Assessing the copula selection for bivariate frequency analysis based on the tail dependence test

The flood characteristics, namely, peak, duration and volume provide important information for the design of hydraulic structures, water resources planning, reservoir management and flood hazard mapping. Flood is a complex phenomenon defined by strongly correlated characteristics such as peak, duration and volume. Therefore, it is necessary to study the simultaneous, multivariate, probabilistic behaviour of flood characteristics. Traditional multivariate parametric distributions have widely been applied for hydrological applications. However, this approach has some drawbacks such as the dependence structure between the variables, which depends on the marginal distributions or the flood variables that have the same type of marginal distributions. Copulas are applied to overcome the restriction of traditional bivariate frequency analysis by choosing the marginals from different families of the probability distribution for flood variables. The most important step in the modelling process using copula is the selection of copula function which is the best fit for the data sample. The choice of copula may significantly impact the bivariate quantiles. Indeed, this study indicates that there is a huge difference in the joint return period estimation using the families of extreme value copulas and no upper tail copulas (Frank, Clayton and Gaussian) if there exists asymptotic dependence in the flood characteristics. This study suggests that the copula function should be selected based on the dependence structure of the variables. From the results, it is observed that the result from tail dependence test is very useful in selecting the appropriate copula for modelling the joint dependence structure of flood variables. The extreme value copulas with upper tail dependence have proved that they are appropriate models for the dependence structure of the flood characteristics and Frank, Clayton and Gaussian copulas are the appropriate copula models in case of variables which are diagnosed as asymptotic independence.     

Impact of copula selection on geotechnical reliability under incomplete probability information

This paper aims to investigate the impact of copula selection on geotechnical reliability under incomplete probability information. The copula theory is introduced briefly. Thereafter, four copulas, namely Gaussian, Plackett, Frank, and No. 16 copulas, are selected to model the dependence structure between cohesion and friction angle. A copula-based approach is used to construct the joint probability density function of cohesion and friction angle with given marginal distributions and correlation coefficient. The reliability of an infinite slope and a retaining wall is presented to demonstrate the impact of copula selection on reliability. The results indicate that the probabilities of failure of geotechnical structures with given marginal distributions and correlation coefficient of shear strength parameters cannot be determined uniquely. The resulting probabilities of failure associated with different copulas can differ considerably. Such a difference increases with decreasing probability of failure. Significant difference in probabilities of failure could be observed for relatively small coefficients of variation of the shear strength parameters or a strong negative correlation between cohesion and friction angle. The Gaussian copula, often adopted out of expedience without proper validation, may not capture the dependence structure between cohesion and friction angle properly. Furthermore, the Gaussian copula may greatly underestimate the probability of failure for geotechnical structures.     

基于三维copula函数的多水文区丰枯遭遇分析

不同水文区的丰枯遭遇概率分析属于多变量概率分布问题,涉及的水文区越多,变量的维数就越高,问题就越复杂.为找到一种简单通用的多变量(n≥3)水文概率问题的求解方法,以不同水文区丰枯遭遇概率分析为例,引入三维copula函数构建多变量联合概率模型,将其用于分析长江、淮河及黄河流域的径流量的联合概率和条件概率问题。研究结果表明,当变量维数n≥3时,由copula函数可以很容易地构建多变量概率分布模型;对一组水文数据系列,有多个不同copula函数可以选择,可采用拟合优度检验方法择优;copula函数构建的多变量概率模型,可以计算各种条件下的联合概率分布,可以分析各种不同量级水文变量的遭遇概率和条件概率;通过与多维转换为一维方法的比较,三维Frank copula函数具有更优良的拟合优度、无偏性及有效性,且计算更简便。     

Interannual variations in length of day with respect to El Niño - Southern Oscillation’s impact (1962–2015)

The objective of research done in this study is to examine the variability of the length of day (LOD) and to investigate its correlation with ENSO (El Niño-Southern oscillation) episodes. For this purpose, the LOD time series (1962–2015), from the International Earth Rotation and Reference Systems Service (IERS), is investigated using the Singular Spectrum Analysis (SSA) technique. The results show that the LOD time series is very complex and is composed of several components: the long-term trend explains 95.97% of the original series, the annual harmonic 1.76% and the semi-annual 1.35%. Considering sea surface temperature anomalies (SSTA) index over the Niño3, Niño4 and Niño3.4 regions, Southern Oscillation Index (SOI) and Multivariate ENSO Index (MEI), the residuals signal, that represents only 0.92% of the initial LOD series, indicate a significant correlation with ENSO occurred during 1965–66, 1972–73, 1982–83 and 1997–98 El Niño events and 1970–71, 1973–74, 1988–89, 2007–08, 2010–11 La Niña ones. This is a pertinent result that suggests that LOD variability is at least partly related to ENSO phenomena.     

