Improving the Near-Surface Wind and Turbulence at the Edge of the Orographic Drag Gray Zone by Tuning the Roughness Length

Mario Hrastinski aCroatian Meteorological and Hydrological Service, Zagreb, Croatia

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Ján Mašek bCzech Hydrometeorological Institute, Praha-Komořany, Czech Republic

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Ana Šljivić aCroatian Meteorological and Hydrological Service, Zagreb, Croatia

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Abstract

In this paper, we present the implementation and evaluate the impact of the new roughness length configuration in the ALARO canonical model configuration of the ALADIN system at the edge of the orographic gravity wave drag gray zone. As an essential input for turbulence parameterization, the roughness length affects the near-surface turbulent fluxes and the screen-level interpolation of meteorological parameters. We utilize GMTED2010 and ECOCLIMAP-II databases to derive orographic and vegetation components of the effective roughness length and introduce tuning parameters enabling us to optimize predicted near-surface turbulent momentum fluxes and 10-m wind speed. Based on sensitivity tests, we (i) prove the necessity of tuning the roughness length fields, (ii) considerably reduce the RMSE of near-surface turbulent momentum fluxes (6%–7%) and 10-m wind speed for different groups of stations (3%–10%), and (iii) identify the tree height as the most influential input parameter in our computational domain. The RMSE decomposition indicates that the improvement of 10-m wind speed mostly comes from a decrease in the random error and bias of the mean. The variability is slightly underestimated, thus reducing the model accuracy for wind speeds above the 95th percentile but at an acceptable level. We explain that roughness length tuning also compensates for the missing roughness sublayer correction in our system. Finally, we show that, although the impact of the orographic gravity wave drag scheme at a horizontal mesh size of 1.8 km is generally small, it is still beneficial for capturing some finer features observed in atmospheric soundings.

Significance Statement

Aiming to improve the 10-m wind speed forecast without sacrificing the accuracy of turbulent momentum fluxes in the kilometric resolution numerical weather prediction model, we derived new roughness length fields from high-resolution physiography databases. Therein, we proved the importance of tuning the input orography and vegetation fields and, depending on the time of day and year, reduced the root-mean-square error of 10-m wind speed by 3%–10%. Further, we demonstrated that orographic gravity wave drag parameterization is still needed to predict finer details seen in wind profiles from atmospheric soundings. Finally, we discussed the related simplifications in our model and their implications and proposed steps toward a more consistent and complete treatment of the near-surface turbulence.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Mario Hrastinski, mario.hrastinski@cirus.dhz.hr

Abstract

In this paper, we present the implementation and evaluate the impact of the new roughness length configuration in the ALARO canonical model configuration of the ALADIN system at the edge of the orographic gravity wave drag gray zone. As an essential input for turbulence parameterization, the roughness length affects the near-surface turbulent fluxes and the screen-level interpolation of meteorological parameters. We utilize GMTED2010 and ECOCLIMAP-II databases to derive orographic and vegetation components of the effective roughness length and introduce tuning parameters enabling us to optimize predicted near-surface turbulent momentum fluxes and 10-m wind speed. Based on sensitivity tests, we (i) prove the necessity of tuning the roughness length fields, (ii) considerably reduce the RMSE of near-surface turbulent momentum fluxes (6%–7%) and 10-m wind speed for different groups of stations (3%–10%), and (iii) identify the tree height as the most influential input parameter in our computational domain. The RMSE decomposition indicates that the improvement of 10-m wind speed mostly comes from a decrease in the random error and bias of the mean. The variability is slightly underestimated, thus reducing the model accuracy for wind speeds above the 95th percentile but at an acceptable level. We explain that roughness length tuning also compensates for the missing roughness sublayer correction in our system. Finally, we show that, although the impact of the orographic gravity wave drag scheme at a horizontal mesh size of 1.8 km is generally small, it is still beneficial for capturing some finer features observed in atmospheric soundings.

Significance Statement

Aiming to improve the 10-m wind speed forecast without sacrificing the accuracy of turbulent momentum fluxes in the kilometric resolution numerical weather prediction model, we derived new roughness length fields from high-resolution physiography databases. Therein, we proved the importance of tuning the input orography and vegetation fields and, depending on the time of day and year, reduced the root-mean-square error of 10-m wind speed by 3%–10%. Further, we demonstrated that orographic gravity wave drag parameterization is still needed to predict finer details seen in wind profiles from atmospheric soundings. Finally, we discussed the related simplifications in our model and their implications and proposed steps toward a more consistent and complete treatment of the near-surface turbulence.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Mario Hrastinski, mario.hrastinski@cirus.dhz.hr

1. Introduction

Having an accurate and timely wind forecast, particularly near the surface, is of great importance for weather forecasters when issuing warnings of different hazards. It is also crucial for various applications, including road, marine, and air traffic as well as air pollution transport and operation of wind farms. Wind forecast also has implications for ocean modeling, including sea currents, sea waves, and storm surges. Despite the continuous improvement of NWP models, their horizontal and vertical resolutions, as well as the description of orography and other surface-related features, accurate positioning of wind systems in time and space remains a challenge.

The orography and other surface-related features (obstacles) considerably affect the atmospheric flow at the range of spatial and temporal scales (e.g., Kanehama et al. 2019). The accuracy of underlying processes in NWP models depends both on gridscale orography (GSO) and subgrid-scale orography (SGSO). The GSO is typically obtained by gridscale averaging and eventual filtering of the real orography from the input data to avoid instability over steep slopes, the appearance of unrealistic gravity waves, and aliasing (e.g., Georgelin et al. 1994; Elvidge et al. 2019). The strength of applied filters and target orographic resolution are model-dependent and considerably affect the SGSO. Typically, the smallest resolved scales related to orography vary between 3 and 8 grid spacing (Δx) (e.g., Elvidge et al. 2019). The unresolved part of the orographic impact on the atmospheric flow is accounted for in the momentum budget with the parameterization of drag processes. These processes typically include the drag due to orographic gravity waves, blocking of the low-level flow and turbulent orographic form drag (TOFD) due to subgrid obstacles (e.g., Beljaars et al. 2004; van Niekerk et al. 2016). The first two processes become mostly resolved below Δx = 2 km (e.g., Vosper et al. 2016, 2020), while the latter one remains unresolved even at hectometric scales (Sandu et al. 2019). However, it should be noted that other drag related processes do exist in reality, but are still not accounted for in parameterizations of mesoscale NWP models, e.g., lee-wave drag and transient wave–mean flow interaction (Sandu et al. 2019).

Given the above discussion, TOFD is the most relevant process from the drag family in this study as our model has Δx = 1.8 km. There are different approaches to its representation available in the literature: (i) the effective roughness length (z0meff) concept (e.g., Fiedler and Panofsky 1972; Hewer and Wood 1998; Grant and Mason 1990) and (ii) the explicit orographic stress profile method (e.g., Wood et al. 2001; Beljaars et al. 2004). The main difference is how they express the total surface drag, i.e., the sum of turbulent shear stress and pressure forces. The first approach assumes increasing the local roughness length (RL) above its vegetative value and thus representing the TOFD by enhanced turbulent shear stress (e.g., Taylor et al. 1989; Wood and Mason 1993). Contrary, the second approach includes adding a new term to the momentum equation, i.e., parameterizing the process outside of the turbulence scheme.

There are more ways to define z0meff, but the common goal of all is to represent a spatially averaged turbulent momentum flux (TMF) in mountainous (hilly) terrain. Although followed with success in many modeling applications, the z0meff approach has some well-identified shortcomings. Those include (e.g., Hignett and Hopwood 1994; Wood et al. 2001; Beljaars et al. 2004; Howard and Clark 2007): (i) possible occurrence of numerical instability if z0meff is enhanced incautiously, (ii) correct surface TMF obtained at the expense of too weak wind at the lowest model level (in areas with high values of z0meff), (iii) the absence of the impact of anisotropy of SGSO (directional dependency), (iv) difficulties in understanding interactions with other drag-related processes, and (v) the existence of alternatives to describe the impact of stability on the TOFD in a more direct and transparent way.

