Tests on the validity of atmospheric torques on Earth computed from atmospheric model outputs

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. B2, 2068, doi: /2001jb001196, 2003 Tests on the validity of atmospheric torques on Earth computed from atmospheric model outputs O. de Viron and V. Dehant Royal Observatory of Belgium, Brussels, Belgium Received 13 September 2001; revised 23 May 2002; accepted 9 October 2002; published 4 February [1] The effect of the atmosphere on the Earth rotation is usually computed using the angular momentum budget equation. In particular, the interaction torque between the solid Earth/ocean and the atmosphere can be computed from the output of global circulation models. This torque is composed of three parts: a mountain torque due to the pressure action on the topography, a gravitational torque due to the interaction between the mass inside the solid Earth and inside the atmosphere, and a friction torque. The purpose of the paper is to test the torque computed from the output of different atmospheric global circulation models (GEOS-1, National Centers for Environmental Protection reanalysis, and ERA-15) in order to see to what extent they are reliable in the frame of Earth rotation studies. The test has been performed by comparing each part of the torque computed from the different models, as well as by verifying of the angular momentum budget equation for the atmosphere. INDEX TERMS: 1227 Geodesy and Gravity: Planetary geodesy and gravity (5420, 5714, 6019); 1239 Geodesy and Gravity: Rotational variations; 1223 Geodesy and Gravity: Ocean/Earth/ atmosphere interactions (3339); KEYWORDS: atmospheric torque, AAM, Earth rotation Citation: de Viron, O., and V. Dehant, Tests on the validity of atmospheric torques on Earth computed from atmospheric model outputs, J. Geophys. Res., 108(B2), 2068, doi: /2001jb001196, Introduction [2] In geophysics, an interdisciplinary approach is increasingly used to interpret observational data, in particular for the study of Earth rotation. The global geophysical fluids such as the ocean and atmosphere are believed to be the major contributors to Earth s rotation fluctuations at timescales from hours to decades. Two approaches are found in the literature for the computation of the effects of the atmosphere and ocean on length-of-day variation, nutation, and polar motion: (1) the angular momentum approach and (2) the torque approach. Both have advantages and disadvantages. [3] Because of the basic principle of conservation of angular momentum, the angular momenta of different parts of a system are perfectly budgeted. Any change of this quantity is associated with torques acting on the system. If the solid Earth-atmosphere system is considered as isolated, any change in angular momentum of the atmosphere (AAM) is associated with an equal and opposite change in the solid Earth angular momentum, and thus in its rotation. We can thus compute the effect of the atmosphere on Earth rotation easily when the AAM is known. The atmospheric angular momentum is computed routinely from atmospheric global circulation models (GCM) and made available to the scientific community by the International Earth Rotation Service (IERS) Special Bureau for the Atmosphere (SBA [see Salstein et al., 1993; Chao et al., 2000]). The AAM is classically decomposed into two parts: Copyright 2003 by the American Geophysical Union /03/2001JB001196$09.00 a matter term (or pressure term), corresponding to the angular momentum of a rigid rotation of the atmosphere with the Earth, and a motion term (or wind term), corresponding to the relative angular momentum of the atmosphere with respect to the Earth. The AAM is an integrated parameter computed from well modeled atmospheric quantities (large-scale surface pressure and three-dimensional wind field), therefore the computation is very robust and the output of the different models are reasonably close one to another when the frequency is not too high (period larger than a few days). [4] Another approach, first used by Munk and Groves [1952] and explained with some more details by Wahr [1982], is the so-called torque approach. The atmosphere and the solid Earth are considered as a coupled system, interacting via three forces: pressure, gravitation and friction. The effect of the atmosphere on the Earth rotation is then computed from the total atmospheric torque acting on the Earth. This approach is numerically much more complicated, as the torque results from compensation of large quantities (numerical instability problems) and because the quantities used in the torque computation (the friction drag and surface pressure in the area where the topography gradient is large) are not well known and not well modeled. The computation of the torque is thus a delicate task and the results have to be considered with some caution. [5] Despite this problem of delicate computation, the torque approaches provides important insights into the reasons why the Earth rotation varies. For instance, there are particular regions of the globe where the interaction between the atmosphere, the ocean, and/or the solid Earth is ETG 3-1

