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 Numerous fields of computational Earth system research require a precise account of variations in the relative atmospheric angular momentum (AAM). Since zonal winds from reanalysis data sets of ERA-40 (ECMWF) and NCEP1 (NCEP/NCAR) are frequently used to compute relative AAM estimates it is critically important to understand uncertainties in these data products. Here, we discuss the varying degree of structural and internal uncertainties associated with ERA-40 and NCEP1 zonal wind data in the tropical Pacific troposphere and lower stratosphere. We assess these uncertainties by quantifying differences in relative AAM computed from reanalyses wind data (1958–2000), that are subsequently compared to a 10-year record of radiosonde observations carried out in the tropical Pacific where reanalyses data differ most. While our analysis suggests that in general differences between reanalysis data and observed tropical winds in the Pacific are not significantly different from each other, we found varying degrees of discrepancies at each radiosonde site. Zonal winds in NCEP1 data (RMS = 1.84 ms−1) reproduce less bias in tropospheric easterly winds than ERA-40 (RMS = 3 ms−1), while for the lower stratosphere ERA-40 data fit better westerly winds (RMS = 3.95 ms−1) than NCEP1 (RMS = 5.03 ms−1). Anomalies in zonal tropical wind fields can be induced by large mountain and friction torques that efficiently affect Earth's rotation rate. Hence, a precise account of the wind term in reanalysis data directly determines the accuracy of computed estimates of relative AAM.
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 On timescales of months to decades the Earth can be considered as a closed system in the absence of external torques exerted by the moon and sun. Thus, any changes in the angular momentum (AM) in one sub-component of the Earth system, such as the atmosphere or the ocean, are compensated by changes in the momentum of the others to conserve Earth's total AM. Barnes et al.  were the first to report that most of the temporal variability in the total global AM results from fluctuations in the angular momentum of the atmosphere (AAM). On interannual time scales fluctuations in the AAM affect Earth's rotation rate that can be assessed by two different approaches [Oort, 1989; Hide and Dickey, 1991]. In the so-called angular momentum approach changes in the AM of the solid Earth are deduced from variations in the AAM. The second method considers the torque-approach where the atmosphere exerts an external torque on the solid Earth causing a change of its angular momentum. The angular momentum of the atmosphere is separated into two components, the pressure (matter) and wind (current) term. The pressure term relates to the momentum corresponding to a global rotation of the masses in the atmosphere with the Earth. Our study is concerned with the wind term that corresponds to the relative angular momentum of the atmosphere with respect to the rotating Earth. Fluctuations in the relative AAM are induced by seasonal and interannual variations in zonal winds through the effect of mountain and friction torques [Oort, 1989; Hide and Dickey, 1991]. To conserve total angular momentum the solid Earth responds to changes in relative AAM by adapting its rotation rate and thus the length of the day (LOD). A major source of the relative AAM are the Tropics where Earth's surface rotates fasted compared to regions at higher latitudes.
 Each of the two AAM approaches provides different assets and drawbacks over the other. The major disadvantage of the torque approach is that its computation requires a precise account of each torque in Earth's subsystems to correctly compute the total torque. Egger et al.  for instance, reported on differences of torques computed from NCEP1 and ERA data due to a computational analysis error in the generation of the reanalysis data sets. Another study by Huang et al.  identified a flawed parameterization scheme used in the NCEP general circulation model (GCM) causing an erroneous calculation of the gravity torque. In both cases, the models were not able to correctly close the balance in the AAM budget as calculated from observations. In contrast, a major advantage of the angular momentum approach is that the straight forward computation of the AAM from data of an atmospheric analysis system. As a result several long-term angular momentum data sets are now available worldwide (i.e., UKMO, http://badc.nerc.ac.uk/view/badc.nerc.ac.uk; JMA-25 [Onogi et al., 2007]) In general, the accessibility and global spatial coverage of these data sets provide a prime choice to conduct climate studies across the globe particularly when observational data are scarce or missing.
 Fluctuations in relative AAM and corresponding changes in LOD are of particular interest for model evaluations since they can be used as diagnostic tools to evaluate the ability of GCMs and weather forecast models to realistically produce the global distribution of wind and pressure patterns [i.e., Hide et al., 1998; Bell et al., 1991; Huang et al., 2004; Marti et al., 2010; Boer and Lambert, 2007]. Some recent research has been carried out assessing the physical characteristics of zonal winds from the ERA-40 and NCEP reanalysis data and others. Masaki  reports on a significant bias in relative AAM computed from ERA-40 and NCEP2 (NCEP1's successor reanalysis data set) in the tropical Pacific due to large annual differences in their wind terms with ERA-40 producing a weaker tropospheric easterly wind component than the NCEP2 data. A study by De Viron and Dehant  identified great discrepancies in the wind term at low frequencies in meteorological data sets from the ECMWF, JMA, NCEP operational data, and NCEP1 reanalysis. However, as long as reanalysis data are not compared to observations it is not possible to assess which reanalysis data set provides the most accurate account of wind information to compute the most precise estimate of relative AAM.