ENSO impacts on salinity in Tampa Bay, Florida

Estuarine salinity distributions reflect a dynamic balance between the processes that control estuarine circulation. At seasonal and longer time scales, freshwater inputs into estuaries represent the primary control on salinity distribution and estuarine circulation. El Niño-Southern Oscillation (ENSO) conditions influence seasonal rainfall and stream discharge patterns in the Tampa Bay, Florida region. The resulting variability in freshwater input to Tampa Bay influences its seasonal salinity distribution. During El Niño events, ENSO sea surface temperature anomalies (SSTAs) are significantly and inversely correlated with salinity in the bay during winter and spring. These patterns reflect the elevated rainfall over the drainage basin and the resulting elevated stream discharge and runoff, which depress salinity levels. Spatially, the correlations are strongest at the head of the bay, especially in bay sections with long residence times. During La Niña conditions, significant inverse correlations between ENSO SSTAs and salinity occur during spring. Dry conditions and depressed stream discharge characterize La Niña winters and springs, and the higher salinity levels during La Niña springs reflect the lower freshwater input levels.     

About the variability in thunderstorm and rainfall activity over India and its association with El Niño and La Niña

Thunderstorms are of much importance in tropics, as this region is considered to have central role in the convective overturn of the atmosphere and play an important role in rainfall activity. It is well known that El Niño and La Niña are well associated with significant climate anomalies at many places around the globe. Therefore, an attempt is made in this study to analyze variability in thunderstorm days and rainfall activity over Indian region and its association with El Niño and La Niña using data of thunderstorm day’s for 64 stations well distributed all over India for the period 1981–2005 (25 years). It is seen that thunderstorm activity is higher and much variable during pre-monsoon (MAM) and southwest monsoon (JJAS) than the rest of the year. Positive correlation coefficients (CCs) are seen between thunderstorms and rainfall except for the month of June during which the onset of the southwest monsoon sets over the country. CCs during winter months are highly correlated. Composite anomalies in thunderstorms during El Niño and La Niña years suggest that ENSO conditions altered the patterns of thunderstorm activity over the country. Positive anomalies are seen during pre-monsoon (MAM) and southwest monsoon months (JAS) during La Niña years. Opposite features are seen in southwest monsoon during El Niño periods, but El Niño favors thunderstorm activity during pre-monsoon months. There is a clear contrast between the role of ENSO during southwest monsoon and post-monsoon on thunderstorm activity over the country. Time series of thunderstorms and precipitation show strong association with similarities in their year-to-year variation over the country.     

Analysis of rainfall and temperature time series to detect long-term climatic trends and variability over semi-arid Botswana

Arid and semi-arid environments have been identified with locations prone to impacts of climate variability and change. Investigating long-term trends is one way of tracing climate change impacts. This study investigates variability through annual and seasonal meteorological time series. Possible inhomogeneities and years of intervention are analysed using four absolute homogeneity tests. Trends in the climatic variables were determined using Mann–Kendall and Sen’s Slope estimator statistics. Association of El Niño Southern Oscillation (ENSO) with local climate is also investigated through multivariate analysis. Results from the study show that rainfall time series are fully homogeneous with 78.6 and 50% of the stations for maximum and minimum temperature, respectively, showing homogeneity. Trends also indicate a general decrease of 5.8, 7.4 and 18.1% in annual, summer and winter rainfall, respectively. Warming trends are observed in annual and winter temperature at 0.3 and 1.5% for maximum temperature and 1.7 and 6.5% for minimum temperature, respectively. Rainfall reported a positive correlation with Southern Oscillation Index (SOI) and at the same time negative association with Sea Surface Temperatures (SSTs). Strong relationships between SSTs and maximum temperature are observed during the El Niño and La Niña years. These study findings could facilitate planning and management of agricultural and water resources in Botswana.     

