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  • View in gallery

    The LWC vs Nd from two FSSP measurements from the 1995 RACE field program. The fits are shown by the solid and dashed lines. The Nd96 and Nd124 are for FSSP-96 (over original size ranges) and FSSP-124 (over extended size ranges) observations, respectively.

  • View in gallery

    Visibility vs Nd from the FSSP measurements; each data point represents a scale of 1 km. The solid-line fit is for FSSP96. The V96 and V124 are for FSSP-96 (over original size ranges) and FSSP-124 (over extended size ranges) observations, respectively.

  • View in gallery

    The visibility calculated from FSSP measurements and from K84 Vis–LWC (as cloud water + fog) and Vis–IWC (as cloud ice + fog) relationships. The V96 and V124 are for FSSP-96 (over original size ranges) and FSSP-124 (over extended size ranges) observations, respectively.

  • View in gallery

    Visibility vs f (LWC, Nd) from in situ observations. The fit is shown with a solid line.

  • View in gallery

    The time series of (a) visibility, (b) temperature, (c) wind speed, and (d) RHw. The heavy-fog region is shown with the line with a double arrow. The model-based data at 0002 UTC at the Zurich airport are shown with filled circles along the dashed line. The model-based Vis is obtained using K84 parameterization.

  • View in gallery

    The RHw distance–height cross section. The airport is located at about 47 km, represented with a black line.

  • View in gallery

    The temperature distance–height cross section. The airport is represented with a black line at 47 km.

  • View in gallery

    The 3D NMM model 10-h simulation results at 0200 UTC: (a) LWC, (b) Nd, (c) Visfi, and (d) VisK. The black line indicates the airport location at 47 km.

  • View in gallery

    The visibility VisP from the present work and those from Meyer et al. (1980) for light-fog (VisML) and heavy-fog (VisMH) conditions, as a function of Nd.

  • View in gallery

    Visibility vs LWC based on assumed Nd (cm−3) values in Eq. (9). The Vis values within the boxes are for an assumed value of LWC of 0.02 g m−3. The Visobs and VisK are obtained from Eqs. (6) and (8), respectively.

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A New Visibility Parameterization for Warm-Fog Applications in Numerical Weather Prediction Models

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  • 1 Cloud Physics and Severe Weather Research Section, Science and Technology Branch, Environment Canada, Toronto, Ontario, Canada
  • | 2 Institute of Meteorology, Climatology and Remote Sensing, University of Basel, Basel, Switzerland
  • | 3 Department of Earth Systems and Geoinformation Sciences, College of Science, George Mason University, Fairfax, Virginia
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Abstract

The objective of this work is to suggest a new warm-fog visibility parameterization scheme for numerical weather prediction (NWP) models. In situ observations collected during the Radiation and Aerosol Cloud Experiment, representing boundary layer low-level clouds, were used to develop a parameterization scheme between visibility and a combined parameter as a function of both droplet number concentration Nd and liquid water content (LWC). The current NWP models usually use relationships between extinction coefficient and LWC. A newly developed parameterization scheme for visibility, Vis = f (LWC, Nd), is applied to the NOAA Nonhydrostatic Mesoscale Model. In this model, the microphysics of fog was adapted from the 1D Parameterized Fog (PAFOG) model and then was used in the lower 1.5 km of the atmosphere. Simulations for testing the new parameterization scheme are performed in a 50-km innermost-nested simulation domain using a horizontal grid spacing of 1 km centered on Zurich Unique Airport in Switzerland. The simulations over a 10-h time period showed that visibility differences between old and new parameterization schemes can be more than 50%. It is concluded that accurate visibility estimates require skillful LWC as well as Nd estimates from forecasts. Therefore, the current models can significantly over-/underestimate Vis (with more than 50% uncertainty) depending on environmental conditions. Inclusion of Nd as a prognostic (or parameterized) variable in parameterizations would significantly improve the operational forecast models.

Corresponding author address: Dr. Ismail Gultepe, Cloud Physics and Severe Weather Research section, Science and Technology Branch, Environment Canada, Toronto, ON M3H 5T4, Canada. Email: ismail.gultepe@ec.gc.ca

