Angular Momentum Budget Research Articles

Atmospheric torques on land and ocean and implications for Earth's angular momentum budget

The exchange of angular momentum between the atmosphere and the oceans and solid Earth is examined using 40 years of atmospheric angular momentum (AAM) and ocean and land torque data from the National Centers for Environmental Prediction/National Center for Atmospheric Research reanalysis. Land torques are the dominant driving mechanism for AAM at submonthly periods. Ocean torques are as important as land torques at periods of 3 months and longer, however. With the exception of the annual and semiannual bands the ocean torque seems to mainly damp the AAM signals. The importance of the ocean torque implies a three‐way interaction among atmosphere, oceans, and solid Earth. For an ocean that simply transmits to the solid Earth the angular momentum exchanged with the atmosphere, with a delay of a few days at most, the analyzed torques imply that AAM should lead the length of day (LOD), which is contrary to the observations at monthly and longer periods. Sources of missing angular momentum variability, either from atmospheric or other origins, that can potentially explain the observed AAM and LOD phase relationship are discussed.

Atmospheric, oceanic and hydrological contributions to seasonal variations in length of day

The annual and semiannual residuals derived in the axial angular momentum budget of the solid Earth–atmosphere system reflect significant signals. They must be caused by further excitation sources. Since, in particular, the contribution for the wind term from the atmospheric layer between the 10 and 0.3 hPa levels to the seasonal variations in length of day (LOD) is still missing, it is necessary to extend the top level into the upper stratosphere up to 0.3 hPa. Under the conservation of the total angular momentum of the entire Earth, variations in the oceanic angular momentum (OAM) and the hydrological angular momentum (HAM) are further significant excitation sources at seasonal time scales. Focusing on other contributions to the Earth's axial angular momentum budget, the following data are used in this study: axial atmospheric angular momentum (AAM) data derived for the 10–0.3 hPa layer from 1991 to 1997 for computing the missing wind effects; axial OAM functions as generated by oceanic general circulation models (GCMs), namely for the ECHAM3 and the MICOM models, available from 1975 to 1994 and from 1992 to 1994, respectively, for computing the oceanic contributions to LOD changes, and, concerning the HAM variations, the seasonal estimates of the hydrological contribution as derived by Chao and O'Connor [(1988) Geophys J 94: 263–270]. Using vector representation, it is shown that the vectors achieve a close balance in the global axial angular momentum budget within the estimated uncertainties of the momentum quantities on seasonal time scales.

Improving ocean angular momentum estimates using a model constrained by data

Ocean angular momentum (OAM) calculations using forward model runs without any data constraints have recently revealed the effects of OAM variability on the Earth's rotation. Here we use an ocean model and its adjoint to estimate OAM values by constraining the model to available oceanic data. The optimization procedure yields substantial changes in OAM, related to adjustments in both motion and mass fields, as well as in the wind stress torques acting on the ocean. Constrained and unconstrained OAM values are discussed in the context of closing the planet's angular momentum budget. The estimation procedure yields noticeable improvements in the agreement with the observed Earth rotation parameters, particularly at the seasonal timescale. The comparison with Earth rotation measurements provides an independent consistency check on the estimated ocean state and underlines the importance of ocean state estimation for quantitative studies of the variable large‐scale oceanic mass and circulation fields, including studies of OAM.

The Energetics of Asian Summer Monsoon

— In this paper, we examine the large-scale balances of kinetic energy, vorticity, angular momentum, heat and moisture over the Asian summer monsoon region. The five year (1986–1990) uninitialized daily analyses for the summer season comprising June, July and August (JJA), produced at the European Centre for Medium Range Weather Forecasts (ECMWF) under the aegis of Tropical Ocean and Global Atmosphere (TOGA) have been considered to carry out the study.¶The following features characterize the Asian summer monsoon domain. It acts as the source of kinetic energy as well as vorticity, and sink of heat and moisture. Kinetic energy and vorticity are produced in the monsoon region and transported horizontally. On the contrary, heat and moisture are transported into the monsoon region. The zonal and meridional components of adiabatic generation of kinetic energy contribute to the production of kinetic energy over the Arabian Sea and Bay of Bengal, respectively. The horizontal advection of relative vorticity is balanced by sub-grid scale generation. The angular momentum generated due to pressure torque (east-west pressure gradient) is balanced by the flux convergence of omega momentum. Further, the angular momentum budget delineates that flux convergence of relative momentum is necessary to maintain the surface westerlies against the friction. The horizontal convergence of heat and moisture facilitates enhancement of diabatic heating, and also leads to the formation of diabatic heat sources, which are crucial to sustain the summer monsoon circulation.

