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DOE OSTI2021

Discrete Graph Structure Learning for Forecasting Multiple Time Series

Time series forecasting is an extensively studied subject in statistics, economics, and computer science. Exploration of the correlation and causation among the variables in a multivariate time series shows promise in enhancing the performance of a time series model. When using deep neural networks as forecasting models, we hypothesize that exploiting the pairwise information among multiple (multivariate) time series also improves their forecast. If an explicit graph structure is known, graph neural networks (GNNs) have been demonstrated as powerful tools to exploit the structure. In this work, we propose learning the structure simultaneously with the GNN if the graph is unknown. We cast the problem as learning a probabilistic graph model through optimizing the mean performance over the graph distribution. The distribution is parameterized by a neural network so that discrete graphs can be sampled differentiably through reparameterization. Empirical evaluations show that our method is simpler, more efficient, and better performing than a recently proposed bilevel learning approach for graph structure learning, as well as a broad array of forecasting models, either deep or non-deep learning based, and graph or non-graph based.

Shang, Chao↗
DOE OSTI2020

Development of a Time-Height Profile Assimilation Technique for Large-Eddy Simulation

Mesoscale-to-microscale coupling (MMC) aims to address the limited scope of traditional large-eddy simulations by driving the microscale flow with information concerning large-scale weather patterns provided by mesoscale models. We present a new offline MMC technique for horizontally homogeneous microscale flow conditions, in which internal forcing terms are computed based on mesoscale time–height profiles of mean-flow quantities. The advantage of such an approach is that it can be used to drive a microscale simulation with either mesoscale or observational data, and that it does not rely on specific terms in the mesoscale budget equations, which are typically not part of the default output of a mesoscale solver. The performance of the proposed profile assimilation technique is assessed based on the simulation of a typical diurnal cycle over the Scaled Wind Farm Technology site in west Texas. Results indicate that simple data assimilation techniques lead to unphysically high levels of shear and turbulence caused by the algorithm’s inability to cope with inaccuracies in the mesoscale time–height profiles. Modifying the algorithm to account for vertical coherence in the mesoscale source terms gives the microscale solver a greater ability to correct the provided mesoscale time–height profiles, leading to improved predictions of shear and turbulence statistics. The resulting turbulence statistics are in good agreement with meteorological tower observations and simulation results obtained with state-of-the-art coupling techniques using mesoscale budget components.

data assimilation↗
DOE OSTI2025

Urban heat islands can influence the wind energy resource during heatwaves

Urban wind energy is critical for sustainable electricity generation in cities. However, little research has explored how the urban heat island (UHI) effect influences wind energy, particularly in heatwaves when energy demand surges. In this study, we examine wind energy distribution in the Boston–Providence metropolitan area during heatwaves, using Weather Research and Forecasting (WRF) model integrated with Building Energy Parameterization/Building Energy Model (BEP/BEM). Two scenarios, a realistic case and a hypothetical case without urban warmth, were compared to isolate UHI impacts. Results reveal that UHI induces a "wind energy loss zone" in this urban area, reducing wind power density (WPD) by 20–30 W/m 2 at 50–100 m, while suburban/rural areas exhibit a "wind energy gain zone," with WPD increases up to 40 W/m 2 at 150–200 m. These losses diminish with distance from urban centers and become negligible beyond main urban and suburban sprawl. Heatwave expands the urban "loss zone", while amplifying wind energy gains in suburban/rural areas, driven by stronger thermal gradients and weakened background winds that intensify air convergence in urban and urban-rural circulations, thereby exacerbating urban wind energy losses by 15–20 %. An analysis of 235 wind farms using turbine power curves reveals that built areas dependent on stand-alone or off-grid turbines face significant energy deficits during a heatwave. Wind energy drops by up to 25 %, while cooling-related building energy demand rises 30–40 % during a heatwave. These findings underscore the need for strategic urban wind energy planning to ensure reliable power during extreme heat.