Abstract

The objective of this work is to suggest a new warm-fog visibility parameterization scheme for numerical weather prediction (NWP) models. In situ observations collected during the Radiation and Aerosol Cloud Experiment, representing boundary layer low-level clouds, were used to develop a parameterization scheme between visibility and a combined parameter as a function of both droplet number concentration Nd and liquid water content (LWC). The current NWP models usually use relationships between extinction coefficient and LWC. A newly developed parameterization scheme for visibility, Vis = f (LWC, Nd), is applied to the NOAA Nonhydrostatic Mesoscale Model. In this model, the microphysics of fog was adapted from the 1D Parameterized Fog (PAFOG) model and then was used in the lower 1.5 km of the atmosphere. Simulations for testing the new parameterization scheme are performed in a 50-km innermost-nested simulation domain using a horizontal grid spacing of 1 km centered on Zurich Unique Airport in Switzerland. The simulations over a 10-h time period showed that visibility differences between old and new parameterization schemes can be more than 50%. It is concluded that accurate visibility estimates require skillful LWC as well as Nd estimates from forecasts. Therefore, the current models can significantly over-/underestimate Vis (with more than 50% uncertainty) depending on environmental conditions. Inclusion of Nd as a prognostic (or parameterized) variable in parameterizations would significantly improve the operational forecast models.

Corresponding author address: Dr. Ismail Gultepe, Cloud Physics and Severe Weather Research section, Science and Technology Branch, Environment Canada, Toronto, ON M3H 5T4, Canada. Email: ismail.gultepe@ec.gc.ca

1. Introduction

Fog formation is directly related to thermodynamical, dynamical, radiative, aerosol, and microphysical processes and to surface conditions. Extinction of light at visible ranges within the fog results in low visibilities that can affect low-level flight conditions, marine traveling, shipping, and transportation. Fog occurrence more than 10% of time in some regions of Canada (Whiffen 2001) demands that fog nowcasting and/or forecasting models should be improved. In particular, fog intensity, represented with visibility (Vis), should be more accurately predicted (better than 30%) to reduce the costs of fog-related accidents and to reduce delays at airports and in marine environments (Pagowski et al. 2004).

The prediction of fog using NWP models is important because satellite observations cannot be used accurately during nighttime and when ice and/or snow cover(s) the earth’s surface. Surface observations over the land are also insufficient to determine the true extent of fog (Ellrod 1995). The NWP models for visibility calculations usually use relationships between visibility and liquid water content (LWC). In real atmospheric conditions, however, visibility (extinction of visible light) is related to droplet number and water mass in a given volume of air (Gultepe et al. 2001). Increasing droplet number concentration Nd in warm-fog conditions (T > 0°C) for a fixed LWC results in decreasing visibility. Also, increasing LWC results in decreasing visibility that is currently represented with Vis–LWC relationships in most of the NWP models (Stoelinga and Warner 1999). However, Meyer et al. (1980) and Gultepe and Isaac (2004a) showed that both Nd and LWC should be included in visibility parameterization for warm-fog conditions.

The forecast and cloud models, in general, use the fog microphysical parameterizations developed by Kunkel (1984, K84 hereinafter) that are based on the relationships between extinction parameter βext and LWC. For example, Bergot and Gudalia (1994a, b) used the Couche Brouillard Eau Liquide (COBEL) 1D model for studying fog and used the K84 relationship. The Rapid Update Cycle (RUC) model that is used commonly for numerical forecasting in North America also utilizes the K84 parameterization (Benjamin et al. 2004) for visibility calculations. Stoelinga and Warner (1999) extensively studied extinction of hydrometeors as a function of their condensed water content. Their work was also performed using the K84 parameterization and was used for warm-fog conditions and liquid clouds.

The earlier studies on Nd and LWC relationships showed that there is usually a large variability on Nd for a given LWC (Gultepe et al. 1996; Gultepe and Isaac 2004b). The work by Gultepe et al. (2005) on fog microphysics suggested that Nd can change from a few droplets per volume to 100 cm−3 for a fixed LWC and that visibility should be function of both Nd and LWC. These works indicated that Nd should be considered in visibility parameterizations. Bott and Trautmann (2002) previously developed a model that predicted both Nd and LWC. Under the saturated conditions, the presence of more cloud concentration nuclei leads to the formation of a large number of small droplets (Gultepe and Isaac 1999), resulting in slower gravitational settling of droplets and thus low visibility. As shown by the experimental relation of Jiusto (1981), visibility is directly related to average cloud droplet radius (and hence number concentration) and is indirectly related to LWC. This situation shows that visibility parameterizations should also include number concentration of droplets as an independent variable.

Brown (1980) and Mason (1982) investigated the effect of radiative cooling on droplet growth and the modification of the droplet spectrum and stated the importance of radiative processes in fog development. Bott et al. (1990) and Bott (1991) studied effects of aerosol activation and composition on fog droplet size distribution and LWC. Bott and Trautmann (2002) developed a computationally very efficient 1D fog model with parameterized microphysics based on the detailed microphysical processes studied in Bott et al. (1990) and Bott (1991). The above studies suggested that fog physics is very important and that LWC alone cannot be sufficient to calculate Vis.