Symmetric Stress Tensor Formulation of Horizontal Momentum Diffusion in Global Models of Atmospheric Circulation

Abstract In climate and weather forecast models, small-scale turbulence in the free atmosphere is usually parameterized by horizontal diffusion of horizontal momentum. This study proposes a formulation that is based on a symmetric stress tensor. The advantage over conventional methods is twofold. First, the Eulerian law of angular momentum conservation is fulfilled. Second, a self-consistent formulation of the momentum and thermodynamic equations of motion becomes possible due to incorporation of the local frictional heating rate, that is, the proper dissipation. The importance of these issues is demonstrated by numerical experiments performed with a simple general circulation model. For example, the new scheme precisely accounts for the irreversible increase of total potential energy during the decay of a baroclinic life cycle. Also the stress generated by horizontal momentum diffusion is found to be significant in the angular momentum budget of multiple life cycle experiments.

A Multiscale Numerical Study of Hurricane Andrew (1992). Part IV: Unbalanced Flows

Despite considerable progress in understanding the hurricane vortex using balanced models, the validity of gradient wind balance in the eyewall remains controversial in observational studies. In this paper, the structure and development of unbalanced forces and flows in hurricanes are examined, through the analyses of the radial momentum and absolute angular momentum (AAM) budgets, using a high-resolution (i.e., Δx = 6 km), fully explicit simulation of Hurricane Andrew (1992). It is found from the radial momentum budgets that supergradient flows and accelerations, even after temporal and azimuthal averaging, are well organized from the bottom of the eye center to the upper outflow layer in the eyewall. The agradient accelerations are on average twice greater than the local Coriolis force, and caused mainly by the excess of the centrifugal force over the pressure gradient force. It is shown by the AAM budgets that supergradient flows could occur not only in the inflow region as a result of the inward AAM transport, but also in the outflow region through the upward transport of AAM. The eyewall is dominated by radial outflow in which the upward transport of AAM overcompensates the spindown effect of the outflow during the deepening stage. The intense upper outflow layer is generated as a consequence of the continuous outward acceleration of airflows in the eyewall updrafts. In spite of the pronounced agradient tendencies, results presented here suggest that the azimuthally averaged tangential winds above the boundary layer satisfy the gradient wind balance within an error of 10%. The analyses of instantaneous fields show pronounced asymmetries and well-organized wavenumber-2 structures of the agradient flows and forces in the form of azimuthally propagating vortex–Rossby waves in the eyewall. These waves propagate cyclonically downstream with a speed half the tangential winds near the top of the boundary layer and vertically upward. Agradient flows/forces and AAM transport in the eye are also discussed.

Seasonal length-of-day changes and atmospheric angular momentum oscillations in their temporal variability

Recently, effective atmospheric-angular-momentum (AAM) functions as calculated from National Centers for Environmental Prediction (NCEP) (formerly National Meteorological Center, NMC) and National Center for Atmospheric Research (NCAR) Reanalyses have become available for the years 1958 to 1998. Concerning the wind terms, the top level in the atmosphere used here is 10 hPa. Compared with earlier NMC model versions, which incorporate wind fields up to 100 hPa since 1976 and up to 50 hPa since 1981, the reanalyses have produced improved data series over a longer period than before. The axial AAM component χ3 is associated with changes in length of day (LOD). Motivated by better quality and continuity of the series AAM (NCEP) Reanalysis, the problem of the seasonal imbalances in the solid Earth–atmosphere axial angular momentum budget is re-examined. To assess better the estimates of the annual and semiannual oscillations in LOD and AAM and of the residual oscillations derived as difference series between LOD and AAM, the series of LOD data from three analysis centers [International Earth Rotation Service (IERS), GeoForschungZentrum Potsdam (GFZ) and Jet Propulsion Laboratory Pasadena (JPL)] and of AAM data in terms of χ3(W), χ3(P) and χ3(P+IB) from four meteorological centers [NCEP, Japan Meteorological Agency (JMA), European Centre for Medium-Range Weather Forecasts (ECMWF) and the UK Meteorological Office (UKMO)] are used in this study. The main analysis steps were removing gaps, filtering out the seasonal oscillations, calculating optimal estimates of the parameters of the oscillations and calculating the difference series between the LOD and AAM systems as well as the residuals in the axial angular momentum budget in the LOD–AAM systems. The results derived as difference series between the different LOD, AAM and LOD–AAM systems show to what extent the variations reflect systematic differences and significant signals, respectively, which is important for future activities in this field.

