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Ruiqiang Ding
and
Jianping Li

Abstract

An analysis has been made of the trend and decadal variability of persistence of daily 500-mb (hPa) geopotential height anomalies for the winter season. The persistence is measured based on autocorrelations at 1- and 5-day lags (denoted r 1 and r 5, respectively) and the effective time between independent samples T 0. The results from linear trend analysis show that there exist significant trends of persistence of daily 500-mb geopotential height anomalies in some regions of the world. The regions with a significant decreasing trend are found to be mainly located at mid–high latitudes of the Northern and Southern Hemispheres, while the regions with a significant increasing trend are mainly located in the tropical Pacific Ocean. For other variables including sea level pressure (SLP), 1000-mb height, and 200-mb height, the persistence of daily anomalies also exhibits similar trends in these regions. It is speculated that the enhanced baroclinicity and advection are possibly responsible for the significant downward trend of persistence mainly occurring in the southern and northern mid–high latitudes, while the increased coupling between the atmospheric circulation and sea surface temperature (SST) could contribute to the increase of persistence in the tropical Pacific. An empirical orthogonal function (EOF) analysis based on the 7-yr Gaussian low-pass-filtered series of winter season r 1 and r 5 of 500-mb height (linear trend removed before the low-pass filtering) is presented. The results suggest that there is prominent decadal variability of persistence in some regions of the Northern and Southern Hemispheres and tropics. When compared with r 1, r 5 has decadal variations with larger magnitude and larger spatial scale. It is found that the decadal variability of persistence is closely related to decadal fluctuations of large-scale atmospheric circulation patterns.

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Jianping Li
and
Ruiqiang Ding

Abstract

To quantify the predictability limit of a chaotic system, the authors recently developed a method using the nonlinear local Lyapunov exponent (NLLE). The NLLE method provides a measure of local predictability limit of chaotic systems and is intended to supplement existing predictability methods. To apply the NLLE in studies of actual atmospheric predictability, an algorithm based on local dynamical analogs is devised to enable the estimation of the NLLE and its derivatives using experimental or observational data. Two examples are given to illustrate the effectiveness of the algorithm, involving the Lorenz63 three-variable model and the Lorenz96 forty-variable model; they reveal that the algorithm is applicable in estimating the NLLE of a chaotic system from its experimental time series. On this basis, the NLLE method is used to investigate temporal–spatial distributions of predictability limits of the daily geopotential height and wind fields. The limit of atmospheric predictability varies widely with region, altitude, and season. The predictability limits of the daily geopotential height and wind fields are generally less than 3 weeks in the troposphere, whereas they are approximately 1 month in the lower stratosphere, revealing a potential predictability source for forecasting weather from the stratosphere. Further work is required to examine broader applications of the NLLE method in predictability studies of the atmosphere, ocean, and other systems.

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Ruiqiang Ding
and
Jianping Li

Abstract

This study confirms a weak spring persistence barrier (SPB) of sea surface temperature anomalies (SSTAs) in the western tropical Indian Ocean (WIO), a strong fall persistence barrier (FPB) in the South China Sea (SCS), and the strongest winter persistence barrier (WPB) in the southeastern tropical Indian Ocean (SEIO). During El Niño events, a less abrupt sign reversal of SSTAs occurs in the WIO during spring, an abrupt reversal occurs in the SCS during fall, and the most abrupt reversal occurs in the SEIO during winter. The sign reversal of SSTA implies a rapid decrease in SSTA persistence, which is favorable for the occurrence of a persistence barrier. The present results indicate that a more abrupt reversal of SSTA sign generally corresponds to a more prominent persistence barrier. El Niño–induced changes in atmospheric circulation result in reduced evaporation and suppressed convection. This in turn leads to the warming over much of the TIO basin, which is an important mechanism for the abrupt switch in SSTA, from negative to positive, in the northern SCS and SEIO. The seasonal cycle of the prevailing surface winds has a strong influence on the timing of the persistence barriers in the TIO.

