# Fog in heterogeneous environments: the relative importance of local and non-local processes on radiative-adptive fog formation

L. Ducongé, C. Lac, B. Vié, T. Bergot, J. Price

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## To cite this version:

L. Ducongé, C. Lac, B. Vié, T. Bergot, J. Price. Fog in heterogeneous environments: the relative importance of local and non-local processes on radiative-adaptive fog formation. Quarterly Journal of the Royal Meteorological Society, 2020, 146 (731), pp.2522-2546. 10.1002/qj.3783. hal-04950242

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Submitted on 23 Oct 2025

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DOI: 10.1002/qj.3783

RESEARCH ARTICLE

Quarterly Journal of the
Royal Meteorological Society

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RMetS

# Fog in heterogeneous environments: the relative importance of local and non-local processes on radiative-adveptive fog formation

L. Ducongé<fnref n="1" /> | C. Lac<fnref n="1" /> | B. Vié<fnref n="1" /> | T. Bergot<fnref n="1" /> | J. D. Price<fnref n="2" />

**Correspondence**

C. Lac, CNRM, 42 avenue Gaspard
Coriolis, Toulouse, France.

Email: christine.lac@meteo.fr

**Abstract**

A 100 m resolution simulation of radiation fog observed during the Local And Non-local Fog Experiment (LANFEX) was performed over the Shropshire hills (UK) in order to understand the impact of local circulation on valley fog formation. The model correctly resolves all valleys and their different geometries, their associated dynamical features, and the different fog conditions between the measurement sites. Passage of stratocumulus during the night led to fog dissipation and gave the opportunity to study two fog formation stages. In the narrow valleys, fog formed at the valley floor and non-local drainage-flow processes acted to dissipate it. This equilibrium determined the fog optical thickness, which varied within and between valleys. Wider basins were more subject to dense fog conditions (due to local formation) than narrower valleys, where advecting fog events are locally observed through basins overflowing. The largest and most open valley of Jay Barns was impacted by numerous circulations from narrower tributary valleys, and their complex interactions affected fog formation differently between events. The impact of cloud microphysics on the simulated fog is studied by comparing simulations with one-moment and two-moment schemes. The use of a two-moment scheme brings improvements when the prognostic number concentration is used to compute cloud optical properties, meaning that the radiative impact of droplet concentration is greater than its gravitational settling effect.

**KEYWORDS**

complex terrain, drainage flow, high-resolution modelling, radiation fog

# 1 | INTRODUCTION

Fog is defined by the World Meteorological Organization as a weather phenomenon where droplets in suspension cause a reduction in horizontal visibility to less than 1 km. Fog is a high-impact weather phenomenon, particularly for the transport sector, human security and health.

Even though the main ingredients for radiative fog formation are well known (such as clear sky, calm winds and high relative humidity), there are complex interactions between microphysical, dynamical, turbulent, surface and radiative processes, from mesoscale to local scale, which make fog forecasting a challenge for numerical weather prediction models. Effort has been made by the

<footnote n="1">¹CNRM, Université de Toulouse,
Météo-France, CNRS, Toulouse France</footnote>

<footnote n="2">²Met Office Research Unit, Cardington
Airfield, Bedford, UK</footnote>
meteorological community over many years to understand fog processes and correctly forecast fog events.

Numerical studies using a 1D configuration have shown the importance of radiative cooling, turbulent mixing, gravitational settling of droplets, surface processes and advection through forcing terms for fog formation and its life cycle (Brown and Roach, 1976; Musson-Genon, 1987; Duynkerke, 1991; Bergot and Guedalia, 1994; Steenveeld and de Bode, 2018). However the strong assumption of horizontal homogeneity strongly impacts the external forcing computation (Gultepe et al., 2007) through a poor representation of horizontal heterogeneities. Recent 3D simulations at metric resolutions (via large-eddy simulations, LESs) using ideal-case configurations have shown that buildings and trees introduce variability on fog formation time (Bergot et al., 2015; Mazoyer et al., 2017). Thus, fog modelling using real and complex topography still remains challenging.

Cold pools appear to bring a favourable environment for fog formation since they are associated with patches of cold air (Gustavsson et al., 1998). The mechanisms by which they form are not well understood. *Insitu* surface radiative cooling is often cited in areas sheltered by surrounding topography, preventing near-surface turbulent mixing with warm air aloft (Thompson, 1986; Vosper and Brown, 2008). Drainage flows are sometimes cited as sources of cold pools by transport of cold air to low-lying places (Bodine et al., 2009). They occur when the valley cold airmass leads to a horizontal pressure gradient which drives the flow in the down-valley direction (Whiteman and Doran, 1993). Drainage flows are affected by valley width; lateral constrictions are favourable to flow acceleration and enhance turbulent mixing (Zängl, 2004). This is mainly true for narrower valleys which are subject to thermally driven circulations while larger valleys are more influenced by large-scale (LS) winds (Duine et al., 2017). In this way, LS winds and pressure gradient can interact differently with valley winds (Whiteman and Doran, 1993; Banta et al., 2004). However, it is not clear if the transport of cold air down the valley is followed by cooling across the valley floor. Drainage flows are intermittent by nature (Whiteman and Zhong, 2008) and could be destructive to cold pool organization (Zängl, 2005), with an increase of near-surface turbulent mixing associated with both regions of advective warming and cooling across the valley floor (Vosper et al., 2014).

Because of the sheltering mechanism and associated weak dynamics, the lowest isolated places, such as basins, appear to be more favourable to fog formation than broader and open valleys (Hodges and Pu, 2016). However, fog over complex terrain shows an important day-to-day variation and cold pools are not systematically foggy (Müller et al., 2010). Drainage flows affect fog depending on the sign of

heat and moisture advection (Pilié et al., 1975; Fitzjarrald and Lala, 1989) and determine the location and timing of fog formation (Golding, 1993; Choi and Speer, 2006). They can blow above fog layers, changing the strength of the thermal inversion, the entrainment velocity across the fog top and turbulent conditions (Cuxart and Jiménez, 2012), and can even control the fog thickness through complex interactions with cold pools and the ambient flow (Hang et al., 2016).

Taking into account advective forcing from local circulations improves LES results in an idealized configuration (Porson et al., 2011). However, such circulations often have dimensions greater than 1 km, which is the domain size classically used in fog LESs. Simulations at metric resolution over domains of a few tens of km are presently difficult to achieve, due to their high computational cost. To study the dynamical processes generated by heterogeneity in the topography impacting the fog life cycle, a good compromise is to use high-resolution mesoscale simulations (Cuxart, 2015) of about 100 m resolution to capture the valleys and hence the thermally driven drainage flows (Vosper et al., 2013; Vosper et al., 2014).

The present study investigates the complexity of advective effects linked to these local circulations and their impact on fog formation. It will be based on the LANFEX (Local And Non-local Fog EXperiment; Price et al. (2018)) campaign, which was designed to improve our understanding of radiation fog formation. A major preliminary result from LANFEX is that wider and more open valleys are often foggier than narrower valleys, even though nocturnal cooling is more rapid in the latter. In the same way, advecting fog events seem to be more common in the narrowest valleys (in this study, “advecting” or “advective” fog refers to an existing fog transported by non-local processes, and not to “advection” fog). Generally, a high variability in fog conditions between the different valleys was observed.

In addition to dynamical processes occurring over complex terrain, the fog life cycle could be very dependent on its microphysical characteristics, as concluded by Müller et al. (2010). A correct representation of the different microphysical fields by numerical models is challenging. The main production of fog droplets is located where the cooling is a maximum and sustains supersaturation. This cooling is firstly driven by radiative flux divergence at the surface and supports the formation of the first droplets. Once the fog layer is sufficiently dense, it becomes opaque to long-wave radiation and the strongest radiative cooling moves to the fog top. The fog layer becomes nearly moist adiabatic, with the development of top to bottom weak convection (Roach et al., 1976; Duynkerke, 1999; Bergot et al., 2007; Price, 2011). These adiabatic fogs are generally more persistent than optically thin fogs associated with thermally stable conditions. Radiative properties of fog
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layers are closely related to droplet size and concentration and their interactions with radiation (Bott et al., 1990). A two-moment microphysical scheme can represent a prognostic droplet concentration in numerical models. This number is linked to characteristics of cloud condensation nuclei (CCN) on which droplets form (Bott, 1991). Zhang et al. (2014), Stolaki et al. (2015) and Maalick et al. (2016) showed, in 1D or 2D configurations, that an increase in CCN concentration has a positive feedback on the fog deepening and its lifetime due to reduced gravitational settling and additional radiative cooling at its top. More precisely, the accumulation mode of aerosols seems to act as the main mode for fog droplet formation (Boutle et al., 2018). Also the relative importance of reduced sedimentation against increased radiative cooling in the increase of the fog depth is not well established. Our study uses a prognostic representation of a realistic aerosol population with a two-moment microphysical scheme over a real hilly terrain in a 3D high-resolution configuration, in order to better characterize the main local and non-local processes leading to fog formation. The differences between one-moment and two-moment microphysical schemes are also addressed.

The main goal of this study is to answer the following questions:

* What role do local circulations play in fog formation over hilly terrain, and what is the relative importance of local and non-local contributions?

* What are the main contributions of a two-moment microphysical scheme on the radiative fog development?

After a description of the observational and numerical set-up in section 2, the simulation is validated by comparison to observations from different valleys in section 3. A numerical analysis based on cloud water content and potential temperature budgets is then conducted in section 4, to characterize the elements leading to fog formation over the different valleys. Sensitivity tests are then applied in section 5 in order to evaluate the impact of the microphysical parametrizations and fog droplet number concentration over the fog life cycle, before conclusions and perspectives presented in section 6.

# 2 | OBSERVATIONS AND NUMERICAL MODEL

## 2.1 | The LANFEX field experiment

The LANFEX experiment (Price et al., 2018) was designed to study the impacts of local circulations on fog over the

Shropshire region, in western England, a region characterized by small hills and a complex valley network. LANFEX was an extension from the Cold-Air Pooling Experiment (COLPEX; Price et al. (2011)) which was conducted to study nocturnal dynamics in dry cases over the same area. The main objective of LANFEX was to better understand why some air masses can support fog or not, or support different fog characteristics, according to the valley configuration. For this purpose, several valleys with different topographical characteristics were widely instrumented, giving an unprecedented three-dimensional (3D) observational coverage of fog heterogeneities over complex terrain.

