Three-Dimensional Atmospheric Angular Momentum Simulated by the ...

Journal of theMeteorologicalSociety of Japan, Vol. 78, No. 2, pp. 111-122, 2000

Three-Dimensional

Atmospheric

Meteorological

Angular

Agency

Momentum

Model

for

By Isao National Astronomical

the

Period

111

Simulated

by

the

Japan

of 1955-1994

Naito

Observatory, Mizusawa, Iwate, Japan Y.-H.

Shang-Hai Astronomical

Zhou

Observatory, Shang-Hai, China

Masato

Sugi

Meteorological Research Institute, Ryuichi

Tsukuba, Japan

Kawamura

Toyama University, Toyama, Japan and Nobuo

Sato

Japan Meteorological Agency, Tokyo, Japan (Manuscript received 27 April 1999, in revised form 11 January 2000)

Abstract Axial and equatorial atmospheric angular momentum (AAM) functions for the rotational dynamics of the Earth are calculated monthly from ensemble mean data of three independent 40-year simulations during 1955-1994 by the global model of the Japan Meteorological Agency (JMA) forced by observed near-global sea surface temperature (SST) conditions. The model results are compared with those from the reanalysis data of the National Centers for Environmental Prediction (NCEP) and the operational objective analysis data of JMA and with the functions inferred from the observed length of day (LOD) and polar motion. The annual term of the simulated axial wind AAM function (dimensionless relative angular momentum of atmosphere due to zonal wind) during 1984-1994 agrees well with those from the two analysis data sets and roughly with the inferred function from LOD, while the semi-annual term is considerably over-estimated, suggesting an incompleteness in the simulated subtropical zonal winds. The annual term of the simulated equatorial pressure AAM function (dimensionlessatmospheric inertia products due to atmospheric mass redistribution) is considerably over-estimated with respect to those from the two analysis data sets, presumably due to the large simulated redistribution of atmospheric mass between the Eurasian continent and the North Pacific Ocean. For interannual variations during 1955-1994, only the axial wind AAM function is reasonably simulated and shows good agreement with that from NCEP data as well as the Southern Oscillation Index. The above results lead to an understanding that the SST-forced ALCM simulates reasonably the atmospheric axial modes exciting LOD change but not the equatorial (non-axial) modes exciting the polar motion.

Corresponding author: Isao Naito, National Astronomical Observatory, 2-12, Hoshigaoka-cyo, Mizusawa 0230861, Japan. E-mail: [email protected] (c) 2000, Meteorological Society of Japan

1. Introduction In 1980,the three-dimensional global meteorological data set obtained from the First GARP (Global

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Atmospheric Research Program) Global Experiment was examined to explain a subseasonal variation in the length-of-day (LOD) determined together with polar motion from the high precision Very Long Base-line Interferometry (VLBI) measurements conducted by NASA (Hide et al. 1980). The former data set is widely referred to as objective analysis data from numerical weather prediction systems, and the latter two data of LOD and polar motion are the three-dimensional Earth rotational parameters (ERPs) now being monitored by various space geodetic techniques (see Clark et al. 1998, for example). To relate variations in ERPs from space geodesy

with

corresponding

atmospheric

parame-

ters, atmospheric angular momentum (AAM) functions have been calculated from the objective analysis data in the world meteorologicalcenters (Barnes et al. 1983; Salstein et al. 1993;Dehant et al. 1997). The AAM functions, dimensionless atmospheric angular momentum normalized by Earth's mean angular momentum, are composed of axial and equatorial components for the LOD change and the polar motion, respectively. Each component has wind and pressure terms reflecting atmospheric relative angular momentum and the redistribution of atmospheric mass (i.e., inertia products and moment of inertia of atmospheric mass), respectively,as defined by Munk and MacDonald (1960) and Lambeck (1980). This information has allowed us to understand Earth's rotational dynamics in considerably closer relation to atmospheric global phenomena than before (see Rosen 1993; Eubanks 1993, and Dickey 1993, for reviews). An outstanding result is that the variation of the wind term in the axial AAM function (i.e., dimensionless atmospheric relative angular momentum) agrees wellwith that of the inferred function from the observed LOD on intraannual to interannual scales. In particular, the LOD data and the axial wind AAM function have been recognized as proxy signals, like the Southern Oscillation Index (SOT), for monitoring the coupled oceanatmosphere dynamics in the tropics that cause El Nino-Southern Oscillation (ENSO) (Rosen et al. 1984; Chao 1989; Hide and Dickey 1991; Dickey et al. 1992b; Dickeyet al. 1994; etc.). It has been found, however, that the equatorial AAM function does not agree with the inferred function from the polar motion data even for seasonal variations (Naito et al. 1987; Eubanks et al. 1988; King and Agnew 1991;etc.). Although the disagreement basically suggests the existence of other contributions from ocean and land water to the polar motion (Wahr 1982, 1983; Chao et al. 1987; Wilson and Kuehne 1990;Kuehne and Wilson 1991; Ponte et al. 1998; etc.), it also reflects discrepancies in the equatorial AAM functions themselves from the meteorologicalcenters, which show different behaviors (Eubanks et al. 1988). In particular, the

