# Assimilation of Ground-Based Microwave Radiometer Temperature Observations Into a Convective-Scale NWP Model for Fog Forecast Improvement

Guillaume Thomas, Pauline Martinet, Pierre Brousseau, Philippe Chambon, Jean-françois Georgis, Maxime Hervo, Thierry Huet, Ulrich Löhnert, Emiliano Orlandi, Vinciane Unger

► To cite this version:

Guillaume Thomas, Pauline Martinet, Pierre Brousseau, Philippe Chambon, Jean-françois Georgis, et al.. Assimilation of Ground-Based Microwave Radiometer Temperature Observations Into a Convective-Scale NWP Model for Fog Forecast Improvement. Quarterly Journal of the Royal Meteorological Society, 2024, 151 (766), 10.1002/qj.4893. hal-04950317

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https://cnrs.hal.science/hal-04950317v1

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RESEARCH ARTICLE

# Assimilation of Ground-Based Microwave Radiometer Temperature Observations Into a Convective-Scale NWP Model for Fog Forecast Improvement

Guillaume Thomas<fnref n="1" /> ID

Pauline Martinet<fnref n="1" />

Pierre Brousseau<fnref n="1" /> ID

Philippe Chambon<fnref n="1" /> ID

Jean-François Georgis<fnref n="2" />

Maxime Hervo<fnref n="3" />

Thierry Huet<fnref n="4" />

Ulrich Löhnert<fnref n="5" /> ID

Emiliano Orlandi<fnref n="6" />

**Correspondence**

Guillaume Thomas, Centre National de
Recherches Météorologiques, Météo
France and CNRS, UMR 3589, 31100,
Toulouse, France.

Email: guillaume.thomas@meteo.fr

**Funding information**

METEO-FRANCE and ANR through
grant AAPG 2018-CE01-0004; European
Cooperation in Science and Technology,
Grant/Award Numbers: CA18235 PROBE,
ES1303 TOPROF

**Abstract**

During the SOuthwest FOGs 3D (SOFOG3D) campaign, a unique network of eight ground-based microwave radiometers (MWRs) has been deployed over the southwestern part of France in order to improve fog forecasting, among other objectives. Observations have been acquired from mid-autumn to mid-spring 2019/2020 with the aim of assessing the impact of the assimilation of such observations in the Application de la Recherche à l'Opérationnel à Méso-Échelle (AROME-France) numerical weather prediction model during fog conditions. For that purpose, temperature profiles derived from MWR measurements at six different locations have been assimilated for a time period of three months with a three-dimensional variational assimilation system similar to the one used operationally in the AROME-France numerical weather prediction model. Positive impacts on AROME-France one-hour background and analysis have been obtained, as well as statistically significant temperature improvements for up to eight hours of forecast during all weather conditions. Positive impacts are also demonstrated during fog conditions, both for a single case study and statistically for temperature and fog forecast scores over several fog events.

**KEYWORDS**

AROME-France, fog, microwave radiometers, SOFOG3D, variational data assimilation

# 1 | INTRODUCTION

Fog is one of the meteorological phenomena most impactful on the socioeconomic system. Gultepe et al. (2009) relate tens of road-transport casualties over North America to fog conditions. They also mention economic losses in the air-transport sector, which can reach several million euros. This was demonstrated in 2006 during a three-day fog event over Great Britain. Nevertheless, fog forecasts remain very challenging, even with convective-scale

numerical weather prediction (NWP) models, due to local
and highly nonlinear processes taking part in the fog life
cycle. Bergot and Guedalia (1994) also demonstrated that
a good initialization of temperature and humidity is essen-
tial to forecast fog properly.

However, the atmospheric boundary layer (hereafter
ABL) is still the part of the atmosphere most undersam-
pled with current operational networks. In fact, though
satellites provide crucial information, especially in areas
where ground observing systems cannot be deployed, the

<footnote n="1">¹Centre National de Recherches
Météorologiques, Météo France and
CNRS, Toulouse, France</footnote>

<footnote n="2">²Laboratoire d'Aérologie, Université de
Toulouse, Toulouse, France</footnote>

<footnote n="3">³Federal Office of Meterology and
Climatology, MeteoSwiss, Payerne,
Switzerland</footnote>

<footnote n="4">⁴The French Aerospace Lab, ONERA,
Toulouse, France</footnote>

<footnote n="5">⁵Institute for Geophysics and Meteorology,
University of Cologne, Cologne, Germany</footnote>

<footnote n="6">⁶European Centre for Medium-Range
Weather Forecasts (ECMWF), Reading,
UK</footnote>
assimilation of satellite observations is still limited in the ABL (Bouchard et al., 2010; Guedj et al., 2011). This limitation is due to large uncertainties in ground emissivity, relatively broad weighting functions close to the ground, and the presence of clouds potentially affecting satellite measurements. Though new ABL thermodynamic profiling systems have been developed in the past decades and are expected to integrate future operational networks, radiosondes are one of the few observing systems used operationally and capable of profiling thermodynamic variables within the ABL with a high vertical resolution. However, due to their cost, such measurements are usually done only twice a day and solely at a few locations. Over the past couple of decades, emerging ground-based remote-sensing technology has reached industrial maturity, enabling the deployment of ABL profilers for future operational networks. This is the case for ground-based microwave radiometers providing well-resolved temperature profiles at a high temporal resolution within the ABL, as well as information on integrated water vapor (IWV) and liquid water path (Rose et al., 2005). Even if such profiling remote-sensing instruments are good candidates for future operational networks, very few studies have investigated their ability to improve weather forecasts. Nonetheless, Otkin et al. (2011) and Hartung et al. (2011) conducted an Observing System Simulated Experiment (OSSE) by simulating 140 synthetic ABL profilers (Doppler wind lidar, Raman lidar, microwave radiometers (MWRs), and the infrared spectrometer known as the Atmospheric Emitted Radiance Interferometer (AERI)). Forecast improvements in thermodynamic parameters up to 6 hours have been demonstrated, leading to better cumulative rainfall forecasts.

Several studies investigated the assimilation of MWR temperature and humidity profiles during precipitation events (Caumont et al., 2016; He et al., 2020; Qi et al., 2021a, 2021b). Slight positive impacts on intensity and cumulative rainfall have been demonstrated.

However, very few MWR data assimilation studies were focused on fog forecasting. The first study of Vandenberghe and Ware (2002) demonstrated, using a single case study, that fog short-term forecasts are improved when MWR observations, IWV from the Global Positioning System (GPS), and wind profiles from wind profilers are assimilated every 10 minutes within a four-dimensional variational (4D-Var) scheme. Using a 3D-Var scheme with only two assimilation cycles (at 1200 and 1500 UTC) also led to improved fog forecasts, but only during the first hour of forecasting, in contrast to 4D-Var, where the fog layer is maintained over the three hours of the assimilation window.

Paving the way for a direct assimilation of MWR observations, Martinet et al. (2015, 2017) investigated the assimilation of brightness temperatures in a simplified 1D-Var data assimilation scheme. They demonstrated root-mean-square error (RMSE) reductions of up to 50% in the temperature analyses compared with the background ones, with a significant reduction of large temperature overestimations during one winter case study of a highly stable boundary layer in complex terrain. In Martinet et al. (2020), the work of Martinet et al. (2015, 2017) was expanded to humidity and liquid water path (LWP) variables, focusing this time on fog events. Investigating one thin fog case, large temperature errors in the Application de la Recherche à l'Opérationnel à Méso-Échelle (AROME-France) NWP model as well as vertical and temporal errors in the fog life cycle could be corrected in the AROME analyses thanks to the assimilation of MWR observations.

Given the encouraging results presented for the AROME-France NWP model with a 1D-Var system, the present study proposes to go further by assimilating MWR observations within the 3D-Var system of the AROME model during a fog dedicated field experiment.

For that purpose, the first part of this article presents the AROME-France NWP model, as well as the SOuthwest FOGs 3D (SOFOG3D) experimental campaign in which this study takes place. After explaining the method used to retrieve temperature profiles from MWR brightness temperatures, data assimilation experiment setups are detailed in the second part. Then, in the third part, the impact of the assimilation of temperature profiles retrieved from MWR observations is studied. After a focus on the AROME background and analysis, the impact on AROME-France forecasts is investigated for the whole winter season as well as solely during fog conditions. Finally, the last section summarizes the main results of this study and proposes further investigations.

## 2 | DATA AND METHODOLOGY

### 2.1 | The AROME-France NWP Model

AROME-France is a convective-scale limited-area NWP model, used operationally at Météo France since December 2008 (Brousseau et al., 2016; Seity et al., 2011). It is centered over France (Figure 1) and has a horizontal resolution of 1.3 km and 90 vertical levels (the first one being 5 m above the ground level and the top one at 10 hPa). It has a non-hydrostatic dynamical core inherited from the Aire Limitée Adaptation dynamique Développement InterNational Non-Hydrostatic (ALADIN-NH) NWP model (Bubnová et al., 1995), while the physical
<figure><img src="image_2.png" /><figcaption>**FIGURE 1** Example of an AROME short-term 2-m temperature forecast for the closest level to the ground, valid on January 13, 2020 at 0700 UTC (the shaded rectangle represents the SOFOG3D domain). [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

parameterizations come from the MESO-NH NWP research model (Lac *et al.*, 2018; Lafore *et al.*, 1998). AROME-France uses 12 prognostic variables: two for the horizontal winds (u for the zonal wind and v for the meridional one), the temperature T, the turbulent kinetic energy (TKE), two non-hydrostatic variables (p̂ for pressure and d for the vertical momentum), and six specific contents (water vapor q_v, rain q_r, snow q_s, graupel q_g, cloud droplets q_l, and ice crystals q_i). The evolution of these contents is governed by the ICE3 one-moment bulk microphysical scheme (Pinty & Jabouille, 1998). As it is a limited-area NWP model, it requires lateral boundary conditions, which are provided by the Météo France global NWP model Action de Recherche Petite Échelle Grande Échelle (ARPEGE). An hourly cycled 3D-Var assimilation scheme is used to provide the initial conditions for five control variables (the two components of the horizontal wind, the temperature, the surface pressure, and the specific humidity), while the rest of the prognostic variables are adjusted to the updated model fields during the first forecast steps (Brousseau *et al.*, 2016).

