droplets remain after successfully competing for water vapor with the smaller activated droplets. These small droplets eventually evaporate (deactivate) again. In the fog dissolution/evaporation stage, only these large droplet need to be evaporated. Therefore, to convert radar reflectivity to visibility for traffic safety products, knowledge of the state of local fog evolution is necessary.

Corresponding author address: R. Boers, KNMI, P.O. Box 201, 3730 AE De Bilt, Netherlands. E-mail: reinout.boers@knmi.nl

Abstract

The development of a radiation fog layer at the Cabauw Experimental Site for Atmospheric Research (51.97°N, 4.93°E) on 23 March 2011 was observed with ground-based in situ and remote sensing observations to investigate the relationship between visibility and radar reflectivity. The fog layer thickness was less than 200 m. Radar reflectivity values did not exceed −25 dBZ even with visibilities less than 100 m. The onset and evaporation of fog produce different radar reflectivity–visibility relationships. The evolution of the fog layer was modeled with a droplet activation model that used the aerosol size distribution observed at the 60-m altitude tower level as input. Radar reflectivity and visibility were calculated from model drop size spectra using Mie scattering theory. Since radiative cooling rates are small in comparison with cooling rates due to adiabatic lift of aerosol-laden air, the modeled supersaturation remains low so that few aerosol particles are activated to cloud droplets. The modeling results suggest that the different radar reflectivity–visibility relationships are the result of differences in the interplay between water vapor and cloud droplets during formation and evaporation of the fog. During droplet activation, only a few large cloud droplets remain after successfully competing for water vapor with the smaller activated droplets. These small droplets eventually evaporate (deactivate) again. In the fog dissolution/evaporation stage, only these large droplet need to be evaporated. Therefore, to convert radar reflectivity to visibility for traffic safety products, knowledge of the state of local fog evolution is necessary.

Corresponding author address: R. Boers, KNMI, P.O. Box 201, 3730 AE De Bilt, Netherlands. E-mail: reinout.boers@knmi.nl

1. Introduction

Low-level moisture, appropriate low wind speed, and nighttime longwave cooling are the primary prerequisites for the development of radiation fog. Initially, most longwave cooling (longwave radiative flux divergence) originates near the ground, but the level of maximum cooling will rise progressively as the fog layer thickens and the emissivity of cloud droplets becomes dominant. If the fog layer is thick enough and the droplet radius approaches 5–10 μm, then most longwave radiative flux divergence is situated near the top of the fog layer. With large fog-top cooling rates, the fog layer will then transform to a wet-adiabatic boundary layer with top-down convection and entrainment of dry air from the top. This process will dry out the fog but will continue to cool it at the same time. Thus, it will provide a self-limiting mechanism that restricts the vertical development of the fog layer. Radiation fog layers are therefore mostly confined to levels below 200 m (Duynkerke 1991). However, since these fogs develop from the ground upward, they are a traffic hazard from the moment they arise. It is paramount that the conditions responsible for the onset of these fog layers are well understood so that nowcasting and other short-term observation and prediction products can be improved.

A large body of literature is now available that describes the onset and evolution of fog layers, and several modeling efforts have demonstrated the importance of atmospheric processes, the most elementary of which were mentioned above. A comprehensive summary of work from the 1980s onward is provided by Gultepe et al. (2007) with an excellent set of references to guide the reader.

One of the more prevailing peculiarities of fog layers is their patchiness, a fact that stands out when satellite data are inspected. Often a local plot of wetland will be shrouded in fog, while the adjacent urbanized area will experience no fog whatsoever. The patchiness makes it very difficult to provide for accurate nowcasting. At the same time, fog layers hazardous for traffic are very difficult to detect from satellites. Satellite radiometers have only limited capability to discriminate between a cloud layer residing at the surface and another one with a cloud base within a couple of hundred meters above the surface. Even though there are now several satellite detection schemes available (Cermak and Bendix 2011, and references therein), these schemes are not widely used in operational applications. Overlying thin cirrus clouds may additionally obstruct accurate fog detection.

Of course, the hazard for traffic is not so much fog itself but its consequence, namely, reduced visibility. Visibility is the end result of a complex interplay between aerosol microphysics, chemistry, radiation cooling, and particle activation (Elias et al. 2009). Before particle activation occurs, visible extinction is not so large, and range variations in visibility can be observed remotely by lidar. However, when particle activation has occurred, visibility can be only locally observed with traditional in situ visibility sensors, while horizontal variations in visibility are undetectable. This makes visibility sensors or lidar as tools for nowcasting of limited use as spatial variations in visibility remain undetected because of signal attenuation.

