In coupled mesoscale–microscale simulations, including horizontal grid resolutions falling within the terra incognita is almost inevitable. The terra incognita, coined by Wyngaard (2004), is the range of horizontal grid spacings where turbulence models used in both mesoscale and LESs do not work properly. The MMC project investigated the impact of the terra incognita in coupled simulations (Rai et al., 2017, 2019). Our work suggests that the impact of the terra incognita can be minimized using an appropriate choice of the horizontal grid spacing, turbulence modeling (dependent on the horizontal grid spacing), and grid refinement ratio (GRR) applied between the mesoscale and microscale simulations. The most important consideration is that the horizontal grid spacing of the mesoscale simulation should be at least comparable to the boundary layer depth. Horizontal grid spacing smaller than the boundary layer depth produces erroneous structures in the simulated flow. Applying a GRR that allows for simulations to jump over the terra incognita not only alleviates the problem but also reduces the number of computational domains. A larger value of GRR, however, also increases the fetch needed to generate turbulence on nested domains due to the inertia of larger structures transported from the parent domain. The need for a larger fetch can be mitigated by applying perturbations along the inflow boundaries of the domain (Sect. 2.4). In situations when the GRR (between mesoscale and microscale domains) becomes large, it can be beneficial to use the LES three-dimensional (3D) turbulence model (e.g., Smagorinsky, 1963) in the terra incognita region, provided that the horizontal grid spacing is closer to 100 m, and then jump to grid spacing larger than the boundary layer depth using the GRR (Rai et al., 2019). However, the use of a 3D LES closure when the grid spacing is too coarse to resolve any of the motions responsible for momentum transport can result in incorrect stress profiles, leading to significant errors in wind speed within the atmospheric boundary layer (ABL). The recently developed 3D planetary boundary layer (PBL) Mellor–Yamada scheme (Juliano et al., 2022) fills a critical gap in this regard, providing for a consistent representation of transport at scales finer than traditional mesoscale applications but at scales too coarse to rely upon a 3D LES turbulence closure (Sect. 4.1).

The surface layer (SL) traditionally represents approximately the lowest 10 % of the atmospheric boundary layer (ABL), within which the vertical fluxes of heat, momentum, and other constituents are assumed to approach nearly constant distributions with height above the surface. Parameterization of the exchanges of these quantities between the surface and the atmosphere within atmospheric models relies upon various SL scaling relationships, since the vertical grid spacing in such models is generally too coarse to use a no-slip boundary condition. The particular SL scaling employed, along with characteristics of the model spatial discretization and the turbulence closure employed to model turbulent exchanges above the surface, all interact to influence the application of the surface boundary condition in atmospheric models and subsequently impact resulting flow and other SL and ABL characteristics.

The most commonly employed SL scaling relationship used within atmospheric models is the Monin–Obukhov similarity theory (MOST; Monin and Obukhov, 1954). MOST provides relationships to parameterize the fluxes between the surface and atmosphere based on a small number of surface and near-surface atmospheric-flow parameters. While MOST is well established, relatively simple, and widely used, it is based on a number of assumptions, including uniform terrain, horizontal homogeneity of both surface and atmospheric variables of interest, steady flow and forcing conditions over time, and the appropriateness of ensemble mean values of the parameterized fluxes. These assumptions are reasonably well satisfied in most historical numerical weather prediction and mesoscale atmospheric simulations, due in part to the use of coarse grid spacing, which satisfies the appropriateness of ensemble mean representations within each grid cell, while also not resolving sharp transitions in terrain features, horizontal heterogeneities, and meteorological forcing. However, the recent transition toward the use of higher resolution in many mesoscale applications sharpens the representation of some or all of these features, all of which increasingly violate the assumptions upon which MOST is based.

While the use of high horizontal resolution violates the applicability of MOST for one set of reasons, the use of high vertical resolution can create additional problems, especially in settings for which a logarithmic mean profile shape is not expected, such as within forest canopies or over significant surface waves or ocean swell. Moreover, care must be taken not to place the lowest model grid cell too close to the surface.

Microscale atmospheric LES models also routinely apply MOST to formulate the surface stresses at each surface grid cell based on the instantaneous time-varying horizontal velocities above. Even under highly idealized conditions satisfying the assumptions of MOST in the aggregate, such models violate the appropriateness of the ensemble mean assumption.