Following the formulation of Berre (2000), the AROME-France 3D-Var assimilation scheme uses an isotropic and homogeneous climatological background-error covariance matrix **B**, estimated by Brousseau *et al.* (2011). In order to update the control variables, observations from weather radar (pseudo-profile of relative humidity and Doppler winds: Wattrelot *et al.* (2014);

Montmerle and Faccani (2009)), weather ground stations, satellites, radiosondes, aircrafts, ground GPS, wind profilers, ships, and buoys are used. Long forecasts (up to 51 hours) are launched eight times a day (every three hours from 0000 to 2100 UTC).

## 2.2 | The SOFOG3D Ground-Based MWR Network

### 2.2.1 | Instrument and Locations

Thanks to the SOFOG3D project, a large set of instruments has been deployed in order to improve fog life-cycle knowledge through the observation of fog-related meteorological variables. This experimental campaign took place for a six-month period, from October 2019–May 2020, over the southwestern part of France, a region prone to fog events. Thanks to an unprecedented set of dedicated observations, the SOFOG3D experiment aimed to provide a complete 3D description of the fog layer during intensive observation periods (IOPs). For that purpose, in situ instruments like local ground stations, radiosoundings, and a fleet of unmanned aerial vehicles (UAVs) have been used. In addition, profiling platforms like tethered balloons, Doppler cloud radar, and a network of ground-based MWRs have been deployed.

The six MWRs used in this study are all manufactured by Radiometer Physics GmbH (RPG) and measure brightness temperature (BT) in two spectral bands. The first one (the K band), with channels from 22.24–31 GHz, corresponds to the water-vapor absorption band. It allows the retrieval of information concerning humidity profiles, integrated water vapor, and liquid water path. The second one, related to the oxygen absorption complex (the V band), enables temperature profiling using channels between 51 and 58 GHz. Figure 2 shows the location of the eight MWR units, while Table 1 indicates the exact location and characteristics of the six RPG Humidity And Temperature PROfiler (HATPRO) MWRs used in this study.

### 2.2.2 | Temperature Retrieval

In order to retrieve temperature profiles from MWR brightness-temperature measurements, a neural network developed by the RPG manufacturer has been used.¹ The neural network has been trained with 25,000 profiles extracted from 3 years of AROME-France one-hour forecasts representative of the whole year. By means of a radiative transfer model, simulated brightness-temperature spectra have been obtained, which are used in order to
(a)

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

(b)

<figure><img src="image_5.png" /><figcaption>FIGURE 2 Positions of observations used within the present study. (a) SOFOG3D MWR network over the southwestern part of France. Red crosses indicate temperature and humidity MWR profilers, the blue cross a temperature MWR profiler, and the yellow one a humidity MWR profiler (from Martinet et al., 2022). (b) Visibilimeter network over the southwestern part of France (blue crosses) and positions of radiosonde launches dedicated to the SOFOG3D observation campaign. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

<table><caption>TABLE 1 Name, location, and characteristics of the six MWRs deployed during the SOFOG3D experiment and used in the present study. For more details, the reader should refer to table 1 of Martinet *et al.* (2022). MWR units specified in gray have not been used in this study.</caption><thead><tr><td>Station</td><td>Lat (°)</td><td>Lon (°)</td><td>Instrument generation</td><td>Expected noise</td><td>Radiometric resolution</td></tr></thead><tbody><tr><td>Agen (AGN)</td><td>44.17</td><td>0.59</td><td>HATPRO G3</td><td>0.5 K</td><td>0.1–0.2 K</td></tr><tr><td>Bergerac (BRG)</td><td>44.82</td><td>0.52</td><td>HATPRO G2</td><td>0.5 K</td><td>0.1–0.2 K</td></tr><tr><td>Biscarrosse (BIS)</td><td>44.37</td><td>-1.13</td><td>HATPRO G5</td><td>0.15 K</td><td>0.07–0.15 K</td></tr><tr><td>Charbonnière (SKO)</td><td>44.42</td><td>-0.59</td><td>HATPRO G5</td><td>0.15 K</td><td>0.07–0.15 K</td></tr><tr><td>Mont-de-Marsan (MDM)</td><td>43.9</td><td>-0.5</td><td>HATPRO G2</td><td>0.5 K</td><td>0.1–0.2 K</td></tr><tr><td>Toulouse-ONERA (TON)</td><td>43.51</td><td>1.47</td><td>HATPRO G2</td><td>0.5 K</td><td>0.1–0.2 K</td></tr></tbody></table>

find the optimal transfer function of the neural network. With this method, several variables and three types of temperature profiles can be retrieved but, in the present work, only temperature profiles optimized for the ABL are retrieved (profiles available every 10 minutes up to 2500 m with 54 discrete levels). In fact, humidity profiles are not well resolved from MWRs only, as the degree of freedom for the signal is only 1. Martinet et al. (2020) already demonstrated the limited impact of humidity on the analyses with the assimilation of MWR observations. However, temperature within the ABL is poorly constrained with the current operational network. Thus, most of the benefit we can expect from MWRs should come from the assimilation of the ABL temperature profiles. More details on the MWR products and the retrieval algorithm used in this study can be found in Martinet *et al.* (2022). Figure 3 shows that bias and RMSE values between MWR temperature profiles and co-located radiosondes typically lie between -0.5 and 0.5 K

and are lower than 1.5 K, respectively, in the ABL during SOFOG3D.

Figure 4 shows a comparison between MWR temperature profiles and co-located radiosoundings during an optically thin fog event dissipated by a stratus cloud advection at 0600 UTC. Figure 4 shows that the MWR profile catches the temperature inversion very well at 0530 UTC when fog stays optically thin with a thickness of less than 100 m. At 0530 UTC, a stratus cloud is advected at 200 m. Though the MWR is not able to resolve the temperature inversion located at the base of the stratus cloud, the MWR temperature profile locates the temperature inversion (peak at 500 m) and cooling at the surface well. At 1130 UTC, the fog layer is dissipated by the stratus cloud. The MWR is able to reproduce the temperature warming close to the ground, as well as the elevation of the temperature inversion, very well.
<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /><figcaption>FIGURE 3 Vertical profiles of temperature bias (solid line) and root-mean-square-error (dashed line) for the two MWRs with colocated radiosoundings. Statistics are performed over (a) 50 profiles at Charbonniere and (b) 49 profiles at Agen. Figure adapted from Martinet *et al.* (2022).</figcaption></figure>

3 | TOWARD THE ASSIMILATION
OF MWR OBSERVATIONS: DATA
QUALITY CONTROL AND
ASSIMILATION EXPERIMENT
SETUP

**3.1** **Data Quality Control**

Despite the good quality of retrieved temperature profiles from MWR observations, their accuracy can still be temporarily degraded in the presence of non-meteorological disturbances (radio-frequency interference, birds, aircraft, tethered balloon, ...), precipitation, or wet radome conditions. In order to cope with such situations, several quality controls have been developed. To filter out non-meteorological disturbances, suitable IWV and BT thresholds have been used. Based on the statistical distribution of the IWV 2-minute standard deviation, a threshold of 5 kg·m⁻² has been chosen. Additionally, a 2 K-threshold on the 22.24-GHz BT standard deviation computed using a 2-minute sliding window was used to assure the selection of only trustworthy data.

In order to remove data affected by rain, the MWR rain
detector has been used to remove observations sampled
in the presence of precipitation. To remove data affected
by the deposition of rain droplets on the radome after the
end of a rain event, a final quality control has been con-
sidered. An ad hoc method, based on cumulative rainfall

(RR, measured by the closest operational rain-gauge) was
developed to evaluate the required time for the MWR
radome to be entirely dry. Considering that the MWR
radome can be considered as dry enough when the bright-
ness temperatures reach values with the same order of
magnitude as the ones observed before a precipitation
event, the cumulative rainfall over a 6-hour sliding win-
dow has been used with the following thresholds:

* if $RR_{6h} \ge 5$ mm, 30 minutes of data are removed after the end of the precipitation event;

* if $RR_{6h} < 5$ mm, only 15 minutes of data are removed after the end of the precipitation event.

3.2 | Data Screening

For the sake of simplicity, MWR retrieved profiles have
been assimilated as conventional radiosoundings within
the AROME 3D-Var system assuming a diagonal **R** matrix.
By using a diagonal **R** matrix in the 3D-Var, we make the
assumption that observation errors are not correlated with
each other. In order to respect this hypothesis and assimi-
late MWR temperature profiles optimally, a thinning of the
high resolution temperature profiles retrieved from MWR
observations can be proposed.

To that end, the expected vertical resolution of a MWR
temperature profile is investigated. It is important to note
that the quantitative estimation of the vertical resolution
<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>FIGURE 4 (a) Cloud radar reflectivity during the fog and stratus cloud advection on December 6, 2019. Bottom panels: temperature profile measurement observed at Charbonnière by radiosounding (black line) and MWR (blue line) at (b) 0526 UTC and (c) 1133 UTC. For both panels, time is defined in UTC and height as altitude above ground level. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

of retrievals obtained from passive instruments depends on the metrics used. In the context of ground-based MWR, several methods have been used for that purpose. For instance, Turner and Löhnert (2021) use the cumulative degrees of freedom of signal, while Hewison (2007) and Blumberg et al. (2015) propose a method based on the diagonal of the averaging kernel matrix. On the other hand, the use of the inter-level error covariance method tends in favor of a thinner vertical resolution, as shown by Liljegren et al. (2005) and Cimini et al. (2006).