 In our study we first compare relative AAM estimates computed from zonal winds in ERA-40 (ECMWF) and NCEP1 (NCEP/NCAR) over a 43-year record for differences in their spatial contributions and over atmospheric layers. Subsequently, we evaluate their spatial discrepancies against radiosonde observations at several sites in the tropical Pacific over a 10-year record. In section 2 we describe the data and the methods used for our assessment. A summary and discussion of results is given in section 3 while the last section provides conclusions from our findings.
2. Data and Methods
2.1. Reanalysis Products and Radiosonde Observations
 Zonal wind fields from the two well-known global meteorological reanalysis products ERA-40 (ECMWF) and NCEP1 (NCEP/NCAR) have been produced with a ‘frozen’ state-of-the-art assimilation and forecast model system that comprises several analysis steps [Uppala et al., 2005; Kalnay et al., 1996]. The final reanalysis data product depends implicitly on the dynamics and physics of the forecast model and the quality of the observations. We used monthly relative AAM estimates because any anomaly that may exist just by persistency from the previous month is averaged out on this time scale [Weickmann et al., 2000]. Then again, zonal wind patterns associated with changes in Earth's rotation rate and thus relate to fluctuations in the relative AAM exhibit on semi-annual, annual and quasi-biennial time scales [i.e., Lambeck and Cazenave, 1973, and references therein]. The ERA-40 product contains data on 23 standard pressure levels (1000–1 hPa) on a reduced Gaussian grid with a spacing of 2.5° while the NCEP1 monthly data were available on a lat/lon 2.5° grid with 17 standard pressure levels (1000–10 hPa). In our analysis we evaluated the reanalysis data against radiosonde data as the most consistent observations carried out throughout the atmosphere [Onogi, 2000]. The radiosonde sites (Table 2) were selected according to their location within the Pacific Tropics and their unique lengthy data record from 1991 to 2000. The radiosonde sites reside within a box region between 20°S to 20°N and 180°W to 60°W (Figure 6) where our study identified the largest bias in relative AAMERA-40 and AAMNCEP1, and in corresponding zonal winds. Radiosonde observations were launched once or twice a day at 00:00 and/or 12:00 UTC. The number of observations, however, taken at each site between surface (1000 hPa) and the upper atmosphere (10 hPa) varies with radiosonde location. For our analysis we selected wind observations in accordance to standard pressure levels between the surface layer (1000 hPa) and lower stratosphere (10 hPa) corresponding to the vertical resolution of the two reanalysis data sets. Since observations at the four radiosonde sites were distributed non-homogeneously in time over the selected analysis period we averaged the wind data at each site and for each pressure level from 1991 to 2000.
 Neglecting height of the atmosphere and small latitude variations in the acceleration of gravity and the radius of Earth, we derived relative AAM values from zonal winds on pressure levels integrated over the total atmosphere, according to the formulation described in Barnes et al. ,
where, R is the mean radius of the Earth (6.37 × 106 m), g is the mean acceleration of gravity (9.81 m/s2), ps is the surface pressure, and u is the zonal component of wind. The right-hand side of this equation is integrated over longitude λ, latitude Φ, and pressure levels p. We estimate AAMRel by approximating the surface pressure ps with a constant p of 1000 hPa and the top pressure level at 10 hPa because both reanalysis data sets exclude ps and include wind data as zonal means on pressure coordinates. Computation of monthly AAMRel from this type of data is straightforward as it only requires the use of monthly mean zonal wind. Since winds near the surface tend to be weak, we found that errors caused by this approximation are likely to be small. From each of the two reanalysis data sets we computed time series of monthly sums of relative AAM (equation (1)) by performing a global mass- and area-weighted vertical integral. In order to compare zonal winds from reanalyses with observations all data were averaged over the time period 1991 to 2000. Since reanalysis data are located on grid points they had to be interpolated by bilinearly interpolation from the four nearest grid points to the coordinates of the radiosonde sites.
 Applying a cross wavelet transform (XWT) on the relative AAMERA-40 and AAMNCEP1 can provide more insight into how both time series relate to climate processes that exist at various time frequencies. The cross wavelet transform (XWT) we used on the relative AAM time series is constructed from the continuous wavelet transform (CWT) from each of the AAMERA-40 and AAMNCEP1 time series. CWT analysis was chosen using the Morlet wavelet to better extract intuitive features in each data set [Torrence and Compo, 1998].
