# Sensitivity analysis of the convective-scale AROME model to physical and dynamical parameters

Meryl Wimmer, Laure Raynaud, Laurent Descamps, Loïk Berre, Yann Seity

► To cite this version:

Meryl Wimmer, Laure Raynaud, Laurent Descamps, Loïk Berre, Yann Seity. Sensitivity analysis of the convective-scale AROME model to physical and dynamical parameters. Quarterly Journal of the Royal Meteorological Society, 2022, 148 (743), pp.920-942. 10.1002/qj.4239. hal-04918247

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DOI: 10.1002/qj.4239

RESEARCH ARTICLE

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# Sensitivity analysis of the convective-scale AROME model to physical and dynamical parameters

Meryl Wimmer* |

Laure Raynaud* |

Laurent Descamps |

Loïk Berre* |

Yann Seity

Centre National de Recherches
Météorologiques, Université
Toulouse III - Paul Sabatier,
Météo-France, Toulouse, France

**Correspondence**

M. Wimmer, Centre National de
Recherches Météorologiques, Université
Toulouse III - Paul Sabatier, 42 Avenue
Gaspard Coriolis, 31057 Toulouse, France.
Email: meryl.wimmer@umr-cnrm.fr

**Abstract**

A global sensitivity analysis of the convective-scale Application of Research to Operations at Mesoscale (AROME) model is performed in order to determine the most influential parameters on the forecast of different near-surface variables. For that purpose, the Morris method is applied to 21 parameters from six different physical and dynamical parametrization schemes, over different seasons. Results highlight a set of eight parameters with a noticeable influence on most variables, in particular 10 m wind speed and precipitation forecasts. The sensitivity of parameter uncertainties is also examined on different spatio-temporal scales. A clear diurnal cycle of parameters influence is observed in summer, in close connection with the convective activity. In addition, the spatial distribution of parameters influence is mostly consistent with the underlying distribution of weather forecasts. A Sobol' sensitivity analysis, based on surrogate models, mostly confirms Morris conclusions and highlights some interactions between parameters.

**KEYWORDS**

AROME, model uncertainty, Morris screening, parametrization, sensitivity analysis, Sobol' indices

# 1 | INTRODUCTION

Convection-permitting numerical weather prediction (NWP) models are now widely used in most operational weather prediction centres, with horizontal resolutions usually between 1 and 4 km (Clark et al., 2016). These models have the advantage, compared to global models, of providing a realistic representation of small-scale phenomena. However, they are still subject to imperfections. One source of forecast error is related to the representation of unresolvable subgrid-scale physical processes with parametrization schemes, which often provide a simplified modelling of complex physical processes (Stensrud, 2011). Furthermore, these schemes involve many uncertain parameters, whose accuracy is crucial for forecast performance. Generally, the calibration of parameter values is

performed manually by searching for the configurations that optimize the forecast–observation comparison. However, in recent years, more objective techniques using emulators have also been developed (Neelin et al., 2010; Gong et al., 2015; Bellprat et al., 2016; Duan et al., 2017; Voudouri et al., 2017; Couvreux et al., 2020).

In addition to deterministic forecasts, convective-scale ensemble prediction systems (EPSs) have been developed to estimate forecast uncertainties (Gebhardt et al., 2008; Bouttier et al., 2012; Romine et al., 2014; Hagelin et al., 2017; Frogner et al., 2019). Properly accounting for model errors in these systems is still challenging and different methods have been proposed (Buizza, 1999; Shutts, 2005; Wang, 2011). Perturbing uncertain parameters is an appealing approach that has lead to promising results using different approaches such as Random Parameter
(McCabe et al., 2016) and Stochastically Perturbed Parametrization (SPP; Ollinaho et al., 2013), which directly perturb some parameters from different parametrization schemes. An efficient implementation of such methods requires identification of the relevant parameters to perturb, along with their uncertainty ranges. These choices of parameter selection often rely on experts' knowledge. However, Marsigli et al. (2019) have proposed a random selection of parameters.

A better understanding of the impact of parameters on forecasts could help to improve the tuning of parameters in deterministic forecasts or the representation of their uncertainty of parameters in EPSs. For that purpose, objective methods such as Sensitivity Analysis (SA) can be used to measure the influence of these parameters. These methods consist of sampling the uncertain input parameter space, in order to identify and sometimes quantify the impact of parameter perturbations on model outputs (Saltelli et al., 2000). One can distinguish between local SA methods which look at the impact of small parameter perturbations around nominal values, and global methods which examine the influence of simultaneous perturbations of all inputs over their entire variation ranges. Global methods are particularly suited for nonlinear behaviours such as those encountered in NWP models.

Global SA has already been applied to complex models from different scientific domains including the atmospheric sciences. For instance, these analyses were conducted for land-surface models (Liu et al., 2004; Bastidas et al., 2006; Hou et al., 2012; Li et al., 2013), coupled ocean-atmosphere models (Marzban et al., 2014), global climate models (Stainforth et al., 2005; Zhang et al., 2012; Covey et al., 2013; Qian et al., 2015) and atmospheric chemical models (Lucas and Prinn, 2005). Regarding NWP models, Di et al., (2015; 2017) and Quan et al. (2016) examined the sensitivity of the Weather Research and Forecasting (WRF) model to a set of parameters from different physical parametrizations, with a focus on five or nine rainy and rainless events. Ji et al. (2018) extended these studies over a one-month summer period and compared results from two SA methods. However, to the authors' knowledge, no global SA has been performed in an operational convective-scale model over long periods.

In this context, the aim of this study is to apply two global SA methods in the French convective-scale Application of Research to Operations at Mesoscale (AROME) model, in order to identify the most influential parameters from all physical parametrizations and some dynamical schemes.

The outline of the paper is as follows. Section 2 describes the global sensitivity analysis methods used. The experimental set-up is introduced in Section 3 and

results are discussed in Section 4. Finally, some concluding remarks are provided in Section 5.

## 2 | GLOBAL SENSITIVITY ANALYSIS

Amongst global SA, three types of method can be distinguished: (a) screening methods as, for instance, the Morris method, (b) variance decomposition methods such as Fourier Amplitude Sensitivity Testing (FAST) or Sobol' indices method, and (c) regression-based methods, for example, Pearson correlation coefficient can be used as a sensitivity measure for a linear model (Wilks, 2011). In this section, the two state-of-the-art SA methods used in this study are presented: Morris screening and Sobol' indices.

### 2.1 | Morris sensitivity analysis

The Morris screening (Morris, 1991), also called Elementary Effect method, is a “One-At-a-Time” (OAT) design, meaning that each parameter is perturbed one after the other. Screening methods are often time-consuming as they require a large number of simulations, especially for a high level of accuracy. However, the Morris approach can give robust results with a small number of simulations (about 10 or 50 per parameter; Campolongo et al., 2007). Furthermore, another noticeable advantage of the Morris approach is that it does not require any specific assumption on output monotony properties or parameters' influence.

This method has been successfully applied to various complex models such as physics-based battery (van Rensburg et al., 2019), building energy budget (Sanchez et al., 2014; Branger et al., 2015; Yang et al., 2016), seismic sources location (Franczyk, 2019), wastewater model (Ruano et al., 2011; Cosenza et al., 2013; Vanrolleghem et al., 2015), hydrothermal of embankment dam (Ren et al., 2019), combat (Alam et al., 2004), agronomics (Confalonieri et al., 2010a; 2010b), and medicine (Wu et al., 2013; Link et al., 2018). In atmospheric sciences, this screening method has been applied to a climate model (Covey et al., 2013) and NWP models (Di et al., 2015; 2017; Quan et al., 2016).

