Convergent Cross Mapping Method Research Articles

Causal mediation of urban temperature by geopotential height in U.S. cities

Excessive warming is the source of many environmental challenges in urban areas. Finding causal interactions between urban ambient temperature and other meteorological variables will greatly facilitate our understanding of the underlying mechanisms of urban heat. In this study, we use the data of 2-m air temperature and 500 hPa geopotential height (GPH) in 520 cities in the contiguous United States (CONUS), from 2016 to 2022, to detect their local and nonlocal causal interactions based on the convergent cross-mapping method. For local (within the same city) interactions between temperature and GPH, there are hubs of strong causal interactions in the northern Appalachian Mountain and inland southwestern CONUS, whereas the leeward side of the southern Rocky Mountains exhibit low causation due to the baroclinic in this area. The nonlocal causal networks exhibit potential long-range connections (teleconnections), largely attributable to the influence of the upstream and downstream westerly circulations on local atmospheric variables. This study can be informative to stakeholders in design sustainable countermeasures to mitigate excessive heat in urban areas.

Observational evidence for detrimental impact of inhaled ozone on human respiratory system

The detrimental influence of inhaled ozone on human respiratory system is ambiguous due to the complexity of dose response relationship between ozone and human respiratory system. This study collects inhaled ozone concentration and respiratory disease data from Shenzhen City to reveal the impact of ozone on respiratory diseases using the Generalized Additive Models (GAM) and Convergent Cross Mapping (CCM) method at the 95% confidence level. The result of GAM exhibits a partially significant lag effect on acute respiratory diseases in cumulative mode. Since the traditional correlation analysis is incapable of capturing causality, the CCM method is applied to examine whether the inhaled ozone affects human respiratory system. The results demonstrate that the inhaled ozone has a significant causative impact on hospitalization rates of both upper and lower respiratory diseases. Furthermore, the harmful causative effects of ozone to the human health are varied with gender and age. Females are more susceptible to inhaled ozone than males, probably because of the estrogen levels and the differential regulation of lung immune response. Adults are more sensitive to ozone exposure than children, potentially due to the fact that children need longer time to react to ozone stress than adults, and the elderly are more tolerant than adults and children, which may be related to pulmonary hypofunction of the elderly while has little correlation with ozone exposure.

Causality analysis in type 1 diabetes mellitus with application to blood glucose level prediction

Effective control of blood glucose level (BGL) is the key factor in the management of type 1 diabetes mellitus (T1D). BGL prediction is an important tool to help maximise the time BGL is in the target range and thus minimise both acute and chronic diabetes-related complications. To predict future BGL, histories of variables known to affect BGL, such as carbohydrate intake, injected bolus insulin, and physical activity, are utilised. Due to these identified cause and effect relationships, T1D management can be examined via the causality context. In this respect, this work initially investigates these relations and quantifies the causality strengths of each variable with BGL using the convergent cross mapping method (CCM). Then, considering the extended CCM, the causality strengths of each variable for different lags are quantified. After that, the optimal time lag for each variable is determined according to the quantified causality effects. Subsequently, the feasibility of leveraging causality information as prior knowledge for BGL prediction is investigated by proposing two approaches. In the first approach, causality strengths are used as weights for relevant affecting variables. In the second approach, the optimal causal lags and the corresponding causality strengths are considered the shifts and weights for the variables, respectively. Overall, the evaluation criteria and statistical analysis used for comparing results show the effectiveness of using causality analysis in T1D management.

Quantifying the Influences of Driving Factors on Land Surface Temperature during 2003–2018 in China Using Convergent Cross Mapping Method

The relationship between land surface temperature (LST) and environmental factors is complex and nonlinear. To determine these relationships for China, this study analyzed the driving effects of air temperature, vegetation index, soil moisture, net surface radiation, precipitation, aerosols, evapotranspiration, and water vapor on LST based on remote-sensing and reanalysis data from 2003–2018, using a convergent cross-mapping method. During the study period, air temperature and net surface radiation were the dominant drivers of LST with a cross-mapping skill above 0.9. Vegetation index and evapotranspiration were the secondary drivers of LST with a cross-mapping skill that was higher than 0.5. Except for air temperature and net surface radiation, the direction and strength of the effects of the driving factors on LST were related to the climate type. The effects of air temperature and net radiation on LST diminished from north to south, indicating that LST was more sensitive to air temperature and net radiation in energy-limited regions. However, the effects of vegetation index and evapotranspiration on LST varied significantly across climate zones; that is, positive effects were mostly in non-monsoonal zones and negative effects were primarily in monsoonal zones. Our results quantified the driving role of environmental factors on LST and provided a comprehensive understanding of LST dynamics.