Despite its shortcomings, z0meff is still frequently utilized concept in NWP and research models. Generally, there are two basic types of methods for its computation (e.g., Han et al. 2014): (i) wind profile-based methods utilizing the bulk similarity approach (e.g., Jacobs and Schols 1986; Sicart et al. 2014; Hintz et al. 2020; Nelli et al. 2020) and (ii) land surface parameter methods based on parameterization schemes (e.g., De Vries et al. 2003; Faivre et al. 2017; Floors et al. 2018). Given the spatial coverage of observations and typical domain sizes of operational NWP models, the second method predominates in such an environment. Besides the orography, these methods typically utilize various input data which link the RL with vegetation and urban structures (e.g., buildings and pillars). Among others, we emphasize the satellite-based LAI or NDVI (e.g., Faroux et al. 2013), laser altimeter data (e.g., De Vries et al. 2003; Floors et al. 2018), lidar and radiometry data (e.g., Faivre et al. 2017), and synthetic aperture radar data (e.g., Zhang et al. 2017). Recently, with the growing number of sources and volume of data, machine learning methods are increasingly used to extract land surface and land cover data (e.g., Walsh et al. 2021) or even the RL itself (e.g., Hu et al. 2020).

Besides the contribution to TMF and turbulent shear stress, the z0meff is used to derive the 10-m wind by applying the Monin–Obukhov similarity theory (MOST). The analogous approach also holds for other screen-level parameters, e.g., 2-m temperature and humidity. In forested and urban environments, the wind profiles obtained by utilizing the MOST need to be modified to include their wake effect, i.e., roughness sublayer correction needs to be applied (e.g., Harman and Finnigan 2007; Lee et al. 2020). More details on the role of RL in the ALARO canonical model configuration (CMC) of the ALADIN system (Termonia et al. 2018), with implications for the verification of 10-m wind, are given in the following section.

The aim of our research is threefold. First, to create a procedure for computation of RL fields from recent high-resolution databases and examine their impact on the near-surface wind (NSW) and turbulence. Second, to optimize the scaling of input fields utilized to derive the RL, e.g., SGSO, LAI, and tree height (HT). Third, to validate the impact of the drag family of schemes at the edge of the orographic drag gray zone. Based on this research, parameters of the final RL configuration will be proposed. The aim is to apply them within the next version of the operational NWP model at Croatian Meteorological and Hydrological Service (CMHS). The paper is organized as follows. Section 2 explains the role of RL in turbulence parameterization of the ALARO CMC. Procedures and data employed to derive RL fields are elaborated in section 3, followed by the description of verification data and methodology, and model settings in section 4. The impact of the orographic gravity wave drag (OGWD) scheme and RL modifications on the NSW and turbulence are shown in section 5. Finally, the summary and conclusions are given in section 6.

2. The role of the roughness length in the TOUCANS turbulence parameterization

Third-Order moments Unified Condensation Accounting and N-dependent Solver (TOUCANS; Bašták Ďurán et al. 2014, 2018) is a turbulence parameterization applied in the ALARO CMC, as well as its version ALARO-HR18 which is in preparation for operational application at CMHS. The description of the ALARO-HR18 model is given in section 4c.

The RL is one of the fundamental quantities of turbulence parameterization in NWP and climate models. Its role is twofold. First, it is utilized to compute the turbulent transport of momentum, heat, and moisture in the surface layer of the planetary boundary layer (PBL). Second, it plays a crucial role in the computation of screen-level meteorological parameters, i.e., construction of their subgrid vertical profiles in the surface layer. In statically neutral conditions, we can express this for wind and dry static energy as follows (e.g., Stull 1988; Foken 2008):
u(z)=u*κln(z+z0mdz0m),
s(z)=s0+Prtns*κln(z+z0hdz0h),
where z is height above the surface, u and s are wind and dry static energy at z, z0m and z0h are RL for momentum and heat, d is a zero-plane displacement height, s0 is dry static energy at z = d, u* and s* are characteristic scales of turbulent fluctuations of wind and dry static energy, Prtn is the turbulent Prandtl number at neutrality, while κ is von Kármán’s constant. Two remarks should be made here: (i) Eqs. (1) and (2) are valid only in the inertial sublayer of the surface layer, i.e., above the so-called blending height, below which the real profiles depart from the logarithmic law, and (ii) in the literature, the logarithmic wind profile is often simplified to: u(z)=(u*/κ)ln[(zd)/z0m], supposing zdz0m. We cannot make this approximation on a gridbox scale, where z0m also contains the orographic component. In such case, z0m can exceed the forcing height (around 10-m in the ALARO-HR18).

The RL is proportional to the height of local obstacles (e.g., rocks, trees, bushes, crops, grass, buildings, pillars, etc.), with a proportionality factor depending on their shape, slope, spacing, and orientation (e.g., Jacobs and Schols 1986). Furthermore, RL carries the information about the surface from different spatial scales, ranging from the microscale to Δx. As can be seen from Eqs. (1) and (2), there are two types of RL, i.e., mechanical (dynamic) and thermal. In NWP models, they are often set to be proportional (z0h = c × z0m), where proportionality constant c is typically in the range 0.01–0.1 (e.g., Betts and Beljaars 1993; Trigo et al. 2015). However, there are alternative and more advanced approaches based on parameterizations (e.g., Raupach 1994; Zheng et al. 2012). The ALARO-HR18 model utilizes the first approach, wherein c = 0.1.

By utilizing the dimensional analysis, the validity of Eqs. (1) and (2) can be extended beyond static neutrality (e.g., Lee et al. 2020):
u(z)=u*κ[ln(z+z0mdz0m)ψm(z+z0mdL)+ψm(z0mL)],
s(z)=s0+Prtns*κ[ln(z+z0hdz0h)ψh(z+z0hdL)+ψh(z0hL)],
where ψm and ψh are integrated similarity functions for momentum and heat, while L is the Monin–Obukhov length given by
L=s¯u*2gκs*.
In the above given expression for L, s¯ is a surface value of dry static energy, while g is acceleration due to gravity. The characteristic quantities u* and s* are given by
u*=[(uw)s¯2+(υw)s¯2]1/4,
s*=1u*(sw)s¯.
Primed quantities in Eqs. (6) and (7) denote turbulent departures from the mean state, while their products are called turbulent fluxes and represent the transport by turbulence within the surface layer. In the ALARO-HR18 model they are expressed in a bulk form (e.g., Louis 1979; Beljaars 1995; Best et al. 2004; Beljaars et al. 2017):
(wϕ)¯s=Cϕ(u2+υ2)[ϕ(Z)ϕs],
where subscript “s” denotes surface values and Z is a height of the lowest model level, ϕ = (u, υ, or s), while Cϕ stands for corresponding drag (transfer) coefficients of momentum (CM) and heat (CH). The CM and CH are given by
CM=CMNFM(Ri),CH=CHNFH(Ri),
where FM and FH are stability functions for momentum and heat such that FM(Ri = 0) = FH(Ri = 0) = 1, while CMN and CHN are corresponding drag (transfer) coefficients at neutrality given by
CMN=κ2ln2(1+zz0m),CHN=1Prtn[κ2ln(1+zz0h)ln(1+zz0m)],
where it is assumed d = 0. More details on the computation of the above types of RL in the ALARO-HR18 model are given in the following section.

Verification of the screen-level wind over land is a nontrivial task for two reasons: (i) a nonrepresentativeness of the measurement locations, given by the subgrid inhomogeneities not resolved by the model and (ii) a lack of the roughness sublayer correction in the ALARO CMC, even though the lowest model level over forested or urban areas typically lies inside the roughness sublayer, where the mean wind profile deviates from the MOST. Applying the MOST from the lowest model level down to the surface requires neglecting the zero-plane displacement so that the model wind speed at the ground is zero.

Both above problems are illustrated in the situation shown in Figs. 1a–c, assuming a statically neutral stratification for simplicity. In reality, there is a forest in the upwind direction from the measurement site (Fig. 1a), while the model grid box is homogeneous and covered with roughness elements of the average height (Fig. 1b). The time-averaged wind profile over the forest departs from the logarithmic law, having an inflection point around the canopy top (Fig. 1c; blue line). The time-averaged wind profile in the measurement point close to the forest is not logarithmic either, i.e., the NSW is decelerated by the forest’s wake (Fig. 1c; violet line). The wind profile averaged over the whole area (solid red line) lies between these two profiles, and its logarithmic extrapolation into the roughness sublayer (dashed red line) vanishes at the mean displacement height indicated by a dashed horizontal line. All three profiles match only outside the roughness sublayer, i.e., above the blending height. The gridbox-averaged wind profile assumed in the model obeys the logarithmic law without the zero-plane displacement (orange line). It is used to obtain surface TMFs as the bottom boundary condition for the turbulence scheme and to perform interpolation of the wind to the screen level. Ideally, the RL should be derived so that the model wind profile matches the actual mean wind profile above the blending height, yielding the correct value of surface TMFs. From Fig. 1c, it is evident that matching the wind in the inertial sublayer leads to a discrepancy in the screen-level wind and vice versa. Therefore, tuning the RL in the model is necessarily a compromise. It must not be based merely on the comparison against the screen-level measurements, but it should also include radiosoundings characterizing the rest of the PBL. However, the latter are scarce both spatially and temporally.

