Oceanic excitation of daily to seasonal signals in Earth rotation: results from a constant-density numerical model

Transcription

1 Geophys. J. Int. (1997) 130,69-7 Oceanic excitation of daily to seasonal signals in Earth rotation: results from a constant-density numerical model Rui M. Ponte Atmospheric and Environmental Research, Inc.. 80 hfemorial Drive, Cumhridggr MA , US.. ponte(@aer.com Accepted 1997 April. Received 1997 April ; in original form 1997 February 6 1 INTRODUCTION In recent years, a significant effort has been devoted to determine the sources of length of day (LOD) and polar motion (PM) excitation, on time scales from days to seasons. A review of relevant results can be found in Wahr (1988), Hide & Dickey (1991). Rosen (1993), Wilson (1995) and references therein. For our purposes, a summary of findings pertaining to scales from several days to seasons will suffice. The role of variable zonal winds as the primary driving source for seasonal fluctuations in LOD is well established. Residuals in seasonal LOD excitation, after accounting for wind effects, have amplitudes of only a few per cent of the seasonal cycle in LOD, and are at the. noise level of present atmospheric wind data sets. At subseasonal time scales, fluctuations in atmospheric zonal winds and the moment of inertia appear to have enough power to excite observed changes in LOD, but the coherence between atmospheric excitation and LOD generally decreases with period and drops below significance levels at periods shorter than one or two weeks, approximately (Rosen, Salstein & Wood 1990; Dickey et al. 1992). Compared to that for LOD, knowledge about the driving mechanisms for PM is much less certain. even at seasonal time SUMMARY Velocity and mass fields from a constant-density, near-global ocean model, driven with observed twice-daily surface wind stresses and atmospheric pressures for the period October 1992-September 1993, are used to calculate oceanic excitation functions for the length of day (LOD) and for polar motion (PM), and results are analysed as a function of the frequency band. Variable currents and mass redistributions are both important in determining oceanic excitation functions. For bands with periods longer than one month, wind-driven variability is the primary cause of oceanic excitation signals. At higher frequency bands, larger deviations from the inverted barometer response occur, and pressure-driven signals contribute more significantly to the variance in the excitation functions. Oceanic LOD excitation is generally small compared to that of the atmosphere, except for the 2-10 day band. At these scales, adding oceanic to atmospheric excitation series does not lead to better agreement with the observed LOD, although this result may be related to data quality issues. With regard to the excitation of PM, the ocean is in general as important as the atmosphere at most time scales. Combined oceanic and atmospheric excitation series compare visibly better with geodetic series than do atmospheric series alone, pointing to the ocean as a source of measurable signals in PM. Key words: Earth's rotation, oceanic currents, oceanic models, oceans, sea-level. scales. A link between atmospheric mass shifts and PM has been established for both seasonal and more rapid time scales (Eubanks et al. 1988; Chao & Au 1991; Chao 1993; Kuehne, Johnson & Wilson 1993), and Gross & Lindqwister (1992) found that winds and mass shifts could largely explain PM during a short intensive observation campaign in early However, the role of atmospheric mass shifts, or equivalently changes in surface pressure, pa, over the ocean is not well understood, as it depends on whether the ocean reacts dynamically to those changes or in a simple isostatic manner, as an inverted barometer (IB). In the latter case, the combined mass of the atmosphere and ocean does not change locally (e.g. Ponte, Salstein & Rosen 1991) and the variance of the effective atmospheric time-series is generally less than that in geodetic series, suggesting other important sources of excitation (e.g. Eubanks et ul. 1988). Whereas atmospheric mechanisms for excitation of variable LOD and PM have been amply investigated, variability in oceanic angular momentum is poorly known, and in the absence of global ocean observations its calculation has relied mostly on output from dynamical models. With the exception of tidal studies, almost invariably the focus has been on the seasonal cycle (e.g. Wilson & Haubrich 1976; Wahr 1983; Q 1997 RAS 69