Despite the abovementioned caveats, MOST is still routinely applied in atmospheric simulations at all scales, owing primarily to a dearth of alternatives. To improve its applicability, as well as the performance of simulating flow within the SL more generally, numerous approaches have been developed, including various damping (Mason and Thomson, 1992) and correction factors (Khani and Porté-Agel, 2017), the use of more advanced turbulence subgrid-scale (SGS) models (Bou-Zeid et al., 2005; Chow et al., 2004), taking care to properly set the computational mesh to have the proper width-to-height ratio (Brasseur and Wei, 2010), and the use of additional near-wall stress parameterizations (Brown et al., 2001) to distribute the surface stresses vertically. The impacts of many of these methods on improving LES performance within the WRF model in wind-energy-relevant applications has been examined in Mirocha et al. (2010), Kirkil et al. (2012), Mirocha et al. (2013), and Mirocha et al. (2014b).

SL modeling has also been extended to applications over forested landscapes for which a logarithmic vertical profile of mean wind speed is not observed (see review by Patton and Finnigan, 2012). These methods are based on the addition of momentum sink terms to the governing horizontal momentum equations to account for the increased drag effects of foliage, with the magnitude of the drag expressed in terms of a leaf area index, which represents the surface area of vegetation as a function of height. Modifications to elements of the SGS model, including eddy viscosity coefficients and SGS turbulence kinetic energy (TKE), may also be included in such formulations.

Arthur et al. (2019) implemented the plant canopy model of Shaw and Patton (2003) into the WRF model and demonstrated the ability of WRF-LES to recover expected distributions of winds and turbulence quantities in an idealized plant canopy. Arthur et al. (2019) additionally combined concepts from the plant canopy approach and the near-wall stress models used in various LES SGS formulations (Kirkil et al., 2012) to develop a novel distributed drag implementation for the parameterized surface stresses. This model applies the expected surface momentum stresses as drag terms in the horizontal momentum equations, distributed vertically over the several lowest model grid cells. When applied in LESs using the MOST surface boundary condition, this approach significantly improves agreement between simulated mean wind speed profiles and their expected similarity relationships.

In addition to improving the implementation of MOST within atmospheric solvers, significant progress has also been achieved in developing an alternative to MOST using machine learning (ML) to relate surface exchange to relevant atmospheric and surface parameters obtained from observations. Details of this approach are provided in Sect. 4.2.

Over the course of this project, we have explored different frameworks for coupling mesoscale simulations to microscale LESs. Figure 2 depicts the various ways of classifying coupling strategies. Coupling approaches can be classified according to the following properties: communication directionality (i.e., one-way or two-way coupling), communication strategy (i.e., online through system memory or offline through file system), information transferred (i.e., direct quantities such as wind speed, temperature, and surface fluxes or indirect quantities such as tendencies from the mesoscale budget), and the information transfer location (i.e., inflow/surface planes at the LES boundary or through the entire flow volume). A comparatively low-cost method for coupling the mesoscale to the microscale is via an offline, periodic LES, which includes internal height–time-varying source terms that provide mesoscale influence on the microscale. For this approach, mesoscale simulation output is saved over a one-dimensional (1D) column at a regular temporal interval (e.g., 10 min); this information is used with data assimilation techniques to force the periodic simulation toward the desired mesoscale behavior. One way to achieve this forcing is through what we term “profile assimilation”, in which the microscale velocity and potential temperature solutions are plane-averaged at each height at a given time. Those resultant mean profiles are compared with the desired mesoscale profiles, and the difference is used to determine the amount of forcing required to drive the microscale mean vertical profiles to match those of the mesoscale. One of the key lessons learned in this study is that with a strong forcing that enforces the microscale mean vertical profiles to very closely match those of the mesoscale (what we term “direct profile assimilation”), unrealistic turbulent fields sometimes form in the microscale simulation. This may be a natural LES response to mesoscale profiles that are superadiabatic over too much of their vertical extent. To deal with this, we developed a method that allows the microscale simulation more freedom to depart from the exact mesoscale vertical structure (what we term “indirect profile assimilation”) but which will follow all the mesoscale trends in time (Allaerts et al., 2020, 2023). Alternatively, the mesoscale forcing can be included by imposing height–time-varying source terms in the microscale LES. The forcing accounts for large-scale advection and the driving pressure gradient and is extracted from the mesoscale simulation (Draxl et al., 2021). Any of these methods, though, assume a horizontally homogeneous forcing field and are applicable only to homogeneous cases that are well represented by periodic boundary conditions. Although it is theoretically possible to apply an internal source term that varies three-dimensionally in space to represent horizontally heterogeneous situations, we have not explored that approach; however, others (Sanz-Rodrigo et al., 2021) have demonstrated the validity of that approach. Instead, for horizontally heterogeneous domains or simulations that resolve turbines, we have focused our attention on boundary-coupled simulations, which provide the highest degree of generality. Boundary-coupled simulations can be conducted via online or offline coupling.