The principle of the method is the following. Let us consider a model with *k* uncertain parameters, denoted $X_i, i = 1...k$, assumed to be continuous and uniformly distributed over specific intervals. After a normalization between 0 and 1, these parameters are discretized into *p* levels. The method starts with initial values of each parameter, randomly sampled in the *k*-parameter space. All parameters are then perturbed one-by-one, in a random order, by a value Δ proportional to $1/(p - 1)$. When
<figure><img src="image_4.png" /><figcaption>FIGURE 1 Example of a Morris design for $k = 2$ parameters ($X_1$ and $X_2$) with the following settings: $r = 5$, $p = 5$, $\Delta = 1/(p-1)$. A, B, C, D and E are the starting points of the Morris trajectories [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

all parameters are perturbed, we obtain $k + 1$ simulations, forming a Morris trajectory. For example, Figure 1 presents a Morris design for $k = 2$ parameters ($X_1$ and $X_2$), perturbed between 0 and 1 and discretized into $p = 5$ values. There are $r = 5$ Morris trajectories with a perturbation step $\Delta = 1/(p-1)$, starting at points A, B, C, D and E, which are randomly chosen.

Along a Morris trajectory, the influence of each parameter $X_i$ is measured with the corresponding elementary effect $EE_i$ defined as follows:

$$EE_i = \frac{f(X_1, X_2, \dots, X_i + \Delta, \dots, X_k) - f(X_1, X_2, \dots, X_i, \dots, X_k)}{\Delta}, \quad (1)$$

where $f(X_1, X_2, \dots, X_k)$ is a scalar model output. Note that the perturbation $\Delta$ can be either positive or negative depending on trajectory orientation (direct or opposite). Therefore, along a trajectory, one elementary effect is computed for each parameter.

As a single Morris trajectory samples a very small part of the $k$-parameter space, $r$ trajectories are necessary to sample the whole domain. For example, in Figure 1, the Morris trajectory starting at point A is not sufficient; four other trajectories starting from points B, C, D and E are needed to better sample the whole parameter space ($X_1, X_2$). In order to properly explore the parameter space, we follow Campolongo et al. (2007), who suggest maximising distances between trajectories. This is achieved by computing the sum of Euclidean distances between points from M different trajectories and by selecting the

$r$ furthest ones. These $r$ trajectories provide a sample of the whole elementary effects distribution, referred as $F_i$ for the parameter $X_i$. The higher $r$ is, the more accurate the estimation of $F_i$ is.

As proposed by Campolongo et al. (2007), the $F_i$ distribution can be summarised with two sensitivity indices, for each parameter $X_i$:

$$\mu_i^* = \mathbb{E}(|EE_i|), \quad \sigma_i = \text{std}(EE_i),$$

where $\mathbb{E}$ is the expected value and $\text{std}$ the standard deviation. $\mu_i^*$ characterises the direct impact of a parameter on model outputs: the higher $\mu_i^*$ is, the more influential the parameter is. $\sigma_i$ represents not only the impact amplitude, but also interactions between parameters and nonlinear effects. High $\sigma_i$ values can correspond to a strong interaction between considered parameters, or to nonlinear effects. As $\mu_i^*$ and $\sigma_i$ represent two complementary measures of the parameters' influence, in the remainder of the paper, the total parameter impact will be evaluated with the Total Morris Indices (TMI), given by $M_{T,i} = \sqrt{\mu_i^{*2} + \sigma_i^2}$, as proposed by Ciric (2012).

A major limitation of this method is that parameters' interactions and nonlinearity properties cannot be distinguished. This is the reason why the Morris approach is mostly used to provide a first insight into the parameters' influence. Generally, it is often completed with other methods such as the Sobol' indices described in the next section. Some improvements have also been proposed to determine second-order effects (Cropp and Braddock, 2002; Campolongo et al., 2007) or to account for dependent parameters (Ge and Menendez, 2017), but they are not considered in this study.

## 2.2 | Sobol' indices method

The second method, proposed by Sobol' (1990), is a variance-based approach. Whatever the method used for Sobol' indices estimation, they have been very popular in several domains such as hydrology (e.g., Nossent et al. (2011); Sarrazin et al. (2016)), climatology (Shi et al., 2019), atmospheric chemistry (Girard et al., 2016) or atmospheric observation (Rieutord, 2017). This approach has the advantage of providing a deep understanding of parameters' influence and interactions without requiring any hypothesis on the studied model. Furthermore, for a more global application, the method has been extended to vectorial outputs (Gamboa et al., 2014) and dependent variables (Chastaing, 2013) in particular.

More precisely, this method uses the Hoeffding decomposition theorem to break down the model output variance
<figure><img src="image_5.png" /></figure>

$V(Y) = V$ (where $Y = f(X_1, X_2, ..., X_i, ..., X_k)$ is the model output and $X_1, X_2, ..., X_i, ..., X_k$ the $k$ parameter value) into a sum of statistics of increasing dimensions:

$$V = \sum_{i=1}^{k} V_i + \sum_{1 \le i < j \le k} V_{ij} + \dots + V_{1,2,...,k}, \quad (2)$$

where:

$V_i = \mathbb{V}(\mathbb{E}[Y|X_i])$ is the output variance due to parameter $i$, and

$V_{ij} = \mathbb{V}(\mathbb{E}[Y|X_i, X_j]) - V_i - V_j$ is the output variance due to the couple of parameters $i$ and $j$.

According to this variance decomposition, Sobol' (1990) defines sensitivity indices as the proportion of the model output variance due to a parameter or a group of parameters. These indices are commonly referred to as the Sobol' indices. The most frequently used are the first-order Sobol' indices, defined, for a $i$th parameter $X_i$, by:

$$S_i = \frac{V_i}{V}, \quad (3)$$

and the second-order indices, defined by:

$$S_{i,j} = \frac{V_{ij}}{V}. \quad (4)$$

These second-order indices provide information about interactions between parameters $X_i$ and $X_j$. As the sum of all Sobol' indices is equal to one, the higher the Sobol' index $S_i$ is, the more influential the parameter $X_i$ is.

However, when the number of parameters is too large, the interpretation of all Sobol' indices can be complex and the total Sobol' indices (Homma and Saltelli, 1996) can be used to summarise the overall contribution of a parameter:

$$S_{Ti} = \sum_{j \ne i} S_j = 1 - \frac{\mathbb{V}(\mathbb{E}[Y|X_{i-1}])}{V}, \quad (5)$$

where $\#i$ represents all indices ensembles containing index $i$, and $X_{i-1}$ corresponds to all parameters except the $i$th one.

Estimation of Sobol' indices requires us to compute the model output variance $Y$, given the parameter $X_i$. According to Jacques (2011), a possible approach is to use a Monte-Carlo sampling with, at least, 1,000 simulations for each parameter. To achieve an accuracy on the Sobol' indices of about 10%, a number of 10,000 simulations per parameter is necessary (Iooss, 2011). Designs such as Latin Hypercube sampling (McKay et al., 1979), stratified sampling or quasi-Monte Carlo can reduce the number of simulations. However, compared to the Morris screening, this method is much more costly.

The use of statistical surrogate models, also called model emulators or metamodels, can be a useful alternative to generate thousands of simulations with a very low computational cost. Surrogate models are simple mathematical functions that aim at approximating a model output in a computationally efficient way. They can be based on polynomials (Neelin et al., 2010; Bellprat et al., 2016; Voudouri et al., 2017), neural networks, kriging or random forests (Faivre et al., 2016). In this paper, the Polynomial Chaos Expansion (PCE) is used. One advantage of that surrogate is that the Sobol' indices can be computed analytically from PCE coefficients.

Consider a model $f(\mathbf{X}) = Y$ that associates the input $\mathbf{X} = \{X_0, ..., X_k\}$ to an output $Y$. That model can be projected on a space defined by orthogonal polynomials $\Psi_\alpha$ and is thus approximated by the following linear combination:

$$f(\mathbf{X}) = \sum_{\alpha \in \mathbb{N}^k} b_{\alpha} \Psi_{\alpha}(\mathbf{X}), \quad (6)$$

where $\Psi_\alpha, \alpha \in \mathbb{N}^k$ are the orthogonal multivariate polynomials, and $b_\alpha$ coefficients to determine. In order to fix the number of coefficients to determine, that PCE $\tilde{f}$ is an approximation of model $f$ with an error $\epsilon$ and only $P$ coefficients are considered:

$$\tilde{f}(\mathbf{X}) = \sum_{\alpha \in \mathbb{A}} b_{\alpha} \Psi_{\alpha}(\mathbf{X}) + \epsilon = \mathbf{B}^{\mathrm{T}} \Psi(\mathbf{X}) + \epsilon, \quad (7)$$

where $\mathbb{A} \subset \mathbb{N}^k$, $\mathbf{B} = \{b_0, ..., b_{P-1}\}$ and $\Psi = \{\Psi_0(\mathbf{X}), ..., \Psi_{P-1}(\mathbf{X})\}$.