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two equatorial wind AAM functions (i.e., dimensionless

equatorial

relative

angular

momentum

of

atmosphere) from the National Centers for Environmental Prediction (NCEP) and the Japan Meteorological Agency (JMA), for example, show a large discrepancy in their contributions to the annual wobble (i.e. the annual variation of the polar motion), suggesting differencesin their data assimilation systems (for details, see Aoyama and Naito 2000). The same equatorial wind AAM functions on time scales near 14 months were found to excite considerably different Chandler wobbles (Furuya et al. 1996, 1997). These are enigmatic results if we take into account that the meteorologicalcenters acquire similar observed meteorologicaldata in their numerical weather prediction systems. Simulation experiments to understand angular momentum exchangesbetween the atmosphere and solid Earth using Atmospheric General Circulation Model (AGCM) are important (Boer 1990). With regard to the different responses of AGCMs to the same observed sea surface temperature (SST) variations over the world oceans, the intercomparison study of the axial wind AAM function suggests that the different responses of AGCMs can be a source for discrepanciesamong objective analysis data sets (Hide et al. 1997). More extended experiments, such as ensemble climate simulations forced by SST, are expected to become a useful method for understanding atmospheric variability (e.g., Harzallah and Sadourny 1995). Therefore, comparisons of the equatorial wind AAM function calculated from such simulated atmospheric data with those from the analysis data of the meteorological centers would also provide valuable insights into the enigma mentioned above. The data obtained from the simulation experiments conducted by using DMA'sAGCM with near-global SST boundary conditions (Sugi et al. 1997; Kawamura et al. 1997), for example, are useful for such comparison studies. More generally, these studies are important for a basic understanding of the seasonal redistribution of atmospheric mass and winds contributing to the annual wobble. In this paper, focusing on the atmospheric seasonal and interannual variations in the extratropics exciting the polar motion, we evaluate the axial and equatorial AAM functions based upon the simulations by JMA's AGCM using SST boundary conditions over the world oceans (Sugi et al. 1997; Kawamura et al. 1997), and compare them with those from the reanalyses data of NCEP and the operational analysis data of JMA, the inferred functions from the observedLOD and polar motion data, and the SOT.In Sections 2 and 3, we outline a basic model for the three-dimensional angular momentum budget and briefly describe the data sets used in this study, respectively. In Section 4, we discuss results for seasonal and interannual variations, and in Sec-

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Lion5 we provide a summary. 2. A basic model for three-dimensional lar momentum budget

angu-

The variation in the orientation of Earth's rotational axis with respect to Earth's figure axis (i.e., the axis for Earth's largest principal moment of inertia) has conventionallybeen referred to as the polar motion or the wobble, while the variation in the Earth's axial angular velocity has often been described in terms of the LOD change. Based on the conservation of Earth's total angular momentum, the polar motion and LOD change are expressed by perturbation equations for the equatorial and axial angular velocities, respectively, of Earth that are given the followingdimensionless equations (1) and (2) normalized by the mean angular velocity of Earth (for details, see Eubanks 1993, for example): (i/o-)dm/dt+m=x

(1)

d/dt(m3+X3)=0,

(2)

where o=0+ia is the complex frequency of the Earth's free wobble (the Chandler wobble) and a is the coefficient for Earth's anelasticity equal to |o|/2Q, and Q is the Earth's Q-value (quality factor). m=m1+im2 in Eq. (1) is the dimensionless equatorial angular velocity in complex form describing polar motion, where ml and m2 are components along 00E and 900E, respectively. m3 in Eq. (2) is the dimensionless small quantity for axial angular velocity equal to -ALOD/(LOD), where (LOD) and LLOD are the standard value of LOD and its deviation from (LOD), respectively. x=x1+ix2 in Eq. (1) is the excitation function for polar motion in complex form, where x1 and x2 are components along 00E and 900E, respectively. Similarly, x3 in Eq. (2) is the excitation function for the LOD change. The axial and equatorial

atmospheric

angular

mo-

mentum functions proposed by Barnes et al. (1983) are approximately applicable to x and x3 in the formulations above. Their pressure and wind terms, respectively,express the effects of inertia product or moment of inertia due to atmospheric mass redistribution and of atmospheric relative angular momentum changes upon polar motion and LOD (see Appendix 1 for details). To evaluate the pressure term, two ideal cases, the inverted-barometer (TB) and non-TB(NIB), are used for the oceanic response to atmospheric pressure variations, where in the TB case the oceans are assumed to respond isostatically and in the NIB case the oceans are assumed to be rigid. It is generally considered that the AAM function expressed by the TB pressure term plus the wind term is an appropriate model for explaining LOD change and polar motion on time scales longer than