Alternatively, the Desroziers diagnostic (Desroziers et al., 2005), commonly used in the satellite data community, has never, to our knowledge, been used for

ground-based instruments. It is an a posteriori diagnostic that uses the analysis residuals $d_a^o$ (corresponding to the distance between the observation and the analysis $x_a$) and the innovations $d_b^o$ (corresponding to the distance between the observation and the background $x_b$) to estimate the full R matrix directly:

$$ \mathbf{R} = \mathbb{E}[d_a^o(d_b^o)^T] = \mathbb{E}[(y - \mathcal{H}(x_a))(y - \mathcal{H}(x_b))^T], \quad (1) $$

where y refers to the observation vector, $x_a$ refers to the analysis, $x_b$ to the background, and $\mathcal{H}$ corresponds to the interpolation operator from the model grid onto the MWR vertical grid.
To be able to diagnose the observation-error covariance matrix with the Desroziers diagnostic, a first data assimilation experiment should be run. A first experiment assimilating MWR temperature profiles at the full vertical resolution within the operational AROME 3D-Var using a diagonal **R** matrix has thus been carried out. Then, the expected full **R** matrix has been computed based on the innovations and analysis residuals over the three-month period of the cycled assimilation experiment. Though the Desroziers diagnostic provides an estimation of the full **R** matrix, the current assimilation system used for the AROME model cannot integrate non-diagonal **R** matrices. This is the reason why the Desroziers diagnostic is only used in this study to get an estimation of the observation-error correlations in order to propose a thinning of the high resolution temperature profiles retrieved from MWR observations.

Figure 5 highlights strong correlations between observation errors when these are associated with spatially close observations. For example, if two observations are about 200 m from each other, the correlation between their errors is about 0.7. However, the correlation values decrease and reach 0 for observations separated by 800 m. For larger distances between observations, some low negative or positive correlation values (between -0.05 and 0.1) are observed. They could correspond to artifact correlations, potentially explained by the non fully respect of the assumptions required for the Desroziers diagnostic (the first assumption is based on the independence of the observation and the background errors, while the second one requires exactly specified **R** and **B** matrices to produce the analysis). For a strict thinning, according to Figure 5, observations separated by less than 800 m should be removed before data assimilation. Consequently, only three vertical levels per assimilated MWR profile have been selected for data assimilation trials.

As a result, for the next part of this work, the data thinning step reduces the number of temperature levels used to three, located at about 50, 900, and 1800 m above the ground. As the estimation of the true MWR vertical resolution is dependent on the chosen methodology as well as on atmospheric conditions, the impact of assimilating MWR observations at the full vertical resolution will be compared with the assimilation of thinned MWR profiles in the next sections.

## 3.3 | Data Assimilation Experiment Description

As previously mentioned, an hourly cycled 3D-Var assimilation scheme is used in the AROME-France model. In

order to assess the impact of temperature profiles derived from the SOFOG3D MWR on the AROME-France forecasts, several experiments have been carried out. The first one, considered as the reference (REF), is equivalent to the operational configuration of the AROME-France NWP model. In the second one, called ALLOBS, temperature profiles from the six sites of MWRs have been assimilated at their full vertical resolution. Finally, the THIN experiment is similar to ALLOBS, but thinned MWR temperature profiles, taking into account only three vertical levels per profile, have been assimilated. These experiments have been conducted over a three-month period approximately, from December 1, 2019–March 9, 2020.

For the present work, the AROME-France operational **B** matrix has been used. It is a climatological matrix that has been computed over a 26-day period, using 312 differences between pairs of 3-h range AROME-France forecasts of a six-member ensemble data assimilation scheme (Brousseau *et al.*, 2011). The use of a static **B** matrix means that the information that comes from an observation is always spread the same way, whatever the weather regime, both geographically and between the different control variables. This is one limitation of this study, as Ménétrier and Montmerle (2011) demonstrated that much shorter vertical correlations are observed at low levels during fog compared with clear-sky conditions, as well as strong positive correlations between temperature and humidity in saturated layers. However, though not available at the time of this study, the upcoming upgrade of the AROME assimilation system from a 3D-Var algorithm to an ensemble data assimilation scheme (3D-EnVar: Brousseau *et al.* (2024)) by the end of 2024 should improve the representation of background-error covariances for future studies.

<figure><img src="image_10.png" /><figcaption>**FIGURE 5** Estimated MWR observation-error correlations as a function of the vertical distance between observations based on the Desroziers diagnostic.</figcaption></figure>
As temperature profiles derived from the SOFOG3D MWRs have been assimilated similarly to radiosonde observations, the same diagonal R matrix has been used for both *ALLOBS* and *THIN* experiments and corresponds to the one used for radiosoundings (with values decreasing from about 1.2 K close to the ground to 0.85 K at 720 hPa).

# 4 | IMPACTS OF MWR TEMPERATURE PROFILES ON THE AROME-FRANCE SYSTEM

## 4.1 | Impact on AROME Backgrounds and Analyses

### 4.1.1 | Statistics With Respect to MWR Temperature Observations

Before assessing a potential impact on forecasts, effects of the assimilation of MWR observations on model analyses and the subsequent backgrounds must be investigated to check that the new observations can be assimilated correctly in the model. Figure 6 represents the innovation and analysis residual probability density functions (PDFs) for the *ALLOBS* and *THIN* experiments. The PDF is computed over the three-month period described above. In order for the two figures to be comparable, only the observations assimilated in both experiments have been used to compute these histograms (solely the three vertical levels corresponding to the vertical thinning applied in *THIN* are used here). For the first one (Figure 6a), the innovation

PDF (blue bars) exhibits a Gaussian shape, with a small bias of -0.19 K and observation minus background differences spanning the range -2.5 to 2.5 K. It denotes that, on average, the AROME-France backgrounds are slightly warmer than the MWR observations. In the analysis residual PDF (orange bars), the bias is significantly reduced by about 40%, reaching -0.11 K. Concerning the standard deviation, this drops from 1.10 to 0.39 K. It indicates that the *ALLOBS* analyses are less spread around a state which is, on average, closer to the observations. To a lesser extent, similar results have been obtained with the *THIN* experiment (Figure 6b). Indeed, the innovations present a larger bias of -0.3 K and the assimilation of MWR observations helps to reduce it by about 17% in the analysis residuals (-0.25 K). The standard deviation is also reduced from 1.24 to 0.85 K.

In both experiments, the assimilation of MWR temperature profiles has a positive effect on the analyses. Nevertheless, the *ALLOBS* experiment presents better statistical values, indicating that the analysis is closer to MWR observations compared with the *THIN* experiment. This result is expected, due to the higher number of MWR observations assimilated in the *ALLOBS* experiment. In fact, the analysis increment in *THIN* is driven by MWR observations at only three levels, but also depends on how the *B* matrix spreads the information from other observing systems through the vertical. In contrast, in *ALLOBS*, the assimilation of MWR profiles at the full resolution constrains the analysis consistently through the different levels, enhancing the impact of MWR observations on the analysis increment.

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

**FIGURE 6** Probability density functions of innovation and analysis residuals for (a) *ALLOBS* (left panel) and (b) *THIN* (right panel) experiments. The histograms in blue (respectively orange) represent the “observation – background” differences (respectively “observation – analysis” differences) for the three levels where data are assimilated in both experiments. [Colour figure can be viewed at wileyonlinelibrary.com]
This section demonstrates that MWR observations can be assimilated properly into the AROME-France model. In a second step, it is also important to assess the impact of the assimilation of MWR profiles with respect to other observing systems assimilated in AROME-France. In fact, the improvement of AROME analyses and backgrounds with respect to MWR temperature profiles that are used within the assimilation experiment is rather straightforward if observations are assimilated properly. However, the propagation of this positive impact with respect to other observations, as well as other prognostic variables such as wind, needs to be evaluated to ensure that the assimilation of MWR observations does not bring any degradation to the other observation types. The next sections aim to evaluate the impact of MWR assimilation on AROME backgrounds and analyses with respect to independent radiosoundings and aircraft observations. It is important to highlight that the conclusions might differ between these two independent sources of information, due to the geographical location of aircraft data (mainly Bordeaux and Toulouse airports) with respect to radiosoundings co-located with MWRs deployed at Charbonnière and Agen. Aircraft data are also representative of all weather conditions during the day, while radiosoundings were only launched during conditions prone to fog and mainly by night.

## 4.1.2 | Statistics With Respect to Radiosonde Observations

During the whole SOFOG3D experimental campaign, about 150 radiosondes have been launched from the Agen, Charbonnière, and Toulouse sites (for this last, radiosondes were launched 10 km away from the MWR site). As these observations have not been assimilated in the AROME-France NWP model, they make a valuable source of independent data to assess the impact of MWR observations on AROME backgrounds and analyses. For that purpose, a total of 93 radiosondes launched during the winter meteorological period have been used, excluding those from the Toulouse site due to the 10-km distance between MWR observations and radiosondes.

Figure 7 presents the biases and associated standard deviations for the AROME backgrounds and analyses with respect to the 93 independent radiosondes launched during SOFOG3D. Concerning the AROME-France backgrounds, the reference experiment has slight warm biases between 0.3 and 0.5 K in the lower part of the atmosphere (between the ground level and 950 hPa, Figure 7a) and larger errors above 850 hPa, reaching -1.5 K. Thanks to the assimilation of MWR observations, background-temperature biases are reduced close

to the ground, with values ranging between -0.3 and 0.3 K. In contrast, between 920 and 980 hPa biases are increased for both experiments, potentially due to errors in the position of the ABL top. Finally, above 920 hPa, depending on the level considered, biases are reduced by 0.2-0.5 K for both experiments in comparison with the reference.