Using a large set of model output data, forming a learning database, the coefficients $b_\alpha$ can be determined by minimizing the mean squared error between that surrogate model $f$ and the real one $f$ (the learning database). After some calculations explained in Sudret (2008), the Sobol' indices for a group of parameters $u$ can be expressed as:

$$S_u = \frac{\sum_{\alpha \in A_u} b_{\alpha}^2}{\sum_{\alpha \in A \setminus \{0\}} b_{\alpha}^2}, \quad (8)$$

where $A_u = \{\alpha \in A : i \in u \Leftrightarrow \alpha_i \ne 0\}$. Sudret (2008) provides more details.

## 3 | EXPERIMENTAL SET-UP AND SENSITIVITY INDICES

In this section we present the NWP model used, the selected parameters, the configuration of the two SA methods and the definition of sensitivity indices.
## 3.1 | AROME model

The French convection-permitting AROME model (Seity et al., 2011) is a spectral and non-hydrostatic limited-area model. Its dynamical core comes from the ALADIN model (Aire Limitée Adaptation Développement INternational; Bénard et al., 2010), while the physical parametrizations are taken from the research model MESO-NH (Lafore et al., 1998).

Microphysics are represented with a bulk, one-moment scheme using six water species: water vapour, cloud liquid water, cloud pristine ice, precipitation rain, snow and graupel (ICE3; Pinty and Jabouille, 1998). Bouteloup et al. (2011) improved this scheme by adding a PDF-based sedimentation scheme. The planetary boundary-layer turbulence is represented with the Cuxart et al. (2000) scheme, which uses a turbulent kinetic energy (TKE) prognostic equation. Shallow convection is simulated with an eddy diffusivity Kain-Fritsch scheme (Pergaud et al., 2009). The surface is described with tiles of land, towns, sea and inland waters for each AROME grid box, in the surface scheme called SURFEX (SURFace EXternalisée; Le Moigne et al., 2009). Finally, AROME uses a previous version of ECMWF's radiation scheme, the Rapid Radiative Transfer Model (RRTM) code, to compute long-wave (Mlawer et al., 1997) and short-wave (Fouquart and Bonnel, 1980) radiation. A semi-Lagrangian horizontal diffusion (SLHD) scheme simulates the dissipation of energy at small scales by controlling the amplitude of numerical diffusion of hydrometeors (Váña et al., 2008). This numerical diffusion scheme can be considered as a parametrization as it represents a subgrid process, despite the fact that it is more related to dynamics.

AROME has been running operationally since 2008 and produces 2-day forecasts, over a limited domain covering Western Europe and centred on France (domain corners at 11.9°W, 54.65°N; 15.975°E, 54.65°N; 8.1°W, 37.5°N; 12.15°E, 37.5°N). This domain covers an area of about 1,600 × 1,600 km with a horizontal resolution of 1.3 km. For the present study, the AROME model has been run with a 2.5 km horizontal resolution and 90 vertical levels. Surface and initial conditions come from the 3D-Var AROME analysis (Brousseau et al., 2016), and lateral conditions are provided by the global operational ARPEGE model (Action de Recherche Petite Echelle Grande Echelle; Courtier et al., 1991; Déqué et al., 1994).

## 3.2 | Set-up for SA parameters

Discussions with experts in physical processes lead to the identification of 21 uncertain parameters from six different parametrizations: radiation, microphysics, turbulence,

surface, convection and SLHD. They are summarised in Table 1.

In the radiation scheme, RSWINHF and RLWINHF are inhomogeneity coefficients for short-wave and long-wave radiations respectively. They represent the inhomogeneity of clouds by weighting optical properties such as diffusion, scattering and optical thickness. The higher these parameters are, the more uniform the cloud is and the higher the optical properties are. On the contrary, the smaller the parameters are, the more heterogeneous the cloud is and the smaller the optical properties are. Consequently, higher values correspond to stratiform clouds and lower values to cumuliform clouds.

Regarding microphysics, RCRIAUTI and RCRIAUTC are autoconversion thresholds for snow and rain respectively. The higher RCRIAUTI is, the less snow is created. The higher RCRIAUTC is, the less rain is produced. VSIGQSAT is a parameter from the subgrid condensation scheme that is linked to the width of the PDF of the subgrid variance of the saturation departure. The higher VSIGQSAT is, the larger the PDF and it is easier for the model to condense water in a fraction of the grid.

In the Cuxart et al. (2000) scheme, seven parameters are selected. XLINI is the minimum of mixing length. The higher XLINI is, the higher the dissipation is. XCTD is a constant in the dissipation of temperature and relative humidity. This parameter is written $C_θ = C_q = C_{qθ}$ in Cuxart et al. (2000). XCTP is a constant for the temperature-vapour pressure correlations, denoted $C_h = C_s = C_s$ in Cuxart et al. (2000). XCEP is a constant for wind-pressure correlations, $C_m$ in Cuxart et al. (2000). XCED is a coefficient involved in the dissipation of the TKE, which corresponds to $C_e$ in Cuxart et al. (2000). XPHI_LIM is a threshold for the reverse Schmidt and Prandtl numbers denoted $Φ_3$ and $Ψ_3$ in Cuxart et al. (2000). Lastly, XCET is a constant in the transport term in the equation for the TKE, referred to as $C_e$ in Cuxart et al. (2000).

In the SLHD scheme, SLHDEPSH is a dimensionless parameter representing the intensity of horizontal Laplacian smoothing. SLHDKMIN and SLHDKMAX are, respectively, the minimum and maximum values for the $κ$ diffusion function described in Váña et al. (2008).

In the surface scheme, XRIMAX is the critical Richardson number which impacts the planetary boundary-layer thickness. The smaller XRIMAX is, the lower the entrainment rate is. XFRACZ0 is a tuning coefficient of orographic drag. The smaller XFRACZ0 is, the stronger the drag is.

Finally, in the shallow convection scheme, XCMF is the closure coefficient at the bottom level, denoted $M_0$ in Pergaud et al. (2009). XABUO and XBDETR are coefficients in the calculation of ascending vertical velocity, particularly, in the buoyancy and entrainment term, respectively.
<figure><img src="image_6.png" /><figcaption>TABLE 1 List of AROME parameters selected for the sensitivity analysis</figcaption></figure>