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a day (see Eubanks 1993, for details). In computing the AAM functions, four numerical coefficients called "transfer functions" should be introduced to consider "Love number" corrections for the elastically deformable Earth with respect to the rigid Earth. This study employs the coefficients under the core-mantle decoupling for LOD mentioned in detail in Appendix 1 (also see Eubanks 1993, and Aoyama and Naito 2000). 3. Data sets used in this analysis 3.1 Simulated atmospheric data byJMA global model The simulated atmospheric data used for calculating AAM functions in this analysis are performed by a global model of the JMA forced by nearly global observed SST data. The model used here is basically equivalent to the JMA model used for the operational global numerical forecast in the JMA, but has a T42 (i.e., triangular truncation at total wave number 42) resolution, which is equivalent to approximately 2.80 latitude-longitude, and 21 levels up to 10hPa (JMA 1993). An ensemble of three independent 40-year integrations for 1955 to 1994 are performed with different initial conditions employing the same prescribed SSTs and climatological sea ice distributions, in which the SST data set of Bottomley et al. (1990) and Parker et al. (1995) are used for the first 34-year period of 1955-1988 and for the latter period of 1989-1994,respectively (Sugi et al. 1997; Kawamura et al. 1997). Global features of the simulated climate by the JMA model have been found to be reasonable in comparison with the observed climate (Sugi et al. 1995). The SST-forced variability of seasonal mean fields in this ensemble experiment has also been estimated and shows that the potential predictability of pressure fields by the SST variations is generally high (50-90%) in the tropics, and low (less than 30%) in the extratropics (Sugi et al. 1997). This suggests that the SST-forced variability has high predictability in LOD change and low predictability in polar motion, since the LOD change and polar motion have their sources basically in the tropics and the extratropics, respectively (see the functional forms of equations in Appendix 1). The axial and equatorial AAM functions are calculated monthly based on the ensemble mean data, which are hereafter referred to as JMA-S. The wind terms are calculated by integrating winds from the surface of real topography up to 10hPa pressure level. The TB and NIB pressure terms are calculated from surface pressures on real topography and sea level pressures over oceans. Surface pressures on real topography have been re-estimated by a leastsquare fitting from geopotential heights in the simulated data (Naito et al. 1987).

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3.2 AAM functions from the operational analysis data in JMA The calculations of AAM functions based upon

J MA's operational objective analysis global data, which are hereafter referred to as JMA-O, start once a day (but as daily means) from late 1983and twice a day from 1988 (Naito et al. 1987). The global numerical weather prediction model used for data assimilation during this period at JMA was T63L16 version or T106L21 version spectral model. The objective analysis was performed with an optimum interpolation method at 2.5x2.5 or 1.875x1.875 latitude-longitude grids on 16 mandatory pressure levels up to 10hPa. Their wind terms reflect winds from tops of real topography to the 10hPa pressure level, as in those based on JMA-S above. Their pressure terms both for TBand NIB cases have also been calculated from surface pressures on real topography that are re-estimated by a least-square fitting from geopotential heights and from sea level pressures over oceans in the objective analysis data. Therefore, it should be noted that the calculated JMA-O AAM functions contain no artificial jumps associated with changes in the lowerboundary of the global model employed in JMA's numerical weather prediction system, for example. For comparisons with the JMA-S AAM functions in this analysis, JMA-O AAM functions during 1984-1994 are employed and averaged into monthly series because of using the monthly series of JMA-S, though we admit that time resolution becomes too low to estimate semiannual variations as will be discussed in Section 4-1. 3.3 AAM functions from the reanalysis data in NCEP/NCAR NCEP and NCAR (National Center for Atmospheric Research) conducted a reanalyses project based upon a long period (1957-1996)of comprehensive observational data, and by using a recent version of NCEP's numerical weather prediction model (Kalnay et al. 1996). The resolution is 2.5 degrees in the horizontal and 17 levels in the vertical up to 10hPa. The AAM functions from NCEP/NCAR's reanalysis data, which are hereafter referred to as NCEP-R, are provided by the SubBureau for AAM of International Earth Rotation Service (IERS). Their wind terms are calculated up to 10hPa from 1000hPa, and their pressure terms are computed on the basis of TBand NIB cases (see Salstein et al. 1993,for details). Note that there is a difference in the computation of the wind terms between NCEP and the others used here (with regard to this point, see Aoyama and Naito 2000). Data were available four-times a day from 1968(but note that it is now available from 1948). In this analysis, NCEP-R AAM functions during 1968-1994 are employed and also averaged into monthly series.

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3.4 ObservedLOD and polar motion data For LOD data, the daily LOD series of "IERS Earth Orientation Parameter (EOP) 97 C04" during 1962-1994 and "SPACE97LOD" during 19761994 (Gross 1996) are employed, which are obtained from combining data observed with modern space-geodeticand classicaloptical astronomical techniques. For comparisons of the axial AAM function with the annual and semiannual LOD variations, however, the latter series is used, in which the effects of all the solid Earth tides on the LOD (Yoder et al. 1981) and the ocean tidal loading corrections to these tides (Dickman 1993) are removed. Both daily series are converted into monthly series of the inferred function equal to m3=-ALOD/. For polar motion data, the daily polar motion series of "IERS EOP 97 C04" during 1968-1994 is used. The inferred excitation function from the observed polar motion that is equal to the left-hand side of Eq. (1) is computed in terms of a discrete equation employing 435 days and 100 for the period and Q value, respectively, for the Chandler wobble in Eq. (1). The daily series of the inferred function is then averagedinto monthly series for comparisons with the calculated equatorial AAM functions. 4. Results and discussions 4.1 Seasonal angular momentum budgetsfor the period 1984-1994 We show here the annual and semiannual variations in the axial and equatorial AAM functions from JMA-S, JMA-O, and NCEP-R in comparison with those of the inferred functions from observed LOD and polar motion data through Eqs. (1) and (2), respectively, during the 1984-1994 period common to all these data sets. The amplitudes and phases of all the annual and semiannual terms are determined by least-squaresfitting of a linear combination of their sinusoidsand trends, the latter determined with a fourth-order polynomial function for the axial component and a linear function for the equatorial component. The phase angles are taken with respect to January 1 using sine functions for the sinusoids. Thus, it should be noticed that the semiannual terms are roughly estimated by this method due to a little longer sampling interval (a month) of data. In the figures, the results of analysis based on JMA-O (the JMA operational objective analysis data), JMA-S (simulated data by JMA model), and NCEP-R (NCEP/NCAR reanalysis data) are simply denoted by O, S, and R, respectively, and their amplitudes and phases are shown by the length of the bar and the position of bold-typed "I", respectively. 4.1.1 Axial component Figure 1 shows the amplitudes and phases in the annual variations for axial component (i.e., x3),

