Abstract. The impact of climate change on weather pattern dynamics over the North Atlantic is explored through the lens of the information theory of forced dissipative dynamical systems. The predictability problem is first tackled by investigating the evolution of block entropies on observational time series of weather patterns produced by the Met Office, which reveals that predictability is increasing as a function of time in the observations during the 19th century and beginning of the 20th century, while the trend is reversed at the end of the 20th century and beginning of the 21st century. This feature is also investigated in the 15-member ensemble of the UK Met Office CMIP5 model for the 20th and 21st centuries under two climate change scenarios, revealing a wide range of possible evolutions depending on the realization considered, with an overall decrease in predictability in the 21st century for both scenarios. Lower bounds of the information entropy production are also extracted, providing information on the degree of time asymmetry and irreversibility of the dynamics. The analysis of the UK Met Office model runs suggests that the information entropy production will increase by the end of the 21st century, by a factor of 10 % in the Representative Carbon Pathway RCP2.6 scenario and a factor of 30 %–40 % in the RCP8.5 one, as compared to the beginning of the 20th century. This allows one to make the conjecture that the degree of irreversibility is increasing, and hence heat production and dissipation will also increase under climate change, corroborating earlier findings based on the analysis of the thermodynamic entropy production.
{"title":"Weather pattern dynamics over western Europe under climate change: predictability, information entropy and production","authors":"S. Vannitsem","doi":"10.5194/npg-30-1-2023","DOIUrl":"https://doi.org/10.5194/npg-30-1-2023","url":null,"abstract":"Abstract. The impact of climate change on weather pattern dynamics over the North Atlantic is explored through the lens of the information theory of forced dissipative dynamical systems. The predictability problem is first tackled by investigating the evolution of block entropies on observational time series of weather patterns produced by the Met Office, which reveals that predictability is increasing as a function of time in the observations during the 19th century and beginning of the 20th century, while the trend is reversed at the end of the 20th century and beginning of the 21st century. This feature is also investigated in the 15-member ensemble of the UK Met Office CMIP5 model for the 20th and 21st centuries under two climate change scenarios, revealing a wide range of possible evolutions depending on the realization considered, with an overall decrease in predictability in the 21st century for both scenarios. Lower bounds of the information entropy production are also extracted, providing information on the degree of time asymmetry and irreversibility of the dynamics. The analysis of the UK Met Office model runs suggests that the information entropy production will increase by the end of the 21st century, by a factor of 10 % in the Representative Carbon Pathway RCP2.6 scenario and a factor of 30 %–40 % in the RCP8.5 one, as compared to the beginning of the 20th century. This allows one to make the conjecture that the degree of irreversibility is increasing, and hence heat production and dissipation will also increase under climate change, corroborating earlier findings based on the analysis of the thermodynamic entropy production.\u0000","PeriodicalId":54714,"journal":{"name":"Nonlinear Processes in Geophysics","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44708779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tobias Necker, David Hinger, P. Griewank, T. Miyoshi, M. Weissmann
Abstract. The success of ensemble data assimilation systems substantially depends on localization, which is required to mitigate sampling errors caused by modeling background error covariances with undersized ensembles. However, finding an optimal localization is highly challenging, as covariances, sampling errors, and appropriate localization depend on various factors. Our study investigates vertical localization based on a unique convection-permitting 1000-member ensemble simulation; 1000-member ensemble correlations serve as truth for examining vertical correlations and their sampling error. We discuss requirements for vertical localization by deriving an empirical optimal localization (EOL) that minimizes the sampling error in 40-member subsample correlations with respect to the 1000-member reference. Our analysis covers temperature, specific humidity, and wind correlations on various pressure levels. Results suggest that vertical localization should depend on several aspects, such as the respective variable, vertical level, or correlation type (self- or cross-correlations). Comparing the empirical optimal localization with common distance-dependent localization approaches highlights that finding suitable localization functions bears substantial room for improvement. Furthermore, we examine approaches for achieving positive semi-definiteness for covariance localization that hardly affect the sampling error reduction. Finally, we discuss the gain of combining different localization approaches with an adaptive statistical sampling error correction.