<table><thead><tr><th>Scheme</th><th>Parameter</th><th>Physical meaning</th><th>Default</th><th>Range</th></tr></thead><tbody><tr><td rowspan="2">Radiation</td><td>RSWINHF</td><td>Short-wave inhomogeneity factor</td><td>1</td><td>0.6 – 1</td></tr><tr><td>RLWINHF</td><td>Long-wave inhomogeneity factor</td><td>1</td><td>0.6 – 1</td></tr><tr><td rowspan="3">Microphysics</td><td>RCRIAUTI</td><td>Snow autoconversion threshold</td><td>0.2 × 10<sup>-3</sup></td><td>(0.02 – 0.25) × 10<sup>-3</sup></td></tr><tr><td>RCRIAUTC</td><td>Rain autoconversion threshold</td><td>1.0 × 10<sup>-3</sup></td><td>(0.4 – 1) × 10<sup>-3</sup></td></tr><tr><td>VSIGQSAT</td><td>Constant for subgrid condensation</td><td>0.02</td><td>0 – 0.1</td></tr><tr><td rowspan="5">Turbulence</td><td>XLINI</td><td>Minimum mixing length</td><td>0</td><td>0 – 0.2</td></tr><tr><td>XCTD</td><td>Constant for dissipation of temperature and vapour pressure fluctuations</td><td>1.2</td><td>0.98 – 1.2</td></tr><tr><td>XCTP</td><td>Constant for temperature and vapour pressure correlations</td><td>4.65</td><td>1.035 – 22.22</td></tr><tr><td>XCEP</td><td>Constant for wind-pressure correlations</td><td>2.11</td><td>0.225 – 4.0</td></tr><tr><td>XCED</td><td>Constant for dissipation of TKE</td><td>0.85</td><td>0.4 – 2</td></tr><tr><td rowspan="3">Diffusion</td><td>XPHI_LIM</td><td>Threshold value for Sc<sup>-1</sup> and Pr<sup>-1</sup></td><td>3</td><td>1 – 4.5</td></tr><tr><td>XCET</td><td>Constant for transport of TKE</td><td>0.4</td><td>0.072 – 1.512</td></tr><tr><td>SLHDEPSH</td><td>Strength of SLHD</td><td>0.060</td><td>0.01 – 0.09</td></tr><tr><td rowspan="3">Surface</td><td>SLHDKMIN</td><td>Diffusion function minimum</td><td>0</td><td>-1 to 1</td></tr><tr><td>SLHDKMAX</td><td>Diffusion function maximum</td><td>6</td><td>4 – 12</td></tr><tr><td>XRIMAX</td><td>Critical Richardson number</td><td>0.2</td><td>0 – 0.3</td></tr><tr><td rowspan="4">Convection</td><td>XFRACZ0</td><td>Coefficient for orographic drag</td><td>5</td><td>2 – 10</td></tr><tr><td>XCMF</td><td>Closure coefficient at bottom level</td><td>0.065</td><td>0 – 0.1</td></tr><tr><td>XABUO</td><td>Coefficient for the buoyancy</td><td>1</td><td>0.7 – 1.5</td></tr><tr><td>XBDETR</td><td>Coefficient for the detrainment</td><td>1 × 10<sup>-6</sup></td><td>0 – 1</td></tr><tr><td></td><td>XENTR_DRY</td><td>Coefficient for dry entrainment</td><td>0.55</td><td>0.1 – 0.699</td></tr></tbody></table>

Note: Default values used in the operational AROME configuration and minimum/maximum allowed values for each parameter are given in columns four and five.

XENTR_DRY is a coefficient in the dry entrainment calculation.

For each parameter, experts also suggested a uniform distribution for the perturbation range reported in Table 1. This table also presents the default values used in the operational AROME. Note that, in some cases, the default value is not in the middle of the proposed range to avoid non-physical settings.

## 3.3 | Experimental design

### 3.3.1 | Morris screening

Regarding the Morris SA, an experimental design of $r = 12$ trajectories using the Campolongo *et al.* (2007) maximizing distance method is applied to the space of the $k = 21$ parameters previously described. Each parameter perturbation range is discretized into $p = 8$ levels

and the perturbation step used is $\Delta = 4/(p - 1)$. This screening thus requires running $r(k + 1) = 12 \times (21 + 1) = 264$ AROME simulations, which is a good compromise between computational efficiency and the robustness of the results. Based on the suggestion in Campolongo *et al.* (2007) and according to findings of Di *et al.* (2015), Quan *et al.* (2016) and Ji *et al.* (2018), this Morris design with $r = 12$ trajectories should be sufficient to provide valuable and robust sensitivity results.

As the parameters' influence is likely to depend on the season and on the day, the analysis is conducted for three periods of 31 days:

* Summer 2018: from 01 May 2018 to 30 July 2018, every three days

* Autumn 2018: from 01 October 2018 to 30 November 2018, every two days

* Winter 2018–2019: from 01 December 2018 to 30 January 2019, every two days
<figure><img src="image_7.png" /></figure>

The 264 AROME simulations are run once per day, starting at 2100 UTC, and provide 48 hr forecasts. Note that, because of the 3- or 2-day interval between successive forecasts, temporal correlations are expected to be small in the dataset.

This configuration thus represents a total of 24,552 AROME forecasts to produce. In order to reduce the computational time, a hydrostatic version of the AROME model with a horizontal resolution of 2.5 km has been used. It has been verified that this hydrostatic option does not degrade the forecast performances (Figure S1). Furthermore, some recent researches question the use of a hydrostatic version at high resolution (Dueben et al., 2020) and suggest a valid use of hydrostatic version at 2.5 km (figure 1 from Burgot et al. (2021)). It is finally important to mention that no simulation crashed or drifted towards unrealistic forecasts.

### 3.3.2 | Scalar model outputs used to evaluate the model sensitivity

The Morris and Sobol' methods measure the parameters' influence with respect to a scalar model output. In this study, scalar outputs considered are either an averaged forecast field or a performance metric such as mean bias, root-mean square error (RMSE) and mean absolute error (MAE). These scores are computed using SYNOP (surface synoptic observations) and the French real-time meteorological observations network (Tardieu and Leroy, 2003), with the following formulae:

$$ 
\begin{aligned}
Bias &= \frac{1}{n} \sum_{k=1}^{n} (y_k - o_k), & RMSE &= \sqrt{\frac{1}{n} \sum_{k=1}^{n} (y_k - o_k)^2}, \\
MAE &= \frac{1}{n} \sum_{k=1}^{n} |y_k - o_k|,
\end{aligned}
\quad (9) $$

where n is the number of in situ measures, $y_k$ is the model output interpolated to the location of the kth observation (with a nearest-neighbour approach) and $o_k$ is the kth observation. Other scores, like Fraction Skill Score can also be considered for precipitation or total cloud cover.

Hence, for all 264 daily simulations, Morris sensitivity indices, $\mu_i^*\{f(d, h)\}$ and $\sigma_i\{f(d, h)\}$, are computed for each parameter, where $f(d, h)$ is a spatially averaged forecast field value or verification metrics, corresponding to the forecast issued on day d and valid at forecast range h.

The parameters' influence is examined on different meteorological variables, including 10 m wind speed (ff10m), 10 m wind gust (ffgust), 1-, 3-, 6- and 24-hourly accumulated precipitation (prec01, prec03, prec06, prec24), total cloud cover (cloud), 2 m relative humidity

(RH2m), 2 m temperature (T2m) and 1-hourly downward global solar radiation (Sol01).

### 3.3.3 | Estimation of Sobol' indices

For the Sobol' method, a PCE is used to compute Sobol' indices analytically. Because of computational cost, storage capacity and time limitations, the 5-order PCE is built directly from the 264 Morris simulations. PCEs are independently computed for each scalar model output (mean bias, MAE, RMSE) of each variable (ff10m, ffgust, prec01, ...), season (summer, autumn, winter), day (31 for each season) and forecast range (16 forecast ranges from 3 to 48 hr lead times). This represents a total of 44,640 PCEs to build. All of these surrogates are validated with the cross-validation Leave-One-Out method (Stone, 1974; Geisser, 1975).

Figure 2 represents this Leave-One-Out relative emulation error, averaged over different seasons, days and forecast ranges, for the different emulated metrics of all meteorological variables. Emulation errors for the three metrics are very small, with values between 0.5 and 2.25%. This indicates a good performance of the PCE method. In more detail, the emulations of wind at 10 m (ff10m), temperature at 2 m (T2m) and solar radiation (Sol01) have the smallest errors (less than 1%), whatever the emulated score (mean bias, MAE, RMSE). However, stronger errors are detected for the mean bias emulation of wind gust at 10 m (ffgust), total cloud cover (cloud) and relative humidity at 2 m (RH2m). On the other hand, emulation of precipitation gives the highest errors with MAE and RMSE.

<figure><img src="image_8.png" /><figcaption>FIGURE 2 Mean Leave-One-Out relative emulation error averaged over all seasons, days and forecast ranges for different meteorological variables and scalar model outputs. The surrogate errors for mean bias emulation are in black, for MAE emulation in grey and for RMSE emulation in white</figcaption></figure>
<figure><img src="image_9.png" /></figure>

## 3.4 | Definition of sensitivity indices

Different points of view of the parameter sensitivity can be considered, leading to TMI calculations with different formulae listed in Table 2.