For offline coupling, the mesoscale output once again needs to be saved at regular temporal intervals to provide boundary forcing for the LES. However, instead of 1D profiles, two-dimensional (2D) planes must be saved, which increases the input/output (I/O) and storage requirements considerably. Boundary coupling allows for simulation of a heterogeneous domain for resolving complex terrain, mesoscale flows with significant horizontal gradients, or wind farms.

Online-coupled cases downscale from the mesoscale through nesting, usually within a single code; this allows for a potentially streamlined workflow, as the downscaling usually involves setting runtime input parameters. Advantages of an online-coupled simulation is the ability to use consistent numerics and complete atmospheric physics across spatial scales, as well as the ability to perform two-way coupling. However, because mesoscale meteorology models are usually not developed with LES applications in mind, this coupling approach requires greater overhead and poorly optimized parallelization of computing resources for the LES domain, imposing severe restrictions on the ability to conduct large numbers of simulations. Note that a current DOE initiative focuses on development of mesoscale (ERF, Energy Research and Forecasting model) and microscale (AMR-Wind; adaptive mesh refinement) models that are aimed at exascale high-performance computing (HPC) platforms. However, also note that online coupling of mesoscale and microscale models that are based on the same formulation, i.e., equations, and use the same numerical discretization simplifies coupling and results in more consistent simulations across scales. Offline boundary-coupled simulations, however, are able to achieve higher simulation throughput, which is crucial for parameter selection, sensitivity studies, or wind plant design applications. We conducted a series of case studies directly comparing these approaches: one in a flat, fairly homogeneous onshore environment (Sect. 3.1, Allaerts et al., 2020; Draxl et al., 2021; Allaerts et al., 2023) and one in the offshore environment (Sect. 3.5, Thedin et al., 2023). Further case studies demonstrate the use of these techniques in complex terrain (Sect. 3.3 and 3.4), resolving the coastal boundary (Sect. 3.6), or in the offshore environment with variable shallow-water roughness and sea surface temperature (Sect. 3.6).

We note that while the stand-alone microscale solver adds complexity to the setup, it allows for greater flexibility. Most importantly, it allows for the study of the interaction of realistic weather conditions, complex terrain, and turbines. The turbines can be coupled with aero-servo-elastic models using OpenFAST (2022; see Sect. 3.5.2). In the workflows presented in this paper, the turbine can be represented by actuator disk or actuator line models. Note that the stand-alone, offline approach even allows for the use of blade-resolved approaches.

LESs are designed to explicitly resolve the energetically important scales of turbulence and the resulting fluxes and transport those motions generate within the flow. Models using grid spacings that are too coarse to resolve those motions must instead rely on parameterizations (e.g., PBL schemes) to represent those processes. Therefore, when forcing LESs with mesoscale atmospheric data at the domain boundaries, either online or offline, a domain fetch is required for the resolved scales of motion to appear within the LES flow field, since those motions are not resolved within the inflow data. A similar issue is encountered when forcing LESs with observations, as most observational datasets do not contain sufficient spatiotemporal frequency to specify the turbulence field. In each of these cases, the fetch required for resolved-scale turbulence motions to form and equilibrate to the large-scale forcing within the LES domain can be extensive and represents a significant computational burden. The amount of fetch required depends on multiple contributing factors, including surface roughness and terrain, wind speed, and atmospheric stability. Generally, for a computation using specified inflow conditions during unstable conditions, the reduction in fetch due to perturbations can be small, perhaps only around 100 grid cells in the direction of the mean flow. However, during neutral or stable conditions, perturbation can foreshorten the fetch by several hundred grid points, which can constitute a computational savings of 50 % or more. Moreover, the flow field within the fetch will not represent either the mean or turbulence fields during the process of turbulence spin-up and equilibration well.

Within the fetch region, both the turbulence and mean flow statistics change rapidly, with turbulence developing and the mean flow responding to those changes. Random perturbations applied just inside the inflow plane(s) produce uncorrelated gradients that, through the action of the governing equations, develop into robust turbulence features with expected correlations and energetics. During this process, there is often an associated reduction in mean wind speeds and a small change in wind direction near the surface, due to a temporary reduction in downward momentum transport – since the mesoscale closure is no longer providing that within the LES domain and the turbulence within the LES domain has not yet developed the correlated structures responsible for downward momentum transport. The length of this region varies with stability and mean wind speed, with more stable and higher wind speeds generating longer transitional fetches. However, the mean and turbulence statistics of the flow do asymptotically approach their equilibrium values, after which no significant changes are observed with increasing distance from the inflow.