Causality analysis and prediction of blast furnace state based on convergence cross mapping

ABSTRACT Blast furnace (BF) ironmaking system is a complex industrial system so this paper proposes a BF state causality analysis method based on the use of convergent cross-mapping method (CCM). This method can accurately describe the causal relationships between states at different locations in the BF system. It can also be used as a feature selection method for prediction models. After obtaining accurate causal characteristics of the BF state covariates, the BF system process theory is used for validation. The causal characteristics are used as input variables to the extreme gradient boosting model (XGboost) for predicting BF state parameters. After testing with industrial data, the model predicted an absolute error control within 2% with an accuracy of over 88%. The CCM approach mentioned in this paper is more suitable for state causal impact analysis and predictive model feature selection for BF systems.

A complex network approach for the model of vehicle emission propagation and intelligently mine the interaction rules

With the increasing number of motor vehicles, exhaust emission has become a major source of urban pollution. Most studies are limited to the prediction of pollutant concentration, which cannot clearly indicate the change of pollution emissions and regional relationship. In this paper, we propose an emission propagation model of vehicle source pollution based on complex network in order to intelligently mine the interaction and propagation rules hidden behind dynamic spatiotemporal data. First, aiming at the problems of low resolution and insufficient data volume of vehicle emission data, a high-resolution pollution emission data is generated based on the COPERT (Computer Program to Calculate Emissions from Road Transport). For study the influence of causality between regions, a propagation model is designed based on the convergent cross mapping method to transform the emission time series into a complex network. In addition, we propose a novel key node mining algorithm using hybrid local and global information to identify areas of heavy pollution. Experimental results on real datasets demonstrate that the spread of pollution follows certain rules and is also affected by regional influences. Moreover, the proposed algorithm is superior to the state-of-the-art methods.

Detecting delay propagation in regional air transport systems using convergent cross mapping and complex network theory

It has been widely recognized that delay propagation is a widespread phenomenon in air transport systems. Regional air transport systems are vulnerable to severe systemic delay propagation because of connected resources and shared airspace. This study presents a two-stage analytical framework to detect delay propagation in regional air transport systems, which is critical to support industrial applications in air transport operations. In the first stage, we propose a delay causality without the strong and independent causality (SIC) assumption to represent the delay propagation effect. A convergent cross mapping method is employed to obtain the delay causality. In the second stage, we build a delay causality graph based on the none SIC assumption (DCG-non-SIC). A complex network analysis of DCG-non-SIC is presented to enhance the understanding of delay propagation patterns. This study carries out a real-world case study and provides some interesting results. Robustness checks are conducted, which verifies that the results derived in the analytical framework are solid. The results show that there is extensive delay causality between airport pairs, and a transitive trait of delay causality is observed in regional air transport systems. In addition, the importance of airports in delay propagation is not exactly in line with the hub class or the airport size.

Convergent cross mapping method and its application in ecology

The convergent cross mapping (CCM) is a method to analyze causality of nonlinear time series variables. Different from the traditional linear system analysis method, CCM gets historical information based on their state space reconstruction. The presence of causality can be confirmed when the estimated values perform convergent with time series extension. Here, we introduced the develop-ment history of CCM and its advantages over the traditional Granger causality test, and elaborated the principle, algorithm process, and implementation approach. As a system analysis method aiming at the coupling relationship between variables from weak to moderate, CCM can effectively solve the complex causality among nonlinear multivariable in ecosystems. When it is applied to the causality analysis of multi-point time series variables with spatial information, the spatial autocorrelation among points should be fully considered and combined with the method that can remove the spatial correlation between variables and sequences, so as to ensure more accurate causality analysis using CCM and more convincing results.

