Atmospheric Angular Momentum Data Research Articles

Short-term prediction of UT1-UTC and LOD via Dynamic Mode Decomposition and combination of least-squares and vector autoregressive model

Abstract This study presents a short-term forecast of UT1-UTC and LOD using two methods, i.e. Dynamic Mode Decomposition (DMD) and combination of Least-Squares and Vector Autoregression (LS+VAR). The prediction experiments were performed separately for yearly time spans, 2018-2022. The prediction procedure started on January 1 and ended on December 31, with 7-day shifts between subsequent 30-day forecasts. Atmospheric Angular Momentum data (AAM) were used as an auxiliary time series to potentially improve the prediction accuracy of UT1-UTC and LOD in LS+VAR procedure. An experiment was also conducted with and without elimination of effect of zonal tides from UT1-UTC and LOD time series. Two approaches to using the best steering parameters for the methods were applied:. First, an adaptive approach, which observes the rule that before every single forecast, a preliminary one must be performed on the pre-selected sets of parameters, and the one with the smallest prediction error is then used for the final prediction; and second, an averaged approach, whereby several forecasts are made with different sets of parameters (the same parameters as in adaptive approach) and the final values are calculated as the averages of these predictions. Depending on the method and data combination mean absolute prediction errors (MAPE) for UT1-UTC vary from 0.63 ms to 1.43ms for the 10th day and from 3.07 ms to 8.05ms for the 30th day of the forecast. Corresponding values for LOD vary from 0.110 ms to 0.245 ms for the 10th day and from 0.148 ms to 0.325 ms for the 30th day.

A comparison of the interannual variability in atmospheric angular momentum and length‐of‐day using multiple reanalysis data sets

This study performs an intercomparison of the interannual variability of atmospheric angular momentum (AAM) in eight reanalysis data sets for the post‐1979 era. The AAM data are further cross validated with the independent observation of length‐of‐day (LOD). The intercomparison reveals a close agreement among almost all reanalysis data sets, except that the AAM computed from the 20th Century Reanalysis (20CR) has a noticeably lower correlation with LOD and with the AAM from other data sets. This reduced correlation is related to the absence of coherent low‐frequency variability, notably the Quasi‐biennial Oscillation, in the stratospheric zonal wind in 20CR. If the upper‐level zonal wind in 20CR is replaced by its counterpart from a different reanalysis data set, a higher value of the correlation is restored. The correlation between the AAM and the Nino3.4 index of tropical Pacific SST is also computed for the reanalysis data sets. In this case, a close agreement is found among all, including 20CR, data sets. This indicates that the upward influence of SST on the tropospheric circulation is well captured by the data assimilation system of 20CR, which only explicitly incorporated the surface observations. This study demonstrates the overall close agreement in the interannual variability of AAM among the reanalysis data sets. This finding also reinforces the view expressed in a recent work by the authors that the most significant discrepancies among the reanalysis data sets are in the long term mean and long‐term trend.

Atmospheric excitation of polar motion

The polar motion excited by the fluctuation of global atmospheric angular momentum (AAM) is investigated. Based on the global AAM data, numerical results demonstrate that the fluctuation of AAM can excite the seasonal wobbles (e.g., the 18-month wobble) and the Chandler wobble, which agree well with previous studies. In addition, by filtering the dominant low frequency components, some distinct polar wobbles corresponding to some great diurnal and semi-diurnal atmospheric tides are found.

Improved near-term Earth rotation predictions using atmospheric angular momentum analysis and forecasts

