A Comparison of Decadal-to-Interdecadal Variability and Trend in Reanalysis Datasets Using Atmospheric Angular Momentum

Houk Paek School for Engineering of Matter, Transport, and Energy, Arizona State University, Tempe, Arizona

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Huei-Ping Huang School for Engineering of Matter, Transport, and Energy, Arizona State University, Tempe, Arizona

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Abstract

An intercomparison of the global relative angular momentum MR in five reanalysis datasets, including the Twentieth Century Reanalysis (20CR), is performed for the second half of the twentieth century. The intercomparison forms a stringent test for 20CR because the variability of MR is known to be strongly influenced by the variability of upper-tropospheric zonal wind whereas 20CR assimilated only surface observations. The analysis reveals good agreement for decadal-to-multidecadal variability among all of the datasets, including 20CR, for the second half of the twentieth century. The discrepancies among different datasets are mainly in the slowest component, the long-term trend, of MR. Once the data are detrended, the resulting decadal-to-multidecadal variability shows even better agreement among all of the datasets. This result indicates that 20CR can be reliably used for the analysis of decadal-to-interdecadal variability in the pre-1950 era, provided that the data are properly detrended. As a quick application, it is found that the increase in MR during the 1976/77 climate-shift event remains the sharpest over the entire period from 1871 to 2008 covered by 20CR. The nontrivial difference in the long-term trend between 20CR and the other reanalysis datasets found in this study provides a caution against using 20CR to determine the trend on the centennial time scale that is relevant to climate change. These conclusions are restricted to the quantities that depend strongly on the upper-tropospheric zonal wind, but the approach adopted in this work will be useful for future intercomparisons of the low-frequency behavior of other climate indices in the reanalysis datasets.

Corresponding author address: Houk Paek, School for Engineering of Matter, Transport, and Energy, Arizona State University, Tempe, AZ 85287-6106. E-mail: hpaek@asu.edu

Abstract

An intercomparison of the global relative angular momentum MR in five reanalysis datasets, including the Twentieth Century Reanalysis (20CR), is performed for the second half of the twentieth century. The intercomparison forms a stringent test for 20CR because the variability of MR is known to be strongly influenced by the variability of upper-tropospheric zonal wind whereas 20CR assimilated only surface observations. The analysis reveals good agreement for decadal-to-multidecadal variability among all of the datasets, including 20CR, for the second half of the twentieth century. The discrepancies among different datasets are mainly in the slowest component, the long-term trend, of MR. Once the data are detrended, the resulting decadal-to-multidecadal variability shows even better agreement among all of the datasets. This result indicates that 20CR can be reliably used for the analysis of decadal-to-interdecadal variability in the pre-1950 era, provided that the data are properly detrended. As a quick application, it is found that the increase in MR during the 1976/77 climate-shift event remains the sharpest over the entire period from 1871 to 2008 covered by 20CR. The nontrivial difference in the long-term trend between 20CR and the other reanalysis datasets found in this study provides a caution against using 20CR to determine the trend on the centennial time scale that is relevant to climate change. These conclusions are restricted to the quantities that depend strongly on the upper-tropospheric zonal wind, but the approach adopted in this work will be useful for future intercomparisons of the low-frequency behavior of other climate indices in the reanalysis datasets.

Corresponding author address: Houk Paek, School for Engineering of Matter, Transport, and Energy, Arizona State University, Tempe, AZ 85287-6106. E-mail: hpaek@asu.edu

1. Introduction

Since the inception of the first National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis (Kalnay et al. 1996), several reanalysis datasets have been created using varied frameworks for data assimilation. These datasets have emerged as a cornerstone of modern climate analysis. Each reanalysis dataset was created using a single numerical model, eliminating temporal discontinuities in the routine daily archive of global analysis that are due to upgrades of weather forecast models. Nevertheless, the known temporal inhomogeneities in the quality and quantity of observations still raise concerns about the feasibility of using reanalysis to determine climate variability and trend on interdecadal and longer time scales (Thorne and Vose 2010, 2011; Dee et al. 2011a). By assimilating only surface observations (Whitaker et al. 2004), the recently released Twentieth Century Reanalysis (20CR; Compo et al. 2006, 2011) [we use version 2, which is described in Compo et al. (2011)] extended reanalysis back to 1871. Because it is based on a temporally more homogeneous subset of observations, the prospect of using 20CR to extract interdecadal and long-term trend has been suggested and debated elsewhere (e.g., Thorne and Vose 2010, 2011; Dee et al. 2011a). To contribute to this line of research, this study will compare the decadal-to-interdecadal variability and trend in 20CR with their counterparts in other reanalysis datasets (that assimilated 3D observations) for the second half of the twentieth century. The outcome will be used to determine the reliability of the interdecadal variability and trend in 20CR in the pre-1950 era.

