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 Interannual length-of-day variations and ENSO indices such as the Southern Oscillation Index (SOI) and Nino 3.4 SST are well correlated as a consequence of angular momentum conservation. During an El Nino event, the westerly winds increase, which raises the atmospheric angular momentum (AAM); as a result, the solid Earth must slow down, which increases the duration of the day (length-of-day: LOD). However, a lag has been observed with the SOI and Nino 3.4 SST leading the LOD and AAM series by one–two months; to date no dynamical explanation has been offered. The dominant excitation mechanism of interannual LOD is the wind term, driven largely by thermal winds arising from the poleward gradient of tropical temperature (TT). We show that the TT gradient (TTG), which peaks 1–2 months after the Nino 3.4 SST anomaly, is the source of the thermal winds that drive the LOD anomaly and account for this well-known ENSO-Earth rotation lag.
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 Numerous papers have pointed out the robust correlation between the El Nino/Southern Oscillation (ENSO) and interannual variations in length-of-day [Rosen et al., 1984; Chao, 1988; Dickey et al., 1993, and references therein]. As studied for example by Mo et al. , this correlation arises because stronger (weaker) sub-tropical jet streams, concentrated in the upper troposphere (∼200 hPa) of both hemispheres, increase (decrease) the axial component of AAM during the mature phase of El Nino (La Nina) events, thereby causing LOD to increase (decrease) in order to conserve the total angular momentum of the Earth system. The increase in jet stream strength during El Nino arises from a general warming of the tropical troposphere associated with the transfer of latent and sensible heat from the equatorial Pacific ocean to the overlying atmosphere, causing geopotential heights and in particular the tropopause to become elevated at low latitudes, thereby increasing the poleward height gradient and geostrophic wind speeds [Reid and Gage, 1984].
 It has long been noted that changes in LOD tend to lag indices of the ENSO cycle by a few months [e.g., Chao, 1988; Dickey et al., 1993]; however, the physical mechanism responsible for this lag has not been elucidated. In this study, we examine the correlation among time series of AAM, LOD, ENSO indices, and the warming of the tropical troposphere, to gain a better understanding of the processes responsible for the observed delay between the mature phase of ENSO and the atmosphere/solid Earth rotational response. Recent findings regarding the propagation of heat from the oceanic mixed layer to the free troposphere during El Nino events [e.g., Su et al., 2005] provide a framework for understanding the origin of the delay in terms of dynamic and thermodynamic meteorological processes.
2. Data Considered
 We used a combination of atmospheric, oceanic, and geodetic data spanning the years 1979–2004 in this study. Time series of AAM were obtained from the NCEP reanalysis [Kalnay et al., 1996]; we binned 6-hourly values to form non-overlapping ten-day averages, with composite seasonal cycles removed. Winds up to the 10 hPa level were included in the calculation, along with changes in planetary AAM computed from surface pressure variations using the inverted barometer approximation [Barnes et al., 1983]. For the ENSO variation, monthly values of the Nino 3.4 SST index (averaged over latitude 5N–5S, longitude 120W–170W) were interpolated to form a ten-day spaced time series with composite seasonal cycle removed; another ENSO series was formed by similar treatment of the monthly values of the Southern Oscillation Index, with sign reversed to form the modified SOI (MSOI). Non-tidal LOD variations were obtained from the SPACE 2004 compilation of the JPL KEOF output [Gross, 2005], with 6-hourly values binned to form ten-day non-overlapping averages with seasonal cycle removed. We also obtained tropical temperatures (TT) from the NCEP-NCAR reanalysis at 25 equally spaced latitudinal bands between 30N and 30S, averaged zonally and vertically from 1000hPa to 10hPa; these were binned in non-overlapping ten-day averages with seasonal cycle removed. In order to focus on interannual variations, all time series were filtered in the 2–7 year band using the phase-neutral recursive algorithm of Murakami .