Energy - Wind↗
DOE OSTI2013

The Role of Gravity Waves in the Formation and Organization of Clouds During TWPICE

All convective clouds emit gravity waves. While it is certain that convectively-generated waves play important parts in determining the climate, their precise roles remain uncertain and their effects are not (generally) represented in climate models. The work described here focuses mostly on observations and modeling of convectively-generated gravity waves, using the intensive observations from the DoE-sponsored Tropical Warm Pool International Cloud Experiment (TWP-ICE), which took place in Darwin, from 17 January to 13 February 2006. Among other things, the research has implications the part played by convectively-generated gravity waves in the formation of cirrus, in the initiation and organization of further convection, and in the subgrid-scale momentum transport and associated large-scale stresses imposed on the troposphere and stratosphere. The analysis shows two groups of inertia-gravity waves are detected: group L in the middle stratosphere during the suppressed monsoon period, and group S in the lower stratosphere during the monsoon break period. Waves belonging to group L propagate to the south-east with a mean intrinsic period of 35 h, and have vertical and horizontal wavelengths of about 5-6 km and 3000-6000 km, respectively. Ray tracing calculations indicate that these waves originate from a deep convective region near Indonesia. Waves belonging to group S propagate to the south-south-east with an intrinsic period, vertical wavelength and horizontal wavelength of about 45 h, 2 km and 2000-4000 km, respectively. These waves are shown to be associated with shallow convection in the oceanic area within about 1000 km of Darwin. The intrinsic periods of high-frequency waves are estimated to be between 20-40 minutes. The high-frequency wave activity in the stratosphere, defined by mass-weighted variance of the vertical motion of the sonde, has a maximum following the afternoon local convection indicating that these waves are generated by local convection. The wave activity is strongest in the lower stratosphere below 22 km and, during the suppressed monsoon period, is modulated with a 3-4-day period. The concentration of the wave activity in the lower stratosphere is consistent with the properties of the environment in which these waves propagate, whereas its 3-4-day modulation is explained by the variation of the convection activity in the TWP-ICE domain. At low rainfall intensity the wave activity increases as rainfall intensity increases. At high values of rainfall intensity, however, the wave activity associated with deep convective clouds is independent of the rainfall intensity. The convection and gravity waves observed during TWP-ICE are simulated with the Weather Research and Forecasting (WRF) Model. These simulations are compared with radiosonde observations described above and are used to determine some of the properties of convectively generated gravity waves. The gravity waves appear to be well simulated by the model. The model is used to explore the relationships between the convection, the gravity waves and cirrus.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2013

Standardized Software for Wind Load Forecast Error Analyses and Predictions Based on Wavelet-ARIMA Models - Applications at Multiple Geographically Distributed Wind Farms

Given the multi-scale variability and uncertainty of wind generation and forecast errors, it is a natural choice to use time-frequency representation (TFR) as a view of the corresponding time series represented over both time and frequency. Here we use wavelet transform (WT) to expand the signal in terms of wavelet functions which are localized in both time and frequency. Each WT component is more stationary and has consistent auto-correlation pattern. We combined wavelet analyses with time series forecast approaches such as ARIMA, and tested the approach at three different wind farms located far away from each other. The prediction capability is satisfactory -- the day-ahead prediction of errors match the original error values very well, including the patterns. The observations are well located within the predictive intervals. Integrating our wavelet-ARIMA (‘stochastic’) model with the weather forecast model (‘deterministic’) will improve our ability significantly to predict wind power generation and reduce predictive uncertainty.

uncertainty analysis, wind generation forecast, wa↗
DOE OSTI2025

Harnessing land-atmosphere interactions to enhance subseasonal-to-seasonal predictability

2025 Advancing Understanding of Land-Atmosphere Interactions and Processes on S2S Predictability Workshop What: 227 registered workshop participants gathered in person (43%) and online (57%) to discuss state-of-the-art scientific understanding and modeling of land-atmosphere interactions and related processes in the context of subseasonal-to-seasonal (S2S) predictability. Topics covered sources of S2S predictability, land model initialization methods, model diagnosis and evaluation metrics, AI/ML analysis and applications, and coordination of future community multi-model S2S forecast focused experiments. To advance the science, this community workshop, organized by NSF NCAR, NOAA, NASA, and DOE, aimed to 1) identify process- and application-oriented metrics for assessing S2S prediction skill and 2) develop experimental protocols for coordinated experiments to isolate, quantify, and understand the role of land-atmosphere interactions in S2S predictability. When: June 16-18, 2025 Where: Boulder, CO, USA, and online.

