A stochastic model of SST for climate simulation experiments

 This study describes the implementation of a statistical method to simulate a multi-century sequence of global sea surface temperature (SST) fields. A multi-variable auto-regressive (AR) model is trained on the observed time series of SST from the data set compiled at the Hadley Centre (GISST 2.0). To reduce the dimensionality of the model, the stochastic process is in practice fitted to empirical orthogonal function (EOF) time coefficients of the SST series, retaining the first 14 EOFs. Selected lag cross-covariances among the EOF time series are retained, based on the structure of the cross-correlation matrix and lags up to 64 months are included. Though the resulting system is quite large (a 14-dimensional AR process, with 400 parameters to be determined) the calculation is possible and a stable process is obtained. The process can then be used to investigate some statistical properties of the SST data set and to generate synthetic SST data that could be used in very long numerical experiments with atmospheric or ocean models in which only the main features of the observed statistics of the SST must be retained. Results indicate that the synthetic SST data set seems to be of usable quality as boundary condition for the atmosphere or the ocean in climate experiments. Analysis of extreme events and extreme decades in the synthetic SST data confirms the exceptional character of the 1980s, but also provides circumstantial evidence that the 1980s were indeed within the limits of the statistics of the previously observed record. Received: 6 August 1996 / Accepted: 29 September 1997     

An objective analysis of the observed spatial structure of the tropical Indian Ocean SST variability

The observed interannual Indian Ocean sea surface temperature (SST) variability from 1950 to 2008 is analyzed in respect to the spatial structure of the variability. The analysis is based on an objective comparison of the leading empirical orthogonal function modes against the stochastic null hypothesis of spatial red noise (isotropic diffusion). Starting from this red noise assumption, the analysis searches for those structures that are most distinct from the red noise hypothesis. This objective approach will put previously well and less known modes of variability into the context of the multivariate SST variability. The Indian Ocean SST variability is marked by relatively weak SST variability, which is strongly dominated by a basin wide monopole pattern that is caused by different processes. The leading modes of variability are the El Nino Southern Oscillation (ENSO) variability and the warming trend, which both project onto the basin wide monopole structure. Other more characteristic spatial patterns of internal variability are much less dominant in the tropical Indian Ocean, which is quite different from all other ocean basin, where characteristic teleconnection patterns exist. The remaining, ENSO independent, detrended variability is dominated by multi-pole patterns from the southern Indian Ocean reaching into the tropical Indian Ocean, which are probably primarily caused by extra-tropical atmospheric forcings. The large scale tropical Indian Ocean internal variability itself has no dominant structure. The currently often used dipole mode index (DMI) does not appear to present a dominant teleconnection pattern of the Indian Ocean internal SST variability. In the context of the objective analysis presented here, the DMI partly reflects the ENSO variability and is also a representation of the multi-dimensional, chaotic spatial red noise (isotropic diffusion) process. As such the DMI cannot be interpreted as a coherent teleconnection between the two poles.     

An evaluation of the CMIP3 and CMIP5 simulations in their skill of simulating the spatial structure of SST variability

The natural sea surface temperature (SST) variability in the global oceans is evaluated in simulations of the Climate Model Intercomparison Project Phase 3 (CMIP3) and CMIP5 models. In this evaluation, we examine how well the spatial structure of the SST variability matches between the observations and simulations on the basis of their leading empirical orthogonal functions-modes. Here we focus on the high-pass filter monthly mean time scales and the longer 5 years running mean time scales. We will compare the models and observations against simple null hypotheses, such as isotropic diffusion (red noise) or a slab ocean model, to illustrate the models skill in simulating realistic patterns of variability. Some models show good skill in simulating the observed spatial structure of the SST variability in the tropical domains and less so in the extra-tropical domains. However, most models show substantial deviations from the observations and from each other in most domains and particularly in the North Atlantic and Southern Ocean on the longer (5 years running mean) time scale. In many cases the simple spatial red noise null hypothesis is closer to the observed structure than most models, despite the fact that the observed SST variability shows significant deviations from this simple spatial red noise null hypothesis. The CMIP models tend to largely overestimate the effective spatial number degrees of freedom and simulate too strongly localized patterns of SST variability at the wrong locations with structures that are different from the observed. However, the CMIP5 ensemble shows some improvement over the CMIP3 ensemble, mostly in the tropical domains. Further, the spatial structure of the SST modes of the CMIP3 and CMIP5 super ensemble is more realistic than any single model, if the relative explained variances of these modes are scaled by the observed eigenvalues.     

