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A covariance decomposition method is applied to a monthly global precipitation dataset to decompose the interannual variability in the seasonal mean time series into an unpredictable component related to “weather noise” and to a potentially predictable component related to slowly varying boundary forcing and low-frequency internal dynamics. The “potential predictability” is then defined as the fraction of the total interannual variance accounted for by the latter component. In tropical oceans (30° E–0° W, 30° S–30° N), the consensus is that the El Nino-Southern Oscillation (ENSO, with 4–8 year cycles) is a dominant driver of the potentially predictable component, while the Madden-Julian Oscillation (MJO, with 30–90 days cycles) is a dominant driver of the unpredictable component. In this study, the consensus is verified by using the Nino3-4 SST index and a popular MJO index. It is confirmed that Nino3-4 SST does indeed explain a significant part of the potential predictable component, but only limited variability of the unpredictable component is explained by the MJO index. This raises the question of whether the MJO is dominant in the variability of the unpredictable component of the precipitation, or the current MJO indexes do not represent MJO variability well.

The patterns of interannual variability that arise from the slow (potentially predictable) and fast or intraseasonal (unpredictable) components of seasonal mean precipitation over eastern China are examined, based on observations from a network of 106 stations for the period 1951–2004. The analysis is done by using a variance decomposition method that allows identification of the sources of the predictability and the prediction uncertainty, from March–April–May (MAM) to September–October–November (SON). The average potential predictability (ratio of slow-to-total variance) of eastern China precipitation is generally moderate, with the highest value of 0.18 in June–July–August (JJA) and lowest value of 0.12 in April–May–June (AMJ). The leading predictable precipitation mode is significantly related to one-season-lead SST anomalies in the area of the Kuroshio Current during AMJ-to-JJA, the Indian-western Pacific SST in July–August–September (JAS), and the eastern tropical Pacific SST in MAM and SON. The prolonged linear trends, which are seen in the principal component time series associated with the second or third predictable precipitation modes in MJJ-to-ASO, also serve as a source of predictability for seasonal precipitation over eastern China. The predictive characteristics of the atmospheric circulation–precipitation relationship indicate that the western Pacific subtropical high plays a key role in eastern China precipitation. In addition, teleconnection patterns that are significantly related to the predictable precipitation component are also identified. The leading/second unpredictable precipitation modes from MAM to SON all show a monopole/dipole structure, which are accompanied by wavy circulation patterns that are related to intraseasonal events.

Decadal and multidecadal variability in the ERSSTv5 global SST dataset are studied in terms of implicit fast (noise) and slow (signal) processes that affect variability on decadal time scales. Using a new method that better estimates the fast, or noise, component of decadal variability, estimates of the modes of variability in the slow component are possible. The fast component of decadal variability has a leading fast mode, which explains 62% of the variance, and it is shown that this fast variability, or decadal climate noise, is well represented by any of the indices associated with intradecadal or interannual variability in the tropical Pacific Ocean. Three slow modes are identified, representing 69% of the slow multidecadal variance, after removing the radiative forcing trend. These modes are shown to be related to variability in the Atlantic multidecadal oscillation (AMO) and SST multidecadal variability in the central western Pacific and in the Indian Ocean gyre region, respectively. The first and third slow modes represent two phases of a propagating mode with a period of about 80 years. The second slow mode represents multidecadal variability of the western Pacific warm pool, which is less robust than the other two and shown to be weakly related to the AMO with a lag of about 30 years; fast variability in this region is related to the leading fast mode. Three regions of significant slow variability are identified south of Australia, south of Africa, and near the Drake Passage in association with the Antarctic Circumpolar Current.

