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DOE OSTI2025

Is There a Scalar Atmospheric Surface Layer Within a Convective Boundary Layer? Implications for Flux Measurements

Top‐down entrainment shapes the vertical gradients of sensible heat, latent heat, and CO 2 fluxes, influencing the interpretation of eddy covariance (EC) measurements in the unstable atmospheric surface layer (ASL). Using large eddy simulations for convective boundary layer flows, we demonstrate that decreased temperature gradients across the entrainment zone increase entrainment fluxes by enhancing the entrainment velocity, amplifying the asymmetry between top‐down and bottom‐up flux contributions. These changes alter scalar flux profiles, causing flux divergence or convergence and leading to the breakdown of the constant flux layer assumption (CFLA) in the ASL. As a result, EC‐measured fluxes either underestimate or overestimate “true” surface fluxes during divergence or convergence phases, contributing to energy balance non‐closure. The varying degrees of the CFLA breakdown are a fundamental cause for the non‐closure issue. These findings highlight the underappreciated role of entrainment in interpreting EC fluxes, addressing non‐closure, and understanding site‐to‐site variability in flux measurements.

eddy covariance fluxes of scalars↗

NASA NTRS1990

Direct numerical simulations of stably-stratified sheared turbulence: Implications for oceanic mixing

Direct numerical simulations of the time evolution of homogeneous stably stratified turbulent shear flows have been performed for several Richardson numbers Ri and Reynolds numbers R(sub lambda) in earlier works. The results show excellent agreement with length scale models developed from laboratory experiments to characterize oceanic turbulence. When the Richardson number Ri is less than the stationary value Ri(sub s), the turbulence intensity grows at all scales, and the growth rate appears to be a function of Ri. The size of the vertical density inversions also increases. On the other hand, when Ri is greater than or equal to Ri(sub s) the largest turbulent eddies become vertically constrained by buoyancy when the Ellison (turbulence) scale L(sub E) and the Ozmidov (buoyancy) scale L(sub O) are equal. At this point, the mixing efficiency is maximal and corresponds to a flux Richardson number R(sub f) = 0.20. The vertical mass flux becomes counter-gradient when epsilon = 19(nu)N(exp 2) and vertical density overturns are suppressed in less than half a Brunt-Vaisala period. The results of the simulations were also recast in terms of the Hydrodynamic Phase Diagram introduced in fossil turbulence models. The so-called point of fossilization occurs when epsilon = 4DCN(exp 2); Gibson proposed 13DCN(exp 2). This value is in agreement with indirect laboratory observations and field observations. Finally, the validity of the steady-state models to estimate vertical eddy diffusivities in the oceanic thermocline is discussed.

Itsweire, E. C.↗

NASA NTRS1987

Deuterium in the daytime thermosphere

Ion concentration measurements for H(+) and D(+) from the magnetic ion mass spectrometer on the Atmosphere Explorer C satellite are used, in conjunction with other atmospheric data, to determine the concentrations of H and D in the nonpolar daytime thermosphere. The ratio of the observed D(+) to H(+) concentrations has essentially the same height dependence in the 300 to 800-km region as expected for their neutral counterparts, even in the presence of ion temperature gradients and probable large vertical ion fluxes. Rapid charge exchange with atomic oxygen ensures that D/H is about equal to D(+)/H(+) at the lower altitudes where the derived D to H concentration ratio is a factor of about 6 larger than its sea level value, for an exospheric temperature of 930 K. This relative enhancement of deuterium arises from the fact that hydrogen more readily escapes the earth, and a large vertical gradient in the H concentration relative to its diffusive equilibrium value is necessary to drive this upward flux through the lower thermosphere. If these planetary losses of hydrogen are much greater than those associated with evaporative escape, as is the current view, then correspondingly larger deuterium loss rates are also likely in order that the thermospheric D/H ratio not increase well above the observed value. The absolute winter daytime concentration of deuterium at 300 km is found to be 210 + or - 50 atoms/cu cm.