Predictability of Indian Ocean sea surface temperature using canonical correlation analysis

There is strong evidence that Indian Ocean sea surface temperatures (SSTs) influence the climate variability of Southern Asia and Africa; hence, accurate prediction of these SSTs is a high priority. In this study, we use canonical correlation analysis (CCA) to design empirical models to assess the predictability of tropical Indian Ocean SST from sea level pressure (SLP) and SST themselves with lead-times up to one year. One model uses the first twelve empirical orthogonal functions (EOFs) of SLP over the Indian Ocean using different lead-times to predict SST. A CCA model with EOFs of SST as the predictor at the same lead-times is compared to SLP as a predictor and shows the auto-correlation of the system. A CCA using the first five extended empirical orthogonal functions (EEOFs) of sea level pressure over the Indian Ocean basin for an interval of two years combined with SST EOFs as predictors is found to produce the greatest correlation between forecast and observed SSTs. This model obtains higher skill by explicitly considering the development in time of SLP anomalies in the region. The skill of this model, assessed from retroactive forecasts of an 18 year period, shows improvement relative to other empirical forecasts particularly for the central and eastern Indian Ocean and boreal autumn months preceding the Southern Hemisphere summer rainfall season. This is likely due to the limited domain of this model identifying modes of variability that are more pronounced in these areas during this season. Finally, a nonlinear canonical correlation analysis (NLCCA) derived from a neural network is used to analyze the leading nonlinear modes. These nonlinear modes differ from the linear CCA modes with distinct cold and warm SST phases suggesting a nonlinear relationship between SST and SLP over the tropical Indian Ocean.     

500hPa月平均高度距平场统一的时空结构研究

大气环流异常的空间分布结构、年内演变和年际演变规律与长期天气和短期气候变化有密切的关系。国内外对它们的基本特征、演变规律以及形成和变化的物理原因作了许多研究;这些研究是长期天气预报和短期气候变化研究很有成就的一个方面。但是上述的多数工作主要是对环流异常的空间分布特征和时间分布规律分别进行研究,以揭示时空各自独立的分布规律,如大气中有空间上的遥相关     

Modelling of Indian monsoon rainfall series by univariate box—Jenkins type of models

The time domain approach, i.e. Autoregressive (AR) processes, of time series analysis is applied to the monsoon rainfall series of India and its two major regions, viz. North-West India and Central India. Since the original time series shows no modelable structure due to the presence of high interannual variability, a 3-point running filter is ap-plied before exploring and fitting appropriate stochastic models. Out of several parsimonious models fitted, AR(3) is found to be most suitable. The usefulness of this fitted model is validated on an independent datum of 18 years and some skill has been noted. These models therefore can be used for low skill higher lead time forecasts of monsoon. Further the forecasts produced through such models can be combined with other forecasts to increase the skill of monsoon forecasts.     

Non‐linear coupling between modes in a low‐dimensional model of ENSO

Abstract

An intermediate coupled model of the tropical Pacific ocean‐atmosphere system was reduced by projecting the non‐linear model onto a truncated basis set of its own empirical orthogonal functions (EOFs). For moderate coupling strengths, the simulated El Niño/Southern Oscillation (ENSO) variability consists of a dominant quasi‐quadrennial mode with a period of approximately four years and a smaller quasi‐biennial mode at a period of approximately two years. In the absence of a seasonal cycle, the leading two EOFs capture the dynamics of the leading interannual mode, with a further two EOFs being required to capture the secondary oscillation. The presence of seasonal forcing increases the EOF requirement by two, the leading pair of EOFs being dominated by the annual cycle. Normal mode analysis of the reduced models indicates that the quasi‐biennial mode manifests itself, even though it is linearly stable, by non‐linear coupling to the quasi‐quadrennial mode. The nonlinearity does not produce the quasi‐biennial signal unless the spatial degrees of freedom associated with the linear quasi‐biennial mode are present. Other linearly stable modes also couple non‐linearly to the leading interannual mode and to the seasonal cycle, but the quasi‐biennial mode is favoured over other, less‐damped linear modes because of its proximity to a multiple of the quasi‐quadrennial frequency.     