For our purpose, global atmospheric relative angular momentum MR is chosen as the key index for the intercomparison. This index is known to usefully represent the variability of tropospheric zonal flow associated with major climatic phenomena ranging from the Madden–Julian oscillation (e.g., Feldstein and Lee 1995; Weickmann et al. 1997) and El Niño (e.g., Black et al. 1996; Huang et al. 2003) to global warming (Abarca del Rio 1999; Huang et al. 2001; de Viron et al. 2002; Räisänen 2003). Although MR is a weighted integral of 3D zonal wind, its variability is dominated by the variability of zonal wind in the upper troposphere (e.g., Huang and Sardeshmukh 2000). Thus, a comparison in the variability of MR with other reanalysis datasets forms a stringent test for 20CR. As a further motivation, previous studies have suggested the possibility of interdecadal climate regime shifts, mostly on the basis of an apparently unique event in 1976/77 [Trenberth (1990), Miller et al. (1994), and recent surveys in Huang et al. (2005) and Meehl et al. (2009)] that is known to be associated with a large upward shift in MR (Huang et al. 2001, 2003) and a shift in surface torques (Marcus et al. 2011). If the 20CR data also exhibit this large shift in MR in 1976/77, one may use such a shift as an indicator to search for other climate-shift events in the pre-1950 era using that dataset.

2. Datasets and analysis method

The reanalysis datasets used to cross validate 20CR are the NCEP–NCAR reanalysis (hereinafter called Reanalysis-I or R-1) (Kalnay et al. 1996; Kistler et al. 2001), the NCEP–U.S. Department of Energy reanalysis (hereinafter called Reanalysis-II or R-2) (Kanamitsu et al. 2002), the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40; Uppala et al. 2005), and the ECMWF Interim Re-Analysis (ERA-Interim; Dee et al. 2011b) (both ECMWF datasets were obtained online at http://data.ecmwf.int/data), as summarized in Table 1. A detailed budget of global angular momentum for Reanalysis-I can be found in Huang et al. (1999).

Table 1.

Summary of reanalysis datasets used in this work.

Table 1.

The global relative angular momentum is evaluated (Peixoto and Oort 1992) as
e1
where a = 6.371 × 106 m is the mean radius of the earth, g = 9.81 m s−2 is gravitational acceleration, and u is the 3D zonal wind as a function of latitude θ, longitude λ, and pressure p. The integral is calculated using the archived zonal wind at pressure levels from 10 to 1000 hPa. Although the two ECMWF reanalysis datasets have a finer pressure-level resolution above 10 hPa, for the intercomparison we keep 10 hPa as the top level for all of the datasets. Calculations that included the detail of the 1–10-hPa data produced little difference. Since the anomaly of MR is generally dominated by the variability of upper-tropospheric zonal wind, we also use another index,
e2
where u200 is the zonal wind at 200 hPa, to quantify the contribution of the upper-level zonal wind to MR.

To focus on low-frequency variability, we first suppressed the high-frequency components and seasonal cycle by applying a 1-yr low-pass filter to the time series of MR or M200. Hereinafter, the symbol MR or M200 denotes this low-pass-filtered quantity. Egger et al. (2003) have previously compared the high-frequency components of angular momentum and surface torques in the NCEP and ECMWF reanalyses. The anomaly of angular momentum, denoted as ΔMR and ΔM200, is defined as the departure from the long-term mean. To further focus on decadal and longer-term variability, a 5-yr running mean is applied to the time series of ΔMR and ΔM200. To deduce the trend in ΔMR or ΔM200, the 5-yr running-averaged time series is least squares fitted with a second-degree polynomial in time. Then, we may detrend the time series by subtracting this second-degree polynomial from ΔMR or ΔM200. To test the robustness of our conclusions, an additional calculation that is based on a linear fit instead of a quadratic fit will also be performed. We have adopted these relatively simple procedures for easy reproducibility and for their flexibility in treating the five reanalysis datasets that have very different lengths and cover different periods. Alternatives of the procedure for filtering were tested to ensure that our conclusions are not sensitive to those details.

