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J. Vanneste
and
T. G. Shepherd

Abstract

The density and the flux of wave-activity conservation laws are generally required to satisfy the group-velocity property: under the WKB approximation (i.e., for nearly monochromatic small-amplitude waves in a slowly varying medium), the flux divided by the density equals the group velocity. It is shown that this property is automatically satisfied if, under the WKB approximation, the only source of rapid variations in the density and the flux lies in the wave phase. A particular form of the density, based on a self-adjoint operator, is proposed as a systematic choice for a density verifying this condition.

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G. J. Boer
and
T. G. Shepherd

Abstract

Global FGGE data are used to investigate several aspects of large-scale turbulence in the atmosphere. The approach follows that for two-dimensional, nondivergent turbulent flows which are homogeneous and isotropic on the sphere. Spectra of kinetic energy, enstrophy and available potential energy are obtained for both the stationary and transient parts of the flow. Nonlinear interaction terms and fluxes of energy and enstrophy through wavenumber space are calculated and compared with the theory. A possible method of parameterizing the interactions with unresolved scales is considered.

Two rather different flow regimes are found in wavenumber space. The high-wavenumber regime is dominated by the transient components of the flow and exhibits, at least approximately, several of the conditions characterizing homogeneous and isotropic turbulence. This region of wavenumber space also displays some of the features of an enstrophy-cascading inertial subrange. The low-wavenumber region, on the other hand, is dominated by the stationary component of the flow, exhibits marked anisotropy and, in contrast to the high-wavenumber regime, displays a marked change between January and July.

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J. F. Scinocca
and
T. G. Shepherd

Abstract

Exact, finite-amplitude, local wave-activity conservation laws are derived for disturbances to steady flows in the context of the two-dimensional anelastic equations. The conservation laws are expressed entirely in terms of Eulerian quantities, and have the property that, in the limit of a small-amplitude, slowly varying, monochromatic wave train, the wave-activity density A and flux F, when averaged over phase, satisfy F = c g A where c g is the group velocity of the waves. For nonparallel steady flows, the only conserved wave activity is a form of disturbance pseudoenergy; when the steady flow is parallel, there is in addition a conservation law for the disturbance pseudomomentum.

The above results are obtained not only for isentropic background states (which give the so-called “deep form” of the anelastic equations), but also for arbitrary background potential-temperature profiles θ 0(z) so long as the variation in θ 0(z) over the depth of the fluid is small compared with θ 0 itself. The Hamiltonian structure of the equations is established in both cases, and its symmetry properties discussed. An expression for available potential energy is also derived that, for the case of a stably stratified background state (i.e., 0/dz > 0), is locally positive definite; the expression is valid for fully three-dimensional flow.

The counterparts to results for the two-dimensional Boussinesq equations are also noted.

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T. J. Shepherd
,
R. J. Barthelmie
, and
S. C. Pryor

Abstract

The Weather Research and Forecasting (WRF) Model has been extensively used for wind energy applications, and current releases include a scheme that can be applied to examine the effects of wind turbine arrays on the atmospheric flow and electricity generation from wind turbines. Herein we present a high-resolution simulation using two different wind farm parameterizations: 1) the “Fitch” parameterization that is included in WRF releases and 2) the recently developed Explicit Wake Parameterization (EWP) scheme. We compare the schemes using a single yearlong simulation for a domain centered on the highest density of current turbine deployments in the contiguous United States (Iowa). Pairwise analyses are applied to diagnose the downstream wake effects and impact of wind turbine arrays on near-surface climate conditions. On average, use of the EWP scheme results in small-magnitude wake effects within wind farm arrays and faster recovery of full WT array wakes. This in turn leads to smaller impacts on near-surface climate variables and reduced array–array interactions, which at a systemwide scale lead to summertime capacity factors (i.e., the electrical power produced relative to nameplate installed capacity) that are 2%–3% higher than those from the more commonly applied Fitch parameterization. It is currently not possible to make recommendations with regard to which wind farm parameterization exhibits higher fidelity or to draw inferences with regard to whether the relative performance may vary with prevailing climate conditions and/or wind turbine deployment configuration. However, the sensitivities documented herein to the wind farm parameterization are of sufficient magnitude to potentially influence wind turbine array siting decisions. Thus, our research findings imply high value in undertaking combined long-term high-fidelity observational studies in support of model validation and verification.