Breig, E. L.↗

NASA NTRS2007

Bulk Crystal Growth of Piezoelectric PMN-PT Crystals Using Gradient Freeze Technique for Improved SHM Sensors

There has been a growing interest in recent years in lead based perovskite ferroelectric and relaxor ferroelectric solid solutions because of their excellent dielectric, piezoelectric and electrostrictive properties that make them very attractive for various sensing, actuating and structural health monitoring (SHM) applications. We are interested in the development of highly sensitive and efficient PMN-PT sensors based on large single crystals for the structural health monitoring of composite materials that may be used in future spacecrafts. Highly sensitive sensors are needed for detection of defects in these materials because they often tend to fail by distributed and interacting damage modes and much of the damage occurs beneath the top surface of the laminate and not detectable by visual inspection. Research is being carried out for various combinations of solid solutions for PMN-PT piezoelectric materials and bigger size crystals are being sought for improved sensor applications. Single crystals of this material are of interest for sensor applications because of their high piezoelectric coefficient (d33 greater than 1700 pC/N) and electromechanical coefficients (k33 greater than 0.90). For comparison, the commonly used piezoelectric ceramic lead zirconate titanate (PZT) has a d33 of about 600 pC/N and electromechanical coefficients k33 of about 0.75. At the present time, these piezoelectric relaxor crystals are grown by high temperature flux growth method and the size of these crystals are rather small (~3x4x5 mm(exp 3). In the present paper, we have attempted to grow bulk single crystals of PMN-PT in a 2 inch diameter platinum crucible and successfully grown a large size crystal of 67%PMN-33%PT using the vertical gradient freeze technique with no flux. Piezoelectric properties of the grown crystals are investigated. PMN-PT plates show excellent piezoelectric properties. Samples were poled under an applied electric field of 5 kV/cm. Dielectric properties at a frequency of 1 kHz are examined. The grown PMN-PT crystals show typical relaxor dielectric properties. Additionally, the thermal properties of the sample are tested. The results are in good agreement with those found in the literature and some are reported for the first time.

Aggarwal, Mohan D.↗

NASA NTRS1986

A dynamically based transport parameterization for one-dimensional photochemical models of the stratosphere

The net vertical tracer flux in the stratosphere is due primarily to advection by the global-scale mean meridional circulation, not to diffusion by turbulent eddies. Using a simple model of this circulation, it is shown that the net flux can be approximated by a flux-gradient relationship in which the vertical 'eddy transport' coefficient is proportional to the square of the diabatic heating rate and inversely proportional to the rate at which meridional tracer gradients are destroyed by horizontal eddy mixing and chemical damping. Thus the transport coefficient will differ for tracers with differing chemical lifetimes. Profiles computed for various source gases (CH4 N2O, CF2Cl2, and CFCl3) show that this parameterization provides an improvement over conventional formulations that utilize a single transport coefficient for all species.

Holton, J. R.↗

DOE OSTI2022

Ocean Surface Flux Algorithm Effects on Tropical Indo-Pacific Intraseasonal Precipitation

Surface latent heat fluxes help maintain tropical intraseasonal precipitation. We develop a latent heat flux diagnostic that depicts how latent heat fluxes vary with the near-surface specific humidity vertical gradient (Δq) and surface wind speed (|V|). Compared to fluxes estimated from |V| and Δq measured at tropical moorings and the Coupled Ocean Atmosphere Response Experiment 3.0 (COARE3.0) algorithm, tropical latent heat fluxes in the National Center for Atmospheric Research CEMS2 and Department of Energy E3SMv1 models are significantly overestimated at |V| and Δq extrema. Madden–Julian oscillation (MJO) sensitivity to surface flux algorithm is tested with offline and inline flux corrections. The offline correction adjusts model output fluxes toward mooring-estimated fluxes; the inline correction replaces the original bulk flux algorithm with the COARE3.0 algorithm in atmosphere-only simulations of each model. Both corrections indicate reduced latent heat flux feedback to intraseasonal precipitation, in better agreement with observations, suggesting that model-simulated fluxes are overly supportive for maintaining MJO convection.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1996