Fig. 1.
Fig. 1.

Schematic situation illustrating the problem of screen-level wind verification. (a) The real area occupying the model grid box is heterogeneous, and the measurement location is not always far enough from obstacles. (b) The model grid box is homogeneous, assuming roughness elements of an average height. (c) The associated wind profiles are shown. In the roughness sublayer, the gridbox-averaged model profile (orange line) differs from the average real wind profile (red line). Ideally, they should match above the blending height. The dashed horizontal line denotes the zero-plane displacement, determined by extrapolating the logarithmic part of the average real wind profile.

Citation: Monthly Weather Review 152, 2; 10.1175/MWR-D-23-0178.1

3. The computation of the roughness length

This section describes the input data and methods used to compute orographic (z0moro) and vegetation roughness length (z0mveg). Further, the effective roughness length (z0meff) is defined as a square root of the quadratic sum of z0moro and z0mveg. Finally, tunable parameters required to adapt z0moro and z0mveg fields to the target model resolution are introduced. The impact of z0moro and z0mveg fields on the NSW and turbulence and their optimization are the main subjects of section 5.

a. The orography and the land cover input data

Many atmospheric processes near the surface are influenced by orography. Accordingly, there is a need for high-quality terrain-related data in NWP models. In this study, the information about orography is obtained from two digital elevation models developed by the United States Geological Survey: Global 30 Arc Second Elevation (GTOPO30; Gesch et al. 1999) and Global Multiresolution Terrain Elevation Data 2010 (GMTED2010; Danielson and Gesch 2011). The GTOPO30 data are available at a horizontal resolution of 30 arc s (∼1 km). The GMTED2010 database contains three datasets and we utilize the one with the finest horizontal resolution, i.e., 7.5 arc s (∼250 m). The GMTED2010 dataset is utilized in this study to derive the GSO, z0moro, and SGSO fields, while the GTOPO30 data are used only to determine the z0moro of the reference experiment. Such an experimental setup allows us to isolate only the impact of RL fields on the NSW and turbulence. At Δx = 1.8 km, the GSO from GTOPO30 and GMTED2010 databases are similar. However, the GMTED2010 data at 250-m horizontal resolution provide more detailed SGSO fields, which is crucial for determining z0moro and characteristics (anisotropy, orientation, and variance of orography) needed for the OGWD scheme.

The information about the land cover is an essential input to NWP models since it affects the surface energy budget and hydrological cycle. Here we are particularly interested in z0mveg due to its impact on the NSW and turbulence. The z0mveg is not a directly measurable quantity, and its estimation is typically based on the correlation with the vegetation type. In its default setup, the ALARO CMC utilizes the Henderson-Sellers et al. (1986) database to determine the z0mveg. However, this database is outdated and unsuitable for the target resolution of the ALARO-HR18 model. For this reason, we aim at utilizing the ECOCLIMAP-II database (Faroux et al. 2013) to retrieve the z0mveg. The ECOCLIMAP-II is a regional upgrade of the global ECOCLIMAP-I database (Masson et al. 2003). Both databases have a horizontal resolution of 1 km, but ECOCLIMAP-II is based on newer input databases and contains more land cover types. For use in meteorological models, each land cover type appears as a partition of four main surface types (tiles): nature, inland water bodies, sea, and urban areas. Further, some of the existing land cover types are split into new ones in ECOCLIMAP-II, which ensures a better regional character. In this research, only the fields necessary to compute z0mveg are adopted from the ECOCLIMAP-II database, i.e., LAI and HT. Other data based on land cover types used in the ALARO-HR18 model come from various older databases. More details on the computation of z0moro and z0mveg are given in the following subsection.

b. The computation of orographic and vegetation roughness length

In the following text, we must distinguish two types of mechanical (dynamical) RL. Both were mentioned earlier but not defined. They mostly differ in the type of roughness elements and the range of represented horizontal scales. The first type is so-called micrometeorological RL or frequently referred to as z0mveg. On the smallest scales (below 10 cm), it is given by the texture of the material surface (e.g., soil, rock, concrete, asphalt, or water surface–not considered here), while on larger scales (0.1–100 m) it is considerably affected by vegetation (e.g., grass, crops, and trees) and urban structures (e.g., buildings, walls, and pillars). The second type of mechanical roughness is z0moro, which carries the impact of the SGSO (scales from the input data resolution to the Δx of the target mesoscale model). The z0moro can be dominant in the mountains, but its contribution generally decreases with increasing the model resolution. Note the additional difference between z0moro and z0mveg, wherein the latter has a pronounced annual cycle due to its link with vegetation. Finally, the z0mveg and z0moro are combined to obtain the effective value, i.e., z0meff:
z0meff=(z0mveg)2+(C1z0moro)2,
where C1 is a tunable parameter initialized as C1 = 1. We note that z0mveg is not scaled as a whole but separately for each patch of the nature tile, i.e., the open land patch and the forest patch. The z0moro and z0mveg in the ALARO-HR18 model are computed in two ways, related to the input databases and methods applied. Hereafter they are denoted as the old and the new way, while the description follows below in the text. An old approach for the computation of z0moro utilizes the GTOPO30 input data, the SGSO variance, and the square root of the gridbox density of isolated peaks:
z0moro=(h2¯h¯2)NS,
where h is the height of the SGSO, bar denotes gridbox average, N is the number of peaks in the grid box, and S is the gridbox area. The new approach utilizes the GMTED2010 input data and the method of Grant and Mason (1990) and Mason (1991), i.e., it computes the z0moro from the amplitude of mean obstacle height (Δh), the frontal area of SGSO roughness elements (A), and the gridbox area (S):
[ln2(Δh2z0moro)]1=0.5CMASκ2,
where CM = 0.6 is a drag coefficient for momentum. More details on the computation of Δh and A/S can be found in Grant and Mason (1990), Mason (1991), and Georgelin et al. (1994).
As already stated, the z0mveg is also computed in two ways. An old approach relates z0mveg to vegetation, following Henderson-Sellers et al. (1986). The new approach adopts methodology from the SURFEX model (Masson et al. 2013; Le Moigne et al. 2020). Its computation procedure relates z0mveg to the vegetation height (HV):
z0mveg=max(0.13HV,0.001m).
The exact value of the scaling parameter in Eq. (14) varies but typically lies between 0.1 and 0.15 (e.g., Duynkerke 1992; Raupach 1992; Floors et al. 2018). However, this holds only if d = 0 in Eqs. (1)(4), while for d > 0, the value of the scaling parameter should be higher (e.g., De Bruin and Moore 1985). For the forest patch, HV depends on the tree height (HT):
HV=C2HT,
where C2 is a tunable parameter initialized as C2 = 1. For the open land patch, HV is derived from LAI:
HV=LAIC3,
where C3 is another tunable parameter initialized as C3 = 6. The gridbox value of z0mveg is finally obtained by averaging the CMN of patches. This value is additionally modified depending on the presence of urban structures. Finally, the z0meff is computed according to Eq. (11).
As already stated in section 2, it is assumed in the ALARO-HR18 model that vegetation-based components of z0m and z0h are proportional:
z0hveg=0.1z0mveg.
Unlike z0meff, the z0heff is not increased due to SGSO. The reason are better temperature and humidity screen-level scores (reduced random error) when only the vegetative component is kept. More details on data and methods used to assess the impact of the new RL fields are given in the following section.

4. Verification data and methods

This section describes the input data used to verify the 10-m wind speed and vertical profiles of TMFs and wind obtained by utilizing different RL settings. Further, it elaborates on the validation strategy and presents the verification methods. Finally, it provides basic information about the model configuration applied in this study.

a. Wind speed and turbulent fluxes data

The impact of RL on the 10-m wind speed is verified utilizing measurements from stations gathered through the global exchange. Before applying the verification procedure, the stations were classified into three groups and thinned. The purpose of the former is to inspect the impact of RL tuning parameters on the 10-m wind speed forecast in different types of terrain. The latter aims to reduce the effect of dependence between time series at various locations during the computation of statistical significance. Three groups of stations are defined as follows (Fig. 2a): lowland (z < 500 m), highland (500 m ≤ z < 1000 m), and mountain (z ≥ 1000 m). For the thinning process, we determine a distance at which the correlation of the model data with the starting point decreases below some objectively chosen level. The model data are chosen since they are approximately equidistant and more correlated than measurements. As a criterion for the loss of correlation, we take a distance at which values of the 2D spatial autocorrelation function decrease below 1/e. The equivalent condition is typically applied in the analysis of spatial and time series (e.g., Kaimal and Finnigan 1994).