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S. C. Pryor
,
J. J. Coburn
,
R. J. Barthelmie
, and
T. J. Shepherd

Abstract

New simulations at 12-km grid spacing with the Weather and Research Forecasting (WRF) Model nested in the MPI Earth System Model (ESM) are used to quantify possible changes in wind power generation potential as a result of global warming. Annual capacity factors (CF; measures of electrical power production) computed by applying a power curve to hourly wind speeds at wind turbine hub height from this simulation are also used to illustrate the pitfalls in seeking to infer changes in wind power generation directly from low-spatial-resolution and time-averaged ESM output. WRF-derived CF are evaluated using observed daily CF from operating wind farms. The spatial correlation coefficient between modeled and observed mean CF is 0.65, and the root-mean-square error is 5.4 percentage points. Output from the MPI-WRF Model chain also captures some of the seasonal variability and the probability distribution of daily CF at operating wind farms. Projections of mean annual CF (CF A ) indicate no change to 2050 in the southern Great Plains and Northeast. Interannual variability of CF A increases in the Midwest, and CF A declines by up to 2 percentage points in the northern Great Plains. The probability of wind droughts (extended periods with anomalously low production) and wind bonus periods (high production) remains unchanged over most of the eastern United States. The probability of wind bonus periods exhibits some evidence of higher values over the Midwest in the 2040s, whereas the converse is true over the northern Great Plains.

Significance Statement

Wind energy is playing an increasingly important role in low-carbon-emission electricity generation. It is a “weather dependent” renewable energy source, and thus changes in the global atmosphere may cause changes in regional wind power production (PP) potential. We use PP data from operating wind farms to demonstrate that regional simulations exhibit skill in capturing actual power production. Projections to the middle of this century indicate that over most of North America east of the Rocky Mountains annual expected PP is largely unchanged, as is the probability of extended periods of anomalously high or low production. Any small declines in annual PP are of much smaller magnitude than changes due to technological innovation over the last two decades.

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I. Polichtchouk
,
T. G. Shepherd
,
R. J. Hogan
, and
P. Bechtold

Abstract

The role of parameterized nonorographic gravity wave drag (NOGWD) and its seasonal interaction with the resolved wave drag in the stratosphere has been extensively studied in low-resolution (coarser than 1.9° × 2.5°) climate models but is comparatively unexplored in higher-resolution models. Using the European Centre for Medium-Range Weather Forecasts Integrated Forecast System at 0.7° × 0.7° resolution, the wave drivers of the Brewer–Dobson circulation are diagnosed and the circulation sensitivity to the NOGW launch flux is explored. NOGWs are found to account for nearly 20% of the lower-stratospheric Southern Hemisphere (SH) polar cap downwelling and for less than 10% of the lower-stratospheric tropical upwelling and Northern Hemisphere (NH) polar cap downwelling. Despite these relatively small numbers, there are complex interactions between NOGWD and resolved wave drag, in both polar regions. Seasonal cycle analysis reveals a temporal offset in the resolved and parameterized wave interaction: the NOGWD response to altered source fluxes is largest in midwinter, while the resolved wave response is largest in the late winter and spring. This temporal offset is especially prominent in the SH. The impact of NOGWD on sudden stratospheric warming (SSW) life cycles and the final warming date in the SH is also investigated. An increase in NOGWD leads to an increase in SSW frequency, reduction in amplitude and persistence, and an earlier recovery of the stratopause following an SSW event. The SH final warming date is also brought forward when NOGWD is increased. Thus, NOGWD is still found to be a very important parameterization for stratospheric dynamics even in a high-resolution atmospheric model.