For the AROME analyses (Figure 7b), temperature biases are slightly degraded compared with the background close to the ground when MWR observations are assimilated, especially with the *ALLOBS* experiment. This degradation might come from non-adapted background-error correlations, probably much larger than expected within fog layers close to the ground (Ménétrier & Montmerle, 2011). Using a diagonal R matrix when assimilating fully resolved temperature profiles could also cause degradations with the *ALLOBS* configuration. In contrast, temperature biases in the analysis are smaller than the background ones between 980 and 920 hPa for both experiments. Compared with the reference, the AROME analyses obtained with *ALLOBS* and *THIN* present smaller biases above 950 hPa. They are also mainly improved below 980 hPa with *THIN*, while slight degradations are observed with *ALLOBS*.

Concerning the temperature-error standard deviations (Figure 7c,d), all three simulations have values relatively close to each other. The assimilation of MWR observations thus has a neutral impact on standard deviation. Values of this range between 1.3 and 1.5 K from ground level up to 980 hPa. Then the temperature-error standard deviation reaches values of 2.0 K at 920 hPa. Finally, in the free troposphere, standard deviation values range between 2.0 and 3.5 K.

## 4.1.3 | Statistics With Respect to Aircraft Observations

In this section, aircraft observations available over the SOFOG3D domain have been used to evaluate the impact of the assimilation of MWR temperature profiles on the NWP model analyses and backgrounds compared with other types of observations. Innovation statistics have been computed for the same three-month winter period, similarly to the previous section.

Figure 8a presents the innovation bias for aircraft temperature measurements, discretized at pressure levels. The red curve, which represents the mean bias of the reference experiment, shows a persistent negative bias with values between 0 and -0.85 K. Similarly to MWR innovations, it indicates that the AROME-France backgrounds are on average warmer than the aircraft temperature measurements. For the *ALLOBS* (blue curve) and *THIN*
<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /><figcaption>FIGURE 7 Bias (top panels) and standard deviation profiles (bottom panels) for the AROME-France backgrounds (left panels) and analyses (right panels) in comparison with 93 radiosondes launched at Agen and Charbonnière during the meteorological winter period of the SOFOG3D observation campaign. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

(green curve) experiments, AROME backgrounds are slightly further than the aircraft measurements between 650 and 850 hPa, while they are significantly closer above 900 hPa. Temperature innovation biases are thus reduced to almost 0 K at 900 hPa. Moreover, most of these modifications are statistically significant according to a Student's t-test with a 95% confidence interval (dots on the curves). Concerning the standard deviation values (Figure 8b), they range between 0.7 and 1.2 K. For *ALLOBS* and *THIN*, a statistically significant increase by 0.1 K is present mainly between 650 and 850 hPa. However, no impact has been found for the other pressure levels.

Due to cross-correlations between temperature and wind within the **B** matrix and the model physics, which propagates the information temporally along the forecast lead time, the assimilation of MWR temperature profiles also impacts forecast winds. Concerning the zonal wind (Figure 8c,d), negative biases are present in the *REF* experiment from the ground level up to 700 hPa, with values

ranging between −0.85 and 0 m·s⁻¹. Then, positive biases can be seen with values reaching up to 0.45 m·s⁻¹. For the two other experiments assimilating MWR observations, biases are reduced at all levels, except between 700 and 750 hPa. While a small statistically significant bias reduction is present for the *THIN* experiment below 800 hPa, a bias reduction of up to 50% can be seen for the *ALLOBS* experiment. Concerning the standard deviations (Figure 8d), *REF* and *THIN* present similar values, which range between 2.0 and 3.0 m·s⁻¹. For *ALLOBS*, despite an error increase by 0.3 m·s⁻¹ between 600 and 900 hPa, no impact has been found for the other pressure levels.

Less impact has been found on the aircraft meridional winds. Figure 8e shows small bias reductions up to 900 hPa for *ALLOBS* and *THIN* in comparison with *REF*. Even if some of these error reductions are statistically significant, the largest bias reduction only reaches about 0.1 m·s⁻¹. Between 200 and 900 hPa, no impact has been found for *THIN*, while an increase of about 0.2 m·s⁻¹ can be seen for
<figure><img src="image_15.png" /></figure>

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

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

FIGURE 8 Aircraft-observation innovation statistics (left panel: bias; right panel: standard deviation) for (a,b) temperature, (c,d) zonal wind, and (e,f) meridional wind. The red, blue, and green curves represent the statistics for the reference, *ALLOBS*, and *THIN* experiments, respectively. The dots indicate statistically significant reductions or increases of the statistics compared with the reference experiment (with a Student's *t*-test with a 95% confidence interval). [Colour figure can be viewed at wileyonlinelibrary.com]

**ALLOBS.** Concerning the standard deviation (Figure 8f), REF and THIN are globally close to each other, with values between 2.0 and 3.2 m·s⁻¹. As for the zonal wind,

**ALLOBS** presents statistically significant standard deviation increases between 600 and 900 hPa, but no impact on the other vertical levels.
For the other observing systems assimilated, neutral impact or similar error reductions have been obtained globally (not shown here). Knowing that information can be extracted from MWR temperature profiles to improve AROME backgrounds and analyses with a positive or neutral impact on other assimilated observations, the next section investigates how these improvement propagate temporally in AROME forecasts.

## 4.2 Evaluation of AROME-France Temperature Forecasts Over the Whole Wintertime Period

In this section, the statistical impact of MWR temperature profiles is investigated for the whole meteorological winter period (2019/2020), taking into account all weather conditions (but precipitations, as explained in Section 3.1).

### 4.2.1 Validation of Temperature Forecasts With Respect to MWR Temperature Profiles

To assess the impact of MWR observations on AROME temperature forecasts specifically, the first 24-h AROME forecasts (from the analysis cycle valid at 0000 UTC) are compared with MWR temperature profiles valid at the same forecast lead time. In this comparison, temperature

profiles retrieved from MWR observations can thus be considered as independent observations for forecast lead times above 1 hour.

Figure 9 presents the temperature absolute mean bias differences computed between two experiments (ALLOBS – REF on the left and THIN – REF on the right) for the three-month period, the absolute mean bias being computed between MWR observations and forecasts valid at the same time. With the ALLOBS experiment, Figure 9a shows large reductions of absolute mean bias (up to 0.5 K) for the first eight hours of the forecast, especially between 960 hPa and the ground level. These error reductions have been found to be statistically significant according to a Student's t-test with a 95% confidence interval. A light increase in the absolute mean bias is nevertheless present between 880 and 920 hPa for the first five hours of the forecast, but only a small fraction is statistically significant. After the first 10 hours of the forecast, a very limited and non statistically significant impact is noticed. Concerning the associated temperature-error standard deviations, Figure 10a shows that, while most standard deviation values are below 2.0 K, those associated with evening and night forecasts reach values up to 3.3 K. The same results have been found for the ALLOBS experiment (Figure 10b), MWR observation assimilation having a very limited impact on standard deviation differences (ranging solely between -0.2 and 0.2 K,

<figure><img src="image_21.png" /><figcaption>**FIGURE 9** Temperature absolute mean bias differences computed over the six MWR sites assimilated within the AROME model for the whole winter period (from December 1, 2019–March 9, 2020), for (a) the ALLOBS – REF case and (b) the THIN – REF experiments. White unfilled squares highlight the statistically significant differences computed with a Student's t-test at 95% confidence interval. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>
<caption>FIGURE 10</caption>

Temperature-error standard
deviation computed over the
six MWR sites assimilated
within the AROME model for
the whole winter period for
(a) reference, (b) ALLOBS,
and (d) THIN experiments.
(c) represents the standard
deviation difference between
ALLOBS and REF, (e) being
similar but between THIN
and REF. A Student's *t*-test at
95% confidence interval was
performed, but differences
were not found to be
statistically significant. The
reader should notice that the
standard deviation color bars
are reduced to values ranging
from 2–3.4 K. [Colour figure
can be viewed at
wileyonlinelibrary.com]

<figure><img src="image_22.png" /></figure>

Figure 10c). Moreover, these last are not statistically
significant according to a Student's *t*-test with 95%
confidence interval.

The assimilation of MWR temperature profiles within
the *THIN* experiment leads to the same conclusions, but
to a lesser extent. Indeed, Figure 9b shows absolute mean
bias reductions at the same pressure levels and forecast lead times as observed with the *ALLOBS* experiment. However, while the absolute mean bias reductions reach 0.5 K in *ALLOBS*, these are lower than 0.2 K with the *THIN* experiment, except for the first two hours of forecast between 780 and 850 hPa for which statistically significant bias reductions reach 0.4 K. A Student's *t*-test with a 95% confidence interval highlights that most of the absolute bias variations are not statistically significant with the *THIN* experiment.

For the temperature-error standard deviations (Figure 10d,e), no impact is noticed (all the standard deviation differences with the reference are very close to 0 K).

This section has demonstrated a significant reduction of temperature biases within the ABL through a 1–8 hour forecast window using non-assimilated MWR observations to validate AROME forecasts. In order to assess the impact of such observations on temperature forecasts with independent observations, the next section proposes forecast scores against radiosondes launched during the SOFOG3D observation campaign.

## 4.2.2 | Validation of Temperature Forecasts With Respect to Radiosoundings

Similarly to the validation of the impact on AROME backgrounds and analyses brought by MWR assimilation, it is important to assess the impact on AROME forecasts with respect to observations other than MWR profiles. In this

section we propose to use the 93 radiosoundings launched during SOFOG3D to evaluate the impact on AROME forecasts brought by the assimilation of MWR data.

