In this article,we first establish a recollement related to projectively coresolved Gorenstein flat(PGF)complexes.Secondly,we define and study PGF dimension of complexes,we denote it PG F(X)for a complex X.It is shown...In this article,we first establish a recollement related to projectively coresolved Gorenstein flat(PGF)complexes.Secondly,we define and study PGF dimension of complexes,we denote it PG F(X)for a complex X.It is shown that the PGF(X)is equal to the infimum of the set{supA|there exists a diagram of morphisms of complexes A←G→X,such that G→X is a special PGF precover of X and G→A is a PGF almost isomorphism}.展开更多
Abstract In this article, the author studies the projectively flat Matsumoto metric F=α^2/(α -β), where α=√αijy^iy^j is a Riemannian metric and β =biy^i is 1-form. Theyconclude that α is locally projectively...Abstract In this article, the author studies the projectively flat Matsumoto metric F=α^2/(α -β), where α=√αijy^iy^j is a Riemannian metric and β =biy^i is 1-form. Theyconclude that α is locally projectively fiat and β is paralled with respect to α. And get the same result for the higher order approximate Matsumoto metric.展开更多
In this paper, the authors study a class of Finsler metric defined by a Rieman- nian metric and a 1-form. We find a necessary and sufficient condition for the metric to be prejectively flat.
In this paper, we study a class of Finsler metric in the form F=αexp(β/α)+εβ, where α is a Riemannian metric and β is a 1-form, ε is a constant. We call F exponential Finsler metric. We proved that exponential...In this paper, we study a class of Finsler metric in the form F=αexp(β/α)+εβ, where α is a Riemannian metric and β is a 1-form, ε is a constant. We call F exponential Finsler metric. We proved that exponential Finsler metric F is locally projectively flat if and only if α is projectively flat and β is parallel with respect to α. Moreover, we proved that the Douglas tensor of expo-nential Finsler metric F vanishes if and only if β is parallel with respect to α. And from this fact, we get that if exponential Finsler metric F is the Douglas metric, then F is not only a Berwald metric, but also a Landsberg metric.展开更多
In this paper, we consider some polynomial (a,fl)-metrics, and discuss the sufficient and necessary conditions for a Finsler metric in the form F=α+α1β+α2β^2/α+α4β^4/α^3 to be projectively flat, where ai...In this paper, we consider some polynomial (a,fl)-metrics, and discuss the sufficient and necessary conditions for a Finsler metric in the form F=α+α1β+α2β^2/α+α4β^4/α^3 to be projectively flat, where ai 0=1,2,4) are constants with a1≠0, a is a Riemannian metric and β is a 1-form. By analyzing the geodesic coefficients and the divisibility of certain polynomials, we obtain that there are only five projectively flat cases for metrics of this type. This gives a classification for such kind of Finsler metrics.展开更多
In this work, we study a class of special Finsler metrics F called arctangent Finsler metric, which is a special (α, β)-metric, where a is a Riemannian metric and β is a 1-form, We obtain a sufficient and necessa...In this work, we study a class of special Finsler metrics F called arctangent Finsler metric, which is a special (α, β)-metric, where a is a Riemannian metric and β is a 1-form, We obtain a sufficient and necessary condition that F is locally projectively fiat if and only if α and β satisfy two special equations. Furthermore we give the non-trivial solutions for F to be locally projectively fiat. Moreover, we prove that such projectively fiat Finsler metrics with constant flag curvature must be locally Minkowskian.展开更多
In this work, we study the Asanov Finsler metric F=α(β^2/α^2+gβ/α+1)^1/2exp{(G/2)arctan[β/(hα)+G/2]}, where α=(αijy^iy^i)^1/2 is a Riemannian metric and β=by^i is a 1-fom, g∈(-2,2), h=(1-g^2/4...In this work, we study the Asanov Finsler metric F=α(β^2/α^2+gβ/α+1)^1/2exp{(G/2)arctan[β/(hα)+G/2]}, where α=(αijy^iy^i)^1/2 is a Riemannian metric and β=by^i is a 1-fom, g∈(-2,2), h=(1-g^2/4)^1/2, G=g/h. We give the necessary and sufficient condition for Asanov metric to be locally projectively flat, i.e., α is projectively flat and ,Sis parallel with respect to α. Moreover, we proved that the Douglas tensor of Asanov Finsler metric vanishes if and only if β is parallel with respect to α.展开更多
In this paper, we study spherically symmetric Finsler metrics. Analyzing the solution of the projectively fiat equation, we construct a new class of projectively flat Finsler metrics.