2 70 R. M. Ponte Brosche et al. 1990; Ponte & Rosen 199; Bryan 1997), basically pointing to small amplitudes of oceanic LOD and PM excitation compared to that of the atmosphere at these time scales. Other ongoing studies, however, suggest a possibly important role of the ocean in the excitation of seasonal PM (Bryan & Smith 1995; Rosen, Salstein & Ponte 1996). At subseasonal time scales, the role of the oceans in the planet's angular momentum budget may be more relevant (Eubanks et al. 1988; Rosen et al. 1990), but besides a crude attempt by Ponte et al. (1991), estimates of the amplitude of subseasonal LOD and PM excitation by the oceans, related to either wind or pressure forcing, are currently missing. To begin filling in this gap, here we use approximately one year of available output from the constant-density model of Gaspar & Ponte (1997) and evaluate the oceanic excitation functions for both, LOD and PM. Output obtained with both surface wind stress and pressure forcing permits an evaluation of the efficiency of the two mechanisms in driving oceanic excitation signals. Effects of both variable currents and mass fields can also be examined. Given the simplicity of the ocean model and the relatively short period studied, the qualitative aspects of the analysis are emphasized. The current effort leads, nevertheless, to significant new insights about the role of the ocean in driving fluctuations in the Earth's rotation. 2 DATA AND METHODOLOGY To calculate the excitation of LOD and PM due to variability in the motion and mass fields of the oceans, we follow the formulation of Barnes et al. ( 1983), originally derived for the atmosphere. Briefly, there are three non-dimensional excitation functions, (xl, xz) and x3, which relate to angular momentum components along the two equatorial axes and the polar axis and thus represent PM and LOD excitation, respectively. Each x can be separated into excitation functions associated with variable velocity and mass fields, denoted here by superscripts V and P, respectively (V stands for velocity and is adopted here as a general notation applicable to both atmosphere and oceans, instead of the conventional atmospheric notation of W for winds; P conventionally stands for pressure and relates to either atmospheric surface or oceanic bottom pressure). To evaluate the oceanic x functions, we use estimates of velocity and bottom pressure fields available from the constantdensity model runs of Gaspar & Ponte (1997). These runs were originally intended to help in the understanding of the relation between sea level and pa as observed by the TOPEX/ Poseidon altimeter. The correlations between wind- and pressure-driven sea-level signals in the model were found to explain, within measurement errors, the IB departures inferred from the altimeter data on the basis of simple regression analysis, indicating the ability of the model to represent the statistical relations between sea level and pa, particularly at subseasonal time scales. The assumption of constant density greatly simplifies the modelling problem, leading to depth-independent flow fields and to a direct correspondence between bottom pressure and sea-level fluctuations. One may think of such a model as representing the evolution of vertically averaged fields, which are the important fields for evaluating x functions. As discussed for example by Hasselman ( 1982), the full equations of motion can be separated into a vertically averaged (barotropic) system and a residual, depth-dependent ( baroclinic) system. The two systems are generally coupled, but if the coupling is weak (see again Hasselman 1982), they can be treated independently. In this study, we assume that the coupling between barotropic and baroclinic systems is negligible, in which case the vertically averaged fields of interest to us are essentially given by the constant-density model used here. The weak-coupling assumption is widely used in oceanographic studies (Gill 1982) because it provides a good qualitative description of oceanic variability in general. Theoretical and numerical studies also suggest that barotropic dynamics capture the essence of atmospherically forced large-scale variability at middle and high latitudes (Willebrand, Philander & Pacanowski 1980 Chao & Fu 1995). Thus, the constant-density model should provide a good qualitative estimate for the vertically averaged fields and the oceanic xs we want to calculate. The ensuing comparisons with geodetic data support this assertion. Modelled flow and sea-level fields from the output of runs forced by twice-daily surface winds and pressure from the US National Centers for Environmental Prediction (NCEP) are used to estimate x functions. Details on the model are provided in Gaspar & Ponte (1997) and references therein. The model conserves total mass (or equivalently volume). For the available runs, integration started from