Most Morris sensitivity indices are calculated from the spatially averaged model outputs $f(d, h) = (1/X) \sum_x f(x, d, h)$ (formulae (11)–(14)) where X is the number of spatial data (number of observations for performance metric (about 1,500) or number of grid points for mean forecast (about 200,000)). From $f(d, h)$, three types of index are computed:

* Global: represents the mean influence of parameters over a year (summer, autumn and winter), obtained from an average over seasons, days and forecast ranges.

* Seasonal: represents the mean influence of parameters for each season, obtained from an average over days and forecast ranges.

* Daily: represents the mean influence of parameters for each day of each season, obtained from an average over forecast ranges.

* Hourly: represents the mean influence of parameters as a function of forecast range, averaged over all days of a season.

The last type of TMI, hereafter called spatial TMI, allows for a spatial analysis of the influence of parameters. In that case, spatial TMI are computed on spatial model outputs but temporally averaged ($f(x, h) = (1/D) \sum_d f(x, d, h)$ where D is the number of days for each season) to reduce computational cost, as defined in (15).

While, concerning the Sobol' method, only Global Total Sobol' Indices (GTSI), averaged over all days, seasons and forecast ranges are considered in the same vein as global TMI ((11)):

$$GTSI_i = \frac{1}{S} \frac{1}{D} \frac{1}{H} \sum_s \sum_d \sum_h S_{T,i} \{f(d, h)\}, \quad (10)$$

where $f(d, h) = (1/X) \sum_x f(x, d, h)$ is the spatial-averaged scores (Mean Bias, MAE, RMSE), and $S_{T,i}$ is the Total Sobol' Indices analytically calculated from PCE coefficients. Hence, GTSI represents an overall sensitivity measure, which can be compared to the global Total Morris Indices ((11)).

## 4 | RESULTS

This section presents sensitivity results from the Morris SA on different variables and model outputs. The last subsection is devoted to results with the Sobol' method,

<table><caption>TABLE 2 Different TMI definitions with $f(x, h, d)$ being the model output depending on the space $x$, the forecast starting day $d$ and the forecast range $h$. $M_{T,i} = \sqrt{\mu_i^{*2} + \sigma_i^{*2}}$ is the TMI calculation, $S$ is the number of seasons of 31 days, $D$ is the number of days for each season and $H$ is the number of forecast ranges</caption><thead><tr><th>Parameters' influence</th><th>TMI<sub>i</sub></th><th></th></tr></thead><tbody><tr><td>Global</td><td>TMI<sub>i</sub> = <sup>1</sup>&frasl;<sub>S D</sub> <sup>1</sup>&frasl;<sub>H</sub> &sum;<sub>s</sub> &sum;<sub>d</sub> &sum;<sub>h</sub> M<sub>T,i</sub> {f(d, h)}</td><td>(11)</td></tr><tr><td>Seasonal</td><td>TMI<sub>i</sub>(s) = <sup>1</sup>&frasl;<sub>D</sub> <sup>1</sup>&frasl;<sub>H</sub> &sum;<sub>d</sub> &sum;<sub>h</sub> M<sub>T,i</sub> {f(d, h)}</td><td>(12)</td></tr><tr><td>Daily</td><td>TMI<sub>i</sub>(d, s) = <sup>1</sup>&frasl;<sub>H</sub> &sum;<sub>h</sub> M<sub>T,i</sub> {f(d, h)}</td><td>(13)</td></tr><tr><td>Hourly</td><td>RTMI<sub>i</sub>(h, s) = <sup>1</sup>&frasl;<sub>D</sub> &sum;<sub>d</sub> M<sub>T,i</sub> {f(d, h)}</td><td>(14)</td></tr><tr><td>Spatial</td><td>TMI<sub>i</sub>(x, s) = <sup>1</sup>&frasl;<sub>H</sub> &sum;<sub>h</sub> M<sub>T,i</sub> {f(x, h)}</td><td>(15)</td></tr></tbody></table>

where TSIs are presented only for the global influence (following (10)).

### 4.1 | Influence of Global parameters with the Morris design

As a first global insight into the parameters' influence, the Total Morris Indices calculated from (11) are considered.

Figure 3 shows the sensitivity of each parameter for different meteorological variables. As results for the four scalar outputs (the averaged field and the three verification scores) are very similar, the sensitivity averaged over these four outputs is presented here and in the remainder of the paper. Furthermore, as TMI values change with the meteorological variable, TMI are normalised for each meteorological variable, by their respective maximum value over all parameters. Hence, normalised values vary between 0 and 1, with higher values corresponding to a larger parameter sensitivity.

In Figure 3, VSIGQSAT, a parameter from the microphysics scheme that controls the cloud formation (especially through subgrid condensation) has a large indirect impact on solar radiation and also on temperature at 2 m through a parasol cooling effect. As a second-order impact, this parameter also indirectly influences the precipitation (all accumulation ranges) and, to a lesser extent, other meteorological fields.

However, as this parameter defines the cloud formation, its influence on total cloud cover is particularly high and the influence of other parameters, such as RSWINHF, seems negligible on that meteorological field. As VSIGQSAT has too strong an influence on total cloud cover, that meteorological field cannot be used to evaluate the impact of parameters on clouds. A solution is to consider an indirect field, also measuring the cloud's presence. The proposition here is the downward solar radiation that
<figure><img src="image_10.png" /><figcaption>FIG URE 3 TMI for each parameter as a function of meteorological variable. The higher the sensitivity, the darker the colour, and the more influential the parameter is [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

can measure the cloud presence through the cloud's shadows. Even if RSWINHF is one of the less influential parameters on total cloud cover, it is the second most important one for the solar radiation influence as it is a parameter involved in the calculation of short-wave optical properties. However, a small part of that influence may be due to the impact on the surface diurnal heating, responsible for the convective plumes at the origin of convective clouds. Thus, the choice of the meteorological field used to study the impact on clouds is important as it can lead to really different conclusions.

Regarding turbulence parameters, three of them have a large influence on several meteorological fields: XCTP, XCEP and XCED. As XCTP occurs in the equations of the correlations between wind and temperature or vapour fluctuations, it has a strong impact on these meteorological fields, near the surface. XCEP is involved directly in the calculation of wind fluctuations. Consequently, its impact on wind at 10 m is the strongest. Finally, XCED defines the diffusion of the TKE. Since the TKE is proportional to the squared wind fluctuations, that parameter clearly affects the wind gust calculation. This parameter also impacts the wind at 10 m. Furthermore, these three parameters also influence the precipitation field but these impacts are more indirect and not clearly understood.

In the diffusion scheme, SLHDEPSH controls the hydrometeors' diffusion. Consequently, this parameter is known to have a large impact on the precipitation rate. We can notice that this impact becomes stronger for longer accumulation ranges, compared to other influential parameters on precipitation. This parameter does not seem to have an influence on other meteorological fields.

In the surface scheme, XFRACZ0 controls the orographic drag, and consequently impacts the friction at the surface and then the near-surface wind.

The XCMF parameter from the shallow convection scheme seems to have an influence on all variables. Since XCMF describes the mass flux at low levels, it impacts the convective clouds' formation, their radiative impact on the ground and also convective precipitation at grid scale. As it characterises the convective plumes at the bottom level, it defines the wind convergence and the wind force at the surface. This explains why this parameter affects winds at 10 m. Furthermore, XCMF also alters the accumulated precipitation, solar radiation, temperature and relative humidity at 2 m. Indeed, this parameter controls the intensity of the mass flux and consequently the activity of the shallow convection scheme. Thus, as already observed by Khain *et al.* (2021), that activity influences the ascending motion of humidity in the free atmosphere and the humidity available for the microphysics scheme to generate grid-scale precipitation.