In this paper we explore a different type of visibility detection, namely, one provided by variations in radar reflectivity. In comparison with lidar extinction, radar signal extinction is small, although in general it cannot be neglected. Therefore, with a wavelength of 35 GHz, reflectivity variations over large horizontal regions should be detectible (Hamazu et al. 2003; Uematsu et al. 2005a,b). If it is possible to fix locally the link between visibility and reflectivity, then one can remotely detect visibility, provided the local link between the two quantities can be assumed to hold regionally. If this technique is sufficiently accurate, then nowcasting and visibility detection of airports and regions of high traffic volumes can be greatly enhanced, as three-dimensional volume scanning is part and parcel of most operational radar systems. In doing so we focus on a radiation fog that adheres to the definition of fog type: RAD (Tardif and Rasmussen 2007), with surface wind speeds less than 2 m s−1.

The purpose of this paper is thus to establish the link between visibility and radar reflectivity in order to investigate the feasibility of developing a radar visibility product for use in (air) traffic management. To this end the remote sensing synergy present at the Cabauw Experimental Site for Atmospheric Research (CESAR, http://www.cesar-observatory.nl) in the western part of the Netherlands is used to detect fog layers. The CESAR 200-m tower is fitted with instruments measuring temperature, humidity, visibility, and aerosol size spectra. The remote sensing platform at CESAR comprises a 35-GHz radar, microwave radiometer, and several lidar systems. The strategy of this work was to capture the link between visibility and radar reflectivity from the CESAR observations, and to model this link using a fog–cloud droplet activation model in order to understand the physics of nucleation and droplet formation. Particle nucleation was simulated using a kappa-Köhler model of droplet activation. The nucleation model was coupled to a traditional Mie scattering model to simulate visibility and radar reflectivity in order to gauge whether the observed coupling between visibility and radar reflectivity can indeed be modeled, and thus can be understood in terms of physical processes.

2. Observations

a. Integrated profiling site CESAR

CESAR is situated at 51.97°N, 4.93°E in a rural flat grassland region between the cities of Rotterdam and Utrecht in the Netherlands (Fig. 1). Cabauw is the meteorological research site of the Royal Netherlands Meteorological Institute (KNMI) and was originally established in 1972. In the first 20 years of its existence, most work focused on exchange processes between the earth and atmosphere (Van Ulden and Wieringa 1996), using the 200-m tower instrumented at regular height intervals. In the mid-1990s, the scope of the work was progressively expanded to include research on the interaction of clouds, aerosols, and radiation, the evaluation of climate and weather models, the validation of satellite retrievals, and the monitoring of climate. To this end additional remote sensing and radiation equipment was installed at the site.

Fig. 1.
Fig. 1.

CESAR site in the Netherlands. The insets show (top left) the location, (top right) the cloud radar with the construction to insert a reflector plate to convert to fog mode operation, and (middle right) the visibility sensor.

Citation: Journal of Atmospheric and Oceanic Technology 30, 2; 10.1175/JTECH-D-12-00081.1

Although KNMI is the Cabauw site manager, it is not solely responsible for running and maintaining all of the scientific instruments there. A number of Dutch universities and scientific and technological research institutes are organized in the CESAR consortium, with the specific aim to jointly plan and execute their research activities at Cabauw and to share responsibility in running field programs. CESAR provides an important platform for collaboration in the field of atmospheric sciences and over the years has attracted many international research groups to temporarily locate their instruments at CESAR. CESAR’s strength lies in the capability for integrated profiling of the atmospheric column. Broadly speaking, there are three sets of instruments, namely, tower-based in situ, ground-based in situ, and ground-based remote sensing instruments. They measure a broad spectrum of thermodynamic, radiation, and chemical parameters, and they contribute to a large variety of national and international research and monitoring programs. Below we will give a short overview of the measured parameters where relevant for this work.

b. Thermodynamic profiling

The 200-m mast is instrumented at the 2-, 10-, 20-, 40-, 80-, 140-, and 200-m levels. Measurements at these levels include temperature, humidity, wind speed, and wind direction. The observations at CESAR are supported by radiosondes that are launched at 12-h intervals at the World Meteorological Organization (WMO) KNMI launch site in De Bilt (52.10°N, 5.18°E), which is at a distance of 22.19 km from Cabauw. Accuracy for the temperature measurement is 0.1°C. Humidity observations are derived from a relative humidity sensor with an accuracy of 1%.