 For atmospheric levels from 1000 hPa to 50 hPa we calculated at each station standard root mean squares (RMS) statistics by averaging the squared differences between reanalysis data and observations and taking from this estimate the square root. Any analysis above the pressure level of 50 hPa was not feasible since radiosonde observations become scarcer and the reanalysis model is stronger constraint by its model physics than by observations [Baldwin and Gray, 2005; Punge and Giorgetta, 2007]. Furthermore, we applied error statistics to evaluate discrepancies between reanalysis data and radiosonde observations itself as well as to examine the variability within the data on tropospheric (1000–200hPa) and stratospheric (200–50 hPa) atmospheric levels at each station. The standard error was calculated by dividing the standard deviation from zonal winds from their mean by the square root of number of measurements. As a more stringent approach to identify the statistical significance of bias between reanalysis data and observations at each radiosonde site we applied the two-sample paired t-test at the 95% significance level.
3.1. Comparison Between ERA-40 and NCEP-1 Reanalysis Products
 Over a time period from 1958 to 2000 we found a positive offset of the mean relative AAMERA-40 (1.50 × 1026kgm2s−1) over AAMNCEP1 (1.41 × 1026kgm2s−1) by 6%. Since the annual cycle of the relative AAM is forced by seasonal fluctuations in zonal winds [i.e., Barnes et al., 1983; Hide and Dickey, 1991] we compared the long-term annual mean cycle of the relative AAMERA-40 and AAMNCEP1 to investigate possible discrepancies in the representation of seasonal processes (Figure 1). The annual mean cycle of both reanalyses exhibit distinct maxima of computed relative AAM for the months December to February (DJF) and September to November (SON), with a minor decrease in winter and a pronounced minimum from June to August (JJA). The minor minimum in winter between January and February has been discussed in previous studies [see Huang and Sardeshmukh, 2000, and references therein] and has been noted as early as in 1953 by Smith and Tucker . Lambeck and Cazenave  were the first who reported that the midwinter minimum also corresponds with observed variations in the length of day (LOD). Since the semi-annual and annual cycle of each of the computed relative AAM estimates explain more than 95% of the seasonal variations with their pronounced winter and summer variations [see Huang and Sardeshmukh, 2000, Figure 1a], our analysis will further focus on those two and differences between the two reanalysis data sets. We found that the resulting amplitude in Figure 1 between seasonal extremes from December to February and June to August (DJF-JJA) in relative AAMERA-40 and AAMNCEP1 is as much as 4 × 1026kgm2s−1. Monthly mean contributions of AAMERA-40 differ from AAMNCEP1, however, as much as by 8% when zonal winds increase on both hemispheres during the boreal seasons of spring (MAM) and fall (SON), while for the season JJA it is less than 5%.
 Comparing monthly mean estimates of AAMERA-40 and AAMNCEP1 over a multidecadal time period from 1958 to 2000 (Figure 2) revealed a persistent positive offset of AAMERA-40 over AAMNCEP1. However, since 1981 this relationship has been even slightly improved with r2 = 70% compared to r2 = 68% from 1958 to 1980. For the last two decades (1981–2000) AAMERA-40 observed a slight increase in variability (s2 = 0.06 × 1026kgm2s−1) compared to AAMNCEP while there were no differences (both s2 = 0.05 × 1026kgm2s−1) in the first two decades of the analyzed time period.
 The large bias between the time series of AAMERA-40 and AAMNCEP1 (Figure 2) that can be seen at certain time periods between 1958 to 2000 is further investigated to determine whether this bias relates to differences in the representation of climate processes. Our cross wavelet analysis indicates high common power for the relative AAMERA-40 and AAMNCEP1 at the semi-annual (6 months period) and annual (12 months period) frequency band that is significant at the 5% level (Figure 3). For the semiannual and annual periods we observe arrows that indicate an in-phase relative relationship by pointing right (60°) while for the marked 24–32 and 24–64 bands arrows indicate a slightly out-of phase relationship by pointing 90° down with the relative AAMERA-40 leading AAMNCEP1. The analysis suggests for the 24 to 64 months band a smaller common power spectrum since the early 1980s when a string of El Niño - Southern Oscillation (ENSO) events occurred that lasted into the late 1990s. The ENSO phenomenon describes a coupled quasiperiodic ocean-climate pattern observed across the tropical Pacific Ocean roughly every two to five years. The ENSO band coincides with high common power in quasiperiodic variations at the 24–32 frequency band for the late 1980s to the mid 1990s. This feature can be attributed to the occurrence of the quasi-biennial oscillation (QBO) of equatorial zonal winds. The QBO is an alternating wind regime between easterlies and westerlies in the tropical stratosphere with a mean period of 28 to 29 months. The relation between QBO and ENSO events as demonstrated in their common time-frequency domain was first revealed by Angell .