Although droplet number concentration can be a prognostic variable in mesoscale models (Rasmussen et al. 2002), the bulk microphysical parameterizations, usually with one or two variables for each hydrometeor category, use predescribed size distributions. Then, mixing ratio is predicted based on assumed size distributions. Rasmussen et al. (2002) used a new microphysical model with 36 bin channels in particle spectra and allowed size distribution to evolve naturally without specifying the spectra shape. Thompson et al. (2004) conducted a comprehensive study on winter precipitation over an idealized two-dimensional mountain to investigate various aspects of a bulk, mixed-phase microphysical parameterization found in the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5), the RUC model, and the Weather Research and Forecast model. They stated that bin models are computationally very expensive and that, for this reason, bin models are not yet viable for real-time operational NWP runs. In their application, Nd was assumed to be 50, 100, 200, and 500 cm−3 to calculate the cloud water mixing ratio for mass conversion.

Currently, Nd is fixed as 100 cm−3 in RUC applications [J. Brown, National Oceanic and Atmospheric Administration (NOAA), 2005, personal communication], and, therefore, Nd could not be considered as an independent variable for visibility applications. In a similar way, the Canadian operational Global Environmental Multiscale (GEM) model (Mailhot et al. 2002) also did not have a prognostic equation for Nd or a fixed value for microphysical scheme; however, it is fixed for the radiation scheme (J. Milbrandt 2005, personal communication). Note also that high-resolution NWP models based on two-moment bulk schemes could predict Nd and LWC independently, and then both parameters can be used for visibility calculation at each time step. On the other hand, Nd was usually calculated as a prognostic variable in fog/cloud models (Müller et al. 2005).

In the present work, a new parameterization scheme for warm-fog visibility as function of both LWC and Nd is suggested and is applied to a nonhydrostatic mesoscale model with a detailed microphysical scheme to show the difference in visibility calculation based on old and new parameterization schemes. The detailed microphysics of the 1D Parameterized Fog (PAFOG) model (Bott and Trautmann 2002) was incorporated and fully coupled with the 3D Nonhydrostatic Mesoscale Model (NMM) of the NOAA National Centers for Environmental Prediction (NCEP) (Janjic et al. 2001; Janjic 2003).

2. Observations

Observations used to develop a new microphysical parameterization for warm fog were collected during the Radiation and Aerosol Cloud Experiment (RACE), representing boundary layer low-level clouds (Gultepe et al. 2001), that took place over eastern Canada during the months of August and October in 1995. During the field program, some low-level clouds with base heights lower than 100-m height occurred. Although fog was also observed over the Atlantic Ocean, observations were limited to higher levels within the clouds because of flight restrictions.

The main in situ measurements such as Nd and droplet size, aerosol number concentrations Na, LWC, temperature T, and relative humidity RHw were collected by the Forward-Scattering Spectrometer Probe (FSSP), Particle Cavity Axial Spectrometer Probe, hot-wire probes (e.g., King Probe), Rosemount T probe, and EG&G dewpoint hygrometer, respectively, over 16 flights that represented low-level clouds with various airmass origins. Concentration Nd was obtained using the FSSP-100 with original size range (2.1–48.4 μm; FSSP-96) and extended size range (4.6–88.7 μm; FSSP-124). Microphysical parameters such as Nd, LWC, and extinction parameters were directly obtained using in situ observations collected along constant-altitude flight legs and aircraft profiles. To represent important scales related to fog formation, measurements were averaged over 1-km scale. Additional information on observations can be found in Gultepe et al. (1996).

Observations obtained from surface instruments nearby the Zurich Airport such as Vis, T, wind speed, and RHw on 28 November 2004 were also used to validate the NMM 3D simulations. The low visibility of less than 100 m (measured with a Belfort visibility meter) occurred between 2200 and 0600 UTC, during which period RHw reached 100%. Heavy-fog conditions were observed along this time period over the airport area.

3. Fog microphysical model

The current operational NWP models cannot resolve processes that play an important role in fog formation, mainly because of coarse vertical grid resolution (e.g., ∼50 m near the surface) and oversimplified cloud microphysics. In these models, excessive cooling is very common during nighttime when the vertical resolution is increased to resolve better the boundary layer (Müller et al. 2005). The development of a very strong surface inversion is mostly related to the turbulence scheme that underestimates mixing under stable conditions that are typical for radiation fog. To overcome such problems, a revised turbulence scheme (Müller et al. 2005) and the detailed microphysics of the 1D PAFOG model (Bott and Trautmann 2002) were incorporated and fully coupled with the 3D NMM from NOAA/NCEP (Janjic 2003). The PAFOG microphysics is limited to the lower 1.5 km of the atmosphere and replaces the condensation/evaporation of cloud water in the precipitation with the cloud physics scheme of Ferrier et al. (2002).