Abstract Predicted values of atmospheric angular momentum (AAM) from the U.S. National Centers for Environmental Prediction (NCEP) were introduced into the International Earth Rotation and Reference Systems Service (IERS) Bulletin A (rapid service/prediction of Earth orientation) combination during 2000 in an effort to improve the near-term universal time–coordinated universal time (UT1–UTC) predictions. In this approach, only the atmospheric contributions to the excitation of UT1 variations were included and contributions from other sources, such as the oceans, were neglected. However, we observed that using this approach the AAM inputs sometimes degraded the UT1 predictions as much as they helped and suspended their use in early 2001 for re-evaluation. This re-evaluation resulted in a greater appreciation of the systematic differences between the AAM and UT1R series as well as suggests that, in the actual Earth system, the oceans balance some of the atmospheric variability on specific time scales between 2 and 15 days. Since near-real time oceanic angular momentum information is currently not available, an improved approach for assimilating AAM data products was developed. These improvements include the use of both pressure and wind AAM terms, use of the previously unavailable AAM analysis data at the 24-h epoch for the latest AAM analysis file, smoothing of the AAM-based Length of day (LOD) to reduce sub-diurnal variability before integrating to UT1R, and removal of a best-fit sinusoid from the AAM UT1R time series. The new procedure reduces the effects of systematic trends (both periodic and linear) that do not appear to be present in actual UT1R variability. Retrospective studies indicate that including this new AAM-derived series may reduce UT1R prediction errors by ∼41% at 5 days into the future. Consequently, AAM-derived estimates of UT1R were restored to IERS Bulletin A starting in the 7 August 2001 issue. Comparisons made after the addition of UTAAM into the Bulletin A UT1–UTC combination solution indicate a better than 50% reduction in prediction errors at 5 and 10 days into the future and an ∼1 ms improvement at 30 days into the future.

Nontidal oceanic excitation of nutation and diurnal/semidiurnal polar motion revisited

A new 7.5‐yearlong time series of hourly estimates of nontidal ocean angular momentum, representing signals forced by 6‐hourly surface atmospheric pressure and winds including those forced by the atmospheric tides, is used to assess the influence of a dynamic ocean on nutation and on diurnal and semidiurnal polar motions. Using available atmospheric angular momentum data, we estimate the total excitation by the dynamically coupled atmosphere‐ocean system and compare it to that of the atmosphere alone. In case of the retrograde diurnal excitation, significant contributions are found for the retrograde annual, prograde annual, and prograde semiannual nutations and for the constant offset of the celestial pole. For the prograde annual nutation corresponding to the retrograde S1 component of excitation, the atmosphere‐ocean model does not improve the agreement with VLBI observations beyond that obtained using the atmosphere model alone. We also considered separately an irregular contribution to nutation, which can excite both the free core nutation signal and other broadband variability. The irregular component of the atmosphere‐ocean model is found to be significantly correlated with that derived from the atmosphere model. For the prograde diurnal component of excitation, which contributes to polar motion, the only nonnegligible effect (∼9 microarc seconds (μas)) is associated with the prograde S1 harmonic. The only significant component of the semidiurnal excitation found is the elliptical oscillation S2 in polar motion with major semiaxis of 9 μas, but this estimate is uncertain because the 6‐hourly atmospheric fields used to force the ocean do not properly resolve semidiurnal signals. In any case, this contribution is much smaller than that from the S2 ocean gravitational tide.

Oceanic excitation of the chandler wobble

We estimate the oceanic contribution to the excitation of the Chandler wobble using an 11-year time series of ocean angular momentum. The time domain comparison of this series with the non-atmospheric excitation inferred from the polar motion and atmospheric angular momentum data shows a high correlation over most of the period of 1985 to 1996 when they overlap. The frequency domain comparison yields a high coherence in the vicinity of the resonant Chandler frequency. In terms of the free wobble excitation power, we compute the ocean contribution to be 11.9 mas 2/cpy, which is approximately the same amount as supplied by the atmosphere. The combined action of the atmosphere and oceans provides about 80% of the power needed to maintain the wobble observed during 1985 to 1996, with the remaining deficit being at the level of one standard deviation of the excitation power estimated from a 100-year record of polar motion data.

Wavelet analysis of interannual LOD, AAM, and ENSO: 1997-98 El Niño and 1998-99 La Niña signals

On the basis of the data series of the length of day (LOD), the atmospheric angular momentum (AAM) and the Southern Oscillation Index (SOI) for January 1970–June 1999, the relationship among Interannual LOD, AAM, and the EL Nino/Southern Oscillation (ENSO) is analyzed by the wavelet transform method. The results suggest that they have similar time-varying spectral structures. The signals of 1997–98 El Nino and 1998–99 La Nina events can be detected from the LOD or AAM data.

Contribution of new AAM data source to δLOD excitation

Data sets of the changes of the length of day (ΔLOD) measured by space geodetic techniques and of the atmospheric angular momentum (AAM) derived from global meteorological data by the National Meteorological Center (NMC) and the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) are used to reanalyze and study the excitations of ΔLOD, and to examine and compare the contribution of each AAM series to ΔLOD. The main results are as follows.