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Fig. 1. Amplitudes and phases for annual variation in the axial AAM function (x3) and the inferred function from the observed LOD change for the period of 1984-1994. Length of bar indicates amplitude in unit of 10-7 (see top scale) while bold-typed "I" indicates phase in unit of degree (see bottom scale). The numerical values of magnitude and phase are also shown in parenthesis. W, PNIB, PIB, and W+PIB denote wind term, NIB-pressure term, IB-pressure term, and wind term plus TB-pressure term, respectively, and O, S, and R are those from JMA-O, JMA-S, and NCEP-R data, respectively.

where OBS indicates those of the inferred function from the observed LOD data through Eq. (2). The amplitudes and phases in the four terms (i.e., wind, NIB-pressure, TB-pressure, and wind+IB-pressure terms) of the AAM functions from the three meteorologicalsources agreewell with each other. Namely, the simulated AAM function (S) by the JMA model agrees wellwith those from the objective and reanalysis data (O and R), but is different from the behavior in the JMA model of the AMIP study by Hide et al. (1997) that showed a slightly larger amplitude overestimation in the seasonal variation due to an overestimation in the semiannualvariation as will be mentioned later. These comparisons thus reconfirm a basic understanding that the axial angular momentum budget of the atmosphere-mantle system on the annual time scale can be almost completed with zonal wind alone (Rosen and Salstein 1985; Naito and Kikuchi 1990, 1991; Rosen and Salstein 1991; Hide et al. 1997; etc.). The pressure term should not be neglected for a more accurate budget (Naito and Kikuchi 1990;also see Aoyama and Naito 2000). Figure 2 shows the same as Fig. 1 but for the semiannual variations. The wind term clearly plays a major role in semiannual variation. However,the amplitude of the wind term from JMA-S is almost two times as large as those from JMA-O and NCEPR (and even larger than the amplitude in its annual variation shown in Fig. 1), in spite of a good agree-

meet in phase. This kind of discrepancy was also found in the semiannual mode of seasonal errors in AMIP (Hide et al. 1997). Actually, we reconfirmed that the seasonal variation of JMA-S show almost same feature as shownin Fig. 7 of Hide et al. (1997). Although semiannual variations of zonal wind generally prevail in the subtropical troposphere and the upper stratosphere, the discrepancy here is likely attributable to an incompletereproduction of the subtropical jet by the simulation, as pointed out by Sugi et al. (1995). This is because the wind term estimated from NCEP's reanalysesdata from surface to 1hPa can completely explain the semiannual variation in LOD (Rosen and Salstein 1991;Aoyama and Naito 2000). 4.1.2 Equatorial component Figure 3 shows the amplitudes and phases in the annual variations for equatorial x1 and x2 components toward 00E and 900E,respectively,where OBS indicate those of the inferred function from the observed polar motion data through Eq. (1). In the x1 component, the NIB- and TB-pressure terms in JMA-S have considerably large amplitudes, amounting to about two times those in JMA-O and NCEPR, while the small wind terms in the three data sets are very different from each other in both amplitude and phase. As a result, the wind+IB-pressure term in JMA-S disagrees considerably with those in

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2. Same

as in Fig.

1, but

the two analysis data, with its amplitude reaching almost four times of the others. Similarly, in the x2 component, the NIB- and TB-pressureterms in JMA-S have large amplitudes compared to those in JMA-O and NCEP-R, which results in large discrepancies in amplitude of the wind+IB-pressure terms in the three meteorologicaldata. The considerablystronger annual variations in the two pressure terms in JMA-S than those in JMA-O and NCEP-R are likely to be closelyconnected with the stronger simulated Aleutian low and Siberian high than the observed ones, as was pointed out by a non-ensemble experiment using the JMA model by Sugi et al. (1995). This suggests that the SST forced AGCM does not reasonably reproduce the observed pressure term, exciting a major part of the annual wobble. Sugi et al. (1997) showed that the pressure field of the SST-forcedvariability of JMA-S has low predictability (less than 30%) in the extratropics compared with high predictability (50-90%) in the tropics, as mentioned in Section 3. All these facts lead to an understanding that the SST-forced pressure fields do not reasonably simulate the annual pressure variation in the extratropics exciting the annual wobble. Therefore, a more sophisticated simulation study focusedon the atmospheric annual variation in the extratropics will be urgently needed. In addition, a much larger relative difference in the wind+IB-pressure terms between the simulated and two analysis data appearing in x1 component than in x2 component mentioned above suggests that the real atmospheric motions over the ocean hemisphere affecting x1 component is more complicated than those over the continent hemisphere