c. Clouds

Several complementary systems are available at Cabauw to obtain detailed cloud information, ranging from cloud fractional coverage to altitude distributions. The principal modes of cloud observation are a cloud radar at 35 GHz, a ceilometer, and a multiwavelength microwave radiometer. As the radar is traditionally operated in the zenith direction, this mode of operation would yield no information about fog, as the first range gate of the radar is at 250 m. Therefore, a lightweight aluminum reflector was procured, and during fog episodes the reflector was placed above the antenna of the cloud radar. The reflector deflects the radar beam in a nearly horizontal direction but slightly upward at an angle of 3.5°. This small angle was chosen for safety purposes and to be able to detect the top of the fog layer. It ensures a transmission path of several kilometers through the fog so that its evolution and reflectivity structure can be probed in detail. The disadvantage of this mode of operation is that the system will suffer from spurious ground reflections, even though the beam divergence is small (5 mrad). The postprocessing of the radar data therefore entails a significant effort to eliminate ground echoes. Another disadvantage is that the fixed position angle of the radar prevents accurate collocation of the radar range gate data with the tower data. The lack of collocation (around 300 m for the nearest range gate and the 20-m tower level) introduces possible temporal differences between the mast data and the reflectivity data. Such differences cannot be avoided. Nevertheless, as we shall see later on, this mode of operation is quite suitable for the detection of fog episodes for the purpose of the research reported here.

d. Aerosols

In 2007, an aerosol inlet was mounted at the 60-m tower level, with the specific aim to facilitate the expansion of the research program to include aerosol size and composition measurements. The aerosol inlet, which retains particles smaller than 5-μm radius, is attached to a piping system in the basement of the Cabauw research facility, where a manifold is in place to distribute the air to various aerosol probes. A TSI scanning mobility particle sizer (SMPS) and a condensation particle counter (CPC) probe are installed to measure dry aerosol spectra and total cloud particle counts. For the purpose of this experiment, only the SMPS data could be used, not only to detect the aerosol structure ahead and during fog episodes, but also to initialize the droplet activation model (to be discussed in the next section). The range of particles measured by the SMPS is between 0.0025 and 1-μm diameter, and the relative humidity at the instrument is kept near 30%.

e. Visibility

Although visibility has been measured at the automated weather station (AWS) station of Cabauw since 2007 with a Vaisala FD12P probe, for the purpose of this experiment, the tower levels 2, 10, and 20 were fitted with Biral SWS-100 sensors with a visibility resolution of 10 m and an accuracy of 10% (maximum). After the day of the experiment (23 March 2011), other tower levels (40, 80, 140, and 200 m) were also fitted with similar instruments.

f. Observation procedures

During the fog season (1 October–31 March), daily forecasts were made of the possibility of fog occurring at CESAR. If conditions were deemed promising, then the aluminum reflector was shifted over the transmitter/receiver in the late afternoon so that the radar beam was deflected in the near-horizontal direction. After fogs lifted at the end of the episode, the reflector was shifted back to its rest position and normal radar operation resumed. Radar data collected during the episode then went through a ground clutter cleaning routine to improve the signal output to be used in the visibility studies. Visibility data at the mast were obtained and visibility–radar reflectivity plots were made for the data points along the radar signal paths at heights where the radar beam pass the tower level of 20 m. These plots were inspected for uniformity, and relationships between the two quantities were obtained. Next, it was assumed that the locally obtained visibility–reflectivity relationships were valid for the entire radar range, so that the radar signal range–time series for the fog episode could be converted into a remote sensing visibility plot. These radar visibility plots are the principal output of this process, and the aim is to determine whether such radar visibility plots can provide added value in detecting range–time variations in visibility on a large spatial scale. As will be discussed later, no uniform radar reflectivity–visibility relationship exists so an informed choice needed to be made.

3. Droplet activation model

A droplet activation model was developed that allows the calculation of wetted aerosol/fog droplet spectra as a function of observed SMPS dry aerosol spectra. Here, a combination of tower-measured temperature and humidity data is used to prescribe particle growth rate and activation. Relevant details of the model are described in the appendix. Issues that cannot be resolved from the available data are the aerosol composition and size-dependent hygroscopicity. Composition determines hygroscopicity, and hygroscopicity will determine droplet activation.

Size-dependent hygroscopicity is important in droplet activation and can be observed by operating a cloud condensation nuclei (CCN) counter side by side with aerosol spectrometers. Roberts et al. (2008) and Gunthe et al. (2009) found that the larger particles are, in general, more hygroscopic than the smaller particles, a fact that they attributed to cloud processing of the larger particles in advance of being detected by the measurement system. This fact adds considerable complexity to a modeling of droplet activation, as it then becomes impossible to attribute a specific value or range of values of hygroscopicity to a particle, which is necessary to calculate its critical supersaturation.

Because of the uncertainty in value of the hygroscopicity and the general absence of droplet data, it was decided to model the droplet activation for three values of the hygroscopicity parameter κ, namely, (i) κ = 1.30 (representing pure sea salt NaCl, e.g., present during northwesterly inflow of clean oceanic air), (ii) κ = 0.67 (representative of ammonium nitrate, NH4NO3, a nitrogen salt that is typically formed in the polluted Dutch environment as a result of the reaction between ammonia and NOx), and (iii) κ = 0.33 (representative of a less soluble organic compound). This range is justified because Mensah et al. (2011) found that for the CESAR site, about 30% of particles are organic matter, which, presumably is less soluble than sea salt, while a large fraction of inorganic aerosol at CESAR turned out to be ammonium nitrate.