Modeling the atmosphere, at both meso- and microscales, is subject to uncertainty from a variety of sources. Uncertainty propagates from the data used to specify initial and boundary conditions (e.g., reanalysis-based flow fields, land surface properties, sea surface temperature data), from the form of model closures, and from specific parameter values used within a closure. Sensitivities to these uncertain factors may display complex, nonlinear interactions. Therefore, constraining the impacts on model predictions – particularly when considering coupled mesoscale–microscale modeling – is difficult. A powerful, albeit computationally intensive, approach to evaluating uncertainty in atmospheric-model closures is to generate an ensemble of simulations that sample across a range of parameter values. To adequately capture potential nonlinearities in the atmospheric-model response, several dozen or more ensemble members are typically required. However, once such a perturbed parameter ensemble is generated, it may be extensively interrogated using a variety of meta-modeling techniques. For example, generalized linear models were used by Yang et al. (2017, 2019) and Berg et al. (2019) for this purpose, while Kaul et al. (2022) performed analyses using random forest representations of the atmospheric-model response.

In the context of wind energy applications, quantities of interest such as hub-height wind speeds, turbulence levels, shear, and veer are known to generally show sensitivity to parameterizations of boundary layer turbulence and surface fluxes, and these kinds of parameterizations have been most extensively targeted for uncertainty quantification under the MMC project and related A2e projects. For example, uncertainty in mesoscale model predictions over complex terrain owing to parameter values of PBL and surface schemes was examined by Yang et al. (2017, 2019) and Berg et al. (2019). Reassuringly, these studies found that only a few parameters accounted for most of the model uncertainty, although the identity of these parameters could vary diurnally and seasonally based on the dominant state of atmospheric stability. Uncertainty owing to LES subgrid-scale turbulence closure parameters in realistic coupled mesoscale–microscale simulations was examined by Kaul et al. (2022) and found to trace predominantly to a single parameter (an eddy viscosity coefficient). However, the sensitivity of the modeled flow to variations in this parameter was noted to vary significantly between two case studies with nominally similar large-scale flow conditions but different smaller-scale flow structures (convective cells vs. rolls) and to show nonlinearity of response. For example, the hub-height wind speed showed much greater sensitivity to the eddy viscosity coefficient, across the full range of eddy viscosity coefficient values that were tested, in the case with roll-type structures. TKE was also more sensitive in the case with rolls to changes in the coefficient value through the lower half of the range of values tested. At higher values of the coefficient, turbulence was effectively damped so that the sensitivity of TKE to further increases in the coefficient became slight. In contrast, the case with a cellular flow structure was better able to sustain turbulence, so sensitivity of TKE to the eddy viscosity coefficient persisted across the full range of tested values, and sensitivities were greater at higher values of the coefficient.

Looking forward, much work remains to better characterize uncertainties within both mesoscale and microscale model predictions across a wider range of flow conditions, especially offshore. However, these initial studies give promising indications that uncertainty can typically be traced to a small number of model parameters and that the importance of these specific parameters can be interpreted in terms of flow physics considerations. Furthermore, the application of meta-modeling techniques and leveraging machine learning approaches can greatly aid in detecting relationships and patterns within atmospheric-model responses. Thus, efforts at uncertainty quantification not only meet a practical need to bound variability in atmospheric-model predictions but also can provide deeper insights to modelers that may ultimately drive improvements in parameterizations.

Complexity comes into play in many manners for atmospheric flow. For the purposes of enhanced MMC for wind energy applications, we have focused on issues relating to complex-terrain and offshore environments, including issues of correctly modeling atmospheric gravity waves but avoiding generating spurious ones.

To enable accurate assessment and repeatability of our science results, we have made all the essential components of our studies publicly available. These components include (1) the problem definition, including data exploration, curation, and transformation into useful simulation inputs; (2) the actual simulation inputs, including model configuration files and scripts; and (3) postprocessing and synthesis of the output. For this purpose, we have established the A2e–MMC GitHub organization for archiving and disseminating our work archived in Quon et al. (2023a, b, c), Gill et al. (2023), and Hawbecker et al. (2023b). This public GitHub organization hosts Python analysis code, Python analysis notebooks, code-specific input files, and our MMC-specific version of the WRF model that tracks the community version (currently v.4.3), each constituting a separate version-controlled repository. For every study in this project, the team has adopted workflows based on a common set of analysis and simulation codes within this framework, thus ensuring apples-to-apples comparisons between results. To complement the technical content on GitHub, we have also created a Read the Docs documentation site to provide an easily accessible high-level overview of our project's accomplishments, describe our capabilities, and link to the resources on GitHub wherever appropriate (Mesoscale-to-Microscale Coupling, 2023). We believe that in combination the GitHub and Read the Docs documentation will serve as a living record of the MMC project, as well as provide flexible and adaptable documentation for future related projects.