In this paper,we find some solutions to a system of partial differential equations that characterize the projectively flat Finsler metrics.Further,we discover that some of these metrics actually have the zero flag cur...In this paper,we find some solutions to a system of partial differential equations that characterize the projectively flat Finsler metrics.Further,we discover that some of these metrics actually have the zero flag curvature.展开更多
In this paper, we study a class of Finsler metrics in the form , where is a Riemannian metric, form, and ∈ and k≠0 are constants. We obtain a sufficient and necessary condition for F to be locally projectively flat ...In this paper, we study a class of Finsler metrics in the form , where is a Riemannian metric, form, and ∈ and k≠0 are constants. We obtain a sufficient and necessary condition for F to be locally projectively flat and give the non-trivial special solutions. Moreover, it is proved that such projectively flat Finsler metrics with the constant flag curvature must be locally Minkowskian.展开更多
In this paper, we study a special class of two-dimensional Finsler metrics defined by a Riemannian metric and 1-form. We classify those which are locally projectively flat with constant flag curvature.
In recent years,the demand for synchronous acquisition of three-dimensional(3D)shape and col-or texture has surged in fields such as cultural heritage preservation and healthcare.Addressing this need,this paper propos...In recent years,the demand for synchronous acquisition of three-dimensional(3D)shape and col-or texture has surged in fields such as cultural heritage preservation and healthcare.Addressing this need,this paper proposes a novel method for simultaneous 3D shape and color texture capture.First,a linear model correlating camera exposure time with grayscale values is established.Through exposure time calibration,the projected red,green and blue(RGB)light and white-light grayscale values captured by a monochrome cam-era are aligned.Then,three sets of color fringes are projected onto the object to identify optimal pixels for 3D reconstruction.And,three pure-color patterns are projected to synthesize the color texture.Experimental res-ults show that this method effectively achieves synchronous 3D shape and color texture acquisition,offering high speed and precision,and avoids color crosstalk interference common in 3D reconstruction of colored ob-jects using a monochrome camera.展开更多
In this paper,we study and characterize locally projectively flat singular square metrics with constant flag curvature.First,we obtain the sufficient and necessary conditions that singular square metrics are locally p...In this paper,we study and characterize locally projectively flat singular square metrics with constant flag curvature.First,we obtain the sufficient and necessary conditions that singular square metrics are locally pro jectively flat.Furthermore,we classify locally pro jectively flat singular square metrics with constant flag curvature completely.展开更多
Projections of future urban land change are essential for a range of sustainability assessments,including those related to biodiversity loss,carbon emissions,and agricultural land conversion.However,to what extent and...Projections of future urban land change are essential for a range of sustainability assessments,including those related to biodiversity loss,carbon emissions,and agricultural land conversion.However,to what extent and where current projections agree or disagree remains unknown.Here,we systematically compare existing global projections that are consistent with the Shared Socioeconomic Pathways.We find that the total global urban land area is expected to increase by 112%between 2020 and 2100(averaged across all projections),with a coefficient of variation of 0.81.This variation is mostly caused by the selection of the underlying drivers that are included in the different models.Regionally,the highest average growth rates are found in sub-Saharan Africa(+679%to+730%),while this region also has the highest variation across projections(coefficient of variation ranging from 2.02 to 2.18).When ranking scenarios within a study from the highest to the lowest projected increase in urban land,rankings are relatively similar for regions in the Global North,but not for regions in the Global South.The large disagreement across projections can lead to high uncertainties in assessments of future urban land change impacts,which can undermine the effectiveness of long-term planning,policymaking,and resource management decisions.展开更多
Climate models are essential for understanding past,present,and future changes in atmospheric circulation,with circulation modes providing key sources of seasonal predictability and prediction uncertainties for both g...Climate models are essential for understanding past,present,and future changes in atmospheric circulation,with circulation modes providing key sources of seasonal predictability and prediction uncertainties for both global and regional climates.This study assesses the performance of models participating in phase 6 of the Coupled Model Intercomparison Project in simulating interannual variability modes of Northern Hemisphere 500-hPa geopotential height during winter and summer,distinguishing predictable(potentially predictable on seasonal or longer timescales)and unpredictable(intraseasonal and essentially unpredictable at long range)components,using reanalysis data and a variance decomposition method.Although most models effectively capture unpredictable modes in reanalysis,their ability to reproduce dominant predictable modes-specifically the Pacific-North American pattern,Arctic Oscillation,and Western Pacific Oscillation in winter,and the East Atlantic and North Atlantic Oscillations in summer-varies notably.An optimal ensemble is identified to distinguish(a)predictable-external modes,dominated by external forcing,and(b)predictable-internal modes,associated with slow internal variability,during the historical period(1950-2014)and the SSP5-8.5 scenario(2036-2100).Under increased radiative forcing,the leading winter/summer predictable-external mode exhibits a more uniform spatial distribution,remarkably larger trend and annual variance,and enhanced height-sea surface temperature(SST)covariance under SSP5-8.5 compared to historical conditions.The dominant winter/summer predictable-internal modes also exhibit increased variance and height-SST covariance under SSP5-8.5,along with localized changes in spatial configuration.Minimal changes are observed in spatial distribution or variance for dominant winter/summer unpredictable modes under SSP5-8.5.This study,from a predictive perspective,deepens our understanding of model uncertainties and projected changes in circulations.展开更多