Decadal mean variables are frequently used to characterize decadal climate variabilities. Decadal means are often calculated using yearly data, which can represent variability at time scales from annual to centennial. Residuals from interannual fluctuations may contribute to the variability in decadal time series. Such variability is more difficult to be predicted at the long range. Removing it from the decadal variability means that the remaining variability is more likely to arise from slowly varying multidecadal or longer time scale external forcing and internal climate dynamics, which are more likely to be predicted. Here, a new approach is proposed to understand the uncertainty, potential predictability, and drivers of decadal mean variables. The covariance matrix of multivariate decadal running means is decomposed into unpredictable fast decadal variability and the potentially predictable slow decadal variability. EOF analysis is then applied to the decomposed matrices to find the dominant modes, which may be related to the drivers of the two types of variabilities in the multivariate decadal means. The methodology has been applied to 140-yr datasets of North Pacific sea surface temperature and the Northern Hemisphere 1000-hPa geopotential height. For sea surface temperature, the Pacific decadal oscillation is the major driver of the fast decadal variability, while the radiative forcing and the Atlantic multidecadal oscillation are major drivers of the slow decadal variability. For the 1000-hPa geopotential height, fast decadal variability is associated with the northern annular mode, the east Atlantic mode, and the Pacific decadal oscillation. Slow decadal variability is associated with the northern annular mode and the Atlantic multidecadal oscillation.

Improvement in the seasonal forecasting of East Asian summer monsoon rainfall (EASMR) remains a great challenge, as it is influenced by varied and complex impacts from (1) external forcings and slowly varying internal variabilities, which are potentially predictable, and (2) internal dynamics on intraseasonal time scales, which is basically unpredictable beyond a season. In this work, a (co-)variance decomposition method is applied to identify the leading potentially predictable (slow) patterns of the EASMR [the seasonal mean rainfall in the region (5°–50° N, 100°–140° E) in June–July–August] during 1979–2019 by separating the unpredictable noise (intraseasonal). We focus on the most critical predictable sources that are additional to the decaying (DC) El Niño–Southern Oscillation (ENSO), developing (DV) ENSO, and spring Arctic Oscillation (AO)—the three most important and well-recognized predictors for EASMR. We find that (1) the indices that represent the EASMR predictability related to the DC ENSO, spring AO and DV ENSO are the preceding November to March Niño1 + 2 sea surface temperature (SST), the April–May AO, and the May Niño4 SST, respectively; (2) the dominant additional predictable EASMR signals that are linearly independent of the DC ENSO, spring AO and DV ENSO have apparent relationships with the interannual variability of the SST in the western North Pacific, tropical and southern Atlantic, southern Indian, and Arctic oceans during boreal springtime, as well as the linear trend; and (3) by applying a principal component regression scheme to evaluate the EASMR predictability arising from DC/DV ENSO–AO and these additional predictors, the cross-validated fraction variance skill of the total seasonal mean EASMR is 11% (8%—land; 13%—ocean) for the former, and 15% (15%—land; 15%—ocean) for the latter, with a total of 26% that comprises more than 80% of the potential predictability of the EASMR. The considerable skill stemming from the predictors additional to DC/DV ENSO–AO indicates that they are worthy of attention in the seasonal forecasting of EASMR, especially for terrestrial areas.

Based on model output from a multi-model ensemble (MME) of coupled atmosphere-ocean general circulation models, it is shown that prolonged trends in Australian rainfall over the southwest during winter and the monsoonal northwest during summer are associated with trends in the large scale Southern Hemisphere circulation. These trends, in turn, are the result of external radiative forcing, including anthropogenic greenhouse gases, ozone, aerosols and land use change. The MME is used in an analysis of covariance method to separate the internal (natural) variability in the coupled rainfall-atmospheric circulation relationship from influences associated with anomalous external radiative forcing. In both seasons, the leading coupled external mode (singular vector) in the twentieth century runs has rainfall and circulation loading patterns with associated time-series that have statistically significant trends. The associated rainfall loading patterns qualitatively resemble the patterns of observed rainfall trends. The circulation loading patterns reflect the thermal expansion of the tropics and the Hadley Cell. A comparison between similar analyses using the second half of the twenty-first century of the representative concentration pathways (RCP) RCP8.5 and RCP4.5 scenarios show that trends in rainfall and the circulation are projected to continue and intensify under increasing anthropogenic greenhouse gas concentrations. The technique developed here is generally applicable to separate the climate change signal from natural variability in any relevant pair of coupled climate fields.

