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The World Health Organization (WHO) declared monkeypox as a public health emergency of international concern (PHEIC) on July 23, 2022, their highest level of alert. This raised concerns about the management of the global monkeypox outbreak, as well as the scientific analysis and accurate prediction of the future course of the epidemic. This study used EpiSIX (an analysis and prediction system for epidemics based on a general SEIR model) to analyze the monkeypox epidemic and to forecast the major tendencies based on data from the USA CDC (https://www.cdc.gov) and the WHO (https://www.who.int/health-topics/monkeypox). The global outbreak of monkeypox started in the UK on May 2, 2022, which marked the beginning of an epidemic wave. As of October 28, 2022, the cumulative number of reported cases worldwide was 77,115, with 36 deaths. EpiSIX simulations predict that the global monkeypox epidemic will enter a low epidemic status on March 1, 2023 with the cumulative number of confirmed cases ranging from 85,000 to 124,000, and the total number of deaths ranging from 60 to 87. Our analysis revealed that the basic reproduction number (R0) of monkeypox virus (MPXV) is near to 3.1 and the percentage of asymptomatic individuals is 13.1%-14.5%, both of which are similar to the data for SARS. The vaccination efficiency against susceptibility (VEs) of individuals who have had monkeypox is ∼79%, and the vaccination efficiency against infectiousness (VEi) of individuals who have had monkeypox is ∼76%-82%. The mean incubation period for monkeypox is 8 days. In total, 94.7% of infected individuals develop symptoms within 20 days and recover within 2 weeks after the confirmation of symptoms. Simulation results using EpiSIX showed that ring vaccination was remarkably effective against monkeypox. Our findings confirmed that a 20-day isolation for close contacts is necessary.

We consider the long-term properties of a stochastic SVIR epidemic model with saturation incidence rates and logistic growth in this paper. We firstly derive the fitness of a unique global positive solution. Then we construct appropriate Lyapunov functions and obtain condition Rs 0 > 1 for existence of stationary distribution, and conditions for persistence in the mean. Moreover, conditions including Re 0 < 1 for exponential extinction to the infected individuals are figured out. Finally, by employing Fokker-Planck equation and stochastic analysis, we derive the probability density function around the quasi-endemic equilibrium point when critical value R p 0 > 1 is valid. Consequently, some examples and illustrative simulations are carried out to verify the main theoretical results.

The dynamical behaviors of a stochastic heroin population model with standard incidence rates between distinct patches are investigated in this paper. We firstly derive the fitness of a global positive solution. Then, under some moderate conditions, we show that the heroin population model always admits a stationary Markov process in the long run. More precisely, the coexistence of the drug users and the susceptible is studied by constructing multiple proper functions when the intensities of the white noises are under control, and the spectral radius of the irreducible matrix is greater than one ( R 0 > 1 ). For the elimination of the drug users, if the intensities of the white noises are large, then the elimination of drug users in a heroin population would exponentially decrease with probability one. Especially, when the spectral radius of the irreducible matrix is less than one ( R 0 1 ), the elimination of drug users who are not in treatment also follows the exponential decline with probability one. As a consequence, two examples and their corresponding numerical simulations are demonstrated to present the validity and feasibility of the theoretical results.

We propose stage-structured single-species population models with psychological effects and partial tolerance in polluted environments in this paper. First, the conditions of extinction and the time for extinction are investigated respectively. Especially, the time for extinction takes longer as the value of the psychological effects increases. Then the weak persistence in the mean around the pollution-free equilibrium and the stochastic permanence have been derived under some moderate conditions. Further, the existence of a periodic solution for the periodic single-species population has been determined. The corresponding numerical simulations verify the efficiency of the main theoretical results.