Fig. 2.
Fig. 2.

(a) Location of stations used for the verification and (b) orography of the ALARO-HR18 model domain. The stations providing 10-m wind speed data are classified as follows: lowland (z < 500 m; green), highland (500 m ≤ z < 1000 m; red), and mountain (z ≥ 1000 m; blue). The locations of atmospheric soundings and the Cabauw tower are denoted with black “x” markers and a purple star.

Citation: Monthly Weather Review 152, 2; 10.1175/MWR-D-23-0178.1

Based on the analysis of detrended wind speed data for model points located in flat (Netherlands and eastern Croatia) and mountainous terrain (Swiss and Austrian Alps), we find that, in most of the cases, the 2D spatial autocorrelation function decreases below the chosen threshold within 50 km of the starting point (Fig. 3). However, in flat terrain, this radius of impact may occasionally exceed 100 km. On average, and for the extremal location of four considered, it reaches a value of 80 km (not shown). To keep a reasonable number of stations in each group (Table 1), we opt for a radius of 50 km. Thus the condition of independence is ensured in the majority of situations.

Fig. 3.
Fig. 3.

The 2D spatial autocorrelation function (ACF) for different locations and weather situations: (a) mountain location and anticyclonic case (ACC; 5 Feb 2020), (b) mountain location and cyclonic case (CYC; 10 Feb 2020), (c) lowland location and ACC, and (d) lowland location and CYC. The elliptic curve in the horizontal plane represents the projection of the 1/e value of the 2D spatial ACF, i.e., the distance at which the model data lose their memory (become independent).

Citation: Monthly Weather Review 152, 2; 10.1175/MWR-D-23-0178.1

Table 1.

The number of stations per group depending on the radius of impact.

Table 1.

Measurements of TMFs at 5, 60, 100, and 160 m above the ground level are taken from the Cabauw tower in the Netherlands (e.g., Bosveld et al. 2020). The station surroundings, instruments and data quality control methods are described in Bosveld (2020). A comparison of measured and predicted TMFs is conducted using values from the nearest vertical level, i.e., without interpolation. The lowest level of measurements lies in the layer where the model applies the assumption of constant fluxes, while the height differences for other levels are within a few meters. The results of this comparison will be used to determine an optimal RL configuration in the ALARO-HR18 model, aiming to achieve a compromise between the accuracy of the 10-m wind forecast and the reality of the turbulence scheme given by TMFs. To further verify the wind profile within the PBL, we utilize atmospheric soundings obtained through the global exchange.

b. Verification methods

The performance of different RL settings in the ALADIN-HR18 model, i.e., the average deviation of related forecasts from measurements, is assessed by considering prognostic variables as continuous and categorical. The first includes the computation of a frequently utilized verification measure, i.e., the RMSE (e.g., Wilks 2011). To quantify different sources of error, RMSE is decomposed into bias of the mean (BM), bias of the standard deviation (BSD), and dispersion error (DISP) [check Eq. (A1) in the appendix]. Finally, the skill score (SS) is computed to assess the relative improvement/deterioration of the RMSE compared to the reference experiment [check Eq. (A2) in the appendix]. To confirm whether the difference in RMSE between various experiments is statistically significant, we utilize the moving-block bootstrap technique (e.g., Wilks 1997), with 1000 resamples at a confidence level of 90%. During the verification, we compare observations with the nearest model point.

The above-described procedure is carried out for all stations together as well as for individual groups. The aim is to identify the most sensitive parameters used for the RL computation and to determine their optimal values concerning the total error and partitioning between different sources.

The categorical verification is performed to assess the impact of RL settings on flows of different intensities. Wind speed data are classified into six categories, with boundaries determined based on percentiles (e.g., Odak Plenković et al. 2018). The boundaries of categories in our study are given by 25th, 50th, 75th, 90th, 95th, and 100th percentile. The categorical verification procedure includes the computation of equitable threat score (ETS; e.g., Hogan et al. 2009, 2010), extremal dependency index [EDI; check Eq. (A3) in the appendix], and relative frequency of events, i.e., forecasts or observations per category. ETS measures the predictive skill by providing the fraction of correctly predicted events adjusted for success related to the random chance. However, its performance for rare situations and a small sample of forecasts is deficient. For this reason, we utilized EDI as a representative categorical metric in our study (particularly for strong wind). Finally, the relative frequency of events is computed to inspect the impact of RL on 10-m wind speed distribution, i.e., the frequency of appearance per category.

c. Numerical model configuration and output data

In this study, we utilize ALARO-HR18 model with Δx = 1.8 km. The model domain consists of 1296 × 1185 grid points on a Lambert conformal projection, thus covering an area of approximately 2330 km × 2070 km (Fig. 2b). The prognostic fields utilize Fourier’s spectral representation in zonal and meridional directions, with elliptic truncation to ensure an isotropic horizontal resolution (Machenhauer and Haugen 1987). The truncation is done at wavenumbers 431 (zonal) and 383 (meridional), meaning that the so-called quadratic grid is applied (Wedi 2014).

ALARO-HR18 has 87 vertical levels of a hybrid mass-based and terrain-following coordinate η (Simmons and Burridge 1981; Laprise 1992), with the lowest level at approximately 10 m. Vertical discretization is performed with the finite difference method (Simmons and Burridge 1981) on a Lorenz grid. The dynamical core is nonhydrostatic, fully compressible, and based on the shallow atmosphere approximation. Temporal discretization is based on the two-time level iterative centered-implicit scheme (Bénard 2003) with two iterations and it is further combined with a semi-Lagrangian advection (Temperton et al. 2001; Váňa et al. 2008), allowing for a time step of 60 s. The latter computation is performed within the gridpoint space, together with lateral boundary coupling (Davies 1976; Radnóti 1995) and contribution of unresolved physical processes, i.e., parameterizations.

The package of applied physical parameterizations (ALARO-1 version B) is described in detail within Termonia et al. (2018), and here we highlight only processes relevant to this research, i.e., turbulence, orographic gravity wave drag (OGWD) and surface (soil).

Turbulence parameterization (TOUCANS; Bašták Ďurán et al. 2014) is based on two prognostic turbulent energies, accounting for moisture effects (Marquet and Geleyn 2013; Bašták Ďurán et al. 2018). The ratio of these energies is utilized as the scheme’s only stability parameter. In TOUCANS, the nonlocal effects are included via third-order moments and optionally by choosing the Bougeault and Lacarrére (1989) type of the mixing length formulation. An integral part of the scheme is also a shallow convection closure after Lewellen and Lewellen (2004).

The drag family of schemes includes the treatment of the wave drag, flow blocking, and mountain lift processes (Catry et al. 2008). In addition, the TOFD process is treated within the TOUCANS scheme by pushing the z0meff above its vegetative value and thus increasing the surface TMFs. The first three processes are switched on for all experiments except the final one. Contrary, the TOFD is ever-present and prone to tuning, which is the subject of the following section.

Finally, the processes within the soil are represented by the two-layer surface scheme called ISBA, which describes the evolution of temperature and specific water content in shallow and deep soil, as well as the interception reservoir (Noilhan and Planton 1989; Giard and Bazile 2000). The surface scheme closely interacts with the atmospheric model by taking the thermodynamic state of its lowest level as an input. On the other hand, the surface scheme produces fluxes that serve as a bottom boundary condition for the turbulence scheme of the atmospheric model.

The model is initialized daily at 0000 UTC, with the output frequency set to 1 h. The hourly lateral boundary conditions are taken from the IFS model of the ECMWF in a lagged mode, i.e., starting from the 6-h forecast of its preceding prognostic run (Tudor et al. 2015). The same forecast is used to prepare the initial conditions, where upper-air fields are obtained by interpolation from the global model. Further, the soil fields are analyzed utilizing conventional measurements, i.e., screen-level temperature and humidity, within the surface data assimilation procedure called CANARI (Mahfouf 1991; Bouttier et al. 1993a,b). To avoid the spinup-related issues of the soil-to-atmosphere coupling (e.g., Cosgrove et al. 2003), we allow a 3-week warm-up period of the system before launching the first forecast.

The primary verification period (6–20 February 2020) is chosen to encompass several strong wind cases, namely, the Ciara and Dennis storms. Additionally, the options with the most successful settings are launched in the summer period (16–30 August 2020), which includes the Francis storm and serves to prove their more general validity. The assessment of the impact of RL settings and OGWD scheme on the 10-m wind and near-surface TMFs is presented in section 5.