Is the Indian Ocean SST variability a homogeneous diffusion process?

Whereas the predominance of El Niño Southern Oscillation (ENSO) mode in the tropical Pacific sea surface temperature (SST) variability is well established, no such consensus seems to have been reached by climate scientists regarding the Indian Ocean. While a number of researchers think that the Indian Ocean SST variability is dominated by an active dipolar-type mode of variability, similar to ENSO, others suggest that the variability is mostly passive and behaves like an autocorrelated noise. For example, it is suggested recently that the Indian Ocean SST variability is consistent with the null hypothesis of a homogeneous diffusion process. However, the existence of the basin-wide warming trend represents a deviation from a homogeneous diffusion process, which needs to be considered. An efficient way of detrending, based on differencing, is introduced and applied to the Hadley Centre ice and SST. The filtered SST anomalies over the basin (23.5N–29.5S, 30.5E–119.5E) are then analysed and found to be inconsistent with the null hypothesis on intraseasonal and interannual timescales. The same differencing method is then applied to the smaller tropical Indian Ocean domain. This smaller domain is also inconsistent with the null hypothesis on intraseasonal and interannual timescales. In particular, it is found that the leading mode of variability yields the Indian Ocean dipole, and departs significantly from the null hypothesis only in the autumn season.     

气象场相关结构对EOFs展开稳定性的影响

本文从矩阵扰动理论出发,提出利用矩阵的范数(norm)作为度量气象场随机扰动的稳定性指标,并由此间接推估EOFs展开的稳定性。经理论论证、数值试验和实例计算表明,气象场的相关性越好,达到稳定相关结构所需样本越小,由此得到的EOFs稳定性也越好,反之则不然。上述规律又直接受样本大小n和站点数目p的影响。对于不同的气象场来说,达到稳定EOFs的样本临界值不同,必须警惕EOFs展开有可能不是稳定的。     

气候反馈对温度空间模态的依赖性:IPCC AR6解读

依据政府间气候变化专门委员会(IPCC)第六次评估报告(AR6)第一工作组(WGI)报告第七章的内容,详细解读了气候反馈对温度空间模态的依赖性。与第五次评估报告(AR5)相比,AR6对于地表温度空间模态演变在驱动气候反馈变化中作用的理解已有了较大提升。AR6认为,在温室气体强迫下,北极在21世纪的增温幅度很可能大于全球平均水平,南极在百年时间尺度上的增温要强于热带地区;同时,在百年时间尺度上热带太平洋东部的变暖幅度大于西部,即热带太平洋东-西向海表温度梯度减弱。极地放大效应(尤其是南半球)和热带太平洋东-西向海表温度梯度随时间的变化是影响未来气候反馈如何演变的关键因素。随着地表增温空间模态的演变,气候反馈(尤其云反馈)预计将在未来几十年的时间尺度上逐渐增加,对气候变化更多是起放大作用。     

东亚夏季风的低频振荡及其与500hPa角动量输送变化的关系

本文用谱分析和经验正交函数分析了1986年夏季风时期亚洲高空越赤道气流和低空赤道西风的低频振荡特征。高低空两支季风气流的30—50天滤波序列的主要经验正交函数能较好地反映亚洲夏季风低频振荡的空间特征。根据EOF1时间序列的振荡位相可以确定东亚夏季风活跃/中断的具体时间。后延相关揭示出北半球500hPa中低纬角动量输送的经向交换同东亚夏季风的低频活动有密切关系。      

A comparative study of mixed exponential and Weibull distributions in a stochastic model replicating a tropical rainfall process