Trends and extreme value analysis of rainfall pattern over homogeneous monsoon regions of India

Trends of pre-monsoon, monsoon and post-monsoon rainfall pattern were studied on decadal basis over different homogeneous monsoon regions in India for the period 1871–2008. It is attempted to understand the relation of monsoon rainfall with the global teleconnections of El Niño and La Niña, for which the correlation analysis has been carried out with Darwin pressure and Niño 3.4 sea surface temperature (Niño 3.4 SST). The correlation analysis inferred that the significant correlations were observed when monsoon rainfall is related to ENSO indices on decadal scale than on annual ones. The study also found that the north-west region is more affected by the moderate El Niño years compared to strong El Niño years. The regions Central North-East and North-East could not make any difference among weak, moderate and strong La Niña events. The authors also have carried out the extreme value analysis over different homogeneous monsoon regions of India as well as for whole India. The results show that the return values of rainfall are increasing with the return periods for the forthcoming 10, 20, 50 and 100 years. The heterogeneity in number of threshold years that were recorded for the extreme rainfall over north-east (humid climatic type) and north-west (arid climatic type) described the climate variability. The results of the present study may be useful for the policy makers in understanding the rainfall exceedance in different return periods for planning the risk management strategies.     

Drought characterization using a new copula-based trivariate approach

Meteorological drought is a natural climatic phenomenon that occurs over various time scales and may cause significant economic, environmental and social damages. Three drought characteristics, namely duration, average severity and peak intensity, are important variables in water resources planning and decision making. This study presents a new method for construction of three-dimensional copulas to describe the joint distribution function of meteorological drought characteristics. Using the inference function for margins, the parameters for six types of copulas were tested to select the best-fitted copulas. According to the values of the log-likelihood function, Galambos, Frank and Clayton were the selected copula models to describe the dependence structure for pairs of duration–severity, severity–peak and duration–peak, respectively. Trivariate cumulative probability, conditional probability and drought return period were also investigated based on the derived copula-based joint distributions. The proposed model was evaluated over the observed data of a Qazvin synoptic station, and the results were compared with the empirical probabilities. For measuring the model accuracy, R ², root mean square error (RMSE) and the Nash–Sutcliffe efficiency (NSE) criteria were used. Results indicated that R ², RMSE and NSE were equal to 0.91, 0.098 and 0.668, respectively, which demonstrate sufficient accuracy of the proposed model. Drought probabilistic characteristics can provide useful information for water resource planning and management.     

Variability of Indian monsoon-ENSO relationship in a 1000-year MRI-CGCM2.2 simulation

There is a close relationship between interannual variability of the Indian summer monsoon rainfall and the El Niño/Southern Oscillation (ENSO) (drought conditions over India accompany warm ENSO events and vice versa). However, recent observations suggest a weakening of this ENSO-monsoon relationship that may be linked to global warming. We report here an analysis of the ENSO-monsoon relationship within the framework of a 1000-year control simulation of the MRI-coupled general circulation model (GCM), MRI-CGCM2.2. An overall correlation between the June-July-August (JJA) Nino3.4 sea surface temperature and the JJA Indian monsoon rainfall is –0.39, with reasonable circulation characteristics associated with the modeled ENSO. The simulated ENSO-monsoon relationship reveals long-term variations, from –0.71 to +0.07, in moving 31-year windows. This modulation in the ENSO-monsoon relationship is associated with decadal variability of the climate system.     

Towards understanding the unusual Indian monsoon in 2009

The Indian summer monsoon season of 2009 commenced with a massive deficit in all-India rainfall of 48% of the average rainfall in June. The all-India rainfall in July was close to the normal but that in August was deficit by 27%. In this paper, we first focus on June 2009, elucidating the special features and attempting to identify the factors that could have led to the large deficit in rainfall. In June 2009, the phase of the two important modes, viz., El Niño and Southern Oscillation (ENSO) and the equatorial Indian Ocean Oscillation (EQUINOO) was unfavourable. Also, the eastern equatorial Indian Ocean (EEIO) was warmer than in other years and much warmer than the Bay. In almost all the years, the opposite is true, i.e., the Bay is warmer than EEIO in June. It appears that this SST gradient gave an edge to the tropical convergence zone over the eastern equatorial Indian Ocean, in competition with the organized convection over the Bay. Thus, convection was not sustained for more than three or four days over the Bay and no northward propagations occurred. We suggest that the reversal of the sea surface temperature (SST) gradient between the Bay of Bengal and EEIO, played a critical role in the rainfall deficit over the Bay and hence the Indian region. We also suggest that suppression of convection over EEIO in association with the El Niño led to a positive phase of EQUINOO in July and hence revival of the monsoon despite the El Niño. It appears that the transition to a negative phase of EQUINOO in August and the associated large deficit in monsoon rainfall can also be attributed to the El Niño.     

