The decadal modulation of coupled bred vectors



[1] This study investigates the nature of a decadal modulation in the coupled bred vectors (BVs) developed to capture the dominant instabilities related to seasonal-to-interannual variability in the Equatorial Pacific using the GEOS-5 atmosphere-ocean general circulation model. It is found that the coupled BVs, with a monthly rescaling period, successfully reflect the observed decadal modulation of zonal location in the El Niño action center over the equatorial Pacific. By dividing the 30 years of BVs into two epochs, it is shown that the leading Empirical Orthogonal Function (EOF) of BV oceanic temperature shifts from the eastern Pacific during 1981–1999 to the central Pacific during 2000–2010, consistent with decadal changes in the location of the El Niño action center. By performing a budget analysis for BV temperature, it is found that the westward shift of the BV temperature is due to the strengthening of the mean zonal temperature gradient, which acts to amplify the BV temperature growth due to the zonal advection of background temperature by the BV current.

1. Introduction

[2] Ensembles of numerical forecasts based on perturbed initial conditions have long been used to improve estimates of both weather and climate forecasts. Since one goal has been the use of the ensemble spread as an indicator of expected forecast skill, bred vectors [Toth and Kalnay, 1993] have been used as perturbations to capture the fastest growing modes on weather time scales. More recently, the coupled breeding method was developed for coupled atmosphere-ocean systems to capture the dominant mode of coupled instabilities associated with the El Niño/Southern Oscillation (ENSO) [Cai et al., 2003; Yang et al., 2006, 2008; Ham et al., 2012]. Several studies have shown that perturbations based on bred vectors (BVs) improve the skill of ensemble forecasts because they capture important aspects of the time-varying initial errors [Yang et al., 2008, 2009].

[3] In addition to providing relevant perturbations for ensemble forecasts, breeding provides information on the characteristics of unstable modes. Yang et al. [2006]showed that in the equatorial Pacific the dominant pattern of the ocean component of the seasonal BV using the NASA Seasonal-to-Interannual Prediction Project coupled general circulation model (CGCM) resembles the dominant pattern of ENSO variability. They investigated the dependency of BVs on the seasonal cycle and phase of El Niño [Cai et al., 2003]. Hoffman et al. [2009] formulated the energy budget equation for the BV to understand the growth of atmospheric flow instabilities over the tropical ocean. While most previous stability analyses have been undertaken with simplified models due to the difficulty of formulating the linear operator [Fedorov and Philander, 2001; Bejarano and Jin, 2008], the breeding method provides an easy mechanism for examining the stability of the fastest growing mode even in CGCMs.

[4] In this study we investigate decadal changes in the dominant EOF calculated from the time series of BV. In particular, we examine whether the occurrence of the “Central Pacific El Niño” [Kao and Yu, 2009; Yeh et al., 2009] in more recent years is reflected in a change in the most unstable mode over the tropical Pacific. Following McPhaden et al. [2011], we divide the last three decades into two epochs (1981 to 1999, and 2000 to 2010), focusing on the physical mechanisms behind changes in the BVs, with the aim of better understanding the nature of the decadal changes in El Niño and how this can be represented in the coupled model. Note that the general conclusion in this study remains when the first epoch covers 1981–1995, and the second spans 1996–2010.

2. Model and Breeding Experiment

[5] The model used in this study is the Goddard Earth Observing System (GEOS) Atmosphere-Ocean General Circulation Model, Version 5 (GEOS-5 AOGCM). The oceanic component consists of the Modular Ocean Model version 4.1 (MOM4.1) with a grid configuration of 40 vertical levels and a 0.5° × 0.5° horizontal grid telescoping to 0.25° meridional spacing near the equator. The atmospheric component has 72 vertical levels using a generalized vertical coordinate and 1.25° latitude by 1° longitude grid spacing. More details about the GEOS-5 atmospheric model are provided inRienecker et al. [2008].

[6] The breeding method is applied from 1980 to 2010 with the aim of capturing the fastest-growing errors in the seasonal forecasts. We applied two-sided breeding, which means positive and negative bred runs are restarted every month by adding and subtracting the bred vector to the initial conditions generated from the Ensemble Optimal Interpolation (EnOI) option of the GEOS ocean data assimilation system, forced with NASA's Modern-Era Retrospective analysis for Research and Applications (MERRA) [Rienecker et al., 2011].