The Indian Ocean dipole (IOD) alone can cause a weak WPB in the SEIO. El Niño events co-occurring with positive IOD further strengthen the SEIO WPB. The SEIO WPB appears to be more strongly influenced by ENSO than by the IOD. In contrast, the WIO SPB and the SCS FPB are relatively independent of the IOD.

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Ruiqiang Ding
and
Jianping Li

Abstract

This study investigates the persistence characteristics of the sea surface temperature anomaly (SSTA) in the northern tropical Atlantic (NTA). It is found that a persistence barrier exists around December and January. This winter persistence barrier (WPB) is prominent during the mature phase of strong ENSO events but becomes indistinct during weak ENSO and normal (non-ENSO) events. During strong El Niño events, the NTA SSTA shows a reversal in sign and a rapid warming during December and January. It is possible that this SSTA sign reversal reduces the persistence, leading to the occurrence of the NTA WPB. The present analyses indicate a dynamic relationship among the Pacific ENSO, the NTA SSTA, and the NTA WPB on a quasi-biennial time scale: a strong El Niño event is usually preceded by a strong La Niña event, which leads to a sign reversal of the NTA SSTA in winter as a delayed response to ENSO, finally resulting in the NTA WPB. Analyses also suggest that the NTA WPB is affected by the North Atlantic Oscillation (NAO). The NAO enhances the persistence of the NTA SSTA during winter, tending to weaken the NTA WPB.

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Jie Feng
,
Ruiqiang Ding
,
Deqiang Liu
, and
Jianping Li

Abstract

Nonlinear local Lyapunov vectors (NLLVs) are developed to indicate orthogonal directions in phase space with different perturbation growth rates. In particular, the first few NLLVs are considered to be an appropriate orthogonal basis for the fast-growing subspace. In this paper, the NLLV method is used to generate initial perturbations and implement ensemble forecasts in simple nonlinear models (the Lorenz63 and Lorenz96 models) to explore the validity of the NLLV method.

The performance of the NLLV method is compared comprehensively and systematically with other methods such as the bred vector (BV) and the random perturbation (Monte Carlo) methods. In experiments using the Lorenz63 model, the leading NLLV (LNLLV) captured a more precise direction, and with a faster growth rate, than any individual bred vector. It may be the larger projection on fastest-growing analysis errors that causes the improved performance of the new method. Regarding the Lorenz96 model, two practical measures—namely the spread–skill relationship and the Brier score—were used to assess the reliability and resolution of these ensemble schemes. Overall, the ensemble spread of NLLVs is more consistent with the errors of the ensemble mean, which indicates the better performance of NLLVs in simulating the evolution of analysis errors. In addition, the NLLVs perform significantly better than the BVs in terms of reliability and the random perturbations in resolution.

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Zongrong Li
,
Ruiqiang Ding
,
Jiangyu Mao
, and
Zhengyi Ren

Abstract

The Victoria Mode (VM) is defined as the second empirical orthogonal function (EOF) of sea surface temperature anomalies (SSTAs) in the North Pacific. It is independent of the Pacific decadal oscillation (PDO) and represents the second climate mode of North Pacific variability. Using a first-order autoregressive model and forcing indices that track the Aleutian low, the North Pacific Oscillation (NPO), anomalous ocean circulation in the Kuroshio–Oyashio Extension (KOE), and the cold tongue (CT) and warm pool (WP) El Niño–Southern Oscillation (ENSO), this study reconstructs the North Pacific SSTAs and examines the relative contributions of different forcing mechanisms to the VM variance. It is found that the NPO and ENSO, especially the WP ENSO, are the dominant sources of VM variability, whereas the contributions of the Aleutian low and zonal advection in the KOE region are relatively small. Further analysis shows that the forcing mechanisms acting on the VM are frequency dependent. At decadal and longer time scales, the VM variance comes mainly from the WP ENSO, whereas at interannual-time-scale contributions from the NPO and CT ENSO are important. This study suggests that the VM is an oceanic response to the NPO forcing and atmospheric teleconnections excited by ENSO events.