{"title":"Guidance on how to improve vertical covariance localization based on a 1000-member ensemble","authors":"Tobias Necker, David Hinger, P. Griewank, T. Miyoshi, M. Weissmann","doi":"10.5194/npg-30-13-2023","DOIUrl":"https://doi.org/10.5194/npg-30-13-2023","url":null,"abstract":"Abstract. The success of ensemble data assimilation systems substantially depends on localization, which is required to mitigate sampling errors caused by modeling background error covariances with undersized ensembles. However, finding an optimal localization is highly challenging, as covariances, sampling errors, and appropriate localization depend on various factors. Our study investigates vertical localization based on a unique convection-permitting 1000-member ensemble simulation; 1000-member ensemble correlations serve as truth for examining vertical correlations and their sampling error. We discuss requirements for vertical localization by deriving an empirical optimal localization (EOL) that minimizes the sampling error in 40-member subsample correlations with respect to the 1000-member reference. Our analysis covers temperature, specific humidity, and wind correlations on various pressure levels. Results suggest that vertical localization should depend on several aspects, such as the respective variable, vertical level, or correlation type (self- or cross-correlations). Comparing the empirical optimal localization with common distance-dependent localization approaches highlights that finding suitable localization functions bears substantial room for improvement. Furthermore, we examine approaches for achieving positive semi-definiteness for covariance localization that hardly affect the sampling error reduction. Finally, we discuss the gain of combining different localization approaches with an adaptive statistical sampling error correction.\u0000","PeriodicalId":54714,"journal":{"name":"Nonlinear Processes in Geophysics","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44031858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract. Motivated by the concept of “location uncertainty”, initially introduced in Mémin (2014), a scheme is sought to perturb the “location” of a state variable at every forecast time step. Further considering Brenier's theorem (Brenier, 1991), asserting that the difference of two positive density fields on the same domain can be represented by a transportation map, we demonstrate that the perturbations consistently define a stochastic partial differential equation (SPDE) from the original PDE. It ensues that certain quantities, up to the user, are conserved at every time step. Remarkably, derivations following both the SALT (stochastic advection by Lie transport; Holm, 2015) and LU (location uncertainty; Mémin, 2014; Resseguier et al., 2017a) settings can be recovered from this perturbation scheme. Still, it offers broader applicability since it does not explicitly rely on Lagrangian mechanics or Newton's laws of force. For illustration, a stochastic version of the thermal shallow water equation is presented.
摘要在“位置不确定性”概念的激励下，最初在msammin(2014)中引入，寻求一种方案来扰动状态变量在每个预测时间步长的“位置”。进一步考虑Brenier定理(Brenier, 1991)，断言同一域上两个正密度场的差可以用运输图表示，我们证明了扰动一致地定义了原始PDE的随机偏微分方程(SPDE)。结果是，在每个时间步上，一定数量的量(由用户决定)是守恒的。值得注意的是，SALT(随机平流由李氏输运;Holm, 2015)和LU (location uncertainty;Memin, 2014;Resseguier et al.， 2017a)设置可以从该摄动方案中恢复。尽管如此，它还是提供了更广泛的适用性，因为它不明确地依赖于拉格朗日力学或牛顿的力定律。为了说明，给出了一个随机版本的浅水热方程。
{"title":"Physically constrained covariance inflation from location uncertainty","authors":"Yicun Zhen, V. Resseguier, B. Chapron","doi":"10.5194/npg-30-237-2023","DOIUrl":"https://doi.org/10.5194/npg-30-237-2023","url":null,"abstract":"Abstract. Motivated by the concept of “location uncertainty”, initially introduced in Mémin (2014), a scheme is sought to perturb the “location” of a state variable at every forecast time step. Further considering Brenier's theorem (Brenier, 1991), asserting that the difference of two positive density fields on the same domain can be represented by a transportation map, we demonstrate that the perturbations consistently define a stochastic partial differential equation (SPDE) from the original PDE. It ensues that certain quantities, up to the user, are conserved at every time step. Remarkably, derivations following both the SALT (stochastic advection by Lie transport; Holm, 2015) and LU (location uncertainty; Mémin, 2014; Resseguier et al., 2017a) settings can be recovered from this perturbation scheme. Still, it offers broader applicability since it does not explicitly rely on Lagrangian mechanics or Newton's laws of force. For illustration, a stochastic version of the thermal shallow water equation is presented.