[7] The rescaling interval chosen for the breeding is one month. The rescaling norm is the RMS difference of the instantaneous sea surface temperatures (SSTs) from the positive and negative bred runs; the region for defining the norm is the tropical Pacific domain over 120°E–90°W, 15°S–15°N [Ham et al., 2012]. At every re-initialization during the breeding cycle, perturbations are re-scaled so that the magnitude of the norm is reduced to 10% of the natural variability of SST over the norm region (i.e. 0.48°C). The first atmospheric and oceanic perturbation is generated by using GEOS-5 analyses on two different days. The norm magnitude of the first initial perturbation is also set to 0.48°C.

3. Decadal Modulation of the BV

[8] Figure 1ashows the Niño-3.4 index (i.e. the SST anomaly over 170–120°W, 5°S–5°N) and the BV growth rate [Yang et al., 2008] with/without a 7-month moving average. The BV growth rate is relatively high during 1998 and 2007 and low during 1982 and 2009. There is negative correlation of −0.37 between the Niño-3.4 SST anomaly and the smoothed BV growth rate with 95% confidence level when the SST is lagged by six months, implying that the BV growth rate is affected by the ENSO phase, with lower growth rates during warm events. A possible explanation for the negative relationship will be discussed in the next section.

Figure 1.

(a) The time series of Niño-3.4 SST anomaly (black) and BV growth rate (red). The 7-month moving average of the BV growth rate is shown with the thick red line. (b) The first Empirical Orthogonal Function (EOF) in the first (shaded) and second (contour) epoch. (c) The location of the maximum in the first EOF during the first (black) and second (red) epoch as a function of depth. The upper and lower boundary of the 95% confidence interval for the difference between epochs is shown as the dotted black line.

[9] Figure 1bshows the leading EOF of equatorially-averaged (5°S–5°N) BV temperature for each epoch. The dominant EOF in the first epoch is confined primarily to the eastern Pacific, with a surface anomaly at 150°W, and a subsurface center at about 130°W. This vertical phase shift is less excessive than that of the CP El Niño calculated from 1950 to 2009 as inKao and Yu [2009], however, the subsurface structure of the CP El Niño between 1981–2010 is similar to that of BV temperature (not shown). Compared to the first epoch, the dominant EOF for the second epoch is shifted to the west. It is also deeper than for the earlier epoch, following the mean thermocline depth. At the surface, the most unstable region also shifts from the central Pacific in the first epoch to the western Pacific in the second epoch. This is consistent with the westward shift of the SST action center to the central Pacific during that period [Yeh et al., 2009]. Figure 1c shows the longitudinal location of the maximum value in 1st EOF as a function of depth. The dotted line denotes the 95% confidence level estimated using the bootstrap method (see auxiliary material for the details). It is clear that the shift of zonal location in the BV action center in the second epoch is statistically significant.

[10] Figure 2shows the regression of the BV SST and surface-layer (0–50 m) currents onto the 1st Principal Component (PC) of BV temperature in each epoch. The regressed BV SST during the second epoch is located over the central Pacific between 150°E and 150°W, while during the first epoch it is located between 180 and 120°W. The surface-layer BV horizontal currents are also shifted to the west in the second epoch. In the first epoch, the dominant mode of BV currents leads surface convergence and downwelling to the west of 120°W, while it is located to the west of 130°W during the second epoch (not shown).

Figure 2.

The regressed BV SST (shading) and surface-layer (0–50 m averages) currents (vector) with respect to the principal component of the first EOF during (a) earlier decades, and (b) the recent decade.

[11] To examine the cause of these decadal differences in the BVs, a budget analysis is performed for the tropical Pacific temperature in the surface-layer (0–50 m) as follows:

display math

where T and T′ denote the temperature in the control run (i.e. average of two bred runs) and BV (i.e. the difference between two bred runs divided by 2) temperature, respectively. In addition, u′, v′, w′, and Q′ denote the BV zonal, meridional, vertical currents, and surface heat-flux. This equation for the BV is similar to that inHoffman et al. [2009], without the nonlinear advection terms (see auxiliary material for detailed derivations).

[12] To examine the temperature budget related to the dominant EOFs, Figure 3shows the composite of BV advection terms from periods when the magnitude of the PC of the first EOF is greater than one standard deviation of its time series. Using a t-test based on the temporal variance of each term in the right hand side ofequation (1), Figure 3 shows the total advection magnitude and only two advection terms (i.e. math formula, and math formula) that are significantly different from zero at the 95% confidence level. The total advection term reflects the spatial pattern of the 1st EOF, which has maximum values over the eastern (central) Pacific during the first (second) epoch. The magnitude of the total advection is mainly determined by zonal and vertical advection terms shown in Figure 3; however, some contributions over the eastern Pacific in the first epoch comes from meridional and vertical advection of BV temperature due to background currents (i.e. math formula, and math formula). However, they did not exceed the 95% confidence level as mentioned earlier.

