二阶奇异动力系统的非平凡周期解

应用Leray-Schauder非线性二择一原理研究二阶动力系统x+k²x=f(t,x)+e(t)非平凡周期解的存在性,其中0<k<π/T,f∈C((R/TZ)×R^N\{0},R^N)在原点具有排斥的奇性.不需要任何的强制性条件,既可以处理强奇性,也可以处理弱奇性.     

A meso-scale three-dimensional dynamical model of orographic rainfall

Summary A mesoscale three-dimensional (3-D) dynamical model is presented to diagnose orographic rainfall, with particular reference to the Western Ghats (WG) in India. This model has two parts, namely, a dynamical part and a thermodynamical part. In the dynamical part the vertical velocity induced by a mesoscale elliptical orographic barrier has been computed using the perturbation technique. In the thermodynamical part rainfall intensity (RFI) has been computed using the computed vertical velocities, with the help of continuity of moisture and mass. The computed RFI has been compared with observed RFI as well as with that computed by 2-D model. The present study shows that during the southwest monsoon season (SWMS), orographic rainfall enhancement in the WG area appears to be solely due to the vertical shear of the basic flow and its variation with height. Stability appears to have very little influence on it. The spatial distribution of RFI across the barrier shows that there are four regions of maximum rainfall, one primary on the windward side behind the peak of the barrier and three secondary on the leeward side. The symmetry in the locations of these secondary rainfall maxima appears to be critically dependent on the component of basic flow parallel to the major ridge axis of the barrier.     

Simplified dynamical anomaly model for long-range numerical forecasts

In this atmosphere-ocean-land coupled model, two basic ideas are developed, One is that the observational climate field is utilized and only the anomalous components are predicted. The other is that the transient Rossby wave is treated as the meteorological "noise" on the long-term variation that must be predicted in a climate forecasting. According to the latter, the transient Rossby wave can be filtered by omitting the partial derivative with respect to time in the atmospheric vorticity equation. But the time derivative term is still kept in the thermal equation for underlying ocean and land. With this assumption, the vorticity equation becomes time-independent, i.e. it is only a balance relationship between the anomaly geopotential height field and earth's surface heating field. This model is different from the usual GCM, so it may be called as the filtered anomaly model (FAM).A dozen examples of one month prediction are summarized in this report.     

Multi-year predictability in a coupled general circulation model

Multi-year to decadal variability in a 100-year integration of a BMRC coupled atmosphere-ocean general circulation model (CGCM) is examined. The fractional contribution made by the decadal component generally increases with depth and latitude away from surface waters in the equatorial Indo-Pacific Ocean. The relative importance of decadal variability is enhanced in off-equatorial “wings” in the subtropical eastern Pacific. The model and observations exhibit “ENSO-like” decadal patterns. Analytic results are derived, which show that the patterns can, in theory, occur in the absence of any predictability beyond ENSO time-scales. In practice, however, modification to this stochastic view is needed to account for robust differences between ENSO-like decadal patterns and their interannual counterparts. An analysis of variability in the CGCM, a wind-forced shallow water model, and a simple mixed layer model together with existing and new theoretical results are used to improve upon this stochastic paradigm and to provide a new theory for the origin of decadal ENSO-like patterns like the Interdecadal Pacific Oscillation and Pacific Decadal Oscillation. In this theory, ENSO-driven wind-stress variability forces internal equatorially-trapped Kelvin waves that propagate towards the eastern boundary. Kelvin waves can excite reflected internal westward propagating equatorially-trapped Rossby waves (RWs) and coastally-trapped waves (CTWs). CTWs have no impact on the off-equatorial sub-surface ocean outside the coastal wave guide, whereas the RWs do. If the frequency of the incident wave is too high, then only CTWs are excited. At lower frequencies, both CTWs and RWs can be excited. The lower the frequency, the greater the fraction of energy transmitted to RWs. This lowers the characteristic frequency (reddens the spectrum) of variability off the equator relative to its equatorial counterpart. At low frequencies, dissipation acts as an additional low pass filter that becomes more effective, as latitude increases. At the same time, ENSO-driven off-equatorial surface heating anomalies drive mixed layer temperature responses in both hemispheres. Both the eastern boundary interactions and the accumulation of surface heat fluxes by the surface mixed layer act to low pass filter the ENSO-forcing. The resulting off-equatorial variability is therefore more coherent with low pass filtered (decadal) ENSO indices [e.g. NINO3 sea-surface temperature (SST)] than with unfiltered ENSO indices. Consequently large correlations between variability and NINO3 extend further poleward on decadal time-scales than they do on interannual time-scales. This explains why decadal ENSO-like patterns have a broader meridional structure than their interannual counterparts. This difference in appearance can occur even if ENSO indices do not have any predictability beyond interannual time-scales. The wings around 15–20°S, and sub-surface variability at many other locations are predictable on interannual and multi-year time-scales. This includes westward propagating internal RWs within about 25° of the equator. The slowest of these take up to 4 years to reach the western boundary. This sub-surface predictability has significant oceanographic interest. However, it is linked to only low levels of SST variability. Consequently, extrapolation of delayed action oscillator theory to decadal time-scales might not be justified.     