A stochastic rainfall model is presented for the generation of hourly rainfall data in an urban area in Malaysia. In view of the high temporal and spatial variability of rainfall within the tropical rain belt, the Spatial–Temporal Neyman–Scott Rectangular Pulse model was used. The model, which is governed by the Neyman–Scott process, employs a reasonable number of parameters to represent the physical attributes of rainfall. A common approach is to attach each attribute to a mathematical distribution. With respect to rain cell intensity, this study proposes the use of a mixed exponential distribution. The performance of the proposed model was compared to a model that employs the Weibull distribution. Hourly and daily rainfall data from four stations in the Damansara River basin in Malaysia were used as input to the models, and simulations of hourly series were performed for an independent site within the basin. The performance of the models was assessed based on how closely the statistical characteristics of the simulated series resembled the statistics of the observed series. The findings obtained based on graphical representation revealed that the statistical characteristics of the simulated series for both models compared reasonably well with the observed series. However, a further assessment using the AIC, BIC and RMSE showed that the proposed model yields better results. The results of this study indicate that for tropical climates, the proposed model, using a mixed exponential distribution, is the best choice for generation of synthetic data for ungauged sites or for sites with insufficient data within the limit of the fitted region.     

Factors that affect the amplitude of El Nino in global coupled climate models

Historically, El Nino-like events simulated in global coupled climate models have had reduced amplitude compared to observations. Here, El Nino-like phenomena are compared in ten sensitivity experiments using two recent global coupled models. These models have various combinations of horizontal and vertical ocean resolution, ocean physics, and atmospheric model resolution. It is demonstrated that the lower the value of the ocean background vertical diffusivity, the greater the amplitude of El Nino variability which is related primarily to a sharper equatorial thermocline. Among models with low background vertical diffusivity, stronger equatorial zonal wind stress is associated with relatively higher amplitude El Nino variability along with more realistic east–west sea surface temperature (SST) gradient along the equator. The SST seasonal cycle in the eastern tropical Pacific has too much of a semiannual component with a double intertropical convergence zone (ITCZ) in all experiments, and thus does not affect, nor is it affected by, the amplitude of El Nino variability. Systematic errors affecting the spatial variability of El Nino in the experiments are characterized by the eastern equatorial Pacific cold tongue regime extending too far westward into the warm pool. The time scales of interannual variability (as represented by time series of Nino3 SSTs) show significant power in the 3–4 year ENSO band and 2–2.5 year tropospheric biennial oscillation (TBO) band in the model experiments. The TBO periods in the models agree well with the observations, while the ENSO periods are near the short end of the range of 3–6 years observed during the period 1950–94. The close association between interannual variability of equatorial eastern Pacific SSTs and large-scale SST patterns is represented by significant correlations between Nino3 time series and the PC time series of the first EOFs of near-global SSTs in the models and observations. Received: 17 April 2000 / Accepted: 17 August 2000     

An empirical model of decadal ENSO variability

This paper assesses potential predictability of decadal variations in the El Ni?o/Southern Oscillation (ENSO) characteristics by constructing and performing simulations using an empirical nonlinear stochastic model of an ENSO index. The model employs decomposition of global sea-surface temperature (SST) anomalies into the modes that maximize the ratio of interdecadal-to-subdecadal SST variance to define low-frequency predictors called the canonical variates (CVs). When the whole available SST time series is so processed, the leading canonical variate (CV-1) is found to be well correlated with the area-averaged SST time series which exhibits a non-uniform warming trend, while the next two (CV-2 and CV-3) describe secular variability arguably associated with a combination of Atlantic Multidecadal Oscillation (AMO) and Pacific Decadal Oscillation (PDO) signals. The corresponding ENSO model that uses either all three (CVs 1–3) or only AMO/PDO-related (CVs 2 and 3) predictors captures well the observed autocorrelation function, probability density function, seasonal dependence of ENSO, and, most importantly, the observed interdecadal modulation of ENSO variance. The latter modulation, and its dependence on CVs, is shown to be inconsistent with the null hypothesis of random decadal ENSO variations simulated by multivariate linear inverse models. Cross-validated hindcasts of ENSO variance suggest a potential useful skill at decadal lead times. These findings thus argue that decadal modulations of ENSO variability may be predictable subject to our ability to forecast AMO/PDO-type climate modes; the latter forecasts may need to be based on simulations of dynamical models, rather than on a purely statistical scheme as in the present paper.     