Wind contributions to the Earth's angular momentum budgets in seasonal variation

The atmospheric contributions to seasonal variations in length of day (LOD) and wobble are discussed for the period 1988–1997. The data sets used here are SPACE97 and EOP97C04 for LOD and wobble, respectively. Two atmospheric angular momentum (AAM) functions are calculated from the operational objective analysis data of the Japan Meteorological Agency (JMA) and the reanalysis data of the National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR). Both the axial AAM functions agree well in annual variation and roughly in semiannual variation, with the function inferred from the observed LOD. The two equatorial AAM functions show the different wind contributions to the function inferred from the observed wobble, in both annual and semiannual variations, which are attributable in part to the different vertical wind integration methods between NCEP/NCAR and JMA. The equatorial tropospheric wind contributions, calculated by the same method, are found to show discrepancies arising from the different tropospheric regional winds associated with the Asian monsoon.

Vortex Merging in a 1½-Layer Fluid on anfPlane*

Mass, angular momentum, and energy budgets are examined in an analytical model of vortex merging relevant to midlatitude mesoscale eddies. The vortices are baroclinic and cyclogeostrophic. The fluid surrounding them is assumed to remain quiescent. It is shown that due to this surrounding fluid, angular momentum is conserved when expressed in both the inertial and rotating frames of reference. Lens-shaped solid-body vortices can conserve mass, angular momentum, and energy when they merge. If an upper-layer of thickness H1 is included in the model, the merged vortex must have either less energy or mass than the sum of the original two vortices. A more complex model of the vortex azimuthal structure is then considered, which includes a constant vorticity shell surrounding the solid-body core. If the shell is large compared to the core, the mass, angular momentum, and energy can all be conserved in the merged vortex. However, if the shell is small, the merged vortex must have less energy or mass than in the solid-body case.

Oceanic angular momentum variability estimated from the Parallel Ocean Climate Model, 1988–1998

This paper describes the use of a global numerical model of the oceans to estimate variations in both the equatorial and axial components of angular momentum resulting from oceanic mass redistribution and circulation. The Parallel Ocean Climate Model, driven by daily wind fields and monthly heat fluxes from the European Centre for Medium‐Range Weather Forecasts for 1988–1998, provides insight into variations in the transport and exchange of angular momentum, a quantity which is essentially conserved within the Earth system. Exchange of angular momentum between the oceans and the solid Earth should be manifest as changes in the Earth's rotation (both polar motion and length of day), and it is possible to compare predicted Earth rotation changes with actual geodetic observations. Using an inverted barometer assumption for oceans, the numerical model predictions of rotation change agree in sign and magnitude and are significantly correlated with observed polar motion and length of day variations after subtracting the dominant atmospheric contributions. The correlation has a seasonal variation which suggests that the role of the oceans in the excitation polar motion is more important during the Northern Hemisphere summer. Our results indicate that the oceans, to a different extent, account for a significant part of the nonatmospheric angular momentum budget for the Earth, and its fluid envelopes on interannual to submonthly timescales.

On Shear-Generated Gravity Waves that Reach the Mesosphere. Part I: Wave Generation

Abstract A long unresolved issue in nonorographic gravity wave generation is whether there is significant emission from Kelvin–Helmholtz (KH) shear instability in the lower stratosphere, for instance, just above tropopause jets. Such emission has often been suggested as significant for the angular momentum budget and hence for the wave-driven circulation of the middle atmosphere, most crucially in the summer mesosphere. An idealized model thought experiment is studied in which it is assumed that the KH shear instability rapidly mixes a thin layer, producing a “pancake” of three-dimensional clear-air turbulence, and emitting low-frequency inertia–gravity waves whose aspect ratio matches that of the turbulent layer and whose horizontal wavelength is large enough to avoid back-reflection and hence reach the summer mesosphere. The wave emission is modeled as a linear initial-value problem in which the rapid mixing of mass and momentum achieved by the turbulence is treated as instantaneous, and hence as determ...

On Shear-Generated Gravity Waves that Reach the Mesosphere. Part II: Wave Propagation

The propagation of Kelvin–Helmholtz (KH) shear-generated gravity waves through the summer stratosphere is investigated using ray tracing, taking into account back-reflection as well as wave dissipation due to precritical-layer breaking, radiative damping, and viscous diffusion. It is found that the transmission rate of upward–eastward waves to the mesosphere is surprisingly good, provided that the horizontal scale of the waves is large enough to prevent back-reflection. A rough upper bound on the net momentum flux into the mesosphere due to a large ensemble of mutually incoherent KH-generated clear-air turbulence events is then estimated, using reasonable-looking assumptions about the statistics of such events. It is found that on this basis the wave source cannot safely be neglected in the global angular momentum budget.

