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 (
There are more ways to define
Despite its shortcomings,
Besides the contribution to TMF and turbulent shear stress, the
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 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.
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.
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 (
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,
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
b. The computation of orographic and vegetation roughness length
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).
(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.
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
The number of stations per group depending on the radius of impact.
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
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
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
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
The original
The orographic roughness
Citation: Monthly Weather Review 152, 2; 10.1175/MWR-D-23-0178.1
The
The vegetation roughness
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
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).
The impact of the orographic roughness (
Citation: Monthly Weather Review 152, 2; 10.1175/MWR-D-23-0178.1
Improving the accuracy of near-surface TMFs by modifying
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
2) The impact of scaling the tree-height-based vegetation height
Since the NRL-related procedure for the computation of
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.
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
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.
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 (
The root-mean-square error (RMSE) of zonal (
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
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
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.
(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.
(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
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.
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
A set of sensitivity tests related to input parameters, used to compute
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
Overall, a positive contribution from new RL fields was demonstrated despite possible drawbacks related to the
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
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
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
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.
REFERENCES
Bašták Ďurán, I., J.-F. Geleyn, and F. Váňa, 2014: A compact model for the stability dependency of TKE production-destruction-conversion terms valid for the whole range of Richardson numbers. J. Atmos. Sci., 71, 3004–3026, https://doi.org/10.1175/JAS-D-13-0203.1.
Bašták Ďurán, I., J.-F. Geleyn, F. Váňa, J. Schmidli, and R. Brožková, 2018: A turbulence scheme with two prognostic turbulence energies. J. Atmos. Sci., 75, 3381–3402, https://doi.org/10.1175/JAS-D-18-0026.1.
Beljaars, A., 1995: The parametrization of surface fluxes in large-scale models under free convection. Quart. J. Roy. Meteor. Soc., 121, 255–270, https://doi.org/10.1002/qj.49712152203.
Beljaars, A., A. R. Brown, and N. Wood, 2004: A new parametrization of turbulent orographic form drag. Quart. J. Roy. Meteor. Soc., 130, 1327–1347, https://doi.org/10.1256/qj.03.73.
Beljaars, A., E. Dutra, G. Balsamo, and F. Lemarié, 2017: On the numerical stability of surface–atmosphere coupling in weather and climate models. Geosci. Model Dev., 10, 977–989, https://doi.org/10.5194/gmd-10-977-2017.
Bénard, P., 2003: Stability of semi-implicit and iterative centered-implicit time discretizations for various equation systems used in NWP. Mon. Wea. Rev., 131, 2479–2491, https://doi.org/10.1175/1520-0493(2003)131%3C2479:SOSAIC%3E2.0.CO;2.
Best, M. J., A. Beljaars, J. Polcher, and P. Viterbo, 2004: A proposed structure for coupling tiled surfaces with the planetary boundary layer. J. Hydrometeor., 5, 1271–1278, https://doi.org/10.1175/JHM-382.1.
Betts, A. K., and A. C. M. Beljaars, 1993: Estimation of effective roughness length for heat and momentum from FIFE data. Atmos. Res., 30, 251–261, https://doi.org/10.1016/0169-8095(93)90027-L.
Bosveld, F. C., 2020: The Cabauw in-situ observational program from 2000–present: Instruments, calibrations and set-up. KNMI Tech. Rep. TR-384, 79 pp., https://cdn.knmi.nl/knmi/pdf/bibliotheek/knmipubTR/TR384.pdf.
Bosveld, F. C., P. Baas, A. C. M. Beljaars, A. A. M. Holtslag, J. V.-G. de Arellano, and B. J. H. van de Wiel, 2020: Fifty years of atmospheric boundary-layer research at Cabauw serving weather, air quality and climate. Bound.-Layer Meteor., 177, 583–612, https://doi.org/10.1007/s10546-020-00541-w.
Bougeault, P., and P. Lacarrére, 1989: Parameterization of orography-induced turbulence in a mesobeta-scale model. Mon. Wea. Rev., 117, 1872–1890, https://doi.org/10.1175/1520-0493(1989)117<1872:POOITI>2.0.CO;2.