Northern hemisphere winter atmospheric climate: modes of natural variability and climate change

Under anthropogenic climate change it is possible that the increased radiative forcing and associated changes in mean climate may affect the “dynamical equilibrium” of the climate system; leading to a change in the relative dominance of different modes of natural variability, the characteristics of their patterns or their behavior in the time domain. Here we use multi-century integrations of version three of the Hadley Centre atmosphere model coupled to a mixed layer ocean to examine potential changes in atmosphere-surface ocean modes of variability. After first evaluating the simulated modes of Northern Hemisphere winter surface temperature and geopotential height against observations, we examine their behavior under an idealized equilibrium doubling of atmospheric CO₂. We find no significant changes in the order of dominance, the spatial patterns or the associated time series of the modes. Having established that the dynamic equilibrium is preserved in the model on doubling of CO₂, we go on to examine the temperature pattern of mean climate change in terms of the modes of variability; the motivation being that the pattern of change might be explicable in terms of changes in the amount of time the system resides in a particular mode. In addition, if the two are closely related, we might be able to assess the relative credibility of different spatial patterns of climate change from different models (or model versions) by assessing their representation of variability. Significant shifts do appear to occur in the mean position of residence when examining a truncated set of the leading order modes. However, on examining the complete spectrum of modes, it is found that the mean climate change pattern is close to orthogonal to all of the modes and the large shifts are a manifestation of this orthogonality. The results suggest that care should be exercised in using a truncated set of variability EOFs to evaluate climate change signals.     

Nonparametric testing of variability and trend in some climatic records

We use the method of surrogates to test the structure of variability in nine paleoclimate reconstructions and to compare temperature trends with that of the modern temperature record in the Northern hemisphere. Three different algorithms are used to generate surrogate time series: the iterated amplitude adjusted Fourier transform (IAAFT), the statically transformed autoregressive process (STAP) and a modification of STAP, which generates surrogates of arbitrary length (STAPL). We assessed through formal statistical tests that the surrogates preserve the LTP structure of the reconstructed time series of global temperature, using different measures (Hurst exponent, DFA exponent and R/S analysis). Then using the same surrogates we tested for the presence of a linear trend at least as great as the trend of the modern time series against the null hypothesis that the observed trend is only due to LTP. The null hypothesis could be rejected at the lowest possible significance level for all but two of the reconstructions. The result from the non-parametric test adds further statistical evidence to that of earlier parametric studies that the observed global warming trend in the modern time series cannot be adequately explained by natural agents of variability.     

耦合模式热带太平洋云—气候反馈模拟误差评估

云—气候反馈是热带海气相互作用的重要过程, 同时也是气候模拟的难点。本文利用IPCC AR4提供的耦合模式20世纪模拟试验结果和观测资料, 通过滤波和经验正交展开 (EOF) 的方法将热带太平洋海表温度的年际变化和年代际变化信号分别提取出来, 然后再分别计算观测和模式在年际和年代际时间尺度上云—辐射和热通量反馈特征, 发现在上述两个时间尺度上, 耦合模式模拟的云—辐射和热通量的反馈都要比观测和再分析资料的偏弱。反馈偏弱的可能原因是模式中热带大气对流和云对海表温度变化的敏感性比真实大气要偏弱。值得注意的是, 尽管耦合模式热带太平洋年代际热力反馈偏弱, 但是耦合模式模拟的热带太平洋南北纬10°之间海表温度的年代际增温趋势与观测相当。进一步分析表明, 只用年代际热力反馈来解释热带太平洋的气候变化是不够的, 还必须考虑动力反馈对于海表温度变化的调节作用。     

Modal aspects of the Northern Hemisphere annular mode as identified from the results of a GCM run