Figure 4 displays from which part of the atmosphere discrepancies in AAMERA-40 and AAMNCEP1 arise. Globally integrated contributions of computed relative AAM is presented as a function of pressure levels from the surface (1000 hPa) to the top of the atmosphere (10 hPa) averaged over the time period 1958 to 2000. Mean contributions of relative AAMERA-40 and AAMNCEP1 steadily increase from small negative amounts near the surface to a maximum of more than 200 × 1023kgm2s−1 in the troposphere (300 hPa) while largest estimates are observed in the troposphere between 500 hPa and 300 hPa where subtropical jets dominate the zonal flow in both hemispheres. However, over most of the troposphere AAMNCEP1 mean contributions are smaller than those from AAMERA-40 (Table 1). Largest differences between computed estimates of relative AAM are found in the middle troposphere between 925 hPa and 400 hPa with a maximum bias on pressure level 600 hPa where AAMERA-40 differs from AAMNCEP1by as much as 15%. At the top of the troposphere (50 hPa–10 hPa) computed estimates of relative AAM become highly uncertain since assimilated stratospheric observations are scarce and do not provide a reliable account of zonal flow with increasing atmospheric heights [Baldwin and Gray, 2005; Punge and Giorgetta, 2007].
Table 1. Mean Differences (1958–2000) in Percent Between Computed Relative AAMNCEP1 Versus AAMERA-40 for Pressure Levels 1000 hPa to 10 hPaa
Pressure Level (hPa)
AAMNCEP1 Versus AAMERA-40 (%)
Numbers in percent (right column) describe how much AAMNCEP1 under/overestimates AAMERA-40.
 To gain better insight into the layer by layer biases in AAMERA-40 and AAMNCEP1 and their seasonal differences we investigated their horizontal distribution.
 Correspondingly to the large vertical bias in computed relative AAM estimates diagnosed in Figure 3 we averaged AAMdiff estimates over pressure levels 925 hPa to 400hP and displayed the relative AAMdiff (AAMERA-40 minus AAMNCEP1) at each grid point averaged over all time steps between 1958 and 2000 and displayed on a 2.5° × 2.5° grid (Figures 5a–5d). All seasons show estimates of AAMdiff that are typically between 3 × 1010kgm2s−1 and 2 × 1010kgm2s−1 or less over most of the globe with instances of both positive and negative bias in different regions. For the analyzed area in the tropical Pacific (20°S to 20°N, 180°W to 60°W) we observe for all seasons large differences between 9 × 1010kgm2s−1 to 15 × 1010kgm2s−1 and more. Regions of maximum AAMdiff are remarkably stable over the seasons. A maximum in AAMdiff of 18 × 1010kgm2s−1 and more resides at the west coast of Central America. Between northern summer (JJA) and fall (SON) the center of largest AAMdiff moves from the region of Central America to the Northwest coast of Chile (12 × 1010kgm2s−1 ≤ ≥ 15 × 1010kgm2s−1). Over all seasons, but in particular during the boreal winter (DJF) a distinct belt of strong low-level westerlies between 30°S and 60°S evolves on the southern hemisphere with estimates of AAMdiff of about 3 × 1010kgm2s−1. Since the equatorial Pacific observes predominately easterly lower level winds (trade winds) in the troposphere (925–400 hPa) relative AAM estimates computed from easterlies are negative for this region. A positive bias, thus, indicates that AAMERA-40 is characterized by weaker easterlies compared to AAMNCEP1 reanalysis data.
 The following section investigates how well zonal winds from ERA-40 and NCEP1 reanalysis products agree with radiosonde data.
3.2. Comparison Between Reanalysis Products and Radiosonde Observations
 When we compare wind observations from radiosonde sites (Figure 6 and Table 2) we have to consider that these observations have been assimilated to some extent into both, ERA-40 and NCEP1 reanalysis products. As a result the reanalysis data are not independent from observations. Over a time period from 1991 to 2000 we compared zonal wind data from each of the two reanalyses to radiosonde observations located in the equatorial Pacific region where we identified the largest bias in computed relative AAM estimates (Figure 7). Since Bogota (Colombia) is located at 2500 amsl radiosonde observations could not be carried out for pressure levels 1000 hPa, 925 hPa, and 850 hPa. We found systematic positive deviations from radiosonde values in both reanalyses with varying degree. Both reanalyses show largest mean differences to observations in the troposphere between pressure levels 925 hPa and 400 hPa corresponding to those levels where they also diverge most from each other (see Figure 4 and Table 1). Since the equatorial troposphere (1000 hPa–200 hPa) observes low-level prevailing easterly winds, our analysis suggests that in both reanalyses the easterly wind component in this region is weaker compared to radiosonde values with ERA-40 exhibiting a larger difference in easterly winds compared to NCEP1. However, for the upper troposphere and lower stratosphere (200 hPa to 50 hPa) with their predominately strong westerly winds we see at all radiosonde sites a negative bias between reanalyses and observations. The negative differences in zonal wind flow suggest that both reanalysis products under predict westerly upper tropospheric and stratospheric winds with ERA-40 data producing a smaller bias.