Purpose-Interface management is the process of managing communications,responsibilities and coordination of project parties,phases or physical entities which are dependent on one another.Interface management is a cruc...Purpose-Interface management is the process of managing communications,responsibilities and coordination of project parties,phases or physical entities which are dependent on one another.Interface management is a crucial part of managing any construction project-but particularly important for high-speed railway projects that often have several contractual parties and stakeholders,very long project timelines and huge upfront cost overlays.This paper discusses how various project interfaces were managed during the design and construction of the civil engineering infrastructure for the High Speed Two(HS2)project in the United Kingdom.Design/methodology/approach-The paper uses the case study methodology.Key interfaces on the HS2 project are grouped into various categories and the paper discusses how they were managed within the Area North Integrated Project Team(IPT)of the HS2 project made up of contractor Balfour Beatty VINCI(BBV),the Mott MacDonald SYSTRA Design Joint Venture(DJV)and client HS2 Ltd.3 different case studies drawn from across the IPT are used,each of them highlighting different interfaces and how these interfaces were managed.Findings-The paper shows how innovative technical designs and modern methods of construction were used to address some of the unique and peculiar challenges of designing a brand-new railway in the United Kingdom.Addressing the contrasting and often competing requirements of different stakeholders,coupled with challenging physical constraints of the very limited land available for the project and the use of a rarely used Act of Parliament in the delivery of the project required different approach to interface management.Collaboration and proactive stakeholder engagement are necessary for successful interface management on megaprojects.The authors posit that adopting an integrated approach to engineering and construction management is an essential ingredient for the successful delivery of high-speed railway projects.Originality/value-With many high-speed railway projects around the world coming up in the next few years,understanding the context and challenges for each country will help engineering and design managers adopt appropriate approaches for their projects.The lessons learned on the HS2 project are also transferable to other mega infrastructure projects with complex project interfaces.展开更多
Global warming induced by increased CO_(2) has caused marked changes in the ocean.Previous estimates of ocean salinity change in response to global warming have considerable ambiguity,largely attributable to the diver...Global warming induced by increased CO_(2) has caused marked changes in the ocean.Previous estimates of ocean salinity change in response to global warming have considerable ambiguity,largely attributable to the diverse sensitivities of surface fluxes.This study utilizes data from the Flux-Anomaly-Forced Model Intercomparison Project to investigate how ocean salinity responds to perturbations of surface fluxes.The findings indicate the emergence of a sea surface salinity(SSS)dipole pattern predominantly in the North Atlantic and Pacific fresh pools,driven by surface flux perturbations.This results in an intensification of the“salty gets saltier and fresh gets fresher”SSS pattern across the global ocean.The spatial pattern amplification(PA)of SSS under global warming is estimated to be approximately 11.5%,with surface water flux perturbations being the most significant contributor to salinity PA,accounting for 8.1% of the change after 70 years in experiments since pre-industrial control(piControl).Notably,the zonal-depth distribution of salinity in the upper ocean exhibits lighter seawater above the denser water,with bowed isopycnals in the upper 400 m.This stable stratification inhibits vertical mixing of salinity and temperature.In response to the flux perturbations,there is a strong positive feedback due to consequent freshening.It is hypothesized that under global warming,an SSS amplification of 7.2%/℃ and a mixed-layer depth amplification of 12.5%/℃ will occur in the global ocean.It suggests that the salinity effect can exert a more stable ocean to hinder the downward transfer of heat,which provides positive feedback to future global warming.展开更多
基金Supported by the National Natural Science Foundation of China(12061061)Young Talents Team Project of Gansu Province(2025QNTD49)+1 种基金Lanshan Talents Project of Northwest Minzu University(Xbmulsrc202412)Longyuan Young Talents of Gansu Province。
文摘In this article,we first establish a recollement related to projectively coresolved Gorenstein flat(PGF)complexes.Secondly,we define and study PGF dimension of complexes,we denote it PG F(X)for a complex X.It is shown that the PGF(X)is equal to the infimum of the set{supA|there exists a diagram of morphisms of complexes A←G→X,such that G→X is a special PGF precover of X and G→A is a PGF almost isomorphism}.