\u0000","PeriodicalId":54714,"journal":{"name":"Nonlinear Processes in Geophysics","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43989736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract. Abrupt and irreversible winter Arctic sea ice loss may occur under anthropogenic warming due to the disappearance of a sea ice equilibrium at athreshold value of CO2, commonly referred to as a tipping point. Previous work has been unable to conclusively identify whether a tippingpoint in winter Arctic sea ice exists because fully coupled climate models are too computationally expensive to run to equilibrium for manyCO2 values. Here, we explore the deviation of sea ice from its equilibrium state under realistic rates of CO2 increase todemonstrate for the first time how a few time-dependent CO2 experiments can be used to predict the existence and timing of sea ice tippingpoints without running the model to steady state. This study highlights the inefficacy of using a single experiment with slow-changing CO2to discover changes in the sea ice steady state and provides a novel alternate method that can be developed for the identification of tippingpoints in realistic climate models.
{"title":"An approach for projecting the timing of abrupt winter Arctic sea ice loss","authors":"Camille Hankel, E. Tziperman","doi":"10.5194/npg-30-299-2023","DOIUrl":"https://doi.org/10.5194/npg-30-299-2023","url":null,"abstract":"Abstract. Abrupt and irreversible winter Arctic sea ice loss may occur under anthropogenic warming due to the disappearance of a sea ice equilibrium at a\u0000threshold value of CO2, commonly referred to as a tipping point. Previous work has been unable to conclusively identify whether a tipping\u0000point in winter Arctic sea ice exists because fully coupled climate models are too computationally expensive to run to equilibrium for many\u0000CO2 values. Here, we explore the deviation of sea ice from its equilibrium state under realistic rates of CO2 increase to\u0000demonstrate for the first time how a few time-dependent CO2 experiments can be used to predict the existence and timing of sea ice tipping\u0000points without running the model to steady state. This study highlights the inefficacy of using a single experiment with slow-changing CO2\u0000to discover changes in the sea ice steady state and provides a novel alternate method that can be developed for the identification of tipping\u0000points in realistic climate models.\u0000","PeriodicalId":54714,"journal":{"name":"Nonlinear Processes in Geophysics","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48467653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
I. Rypina, Timothy R. Getscher, L. Pratt, Tamay Ozgokmen
Abstract. This paper presents the first comprehensive comparison of several differentdynamical-systems-based measures of stirring and Lagrangian coherence,computed from real ocean drifters. Seven commonly used methods (finite-timeLyapunov exponent (FTLE), trajectory path length, trajectory correlation dimension,trajectory encounter volume, Lagrangian-averaged vorticity deviation,dilation, and spectral clustering) were applied to 144 surface drifters inthe Gulf of Mexico in order to map out the dominant Lagrangian coherentstructures. Among the detected structures were regions of hyperbolic natureresembling stable manifolds from classical examples, divergent andconvergent zones, and groups of drifters that moved more coherently andstayed closer together than the rest of the drifters. Many methodshighlighted the same structures, but there were differences too. Overall, fiveout of seven methods provided useful information about the geometry of transport within the domain spanned by the drifters, whereas the path length and correlation dimension methods were less useful than others.