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variation.

affecting x2 component. On the other hand, a smaller difference in the amplitudes of the wind+IBpressure term of the two analysis data and of OBS in xi component than in x2 component may reflect that the continental water contribution to the annual wobble is required more in x2 component than in xi component for the complete budget. In Fig. 3, the wind terms in the two analysis data as well as the simulated one are also found to have considerably different amplitudes. This disagreement arises not only from the difference in the method of computation of the wind terms mentioned in Section 3 but also from differences in the data assimilation system of the two meteorological cen-

ters (see Aoyama and Naito 2000, for detail). Also, the different wobbles simulated by the wind terms from the above two analysis data (Furuya et al. 1996, 1997) could be attributed to the same reasons above. These discrepancies will not be resolved without a further advancement of AMIP (see Gates 1992, for example). The semiannual wobble is not mentioned here because of its small amplitude compared to the annual wobble and of little reliability of this simulation experiment in reproducing the semiannual variation. 4.2 Irregular variations in the axial AAM functions for the period of 1955-1994 Figure 4 shows the irregular variations in the axial wind term (i.e., dimensionlessaxial relative angular momentum of atmosphere) from the simulated (JMA-S) and reanalyses (NCEP-R) data during 1968-1994 obtained after removing their sea-

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Fig. 3. Amplitudes and phases for annual variation in the equatorial AAM function (x) and the inferred function from the observed polar motion determined for the period of 1984-1994. Legends are as same as those in Fig. 1.

sonal terms and trends. They are quite similar to each other, though showinga small differencein amplitude (as will be confirmed in Fig. 5). In particular, the strong variations of ENSO event such as in 1982-1983 are successfullyreproduced (see Dickey et al. 1994,and Hide et al. 1997, for example). Figures 5, 6a, and 6b show their spectra, squared coherence, and coherence phase, respectively, computed by the multitaper method (Thomson 1982). JMA-S has a smaller power than NCEP-R at nearly all frequencies; but note that it showed a little larger amplitude than NCEP-R in annual variation of Fig. 1. Since the squared-coherence is significant and the coherence phase is stable around 0 degree for fre-

quencies lower than a cycle/year, a spectral peak and a large squared coherence near timescales of 2-4 years shown in Figs. 5 and 6a, respectively, reconfirm a strong connection between atmospheric relative angular momentum variations and ENSO events (Dickey et al. 1994; Mo et al. 1997; etc.). On the other hand, Fig. 6 surprisingly shows general loss of coherence for frequencieshigher than a cycle/year. This, in addition to the overestimations in the semiannual variation, can be considered to result from a limitation of the model simulation forced by SST. A more sophisticated simulation study focused on the annual and sub-annual variations using AGCM will be urgently needed, to which the Earth

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4.

Interannual

variations

in

ial wind+IB-pressure

AAM

function

JMA-S

data

for the

and

NCEP-R


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axfrom

period

of 1968-1994.

Fig. 6. Squared coherence (a) and coherence phase (b) between the interannual variations in the axial wind+IB-pressure AAM function from JMA-S and NCEP-R data for the period of 1968-1994 determined by Multitaper method (Thompson 1982). Horizontal dashed line indicates 95% confidence threshold.

Fig. 5. Multitaper power spectra of the interannual variations in the axial wind+IB-pressure AAM function from JMA-S and NCEP-R data for the period of 1968-1994. Double-arrow indicates 90% confidence interval.

Fig.

7.

Interannual

wind+IB-pressure

rotation data will contribute as one of the observed global signals. Figure 7 compares the interannual variation of the axial wind+IB-pressure terms from JMA-S and NCEP-R, and the inferred function (OBS) from the observed LOD data during 1968-1994 obtained through a zero-phase Butterworth low-passfilter of order 2 with cut-off frequencyof a cycle/year. Both JMA-S and NCEP-R vary coherently with OBS but in general show a little smaller amplitude than in OBS. This is presumably because we have neglected the contribution of wind above 10hPa and because possible sourcesfrom ocean currents may exist (Dickey et al. 1994). Figure 7 also indicates that JMA-S tends to underestimate and overestimate ENSO signals with respect to NCEP-R during 1982-1983and 1972-1973, respectively. The same features were found during 1982-83 in AMIP (Hide et al. 1997). During 197273, however, both NCEP-R and JMA-Sshow underestimation with respect to LOD. Figure 8 shows the

variations AAM

function

in

the from

JMA-S and NCEP-R ferred function from

data and in the inthe observed LOD

change

of 1968-1994.

for the

period

interannual variations in the axial wind+IB-pressure terms from JMA-S and in the ModifiedSouthern Oscillation Index (MSOI) during 1955-1994 (see Appendix 2), where each series is normalized by its standard deviation. It reconfirms that there is a striking similarity between AAM and MSOI (see Mo et al. 1997, for example), demonstrating that the simulation successfullyreproduces ENSO signals over the last 40 years. In the present paper, we do not discuss interannual variations in the equatorial AAM functions because their behavior is too noisy to compare with those of the inferred functions from the observedpolar motion. These discussions will also be urgently needed by collaboration of the Earth rotation with the AGCM.

