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The accurate modelling of the wind speed profile at altitudes relevant to wind energy (i.e. up to 200m) is important for preliminary wind resource assessments, forecasting of the wind resource, and estimating shear loads on turbine blades. Modelling of the wind profile at these altitudes is particularly challenging in stable stratification due to weak turbulence and the influence of a broad range of additional processes. Models used to simulate the wind profile range from equilibrium-based 1D analytic extrapolation models to time-evolving 3D atmospheric models. Extrapolation models are advantageous due to their low computational requirements but provide a very limited account of atmospheric physics. Conversely, 3D models are more physically comprehensive but have considerably higher computational cost and data requirements. The middle ground between these two approaches has been largely unexplored. The intent of this research is to compare the ability of a range of models of varying complexity to model the wind speed profile up to 200m under stable stratification. I focus in particular on models that are more physically robust than conventional extrapolation models but less computationally expensive than a 3D model. Observational data taken from the 213-m Cabauw meteorological tower in the Netherlands provide a basis for much of this analysis. I begin with a detailed demonstration of the limitations and breakdown in stable stratification of Monin-Obukhov similarity theory (MOST), the theoretical basis for the logarithmic wind speed profile model. I show that MOST (and its various modifications) are reasonably accurate up to 200m for stratification no stronger than weakly stable. At higher stratifications, the underlying assumptions of MOST break down and large errors in the modelled wind profiles are found. I then consider the performance of a two-layer MOST-Ekman layer model, which provides a more physically-comprehensive description of turbulence compared to MOST-based models and accounts for the Coriolis force and large-scale wind forcing (i.e. geostrophic wind). I demonstrate considerable improvements in wind profile accuracy up to 200m compared to MOST-based approaches. Next, I contrast the performance of a two-layer model with a more physically-comprehensive equilibrium-based single-column model (SCM) approach. I demonstrate several limitations of the equilibrium SCM approach - including frequent model breakdown - that limit its usefulness. I also demonstrate no clear association between the accuracy of the wind profile and the order of turbulence closure used in the SCM. Furthermore, baroclinic influences due to the land-sea temperature gradient are shown to have only modest influence on the SCM wind speed profile in stable conditions. Overall, the equilibrium SCM (when it does not break down) is found to generally outperform the two-layer model. Finally, I contrast the performance of the equilibrium SCM with a time-evolving SCM and a time-evolving 3D mesoscale model using a composite set of low-level jet (LLJ) case studies as well as a 10-year dataset at Cabauw. For the LLJ case studies, the time-evolving SCM and 3D model are found to accurately simulate the evolving stratification, the inertial oscillation, and the LLJ. The equilibrium SCM is shown to have comparatively less skill. Over the full 10-year data set, the sensitivity of the time-evolving SCM to horizontally-driven temperature changes in the ABL is found to be a considerable limitation. Despite its various limitations and simplified physics, the time-evolving SCM is generally found to be equally as accurate as the mesoscale model while using a fraction of the computational cost and requiring only a minimal amount of easily attainable local observations. Overall, the time-evolving SCM model is found to perform the best (considering both accuracy and robustness) compared to a range of equilibrium approaches as well as a time-evolving 3D model, while offering the best balance of observational data requirements, physical applicability, and computational requirements. This thesis presents a compelling case for the use of SCMs in the field of wind energy meteorology. / Graduate

This work approaches the topic of modeling the atmospheric boundary layer in four research projects, which are summarized below. i) The diurnal cycles of near-surface meteorological parameters over Antarctic sea ice in six widely used atmospheric reanalyses were validated against observations from Ice Station Weddell. The station drifted from February through May 1992 and provided the most extensive set of meteorological observations ever collected in the Antarctic sea ice zone. For the radiative and turbulent surface fluxes, both the amplitude and shape of the diurnal cycles varied considerably among different reanalyses. Near-surface temperature, specific humidity, and wind speed in the reanalyses all featured small diurnal ranges, which, in most cases, fell within the uncertainties of the observed cycle. A skill score approach revealed the superiority of the ERA-Interim reanalysis in reproducing the observed diurnal cycles. An explanation for the shortcomings in the reanalyses is their failure to capture the diurnal cycle in cloud cover fraction, which leads to errors in other quantities as well. Apart from the diurnal cycles, NCEP-CFSR gave the best error statistics. ii) The accuracy of prediction of stable atmospheric boundary layers depends on the parameterization of the surface layer which is usually derived from the Monin-Obukhov similarity theory. In this study, several surface-layer models in the format of velocity and potential temperature Deacon numbers were compared to observations from CASES-99, Cardington, and Halley datasets. The comparisons were hindered