Wind energy is the leading renewable technology in the U.S., generating over 10% of utility-scale electricity in recent years. Rapid growth in wind energy installations has made modeling and prediction of atmospheric boundary layer (ABL) wind speeds and the associated turbulence critical for wind turbine siting, resource assessment, and operational power forecasting. A number of modeling challenges currently exist, such as representing the impact of terrain on wind turbine wakes and capturing small-scale turbulence in stably-stratified conditions. Many low-fidelity wind turbine simulation methods fail to incorporate topography and struggle to account for dynamic flow behavior. In this dissertation, results are presented using high-fidelity large-eddy simulation (LES), which captures the dynamic and turbulent behavior of ABL winds, providing a framework to simulate a wide variety of turbulent atmospheric phenomena with a wind turbine parameterization to understand turbine-airflow interactions.

First, high-resolution simulations of the 2017 Perdigão field campaign in Portugal are conducted. The Perdigão site consists of two parallel ridges with a wind turbine located on top of one of the ridges. Both convective and stable atmospheric conditions are simulated to understand how the wind turbine wake behaves in complex terrain in two representative flow regimes. For the convective case study, flow recirculation in the lee of the ridge occurred, thus deflecting the wake upwards. For the stable case study, the wake deflected downwards following the terrain due to a mountain wave that occurred. The vertical behavior of the wind turbine wake can be detrimental to downwind turbines; however, this vertical behavior is not accounted for in current wind farm design wake models. These case studies demonstrate the dependence of the wind turbine wake behavior on terrain-induced flow phenomena, which, in-turn, depend on the thermal stratification of the atmosphere.

The stable case study from Perdigão is then studied in more depth to better understand both the ambient and wind turbine wake turbulence characteristics. Novel derived measurements of the turbulence dissipation rate are available from the field campaign, providing an opportunity to further examine the spatial structure of turbulence predicted by the model. Additionally, in this study, the dynamic reconstruction model (DRM) LES turbulence closure is used to better represent smaller-scale turbulence. The DRM closure more accurately predicts turbulence metrics, including the turbulence dissipation rate, most notably upwind of the major topographic features. After the flow passes over the first ridge, the differences between the DRM and a standard eddy-viscosity closure are small close to the surface, although the DRM closure does better predict the turbulence dissipation rate in the upper atmosphere in this region. Because the DRM closure is not a standard eddy-viscosity closure, negative turbulence dissipation rate or the backscatter of energy from smaller scales to larger scales is predicted; however, backscatter cannot be derived from Perdigão measurements due to the experimental setup and analysis methods used, thus leaving validation of this aspect for future work.

Next, a range of idealized stable boundary layer (SBL) conditions are modeled in support of the American Wake Experiment (AWAKEN) field campaign to address: (1) the effect of wind turbines on SBL development, and (2) the effect of intermittent turbulence on wind farm performance. In weak SBL conditions, turbulence is continuous and easier to simulate. With the intermittent turbulence that occurs in strongly stable conditions, only the DRM closure can resolve realistic turbulence. For all SBL conditions simulated, the wind farm significantly impacts wind speeds and thermal structure well downwind (greater than 30 rotor diameters or 2.4 km) of the farm. Wind speeds in the wakes are reduced, and the increased mixing as a result of the wakes weakens the stable stratification in the boundary layer.

Finally, simulations are performed of a real case study of intermittent turbulence observed during the AWAKEN field campaign. The intermittent turbulence event is determined to be driven by a nocturnal mesoscale convective system (MCS). The MCS results in a cold pool, which radiates outwards as a density current. This density current perturbs the SBL, thus inducing gravity waves. The structure of the simulated gravity waves is found to be especially sensitive to the parameterization of cloud and precipitation processes (microphysics). The gravity waves have very strong effects on the flow in the upper atmosphere; however, closer to the surface where there is additional ambient turbulence and turbulence generated by wakes, the effect of the waves is more nuanced. Notably, the waves induce local wind direction variation, which leads to fluctuations in the power output as various turbines within the farm are subjected to the wakes of nearby turbines.

The findings presented in this dissertation provide insight into wind farm performance in a broad range of atmospheric conditions by incorporating both terrain effects and thermal stratification. Specifically, these conditions include dynamic turbulent phenomena that current wind farm design tools are unable to capture. The advances in this dissertation related to high-resolution LES reveal novel and complex relationships between wind turbines and the atmosphere that can significantly improve wind farm power predictions at large.