In the model, liquid water content is a prognostic variable, and, once it forms, it is transported by both turbulence and advection. In addition, droplet number concentration is introduced as a prognostic variable to the NMM. Overall, both Nd and LWC change as a function of advection in the horizontal and vertical directions, sedimentation, and phase changes, as well as activation and condensation/evaporation processes.

A lognormal droplet size distribution with dispersion parameter of 0.2 is assumed in the calculations. Details on the microphysics of this work can be found in Bott and Trautmann (2002). For 3D simulations in complex topography, a 50-km innermost-nested domain with a horizontal grid resolution of 1 km centered at Zurich Unique Airport in Switzerland is used. The vertical grid uses 45 levels, with 27 covering the lowest 1 km above the ground. In the soil, 11 layers are used for heat and moisture equations, where the first layer has a thickness of 0.25 cm. This grid structure is chosen to resolve the small-scale effects on boundary layer processes. Initial and hourly boundary conditions for the 3D fog simulation are derived from the NMM forecasts with 4-km spacing. The 4-km grid was nested into a 22-km grid covering Europe driven by the Global Forecast System model.

4. Method and parameterization development

a. Summary of visibility calculation

From the in situ observations collected during RACE, LWC, Nd, and the extinction parameter βext are used to obtain a relationship between Vis and Nd and LWC, and then Vis = f (LWC, Nd) is derived. The extinction parameter was calculated from FSSP probe measurements as follows:
i1558-8432-45-11-1469-e1
where n is the number density of particles in a bin size as radius r and Qext is the Mie extinction coefficient; Qext is related to number concentration, particle radius, and wavelength of visible light. When drop size increases to larger than about 4 μm, Qext becomes 2. It fluctuates between 3.8 and 0.9 for particle sizes of less than 4 μm (Koenig 1971; Brenguier et al. 2000). The extinction parameter is converted to Vis using an equation given by (Stoelinga and Warner 1999) as
i1558-8432-45-11-1469-e2

b. Parameterization of visibility versus either Nd or LWC

The new parameterization is developed after showing the relationships between Vis and LWC, and between Vis and Nd. Figure 1 shows LWC obtained from hot-wire probes versus Nd that is based on FSSP-100 measurements with original size range (2.1–48.4 μm; FSSP-96) and extended size range (4.6–88.7 μm; FSSP-124). The LWC increases with increasing Nd, but, for a given LWC, Nd changes from a few droplets per volume up to 100 cm−3. The fitted lines in Fig. 1 for FSSP-96 and FSSP-124 are given as
i1558-8432-45-11-1469-e3
and
i1558-8432-45-11-1469-e4
respectively. The root-mean-square error (rmse) and mean relative error (mre) in LWC estimation are 0.02 g m−3 and 76%, respectively, indicating large variability in the observations. The fits to the FSSP data show significant differences related to their size ranges; here, the FSSP96 observations were considered in the calculations because of the existence of small fog droplets (<50 μm). This size range was also used in Meyer et al. (1980).
Figure 2 shows Vis versus Nd obtained from the FSSP (with original size range) measurements and a fit to data. This figure also shows that Vis decreases quickly while Nd increases for Nd < 100 cm−3 and then decreases gradually for Nd > 100 cm−3. Its equation for observations (Visobs) is obtained as
i1558-8432-45-11-1469-e5
with a correlation coefficient of R = 0.85, and the rmse and mre in Vis estimation are 18 m and 46%, respectively. Large changes in Vis occur when Nd changes from a few droplets up to 100 cm−3. Above 100 cm−3, Vis becomes less than 100 m.
Figure 3 shows both Vis versus LWC and Vis versus ice water content (IWC) for reference. It is seen that variability in Vis as a function of condensed water content is comparable to the variability in Vis as a function of Nd shown earlier. The fit for Vis (Visobs) versus LWC based on observations is obtained as
i1558-8432-45-11-1469-e6
The Visobs (Fig. 3) becomes smaller at LWC >0.03 g m−3 relative to the K84 fit (VisK) and becomes larger at LWC <0.03 g m−3. The rmse and mean relative error in Vis estimation are about 37 m and 44%, respectively.