Time-varying causality inference of different nickel markets based on the convergent cross mapping method

Most previous studies ignored the nonlinear dynamic mechanism of the interaction between variables when exploring the causal relationship between economic and financial time series. Moreover, the dynamic interactions between these prices are time-varying. Therefore, we divide the whole time series into segments and use the convergent cross mapping method in each window to detect the causality among prices, which are defined as the causality patterns. The transition of these patterns over time can form a causal evolutionary network. Thus, we analyze and explore the time-varying characteristics of causality among spot prices, futures prices and stock prices in nickel markets through the structural characteristics of the constructed network. The results indicate that the diversity of causality patterns decreases with an increasing time scale. We selected 600 days as the study time scale to ensure the diversity and stability of causality patterns. However, only a few patterns play an important role in the evolution of causality, and when identified from different perspectives, the important patterns are not the same. However, these important patterns are all characterized by the fact that the influence of the stock market on other nickel markets is weaker than the influence of other nickel markets on the stock market. Moreover, some causality patterns can form clusters due to their frequent interactions. There is a certain preference in the transition between patterns or clusters. Our results can help market participants understand and monitor the dynamic process of causality among nickel prices in different markets.

On the cause-and-effect relations between aerosols, water vapor, and clouds over East Asia

Atmosphere is a complex dynamical system. Here, we investigated the causal links between aerosols, water vapor, and clouds, using the convergent cross mapping (CCM) method, which is based on nonlinear state space reconstruction. We utilized remote sensing data of aerosol optical depth at 550 nm (AOD), water vapor (WV), cloud cover (CC), cloud optical depth (COD), cloud effective radius-ice (CERI), and cloud effective radius-liquid (CERL) from Moderate Resolution Imaging Spectro-radiometer (MODIS) sensor over East Asia, for the period 2003–2018. Our analysis shows that there is a bidirectional forcing between AOD, CC, and COD which could be attributed to the invigoration effect of aerosols on clouds. In addition, there is a bidirectional forcing between AOD and WV and AOD and CERL, which could be attributed to the first indirect effect of aerosols on clouds, while there is no causality among AOD and CERI, probably because of strong coupling among aerosols and ice nuclei. Based on our analysis, we conclude that CCM method can effectively be used in all aerosol–cloud interactions’ studies, searching for causality among the parameters.

Selection of EMG Sensors Based on Motion Coordinated Analysis.

The intelligent prosthesis driven by electromyography (EMG) signal provides a solution for the movement of the disabled. The proper position of EMG sensors can improve the prosthesis’s motion recognition ability. To exert the amputee’s action-oriented ability and the prosthesis’ control ability, the EMG spatial distribution and internal connection of the prosthetic wearer is analyzed in three kinds of movement conditions: appropriate angle, excessive angle, and angle too small. Firstly, the correlation characteristics between the EMG channels are analyzed by mutual information to construct a muscle functional network. Secondly, the network’s features of different movement conditions are analyzed by calculating the characteristic of nodes and evaluating the importance of nodes. Finally, the convergent cross-mapping method is applied to construct a directed network, and the critical muscle groups which can reflect the user’s movement intention are determined. Experiment shows that this method can accurately determine the EMG location and simplify the distribution of EMG sensors inside the prosthetic socket. The network characteristics of key muscle groups can distinguish different movements effectively and provide a new strategy for decoding the relationship between limb nerve control and body movement.

Research on the Interannual Variation Characteristics of the Causal Relationship between the Northern Hemisphere Annular Mode and Northeast Asia Winter Surface Air Temperature Based on Convergent Cross Mapping Method