The influence of global warming in Earth rotation speed

Abstract. The tendency of the atmospheric angular momentum (AAM) is investigated using a 49-year set of monthly AAM data for the period January 1949-December 1997. This data set is constructed with zonal wind values from the reanalyses of NCEP/NCAR, used in conjunction with a variety of operationally produced AAM time series with different independent sources and lengths over 1976-1997. In all the analyzed AAM series the linear trend is found to be positive. Since the angular momentum of the atmosphere-earth system is conserved this corresponds to a net loss of angular momentum by the solid earth, therefore decreasing the Earth rotation speed and increasing the length of day (LOD). The AAM rise is significant to the budget of angular momentum of the global atmosphere-earth system; its value in milliseconds/century (ms/cy) is +0.56 ms/cy, corresponding to one-third of the estimated increase in LOD (+1.7 ms/cy). The major contribution to this secular trend in AAM comes from the equatorial Tropopause. This is consistent with results from a previous study using a simplified aqua-planet model to investigate the AAM variations due to near equatorial warming conditions. During the same time interval, 1949-1997, the global marine + land-surface temperature increases by about 0.79 °C/cy, showing a linear correspondence between surface temperature increase and global AAM of about 0.07 ms per 0.1 °C. These results imply that atmospheric angular momentum may be used as an independent index of the global atmosphere's dynamical response to the greenhouse forcing, and as such, the length of day may be used as an indirect indicator of global warming.Key words. Meteorology and atmospheric dynamics (general circulation) · Geodesy

The Role of diabatic heating, torques and stabilities in forcing the radial- vertical circulation within cyclones part iii: case study of lee-side cyclones

Two phases of extratropical cyclone development identified in previous mass and angular momentum budget studies have been confirmed through the numerical simulations of the azimuthally-averaged mass-weighted radial motion within two leeside cyclones: a Mediterranean and an Alberta cyclone. In the Mediterranean cyclone, a moist baroclinic phase is identified with inward (outward) mass and storm angular momentum transport in the lower (higher) value isentropic layers. The mass and storm angular momentum are then transported diabatically from lower to higher value isentropic layers through latent heat release. In addition, storm angular momentum is transferred horizontally across the inclined isentropic surfaces by pressure stresses due to the paired negative and positive pressure torque in lower and higher value isentropic layers respectively. A dry-leeside baroclinic phase is identified in the early stage of the Alberta cyclone with inward (outward) transport of mass and angular momentum in the higher (lower) value isentropic layers. The redistribution of angular momentum is associated with the virtual transfer by torques. A transition from dry to moist phase is identified in the life cycle of the Alberta cyclone.

The balance of global angular momentum in a long‐term atmospheric data set

The balance of global atmospheric angular momentum is examined in a long time series of “reanalysis” data generated at the National Centers for Environmental Prediction (NCEP). A systematic negative bias of about −10 Hadleys (1018 kg m2 s−2) is obtained in the total torque in all seasons. The sum of the frictional (TF) and mountain (TM) torques contributes about half of this negative bias in the northern summer and autumn. The torque due to the parameterized gravity wave drag, TG, contributes the other half of the negative bias in summer but contributes the whole of it in winter. In the annual mean the projected angular momentum imbalance due to TG exceeds that due to TM + TF. Consistent with the budget analysis of the assimilated data, losses of angular momentum are also found in an extensive set of medium‐range forecasts made with the NCEP reanalysis model. The average rates of loss of relative angular momentum in these forecasts, −7 Hadleys in January and −6 in July, are comparable to the bias of the total torque in the angular momentum budget. Further investigations are suggested to determine the model error, especially that associated with the parameterized gravity wave drag, related to the budget imbalance found in this study.

Semidiurnal Variations in the Budget of Angular Momentum in a General Circulation Model and in the Real Atmosphere

Abstract Diurnal and semidiurnal variations in the budget of atmospheric angular momentum are evident in a simulation by the NCAR Community Climate Model (CCM2). These variations depicted with 20-min time resolution (each time step) are used as guides to study similar variations determined from 6-hourly NCEP/NCAR Reanalysis data. A semidiurnal variation in relative angular momentum and in angular momentum related to solid body rotation of the atmosphere is found in the reanalysis. Although there is evidence that both frictional and gravity-wave drag torques play roles, the effects of semidiurnal variations in mountain torque, resulting from the migrating semidiurnal pressure wave, are most thoroughly documented.

