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Kevin E. Trenberth

Abstract

Possible methods for estimating surface fluxes include (i) use of bulk fluxes and in situ observations, (ii) use of model parameterizations to interpret specified inputs and compute surface fluxes, and (iii) various indirect methods, which rely on the fact that the mass and surface heat, energy, and momentum budgets must balance and so, given computations of all the other components in the various budget equations applied to fields either within the ocean or the atmosphere, fluxes may be inferred as a residual. This paper reviews the third approach using indirect methods and outlines the advantages associated with the use of global atmospheric analyses from four-dimensional data assimilation (4DDA). The time mean increment required in producing analyses in 4DDA is identical to the systematic short-term (6 h) assimilating model forecast error and is most likely due to errors in the model physics. Therefore, the analyses include a desirable fix, which allows the sum of the “physics” to be deduced from “dynamics.” The focus is on the heat and moisture budgets to infer surface heat fluxes and freshwater fluxes, but with the recognition of the need to balance the mass budget as well. The diurnal cycle of the vertically integrated mass budget for July 1985 and January 1996 from National Centers for Environmental Prediction (formerly the National Meteorological Center) reanalyses is presented, revealing the strong semidiurnal tide and highlighting the need for at least four-times-daily data. The new results reveal that gross violations of the mass budget continue to be present, but these can be allowed for. A discussion is given of other sources of errors contributing to the heat and moisture budgets.

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Kevin E. Trenberth

Abstract

An approximate formulation of how much moisture that precipitates out comes from local evaporation versus horizontal transport, referred to as “recycling,” has allowed new estimates of recycling to be mapped globally as a function of length scale. The recycling is formulated in terms of the “intensity of the hydrological cycle” I, which is alternatively referred to as a “precipitation efficiency” as it denotes the fraction of moisture flowing through a region that is precipitated out, and a “moistening efficiency,” M, which is defined as the fraction of moisture evaporated from a region to that flowing through. While datasets of the pertinent quantities have improved, they still contain uncertainties. Results show that often the intensity is not greatest at times of greatest precipitation because moisture transport into the region is also a maximum, especially in the monsoonal regions. The annual cycle variations of I are fairly small over North America and Europe while large seasonal variations in M occur in most places. Seasonal mean maps of precipitation, evaporation (E), and atmospheric moisture transport are presented and discussed along with the seasonal and annual means of derived precipitation and moisture efficiencies and the recycling fraction. The recycling results depend greatly on the scale of the domain under consideration and global maps of the recycling for seasonal and annual means are produced for 500- and 1000-km scales that therefore allow the heterogeneity of the fields across river basins to be captured. Global annual mean recycling for 500-km scales is 9.6%, consisting of 8.9% over land and 9.9% over the oceans. Even for 1000-km scales, less than 20% of the annual precipitation typically comes from evaporation within that domain. Over the Amazon, strong advection of moisture dominates the supply of atmospheric moisture over much of the river basin but local evaporation is much more prominent over the southern parts, and, for the annual cycle as a whole, about 34% of the moisture is recycled. Over the Mississippi Basin, the recycling is about 21%. The smaller number mostly reflects the smaller domain size. Relatively high annual values of recycling (>20%) occur in the subtropical highs, where E is high and the advective moisture flux is small, and in convergence zones where, again, the advective moisture flux is small. Low annual values occur over the southern oceans, the North Pacific, and the eastern equatorial Pacific, where the moisture flux is at a maximum.

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Kevin E. Trenberth

Abstract

The distribution of the mean westerly wind over the globe is described for June, July and August, the southern winter, using analyses from the European Centre for Medium Range Weather Forecasts (ECMWF) from 1979 to 1982. The tropospheric momentum budget is analyzed from both the traditional Eulerian and the transformed Eulerian perspectives. Thus an assessment is made of the Eliassen-Palm flux divergence and the diabatically driven residual mean circulation. The vertical mean budget is also analyzed to allow deductions about the mean surface torque by the atmosphere on the earth and the grow surface stress.

In the southern winter, transient eddies dominate the poleward momentum transports in both hemispheres, and total transports are somewhat larger than found in previous studies. Values of the deduced mean westerly surface stress are therefore larger than most previous estimates, but seem very reasonable and are probably more reliable in midlatitudes. A strange vertical structure analyzed to be present in the ECMWF zonal mean meridional wind is found to be inconsistent with the momentum budget, and the analyzed Hadley circulation is shown to be much too weak. The latter was expected since diabatic effects were not included in the initialization at ECMWF for this period. The total momentum budget is determined without including vertical eddy fluxes of momentum, but the residual is fairly small outside of the tropics and can probably be accounted for by fairly small errors in the analyzed divergent wind component.