We finally notice that all parameters impact the precipitation forecasts. That result shows the implication of all parametrizations in the calculation of precipitation.

From the above analysis, one can deduce a list of the eight most influential parameters on all meteorological variables: RSWINHF, VSIGQSAT, XCTP, XCEP, XCED, SLHDEPSH, XFRACZ0 and XCMF. These parameters appear in the top five ranking for at least one meteorological variable. Furthermore, they are involved in all parametrizations.

The 13 remaining parameters have only marginal impacts on model outputs. The limited sensitivity of AROME forecasts to these parameters can be explained either by their contribution to second-order physical phenomena (e.g., XCTD is involved in second-order temperature, humidity fluctuations), or possibly by a too small variation range.

## 4.2 | Influence of seasonal parameters

As a second step, we examine the seasonal dependence of the parameter influence, using seasonal TMI calculated with (12). Figures 4a, b present, respectively for summer and winter, TMI (averaged for all model outputs: Mean Bias, MAE, RMSE, mean field) for each parameter and meteorological field. To better compare TMI for different model outputs and seasons they are normalized, for each meteorological field, by the maximum TMI value of the three seasons (summer, autumn, winter).

All the most influential parameters have a strong variability according to season. In particular, we can notice that parameters from radiation, microphysics and shallow
<figure><img src="image_11.png" /><figcaption>FIGURE 4 TMI for each parameter as a function of meteorological variable, and for each season: (a) summer and (b) winter. The higher the sensitivity, the darker the colour, and the more influential the parameter is [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

convection schemes (RSWINHF, VSIGQSAT and XCMF) have a larger influence on model outputs during summer (Figure 4a) than in winter (Figure 4b). Indeed, during summertime, there are more convective clouds and the radiation intensifies. That is why radiating parameters (RSWINHF) are more sensitive to downward solar radiation (Sol01) in summer (Figure 4a). Furthermore, as shallow convection and microphysics schemes are more active to represent convective clouds, parameters from these parametrizations (XCMF and VSIGQSAT) have a stronger influence. Moreover, as the convective activity induces higher hydrometeor contents and the associated precipitation is mainly convective, hydrometeor contents and consequently precipitations are more smoothed by the diffusion scheme in convective situations. This is particularly true as the SLHD scheme takes more action in convective plumes where the wind strain field is more important due to high values of vertical velocity. This explains why SLHDEPSH has a stronger influence in summer than in winter.

Generally, all major parameters have a larger influence on model outputs during summer. Indeed, physical parametrizations are more active in AROME forecasts for summer than for winter especially regarding convection over land. This is particularly true as TMI are calculated from land station observations used for the scores computation.

On the other hand, parameters from turbulence schemes (XCTP, XCEP and XCED) and from orographic drag representation (XFRACZ0) have a larger influence on wind and wind gust in winter. Hence, the variations of wind forecast performance are mainly related

to turbulence parameters. We explain this behaviour by a stronger average wind shear during wintertime in the AROME-France domain, and also by more frontal turbulence and storms in winter.

Finally, the eight most influential parameters identified with the global analysis remain the most influential ones for summertime. For wintertime this list can be reduced to only four (VSIGQSAT, XCTP, XCEP and XCED).

## 4.3 | Influence of daily parameters

In this section, we examine the daily variations of the influence of the parameters over a season. These daily results are obtained using (13). Because of a larger influence of parameters during summer, here we present results only for that period.

Figure 5 shows the parameters’ influence averaged over the different forecast ranges (from 3 to 48 hr lead time), for each day of the summer period. In the same vein as global and seasonal TMI, the daily TMI are averaged over all model outputs: Mean Bias, MAE, RMSE, mean meteorological field. The different values for a given variable are normalized by the corresponding maximum value over the considered period.

The most influential parameters remain the same over the whole period, but we can notice some daily variations in the sensitivity intensity. For example, in Figure 5a, b the influence of the most influential parameters on wind at 10 m and wind gusts (VSIGQSAT, XCTP, XCEP, XCED
<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /><figcaption>**FIGURE 5** Daily TMI for each day of the summer 2018 period, for each parameter and for (a) wind at 10 m, (b) wind gust at 10 m and (c) 3 hr precipitation. The higher the sensitivity, the darker the colour, and the more influential the parameter is [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

and XCMF) is generally unchanged. However, a larger sensitivity in the forecast of 27 July 2018 at 2100 UTC is detected for XCEP and XCED from the boundary-layer scheme. On this day, an extratropical cyclone crossed the AROME-France domain. Its pressure minimum passed over the north of the domain, near the United Kingdom. A cold front crossed France during 28 and 29 July 2018. Hence, this stronger influence on wind at 10 m and wind gust may be due to the gust front associated with the cold front.

On Figure 5c, the daily parameters' influence on 3-hourly accumulated precipitation is much more variable according to the weather situation. In particular,

VSIGQSAT and SLHDEPSH have a larger influence for forecasts initialised from 28 May to 9 June and from 30 June to 3 July 2018. These periods correspond to stronger convective situations with many warnings for thunderstorms. Thus, the impact of these parameters is clearly linked to the convective activity in the model. On the contrary, no significant rainfall was observed between 12 and 27 June, which explains the small influence of parameters during that period.

The parameters' influence clearly depends on the weather situation. The interpretation of the parameters' sensitivity may change significantly. This shows the need to perform SA over large periods in order to cover a large
<figure><img src="image_14.png" /><figcaption>FIGURE 6 TMI as a function of forecast range, for each parameter during the summer 2018 period. (a) 10 m wind, (b) 6 hr accumulated precipitation and (c) temperature at 2 m. The higher the sensitivity, the darker the colour, and the more influential the parameter is [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

number of different meteorological situations to get more
robust results.

**4.4** | Influence of hourly parameters

We present in this section the diurnal cycle of parameters'
influence on some meteorological variables and for the
summer and winter periods. TMI are computed using (14).
Similarly to previous results, these hourly TMI are aver-
aged over all model outputs considered, for wind at 10 m,
6-hourly accumulated precipitation and temperature at
2 m in summer (Figure 6a-c) and winter (Figure 7a-c).

TMI are normalized by the maximum value over all fore-
cast ranges. We note that the 0 hr lead time in Figures 6
and 7 corresponds to 2100 UTC.

In Figure 6, we can point out that the most influen-
tial parameters are consistent with those identified in
the global SA, namely: RSWINHF, XCTP, XCEP, XCED,
XFRACZ0, SLHDEPSH, XCMF and VSIGQSAT. How-
ever, their effects on model outputs differ according to the
lead time. For wind at 10 m (Figure 6a), VSIGQSAT and
XCMF influences exhibit a clear diurnal cycle with an
increase between 12–18 hr and 36–42 hr forecast ranges,
which correspond to the periods of convective activity. We
notice that VSIGQSAT presents a slightly 3-hour temporal
<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /><figcaption>FIGURE 7 TMI as a function of forecast range, for each parameter during winter 2018–2019. (a) 10 m wind, (b) 6 hr accumulated precipitation and (c) temperature at 2 m. The higher the sensitivity, the darker the colour, and the more influential the parameter is [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

shift compared to XCMF. This shift can be explained by
the time difference between the formation of convective
plumes in the boundary layer and the creation of clouds
at the top of the boundary layer. Turbulence parameters
also present a diurnal cycle but it is less noticeable. XCEP
(wind/pressure correlation) and XCTP (temperature/-
vapour pressure correlation) affect wind at 10 m between
15–18 hr and 39–42 hr lead times, during afternoons when
the turbulence in the boundary layer is more intense and
correlations between wind fluctuations are stronger. On
the contrary, XCED (diffusion of TKE) has a larger sensi-
tivity at night (3–9 hr and 24–30 hr lead times) due to the
increase of the TKE dissipation during that time of the day.

Regarding precipitation (Figure 7b), all turbulence
parameters have the same diurnal cycle with a slightly
larger influence during the afternoon (18–30 hr and
42–48 hr), clearly linked to convective precipitation. We
can also notice that the sensitivities of SLHDEPSH and
VSIGQSAT on precipitation present a strong diurnal cycle,
particularly correlated with the convection activity (at
18–24 hr and 42–48 hr).