We formulate a single-species population model with fluctuations and migrations between two different patches (the nature reserve and the natural environment) to describe the situation that endangered species often meets with. Firstly, we prove that there exists a unique global positive solution to a stochastic single-species model with any positive initial value. Then, sufficient conditions that guarantee extinction and persistence in the mean of solutions are derived as the main results. It turns out that, under moderate fluctuation conditions, migration rates play significant roles for the persistence of endangered species in nature reserve and the natural environment. We further provide the sustainable strategies for local managers to avoid the extinction of endangered species, and separately carry out illustrative examples and numerical simulations at the end of this contribution.

We investigate the global asymptotic stabilities of disease-free equilibrium and endemic equilibrium of the deterministic susceptible–exposed–infected–recovered epidemic model (short for SEIR model). The basic reproduction number R 0 , depends on constant contact rate β and natural death rate d and other parameters as well, indicates the critical value of stability, and completely determines the dynamical behavior of the deterministic model. After taking the perturbations of the environments into account, the corresponding stochastic SEIR model with generalized nonlinear incidence is discussed in existence and uniqueness, the extinction in the mean, and the existence of the unique stationary distribution as well. As a consequence, we carry out several numerical simulations to support the main theoretical results of this paper.

We establish a stochastic HIV/AIDS model for the individuals with protection awareness and reveal how the protection awareness plays its important role in the control of AIDS. We firstly show that there exists a global positive solution for the stochastic model. By constructing Lyapunov functions, the ergodic stationary distribution when $R_{0}^{s}>1$ and the extinction when $R_{0}^{e}

A stochastic susceptible–exposed–infected–recovered (SEIR) model with nonlinear incidence rate is investigated. Under suitable conditions, existence and uniqueness of a global solution, stationary distribution with ergodicity, persistence in the mean, and extinction of the disease are obtained. Numerical simulations and conclusions are separately carried out at the end of this paper.

We formulate an epidemic model with age of vaccination and generalized nonlinear incidence rate, where the total population consists of the susceptible, the vaccinated, the infected and the removed. We then reach a stochastic SVIR model when the fluctuation is introduced into the transmission rate. By using Ito’s formula and Lyapunov methods, we first show that the stochastic epidemic model admits a unique global positive solution with the positive initial value. We then obtain the sufficient conditions of the stochastic epidemic model. Moreover, the threshold tells the disease spreads or not is derived. If the intensity of the white noise is small enough and R ˜ 0 1 , then the disease eventually becomes extinct with negative exponential rate. If R ˜ 0 > 1 , then the disease is weakly permanent. The persistence in the mean of the infected is also obtained when the indicator R ˆ 0 > 1 , which means the disease will prevail in a long run. As a consequence, several illustrative examples are separately carried out with numerical simulations to support the main results of this paper.

In this paper, the dynamics of a stochastic susceptible–infected–removed model in a population with varying size is investigated. We firstly show that the stochastic epidemic model has a unique global positive solution with any positive initial value. Then we verify that random perturbations lead to extinction when some conditions are being valid. Moreover, we prove that the solution of the stochastic epidemic model is persistent in the mean by building up a suitable Lyapunov function and using generalized Ito’s formula. Further, the stochastic epidemic model admits a stationary distribution around the endemic equilibrium when parameters satisfy some sufficient conditions. To end this contribution and to check the validity of the main results, numerical simulations are separately carried out to illustrate these results.

In this paper we investigate the persistence and extinction of a stochastic epidemic model with a varying population environment in the long-term behavior. Our model consists of two stochastic differential equations: one for the susceptible individuals in which the transmission rate is disturbed by white noise, one for the exposed individuals in which the same perturbation occurs, and one ordinary differential equation in which describes the infective individuals in a varying population environment. We derive sufficient conditions for the extinction and persistence of the epidemic model depending on the constant contact rate. Moreover, we carry out several numerical simulations to illustrate the main results of this contribution.

We propose a single-species population model with partial pollution tolerance in a polluted environment in this contribution, and introduce the random perturbation of the birth rate of single-species population into this model. The extinction occurs around the pollution-free equilibrium under some moderate conditions, and the stationary distribution with ergodicity is derived around the positive equilibrium. Numerical simulations demonstrate the efficiency of our main results.