文摘Abstract In this article, the author studies the projectively flat Matsumoto metric F=α^2/(α -β), where α=√αijy^iy^j is a Riemannian metric and β =biy^i is 1-form. Theyconclude that α is locally projectively fiat and β is paralled with respect to α. And get the same result for the higher order approximate Matsumoto metric.
基金Supported by the National Natural Science Foundation of China (Grant No.11071005)
文摘In this paper, the authors study a class of Finsler metric defined by a Rieman- nian metric and a 1-form. We find a necessary and sufficient condition for the metric to be prejectively flat.
基金Project (No. 10571154) supported by the National Natural ScienceFoundation of China
文摘In this paper, we study a class of Finsler metric in the form F=αexp(β/α)+εβ, where α is a Riemannian metric and β is a 1-form, ε is a constant. We call F exponential Finsler metric. We proved that exponential Finsler metric F is locally projectively flat if and only if α is projectively flat and β is parallel with respect to α. Moreover, we proved that the Douglas tensor of expo-nential Finsler metric F vanishes if and only if β is parallel with respect to α. And from this fact, we get that if exponential Finsler metric F is the Douglas metric, then F is not only a Berwald metric, but also a Landsberg metric.
文摘In this paper, we consider some polynomial (a,fl)-metrics, and discuss the sufficient and necessary conditions for a Finsler metric in the form F=α+α1β+α2β^2/α+α4β^4/α^3 to be projectively flat, where ai 0=1,2,4) are constants with a1≠0, a is a Riemannian metric and β is a 1-form. By analyzing the geodesic coefficients and the divisibility of certain polynomials, we obtain that there are only five projectively flat cases for metrics of this type. This gives a classification for such kind of Finsler metrics.
基金Project (No. 10571154) supported by the National Natural Science Foundation of China
文摘In this work, we study a class of special Finsler metrics F called arctangent Finsler metric, which is a special (α, β)-metric, where a is a Riemannian metric and β is a 1-form, We obtain a sufficient and necessary condition that F is locally projectively fiat if and only if α and β satisfy two special equations. Furthermore we give the non-trivial solutions for F to be locally projectively fiat. Moreover, we prove that such projectively fiat Finsler metrics with constant flag curvature must be locally Minkowskian.
基金Project (No. 10571154) supported by the National Natural Science Foundation of China
文摘In this work, we study the Asanov Finsler metric F=α(β^2/α^2+gβ/α+1)^1/2exp{(G/2)arctan[β/(hα)+G/2]}, where α=(αijy^iy^i)^1/2 is a Riemannian metric and β=by^i is a 1-fom, g∈(-2,2), h=(1-g^2/4)^1/2, G=g/h. We give the necessary and sufficient condition for Asanov metric to be locally projectively flat, i.e., α is projectively flat and ,Sis parallel with respect to α. Moreover, we proved that the Douglas tensor of Asanov Finsler metric vanishes if and only if β is parallel with respect to α.
基金Supported by the National Natural Science Foundation of China(Grant No.11071005)
文摘In this paper, we study spherically symmetric Finsler metrics. Analyzing the solution of the projectively fiat equation, we construct a new class of projectively flat Finsler metrics.
