Further Study Of The Eddy Heat Flux Approximation Theory Of Stratospheric Temperature Variatio

Under quasigeostrophic scaling,the eddy heat flux approximation theory within the transformed Eulerian-mean framework is usually utilized to calculate the dynamical and radiative heating contributions to the Arctic stratospheric temperature changes,but this may bring certain error.In this paper,according to a new area-weighted averaged thermodynamic equation within the Eulerian-mean framework proposed by Liu and Fu(2019),a monthly temperature change equation is constructed by time-sliding accumulation.Then using three sets of reanalysis data(ERA-Interim,ERA5 and MERRA-2),we calculate the climatological monthly temperature increment,dynamical heating,diabatic heating and convective heating term(W term)of the new equation at 100 h Pa in the Arctic lower stratosphere,respectively,during the whole period 1981—2018 and two sub-periods(1981—1999 and 2000—2018),and carry out the balance test.Next,the contribution and physical significance of the newly derived W term are analyzed,and then the optimal conditions for the establishment of the eddy heat flux approximation theory are given.Finally,the equation is applied in the stratosphere of the Northern Hemisphere to quantitatively explain the cause of temperature trend change.The main conclusions are summarized as follows:(1)Compared with the eddy heat flux approximation theory,the new form of temperature change equation only increases the W term,but during different periods,the newly derived W term reduces the imbalance between the Arctic temperature increment term and the sum of cumulative dynamical and diabatic heating by half in winter and spring.(2)At 100 h Pa,W term and its correlation with temperature increment change with month and latitude,nontrivial especially in winter and spring,which contributes significantly to temperature change and has strong correlation.As the weighted average of the area of the vertical component of the mean meridional circulation,the W term is directly proportional to the mass flow function at the reference latitude,thus indicating that the W term can be interpreted as either net adiabatic heating or net vertical mass transport.Therefore,the best reference latitude for the eddy heat flux approximation theory should be near the zero contour line of the W term.Further verification also shows that the sum of the action terms of the eddy heat flux approximation theory is basically equal to the sum of the action terms of the new form of temperature change equation when the reference latitude is taken at 50°N.In addition,different integration time scales will also have an impact on the accurate use of the eddy heat flux approximation theory.The shorter the integration time scale,the smaller the imbalance between the temperature increment and the sum of each action item.(3)In the extension and application of the eddy heat flux approximation theory and the new form of temperature change equation,multiple regression can be used to separate each action item of the stratospheric temperature trend,so as to quantitatively explain the contribution of each action item to the stratospheric monthly temperature.When the reference latitude is taken at 60°N,the current monthly temperature trend change can be explained by using the dynamical,diabatic heating and W term,that is,using the new form of temperature change equation;When the reference latitude is taken at 50°N,the current monthly temperature trend can be explained only by the dynamical and diabatic heating term,that is,the eddy heat flux approximation theory.