Climate predictability experiments with a general circulation model

The atmospheric response to the evolution of the global sea surface temperatures from 1979 to 1992 is studied using the Max-Planck-Institut 19 level atmospheric general circulation model, ECHAM3 at T 42 resolution. Five separate 14-year integrations are performed and results are presented for each individual realization and for the ensemble-averaged response. The results are compared to a 30-year control integration using a climate monthly mean state of the sea surface temperatures and to analysis data. It is found that the ECHAM3 model, by and large, does reproduce the observed response pattern to El Nino and La Niña. During the El Nino events, the subtropical jet streams in both hemispheres are intensified and displaced equatorward, and there is a tendency towards weak upper easterlies over the equator. The Southern Oscillation is a very stable feature of the integrations and is accurately reproduced in all experiments. The inter-annual variability at middle- and high-latitudes, on the other hand, is strongly dominated by chaotic dynamics, and the tropical SST forcing only modulates the atmospheric circulation. The potential predictability of the model is investigated for six different regions. Signal to noise ratio is large in most parts of the tropical belt, of medium strength in the western hemisphere and generally small over the European area. The ENSO signal is most pronounced during the boreal spring. A particularly strong signal in the precipitation field in the extratropics during spring can be found over the southern United States. Western Canada is normally warmer during the warm ENSO phase, while northern Europe is warmer than normal during the ENSO cold phase. The reason is advection of warm air due to a more intense Pacific low than normal during the warm ENSO phase and a more intense Icelandic low than normal during the cold ENSO phase, respectively.     

A minimal model of the Atlantic Multidecadal Variability: its genesis and predictability

Through a box model of the subpolar North Atlantic, we examine the genesis and predictability of the Atlantic Multidecadal Variability (AMV), posited as a linear perturbation sustained by the stochastic atmosphere. Postulating a density-dependent thermohaline circulation (THC), the latter would strongly differentiate the thermal and saline damping, and facilitate a negative feedback between the two fields. This negative feedback preferentially suppresses the low-frequency thermal variance to render a broad multidecadal peak bounded by the thermal and saline damping time. We offer this “differential variance suppression” as an alternative paradigm of the AMV in place of the “damped oscillation”—the latter generally not allowed by the deterministic dynamics and in any event bears no relation to the thermal peak. With the validated dynamics, we then assess the AMV predictability based on the relative entropy—a difference of the forecast and climatological probability distributions, which decays through both error growth and dynamical damping. Since the stochastic forcing is mainly in the surface heat flux, the thermal noise grows rapidly and together with its climatological variance limited by the THC-aided thermal damping, they strongly curtail the thermal predictability. The latter may be prolonged if the initial thermal and saline anomalies are of the same sign, but even rare events of less than 1% chance of occurrence yield a predictable time that is well short of a decade; we contend therefore that the AMV is in effect unpredictable.     

A low latitude general circulation model

Summary The primitive equations of motion are solved to find peak latitudes of families of trajectories of air moving from low latitudes towards the pole from a state of rest under the action of a constant meridional pressure gradient. The general case is discussed first and then calculations are applied to the 20° West meridian in January and July for the Northern Hemisphere.The resulting mass transposition indicates that a belt of convergence should occur at about 32° N in January; this agrees well with the latitude of the axis of the mean sub-tropical high pressure belt at that time of year.The nature of the climatological model in low latitudes suggested by the calculation is then discussed.

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Zusammenfassung Die vereinfachten Bewegungsgleichungen werden gelöst, um Scheitelbreiten für Trajektorienscharen der Luftbewegungen zu finden, die ausgehend von dem Ruhezustand unter Einwirkung eines konstanten meridionalen Druckgradienten polwärts gerichtet sind. Der allgemeine Fall wird diskutiert und es werden Berechnungen für den 20. westlichen Längengrad der Nordhemisphäre für Januar und Juli durchgeführt.Der resultierende Massentransport zeigt, daß im Januar in 32° N ein Konvergenzgürtel auftreten sollte. Dies stimmt gut überein mit der geographischen Breite der Achse des mittleren subtropischen Hochdruckgürtels zu dieser Jahreszeit.Schließlich wird die Form des klimatologischen Modells für niedere Breiten, das durch diese Berechnungen nahegelegt wird, diskutiert.