3. Decadal-to-interdecadal variability

The 5-yr running means of ΔMR and ΔM200 (with the long-term mean removed but without further detrending) for the five reanalysis datasets are shown in Figs. 1a and 1b. In the post-1970 era, all five datasets qualitatively agree on the up and down in decadal variability of ΔMR, although 20CR exhibits an overall upward trend from 1970 to the present that differs from the other datasets. (We will later demonstrate that the agreement among the five datasets improves dramatically if the data are detrended.) The sharp increase in MR during the 1976/77 transition, previously shown by Huang et al. (2001, 2003) using Reanalysis-I, is robustly reproduced in the other datasets, including 20CR. In Fig. 1b, for ΔM200 the departure of 20CR from the other four datasets is substantial, whereas those four other datasets are tightly packed together for the last 20 yr of record. This indicates that the discrepancy in ΔMR between 20CR and the other datasets in Fig. 1a comes mainly from the differences in the upper-level zonal wind. (The similarity of the temporal patterns of ΔMR and ΔM200 in Figs. 1a and 1b corroborates our earlier assertion that the upper-tropospheric zonal wind is a major contributor to ΔMR.)

Fig. 1.
Fig. 1.

(a) The 5-yr running-averaged monthly anomalies of (a) ΔMR (global relative angular momentum) and (b) ΔM200 [angular momentum (per unit pressure thickness) calculated at only 200 hPa level] for the five reanalysis datasets.

Citation: Journal of Climate 25, 13; 10.1175/JCLI-D-11-00358.1

Given the agreement among all of the datasets on the increase in MR during the 1976/77 transition, it is interesting to note that in the 140 yr of record of 20CR the 1976/77 event has the most dramatic increase in MR, followed by two other events in the 1940s and the 1890s (which, however, recovered immediately at the turn of the twentieth century).

4. Comparison of trend and the effect of detrending

Because the five reanalysis datasets have varied lengths and cover very different periods, we investigate the trend in these datasets by looking at two periods, 1949–78 and 1979–2008, each of which sees a substantial overlap of coverage by multiple datasets. A least squares quadratic fit is applied to the ΔMR time series to deduce the trend, and detrending is done by subtracting the quadratic curve from the time series as described in section 3. Figure 2a shows the quadratic fits for ΔMR for Reanalysis-I, 20CR, and ERA-40 for 1949–78. Aside from the disagreement in the pre-1960 era between 20CR and Reanalysis-I (which might be related to the quality of upper-air observations in the pre-1960 era; see Kistler et al. 2001), good agreement is found in the post-1960 era among the three datasets for the overall trend and for the decadal variability after the data are detrended, as shown in Fig. 2b. Figures 2c and 2d are similar to Figs. 2a and 2b, but they are for 1979–2008 and with the addition of Reanalysis-II and ERA-Interim data. Notably, while all of the datasets that assimilated 3D winds exhibit a downward trend in ΔMR for this period, the 20CR data show a mild upward trend instead. Nevertheless, once the data are detrended (Fig. 2d), all five datasets show remarkable agreement on the decadal-to-multidecadal variability over this period. In particular, detrending brings 20CR into tighter agreement with all of the other datasets. This result implies that the decadal-to-multidecadal variability in 20CR is trustworthy but that the long-term trend needs to be treated with caution.

Fig. 2.
Fig. 2.

(a) The least squares quadratic fit (dashed curves) to ΔMR for Reanalysis-I, ERA-40, and 20CR for 1949–78. (b) The “detrended” time series for the same period, with the quadratic curve removed from the time series. (c),(d) As in (a),(b), but for 1979–2008 and with the addition of Reanalysis-II and ERA-Interim.

Citation: Journal of Climate 25, 13; 10.1175/JCLI-D-11-00358.1

We regarded the quadratic curves from the least squares fit in Figs. 2a and 2c as the “trend,” but they might alternatively be viewed as part of the ultralow-frequency variability on the centennial time scale, for which the 1979–2008 segment shown in Fig. 2c could be just one-quarter of a full period (analogous to a winter season vs the whole year). In this context, our use of the quadratic fit is meaningful, since the time evolution within one-quarter of an oscillation need not be linear. Nevertheless, since the choice of the quadratic fit is somewhat of a mathematical convenience, we next test the robustness of our conclusions by replacing it with a least squares linear fit. Detrending is then performed by removing the straight line from the time series of ΔMR. Figures 3a–d show the counterparts of Figs. 2a–d but based on the linear trend. In general, it remains true that detrending leads to much closer agreements among the reanalysis datasets.

Fig. 3.
Fig. 3.

As in Fig. 2, but with the quadratic fit in (a) and (c) replaced by a linear fit. The detrended time series of ΔMR in (b) and (d) are with the linear fit removed.