{"title":"Applying dynamical systems techniques to real ocean drifters","authors":"I. Rypina, Timothy R. Getscher, L. Pratt, Tamay Ozgokmen","doi":"10.5194/npg-29-345-2022","DOIUrl":"https://doi.org/10.5194/npg-29-345-2022","url":null,"abstract":"Abstract. This paper presents the first comprehensive comparison of several different\u0000dynamical-systems-based measures of stirring and Lagrangian coherence,\u0000computed from real ocean drifters. Seven commonly used methods (finite-time\u0000Lyapunov exponent (FTLE), trajectory path length, trajectory correlation dimension,\u0000trajectory encounter volume, Lagrangian-averaged vorticity deviation,\u0000dilation, and spectral clustering) were applied to 144 surface drifters in\u0000the Gulf of Mexico in order to map out the dominant Lagrangian coherent\u0000structures. Among the detected structures were regions of hyperbolic nature\u0000resembling stable manifolds from classical examples, divergent and\u0000convergent zones, and groups of drifters that moved more coherently and\u0000stayed closer together than the rest of the drifters. Many methods\u0000highlighted the same structures, but there were differences too. Overall, five\u0000out of seven methods provided useful information about the geometry of transport within the domain spanned by the drifters, whereas the path length and correlation dimension methods were less useful than others.\u0000","PeriodicalId":54714,"journal":{"name":"Nonlinear Processes in Geophysics","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43345946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Khedhaouiria, S. Bélair, V. Fortin, G. Roy, F. Lespinas
Abstract. Several data assimilation (DA) approaches exist to generate consistent and continuous precipitation fields valuable for hydrometeorological applications and land data assimilation. Usually, DA is based on either static or dynamic approaches. Static methods rely on deterministic forecasts to estimate background error covariance matrices, whereas dynamic approaches use ensemble forecasts. Associating the two methods is known as hybrid DA, and it has proven beneficial for different applications as it combines the advantages of both approaches. The present study intends to explore hybrid DA for the 6 h Canadian Precipitation Analysis (CaPA). Based on optimal interpolation (OI), CaPA blends forecasts and observations from surface stations and ground-based radar datasets to provide precipitation fields over the North American domain. The application of hybrid DA to CaPA consisted of finding the optimal linear combination between (i) an OI based on the Regional Deterministic Prediction System (RDPS) and (ii) an ensemble Kalman filter (EnKF) based on the 20-member Regional Ensemble Prediction System (REPS). The results confirmed the known effectiveness of the hybrid approach when low-density observation networks are assimilated. Indeed, the experiments conducted for the summer without radar datasets and for the winter (characterized by very few observations in CaPA) showed that attributing a relatively high weight to the EnKF (50 % and 70 % for summer and winter, respectively) resulted in better analysis skill and a reduction in false alarms compared with the OI method. A deterioration in the moderate- to high-intensity precipitation bias was, however, observed during summer. Reducing the weight attributed to the EnKF to 30 % alleviated the bias deterioration while improving skill compared with the OI-based CaPA.