Concerning temperature at 2 m (Figure 6c), the diurnal cycle is clearly more evident than for 10 m wind and precipitation. XCTP exhibits a smaller but noticeable effect on temperature during the night, between 3–6 hr and 24–30 hr, in addition to the one observed during the day.
We also notice that the influence of parameters linked to the convective activity (VSIGQSAT and XCMF) is slightly delayed by 6 hr relative to the meteorological variables: from 12–18 hr forecast ranges for 10 m wind and temperature to 18–24 hr for 6 hr precipitation (for J + 1). This is due to the accumulation range of precipitation.

Regarding the winter period (Figure 7), consistently with the seasonal analysis, a much smaller influence of convection, diffusion and microphysic parameters, such as XCMF, SLHDEPSH and VSIGQSAT, is observed for 10 m wind, precipitation and 2 m temperature. The main difference is the absence of diurnal cycles particularly for 10 m wind (Figure 7a). A diurnal cycle is still observed for the impact of XCTP and XCED on 2 m temperature (Figure 7c),

but it is much smaller than in summer (Figure 6c). Finally, no diurnal cycle appears in the influence of parameters on precipitation during winter (Figure 7b). However, for the two seasons, an increase of the parameters’ impact on precipitation according to forecast lead time is noticed (Figures 6b and 7b), suggesting cumulative effects of impact over the forecast range.

## 4.5 | Spatial influence of the most influential parameters

In order to examine the spatial distribution of parameters' sensitivity, Figures 8a, b, 9a, 10a and 11a map the response

<figure><img src="image_17.png" /><figcaption>**FIGURE 8** Comparison between influences of (a) XCEP and (b) XCFRACZ0 on the 10 m wind. (c) shows the AROME forecasts of 10 m wind field, averaged over summer 2018 and forecast ranges [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>
<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /><figcaption>FIGURE 9 Comparison between (a) the influence of XCED on wind gust and (b) the AROME forecasts of wind gust field at 10 m, averaged over summer 2018 and forecast ranges [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>FIGURE 10 Comparison between (a) the influence of SLHDEPSH on 6 hr precipitation and (b) the AROME forecasts of 6 hr precipitation field, averaged over summer 2018 and forecast ranges [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

of seasonal mean forecasts to the parameters' variations during summertime. These TMI are computed following (15) and are normalized by the maximum value in the AROME-France domain.

Similar calculations can be performed using forecast
verification metrics as scalar outputs. However, these
scores provide sparse information with only one sensitiv-
ity value at each observation location. The advantage of
directly looking at the forecast fields is that it provides
an information over the whole AROME-France domain.
Sensitivities are presented for five of the most influential

parameters regarding 10 m wind, 10 m wind gust, 6-hr pre-
cipitation and total cloud cover. As the interpretation of
results for the different seasons is very similar, only the
summer period is shown here.

In addition to the sensitivity maps, Figures 8c, 9b, 10b and 11b also present the AROME forecast fields, averaged over the summer period and all forecast ranges.

Figure 8a, b present the sensitivity of the 10 m
wind forecast field to parameters XCEP (constant for
wind-pressure correlations) and XFRACZ0 (coefficient for
orographic drag) respectively, during the summer period.
<figure><img src="image_21.png" /><figcaption>FIGURE 11 Comparison between (a) the influence of VSIGQSAT on total cloud cover and (b) the AROME forecasts of total cloud cover, averaged over summer 2018 and forecast ranges [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

According to previous results, XCEP is certainly one of the most important parameters for that meteorological variable. Its sensitivity is particularly high in the Channel and in the Gulf of Lion (Figure 8a). Figure 8c presents the seasonal mean of operational AROME forecast of wind at 10 m during this summer, and these two regions correspond to windy zones. Thus, this parameter seems to have a stronger influence on windy areas. XFRACZ0, used in the SURFEX scheme, is one of the eight most influential parameters on wind. Contrary to XCEP, this parameter has a very local impact and its influence does not depend on seasonal wind. One can see in Figure 8b that its impact predominates in orographic areas such as the Alps and the Pyrenees.

XCED was previously identified as the most influen-
tial parameter for 10 m wind gusts. Figure 9a indicates a
clear land/sea contrast of its impact during summer, with
higher sensitivity values over land, where the turbulence
is more active than over sea, due to a larger roughness over
land. Thus, no clear link with the seasonal mean wind gust
forecast can be found (Figure 9b). However, the sensitivity
to XCED is locally enhanced in well-known windy regions
such as the Rhône valley.

Figure 10a presents the sensitivity of precipitation to
the diffusion parameter SLHDEPSH, during summer. Its
sensitivity is clearly correlated with the seasonal field
of precipitation (Figure 10b). For example, the western
part of France, the north of Spain, the southwest of Ger-
many and the Alps are rainy locations, where SLHDEPSH
has a strong influence. On the contrary, the sensitivity
is much more limited in the rainy region near Ireland,
United Kingdom or Sardinia. This may be due to less
convective precipitation but more stratiform precipitation
on these areas.

Finally, the sensitivity of total cloud cover to VSIGQSAT is shown in Figure 11a. This parameter has a stronger influence over the sea, which can be explained by a higher relative humidity that favours subgrid condensation. However, we note a higher influence over the Mediterranean and North Seas than over the Atlantic. This behaviour does not seem to be correlated with the mean total cloud cover field (Figure 11b). This behaviour could be explained by a stronger evaporation rate over Mediterranean Sea. This is not a surprise that VSIGQSAT has a high influence over this region: as the relative humidity is higher, the condensation point is easier to reach. However, for the cold North Sea, which is not particularly known to have a high evaporation rate, the strong influence of VSIGQSAT is not clearly understood.

The spatial distribution of parameters' sensitivity is overall consistent with the underlying distribution of weather forecasts. However, this spatial study shows that some parameters, as XCED or VSIGQSAT, can have a spatially wide influence related to sea/land differences for instance, while others, as XFRACZ0 or SLHDEPSH, have a more local impact, for example relative to orographic features.

4.6 | Interactions between parameters with the Sobol' method

In addition to the Morris SA, a Sobol' analysis has also
been conducted. However, because of the high number
of meta-models needed, the first-order, second-order and
Total Sobol' Indices are analytically calculated from PCE
coefficients built only for the spatially averaged scores
as scalar model outputs. Furthermore, the same global
<figure><img src="image_22.png" /><figcaption>FIGURE 12 Total Sobol' indices, for each parameter as a function of meteorological variable. The higher the Total Sobol' Index, the darker the colour, and the more influential the parameter is [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>

averaging (over all days, seasons and forecast ranges) used in Section 4.1 is applied to compute the Global Total Sobol' Indices (GTSI; (10)).

Figure 12 presents the GTSI for each parameter and for different meteorological variables. This figure can directly be compared to Figure 3. Generally, the information provided by GTSI is quite similar to that provided by TMI. However some differences can be noticed. It is interesting to observe that there is a higher contrast between the impact of the most influential parameters and the lesser influential ones. For example, the impact of XCEP on 10 m wind dominates, in particular in comparison with parameters XCED and XCTP, whose impact was larger according to the Morris sensitivity (Figure 3). The same remark is true for all meteorological variables and particularly for precipitation: the Morris sensitivity indicated a relatively high impact of most parameters, while the Sobol' indices better highlight the contributions of VSIGQSAT, XCEP and SLHDEPSH. Furthermore, the impact of XCEP and XCED on precipitation and solar radiation is smaller with the Sobol' method. Finally, the list of the most influential parameters according to the Sobol' method may change: it suggests reducing the list to VSIGQSAT, XCTP, XCEP, XCED and SLHDEPSH.

The good agreement between Morris and Sobol' results tend to confirm the robustness of the PCEs. It is then interesting to look at the additional information about interactions between parameters, provided by the second-order Sobol' indices. It is worth mentioning, however, that given the relatively basic sampling used for training the PCEs, these interactions may be only partially estimated.