Several observation sites were set up across the Shropshire hills (Figure 1): five main sites and eight secondary sites to capture the local meteorological conditions corresponding to different terrain geometries. The first valley, containing the Jay Barns main site, is 10 km wide and open to its northeast and southeast sides, with connections in the northwest and west through smaller valleys. The other main sites are: Whitcott-Keysett (valley oriented west to southeast, 1 to 3 km wide), Skyborry (valley oriented northwest to southeast, 1–1.5 km wide) and Pentre, the narrowest valley (oriented northwest to southeast, a few hundred metres wide). Skyborry valley has a relatively constant width along its axis, but Pentre and Whitcott-Keysett valleys are more variable in width with both basins and narrower regions present. The last main site, Springhill, is situated at the top of a hill at 400 m a.m.s.l. (above mean sea level), mainly to measure LS conditions and to detect whether fog reaches the hilltop.

Main sites (black stars in Figure 1b) were instrumented with towers measuring wind, temperature, relative humidity and turbulent fluxes at different heights: 2, 10, 25 and 50 m at Jay Barns and Skyborry, 2 and 16 m at Pentre and Whitcott-Keysett, 2 and 10 m at Springhill, in addition to surface energy balance, soil characteristics, 2 m horizontal visibility and cloud-base height. A set of dewmeters (Price and Clark, 2014) were deployed at each main site to estimate the total amount of water deposited on the ground, resulting from either droplet turbulent deposition, gravitational settling or dew formation. The smaller secondary sites measured temperature, pressure, relative humidity at 1.2 m, and wind speed and direction at 2.5 m above the ground. All available observations are listed in tables 1 and 2 of Price et al. (2018).

In this study, we focus on the Intense Observation Period (IOP) 12 of LANFEX, during the night of 01–02 October 2015, as the fog showed strong horizontal heterogeneities. In addition to measurements described above, radiosondes were launched at different times (1616, 2002 and 2356 UTC on 01 October, and 0307, 0436, 0604
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<figure><img src="image_7.png" /><figcaption>**FIGURE 1** Domains used for (a) the 500 m simulation and (b) the 100 m simulation. Main sites are in upper-case letters and marked with stars, secondary sites are in lower-case and marked with dots. The colour shading represents the orography (m)</figcaption></figure>

and 0730 UTC on 02 October) from the Jay Barns site. An aerosol spectrometer measured the aerosol particle size distribution between 0.25 and 10 µm. [TYPESETTER: Make µ roman, not italic (and below).] Apart from that, there were no microphysical measurements for this IOP.

## 2.2 | Numerical set-up

To simulate this fog case, we use the non-hydrostatic anelastic research model Meso-NH (Lac *et al.*, 2018) at 100 m resolution. A downscaling method is applied from the Météo-France operational model AROME (Seity *et al.*, 2011; Brousseau *et al.*, 2016) analysis at 1.3 km resolution, used for initial and hourly coupling conditions at boundaries of a 500 m horizontal resolution model, over a domain size of 250 × 250 grid points. The 100 m horizontal resolution model, over 270 × 225 grid points, is nested inside in a two-way interactive mode (Figure 1). A nudging to LS fields from analysis is imposed above 500 m height above ground (the vertical coordinate follows the topography) through an absorbing layer where the prognostic variables are relaxed towards the LS fields, since LS conditions, such as the passage of stratocumulus cloud, are influencing factors in the fog case studied.

Both nested models have 148 vertical levels, with a 1 m vertical grid size for the first 70 m – essential for fog and complex terrain dynamics modelling (Tardif, 2007; Vosper

*et al.*, 2013; Philip *et al.*, 2016). The resolution is stretched above this level up to a vertical grid size of 50 m at 1430 m, which is the model top. The orography data come from the Shuttle Radar Topography Mission (SRTM; Farr *et al.*, (2007)), at resolution 90 m for the 500 m model, 30 m for the 100 m model.

The advection scheme for momentum variables is a centred scheme of fourth-order in space, and a Runge-Kutta time-splitting of fourth-order in time. For the scalar variables, the advection scheme is PPM (Piecewise Parabolic Method) from Colella and Woodward (1984).

The atmospheric model is coupled with the Interaction between Soil Biosphere and Atmosphere (ISBA) surface scheme (Noilhan and Planton, 1989) through the EXternalized SURFace (SURFEX) model (Masson *et al.*, 2013). Surface cover data are provided by the Corine Land Cover program (Büttner and Eiselt, 2013) at 100 m horizontal resolution.

Meso-NH uses a turbulent scheme with a prognostic TKE (Cuxart *et al.*, 2000), in a 1D mode with the Bougeault and Lacarrere (1989) mixing length at 500 m resolution, and in a 3D mode with the Deardorff (1980) mixing length at 100 m. Considering an effective resolution around 5 Δx as a function of numerical schemes (Lac *et al.*, 2018), most of the eddies are parametrized at 100 m resolution in a stable boundary layer.

To take into account the dynamical impact of forested areas over the Shropshire hills, a drag approach, developed in Aumond *et al.* (2013), is used instead of a traditional
roughness length, as the first vertical levels are located below the height of the trees (15 m considered). The drag force acts as an additional sink term in the momentum and TKE equations and has already been used in fog simulations (Mazoyer *et al.*, 2017).

The microphysical scheme is the two-moment Liquid Ice Multiple Aerosol (LIMA) scheme (Vié *et al.*, 2016) considering prognostic droplet and drop concentrations and a multimodal aerosol population, with a detailed treatment of aerosol-cloud interactions. Each CCN mode is defined by its chemical composition and nucleation properties. The main processes acting on each CCN mode are included, such as resolved and turbulent transport, below-cloud scavenging by rain, and replenishment by cloud droplet evaporation. The CCN activation rate is computed with a diagnostic of maximum supersaturation, S, which depends on vertical velocity, radiative cooling and available CCNs. For the simulation considered here, a homogeneous initialization with sulphate aerosol concentration of $600 \text{ cm}^{-3}$ was used, with a size distribution centred around the mean diameter of $0.25 \ \mu\text{m}$. This aerosol distribution has been chosen according to aerosol spectrometer measurements at Jay Barns, which count the number of aerosols per size class for sizes higher than $0.25 \ \mu\text{m}$, corresponding to a total aerosol concentration of $300 \text{ cm}^{-3}$ above $0.2 \ \mu\text{m}$. The observed distribution was extrapolated below this minimum measured diameter considering a log-normal distribution leading to a doubling of the measured concentration. No observation about aerosol species was available.

In addition to droplet sedimentation, parametrized by Stokes' law, fog deposition is also included to represent direct capture of droplets by the plant canopies, in a simplistic way as it acts as an additional sedimentation velocity of $2 \text{ cm} \cdot \text{ s}^{-1}$ at the first level for grass and 15 m height for trees (Mazoyer *et al.*, 2017).

The ECMWF radiation code is used to compute the radiative transfer, with the Rapid Radiation Transfer Model (RRTM; Mlawer *et al.*, (1997)) for long-wave radiation and Morcrette (1991) for short-wave radiation. Cloud optical properties for long-wave and short-wave radiation take into account the explicit cloud droplet concentration, according to Savijärvi *et al.* (1997).

For the case-study, the 500 m model run started at 1200 UTC on 01 October 2015, initialized from the AROME analysis, and the nested 100 m model run started at 1800 UTC. Both models ran interactively until 02 October at 1200 UTC. In Price *et al.* (2018), results of a Meso-NH simulation during IOP 12 have already been presented and compared with the Met Office Unified Model results in the same configuration, except that it used one-moment microphysics and subgrid cloud schemes.

# 3 | OBSERVATIONS AND REFERENCE SIMULATION OF IOP 12

## 3.1 | Description of the observed case

One of the characteristics of IOP 12 was a stratocumulus passage between 0000 and 0300 UTC over the whole domain (Figure 2, left column) which led to fog dissipation at Jay Barns, Skyborry and Whitcott-Keysett. This gave the opportunity to study two incidents of fog formation for each site, as fog was seen to re-form at the same sites after the cloudy interlude.

No fog was observed over the Pentre site before the cloudy interlude, but the observed horizontal visibility at 1.5 m reduced to 1.5 km between 2145 and 0000 UTC, while fog formed at 2130 and 2200 UTC at the Jay Barns and Skyborry sites respectively (Figure 3a, dashed lines). The fog was confirmed by visibility less than 1 km at 1.5 m, but was thin with values of downward long-wave (LWD) fluxes almost similar to clear-sky values (Figure 3b), and its formation was also intermittent at Jay Barns with an oscillation in the visibility. This formation occurred with similar near-surface temperatures at the two sites (Figure 3c), but in the presence of different dynamical features: the 10 m wind speed remained generally $\le 0.5 \text{ m} \cdot \text{s}^{-1}$ with varying direction at Jay Barns, while a northwesterly drainage flow was formed over Skyborry with wind speed around $1 \text{ m} \cdot \text{s}^{-1}$ (Figure 3d,e). The flow pattern observed at Pentre was similar to that at Skyborry. For both sites, the formation of drainage flow was accompanied by a sudden near-surface cooling of up to $7 \ ^{\circ}\text{C}$ in 1 hr, followed by a smoother decrease; this could be associated with a microfront type of structure as described by Mahrt *et al.* (2010). At Jay Barns, the near-surface temperature decreased more gradually. A transient dissipation of the fog occurred at Jay Barns between 2230 and 2300 UTC, associated with a near-surface warming of $2 \ ^{\circ}\text{C}$ and an intrusion of a northwesterly flow up to $2 \text{ m} \cdot \text{s}^{-1}$.

The stratocumulus passage was almost the same for all the sites with a sharp LWD flux increase and an increase of visibility, creating more homogeneous near-surface meteorological conditions.