Additionally, recent work has established the possibility that the surface tension of individual wetted particles may vary between the value of that of pure water (0.072 N m−1) and lower values that are representative of water surfaces contaminated by organic material (Irwin et al. 2010). Lower values of surface tension lead to lower values of the critical supersaturation, so that particles are activated at a smaller size. Even though the presence of organics at CESAR has been detected, it is impossible to assign a precise value of the surface tension to individual particles. In practice this issue is partly circumvented by assuming that the chosen value of κ is an effective hygroscopicity, thus lumping the surface tension effects and the hygroscopicity effects into one parameter only.

To convert the computed spectra to visibility, the particles were binned at time steps of 1 min in 150 size bins, and Mie code was used to calculate the scattering properties of the wetted aerosols at a wavelength of 550 nm. The index of refraction was allowed to vary between the value of the pure dry aerosol to that of pure water depending on the mole fraction of soluble material in the water droplet according to traditional mixing rules. The imaginary part of the index of refraction of the pure dry aerosol was not known, so it was put to zero. Therefore, the imaginary part of the index of refraction of the wetted aerosol/fog droplet follows that of pure water.

Extinction coefficient σext was calculated according to
e1
where Qext,i is the extinction efficiency in bin i and is output of the Mie calculations, Ni is the number of particles in spectral bin i, and ri is the mean radius of spectral bin i. Visibility can then be calculated according to the standard formula
e2
see Clarke et al. (2008) for definitions of both (1) and (2). Here σext,part is the particulate extinction at the wavelength of 550 nm, which is output from the Mie calculations, and σray is the Rayleigh scatter at the same wavelength, which can be calculated separately using the surface pressure as input.
To convert the computed spectra to radar reflectivity, use was made of the standard conversion formula
e3
(Battan 1973), where R is the radar reflectivity in decibels of Z (dBZ) and the index i refers to the summation over the 150 spectral bins.

4. Results

a. CESAR observations

The observations of the radiation fog that developed in the night from 22 to 23 March 2011 are presented in Figs. 25. The time–height cross sections of potential temperature (Fig. 2a) and relative humidity (Fig. 2b), the longwave downward radiation (uncertainty 10 W m−2, Fig. 2c) at the Baseline Surface Radiation Network (BSRN) site at CESAR (Ohmura et al. 1998), the time series of SMPS aerosol concentration (Fig. 2d), and the time–height cross section of tower wind speed (Fig. 2e) are shown. The data displayed are obtained from the standard tower data levels of 200, 140, 80, 40, 20, 10, and 2 m, and are presented in a contour plot. After 1800 UTC 22 March, radiative cooling quickly established a surface inversion that by midnight resulted in a temperature jump of 6°C between the surface and the 200-m tower level. From here onward the cold layer develops upward. This layer has a relative humidity close to or in excess of 100%, indicative of fog. Figure 2b shows that relative humidity is an imprecise measurement, so it is difficult to assign fog condition based on this observation only. Nevertheless, based on the (potential) temperature and relative humidity, without being too precise, it is clear that the top of the fog layer evolves from levels of below 20 m around 0300 UTC to between 80 and 140 m 3 h later. Between 0400 and 0800 UTC, the temperature rises 2°C even though the relative humidity remains close to 100%. After 0800 UTC, the fog quickly evaporates as the surface heats up and the maximum temperature of 11°C is reached by 1500 UTC.

Fig. 2.
Fig. 2.

(a) The potential temperature and (b) relative humidity cross sections, (c) longwave downward radiation at the BSRN station, (d) the SMPS particle concentrations, and (e) the wind speed cross section for 23 Mar 2011.

Citation: Journal of Atmospheric and Oceanic Technology 30, 2; 10.1175/JTECH-D-12-00081.1

Fig. 3.
Fig. 3.

Radar reflectivity time–height cross section for the first 10 h on 23 Mar 2011. Data are filtered to remove noise and clutter. However, some clutter still remains near the 140-m level. The lower two gates show some distortion in signal strength, possibly due to receiver saturation.

Citation: Journal of Atmospheric and Oceanic Technology 30, 2; 10.1175/JTECH-D-12-00081.1

Fig. 4.
Fig. 4.

Visibility observations at 2, 10, and 20 m for 23 Mar 2011.

Citation: Journal of Atmospheric and Oceanic Technology 30, 2; 10.1175/JTECH-D-12-00081.1

Fig. 5.
Fig. 5.