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

Seasonal variations in length of day and atmospheric angular momentum

The seasonal variations of the Earth’s rotation are still not sufficiently well explained in terms of their causes. Quantitative estimates of the variability of the oscillations in length of day (LOD) and atmospheric angular momentum (AAM) have been applied very seldom. Therefore, the problem is re-examined.  In particular, the axial AAM component labelled χ3 is related to changes in LOD. For this reason, the following series of data at one-day intervals is used in this study: (a) LOD from the series EOP (IERS) C04 from 1962 to 1996, (b) χ3 (W ), χ3(P) and χ3 (P + IB) from the series AAM (NMC) from 1976 to 1995 and (c) χ3 (W ), χ3 (P) and χ3 (P + IB) from the series AAM (JMA) from 1983 to 1995. Here, χ3 (W ) is the wind term, χ3 (P) the pressure term and χ3 (P + IB) the pressure term with inverted-barometer response.  First, the seasonal oscillations are separated from the various time-series by filtering. To illustrate their characteristics, the amplitudes, periods and phases of the annual and semi-annual oscillations are then derived and presented in terms of their temporal variability. The discrepancies between the magnitudes of the annual and semi-annual components of LOD without the tidal effects Sa and without Ssa and of χ3 (W ), χ3(W ) + χ3 (P) and χ3 (W ) + χ3 (P + IB) show to what extent uncertainties are present in the data, which portions of AAM originate from χ3(W ), χ3 (P) and χ3 (P + IB), and whether another excitation source contributes to seasonal LOD variations. At the annual frequency, the wind term from the upper stratosphere that is neglected is evidently responsible for the imbalance between the LOD and AAM data. However, at the semi-annual frequency, the discrepancy is not fully explained by the missing stratospheric wind term, and a contribution from the global surface water redistribution is likely.

Regional Sources of Mountain Torque Variability and High-Frequency Fluctuations in Atmospheric Angular Momentum

Abstract The sources of high-frequency (⩽14 day) fluctuations in global atmospheric angular momentum (AAM) are investigated using several years of surface torque and AAM data. The midlatitude mountain torque associated with the Rockies, Himalayas, and Andes is found to be responsible for much of the high-frequency fluctuations in AAM, whereas the mountain torque in the Tropics and polar regions as well as the friction torque play a much lesser role on these timescales. A maximum in the high-frequency mountain torque variance occurs during the cool season of each hemisphere, though the Northern Hemisphere maximum substantially exceeds that of the Southern. This relationship indicates the seasonal role played by each hemisphere in the high-frequency fluctuations of global AAM. A case study reveals that surface pressure changes near the Rockies and Himalayas produced by mobile synoptic-scale systems as they traversed these mountains contributed to a large fluctuation in mountain torque and a notable high-fre...

Angular momentum exchange among the solid Earth, atmosphere, and oceans: A case study of the 1982–1983 El Niño event

The 1982–1983 El Nino/Southern Oscillation (ENSO) event was accompanied by the largest interannual variation in the Earth's rotation rate on record. In this study we demonstrate that atmospheric forcing was the dominant cause for this rotational anomaly, with atmospheric angular momentum (AAM) integrated from 1000 to 1 mbar (troposphere plus stratosphere) accounting for up to 92% of the interannual variance in the length of day (LOD). Winds between 100 and 1 mbar contributed nearly 20% of the variance explained, indicating that the stratosphere can play a significant role in the Earth's angular momentum budget on interannual time scales. Examination of LOD, AAM, and Southern Oscillation Index (SOI) data for a 15‐year span surrounding the 1982–1983 event suggests that the strong rotational response resulted from constructive interference between the low‐frequency (∼4–6 year) and quasi‐biennial (∼2–3 year) components of the ENSO phenomenon, as well as the stratospheric Quasi‐Biennial Oscillation (QBO). Sources of the remaining LOD discrepancy (∼55 and 64 μs rms residual for the European Centre for Medium‐Range Forecasting (EC) and U.S. National Meteorological Center (NMC) analyses) are explored; noise and systematic errors in the AAM data are estimated to contribute 18 and 33 μs, respectively, leaving a residual (rms) of 40 (52) μs unaccounted for by the EC (NMC) analysis. Oceanic angular momentum contributions (both moment of inertia changes associated with baroclinic waves and motion terms) are shown to be candidates in closing the interannual axial angular momentum budget.