Land-Atmosphere Interaction↗
DOE OSTI2022

The United States COVID-19 Forecast Hub dataset

Academic researchers, government agencies, industry groups, and individuals have produced forecasts at an unprecedented scale during the COVID-19 pandemic. To leverage these forecasts, the United States Centers for Disease Control and Prevention (CDC) partnered with an academic research lab at the University of Massachusetts Amherst to create the US COVID-19 Forecast Hub. Launched in April 2020, the Forecast Hub is a dataset with point and probabilistic forecasts of incident cases, incident hospitalizations, incident deaths, and cumulative deaths due to COVID-19 at county, state, and national, levels in the United States. Included forecasts represent a variety of modeling approaches, data sources, and assumptions regarding the spread of COVID-19. The goal of this dataset is to establish a standardized and comparable set of short-term forecasts from modeling teams. These data can be used to develop ensemble models, communicate forecasts to the public, create visualizations, compare models, and inform policies regarding COVID-19 mitigation. These open-source data are available via download from GitHub, through an online API, and through R packages.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Exploration of turbulent heat fluxes and wind stress curl in WRF and ERA‐Interim during wintertime mesoscale wind events around southeastern Greenland

Abstract The strong, mesoscale tip jets and barrier winds that occur off the coast of southeastern Greenland drive large surface turbulent heat fluxes that may impact deep ocean convection. The turbulent fluxes and wind stress curl associated with 10 m wind patterns identified using the self‐organizing map technique are investigated for 10 winters (1997–2007, November‐December‐January‐February‐March) in the European Centre for Medium‐Range Weather Forecasts Interim Reanalysis (ERA‐I) and a regional simulation using the Weather Research and Forecasting (WRF) model at 50 km. Sensible heat flux differences between WRF and ERA‐I are primarily due to differences in near‐surface temperature, while latent heat flux differences are driven by both moisture and wind speed differences. The largest turbulent flux differences occur over the marginal ice zone where the fluxes in WRF are larger than in ERA‐I due to specified sea ice thickness that influences the near‐surface atmospheric temperature and moisture; WRF has larger magnitude wind stress curl over the Irminger Sea. Patterns of strong westerly tip jet with barrier flow are most likely to impact preconditioning and convection in the Irminger Sea compared to other manifestations of westerly tip jets, and easterly tip jets are expected to have localized ocean impacts south of Cape Farewell.

DuVivier, Alice K.↗
DOE OSTI2015

The climatological distribution of extreme Arctic winds and implications for ocean and sea ice processes

Abstract Some of the strongest near‐surface winds on Earth form in the Arctic and sub‐Arctic due to intense midlatitude cyclones and mesoscale processes, and these strong surface winds have important impacts on ocean and sea ice processes. We examine the climatological distribution of over‐ocean, near‐surface wind speeds within a Pan‐Arctic domain for 18 years (1990–2007) in four gridded data sets: the European Centre for Medium‐Range Weather Forecasts Interim reanalysis (ERA‐I), the Climate Forecast System Reanalysis, version 2 of the Common Ocean‐Ice Reference Experiment data set, and a regional climate simulation generated using the Weather Research and Forecasting (WRF) model run at 50 km (WRF50) horizontal resolution with ERA Interim as lateral boundary conditions. We estimate probability density functions, the annual cycle, and map the 50th and 99th percentile winds. We then perform the same statistical analysis of winds for 2 years when 10 km WRF data are available (June 2005 to May 2007); despite the much shorter time period, the Pan‐Arctic statistics are very similar to those from the 18 year analysis. We repeat the wind speed statistical analysis within a subdomain surrounding Greenland and find that WRF10 has consistently larger maximum wind speeds, but this difference only appears at wind speed percentiles higher than 99%. Differences in the 99th percentile wind speeds are spatially heterogeneous. An investigation of surface fluxes within WRF50 and WRF10 reveals unrealistically large sensible heat fluxes along the sea ice edge, and the geographic distribution and magnitude of these fluxes is shown to be sensitive to sea ice representation in WRF.