Radar reflectivity vs visibility (20 m) for 23 Mar 2011.

Citation: Journal of Atmospheric and Oceanic Technology 30, 2; 10.1175/JTECH-D-12-00081.1

The longwave downward radiation (Fig. 2c) measured at the surface shows a gradual change around 0300 UTC, changing from 275 to 335 W m−2, which indicates the transition from radiation emanating from a clear sky to one coming from a fog/cloud layer. This transition is not very abrupt, as the cloud layer will be initially partly transparent to longwave radiation. After 0800 UTC the radiation levels change back to the clear-sky conditions as the fog evaporates. Figure 2d shows the SMPS dry aerosol data ingested at the 60-m tower level for 23 March 2011. During the fog episode, particle number concentrations were between 7000 and 11 000 cm−3 and gradually decrease during the day. Wind speed observation (Fig. 2e) indicate that the surface wind speeds were less than 2 m s−1; however, at the top tower level of 200 m, the wind speed was more than 7 m s−1.

Figure 3 shows the radar reflectivity on 23 March 2011. Reflectivity values above the near-field noise level of −55 dBZ appeared at the surface near 0300 UTC and developed upward to 150 m in the course of the next 3 h. Figure 4 shows the visibility observed at 2, 10, and 20 m (the only levels where sensors were located that night), from which it appears that the 2-m sensor was the only one detecting low visibilities (<100 m) prior to 0300 UTC. The low visibilities at this level extended backward in time to 2200 UTC 22 March 2011, so it appears that ground fog of a depth of less than 10 m existed for at least 5–6 h prior to 0300 UTC. This ground fog was undetectable by the radar, as the first gate is at 20 m above ground level. At 0200 UTC the 10-m level becomes enveloped in fog followed by the 20-m level 1 h later. In accordance with the increasing temperatures at 0800 UTC, the fog disappears and the radar reflectivity in Fig. 3 quickly drops to levels below −50 dBZ. Interestingly, the radar reflectivity shows distinct patches of alternating high or low reflectivity extending from the top of the fog layer to the surface, suggesting coupling of the top and bottom of the fog layer, which may be due to convection induced by fog-top longwave radiative cooling. Alternating patches of higher and lower radar reflectivity in a fog layer have been observed before, a fact that Uematsu et al. (2005b) attribute to wind shear.

Figure 5 shows radar reflectivity versus visibility. The comparison was done for the 20-m tower level using the third range gate of the radar return signal, which is the first gate not affected by ground clutter as shown in Fig. 3. Maximum reflectivity values are in excess of −30 dBZ. These values are well below those expected of minor drizzle formation (−10 to −20 dBZ), so it is clear that no precipitation occurred during the fog episode. None was measured at the surface automatic weather station. It appears that for this day, there is not a uniform link between visibility and radar reflectivity. There are two branches, with the lower branch representing the early hour of fog development and the second—steeper—branch representing the later hours and bulk of the data. A regression through the steeper branch of the visibility–reflectivity plot yields an RMS error of 3 dBZ. We expect that the lack of collocation between the radar and tower data contributes to this error. We suggest a possible physical explanation for the two branches in the discussion of the modeling results below.

b. Simulation of droplet activation and evaporation

To understand the microphysical aspects of the fog layer, a modeling effort was undertaken to simulate droplet spectra and the visibility and radar reflectivity derived from these spectra. Even though we did not have access to a complete boundary model with interactive physics between radiation, droplet formation, turbulence, and precipitation, the model can elucidate the droplet activation process, including its dependence on chemical properties of the dry aerosol. Also, the radar data clearly show no high reflectivity values associated with precipitation, so precipitation can be neglected altogether. The simplest way to model droplet formation and evaporation is to simulate a single cooling and warming cycle, during which aerosol/droplet spectra evolve from their incipient wet aerosol state, through droplet activation, droplet growth, and eventual evaporation as the layer heats up after sunrise. Although it is realized that this simple model will neglect microphysics/turbulence interactions altogether, it will provide a first-order idea of the evolution of the droplet spectra. To this end the temperature/humidity variations as observed at the tower levels and the SMPS-observed aerosol spectra at the 60-m level at 0000 UTC were used to constrain the model (Fig. 6). The black solid lines show the temperature and dewpoint temperature as observed at the 40-m level, while the broken lines represent their modeled counterparts. The modeled temperatures and dewpoint temperatures represent conditions under which total water content was preserved, so their values depart somewhat from the observations. Given the modeled temperatures, this constraint implies complete evaporation of the fog by 0800 UTC. However, the 40-m level suggested complete evaporation 1 h later. As vertical wind speeds could not be measured, and given the lack of precision in the relative humidity data, it is unclear whether this later evaporation point is the result of imprecise observations, sudden vertical movements, or an inflow of humid air during the fog episode. After the relative humidity reaches 100% (near 0145 UTC), the cooling rates increase and minimum temperature is reached at 0400 UTC. Then the temperature started to increase at a constant rate. As the precise chemical composition of the aerosol was not known, the hygroscopicity was prescribed for three different model runs, namely, at κ = 1.3 (NaCl), κ = 0.67 (NH4NO3), and κ = 0.33 (malonic acid) to understand spectral behavior over a realistic range of highly soluble to relatively insoluble aerosol particles.