Energy production from wind is an increasingly important component of overall

global power generation, and will likely continue to gain an even greater share

of electricity production as world governments attempt to mitigate climate

change and wind energy production costs decrease. Wind energy generation

depends on wind speed, which is greatly influenced by local and synoptic

environmental forcings. Synoptic forcing, such as a cold frontal passage,

exists on a large spatial scale while local forcing manifests itself on a much

smaller scale and could result from topographic effects or land-surface heat

fluxes. Synoptic forcing, if strong enough, may suppress the effects of

generally weaker local forcing. At the even smaller scale of a wind farm,

upstream turbines generate wakes that decrease the wind speed and increase the

atmospheric turbulence at the downwind turbines, thereby reducing power

production and increasing fatigue loading that may damage turbine components,

respectively. Simulation of atmospheric processes that span a considerable

range of spatial and temporal scales is essential to improve wind energy

forecasting, wind turbine siting, turbine maintenance scheduling, and wind

turbine design.

Mesoscale atmospheric models predict atmospheric conditions using observed

data, for a wide range of meteorological applications across scales from

thousands of kilometers to hundreds of meters. Mesoscale models include

parameterizations for the major atmospheric physical processes that modulate

wind speed and turbulence dynamics, such as cloud evolution and

surface-atmosphere interactions. The Weather Research and Forecasting (WRF)

model is used in this dissertation to investigate the effects of model

parameters on wind energy forecasting. WRF is used for case study simulations

at two West Coast North American wind farms, one with simple and one with

complex terrain, during both synoptically and locally-driven weather events.

The model's performance with different grid nesting configurations, turbulence

closures, and grid resolutions is evaluated by comparison to observation data.

Improvement to simulation results from the use of more computationally

expensive high resolution simulations is only found for the complex terrain

simulation during the locally-driven event. Physical parameters, such as soil

moisture, have a large effect on locally-forced events, and prognostic

turbulence kinetic energy (TKE) schemes are found to perform better than

non-local eddy viscosity turbulence closure schemes.

Mesoscale models, however, do not resolve turbulence directly, which is

important at finer grid resolutions capable of resolving wind turbine

components and their interactions with atmospheric turbulence. Large-eddy

simulation (LES) is a numerical approach that resolves the largest scales of

turbulence directly by separating large-scale, energetically important eddies

from smaller scales with the application of a spatial filter. LES allows

higher fidelity representation of the wind speed and turbulence intensity at

the scale of a wind turbine which parameterizations have difficulty

representing. Use of high-resolution LES enables the implementation of more

sophisticated wind turbine parameterizations to create a robust model for wind

energy applications using grid spacing small enough to resolve individual

elements of a turbine such as its rotor blades or rotation area.

Generalized actuator disk (GAD) and line (GAL) parameterizations are integrated

into WRF to complement its real-world weather modeling capabilities and better

represent wind turbine airflow interactions, including wake effects. The GAD

parameterization represents the wind turbine as a two-dimensional disk

resulting from the rotation of the turbine blades. Forces on the atmosphere are

computed along each blade and distributed over rotating, annular rings

intersecting the disk. While typical LES resolution (10-20 m) is normally

sufficient to resolve the GAD, the GAL parameterization requires significantly

higher resolution (1-3 m) as it does not distribute the forces from the blades

over annular elements, but applies them along lines representing individual

blades.

In this dissertation, the GAL is implemented into WRF and evaluated against the

GAD parameterization from two field campaigns that measured the inflow and

near-wake regions of a single turbine. The data-sets are chosen to allow

validation under the weakly convective and weakly stable conditions

characterizing most turbine operations. The parameterizations are evaluated

with respect to their ability to represent wake wind speed, variance, and

vorticity by comparing fine-resolution GAD and GAL simulations along with

coarse-resolution GAD simulations. Coarse-resolution GAD simulations produce

aggregated wake characteristics similar to both GAD and GAL simulations (saving

on computational cost), while the GAL parameterization enables resolution of

near wake physics (such as vorticity shedding and wake expansion) for high

fidelity applications.