The Northern Hemisphere Annular Mode (NAM) is the main circulation mode in the Northern Hemisphere in winter, with a significant impact on the winter climate variability in the Northern Hemisphere. There are a number of studies that use statistical methods such as correlation analysis and synthetic analysis to discuss NAM and other climatic factors but rarely with the perspective of causality. In this research, the authors apply the Convergent Cross Mapping (CCM) method and use the NAM index provided by the Climate Prediction Center (CPC) from 1960 to 2018 as well as reanalysis data provided by NCEP/NCAR to analyze the impact of NAM on the winter Surface Air Temperature (SAT) in Northeast Asia. Causality changes its strength and weakness year by year and its possible physical mechanism. Our analysis indicates the following: 1) NAM has a one-way causal relationship with the winter SAT in Northeast Asia, and the strength of the relationship has interannual changes. The maximum and minimum years of causal effects are 2006 and 1982, respectively. 2) The winter NAM index has a significant 8−9-year scale main cycle, which is the driving factor for the winter NAM to affect the SAT in Northeast Asia, and to some extent, its change has affected the interannual change of NAM on the SAT causality in Northeast Asia. 3) Comparing the circulation situation of the maximum (2006) and minimum (1982) years of the causal relationship of the impact of NAM on the SAT, it can be seen that the “seesaw” structure of NAM in the year of maximum causality (2006) is obvious. However, the form of NAM’s north–south oscillation in the year of minimum causality (1982) is not obvious. This work may therefore provide a new idea in analyzing the interannual and inter-decadal changes of causality.

Improved CCM for variable causality detection in complex systems

Convergent cross-mapping (CCM), has been largely implemented for variable causality detection in complex systems like chemical process. However, this method is susceptible to problems regarding parameter selection and threshold determination. The synchronization phenomenon and the Moran effect, which are two interference terms in causality detection, must also be addressed. Therefore, an improved CCM is proposed to overcome these limitations in this paper. In the improved CCM, the optimal embedding dimension is selected based on the pseudo-nearest-neighbor theory. Also, Monte Carlo simulation is adopted to evaluate the convergence threshold. Next, by using the defined time delay detection function, the synchronization phenomenon and the Moran effect are identified to reduce the interference terms and further improve the accuracy. Finally, the improved CCM method is applied in a numerical example and a hydrocracking process to demonstrate its feasibility and superior performance than other methods.

Detecting the Causal Effect of Soil Moisture on Precipitation Using Convergent Cross Mapping

As a vital land surface parameter, soil moisture influences climate through its impact on water and energy cycles. However, the effect of soil moisture on precipitation has been strongly debated. In this study, a new causal detection method, convergent cross mapping (CCM), was applied to explore the causality between soil moisture and precipitation over low- and mid- latitude regions in the Northern Hemisphere. CCM method generally identified a strong effect of soil moisture on precipitation. Specifically, the optimal effect of soil moisture on precipitation occurred with a lag of one month and clearly decreased after four months, suggesting that soil moisture has potentials to improve the accuracy of precipitation forecast at a sub-seasonal scale. In addition, as climate (i.e., aridity index) changed from dry to wet, the effect of soil moisture on precipitation first increased and then decreased with peaks in semi-arid and semi-humid areas. These findings statistically support the hypothesis that soil moisture impacts precipitation and also provide a reference for the design of climate prediction systems.

Understanding meteorological influences on PM<sub>2.5</sub> concentrations across China: a temporal and spatial perspective

Abstract. With frequent air pollution episodes in China, growing research emphasis has been put on quantifying meteorological influences on PM2.5 concentrations. However, these studies mainly focus on isolated cities, whilst meteorological influences on PM2.5 concentrations at the national scale have not yet been examined comprehensively. This research employs the CCM (convergent cross-mapping) method to understand the influence of individual meteorological factors on local PM2.5 concentrations in 188 monitoring cities across China. Results indicate that meteorological influences on PM2.5 concentrations have notable seasonal and regional variations. For the heavily polluted North China region, when PM2.5 concentrations are high, meteorological influences on PM2.5 concentrations are strong. The dominant meteorological influence for PM2.5 concentrations varies across locations and demonstrates regional similarities. For the most polluted winter, the dominant meteorological driver for local PM2.5 concentrations is mainly the wind within the North China region, whilst precipitation is the dominant meteorological influence for most coastal regions. At the national scale, the influence of temperature, humidity and wind on PM2.5 concentrations is much larger than that of other meteorological factors. Amongst eight factors, temperature exerts the strongest and most stable influence on national PM2.5 concentrations in all seasons. Due to notable temporal and spatial differences in meteorological influences on local PM2.5 concentrations, this research suggests pertinent environmental projects for air quality improvement should be designed accordingly for specific regions.