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S. C. Pryor
,
F. Letson
,
T. Shepherd
, and
R. J. Barthelmie

Abstract

The Southern Great Plains (SGP) region exhibits a relatively high frequency of periods with extremely high rainfall rates (RR) and hail. Seven months of 2017 are simulated using the Weather Research and Forecasting (WRF) Model applied at convection-permitting resolution with the Milbrandt–Yau microphysics scheme. Simulation fidelity is evaluated, particularly during intense convective events, using data from ASOS stations, dual-polarization radar, and gridded datasets and observations at the DOE Atmospheric Radiation Measurement site. The spatial gradients and temporal variability of precipitation and the cumulative density functions for both RR and wind speeds exhibit fidelity. Odds ratios > 1 indicate that WRF is also skillful in simulating high composite reflectivity (cREF, used as a measure of widespread convection) and RR > 5 mm h−1 over the domain. Detailed analyses of the 10 days with highest spatial coverage of cREF > 30 dBZ show spatially similar reflectivity fields and high RR in both radar data and WRF simulations. However, during periods of high reflectivity, WRF exhibits a positive bias in terms of very high RR (>25 mm h−1) and hail occurrence, and during the summer and transition months, maximum hail size is underestimated. For some renewable energy applications, fidelity is required with respect to the joint probabilities of wind speed and RR and/or hail. While partial fidelity is achieved for the marginal probabilities, performance during events of critical importance to these energy applications is currently not sufficient. Further research into optimal WRF configurations in support of potential damage quantification for these applications is warranted.

Significance Statement

Heavy rainfall and hail during convective events are challenging for numerical models to simulate in both space and time. For some applications, such as to estimate damage to wind turbine blades and solar panels, fidelity is also required with respect to hail size and joint probabilities of wind speed and hydrometeor type and rainfall rates (RR). This demands fidelity that is seldom evaluated. We show that, although this simulation exhibits fidelity for the marginal probabilities of wind speed, RR, and hail occurrence, the joint probabilities of these properties and the simulation of maximum size of hail are, as yet, not sufficient to characterize potential damage to these renewable energy industries.

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F. Letson
,
T. J. Shepherd
,
R. J. Barthelmie
, and
S. C. Pryor

Abstract

Deep convection and the related occurrence of hail, intense precipitation, and wind gusts represent a hazard to a range of energy infrastructure including wind turbine blades. Wind turbine blade leading-edge erosion (LEE) is caused by the impact of falling hydrometeors onto rotating wind turbine blades. It is a major source of wind turbine maintenance costs and energy losses from wind farms. In the U.S. southern Great Plains (SGP), where there is widespread wind energy development, deep convection and hail events are common, increasing the potential for precipitation-driven LEE. A 25-day Weather Research and Forecasting (WRF) Model simulation conducted at convection-permitting resolution and using a detailed microphysics scheme is carried out for the SGP to evaluate the effectiveness in modeling the wind and precipitation conditions relevant to LEE potential. WRF output for these properties is evaluated using radar observations of precipitation (including hail) and reflectivity, in situ wind speed measurements, and wind power generation. This research demonstrates some skill for the primary drivers of LEE. Wind speeds, rainfall rates, and precipitation totals show good agreement with observations. The occurrence of precipitation during power-producing wind speeds is also shown to exhibit fidelity. Hail events frequently occur during periods when wind turbines are rotating and are especially important to LEE in the SGP. The presence of hail is modeled with a mean proportion correct of 0.77 and an odds ratio of 4.55. Further research is needed to demonstrate sufficient model performance to be actionable for the wind energy industry, and there is evidence for positive model bias in cloud reflectivity.