Figure 11 presents the biases and associated standard deviations for the AROME forecasts, all of them being valid at radiosonde launch time. Knowing that the impact of MWR on forecasts is statistically significant up to 10 hours only, the score computation uses the long-term forecasts closest in time to the radiosonde launch time. Since those forecasts are run at either 0000 UTC or 1800 UTC, comparisons with radiosondes are made with different forecast lead times up to 6 hours only.

Thanks to MWR assimilation, biases are reduced close to the ground (with values nearly equal to 0 K), as well as above 920 hPa for both experiments. However, a slight bias increase is noticed at 950 hPa, this degradation being slightly larger with *ALLOBS*. Though both reductions and increases are observed in the temperature biases, these changes were not found to be statistically significant with a Student's *t*-test with a 95% confidence interval.

Concerning the temperature-error standard deviations, all three simulations have values relatively close to each other. They range between 1.3 and 1.5 K from the ground level up to 980 hPa, before reaching 2.0 K between 850 and 920 hPa and increasing up to 3.5 K above 850 hPa. A slight increase in standard deviation is present below 980 hPa and above 850 hPa, while standard deviation is reduced between 850 and 980 hPa when MWR observations are assimilated. However, the differences are quite small and the impact is neutral overall.

<figure><img src="image_23.png" /><figcaption>**FIGURE 11** Bias (left panel) and standard deviation profiles (right panel) for the AROME-France forecasts in comparison with 93 radiosondes launched at Agen and Charbonnière during the meteorological winter period of the SOFOG3D observation campaign. Only forecast lead times from 2–6 hours are considered. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>
# 4.3 | Impacts on Forecast Scores During Low-Visibility Conditions

## 4.3.1 | Study of a Missed Fog Case

On January 13, 2020, a radiative fog event was observed at Agen. According to visibility observations (Figure 12), its duration was about 12 hours (approximately from 0200–1400 UTC). Thanks to the bistatic radar system for atmospheric studies cloud radar (Delanoë et al., 2016) deployed during the experimental campaign, the fog vertical development can be derived directly from reflectivity observations. Figure 13 shows that, during the formation phase (from 0200–0600), the fog thickness increases from a few tens of meters to 100 m, while in the mature phase (0600–1100) the fog thickness remains stable around 200 m. Afterwards, the fog dissipation phase occurs with a decreased fog thickness until evaporation of the remaining water droplets.

Figure 14a represents the 0–24 h AROME liquid water content (LWC) forecasts extracted from the *REF* experiment, valid at 0000 UTC on January 13, 2020. It shows that

this thick and long fog event was not simulated by the AROME-France NWP model. Nevertheless, a stratus cloud is present from 0000–0900 UTC between approximately 400 and 1200 m altitude, probably limiting the radiative cooling in the model. In order to assess the impact of the SOFOG3D MWR observations during this fog event, Figures 14 and 15 show the 24-hour forecasts of LWC and temperature for both *ALLOBS* and *THIN* experiments compared with the reference experiment.

In Figure 15, MWR temperature observations (black curves) are compared with AROME forecasts (red, blue, and green curves, representing forecasts from the *REF*, *ALLOBS*, and *THIN* experiments respectively) for the three levels for which MWR observations have been assimilated, whatever the assimilation experiment considered.

At 1800 m above ground level (Figure 15a), temperature forecasts are underestimating the observed ones by up to 2 K within the *REF* experiment. For the first 10 hours of forecast, *ALLOBS* and *THIN* present temperatures 1–2 K higher than *REF*, leading to light overestimations (especially for *THIN*). Between 1000 and 1600 UTC, this warming is still present in the simulations but limited

<figure><img src="image_24.png" /><figcaption>FIGURE 12 Visibility time series at Agen on January 13, 2020. The dotted gray line represents the visibility threshold under which a fog event is observed (visibility below 1000 m).</figcaption></figure>

<figure><img src="image_25.png" /><figcaption>FIGURE 13 Basta radar reflectivity time series for a fog event missed in the *REF* experiment, observed at Agen on January 13, 2020. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>
<figure><img src="image_26.png" /><figcaption>FIGURE 14 Agen 24-hour liquid water content forecasts for (a) REF, (b) ALLOBS, and (c) THIN experiments. Only liquid water content within cloud layers is taken into account and not rain hydrometeors. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

to less than 1 K. Afterwards, the three forecasts are equivalent. Thanks to the assimilation of MWR temperature observations, the daily RMSEs (computed between the forecasts and the observations) are significantly reduced, decreasing from 1.29 K in the REF experiment to 0.93 K in ALLOBS (−28%) and to 0.78 K in THIN (−40%).

At 900 m above the ground, temperature forecasts (Figure 15b) are located within the stratus cloud simulated by AROME. At 0000 UTC, all forecasts underestimate the temperature (around 2 K for REF and 1 K for ALLOBS and THIN). Up to 0800 UTC, globally ALLOBS presents higher temperatures than REF, thus being closer to the observations. Excepting the fifth hour of the forecast, THIN is close to REF, a result that can also be seen in RMSE values. Indeed, while ALLOBS presents a RMSE reduced by about 10% in comparison with REF (2.04 and 2.27 K, respectively), the THIN one is equivalent to the reference (2.28 K). Though temperature forecasts are quite similar between REF and THIN at 900 m, a significant evaporation of the stratus cloud is observed. In fact, while the stratus cloud is forecast for nine hours (0000–0900 UTC) in REF, its life cycle is reduced to three hours (0000–0300 UTC) in ALLOBS and five hours (0000–0500 UTC) in THIN. Moreover, the cloud thickness is also reduced in ALLOBS and THIN in comparison with the REF forecast (the cloud thickness is approximately half of the reference one). This evaporation is probably due to the drying of the layer at 900 m, which is probably driven by the cross-correlations and vertical correlations of the B matrix (not shown here).

At 50 m above the ground level (Figure 15c), REF and THIN are close to the observations at the beginning of the forecast, while ALLOBS presents a temperature underestimation by about 1 K. These differences are due

to the cycled 3D-Var data assimilation scheme used in the present study. Due to the cooler conditions present in ALLOBS, a longer period of temperature underestimation is impacting this experiment and the associated RMSE value. Indeed, while the THIN experiment presents a degradation of 8%, the ALLOBS one is degraded by 34%. Due to the radiative cooling simulated in both experiments, water-vapor condensation can be noticed close to the ground in Figure 14b,c. In the case of the ALLOBS forecasts, it even leads to the formation of a thin cloud layer around 50 m above ground level. This water-vapor condensation is also allowed by the lower-level moistening (Figure 16d,f), due to humidity increments provided by the B-matrix covariances.

In order to understand the impact of MWR assimilation better, Figure 16 shows the 2D distribution of analysis increments for both temperature and humidity at 50 m above ground and for all configurations. As expected, one main limitation of 3D-Var is to spread the analysis increment over large areas around the assimilated observations, whereas, particularly during fog conditions, we expect the analysis increment to be more localized. For the temperature increment, all three configurations tend to cool down the south part of the domain, while an increase in temperature is observed in the northeast part of the domain. However, we can note a larger cooling around the positions of the assimilated MWRs in ALLOBS and THIN. The spread of the analysis increment is also larger with ALLOBS compared with THIN. In terms of humidity, all configurations tend to increase humidity in the southwest part of the domain while decreasing humidity in the north part of the domain. However, significant differences are observed between each configuration: while humidification is only located in the southwest part of
<figure><img src="image_27.png" /><figcaption>**FIGURE 15** Temperature time series at (a) 1800 m above the ground, (b) 900 m above the ground, and (c) 50 m above the ground. The thick black curves represent temperature retrieved from the Agen MWR and the colored ones the different temperature forecasts (red: REF, blue: ALLOBS, green: THIN). [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

the domain in the *REF* configuration, it extends over a larger domain in the north direction with *ALLOBS*. The humidity increment with *THIN* is closer to *REF* compared with *ALLOBS*, except for an increase in humidity observed in the northeast direction instead of a drying. If we focus on the Agen site, represented by the black

cross, all configurations tend to decrease the temperature at 50 m. However, while *REF* and *THIN* tend to dry the layer, the *ALLOBS* configuration increases the humidity. As the only difference between *ALLOBS* and *THIN* comes from the number of vertical levels that are assimilated, this humidification probably comes from the *B*-matrix correlations, which spread the increment vertically and between variables. This is probably the conjunction of the large temperature cooling as well as the increased humidity present in *ALLOBS*, which leads to the saturation of the layer close to the ground after a few hours of forecast.

Despite an improved representation of this fog event, the fog layer is still underestimated even with the additional MWR data. Several reasons could explain this difficulty: as the stratus cloud is not entirely dissipated, the radiative scheme might not be able to get the exact cooling at the ground. The microphysical scheme is also prone to errors during fog conditions, and the use of a two-moment microphysical scheme like liquid Ice multiple aerosols (Vié *et al.*, 2016) with a better initialization of aerosols would also be beneficial to get an improvement in liquid water content after a modification of temperature. Humidity is also a key variable for fog forecasting and this variable might not be properly constrained, as no other observations are assimilated within the ABL.

### 4.3.2 | Statistical Impact on Temperature Forecasts During Local Fog Conditions

In order to obtain a statistical evaluation of the impact of MWR observations on AROME-France temperature forecasts during fog conditions, we focus on the Agen MWR. Indeed, the largest number of fog events during the meteorological winter period (from December 1–March 9, Table 2) were observed at the Agen site.