c. The K84 visibility parameterization as a function of LWC

The VisK parameterization was also based on FSSP measurements in the size range of 0.5–45 μm. The parameterizations for extinction coefficient βext versus LWC from K84 and versus IWC from Stoelinga and Warner (1999) are given, respectively, as
i1558-8432-45-11-1469-e7a
and
i1558-8432-45-11-1469-e7b
where βext and LWC have units of inverse kilometers and grams per cubic meter, respectively. Then, βext from Eq. (7a) is converted to VisK using Eq. (2). After conversion, VisK versus LWC is obtained as
i1558-8432-45-11-1469-e8
Equation (8) is commonly used for visibility parameterization in many operational forecast models.

d. New visibility parameterization as a function of both LWC and Nd

Using information that Vis decreases with increasing Nd and LWC as shown in Figs. 2 and 3, a relationship between Visobs and (LWC × Nd)−1 is investigated. Then, as described in Gultepe et al. (2005), Vis is parameterized as a function of both Nd and LWC (Fig. 4), because Vis is also a strong function of Nd. The power fit to observed visibility versus xfi (fog index) is defined as (LWC × Nd)−1 and is obtained as
i1558-8432-45-11-1469-e9
This fit indicates that Vis is inversely related to both LWC and Nd. The rmse and mre in Vis estimation are 37 m and 44%, respectively. The larger values of xfi (corresponding to Vis > 100 km) suggest that variability (and also problems in measurements) in Vis increase with increasing xfi, and this increase can be related to uncertainties in the observations at small values of LWC < 0.005 g m−3. The maximum limiting LWC and Nd values used in derivation of Eq. (9) are about 400 cm−3 and 0.5 g m−3, respectively. The minimum limiting Nd and LWC values are 1 cm−3 and 0.005 g m−3, respectively. The results can be extended down to 0.001 g m−3 because of averaging used in deriving Eq. (9).

In the next section, Eqs. (8) and (9) are used in the NMM 3D fog model (Müller et al. 2005), with detailed microphysics from the 1D PAFOG model (Bott and Trautmann 2002), to study a fog case at the Zurich Unique Airport in Switzerland. The parameterizations are tested at this airport because of availability of surface observations and the model setup over an inhomogeneous terrain.

5. Results

The main results of this study are related to the 3D fog model response to the previous and new parameterization schemes. Here, general observations related to fog formed at the Zurich Unique Airport are summarized and then the effect of the new parameterization scheme on visibility calculations in 3D NMM model is emphasized. Details on this case and information on both the microphysics and turbulence parameterizations of the 3D NMM can be found in Müller et al. (2005) and Bott and Trautmann (2002).

Surface observations from a nearby ground station close to the airport and model-based output at 0002 UTC (shown as circles) are summarized in Fig. 5. Figure 5a shows that during the heavy fog time period, Vis was about 100 m and was comparable with a model-based value of 200 m. The difference between them likely occurred because of the underestimation of Nd from the model. Temperature T increased gradually from 0°C at 0000 UTC to 1.5°C at 0200 UTC (Fig. 5b). Model-based T (−2°C) was comparable to the observed T (0°C). The fog lifted shortly after sunrise, likely as a result of solar radiative heating, indicated with increasing T at the surface. During the heavy-fog conditions, wind speed ranged between 2 and 6 m s−1 (Fig. 5c). The observed and model-based RHw were close to 100% during heavy-fog conditions (Fig. 5d).

The LWC values obtained from a prognostic equation using the 3D NMM model were used to calculate Vis values that were related only to LWC (K84) and to both Nd and LWC (called xfi index). The NMM 10-h forecast valid at 0200 UTC 28 November 2004 is summarized for the Zurich Unique Airport. The fog at the airport area on this day likely formed because of radiative cooling; however, the complex terrain resulted in cold-air drainage flows from the mountains into the “valleys,” which also contributed to the fog formation.

Figure 6 shows that RHw is close to saturation at levels below 600 m. The Zurich Unique Airport is located at 47 km approximately along the south-to-north cross section. The finescale fluctuations of RHw are seen in this figure, indicating the large variability in the moisture field. The T cross section corresponding to RHw values is shown in Fig. 7. The details on boundary layer processes used in this simulation can be found in Müller et al. (2005). The fog is seen below 600 m in this figure where T ranges from 0° down to −2°C.

Figure 8 shows the distance–height cross section of LWC, Nd, and Vis values calculated using Eq. (8) (K84: VisK; Fig. 8d) and using Eq. (9) (new parameterization: Visfi; Fig 8c). The LWC and Nd values are approximately 0.30 g m−3 and 50 cm−3 at the airport location (x = 47 km), but these values cannot be verified because of a lack of observations at the surface site. Corresponding values of VisK and Visfi are estimated to be about 200 and 100 m, respectively, and both Vis calculations are found to be comparable to observed Vis values of about 150 m (Fig. 5a). This difference indicates that the Vis calculation in the forecasting models should include both Nd and LWC and that their uncertainty is very important in estimating accurate Vis. The large values of model-based Vis are likely due to an underestimation of Nd (Fig. 8b). If Nd is not included in the K84 parameterization, Vis can be either underestimated or overestimated, depending on the microphysical conditions, and this issue is addressed in the discussion section. It suggests that detailed comparisons should be made for various forecasting models. The main difficulty, however, remains in the accurate prediction of both LWC and Nd over complex terrain in a numerical model.