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Jianping Li
,
Richard Swinbank
,
Ruiqiang Ding
, and
Wansuo Duan
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Jie Feng
,
Jianping Li
,
Ruiqiang Ding
, and
Zoltan Toth

Abstract

Instabilities play a critical role in understanding atmospheric predictability and improving weather forecasting. The bred vectors (BVs) are dynamically evolved and flow-dependent nonlinear perturbations, indicating the most unstable modes of the underlying flow. Especially over smaller areas, however, BVs with different initial seeds may to some extent be constrained to a small subspace, missing potential forecast error growth along other unstable perturbation directions.

In this paper, the authors study the nonlinear local Lyapunov vectors (NLLVs) that are designed to capture an orthogonal basis spanning the most unstable perturbation subspace, thus potentially ameliorating the limitation of BVs. The NLLVs are theoretically related to the linear Lyapunov vectors (LVs), which also form an orthogonal basis. Like BVs, NLLVs are generated by dynamically evolving perturbations with a full nonlinear model. In simulated forecast experiments, a set of mutually orthogonal NLLVs show an advantage in predicting the structure of forecast error growth when compared to using a set of BVs that are not fully independent. NLLVs are also found to have a higher local dimension, enabling them to better capture localized instabilities, leading to increased ensemble spread.

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Ruiqiang Ding
,
Jianping Li
, and
Kyong-Hwan Seo

Abstract

Existing numerical models produce large error in simulating the Madden–Julian oscillation (MJO), thereby underestimating its predictability. In this paper, the predictability limit of the MJO is determined by the nonlinear local Lyapunov exponent approach, which provides an estimate of atmospheric predictability based on the observational data. The results show that the predictability limit of the MJO obtained from the bandpass-filtered (30–80 days) outgoing longwave radiation and wind fields, which serves as an empirical estimate of the theoretical potential predictability of the MJO, can exceed 5 weeks, which is well above the 1-week predictability of background noise caused by bandpass filtering. In contrast, a real-time analysis of MJO predictability using the real-time multivariate MJO (RMM) index, as introduced by Wheeler and Hendon, reveals a predictability limit of about 3 weeks. The findings reported here raise the possibility of obtaining a higher predictability limit in real-time prediction by improving the RMM index or by introducing a better method of extracting intraseasonal signals.

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Ruiqiang Ding
,
Jianping Li
, and
Kyong-Hwan Seo

Abstract

Tropical intraseasonal variability (TISV) shows two dominant modes: the boreal winter Madden–Julian oscillation (MJO) and the boreal summer intraseasonal oscillation (BSISO). The two modes differ in intensity, frequency, and movement, thereby presumably indicating different predictabilities. This paper investigates differences in the predictability limits of the BSISO and the boreal winter MJO based on observational data. The results show that the potential predictability limit of the BSISO obtained from bandpass-filtered (30–80 days) outgoing longwave radiation (OLR), 850-hPa winds, and 200-hPa velocity potential is close to 5 weeks, comparable to that of the boreal winter MJO. Despite the similarity between the potential predictability limits of the BSISO and MJO, the spatial distribution of the potential predictability limit of the TISV during summer is very different from that during winter. During summer, the limit is relatively low over regions where the TISV is most active, whereas it is relatively high over the North Pacific, North Atlantic, southern Africa, and South America. The spatial distribution of the limit during winter is approximately the opposite of that during summer. For strong phases of ISO convection, the initial error of the BSISO shows a more rapid growth than that of the MJO. The error growth is rapid when the BSISO and MJO enter the decaying phase (when ISO signals are weak), whereas it is slow when convection anomalies of the BSISO and MJO are located in upstream regions (when ISO signals are strong).

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