Fig. 6.
Fig. 6.

Observed temperature and dewpoint temperature at 40 m, and their modeled counterparts, which were used to constrain the droplet activation model, for 23 Mar 2011.

Citation: Journal of Atmospheric and Oceanic Technology 30, 2; 10.1175/JTECH-D-12-00081.1

Figure 7 shows the modeled activated droplet concentration as a function of time for the three chosen values of the hygroscopicity. There are several noteworthy elements in this graph. First, according to the model first droplet activation occurs at 0145 UTC. Yet, for all hygroscopicity values, the initial concentration of activated droplets is higher than the later concentrations, even though the layer continues to cool. Close examination of the output reveals that this is because the supersaturation is very low (less than 0.04%). This means that the group of activated aerosols with the higher critical supersaturation grows so slowly that the larger droplets attract sufficient water vapor to suppress further increase in the ambient relative humidity. Thus, the ambient relative humidity starts to drop below the critical supersaturation of the group of the smallest activated droplets, so they evaporate again. Second, when the cooling rate increases at 0300 UTC, a second set of droplets activate for the two highest values of hygroscopicity but not for the lowest hygroscopicity. Only for κ = 0.33 is a stable droplet concentration of 100 cm−3 reached. For κ = 1.30 no equilibrium number of activated droplet concentration is reached at all.

Fig. 7.
Fig. 7.

Modeled-activated droplet concentration for three values of the hygroscopicity parameter for 23 Mar 2011.

Citation: Journal of Atmospheric and Oceanic Technology 30, 2; 10.1175/JTECH-D-12-00081.1

Clearly, the picture emerges that the process of condensation/activation is different from the process of evaporation/deactivation. Even though initially a set of droplets is activated, some of this set will grow rapidly at the expense of others, which will evaporate again during the first hours. Only after the early hours will a more permanent and stable set of droplets dominate fog evolution. When the layer starts to warm. this later stable set of droplets will evaporate eventually.

Once the droplet spectra are modeled, the associated visibility and radar reflectivity values can be obtained as well according to Eqs. (1)(3). Figure 8 shows the comparison of modeled visibility with observed visibility at the 20-m tower level. Clearly, visibility remains the highest for the lower value of κ = 0.33 on account of the fact that for this value the least number of droplets is activated and the wet aerosols are the smallest. The simulations are not synchronized with the observations because saturation in the observations is reached at a different time than in the model. The reason is that the temperature/dewpoint observations were taken at the 40-m altitude to adhere as closely as possible to the 60-m altitude aerosol intake point, while the visibility observations were taken at the 20-m tower level. Possible other factors influencing the lack of synchronicity are the imprecision in modeling the exact time when saturation occurs and inaccuracies in the relative humidity instrument, which will affect the dewpoint determination. At any rate, if the modeled time series is shifted by 1 h, then it is clear that the variation in visibility follows that of an activated aerosol layer of moderate hygroscopicity (κ = 0.4–0.7), even though the modeled minimum visibility is slightly lower than observed for all values of κ. It is important to note that for visibilities higher than 800 m, which is the regime for which very few—if any—aerosol particles are activated to cloud droplets, the visibility is quite sensitive to variations in κ (a range of several kilometers in visibility for the applied range in κ). This is the regime of haze droplets, which are unactivated aerosol particles that have taken up water in amounts that are dependent on the value of their hygroscopicity. However, at small visibilities, when enough fog droplets are present, they dominate the visibility reduction, and the hygroscopicity of the original aerosol particle is practically irrelevant in determining visibility.

Fig. 8.
Fig. 8.

A comparison of the observed visibility at the 20-m tower level with modeled visibility for three values of the hygroscopicity factor for 23 Mar 2011.

Citation: Journal of Atmospheric and Oceanic Technology 30, 2; 10.1175/JTECH-D-12-00081.1

Figure 9 shows the modeled relationship between visibility and radar reflectivity for the three values of κ. For each simulation two branches are apparent that reflect the process of activation (lower branch) and that of deactivation (upper branch). The largest values of reflectivity (−20 dBZ) are somewhat larger than observed (−30 dBZ), which is consistent with the lower values of modeled visibility as well, so this suggests that too many droplets were activated in our model even though the number is already quite small, or that they grew too large or both. For comparison purposes, a modeled factor of 10 dBZ larger than observed is equivalent to an increase of 10 in number concentration and an increase of 1.5 μm in diameter. Such errors are to be expected in a modeling environment with uncertain input conditions.