6. Discussion

In this section, issues related to the accurate calculation of Vis for numerical models and observations are discussed and improvements for simulations are emphasized.

a. Vis and Nd relationships

Earlier studies suggested that visibility is indirectly related to Nd. For example, Meyer et al. (1980) showed that Vis is a function of Nd and changes with fog intensity. The Vis values calculated from their equations are described as VisML and VisMH for light-fog and heavy-fog conditions, respectively. As shown in Fig. 9, VisML is larger than Visobs [Eq. (5)] when light-fog conditions occur. In heavy-fog conditions, VisP (the value from the current work) is almost one order of magnitude less than that for the light-fog cases of Meyer et al. (1980). The VisP values are smaller than heavy-fog conditions obtained from the VisMH. The parameterizations of Meyer et al. (1980) for light and heavy fog are given, respectively, as
i1558-8432-45-11-1469-e10
i1558-8432-45-11-1469-e11
It can be seen that visibility according to Eq. (5) decreases much faster than visibilities of Meyer et al. (1980). These differences can be related to uncertainties in Nd measurements in earlier studies or to in situ measurements collected within the low-level clouds. Overall, the results indicate that Nd should be considered in Vis parameterizations as an independent variable.

b. Cold biases at low levels in the simulations

A cold bias with a strong inversion develops in the lowest levels of the boundary layer. This shows that cold biases in high-resolution models (Müller et al. 2005) and operational models (Wilson and Vallée 2002, 2003) should be studied and their consequences should be quantified. In the current study, the cold bias was not an issue, as described in (Müller et al. 2005; Müller 2006). The numerical models can have a large uncertainty in simulating surface temperatures, because of their limitation in representing the stable nocturnal boundary layer (Duynkerke et al. 1999; Bergot et al. 2005). This result shows that, to improve fog forecasting, predicted T values should have accuracy within 1°C of observed T obtained from the surface instruments (Gultepe et al. 2006c); otherwise, a significant difference between model-predicted surface T and observed T can occur, which may affect fog physical characteristics. Note also that uncertainty in vapor mixing ratio observations can be as high as 20%, dependent on T and model type (Gultepe et al. 2006c).

c. Uncertainties in Vis parameterization

Visibility can be calculated from LWC, Nd, f (Nd, LWC), or directly from a droplet spectra that can explicitly be obtained from a high-resolution size bin droplet model or from a bulk microphysical scheme assuming a particle size spectra shape. Table 1 summarizes all of the parameterizations and their relative uncertainties. At present, large-scale models (e.g., RUC) use only LWC as an independent variable, which may result in more than 50% uncertainty in Vis (Fig. 10). Detailed microphysical models can generate droplet spectra explicitly, but, because of high computational cost, they cannot be used even for 1D forecast models. For this reason, visibility calculations should be done using both LWC and total droplet number concentration, and the results can be verified using a 3D detailed cloud microphysical model.

Using Eq. (6), K84 parameterization [Eq. (8)], and Eq. (9), the effect of uncertainties in Nd and LWC on visibility calculation is shown in Fig. 10. It shows that 30% uncertainty in Nd and 15% uncertainty in LWC, assuming that fractional uncertainty in Vis is equal to the sum of the fractional uncertainties in Nd and LWC, results in about 29% uncertainty in visibility values. If Vis is calculated using either the K84 parameterization or Eq. (6), however, then Vis uncertainty can be more than 75% (see Fig. 10). This uncertainty is much worse than the uncertainty in Visfi calculated from Eq. (9), which is a function of both Nd and LWC. In real observations, uncertainty in LWC and Nd can be better than 10% and 30%, respectively, and Visfi [from Eq. (9)] can have an uncertainty better than about 29%. Note that the difference between Visobs [Eq. (6)] and VisK [Eq. (8)] is about 15% (500 m) at lower LWC values (<0.01 g m−3); therefore, Eq. (6) can be used to replace VisK parameterization but not Visfi because of its detailed physics and smaller uncertainty.

d. Uncertainties in microphysical parameters

The LWC and Nd values from the optical probes can include uncertainties of about 15% and 30%, respectively (Baumgardner et al. 1990). If Nd is used as an additional independent parameter in visibility parameterization, then Nd spectra from the FSSP should be obtained accurately. Although the spectra are measured accurately enough for total Nd, changes in the lowest bins of the FSSP can cause significant uncertainty in visibility calculations, and this fact needs to be addressed in future studies. Droplet measurements from a new fog instrument (Droplet Measurement Technologies, Inc., Boulder, Colorado) collected during the Fog Remote Sensing and Modeling (FRAM) project, which took place over the Ontario and Nova Scotia regions of Canada during the winter of 2005/06 and the summer of 2006 (Gultepe et al. 2006b), can be used to validate the results from the current work.