5. Results

The RL is an essential input parameter for turbulence parameterization of nowadays NWP models. One should note that neither z0moro nor z0mveg is a directly measurable quantity but the result of empirical estimation. Relevant databases typically rely on the correlation between z0mveg and vegetation type, where the latter can be retrieved from the corresponding satellite data. Furthermore, z0moro carries additional uncertainty related to its heuristic nature. The RL primarily affects the NSW. Therefore it is justified to scale and filter RL fields obtained by previously explained procedures while seeking a compromise between the optimal verification scores for the 10-m wind and realistic TMFs affected by turbulence and OGWD processes. The scaling adjusts mean RL values, while smoothing adapts the level of details to a given model resolution. Their impact on the NSW and TMFs is evaluated in the following subsections.

Before the presentation of results, we provide a general remark on RL tuning. Our goal of finding an optimal RL configuration can be viewed as an optimization task, i.e., minimizing a cost function based on the model scores. Indeed, a direct approach would be to set meaningful optimization area in the parameter space (C1, C2, C3, and FA) and seek the cost function minimum. However, such a search is restricted by two complications: (i) each evaluation of the model scores requires months-long integration of a high-resolution NWP model (high cost), and (ii) the weighting of different scores in the cost function is somewhat subjective, i.e., influenced by the experience of human expert (subjective stop criterion). Common NWP practice with multiparameter optimization is splitting it into a series of 1D optimizations. Accordingly, only a few values of each parameter are tested, while parameters are optimized consecutively. A rule of thumb is to vary physical parameters, like HT, between one-half and twice their unscaled values unless the tuning indicates that an extension of the range might be beneficial. For heuristic parameters, like z0moro, the tuning range is less certain. Thanks to the fact that RMSE is usually a flat function of the tuning parameters, it is not necessary to sample parameter space densely enough, i.e., one can improve the model scores by taking an optimization path with a modest number of steps, and fine-tuning would bring only a slight additional gain. To explain our final roughness length configuration, we describe in detail the undertaken path in the following subsections.

a. The new roughness length fields and their impact on the forecast

Following the procedures described in section 3, we create two RL configurations and corresponding fields for each month of the year. The first configuration (hereafter ORL) is based on the previous practices applied in the ALADIN community. These practices include: (i) computation of the z0moro according to Eq. (12), utilizing the GTOPO30 data as an input, (ii) interpolation of z0mveg from precomputed low resolution datasets based on the land use, and (iii) application of scaling and smoothing on z0moro. The second configuration (hereafter NRL) differs in the input data and methods utilized to compute z0moro and z0mveg. The z0moro is computed using the GMTED2010 data and Eq. (13), while z0mveg procedure is based on the ECOCLIMAP-II data and Eqs. (14)(16). However, the GSO and other SGSO fields (anisotropy, orientation, and variance of orography) are the same for both configurations and are calculated from the GMTED2010 database. The latter fields are used within the OGWD scheme. Thus, by comparing simulations based on ORL and NRL configurations, we only assess the impact of different RL fields on the NSW and turbulence.

The original z0moro field (without scaling and filtering) from ORL and NRL configurations is shown in Figs. 4a and 4b. The highest values are observed in the mountains, regardless of the computation method and input data. However, the mean, maximum, and variability are considerably smaller for the NRL configuration (not shown). Furthermore, the NRL field is much smoother, while the ORL field seems a bit grainy. Finally, the ORL field contains highly localized maxima that may pose a problem for the numerical stability of the model. Tuned z0moro fields from ORL and NRL configurations are shown in Figs. 4c and 4d. The selection of tunable parameters is elaborated in the following subsections. Here we only note that z0moro fields are scaled for both configurations and additionally filtered in the case of ORL.

Fig. 4.
Fig. 4.

The orographic roughness z0moro (m) computed by utilizing the following: (a) the old computation procedure with GTOPO30 orography data as input; (b) the new computation procedure with GMTED2010 orography data as input; (c) as in (a), but with scaled and filtered output (C1 = 0.50 and FA = 3); and (d) as in (b), but with scaled output (C1 = 0.25). Panels (c) and (d) correspond to the final setup of different z0moro configurations.

Citation: Monthly Weather Review 152, 2; 10.1175/MWR-D-23-0178.1

The z0mveg field from ORL and NRL configurations, including one winter and one summer month, is shown in Figs. 5a–d. As for its spatial characteristics, higher values are observed in the forested areas. The impact of urban environments, e.g., Paris, Rome, or German Ruhr, on z0mveg can be seen in Figs. 5b and 5d. Similar to z0moro, we notice that z0mveg fields from the NRL configuration are much smoother than those from the ORL. Another feature related to the ORL configuration is a square-like pattern (obvious in Figs. 5a and 5c when zoomed) which seems inappropriate for the target resolution. By analyzing the annual cycle of the mean z0mveg, we notice that untuned NRL values are considerably smaller than ORL values (not shown). The same holds for the amplitude of the annual cycle. Therefore, we perform a preliminary tuning of z0mveg before the first sensitivity tests by increasing the tree height (HT) via the C2 parameter. The aim is to get closer to the corresponding mean value of the ORL configuration for the month in which sensitivity tests are carried out, i.e., February. Additionally, the analysis points out that increasing z0mveg in such a way improves the 10-m wind speed scores and near-surface TMFs (not shown). Finally, this approach should reduce the number of iterations in seeking the optimal setup of the NRL configuration. For additional confirmation, the chosen setup is also validated in the summer period. The impact is smaller than in winter but still positive (not shown).

Fig. 5.
Fig. 5.

The vegetation roughness z0mveg (m) computed by utilizing the following: (a) the old procedure with Henderson-Sellers et al. (1986) data as input (for February); (b) the new procedure with ECOCLIMAP II data as input (for February); (c) as in (a), but for August; and (d) as in (b), but for August. Panels (b) and (d) correspond to the optimal setup of related tuning parameters, i.e., C2 = 1.75, C3 = 6.0 and FA = 0.

Citation: Monthly Weather Review 152, 2; 10.1175/MWR-D-23-0178.1

In the following subsections, we present the impact of RL settings on the 10-m wind speed forecast and near-surface TMFs. Conclusively, we explain the selection of the final RL configuration in the ALARO-HR18 model.

1) The impact of the orographic roughness length scaling

The z0moro is an essential parameter for the accuracy of NSW forecast in mountainous areas. Given that we base our classification of stations only on height, even the lowland stations may feel some impact if located near the mountain foothill. For the reasons mentioned in the preceding subsection, we start the z0moro-related sensitivity tests with HT scaled by C2 = 1.5. The other parameters for the computation of NRL, discussed individually in the following subsections, are set to: C1 = 1 (z0moro scaling), C3 = 6 (HV scaling for the open land patch), and FA = 0 (number of filter applications on z0moro and z0mveg) while the OGWD scheme is active.

We conduct a set of sensitivity tests with a modified value of the C1 parameter, i.e., 0.75, 0.5, and 0.25, keeping other parameters constant. The lower limit of the C1 parameter results from preliminary tests for a shorter period with the strongest wind, where the criterion was the most favorable ratio of random (DISP) to total error (RMSE). Further decrease of C1 led to an increase in DISP, with a nearly constant RMSE. On the other hand, starting from C1 = 1, each decrease of its value within the above interval results in a reduction of RMSE (not shown). A comparison of the initial experiment (C1 = 1) and the final one (C1 = 0.25) in the period 6–20 February 2020 is shown in Fig. 6. The decrease of C1 results in a small improvement of BSD and DISP (Fig. 6a). The only drawback is a deterioration in BM during the night and morning hours. The overall minor sensitivity to the C1 parameter results from a slightly negative impact on the lowland group of stations which are the most represented (Fig. 6b). However, the impact on other two groups is either neutral (highland) or very positive (mountain).

Fig. 6.
Fig. 6.

The impact of the orographic roughness (z0moro) scaling on the 10-m wind speed forecast during the period 6–20 Feb 2020: (a) the root-mean-square error (RMSE) decomposition for all stations and (b) the skill score (SS) for all stations and individual groups.

Citation: Monthly Weather Review 152, 2; 10.1175/MWR-D-23-0178.1

Improving the accuracy of near-surface TMFs by modifying z0meff can deteriorate the wind forecast at the lowest model levels and vice versa. To confirm this does not happen in our case, i.e., that the potential deterioration of near-surface TMFs does not affect the wind profile above the first model level, we perform its comparison with available atmospheric soundings in mountainous areas. Based on verification scores for 925- and 850-hPa wind, we conclude that the impact on the profile within the PBL due to z0moro tuning is negligible (not shown). Although desirable, the analysis of TMFs is not conducted as such measurements are rare in the mountains, their vertical extent is typically insufficient, and conclusions may strongly depend on the characteristics of the location itself.