To develop and test methods for coupling so that the microscale follows changes at the mesoscale, an early case study of a diurnal cycle in flat conditions was chosen. This nonstationary case includes time-varying hub-height wind speed and direction, shear and veer, and turbulence intensity. For such a case, accurate downscaling of energy from the mesoscale is important for predicting realistic turbulent flow features in the wind farm operating environment.

Surrounded by grassland with no significant terrain changes within hundreds of miles, the Scaled Wind Farm Technology (SWiFT) facility located in the southern Great Plains in West Texas forms an ideal flat-terrain test site. There are several meteorological measurement facilities near the SWiFT site hosted by Texas Tech University's National Wind Institute (Sandia National Laboratories, 2023), including a tall meteorological tower and a radar wind profiler with a radio acoustic sounding system. In addition to the ideal terrain and availability of observational data, the site is also chosen for its relevance to onshore wind energy installations in the United States. Details of the atmospheric characterization are provided in Kelley and Ennis (2016).

From available data, the evening transition from 8 to 9 November 2013 was identified as a synoptically quiescent diurnal cycle leading to nonstationary flow conditions at heights relevant to wind energy. The evolution of flow parameters including wind speed, turbulence intensity, and virtual potential temperature follows a typical diurnal pattern, featuring a morning transition, daytime convective boundary layer, afternoon–evening transition, and nocturnal low-level jet. The relatively simple geographical and meteorological conditions of the SWiFT diurnal cycle make it an ideal case to study the performance of internal coupling methods throughout various atmospheric-stability regimes. The case has been used to evaluate existing coupling methodologies (Draxl et al., 2021) as well as to develop new techniques (Allaerts et al., 2020, 2023). The WRF mesoscale simulation setup contains three nested domains with 27, 9, and 3 km grid spacing, centered at the SWiFT site. The LES domains included 270, 90, and 30 m resolutions.

Among the various lessons learned from this flat-terrain diurnal-cycle case, perhaps the most important one was regarding the division of responsibilities between the mesoscale and the microscale solvers in an MMC framework. The trends in the mean flow are set at the mesoscale level, and the microscale solver cannot correct for large biases in mean flow quantities or erroneous timing of large-scale events like the evening transition. The task of the microscale solver is to fill in information on the unsteady, three-dimensional turbulent structures, which was often accompanied by an improvement in the prediction of wind shear and mean turbulence statistics inside the boundary layer, even in the relatively simple conditions of the SWiFT diurnal cycle. Further, the SWiFT case also highlighted the need for more high-quality data extending up to higher altitudes for validation purposes. Despite the available meteorological tower being taller than typically deployed towers, many boundary layer processes with relevance to wind energy take place above 200 m. For example, the low-level jet that developed during the SWiFT diurnal cycle was predicted to attain its maximum wind speeds at a height between 250 and 350 m, but there were insufficient data to validate this finding. Moreover, meteorological towers only present observations from a single column, which means they cannot be used to assess how well the spatial variations in the turbulent flow fields are predicted. Note that similar work has been carried out using data from the GABLS3 diurnal-cycle case that included high-altitude measurements to over 1000 m. Benchmark results are archived at Sanz Rodrigo et al. (2017a) with mesoscale–microscale coupling results described by Sanz Rodrigo et al. (2017b) and archived in Sanz Rodrigo (2017b, c).

A second case study (Arthur et al., 2020) leveraged MMC techniques to conduct simulations of a wind farm during a frontal passage, for which rapid changes in wind speed, direction and temperature, and atmospheric turbulence were observed. One of the key benefits of mesoscale–microscale coupling is the ability to examine wind energy phenomena at the wind plant scale while resolving time-varying forcing from the mesoscale. The simulations demonstrated the ability to capture the relevant mesoscale meteorological phenomena on a typical mesoscale simulation domain; downscale those features to an LES domain containing a section of an operating wind plant, represented as generalized actuator disks (GADs; Mirocha et al., 2014a); and simulate the interactions between the time-varying meteorological flow and turbines, including wakes, power extracted, and turbulence phenomena. This case study demonstrates the viability of fully online-coupled MMC simulations in WRF to address important issues in wind plant behavior under realistic atmospheric operating conditions.

The purpose of a first complex-terrain case study was to examine the flow structures near the surface, which depend on many factors, including surface forcing. We investigated coherent structures present in the flow measured using scanning lidar deployed near Wasco, Oregon, during the WFIP2 (Wind Forecast Improvement Project) campaign (Wilczak et al., 2019; Shaw et al., 2019) and those simulated using WRF LES. The simulations utilized WRF to WRF-LES for the unstable condition case on 21 August and stable conditions on 14 August 2016 for the westerly flow. The model output was sampled in a way consistent with scanning lidar data using plan position indicator scanning. We used the wind field of the innermost domain that has a horizontal grid spacing of 10 m.