The Nd estimation from temperature measurements can include large uncertainties because of its dependency on other physical (e.g., nucleation) and dynamical (e.g., turbulence) parameters. This possibility shows that the uncertainties may also be related to both RHw and Na, which can be obtained from observational datasets. Using Nd = f (T) (Gultepe and Isaac 2004a) may cause a cold bias in the boundary layer if Nd is underestimated. Because in this case droplets will likely absorb less energy than what it should be, this process may also affect turbulent heat and mass fluxes in the boundary layer. This problem is left for a future study when a new dataset from the FRAM fog project becomes available.

e. Nd–Na relationships

Accurate calculation of visibility requires accurate observations of Nd and therefore Na. If aerosol number concentration can be accurately measured or obtained from model variables, for example, RHw and T, the relationships between Nd and both Na and supersaturation (Bott and Trautmann 2002) can be used in visibility calculations. Gultepe and Isaac (1999) summarized the relationships between Nd and Na for various cloud types for low-level clouds. It is hoped that the new field program (FRAM) can also address this problem so that visibility can be obtained as a function of both LWC and Na from an NWP model. It should be emphasized that aerosols are even harder to model than Nd because there are many unknown sources of all kinds of aerosols. At present, an initial aerosol size distribution typical for rural areas was assumed in the model runs and therefore Nd–Na relationships cannot be used efficiently for fog forecasts.

f. FRAM field program for model simulations and remote sensing retrievals

The new field program FRAM is being performed to develop model parameterizations, validate model simulations, and verify remote sensing retrievals. This project took place over the Ontario region from November 2005 to May 2006 and is continuing into the 2006–07 time period over eastern Canada for marine fog studies. During this field program, extensive measurements of Nd, LWC, and visibility were made, representing various atmospheric conditions. It is expected that new observations will be very useful for fog-related instrument development, model validations, and development of the satellite algorithms.

7. Conclusions

In this work, observations collected within low-level clouds during the RACE field program were used in the analysis of visibility parameterizations. The results are applied to a high-resolution 3D fog model to test the new visibility relations against other formulations. The following six conclusions can be drawn:

  1. The Nd ranges from a few droplets per cubic centimeter up to a few hundred per cubic centimeter for a given LWC, which indicates that visibility should be parameterized as a function of both Nd and LWC.
  2. Uncertainty in a new visibility parameterization based on both LWC and Nd is found to be about 29%, indicating that it still needs to be improved but is much more accurate than that of K84. His work was developed using LWC alone, which caused over-/underestimation of the visibility (by more than 50%) depending on environmental conditions (Fig. 10).
  3. The detailed microphysical scheme adapted from the 1D PAFOG model and used in the 3D NMM fog model significantly improved visibility calculations with the new parameterization. It is also shown by Gultepe et al. (2006a) that the new visibility parameterization was successfully incorporated into the Canadian Mesoscale Cloud Model (MC2), indicating applicability of the new visibility parameterization.
  4. The cloud condensation nuclei can be directly related to Na, which can be used as an independent variable to estimate the effect of aerosols on fog formation in large-scale models. At present, aerosol size distribution is fixed for these simulations, and so Na cannot be used directly for Nd prediction, indicating that better parameterizations are needed.
  5. If Nd is obtained as a function of environmental conditions such as T (Gultepe and Isaac 2004a), more accurate Vis predictions can be made with current operational forecast models without a prognostic Nd. Thus, visibility estimates based on Nd and LWC can be obtained from bulk microphysical schemes used in operational forecast models.
  6. To improve physically based parameterizations of visibility, field projects with detailed microphysical observations and 2D and 3D models with small-scale turbulence and nucleation schemes are needed.