For the first time, to our knowledge, this dissertation combines the

capabilities of a mesoscale weather prediction model, LES, and high-resolution

wind turbine parameterizations into one model capable of simulating a real

array of wind turbines at a wind farm. WRF is used due to its sophisticated

environmental physics models, frequent use in the atmospheric modeling

community, and grid nesting with LES capabilities. Grid nesting is feeding

lateral boundary condition data from a coarse resolution simulation to a finer

resolution simulation contained within the coarse resolution simulation's

domain. WRF allows the development of a grid nesting strategy from

synoptic-scale to microscale LES relevant for wind farm simulations; this is

done by building on the results from the investigation of model parameters for

wind energy forecasting and the implementation of the GAD and GAL wind turbine

parameterizations. The nesting strategy is coupled with a GAD parameterization

to model the effects of wind turbine wakes on downstream turbines at a

utility-scale Oklahoma wind farm. Simulation results are compared to

dual-Doppler measurements that provide three-dimensional fields of horizontal

wind speed and direction. The nesting strategy is able to produce realistic

turbine wake effects, while differences with the measurements can mostly be

attributed to the quality of the available weather input data.

A stable atmospheric boundary layer (ABL) develops over land at night due to radiative surface cooling. The state of turbulence in the stable boundary layer (SBL) is determined by the competing forcings of shear production and buoyancy destruction. When both forcings are comparable in strength, the SBL falls into an intermittently turbulent state, where intense turbulent bursts emerge sporadically from an overall quiescent background. This usually occurs on clear nights with weak winds when the SBL is strongly stable. Although turbulent bursts are generally short-lived (half an hour or less), their impact on the SBL is significant since they are responsible for most of the turbulent mixing.

The nighttime SBL can be modeled with large-eddy simulation (LES). LES is a turbulence-resolving numerical approach which separates the large-scale energy-containing eddies from the smaller ones based on application of a spatial filter. While the large eddies are explicitly resolved, the small ones are represented by a subfilter-scale (SFS) stress model. Simulation of the SBL is more challenging than the daytime convective boundary layer (CBL) because nighttime turbulent motions are limited by buoyancy stratification, thus requiring fine grid resolution at the cost of immense computational resources. The intermittently turbulent SBL adds additional levels of complexity, requiring the model to not only sustain resolved turbulence during quiescent periods, but also to transition into a turbulent state under appropriate conditions. As a result, LES of the strongly stable SBL potentially requires even finer grid resolution, and has seldom been attempted.

This dissertation takes a different approach. By improving the SFS representation of turbulence with a more sophisticated model, intermittently turbulent SBL is simulated, to our knowledge, for the first time in the LES literature. The turbulence closure is the dynamic reconstruction model (DRM), applied under an explicit filtering and reconstruction LES framework. The DRM is a mixed model that consists of subgrid scale (SGS) and resolved subfilter scale (RSFS) components. The RSFS portion is represented by a scale-similarity model that allows for backscatter of energy from the SFS to the mean flow. Compared to conventional closures, the DRM is able to sustain resolved turbulence under moderate stability at coarser resolution (thus saving computational resources). The DRM performs equally well at fine resolution. Under strong stability, the DRM simulates an intermittently turbulent SBL, whereas conventional closures predict false laminar flows. The improved simulation methodology of the SBL has many potential applications in the area of wind energy, numerical weather prediction, pollution modeling and so on.

The SBL is first simulated over idealized flat terrain with prescribed forcings and periodic lateral boundaries. A wide range of stability regimes, from weakly to strongly stable conditions, is tested to evaluate model performance. Under strongly stable conditions, intermittency due to mean shear and turbulence interactions is simulated and analyzed. Furthermore, results of the strongly stable SBL are used to improve wind farm siting and nighttime operations. Moving away from the idealized setting, the SBL is simulated over relatively flat terrain at a Kansas site over the Great Plains, where the Cooperative Atmospheric-Surface Exchange Study - 1999 (CASES-99) took place. The LES obtains realistic initial and lateral boundary conditions from a meso-scale model reanalysis through a grid nesting procedure. Shear-instability induced intermittency observed on the night of Oct 5th during CASES-99 is reproduced to good temporal and magnitude agreement. The LES locates the origin of the shear-instability waves in a shallow upwind valley, and uncovers the intermittency mechanism to be wave breaking over a standing wave (formed over a stagnant cold-air bubble) across the valley. Finally, flow over the highly complex terrain of the Owens Valley in California is modeled with a similar nesting procedure. The LES results are validated with observation data from the 2006 Terrain-Induced Rotor Experiment (T-REX). The nested LES reproduces a transient nighttime warming event observed on the valley floor on April 17 during T-REX. The intermittency mechanism is shown to be through slope-valley flow transitions. In addition, a cold-air intrusion from the eastern valley sidewall is simulated. This generates an easterly cross-valley flow, and the associated top-down mixing through breaking Kelvin-Helmholtz billows is analyzed. Finally, the nesting methodology tested and optimized in the CASES-99 and T-REX studies is transferrable to general ABL applications. For example, a nested LES is performed to model daytime methane plume dispersion over a landfill and good results are obtained.