基金supported by the National Natural Science Foundation of China(Grant Nos.10371138&10471001).
文摘In this paper,we find some solutions to a system of partial differential equations that characterize the projectively flat Finsler metrics.Further,we discover that some of these metrics actually have the zero flag curvature.
基金This work was supported by the National Natural Science Foundation of China (Grant No.10571154).
文摘In this paper, we study a class of Finsler metrics in the form , where is a Riemannian metric, form, and ∈ and k≠0 are constants. We obtain a sufficient and necessary condition for F to be locally projectively flat and give the non-trivial special solutions. Moreover, it is proved that such projectively flat Finsler metrics with the constant flag curvature must be locally Minkowskian.
基金Supported by the Fundamental Research Funds for the Central Universities
文摘In this paper, we study a special class of two-dimensional Finsler metrics defined by a Riemannian metric and 1-form. We classify those which are locally projectively flat with constant flag curvature.
文摘In recent years,the demand for synchronous acquisition of three-dimensional(3D)shape and col-or texture has surged in fields such as cultural heritage preservation and healthcare.Addressing this need,this paper proposes a novel method for simultaneous 3D shape and color texture capture.First,a linear model correlating camera exposure time with grayscale values is established.Through exposure time calibration,the projected red,green and blue(RGB)light and white-light grayscale values captured by a monochrome cam-era are aligned.Then,three sets of color fringes are projected onto the object to identify optimal pixels for 3D reconstruction.And,three pure-color patterns are projected to synthesize the color texture.Experimental res-ults show that this method effectively achieves synchronous 3D shape and color texture acquisition,offering high speed and precision,and avoids color crosstalk interference common in 3D reconstruction of colored ob-jects using a monochrome camera.
基金Supported by the National Natural Science Foundation of China(Grant No.11871126)the Science Foundation of Chongqing Normal University(Grant No.17XLB022)。
文摘In this paper,we study and characterize locally projectively flat singular square metrics with constant flag curvature.First,we obtain the sufficient and necessary conditions that singular square metrics are locally pro jectively flat.Furthermore,we classify locally pro jectively flat singular square metrics with constant flag curvature completely.
基金supported by the Netherlands Organization for Scientific Research NWO in the form of a VIDI grant(Grant No.VI.Vidi.198.008).
文摘Projections of future urban land change are essential for a range of sustainability assessments,including those related to biodiversity loss,carbon emissions,and agricultural land conversion.However,to what extent and where current projections agree or disagree remains unknown.Here,we systematically compare existing global projections that are consistent with the Shared Socioeconomic Pathways.We find that the total global urban land area is expected to increase by 112%between 2020 and 2100(averaged across all projections),with a coefficient of variation of 0.81.This variation is mostly caused by the selection of the underlying drivers that are included in the different models.Regionally,the highest average growth rates are found in sub-Saharan Africa(+679%to+730%),while this region also has the highest variation across projections(coefficient of variation ranging from 2.02 to 2.18).When ranking scenarios within a study from the highest to the lowest projected increase in urban land,rankings are relatively similar for regions in the Global North,but not for regions in the Global South.The large disagreement across projections can lead to high uncertainties in assessments of future urban land change impacts,which can undermine the effectiveness of long-term planning,policymaking,and resource management decisions.
基金supported by the National Natural Science Foundation of China(Grant Nos.U2342210 and 42275043)the National Institute of Natural Hazards,Ministry of Emergency Management of China(Grant Nos.J2223806,ZDJ2024-25 and ZDJ2025-34)。
文摘Climate models are essential for understanding past,present,and future changes in atmospheric circulation,with circulation modes providing key sources of seasonal predictability and prediction uncertainties for both global and regional climates.This study assesses the performance of models participating in phase 6 of the Coupled Model Intercomparison Project in simulating interannual variability modes of Northern Hemisphere 500-hPa geopotential height during winter and summer,distinguishing predictable(potentially predictable on seasonal or longer timescales)and unpredictable(intraseasonal and essentially unpredictable at long range)components,using reanalysis data and a variance decomposition method.Although most models effectively capture unpredictable modes in reanalysis,their ability to reproduce dominant predictable modes-specifically the Pacific-North American pattern,Arctic Oscillation,and Western Pacific Oscillation in winter,and the East Atlantic and North Atlantic Oscillations in summer-varies notably.An optimal ensemble is identified to distinguish(a)predictable-external modes,dominated by external forcing,and(b)predictable-internal modes,associated with slow internal variability,during the historical period(1950-2014)and the SSP5-8.5 scenario(2036-2100).Under increased radiative forcing,the leading winter/summer predictable-external mode exhibits a more uniform spatial distribution,remarkably larger trend and annual variance,and enhanced height-sea surface temperature(SST)covariance under SSP5-8.5 compared to historical conditions.The dominant winter/summer predictable-internal modes also exhibit increased variance and height-SST covariance under SSP5-8.5,along with localized changes in spatial configuration.Minimal changes are observed in spatial distribution or variance for dominant winter/summer unpredictable modes under SSP5-8.5.This study,from a predictive perspective,deepens our understanding of model uncertainties and projected changes in circulations.