Nonstationary Gravity Wave Forcing of the Stratospheric Zonal Mean Wind

The role of gravity wave forcing in the zonal mean circulation of the stratosphere is discussed. Starting from some very simple assumptions about the momentum flux spectrum of nonstationary (non-zero phase speed) waves at forcing levels in the troposphere, a linear model is used to calculate wave propagation through climatological zonal mean winds at solstice seasons. As the wave amplitudes exceed their stable limits, a saturation criterion is imposed to account for nonlinear wave breakdown effects, and the resulting vertical gradient in the wave momentum flux is then used to estimate the mean flow forcing per unit mass. Evidence from global, assimilated data sets are used to constrain these forcing estimates. The results suggest the gravity-wave-driven force is accelerative (has the same sign as the mean wind) throughout most of the stratosphere above 20 km. The sense of the gravity wave forcing in the stratosphere is thus opposite to that in the mesosphere, where gravity wave drag is widely believed to play a principal role in decelerating the mesospheric jets. The forcing estimates are further compared to existing gravity wave parameterizations for the same climatological zonal mean conditions. Substantial disagreement is evident in the stratosphere, and we discuss the reasons for the disagreement. The results suggest limits on typical gravity wave amplitudes near source levels in the troposphere at solstice seasons. The gravity wave forcing in the stratosphere appears to have a substantial effect on lower stratospheric temperatures during southern hemisphere summer and thus may be relevant to climate.

Alexander, M. J.↗

DOE OSTI2022

A Hierarchy of Global Ocean Models Coupled to CESM1

Abstract We develop a hierarchy of simplified ocean models for coupled ocean, atmosphere, and sea ice climate simulations using the Community Earth System Model version 1 (CESM1). The hierarchy has four members: a slab ocean model, a mixed‐layer model (MLM) with entrainment and detrainment, an Ekman MLM, and an ocean general circulation model (OGCM). Flux corrections of heat and salt are applied to the simplified models ensuring that all hierarchy members have the same climatology. We diagnose the needed flux corrections from auxiliary simulations in which we restore the temperature and salinity to the daily climatology obtained from a target CESM1 simulation. The resulting three‐dimensional corrections contain the interannual variability fluxes that maintain the correct vertical gradients of temperature and salinity in the tropics. We find that the inclusion of mixed‐layer entrainment and Ekman flow produces sea surface temperature and surface air temperature fields whose means and variances are progressively more similar to those produced by the target CESM1 simulation. We illustrate the application of the hierarchy to the problem of understanding the response of the climate system to the loss of Arctic sea ice. We find that the shifts in the positions of the mid‐latitude westerly jet and of the Inter‐tropical Convergence Zone (ITCZ) in response to sea‐ice loss depend critically on upper ocean processes. Specifically, heat uptake associated with the mixed‐layer entrainment influences the shift in the westerly jet and ITCZ. Moreover, the shift of ITCZ is sensitive to the form of Ekman flow parameterization.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

A hierarchy of global ocean models coupled to CESM1

We develop a hierarchy of simplified ocean models for coupled ocean, atmosphere, and sea ice climate simulations using the Community Earth System Model version 1 (CESM1). The hierarchy has four members: a slab ocean model, a mixed-layer model (MLM) with entrainment and detrainment, an Ekman MLM, and an ocean general circulation model (OGCM). Flux corrections of heat and salt are applied to the simplified models ensuring that all hierarchy members have the same climatology. We diagnose the needed flux corrections from auxiliary simulations in which we restore the temperature and salinity to the daily climatology obtained from a target CESM1 simulation. The resulting three-dimensional corrections contain the interannual variability fluxes that maintain the correct vertical gradients of temperature and salinity in the tropics. We find that the inclusion of mixed-layer entrainment and Ekman flow produces sea surface temperature and surface air temperature fields whose means and variances are progressively more similar to those produced by the target CESM1 simulation. We illustrate the application of the hierarchy to the problem of understanding the response of the climate system to the loss of Arctic sea ice. We find that the shifts in the positions of the mid-latitude westerly jet and of the Inter-tropical Convergence Zone (ITCZ) in response to sea-ice loss depend critically on upper ocean processes. Specifically, heat uptake associated with the mixed-layer entrainment influences the shift in the westerly jet and ITCZ. Moreover, the shift of ITCZ is sensitive to the form of Ekman flow parameterization.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2012