Soil moisture affects flow in the atmospheric boundary layer (ABL) through relative partitioning of surface energy fluxes. Surface conditions significantly affect flow in the ABL under quiescent synoptic conditions (weak forcing) over flat terrain, but strong wind forcing often dominates land surface effects. Over complex terrain, it is unclear what role soil moisture plays. Due to a lack of data at the appropriate resolution, surface conditions are often interpolated from coarse grids as part of a standard intialization procedure for mesoscale atmospheric models. In this work, simulations of the ABL are performed using the Advanced Regional Prediction System (ARPS) in a horizontally nested grid configuration for the complex terrain of Owens Valley, California, site of the Terrain-Induced Rotor Experiment (T-REX) in March and April, 2006. Effects of surface

conditions on simulations of ABL flow in complex terrain under both weak and strong synoptic

forcing are investigated through a sensitivity study and through comparisons to observations. Coupled hydrologic modeling using PF.CLM, a coupled groundwater-land-surface model, is presented as a physically-based alternative to standard initialization procedures. Soil moisture measurements were carried out during T-REX and are used to validate results of the coupled hydrologic modeling. Results of the sensitivity study indicate that simulations of the ABL are sensitive to surface soil moisture initialization under both weak and strong synoptic forcing. Comparisons of simulation results to observations show significant improvements in most simulations with more accurate soil moisture. Coupled hydrologic modeling is a promising alternative to standard initialization procedures; even simple two-dimensional simulations successfully capture soil moisture trends across Owens Valley. Simple adjustments to standard initial soil moisture based on field observations yield significant improvements in comparisons to observations as well.

Since the beginning of numerical weather prediction (NWP), which was performed on O(700 km) grids, advances in computing technology have driven corresponding advances in model resolution. In recent years, operational NWP efforts have reached O(1 km) horizontal resolutions, leading to the use of large-eddy simulation (LES) to simulate the atmospheric boundary layer (ABL). However, the available turbulence closure models for atmospheric LES were designed to model the smallest scales of atmospheric turbulence, leaving operational forecasters and researches in many diverse fields alike without a turbulence model fit for the computing power available to them. This range of resolutions is known as the "gray zone" or "terra incognita" in the atmospheric turbulence literature, and will be the focus of much discussion in this dissertation. Further, the results will be presented in a way that is visual and digestible to a user of LES whose expertise is not necessarily in theoretical turbulence.

Here, the Weather Research and Forecasting (WRF) model is used to give a thorough and visual demonstration of the inadequacies of the more popular LES turbulence closure models, the Smagorinsky-Lilly and TKE-1.5 models, at gray-zone resolutions, and an explanation of the behavior is offered. Two alternatives, both with multiple flavors, the dynamic reconstruction model (DRM) and an alternative-anisotropic formulation of the classical eddy-viscosity models, are presented as potential remedies to the gray-zone issue. Studies are conducted first for an idealized free-convection case with constant surface heat flux and zero mean wind. A more realistic initial profile with an initial wind and geostrophic forcing is then considered. Finally, three more cases are considered with various surface heat flux values and initial wind profiles.

Both the DRM and alternative-anisotropic eddy-viscosity models are able to deliver much more consistent results at coarse resolutions when considering planar-averaged profiles of potential temperature and velocity, resolved velocity fields and resolved turbulent kinetic energy, and their performance inspires interesting topics of future work regarding the representation of scales of energy in the atmosphere. The implementation of the anisotropic eddy-viscosity model in general, as well as the anisotropic Smagorinsky-Lilly model specifically, in the WRF model is also considered, resulting in a change in the WRF turbulent diffusion routines and a demonstration of improvement seen at coarse resolutions by reformulating the anisotropic Smagorinsky-Lilly model to partition stress terms into horizontal and vertical components. An additional chapter presents the gray zone problem as it relates to complex terrain.