We introduce the stochasticity into a deterministic model which has state variables susceptible–exposed–infected with varying population size in this paper. The infected individuals could return into susceptible compartment after recovering. We show that the stochastic model possesses a unique global solution under building up a suitable Lyapunov function and using generalized Ito’s formula. The densities of the exposed and infected tend to extinction when some conditions are being valid. Moreover, the conditions of persistence to a global solution are derived when the parameters are subject to some simple criteria. The stochastic model admits a stationary distribution around the endemic equilibrium, which means that the disease will prevail. To check the validity of the main results, numerical simulations are demonstrated as end of this contribution.

This article discusses a stochastic SIQS epidemic model with saturated incidence. We assume that random perturbations always fluctuate at the endemic equilibrium. The existence of a global positive solution is obtained by constructing a suitable Lyapunov function. Under some suitable conditions, we derive the stochastic boundedness and stochastic permanence of the solutions of a stochastic SIQS model. Some numerical simulations are carried out to check our results.

In the winters of 2012–2018, a total of 25 ‘ultra-long’ (≥6 days), wide-ranging pollution events occurred in northern China. The results showed that the atmospheric circulation pattern corresponding to 62.5% of the persistent ‘most serious’ and ‘more serious’ air pollution events in northern China were the blocking structures, and that 43.75% of the 500-hPa atmospheric circulation anomalies in the middle and high latitudes of Eurasia were ‘dual-blocking’, 18.75% of them were ‘single-blocking’. The abnormally stable blocking situation provided a special circulation background for the occurrence and maintenance of persistent heavy air pollution in northern China. The Okhotsk blocking is significantly positively correlated with the persistent ‘most serious’ air pollution events. ‘Stagnation’ of the blocking system and its dynamic effect play an important role in regulating atmospheric environmental capacity and accelerating the accumulation of aerosols during the persistent heavy pollution episodes. Due to the synergy between the weak wind effect of the leeward slope on the eastern side of the Loess Plateau in this region and the downward airflow of the large-scale blocking system, the effect of sustained suppression of atmospheric pollutant diffusion in northern China is more significant. The downward air flow along the eastern leeward slope of the Loess Plateau is very important for accumulation of air pollutants, which is controlled by the tropospheric blocking high. In addition, the ‘subsidence (temperature) inversion’ effect produced by the synergy between the downward airflow of the eastern leeward slope of the Loess Plateau and the large-scale blocking system creates a continuous and stable ‘warm-cover’ structure in the middle of the troposphere on the eastern of the Loess Plateau; this effect strengthens the radiation effect of aerosols in the atmospheric pollutants, as well as the ‘two-way feedback’ mechanism between adverse meteorological conditions in the boundary layer and atmospheric pollutants.

A stochastic susceptible–infected–vaccinated model with a general incidence rate and varying population size is considered in this paper. By means of constructing a suitable Lyapunov function, the sufficient conditions for the extinction are derived. Further, some conditions that guarantee the existence of a unique stationary distribution is obtained. The main results are illustrated by computer simulations.

In this paper, we have completely studied a four-parameter family of continuous piecewise linear differential systems with three linear regions and no symmetry in the compactification space of R 2 . The bifurcation diagram and the corresponding global phase portraits of the continuous piecewise linear system are derived. It is shown that the continuous piecewise linear system has rich dynamics such as three isolated equilibria, three limit cycles, a figure-eight loop and a homoclinic loop which likes a cuspidal loop in R 2 for some parameters values, respectively. As applications of our results, we can obtain the global dynamics of continuous piecewise linear FitzHugh-Nagumo equation and non-symmetric memristor-based electronic oscillators, respectively.