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Fig. 8. Interannual variations in the axial wind+IB-pressure AAM function from JMA-S data and in Modified Southern Oscillation Index (MSOI) for the period of 1955-1994, where each series is normalized by its standard deviation.

5. Summary The axial and equatorial AAM functions are calculated monthly from the ensemble mean data of three independent 40-year simulationsfor the period of 1955-1994by the JMA model forced by observed near-global SST conditions. These results are discussed in comparison with those from the reanalysis data of NCEP/NCAR and the operational objective analysis data of JMA and with inferred functions from the observed LOD and polar motion data, respectively. The results of the analysis are summarized below. With regard to seasonal variations during 19841994,the annual signal in the simulated wind term for the axial AAM function (dimensionless relative angular momentum of atmosphere due to zonal wind) agrees well with those from DMA's operational and NCEP's reanalysis data and the inferred function from the observed LOD. However,its semiannual term is considerably over-estimated,suggesting an incompleteness in the simulated subtropical zonal winds. On the other hand, the simulated pressure term for the equatorial AAM function (dimensionlessatmospheric inertia products due to atmospheric mass redistribution) on annual time scales is considerably over-estimated with respect to those from DMA'soperational and NCEP's reanalysis data, presumably due mainly to the considerably larger simulated redistribution of atmospheric mass between the Eurasian continent and the North Pacific Ocean. With regard to the interannual variations during 1968-1994, only the wind term for the axial AAM function is reasonably simulated among all the terms in the AAM functions compared to those from NCEP's reanalysis data and the inferred functions from the observedLOD and polar motion data. The model, however, underestimates this term in ENSO events for 1982-1983but overestimates it for

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1972-1973, compared to that from NCEP's reanalysis data. The simulated wind term also shows a good relationship with the Southern Oscillation Index through all the simulated period of 1955-1994. The above results lead to an understanding that the SST-forcedAGCM simulates reasonably the atmosphericaxial modes exciting LOD change but not the equatorial (non-axial) modes exciting the polar motion. An AGCM study focused on the atmosphericequatorial (non-axial) modes dominant in the extratropics will be urgently needed to improve AGCM as well as to obtain a more complete understanding of Earth's three-dimensional angular momentum budget, in which the Earth rotation data will play a key role. Acknowledgments The authors thank anonymous reviewersfor providing invaluable comments in improving the paper, R. Gross for providing the LOD data, D. Salstein for providing the AAM function data based on the reanalysis data of NCEP/NCAR, JMA for providing the operational objective data since 1983,and R. Rosen and T. Iwasaki for discussions. Y.-H. Zhou thanks T. Iwabuchi and Y. Aoyama for kind helps during this work. Appendix 1 Atmospheric Angular Momentum (AAM) Functions The axial and equatorial components of the atmospheric angular momentum (AAM) functions x and x3 in Eqs. (1) and (2), respectively,are given as below (Barnes et al. 1983). x =1.00AI/(C-A)+1.43Ah/[SZ(C-A)]

(A1)

x3=0.70DI33/Ci+1.00AtL3/[cC],

(A2)

where each component is composed of "pressure term" and "wind term" corresponding to the first and second terms, respectively, of right side in Eqs. (A1) and (A2). In Eq. (A1), LEI and Oh are, respectively,inertia products and equatorial component of relative angular momentum of atmosphere in complex form, C and A are the Earth's axial and equatorial principal moments of inertia, respectively, and is the Earth's mean angular velocity. In Eq. (A2), AI33, and Ah3 are, respectively, changes in moment of inertia and axial component of relative angular momentum of atmosphere. Four numerical coefficientsin Eqs. (A1) and (A2) are the transfer functions indicating "Love number" corrections for the elastically deformable Earth with respect to the rigid Earth. Note, however,that this study employs the coefficientsfor the constants C and A of the

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mantle under the core-mantle decoupling as mentioned in Section 2. Namely, we use here the AAM functions for LOD change multiplying 1.12 to those calculated through Eq. (A2), where 1.12 is equal to ratio of C for the wholeEarth to that for the mantle. However, we use the AAM functions for polar motion without correction because they approximately equal to those in Eq. (A1) within error of 1-2% (Eubanks 1993). We thus add the corrections to the archived AAM functions for LOD change from JMA-O and NCEP-R published through IERS. In general, AI, Ah AI33, and Ah3 in equations (A1) and (A2), are expressed as the following integration.