a resting, IB solution and was carried out for the period 1992 September September 20. The first month's output is excluded from the analysis to avoid effects of transients during the spin-up process. Given typical barotropic adjustment times of a few days, one month is sufficient for the model ocean to forget initial conditions. Integrals over the ocean volume, involved in the calculation of x functions, are approximated as simple sums. The calculation of xp needs some discussion. One can write the oceanic bottom pressure as P =gp(h + i) + Par (1) where H is the oceanic depth, [ is sea level, g = 9.8 m s-' is the acceleration of gravity and p = lo3 kg m-3 is a typical density of water. Such a value of p corresponds to the combined ocean-atmosphere mass over ocean-covered areas. For our purposes, we would like to separate oceanic and atmospheric contributions to the excitation. The partition is somewhat arbitrary, but given the general tendency for an IB response to pa (Gaspar & Ponte 1997), we assume without loss of generality that i = Fb + i' (that is an IB term plus dynamical signals i' related to pressure, wind or any other forcing), where as usual (Ponte et al. 1991), and P, is the averaged atmospheric pressure over the global oceans. Then, ( 1 ) reduces to p =gpw + i') + P,. (3) The effects of variable P, are taken to represent atmospheric excitation; these are commonly included in estimates of atmospheric xs based on the IB assumption (Salstein et al. 1993). The relevant oceanic contribution to the excitation of PM and LOD changes is contained in ('; H is time-invariant and does not matter here. We use, therefore, p = gpi' when calculating oceanic xp. To compare with oceanic xs, atmospherically and geodetically derived excitation functions, denoted xa and xg, respectively, are also used. Time-series of xa are those pro RAS, GJI 130,69-7

3 ~ ~~ ~ ~ ~ ~ ~ ~ ~ vided routinely by the Sub-bureau for Atmospheric Angular Momentum of the International Earth Rotation Service (IERS) and based on the NCEP fields (Salstein et al. 1993). Winds up to 50 mb pressure level are included in xv, and unless specified otherwise, xp includes the basic IB assumption described by Salstein et al. (1993). Thus, apart from small effects due to the different ocean-land masks in the ocean model and the NCEP model, the sum xp + xp(*' represents the excitation due to mass shifts in the atmosphere-ocean system. For xy we use daily time-series described in Salstein et al. ( 1993); xf,2 are calculated from the EOP C 0 pole positions reported by IERS (1995) using the method of Wilson (1985). Daily pole positions are provided, but smoothing removes all power at periods of three days and shorter and retains all power only at periods of15 days and longer (Gambis 1995, private communication). Given that the various excitation functions have different time resolutions and smoothing at the high-frequency end of the spectrum, comparative analyses are restricted to periods longer than 2 and 10 days for x3 and (xl, x2), respectively. Notice, however, that xfz signals at periods between 10 and 15 days may be somewhat attenuated by the smoothing applied to the original pole-position data. 3 OCEANIC EXCITATION OF LOD Time-series of x;.' and their sum ( x3) were calculated twice daily using output from model runs forced with both winds and pressure, and only pressure. Table 1 provides the variance for each oceanic, atmospheric and geodetic x3 function for four different frequency bands: seasonal (3 months-1 year), intraseasonal (1-3 months), submonthly (10 days-1 month), and daily (2-10 days) bands. The variance is calculated by summing the squared amplitudes of the Fourier harmonics contained in each band-3, 8, 23 and 11 harmonics for the seasonal, intraseasonal, submonthly and daily bands, respectively. Comparison of results from the two runs with different forcing clearly shows the dominant effect of wind driving at seasonal and intraseasonal bands, with pressure driving becoming more comparable at submonthly and daily bands. These results are expected, given the predominantly IB response of the ocean to pa at periods longer than a few days and the comparable importance of winds and pressure in driving dynamical signals in the ocean at short periods (Ponte 1993, 199). Comparing x: and x: with x3 shows that both currents and bottom pressure fluctuations contribute significant variance to the oceanic excitation, with a tendency for xy (xi) to be more important at high (low) frequencies. Table 1. Variance of oceanic, atmospheric and geodetic x3 functions as a function of frequency band. Oceanic values in the second line for each band are calculated from the output of run with pressure