Determing the effects of El Niño-Southern Oscillation events on coastal water quality

The importance of the El Niño-Southern Oscillation (ENSO) on regional-scale climate variability is well recognized although the associated effects on local weather patterns are poorly understood. Little work has addressed the ancillary impacts of climate variability at the community level, which require analysis at a local scale. In coastal communities water quality and public health effects are of particular interest. Here we describe the historical influence of ENSO events on coastal water quality in Tampa Bay, Florida (USA) as a test case. Using approximate randomized statistics, we show significant ENSO influences on water quality particularly during winter months, with significantly greater fecal pollution levels during strong El Niño winters and significantly lower levels during strong La Niña winters as compared to neutral conditions. Similar significant patterns were also noted for El Niño and La Niña fall periods. The success of the analysis demonstrates the feasibility of assessing local effects associated with large-scale climate variability. It also highlights the possibility of using ENSO forecasts to predict periods of poor coastal water quality in urban region which local agencies may use to make appropriate prepations.     

Comparison of 1982–1983 and 1997–1998 El Niño effects on the shallow-water fish assemblage of the Patos Lagoon estuary (Brazil)

Meteorological impacts of El Niño events of 1982–1983 and 1997–1998 were observed in locations throughout the world. In southern Brazil, El Niño events are associated with increased rainfall and higher freshwater discharge into Patos Lagoon, a large coastal lagoon that empties into the Atlantic Ocean. Based on interdecadal meteorological and biological data sets encompassing the two strongest El Niño events of the last 50 yr, we evaluated the hypothesis that El Niño-induced hydrological changes are a major driving force controlling the interannual variation in the structure and dynamics of fishes in the Patos Lagoon estuary. High rainfall in the drainage basin of the lagoon coincided with low salinity in the estuarine area during both El Niño episodes. Total rainfall in the drainage basin was higher (767 versus 711 mm) and near-zero salinity conditions in the estuarine area lasted about 3 mo longer during the 1997–1998 El Niño event compared with the 1982–1983 event. Hydrological changes triggered by both El Niño events had similar relationships to fish species composition and diversity patterns, but the 1997–1998 event appeared to have stronger effects on the species assemblage. Although shifts in species composition were qualitatively similar during the two El Niño events, distance between El Niño and non-El Niño assemblage multivariate centroids was greater during the 1996–2000 sampling period compared with the 1979–1983 period. We provide a conceptual model of the principal mechanisms and processes connecting the atmospheric-oceanographic interactions triggered by the El Niño phenomena and their effect on the estuarine fish assemblage.     

Study of the global and regional climatic impacts of ENSO magnitude using SPEEDY AGCM

ENSO is considered as a strong atmospheric teleconnection that has pronounced global and regional circulation effects. It modifies global monsoon system, especially, Asian and African monsoons. Previous studies suggest that both the frequency and magnitude of ENSO events have increased over the last few decades resulting in a need to study climatic impacts of ENSO magnitude both at global and regional scales. Hence, to better understand the impact of ENSO amplitude over the tropical and extratropical regions focussing on the Asian and African domains, ENSO sensitivity experiments are conducted using ICTPAGCM (‘SPEEDY’). It is anticipated that the tropical Pacific SST forcing will be enough to produce ENSO-induced teleconnection patterns; therefore, the model is forced using NINO3.4 regressed SST anomalies over the tropical Pacific only. SPEEDY reproduces the impact of ENSO over the Pacific, North and South America and African regions very well. However, it underestimates ENSO teleconnection patterns and associated changes over South Asia, particularly in the Indian region, which suggests that the tropical Pacific SST forcing is not sufficient to represent ENSO-induced teleconnection patterns over South Asia. Therefore, SST forcing over the tropical Indian Ocean together with air–sea coupling is also required for better representation of ENSO-induced changes in these regions. Moreover, results obtained by this pacemaker experiment show that ENSO impacts are relatively stronger over the Inter-Tropical Convergence Zone (ITCZ) compared to extratropics and high latitude regions. The positive phase of ENSO causes weakening in rainfall activity over African tropical rain belt, parts of South and Southeast Asia, whereas, the La Niña phase produces more rain over these regions during the summer season. Model results further reveal that ENSO magnitude has a stronger impact over African Sahel and South Asia, especially over the Indian region because of its significant impact over the tropical Atlantic and the Indian Ocean through Walker circulation. ENSO-induced negative (positive) NAO-like response and associated changes over Southern Europe and North Africa get significantly strong following increased intensity of El Niño (La Niña) in the northern (southern) hemisphere in the boreal winter (summer) season. We further find that ENSO magnitude significantly impacts Hadley and Walker circulations. The positive phase of ENSO (El Niño) overall strengthens Hadley cell and a reverse is true for the La Niña phase. ENSO-induced strengthening and weakening of Hadley cell induces significant impact over South Asian and African ITCZ convective regions through modification of ITCZ/monsoon circulation system.     