Similarly to the precedent case study, the *REF*, *ALLOBS*, and *THIN* simulations have been used, but statistics have been computed over both observed and simulated fog events. Fog is considered in the model space and observation space when visibility (simulated or observed) is lower than 1 km during a period of at least 30 minutes over a one-hour time window.

To assess the impact of MWR observations on temperature forecasts specifically in fog conditions, the first 24-h AROME forecasts (valid at 0000 UTC) are compared with MWR temperature profiles valid at the same time. In this comparison, temperature profiles retrieved from MWR observations can be considered as independent observations for forecast lead times above 1 hour.

Figure 17 presents the temperature absolute mean bias differences computed between two experiments, the absolute mean bias being computed between MWR
Temperature
analysis increments

<figure><img src="image_28.png" /><figcaption>REF</figcaption></figure>

<figure><img src="image_29.png" /><figcaption>ALLOBS</figcaption></figure>

<figure><img src="image_30.png" /><figcaption>THIN</figcaption></figure>

Specific humidity
analysis increments

<figure><img src="image_31.png" /><figcaption>(d)</figcaption></figure>

<figure><img src="image_32.png" /><figcaption>(f)</figcaption></figure>

<figure><img src="image_33.png" /></figure>

FIGURE 16 Temperature (left panels) and specific humidity (right panels) analysis increments at 50 m above ground on January 13, 2020 at 0000 UTC for REF (top panels), ALLOBS (middle panels), and THIN (bottom panels). The black cross represents the location of the Agen site. [Colour figure can be viewed at wileyonlinelibrary.com]

observations and forecasts valid at the same time.
Figure 17a shows that the ALLOBS experiment presents
large absolute mean bias reductions in comparison with
REF, reaching up to 0.5 K decrease. Such results are

present up to 10 hours of forecast lead time, espe-
cially close to the ground or above the ABL top. A
Student's t-test performed with a 95% confidence inter-
val highlights that these bias reductions are statistically
<figure><img src="image_34.png" /><figcaption>TABLE 2 Number of fog events observed with the operational Météo-France network of visibility sensor during the 2019/2020 meteorological winter.</figcaption></figure>

<table><thead><tr><td>Visibility station</td><td>Fog events</td></tr></thead><tbody><tr><td>Agen</td><td>64</td></tr><tr><td>Bergerac</td><td>46</td></tr><tr><td>Biscarrosse</td><td>7</td></tr><tr><td>Charbonnière</td><td>31</td></tr><tr><td>Mont-de-Marsan</td><td>44</td></tr><tr><td>Toulouse</td><td>26</td></tr></tbody></table>

significant (represented by white squares) only for the first two hours of forecast. Figure 18a-c indicates that large errors are made close to the ground during fog conditions. Nevertheless, the assimilation of MWR observations has a very small impact on standard deviation values, with error increases or decreases solely up to 0.2 K (Figure 18c).

For the *THIN* experiment (Figure 17b), though smaller differences from the reference experiment have been found in comparison with *ALLOBS*, a positive impact on temperature biases has been observed. Indeed, a slight reduction of absolute bias values has been found up to 2 hours of forecast close to the ground. Moreover, these differences are statistically significant over a limited height-time area. A neutral impact on the associated temperature-error standard deviation values has been observed (Figure 18d,e), with values closer to the

*REF* standard deviation in comparison with the *ALLOBS* experiment.

This section has demonstrated a positive impact on temperature forecasts specifically during fog conditions by reducing temperature biases up to 10 hours of forecast. Figure 14 also demonstrated how small changes in temperature can significantly impact the LWC forecast. The next section aims to evaluate the statistical impact of MWR assimilation on fog forecast scores through comparison with visibility measurements during the whole winter period.

### 4.3.3 | Statistical Impact on Fog Forecast Scores

To assess the impact of MWR temperature profiles on fog forecasts, additional scores based on visibility have been computed. As a reference, about 20 operational visibility sensors present in the SOFOG3D domain (Figure 2) have been used while a visibility diagnostic has been employed on the model side. Knowing that visibility is reversely proportional to the extinction coefficient (Koschmieder, 1924), relations between both can be retrieved similarly to the empirical formula derived by Kunkel (1984). At Météo France, a new visibility diagnostic has been implemented. It is based on a second-degree polynomial relation that links six months of observed visibility (from about 100 operational visibility sensors) to AROME-France forecasts of liquid water and rain contents (I. Etchevers,

<figure><img src="image_35.png" /><figcaption>FIGURE 17 Temperature absolute mean bias differences at Agen during fog conditions (observed and/or forecast), for (a) *ALLOBS-REF* and (b) *THIN-REF*. White unfilled squares highlight the statistically significant differences computed with a Student's *t*-test at 95% confidence interval. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>
<figure><img src="image_36.png" /></figure>

<figure><img src="image_37.png" /></figure>

<figure><img src="image_38.png" /></figure>

<figure><img src="image_39.png" /></figure>

<figure><img src="image_40.png" /></figure>

<figure><img src="image_41.png" /><figcaption>FIGURE 18</figcaption></figure>

Temperature-error standard
deviations at Agen during fog
conditions (observed and/or
forecast), for (a) reference,
(b) *ALLOBS*, and (d) *THIN*
experiments. (c) represents
the standard deviation
difference between *ALLOBS*
and *REF*, (e) being similar
but between *THIN* and *REF*
experiments. A Student's
t-test at 95% confidence
interval was performed, but
differences were not found to
be statistically significant.
[Colour figure can be viewed
at wileyonlinelibrary.com]

personal communication, 2021). In the present study,
this diagnostic has been used in order to detect fog
occurrence in the forecasts issued from the *REF*, *ALLOBS*,

and *THIN* experiments. During 19 SOFOG3D intensive
observation periods, 24-h forecasts have been produced
every two hours from 1800-0600 UTC (for a total of 133
forecasts). Considering that fog is forecast if the diagnosed visibility is lower than 1 km and observed if the observed visibility is below 1 km, contingency table scores have been computed for each forecast lead time of the 133 forecasts. Similar scores have also been computed with a visibility threshold of 500 m to consider thicker fog events. It is important to note that spatio-temporal errors in the AROME forecast are not taken into account in the score computation and might lead to a double penalty by comparing the AROME grid point that is closest to the visibility sensor. Though the exact value of forecast scores (probability of detection (POD), false-alarm ratio (FAR),

etc.) could be improved by limiting the double penalty, this section mainly aims at evaluating how the assimilation of MWR observations can lead to improved fog forecasts, rather than the exact value of fog forecast score. In this sense, the most important aspect is to use the same methodology for all configurations.

Figure 19a represents the probability of detection for visibility lower than 500 m. At the beginning of the forecast, both *ALLOBS* and *THIN* are improving the fog detection, with a POD increase from 0.255 to 0.35 and 0.32 respectively (both increases being statistically significant according to a Bootstrap test with 95% confidence). Then,

<figure><img src="image_42.png" /><figcaption>FIGURE 19 Probability Of Detection (POD, upper figures) and Heidke Skill Score (HSS, lower figures) for visibility thresholds of 500 m (left) and 1000 m (right) for the 24 hours of forecast lead time of the 133 forecasts run for 19 special observation periods. The red curve represents the *REF* experiment, while the blue and green ones represent *ALLOBS* and *THIN*, respectively. The dots on the curves represent statistically significant differences according to a bootstrap test with 95% confidence. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>
<figure><img src="image_43.png" /></figure>

<figure><img src="image_44.png" /><figcaption>**FIGURE 20** Same as Figure 19 but for the frequency bias index (FBI, upper figures) and false-alarm ratio (FAR, lower figures).
[Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

while the *ALLOBS* POD decreases, its values becomes lower than the *REF* experiment after 4 hours of forecast lead time. At the same time, *THIN* POD values increase with values higher than the *REF* experiment, these improvements being statistically significant. From 6–20 h of forecast lead time, POD values are close to each other for the three experiments. Finally, while *REF* and *ALLOBS* remain close for the last four hours of forecast lead time, POD values associated with *THIN* are higher, part of these improvements being statistically significant. The results obtained with a visibility threshold of 1000 m (Figure 19b) are close to the ones presented for a threshold of 500 m, though they are statistically less significant for the first two hours. This might be explained by a larger impact on thick fog events compared with thin fog events.

Figure 19c shows the Heidke Skill Score (HSS) obtained with the same forecasts. Once again, *ALLOBS* and *THIN* forecasts perform better than *REF* at the beginning of the forecast, the HSS score being increased from 0.3 to 0.385 and 0.375 respectively. Then, up to 24 hours of forecast, *ALLOBS* degrades the HSS score compared with the one obtained with *REF*, most of the degradation being statistically significant between 0 and 12 hours of forecast. On the other hand, *THIN* improves the HSS score up to 8 hours of forecast before staying close to *REF* up to 20 hours of forecast (with the exception of the 14th forecast lead time, where a statistically significant degradation can be noticed). Afterwards, fog forecasts are improved in *THIN*, reaching HSS values up to 0.4. Concerning fog forecasts based on a visibility threshold lower
than 1000 m (Figure 19d), results similar to the ones computed with a 500-m threshold have been obtained, with less statistically significant results.

Frequency bias index (FBI) and FAR have also been computed over the same period of interest for both visibility thresholds. Figure 20a,b shows that FBI values associated with *ALLOBS* and *THIN* forecasts are higher than the *REF* ones up to 10 hours of forecast lead time and are closer to the optimal value of 1. This indicates that new forecasts simulate a larger number of fog events compared with *REF* and get closer to the number of observed fog events. Then, from 12–24 hours of forecast, *ALLOBS* presents lower FBI values than *REF*, degrading the FBI score. For *THIN*, FBI scores are similar to *REF* between 10 and 18 hours of forecast and are significantly improved between 20 and 24 hours of forecast. This result shows that *THIN* estimates the number of fog events better for long-term forecasts.