DI=-r4/g

PS cost sin exp(ia)dad

(A3)

Ah=r3/9

AI33=r4/gIPscos3gdadb

(A5)

Ah3=-r3/g///ucostcbdpdAdb,(A6) where r is the Earth's mean radius, b and A are latitude and longitude, respectively, PS is surface pressure, u and v are eastward and northward velocities, respectively, g is the Earth's mean gravity, and dp denotes pressure integral from bottom to top of atmosphere. Appendix 2 Southern Oscillation Index Data The Southern Oscillation Index (SOT)is a proxy measure for the strength of ENSO and is conventionally definedas the differenceof atmospheric sea-level pressure in hPa between Tahiti and Darwin. In this study, the standard monthly SOTseries during 19551994 provided from NOAA is used to define a modified SOT (MSOI) equal to SOTmultiplied by -1, which is positively correlated with the LOD change (see Dickey 1993, for example). References Aoyama, Y. and I. Naito, 2000: Wind Contribution to the Earth's Angular Momentum Budget in Seasonal Variation, J. Geophys. Res., in press. Barnes, R.T., R. Hide, A.A. White and C.A. Wilson, 1983: Atmospheric angular momentum fluctuations, length-of-day changes and polar motion. Proc. R. Soc. London A, 387, 31-73. Boer, G.J., 1990: Earth-atmosphere exchange of angular momentum simulated in a general circulation model

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2

and implications for the length of day, J. Geophys. Res., 95, 5511-5531. Bottomley, M., C.K. Folland, J. Hsiung, RE. Newell and D.E. Parker, 1990: Global Ocean Surface Temperature Atlas (COSTA) HMSO, London. Chao, B.F, W.P. O'Connor, A.T.C. Chang, D.K. Hall and J.L. Foster, 1987: Snow Load Effects on the Earth's Rotation and Gravitational Field, 19791985, J. Geophys. Res., 92, 9415-9422. -, 1989: Length-of-day variations caused by El Nino-Southern Oscillation and Quasi-Biennial Oscillation, Science, 243, 923-925. Clark, TA., C. Ma, J.W. Ryan, B.F. Chao, J.M. Gipson, D.S. MacMillan, N.R. Vandenberg, TM. Eubanks and A.E. Niel, Earth Rotation Measurement Yields Valuable Information About the Dynamics of the Earth System, Eos, Transactions, AGU, 79, 205, 209. Dehant et al., Study of Earth's Rotation and Geophysical Fluids Progresses, Eos, Transactions, AGU, 78, 357, 360. Dickman, S.R., 1993: Dynamic ocean tide effects on the Earth Rotation, Geophys. J. Int., 112, 448-470. Dickey, J.O., S.L. Marcus and R. Hide, 1992a: The Earth's Angular Momentum Budget on subseasonal time scales, Science, 225, 321-324. -, and -, 1992b: Global Propagation of Interannual Fluctuations of Atmospheric Angular Momentum, Nature, 357, 484-488. -, 1993: Atmospheric Excitation of the Earth's Rotation: Progress and Prospects Via Space Geodesy, in Contributions of Space Geodesy to Geodynamics: Earth Dynamics, ed. by D.E. Smith and D.L. Turcotte, Am. Geophys. Union, 56-70. -, S.L. Marcus, R. Hide, T.M. Eubanks and D.H. Boggs, 1994: Angular momentum exchange among the solid Earth, atmosphere, and oceans: A case study of the 1982-1983 El Nino event, J. Geopys. Res., 99, B12, 23921-23937. Eubanks, TM., J.A. Steppe, JO. Dickey, RD. Rosen and D.A. Salstein, 1988: Causes of rapid motions of the Earth's pole, Nature, 334, 115-119. -, 1993: Variation in the orientation of the Earth, in Contributions of Space Geodesy to Geodynamics: Earth Dynamics, edd by D.E. Smith and D.L. Turcotte, Am. Geophys. Union, 1-54. Furuya, M., Y. Hamano and I. Naito, 1996: Quasiperiodic wind signal as a possible excitation of Chandler wobble, J. Geophys. Res., 101, 25537-25546. -, - and -,1997: Importance of Wind for the Excitation of Chandler Wobble as Inferred from Wobble Domain Analysis, J. Phys. Earth, 45, 177-188. Gates, W.L., 1992: AMIP: The Atmospheric Model Intercomparison Project, Bull. Amer. Meteor. Soc., 73, 1962-1970. Gross, R.S., 1996: Combinations of Earth orientation measurements; SPACE94, COMB94, and POLE94, J. Geophys. Res., 101, 8729-8740. Harzallah, A. and R. Sadourny, 1995: Internal versus SST-forced atmospheric variability as simulated by an atmospheric general circulation model, J. Climate, 8, 474-495.

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Hide, R., N.T. Birch, L.V. Morrison, D.J. Shea and A.A White, 1980: Atmospheric angular momentum fluctuations and changes in the length of day, Nature, 286, 114-117. - and J.O. Dickey, 1991: Earth's Variable Rotation, Science, 253, 629-637. -, J.O. Dickey, S.L. Marcus, R.D. Rosen and D.A. Saltein, 1997: Atmospheric angular momentum fluctuations during 1979-1988 simulated by global circulation models, J. Geophys. Res., 102, 16423-16438. JMA, 1993: Outline of operational numerical weather prediction at Japan Meteorological Agency, NPD/JMA. Kalnay, E., M. Kanamitsu, R. Kistler, W. Collins, D Deaven, L. Gandin, M Iredell, S. Saha, G. White, J. Woollen, Y. Zhu, A. Wang, Roy Jenne and Dennis Joseph, 1996: The NCEOP/NCAR 40-year reanalysis project, Bull. Amer. Meteor. Soc., 77, 437-471. Kawamura, R., M. Sugi and N. Sato, 1997: Interdecadal and Interannual Variations over the North Pacific Simulated by a Set of Three Climate Experiments, J. Climate, 10, 2115-2121. King, N.E. and D.C. Agnew, 1991: How large is the retrograde annual wobble?, Geophys. Res. Lett., 18, 1735-1738. Kuehne, J. and C. Wison, 1991: Terrestrial water storage and polar motion, J. Geophys. Res., 96, 43374345. Lambeck, K., 1980: The Earth's Variable Rotation, Cambridge University Press. Marcus, S.L., Y. Chao, J.O. Dickey and P. Gegout,1998: Detection and modeling of nontidal oceanic effects on Earth's Rotation Rate, Science, 281, 1656-1659. Mo, K.C., et al, 1997: Interannual fluctuations in atmospheric angular momentum simulated by the National Centers for Environmental Prediction medium range forecast model, J. Geophys. Res., 102, 67036713. Munk, W.H. and G.J.F. MacDonald, 1960: The Rotation of the Earth, Cambridge Univ. Press. Naito, I., N. Kikuchi and K. Yokoyama, 1987: Results of estimating the atmospheric momentum functions based on the JMA global analysis data, Publ. Int. Latit. Obs. Mizusawa, 20, 1-11.