forcing only. Variance (x lo-'') Bands x! x: x3 x: x? xy-x: 3 mo-1 yr mo-3 mo d-1 mo d-10 d RAS, GJI 130, 69-7 Oceanic excitation of Earth rotation 71 At seasonal, intraseasonal and submonthly bands the variance in x3 is smaller than that in either x$ or x$ by one or two orders of magnitude, confirming the expected small oceanic LOD excitation, compared to the atmosphere. In addition, the variance in x3 is only 20 to 0 per cent of the variance in the residual series xy - xf. Excluding significant underestimation of the power in oceanic excitation, the corollary is that either other sources of excitation are important to explain those residuals, including stratospheric wind effects not considered here (Rosen et al j, or that the residuals are at the noise level of current observations (Dickey et al j. For the daily band, the variances in x3, x$ and x: are all comparable, with currents being most important to the variability in x3. The oceans and atmosphere are thus likely to contribute equally to the excitation of rapid fluctuations in LOD. The daily-band coherence amplitude between xy and either x3 or x$ is nevertheless quite small, and adding x3 to x$ does not increase the coherence with xf. These results are not surprising, given the expected lower signal-to-noise ratios in x$" functions (Dickey et al. 1992; Rosen 1993) and in atmospheric fields used to force the ocean model, at these high frequencies, and given the simplified ocean dynamics considered here. OCEANIC EXCITATION OF POLAR MOTION Table 2 shows the variance contained in the frequency bands previously defined for the xl,z functions related to PM. As for x3, currents and mass variability are both important contributors to oceanic excitation signals, and wind-driven signals dominate at periods longer than one month, with pressuredriven signals also becoming important at shorter periods. Comparison of the variance in x1,2 in Table 2 with respective atmospheric values indicates that, with the exception of the seasonal and intraseasonal bands for x2, the levels of excitation of PM are similar for the oceans and atmosphere. The potential role of oceanic excitation of seasonal PM (for xl) is in Table 2. Variance of oceanic, atmospheric and geodetic x1 and x2 (as in Table 1). Variance (x Bands x: x: X1 x: x? 3 mo-1 yr mo-3 mo d-1 mo d-10 d x: mo-1 yr x 10-7 Y mo-3 mo d-1 mo d-10 d

4 ~ Y,*' 72 R. M. Ponte agreement with other current work using more sophisticated ocean models (Bryan & Smith 1995; Rosen et ul. 1996). Over most bands, the level of contribution of both geophysical fluids to the observed excitation of PM remains uncertain, however, given the spread of values for the variances in oceanic and atmospheric series compared to the geodetic series in Table 2. Previous studies by Eubanks et ui. (1988) and others have noted the less-than-perfect agreement between atmospheric and geodetic x1,2 functions. A pertinent question is whether inclusion of the oceanic functions derived here leads to better agreement. Figs 1 and 2 (top and middle panels) display the comparison between time-series of x& and corresponding series for the atmosphere, and for the atmosphere and oceans combined. All time-series were filtered to remove variability at periods shorter than 10 days. Rather than addressing how well one can explain the geodetic records, we focus on the effects of including the ocean in the comparison with xg. Visual inspection of Figs 1 and 2 indicates that, when oceanic excitation is included, there is a substantial improvement, both in amplitude and timing of events, in the agreement with the observed x& series at given times: notice for example the variability between days 0 and 50 in xl, between days 200 and 20 in x2 or during the last month in both series. Overall, the correlations with the geodetic curves are still small, particularly for xl, but improve slightly from 0.38 to 0.1 and from 0.68 to 0.7 for x1 and x2, respectively, when oceanic signals are included. Coherence amplitudes and phases for the frequency bands previously defined are reported in Table 3. Results suggest that the oceans contribute coherent power to the geophysical excitation series. With the exception of the intraseasonal band for xl, coherence amplitudes are generally higher when the combined oceanic x, 'i,c.. XIC DAYS SINCE OCTOBEK 1, 1992 Figure 1. Time-series of xp (dotted line) on all panels and xi', xf+xl and x: calculated without the IB assumption (solid line) on the upper, middle and bottom panels, respectively. All series have been filtered to remove signals at periods shorter than 10 days. The correlation coefficients for each pair of curves are shown in the lower-right corner of the respective plot DAYS