 We seek to understand the origin of the delayed rotational response of the Earth to oceanic and atmospheric indicators of the ENSO cycle, both through comparisons with geodetically-measured LOD changes and through examination of the atmospheric response to the associated lower-boundary forcing. Changes in LOD are commonly referenced to monthly values of the SOI or to indicators of equatorial Pacific sea surface temperature such as the Nino 3.4 SST index, with lags of a few months typically found. Figure 1 shows lag correlations of solid Earth and atmospheric quantities with Nino 3.4 SST (solid lines) and with MSOI (dashed lines) computed for the period 1979–2004, with all series filtered in the 2–7 year band to focus on ENSO-related variability. For the time span considered, correlations of LOD (green curves) and AAM (red curves) with both SST and MSOI peak with a one-month lag after the ENSO indices. The equal lags of AAM and LOD confirm the dominant role of the atmosphere in driving interannual Earth rotation variations, while the slightly smaller magnitude of the LOD correlation may indicate “leakage” of decadal core-mantle effects into the 2–7 year band (ocean angular momentum, not considered here, can also affect interannual LOD at detectable levels [cf. Marcus et al., 1998]).
 Similar or longer lags have been noted between Nino 3.4 SST and different aspects of the global atmosphere/ocean response; Su et al. , in particular, have investigated the reasons for lags between Nino 3.4 SST and the response of the tropical tropospheric temperature during recent ENSO events. Here, we follow up on their results to investigate the mechanism responsible for the delayed response of Earth rotation to ENSO forcing. The light blue curves in Figure 1 show that during the interval of our study, the average TT was well-correlated with both ENSO indices, but at a lag (four months) far longer than that associated with the rotational/AAM response.
 Since zonal wind anomalies are linked to the meridional temperature gradient through the thermal wind equation (see Appendix A), we also examined the difference between average equatorial (15N–15S) and subtropical (30N–15N, 30S–15S) TT as an approximate index of the tropical temperature gradient (TTG). The resulting correlations (Figure 1, dark blue curves) maximize at the same one-month lag as the LOD and AAM, indicating that the poleward gradient of the temperature response, rather than the temperature anomaly itself, controls the timing of the Earth rotation response to ENSO forcing. Interestingly the TTG has a higher correlation with the ENSO indices than either AAM or LOD, consistent with its role as an intermediary in transmitting the ENSO signal to the atmosphere and solid Earth through angular momentum forcing. It is also interesting to note that the magnitude of the TTG correlation is larger than the maximum TT correlation, confirming the robust signature of the ENSO cycle on the atmospheric temperature gradient as well as on the temperature itself.
 In order to investigate the origin and timing of the TTG associated with ENSO, we regressed the TT anomaly on Nino 3.4 SST as a function of latitude and lag, using vertically- and zonally-averaged temperature data from the NCEP reanalysis for 1979–2004 (Figure 2a). These results are quite similar to those obtained by Su et al. [2005, Figure 1a], with the regressed temperature anomalies slightly in excess of 0.3C per degree of SST change and maxima located slightly off the equator in both hemispheres. The response reaches its peak about 4 months following the Nino 3.4 SST anomaly, and spreads progressively from the deep tropics (within about 15° of the equator) to higher latitudes in both hemispheres.
 In order to quantitatively assess the role of thermal wind anomalies in driving the Earth's rotational response to ENSO, we evaluated the AAM anomaly in each latitude belt due to thermal wind forcing based on the poleward gradient of TT regressed on Nino 3.4 SST (see Appendix A). The results are shown in Figure 2b, in terms of equivalent LOD forcing for each 2.5°-wide latitude belt; note that in this calculation the geostrophic approximation is applied to all latitude belts, with the Coriolis parameter not allowed to decrease below its absolute value at 15° latitude in either hemisphere. The thermal wind forcing is seen to maximize in both hemispheres at about 20° latitude, with a stronger response in the Northern Hemisphere reflecting the preference of El Nino (warm) events for the boreal winter, when the northern branch of the Hadley cell is more active. The maximum forcing is seen to occur at a one (two) month lag in the Northern (Southern) hemisphere, consistent with the overall one-month lags for LOD, AAM and TTG seen in Figure 1 with respect to ENSO forcing.
Figure 3 shows the thermal wind AAM computed from the TT data and summed over latitudes 15°–30° in each hemisphere (red line, left axis), along with 2–7 year filtered values of the Nino 3.4 SST index (blue line, right axis). The thermal wind AAM is seen to maintain a robust and stable phase relationship with the SST anomaly, with a consistent lag throughout most of the record. The dashed line shows the 2–7 year filtered time series of LOD regressed onto the Nino 3.4 SST index at a one-month lag, for which the response is largest. The regressed LOD is seen to track the thermal wind forcing quite well in both amplitude and phase, indicating that the anomalous poleward temperature gradient associated with the ENSO cycle is responsible for that part of the interannual LOD variability which is linearly related to Nino 3.4 SST forcing.