To further confirm the results, the same experiment is conducted during the summer, i.e., in the period 16–30 August 2020. The only differences are in RMSE (smaller in summer) and a slightly improved results for the highland group of stations (not shown). In addition, the categorical verification of 10-m wind speed is performed. The results indicate that scaling z0moro improves the model performance in forecasting moderate and strong wind at highland and mountain stations (not shown). Based on the analysis performed, we conclude that scaling z0moro brings satisfactory results. Hence, C1 = 0.25 is identified as a new reference when testing other RL tuning parameters.

2) The impact of scaling the tree-height-based vegetation height

Since the NRL-related procedure for the computation of z0mveg includes different approaches for open land and forest patches, its scaling offers an opportunity to adopt the parameter-by-parameter approach. In perspective, HT is the most influential parameter, affecting the forest patch. For the reasons explained previously (and partly shown), scaling its contribution considerably improves the NSW forecast for all groups of stations. Based on previous results, we select the following starting setup: C1 = 0.25, C2 = 1.5, C3 = 6, and FA = 0.

We execute sensitivity tests with different values of the C2 parameter, i.e., 1.0, 1.5, 1.75, and 1.875, keeping other parameters constant. The criterion for selecting the upper limit of the C2 parameter coincides with the preceding test, minimizing the ratio of random (DISP) to total error (RMSE). In addition, its further increase deteriorates the predictability of moderate and strong wind. The validation period corresponds to the previous set of experiments, i.e., 6–20 February 2020. The RMSE and DISP are reduced with each increase in C2, while BSD in whole and daily BM deteriorate for C2 > 1.5 (not shown). The RMSE decomposition for nonscaled (C2 = 1.0) and chosen setups (C2 = 1.875) are shown in Fig. 7a. The improvement in RMSE is mainly a result of the reduction in DISP. During the nighttime, there is an additional contribution from the BM. However, during the daytime, BM works in the opposite direction, i.e., it increases the RMSE. The diurnal variation of BM mainly comes from the lowland group of stations (Fig. 7b) and suggests some difficulties in representing the daily cycle of the wind. The only real drawback with the increase of C2 is a reduction in model variability reflected through BSD. Considering that by scaling HT, we considerably decrease the random error, i.e., DISP, we are willing to accept reduced variability. Since underestimation of BSD affects the model’s ability to simulate strong wind, we need to assess a categorical skill given by ETS and EDI (not shown). However, the final decision will depend on the results of sensitivity tests for the remaining parameters and the accuracy of TMFs. The results for the summer period are similar, but the overall impact of tuned C2 is somewhat smaller. For additional and more physical confirmation, measured and predicted TMFs from the Cabauw tower are compared. The results are shown and discussed at the end of the following subsection.

Fig. 7.
Fig. 7.

The impact of scaling the tree-height-based vegetation height on the 10-m wind speed forecast during the period 6–20 Feb 2020: (a) the root-mean-square error (RMSE) decomposition for all stations and (b) the skill score (SS) for all stations and individual groups.

Citation: Monthly Weather Review 152, 2; 10.1175/MWR-D-23-0178.1

3) The impact of scaling the LAI-based vegetation height

The second parameter for scaling the z0mveg, i.e., C3, affects the open land patch containing low vegetation and crops. Based on previous experiments, we select the following starting setup: C1 = 0.25, C2 = 1.875, C3 = 6, and FA = 0. The sensitivity tests are conducted in the winter period, i.e., 6–20 February 2020, wherein the values of the C3 parameter are set to 1.5, 3, 6, and 12. The latter is introduced following the results of the complementary diagnostics of TMFs, aiming to optimize the final value (see below).

The results for the starting setup (C3 = 6) and an experiment with C3 = 1.5 are shown in Figs. 8a and 8b. The decrease in C3 value, and related increase of RL, results in a reduction of RMSE. This is related to a decrease in DISP, but it is accompanied by an increase in BSD, as in the case of experiments with the C2 parameter. The impact is largest at mountain stations. However, the overall signal follows the behavior of lowland stations and is slightly positive. Although the RMSE improves with changes in C3 value, the trade-off between DISP and BSD seems less favorable than for the C2 parameter. To determine the most acceptable values of both parameters, we analyze the EDI of 10-m wind speed and TMFs.

Fig. 8.
Fig. 8.

The impact of scaling the LAI-based vegetation height on 10-m wind speed forecast during the period 6–20 Feb 2020: (a) the root-mean-square error (RMSE) decomposition for all stations and (b) the skill score (SS) for all stations and individual groups.

Citation: Monthly Weather Review 152, 2; 10.1175/MWR-D-23-0178.1

The EDI for strong wind, and thus the predictive skill, slightly deteriorates as C2 increases from 1.5 to 2.0. Similar is observed when C3 is decreased from 6 to 1.5 (not shown). In both cases, the RMSE of 10-m wind speed is improved. However, the overall signal is much stronger for C2.

To measure the discrepancy between measured and predicted TMFs, we utilize RMSE. Its computation is based on five 72-h forecasts at a single location (Cabauw tower) and four vertical levels for different meteorological conditions in summer and winter periods. The selected cases include a stable winter situation with weak wind and turbulence activity, three windstorms (two in the winter; Ciara and Dennis, and one in the summer; Francis), and a part of the anticyclonic summer period. Since the model performance in the simulation of TMFs varies considerably for any RL configuration, we need a robust measure like RMSE to make an objective decision. In total, five different NRL settings are compared with the ORL configuration. The reference NRL configuration (REF) has the following settings: C1 = 0.25, C2 = 1.0, C3 = 6, and FA = 0. Additional experiments differ in the following: EXP1 (C2 = 1.5), EXP2 (C2 = 1.875), EXP3 (C2 = 1.875 and C3 = 3) and EXP4 (C2 = 1.875 and C3 = 1.5).

The RMSE of zonal (uw¯) and meridional (υw¯) TMF computed over five selected cases and all forecast lead times is shown in Table 2. As can be seen, TMFs obtained with an untuned setup of the NRL configuration have a larger RMSE than those of the ORL configuration, which underlines the necessity of retuning when the model physiography is changed. The signal is consistent for most of the levels and both TMF components. By adjusting the C2 parameter to increase z0mveg, the RMSE of TMFs considerably reduces until the value C2 = 1.5 (EXP1). With a further increase in C2 (EXP2), the RMSE of TMFs changes only marginally. The impact of C2 tuning is the largest within the constant fluxes layer, wherein the RMSE is decreased by 6%–7% compared to ORL configuration. Above it, the results are mixed, and the impact is weaker.

Table 2.

The root-mean-square error (RMSE) of zonal (uw¯) and meridional (υw¯) turbulent momentum flux at four vertical levels over five selected cases and all forecast lead times for the Cabauw tower.

Table 2.

At the same time, the RMSE of 10-m wind is somewhat reduced, but the forecast performance for strong wind given by EDI deteriorates. Considering this and the aim to modify the input fields of the NRL configuration as little as possible, the value C2 = 1.75 is chosen as optimal. The selected value of the C2 parameter is a compromise between the RMSE of 10-m wind speed, distribution of its components (BSD and DISP in particular), categorical skill given by EDI and the matching of measured and predicted TMFs. The decision on the optimal C2 value is somewhat subjective, and any other choice with 1.5 < C2 < 1.875, i.e., having satisfying TMFs, is equally justified. The impact of changes in the C3 parameter on the RMSE of TMFs is negative for most of the levels and both TMF components. At the same time, the BSD of 10-m wind speed and categorical skill deteriorate. The only positive feature is a decrease in RMSE due to the reduction of DISP. Aiming to optimize its final value, we conducted an experiment with C3 = 12. Compared to the increase in HT scaling above C2 = 1.5, the impact on RMSE is weaker, while other indicators remain neutral. For this reason, we decided to keep the C3 = 6 as an optimal value.

Assessing TMF’s behavior based on a single location has its weaknesses. Since it is placed in a relatively homogeneous terrain, and the impact of C2 and C3 parameters is largest at lowland stations, we believe that our conclusions apply to the majority of similar locations and that the analysis carried out gives an additional value to our research.

4) The impact of the roughness length filtering

After adjusting z0moro and z0mveg by scaling the related parameters, we examine the impact of their filtering. For this purpose, we utilize a 5-point 2D spatial Laplacian filter, masking the sea points. The weights assigned to the central and surrounding four points are 1/2 and 1/8, respectively. To simplify the process, the number of FA is always the same for both components of z0meff. Based on the results from previous experiments, we select the following starting setup: C1 = 0.25, C2 = 1.75, C3 = 6, and FA = 0.