Table 2. Radiosonde Sites Located Within the Analyzed Tropical Region (20°S–20°N and 180°W–60°W) Listed With Their World Meteorological Organization (WMO) Numbers, Coordinates and Location Above Mean Sea Level (amsl)
Atuona, French Polynesia
San Cristobal (Galapagos), Ecuador
San Jose, Costa Rica
 Correspondingly to Figure 7 we assessed statistically the mean magnitude of the varying differences in zonal winds between reanalyses and at each radiosonde site. We found that at all sites the ERA-40 reanalysis showed weaker easterly winds (RMSNCEP1 = 3.0 ms−1; RMSERA-40 = 1.84 ms−1) than NCEP data between 1000 hPa and 200 hPa compared to radiosonde observations. Both reanalysis products show largest discrepancies to radiosonde observations for Atuona, French Polynesia (RMS = 5.0 ms−1) while smallest deviations are observed for both at San Jose, Costa Rica, (RMSERA-40 = 3.46 ms-1 and RMSNCEP1 = 2.74 ms-1). Our analysis found that for the upper troposphere and lower stratosphere (200 hPa–50 hPa) westerly winds in both reanalysis sets are weaker than in radiosonde data with ERA-40 reanalysis being closer (RMS = 3.95 ms−1) to radiosonde values than NCEP1 data (RMS = 5.03 ms−1). The largest deviation showed both reanalysis data again at Atuona (French Polynesia) with a RMS of more than 9.0 ms−1. Overall, the easterly flow of low-level trade winds in the analyzed area of the equatorial Pacific is slightly better reproduced by NCEP1 data while for the lower stratosphere ERA-40 winds fit closer observations.
 We further assessed graphically the uncertainty in discrepancies between the data at each radiosonde site for troposphere (Figure 8a) and stratosphere (Figure 8b). Both figures display the results of the mean zonal wind and its variability shown here as error bars with their ends representing the value for the respective standard error for each data set. Figure 8a shows the mean values and standard errors from reanalysis and observations that are all negative indicating an easterly wind component. The error bars at Atuona (French Polynesia) from reanalysis data and observations fall within each other's intervals, suggesting they are not significantly different from each other [Lanzate, 2005]. At this site, however, the mean observed easterly wind component (meanobs = 9.5 ± 1.32 ms−1) is clearly underestimated in ERA-40 by 33% and in NCEP1 by 15%. The variability in zonal winds from both reanalysis data sets (meanERA-40 = 2.65 ± 1.03 ms−1, meanNCEP1 = 3.38 ± 1.26 ms−1) is also smaller than in observed winds. Similar results are found at the Bogota (Columbia) site where variability in zonal winds from both reanalysis data (meanNCEP1 = 4.84 ± 0.62 ms−1, meanERA-40 = 3.55 ± 0.41 ms−1) is smaller (ERA-40 = 42%, NCEP1 = 21%) than in observed tropospheric easterly winds (meanobs = 6.12 ± 0.97 ms−1). Since error bars from the NCEP1 mean zonal wind overlap with the observed mean wind estimate suggesting no significant difference between both data. However, the error bars for ERA-40 and observed easterly winds fall not within each other indicating significant differences between both data sets. At San Cristobal (Ecuador) ERA-40 (meanERA-40 of 2.83 ± 0.32 ms−1) underestimates the mean observed easterly wind component (meanobs of 2.95 ± 1.32 ms−1) by only 4% while the mean NCEP1 zonal wind is stronger than observed by 21% (meanNCEP1 of 3.56 ± 0.69 ms−1). At the radiosonde site at San Jose (Costa Rica) the observed mean easterly wind component (meanobs = 2.95 ± 0.99 ms−1) is largely underestimated by both reanalyses (meanERA-40 = 0.65 ± 0.20 ms−1; meanNCEP1 = 1.11 ± 0.52 ms−1) by 62% for NCEP1 and 78% for ERA-40. Figure 8b shows the mean of zonal winds and its standard error for the stratosphere for all four radiosonde sites. At Atuona (French Polynesia), mean zonal winds from reanalysis data (meanERA-40 = 2.59 ± 2.03 ms−1, meanNCEP1 = 3.58 ± 1.58 ms−1) underestimate the observed mean westerly wind component by 65% (NCEP1) and 74% (ERA-40). However, zonal winds from both reanalysis data still vary within observed variability (meanObs = 10.14 ± 5.82 ms−1) suggesting that differences between the data are not significant. At Bogota (Columbia) reanalyses mean zonal winds also strongly underestimate the observed mean wind (meanObs = −2.67 ± 1.87 ms−1) by 82% (NCEP1) and 97% (ERA-40). The variability of ERA-40 and NCEP1 zonal winds (meanERA-40 = −0.09 ± 0.86 ms−1, meanNCEP1 = −0.48 ± 1.03−1), however still falls within error bars from observations. Thus, differences in data can be considered as insignificant. At San Cristobal (Ecuador) the variability of stratospheric westerly winds from both reanalysis data (meanERA-40 = 1.61 ± 1.20 ms−1, meanNCEP1 = 0.75 ± 1.25 ms−1) strongly underestimates observations (meanObs = 6.46 ± 2.73 ms−1). NCEP1 westerly winds underestimate mean observed winds in average by 88% while ERA-40 west winds are 75% less than observed. Since variability in both reanalysis data is within standard error for observations the data show no significant differences. San Jose (Costa Rica) stratospheric winds have an easterly component (meanObs = −2.65 ± 3.04 ms−1) while the trend in ERA-40 is stronger westerly (meanERA-40 = 1.33 ± 1.67 ms−1) and largely underestimates the east wind component by 150%. NCEP1 mean zonal winds evolve around zero (meanNCEP1 = −0.53 ± 1.28 ms−1) underestimating the easterly wind by 88%.