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and N. Kikuchi, 1990: A seasonal budget of the Earth's axial angular momentum, Geophys. Res. Lett., 17, 631-634. - and N. Kikuchi, 1991: Reply to Rosen & Salstein's comment, Geophys. Res. Lett., 18, 1927-1928. Parker, D.E., C.K. Folland and M. Jackson, 1995: Marine surface temperature: Observed variations and data requirements, Climatic Change, 31, 559-600. Ponte, R.M., D. Stammer and J. Marshall, 1998: Oceanic signals in observed motions of the Earth's pole of rotation, Nature, 391, 476-479. Rosen, R.D. and D.A. Sastein, 1985: Contribution of Stratospheric Winds to Annual and Semi-Annual Fluctuations in Atmospheric Angular Momentum and the Length of Day, J. Geophys. Res., 90, 80338041. - and -, 1991: Comment on "A seasonal budget of the Earth's axial angular momentum" by Naito and Kikuchi, Geophys. Res. Lett., 18, 19251926. -, 1993: The Axial Momentum Balance of Earth and its Fluid Envelope, Survey in Geophysics, 14, 1-29. Salstein, D.A., D.M. Kann, A.J. Miller and R.D. Rosen, 1993: The Sub-Bureau for Angular Momentum of the International Earth Rotation Service (IERS): A meteorological data center with geodetic applications, Bull. Amer. Meteor. Soc., 74, 67-80. Smith, D.E and D.L. Turco, 1993: Contributions of Space Geodesy to Geodynamics, Earth Dynamics, Am. Geophys. Union. Sugi, M., R. Kawamura and N. Sato, 1995: The Climate Simulated by the JMA Global Model, Part 1: Global Feature, Report Nat. Res. Inst. Earth Sci. Disast. Prevent., 54, 155-180. -, and -, 1997: A study of SSTforced variability and predictability using the JMA global model., J. Meteor. Soc. Japan, 75, 717-736. Thomson, D.J., 1982: Spectrum estimation and harmonic analysis, Proc. IEEE, 70, 1055-1096. Yoder, C.F., J.G. Williams and ME. Parkes, 1981: Tidal Variations of Earth Rotation, J. Geophys. Res., 86, 881-891.

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Vol. 78, No. 2

気象庁モデルによってシミュレートされた1955年-l994年 3次元大気角運動量

の

内藤勲夫 (国立天文台地球回転研究系) Y.-H.

Zhou

(上海天文台) 杉正人 (気象研究所気象研究部) 川村隆一 (富山大学理学部) 佐藤信夫 (気象庁観測部)

1955年

から1994年

までの40年

間の世界の海面水温データを境界条件として、気象庁全球モデルでシ

ミュレートされたアンサンブル平均の大気運動データから、地球回転力学に必要な極軸および赤道軸成分の大気角運動量 (AAM)

関数を月毎に算出し、それらをNCEPの

析データから算出されたAAM関 1984年-1994年

再解析データおよび気象庁のルーチン解

数および観測された一日の長さ (LOD)

の期間でのシミュレートされた極軸成分のAAM関

および極運動データと比較した。

数の風速項 (帯状風による無次元大気

相対角運動量) の年周変化は二つの解析データに基づく計算値およびLODか

らの推測値に良い一致を示

した。しかし、半年周変化ではシミュレーションは著しく過剰な振幅を示した。これは亜熱帯帯状風の不完全な再現によると示唆される。同様にシミュレートされた赤道軸成分のAAM関

数の気圧項 (大気の質

量再分布による無次元大気慣性乗積) の年周変化は二つの解析データに基づく計算値を大幅に上回る振幅を示した。これはシミュレートされたユーラシア大陸と北太平洋の間の大気質量循環が、解析データのそれに比べて、過剰であることによる。1955年-1994年現され、それはNCEPのの結果から、SSTで

の期間の年々変動では、極軸成分の風速項のみが再

再解析データに基づく計算値および南方指数の変動とよい相関を示した。以上

強制された大気モデルはLOD変

動を励起する大気の極軸モードをよく再現するが、

極運動を励起する大気の非極軸モードの再現性は悪いことが分かる。