P372 Inference of intra and inter hippocampal directed causal relationships based on foramen ovale recordings

Objectives The traditional method for seizure onset zone determination is based on the temporal order in the appearance of pathological waveforms. However, this method assumes, that the well observable pathological waveforms are really the first signs of those processes, which play important role in the seizure generation. Our objective is to develop and apply new mathematical methods to identify the causal relations between brain areas during epileptic activity. Methods The Convergent Cross Mapping method of Sugihara was modified to reveal temporal dynamics of causal connections, and applied to current source density distribution data calculated from multichannel foramen ovale electrode recordings. Results The causality analysis revealed directed connections between the two hippocampi and specific changes in intra and inter-hippocampal connections comparing interictal and ictal periods: intrahippocampal connections get stronger and spread away spatially, while inter-hippocampal connections show more complex temporal development patterns during the seizures: the functional connectivity decreases during initial phase of the seizures in some cases, while increases during the full blown seizures. Onset of the tonic phases accompanied by temporal increase of the causal connections between the two hippocampi as well. Conclusions New mathematical analysis method, such as Convergent Cross Mapping raise the possibility of objective determination the causal relationships at the initiation of the seizure, without specific assumptions about the waveforms. Significance Causality analysis can support more precise identification of seizure onset zones, thus results in better surgical outcome.

Causative impact of air pollution on evapotranspiration in the North China Plain

Atmospheric dispersion conditions strongly impact air pollution under identical surface emissions. The degree of air pollution in the Jing-Jin-Ji region is so severe that it may impose feedback on local climate. Reference evapotranspiration (ET0) plays a significant role in the estimation of crop water requirements, as well as in studies on climate variation and change. Since the traditional correlation analysis cannot capture the causality, we apply the convergent cross mapping method (CCM) in this study to observationally investigate whether the air pollution impacts ET0. The results indicate that southwest regions of Jing-Jin-Ji always suffer higher PM2.5 concentration than north regions through the whole year, and correlation analysis suggests that PM2.5 concentration has a significant negative effect on ET0 in most cities. The causality detection with CCM quantitatively demonstrates the significantly causative influence of PM2.5 concentration on ET0, higher PM2.5 concentration decreasing ET0. However, CCM analysis suggests that PM2.5 concentration has a relatively weak causal influence on ET0 while the correlation analysis gives the near zero correlation coefficient in Zhangjiakou city, indicating that the causative influence of PM2.5 concentration on ET0 is better revealed with CCM method than the correlation analysis. Considering that ET0 is strongly associated with crop water requirement, the amount of water for agricultural irrigation could be reduced at high PM2.5 concentrations. These findings can be utilized to improve the efficiency of water resources utilization, and reduce the exploiting amount of groundwater in the Jing-Jin-Ji region, although PM2.5 is detrimental to human health.

Detecting the causality influence of individual meteorological factors on local PM2.5 concentration in the Jing-Jin-Ji region

Due to complicated interactions in the atmospheric environment, quantifying the influence of individual meteorological factors on local PM2.5 concentration remains challenging. The Beijing-Tianjin-Hebei (short for Jing-Jin-Ji) region is infamous for its serious air pollution. To improve regional air quality, characteristics and meteorological driving forces for PM2.5 concentration should be better understood. This research examined seasonal variations of PM2.5 concentration within the Jing-Jin-Ji region and extracted meteorological factors strongly correlated with local PM2.5 concentration. Following this, a convergent cross mapping (CCM) method was employed to quantify the causality influence of individual meteorological factors on PM2.5 concentration. The results proved that the CCM method was more likely to detect mirage correlations and reveal quantitative influences of individual meteorological factors on PM2.5 concentration. For the Jing-Jin-Ji region, the higher PM2.5 concentration, the stronger influences meteorological factors exert on PM2.5 concentration. Furthermore, this research suggests that individual meteorological factors can influence local PM2.5 concentration indirectly by interacting with other meteorological factors. Due to the significant influence of local meteorology on PM2.5 concentration, more emphasis should be given on employing meteorological means for improving local air quality.