 As a more stringent approach to determine the statistical significance of differences between reanalysis data and observations we applied the two-tailed paired t-test. In general, at all four radiosonde stations reanalysis data show a less strong easterly wind component than observations. The t-statistic at the 95% confidence level suggests, however, that tropospheric zonal winds from NCEP1 are not significantly different from observations. Tropospheric zonal winds in ERA-40 data show that at San Jose (Costa Rica) tropospheric zonal winds are significantly less easterly than observations suggest. For the stratosphere trends in reanalysis data from Atuona (French Polynesia) and San Cristobal (Ecuador) show a weaker westerly wind component compared to observations. At Bogota (Columbia) and San Jose (Costa Rica) mean zonal winds from observations show an easterly component while it is only weakly expressed in both reanalysis data sets. Overall, t-statistic results suggest that discrepancies between the two reanalysis data and radiosonde values at all four sites can be considered as not significant.
4. Summary and Discussion
 The major goal of our study was to determine uncertainties in relative AAM contributions computed from zonal winds from the ERA-40 and NCEP1 reanalysis data products. The relative AAM is a quantity frequently used as a diagnostic tool in model evaluation and its estimates can be compared to observed geodetic time series. We discuss differences between the two reanalyses over a multidecade time period (1958–2000) and with regard to zonal winds from radiosonde observations (1991–2000). Since ERA-40 and NCEP1 reanalyses both used the same radiosonde wind observations to produce their final data products they should be qualitatively very similar [Onogi, 2000; Kistler et al., 2001, Uppala et al., 2005].
4.1. Relation Between Relative AAM Estimates Computed From ERA-40 and NCEP1 Reanalyses
 Since the early 1980s additional data sources such as satellite and ship data where introduced into the reanalysis data products that led to an improved relation between AAMERA-40 and AAMNCEP1 compared to the epoch 1958–1980. Although ECMWF and NCAR/NCEP share the various databases for producing their reanalysis data, we assume that differences in computational schemes, such as bias correction issues in their assimilation models lead to differences in the ERA-40 and NCEP1 reanalysis products. This is best shown for the period from 1979 to 1986, when during the extreme El Niño event from 8/1982–8/1983, AAMERA-40 estimates exceed AAMNCEP1 by 16% with a dominant AAMERA-40 peak that rises above AAMNCEP1's maximum by 25% (Figure 2). Simmons et al.  reported that the prominent peak of AAMERA-40 over AAMNCEP1 arises apparently from problems with ERA-40 bias adjustment in temperature data from satellite observations due early TIROS-N Operational Vertical Sounder (TOVS) data. This bias has also an effect on the representation of winds in the reanalysis data in particular since in the Tropics reanalysis wind fields are mostly computed from observed convergence flow [Kistler et al., 2001]. Thus, differences in the vertical profile of temperature can directly affect the determination of the tropical wind field. Overall, harmonization efforts between the two reanalysis data sets have been successful as results from a cross wavelet analysis (Figure 3) show. Additional data sources have been assimilated into the two data sets since the early 1980s. Since that time additional satellite data were introduced into the assimilation process of the final reanalysis products. As a result from this time epoch on both data sets show a high coherency in the frequency bands of ENSO and the QBO that relate to teleconnection patterns associated with variations in zonal winds. However, although the relation between time series of globally integrated AAMERA-40 and AAMNCEP1 improved, the large positive bias in AAMERA-40 minus AAMNCEP1 for the troposphere (925–400 hPa) of the equatorial Pacific (180°W to 60°E and 20°S to 20°N) and on the southern hemisphere in the region of the tropospheric jets (30°S and 60°S) points to the challenge to correctly determine tropical wind fields.