After 0300 UTC, conditions were again favourable for fog formation, but each site responded differently. The LWD flux did not increase at the same rate at Jay Barns and Pentre once the fog appeared. The LWD flux increase started 2.5 hr after fog formation at Jay Barns. It was almost instantaneous at Pentre when visibility decreased below 1 km at 0400 UTC, and was associated with weakening or dissipation of the thermal stratification (not shown), and a small increase in drainage speed from $1.5 \text{ to } 2 \text{ m} \cdot \text{s}^{-1}$. As explained in Price *et al.* (2018), it could be the signature of a well-developed fog that had formed elsewhere in the
<figure><img src="image_8.png" /><figcaption>**FIGURE 2** Time series of vertical profiles of (left) backscatter (SI unit 10,000 sr·km⁻¹) observed by a ceilometer for each main site, and (right) cloud mixing ratio (g·kg⁻¹) simulated in REF at each main site during the night of 1–2 October 2015. Note that ceilometer measurements are not available below 30 m</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>**FIGURE 3** Time series of 30 min moving averages of (a) 1.5 m horizontal visibility (km), (b) surface downward long-wave radiation (W·m⁻²), (c) 2 m temperature (°C), (d) 10 m wind direction and (e) 10 m wind speed (m·s⁻¹), for sites Jay Barns (red), Skyborry (green) and Pentre (blue). Observations are in dashed lines, and results from REF simulation in solid lines. Sunrise is marked by the vertical dashed orange line in (c)</figcaption></figure>

valley and been advected over the site by local circulations. In contrast, fog at Jay Barns and Skyborry formed in a thermally stable and less dynamic environment. Only Springhill remained clear of fog throughout the night, while Whitcott and Skyborry fog conditions were almost similar.

To summarize, the 3D observational approach of fog during IOP 12 of LANFEX showed differences between sites in terms of fog formation and thermodynamic conditions. Over Jay Barns and Skyborry, fog formed first in a calm environment and remained thermally stable and optically thin, while Pentre remained clear but with a reduction of visibility to 1.5 km. After the cloudy interlude,

fog formed over all sites except Springhill, but at different rates. For the Pentre site, the fast increase in the LWD flux, the higher wind speed and the vertical temperature profile suggest that the fog could have been advected from elsewhere.

For this IOP, fog formation appears very site-dependent. A numerical study of this case will now be presented in order to identify the contributions of local versus non-local effects and to explain the differences between the sites.

## 3.2 Validation of the reference simulation of IOP 12

The set-up chosen for the reference simulation (hereafter denoted REF) was detailed in section 2.2. The simulated 1.5 m horizontal visibility is here calculated according to the Koschmieder (1924) equation, linking the visibility to an extinction coefficient function of the droplet size distribution, through the Mie theory applied to spherical particles (Bohren and Huffman, 1983). The main differences between REF and observations are an overestimation of relative humidity in the afternoon (75% instead of 60% observed at 1600 UTC, as shown in figure 9 of Price et al. (2018)), and a 1.5 hr delay on the stratocumulus arrival also present in LS fields. Both errors led to an excess of simulated fog water content and a too large vertical extension of the fog layer up to 0200 UTC over all sites except Springhill (Figure 2). These induce an underestimation of the visibility (Figure 3a), and also a thin fog formation at Pentre where no fog was observed at this time but only a reduction of visibility to 1.5 km. Despite a simulated visibility decrease occurring between 2130 and 2200 UTC at the three sites, the thickening of the fog is simulated at different rates.

The first fog formation is correctly reproduced at Skyborry at 2200 UTC, while it is delayed by about 30 min at Jay Barns. This delayed formation is associated with the stronger simulated northerly flow earlier, leading to higher near-surface temperature than observed, but the visibility lowering is consistent with the reduction of wind speed (Figure 3c-e). At Jay Barns, fog formed within a steady southeasterly flow of about 1 m·s⁻¹, which lasted until 0000 UTC. In contrast to the observations, there is no intrusion of northerly flow once fog forms in the model, and no increase in 1.5 m visibility above 1 km. The influence of such flow on fog formation at Jay Barns will be discussed later.

The direction and speed during the drainage flow onset, and the associated drop in near-surface temperature, are fairly well represented over the narrow valley sites (Figure 3c-e). The stratocumulus delay caused the
drainage to strengthen at Pentre, through prolonged surface radiative cooling on the sloping surfaces.

Conforming to the stratocumulus delay, the second fog formation is fairly well simulated over the Pentre and Skyborry sites in terms of LWD fluxes and thermodynamical fields. The model captures the dynamical characteristics at Jay Barns but fog remains optically too thick compared to observations, leading to an overestimation of near-surface temperature after the cloud cover. Following the overestimation of fog water content before the cloudy interlude, the lower layers remain colder and wetter than observed under cloud cover (not presented here), enhancing the fog thickening for the second event.

Nevertheless, a fairly good agreement with observations was identified in terms of thermodynamic conditions accompanying the different fog formations over the various sites, in addition to the simulated different thickening rates between the sites once visibility decreased below 1 km. This simulation will be used in the next section to explore the processes driving the fog events at the different sites.

## 4 | IMPACT OF LOCAL CIRCULATIONS ON FOG FORMATION

The simulated liquid water path (LWP) is presented in Figure 4 for the first fog event. Valleys appear foggy and the thickest fog is produced in the Jay Barns valley with LWP values up to $50 \text{ g} \cdot \text{m}^{-2}$, while they are less than $1 \text{ g} \cdot \text{m}^{-2}$ at Pentre. Heterogeneities in fog thickness also exist within the valleys. This justifies conducting the analysis over the whole valley system and not just at the instrumented sites. The analysis is based on heat and cloud water budgets in order to separate local and non-local contributions to formation and optical thickening of the fog. We will mainly focus on the Jay Barns, Skyborry and Pentre valleys as Whitcott presents strong similarities with Skyborry in the configuration of the valley.

### 4.1 | Fog in the large open valley of Jay Barns

Vertical profiles of tendencies at the Jay Barns site for both events at formation time are presented in Figure 5a,d for potential temperature and cloud water respectively during the first event, and Figure 6a,d for the same parameters during the second event. The southeasterly flow previously identified over Jay Barns during the first formation sequence has the characteristics of a low-level jet (LLJ) below 35 m height resulting in cold advection up

to $-2 \text{ K} \cdot \text{hr}^{-1}$ over the site. Consequently, fog droplets are mainly produced through the condensation process and there is also a small positive contribution from advective processes within the LLJ, leading to an important total cloud water tendency of up to $0.4 \text{ g} \cdot \text{kg}^{-1} \cdot \text{hr}^{-1}$. Both processes are favourable to a rapid optical thickening over this site. The two sink terms limiting cloud water production in the fog layer are turbulent diffusion below 30 m and deposition of fog droplets onto the surface, brought near the surface by both sedimentation and turbulent processes. The fog layer spreads upwards, associated with a vertical advection of the cold foggy airmass between 30 and 50 m height, where it reaches the northwesterly ambient flow. Evaporation due to entrainment limits the vertical extension of the fog layer which remains constrained within the southeasterly LLJ. Northwesterly winds above 35 m mainly come from the northern valleys and pass above the fog layer at the Jay Barns site (not shown). They are associated with a decrease in total cloud water production in the northwestern part of the Jay Barns valley (Figure 7a), with evaporation at the fog edges (Figure 7b) by advection of warmer air which prevents local formation (Figure 7d). Advection of fog water appears highly variable across the valley (Figure 7c). The rapid fog thickening over the site is explained here by local and non-local contributions, both favourable to a production of fog droplets, but constrained

<figure><img src="image_10.png" /><figcaption>**FIGURE 4** Map of liquid water path (LWP, colour shading) between 0 and 150 m ($\text{g} \cdot \text{m}^{-2}$) from the 100 m resolution model averaged between 2200 and 0200 UTC. Black contours represent the orography, from 100 to 500 m a.m.s.l., every 25 m. The five main sites are marked by black circles. Rectangles show the subdomains used to compute PDF in Figures 11, 12 (solid lines), and 13 (dashed lines indicating basins)</figcaption></figure>
<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /><figcaption>**FIGURE 5** Vertical profiles of budget terms at the three main sites of (a, b, c, bottom axis, Khr⁻¹) potential temperature θ, and (d, e, f, bottom axis, g·kg⁻¹·hr⁻¹) cloud mixing ratio. ADV=advection, COND=microphysical processes, TURB=turbulence, SEDI=sedimentation and surface deposition, RAD=radiative processes and TOT=total tendency. Data are averaged over the formation times of the first fog event: 2200–0000 UTC at Jay Barns and Skyborry, 0000–0200 UTC at Pentre. Zonal, meridional and vertical wind speeds are averaged for the same periods (top axis, m·s⁻¹) and shown by dotted, dashed and dot-dashed lines respectively. For clarity, vertical velocity has been multiplied by 20</figcaption></figure>

in the vertical because of circulations from tributary valleys.

The second period of fog formation shows an influence of a westnorthwesterly flow between the surface and 90 m height over the Jay Barns site, leading to a warm advection and a decrease in the local contribution of fog

water to near-zero values compared to the previous event. This time, fog is mainly brought by advection between 30 and 90 m height, explaining that the fog top reaches 100 m height almost instantaneously, with a total cloud water tendency half that of the first event. The formation at Jay Barns is sensitive to local circulations from the northern
<figure><img src="image_13.png" /><figcaption>**FIGURE 6** As Figure 5, but averaged over the formation times of the second fog event: 0400–0530 UTC at Jay Barns, 0600–0730 UTC at Pentre and Skyborry</figcaption></figure>

tributary valleys, but now with an opposite impact to that
during the first event. Considering the whole valley, flow
from the narrow tributary valleys is from the northwest
towards the southeastern aperture of the valley, and local
(Figure 8b) and non-local (Figure 8c) processes have oppo-
site impacts; regions of local fog formation are subjected
to non-local destruction. On the contrary, fog evaporation
occurs when it is brought through advection. The com-
bination of both processes leads to a loss of cloud water
in the northern part of the valley at the expense of the
southern part, where total cloud water tendency remains

positive (Figure 8a). Because of warmer advective effects
(Figure 8d), the local contribution is generally weaker than
during the first fog event within this valley.