Citation: Journal of Climate 25, 13; 10.1175/JCLI-D-11-00358.1

5. Long-term mean

In the preceding sections, we have removed the long-term mean in MR to focus on low-frequency variability and trend. If the long-term mean is retained, that is, if we consider MR instead of ΔMR, a systematic negative bias is found in 20CR when compared with other reanalysis datasets, as shown in Fig. 4a for MR and Fig. 4b for M200. There also exist systematic differences in MR among the other four reanalysis datasets, but they are much smaller and the differences appear to diminish toward the last 20 yr of record. For M200, from 1990 to the present, Reanalyses I and II clustered together while ERA-40 agreed with ERA-Interim, but a systematic difference still exists between these two groups.

Fig. 4.
Fig. 4.

The (a) MR and (b) M200, with the long-term mean retained, for the five reanalysis datasets. (c) As in (a), but with the integration in Eq. (1) carried out only from 150 to 10 hPa and from 10°S to 10°N to show the contribution from the tropical upper atmosphere.

Citation: Journal of Climate 25, 13; 10.1175/JCLI-D-11-00358.1

To visualize the differences in zonal-mean zonal wind that contribute to the biases shown in Fig. 4, Figs. 5a, 5b, 5e, 5f, 5i, and 5j show the 1979–2008 seasonal (June–August for summer and December–February for winter) and annual climatology of zonal-mean zonal velocity for 20CR and ERA-Interim. The most notable difference is a stronger upper-tropospheric easterly flow on the equator in 20CR, which is further highlighted in Figs. 5c, 5g, and 5k, which show the difference between 20CR and ERA-Interim. Figures 5c, 5g, and 5k also show that the upper-tropospheric zonal wind is stronger in 20CR in the higher latitudes. This, however, does not overcome the negative bias in the tropics, which is more important for angular momentum because of the latitudinal weight cos2θ in the integral for MR. Figures 5d, 5h, and 5l are similar to Figs. 5c, 5g, and 5k but show the difference between Reanalysis-II and ERA-Interim, which is considerably smaller than the difference between 20CR and ERA-Interim. The slightly lower value of the long-term mean of MR in Reanalysis-II is also due to a stronger tropical easterly zonal wind.

Fig. 5.
Fig. 5.

The summer (June–August) climatology of zonal-mean zonal wind from 1979 to 2008 for (a) 20CR and (b) ERA-Interim. (c) The difference between 20CR and ERA-Interim, i.e., (b) minus (a). (d) As in (c), but for the difference between Reanalysis-II and ERA-Interim. (e)–(h) As in (a)–(d), but for winter (December-February). (i)–(l) As in (a)–(d), but for the annual mean. Also shown are the 1979–2008 linear trends for (m) 20CR and (n) ERA-Interim. Contour intervals are 4 m s−1 for (a),(b),(e),(f),(i), and (j) and 1 m s−1 for (c),(d),(g),(h),(k),(l),(m), and (n). Color scales are shown at right.

Citation: Journal of Climate 25, 13; 10.1175/JCLI-D-11-00358.1

Although multiple factors may contribute to the difference in the long-term mean of MR between 20CR and the other reanalysis datasets, an important factor to consider is the lack of realism in the stratosphere in 20CR. For example (as pointed out by a reviewer), quasi-biennial oscillation (QBO) is entirely missing in 20CR, as demonstrated in Fig. 6. This leads to a perpetual easterly zonal wind on the equator for 20CR, which contributes to a negative bias in MR, as further illustrated in Fig. 4c (note that QBO itself has a nontrivial contribution to the variability of MR; e.g., Chao 1989). This is not surprising since 20CR only assimilated the surface observations. A phenomenon that is initiated in the stratosphere and then propagates or extends downward [e.g., in the sense of Baldwin and Dunkerton (1999) or Haynes et al. (1991)] would not be correctly captured in the data-assimilation process for 20CR. Although many of these phenomena have shorter periods, their absence could affect the long-term climatology.

Fig. 6.
Fig. 6.

The time–pressure plots of zonal-mean zonal wind on the equator from 150 to 10 hPa that illustrate the structure of QBO (or the lack of it) in (a) 20CR, (b) Reanalysis-II, and (c) ERA-Interim. Monthly mean data are used without the 5-yr running mean.

Citation: Journal of Climate 25, 13; 10.1175/JCLI-D-11-00358.1

Last, it is also interesting to show the trend in the zonal-mean zonal wind that accompanies the trend in MR. Figures 5m and 5n show the 1979–2008 linear trend of the zonal wind for 20CR and ERA-Interim. The increase in MR during this period is associated in part with the strengthening of the two midlatitude zonal jets, especially the one in the Southern Hemisphere; the trend has a strongly barotropic structure. The trend in the Southern Hemisphere zonal jet in 20CR is stronger than its counterpart in ERA-Interim. Again, this difference might ultimately come from the misrepresentation in 20CR of stratospheric processes that exert a downward influence on the zonal wind in the upper troposphere. The strengthening and poleward shift of the Southern Hemisphere zonal jet [which somewhat resembles the trend produced by doubled carbon dioxide in climate model simulations, e.g., Huang et al. (2001) and Kushner et al. (2001), and is consistent with the findings on the expansion of the Hadley circulation, e.g., Seidel et al. (2008)] is nevertheless qualitatively consistent between the two reanalysis datasets.