SINCE OCTOBEK 1, 1992 Figure 2. As for Fig. 1 but for time-series related to,y2. and atmospheric excitation is used. This is particularly true for the submonthly band, for which oceanic and atmospheric excitation levels are more comparable (see Table 2) and for which the larger bandwidth makes the results statistically more significant. In the absence of estimates for oceanic excitation, previous studies (e.g. Eubanks et ul. 1988) have compared observed PM with atmospheric excitation based on a rigid ocean response to pressure (that is atmospheric xp functions calculated with no IB assumption). For completeness, such a comparison is also provided in Figs 1 and 2 (bottom panel) and Table 3. Although the correspondence between some high-frequency signals seems to improve in places, the correlation between xg and xa (no IB) curves is worse than in the other two cases considered. The coherences in Table 3 show mixed results, with the use of xa (no IB) leading to larger coherence amplitudes than those obtained with xa (IB) at some bands. This behaviour seems counterintuitive given the expected validity of the IB assumption at these time scales. One possible explanation is that, because dynamic sea-level signals are generally correlated with pa (vandam & Wahr 1993; Ponte 199; Gaspar & Ponte 1997), and because oceanic currents are also related to pressure gradients implied by sea-level fields (e.g. Gill 1982), the use of xa (no IB) may capture some of the excitation related to dynamic oceanic effects. In any case, with the exception of the intraseasonal band for xl, use of xa (no IB) always leads to coherence amplitudes lower than those obtained when the effects of the dynamical ocean are included. 5 FINAL REMARKS In summary, the model results suggest that, in comparison with the atmosphere, the role of the oceans in LOD excitation cannot be neglected at periods shorter than 10 days, and at periods ranging from seasonal to daily in the case of PM. To capture the variability in oceanic x functions, one should RAS, GJI 130, 69-7

5 Oceanic excitation of Earth rotation 73 Table 3. Coherence amplitude and phase for a given pair of x, and x2 functions. Amplitudes given in bold face are significantly different than zero with 95 per cent confidence; significant levels are 0.88,0.59 and 0.36 for the seasonal, intraseasonal and submonthly bands, respectively, and based on the number of frequencies averaged in each band. Values in the second line for each band are based on atmospheric xp functions calculated without the IB assumption. (lit> rf, (xf' + x1,?if, (xf, xf) (ui + XZI u,", Rands Amp Phase Amp Phase Amp Phase Amp Phase 3 nro-1 yr mo-3 mo d-1 mo consider the effects of both currents and mass field fluctuations, forced either by winds at low frequencies or both winds and pressure at short periods. These findings stem from a nearly 1 yr case study with a simple ocean model and should be regarded in the proper context. Longer model runs, to permit better frequency resolution and statistics, are currently being pursued, in conjunction with the analysis of output from more complex ocean models. Despite the qualitative nature of our results, including the estimated x1,2 functions leads to an improved agreement between geophysical excitation and observed PM over what is achieved by solely using atmospheric excitation (either with or without the IB assumption), particularly for the submonthly band. The role of oceanic excitation at shorter periods is potentially more important, but the smoothed PM data prevented such an analysis, and in the case of LOD the coherence between xy and either x$, x3 or x$ + x3 is poor. Improving the agreement at these high frequencies may require better estimates for all x functions. For the oceanic xs, this will probably involve state-of-the-art ocean models, together with data assimilation, but given the present results, the prospects for firmly establishing the role of the ocean in the excitation of LOD and PM signals look promising. ACKNOWLEDGMENTS I. Fukumori (JPL), P. Nelson and K. Cady-Pereira (AER) helped with data sets and with numerical runs. Comments by two anonymous reviewers led to significant improvements in the manuscript. This work was supported by the NASA EOS project under grant NAGW-2615, with additional support from NASA contracts NASW-713 and NASW-731. Model runs were performed at the JPL Cray supercomputer, which is supported by the NASA Offices of Mission to Planet Earth, Aeronautics, and Space Science. REFERENCES Barnes, R.T.H., Hide, R., White, A.A. & Wilson, C.A., Atmospheric angular momentum fluctuations, length-of-day changes and polar motion, Proc. R. Soc. 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