The traditional Eulerian view reveals that the midlatitude westerlies are maintained mainly by convergence of westerly momentum by the transient eddies, while the induced Ferrel cell decelerates the westerlies aloft and transports momentum down to the surface to balance losses by surface friction. The transformed Eulerian view shows that the net effect of the eddies in the upper troposphere, above 300 mb, is small, but there is a marked net deceleration by the transient eddies between 700 and 300 mb, and the westerlies there are maintained by the Coriolis torque acting on the diabatically driven residual mean circulation. The observed Ferrel cell is thus revealed to be a fairly small residual of the direct diabatically driven cell and the eddy-induced indirect cell. However, the vertical mean budget clearly shows that it is the meridional transport of westerly momentum by the eddies that is primarily acting to maintain the midlatitude westerlies against losses by surface friction.

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Kevin E. Trenberth

Abstract

Two major blocking events took place over the South Pacific Ocean east of New Zealand, 23 July-4 August and 19–27 August 1979. The configuration of the overall flow, including the split in the westerlies, the location of the blocking highs, and the wavenumber breakdown were very similar. The tendency for blocking highs to reform in the same location in close sequence is referred to as a blocking episode.

The blocking events are analyzed in detail and the imprint they left on the general circulation statistics for the winter as a whole are presented. Since the blocking episode mostly prevented eddies from moving through the region, the variance of meridional velocity is small. Nevertheless, owing to the sequence of blocks the variance of geopotential height is a maximum. This signature on the general circulation is in marked contrast to that in storm track regions where the variance of geopotential height and meridional wind are both a maximum. A global-scale redistribution of mass was associated with the blocking episode.

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Kevin E. Trenberth

Abstract

The Eliassen-Palm (E-P) flux, applied to zonal men flows, is an indicator of both the flux of eddy activity and the eddy forcing of the zonal mean flow. For time mean flows, a localized E-P flux is derived and used diagnostically to assess the impact of transient eddies on a major blocking episode that occurred over the South Pacific during the Southern Hemisphere winter of 1979. In contrast to previous studies that have focused on the mean quasi-geostrophic potential vorticity equation, the focus here is on the mean momentum equations. Eddy transports and the associated induced meridional circulation and other internal adjustments necessary to maintain the thermal wind balance, are gathered together allowing the residual circulation and the effects of the eddies to be determined. The time-mean equations of motion are thus transformed to consist of mean terms, the residual circulation and the divergence of a localized E-P flux vector. The latter is a measure of the eddy forcing of the mean flow, and the east-west component is shown to be related to the flux of wave activity. For the zonal mean case it is identical to the E-P flux. The local E-P flux is closely related to, but differs from, the E-vector of Hoskins et al. and Plumb's radiative wave activity flux, but has several advantages over both.

For the blocking episode, defined as 20 July-31 August 1979, transient eddies were steered around the location of the blocking anticyclones following the two branches of the split westerly jet. However, the transient eddies in each branch differed in character, both from each other and from those in the main Southern Hemisphere storm track that extends across the southern Indian Ocean near 50°S. In the latter, the high frequency synoptic-scale baroclinic eddies are barotropically damped. The eddies have similar character to the south of the block but consist mainly of zonal wavenumbers 3 and 4 with periods shorter than a week. In contrast, the transient eddies in the subtropical branch of the jet are higher wavenumber (mostly waves 5 and 6) with periods longer than a week and, although primarily baroclinic, they are also maintained by barotropic processes. Most transient wave energy propagates eastward and wave packets can be followed around the entire hemisphere, mostly following the split westerly jet, with a period of about six days.

The local E-P flux divergence is divided into barotropic and baroclinic components. The former is coherent in the vertical but strongest at 300 mb near the tropopause. The transient eddies barotropically accelerate the westerlies in the main storm track and branch south of the block, and this is partially balanced by the baroclinic component. Thus a large part of the momentum balance is between transient eddy momentum convergence and the Coriolis torque arising from the poleward heat transport induced Ferrel cell, in combination with Surface friction.

Where the main westerly jet splits as part of the blocking flow configuration, both the barotropic and baroclinic local E-P flux components are acting to decelerate the westerlies and thus the transient eddies are helping to maintain the blocking episode. The main differences between the storm track and blocking regions arise in the barotropic component of the local E-P flux. It appears that the configuration of the split westerly jet acts to systematically deform the transient eddies in such a way that they feed back to help maintain the split structure.