To summarize, local processes are helped by advective
cooling from the southeastern valley aperture and sus-
tain a fast fog growth within the Jay Barns valley for the
first event. Non-local processes are favourable to fog for-
mation over the measurement site also, but are highly
variable throughout the whole valley. Fog formation is at
first constrained in the vertical over Jay Barns because of
a destructive effect from a circulation coming from the
<figure><img src="image_14.png" /><figcaption>**FIGURE 7** Maps showing temporal averages between 2200 and 0000 UTC on 01 October 2015 and vertical averages from the surface to 40 m height, over the Jay Barns valley. Wind vectors and (a) total, (b) condensation and (c) advective tendencies of cloud water (g·kg⁻¹·hr⁻¹). (d) shows advective tendency of potential temperature (Khr⁻¹). The Jay Barns site is marked with a black circle. Orography is shown by black contours, from 100 to 600 m a.m.s.l. every 20 m</figcaption></figure>

northwestern tributary valleys. For the second event, the same circulation blows across the valley and is associated with an advective warming, leading to a weaker local contribution and an advection of the foggy airmass to its southern area. The ability of flows from tributary valleys and surrounding plains to pass through the valley, and to interact with each other, controls the fog characteristics with a high variability from one event to another.

## 4.2 | Fog in the narrowest valley of Pentre

For the first event, the cloud mixing ratio budget shows that fog droplets are advected over the site and evaporated (Figure 5e). This results in a near-zero total cloud water tendency, forming a very shallow fog layer of 20 m depth. This evaporation is supported by a warm
<figure><img src="image_15.png" /><figcaption>**FIGURE 8** As Figure 7, but tendencies are averaged between 0400 UTC and 0530 UTC on 02 October 2015, from the surface to 90 m height</figcaption></figure>

<figure><img src="image_16.png" /></figure>

advection through the fog layer up to 10 K·hr⁻¹ at the surface, with subsidence of warmer air from upper layers within the drainage flow (Figure 5b). This balance exists within the whole valley, but the sign of each component changes: regions of local and non-local formation exist, partially offset by non-local and local processes respectively (Figure 9b,c). Over the main part of the valley, local and non-local effects have opposite effects, which leads to a cloud water production lower than 0.1 g·kg⁻¹·hr⁻¹,

explaining the shallow fog. This is not the case in the basin, in the upstream part of the valley, where an important local formation sustains a total cloud water production of up to 0.15 g·kg⁻¹·hr⁻¹. The fog produced in this basin is then advected down the valley. Drainage flow is associated with a null or positive advective heating along the valley axis, less pronounced than that on surrounding hills, which acts to limit the local formation, or even cause evaporation (Figure 9.d).
<figure><img src="image_17.png" /><figcaption>**FIGURE 9** As Figure 7, but for the Pentre valley with tendencies averaged between 0000 and 0200 UTC on 02 October 2015, between the surface and 20 m height. The Pentre site is marked with a black circle</figcaption></figure>

For the second event (Figure 10), the main difference is that the total cloud water production is generalized to the whole valley with higher values mainly because of local production. The advection of cloud water has a positive contribution near the surface only around Pentre at the basin aperture (Figure 6e and Figure 10c), but has a destructive effect on the local production for the rest of the valley.

Over the specific location of the site, model results for both events confirm observational results from Price *et al.* (2018), but this advective component is linked to the lateral valley constriction in the local topography around Pentre which creates a strengthening of the drainage flow. As in the study of Zängl (2004) for an Alpine valley, the acceleration of the drainage due to the lateral valley constriction is accompanied by a decrease in the height of the flow
<figure><img src="image_18.png" /><figcaption>**FIGURE 10** As Figure 9, but tendencies are averaged between 0600 and 0730 UTC on 02 October 2015, between the surface and 50 m height</figcaption></figure>

and a warm vertical advection from upper layers to the surface. Such subsidence and warming are simulated over the Pentre site (Figures 5b,e), inducing evaporation of the advecting fog, because a part of the airmass at Pentre originates from the surrounding northeast and northwest hills. For the rest of the valley, mainly local processes drive the fog formation and are almost balanced by non-local effects. This non-local destruction is less pronounced during the

second event than during the first, explaining the thicker fog formation after the stratocumulus interlude.

## 4.3 | Fog in the narrow valley of Skyborry

Except near the surface, drainage flow over the Skyborry site is associated with an advective cooling which supports
a local formation of fog during both the first (Figure 5c,f) and the second event (Figure 6c,f). Non-local processes partially oppose the local contribution during the first event and result in half the total cloud water tendency at the Jay Barns site. This behaviour is quite similar over the whole Skyborry valley where fog is mainly produced by condensation, while non-local processes partially offset this local production (not shown). During the second event, a null or positive non-local cloud water contribution appears in addition to local processes, which remains favourable to fog droplet production (Figure 6f), leading to a higher total cloud water production and a higher fog optical thickness than during the first event.

To summarize, model results show that the first fog event in narrow valleys is less developed than in the large valley because of opposite effects of local and non-local processes, while both processes are favourable to a rapid fog growth above the Jay Barns site, with an important contribution from local circulations within the valley. For the second event, the origin of the fog is non-local at Jay Barns, created by the same northwestern circulation which acted to limit the vertical extension of the first fog event, while the local component is weaker than in the first event. It shows that similar circulation results in different fog behaviour between the two events. Non-local processes also have a null or positive contribution at Skyborry, explaining its rapid optical thickening. The site at Pentre is subject to fog overflowing from an upstream basin where fog is mainly produced through local processes, explaining the advective origin shown around the site for both events, as a result of its specific location.

## 4.4 | Relative importance of local and non-local processes

To illustrate the relative importance of local and non-local processes which trigger and affect both fog events around the main sites of LANFEX, probability density functions of the main source terms of the cloud water budget were computed for identified formation periods, over the sub-domains shown in Figure 4. Each point of these domains where fog is present are defined by a value of local (COND) and non-local (ADV) cloud water budget, and resulting scatter plots are presented (Figures 11 to 13) in the form of a fraction of the total number of points in the sub-domain, i.e., normalized by the maximum for an easier comparison.

For the first fog event, most of the points (red colour) around the Jay Barns, Skyborry and Whitcott sites experienced a positive contribution from both local and non-local processes, with the maximum of the distributions centred around +0.05 g·kg⁻¹·hr⁻¹ for both

contributions (Figure 11a,c,d for Jay Barns, Skyborry and Whitcott valleys respectively). However, considering the shape of the distribution for Jay Barns, aligned with the axis where advective tendency is near-zero, this valley experiences rather more local formation than non-local, driving a continuous thickening of the fog. For the narrow valleys, since the shape of their distribution is more aligned with the (dashed) line where both processes balance (but not completely), the local formation around the Skyborry and Whitcott sites is partially balanced by non-local destruction at half the magnitude, resulting in thinner fog in these valleys than in the Jay Barns valley. For these three sites, almost all points are situated above the dashed line, indicating that the total tendency resulting from the sum of the two processes remains positive and favourable to fog growth at different rates. This is not the case around the Pentre site where a non-negligible part of the distribution is located below the dashed line (Figure 11b). A larger fraction of points than in other valleys is subject to a local formation of 0.5 g·kg⁻¹·hr⁻¹ balanced by non-local processes at -0.25 g·kg⁻¹·hr⁻¹, explaining that the fog within this valley remains the thinnest for the first event.

The second event shows that fewer points are subject to non-local destruction in the Pentre valley. The maximum of the distribution is now situated where both processes are favourable to fog formation (Figure 12.b), leading to thicker fog than during the first event. It makes this distribution shape close to that obtained around Skyborry and Whitcott for the first event. For these sites, the non-local sink is reduced compared to the first event and fog is mainly formed through local processes (Figure 12c,d). This is especially the case around Skyborry which becomes the most optically thick fog by the end of the event. At Jay Barns, the distribution is less spread for the second event. The local component shows less extreme values than during the first event, while the non-local one remains the same order of magnitude. There is an almost equivalent distribution between local and non-local formation and destruction, creating a patchy fog behaviour. Around all sites, the maximum of the distribution (red colour) indicates that most of the points are subject to positive contributions from both processes.

Distributions are computed separately for the “basin” regions (i.e., those areas not completely isolated but relatively larger than the rest of the valley considered) in the Pentre and Whitcott valleys (Figure 13), where LWP values are generally higher than the rest of the valley (Figure 4). These show a decrease in the destructive effect from non-local processes, leading to a fog mainly formed through local processes and thicker than in other narrower regions in the valleys. This difference between the basin and the rest of the valley is especially apparent for the
<figure><img src="image_19.png" /><figcaption>**FIGURE 11** Probability density functions normalized by their respective maximum during the first fog formation around the main sites, taking into account only points where cloud mixing ratio is positive between surface and 200 m above ground level (a.g.l.), in domains defined in Figure 4. Tendencies are computed every 5 min between 2200 and 0000 UTC on 01 October 2015 for (a) Jay Barns valley, (c) Skyborry valley and (d) Whitcott-Keysett valley and between 0000 and 0200 UTC on 02 October 2015 for (b) Pentre valley. The pink dashed lines indicate the points where the two processes balance each other</figcaption></figure>

Pentre valley during the first event, while the difference is reduced during the second event when fog is more developed and homogeneous across the valley. In contrast, the downstream largest part of the Whitcott valley experiences a down-valley drainage throughout the night coming from tributary valleys, while this is less the case in the Pentre basin since it is situated in the upstream part of the valley. Thus, for the Whitcott valley, differences between the distribution shapes with the upstream narrower part of the valley are less apparent than in Pentre valley, but still exist with distributions slightly more aligned horizontally for the basin than for the narrower places.

This last analysis shows that, depending on valley geometry, the processes involved are different between valleys and between areas within the same valley. For narrow valleys, the general pattern shows that local formation occurs at valley floors and is partially removed by non-local processes within drainage flows. This non-local destruction is more pronounced in constricted places than basins where drainage is weaker: this is the reason why basins remain foggier than other parts of the valley due to local effects. Such "basin fogs" can overflow downstream,

explaining the non-local origin identified at Pentre for both events. The same process is identified in the Whitcott valley where the basin at the east of the valley is followed downstream by a lateral constriction (not shown).