6. Conclusions

An intercomparison of the global relative angular momentum in five reanalysis datasets reveals good agreement for decadal-to-multidecadal variability among all of the datasets, including 20CR, for the second half of the twentieth century. The discrepancies among the different datasets are found to come mainly from the slowest component—the long-term trend—in the time series of angular momentum. Once the time series of ΔMR are detrended, the resulting decadal-to-multidecadal variability shows even better agreement among all of the datasets. This key result, shown in Fig. 2d, is remarkable given that the variability of MR is dominated by upper-tropospheric zonal wind whereas the 20CR dataset only assimilated surface observations. It indicates that 20CR can be reliably used for the analysis of decadal-to-interdecadal variability in the pre-1950 era, provided that the data are properly detrended. On the other hand, a nontrivial difference in the long-term trend exists between 20CR and the other reanalysis datasets. Thus, one must exercise extreme caution when using 20CR to determine the trend on the centennial time scale that is relevant to climate change. Although we have focused on angular momentum and zonal wind, the trend and low-frequency variability in MR and zonal wind could potentially be used to cross validate those in temperature (e.g., Räisänen 2003; Allen and Sherwood 2008). Our results may provide a useful reference for such an analysis. Our conclusions pertain to the quantities that depend strongly on the upper-tropospheric zonal wind. The behavior of 20CR might be different for other climate indices that depend strongly on near-surface circulation and processes. A further intercomparison on those quantities will be an interesting follow-up to this work.

Acknowledgments

This research was supported by the Office of Science (BER) of the U.S. Department of Energy. The authors thank three anonymous reviewers for their useful comments that led to improvement of the manuscript. The Reanalysis-I and Reanalysis-II and the 20CR data were obtained from the NOAA ESRL/PSD Internet archive (www.esrl.noaa.gov/psd), and the two ECMWF reanalysis datasets were obtained from the ECMWF data portal (http://data.ecmwf.int/data).

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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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  • Fig. 1.

    (a) The 5-yr running-averaged monthly anomalies of (a) ΔMR (global relative angular momentum) and (b) ΔM200 [angular momentum (per unit pressure thickness) calculated at only 200 hPa level] for the five reanalysis datasets.

  • Fig. 2.

    (a) The least squares quadratic fit (dashed curves) to ΔMR for Reanalysis-I, ERA-40, and 20CR for 1949–78. (b) The “detrended” time series for the same period, with the quadratic curve removed from the time series. (c),(d) As in (a),(b), but for 1979–2008 and with the addition of Reanalysis-II and ERA-Interim.

  • Fig. 3.

    As in Fig. 2, but with the quadratic fit in (a) and (c) replaced by a linear fit. The detrended time series of ΔMR in (b) and (d) are with the linear fit removed.

  • Fig. 4.

    The (a) MR and (b) M200, with the long-term mean retained, for the five reanalysis datasets. (c) As in (a), but with the integration in Eq. (1) carried out only from 150 to 10 hPa and from 10°S to 10°N to show the contribution from the tropical upper atmosphere.

  • Fig. 5.

    The summer (June–August) climatology of zonal-mean zonal wind from 1979 to 2008 for (a) 20CR and (b) ERA-Interim. (c) The difference between 20CR and ERA-Interim, i.e., (b) minus (a). (d) As in (c), but for the difference between Reanalysis-II and ERA-Interim. (e)–(h) As in (a)–(d), but for winter (December-February). (i)–(l) As in (a)–(d), but for the annual mean. Also shown are the 1979–2008 linear trends for (m) 20CR and (n) ERA-Interim. Contour intervals are 4 m s−1 for (a),(b),(e),(f),(i), and (j) and 1 m s−1 for (c),(d),(g),(h),(k),(l),(m), and (n). Color scales are shown at right.

  • Fig. 6.

    The time–pressure plots of zonal-mean zonal wind on the equator from 150 to 10 hPa that illustrate the structure of QBO (or the lack of it) in (a) 20CR, (b) Reanalysis-II, and (c) ERA-Interim. Monthly mean data are used without the 5-yr running mean.

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