by a large amount of scatter within and among datasets. Tests utilizing R2 demonstrated that the Quasi-Normal Scale Elimination (QNSE) theory exhibits the best overall performance. Further proof of this was provided by 1D simulations with the Weather Research and Forecasting (WRF) model. iii) The increasing number of physics parameterization schemes adopted in numerical weather forecasting models has resulted in a proliferation of inter-comparison studies in recent years. Many of these studies concentrated on determining which parameterization yields results closest to observations rather than analyzing the reasons underlying the differences. In this work, the performance of two 1.5-order boundary layer parameterizations was studied, the QNSE and Mellor-Yamada-Janjić (MYJ) schemes, in the Weather Research and Forecasting (WRF) model. The objectives were to isolate the effect of stability functions on the near-surface values and vertical profiles of virtual temperature, mixing ratio and wind speed. The results demonstrate that the QNSE stability functions yield better error statistics for 2-m virtual temperature but higher up the errors related to QNSE are slightly larger for virtual temperature and mixing ratio. A surprising finding is the sensitivity of the model results to the choice of the turbulent Prandtl number for neutral stratification (Prt0): in the Monin-Obukhov similarity function for heat, the choice of Prt0 is sometimes more important than the functional form of the similarity function itself. There is a stability-related dependence to this sensitivity: with increasing near-surface stability, the relative importance of the functional form increases. In near-neutral conditions, QNSE exhibits too strong vertical mixing attributed to the applied turbulent kinetic energy subroutine and the stability functions including the effect of Prt0. iv) In recent years, many eddy-diffusivity mass flux (EDMF) planetary boundary layer (PBL) parameterizations have been introduced. Yet, most validations are based on idealized setups and/or single column models. To address this gap, this study focused on the effect the mass flux part has on the performance in the QNSE-EDMF PBL scheme in the WRF model by comparing the results to observations from the CASES-97 field campaign. In addition, two refined versions, one introducing the parameterized clouds to the WRF radiation scheme, and the second adding a different entrainment formulation, were evaluated. The introduction of mass flux reduced errors in the average moisture profile but virtual temperature and wind speed profiles did not change as much. The turbulent flux profiles for modeled virtual potential temperature were little affected, with consistent reasonable agreement with observations, if one allows for biases in the observed data and modeled surface fluxes. However, the water vapor flux divergences from QNSE tend to be more negative than observed, while including the mass flux part tends to make the divergences more positive, the latter at least partially due to deeper model PBLs resulting from excessive model surface virtual temperature fluxes. Further, both virtual potential temperature and water vapor flux profiles display spurious spikes attributed to the way the non-local and local terms interact in the model. The influence of the mass flux schemes extends to 60 – 100-km scale circulation features, which were greatly modified by both the inclusion of mass flux and the new entrainment formulation. Adding mass flux based clouds to the radiation calculation improved the time and space averaged modeled incoming shortwave flux. The choice of the representation for entrainment/detrainment often affected the results to the same extent as adding mass flux did.

Turbulent flows affected by buoyancy lie at the basis of many applications, both within engineering and the atmospheric sciences. A prominent example of such an application is the atmospheric boundary layer, the lowest layer of the atmosphere, in which many physical processes are heavily influenced by both stably stratified and convective turbulent transport. Modelling these turbulent flows correctly, especially in the presence of stable stratification, has proven to be a great challenge and forms an important problem in the context of climate models. In this thesis, we address this issue considering an advanced class of turbulence models, the so-called explicit algebraic models.In the presence of buoyancy forces, a mutual coupling between the Reynolds stresses and the turbulent heat flux exists, which makes it difficult to derive a fully explicit turbulence model. A method to overcome this problem is presented based on earlier studies for cases without buoyancy. Fully explicit and robust models are derived for turbulence in two-dimensional mean flows with buoyancy and shown to give good predictions compared with various data from direct numerical simulations (DNS), most notably in the case of stably stratified turbulent channel flow. Special attention is given to the problem of determining the production-to-dissipation ratio of turbulent kinetic energy, for which the exact equation cannot be solved analytically. A robust approximative method is presented to calculate this quantity, which is important for obtaining a consistent formulation of the model.The turbulence model derived in this way is applied to the atmospheric boundary layer in the form of two idealized test cases. First, we consider a purely stably stratified boundary layer in the context of the well-known GABLS1 study. The model is shown to give good predictions in this case compared to data from large-eddy simulation (LES). The second test case represents a full diurnal cycle containing both stable stratification and convective motions. In this case, the current model yields interesting dynamical features that cannot be captured by simpler models. These results are meant as a first step towards a more thorough investigation of the pros and cons of explicit algebraic models in the context of the atmospheric boundary layer, for which additional LES data are required. / <p>QC 20150522</p>