2 ETG 3-2 DE VIRON AND DEHANT: TEST OF THE ATMOSPHERIC TORQUES stronger than in others. The torque approach allows a geographical study of the interaction which are particularly enlightening [see, e.g., de Viron et al., 2001a]. As an example, the most important contribution to the mountain (topographic) torque can be obtained from places where the gradients of the topography in the zonal (for the axial component) and meridional (equatorial components) directions are important [see de Viron et al., 2001b, Figure 1]. The equatorial mountain torques have been shown to be mainly associated with pressure effects on the Antarctica, the Himalayas, and the Rockies, the axial mountain torque being mainly generated in the Himalayas and Andes areas. [6] Before using the torque to study the Earth-atmosphere interaction, it is necessary to test the torque computations by comparing these torques to other quantities. An obvious test is to test the AAM budget equation (equation (1) applied to the atmosphere). This has been done for the axial component first by Wahr and Oort [1983], who have shown that the AAM time derivative was reasonably close to the total torque, and for the equatorial component, by de Viron et al. [1999], who have shown an even better agreement. [7] The purpose of this paper is to examine the torques from reanalysis of different atmospheric GCMs, in order to study to what extent the computation of torques from outputs of these different models are reliable and to assess the uncertainty of these modeled quantities. [8] In section 2, the data used are briefly described. In section 3, the comparison methods for the torques are explained with some details. Section 4 will be devoted to the comparison of the same torques from different models. In section 5, the angular momentum budget equation is tested for each of the model. Concluding remarks are given in section Data Used and Their Preparation [9] We have used the outputs of reanalysis runs of three different atmospheric models: (1) the NASA Data Assimilation Office (DAO) Earth Observation System-1 (GEOS-1) model: this model has a degree of resolution, with data every 3 hours, from March 1980 to February 1994; (2) the National Center for Environmental Prediction (NCEP) reanalysis model: the outputs used are given on a Gaussian grid every 6 hours, from January 1968 to December 1999, and (3) the European Center for Medium-range Weather Forecast (ECMWF) reanalysis model (ERA-15): the outputs used have a 1 1 degree resolution, every 6 hours, from December 1978 to February [10] We used the surface pressure and the friction drag fields, as well as a topography files, to compute the torques. In the case of the NCEP reanalysis, the topography was given in spherical harmonics; this allows a more precise computation of the derivative of the topography. For the other models, the topography is given on the same grid as the data fields. [11] The torque has been computed for the three components: (1) the axial torque, along the Z axis, inducing an incremental rotation around the mean rotation axis, and (2) and (3) the two equatorial torque components inducing a motion of the rotation axis in the plan perpendicular to the mean rotation axis. The X axis is materialized by the axis in the equator passing through the Earth center and the 0 longitude meridian. With the X and Z axes, the Y axis forms a rectangular coordinate system. [12] The AAM series used in this work are provided by the SBA, with a 6 hour time step. The torque series have been computed using the classical expression given, for instance, by de Viron et al. [2001b]: the total torque is composed of a pressure torque on the topography (mountain torque), a friction torque, and a gravitational torque due to the gravitational coupling between mass anomalies inside the Earth and in the atmosphere. For the equatorial component, the major part of the mountain torque is due to the Earth flattening and the major part of the gravitational torque is due to the ellipsoidal part of the of the gravitational potential, related to the coefficient of degree 2order0(J 2 ) of its spherical harmonic development. As explained by Wahr [1982], the sum of those two effects is given by & Pressure on ellipsoidal þ & Gravitational on J2 ¼ & Ellipsoidal ¼ 6 ^ H Matter : ð1þ The remaining part of the gravitational torque has been shown to be negligible [see, e.g., de Viron et al., 1999], and it will not be addressed in what follows. 