Figure 3.

The composite of equatorially-averaged (5°S–5°N) advection terms when the magnitude of the PC of the 1st EOF is greater than one standard deviation. The total (i.e. all terms on the right-hand side ofequation (1)), zonal advection ( math formula), and vertical advection ( math formula) due to BV currents are denoted with black, red, and blue lines, respectively. The values for the 1st and 2nd epoch are denoted as solid and dotted lines, respectively. Values are denoted with a thick line when they are significantly different from zero at the 95% confidence level. The gray shading shows the 95% confidence interval for the difference between the zonal advection terms in each epoch.

[13] Zonal advection is generally important over the central Pacific, while the vertical advection term is dominant over the eastern Pacific. Interestingly, the magnitude of the zonal advection composite during the second epoch is significantly higher than that during the first epoch over 180–150°W, while that of vertical advection is significantly reduced. Note that the significance test is quite similar to that used in Figure 1c, whose detailed procedure can be found in auxiliary material. The result is consistent with the finding of Kug et al. [2009] that zonal advection of the mean SST plays a critical role in the development of the Central Pacific El Niño. Since the zonal advection is determined by the BV current and background zonal temperature gradient, the strength of the zonal temperature gradient in the control run affects the BV temperature growth rate over the central Pacific.

[14] Figure 4shows the difference (second – first epoch) between the two epochs of the mean surface-layer temperature and the vertical temperature difference between the surface and 50 m based on the GMAO's ocean analysis. The results show that the equatorial temperature has increased over the western Pacific, while it has changed little to the east of 150°W (consistent withKarnauskas et al. [2009]). The results from Figure 3 indicate that the stronger zonal temperature gradient over the tropical central Pacific in the recent decade should increase the strength of zonal advection by BV currents and the growth of BV temperature over the central Pacific. As a result, the leading BV temperature signal has shifted from the eastern to the central Pacific in the recent decade. On the other hand, the vertical temperature gradient, which is related to the vertical BV temperature advection, has decreased slightly over most of the Pacific region, except over the far eastern Pacific. The mean difference of the meridional temperature gradient is also small, implying that the contribution of the meridional advection term would be similar in both epochs.

Figure 4.

(a) The difference of the mean equatorial (5°S–5°N) surface-layer temperature (red) and temperature difference between the surface and 50 m (black) between the two epochs (second – first epoch) using the GMAO's ocean analysis. (b) The difference of the mean surface-layer temperature averaged over the eastern-Pacific (140–100°W) between the two epochs.

4. Summary and Discussion

[15] In this study, we investigated the decadal modulation of the BVs that are applied to the GEOS-5 AOGCM. It was shown that the dominant BV temperature over the equatorial Pacific shifts from the eastern to the central Pacific in the second epoch. By performing a budget analysis for the BV, it was found that this westward shift of the dominant BV temperature is due to the strengthening of the zonal temperature gradient in the western-to-central Pacific in the second epoch. The increase of mean temperature over the western Pacific leads to a stronger zonal temperature gradient in the second epoch, resulting in the amplification of the BV temperature growth due to the zonal advection of temperature by BV currents.

[16] We noted from Figure 1athat there is lagged negative relationship between the Niño-3.4 SST anomaly and the 7-month moving average of the growth rate. According to the temperature budget analysis, stronger zonal and vertical temperature gradients can increase the BV growth. During canonical El Niño events, the zonal temperature gradient tends to decrease over the central Pacific, and meridional and vertical temperature gradients are also decreased over the eastern Pacific, which implies that the BV growth rate is expected to be relatively smaller during the canonical El Niño events (i.e. an inverse relationship). The six-month lag might be attributed to the fact that the ENSO-related vertical temperature gradient is maximum several months before the ENSO mature phase [An and Jin, 2004].

[17] This study shows that the change of the mean background state in the tropical Pacific can lead to different unstable modes of ENSO events. The results are consistent with other studies that have investigated the relationship between the oceanic basic state and ENSO growth with intermediate models [e.g., Bejarano and Jin, 2008]. Thus, this study also shows that the breeding method can be a powerful tool to understand climate variability with full AOGCMs.


[18] The authors thank the reviewer for helpful comments to improve the paper. Support for this project was provided by the NASA Modeling, Analysis and Prediction (MAP) Program under WBS 802678. S.-W. Yeh was funded by the Korea Meteorological Administration Research and Development Program under grant CATER 2012–3041. Computing resources for this study were provided by the NASA Center for Climate Simulation at the Goddard Space Flight Center.

[19] The Editor thanks an anonymous reviewer for assistance in evaluating this paper.