CO2 Flux Estimation Errors Associated with Moist Atmospheric Processes

Vertical transport by moist sub-grid scale processes such as deep convection is a well-known source of uncertainty in CO2 source/sink inversion. However, a dynamical link between vertical transport, satellite based retrievals of column mole fractions of CO2, and source/sink inversion has not yet been established. By using the same offline transport model with meteorological fields from slightly different data assimilation systems, we examine sensitivity of frontal CO2 transport and retrieved fluxes to different parameterizations of sub-grid vertical transport. We find that frontal transport feeds off background vertical CO2 gradients, which are modulated by sub-grid vertical transport. The implication for source/sink estimation is two-fold. First, CO2 variations contained in moist poleward moving air masses are systematically different from variations in dry equatorward moving air. Moist poleward transport is hidden from orbital sensors on satellites, causing a sampling bias, which leads directly to small but systematic flux retrieval errors in northern mid-latitudes. Second, differences in the representation of moist sub-grid vertical transport in GEOS-4 and GEOS-5 meteorological fields cause differences in vertical gradients of CO2, which leads to systematic differences in moist poleward and dry equatorward CO2 transport and therefore the fraction of CO2 variations hidden in moist air from satellites. As a result, sampling biases are amplified and regional scale flux errors enhanced, most notably in Europe (0.43+/-0.35 PgC /yr). These results, cast from the perspective of moist frontal transport processes, support previous arguments that the vertical gradient of CO2 is a major source of uncertainty in source/sink inversion.

moist atmospheric processes↗

NASA NTRS2004

Nucleation in Synoptically Forced Cirrostratus

Formation and evolution of cirrostratus in response to weak, uniform and constant synoptic forcing is simulated using a one-dimensional numerical model with explicit microphysics, in which the particle size distribution in each grid box is fully resolved. A series of tests of the model response to nucleation modes (homogeneous-freezing-only/heterogeneous nucleation) and heterogeneous nucleation parameters are performed. In the case studied here, nucleation is first activated in the prescribed moist layer. A continuous cloud-top nucleation zone with a depth depending on the vertical humidity gradient and one of the nucleation parameters is developed afterward. For the heterogeneous nucleation cases, intermittent nucleation zones in the mid-upper portion of the cloud form where the relative humidity is on the rise, because existent ice crystals do not uptake excess water vapor efficiently, and ice nuclei (IN) are available. Vertical resolution as fine as 1 m is required for realistic simulation of the homogeneous-freezing-only scenario, while the model resolution requirement is more relaxed in the cases where heterogeneous nucleation dominates. Bulk microphysical and optical properties are evaluated and compared. Ice particle number flux divergence, which is due to the vertical gradient of the gravity-induced particle sedimentation, is constantly and rapidly changing the local ice number concentration, even in the nucleation zone. When the depth of the nucleation zone is shallow, particle number concentration decreases rapidly as ice particles grow and sediment away from the nucleation zone. When the depth of the nucleation zone is large, a region of high ice number concentration can be sustained. The depth of nucleation zone is an important parameter to be considered in parametric treatments of ice cloud generation.

Lin, R.-F.↗

NASA NTRS1991

Momentum and heat flux estimation in the planetary boundary layer (PBL) with a 10.6-micron Doppler lidar

The mean wind, its standard deviation, and the momentum fluxes in the PBL are estimated with a 10.6-micron Doppler lidar. Spectral analysis of the radial velocities was performed, from which, by examining the amplitude of the power spectrum at the inertial range, the kinetic energy dissipation was deduced. The statistical form of the Navier-Stokes equations was used to derive the surface heat flux as the residual balance between the vertical gradient of the third moment of the vertical velocity and the kinetic energy dissipation.

Gal-Chen, Tzvi↗

NASA NTRS2023

Assessment of Oceanographic Conditions during the North Atlantic EXport Processes in the Ocean from RemoTe Sensing (EXPORTS) Field Campaign