<p>The boundary layer is the part of the atmosphere that is in direct contact with the ground via turbulent motion. At mid-latitudes the boundary layer is usually one or a few kilometers deep, while in the Arctic it is much more shallow, typically a few hundred meters or less. The reason is that here the absolute temperature increases in the lowest kilometer, making the boundary layer semi-permanently stably stratified. The exchange of heat, momentum and tracers between the atmosphere, ocean and ground under stable stratification is discussed from an observational, modeling and climate-change point of view. A compilation of six observational datasets, ordered by the Richardson number (rather than the widely used Monin-Obukhov length) reveals new information about turbulence in the very stably stratified regime. An essentially new turbulence closure model, based on the total turbulent energy concept and these observational datasets, is developed and tested against large-eddy simulations with promising results. The role of mesoscale motion in the exchange between the atmosphere and surface is investigated both for observations and in idealized model simulations. Finally, it is found that the stably stratified boundary layer is more sensitive to external surface forcing than its neutral and convective counterparts. It is speculated that this could be part of the explanation for the observed Arctic amplification of climate change.</p>

The boundary layer is the part of the atmosphere that is in direct contact with the ground via turbulent motion. At mid-latitudes the boundary layer is usually one or a few kilometers deep, while in the Arctic it is much more shallow, typically a few hundred meters or less. The reason is that here the absolute temperature increases in the lowest kilometer, making the boundary layer semi-permanently stably stratified. The exchange of heat, momentum and tracers between the atmosphere, ocean and ground under stable stratification is discussed from an observational, modeling and climate-change point of view. A compilation of six observational datasets, ordered by the Richardson number (rather than the widely used Monin-Obukhov length) reveals new information about turbulence in the very stably stratified regime. An essentially new turbulence closure model, based on the total turbulent energy concept and these observational datasets, is developed and tested against large-eddy simulations with promising results. The role of mesoscale motion in the exchange between the atmosphere and surface is investigated both for observations and in idealized model simulations. Finally, it is found that the stably stratified boundary layer is more sensitive to external surface forcing than its neutral and convective counterparts. It is speculated that this could be part of the explanation for the observed Arctic amplification of climate change.

<p>Knowledge of the turbulent fluxes at the sea surface is important for understanding the interaction between atmosphere and ocean. With better knowledge, improvements in the estimation of the heat exchange coefficients can be made and hence models are able to predict the weather and future climate with higher accuracy.</p><p>The exchange coefficients of latent and sensible heat during stable stratification vary in the literature. Therefore it is necessary to investigate the processes influencing the air-sea exchange of water vapour and heat in order to estimate these values. With measurements from a tower and a directional waverider buoy at the site Östergarnsholm in the Baltic Sea, data used in this study have been sampled from the years 2005-2007. This site represents open-ocean conditions during most situations when the wind comes from the south-east sector. The neutral exchange coefficients, CEN and CHN, have been calculated along with the non-dimensional profile functions for temperature and wind to study the dependence of stability and other parameters of relevance.</p><p>It was found that CEN increased slightly with wind speed and reached a mean value of approximately 1.45×10-3. The highest values of CEN were observed during near neutral conditions and low wave ages. CHN attained a mean value of approximately 0.77×10-3 and did not show any relation to wind speed or to wave age. No significant dependence with wind or wave direction could be shown for either CEN or CHN in the sector 80-220°. The stability correction, performed to reduce the dependence on stratification for CEN and CHN, was well performed for stabilities higher than 0.15. The stability is represented by a relationship between the height and the Obukhov-length (z/L).</p><p>Validity of the non-dimensional profile functions for temperature and wind showed that, for smaller stabilities, these functions gave higher values than the corresponding functions recommended by Högström (1996). The profile funtions for temperature was shown to have a larger scatter while the profile functions for wind was less scattered and deviated more from the functions given by Högström</p> / <p>Kunskap om turbulenta flöden i det marina gränsskiktet är viktigt för att förstå växelverkan mellan atmosfär och hav. Med bättre kunskap kan förbättringar i bestämningen av utbyteskoefficienterna för latent och sensibelt värme erhållas. Det medför att modeller kan prognostisera väder och framtida klimat med högre noggrannhet.