Figure 13 presents the second-order Sobol' indices for each couple of parameters and for different meteorological variables. Similarly to the Global Total Sobol' Indices, these second-order indices are computed from the spatially averaged scores and are then temporally averaged as in (10).

First of all, we remark on numerous interactions for wind gusts and 6 hr precipitation, suggesting high interactions between parametrizations, as previously noticed in Section 4.1 (Figure 13b, c). On the other hand, only few strong interactions are noticeable for 10 m wind, total cloud cover, relative humidity and temperature.

For wind gusts (Figure 13b), interactions occur mainly between parameters from the turbulence scheme. Two interactions seem particularly important: XCED (diffusion of TKE) with XCEP (wind/pressure correlation) and with XCTP (temperature/vapour pressure correlation). As XCEP and XCTP are involved indirectly in the wind gust calculation, which strongly depends on XCED, these interactions are not surprising. We also remark that the interaction between XCED and XCEP also appears for 6 hr precipitation (Figure 13c), temperature at 2 m (Figure 13f) and particularly for 10 m wind (Figure 13a). Indeed, it involves XCED which occurs in the wind gust calculation and XCEP in the wind correlation. The interaction between XCED and XCTP for wind gusts (Figure 13b) also appears for relative humidity and temperature (Figure 13e, f). For these two meteorological variables, the interaction between XCTP and XCMF is also quite important. This shows the link between the turbulence and the shallow convection schemes.

The most influential parameter on total cloud cover is VSIGQSAT, and this parameter is in interaction with several others (Figure 13d), in particular with XCEP. This interaction also appears for the impact on precipitation (Figure 13c).

Some other interactions can be noticed such as

(i) RSWINHF with XCEP (XCED) on the precipitation (wind gust) forecasts (Figures 13c and 13b),

(ii) XCEP with XCMF and XCED on the wind gust forecasts (Figure 13b) and

(iii) VSIGQSAT with XCTP on the total cloud cover forecasts (Figure 13d).

For downward solar radiation (not shown) there is only one interaction between RSWINHF and VSIGQSAT. This result is not surprising since this meteorological variable clearly depends on the solar optical properties altered by RSWINHF and on the cloud parasol effect linked to the cloud formation controlled by VSIGQSAT.

Finally, we can notice that XLINI (minimum mixing length), which has one of the smallest direct influence
<figure><img src="image_23.png" /><figcaption>FIGURE 13 Second-order Sobol' indices calculated for (a) 10 m wind, (b) 10 m wind gust, (c) 6 hr precipitation, (d) total cloud cover, (e) 2 m relative humidity and (f) 2 m temperature. The higher the Sobol' index, the darker the colour, and the higher the interaction between the parameters is [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>
on AROME forecasts, seems to have a significant indi-
rect impact through its interaction with XCEP on the 10 m
wind. This interaction also appears for the precipitation
forecasts (Figure 13c).

Thus, regarding Figure 13, five main interactions
are detected for the influence on different meteorologi-
cal variables: XCED-XCEP, XCED-XCTP, XCMF-XCTP,
VSIGQSAT-XCEP and XLINI-XCEP. These interactions
mainly concern the eight most influential parameters
except the last one.

5 | OUTLOOK AND CONCLUSIONS

In this study, a sensitivity analysis of the French convective-scale AROME model to a set of 21 parameters from physical and dynamical schemes has been presented and discussed. The Morris screening, which perturbs one parameter at a time, has been successfully applied to several meteorological variables and scalar model outputs, in order to examine the parameters’ influence on different spatial and temporal scales. In addition, the Sobol’ method has mostly confirmed the Morris results.

The global parameters' influence, averaged over approximately a year of data, allows us to identify eight major parameters, namely, RSWINHF, VSIGQSAT, XCTP, XCEP, XCED, SLHDEPSH, XFRACZ0 and XCMF, which have a noticeable impact on different near-surface meteorological variables, especially wind and precipitation. Three parameters in this list occur in the turbulence scheme (XCTP, XCEP and XCED) and affect almost all weather variables, which highlights the importance of properly tuning this parametrization. VSIGQSAT, a parameter from the subgrid condensation scheme, such as XCMF from the shallow convection scheme, have large direct or indirect impacts on most meteorological variables. These two parameters seem to be relevant for the cloud representation in the AROME model. Finally, parameters RSWINHF, SLHDEPSH and XFRACZ0 are in the top five of the most influential parameters for at least one meteorological variable. RSWINHF, which controls the short-wave inhomogeneity factor, is obviously one of the most sensitive parameters on solar radiation at the surface. SLHDEPSH has a strong influence only on precipitation. XFRACZ0, from the SURFEX scheme, particularly affect the wind at 10 m. The Sobol' method suggests reducing the list to five parameters: VSIGQSAT, XCTP, XCEP, XCED and SLHDEPSH.

A deeper investigation of sensitivity results also
revealed interesting variations on different temporal
scales. In particular, a diurnal cycle is observed for several
parameters in the summer period, and is closely related to
convective activity. It is also shown that convection-related

parameters have a larger influence in summer. Spatial
sensitivities also indicate that the spatial distribution of
parameters' influence is closely linked to the underlying
distribution of the forecast field. Finally, the Sobol' sen-
sitivity analysis gives a first insight into the interactions
between parameters.

This work provides a helpful insight into the “black
box” of parametrizations and may serve as a baseline
for different applications. For instance, the tuning of
parameters’ values for deterministic forecasting could
primarily focus on the most influential parameters iden-
tified. In addition, this study can be seen as a preliminary
step towards the implementation of perturbed parameter
approaches in EPSs in order to define the most important
parameters to perturb. This aspect will be further explored
in a forthcoming paper. Moreover, the daily variations of
parameters’ impacts suggest that it is necessary to per-
turb parameters during the integration of each forecast.
More specifically, a time-scale of 6 hr is recommended.
In the same way, the spatial study indicates the need to
perturb parameters in space. Spatial scale must cover all
the scales between the land/sea (synoptic) to plain/relief
scale (local).

Finally, some influences of the parameters are still
not clearly understood and no information about the
direction of the effect of parameters on model out-
puts are detected with these global sensitivity analyses.
A more detailed study on physical processes based on
the impact on physical tendencies could help to better
understand impacts and interactions of these parame-
ters. Furthermore, sensitivity analyses using local meth-
ods could also give a more detailed estimation of the
impact of parameters, in particular the direction of these
effects.

ACKNOWLEDGEMENTS

The authors would like to thank Agnès Lagnoux, Clé-
mentine Prieur, Robert Faivre and Bruno Sudret for their
help and advice on sensitivity analysis, and also Rachel
Honnert for expertise on the turbulence scheme. Our
sincere gratitude also goes to Inger-Lise Frogner, the
HIRLAM-EPS team, François Bouttier and Philippe Arbo-
gast for their suggestions and remarks.

AUTHOR CONTRIBUTIONS

**Meryl Wimmer:** data curation; formal analysis; investigation; methodology; software; visualization; writing – original draft. **Laure Raynaud:** Laurent **Descamps:** conceptualization; methodology; project administration; supervision; validation; writing – review and editing. **Loïk Berre:** conceptualization; methodology; project administration; supervision; validation; writing – review and editing. **Yann Seity:** conceptualization;
methodology; supervision; validation; writing – review
and editing.

ORCID

Meryl Wimmer https://orcid.org/0000-0002-9639-9145

Laure Raynaud https://orcid.org/0000-0003-1656-9982

Loïk Berre https://orcid.org/0000-0002-3093-7668

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## SUPPORTING INFORMATION

Additional supporting information may be found online in the Supporting Information section at the end of this article.

**How to cite this article:** Wimmer, M., Raynaud, L., Descamps, L., Berre, L. & Seity, Y. (2022) Sensitivity analysis of the convective-scale AROME model to physical and dynamical parameters. *Quarterly Journal of the Royal Meteorological Society*, 148(743), 920–942. Available from: https://doi.org/10.1002/qj.4239