Spatial hydrological drought characteristics in Karkheh River basin,southwest Iran using copulas

Investigation on drought characteristics such as severity, duration, and frequency is crucial for water resources planning and management in a river basin. While the methodology for multivariate drought frequency analysis is well established by applying the copulas, the estimation on the associated parameters by various parameter estimation methods and the effects on the obtained results have not yet been investigated. This research aims at conducting a comparative analysis between the maximum likelihood parametric and non-parametric method of the Kendall \(\tau \) estimation method for copulas parameter estimation. The methods were employed to study joint severity–duration probability and recurrence intervals in Karkheh River basin (southwest Iran) which is facing severe water-deficit problems. Daily streamflow data at three hydrological gauging stations (Tang Sazbon, Huleilan and Polchehr) near the Karkheh dam were used to draw flow duration curves (FDC) of these three stations. The \(Q_{75}\) index extracted from the FDC were set as threshold level to abstract drought characteristics such as drought duration and severity on the basis of the run theory. Drought duration and severity were separately modeled using the univariate probabilistic distributions and gamma–GEV, LN2–exponential, and LN2–gamma were selected as the best paired drought severity–duration inputs for copulas according to the Akaike Information Criteria (AIC), Kolmogorov–Smirnov and chi-square tests. Archimedean Clayton, Frank, and extreme value Gumbel copulas were employed to construct joint cumulative distribution functions (JCDF) of droughts for each station. Frank copula at Tang Sazbon and Gumbel at Huleilan and Polchehr stations were identified as the best copulas based on the performance evaluation criteria including AIC, BIC, log-likelihood and root mean square error (RMSE) values. Based on the RMSE values, nonparametric Kendall-\(\tau \) is preferred to the parametric maximum likelihood estimation method. The results showed greater drought return periods by the parametric ML method in comparison to the nonparametric Kendall \(\tau \) estimation method. The results also showed that stations located in tributaries (Huleilan and Polchehr) have close return periods, while the station along the main river (Tang Sazbon) has the smaller return periods for the drought events with identical drought duration and severity.     

The influence of groundwater abstraction on interpreting climate controls and extreme recharge events from well hydrographs in semi-arid South Africa

There is a scarcity of long-term groundwater hydrographs from sub-Saharan Africa to investigate groundwater sustainability, processes and controls. This paper presents an analysis of 21 hydrographs from semi-arid South Africa. Hydrographs from 1980 to 2000 were converted to standardised groundwater level indices and rationalised into four types (C1–C4) using hierarchical cluster analysis. Mean hydrographs for each type were cross-correlated with standardised precipitation and streamflow indices. Relationships with the El Niño–Southern Oscillation (ENSO) were also investigated. The four hydrograph types show a transition of autocorrelation over increasing timescales and increasingly subdued responses to rainfall. Type C1 strongly relates to rainfall, responding in most years, whereas C4 notably responds to only a single extreme event in 2000 and has limited relationship with rainfall. Types C2, C3 and C4 have stronger statistical relationships with standardised streamflow than standardised rainfall. C3 and C4 changes are significantly (p <?0.05) correlated to the mean wet season ENSO anomaly, indicating a tendency for substantial or minimal recharge to occur during extreme negative and positive ENSO years, respectively. The range of different hydrograph types, sometimes within only a few kilometres of each other, appears to be a result of abstraction interference and cannot be confidently attributed to variations in climate or hydrogeological setting. It is possible that high groundwater abstraction near C3/C4 sites masks frequent small-scale recharge events observed at C1/C2 sites, resulting in extreme events associated with negative ENSO years being more visible in the time series.