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P. H. Haynes
,
M. E. McIntyre
,
T. G. Shepherd
,
C. J. Marks
, and
K. P. Shine

Abstract

The situation considered is that of a zonally symmetric model of the middle atmosphere subject to a given quasi-steady zonal force , conceived to be the result of irreversible angular momentum transfer due to the upward propagation and breaking of Rossby and gravity waves together with any other dissipative eddy effects that may be relevant. The model's diabatic heating is assumed to have the qualitative character of a relaxation toward some radiatively determined temperature field. To the extent that the force may be regarded as given, and the extratropical angular momentum distribution is realistic, the extratropical diabatic mass flow across a given isentropic surface may be regarded as controlled exclusively by the distribution above that surface (implying control by the eddy dissipation above that surface and not, for instance, by the frequency of tropopause folding below). This “downward control” principle expresses a critical part of the dynamical chain of cause and effect governing the average rate at which photochemical products like ozone become available for folding into, or otherwise descending into, the extratropical troposphere. The dynamical facts expressed by the principle are also relevant, for instance, to understanding the seasonal-mean rate of upwelling of water vapor to the summer mesopause, and the interhemispheric differences in stratospheric tracer transport.

The robustness of the principle is examined when is time-dependent. For a global-scale, zonally symmetric diabatic circulation with a Brewer-Dobson-like horizontal structure given by the second zonally symmetric Hough mode, with Rossby height HR = 13 km in an isothermal atmosphere with density scale height H = 7 km, the vertical partitioning of the unsteady part of the mass circulation caused by fluctuations in confined to a shallow layer L is always at least 84% downward. It is 90% downward when the force fluctuates sinusoidally on twice the radiative relaxation timescale and 95% if five times slower. The time-dependent adjustment when is changed suddenly is elucidated, extending the work of Dickinson (1968), when the atmosphere is unbounded above and below. Above the forcing, the adjustment is characterized by decay of the meridional mass circulation cell at a rate proportional to the radiative relaxation rate τ r −1 divided by {1 + (4H 2/H R 2)} . This decay is related to the boundedness of the angular momentum that can be taken up by the finite mass of air above L without causing an ever-increasing departure from thermal wind balance. Below the forcing, the meridional mass circulation cell penetrates downward at a speed τ r −1 HR 2/H . For the second Hough mode, the time for downward penetration through one density scale height is about 6 days if the radiative relaxation time is 20 days, the latter being representative of the lower stratosphere. At any given altitude, a steady state is approached. The effect of a rigid lower boundary on the time-dependent adjustment is also considered. If a frictional planetary boundary layer is present then a steady state is ultimately approached everywhere, with the mass circulation extending downward from L and closing via the boundary layer.

Satellite observations of temperature and ozone are used in conjunction with a radiative transfer scheme to estimate the altitudes from which the lower stratospheric diabatic vertical velocity is controlled by the effective in the real atmosphere. The data appear to indicate that about 80% of the effective control is usually exerted from below 40 km but with significant exceptions up to 70 km (in the high latitude southern hemispheric winter). The implications for numerical modelling of chemical transport are noted.

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V. I. Fomichev
,
A. I. Jonsson
,
J. de Grandpré
,
S. R. Beagley
,
C. McLandress
,
K. Semeniuk
, and
T. G. Shepherd

Abstract

The Canadian Middle Atmosphere Model (CMAM) has been used to examine the middle atmosphere response to CO2 doubling. The radiative-photochemical response induced by doubling CO2 alone and the response produced by changes in prescribed SSTs are found to be approximately additive, with the former effect dominating throughout the middle atmosphere. The paper discusses the overall response, with emphasis on the effects of SST changes, which allow a tropospheric response to the CO2 forcing. The overall response is a cooling of the middle atmosphere accompanied by significant increases in the ozone and water vapor abundances. The ozone radiative feedback occurs through both an increase in solar heating and a decrease in infrared cooling, with the latter accounting for up to 15% of the total effect. Changes in global mean water vapor cooling are negligible above ∼30 hPa. Near the polar summer mesopause, the temperature response is weak and not statistically significant. The main effects of SST changes are a warmer troposphere, a warmer and higher tropopause, cell-like structures of heating and cooling at low and middlelatitudes in the middle atmosphere, warming in the summer mesosphere, water vapor increase throughout the domain, and O3 decrease in the lower tropical stratosphere. No noticeable change in upward-propagating planetary wave activity in the extratropical winter–spring stratosphere and no significant temperature response in the polar winter–spring stratosphere have been detected. Increased upwelling in the tropical stratosphere has been found to be linked to changed wave driving at low latitudes.

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