4. Discussion and Conclusions
 In this study, we examine the link between tropical warming and the rotational response of the atmosphere/solid Earth system to ENSO forcing. The main response of the tropical temperature (TT) to ENSO forcing, as indicated by the Nino 3.4 SST index, takes place at a lag of approximately four months (Figures 1 and 2a). The reasons for this lag are explored in some detail by Su et al. , and involve interactions with remote ocean basins as well as the extratropics. The response of both atmospheric angular momentum (AAM) and length-of-day (LOD) to Nino 3.4 SST anomalies was found to occur on a far shorter time scale (1-month lag) than that of the TT (4-month lag), over the period of the study (1979–2004). By contrast the tropical temperature gradient (TTG), taken to be the difference between “equatorial” (15N–15S) and “subtropical” (30N–15N and 30S–15S) TT showed the same one-month lag with respect to Nino 3.4 SST, indicating that the rotational response to ENSO is driven by angular momentum associated with thermal wind anomalies. The high correlation of the TTG with Nino 3.4 SST shows that the poleward temperature gradients, and associated thermal wind anomalies, are a robust feature of the ENSO cycle (Figure 1).
 Numerical computation of AAM anomalies arising from thermal wind regressed on the Nino 3.4 SST index (Figure 2b) showed that the largest forcing occurs near 20° latitude in both hemispheres, with the stronger NH response presumably arising from the preference of El Nino (warm) episodes for boreal winter, when the northern branch of the Hadley cell is most active [e.g., Su et al., 2005]. When summed over latitudes poleward of 15° (where the geostrophic and thermal wind equations are accurate), the implied AAM anomaly maintains a robust phase relationship with Nino 3.4 SST anomalies, with a consistent lag over most of the study period (Figure 3). The phase and amplitude of the thermal wind AAM is similar to that of interannual LOD regressed on the Nino 3.4 SST index, indicating that thermal winds arising from the evolving meridional gradient of the TT control the lagged rotational response of the solid Earth to ENSO forcing.
 An intriguing feature of the TT response is the reversal of the meridional temperature gradient in both hemispheres, equatorward of latitude 8° (Figure 2a) [see also Su et al., 2005, Figure 1]. Although the geostrophic approximation is not valid in the immediate vicinity of the equator, the implied thermal winds are easterly, increasing in both latitudinal extent and strength as the ENSO cycle evolves (Figure 2b). The effect of these features on the rotational response of the Earth to ENSO forcing, and their possible role in the evolution of the ENSO cycle itself, will be the subject of future studies.
Appendix A:: Thermal Wind Forcing of AAM
 The thermal wind equation may be written as
where u is the zonal (west-to-east) wind speed, p is the pressure, R the specific gas constant for a dry atmosphere, f is the Coriolis parameter, T is the temperature and y the northward displacement from the equator. Assuming the surface wind is zero, the equation can be integrated vertically to give
where M is the westerly linear momentum per unit area, the meridional temperature gradient ∂T/∂y is assumed to be uniform with longitude and height, and the integration extends over the full depth of the atmosphere. The calculation invokes both the hydrostatic and geostrophic approximations, with the latter not being applicable in the immediate vicinity of the equator.
 The angular momentum for a given latitude belt is obtained by multiplication by the lever arm acos(ϕ) and the area 2πa2 cos(ϕ)Δϕ, where ϕ is the latitude, a is the Earth's radius, and Ω its angular velocity, to give
 Note that for a narrow belt (or an arbitrary belt on an f-plane) the AAM contribution from the vertically integrated thermal wind is independent of the width of the belt, and depends on only the northward temperature change ΔT between its latitudinal boundaries.
 The authors gratefully acknowledge discussions (both oral and via e-mail) with H. Su, D. Neelin and M. Ghil and suggestions from two reviewers. The work of J.O.D., S.L.M., and T.M.C. presents the results of one phase of research carried out at the Jet Propulsion Laboratory, under contract with the National Aeronautics and Space Administration.