The sign of the temperature advection associated with drainage flows seems to trigger the local occurrence of fog: over all sites, cold advection is followed by local formation, while a warming effect acts to evaporate fog, but could also be sometimes associated with fog advection. Finally, the scenario seems relatively simple in narrow valleys, summarized by a local formation partially offset by non-local processes. In the largest and open valley (Jay Barns), many circulations from tributary valleys and surrounding plains interact to modulate the fog formation and development, with a high variability for the main contributor to fog dynamics (local or non-local) from one event to another.

The behaviour in the two fog events could be summarized as follows. The first event is characterized by local and non-local contributions favourable to fast fog growth in the largest valley, while balance between the two makes the fog thinner in narrow valleys. Inversely,
<figure><img src="image_20.png" /><figcaption>**FIGURE 12** As Figure 11, but for the second fog formation. Tendencies are between 0400 and 0530 UTC for (a) Jay Barns and between 0600 and 0730 UTC for (b) Pentre, (c) Skyborry and (d) Whitcott-Keysett valleys</figcaption></figure>

for the second event, local production dominates over non-local destruction in narrow valleys, leading to thicker fog after the stratocumulus passage. The influence of LS conditions is suggested to explain the decrease of the non-local destruction in narrow valleys; winds above hills are more oriented from eastsoutheast during the second fog event, in contrast to eastnortheast for the first event (not shown), and could brake the drainage of cold air and associated non-local impacts, within valleys oriented from northwest to southeast, as is Skyborry. In the same way, a pressure-driven channelling effect (Whiteman and Doran, 1993), which results from a valley wind forced by the LS pressure gradient force, could be the reason to explain the stronger drainage during the first event than during the second event. Indeed, pressure gradient force is oriented towards the southeast for the first event, and towards the southwest for the second event (not shown). Banta et al. (2004) showed that the direction of such LS forces could enhance, or reduce, the strengthening of the drainage flow depending on its alignment with the valley pressure gradient driving the drainage flow.

5 | MICROPHYSICAL
SENSITIVITY TESTS

Another objective of this study is to evaluate the contribu-
tion of a two-moment microphysical scheme which explic-
itly predicts the droplet number concentration. Some
microphysical and radiative fields from the REF simula-
tion are presented in Figure 14 for Jay Barns. Although the
absence of microphysical measurements prevents a quan-
titative validation, the droplet number variability through
the fog depth seems realistic (Figure 14a); fog droplet con-
centration is a maximum where radiative cooling allows
CCN activation, first occurring near the surface before
0000 UTC and then moving to the fog top when fog devel-
ops into a well-mixed adiabatic layer (Figure 14b). Sim-
ulated droplet concentrations are in the same range as
those observed in other field experiments, between 50 and
300 cm⁻³ (Wendisch, 1998; García-García et al., 2002; Lu
et al., 2013; Mazoyer et al., 2017). For the second event,
droplet concentration is lower than during the first event
because of a lower number of CCNs available for droplet
<figure><img src="image_21.png" /><figcaption>**FIGURE 13** As Figure 11, but for the basins of (a, b) Pentre valley and (c, d) Whitcott valley. Points are taken between (a) 0000 and 0200 UTC, (b) 0600 and 0730 UTC, (c) 2200 and 0000 UTC, and (d) 0600 and 0730 UTC. (a, c) are for the first fog formation, and (b, d) for the second</figcaption></figure>

formation (Figure14c). This aerosol concentration depletion is caused by two main factors:

(a) a decrease in concentration within valleys during the first fog event through droplet sedimentation and deposition to the surface (from 600 cm⁻³ at 2000 UTC to 150 cm⁻³ at 0400 UTC; Figure 14c), leading to a loss of CCN from the atmosphere, and

(b) the stratocumulus passage which leads to an aerosol concentration depletion in the free atmosphere above hills (from 600 cm⁻³ at 0130 UTC to 250 cm⁻³ at 0500 UTC; not shown).

Sensitivity tests from the REF simulation were performed in order to evaluate the impact of microphysics on the fog life cycle:

* The NRAD simulation, using the same model set-up except for the absence of radiative impact of explicit droplet concentration. Cloud optical depth is then calculated according to Martin *et al.* (1994) without consideration of droplet concentration. This means that the prognostic droplet concentration is taken into account only through the sedimentation process.

* The N300 simulation which uses the one-moment scheme ICE3 (Pinty and Jabouille, 1998) currently used in AROME, from which LIMA was built. It considers a fixed droplet number concentration of 300 cm⁻³, as in the operational configuration. This value also matches the upper bound of droplet concentrations reached with the REF simulation.

* Considering the range of droplet number concentration predicted with simulations using the two-moment scheme (between 50 and 300 cm⁻³), an additional sensitivity test with the one-moment scheme has been performed and considers a constant droplet number of 50 cm⁻³ (N50 simulation).

Figure 15 compares simulations and observations of near-surface LWD flux and mass of water on the surface at Jay Barns and Pentre. Taking into account the droplet concentration in cloud optical properties computing limits the fog thickening. Its transition to an optically thick fog is slower (NRAD compared to REF in Figure 15). After the cloudy interlude, LWD fluxes are strongly reduced in REF while fog immediately reforms in NRAD. In this way, REF
<figure><img src="image_22.png" /><figcaption>**FIGURE 14** Temporal evolution of vertical profiles at Jay Barns of (a) droplet number concentration (cm⁻³), (b) radiative cooling (K·hr⁻¹), (c) total CCN concentration (cm⁻³) for the REF simulation, (d, e) cloud water mixing ratio (g·kg⁻¹) for REF and N300 simulations respectively</figcaption></figure>

brings improvements with more realistic optical thickness at the Jay Barns and Pentre sites.

Results from the two-moment microphysical scheme without the radiative impact of droplet concentration (NRAD) are close to that obtained with the one-moment scheme (N300 in Figure 15a,b). Since no rain was produced

in the NRAD simulation, the droplet number concentration only impacts droplet sedimentation in both NRAD and N300 simulations. For this case, the change in droplet settling speed has much less impact on fog characteristics than the change in radiative properties linked to droplet size.

Decreasing the droplet number concentration to 50 cm⁻³ with the one-moment scheme shows similar results to Boutle *et al.* (2018), with a decrease in optical thickness of the fog layer. Indeed, for the same amount of condensed water, decreasing the droplet concentration results in an increase of the mean droplet diameter and subsequent gravitational settling. The mass of water on the surface shows that the increase in gravitational settling when droplet concentration decreases leads to delay in the increase in LWD flux at the Jay Barns site from 2200 to 2300 UTC in N50 compared to other simulations. It is associated with up to 0.01 mm of water mass on the ground (corresponding to 0.01 litre of liquid water per square metre) more in N50 than in other simulations and observations between 2130 and 2300 UTC (Figure 15c). It leads to an optically thinner fog, with subsequent lower LWC and water mass at the surface after 2300 UTC in N50 than in other simulations. The overestimation of simulated water mass on the surface after 0000 UTC in all simulations, compared to observations, comes from the stratocumulus delay and enhanced simulated fog development at Jay Barns. Such errors are partially offset with N50 because of lower fog water content than in other simulations.

Although the number concentration only impacts the sedimentation process in N50, the fog characteristics are very different from N300. This effect is much stronger than it was between the N300 and NRAD simulations. It is explained by the constant value used in the one-moment scheme, leading to an increase in gravitational settling uniformly through the fog depth when the droplet concentration decreases. On the contrary, though the use of a two-moment scheme shows similar droplet concentrations of 50 cm⁻³ at some locations, such values are not uniform through the fog depth with, for example, values at fog top closer to 300 cm⁻³, associated with weaker gravitational settling and higher fog water content. N50 brings improvements in the fog optical thickness simulated at the Jay Barns site but not at Pentre, showing the importance of considering droplet and aerosol concentration heterogeneities between sites, though they are close to each other and in a similar rural environment. Currently, many numerical models consider a homogeneous droplet concentration for a given environment (i.e., urban, rural or maritime) and cannot fully represent such heterogeneities.

Both at Jay Barns and Pentre, modelled dew formation is visible before 2130 UTC, corresponding to fog formation. The evaporation and evapotranspiration processes
<figure><img src="image_23.png" /><figcaption>**FIGURE 15** Time series of 30 min-averaged surface downward long-wave radiations (W·m⁻²) at (a) Jay Barns and (b) Pentre. Grey shaded areas show measurement uncertainty. (c, d) show time series of mass of water at the ground (mm) at (c) Jay Barns and (d) Pentre. Observation are in black, and simulations in colours</figcaption></figure>

are negligible during the night in near-saturated conditions at the surface. Moreover, the simulated water mass onto the surface is still lower than 0.52 mm, which is the maximum value of the water interception capacity by vegetation canopy in our conditions, excluding runoff to the ground. In this way, dew formation is well predicted by the model over the Jay Barns site before the formation of the first fog droplets, with 0.04 mm of water lost from the atmosphere through this process, while the dew formation rate seems underestimated at Pentre (Figure 15d). More generally, sensitivity to the microphysical schemes is higher at Jay Barns than at Pentre, confirming that the fog at Pentre is mainly driven by dynamics rather than microphysics, in contrast with Jay Barns where local effects are more important.

# 6 | DISCUSSION

The LANFEX climatology (table 3 of Price et al., 2018) shows that fog forms primarily at Jay Barns and Skyborry sites, and is also generally thicker there than at Pentre. As well, advective fogs were more common at Pentre than elsewhere during LANFEX. The fog formation and life cycle during IOP 12 are therefore representative of the

LANFEX fog climatology. Moreover, the LS conditions for this IOP are quite representative of anticyclonic conditions occurring during other IOPs (including IOPs 9, 10 and 11) of LANFEX, associated with an easterly synoptic flow and the development of nocturnal drainage flows in narrow valleys opposing the LS wind.