Bouttier, F., J.-F. Mahfouf, and J. Noilhan, 1993a: Sequential assimilation of soil moisture from atmospheric low-level parameters. Part I: Sensitivity and calibration studies. J. Appl. Meteor., 32, 1335–1351, https://doi.org/10.1175/1520-0450(1993)032<1335:SAOSMF>2.0.CO;2.
Bouttier, F., J.-F. Mahfouf, and J. Noilhan, 1993b: Sequential assimilation of soil moisture from atmospheric low-level parameters. Part II: Implementation in a mesoscale model. J. Appl. Meteor., 32, 1352–1364, https://doi.org/10.1175/1520-0450(1993)032<1352:SAOSMF>2.0.CO;2.
Catry, B., J.-F. Geleyn, F. Bouyssel, J. Cedilnik, R. Brožková, M. Derková, and R. Mladek, 2008: A new sub-grid scale lift formulation in a mountain drag parameterisation scheme. Meteor. Z., 17, 193–208, https://doi.org/10.1127/0941-2948/2008/0272.
Cosgrove, B. A., and Coauthors, 2003: Land surface model spin-up behavior in the North American Land Data Assimilation System (NLDAS). J. Geophys. Res., 108, 8845, https://doi.org/10.1029/2002JD003316.
Danielson, J. J., and D. B. Gesch, 2011: Global multi-resolution terrain elevation data 2010 (GMTED2010). USGS Open-File Rep. 2011–1073, U.S. Geological Survey, 34 pp., https://pubs.usgs.gov/of/2011/1073/pdf/of2011-1073.pdf.
Davies, H. C., 1976: A lateral boundary formulation for multi-level prediction models. Quart. J. Roy. Meteor. Soc., 102, 405–418, https://doi.org/10.1002/qj.49710243210.
De Bruin, H. A. R., and C. J. Moore, 1985: Zero-plane displacement and roughness length for tall vegetation, derived from a simple mass conservation hypothesis. Bound.-Layer Meteor., 31, 39–49, https://doi.org/10.1007/BF00120033.
De Vries, A. C., W. P. Kustas, J. C. Ritchie, W. Klaassen, M. Menenti, A. Rango, and J. H. Prueger, 2003: Effective aerodynamic roughness estimated from airborne laser altimeter measurements of surface features. Int. J. Remote Sens., 24, 1545–1558, https://doi.org/10.1080/01431160110115997.
Doswell, C. A., III, R. Davies-Jones, and D. L. Keller, 1990: On summary measures of skill in rare event forecasting based on contingency tables. Wea. Forecasting, 5, 576–586, https://doi.org/10.1175/1520-0434(1990)005<0576:OSMOSI>2.0.CO;2.
Duynkerke, P. G., 1992: The roughness length for heat and other vegetation parameters for a surface of short grass. J. Appl. Meteor., 31, 579–586, https://doi.org/10.1175/1520-0450(1992)031<0579:TRLFHA>2.0.CO;2.
Elvidge, A. D., and Coauthors, 2019: Uncertainty in the representation of orography in weather and climate models and implications for parameterized drag. J. Adv. Model. Earth Syst., 11, 2567–2585, https://doi.org/10.1029/2019MS001661.
Faivre, R., J. Colin, and M. Menenti, 2017: Evaluation of methods for aerodynamic roughness length retrieval from very high-resolution imaging LIDAR observations over the Heihe Basin in China. Remote Sens., 9, 63, https://doi.org/10.3390/rs9010063.
Faroux, S., A. T. Kaptué Tchuenté, J.-L. Roujean, V. Masson, E. Martin, and P. Le Moigne, 2013: ECOCLIMAP-II/Europe: A twofold database of ecosystems and surface parameters at 1 km resolution based on satellite information for use in land surface, meteorological and climate models. Geosci. Model Dev., 6, 563–582, https://doi.org/10.5194/gmd-6-563-2013.
Ferro, C. A. T., and D. B. Stephenson, 2011: Extremal dependence indices: Improved verification measures for deterministic forecasts of rare binary events. Wea. Forecasting, 26, 699–713, https://doi.org/10.1175/WAF-D-10-05030.1.