We investigate the long-term properties of a stochastic Lotka–Volterra model with infinite delay and Markovian chains on a finite state space. We investigate that the stochastic model admits a unique positive global solution which stays in the way of stochastically ultimate boundedness by constructing Lyapunov functions. Furthermore, the main results that the growth of the solution is slower than time under moderate condition and moment estimation in time average with the power p could be controlled are derived, which modified the known ones in recent literatures.

A kind of stage-structured predator–prey model with Beddington–DeAngelis functional response incorporating a prey refuge is investigated in this paper. By analyzing the corresponding characteristic equations, the local stability of the equilibria is investigated. Moreover, Hopf bifurcations occur at the positive equilibrium as the delay τ crosses some critical values. Further, the influence of prey refuge on densities of predator species and prey species is investigated. Numerical simulations are carried out to illustrate our main results.

The dynamical properties of a stochastic susceptible-infected epidemic model with Logistic growth are investigated in this paper. We show that the stochastic model admits a nonnegative solution by using the Lyapunov function method. We then obtain that the infected individuals are persistent under some simple conditions. As a consequence, a simple sufficient condition that guarantees the extinction of the infected individuals is presented with a couple of illustrative examples.

We formulate and investigate the psychological effect of single-species population models in a polluted environment in this paper. For the deterministic single-species population model, the conditions that guarantee the local extinction and persistence in the mean are derived firstly. We then show that, around the pollution-free equilibrium, the stochastic single-species population is weakly persistent in the mean, and is stochastically permanent under some conditions. As a consequence, some numerical simulations demonstrate the efficiency of the main results.

The intraseasonal oscillation (ISO) in the South China Sea summer monsoon (SCSSM) and its influence on regionally persistent heavy rain (RPHR) over southern China are examined by using satellite outgoing long wave radiation, NCEP/NCAR reanalysis, and gridded rainfall station data in China from 1981 to 2010. The most important feature of the ISO in SCSSM, contributing to the modulation of RPHR, is found to be the fluctuation in the western Pacific subtropical high (WPSH), along with a close link to the Madden-Julian oscillation (MJO). Southern China is divided into three regions by using rotated empirical orthogonal functions (REOFs) for intraseasonal rainfall, where the incidence rate of RPHR is closely linked to the intraseasonal variation in rainfall. It is found that SCSSM ISOs are the key systems controlling the intraseasonal variability in rainfall and can be described by the leading pair of empirical orthogonal functions (EOFs) for the 850-hPa zonal wind over the SCS and southern China. Composite analyses based on the principal components (PCs) of the EOFs indicate that the ISO process in SCSSM exhibits as the east-west oscillation of the WPSH, which is coupled with the northward-propagating MJO, creating alternating dry and wet phases over southern China with a period of 40 days. The wet phases provide stable and lasting circulation conditions that promote RPHR. However, differences in the ISO structures can be found when RPHR occurs in regions where the WPSH assumes different meridional positions. Further examination of the meridional-phase structure suggests an important role of northward-propagating ISO and regional air-sea interaction in the ISO process in SCSSM.

The stability of a kind of cooperative models incorporating harvesting is considered in this paper. By analyzing the characteristic roots of the models and constructing suitable Lyapunov functions, we prove that nonnegative equilibrium points of the models are globally asymptotically stable. Further, the corresponding nonautonomous cooperative models have a unique asymptotically periodic solution, which is uniformly asymptotically stable. An example is given to illustrate the effectiveness of our results.