This manuscript presents an overview of NASA’s EXport Processes in the Ocean from Remote Sensing 2021 Field Campaign in the North Atlantic (EXPORTS NA) and provides quantitative and dynamical descriptions of the physical processes modulating water transformations during the study. A major programmatic goal was to conduct the sampling in a Lagrangian mode so that ocean ecological and biogeochemical changes can be observed independent from physical advective processes. To accomplish this goal, EXPORTS NA conducted a multi-ship, multi-asset field sampling program within a retentive, anticyclonic mode water eddy. Beneath depths of ∼100 m, Lagrangian sampling assets remained within the eddy core waters (ECWs) throughout the experiment, demonstrating that the ECWs within the mode water eddy were retentive. However, strong westerly winds from four storm events deepened the mixed layer (ML) of the surface core waters (SCWs) above the eddy’s mode water core by 25-40 m and exchanged some of the SCWs with surface waters outside of the eddy via Ekman transport. Estimates of flushing times ranged from 5-8 days, with surface exchange fractions ranging from 20-75% and were consistent with particle tracking advected by combined geostrophic and Ekman velocities. The relative contributions of horizontal and vertical advection on changes in ECW tracers depended on the horizontal and vertical gradients of that tracer. For example, horizontal advection played a large role in ECW salinity fluxes, while vertical entrainment played a larger role in the fluxes of nutrients into SCW ML. Each storm injected nutrients and low oxygen waters into the ML, after which the surface ocean ecosystem responded by reducing nutrient concentrations and increasing %O2 saturation levels. Overall, ECW values of chlorophyll and POC were the largest at the onset of the field program and decreased throughout the campaign. The analysis presented provides a physical oceanographic context for the many measurements made during the EXPORTS NA field campaign while illustrating the many challenges of conducting a production-flux experiment, even in a Lagrangian frame, and the inherent uncertainties of interpreting biological carbon pump observations that were collected in a Eulerian frame of reference.

oceanography↗

NASA NTRS1993

Coupled ice-ocean variability in the Greenland Sea

A major surface feature of the Greenland Sea during winter is the frequent eastward extension of sea ice south of 75 deg N and an associated embayment to the north. These features are nominally connected with the East Greenland Current, and both the promontory) and the embayment are readily apparent on climatic ice charts. However, there are significant changes in these features on time-scales as short as a few days. Using a combination of satellite microwave images (SSM/I) of ice cover, meteorological data and in situ velocity, temperature and salinity records, we relate the ice distribution and its changes to the developing structure and circulation of the upper ocean during winter 1988-1989. Our measurements illustrate the preconditioning that leads to convective overturn, which in turn brings warmer water to the surface and results in the rapid disappearance of ice. In particular, the surface was cooled to the freezing point by early December and the salinity then increased through ice formation (about 0.016 m/d) and brine rejection. Once the vertical density gradient was sufficiently eroded, a period of high heat flux (greater than 300 W/sq m) in late January provided enough buoyancy loss to convectively mix the upper water column to at least 200 m. We estimate vertical velocities at about 3 cm/s downward during the initial sinking. The deepening of the thermocline raised surface temperatures by over 1 C resulting in nearly 1.5 x 105 km of ice-melt within two days. Average rates of ice retreat are about 2 km/d southwestward, generally consistent with a wind-driven flow. Comparison of hydrographic surveys from before and after the overturning indicate the fresh water was advected out of the area, possibly to the south and east of our moorings.

Roach, A. T.↗

NASA NTRS2012

Characterization of Turbulent Latent and Sensible Heat Flux Exchange Between the Atmosphere and Ocean in MERRA

Turbulent fluxes of heat and moisture across the atmosphere-ocean interface are fundamental components of the Earth's energy and water balance. Characterizing both the spatiotemporal variability and the fidelity of these exchanges of heat and moisture is critical to understanding the global water and energy cycle variations, quantifying atmosphere-ocean feedbacks, and improving model predictability. This study examines the veracity of the recently completed NASA Modern-Era Retrospective analysis for Research and Applications (MERRA) product with respect to its representation of the surface turbulent heat fluxes. A validation of MERRA turbulent heat fluxes and near-surface bulk variables at local, high-resolution space and time scales is achieved by making comparisons to a large suite of direct observations. Both in situ and satellite-observed gridded surface heat flux estimates are employed to investigate the spatial and temporal variability of the surface fluxes with respect to their annual mean climatologies, their seasonal covariability of near-surface bulk parameters, and their representation of extremes. The impact of data assimilation on the near-surface parameters is assessed through evaluation of incremental analysis update tendencies produced by the assimilation procedure. It is found that MERRA turbulent surface heat fluxes are relatively accurate for typical conditions but have systematically weak vertical gradients in moisture and temperature and have a weaker covariability between the near-surface gradients and wind speed than found in observations. This results in an underestimate of the surface latent and sensible heat fluxes over the western boundary current and storm track regions. The assimilation of observations mostly acts to bring MERRA closer to observational products by increasing moisture and temperature near the surface and decreasing the near-surface wind speeds. The major patterns of spatial and temporal variability of the turbulent heat fluxes produced by MERRA compare favorably to observationally based estimates. However, MERRA is distinct in terms of amplitude. These results suggest that MERRA is likely to be a valuable resource for a number of research applications though, as with all turbulent flux estimates, systematic issues should be taken into account