 Previous studies, although they may vary in intent and data from our analysis, provide some insight in the difficulty in determining tropical wind fields. They claimed as a major reason for discrepancies in reanalysis data sets a lack of meteorological observation points. A recent study by Masaki , for example, identified differences in equatorial westerly winds from ERA-40 and NCEP2 (NCEP1successor data set since 1979) of 4 ms−1 magnitude. The analysis was restricted to a box region of 10° × 10° × 200hP and the bias corresponds to differences in relative AAM from ERA-40 and NCEP2 of 1.2 × 10−11kgm2s−1. Kistler et al.  also reported on large differences along the equator in the zonal averaged u wind component between NCEP1 and an older ECMWF reanalysis product, the ERA-15 reanalysis. From 1973 to 1994 this study identified tropospheric (1000 hPa–50 hPa) easterly winds from ERA-15 that were about 3% weaker than in NCEP1 data. For the upper troposphere (100 hPa–10 hPa), however, zonally averaged ERA-15 u winds show a westerly component that is 2–6% stronger than in NCEP1 data with maximum bias on the southern hemisphere. In an early study, Rosen at al.  reported on discrepancies in tropical zonal wind fields from operational data from NMC (National Meteorological Center, NOAA/NCEP, U.S.) and ECMWF. The bias in the u wind component varied around 0.5 ms−1 for tropospheric layers from 1000 hPa to 700 hPa and from 400 hPa to 200 hPa.
4.2. Relation Between Zonal Winds From ERA-40 and NCEP1 Reanalysis Data Sets and Radiosonde Observations
 To determine the accuracy of tropical wind fields from ERA-40 and NCEP1 reanalysis data we compared them against radiosonde observations carried out in the east equatorial Pacific, the core region of reanalysis data bias.
 During the decade from 1991 to 2000 our analysis clearly identified that each of the data products performs differently well for the tropical troposphere (1000–200 hPa) and lower stratosphere (200 hPa–50 hPa). In general differences between reanalysis data and observations in troposphere and stratosphere are not significant with the only exemption at San Jose (Costa Rica) where stratospheric zonal winds from ERA-40 significantly differ from radiosonde observations.
 A study by Haimberger  found that radiosonde sites used in this study have been identified to produce a subset of measurements with relatively small biases to reanalysis data up to the 10 hPa level where overall the climatology is considered unbiased after homogenization due to high quality instrumentation. However, at all sites the homogenized time series still contain some bias due to large time gaps or change in location of radiosonde launches (San Cristobal, Ecuador). Also larger misfits are noticed between observations and reanalysis data when strong El Niño events were in progress [Uppala et al., 2005, Figure 13]. For these reasons even a broad availability of observations assimilated into the reanalysis assimilation models can cause a reanalysis data product that is flawed for certain time periods. The ERA-40 data assimilation system produced a range of BUFR-encoded feedback data relating to each observation presented to it [Kållberg et al., 2005]. The BUFR information on all quality controlled observations presented to the ERA-40 data assimilation system is provided by the MARS archive (MARS, accessed March 2011, http://www.ecmwf.int/services/archive). However, a detailed analysis of the BUFR information is beyond the scope of this paper, considering that at that time the option to retrieve a specific radiosonde point location from ECMWF's Observation Feedback Archive (OFA) is still in progress.
 In general 40% of all measurements were taken in the lower stratosphere and more than half (60%) within the troposphere. The RMS in zonal tropospheric and lower stratospheric winds in both reanalysis data products is largest to observations taken at Atuona (French Polynesia). Nevertheless, this site provides for troposphere and lower stratosphere 47% of all radiosonde data. We suggest that the varied but overall poor performance in zonal winds at Atuona (French Polynesia) from both reanalyses is related to poor quality of observations causing the large misfits. However, periodic oscillation patterns in the lower stratosphere, such as prolonged westerly phases of the QBO between 1992 and 1997 have been well captured by mean zonal wind observations at San Cristobal (Ecuador, 00.54°S) and Atuona (French Polynesia, 09.49°S) in the equatorial Pacific.