Fiedler, F., and H. Panofsky, 1972: The geostrophic drag coefficient and the ‘effective’ roughness length. Quart. J. Roy. Meteor. Soc., 98, 213–220, https://doi.org/10.1002/qj.49709841519.
Floors, R., P. Enevoldsen, N. Davis, J. Arnqvist, and E. Dellwik, 2018: From lidar scans to roughness maps for wind resource modelling in forested areas. Wind Energy Sci., 3, 353–370, https://doi.org/10.5194/wes-3-353-2018.
Foken, T., 2008: Micrometeorology. 2nd ed. Springer-Verlag, 328 pp.
Georgelin, M., E. Richard, M. Petitdidier, and A. Druilhet, 1994: Impact of subgrid-scale orography parameterization on the simulation of orographic flows. Mon. Wea. Rev., 122, 1509–1522, https://doi.org/10.1175/1520-0493(1994)122<1509:IOSSOP>2.0.CO;2.
Gesch, D., K. Verdin, and S. Greenlee, 1999: New land surface digital elevation model covers the Earth. Eos, Trans. Amer. Geophys. Union, 80, 69–70, https://doi.org/10.1029/99EO00050.
Giard, D., and E. Bazile, 2000: Implementation of a new assimilation scheme for soil and surface variables in a global NWP model. Mon. Wea. Rev., 128, 997–1015, https://doi.org/10.1175/1520-0493(2000)128<0997:IOANAS>2.0.CO;2.
Grant, A. L. M., and P. J. Mason, 1990: Observations of boundary-layer structure over complex terrain. Quart. J. Roy. Meteor. Soc., 116, 159–186, https://doi.org/10.1002/qj.49711649107.
Han, C., Y. Ma, Z. Su, X. Chen, L. Zhang, M. Li, and F. Sun, 2014: Estimates of effective aerodynamic roughness length over mountainous areas of the Tibetan Plateau. Quart. J. Roy. Meteor. Soc., 141, 1457–1465, https://doi.org/10.1002/qj.2462.
Harman, I. N., and J. J. Finnigan, 2007: A simple unified theory for flow in the canopy and roughness sublayer. Bound.-Layer Meteor., 123, 339–363, https://doi.org/10.1007/s10546-006-9145-6.
Henderson-Sellers, A., M. F. Wilson, G. Thomas, and R. E. Dickinson, 1986: Current global land-surface data sets for use in climate-related studies. NCAR Tech. Note NCAR/TN-272+STR, 123 pp., https://opensky.ucar.edu/islandora/object/technotes%3A381/datastream/PDF/view.
Hewer, F. E., and N. Wood, 1998: The effective roughness length for scalar transfer in neutral conditions over hilly terrain. Quart. J. Roy. Meteor. Soc., 124, 659–685, https://doi.org/10.1002/qj.49712454702.
Hignett, P., and W. P. Hopwood, 1994: Estimates of effective surface roughness over complex terrain. Bound.-Layer Meteor., 68, 51–73, https://doi.org/10.1007/BF00712664.
Hintz, K. S., H. Vedel, E. Kaas, and N. W. Nielsen, 2020: Estimation of wind speed and roughness length using smartphones: Method and quality assessment. J. Atmos. Oceanic Technol., 37, 1319–1332, https://doi.org/10.1175/JTECH-D-19-0037.1.
Hogan, R. J., E. J. O’Connor, and A. J. Illingworth, 2009: Verification of cloud-fraction forecasts. Quart. J. Roy. Meteor. Soc., 135, 1494–1511, https://doi.org/10.1002/qj.481.
Hogan, R. J., C. A. T. Ferro, I. T. Jolliffe, and D. B. Stephenson, 2010: Equitability revisited: Why the “equitable threat score” is not equitable. Wea. Forecasting, 25, 710–726, https://doi.org/10.1175/2009WAF2222350.1.
Horvath, K., D. Koračin, R. Vellore, J. Jiang, and R. Belu, 2012: Sub-kilometer dynamical downscaling of near-surface winds in complex terrain using WRF and MM5 mesoscale models. J. Geophys. Res., 117, D11111, https://doi.org/10.1029/2012JD017432.