3. Comparison Methods [13] We test the torque series by two different ways. First, we compare the same torques in different GCMs. As the quantities used to compute the torque are not as robust as the quantities used in the AAM computation, and as there is possibility of numerical instability due to the difference of large close numbers in the computation, it is desirable to verify whether the models give the same results when the total torque is integrated. This test will be done in two parts: (1) we compute the coherence between the torque series for each pair of models by Fourier cross spectrum; and (2) we compute the Fourier spectrum of the different torques for the different models. This gives the relative magnitude of the different torque inside one model (mountain, ellipsoid and friction) and from one model to another. [14] As a second test, we will verify the AAM budget equation. This is not a very convincing test for the equatorial components, as the effect of the ellipsoid is important in both the torque and the AAM. Indeed, the time derivative of the AAM can be written, in the nonrotating frame, dh dt ¼ dh Nonrotating dt þ 6 ^ H Rotating ¼ dh dt þ 6 ^ H Matter þ 6 ^ H Wind : ð2þ Rotating The total torque acting on the atmosphere, using equation (1), can be written & Total ¼ & Ellipsoidal þ & Pressure nonellipsoid þ & Friction ¼ 6 ^ H Matter þ & Pressure nonellipsoid þ & Friction : The two equations have a common term, ^ H matter, which is about 95% of the signal. Therefore the AAM budget ð3þ

3 DE VIRON AND DEHANT: TEST OF THE ATMOSPHERIC TORQUES ETG 3-3 Figure 1. Coherence between the local mountain torques obtained from different atmospheric models. equation is easily satisfied in the equatorial component at at least the 95% level. As this part corresponds to the same terms in the torque and angular momentum changes, only the comparison of the remaining terms constitutes an effective test of the quality of the computation. Thus we remove these common terms from the equations and consider the residuals dh dt 6 ^ H Matter ¼ dh Nonrotating dt þ 6 ^ H Wind Rotating & Total 6 ^ H Matter ¼ & Pressure nonellipsoid þ & Friction : A test of the equality of both right-hand sides of (4) and (5) is used to test the validity of the angular momentum budget. Nevertheless, we have to keep in mind that we are dealing then with only about 5% of the signal. This system is tested both in the time and in the frequency domain. 4. Comparison of the Torques Derived From Different Models 4.1. Ellipsoidal Torque [15] The coherency between the ellipsoidal torque of each pair of models (not shown) is very high for the periods not too short (more than 10 days). The coherency is higher between the ERA and NCEP model than the respective coherency with the GEOS-1. For periods shorter than 10 days, the three models give results that differ very much. This was already obtained in the particular case of the retrograde diurnal motion by Yseboodt et al. [2002], for the matter term of the AAM. The coherence is usually fairly ð4þ ð5þ close to one, and stays in general very high for periods longer than annual. The coherency is slightly better for Y than for X at low frequency. This is probably due to geometrical considerations, the X component being associated mainly with continents (Eurasia and America) and the Y component being more associated with oceans, as the large-scale pressure at the surface of the oceans might be easier to model than the large-scale surface pressure over the continents, mainly where large topographic gradients are present. It must be noted that the ellipsoidal torque is a global computation of a large-scale phenomenon, it is an integrating operation, and is consequently not very sensitive to local error into the data. [16] From the spectrum of the ellipsoidal torque (not shown), some interesting differences between the models can be noticed: (1) at diurnal frequency, the ERA model has an ellipsoidal torque much larger than the others; this is interesting because de Viron et al. [2001b] have shown that the total torque is too small at diurnal frequency to explain the AAM time variation for the NCEP model; (2) for the day periods, the GEOS-1 model has more energy in X and the ERA model has more energy than the others in Y; and (3) at annual frequency, the ERA model has less energy than the others for both components. Nevertheless, for the ellipsoidal torque, the coherence between the series remains in general very good The (Local) Mountain Torque [17] Figure 1 shows the coherences between the local mountain torques obtained from the different atmospheric models. The coherences are rather good between the different models but not as good as for the ellipsoidal torque. This is not surprising as the mountain torque is