文摘Purpose-Interface management is the process of managing communications,responsibilities and coordination of project parties,phases or physical entities which are dependent on one another.Interface management is a crucial part of managing any construction project-but particularly important for high-speed railway projects that often have several contractual parties and stakeholders,very long project timelines and huge upfront cost overlays.This paper discusses how various project interfaces were managed during the design and construction of the civil engineering infrastructure for the High Speed Two(HS2)project in the United Kingdom.Design/methodology/approach-The paper uses the case study methodology.Key interfaces on the HS2 project are grouped into various categories and the paper discusses how they were managed within the Area North Integrated Project Team(IPT)of the HS2 project made up of contractor Balfour Beatty VINCI(BBV),the Mott MacDonald SYSTRA Design Joint Venture(DJV)and client HS2 Ltd.3 different case studies drawn from across the IPT are used,each of them highlighting different interfaces and how these interfaces were managed.Findings-The paper shows how innovative technical designs and modern methods of construction were used to address some of the unique and peculiar challenges of designing a brand-new railway in the United Kingdom.Addressing the contrasting and often competing requirements of different stakeholders,coupled with challenging physical constraints of the very limited land available for the project and the use of a rarely used Act of Parliament in the delivery of the project required different approach to interface management.Collaboration and proactive stakeholder engagement are necessary for successful interface management on megaprojects.The authors posit that adopting an integrated approach to engineering and construction management is an essential ingredient for the successful delivery of high-speed railway projects.Originality/value-With many high-speed railway projects around the world coming up in the next few years,understanding the context and challenges for each country will help engineering and design managers adopt appropriate approaches for their projects.The lessons learned on the HS2 project are also transferable to other mega infrastructure projects with complex project interfaces.
基金supported by the Laoshan Laboratory[grant number LSKJ202202403]the National Natural Science Foundation of China[grant number 42030410]+1 种基金additionally supported by the Startup Foundation for Introducing Talent of NUISTJiangsu Innovation Research Group[grant number JSSCTD202346]。
文摘Global warming induced by increased CO_(2) has caused marked changes in the ocean.Previous estimates of ocean salinity change in response to global warming have considerable ambiguity,largely attributable to the diverse sensitivities of surface fluxes.This study utilizes data from the Flux-Anomaly-Forced Model Intercomparison Project to investigate how ocean salinity responds to perturbations of surface fluxes.The findings indicate the emergence of a sea surface salinity(SSS)dipole pattern predominantly in the North Atlantic and Pacific fresh pools,driven by surface flux perturbations.This results in an intensification of the“salty gets saltier and fresh gets fresher”SSS pattern across the global ocean.The spatial pattern amplification(PA)of SSS under global warming is estimated to be approximately 11.5%,with surface water flux perturbations being the most significant contributor to salinity PA,accounting for 8.1% of the change after 70 years in experiments since pre-industrial control(piControl).Notably,the zonal-depth distribution of salinity in the upper ocean exhibits lighter seawater above the denser water,with bowed isopycnals in the upper 400 m.This stable stratification inhibits vertical mixing of salinity and temperature.In response to the flux perturbations,there is a strong positive feedback due to consequent freshening.It is hypothesized that under global warming,an SSS amplification of 7.2%/℃ and a mixed-layer depth amplification of 12.5%/℃ will occur in the global ocean.It suggests that the salinity effect can exert a more stable ocean to hinder the downward transfer of heat,which provides positive feedback to future global warming.