For both stability conditions, 90 east sectors, each 1 min apart, were selected from the simulations and used to compute the spatial proper orthogonal decomposition (POD) modes and energy (Berkooz et al., 1993). The actual lidar data for the unstable case uses 49 east sectors with wind speed and heat flux values similar to those in the simulations, 5–7 m s-1 and ∼ 350 W m-2, respectively. For the stable case, the actual lidar data employ 160 east sectors with a wind speed of 10–12 m s-1 and heat flux of ∼-30 W m-2, similar to the simulated values. Figure 3 shows the spatial POD modes 1 and 21 and the POD energy (λ, which denotes kinetic energy per unit mass of the flow) distributed among many modes for the simulated and actual lidar data for two stability conditions. The first POD mode in all cases shows the most significant coherent structures, followed by smaller structures for increasing mode numbers. For the given stability conditions, the simulated and lidar cases showed similar shape and size variations for all modes. The first few modes (modes < 5) show similar spatial structures in the POD modes for all stability conditions. However, they exhibit different spatial structures for the higher POD modes. For instance, mode 21 in the unstable case shows large open-cell-like structures, whereas mode 21 in the stable case shows streak-like structures oriented in the predominant wind direction. This variation in flow structures in different modes can be attributed to the forcing function. POD energy shown in Fig. 3 (right panels) depicts the turbulent energy associated with each coherent structure starting from mode 2. The unstable conditions consistently exceed the POD energy (for mode > 1) in both simulated and observed lidar data. The cumulative energy (Fig. 3, inset) indicates that the first mode of the stable condition case contains larger POD energy than the unstable condition case and requires larger modes to represent the energy in the flow in observational data. Although the trend of varying POD energy shows similarities between the two cases, the magnitude and the energy spread among the modes differ. Overall, the POD modes of the different stability cases demonstrate that the simulations capture the important features of coherent structures present in actual lidar data.

This second complex-terrain case also leverages measurements made during the WFIP2 campaign, which covered many stability conditions, including cold-air pools (CAPs) that tend to develop during synoptically quiescent periods. To study the ability of the 3D PBL scheme to capture such features, we chose a case from 10–20 January 2017 when a robust CAP was observed in the Columbia River Gorge. Such events are often challenging to represent accurately in mesoscale simulations due to the relatively small-scale boundary layer processes that must be parameterized. To better understand the spatial variability in meteorological and turbulence characteristics during the CAP lifecycle, we conducted WRF simulations following the High-Resolution Rapid Refresh (HRRR) reforecast configurations that were run for the WFIP2 project. For these simulations, the Mellor–Yamada–Nakanishi–Niino (MYNN; Nakanishi and Niino, 2006) scheme is run in the inner domain (horizontal grid cell spacing, Δ=750 m) of a nested two-domain setup. A novelty of this study is the use of NCAR's (National Center for Atmospheric Research) 3D PBL parameterization (Kosović et al., 2020; Juliano et al., 2022; Eghdami et al., 2022; Rybchuk et al., 2022), which was implemented into the WRF model for high-resolution mesoscale simulations. More information about the modeling setup and codes may be found in Mesoscale-to-Microscale Coupling (2023).

Several key findings emerged from the WFIP2 CAP study, with additional details reported by Arthur et al. (2022). First, turbulence kinetic energy (TKE) measurements from the profiling lidar at the Gordon's Ridge site reveal that, compared to MYNN, the 3D PBL simulation more accurately represents the vertical and temporal variability in TKE. As a result, wind speed errors were lower in the 3D PBL simulation, especially during the CAP erosion period, which has been especially difficult to model (Adler et al., 2021). To better understand the leading cause of the improved performance by the 3D PBL compared with MYNN, we performed a sensitivity analysis using the 3D PBL scheme framework. More specifically, we modified the turbulence closure approach as well as the turbulent length scale–closure constant formulation. The main reason for the improvement in TKE prediction is primarily related to the different turbulent length scale–closure constant formulation. For 3D PBL simulations under convective conditions, Juliano et al. (2022) reported similar findings regarding the primary importance of the turbulent length scale–closure constant formulation.

The MMC techniques developed for onshore studies were tested for a first offshore scenario at the FINO1 research tower, located in the North Sea. This case is representative of low roughness and low turbulence and leverage measurements from the FINO towers and data from the Alpha Ventus wind energy plant.