Howard, T., and P. Clark, 2007: Correction and downscaling of NWP wind speed forecasts. Meteor. Appl., 14, 105–116, https://doi.org/10.1002/met.12.
Hu, X., L. Shi, L. Lin, and V. Magliulo, 2020: Improving surface roughness lengths estimation using machine learning algorithms. Agric. For. Meteor., 287, 107956, https://doi.org/10.1016/j.agrformet.2020.107956.
Jacobs, A. F. G., and E. Schols, 1986: Surface roughness parameter estimated with a drag technique. J. Climate Appl. Meteor., 25, 1577–1582, https://doi.org/10.1175/1520-0450(1986)025<1577:SRPEWA>2.0.CO;2.
Kaimal, J. C., and J. J. Finnigan, 1994: Atmospheric Boundary Layer Flows: Their Structure and Measurement. 1st ed. Oxford University Press, 302 pp.
Kanehama, T., I. Sandu, A. Beljaars, A. van Niekerk, and F. Lott, 2019: Which orographic scales matter most for medium-range forecast skill in the Northern Hemisphere winter? J. Adv. Model. Earth Syst., 11, 3893–3910, https://doi.org/10.1029/2019MS001894.
Laprise, R., 1992: The Euler equations of motion with hydrostatic pressure as an independent variable. Mon. Wea. Rev., 120, 197–207, https://doi.org/10.1175/1520-0493(1992)120<0197:TEEOMW>2.0.CO;2.
Lee, J., J. Hong, Y. Noh, and P. A. Jiménez, 2020: Implementation of a roughness sublayer parameterization in the Weather Research and Forecasting model (WRF version 3.7.1) and its evaluation for regional climate simulations. Geosci. Model Dev., 13, 521–536, https://doi.org/10.5194/gmd-13-521-2020.
Le Moigne, P., and Coauthors, 2020: The latest improvements with SURFEX v8.0 of the Safran–Isba–Modcou hydrometeorological model for France. Geosci. Model Dev., 13, 3925–3946, https://doi.org/10.5194/gmd-13-3925-2020.
Lewellen, D. C., and W. S. Lewellen, 2004: Buoyancy flux modeling for cloudy boundary layers. J. Atmos. Sci., 61, 1147–1160, https://doi.org/10.1175/1520-0469(2004)061<1147:BFMFCB>2.0.CO;2.
Louis, J.-F., 1979: A parametric model of vertical eddy fluxes in the atmosphere. Bound.-Layer Meteor., 17, 187–202, https://doi.org/10.1007/BF00117978.
Machenhauer, B., and J. E. Haugen, 1987: Test of a spectral limited area shallow water model with time-dependent lateral boundary conditions and combined normal mode/semi-Lagrangian time integration schemes. Workshop on Techniques for Horizontal Discretization in Numerical Weather Prediction Models, Reading, United Kingdom, ECMWF, 361–377, https://www.ecmwf.int/node/10904.
Mahfouf, J.-F., 1991: Analysis of soil moisture from near-surface parameters: A feasibility study. J. Appl. Meteor., 30, 1534–1547, https://doi.org/10.1175/1520-0450(1991)030<1534:AOSMFN>2.0.CO;2.
Marquet, P., and J.-F. Geleyn, 2013: On a general definition of the squared Brunt–Väisälä frequency associated with the specific moist entropy potential temperature. Quart. J. Roy. Meteor. Soc., 139, 85–100, https://doi.org/10.1002/qj.1957.
Marzban, C., 1998: Scalar measures of performance in rare-event situations. Wea. Forecasting, 13, 753–763, https://doi.org/10.1175/1520-0434(1998)013<0753:SMOPIR>2.0.CO;2.
Mason, P. J., 1991: Boundary-layer parametrization in heterogeneous terrain. Workshop on Fine-Scale Modelling and the Development of Parametrization Schemes, Reading, United Kingdom, ECMWF, 275–288, https://www.ecmwf.int/sites/default/files/elibrary/1991/11011-boundary-layer-parametrization-heterogeneous-terrain.pdf.