In order to study the physical nature of the Arctic Oscillation (AO) or the Northern Hemisphere annular mode (NAM), the linear stochastic model, constructed empirically from the output of a GCM run, is used to investigate the modal aspects of this climate variability mode. Theoretical analysis on the dominant modal response to the stochastic forcing is performed in terms of the maximum variance contribution. As the modal aspect of AO/NAM, two dominant normal modes are found to resemble the spatial structure of the AO/NAM represented by the leading EOF. These stochastically forced normal modes are regarded to be physical modes and thus can explain many fundamental features of the AO/NAM such as the barotropic annular dipole, tropospher–stratosphere coupling, and its dominance over the wintertime Northern Hemisphere. It then follows that the origin or physical nature of the AO/NAM can be attributed to the behaviors of the dominant annular normal modes. A key distinction of this study from previous eddy driving theories is that, to drive the variability, eddy forcing needs not to have a spatial structure completely coinciding with the pattern of the NAM, since the latter is mainly decided by the linear normal modes.     

Global and regional variability in a coupled AOGCM

 The variability of near surface temperature on global and regional spatial scales and interannual time scales from a 1000 year control integration of the Hadley Centre coupled model (HADCM2-CTL) are compared with the observational record of surface temperature. The model succeeds in reproducing the observed patterns of natural variability, with high variability over the northern continents and low variability over much of the tropics. The model global mean variability has similar strength to observed global mean variability on time scales less than 20 years. The warming seen in the historical record is outside the range of natural variability as simulated in HADCM2-CTL. The model has El-Ni?o/Southern Oscillation (ENSO)-like behaviour with a central Pacific, peak to peak, strength of approximately 3 K. Changes in near surface temperature in the central Pacific are strongly correlated with changes in near surface temperature over most of the tropics, large regions of the extra-tropics and changes in tropical ocean upper 250 m heat content. Tropospheric temperature changes and tropical surface pressure changes are also strongly correlated with changes in the central Pacific surface temperature. Oceanic regions show significant departures from an AR1 or first order Markov behaviour in the Northwest Atlantic, Northwest Pacific and Arctic oceans. The Northwest Atlantic region has large amounts of variability over periods greater than 50 years. This variability is associated with a jump in the strength of North Atlantic meridional stream function. The spectra of the Western European and Continental US land regions are not significantly different from an AR1 process. The flow through the Drake Passage has an interannual standard deviation of approximately 2.5 Sv with significant departures from an AR1 process at time scales greater than 40 years. Winter northern hemispheric 500 hPa geopotential height shows some evidence of multiple regimes but no year to year persistence of these regimes. Received: 31 January 1996/Accepted: 22 July 1996     

Modes of variability of global sea surface temperature,free atmosphere temperature and oceanic surface energy flux

Monthly mean sea surface temperature (SST), free air temperature from satellite microwave sounding units (MSU) and oceanic surface energy fluxes are subjected to empirical orthogonal function (EOF) analysis for a common decade to investigate the physical relationships involved. The first seasonal modes of surface solar energy flux and SST show similar inter-hemispheric patterns with an annual cycle. Solar flux appears to control this pattern of SST. The first seasonal mode of MSU is similar with, additionally, land-sea differences; MSU is apparently partly controlled by absorption of solar near-infrared radiation and partly by sensible heat from the land surface. The second and third seasonal eigenvector of SST and solar flux exhibit semi-annual oscillations associated with a pattern of cloudiness in the subtropics accompanying the translation of the Hadley cell rising motion between the hemispheres. The second seasonal mode of MSU is dominated by an El Niño signal. The first nonseasonal EOFs of SST and solar flux exhibit El Niño characteristics with the solar pattern being governed by west-to-east translation of a Walker cell type pattern. The first non-seasonal EOF of MSU shows a tropical strip pattern for the El Niño mode, which is well correlated with the latent heat fluxes in the tropical east Pacific but not in the tropical west Pacific. Two possible explanations are: an increase in subsidence throughout the tropical strip driven by extra evaporation in the tropical east Pacific and consequent additional latent heat liberation; a decrease of meridional heat flux out of the tropics.