     

Stochastic response surface method for reliability problems involving correlated multivariates with non-Gaussian dependence structure: Analysis under incomplete probability information

This paper aims to provide a stochastic response surface method (SRSM) that can consider non-Gaussian dependent random variables under incomplete probability information. The Rosenblatt transformation is adopted to map the random variables from the original space into the mutually independent standard normal space for the stochastic surrogate model development. The multivariate joint distribution is reconstructed by the pair-copula decomposition approach, in which the pair-copula parameters are retrieved from the incomplete probability information. The proposed method is illustrated in a tunnel excavation example. Three different dependence structures characterized by normal copulas, Frank copulas, and hybrid copulas are respectively investigated to demonstrate the effect of dependence structure on the reliability results. The results show that the widely used Nataf transformation is actually a special case of the proposed method if all pair-copulas are normal copulas. The effect of conditioning order is also examined. This study provides a new insight into the SRSM-based reliability analysis from the copula viewpoint and extends the application of SRSM under incomplete probability information.     

Tropospheric biennial oscillation and south Asian summer monsoon rainfall in a coupled model

In this study Tropospheric Biennial Oscillation (TBO) and south Asian summer monsoon rainfall are examined in the National Centers for Environmental Prediction (NCEP) Climate Forecast System (CFSv2) hindcast. High correlation between the observations and model TBO index suggests that the model is able to capture most of the TBO years. Spatial patterns of rainfall anomalies associated with positive TBO over the south Asian region are better represented in the model as in the observations. However, the model predicted rainfall anomaly patterns associated with negative TBO years are improper and magnitudes are underestimated compared to the observations. It is noted that positive (negative) TBO is associated with La Niña (El Niño) like Sea surface temperature (SST) anomalies in the model. This leads to the fact that model TBO is El Niño-Southern Oscillation (ENSO) driven, while in the observations Indian Ocean Dipole (IOD) also plays a role in the negative TBO phase. Detailed analysis suggests that the negative TBO rainfall anomaly pattern in the model is highly influenced by improper teleconnections allied to IOD. Unlike in the observations, rainfall anomalies over the south Asian region are anti-correlated with IOD index in CFSv2. Further, summer monsoon rainfall over south Asian region is highly correlated with IOD western pole than eastern pole in CFSv2 in contrast to the observations. Altogether, the present study highlights the importance of improving Indian Ocean SST teleconnections to south Asian summer rainfall in the model by enhancing the predictability of TBO. This in turn would improve monsoon rainfall prediction skill of the model.     

Quantile regression C-vine copula model for spatial extremes

A spatial quantile regression model is proposed to estimate the quantile curve for a given probability of non-exceedance, as function of locations and covariates. Canonical vines copulas are considered to represent the spatial dependence structure. The marginal at each location is an asymmetric Laplace distribution where the parameters are functions of the covariates. The full conditional quantile distribution is given using the Joe–Clayton copula. Simulations show the flexibility of the proposed model to estimate the quantiles with special dependence structures. A case study illustrates its applicability to estimate quantiles for spatial temperature anomalies.     

Chandler wobble of the poles as part of the nutation of the atmosphere-ocean-Earth system

The paper presents calculated spectra of El Niño Southern oscillation (ENSO) indices. The ENSO spectra have components with periods that are multiples of the Earth’s free (1.2 years) and forced (18.6 years) nutation periods. Analysis of a 41-year series of exciting functions for the atmospheric angular momentum confirms the existence of such periodicity. Nutation waves responsible for the El Niño phenomena in the ocean, the Southern oscillation in the atmosphere, and the presence of subharmonics of the Chandler period (1.2 years) and superharmonics of the lunar period (18.6 years) in the ENSO spectra are described. A model for the nonlinear nutation of the Earth-ocean-atmosphere system is constructed. In this model, the ENSO, acting at frequencies of combinational resonances, excites the Chandler wobble of the Earth’s poles. At the same time, this wobble interacts with the nutation motions of the atmosphere and World Ocean.