These results suggest that the new visibility parameterization can significantly improve visibility estimates, and additional tests are required using other mesoscale models [e.g., RUC, Operational Multiscale Environment Model with Grid Adaptivity (OMEGA), and GEM models] in the near future in which Nd can be diagnostically obtained from environmental conditions (e.g., temperature; see Gultepe and Isaac 2004a). Additional improvements and validations will also be performed based on the new dataset that will be gathered during the FRAM field program. In the near future, a new three-moment bulk microphysical scheme developed by Milbrandt and Yau (2005), which includes independent predictive equations for the number concentration, mass content, and spectral dispersion for six different hydrometeor categories, will be tested in the GEM model whereby the new visibility parameterization can be directly applied.

Acknowledgments

Funding for this work was provided by the Canadian National Search and Rescue Secretariat and Environment Canada. Some additional funding was also provided by the European COST-722 fog initiative project office. Technical support for the data collection was provided by both NRC, Ottawa, Ontario, Canada, and MSC Cloud Physics and Severe Weather Research Division, Toronto, Ontario, Canada. The authors are also thankful to S. Benjamin, and J. Brown of NOAA, Boulder, Colorado, J. Milbrandt and S. Belair of RPN, Environment Canada, Montreal, Quebec, Canada, B. Ferrier of NOAA, Camp Spring, Maryland, and Dr. W. Jacobs, Langen, Germany, for discussions on cloud microphysical parameterizations related to droplet number concentrations and visibility calculations.

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Fig. 1.
Fig. 1.

The LWC vs Nd from two FSSP measurements from the 1995 RACE field program. The fits are shown by the solid and dashed lines. The Nd96 and Nd124 are for FSSP-96 (over original size ranges) and FSSP-124 (over extended size ranges) observations, respectively.

Citation: Journal of Applied Meteorology and Climatology 45, 11; 10.1175/JAM2423.1

Fig. 2.
Fig. 2.

Visibility vs Nd from the FSSP measurements; each data point represents a scale of 1 km. The solid-line fit is for FSSP96. The V96 and V124 are for FSSP-96 (over original size ranges) and FSSP-124 (over extended size ranges) observations, respectively.

Citation: Journal of Applied Meteorology and Climatology 45, 11; 10.1175/JAM2423.1

Fig. 3.
Fig. 3.

The visibility calculated from FSSP measurements and from K84 Vis–LWC (as cloud water + fog) and Vis–IWC (as cloud ice + fog) relationships. The V96 and V124 are for FSSP-96 (over original size ranges) and FSSP-124 (over extended size ranges) observations, respectively.

Citation: Journal of Applied Meteorology and Climatology 45, 11; 10.1175/JAM2423.1

Fig. 4.
Fig. 4.

Visibility vs f (LWC, Nd) from in situ observations. The fit is shown with a solid line.

Citation: Journal of Applied Meteorology and Climatology 45, 11; 10.1175/JAM2423.1

Fig. 5.
Fig. 5.

The time series of (a) visibility, (b) temperature, (c) wind speed, and (d) RHw. The heavy-fog region is shown with the line with a double arrow. The model-based data at 0002 UTC at the Zurich airport are shown with filled circles along the dashed line. The model-based Vis is obtained using K84 parameterization.

Citation: Journal of Applied Meteorology and Climatology 45, 11; 10.1175/JAM2423.1

Fig. 6.
Fig. 6.

The RHw distance–height cross section. The airport is located at about 47 km, represented with a black line.

Citation: Journal of Applied Meteorology and Climatology 45, 11; 10.1175/JAM2423.1

Fig. 7.
Fig. 7.

The temperature distance–height cross section. The airport is represented with a black line at 47 km.

Citation: Journal of Applied Meteorology and Climatology 45, 11; 10.1175/JAM2423.1

Fig. 8.
Fig. 8.

The 3D NMM model 10-h simulation results at 0200 UTC: (a) LWC, (b) Nd, (c) Visfi, and (d) VisK. The black line indicates the airport location at 47 km.

Citation: Journal of Applied Meteorology and Climatology 45, 11; 10.1175/JAM2423.1

Fig. 9.
Fig. 9.

The visibility VisP from the present work and those from Meyer et al. (1980) for light-fog (VisML) and heavy-fog (VisMH) conditions, as a function of Nd.

Citation: Journal of Applied Meteorology and Climatology 45, 11; 10.1175/JAM2423.1

Fig. 10.
Fig. 10.

Visibility vs LWC based on assumed Nd (cm−3) values in Eq. (9). The Vis values within the boxes are for an assumed value of LWC of 0.02 g m−3. The Visobs and VisK are obtained from Eqs. (6) and (8), respectively.

Citation: Journal of Applied Meteorology and Climatology 45, 11; 10.1175/JAM2423.1

Table 1.

The summary of parameterizations used in this work. The εRel represents relative error calculated using Σ|(xobsxcal)|/ Σxobs, where x represents any dependent parameter.

Table 1.
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