Results over the LANFEX area are in agreement with previous studies focusing on more pronounced topography, suggesting that they are not specific to the Shropshire hills and indicate a general applicability. Indeed, the fact that narrow valleys are more exposed to drainage flows than large valleys is a known feature over complex terrain (Duine et al., 2017). Such valley circulations are impacted by the local valley geometry; the “near-basin” configuration of the Pentre valley is similar to the configuration studied by Arduini et al. (2017), where a stronger cold pool developed in the upstream basin. In our study, fog forms first in the basin, before reaching the rest of the valley. At the valley constriction, drainage flow accelerates, as shown by Zängl (2004) for an Alpine valley. For the largest valley, circulations are more complex due to numerous apertures resulting in a competition between different circulations. The novel aspect of this work is the evaluation of the impact of such geometry-dependent valley circulations in the generation of fog heterogeneities, considering
<figure><img src="image_24.png" /></figure>

closely located valleys. Finally, it is known that fog over complex terrain shows an important variability at different scales (Müller *et al.*, 2010; Bergot and Lestringant, 2019). The complex interactions between local and non-local processes partly explain the variability of fog between valleys observed during LANFEX.

One of the strengths of the simulations was the use of 1 m vertical resolution up to 70 m above the surface, strongly impacting fog onset and enhancing turbulence near the ground and at fog top. Philip *et al.* (2016) have also shown that fine vertical resolution is crucial to simulate advection-radiation fog by introducing horizontal circulations. A comparison between Meso-NH and Unified Model (UM) over the IOP 12, presented in Price *et al.* (2018), showed that fog is less well represented in UM than in Meso-NH, mainly because of the coarser vertical resolution. The horizontal grid length at 100 m is similar to that used by Vosper *et al.* (2014) over the same area, and allowed the correct representation of local thermally driven circulations. Additionally, numerical schemes such as the fourth-order centred scheme for wind advection combined with the fourth-order Runge-Kutta temporal scheme offered a high effective resolution (around 5 Δx), enhancing the entrainment of environmental air at the fog edges (Lac *et al.*, 2018). High-resolution surface cover and orography maps also brought more realism.

Linked to the fine vertical resolution, a drag approach was used instead of a roughness length in order to better represent the flow dynamics near the ground in the presence of trees. This parametrization had been successfully used by Mazoyer *et al.* (2017) in LES to study the impact of a tree barrier on the fog life cycle. Over Shropshire, tree surfaces contribute to less than 20% of the 100 m resolution domain, considering that the drag force is not applied to subgrid patches of trees. The impact of the tree drag on the fog formation at the different sites was small; a 30 min delay was noticed at Jay Barns on the fog formation and the depth of the fog layer was slightly reduced (10 m on average) at most of the foggy sites, without modification of the rest of the fog life cycle (not shown). This parametrization moved towards a more realistic representation of the vegetation than with a roughness approach, but the effect was limited at the scale of the Shropshire hills due to the coarse horizontal resolution compared to LES.

A key parametrization was the turbulence scheme used in its 3D configuration to represent thermally driven circulations in stable conditions as shown by Goger *et al.* (2018). However, the difference between the 3D and the 1D configuration of the turbulence scheme at 100 m resolution has not been evaluated here as it is not part of the objectives of the study.

A difficulty of the IOP 12 simulation was to correctly simulate the stratocumulus passage. Preliminary tests

have shown that it was necessary to configure the model with a base of the top absorbing layer at 500 m above the ground. This allowed a relaxation towards the LS analyses above this height in order to accurately drive the height and timing of the stratocumulus layer. Another simulation, which tested the same vertical resolution below 500 m height but with the domain extended to 12,000 m height with a relaxation layer above 9,000 m, affected the height and the appearance time of the stratocumulus and consequently the two fog events.

Concerning the microphysics, the aerosol distribution was chosen according to aerosol spectrometer measurements at Jay Barns. As there was no information about their chemical nature, an initial population of sulphate was assumed. A test using organic aerosols did not produce differences in the fog life cycle. Another test halving the CCN concentration had an impact on the dissipation time only at Jay Barns (1 hr earlier), and no impact at the other sites. This corroborates the assumption that microphysics has an impact when fog is driven by local processes, as in the Jay Barns valley, and that aerosol number concentration only modifies fog development and dissipation, in agreement with Zhang *et al.* (2014). On the contrary, in narrow valleys, the fog life cycle is less influenced by microphysics and is mainly driven by non-local processes. Moreover, the choice of one-moment or two-moment microphysics did not impact the fine-scale circulations. This contributes to the robustness of the dynamical analysis and its influence on fog.

The “real-case configuration” approach made it difficult to separate the impact of the different characteristics of the simulation on the circulations. In order to go further in the use of the model as a laboratory, a “semi-idealized” approach could be used as in Sabatier *et al.* (2020) (realistic orography, simplified initialization, no LS forcing) so as to focus on local thermally driven circulations. Beyond that, a complete idealized approach could be useful to study the sensitivity of the local/non-local partition to different valley geometries up to complex tributary valley networks.

This study has shown that radiative fog is mainly driven by advective processes in narrow valleys, and circulations from tributary valleys also operate in the largest one and impact the fog-top height. A 1 m vertical resolution and 100 m horizontal resolution are necessary to capture these circulations, and the 3D approach of the turbulence scheme is also probably essential, although it has not been demonstrated here. So forecasting fog over such hilly terrain remains challenging for lower-resolution operational NWP models. In this framework, a physical downscaling method as proposed by Sheridan *et al.* (2018) should be beneficial to include sidewall sheltering effects leading to lower temperatures on clear and calm nights.
When non-local effects are not predominant, as in the largest valley, microphysical processes become a major factor controlling the fog optical thickening after the formation phase. Therefore, a correct representation of the microphysical processes, through the use of a realistic representation of aerosol-cloud interactions with a two-moment microphysical scheme, appears necessary for fog prediction, and is considered in different NWP models. Consistency is also needed between microphysics and radiation by taking into account the droplet concentration in cloud optical properties.

7 | CONCLUSIONS AND OUTLOOK

This study has presented one of the first high-resolution mesoscale simulations of fog over hilly terrain to improve understanding of fog heterogeneities between valleys with different geometries. A 100 m resolution simulation has been performed with the Meso-NH model over the hilly area of the LANFEX campaign, during IOP 12, in order to analyze the dynamic processes involved in fog formation in different valley configurations. Despite errors from initial and coupling conditions, resulting in the fog developing too quickly, the main features are correctly reproduced, such as drainage flows, the cloudy interlude separating two fog events, the occurrence of fog and the differences in fog conditions between the sites. The numerical simulation has facilitated a greater understanding of the main processes involved in the two fog formation events.

The large, open valley of Jay Barns is subject to numerous circulations and complex interactions between surrounding plains and tributary valleys. These conditions produce fog through both local and non-local processes for the first fog event, and the vertical extension was firstly limited by flow from tributary valleys at 40 m height which passes above the fog layer, causing evaporation at the fog top until 0000 UTC and vertical development. During the second fog event, the same circulation pattern advects fog from tributary valleys over the site between the surface and 90 m height. Although the optical thickness of both fog events are similar over the site, their origins are different: the first is more local than the second which is rather non-local.

Narrow valleys show faster cooling than the large and open valley during the early evening transition creating drainage flows. Such flows act as a limiting factor in the local formation of the fog across the valley floor; non-local processes acted to remove locally formed fog, resulting in optically thinner fog than in the larger valley, particularly for the first event. As suggested by Fitzjarrald and Lala (1989), the sign of heat advection associated with drainage flows affects the fog formation; cold advection

supports local formation while a warming effect limits it, or could even cause fog evaporation. Local formation is enhanced within relatively large areas, such as basins, as illustrated with the 10-year observational results from Hodges and Pu (2016) in Utah, USA. The limiting impact of non-local effects is less pronounced in basins than in narrower places, leading to a denser fog.

The non-local origin of the fog identified in observations over Pentre in Price et al. (2018) results from its specific location at a basin aperture. The site is situated in a valley lateral contraction and subjected to an along-valley flow acceleration, supporting results from Zängl (2004). It leads to a fog overflowing from the upstream basin, which evaporates partly over the site, resulting in an optically thinner fog than that over other sites. The same scenario occurs at the end of Whitcott valley where the valley geometry is similar. A higher resolution observational network would be helpful to better capture such non-local behaviour depending on local valley geometry.

Microphysical sensitivity tests show that the use of a two-moment scheme brings improvements in the simulated fog development, in terms of optical thickness, and realistic vertical structure provided that the explicit droplet number concentration is taken into account when calculating cloud optical properties. Without this, differences in liquid water path between one-moment and two-moment schemes come only from the gravitational settling formulation, and are much smaller in magnitude.

The decrease in the fixed droplet concentration with the use of a one-moment scheme is followed by a decrease in fog water content through gravitational settling of bigger droplets. This is mainly true during the formation phase when optical thickness of the fog is not too strong. This leads to a slower optical thickening, in agreement with Boutle et al. (2018), but does not bring a more realistic optical thickness of the fog at all sites, showing the importance of considering droplet concentration variability in space and time to represent correctly fog optical thickness heterogeneities. The sensitivity to microphysical parametrization seems to be important where the development of the fog is local rather than non-local.

Regarding all of these conclusions, a heterogeneous initialization of aerosols and the use of a multimodal aerosol population could be interesting to investigate. In order to use microphysical measurements for validation, an intercomparison exercise is in progress on IOP 1 of LANFEX, over the flatter region at Cardington (UK), for which microphysical observations are available.

Recent studies of IOP 1 have shown that humidity and wind speed in the residual layer control the optical thickening of the fog (Smith et al., 2018), in addition to the hygroscopic growth and the fraction of CCN activated into droplets (Boutle et al., 2018). Over the same case, Poku
et al. (2019) recently showed, with a two-moment micro-
physical scheme using a single mode of CCN, that the CCN
number concentration has a greater impact on fog water
content than the CCN soluble fraction. The LES intercom-
parison will be helpful to investigate the added value of
the two-moment bulk microphysical scheme LIMA using
a prognostic and multimodal representation of an aerosol
population. In the same way, the use of a prognostic pop-
ulation of CCN will allow study of the impact of their
repartition across Shropshire, through the action of local
circulations, and subsequent impacts on local fog micro-
physical characteristics.