Hughes, Mimi↗
DOE OSTI2015

Roles of Wind Shear at Different Vertical Levels, Part I: Cloud System Organization and Properties

Understanding of critical processes that contribute to the organization of mesoscale convective systems is important for accurate weather forecast and climate prediction. In this study, we investigate the effects of wind shear at different vertical levels on the organization and properties of cloud systems using the Weather Research & Forecasting (WRF) model with a spectral-bin microphysical scheme. The sensitivity experiments are performed by increasing wind shear at the lower (0-5 km), middle (5-10 km), upper (> 10 km) and the entire troposphere, respectively, based on a control run for a mesoscale convective system (MCS) with weak wind shear. We find that increasing wind shear at the both lower and middle vertical levels reduces the domain-accumulated precipitation and the occurrence of heavy rain, while increasing wind shear at the upper levels changes little on precipitation. Although increasing wind shear at the lower-levels is favorable for a more organized quasi-line system which leads to enlarged updraft core area, and enhanced updraft velocities and vertical mass fluxes, the precipitation is still reduced by 18.6% compared with the control run due to stronger rain evaporation induced by the low-level wind shear. Strong wind shear in the middle levels only produces a strong super-cell over a narrow area, leading to 67.3% reduction of precipitation over the domain. By increasing wind shear at the upper levels only, the organization of the convection is not changed much, but the increased cloudiness at the upper-levels leads to stronger surface cooling and then stabilizes the atmosphere and weakens the convection. When strong wind shear exists over the entire vertical profile, a deep dry layer (2-9 km) is produced and convection is severely suppressed. There are fewer very-high (cloud top height (CTH) > 15 km) and very-deep (cloud thickness > 15 km) clouds, and the precipitation is only about 11.8% of the control run. The changes in cloud microphysical properties further explain the reduction of surface rain by strong wind shear especially at the lower- and middle-levels. The insights obtained from this study help us better understand the cloud system organization and provide foundation for better parameterizing organized MCS.

cloud system organization↗
DOE OSTI2015

Simulations of cloud‐radiation interaction using large‐scale forcing derived from the CINDY/DYNAMO northern sounding array

Abstract The recently completed CINDY/DYNAMO field campaign observed two Madden‐Julian oscillation (MJO) events in the equatorial Indian Ocean from October to December 2011. Prior work has indicated that the moist static energy anomalies in these events grew and were sustained to a significant extent by radiative feedbacks. We present here a study of radiative fluxes and clouds in a set of cloud‐resolving simulations of these MJO events. The simulations are driven by the large‐scale forcing data set derived from the DYNAMO northern sounding array observations, and carried out in a doubly periodic domain using the Weather Research and Forecasting (WRF) model. Simulated cloud properties and radiative fluxes are compared to those derived from the S‐PolKa radar and satellite observations. To accommodate the uncertainty in simulated cloud microphysics, a number of single‐moment (1M) and double‐moment (2M) microphysical schemes in the WRF model are tested. The 1M schemes tend to underestimate radiative flux anomalies in the active phases of the MJO events, while the 2M schemes perform better, but can overestimate radiative flux anomalies. All the tested microphysics schemes exhibit biases in the shapes of the histograms of radiative fluxes and radar reflectivity. Histograms of radiative fluxes and brightness temperature indicate that radiative biases are not evenly distributed; the most significant bias occurs in rainy areas with OLR less than 150 W/m 2 in the 2M schemes. Analysis of simulated radar reflectivities indicates that this radiative flux uncertainty is closely related to the simulated stratiform cloud coverage. Single‐moment schemes underestimate stratiform cloudiness by a factor of 2, whereas 2M schemes simulate much more stratiform cloud.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

“Prophetic vision, vivid imagination”: The 1927 Mississippi River flood

The 1927 flood in the Lower Mississippi River was the most destructive flood in American history, inundating more than 70,000 km 2 of land, resulting in approximately 500 fatalities and leaving more than 700,000 people homeless. Despite the prominence of the 1927 flood, details on the flood, and the storms that produced the flood, are sparse. We examine the hydrometeorology and hydroclimatology of the 1927 flood in the Lower Mississippi River through downscaling simulations of the storms that were responsible for catastrophic flooding and through empirical analyses of rainfall and streamflow records. We use Twentieth Century Reanalysis fields as boundary conditions and initial conditions for downscaling simulations using the Weather Research and Forecasting (WRF) model. We place the hydrometeorological analyses of the 1927 storms in a hydroclimatological context through analyses of the Twentieth Century Reanalysis fields. Analyses are designed to assess the physical processes that control the upper tail of flooding in the Lower Mississippi River. We compare the 1927 flood in the Lower Mississippi River to floods in 1937 and 2011 that represent the most extreme flooding in the Lower Mississippi River.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Analysis of WRF extreme daily precipitation over Alaska using self‐organizing maps