Fig. 9.
Fig. 9.

Modeled relationships between visibility and radar reflectivity (black, red, and blue) superimposed on the measured relationship (purple), for 23 Mar 2011.

Citation: Journal of Atmospheric and Oceanic Technology 30, 2; 10.1175/JTECH-D-12-00081.1

Figure 10 shows the evolution of the aerosol/droplet spectrum, and the spectral contribution to the visible Qext and to the radar reflectivity R at four stages of the fog episode. The first (Fig. 10a) and second stages (Fig. 10b) represent conditions soon after the onset of fog. For stage A the activated droplet spectral region is still attached to the wetted aerosol distribution, and both R and Qext exhibit smooth transitions between the two parts of the spectrum. For Qext the contributions for both parts of the spectrum are about equal. As the fog layer evolves and droplet continue to grow, the two parts of the spectrum separate and the contribution of the droplets to Qext and R far exceed the contribution of the wetted aerosols by one to three orders of magnitude. At stage C the temperature is at its minimum and the fog layer is fully developed. Radii of mature droplets are typically 10–15 μm, a size that is so small that significant precipitation seems unlikely. In fact, observations from clean clouds over the Southern Ocean (Boers and Rotstayn 2001) indicate that drizzle production is absent when droplet radii are smaller than 10 μm. Added to this is the limited depth of the fog layer, which inhibits coalescence that can create the larger precipitation size droplets. At any rate, had there been significant drizzle production, far higher reflectivities would have been present than were observed in the data. At the last stage D, the fog is evaporating. Note the difference in spectral shape between stages A and D. At stage D the remaining droplets simply all evaporate and no “bridge” in the spectra of the wetted aerosol and evaporated droplets ever occurs.

Fig. 10.
Fig. 10.

Droplet concentration, extinction coefficients, and radar reflectivity at four different times during the evolution of the fog layer for 23 March 2011. Each panel under (a)–(d) consists of three subfigures. The first of the three subfigures indicates in black the original aerosol size distribution and in blue (left) the size distribution of aerosols and (right) the aerosol particles activated to fog droplets. The second subfigure represents the contribution of the inactivated and activated aerosol particles to the extinction coefficient. The third subfigure represents the contributions of the inactivated and activated aerosol particles to the radar reflectivity.

Citation: Journal of Atmospheric and Oceanic Technology 30, 2; 10.1175/JTECH-D-12-00081.1

Figure 11 shows a plot of the radar reflectivity of Fig. 3 converted to visibility using a least squares fit through the upper branch of the visibility–radar reflectivity relationship from Fig. 5. For this relationship the radar is able to distinguish visibilities of 500 m or less at distances of several kilometers away from the observer. It is even possible to discern visibility variation at very high temporal evolution. However, these visibility estimates are limited by the sensitivity of the radar. Figure 9 suggests that a better dynamic range in radar visibility is expected for lower values of κ. The reason is that at high values of κ, visibilities are quickly reduced to very low levels anyway, so that limited extra information is available when visibility is reduced from 100 to 50 m.

Fig. 11.
Fig. 11.

Color plot of the time–height cross section of visibility as derived by radar reflectivity converted to visibility by means of the relationship established from Fig. 9 for 23 Mar 2011.

Citation: Journal of Atmospheric and Oceanic Technology 30, 2; 10.1175/JTECH-D-12-00081.1

5. Discussion and conclusions

The comparison of fog-related observations on 23 March 2011 with a simulation using a microphysical model of particle activation shows a number of important points.

  1. The link between visibility and radar reflectivity does not follow an unambiguous universal curve. Early on during fog formation, the link shows comparative little variation in visibility and large variation in radar reflectivity. Later on, as the fog is in its mature stage and show signs of dissolution, the relationship shifts toward a large variation in visibility and a comparatively smaller variation in radar reflectivity.
  2. A model simulation of this fog episode indicates that one possible reason for the two branches in the visibility–radar reflectivity plot is that during condensation, a portion of activated aerosol particles evaporated well ahead of their reaching a mature stage as they lose the competition for water vapor with the larger drops. Droplet activation can thus be viewed as a two-step process. Initially, a number of aerosol particles are activated, but a large fraction will deactivate after some time as they lose competition for water vapor.
  3. Simulation suggests that only about 1% of available aerosol particles remain activated and grow to the size of fog droplets. This is a very small number and entirely because the cooling rate for this fog is an order of magnitude less than that of a parcel of moist air moving at an updraft speed of 0.5 m s−1, assuming ideal adiabatic conditions. Thus, the total number of fog droplets is much lower than expected from a typical cloud for which the droplet concentration is controlled by convective motions.
  4. The chemistry of the fog layer has a significant impact on the link between visibility and radar reflectivity. The lower the value of κ, the more dynamic resolution is expected to be in the sensitive transition region, where a layer changes from haze to fog to dense fog. Once a fog has been established, the original hygroscopicity of the particle giving rise to the fog droplet is no longer important.