A second offshore case is archived that studies the impact of different ways of representing surface roughness and providing sea surface boundary conditions. The offshore environment in the United States Northeast is an active area of research for wind energy development. Observations have recorded occurrences of persistent low-level jets (LLJs) with jet noses commonly below hub height (Debnath et al., 2021). In this study we assess the sensitivity of LLJ characteristics (e.g., jet nose height, maximum wind speed, low-level shear) to SST. We utilize six freely available satellite-derived SST datasets from the Group for High Resolution Sea Surface Temperature website (Table 1 and Fig. 8) to vary the lower boundary condition of surface temperature in online WRF simulations.

The simulations consist of five domains with grid spacing spanning from 6250 down to 10 m. We used 88 vertical levels with 20 m spacing below 1 km. We compare model results against observations from the New York State Energy Research and Development Authority floating lidars. We assess model performance in capturing the LLJ nose height, maximum wind speed, and low-level shear on each domain in order to compare how sensitive the results are to SST on the mesoscale and microscale. With this comparison, we aim to determine whether model sensitivity on the mesoscale translates directly to the microscale. In other words, can we expect the best-performing mesoscale model setup to be the best setup on the microscale?

Results indicate that ensemble mean error and spread for various characteristics of the offshore LLJ vary between the mesoscale solutions and microscale solutions. However, variance within the microscale domains (domains 4 and 5) is small. The ensemble mean error of EME =(so-s‾)2 (where so is the observed quantity and s‾ is the ensemble mean) and bias of the low-level shear, hub-height wind speed (assumed to be at 118 m in this case), and jet nose height vary across scales from the mesoscale to the microscale (Fig. 9). Additionally, the best mesoscale performer did not lead to the best-performing microscale setup in this case when considering these metrics. On the mesoscale, the shear produced in the lowest levels was lower than what was observed. The LES results improved upon the low-level shear but overcorrected the lowest-level wind speeds and produced values lower than what were observed. It is suspected that using a drag force locally consistent with MOST within the heterogeneous microscale simulation is the root cause of this overcorrection of low-level winds. Future work must focus on generalizing this finding in order to determine if mesoscale simulations can inform performance on the microscale prior to running simulations.

Traditional PBL schemes in mesoscale models are one-dimensional – that is, they parameterize only the vertical turbulent mixing under the assumption of horizontal homogeneity. In this sense, the vertical turbulent fluxes of momentum (<u′w′> and <v′w′>), potential temperature (<θ′w′>), water vapor mixing ratio (<qv′w′>), and any other relevant scalars (<φ′w′>, where φ is a scalar variable, such as the cloud water mixing ratio) are computed. By definition, the horizontal homogeneity assumption neglects horizontal gradients in resolved quantities, as well as the vertical gradient in vertical velocity. Therefore, the vertical turbulent fluxes are dependent on only vertical gradients. However, this assumption is not justified at model resolutions in the terra incognita (Δ≈100–1000 m), where turbulence is partially resolved, and, thus, horizontal gradients play an important role (e.g., Kosović et al., 2021). A main consequence of ignoring horizontal gradients in the terra incognita and under convective conditions is the development of spurious structures (termed modeled convectively induced secondary circulations, or M-CISCs, by Ching et al., 2004), which can have a deleterious effect on the model solution. Furthermore, most 1D PBL parameterizations rely on the 2D horizontal diffusion scheme of Smagorinsky; however, this scheme was originally introduced for numerical stability and is therefore not physically motivated (Smagorinsky, 1990).

To address the fundamental research challenge of modeling in the terra incognita, our team has implemented the 3D PBL parameterization of Mellor and Yamada (Mellor, 1973; Mellor and Yamada, 1974, 1982) into the WRF model. This new parameterization does not impose the assumption of horizontal homogeneity; thus, it considers both vertical and horizontal gradients when computing all six momentum stresses and the full tensor for scalars (namely, θ and qv), in addition to all components of the flux divergences. As a result, this approach does not require the use of Smagorinsky's 2D horizontal diffusion scheme and shows promise at grid resolutions in the terra incognita, especially under convective conditions. To examine the influence of accounting for horizontal gradients, we set up different idealized model configurations under convective conditions and at a high-resolution mesoscale grid spacing (Δ=250 m). This grid spacing is considered to be mesoscale resolution because it is not fine enough to fully resolve the most energetic eddies (i.e., the LES limit) due to the model's effective resolution. The three single-domain, doubly periodic configurations are homogeneous surface forcing (rolls and cells), sea breeze front initiation, and mountain–valley circulation. Results clearly depict the suppression of M-CISCs by the 3D PBL scheme compared to a traditional 1D PBL scheme (Kosović et al., 2021; Juliano et al., 2022). The impact of the turbulent length scale–closure constant formulation is found to be very important, such that M-CISCs may be present in the 3D PBL solution when the length scale is insufficiently large and thus vertical mixing is not strong enough. In general, we believe that the 3D PBL parameterization has the potential to be useful both as a mesoscale-only approach and as part of a mesoscale–microscale coupling strategy.