Poleward-Propagating Angular Momentum Perturbations Induced by Zonally Symmetric Heat Sources in the Tropics

Abstract A series of experiments has been performed using an idealized model of the global atmosphere to study the role eddies play in communicating changes in the zonal mean state between the Tropics and extratropics. When an oscillatory heating perturbation centered about the equator is imposed, the author found a poleward-propagating zonal wind anomaly emanating from the Tropics into the midlatitudes when the heat source oscillates with a period of around 25–100 days. At higher frequency, most of the zonal wind perturbation is confined within the Tropics, while at lower frequency, the main signal occurs in the midlatitudes. The angular momentum budget and Eliassen–Palm cross sections have been examined. The results suggest that eddies act to communicate changes in the Tropics into the midlatitudes in at least two ways. First, changes in zonal mean zonal wind in the Tropics lead to a shift in the eddy angular momentum divergence pattern. Second, heating in the Tropics changes the temperature gradients b...

Mean dynamical characteristics of the Asian summer monsoon with a global analysis ? Forecast system

The dynamical characteristics of Asian summer monsoon are examined with a global spectral model. In addition to the seasonal circulation features, the large scale budgets of kinetic energy, vorticity and angular momentum are examined making use of mean analysis and forecast fields (upto day 5) for summer season comprising June, July and August, (JJA) 1994. Apart from elucidating the systematic errors over the monsoon region, the study expounded the influence of these errors on associated dynamics. The significant errors in the low level flow (850 hPa) evince (i) weakening of south easterly trades and cross equatorial flow into the Northern Hemisphere and (ii) weakening of westerly flow over the North Indian Ocean. Similarly, in the upper level flow (200 hPa) they indicate (i) weakening of Tibetan anti-cyclone and (ii) reduction of return flow into the Southern Hemisphere. The balance requirements in the mean analysis as well as forecast fields are fairly in agreement with the observed over the summer monsoon. The monsoon domain is discerned as the source region of kinetic energy and vorticity. Both are produced in the monsoon region and transported horizontally across. The model forecasts fail to retain the analyzed atmospheric variability in terms of mean as well as transient circulations which is revealed by kinetic energy budget. This is further corroborated by vorticity and angular momentum budgets. It is noticed that the forecasts in all ranges produce feeble monsoon circulation which weakens considerably with increase in the forecast period.

The poleward propagation of atmospheric angular momentum with a 30–60-day time scale

Abstract The existence of the intraseasonal variation of relative atmospheric angular momentum and the poleward propagation of this physical quantity by the intraseasonal mode of atmospheric circulation have been amply demonstrated in previous studies. However, the temporal relationship between the intraseasonal variation and poleward propagation is not well understood and the possible mechanism causing the poleward propagation is unknown. Analyzing the 15-year (1979–1993) upper-air data of the National Meteorological Center (currently the National Centers for Environmental Prediction), we explored these two intriguing issues related to atmospheric angular momentum via case-study analyses. The major findings are as follows: 1. 1. The maximum (minimum) 30–60-day globally integrated atmospheric angular momentum occurs when the positive (negative) angular momentum anomalies of a 30–60-day cycle appear in the tropics-subtropics and those of the previous 30–60-day cycle propagate to the northern and southern midlatitudes. 2. 2. The eastward propagation of the 30–60-day global divergent circulation induces a 30–60-day flip-flop oscillation in the meridional circulation which in turn results in a similar alternation in the angular momentum tendency caused by the Coriolis torque. It was inferred from the zonal-mean angular momentum budget analysis that the 30–60-day variation of atmospheric angular momentum and its poleward propagation are results of the 30–60-day variation of the aforementioned momentum tendency.

The phase difference between length of day and atmospheric angular momentum at subannual frequencies and the possible role of core‐mantle coupling

We examine discrepancies in the angular momentum budget of the Earth on subannual timescales. We find that for signals with long periods (> 30 days) the phase of the length of day (ΔLOD) significantly leads that of the atmospheric angular momentum (AAM). The discrepancy has an amplitude of ≃ 15% of the observed AAM at periods of around 100 days. We show that if changes in the ΔLOD are driven by the atmosphere, then this is diagnostic either of the importance of the oceans or of dynamical coupling between the core and mantle for these frequencies. We find that a simple model of core‐mantle coupling can cause a phase lead of ΔLOD of the correct magnitude. We attempt to fit the transfer function with a simple three‐layer model of the Earth, treating the core as a rotating solid body coupled to the mantle by a specified function. Although our simple model can supply sufficient phase lead of the ΔLOD, the fit to the frequency dependence is poor and it can not fit the magnitude of the transfer function. Nevertheless, this suggests that core‐mantle coupling is a plausible explanation of the observed phase difference. Better fits might be obtained with more realistic models of the core.