This paper gives a new insight on how fog forms and
develops in a region of complex terrain, in the presence
of different valley geometries. It shows that the use of
high-resolution mesoscale simulations have a great poten-
tial to further our understanding of fog over heterogeneous
regions.

ACKNOWLEDGEMENTS

Our thanks go to the Met Office staff involved in the LAN-
FEX campaign for sharing the discussions and providing
us with the observations of IOP 12. We thank the editor and
the two anonymous reviewers for their detailed comments,
which helped to improve this paper.

ORCID

L. Ducongé https://orcid.org/0000-0003-1514-1925

C. Lac https://orcid.org/0000-0003-0324-3991

T. Bergot https://orcid.org/0000-0002-7704-5974

REFERENCES

Arduini, G., Chemel, C. and Staquet, C. (2017) Energetics of deep alpine valleys in pooling and draining configurations. *Journal of the Atmospheric Sciences*, 74(7), 2105–2124.

Aumond, P., Masson, V., Lac, C., Gauvreau, B., Dupont, S. and Berengier, M. (2013) Including the drag effects of canopies: real case large-eddy simulation studies. *Boundary-Layer Meteorology*, 146(1), 65–80.

Banta, R.M., Darby, L.S., Fast, J.D., Pinto, J.O., Whiteman, C.D., Shaw, W.J. and Orr, B.W. (2004) Nocturnal low-level jet in a mountain basin complex. Part I: evolution and effects on local flows. *Journal of Applied Meteorology*, 43(10), 1348–1365.

Bergot, T., Escobar, J. and Masson, V. (2015) Effect of small-scale surface heterogeneities and buildings on radiation fog: large-eddy simulation study at Paris–Charles de Gaulle airport. *Quarterly Journal of the Royal Meteorological Society*, 141, 285–298.

Bergot, T. and Guedalia, D. (1994) Numerical forecasting of radia-
tion fog. Part I: numerical model and sensitivity tests. *Monthly
Weather Review*, 122, 1218–1230.

Bergot, T. and Lestringant, R. (2019) On the predictability of radiation fog formation in a mesoscale model: a case study in heterogeneous terrain. *Atmosphere*, 10(4), 165

Bergot, T., Terradellas, E., Cuxart, J., Mira, A., Liechti, O., Mueller, M. and Nielsen, N.W. (2007) Intercomparison of single-column

numerical models for the prediction of radiation fog. *Journal of Applied Meteorology and Climatology*, 46(4), 504–521.

Bodine, D., Klein, P.M., Arms, S.C. and Shapiro, A. (2009) Variability of surface air temperature over gently sloped terrain. *Journal of Applied Meteorology and Climatology*, 48(6), 1117–1141.

Bohren, C.F. and Huffman, D.R. (1983). Absorption and scattering by a sphere, Chapter 4 in Absorption and scattering of light by small particles. Wiley, New York, NY.

Bott, A. (1991) On the influence of the physico-chemical properties of aerosols on the life cycle of radiation fogs. *Boundary-Layer Meteorology*, 56(1-2), 1–31.

Bott, A., Sievers, U. and Zdunkowski, W. (1990) A radiation fog model with a detailed treatment of the interaction between radiative transfer and fog microphysics. *Journal of the Atmospheric Sciences*, 47, 2153–2166.

Bougeault, P. and Lacarrere, P. (1989) Parameterization of orography-induced turbulence in a mesobeta-scale model. *Monthly Weather Review*, 117(8), 1872–1890.

Boutle, I., Price, J., Kudzotsa, I., Kokkola, H. and Romakkaniemi, S. (2018) Aerosol–fog interaction and the transition to well-mixed radiation fog. *Atmospheric Chemistry and Physics*, 18(11), 7827–7840.

Brousseau, P., Seity, Y., Ricard, D. and Léger, J. (2016) Improvement of the forecast of convective activity from the AROME-France system. *Quarterly Journal of the Royal Meteorological Society*, 142, 2231–2243.

Brown, R. and Roach, W.T. (1976) The physics of radiation fog: II – a numerical study. *Quarterly Journal of the Royal Meteorological Society*, 102, 335–354.

Büttner, G. and Eiselt, B.L. (2013) CORINE Land Cover. EEA and Eurostat: Luxembourg.

Choi, H. and Speer, M.S. (2006) The influence of synoptic-mesoscale winds and sea surface temperature distribution on fog formation near the Korean western peninsula. *Meteorological Applications*, 13(4), 347–360.

Colella, P. and Woodward, P.R. (1984) The piecewise parabolic method for gas-dynamical simulations. *Journal of Computational Physics*, 54(1), 174–201.

Cuxart, J. (2015) When can a high-resolution simulation over com-
plex terrain be called LES?. *Frontiers in Earth Science*, 3(87).
https://doi.org/10.3389/feart.2015.00087

Cuxart, J., Bougeault, P. and Redelsperger, J.L. (2000) A turbu-
lence scheme allowing for mesoscale and large-eddy simulations.
*Quarterly Journal of the Royal Meteorological Society*, 126, 1–30.

Cuxart, J. and Jiménez, M. (2012) Deep radiation fog in a wide closed valley: study by numerical modeling and remote sensing. *Pure and Applied Geophysics*, 169(5-6), 911–926.

Deardorff, J.W. (1980) Stratocumulus-capped mixed layers derived from a three-dimensional model. *Boundary-Layer Meteorology*, 18(4), 495–527.

Duine, G.J., Hedde, T., Roubin, P., Durand, P., Lothon, M., Lohou, F., Augustin, P. and Fourmentin, M. (2017) Characterization of valley flows within two confluent valleys under stable conditions: observations from the KASCADE field experiment. *Quarterly Journal of the Royal Meteorological Society*, 143, 1886–1902.

Duynkerke, P.G. (1991) Radiation Fog: a comparison of model sim-
ulation with detailed observations. *Monthly Weather Review*, 119,
324–341.

Duynkerke, P.G. (1999) Turbulence, radiation and fog in Dutch stable boundary layers. *Boundary-Layer Meteorology*, 90(3), 447–477.
Farr, T.G., Rosen, P.A., Caro, E., Crippen, R., Duren, R., Hensley, S., Kobrick, M., Paller, M., Rodriguez, E., Roth, L., Seal, D., Shaffer, S., Shimada, J., Umland, J., Werner, M., Oskin, M., Burbank, D. and Alsdorf, D. (2007) The Shuttle Radar Topography Mission. *Reviews of Geophysics*, 45(2). https://doi.org/10.1029/2005RG000183

Fitzjarrald, D.R. and Lala, G.G. (1989) Hudson Valley fog environments. *Journal of Applied Meteorology*, 28(12), 1303-1328.

García-García, F., Virafuentes, U. and Montero-Martinez, G. (2002) Fine-scale measurements of fog-droplet concentrations: a preliminary assessment. *Atmospheric Research*, 64(1-4), 179-189.

Goger, B., Rotach, M.W., Gohm, A., Fuhrer, O., Stiperski, I. and Holtslag, A.A. (2018) The impact of three-dimensional effects on the simulation of turbulence kinetic energy in a major alpine valley. *Boundary-Layer Meteorology*, 168(1), 1-27.

Golding, B. (1993) A study of the influence of terrain on fog development. *Monthly Weather Review*, 121, 2529-2541.

Gultepe, I., Tardif, R., Michaelides, S., Cermak, J., Bott, A., Bendix, J., Müller, M.D., Pagowski, M., Hansen, B., Ellrod, G., Jacobs, W., Toth, G. and Cober, S.G. (2007) Fog research: a review of past achievements and future perspectives. *Pure and Applied Geophysics*, 164(6-7), 1121-1159.

Gustavsson, T., Karlsson, M., Bogren, J. and Lindqvist, S. (1998) Development of temperature patterns during clear nights. *Journal of Applied Meteorology*, 37(6), 559-571. https://doi.org/10.1175/1520-0450(1998)037<0559:DOTPDC>2.0.CO;2

Hang, C., Nadeau, D., Gultepe, I., Hoch, S., Román-Cascón, C., Pryor, K., Fernando, H., Creegan, E., Leo, L., Silver, Z. and Pardyjak, E.R. (2016) A case study of the mechanisms modulating the evolution of valley fog. *Pure and Applied Geophysics*, 173(9), 3011-3030.

Hodges, D. and Pu, Z. (2016) The climatology, frequency, and distribution of cold season fog events in northern Utah. *Pure and Applied Geophysics*, 173(9), 3197-3211.

Koschmieder, H. (1924) Theorie der horizontalen Sichtweite: Kontrast und Sichtweite. *Beitraege zur Physik der freien Atmosphere*, 12, 171-181.

Lac, C., Chaboureau, J.P., Masson, V., Pinty, J.P., Tulet, P., Escobar, J., Leriche, M., Barthe, C., Aouizerats, B., Augros, C., Aumond, P., Auguste, F., Bechtold, P., Berthet, S., Bielli, S., Bosseur, F., Caumont, O., Cohard, J.M., Colin, J., Couvreux, F., Cuxart, J., Delautier, G., Dauhut, T., Ducrocq, V., Filippi, J.B., Gazen, D., Geoffroy, O., Gheusi, F., Honnert, R., Lafore, J.P., Lebeaupin Brossier, C., Libois, Q., Lunet, T., Mari, C., Maric, T., Mascart, P., Mogé, M., Molinié, G., Nuissier, O., Pantillon, F., Peyrillé, P., Pergaud, J., Perraud, E., Pianezze, J., Redelsperger, J.L., Ricard, D., Richard, E., Riette, S., Rodier, Q., Schoetter, R., Seyfried, L., Stein, J., Suhre, K., Taufour, M., Thouron, O., Turner, S., Verelle, A., Vié, B., Visentin, F., Vionnet, V. and Wautelet, P. (2018) Overview of the meso-NH model version 5.4 and its applications. *Geoscientific Model Development*, 11(5), 1929-1969.