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Kevin E. Trenberth

Abstract

A comprehensive analysis has been made of the atmospheric planetary wave response to orographic and thermal forcing in midlatitudes using a simple model. Vertical heating profiles with maxima at the surface and in the mid-troposphere are considered. The model is quasi-geostrophic on a beta-plane, and has a constant zonal mean basic-state wind. With these simplifications it is possible to obtain complete analytic solutions, not only for the wave response with and without Ekman pumping, but also for the secondary effects of the waves on the zonal mean flow. The presence of diabatic heating in the waves results in significant non-zero Eliassen-Palm fluxes and violates conditions for non-acceleration of the zonal mean flow, both for propagating and trapped waves. The potential vorticity transport or, alternatively, the Eliassen-Palm flux divergence is shown to be directly related to the vertical heating profile. However, it is the interaction between orographic and thermally forced waves that is mainly responsible for change in the zonal mean flow, and the results therefore strongly depend upon the relative phase of the thermal and orographic forcing.

At large heights, remote from the heating it is shown that it is possible to choose an equivalent mountain that would produce the same response in the planetary waves as the thermal forcing. The equivalent mountain height varies inversely as zonal wavenumber. In addition the mid-tropospheric heating profile produces a wave with 4-5 times the amplitude of the wave response to the surface heating profile with the same vertically integrated total heating. Consequently it is mainly in zonal waves 1 and 2 where a mid-tropospheric thermally forced wave can dominate or be comparable to the orographic waves.

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Kevin E. Trenberth

Abstract

From 1979 to 1989, global European Centre for Medium Range Weather Forecasts (ECMWF) analyses of many meteorological variables important in baroclinic storms have been bandpass filtered to highlight fluctuations on 2- to 8-day time scales in order to illuminate the relationships among the variables in baroclinic storm-track regions. Because of the greater zonal symmetry in the Southern Hemisphere (SH) versus the Northern Hemisphere (NH), it is possible to examine these relationships over a zonal sector without being dominated by local effects associated with jet stream entrance and exit regions of the storm tracks. The bandpassed variance of geopotential height is used to define the storm track, and its meridional profile has a pronounced midlatitude maximum in the SH. The locations of the jet stream and the variance maxima of meridional and zonal velocity components, vorticity, vertical motion, specific humidity, and temperature all bear a distinctive relationship to the storm track, but the latitudes of their maxima are displaced from the center of the storm track. Many covariance quantities such as the transient eddy temperature, moisture, vorticity, and vertical and horizontal momentum fluxes also exhibit a strong storm-track signature. The observed relationships among the eddy quantities can generally be understood in terms of geostrophic theory and perturbation analysis applied to baroclinic systems.

Storm-track activity is remarkably persistent throughout the year in both location and intensity in the SH. The storm track is farthest poleward in the transition seasons as part of a semiannual cycle, but remains near 50°S year round, and is strongest in the southern Indian Ocean and weakest in the South Pacific. There is a strong relationship between the storm track and the major tropospheric polar jet stream and its associated lower-level baroclinicity throughout the year, and the distribution of storm-track activity can be accounted for by baroclinic theory. In contrast to the NH, strongest meridional temperature gradients in middle latitudes are found in the summer half-year in the SH. Whereas the NH storm-track activity is much weaker in summer and shifts poleward, the SH activity is as strong as in winter and, if anything, shifts slightly equatorward. The zonal symmetry is greater in summer and meridional profiles are sharper, implying less variability in the storm track both within and between seasons. In winter, high-frequency storm-track activity extends over a broader range of latitudes and continues to be mainly associated with the polar jet stream.

The question of the impact of the storm-track eddies on the mean flow is examined using zonal mean and a localized Eliassen–Palm flux. Baroclinic effects from the poleward heat flux dominate in winter and the eddies act to decelerate the upper tropospheric westerlies. Barotropic effects in the upper troposphere, mostly from the meridional momentum flux convergence, help to maintain the mean westerly distribution by accelerating the main polar jet and maintaining the mean split in the flow near New Zealand in both summer and winter and even dominate the baroclinic component in the storm track in summer. Diabatic heating by the eddies may also help maintain the mean flow.

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Kevin E. Trenberth

Abstract

An analysis has been made of the spatial and frequency dependence of transient eddy statistics in the Southern Hemisphere at 500 mb. This study emphasizes summer versus winter differences in order to complement previous results of Trenberth (1981), which are shown to nearly correspond to the mean of the summer plus winter statistics. Variance fields of geopotential height, the north–south and east–west geostrophic velocity components, the transient kinetic energy and the poleward transient eddy momentum flux have been analyzed for nine winter and eight summer 128-day seasons from 1972–80. The fields are examined in the frequency domain using Lorenz' (1979) “poor man's spectral analysis” technique. The total fields and the contributions from two broad frequency bands covering periods of 2–8 and 8–64 days are geographically mapped and their zonal means are presented.