{"title":"Using a hybrid optimal interpolation–ensemble Kalman filter for the Canadian Precipitation Analysis","authors":"D. Khedhaouiria, S. Bélair, V. Fortin, G. Roy, F. Lespinas","doi":"10.5194/npg-29-329-2022","DOIUrl":"https://doi.org/10.5194/npg-29-329-2022","url":null,"abstract":"Abstract. Several data assimilation (DA) approaches exist to generate consistent and continuous precipitation fields valuable for hydrometeorological applications and land data assimilation. Usually, DA is based on either static or dynamic approaches. Static methods rely on deterministic forecasts to estimate background error covariance matrices, whereas dynamic approaches use ensemble forecasts. Associating the two methods is known as hybrid DA, and it has proven beneficial for different applications as it combines the advantages of both approaches. The present study intends to explore hybrid DA for the 6 h Canadian Precipitation Analysis (CaPA). Based on optimal interpolation (OI), CaPA blends forecasts and observations from surface stations and ground-based radar datasets to provide precipitation fields over the North American domain. The application of hybrid DA to CaPA consisted of finding the optimal linear combination between (i) an OI based on the Regional Deterministic Prediction System (RDPS) and (ii) an ensemble Kalman filter (EnKF) based on the 20-member Regional Ensemble Prediction System (REPS). The results confirmed the known effectiveness of the hybrid approach when low-density observation networks are assimilated. Indeed, the experiments conducted for the summer without radar datasets and for the winter (characterized by very few observations in CaPA) showed that attributing a relatively high weight to the EnKF (50 % and 70 % for summer and winter, respectively) resulted in better analysis skill and a reduction in false alarms compared with the OI method. A deterioration in the moderate- to high-intensity precipitation bias was, however, observed during summer. Reducing the weight attributed to the EnKF to 30 % alleviated the bias deterioration while improving skill compared with the OI-based CaPA.\u0000","PeriodicalId":54714,"journal":{"name":"Nonlinear Processes in Geophysics","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42501908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract. Localization is an essential technique for ensemble-baseddata assimilations (DAs) to reduce sampling errors due to limited ensembles. Unlike traditional distance-dependent localization, the correlation cutoff method (Yoshida and Kalnay, 2018; Yoshida, 2019) tends to localize the observation impacts based on their background error correlations. This method was initially proposed as a variable localization strategy for coupled systems, but it can also can be utilized extensively as a spatial localization. This study introduced and examined the feasibility of the correlation cutoff method as an alternative spatial localization with the local ensemble transform Kalman filter (LETKF) preliminary on the Lorenz (1996) model. We compared the accuracy of the distance-dependent and correlation-dependent localizations and extensively explored the potential of the hybrid localization strategies. Our results suggest that the correlation cutoff method can deliver comparable analysis to the traditional localization more efficiently and with a faster DA spin-up. These benefits would become even more pronounced under a more complicated model, especially when the ensemble and observation sizes are reduced.
摘要定位是基于集成的数据同化(DAs)的一项重要技术，可以减少由于有限集成造成的采样误差。与传统的距离依赖定位不同，相关截断方法(Yoshida and Kalnay, 2018;Yoshida, 2019)倾向于基于背景误差相关性来定位观测影响。该方法最初是作为耦合系统的一种变量定位策略提出的，但它也可以作为一种空间定位方法广泛应用。本文在Lorenz(1996)模型上初步介绍并检验了相关截断法作为局部集合变换卡尔曼滤波(LETKF)替代空间定位方法的可行性。我们比较了距离依赖定位和相关依赖定位的精度，并广泛探索了混合定位策略的潜力。研究结果表明，相关截断方法可以更有效地提供与传统定位相比较的分析，并且具有更快的数据分析自旋速度。在一个更复杂的模型下，这些好处将变得更加明显，特别是当集合和观测规模缩小时。
{"title":"Applying prior correlations for ensemble-based spatial localization","authors":"Chu-Chun Chang, E. Kalnay","doi":"10.5194/npg-29-317-2022","DOIUrl":"https://doi.org/10.5194/npg-29-317-2022","url":null,"abstract":"Abstract. Localization is an essential technique for ensemble-based\u0000data assimilations (DAs) to reduce sampling errors due to limited ensembles. Unlike traditional distance-dependent localization, the correlation cutoff method (Yoshida and Kalnay, 2018; Yoshida, 2019) tends to localize the observation impacts based on their background error correlations. This method was initially proposed as a variable localization strategy for coupled systems, but it can also can be utilized extensively as a spatial localization. This study introduced and examined the feasibility of the correlation cutoff method as an alternative spatial localization with the local ensemble transform Kalman filter (LETKF) preliminary on the Lorenz (1996) model. We compared the accuracy of the distance-dependent and correlation-dependent localizations and extensively explored the potential of the hybrid localization strategies. Our results suggest that the correlation cutoff method can deliver comparable analysis to the traditional localization more efficiently and with a faster DA spin-up. These benefits would become even more pronounced under a more complicated model, especially when the ensemble and observation sizes are reduced.\u0000","PeriodicalId":54714,"journal":{"name":"Nonlinear Processes in Geophysics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70695249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract. Nonlinear oceanic internal solitary waves are considered under the influence of the combined effects of saturating nonlinearity, Earth's rotation, and horizontal depth inhomogeneity. Here the basic model is the extended Korteweg–de Vries equation that includes both quadratic and cubic nonlinearity (the Gardner equation) with additional terms incorporating slowly varying depth and weak rotation. The complicated interplay between these different factors is explored using an approximate adiabatic approach and then through numerical solutions of the governing variable depth, i.e., the rotating Gardner model. These results are also compared to analysis in the Korteweg–de Vries limit to highlight the effect of the cubic nonlinearity. The study explores several particular cases considered in the literature that included some of these factors to illustrate limitations. Solutions are made to illustrate the relevance of this extended Gardner model for realistic oceanic conditions.