Our computations neglect other physical processes that can influence particle growth and fog evolution, such as turbulence, convection induced by longwave radiative cooling, large-scale vertical motions, and advection. To our knowledge our observations are the first to link radar reflectivity and visibility through direct observations of these two quantities. Some indirect results have been presented before. Gultepe et al. (2009) used output of microphysical probes to establish this link for radar values of −100 to 0 dBZ. However, they produced no direct radar data. In their intermediate radar range between −60 and −30 dBZ, they also found a comparatively large spread in visibility values, suggesting that the link between radar reflectivity and visibility may not be uniform. Despite this nonuniformity it is clear that radar reflectivity can be converted to visibility, opening the way for a powerful tool to augment the detection capability of reduced visibility at airports or roads. However, if there is a larger number of droplets or if the fog droplets attain larger sizes, then reflectivity changes will not incur much difference in visibility. So, the possibility of resolving visibility variations using radar for visibilities less than 100 m will always be limited. Depending on the chemistry of the dry aerosol and given the fact that 10 000 particles per cubic centimeter is a useful number to approximate the typical aerosol concentrations at CESAR, the current radar will yield credible values of visibility from 600 to 800 m downward to 50 m. It would be useful to increase radar sensitivity to −60 to −65 dBZ, so that the dynamic range of the radar–visibility product is improved. Further research presently under way will focus on continued analysis of fog episodes with an emphasis on chemical composition, different cooling rates, and the measurement of fog droplet concentration at the 60-m altitude inlet.

APPENDIX

Droplet Activation Model

The droplet activation model used in this study is a standard kappa-Köhler model (Petters and Kreidenweis 2007), where the Köhler curve per particle is described by
ea1
Here r is the radius of the wetted particle, rd is the dry particle radius, σtens is the surface tension over a droplet of radius r, Rυ is the thermodynamic constant of water vapor, T is temperature, ρw is the density of pure water, and κ is the hygroscopicity of the particle (as defined in the main text). The R term refers to the Raoult effect and the K term to the Kelvin (curvature) effect. The Raoult term is a simplification of the more traditional expression for R in (A1), where R is replaced by the water activity term. This term is complex and depends on the value in the exact chemical balance in the droplet. The activity term can be measured in the laboratory for individual chemical species, but it is more often than not calculated from chemical models.

So, Eq. (A1) is an elegant simplification that allows the investigator to quickly calculate Köhler curves for many different species, where the only two variables pertaining to the chemical composition are κ and σtens. In this work (A1) is further simplified by replacing the surface tension of the droplet by its equivalent of pure water. This simplification is likely to introduce inaccuracies in the calculation but given the uncertain nature of the chemical composition of the aerosols that activate to cloud droplets, it is not unreasonable.

The dry aerosol spectra are separated into two parts, namely, a nonactivated part (NAP) and a potentially activated part (PAP). The NAP consists of the dry aerosol spectrum up a size range for which it is expected that none of the aerosol particles are activated. In the model the mean and upper and lower bin-bound radii of the individual size bins are used to calculate aerosol growth rates as a function of relative humidity. The PAP consists of individual particles beyond the upper bound of the NAP that can be activated once the relative humidity exceeds their critical supersaturation. Of course, it is not possible to predict ahead of time how many particles will be activated. Therefore, the investigator is allowed some leeway to set the number of particles in the PAP depending on the application. The more particles chosen, the smaller the range of particles in the NAP and vice versa. In our simulations the number of particles in the PAP was chosen to be 660 cm−3. Thus, during the computation of the wetted aerosol–fog droplet spectra, the PAP is treated as a series of individual particles. This is a method that ensures the highest accuracy in calculating the activation process. The time step was 0.1 s and a first-order Adam–Bashford scheme was used to advance from one time step to next.

Every 12 s (i.e., 120 iterations) the complete particle spectrum was recomposed out of the NAP and the PAP, and Mie calculations were performed to determine the visible extinction efficiency. The latter can then be used to calculate the visibility as per Eq. (2). At the same time the binned spectra are used to calculate the radar reflectivity as per Eq. (3). As a double check of the accuracy of Eq. (3), the Mie code was also used to calculate the scattering properties of the particles at the radar frequency of 35 GHz. The two calculations agreed to within 2 dBZ.

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