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Résumé Résolution des équations simpflifiées du mouvement pour déterminer l'origine des faisceaux de trajectoires des courants aériens qui, partant du repos, sont dirigés vers le pôle sous l'effet d'un gradient constant de pression méridien. Discussion du cas général; calcul pour le 20^e méridien Ouest de l'hémisphère Nord en janvier et en juillet.Le transport de masse résultant montre qu'il doit y avoir en janvier, a 32° de latitude Nord, une ceinture de convergence ce qui concorde bien avec la latitude de l'axe de la zone moyenne des hautes pressions subtropicales en cette saison.Forme du modèle climatologique aux basses latitudes suggéré par ces calculs.

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With 1 Figure     

An analysis of seasonal predictability in coupled model forecasts

In the recent decade, operational seasonal prediction systems based on initialized coupled models have been developed. An analysis of how the predictability of seasonal means in the initialized coupled predictions evolves with lead-time is presented. Because of the short lead-time, such an analysis for the temporal behavior of seasonal predictability involves a mix of both the predictability of the first and the second kind. The analysis focuses on the lead-time dependence of ensemble mean variance, and the forecast spread. Further, the analysis is for a fixed target season of December?CJanuary?CFebruary, and is for sea surface temperature, rainfall, and 200-mb height. The analysis is based on a large set of hindcasts from an initialized coupled seasonal prediction system. Various aspects of predictability of the first and the second kind are highlighted for variables with long (for example, SST), and fast (for example, atmospheric) adjustment time scale. An additional focus of the analysis is how the predictability in the initialized coupled seasonal predictions compares with estimates based on the AMIP simulations. The results indicate that differences in the set up of AMIP simulations and coupled predictions, for example, representation of air?Csea interactions, and evolution of forecast spread from initial conditions do not change fundamental conclusion about the seasonal predictability. A discussion of the analysis presented herein, and its implications for the use of AMIP simulations for climate attribution, and for time-slice experiments to provide regional information, is also included.     

A data-driven SVR model for long-term runoff prediction and uncertainty analysis based on the Bayesian framework

Accurate and reliable long-term forecasting plays an important role in water resources management and utilization. In this paper, a hybrid model called SVR-HUP is presented to predict long-term runoff and quantify the prediction uncertainty. The model is created based on three steps. First, appropriate predictors are selected according to the correlations between meteorological factors and runoff. Second, a support vector regression (SVR) model is structured and optimized based on the LibSVM toolbox and a genetic algorithm. Finally, using forecasted and observed runoff, a hydrologic uncertainty processor (HUP) based on a Bayesian framework is used to estimate the posterior probability distribution of the simulated values, and the associated uncertainty of prediction was quantitatively analyzed. Six precision evaluation indexes, including the correlation coefficient (CC), relative root mean square error (RRMSE), relative error (RE), mean absolute percentage error (MAPE), Nash-Sutcliffe efficiency (NSE), and qualification rate (QR), are used to measure the prediction accuracy. As a case study, the proposed approach is applied in the Han River basin, South Central China. Three types of SVR models are established to forecast the monthly, flood season and annual runoff volumes. The results indicate that SVR yields satisfactory accuracy and reliability at all three scales. In addition, the results suggest that the HUP cannot only quantify the uncertainty of prediction based on a confidence interval but also provide a more accurate single value prediction than the initial SVR forecasting result. Thus, the SVR-HUP model provides an alternative method for long-term runoff forecasting.     

The Interannual Variability and Predictability in a Global Climate Model

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GRAPES区域扰动预报模式动力框架设计及检验

设计了适用于四维变分同化系统的扰动预报模式GRAPES_PF。根据GRAPES的地形追随坐标非静力原始方程组,采用小扰动分离方法推导微分形式的线性扰动预报方程组,并利用与GRAPES非线性模式相似的数值求解方案求解线性扰动微分方程组。在设计扰动预报模式时采用了两个时间层半隐式半拉格朗日方案对动量方程、热力学方程、水汽方程和连续方程进行时间差分,空间差分方案的变量分布水平方向采用Arakawa C跳点网格,垂直方向采用Charney/Phillips跳层。利用代数消元法进一步推导得到只包含未来时刻扰动Exner气压的亥姆霍兹方程,进而通过广义共轭余差法(GCR)求解,在此基础上得到未来时刻扰动量的预报值。基于所开发的扰动模式开展了数值试验。首先在非线性模式中施加一个中尺度初始扰动高压,得到初始扰动在非线性模式中的后续演变,然后将相同的初始扰动作为扰动模式的初值进行时间积分,将扰动模式预报的结果与非线性模式的结果做了对比。结果表明,所开发的扰动模式GRAPES_PF较好地模拟了惯性重力内波的传播过程:初始高压扰动激发了一个迅速向外传播的惯性重力内波,...     