Abstract We analyze daily precipitation extremes from simulations of a polar‐optimized version of the Weather Research and Forecasting (WRF) model. Simulations cover 19 years and use the Regional Arctic System Model (RASM) domain. We focus on Alaska because of its proximity to the Pacific and Arctic oceans; both provide large moisture fetch inland. Alaska's topography also has important impacts on orographically forced precipitation. We use self‐organizing maps (SOMs) to understand circulation characteristics conducive for extreme precipitation events. The SOM algorithm employs an artificial neural network that uses an unsupervised training process, which results in finding general patterns of circulation behavior. The SOM is trained with mean sea level pressure (MSLP) anomalies. Widespread extreme events, defined as at least 25 grid points experiencing 99th percentile precipitation, are examined using SOMs. Widespread extreme days are mapped onto the SOM of MSLP anomalies, indicating circulation patterns. SOMs aid in determining high‐frequency nodes, and hence, circulations are conducive to extremes. Multiple circulation patterns are responsible for extreme days, which are differentiated by where extreme events occur in Alaska. Additionally, several meteorological fields are composited for nodes accessed by extreme and nonextreme events to determine specific conditions necessary for a widespread extreme event. Individual and adjacent node composites produce more physically reasonable circulations as opposed to composites of all extremes, which include multiple synoptic regimes. Temporal evolution of extreme events is also traced through SOM space. Thus, this analysis lays the groundwork for diagnosing differences in atmospheric circulations and their associated widespread, extreme precipitation events.

Glisan, Justin M.↗
DOE OSTI2016

Comparison of observed and simulated spatial patterns of ice microphysical processes in tropical oceanic mesoscale convective systems

To equitably compare the spatial pattern of ice microphysical processes produced by three microphysical parameterizations with each other, observations, and theory, simulations of tropical oceanic mesoscale convective systems (MCSs) in the Weather Research and Forecasting (WRF) model were forced to develop the same mesoscale circulations as observations by assimilating radial velocity data from a Doppler radar. The same general layering of microphysical processes was found in observations and simulations with deposition anywhere above the 0°C level, aggregation at and above the 0°C level, melting at and below the 0°C level, and riming near the 0°C level. Thus, this study is consistent with the layered ice microphysical pattern portrayed in previous conceptual models and indicated by dual-polarization radar data. Spatial variability of riming in the simulations suggests that riming in the midlevel inflow is related to convective-scale vertical velocity perturbations. Lastly, this study sheds light on limitations of current generally available bulk microphysical parameterizations. In each parameterization, the layers in which aggregation and riming took place were generally too thick and the frequency of riming was generally too high compared to the observations and theory. Additionally, none of the parameterizations produced similar details in every microphysical spatial pattern. Discrepancies in the patterns of microphysical processes between parameterizations likely factor into creating substantial differences in model reflectivity patterns. It is concluded that improved parameterizations of ice-phase microphysics will be essential to obtain reliable, consistent model simulations of tropical oceanic MCSs.

58 GEOSCIENCES↗
DOE OSTI2017

Exploring the effects of a nonhydrostatic dynamical core in high-resolution aquaplanet simulations

This study explores the impact of a nonhydrostatic dynamical core in high-resolution regional climate simulations using an aquaplanet framework. The Weather Research and Forecasting (WRF) model is used to conduct simulations with both hydrostatic (H) and nonhydrostatic (NH) solvers at horizontal grid spacings (?x) of 36, 12, and 4 km. The differences between the H and NH simulated precipitation (?P) are notable even at ?x = 12 km in the inter-tropical convergence zone and the transition region to the drier subtropics. At gray-zone grid spacing (12 km and 4 km) over the tropics, ?P is sensitive to whether a cumulus parameterization scheme is used or not. With an idealized Witch of Agnesi land mountain, differences in the precipitation and circulation (vertical velocity) between the H and NH simulations are significant even at ?x = 36 km in the tropics due largely to the strong feedbacks related to moist processes. The differences increase as the model grid spacing and mountain half width (a) are reduced, accompanied by a shift towards a more nonhydrostatic flow regime at a = 24 km. Latent heat release drastically enhances the differences between the NH and H simulations and extends the effect of nonhydrostatic dynamics to a broader region over the mountain and downstream over the tropics. Overall, differences exist between H and NH simulations even at resolutions between 12 and 36 km, but the differences are sensitive to the representations of moist physics and other features such as horizontal diffusion used in the WRF model.