Understanding agricultural productivity under climate change is critical to helping global food systems tackle impending challenges in supply and demand. Crucially, this requires us to understand planting dates: by controlling the yield and cropping intensity of rainfed agriculture, planting dates could serve as a major adaptation strategy under climate pressure. Currently, the lack of spatiotemporally resolved crop timing information makes it difficult to produce insights into planting behavior, which is the result of complex human decisions made under varying socio-economic and climatic contexts. This data gap hinders our ability to understand how farmers will adapt to climate change by shifting planting dates, and may negatively impact the accuracy of yield predictions. This dissertation addresses this data gap by introducing a scalable method to estimate planting dates. I apply this method to generate insights into historical and future planting dates of soy (Glycine max) in the heavily agricultural state of Mato Grosso, Brazil (MT). My work begins with a remote sensing-based method to estimate field-scale (500 m) planting and harvest dates over large (100,000 km2), and therefore computationally challenging areas, with sparse ground truth information. The method pairs (1) a timeseries analysis algorithm for MODIS imagery, implementable on the cloud computing platform Google Earth Engine (GEE), to extract 500 m phenological milestones and (2) proxy ground truth data based on Planet Labs imagery to relate phenological milestones to observed planting and harvest dates. Next, I build a statistical model of satellite-estimated planting dates as a function of the wet season onset. This model reveals several novel insights about agricultural behavior in Mato Grosso. First, traditional climatological definitions of wet season onset are less correlated to observed planting dates than alternative, easily observable definitions based on rainfall frequency, highlighting the need to explore farmer-relevant definitions of climate. Second, planting dates' sensitivity to wet season onset varies dramatically among fields and with cropping intensity; this heterogeneous response produces a wide range of planting dates that are rarely included in crop models. Finally, a trend toward earlier planting dates, independent of wet season onset, reveals nonstationary behavior that cannot be captured with the historical survey data used by some yield prediction efforts. My findings suggest that under RCP 8.5 climate conditions, climatic windows will constrain planting dates relative to agronomically preferred times, and the feasibility of double cropping will be endangered for vulnerable portions of Mato Grosso. Both delayed planting dates and loss of double cropping suitability are problematic for an economy that largely depends on agribusiness and that is central to international soy supply. While Mato Grosso is the focus of this dissertation, the methods developed here lay the groundwork for similar studies globally. By introducing a scalable method to close the information gap on planting dates and generating new insights into the planting dates of tropical rainfed crops, this work provides a foundation for investigating planting date behavior and climate change adaptation in vulnerable, data-scarce agricultural regions worldwide.