The experiments with FA = 1, 2, and 3 filter applications are conducted for the winter period, i.e., 6–20 February, while other parameters are kept constant. In general, the impact of filtering on RMSE is small and slightly negative, except for mountain stations (not shown). However, in the mountains, any decrease in RL improves the scores as it accelerates the 10-m wind and thus reduces the negative BM. Further, the impact of filtering considerably decreases after FA = 1. Among the positive features of RL filtering, we point to a reduction in BSD, previously identified as a drawback of the NRL configuration. The additional analysis of time series and vertical wind profiles at selected locations confirmed existing results (not shown). For this reason, filtering is excluded from the final RL setup in the ALARO-HR18 model.

b. Do we still need the gravity wave drag parameterization?

The OGWD scheme is an essential component of NWP and climate models for successful wind forecasts. The typical resolution of nowadays regional NWP models is a few kilometers or less, where the OGWD is mainly resolved, i.e., there is no need to parameterize it. In this subsection, we examine the need to utilize the OGWD scheme in the ALARO-HR18 model and assess its impact on the wind forecast within the PBL. Based on previous experiments, we select the following starting setup: C1 = 0.25, C2 = 1.75, C3 = 6.0, and FA = 0.

The impact of the OGWD scheme on the 10-m wind speed forecast is relatively small in a statistical sense and lies between z0moro scaling and RL filtering (not shown). With the OGWD scheme switched off, the 10-m wind is accelerated during more stable situations (night and winter), which increases the amplitude of the daily cycle of the BM. Already negative BSD further decreases. Finally, the RMSE is slightly improved following the signal of DISP. As expected, the overall impact is the largest at mountain stations.

Unlike RL, the impact of the OGWD scheme can extend much farther than the relatively shallow near-surface layer. For that reason, we conduct the analysis of vertical wind profiles based on atmospheric soundings obtained from several locations in or near mountains, i.e., Innsbruck and Cuneo (Alps), Zadar (Velebit mountain, Croatia) and Prague-Libuš (∼100 km from Krušné Hory mountains, Czech Republic). Due to the coarse spatial (horizontal) and temporal resolution of atmospheric soundings and a relatively small number of detected orographic gravity wave events, we could not find the impact of the OGWD scheme on the wind forecast in the PBL in a statistical sense. For this reason, we approach the analysis of individual cases.

The model budgets of wind components with the OGWD scheme on, differences between simulations with the OGWD scheme on and off, profiles of wind components, wind speed and direction for location Prague-Libuš at 1200 UTC 12 February 2019 are shown in Figs. 9a–h. As can be seen, the near-surface total tendency of zonal and meridional wind budget is mainly affected by the vertical turbulent diffusion. The contribution of the OGWD scheme is relatively small. When switched off, the turbulence tries to compensate for its absence and mostly succeeds in a shallow near-surface layer. Above it, the turbulence scheme is not adapting, while the model dynamics becomes the driving force. Consequently, local variations in total tendency occur, affecting the wind profile. Although their impact is small, the model’s ability to reproduce observed wind profiles is deteriorated, as in the Prague-Libuš location (Figs. 9f and 9g). The number of such favorable situations is small in the analyzed period, while the impact of the OGWD scheme is always neutral or slightly positive. Since the scheme is computationally relatively inexpensive, the contribution in the middle and higher PBL proven, the decision is to keep it as a part of the final configuration in the ALARO-HR18 model.

Fig. 9.
Fig. 9.

(a)–(d) Model budgets of wind components and their relative differences due to the OGWD scheme and (e)–(h) wind profiles derived from atmospheric soundings at Prague-Libuš station, 1200 UTC 12 Feb 2019. DYN, OGWD, TUR, and TND denote dynamical, orographic gravity wave drag, turbulence, and overall tendency, respectively, while SND stands for atmospheric soundings data. All wind budgets are domain averaged.

Citation: Monthly Weather Review 152, 2; 10.1175/MWR-D-23-0178.1

c. Validation of the final roughness length configuration

Finally, we approach the validation of configuration created based on the previous sensitivity tests. As explained in previous subsections, it is a compromise between the model’s ability to simulate the NSW and TMFs as well as the overall wind profile within the PBL. Its settings are as follows: C1 = 0.25, C2 = 1.75, C3 = 6.0, FA = 0, and OGWD scheme is switched on. The simulations with ORL, untuned NRL (NRLs) and final NRL (NRLf) configurations are launched in periods 31 January–29 February 2020 and 1–30 August 2020. The validation is focused on 10-m wind speed and conducted for each period individually. It is based on the RMSE decomposition, SS computation and categorical assessment given by EDI.

The RMSE decomposition and SS for the winter and summer period are shown in Figs. 10 and 11. As can be seen, it is crucial to tune the RL settings of the NRL configuration to reduce the RMSE of the 10-m wind speed, i.e., to improve the performance compared to the ORL configuration. The impact is considerably larger in winter than in the summer (Figs. 10 and 11). The improvement is mainly seen during the nighttime and comes from a reduction in DISP and BM. During the daytime, the impact of DISP is relatively small, while BM slightly deteriorates. The only drawback of the NRLf configuration is somewhat reduced variability given by BSD. The RMSE differences between NRLf and ORL configurations are statistically significant at the 90% level, i.e., α = 0.1, for around 50% of nighttime hours in the winter and 15%–20% in the summer.

Fig. 10.
Fig. 10.

(a) The root-mean-square error (RMSE) decomposition and (b) the skill score (SS) for the old roughness length (ORL) configuration, untuned (NRLs) and tuned version of the new roughness length configuration (NRLf) of the ALARO-HR18 model in the period 31 Jan–29 Feb 2020. Circles on the RMSE curves at (a) indicate forecast lead times for which the RMSE difference of the corresponding experiment compared to the reference (ORL) is statistically significant at the 90% level (α = 0.1).

Citation: Monthly Weather Review 152, 2; 10.1175/MWR-D-23-0178.1

Fig. 11.
Fig. 11.

As in Fig. 10, but in the period 1–30 Aug 2020.

Citation: Monthly Weather Review 152, 2; 10.1175/MWR-D-23-0178.1

The C2 is proved as the most influential parameter, while its tuning produced statistically significant differences for lowland stations (in the winter period). The overall impact on the RMSE in winter is the largest for lowland stations, followed by the mountain and highland groups. During the summer, the improvements are generally smaller. They are also very similar for lowland and mountain stations and barely notable for the highland group.

The categorical skill for different groups of stations, given by EDI, is shown in Figs. 12a and 12b for both winter and summer periods. Overall, the skill is higher in winter than in the summer and is the highest for lowland stations, followed by highland and mountain groups. The neutral or positive impact of the NRLf configuration (over ORL) is observed for lowland and mountain stations and for categories up to the 95th percentile. At mountain stations, this also holds for the strongest wind category. The results for highland stations are comparable to ORL configuration or slightly degraded, while for NRLs configuration they are slightly better than for the other two.

Fig. 12.
Fig. 12.

The extremal dependency index (EDI) for the old roughness length (ORL) configuration, untuned (NRLs) and tuned version of the new roughness length configuration (NRLf) and three groups of stations during (a) the winter (31 Jan–29 Feb 2020) and (b) the summer period (1–30 Aug 2020). The categories are defined as percentiles for each group and period, with values of upper boundaries (in m s−1) printed above the corresponding markers.

Citation: Monthly Weather Review 152, 2; 10.1175/MWR-D-23-0178.1

Finally, the total error of the 10-m wind speed forecast, measured by the RMSE, decreases with the introduction and tuning of the new RL fields. It is mainly a result of the improvement related to weak and moderate winds. The price to be paid is a minor degradation of the predictive skill for the strongest wind, i.e., above the 95th percentile. The latter can be improved with further model tuning (e.g., turbulence scheme parameters, stability functions, horizontal diffusion, etc.) or by applying postprocessing techniques.

To confirm that tuning RL fields and 10-m wind does not lead to deterioration of the wind profile, we compared its forecast with available atmospheric soundings. Based on 27 locations in both winter and summer monthly periods, only a minor impact due to RL tuning is observed at the lowest analyzed level, i.e., 925 hPa. However, the verification measures RMSE and BIAS are overall neutral, with NRLf configuration being more successful during the daytime and NRLs during the nighttime (not shown).