一种基于全球动力模式和SMART原理结合的统计降尺度区域季节气候预测方法

针对江苏夏季旱涝和高温热浪等异常气候的预测难题,以江苏夏季站点降水和气温为预测目标,建立了一种基于全球动力模式BCC_CSM1.1（m）和最优可预测气候模态和异常相对倾向（SMART）原理结合的统计降尺度季节气候预测方法。利用历史观测资料和SVD方法提取决定中国夏季降水异常相对倾向的同期热带地区向外长波辐射（Outgoing Longwave Radiation,OLR）和北半球中高纬500 hPa位势高度场异常相对倾向的最优可预测气候模态,并利用逐步回归法构建其与同期江苏站点降水和气温异常相对倾向同期关系的统计降尺度模型;将动力模式对最优可预测气候模态的预测带入统计降尺度模型,实现对区域降水和气温异常相对倾向的预测;最后通过引入观测的近期背景异常实现对降尺度的降水和气温总距平的预测。通过对1991—2019年江苏夏季降水和气温的回报检验表明,本文建立的统计降尺度模型效果较BCC_CSM1.1（m）动力模式的直接预测效果有显著提高,为区域精细化季节气候预测提供了一种有效的手段。     

The regional dynamical model of the atmospheric ozonosphere

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Validating the Runoff from the PRECIS Model Using a Large-Scale Routing Model

The streamflow over the Yellow River basin is simulated using the PRECIS （Providing REgional Climates for Impacts Studies） regional climate model driven by 15-year （1979-1993） ECMWF reanalysis data as the initial and lateral boundary conditions and an off-line large-scale routing model （LRM）. The LRM uses physical catchment and river channel information and allows streamflow to be predicted for large continental rivers with a 1°×1° spatial resolution. The results show that the PRECIS model can reproduce the general southeast to northwest gradient distribution of the precipitation over the Yellow River basin, The PRECIS- LRM model combination has the capability to simulate the seasonal and annual streamflow over the Yellow River basin. The simulated streamflow is generally coincident with the naturalized streamflow both in timing and in magnitude.     

Role of Parameter Errors in the Spring Predictability Barrier for ENSO Events in the Zebiak–Cane Model

ABSTRACT The impact of both initial and parameter errors on the spring predictability barrier （SPB） is investigated using the Zebiak Cane model （ZC model）. Previous studies have shown that initial errors contribute more to the SPB than parameter errors in the ZC model. Although parameter errors themselves are less important, there is a possibility that nonlinear interactions can occur between the two types of errors, leading to larger prediction errors compared with those induced by initial errors alone. In this case, the impact of parameter errors cannot be overlooked. In the present paper, the optimal combination of these two types of errors [i.e., conditional nonlinear optimal perturbation （CNOP） errors] is calculated to investigate whether this optimal error combination may cause a more notable SPB phenomenon than that caused by initial errors alone. Using the CNOP approach, the CNOP errors and CNOP-I errors （optimal errors when only initial errors are considered） are calculated and then three aspects of error growth are compared： （1） the tendency of the seasonal error growth; （2） the prediction error of the sea surface temperature anomaly; and （3） the pattern of error growth. All three aspects show that the CNOP errors do not cause a more significant SPB than the CNOP-I errors. Therefore, this result suggests that we could improve the prediction of the E1 Nifio during spring by simply focusing on reducing the initial errors in this model.     

Quantifying Arctic contributions to climate predictability in a regional coupled ocean-ice-atmosphere model

The relative importance of regional processes inside the Arctic climate system and the large scale atmospheric circulation for Arctic interannual climate variability has been estimated with the help of a regional Arctic coupled ocean-ice-atmosphere model. The study focuses on sea ice and surface climate during the 1980s and 1990s. Simulations agree reasonably well with observations. Correlations between the winter North Atlantic Oscillation index and the summer Arctic sea ice thickness and summer sea ice extent are found. Spread of sea ice extent within an ensemble of model runs can be associated with a surface pressure gradient between the Nordic Seas and the Kara Sea. Trends in the sea ice thickness field are widely significant and can formally be attributed to large scale forcing outside the Arctic model domain. Concerning predictability, results indicate that the variability generated by the external forcing is more important in most regions than the internally generated variability. However, both are in the same order of magnitude. Local areas such as the Northern Greenland coast together with Fram Straits and parts of the Greenland Sea show a strong importance of internally generated variability, which is associated with wind direction variability due to interaction with atmospheric dynamics on the Greenland ice sheet. High predictability of sea ice extent is supported by north-easterly winds from the Arctic Ocean to Scandinavia.     

动态调节模型的三阶段最小二乘辨识方法

针对动态调节模型提出一种三阶段最小二乘辨识方法.先将模型变换为CARMA模型,估计出变换后的CARMA模型参数,再利用已得到的参数估计依次辨识原模型中的系统模型参数和噪声模型参数.该方法原理简单,有效可行.