A close relationship between sea level pressure (SLP) over East Asia and precipitation indices (PIs) in eastern China was observed in the summers (June–August) of 1850–2008 using singular value decomposition (SVD) analysis. To investigate this relationship over a longer period, the SLP fields were reconstructed back to 1470 based on a mathematical model and the historical precipitation indices of eastern China. A cross-validation test of independent samples suggests that the reconstructed SLPs are statistically acceptable. According to the first three predominant SVD modes of the SLP field, three SLP index series (SLPI1–SLPI3) were developed to quantify the thermodynamic differences among the critical SLP centers of East Asia. Both SLPI1 and SLPI2 are highly correlated with the East Asian summer monsoon index, whereas SLPI3 is related to the index of Eurasian meridional atmospheric circulation. The temporal scales of SLP indices were examined during 1470–2008 using the wavelet power spectra. Results indicate that there is significant variance at a 2–5-yr band in the power spectra of the three SLP indices, suggesting SLPI1–SLPI3 have evident interannual variability. Moreover, the wavelet power spectra of SLPI1 and SLPI2 show significantly higher power at the 8–12-yr scale from 1470 to 1750 and at the 60–90-yr scale after 1750. For SLPI3, besides the interannual variability, it has additional periodical variability of 6–11 and 23–33 yr.

Based on the drought/flood grades of 90 meterological stations over eastern China and summer average sea-level pressure (SLP) during 1850–2008 and BPCCA statistical methods, the coupling relationship between the drought/flood grades and the East Asian summer SLP is analyzed. The East Asian summer monsoon index which is closely related with interdecadal variation of drought/flood distribution over eastern China is defined by using the key areas of SLP. The impact of the interdecadal variation of the East Asian summer monsoon on the distribution of drought/flood over eastern China in the last 159 years is researched. The results show that there are four typical drought and flood spatial distribution patterns in eastern China, i.e. the distribution of drought/flood in southern China is contrary to the other regions, the distribution of drought/flood along the Huanghe River-Huaihe River Valley is contrary to the Yangtze River Valley and regions south of it, the distribution of drought/flood along the Yangtze River Valley and Huaihe River Valley is contrary to the other regions, the distribution of drought/flood in eastern China is contrary to the western. The main distribution pattern of SLP in summer is that the strength of SLP is opposite in Asian continent and West Pacific. It has close relationship between the interdecadal variation of drought/flood distribution patterns over eastern China and the interdecadal variation of the East Asian summer monsoon which was defined in this paper, but the correlation is not stable and it has a significant difference in changes of interdecadal phase. When the East Asian summer monsoon was stronger (weaker), regions north of the Yangtze River Valley was more susceptible to drought (flood), the Yangtze River Valley and regions south of it were more susceptible to flood (drought) before the 1920s; when the East Asian summer monsoon was stronger (weaker), the regions north of the Yangtze River Valley was prone to flood (drought), the Yangtze River Valley and regions south of it were prone to drought (flood) after the 1920s. It is indicated that by using the data of the longer period could get much richer results than by using the data of the last 50–60 years. The differences in the interdecadal phase between the East Asian summer monsoon and the drought/flood distributions in eastern China may be associated with the nonlinear feedback, which is the East Asian summer monsoon for the extrinsic forcing of solar activity.

This paper is concerned with a periodic predator–prey system with Holling III functional response and harvesting terms. By means of the coincidence degree theory, we establish the existence of at least eight positive periodic solutions for the system. An example is given to illustrate the effectiveness of our results.

A susceptible–infected–vaccinated epidemic model with proportional vaccination and generalized nonlinear rate is formulated and investigated in the paper. We show that the stochastic epidemic model admits a unique and global positive solution with probability one when constructing a proper [Formula: see text]-function therewith. Then a sufficient condition that guarantees the disappearances of diseases is derived when the indicator [Formula: see text]. Further, if [Formula: see text], then we obtain that the solution is weakly permanent with probability one. We also derived the sufficient conditions of the persistence in the mean for the susceptible and infected when another indicator [Formula: see text].

The existence of periodic solution of a kind of functional differential equation with infinite delay was investigated in this paper. By constructing moderate functional V ( t , φ ) , making use of the Schauder fixed point theory, the main result that the system has a positive periodic solution was obtained.

The periodic solution and global stability for a nonautonomous competitive Lotka–Volterra diffusion system is considered in this paper. By using of Brouwer fixed point theorem and constructing a suitable Liapunov function, under some appropriate conditions, the system has a unique periodic solution which is globally stable.