Masson, V., J.-L. Champeaux, F. Chauvin, C. Meriguet, and R. Lacaze, 2003: A global database of land surface parameters at 1-km resolution in meteorological and climate models. J. Climate, 16, 1261–1282, https://doi.org/10.1175/1520-0442-16.9.1261.
Masson, V., and Coauthors, 2013: The SURFEXv7.2 land and ocean surface platform for coupled or offline simulation of Earth surface variables and fluxes. Geosci. Model Dev., 6, 929–960, https://doi.org/10.5194/gmd-6-929-2013.
Murphy, A. H., 1988: Skill scores based on the mean square error and their relationships to the correlation coefficient. Mon. Wea. Rev., 116, 2417–2424, https://doi.org/10.1175/1520-0493(1988)116<2417:SSBOTM>2.0.CO;2.
Nelli, N. R., and Coauthors, 2020: Impact of roughness length on WRF simulated land-atmosphere interactions over a hyper-arid region. Earth Space Sci., 7, e2020EA001165, https://doi.org/10.1029/2020EA001165.
Noilhan, J., and S. Planton, 1989: A simple parameterization of land surface processes for meteorological models. Mon. Wea. Rev., 117, 536–549, https://doi.org/10.1175/1520-0493(1989)117<0536:ASPOLS>2.0.CO;2.
Odak Plenković, I., L. Delle Monache, K. Horvath, and M. Hrastinski, 2018: Deterministic wind speed predictions with analog-based methods over complex topography. J. Appl. Meteor. Climatol., 57, 2047–2070, https://doi.org/10.1175/JAMC-D-17-0151.1.
Radnóti, G., 1995: Comments on “a spectral limited-area formulation with time-dependent boundary conditions applied to the shallow-water equations.” Mon. Wea. Rev., 123, 3122–3123, https://doi.org/10.1175/1520-0493(1995)123<3122:COSLAF>2.0.CO;2.
Raupach, M. R., 1992: Drag and drag partition on rough surfaces. Bound.-Layer Meteor., 60, 375–395, https://doi.org/10.1007/BF00155203.
Raupach, M. R., 1994: Simplified expressions for vegetation roughness length and zero-plane displacement as functions of canopy height and area index. Bound.-Layer Meteor., 71, 211–216, https://doi.org/10.1007/BF00709229.
Sandu, I., and Coauthors, 2019: Impacts of orography on large-scale atmospheric circulation. npj Climate Atmos. Sci., 2, 10, https://doi.org/10.1038/s41612-019-0065-9.
Sicart, J. E., M. Litt, W. Helgason, V. B. Tahar, and T. Chaperon, 2014: A study of the atmospheric surface layer and roughness lengths on the high-altitude tropical Zongo glacier, Bolivia. J. Geophys. Res. Atmos., 119, 3793–3808, https://doi.org/10.1002/2013JD020615.
Simmons, A. J., and D. Burridge, 1981: An energy and angular-momentum conserving vertical finite-difference scheme and hybrid vertical coordinates. Mon. Wea. Rev., 109, 758–766, https://doi.org/10.1175/1520-0493(1981)109<0758:AEAAMC>2.0.CO;2.
Stephenson, D. B., B. Casati, C. A. T. Ferro, and C. A. Wilson, 2008: The extreme dependency score: A non-vanishing measure for forecasts of rare events. Meteor. Appl., 15, 41–50, https://doi.org/10.1002/met.53.
Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology. 1st ed. Kluwer Academic Publishers, 670 pp.
Taylor, P. A., R. I. Sykes, and P. J. Mason, 1989: On the parameterization of drag over small-scale topography in neutrally-stratified boundary-layer flow. Bound.-Layer Meteor., 48, 409–422, https://doi.org/10.1007/BF00123062.
Temperton, C., M. Hortal, and A. Simmons, 2001: A two-time-level semi-Lagrangian global spectral model. Quart. J. Roy. Meteor. Soc., 127, 111–127, https://doi.org/10.1002/qj.49712757107.