6. Summary and conclusions

RL is a fundamental input parameter of turbulence parameterization, affecting the computation of near-surface turbulent fluxes and diagnostics of screen-level parameters, i.e., 2-m temperature and humidity, 10-m wind, etc. Given its impact on the forecast within the surface layer of the PBL, and thus various aspects of human lives, it is necessary to improve input databases and methods for estimating RL fields. Considering the screen-level parameters, RL mainly affects wind. For this reason, we evaluated the impact of newly derived z0moro and z0mveg on the screen-level wind speed and TMFs, in the ALARO CMC of the ALADIN system. To determine specified components of the NRL configuration, we utilized orography and vegetation fields from GMTED2010 and ECOCLIMAP-II databases. During the verification process, the wind speed and TMFs were considered continuous variables, and the former was additionally categorical. Further, the contribution of the OGWD scheme was examined near the edge of its gray zone, i.e., at a horizontal resolution where involved processes are mainly resolved by the model dynamics. Finally, we evaluated the optimized setup of the NRL configuration against its untuned counterpart and the ORL configuration throughout winter and summer monthly periods.

A set of sensitivity tests related to input parameters, used to compute z0moro and z0mveg fields, was created to optimize the performance of the NRL configuration. Overall, the 10-m wind and near-surface TMFs proved to be the most sensitive to HT scaling via the C2 parameter. Increasing its value to C2 = 1.75 led to a considerable reduction in RMSE of 10-m wind, especially at lowland stations. It was mainly the result of a decrease in DISP and BM, wherein BSD was somewhat increased. The latter was accompanied by slightly deteriorated performance for the extreme wind, i.e., above the 95th percentile. At the same time, the RMSE of near-surface TMFs at the Cabauw tower was also decreased. Finally, the chosen value of the C2 parameter was a compromise between the continuous and categorical scores for 10-m wind and RMSE of TMFs. Although its optimal value may vary depending on the application, and its choice was partly subjective, we believe that the range proposed here., i.e., between 1.5 and 1.875, was sufficiently well founded.

Testing the LAI scaling for the open land patch was conducted equivalently. Increasing the scaling parameter value had a practically negligible impact. Contrary, decreasing it worsened the BSD and EDI of the 10-m wind and the RMSE of near-surface TMFs. Therefore, its initial value, i.e., C3 = 6, remained optimal.

The impact of tuning the other parameters was relatively small. Scaling the z0moro via the C1 parameter considerably improved the 10-m wind speed only at mountain stations. For other groups, the results were either neutral or mixed. As mentioned previously, the accuracy of near-surface TMFs in the mountains typically comes at the expense of too weak winds at a few lowest model levels. Hence, while seeking the optimal value of the C1 parameter, we analyzed whether the reduction in RMSE and BM of the 10-m wind speed and eventual deterioration of near-surface TMFs affected the upper-air wind, i.e., at 925 and 850 hPa from atmospheric soundings. Given that the impact was practically negligible, we opted for C1 = 0.25 as the optimal value. Finally, the impact of the RL filtering was found as slightly negative, except in the mountains. However, as previously shown, the results can improve there with a more positive impact on other groups of stations. Given the impact and number of affected stations, filtering was excluded from the final RL setup.

Overall, a positive contribution from new RL fields was demonstrated despite possible drawbacks related to the z0meff approach. Compared to the ORL configuration, the RMSE of 10-m wind was reduced by 3%–10%, depending on the location, time of the day, and year. At the same time, the RMSE of TMFs for the analyzed station was reduced by 6%–7% (depending on the component) within the layer of constant fluxes. Above it, the impact of the NRL configuration was mixed but considerably smaller. Accounting for the limited nature of conclusions based on a single location, we add that the latter coincides with results for vertical wind profiles, i.e., the impact above the layer of constant fluxes is practically negligible.

The main weakness of the final RL configuration in the ALARO-HR18 model is an underestimation in the variability of 10-m wind speed and related deterioration for extreme situations, i.e., above the 95th percentile. One of the possibilities to improve this aspect is the adjustment of turbulence parameterization, namely, the basic closure parameters and stability functions. In the context of RL, the following upgrades are possible in the short term: (i) introduction of the roughness sublayer correction and (ii) including the directional dependence of z0moro, accounting for the SGSO anisotropy. In future analysis over such a large area as the ALARO-HR18 model domain, a more advanced categorization of stations should be considered, e.g., highland and mountain groups redefined as slope and mountain top, and the lowland group separated into at least continental and coastal subgroups.

Finally, it was confirmed that the influence of the OGWD scheme at Δx = 1.8 km is relatively small. However, it may still be essential for predicting finer structures in the wind profile in and near mountainous regions. Analysis of the momentum budgets, with and without the OGWD scheme, indicated the possibility of missing or insufficiently well-represented processes in the ALARO-HR18 model. One of the candidates is TOFD, represented by artificially increased z0meff, and with related weaknesses discussed in the introduction. Our aim was not to replace the z0meff approach but to try to still profit from it by introducing the new high-resolution RL fields. However, this needs to be one of the first next steps to improve the performance of the ALARO-HR18 model, followed by including other drag-related processes relevant to (sub)kilometric resolution and above discussed RL developments.

Acknowledgments.

The authors thank Endi Keresturi, Iris Odak Plenković, and Suzana Panežić, who helped to shape this paper with their constructive suggestions. They are also grateful to Ivan Bašták Ďurán for his help in better understanding the relevant aspects of the TOUCANS parameterization. Finally, we thank two anonymous reviewers for their comments and valuable suggestions, which considerably improved our paper. This publication is funded by the Croatian Meteorological and Hydrological Service.

Data availability statement.

The observed and predicted 10-m wind speed, and observed and predicted near-surface turbulent momentum fluxes and data utilized to compute the 2D spatial autocorrelation function are available in ASCII format at Zenodo (https://doi.org/10.5281/zenodo.8247695). For accessibility to other data from 3D model simulations, contact the corresponding author.

APPENDIX

The Verification Metrics

a. The root-mean-square error decomposition and skill score

The root-mean-square error (RMSE) is a typically used point-based verification measure affected by the uncertainty of the forecast both in space and time. To distinguish between different sources contributing to the RMSE, we perform its decomposition into the following (e.g., Murphy 1988; Horvath et al. 2012):
RMSE2(F,O)=(FO)2¯=(F¯O¯)2+(σFσO)2+2σFσO(1rFO),
where F and O denote forecast and observations, overbars represent mean values, σ is a standard deviation, and rFO is a correlation coefficient between F and O. All the above values are computed over a sample of M stations and time series of length N. The terms on the right-hand side (RHS) of Eq. (A1) are as follows: (i) the square of the bias of the mean (BM), (ii) the square of the bias of the standard deviation (BSD), and (iii) the square of the dispersion/phase error (DISP). To confirm whether the forecast overestimates or underestimates the observed mean and standard deviation, the related figures in this paper show the values of the first two terms on the RHS of Eq. (A1) before squaring. For consistency, the left-hand side of Eq. (A1) and the third term on the RHS are shown as square root values.
To quantify the relative improvement/deterioration in the RMSE of the forecast of interest (F) compared to the reference forecast (R), we compute the skill score (SS; e.g., Murphy 1988):
SS(F,R,O)=[1RMSE2(F,O)RMSE2(R,O)]×100(%).
A positive SS value means that the accuracy of the forecast F is larger than the accuracy of the forecast R, while a negative value means that it is smaller. The role of SS in this paper is to enable a simple comparison of the impact of different tuning parameters within the roughness length computation procedure on the prediction of 10-m wind speed and near-surface turbulent momentum fluxes.

b. The extremal dependence index

The extremal dependence index (EDI) is a categorical verification measure analyzed in this paper. It is based on a contingency table of predicted versus observed events. The members of the contingency table are as follows: (i) hits (h; the frequency of events predicted to occur and did occur), (ii) misses (m; the frequency of events predicted not to occur but did occur), (iii) false alarms (f; the frequency of events predicted to occur but did not occur) and correct negatives (n; the frequency of events predicted not to occur and did not occur). Note that the perfect forecast system would produce only hits and correct negatives.

EDI is truly equitable verification measure, nondegenerate for rare events and base-rate independent (e.g., Ferro and Stephenson 2011). It is given by
EDI=logFlogHlogF+logH,
where F is false alarm rate [F = f/(f + n)] and H is hit rate [H = h/(h + m)]. EDI takes values between −1 and 1. The higher its value, the higher the predictive skill in the categorical sense. More details on EDI and other categorical verification measures can be found in, e.g., Doswell et al. (1990), Marzban (1998), Stephenson et al. (2008), Ferro and Stephenson (2011).

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