An analysis is made of the coherent patterns, or modes, of interannual variability of Southern Hemisphere 500 hPa geopotential height field under current and projected climate change scenarios. Using three separate multi-model ensembles (MMEs) of coupled model intercomparison project phase 5 (CMIP5) models, the interannual variability of the seasonal mean is separated into components related to (1) intraseasonal processes; (2) slowly-varying internal dynamics; and (3) the slowly-varying response to external changes in radiative forcing. In the CMIP5 RCP8.5 and RCP4.5 experiments, there is very little change in the twenty-first century in the intraseasonal component modes, related to the Southern annular mode (SAM) and mid-latitude wave processes. The leading three slowly-varying internal component modes are related to SAM, the El Niño–Southern oscillation (ENSO), and the South Pacific wave (SPW). Structural changes in the slow-internal SAM and ENSO modes do not exceed a qualitative estimate of the spatial sampling error, but there is a consistent increase in the ENSO-related variance. Changes in the SPW mode exceed the sampling error threshold, but cannot be further attributed. Changes in the dominant slowly-varying external mode are related to projected changes in radiative forcing. They reflect thermal expansion of the tropical troposphere and associated changes in the Hadley Cell circulation. Changes in the externally-forced associated variance in the RCP8.5 experiment are an order of magnitude greater than for the internal components, indicating that the SH seasonal mean circulation will be even more dominated by a SAM-like annular structure. Across the three MMEs, there is convergence in the projected response in the slow-external component.

The modes of variability that arise from the slow-decadal (potentially predictable) and intra-decadal (unpredictable) components of decadal mean temperature and precipitation over China are examined, in a 1000 year (850–1850 AD) experiment using the CCSM4 model. Solar variations, volcanic aerosols, orbital forcing, land use, and greenhouse gas concentrations provide the main forcing and boundary conditions. The analysis is done using a decadal variance decomposition method that identifies sources of potential decadal predictability and uncertainty. The average potential decadal predictabilities (ratio of slow-to-total decadal variance) are 0.62 and 0.37 for the temperature and rainfall over China, respectively, indicating that the (multi-)decadal variations of temperature are dominated by slow-decadal variability, while precipitation is dominated by unpredictable decadal noise. Possible sources of decadal predictability for the two leading predictable modes of temperature are the external radiative forcing, and the combined effects of slow-decadal variability of the Arctic oscillation (AO) and the Pacific decadal oscillation (PDO), respectively. Combined AO and PDO slow-decadal variability is associated also with the leading predictable mode of precipitation. External radiative forcing as well as the slow-decadal variability of PDO are associated with the second predictable rainfall mode; the slow-decadal variability of Atlantic multi-decadal oscillation (AMO) is associated with the third predictable precipitation mode. The dominant unpredictable decadal modes are associated with intra-decadal/inter-annual phenomena. In particular, the El Niño–Southern Oscillation and the intra-decadal variability of the AMO, PDO and AO are the most important sources of prediction uncertainty.

A methodology is proposed that allows an estimate of the contribution of decadal noise to the inter-decadal variability of climate variables. By removing this decadal noise, or unpredictable decadal variability, from the total inter-decadal variability, the residual variability is more likely to be associated with potentially predictable slow processes. This residual variability may be considered to be potentially predictable. We apply the method to sea surface temperature from a 1000 year (850–1850 AD) experiment with the CCSM4 model forced by solar variations, volcanic aerosols, orbital forcings, land use and greenhouse gas concentrations. Our analysis shows large potential SST inter-decadal predictability in the extra-tropical regions in both hemispheres, as well as in the subtropical/tropical Indian Ocean, the western Pacific and the Atlantic. In the tropical eastern Pacific, inter-decadal variability is dominated by unpredictable decadal noise. The two leading unpredictable modes of inter-decadal variability have features related to the two leading ENSO modes, and the PDO. The four leading potentially predictable modes of inter-decadal variability are shown to be related to the external forcing, the IPO, inter-hemispheric SST fluctuations and the AMO, and decadal/multi-decadal AO/NAO variability.