Sea level changes play an important role in current climate change and cause serious economic consequences.It is crucial to determine the rate at which the sea level rises.Traditionally,least squares method is used to calculate the linear trend of sea level changes for a common period.However,a recent study has shown that least squares method is sensitive to the interannual variability.For example,the global mean sea level(GMSL)rate for 20032011 increases from 2.4 mm·a~(-1) to 3.3mm·a~(-1) after the interannual variability is corrected.It is well known that sea level changes are non-stationary,which means that the rate varies with time.To exclude the effect of interannual variability and reveal the temporal evolution of the rate of GMSL,we propose a method for computing the instantaneous rate of sea level rise.Firstly,we use Ensemble Empirical Mode Decomposition(EEMD)to extract the non-linear trend from time series of sea level.The combination of the last two intrinsic functions is treated as the non-linear trend.Then we use cubic Spline smoothing to fit the non-linear trend.The first-order derivative derived by cubic Spline smoothing is the instantaneous rate.This method is applied to the GMSL time series(20022014)from an inversion result which can close the sea level budget on global scale.This inversion result divided the GMSL into six components including steric sea level,ocean mass contributions from Greenland,Antarctica,glaciers and land hydrology,and a non-stochastic residual signal.Our results show that the instantaneous rate of GMSL slowly decreases from 2.7 to 2.5mm·a~(-1) during 20022010.After 2010,the rate of GMSL rapidly increases to 3.8mm·a~(-1) in November 2014.The overall linear trend of steric GMSL is 1.38mm·a~(-1) which is greater than previous studies,however,its instantaneous rate suggests a descending trend.The steric rate decreases from 1.6mm·a~(-1) at 2002 to 1.0 mm·a~(-1) at 2014.The rate of Greenland's contribution to GMSL increases from 0.51 to 0.87mm·a~(-1) during 20022012,and becomes relative stable during 20122014.Antarctica' s contribution to GMSL experiences an overall increase in the instantaneous rate which increases from 0.13 to 0.34 mm·a~(-1) for the period 20022014.The contribution from glacier indicates a slightly decreased trend for 20022012,declining from 0.43 to 0.35mm·a~(-1).In contrast to the other mass contributions,hydrology has slowed down the GMSL rise.We note,however,the mitigation is becoming smaller and smaller during 20022012.The instantaneous rate increases from-0.24 to-0.02mm·a~(-1).Hydrology starts to make positive contributions to sea level rise after 2013.To close the sea level budget,a non-stochastic residual signal is necessarily derived.This signal only shows an overall trend of 0.22mm·a~(-1) during 20022014.However,we find that the instantaneous rate increases rapidly from 0.16 to 0.82mm·a~(-1) for the period 20102014.If we attribute this residual signal to the mass-induced sea level rise,then the mass contributions to GMSL is about 70%in 2014.