Based on the summer precipitation data from the Huaihe River valley and the middle and lower reaches of the Yangtze River from 1922 to 2007, we analyzed the interannual and interdecadal oscillation and probability distribution characteristics of summer precipitation in the Huaihe River valley during the same period, using the wavelet transform and generalized extreme distribution methods. Whereby, we studied the climate background of East Asia Summer Monsoon (EASM), Sea Surface Temperature (SST), East Asia telecorrelation circulation, and their relationship with the interannual and interdecadal oscillation of summer precipitation in the Huaihe River valley. We further compared the difference of interdecadal oscillation of summer precipitation and the relevant climate background between the Huaihe River valley and the middle and lower reaches of the Yangtze River. The results show that: 1) The intensity change of quasi-biennial oscillation (QBO) of summer precipitation in the Huaihe River valley is consistent with that of interdecadal oscillation. The summer precipitation in the Huaihe River valley has been more than normal since the end of the 1990s, and the QBO is very significant. Meanwhile, the probability of occurrence of extreme heavy rainfall increased obviously. 2) The interdecadal oscillation of summer precipitation in the Huaihe River valley has a close relationship with the Pacific Decadal Oscillation (PDO) and interdecadal oscillation of EASM. When PDO is in the cold phase and EASM weakens, the summer precipitation will be greater than normal. 3) QBO of summer precipitation in the Huaihe River valley is mainly controlled by that of EASM, and it has a relationship with a circulation pattern of “positive-negative-positive” from the high to the low latitudes in East Asia. 4) There is interdecadal phase difference in summer precipitation between the Huaihe River valley and the middle and the lower reaches of the Yangtze River, which is mainly related to the intensity and position of West Pacific subtropical high.

The spatio-temporal variability of Northern Hemisphere Sea Level Pressure (SLP) and precipitation over the mid-to-low reaches of the Yangtze River (PMLY) is analyzed jointly using the multi-taper /singular value decomposition method (MTM-SVD). Statistically significant narrow frequency bands are obtained from the local fractional variance (LFV) spectrum. Significant interdecadal (i.e., 16-to-18-year periods) and interannual (i.e., 3-to-6-year periods) signals are identified. Moreover, a significant quasi-biennial signal is identified but only for PMLY data. The spatial joint evolution of patterns obtained for peaks in the LFV spectrum sheds light on relationships between SLP and PMLY: the Arctic Oscillation (AO) modulates the variability of the PMLY while the interannual variability of PMLY is in phase with the Northern Atlantic Oscillation (NAO) and the Northern Pacific Oscillation (NPO).

The existence of positive periodic solution of n-species ecological system with infinite delayx˙i(t)=hi(t,xt)bi(t,xt)-ai(t,xt)xi(t)-∫-∞tGi(t,s,x1(s),…,xn(s))ds,i=1,…,nis studied by the authors. Under the suitable conditions, the main results are obtained by using of the method developed by Wang [On the existence of periodic solutions of functional differential equations, Chinese Ann. Math. 10A(3) (1989) 366–372 (in Chinese)] and the essential Theorems 2.1–2.3 of Sawano [Exponential asymptotic stability for functional differential equations with infinite retardations, Tohoku Math. J. 31 (1979) 363–382]. Our results differ from the ones given by Wang [Positive periodic solutions of an n-species ecological system, Acta Math. Appl. Sinica 17(1) (1994) 1–8 (in Chinese)].

This paper is devoted to build the existence-and-uniqueness theorem of solutions to stochastic functional differential equations with infinite delay (short for ISFDEs) at phase space BC ( ( − ∞ , 0 ] ; R d ) . Under the uniform Lipschitz condition, the linear growth condition is weaked to obtain the moment estimate of the solution for ISFDEs. Furthermore, the existence-and-uniqueness theorem of the solution for ISFDEs is derived, and the estimate for the error between approximate solution and accurate solution is given. On the other hand, under the linear growth condition, the uniform Lipschitz condition is replaced by the local Lipschitz condition, the existence-and-uniqueness theorem is also valid for ISFDEs on [ t 0 , T ] . Moreover, the existence-and-uniqueness theorem still holds on interval [ t 0 , ∞ ) , where t 0 ∈ R is an arbitrary real number.