 Only few studies have examined the relation between zonal winds from reanalysis data products and observations in the Tropics. Although these studies used different data and statistical assessments their findings strongly imply that it is in general difficult to accurately determine wind fields from reanalysis data at low latitudes. For example, Uppala  reported for the Tropics RMS misfits of 1 to 3 ms−1 for the mean low-level (1000 hPa, 850 hPa, 700 hPa) u wind component in 1993 with ERA-15 reanalysis data exhibiting a weaker easterly flow. A study by Hastenrath and Polzin  compared different time slides of a short time series of wind soundings (1967–71) at Galapagos to ERA-15 and NCEP1 data (1979–1993). They claim that mid-tropospheric (600–700 hPa) easterly winds are weaker in ERA-15 compared to observations, while in NCEP1 they are stronger. An analysis on wind velocities from profiler observations and NCEP-1 data by Schafer et al.  found standard deviations of differences ranging between 2 and 8 ms−1. Masaki  considered a range of RMS between 1 to 3 ms−1 to be a typical value for bias in wind speed between reanalysis data and observations. Our findings, however, result in somewhat larger deviations for the troposphere (RMSERA-40 = 3.46–5.18 ms−1; RMSNCEP1 = 2.73–4.51 ms−1) and lower stratosphere (RMSERA-40 = 3.55–9.25 ms−1; RMSNCEP1 = 4.29–9.24 ms−1) that may be related to our larger database. Thus, larger deviations of reanalysis data from radiosonde values indicate that the time variation of ERA-40 and NCEP1 zonal wind in our analysis is larger than those of the wind fields in the studies discussed above. A small RMS is common in smaller sample sizes but can be misleading and not appropriately representing uncertainties. In general, the less observations are available for the assimilation process of the reanalysis product, the more the final reanalysis output is constrained by the reanalysis model computations themselves. We suggest that the NCEP1 model is stronger observation constrained than the ERA-40 reanalysis model for the troposphere (1000 hPa–200 hPa), while for the lower stratosphere (200 hPa–50 hPa), it is the ERA-40 reanalysis model that appears to be more observation constrained. Kistler et al.  emphasized that such conditions for the realization of the final reanalysis product are typically found in the Tropics. In their study they discuss that in the Tropics where mostly convergence flow is observed, differences in the vertical resolution of models directly affect the determination of the tropical wind field. Thus, they claim that differences in the two reanalysis products relate to differences in the ECMWF and NCEP/NCAR models since each model assesses differently the vertical motion related to divergent flow for the computation of reanalysis data and operational analysis.
 One of the persuasive features of reanalysis data is that they provide a uniformly gridded and globally available homogenous data set based on model-constraint observations. In our analysis we show that harmonization efforts between ERA-40 and NCEP1 zonal winds led in particular to an improved time-frequency behavior which is of importance when researching earth-atmosphere feedback processes. However, despite the harmonization efforts of zonal wind fields in the two reanalyses, the large geographical bias in computed relative AAM in the equatorial Pacific should be a reminder that the Tropics is a region where reanalysis results still differ strongly. Our study suggests that deficiencies in computational processes of assimilating observational data lead to structural uncertainties while uncertainties internal to the reanalysis data sets can be associated with low-quality measurements assimilated into the reanalysis process. From our findings we conclude that tropospheric ERA-40 zonal winds are associated with larger structural uncertainties than the more data constraint NCEP1 reanalysis model. It is beyond the scope of this paper, however, to reconcile differences among observations that had been available for the reanalysis assimilation process and data that had been effectively assimilated to build the final reanalysis data product. Whereas discrepancies between reanalyses and observed tropical zonal wind data appear to be small, differences of such magnitude are important when computing relative AAM estimates because the annual amplitude of zonal winds in the Tropics is much smaller than in the midlatitudes. In conclusion we suggest further improvement of reanalysis data products that concerns assimilating additional and improved quality checked measurements from the data-sparse Pacific Tropics and to further improve harmonization efforts of the two reanalysis models. As a result reanalysis data products will be achieved that provide more reliability and consistency with reality.
 This study was supported by a grant from the Deutsche Forschungsgemeinschaft (DFG) research group FOR 584 ‘Earth rotation and global dynamic processes.’ ERA-40 reanalysis data were provided by the ECMWF data service, Reading, U.K. NCEP1 reanalysis data were provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA. Raw radiosonde data were provided by the German Weather Service (DWD) in Offenbach, Germany. We thank Uwe Ulbrich, Institute of Meteorology, Freie Universität Berlin, and G. C. Leckebusch, University of Birmingham, U.K., for discussion and comments. We are also grateful to Eberhard Reimer and Philipp Griewank who provided technical support for some of the discussed analysis. The authors further wish to acknowledge comments made by three anonymous reviewers who helped to improve this manuscript.