Figure 20c,d shows that *ALLOBS* increases the FAR globally throughout the 24 hours of forecast compared with *REF*, whatever the visibility threshold used to compute FAR. On the other hand, *THIN* presents lower FAR for the first 6 hours of forecast lead time, but similar or increased FAR values beyond 6 hours of forecast. We note that the impact obtained with *THIN* has almost no statistical significance.

We note that, for all scores and all experiments, a similar pattern of increased accuracy is observed at 14-h forecast range. As only model cycles between 1800 and 0600 UTC have been used, this forecast range corresponds to daily hours between 0800 and 2000 UTC. As fog occurrence is less important during the day compared with night-time, fog forecast scores are thus all improved.

These results demonstrate the capability of MWR temperature profiles to improve fog forecasts. In fact, using a simplified data assimilation framework, accounting for temperature observations only, an improved LWC forecast at ground is obtained with the *THIN* experiment. However, while positive impact on the temperature field was demonstrated with *ALLOBS*, significant degradations in POD, FAR, and HSS are observed with this configuration. Several issues might lead to inconsistency between the improved temperature field observed with *ALLOBS* and degradation in the fog forecast scores, described below.

* In this article, only temperature has been assimilated, without information on humidity or liquid water content. Thus, we expect that the model physics will be good enough to modify the liquid water content at the ground, and hence the visibility diagnostics on which fog forecast scores are based, only with a better temperature forecast. However, the model physics is known to be prone to significant errors during fog conditions.

In addition, MWR temperature profiles are only assimilated starting at 10 m above ground and most of the positive impact obtained with *ALLOBS* is located above ground. Thus, it might be difficult to be entirely consistent between a better temperature forecast in the ABL and better fog forecast scores based on visibility diagnostics at the ground.

* The background-error covariance matrix used in this study is also sub-optimal for fog and might lead to inconsistency between the temperature increment at one vertical level and the increment at adjacent levels, but also with the humidity increment. In fact, as demonstrated by Ménétrier and Montmerle (2011), much shorter vertical correlations are observed at low levels during fog compared with clear-sky conditions, as well as strong positive correlations between temperature and humidity in saturated layers. Using the operational B matrix computed from a wide range of weather conditions might thus lead to inconsistent increments. The upcoming upgrade of the AROME assimilation system from a 3D-Var algorithm to an ensemble data assimilation scheme (3D-EnVar: Brousseau et al. (2024)) by the end of 2024 should improve the representation of background-error covariances.

* Finally, using a full observation-error covariance matrix **R** is also a crucial aspect when assimilating fully resolved temperature profiles. As a diagonal **R** matrix has been used in this study, assimilating a too-resolved temperature profile without taking into account observation-error correlations might lead to a sub-optimal solution.

An improved fog forecast might thus be expected by improving the data assimilation framework (like dedicated **B** and **R** matrices).

## 5 | SUMMARY AND OUTLOOK

In this study, the impact of the assimilation of ground-based MWR on AROME-France backgrounds, analyses, and forecasts has been studied. Such work was motivated by the SOFOG3D field experiment, from which an unprecedented database for fog study has been built (Martinet et al., 2022), and by the encouraging results shown by the studies of (Martinet et al., 2015, 2017, 2020).

In the present work, an indirect assimilation of MWR retrieved temperature profiles has been chosen. This choice has been motivated by that fact that hydrometeors were not available in the operational 3D-Var system of the AROME model and would have limited the direct assimilation of brightness temperatures to clear-sky
only. Choosing an indirect assimilation of temperature profiles enables the use of MWR observations in all-sky conditions and particularly during fog. In addition to the REF configuration corresponding to the operational AROME 3D-Var system, two new assimilation experiments have been carried out: the ALLOBS experiment, in which MWR profiles are assimilated at their full vertical resolution, and the THIN experiment, which only assimilates three vertical levels in order to assure uncorrelated observation errors. Overall, a positive impact on model analyses and backgrounds has been demonstrated, with smaller differences with respect to MWR observations and also to other observations like aircraft of radiosonde data. However, slight degradations have been found when MWR profiles at their full vertical resolution are assimilated.

Our results also show that temperature biases of AROME forecasts up to 10 hours are significantly improved in the ABL when MWR observations are assimilated. Despite a decrease in temperature biases close to the ground, an improvement in fog forecasts is not straightforward, as fog formation also depends on humidity and the capability of the microphysical scheme to initiate droplet condensation. After demonstrating that the assimilation of temperature profiles can significantly improve fog formation during a missed fog event, a statistical evaluation has been conducted over the whole winter period. Based on a contingency table against surface visibility measurements, forecast scores (detection, false alarms, frequency bias, etc.) are improved with the THIN experiment, while they are often degraded with the ALLOBS experiment. These degradations observed within the ALLOBS forecasts are not entirely understood, but could be due to the violation of the assumption of non-correlated observation errors in this configuration and the use of a sub-optimal B matrix for fog. It is also important to note that, in these experiments, only the temperature profile starting at 10 or 50 m above ground is modified with the assimilation of MWR observations, and not the liquid water content directly. However, fog forecast scores are computed based on a diagnostic of visibility calculated from liquid water content at the ground. An improvement in surface visibility due to an improvement in temperature above ground is thus not straightforward.

These first results of 3D-Var assimilation of MWR temperature profiles are very encouraging, but the degradations observed with the ALLOBS experiment also demonstrate that further improvement of the impact of MWR observations could be obtained with a more optimal configuration of the assimilation system. First of all, a thorough evaluation of the appropriate observation thinning is a non-negligible aspect if a diagonal R matrix is used. To assimilate MWR temperature profiles optimally at their full vertical resolution and to take advantage

of a detailed description of the temperature inversion, which is key in fog formation and dissipation, a full observation-error covariance matrix has to be determined and used in order to take these correlations into account within the assimilation system.

One way to increase the impact of MWR observations could be to consider a direct assimilation of MWR brightness temperature. This method enables a more optimal assimilation of raw observations by limiting additional errors during the retrieval process. Additionally, a direct assimilation of brightness temperatures is used to modify not only the temperature initial state but also humidity and potentially cloud variables when channels sensitive to humidity and liquid water content are used. Assimilating brightness temperatures in all-sky conditions and particularly fog conditions can thus only be possible if hydrometeors are included in control variables. The new 3D-EnVar data assimilation scheme of the AROME model that should soon be implemented operationally paves the way for a direct assimilation of MWR observations. The 3D-EnVar scheme will also contribute to more realistic structure functions within the B matrix, more adapted to fog than those used in this study (which rely on climatology). This new data assimilation scheme should be operational by the end of 2024. Though it might be too difficult to use it over a quite old field experiment like SOFOG3D, a new fog experiment is already scheduled in the Paris-Charles de Gaulle airport during the winter of 2024. During this experiment, MWR but also cloud radar observations will be available at three sites: the Site Instrumenté Régional de Télédétection Atmosphérique observatory, the center of Paris, and Paris-Charles de Gaulle airport. New data assimilation experiments using the operational AROME 3D-EnVar scheme would be very valuable with this new dataset.

Finally, in order to potentially increase the impact of such observations, the ongoing development of the AROME-France 4D-EnVar data assimilation scheme could be considered. Indeed, the addition of a fourth dimension will allow the assimilation of observations every 15 minutes instead of an hourly scheme as is implemented in the operational version of the NWP model. Moreover, it would also be helpful to take temporal covariances within the B matrix into account and adapt more to fog conditions.

Though a better initialization of thermodynamics and cloud variables is essential to improve fog forecasts, an improved representation of surface heterogeneities as well as the impact of vegetation on droplet deposition is also key to improve fog forecasts (Mazoyer et al., 2017). An improved description of turbulence is also essential, both by the assimilation of new observations like wind Doppler lidar measurements and by improved modeling through a
finer vertical grid close to the ground (Antoine *et al.*, 2023) or improved parameterization. A better description of the aerosol population in terms of both size distribution and chemical composition is also essential to represent aerosol activation better, in order to constrain the size distribution and concentration of cloud droplets within the fog layer. Using an advanced two-moment microphysical scheme in the near future within the AROME model should lead to improved fog modeling (Antoine *et al.*, 2023; Vié *et al.*, 2016) and to a larger impact of MWR observations.

## ACKNOWLEDGEMENTS

Data are managed by the French national center for Atmospheric data and services AERIS. This article is based upon work from COST actions ES1303 TOPROF and CA18235 PROBE supported by the European Cooperation in Science and Technology (COST, https://www cost.eu). The SOFOG3D field campaign was supported by METEO-FRANCE and ANR through grant AAPG 2018-CE01-0004. The MWR network deployment was carried out thanks to support by IfU GmbH, the University of Cologne, the Met Office, Laboratoire d'Aérologie, Meteoswiss, ONERA, and Radiometer Physics GmbH. Finally, we sincerely thank the anonymous reviewers, who helped improve the quality of this article.

## DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available on the AERIS website: https://www.aeris-data.fr/projects/sofog-3d/

## ENDNOTE

¹https://www.radiometer-physics.de/download/PDF/Radiometers/HATPRO/RPG_MWR_STD_Software_ManualG5.pdf.

## ORCID

Guillaume Thomas ID https://orcid.org/0000-0001-8285-5915

Pierre Brousseau ID https://orcid.org/0009-0005-3758-7524

Philippe Chambon ID https://orcid.org/0000-0002-3531-8890

Ulrich Löhnert ID https://orcid.org/0000-0002-9023-0269

## REFERENCES

Antoine, S., Honnert, R., Seity, Y., Vié, B., Burnet, F. & Martinet, P. (2023) Evaluation of an improved AROME configuration for fog forecasts during the SOFOG3D campaign. *Weather and Forecasting*, 38, 1605–1620.