{"title":"Effects of rotation and topography on internal solitary waves governed by the rotating Gardner equation","authors":"K. Helfrich, L. Ostrovsky","doi":"10.5194/npg-29-207-2022","DOIUrl":"https://doi.org/10.5194/npg-29-207-2022","url":null,"abstract":"Abstract. Nonlinear oceanic internal solitary waves are considered under the influence of the combined effects of saturating nonlinearity, Earth's rotation, and horizontal depth inhomogeneity. Here the basic model is the extended Korteweg–de Vries equation that includes both quadratic and cubic nonlinearity (the Gardner equation) with additional terms incorporating slowly varying depth and weak rotation. The complicated interplay between these different factors is explored using an approximate adiabatic approach and then through numerical solutions of the governing variable depth, i.e., the rotating Gardner model. These results are also compared to analysis in the Korteweg–de Vries limit to highlight the effect of the cubic nonlinearity. The study explores several particular cases considered in the literature that included some of these factors to illustrate limitations. Solutions are made to illustrate the relevance of this extended Gardner model for realistic oceanic conditions.\u0000","PeriodicalId":54714,"journal":{"name":"Nonlinear Processes in Geophysics","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47403372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wenhao Fan, Haibin Song, Y. Gong, Shun-Hsing Yang, Kun Zhang
Abstract. In this paper, a regional study of mode-2 internalsolitary waves (ISWs) at the Pacific coast of Central America is carried out using the seismic reflection method. The observed relationship betweenthe dimensionless propagation speed and the dimensionless amplitude (DA) ofthe mode-2 ISW is analyzed. When DA < 1.18, the dimensionlesspropagation speed seems to increase with increasing DA, divided into two parts with different growth rates. WhenDA > 1.18, the dimensionless propagation speed increases withincreasing DA at a relatively small growth rate. Wesuggest that the influences of seawater depth (submarine topography),pycnocline depth, and pycnocline thickness on the propagation speed of themode-2 ISW in the study area cause the relationship betweendimensionless propagation speed and DA todiversify. The observed relationship between the dimensionless wavelengthand the DA of the mode-2 ISW is also analyzed. WhenDA < 1, the nondimensional wavelengths seem to change from 2.5 to 7for a fixed nondimensional amplitude. When DA > 1.87, thedimensionless wavelength increases with increasing DA. Additionally, the seawater depth has a great influence on thewavelength of the mode-2 ISW in the study area. Overall, the wavelengthincreases with increasing seawater depth. As for the vertical structureof the amplitude of the mode-2 ISW in the study area, we find that it isaffected by the nonlinearity of the ISW and the pycnocline deviation(especially the downward pycnocline deviation).