Specifying lower boundary conditions in numerical simulations of high-Reynolds-number atmospheric boundary layer flows requires estimating turbulent fluxes of momentum, heat, moisture, and other constituents. However, these fluxes are not known a priori and therefore must be parameterized. Parameterization of surface fluxes in atmospheric-flow models at any scale, from global to turbulence-resolving large-eddy simulations, are based on MOST where atmospheric-stability effects are accounted for through universal, semi-empirical stability functions. The stability functions are a function of the nondimensional stability parameter, a ratio of distance from the surface and the Obukhov length scale z/L (Monin and Obukhov, 1954). However, their functional form is determined based on observations using simple regression that cannot represent the surface-layer structure and governing parameters under a wide range of conditions. We have therefore developed and tested a neural network (NN) ML model for surface-layer parameterization (McCandless et al., 2022). We trained and tested the ML model using long-term observations from the National Oceanic and Atmospheric Administration's Field Research Division tower in Idaho and the Cabauw mast in the Netherlands. The offline comparison of MOST and the NN model surface-layer parameterizations with observations from the Cabauw mast are shown in Fig. 10. We then implemented the ML model in the FastEddy GPU-native LES model (Muñoz-Esparza et al., 2022) and the WRF single-column model. The ML model implementation in FastEddy demonstrates that it can accurately capture the diurnal evolution of an atmospheric boundary layer as shown in Fig. 11.

The ML model implementation in the WRF model was tested using a single-column model (SCM) based on the GABLS3 intercomparison study case defined by Bosveld et al. (2014). The comparison of SCM simulations using the ML model surface-layer parameterization with observations and the MOST parameterization demonstrates that it can capture the sensible heat flux, the skin temperature, the surface friction velocity, and the planetary boundary layer height well but underestimates the latent heat flux (Fig. 12).

A potential reason for discrepancies between the ML-model-predicted and observed latent heat flux is that the ML model for the surface-layer parameterization implemented in WRF interacts with a land–surface model, which is based on MOST.

The ML model for surface-layer parameterization demonstrates the potential to provide better estimates of surface fluxes in comparison to commonly used MOST-based parameterizations. However, to develop a generally applicable ML model it must be trained using long-term, consistent, complete, and quality-controlled observations from a wide range of environments. Future research could focus on expanding the training dataset and testing the model in mesoscale simulations over diverse locations.

Microscale simulations, like WRF-LES (30 m), generated over the Columbia River basin for the Wind Forecast Improvement Project 2 (WFIP2), are able to model the very complicated flow associated with complex terrain including downslope flows, mountain wakes, mountain–valley circulations, gravity waves, cold pools, and gap flows. However, such simulations are currently too complex to configure and computationally expensive for use outside the scientific research community. Here we tested using deep artificial neural networks on the LES to directly downscale from the mesoscale to the microscale in complex terrain. Once trained, deep learning models can generate high-resolution simulations from a coarse image in just a few seconds from mesoscale input. In addition, we wished to demonstrate that the deep network models can then potentially be applied to regions other than the LES domain on which they were trained.

We created high-resolution–low-resolution training sample pairs by subtiling relevant vertical levels of the LES on the eastern portion of the domain and coarsening the tiles with average filters. We trained two separate enhanced super-resolution generative adversarial networks (ESRGANs; Ledig et al., 2017; Wang et al., 2018) to accomplish the downscaling by training one GAN to downscale from 960 to 240 m and the second GAN to downscale from 240 to 30 m and applying the models successively. We set aside data from every third time step in the LES for testing. Visually, the performance of the compound GAN architecture on testing data samples and the larger domain was impressive (Fig. 13). We performed statistical analysis of the high-resolution GAN-generated wind and compared it with the LES, finding good agreement in the power spectra, velocity gradient distributions, and wind speed and wind direction distributions (Dettling et al., 2023). We found high Pearson correlation coefficients and very low mean bias between the tiles of GAN-generated wind components and LESs, as well as good agreement in the moments of GAN-generated wind components with the LES, even in the higher-order moments, skewness, and kurtosis (Dettling et al., 2023).

To demonstrate the potential of transfer learning, we extended the testing sample set to include the western half of WRF-LES, which contains part of the Cascade Range including Mt. Hood. The western region is not only very unique when compared to the training region in the east but also topographically much more complex. We performed the same statistical analysis to compare the GAN-generated wind to the LES in the transfer learning region, and the results were encouraging (Dettling et al., 2023).