Traditional weather models struggle to resolve the details of complex terrain and the strongly stable stratification often observed in near surface temperature inversions. Conversely, traditional engineering computational fluid dynamics codes often use high resolution grid meshes, but do not include forcing from synoptic scale weather. As computational power grows, a new class of models is emerging. These are nested large-eddy simulations (LES), which are both highly resolved and include large scale weather forcing. In this case, high resolution implies grid meshes that are fine enough to resolve the most energetic eddies in the atmospheric boundary layer. These high resolution domains are nested, i.e. forced at the lateral boundaries, by coarser mesoscale models. The role of nested large-eddy simulation in the study of atmospheric boundary layer is twofold. First, trusted LES data allow the study of important dynamics with all the relevant forcing of real flow, but without dense observation networks. Though observations are still critical to the validation of these models, in some cases, as in fire weather, sufficiently detailed observations are very difficult to carry out due to practical concerns. In other cases, simulation is simply a less expensive means to achieve higher resolution data than even the densest sensor network can provide. In this sense, LES is a valuable tool for the research community. For the forecasting community, however, LES cannot be used in place of coarser models given current computational power. As prediction is an ultimate goal of weather modeling, we turn to the second role of LES, the generation of subgrid parameterizations for use in coarse models that can be run for real-time forecasting. The dual purpose of LES, the direct study of atmospheric boundary layer dynamics and the development of parameterizations for mesoscale models, motivate three investigations into the dynamics of the atmospheric boundary layer presented here. Each study conducts LES with the Weather Research and Forecasting (WRF) model, an advanced numerical weather prediction (NWP) code. Unlike traditional NWP or engineering codes, these simulations include both complex terrain as well as realistic weather forcing to advance our understanding of atmospheric boundary layer dynamics and the LES technique itself. The first project is conducted as part of the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) program. During the field campaign of the MATERHORN, large temperature fluctuations were observed on the slope of Granite Peak, Utah, which partially encloses a cold-air pool in the east basin. These flow features are able to be resolved using LES within the WRF model with ∆x = 100 m, allowing accurate representation of lee vortices with horizontal length scale of O(1 km). At this resolution, terrain slopes become quite steep, and some model warm biases remain in the east basin due to limits on terrain-following coordinates that prevent the model from fully resolving drainage flows with this steep terrain. A new timestep limit for the WRF model related to these steep slopes is proposed. In addition, the initialization of soil moisture is adjusted by drying the shallowest layer to assist the formation of a cold pool in the LES. These real case simulations compare well to observations and also to previously published simulations using idealized configurations to study similar phenomena. For instance, the values of non-dimensional mountain height, which characterize flow regimes in idealized studies, are similar in the real case. With their predictive capabilities established, these non-dimensional numbers are likely to provide the future basis for parameterization of the lee vortices which cannot be resolved by NWP models. The second study addresses a challenge to simulating turbulent flow in multiscale atmospheric applications, the efficient generation of resolved turbulence motions over an area of interest. One approach is to apply small perturbations to flow variables near the inflow planes of turbulence-resolving simulation domains nested within larger mesoscale domains. While this approach has been examined in numerous idealized and simple terrain cases, its efficacy in complex terrain environments has not yet been fully explored. Here, we examine the benefits of the stochastic cell perturbation method (CPM) over real complex terrain using data from the 2017 Perdigão field campaign, conducted in an approximately 2-km wide valley situated between two nearly parallel ridges. Following a typical configuration for multiscale simulation using nested domains within the WRF model to downscale from a mesoscale to an LES, we apply the CPM on a domain with a relatively coarse LES mesh spacing of 150 m. LES at this resolution often generates spurious coherent structures under unstable atmospheric conditions with moderate mean wind speeds. We examine the impacts of the CPM on the representation of turbulence within the nested LES domain under moderate mean flow conditions in three different stability regimes: weakly convective, strongly convective, and weakly stable. In addition, two different resolutions of the underlying terrain are used to explore the role of the complex topography itself in generating turbulent structures. We demonstrate that the CPM improves the representation of turbulence within the LES domains, relative to the use of high-resolution complex terrain alone. During the convective conditions, the CPM improves the rate at which smaller-scales of turbulence form, while also accelerating the attenuation of the spurious numerically-generated roll structures near the inflow boundary. During stable conditions, the coarse mesh spacing of the LES used herein was insufficient to maintain resolved turbulence using CPM as the flow develops downstream, highlighting the need for yet higher resolution under even weakly stable conditions. The CPM was particularly efficient during the evening transition period. A final study investigates fundamental controls on drainage flow dynamics. Historically called katabatic flow, drainage flow is buoyancy driven and directed downslope in response to surface cooling typical of the nocturnal period. Analogous upslope flow due to surface heating during the day is often called anabatic flow. A fundamental question is at what time during the evening transition does the slope wind system switch from anabatic to drainage flow. A natural benchmark for this transition is sunset, but the presence of terrain results in shadows cast onto east-facing slopes which can complicate this analysis. To guide this analysis, functional forms for the time of the shadow front propagation are presented for an idealized terrain shape used for an LES in WRF. Even with idealized topography, the present LES are significantly more advanced than previous models used to investigate idealized drainage flow, which prescribed surface cooling rather than prognosticating the cooling in response to the diurnal cycle of insolation and the characteristics of the surface and soil types, as done here. This complexity allows for potentially counterintuitive results, such as the onset of drainage flow occurring on the shadow-cast eastern slopes later than on the sunnier western slopes due to convective structures which persist after sunset. Despite these complications during the development of drainage flow in the evening, there are periods during the night when analytical solutions compare well to the LES solution of drainage flow profiles. A novel analytical solution also explains a dependence on the angle of the slope found in observation data but missing in the original (Prandtl 1942) solution by replacing the traditional Dirichlet with a Neumann boundary condition. The favorable comparison between analytical solutions and results from the high resolution numerical model are a first step towards the ultimate parameterization of drainage flow in coarser NWP models.