4 ETG 3-4 DE VIRON AND DEHANT: TEST OF THE ATMOSPHERIC TORQUES Figure 2. Coherence between the friction torques obtained from different atmospheric models. highly sensitive to the short scale of the surface pressure and topography. A part of the discrepancy is probably related to the difference of resolution of the three models. The coherency is better for X and Y than for Z. As explained by de Viron et al. [2001b], the equatorial mountain torques (X and Y components) are mainly related to pressure differences on the south and north sides of mountains, the major contribution coming from Antarctica, Asia, and North America. Conversely, the axial mountain torque (Z ) is only due to differences of pressure between the East and West sides of mountains, the major contribution being given by Asia, South America, and, to a lesser extent, North America. The explanation of the better coherence for X and Y probably originates in the precision obtained by the models in the locations mentioned above. The coherency is usually better for the pair composed by NCEP and ERA, nevertheless, at low frequency, the GEOS-NCEP pair seems to be more coherent in Y and Z and the ERA model seems to have low coherence for these components with any of the two other models. [18] From the spectrum of the local mountain torque for the three components (not shown), a good agreement is found between the three models, but not as good as for the ellipsoidal torque. In particular, the ERA model gives a much larger axial torque than the two others. The difference is very large for the annual component; one of the results is that, in this model, the mountain torque is the dominant effect for the annual component. The GEOS-1 model shows smaller annual effect for the equatorial components than the two others. This difference can be due to the orography used in the model, or to the local pressure distribution Friction Torque [19] Figure 2 shows the coherency for the three components of the friction torque. It is very high between the NCEP and ERA models at all the periods longer than 20 days. The GEOS-1 model is very different from the two other models in the equatorial components but shows a good agreement for the axial torque. This good agreement for the friction torque is perhaps surprising as the friction drag is a quantity whose modeling is still difficult. Nevertheless, the better quality for the Z component is not surprising, as the zonal wind (that is associated with zonal friction drag) is usually better modeled that the meridional wind. [20] In Figure 3, we have drawn the spectrum of the friction torque for the three models and the three components. As for the coherency, the GEOS-1 model is very different from the two others in the equatorial components, and has a clearly smaller friction torque. The two other models agree quite well for nearly all the frequencies. 5. Angular Momentum Budget Equation for the Different Models [21] The coherence between the total torque and the AAM time derivative has been computed for the three components and for the three models has been computed. As expected from section 4.1, the coherence is very high for the X and Y component, for all the models, as already shown in the case of the GEOS-1 de Viron et al., 1999] and NCEP [Dehant and de Viron, 2002], except at high frequency (period smaller than 10 days). When the ellipsoidal torque is removed from the torque and AAM time derivative, the coherency in X and Y decrease strongly, as shown in the

5 DE VIRON AND DEHANT: TEST OF THE ATMOSPHERIC TORQUES ETG 3-5 Figure 3. Spectrum of the friction for the different models, unit Nm. case of the ERA model in Figure 4. The situation is even worse for GEOS-1 and NCEP. [22] Even if the coherency is poor, we keep a fair match between the AAM time derivative and the torque for the equatorial component for the NCEP model and the ERA model (see Figures 5 and 6). This is not the case for the GEOS-1 model. Note that if both ERA and NCEP models show a fair match in the residuals when testing the Figure 4. Coherence between total torque and AAM time derivative for the ERA model.