The spatial distribution of the eddy statistics is quite similar in summer and winter, although the variances in winter are larger and of broader latitudinal extent, thereby indicating a more vigorous circulation overall than in summer. The seasonal changes in eddy statistics closely follow corresponding changes in the mean westerly wind field and are very small over the Indian Ocean, while the largest changes occur in the Pacific Ocean region. A storm track, as indicated by the high frequency fluctuations, exists in the Indian Ocean along 50°S in both summer and winter. The main low frequency variations including blocking-type phenomena occur south of New Zealand and southeast of South America in both seasons, but with small changes in location. Storms in the Pacific Ocean region have a somewhat longer time scale than over the Indian Ocean.

A comparison has been made with results from previous studies and, in particular, with statistics based upon station data analyzed at GFDL. The GFDL analyses produce relatively weaker wind speeds over the data sparse oceans. The variance fields are comparable in magnitude but differ in detail, and the GFDL analyses fail to capture the characteristic patterns in the storm track and blocking regions of the hemisphere.

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Kevin E. Trenberth

Abstract

Nearly eight years of daily Southern Hemisphere analyses at 500 mb have been used to define the spatial dependence of the variance fields of geopotential height and the two geostrophic wind components, the corresponding covariance fields, and the transient kinetic energy. The fields are further examined in the frequency domain by using Lorenz' (1979) “poor man's spectral analysis” technique. In view of the small variation in eddy statistics as a function of the time of the year in the SH, this study removes the first four harmonies of the annual cycle and then considers all data together, so that contributions from all time scales from 2 to 4096 days (∼11 years) can be resolved. The main results are based on analyses from May 1972–January 1978 but are verified with analyses from the relatively data-rich FGGE period.

Results for the zonal mean statistics are compared with those from previous studies. The zonal means of the geopotential height and westerly wind component have spectra which roughly follow that of red noise with an autocorrelation of about 0.5, whereas the northward wind component spectra closely resembles red noise with autocorretation of 0.2, resulting in considerable anisotropy in the wind fields. The northward component of transient kinetic energy is larger than the eastward component at high frequencies in middle latitudes but the reverse is true for periods of greater than two months. The westerly momentum flux by the transient eddies has a broad spectral peak at 8–32 days and is dominated by contributions from fluctuations of less than about two weeks period.

The geographical dependence of the eddy statistics is mapped for four broad frequency bands covering periods of roughly less than one week, one week to two months, two months to two years, and greater than two years, thereby separating out contributions from transient baroclinic eddies, episodes of blocking, and intermonthly and interannual variability. The spatial patterns of the statistics are interpreted in the light of synoptic behavior of systems and storm tracks as defined by synoptic studies and satellite observations in the Southern Hemisphere. For periods less than a week, variances are largest in the southern Indian Ocean and relationships between the storm tracks and eddy statistics are similar to those found in the Northern Hemisphere by Blackmon, Lau, Wallace and others. However, there also are differences associated with the differences in the mean flow in each hemisphere and these are discussed in the context of baroclinic theory. At periods longer than a week geopotential height variances are largest near southern New Zealand and, to a lesser extent, southeast of South America and appear to be related to the incidence of blocking in the Southern Hemisphere. The corresponding transient kinetic energy has a maximum further north in association with cutoff cold-centered lows. In general, the high-frequency transient eddies play a much larger role in the circulation of the Southern Hemisphere than is true for the winter circulation of the Northern Hemisphere, and the eddy statistics are more zonally symmetric.

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Kevin E. Trenberth

The concept of dividing the year into four seasons is reexamined to appraise critically the relative merit of two commonly used definitions of the seasons: 1) the astronomical definition; and 2) the meteorological breakdown into four three-month periods. These are compared with the definition of winter as the coldest season, summer as the warmest season, and spring and autumn as the transition seasons. Observational data on surface temperatures over the entire globe and, in particular, over the United States, are used to determine what the seasons should be. Presented here is an analysis of the amplitude, and phase of and percentage variance explained by the first harmonic of solar radiation at the top of the atmosphere and surface temperatures.

Annual changes in surface temperature associated with the seasons are much larger over land than over the oceans. Surface temperatures lag the solar cycle by 27½ days over the United States, compared with 32½ days in mid-latitudes over the Northern Hemisphere as a whole, and 44 days in mid-latitudes of the Southern Hemisphere.

The astronomical definition of seasons is appropriate only over the oceanic regions of the Southern Hemisphere. Over the continental regions of the Northern Hemisphere, the “meteorological” seasons in which winter is December, January, and February, etc., agree reasonably well with observed events and are recommended for general usage.

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