Lu, C., Liu, Y., Niu, S., Zhao, L., Yu, H. and Cheng, M. (2013) Examination of microphysical relationships and corresponding microphysical processes in warm fogs. *Acta Meteorologica Sinica*, 27(6), 832-848.

Maalick, Z., Kühn, T., Korhonen, H., Kokkola, H., Laaksonen, A. and Romakkaniemi, S. (2016) Effect of aerosol concentration and absorbing aerosol on the radiation fog life cycle. *Atmospheric Environment*, 133, 26-33.

Mahrt, L., Richardson, S., Seaman, N. and Stauffer, D. (2010) Non-stationary drainage flows and motions in the cold pool. *Tellus A*, 62(5), 698-705.

Martin, G., Johnson, D. and Spice, A. (1994) The measurement and parameterization of effective radius of droplets in warm stratoscumulus clouds. *Journal of the Atmospheric Sciences*, 51(13), 1823-1842.

Masson, V., Le Moigne, P., Martin, E., Faroux, S., Alias, A., Alkama, R., Belamari, S., Barbu, A., Boone, A., Bouyssel, F., Brousseau, P., Brun, E., Calvet, J.-C., Carrer, D., Decharme, B., Delire, C., Donier, S., Essaouini, K., Gibelin, A.-L., Giordani, H., Habets, F., Jidane, M., Kerdraon, G., Kourzeneva, E., Lafaysse, M., Lafont, S., Lebeaupin Brossier, C., Lemonsu, A., Mahfouf, J.-F., Marguinaud, P., Mokhtari, M., Morin, S., Pigeon, G., Salgado, R., Seity, Y., Taillefer, F., Tanguy, G., Tulet, P., Vincendon, B., Vionnet, V. and Voldoire, A. (2013) The SURFEX v7. 2 land and ocean surface platform for coupled or offline simulation of earth surface variables and fluxes. *Geoscientific Model Development.*, 6, 929-960.

Mazoyer, M., Lac, C., Thouron, O., Bergot, T., Masson, V. and Musson-Genon, L. (2017) Large-eddy simulation of radiation fog: impact of dynamics on the fog life cycle. *Atmospheric Chemistry and Physics*, 17(21), 13017

Mlawer, E.J., Taubman, S.J., Brown, P.D., Iacono, M.J. and Clough, S.A. (1997) Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave. *Journal of Geophysical Research*, 102(D14), 16663-16682.

Morcrette, J.-J. (1991) Radiation and cloud radiative properties in the European Centre for Medium Range Weather Forecasts forecasting system. *Journal of Geophysical Research*, 96(D5), 9121-9132.

Müller, M.D., Masbou, M. and Bott, A. (2010) Three-dimensional fog forecasting in complex terrain. *Quarterly Journal of the Royal Meteorological Society*, 136, 2189-2202.

Musson-Genon, L. (1987) Numerical simulation of a fog event with a one-dimensional boundary layer model. *Monthly Weather Review*, 115, 592-607.

Noilhan, J. and Planton, S. (1989) A simple parameterization of land surface processes for meteorological models. *Monthly Weather Review*, 117(3), 536-549.

Philip, A., Bergot, T., Bouteloup, Y. and Bouyssel, F. (2016) The impact of vertical resolution on fog forecasting in the kilometric-scale model AROME: a case study and statistics. *Weather Forecasting*, 31(5), 1655-1671.

Pilié, R., Mack, E., Kocmond, W., Rogers, C. and Eadie, W. (1975) The life cycle of valley fog. Part I: micrometeorological characteristics. *Journal of Applied Meteorology*, 14(3), 347-363.

Pinty, J.-P. and Jabouille, P. (1998). A mixed-phased cloud parameterization for use in a mesoscale non-hydrostatic model: simulations of a squall line and of orographic precipitation, pp. 217-220 in Conference on Cloud Physics: 14th Conference on Planned and Inadvertent Weather Modification, Everett, WA. American Meteorological Society, Boston, MA.

Poku, C., Ross, A.N., Blyth, A.M., Hill, A.A. and Price, J.D. (2019) How important are aerosol-fog interactions for the successful modelling of nocturnal radiation fog? *Weather*, 74, 237-243.

Porson, A., Price, J.D., Lock, A.P. and Clark, P.A. (2011) Radiation fog. Part II: large-eddy simulations in very stable conditions. *Boundary-Layer Meteorology*, 139(2), 193-224.
Price, J.D. (2011) Radiation fog. Part I: observations of stability and drop size distributions. *Boundary-Layer Meteorology*, 139(2), 167–191.

Price, J.D. and Clark, R. (2014) On the measurement of dewfall and fog-droplet deposition. *Boundary-Layer Meteorology*, 152(3), 367–393.

Price, J.D., Lane, S., Boutle, I., Smith, D., Bergot, T., Lac, C., Ducongé, L., McGregor, J., Kerr-Munslow, A., Pickering, M. and Clark, R. (2018) LANFEX: a field and modeling study to improve our understanding and forecasting of radiation fog. *Bulletin of the American Meteorological Society*

Price, J.D., Vosper, S.B., Brown, A.R., Ross, A., Clark, P.A., Davies, F., Horlacher, V., Claxton, B., McGregor, J.R., Hoare, J.S., Jemmett-Smith, B. and Sheridan, P.F. (2011) COLPEX: field and numerical studies over a region of small hills. *Bulletin of the American Meteorological Society*, 92(12), 1636–1650.

Roach, W.T., Brown, R., Caughey, S.J., Garland, J.A. and Readings, C.J. (1976) The physics of radiation fog: I – a field study. *Quarterly Journal of the Royal Meteorological Society*, 102, 313–333.

Sabatier, T., Largeron, Y., Paci, A., Lac, C., Rodier, Q., Canut, G. and Masson, V. (2020) Semi-idealized simulations of wintertime flows and pollutant transport in an Alpine valley: passive tracer tracking. Part II: Passive tracer tracking. *Quarterly Journal of the Royal Meteorological Society*, 146, 827–845.

Savijärvi, H., Arola, A. and Räisänen, P. (1997) Short-wave optical properties of precipitating water clouds. *Quarterly Journal of the Royal Meteorological Society*, 123, 883–899.

Seity, Y., Brousseau, P., Malardel, S., Hello, G., Bénard, P., Bout-
tier, F., Lac, C. and Masson, V. (2011) The AROME-France convective-scale operational model. *Monthly Weather Review*,
139(3), 976–991.

Sheridan, P.F., Vosper, S.B. and Smith, S. (2018) A physically based algorithm for downscaling temperature in complex terrain. *Journal of Applied Meteorology and Climatology*, 57(8), 1907–1929.

Smith, D., Renfrew, I., Price, J.D. and Dorling, S. (2018) Numerical modelling of the evolution of the boundary layer during a radiation fog event. *Weather*, 73(10), 310–316.

Steeneveld, G.J. and de Bode, M. (2018) Unravelling the relative roles of physical processes in modelling the life cycle of a warm radiation fog. *Quarterly Journal of the Royal Meteorological Society*, 144, 1539–1554.

Stolaki, S., Haeffelin, M., Lac, C., Dupont, J.C., Elias, T. and Mas-
son, V. (2015) Influence of aerosols on the life cycle of a radiation
fog event. A numerical and observational study. *Atmospheric
Research*, 151, 146–161.

Tardif, R. (2007). The impact of vertical resolution in the explicit numerical forecasting of radiation fog: a case study,

pp. 1221–1240 in Fog and Boundary Layer Clouds: Fog Visibility and Forecasting. Gultepe, I. (ed.), Springer, Berlin.

Thompson, B. (1986) Small-scale katabatics and cold hollows. *Weather*, 41(5), 146–153.

Vié, B., Pinty, J.P., Berthet, S. and Leriche, M. (2016) LIMA (v1. 0): A quasi two-moment microphysical scheme driven by a multi-modal population of cloud condensation and ice freezing nuclei. *Geoscientific Model Development*, 9(2), 567–586.

Vosper, S.B. and Brown, A.R. (2008) Numerical simulations of sheltering in valleys: the formation of nighttime cold-air pools. *Boundary-Layer Meteorology*, 127(3), 429–448.

Vosper, S.B., Carter, E., Lean, H.W., Lock, A.P., Clark, P.A. and Web-
ster, S. (2013) High-resolution modelling of valley cold pools.
*Atmospheric Science Letters*, 14(3), 193–199.

Vosper, S.B., Hughes, J., Lock, A.P., Sheridan, P.F., Ross, A., Jemmett-Smith, B. and Brown, A.R. (2014) Cold-pool formation in a narrow valley. *Quarterly Journal of the Royal Meteorological Society*, 140, 699–714.

Wendisch, M. (1998) A quantitative comparison of ground-based FSSP and PVM measurements. *Journal of Atmospheric and Oceanic Technology*, 15(4), 887–900.

Whiteman, C.D. and Doran, J.C. (1993) The relationship between overlying synoptic-scale flows and winds within a valley. *Journal of Applied Meteorology*, 32(11), 1669–1682.

Whiteman, C.D. and Zhong, S. (2008) Downslope flows on a low-angle slope and their interactions with valley inversions. Part I: observations. *Journal of Applied Meteorology and Climatology*, 47(7), 2023–2038.

Zängl, G. (2004) A re-examination of the valley wind system in the Alpine Inn Valley with numerical simulations. *Meteorology and Atmospheric Physics*, 87(4), 241–256.

Zängl, G. (2005) Dynamical aspects of wintertime cold-air pools in an alpine valley system. *Monthly Weather Review*, 133(9), 2721–2740.

Zhang, X., Musson-Genon, L., Dupont, E., Milliez, M. and Carissimo, B. (2014) On the influence of a simple microphysics parametriza-
tion on radiation fog modelling: a case study during ParisFog.
*Boundary-Layer Meteorology*, 151(2), 293–315.

**How to cite this article:** Ducongé L, Lac C, Vié B, Bergot T, Price JD. Fog in heterogeneous environments: the relative importance of local and non-local processes on radiative-adveptive fog formation. *Q J R Meteorol Soc.* 2020;146:2522–2546. https://doi.org/10.1002/qj.3783