6 ETG 3-6 DE VIRON AND DEHANT: TEST OF THE ATMOSPHERIC TORQUES Figure 5. Time series of the AAM budget for the NCEP model, when the ellipsoidal effect is removed. individual AAM budget, they do not agree very much with one another. 6. Discussion and Conclusions [23] The mean purpose of this paper is to test the reliability of the gravitational, pressure and friction torques computed from the outputs of global atmospheric circulation reanalysis models. The classical way of testing the torques is to compare their sum with the AAM time derivative. We extend the analysis with some more discriminating tests. [24] First, we compare the series of values of the same torque coming from different models (ERA, NCEP reanalysis, and GEOS-1). The results are summarized in Figures 7 Figure 6. Time series of the AAM budget for the ERA model, when the ellipsoidal effect is removed.

7 DE VIRON AND DEHANT: TEST OF THE ATMOSPHERIC TORQUES ETG 3-7 Figure 7. Summary of the coherency between the torque series obtained from different models. See color version of this figure at back of this issue. and 8. Figure 7 summarizes the coherency between the same torques in different models. We show a good agreement at long period between the series for all the torques except the equatorial friction torque. The mountain and ellipsoidal equatorial torque are usually in better agreement than the corresponding axial torques, except at high frequencies. This agreement shows that torques are not too model-dependent. Figure 8 summarizes the comparison of the spectrum. It can be seen that it is usually good. [25] Second, we verify the AAM budget equation. Figure 9 summarizes the AAM budget equation for all the models. The AAM budget equation is verified for the equatorial components, except at high frequencies; for the axial component, it is verified except at very high and very low frequencies. This verification was then completed by comparing the two sides of the equation subtracting the common term ( ^ H matter ). When the ellipsoidal effect is removed, the situation get worse, as expected. Nevertheless, the computation conserves the AAM for two of the models at frequencies between 10 and 100 days. From our study, the tests in the frequency domain give more detailed and results show worse disagreements than what is apparent in the time domain. Indeed the AAM budget equation seems reasonably well verified for two of the models in the time domain, while Figure 9 presents existing discrepancies. [26] The two tests that we have performed show that when the frequency considered is not too high, the torque series are reliable, and can be used to study the global dynamics of the atmosphere. In this case, they explain indeed quite well the AAM variation in the time domain. Nevertheless, there are still differences between the models, and there is no exact matching of the AAM time derivative and the total torque; the level of disagreement is large enough to obtain observable discrepancies in the atmospherically induced Earth rotation at an observable level. In particular, the different equatorial torques show quite different residuals when the ellipsoidal parts are removed, even if, for two of the models, there is good agreement in the time domain between the equatorial torque and the AAM time derivative when the ellipsoidal effect is removed. [27] Our conclusion from this study is that the torques computed from the outputs of the atmospheric models should not be used to make computational predictions for geodesy, as they are not precise enough to provide Earth rotation corrections with accuracy comparable to the observation accuracy. The AAM is thought to be more reliable for geodesy applications, as it is less sensitive to delicate computations from the numerical point of view than it is for the torques. [28] Any differences between the models can be the cause of differences between the torques. In our opinion, several causes are likely to create nonnegligible torque problems: 1. As we said in section 1, unlike the AAM, the torque is the result of the difference of large numbers, which requires a high precision in the knowledge of each quantity. This is not an error source by it-self, but it will amplify the other errors. 2. The models do not have the same spatial resolution. This can affect strongly the torques, mainly at high frequency. The AAM is not much affected by these differences. 3. The topographies inside the models are not exactly the same. This affects the mountain torque. 4. The parameterization of the friction drag may differ somewhat, as it is a parameter not very well constrained in the models. 5. The mass exchange between the atmosphere, the ocean and the hydrosphere are probably different between the different models, which has repercussion on the torques. Figure 8. Summary of the comparison of the torque series obtained from different models. See color version of this figure at back of this issue.