nonhydrostatic dynamics, latent heating, nonhydros↗
DOE OSTI2016

Simulating effects of a wind-turbine array using LES and RANS

Growth in wind power production has motivated investigation of wind-farm impacts on in situ flow fields and downstream interactions with agriculture and other wind farms. These impacts can be simulated with both large-eddy simulations (LES) and mesoscale wind-farm parameterizations (WFP). The Weather Research and Forecasting (WRF) model offers both approaches. We used the validated generalized actuator disk (GAD) parameterization in WRF-LES to assess WFP performance. A 12-turbine array was simulated using the GAD model and the WFP in WRF. We examined the performance of each scheme in both convective and stable conditions. The GAD model and WFP produced qualitatively similar wind speed deficits and turbulent kinetic energy (TKE) production across the array in both stability regimes, though the magnitudes of velocity deficits and TKE production levels were underestimated and overestimated, respectively. While wake growth slowed in the latter half of the WFP array as expected, wakes did not approach steady state by the end of the array as simulated by the GAD model. A sensitivity test involving the deactivation of explicit TKE production by the WFP resulted in turbulence levels within the array well that were below those produced by the GAD in both stable and unstable conditions. Finally, the WFP overestimated downwind power production deficits in stable conditions because of the lack of wake stabilization in the latter half of the array.

17 WIND ENERGY↗
DOE OSTI2013

Impacts of Microphysical Scheme on Convective and Stratiform Characteristics in Two High Precipitation Squall Line Events

This study investigates the impact of snow, graupel, and hail processes on the simulated squall lines over the Southern Great Plains in the United States. Weather Research and Forecasting (WRF) model is used to simulate two squall line events in May 2007, and the results are validated against radar and surface observations in Oklahoma. Several microphysics schemes are tested in this study, including WRF 5-Class Microphysics Scheme (WSM5), WRF 6-Class Microphysics Scheme (WSM6), Goddard Three Ice scheme (Goddard 3-ice) with graupel, Goddard Two Ice scheme (Goddard 2-ice), and Goddard 3-ice hail scheme. The simulated surface precipitation is sensitive to the microphysics scheme, and especially to whether graupel or hail category is included. All of the three ice (3-ice) schemes overestimated the total precipitation, within which WSM6 has the highest overestimation. Two ice (2-ice) schemes, missing a graupel/hail category, produced less total precipitation than 3-ice schemes. By applying a radar-based convective/stratiform partitioning algorithm, we find that by including the graupel/hail processes, there is an increase in areal coverage, precipitation intensity, updraft and downdraft intensity in convective region and a reduction of areal coverage and its precipitation intensity in stratiform region. For vertical structures, all the bulk schemes, especially 2-ice schemes, have the highest reflectivity located at upper levels (~8 km), which is unrealistic compared to observations. In addition, this study shows the radar-based convective/stratiform partitioning algorithm can reasonably identify WRF simulated precipitation, wind and microphysics fields in both convective and stratiform regions.

characteristics↗
DOE OSTI2023

New insights on wind turbine wakes from large‐eddy simulation: Wake contraction, dual nature, and temperature effects

Abstract Large‐eddy simulation (LES) has been adopted to study wind turbine wakes because it can capture fine‐scale details of turbulent wind flows and interactions with wind turbines. Here, we use the LES version of the Weather Research and Forecasting (WRF) model with an actuator disk model to gain insights on several wake effects that have been traditionally difficult to measure. The first finding is that the wake has a “dual nature,” meaning that the wind speed deficit behaves differently from the added turbulent kinetic energy (TKE) and the two are not co‐located in space. For example, the wind speed deficit peaks at hub height and reaches the ground within 8D (D is the rotor diameter), but added TKE peaks near the rotor tip and generally remains aloft. Second, temperature changes near the ground are driven by the added TKE in the rotor area and by atmospheric stability. The combination of these two factors determines the sign and intensity of the vertical heat flux divergence below the rotor, with convergence and warming associated with stable conditions and weak divergence and modest cooling with unstable conditions. Third, wakes do not expand indefinitely, as suggested by similarity theory applied to the wind speed deficit, but eventually stop expanding and actually contract, at different rates depending on atmospheric stability. The implication of these findings is that, in order to study wakes, it is not sufficient to focus on wind speed deficit alone, because TKE is also important and yet behaves differently from the wind speed deficit.

17 WIND ENERGY↗