{"title":"Regional study of mode-2 internal solitary waves at the Pacific coast of Central America using marine seismic survey data","authors":"Wenhao Fan, Haibin Song, Y. Gong, Shun-Hsing Yang, Kun Zhang","doi":"10.5194/npg-29-141-2022","DOIUrl":"https://doi.org/10.5194/npg-29-141-2022","url":null,"abstract":"Abstract. In this paper, a regional study of mode-2 internal\u0000solitary waves (ISWs) at the Pacific coast of Central America is carried out using the seismic reflection method. The observed relationship between\u0000the dimensionless propagation speed and the dimensionless amplitude (DA) of\u0000the mode-2 ISW is analyzed. When DA < 1.18, the dimensionless\u0000propagation speed seems to increase with increasing DA, divided into two parts with different growth rates. When\u0000DA > 1.18, the dimensionless propagation speed increases with\u0000increasing DA at a relatively small growth rate. We\u0000suggest that the influences of seawater depth (submarine topography),\u0000pycnocline depth, and pycnocline thickness on the propagation speed of the\u0000mode-2 ISW in the study area cause the relationship between\u0000dimensionless propagation speed and DA to\u0000diversify. The observed relationship between the dimensionless wavelength\u0000and the DA of the mode-2 ISW is also analyzed. When\u0000DA < 1, the nondimensional wavelengths seem to change from 2.5 to 7\u0000for a fixed nondimensional amplitude. When DA > 1.87, the\u0000dimensionless wavelength increases with increasing DA. Additionally, the seawater depth has a great influence on the\u0000wavelength of the mode-2 ISW in the study area. Overall, the wavelength\u0000increases with increasing seawater depth. As for the vertical structure\u0000of the amplitude of the mode-2 ISW in the study area, we find that it is\u0000affected by the nonlinearity of the ISW and the pycnocline deviation\u0000(especially the downward pycnocline deviation).\u0000","PeriodicalId":54714,"journal":{"name":"Nonlinear Processes in Geophysics","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45399923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract. In numerical weather prediction (NWP), sensitivity to initial conditions brings chaotic behaviors and an intrinsic limit topredictability, but it also implies an effective control in which a smallcontrol signal grows rapidly to make a substantial difference. The ObservingSystems Simulation Experiment (OSSE) is a well-known approach to studypredictability, where “nature” is synthesized by an independent NWP model run. In this study, we extend the OSSE and design the controlsimulation experiment (CSE), where we apply a small signal to control “nature”. Idealized experiments with the Lorenz-63 three-variable system show that we can control “nature” to stay in a chosen regime withoutshifting to the other, i.e., in a chosen wing of Lorenz's butterfly attractor, by adding small perturbations to “nature”. Using longer-lead-time forecasts, we achieve more effective control with aperturbation size of less than only 3 % of the observation error. We anticipate our idealized CSE to be a starting point for a realistic CSE using the real-world NWP systems, toward possible future applications to reduceweather disaster risks. The CSE may be applied to other chaotic systemsbeyond NWP.
{"title":"Control simulation experiment with Lorenz's butterfly attractor","authors":"T. Miyoshi, Qiwen Sun","doi":"10.5194/npg-29-133-2022","DOIUrl":"https://doi.org/10.5194/npg-29-133-2022","url":null,"abstract":"Abstract. In numerical weather prediction (NWP), sensitivity to initial conditions brings chaotic behaviors and an intrinsic limit to\u0000predictability, but it also implies an effective control in which a small\u0000control signal grows rapidly to make a substantial difference. The Observing\u0000Systems Simulation Experiment (OSSE) is a well-known approach to study\u0000predictability, where “nature” is synthesized by an independent NWP model run. In this study, we extend the OSSE and design the control\u0000simulation experiment (CSE), where we apply a small signal to control “nature”. Idealized experiments with the Lorenz-63 three-variable system show that we can control “nature” to stay in a chosen regime without\u0000shifting to the other, i.e., in a chosen wing of Lorenz's butterfly attractor, by adding small perturbations to “nature”. Using longer-lead-time forecasts, we achieve more effective control with a\u0000perturbation size of less than only 3 % of the observation error. We anticipate our idealized CSE to be a starting point for a realistic CSE using the real-world NWP systems, toward possible future applications to reduce\u0000weather disaster risks. The CSE may be applied to other chaotic systems\u0000beyond NWP.\u0000","PeriodicalId":54714,"journal":{"name":"Nonlinear Processes in Geophysics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41399186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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