Termonia, P., and Coauthors, 2018: The ALADIN system and its canonical model configurations AROME CY41T1 and ALARO CY40T1. Geosci. Model Dev., 11, 257–281, https://doi.org/10.5194/gmd-11-257-2018.
Trigo, I. F., S. Boussetta, P. Viterbo, G. Balsamo, A. Beljaars, and I. Sandu, 2015: Comparison of model land skin temperature with remotely sensed estimates and assessment of surface-atmosphere coupling. J. Geophys. Res. Atmos., 120, 12 096–12 111, https://doi.org/10.1002/2015JD023812.
Tudor, M., S. Ivatek-Šahdan, A. Stanešić, K. Horvath, M. Hrastinski, I. Odak Plenković, A. Bajić, and T. Kovačić, 2015: Changes in the ALADIN operational suite in Croatia in the period 2011-2015. Croat. Meteor. J., 50, 71–89.
Váňa, F., P. Bénard, J.-F. Geleyn, A. Simon, and Y. Seity, 2008: Semi-Lagrangian advection scheme with controlled damping: An alternative to nonlinear horizontal diffusion in a numerical weather prediction model. Quart. J. Roy. Meteor. Soc., 134, 523–537, https://doi.org/10.1002/qj.220.
van Niekerk, A., T. G. Shepherd, S. B. Vosper, and S. Webster, 2016: Sensitivity of resolved and parametrized surface drag to changes in resolution and parametrization. Quart. J. Roy. Meteor. Soc., 142, 2300–2313, https://doi.org/10.1002/qj.2821.
Vosper, S. B., A. R. Brown, and S. Webster, 2016: Orographic drag on islands in the NWP mountain grey zone. Quart. J. Roy. Meteor. Soc., 142, 3128–3137, https://doi.org/10.1002/qj.2894.
Vosper, S. B., A. van Niekerk, A. Elvidge, I. Sandu, and A. Beljaars, 2020: What can we learn about orographic drag parametrisation from high-resolution models? A case study over the Rocky Mountains. Quart. J. Roy. Meteor. Soc., 146, 979–995, https://doi.org/10.1002/qj.3720.
Walsh, E., G. Bessardon, E. Gleeson, and P. Ulmas, 2021: Using machine learning to produce a very high resolution land-cover map for Ireland. Adv. Sci. Res., 18, 65–87, https://doi.org/10.5194/asr-18-65-2021.
Wedi, N., 2014: Increasing horizontal resolution in numerical weather prediction and climate simulations: Illusion or panacea? Philos. Trans. Roy. Soc., A372, 20130289, https://doi.org/10.1098/rsta.2013.0289.
Wilks, D. S., 1997: Resampling hypothesis tests for autocorrelated fields. J. Climate, 10, 65–82, https://doi.org/10.1175/1520-0442(1997)010<0065:RHTFAF>2.0.CO;2.
Wilks, D. S., 2011: Statistical Methods in the Atmospheric Sciences. 3rd ed. International Geophysics Series, Vol. 100, Elsevier, 704 pp.
Wood, N., and P. J. Mason, 1993: The pressure force induced by neutral, turbulent flow over hills. Quart. J. Roy. Meteor. Soc., 119, 1233–1267, https://doi.org/10.1002/qj.49711951402.
Wood, N., A. R. Brown, and F. E. Hewer, 2001: Parametrizing the effects of orography on the boundary layer: An alternative to effective roughness lengths. Quart. J. Roy. Meteor. Soc., 127, 759–777, https://doi.org/10.1002/qj.49712757303.
Zhang, F., M. Sha, G. Wang, Z. Li, and Y. Shao, 2017: Urban aerodynamic roughness length mapping using multitemporal SAR data. Adv. Meteor., 14, 8958926, https://doi.org/10.1155/2017/8958926.
Zheng, W., H. Wei, Z. Wang, X. Zeng, J. Meng, M. Ek, K. Mitchell, and J. Derber, 2012: Improvement of daytime land surface skin temperature over arid regions in the NCEP GFS model and its impact on satellite data assimilation. J. Geophys. Res., 117, D06117, https://doi.org/10.1029/2011JD015901.