Interannual variations in the Earth's polar motion for 1963–1991: Comparison with atmospheric angular momentum over 1980–1991

Analysis of interannual variations in polar motion for the period 1963–1991 reveals two prominent components, a quasi biennial component and a lower frequency component of ∼ 4–6 yr period. These frequencies, previously reported in the length of day, are possibly related to the El Niño‐Southern Oscillation and Quasi Biennial Oscillation of the coupled ocean‐atmosphere system. Over the overlapping period (1980–1991), we compared the geodetically‐derived polar motion excitation with equatorial atmospheric angular momentum (AAM). At the biennial frequency polar motion and AAM are well correlated, when the pressure excitation is estimated assuming a non‐inverted barometer response of the oceans. However AAM alone is unable to explain the total observed polar motion. An oceanic contribution associated with the dynamical response of the oceans to pressure‐derived wind stress is a likely candidate to explain the missing signal. At longer periods (4–6‐yr), the east components of polar motion and AAM vary coherently. No clear conclusion can be drawn however for the north components because of large uncertainties reported in the corresponding AAM data at low frequency.

Measurement of diurnal and semidiurnal rotational variations and tidal parameters of Earth

We discuss the determination of diurnal and semidiurnal variations in the rotation rate and the direction of rotation axis of Earth from the analysis of 8 years of very long baseline interferometry (VLBI) data. This analysis clearly show that these variations are largely periodic and tidally driven; that is, the periods of the variations correspond to the periods of the largest lunar and solar tides. For rotation rate variations, expressed in terms of changes in universal time (UT), the tidal lines with the largest observed signals are O1 (amplitude 23.5 microseconds in time (μs), period 25.82 solar hours); K1 (18.9 μs, 23.93 hours); M2 (17.9 μs, 12.54 hours); and S2 (8.6 μs, 12.00 hours). For variations in the direction of the rotation axis (polar motion), significant signals exist in the retrograde semidiurnal band at the M2 and S2 tides (amplitudes 265 and 119 microarc seconds (μas), respectively); the prograde diurnal band at the O1, K1, and P1 tides (amplitudes 199,152, and 60 μas, respectively); and the prograde semidiurnal band at the M2 and K2 tides (amplitudes 58 and 39 μas, respectively). Variations in the retrograde diurnal band are represented by corrections to the nutations of Earth's body axes, and our estimates here are consistent with previous estimates except that a previously noted discrepancy in the 13.66‐day nutation (corresponding to the O1 tide) is largely removed in this new analysis. We estimate that the standard deviations of these estimates are 1.0 μs for the UTl variations and 14–16 μas for the polar motion terms. These uncertainties correspond to surface displacements of ∼0.5 mm. From the analysis of atmospheric angular momentum data we conclude that variations in UTl excited by the atmosphere with subdaily periods are small (∼1 μs). We find that the average radial tidal displacements of the VLBI sites in the diurnal band are largely consistent with known deficiencies in current tidal models, i.e., deficiencies of up to 0.9 mm in the treatment of the free core nutation resonance. In the semidiurnal band, our analysis yields estimates of the second‐degree harmonic radial Love number h2 at the M2 tide of 0.604+i0.005±0.002. The most likely explanation for the rotational variations are the effects of ocean tides, but there may also be some contributions from atmospheric tides, the effects of triaxiality of Earth, and the equatorial second‐degree‐harmonic components of the core‐mantle boundary.

The Earth's Angular Momentum Budget on Subseasonal Time Scales

Irregular length of day (LOD) fluctuations on time scales of less than a few years are largely produced by atmospheric torques on the underlying planet. Significant coherence is found between the respective time series of LOD and atmospheric angular momentum (AAM) determinations at periods down to 8 days, with lack of coherence at shorter periods caused by the declining signal-to-measurement noise ratios of both data types. Refinements to the currently accepted model of tidal Earth rotation variations are required, incorporating in particular the nonequilibrium effect of the oceans. The remaining discrepancies between LOD and AAM in the 100- to 10-day period range may be due to either a common error in the AAM data sets from different meteorological centers, or another component of the angular momentum budget.