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

Berre, L. (2000) Estimation of synoptic and mesoscale forecast error covariances in a limited-area model. *Monthly Weather Review*, 128, 644–667.

Blumberg, W.G., Turner, D.D., Löhnert, U. & Castleberry, S. (2015) Ground-based temperature and humidity profiling using spectral infrared and microwave observations. Part II: Actual retrieval performance in clear-sky and cloudy conditions. *Journal of Applied Meteorology and Climatology*, 54, 2305–2319.

Bouchard, A., Rabier, F., Guidard, V. & Karbou, F. (2010) Enhancements of satellite data assimilation over Antarctica. *Monthly Weather Review*, 138, 2149–2173.

Brousseau, P., Berre, L., Bouttier, F. & Desroziers, G. (2011) Background-error covariances for a convective-scale data-assimilation system: Arome-France 3d-var. *Quarterly Journal of the Royal Meteorological Society*, 137, 409–422.

Brousseau, P., Seity, Y., Ricard, D. & 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.

Brousseau, P., Vogt, V., Arbogast, E., Martet, M. & Thomas, G. (2024) Configuration and evaluation of a 3DEnVar data assimilation scheme for the Météo-France operational convective model AROME-France. *Quarterly Journal of the Royal Meteorological Society* (to be submitted).

Bubnová, R., Hello, G., Bénard, P. & Geleyn, J.-F. (1995) Integration of the fully elastic equations cast in the hydrostatic pressure terrain-following coordinate in the framework of the arpege/aladin nwp system. *Monthly Weather Review*, 123, 515–535.

Caumont, O., Cimini, D., Löhnert, U., Alados-Arboledas, L., Bleisch, R., Buffa, F. et al. (2016) Assimilation of humidity and temperature observations retrieved from ground-based microwave radiometers into a convective-scale NWP model. *Quarterly Journal of the Royal Meteorological Society*, 142, 2692–2704.

Cimini, D., Hewison, T.J., Martin, L., Güldner, J., Gaffard, C. & Marzano, F.S. (2006) Temperature and humidity profile retrievals from ground-based microwave radiometers during TUC. *Meteorologische Zeitschrift*, 15, 45–56.

Delanoë, J., Protat, A., Vinson, J.-P., Brett, W., Caudoux, C., Bertrand, F. et al. (2016) Basta: a 95-GHz FMCW doppler radar for cloud and fog studies. *Journal of Atmospheric and Oceanic Technology*, 33, 1023–1038.

Desroziers, G., Berre, L., Chapnik, B. & Poli, P. (2005) Diagnosis of observation, background and analysis-error statistics in observation space. *Quarterly Journal of the Royal Meteorological Society: A Journal of the Atmospheric Sciences, Applied Meteorology and Physical Oceanography*, 131, 3385–3396.

Guedj, S., Karbou, F. & Rabier, F. (2011) Land surface temperature estimation to improve the assimilation of SEVIRI radiances over land. *Journal of Geophysical Research*, 116, 1–18.

Gultepe, I., Pearson, G., Milbrandt, J.A., Hansen, B., Platnick, S., Taylor, P. et al. (2009) The fog remote sensing and modeling field project. *Bulletin of the American Meteorological Society*, 90, 341–360.

Hartung, D.C., Otkin, J.A., Petersen, R.A., Turner, D.D. & Feltz, W.F. (2011) Assimilation of surface-based boundary layer profiler
observations during a cool-season weather event using an observ-
ing system simulation experiment. Part II: Forecast assessment.
*Monthly Weather Review*, 139, 2327–2346.

He, W., Chen, H. & Li, J. (2020) Influence of assimilating ground-based microwave radiometer data into the wrf model on precipitation. *Atmospheric and Oceanic Science Letters*, 13, 107–112.

Hewison, T.J. (2007) 1d-var retrieval of temperature and humidity profiles from a ground-based microwave radiometer. *IEEE Transactions on Geoscience and Remote Sensing*, 45, 2163–2168.

Koschmieder, H. (1924) *Theorie der horizontalen Sichtweite. Beitr. Phys. Atmos*, Vol. 11,12. Frankfurt, Germany: Keim & Nemnich.

Kunkel, B.A. (1984) Parameterization of droplet terminal velocity and extinction coefficient in fog models. *Journal of Applied Meteorology and Climatology*, 23, 34–41.

Lac, C., Chaboureau, J.-P., Masson, V., Pinty, J.-P., Tulet, P., Escobar, J. et al. (2018) Overview of the meso-nh model version 5.4 and its applications. *Geoscientific Model Development*, 11, 1929–1969.

Lafore, J.P., Stein, J., Asencio, N., Bougeault, P., Ducrocq, V., Duron, J. et al. (1998) The meso-nh atmospheric simulation system. Part I: Adiabatic formulation and control simulations. In: *Annales geophysicae*, Vol. 16. Göttingen, Germany: Copernicus GmbH, pp. 90–109.

Liljegren, J.C., Boukabara, S.-A., Cady-Pereira, K. & Clough, S.A. (2005) The effect of the half-width of the 22-GHz water vapor line on retrievals of temperature and water vapor profiles with a 12-channel microwave radiometer. *IEEE Transactions on Geoscience and Remote Sensing*, 43, 1102–1108.

Martinet, P., Cimini, D., Angelis, F.D., Canut, G., Unger, V., Guillot, R. et al. (2017) Combining ground-based microwave radiometer and the AROME convective scale model through 1DVAR retrievals in complex terrain: an alpine valley case study. *Atmospheric Measurement Techniques*, 10, 3385–3402.

Martinet, P., Cimini, D., Burnet, F., Ménétrier, B., Michel, Y. & Unger, V. (2020) Improvement of numerical weather prediction model analysis during fog conditions through the assimilation of ground-based microwave radiometer observations: a 1D-VAR study. *Atmospheric Measurement Techniques*, 13, 6593–6611.

Martinet, P., Dabas, A., Donier, J.-M., Douffet, T., Garrouste, O. & Guillot, R. (2015) 1D-VAR temperature retrievals from microwave radiometer and convective scale model. *Tellus A: Dynamic Meteorology and Oceanography*, 67, 27925.

Martinet, P., Unger, V., Burnet, F., Georgis, J.-F., Hervo, M., Huet, T. et al. (2022) A dataset of temperature, humidity, and liquid water path retrievals from a network of ground-based microwave radiometers dedicated to fog investigation. *Bulletin of Atmospheric Science and Technology*, 3, 1–16.

Mazoyer, M., Lac, C., Thouron, O., Bergot, T., Masson, V. & Musson-Genon, L. (2017) Large eddy simulation of radiation fog: impact of dynamics on the fog life cycle. *Atmospheric Chemistry and Physics*, 17, 13017–13035.

Ménétrier, B. & Montmerle, T. (2011) Heterogeneous background-error covariances for the analysis and forecast of fog events. *Quarterly Journal of the Royal Meteorological Society*, 137, 2004–2013.

Montmerle, T. & Faccani, C. (2009) Mesoscale assimilation of radial velocities from doppler radars in a preoperational framework. *Monthly Weather Review*, 137, 1939–1953.

Otkin, J.A., Hartung, D.C., Turner, D.D., Petersen, R.A., Feltz, W.F. & Janzon, E. (2011) Assimilation of surface-based boundary layer profiler observations during a cool-season weather event using an observing system simulation experiment. Part s impact. *Monthly Weather Review*, 139, 2309–2326.

Pinty, J.-P. & Jabouille, P. (1998) A mixed-phase cloud param-
eterization for use in mesoscale non-hydrostatic model: sim-
ulations of a squall line and of orographic precipitations.
In: *Conf. On cloud physics*. WA: Amer. Meteor. Soc. Everett,
pp. 217–220.

Qi, Y., Fan, S., Li, B., Mao, J. & Lin, D. (2021a) Assimilation of ground-based microwave radiometer on heavy rainfall forecast in beijing. *Atmosphere*, 13, 74.

Qi, Y., Fan, S., Mao, J., Li, B., Guo, C. & Zhang, S. (2021b) Impact of assimilating ground-based microwave radiometer data on the precipitation bifurcation forecast: a case study in beijing. *Atmosphere*, 12, 551.

Rose, T., Crewell, S., Löhnert, U. & Simmer, C. (2005) A network suitable microwave radiometer for operational monitoring of the cloudy atmosphere. *Atmospheric Research*, 75, 183–200.

Seity, Y., Brousseau, P., Malardel, S., Hello, G., Bénard, P., Bouttier, F. et al. (2011) The arome-France convective-scale operational model. *Monthly Weather Review*, 139, 976–991.

Turner, D.D. & Löhnert, U. (2021) Ground-based tempera-
ture and humidity profiling: combining active and passive
remote sensors. *Atmospheric Measurement Techniques*, 14,
3033–3048.

Vandenberghe, F. & Ware, R. (2002) 4-dimensional variational assimilation of ground-based microwave observations during a winter fog event.

Vié, B., Pinty, J.-P., Berthet, S. & 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, 567–586.

Wattrelot, E., Caumont, O. & Mahfouf, J.-F. (2014) Operational implementation of the 1d+ 3d-var assimilation method of radar reflectivity data in the arome model. *Monthly Weather Review*, 142, 1852–1873.

**How to cite this article:** Thomas, G., Martinet, P., Brousseau, P., Chambon, P., Georgis, J.-F., Hervo, M. *et al.* (2025) Assimilation of Ground-Based Microwave Radiometer Temperature Observations Into a Convective-Scale NWP Model for Fog Forecast Improvement. *Quarterly Journal of the Royal Meteorological Society*, 151:e4893. Available from: https://doi.org/10.1002/qj.4893