8 ETG 3-8 DE VIRON AND DEHANT: TEST OF THE ATMOSPHERIC TORQUES Figure 9. Verification of the AAM budget for the different models. See color version of this figure at back of this issue. 6. The subgrid scale interaction (gravity-wave drag) between the Earth and the atmosphere is most probably modeled differently in the different model. This affects mainly the short timescale. [29] Nevertheless, the torque approach can and should be considered in improving the physical understanding of the dynamics of the momentum exchange between the atmosphere and the Earth, as it provides insight about how and where this exchange takes place. The estimates of the variations in the Earth rotation due to the atmosphere from the torque approach can only be considered as crude, but their relative influences as functions of the geophysical sources (pressure, gravitation and friction) and their dependence on the spatial distribution, can be studied. This has been done in several studies, for instance, in the case of the 1989 La Nina event, by de Viron et al. [2001a] or at the diurnal frequency, by de Viron et al. [2001b]. [30] The postprocessing associated with the torque computation is also a source of computational errors. Consequently, it would be very useful for geodesy if the torque series are computed routinely as output of the atmospheric models. [31] The success of the test at periods between 20 days and 2 years encourages us to use the torque in the study of atmospheric forcing on Earth rotation at those periods, with some caution at the annual period for the ERA model. [32] Acknowledgments. The NCEP Reanalysis data were provided by the NOAA-CIRES Climate Diagnostic Center, Boulder, Colorado, from their web site at The ERA-15 data were provided by the ECMWF; the help of D. Lucas (ECMWF) in the processing of those data is gratefully acknowledged. The GEOS-1 data originate from NASA s Data Assimilation Office, provided to us by D. Salstein under a NASA grant. O.d.V. is postdoctoral researcher of the Belgian Fonds National de la Recherche Scientifique. References Chao, B. F., V. Dehant, R. S. Gross, R. D. Ray, D. A. Salstein, M. M. Watkins, and C. R. Wilson, Space geodesy monitors mass transports in global geophysical fluids, Eos Trans. AGU, 81(22), , Dehant, V., and O. de Viron, Earth rotation as an interdisciplinary topic shared by astronomers, geodesists and geophysicists, Adv. Space Res., in press, de Viron, O., C. Bizouard, D. Salstein, and V. Dehant, Atmospheric torque on the Earth and comparison with atmospheric angular momentum variations, J. Geophys. Res., 104, , de Viron, O., S. L. Marcus, and J. Dickey, Atmospheric torques during the winter: Impact of ENSO and NAO positive phase, Geophys. Res. Lett., 28(10), , 2001a. de Viron, O., S. L. Marcus, and J. O. Dickey, Diurnal angular momentum budget of the atmosphere and its consequences for the Earth s nutation, J. Geophys. Res., 106, 26,747 26,759, 2001b. Munk, W., and G. Groves, The effect of winds and ocean currents on the annual variation in latitude, J. Meteorol., 9, , Salstein, D. A., D. M. Kann, A. J. Miller, and R. D. Rosen, The Sub-Bureau for Atmospheric Angular Momentum of the International Earth Rotation Service A meteorological data center with geodetic applications, Bull. Am. Meteorol. Soc., 74, 67 80, Wahr, J. M., The effects of the atmosphere and oceans on the Earth s wobble, 1, Theory, Geophys. J. R. Astron. S., 70(2), , Wahr, J. M., and A. H. Oort, Friction- and mountain-torques estimates from global atmospheric data, J. Atmos. Sci., 41, , Yseboodt, M., O. de Viron, T. M. Chin, and V. Dehant, Atmospheric excitation of the Earth nutation: Comparison of different atmospheric models, J. Geophys. Res., 107(B2), 2036, /2000JB000042, V. Dehant and O. de Viron, Royal Observatory of Belgium, Avenue Circulaire, 3, B-1180 Brussels, Belgium. (o.deviron@oma.be; v.dehant@ oma.be)

9 DE VIRON AND DEHANT: TEST OF THE ATMOSPHERIC TORQUES Figure 7. Summary of the coherency between the torque series obtained from different models. Figure 8. Summary of the comparison of the torque series obtained from different models. Figure 9. Verification of the AAM budget for the different models. ETG 3-7 and ETG 3-8