In this paper, we study some ecosystem with asymptotically periodic coefficients. We obtain the existence and uniqueness of asymptotically periodic solution of asymptotically periodic ecosystem.

In this paper, we studied the persistence of the asymptotically periodic multispecies competition predator-prey system with Holling III type functional response. Further, by use of the Standard Comparison Theorem, we improved the results of paper [C. Chen, F. Chen, Conditions for global attractivity of multispecies ecological competition-predator system with Holling III type functional response, Journal of Biomathematics 19(2) (2004) 136-140].

Choosing space as the phase space, the existence, uniqueness and stability of the solution to neutral stochastic functional differential equations with infinite delay (short for INSFDEs) are studied in this paper. Under non-Lipschitz condition, weakened linear growth condition and contractive condition, the existence-and-uniqueness theorem of the solution to INSFDEs by means of the Picard iteration, Doob’s martingale inequalities, Gronwall’s inequality and Bihari’s inequality is obtained. Furthermore, the continuous dependence of the solutions on the initial value to INSFDEs are derived. MSC:65C30, 60H10.

This paper focuses on the stabilities of the equilibria to a predator–prey model with stage structure incorporating prey refuge. By analyzing the characteristic functions, we obtain that the equilibria of the model are locally stable when some suitable conditions are being satisfied. According to the comparison theorem and iteration technique, the globally asymptotic stability of the positive equilibrium is discussed. And, the sufficient conditions of the global stability to the trivial equilibrium and the boundary equilibrium are derived. The study shows that the prey refuge will enhance the density of the prey species, and it will decrease the density of predator species. Finally, some numerical simulations are carried out to show the efficiency of our main results.

The two-patch predator-prey system with diffusion and harvesting is concerned in this paper. By means of the coincidence degree theory and comparison theorem, we establish the existence of at least eight positive periodic solutions for this system. Further, an example is given to illustrate the effectiveness of our results.

[1] The interdecadal variability of summer precipitation in Beijing from 1724 to 2005 is analyzed using a filter, keeping the true trends at time series ends. A probability distribution, Pearson type III, was applied to the summer precipitation series to estimate the probability of anomalous rainfall. This study includes the correlation between the interdecadal variations of the summer precipitation in Beijing and those of the indices of Northern Atlantic Oscillation (NAO), Southern Oscillation (SOI), Pacific Decadal Oscillation (PDO), and summer monsoon (SMS) of East Asia indices are computed. A methodology is thus developed to forecast the probable distribution of precipitation intensities in Beijing. Results show that the probability of drought in Beijing has greatly increased since the middle of the 1960s. The interdecadal variability of NAO, PDO, and SMS are extremely important for the low-frequency forecast of anomalous summer rainfall in Beijing. The method developed here seems appropriate to estimate the probability of future anomalous summer rainfall.

[1] In this paper, we use growing season Normalized Difference Vegetation Index (NDVI) as an indicator of plant growth to quantify the relationships between vegetation production and intra-annual precipitation patterns for three major temperate biomes in China: grassland, deciduous broadleaf forest, and deciduous coniferous forest. With increased precipitation, NDVI of grassland and deciduous broadleaf forest increased, but that of deciduous coniferous forest decreased. More frequent precipitation significantly increased growth of grassland and deciduous broadleaf forest, but did not alter that of deciduous coniferous forest at low precipitation levels and constrained its growth at high precipitation levels. The relationships between NDVI and average precipitation per event were opposite to those between NDVI and precipitation frequency. Such nonlinear feedback suggests that the responses of vegetation production to changes in precipitation patterns differ by both biome type and precipitation amount.