Extratropical aspects of the 40–50 day oscillation in length‐of‐day and atmospheric angular momentum

Fluctuations in Earth rotation over time scales of 2 years or less are dominated by atmospheric effects; spectral analyses of length‐of‐day (LOD) and atmospheric angular momentum (AAM) data show significantly increased variability in the 40–50 day band. LOD and AAM fluctuations on the 40–50 day time scale have previously been linked to tropical, convectively driven waves of the type first described by Madden and Julian (1971) (referred to as MJ hereinafter). A significant spectral peak centered at 42 days has also been found, however, in the AAM of a 3‐year (1120‐day) perpetual‐January simulation of the global atmosphere, performed using a version of the University of California at Los Angeles (UCLA) general circulation model (GCM) which does not give rise to MJ oscillations in the tropics. In the present work the 40–50 day oscillation is studied using the 12‐year overlap between two records: (1) AAM data, compiled from the National Meteorological Center (NMC); and (2) LOD variation from the Jet Propulsion Laboratory Kalman‐filtered Earth rotation series. We analyze the NMC records by latitude belts, in light of the UCLA GCM results, in order to identify possibly distinct sources of the AAM oscillation in the mid‐latitudes and the tropics. Results suggest that two intraseasonal oscillations exist in the Earth‐atmosphere system: a tropical, 50‐day oscillation associated with the convectively driven MJ wave and a mid‐latitude, 40‐day oscillation associated with the interaction of nonzonal flow with topography.

Adaptive filtering and maximum entropy spectra with application to changes in atmospheric angular momentum

The spectral resolution and statistical significance of a harmonic analysis obtained by low‐order maximum entropy methods (MEM) can be improved by subjecting the data to an adaptive filter. This adaptive filter consists of projecting the data onto the leading temporal empirical orthogonal functions obtained from singular spectrum analysis (SSA). The combined SSA‐MEM method is applied both to a synthetic time series and a time series of atmospheric angular momentum (AAM) data. The procedure is very effective when the background noise is white and less so when the background noise is red. The latter case obtains in the AAM data. Nevertheless, we detect reliable evidence for intraseasonal and interannual oscillations in AAM. The interannual periods include a quasi‐biennial one and a low‐frequency one, of 5 years, both related to the El Niño/Southern Oscillation. In the intraseasonal band, separate oscillations of about 48.5 and 51 days are ascertained.

A seasonal budget of the Earth's axial angular momentum

The seasonal variation of the earth's axial angular momentum budget is discussed with an error on the order of a few percent. The budget is based on the core‐mantle decoupling (CMD) hypothesis, using the length of day (LOD) data observed astronomically by the International Radio Interferometry Surveying and the atmospheric angular momentum data calculated from the forecast/analysis data set for numerical weather prediction of the Japan Meteorological Agency. The atmospheric relative angular momentum changes due to zonal wind account for an additional 23 % contribution over the annual budget. However, this is counterbalanced by the effects of the redistributions of air and water masses. Namely, about 16 % is accounted for by the redistribution of air mass, and remained about 7 % agrees with the contribution from surface water storage estimate on continents by Chao & O'Connor [1988]. These facts demonstrate a confirmation of the CMD hypothesis on time scale of a year. At the semi‐annual period, however, there still is a shortage of about 6 % in atmospheric and hydrospheric contributions to the budget.

A damped oscillator model of the 50-day oscillation in the length of the day

Abstract The changes in the length of day with periods near 50 days appear to be driven by resonance in the atmospheric angular momentum. We use a damped harmonic oscillator model, characterized by a resonance period and a Q -factor, to describe this behaviour. Estimates of the period and Q have been obtained by fitting autoregressive (AR) and autoregressive moving average (ARMA) time series models to the length of day and atmospheric angular momentum data. Estimates of the period near 50 days were obtained, but a precise value is probably unobtainable because the low Q value indicates that the degree of resonance is slight.

Atmospheric angular momentum and its relation to the length of day

The U.S. Naval Observatory is responsible for the determination and prediction of UT1-UTC. An investigation was begun to determine if atmospheric angular momentum (AAM) data could be useful in the National Earth Orientation Service (NEOS) combined solution and in the prediction of UT1-UTC. The investigation found AAM data to be useful possibly in the combined solution, but predictions of UT1-UTC were adversely affected when predictions of AAM data were introduced.