</p><p>Utbyteskoefficienterna för latent och sensibelt värme har för stabil skiktning olika värden i litteraturen. Detta gör det nödvändigt att undersöka de processer som påverkar utbytet av vattenånga och värme mellan luft och hav för att kunna bestämma dessa värden. Data som har använts i den här studien insamlades mellan år 2005 och 2007 från en boj och ett torn vid mätplatsen Östergarnsholm i Baltiska havet. För det flesta situationer, när vinden blåser från syd-ost, representerar mätplatsen ett förhållande likvärdigt det över öppet hav. De neutrala utbyteskoefficienterna, CEN och CHN, och de dimensionslösa profilfunktionera för temperatur och vind, och , har beräknats för att studera beroendet av stabilitet samt andra relevanta parametrar.</p><p>Beräkningarna visade att CEN ökade något med vindhastighet och hamnade på ett medelvärde av ungefär 1.45×10-3. De högsta värdena på CEN observerades vid nära neutrala förhållanden och låga vågåldrar. CHN uppmättes till att ha ett medelvärde på ungefär 0.77×10-3 och uppvisade inget beroende med vindhastighet eller vågålder. Inget märkbart beroende med vind- eller vågriktning kunde visas för CEN eller CHN i sektorn 80-220°. Stabilitetskorrektionen, utförd för att reducera beroendet av atmosfärens skiktning för CEN och CHN, var bra för stabiliteter högre än 0.15. Stabiliteten representeras av förhållandet mellan höjden och Obukhov-längden (z/L).</p><p>Utvärdering av de dimensionslösa funktionerna för temperatur och vind visade att dessa funktioner, för små stabiliteter, gav högre värden än motsvarande funktioner som rekommenderas av Högström (1996). Värdena på profilfunktionerna för temperatur hade större spridning än värdena på profilfunktionerna för vind och avvek mer från funktionerna givna av Högström.</p>

Knowledge of the turbulent fluxes at the sea surface is important for understanding the interaction between atmosphere and ocean. With better knowledge, improvements in the estimation of the heat exchange coefficients can be made and hence models are able to predict the weather and future climate with higher accuracy. The exchange coefficients of latent and sensible heat during stable stratification vary in the literature. Therefore it is necessary to investigate the processes influencing the air-sea exchange of water vapour and heat in order to estimate these values. With measurements from a tower and a directional waverider buoy at the site Östergarnsholm in the Baltic Sea, data used in this study have been sampled from the years 2005-2007. This site represents open-ocean conditions during most situations when the wind comes from the south-east sector. The neutral exchange coefficients, CEN and CHN, have been calculated along with the non-dimensional profile functions for temperature and wind to study the dependence of stability and other parameters of relevance. It was found that CEN increased slightly with wind speed and reached a mean value of approximately 1.45×10-3. The highest values of CEN were observed during near neutral conditions and low wave ages. CHN attained a mean value of approximately 0.77×10-3 and did not show any relation to wind speed or to wave age. No significant dependence with wind or wave direction could be shown for either CEN or CHN in the sector 80-220°. The stability correction, performed to reduce the dependence on stratification for CEN and CHN, was well performed for stabilities higher than 0.15. The stability is represented by a relationship between the height and the Obukhov-length (z/L). Validity of the non-dimensional profile functions for temperature and wind showed that, for smaller stabilities, these functions gave higher values than the corresponding functions recommended by Högström (1996). The profile funtions for temperature was shown to have a larger scatter while the profile functions for wind was less scattered and deviated more from the functions given by Högström / Kunskap om turbulenta flöden i det marina gränsskiktet är viktigt för att förstå växelverkan mellan atmosfär och hav. Med bättre kunskap kan förbättringar i bestämningen av utbyteskoefficienterna för latent och sensibelt värme erhållas. Det medför att modeller kan prognostisera väder och framtida klimat med högre noggrannhet. Utbyteskoefficienterna för latent och sensibelt värme har för stabil skiktning olika värden i litteraturen. Detta gör det nödvändigt att undersöka de processer som påverkar utbytet av vattenånga och värme mellan luft och hav för att kunna bestämma dessa värden. Data som har använts i den här studien insamlades mellan år 2005 och 2007 från en boj och ett torn vid mätplatsen Östergarnsholm i Baltiska havet. För det flesta situationer, när vinden blåser från syd-ost, representerar mätplatsen ett förhållande likvärdigt det över öppet hav. De neutrala utbyteskoefficienterna, CEN och CHN, och de dimensionslösa profilfunktionera för temperatur och vind, och , har beräknats för att studera beroendet av stabilitet samt andra relevanta parametrar. Beräkningarna visade att CEN ökade något med vindhastighet och hamnade på ett medelvärde av ungefär 1.45×10-3. De högsta värdena på CEN observerades vid nära neutrala förhållanden och låga vågåldrar. CHN uppmättes till att ha ett medelvärde på ungefär 0.77×10-3 och uppvisade inget beroende med vindhastighet eller vågålder. Inget märkbart beroende med vind- eller vågriktning kunde visas för CEN eller CHN i sektorn 80-220°. Stabilitetskorrektionen, utförd för att reducera beroendet av atmosfärens skiktning för CEN och CHN, var bra för stabiliteter högre än 0.15. Stabiliteten representeras av förhållandet mellan höjden och Obukhov-längden (z/L). Utvärdering av de dimensionslösa funktionerna för temperatur och vind visade att dessa funktioner, för små stabiliteter, gav högre värden än motsvarande funktioner som rekommenderas av Högström (1996). Värdena på profilfunktionerna för temperatur hade större spridning än värdena på profilfunktionerna för vind och avvek mer från funktionerna givna av Högström.