Robert, J. Brent↗

NASA NTRS2012

Characterization of Turbulent Latent and Sensible Heat Flux Exchange Between the Atmosphere and Ocean in MERRA

Turbulent fluxes of heat and moisture across the atmosphere-ocean interface are fundamental components of the Earth s energy and water balance. Characterizing both the spatiotemporal variability and the fidelity of these exchanges of heat and moisture is critical to understanding the global water and energy cycle variations, quantifying atmosphere-ocean feedbacks, and improving model predictability. This study examines the veracity of the recently completed NASA Modern-Era Retrospective analysis for Research and Applications (MERRA) product with respect to its representation of the surface turbulent heat fluxes. A validation of MERRA turbulent heat fluxes and near-surface bulk variables at local, high-resolution space and time scales is achieved by making comparisons to a large suite of direct observations. Both in situ and satellite-observed gridded surface heat flux estimates are employed to investigate the spatial and temporal variability of the surface fluxes with respect to their annual mean climatologies, their seasonal covariability of near-surface bulk parameters, and their representation of extremes. The impact of data assimilation on the near-surface parameters is assessed through evaluation of incremental analysis update tendencies produced by the assimilation procedure. It is found that MERRA turbulent surface heat fluxes are relatively accurate for typical conditions but have systematically weak vertical gradients in moisture and temperature and have a weaker covariability between the near-surface gradients and wind speed than found in observations. This results in an underestimate of the surface latent and sensible heat fluxes over the western boundary current and storm track regions. The assimilation of observations mostly acts to bring MERRA closer to observational products by increasing moisture and temperature near the surface and decreasing the near-surface wind speeds. The major patterns of spatial and temporal variability of the turbulent heat fluxes produced by MERRA compare favorably to observationally based estimates. However, MERRA is distinct in terms of amplitude. These results suggest that MERRA is likely to be a valuable resource for a number of research applications though, as with all turbulent flux estimates, systematic issues should be taken into account.

Roberts, J. Brent↗

NASA NTRS1981

The effects of surface evaporation parameterizations on climate sensitivity to solar constant variations

The effects of two different evaporation parameterizations on the sensitivity of simulated climate to solar constant variations are investigated by using a zonally averaged climate model. One parameterization is a nonlinear formulation in which the evaporation is nonlinearly proportional to the sensible heat flux, with the Bowen ratio determined by the predicted vertical temperature and humidity gradients near the earth's surface (model A). The other is the formulation of Saltzman (1968) with the evaporation linearly proportional to the sensible heat flux (model B). The computed climates of models A and B are in good agreement except for the energy partition between sensible and latent heat at the earth's surface. The difference in evaporation parameterizations causes a difference in the response of temperature lapse rate to solar constant variations and a difference in the sensitivity of longwave radiation to surface temperature which leads to a smaller sensitivity of surface temperature to solar constant variations in model A than in model B. The results of model A are qualitatively in agreement with those of the general circulation model calculations of Wetherald and Manabe (1975).

Chou, S.-H.↗

NASA NTRS1984

Numerical Modeling of the Atmosphere

Numerical models and numerical analyses of observations were used to improve the understanding of the physical processes important in global weather and climate. Results from a study of the effect of baroclinic waves on mid-latitude vertical temperature structure show that the waves' vertical eddy heat flux tend to eliminate the potential vorticity gradient near the steering level by causing the static stability to decrease rapidly with height in the lower troposphere above the boundary layer. An empirical study of the relationship between eddy heat fluxes and the meridional temperature gradient has been completed. The results indicate that the feedback in the flux-gradient system is comparable to dissipation on all time scales between the synoptic and the seasonal. The definition of the Eliassen-Palm flux and the Eliassen-Palm and non-acceleration theorems has been generalized to include eddy forcing of condensation. Calculations based on the generalized diagnostics showed that the annual mean eddy forcing of the zonal mean zonal wind is two and one half times stronger when the condensation effects are included.

Stone, P. H.↗