Data assimilation and ensemble method applied to Upernavik Isstrom
Authors: Jager Eliot , Gillet-Chaulet Fabien , Mouginot Jérémie 
Published: March 2021

&lt;p&gt;Lack of observation is one of the main limitations for improving model prediction in glaciology. However, over the past few years, the amount of observations from satellites has increased at a phenomenal rate. Hopefully, this amount of data will allow to validate the models and their parameterizations. In addition, data assimilation seems to be an optimal method to combine the model and these frequent observations, allowing to reduce the uncertainties of the model and thus potentially improve the projections. While inverse methods are now common in glaciology to infer uncertain parameters from observed surface velocities acquired at a given date, transient data assimilation algorithms are still under development. Recently, the performance of an Ensemble Kalman Filter has been studied on a synthetic case. Here, the goal of this study is to investigate the feasibility of applying this assimilation scheme on a real case : evolution of Upernavik Isstr&amp;#248;m since 1985 using the open source finite element software Elmer/Ice. To do so, we first need to generate an ensemble of simulations that sample the model uncertainties and to evaluate this ensemble against available observations.&lt;/p&gt;&lt;p&gt;We first assemble a set of observations that will serve for model setup and validation. In this sense, we have collected ice velocity measurements, from optical and radar source, surface elevation and bed topography, ice front position and surface mass balance that give us a fairly good a priori knowledge of the evolution of Upernavik Isstr&amp;#248;m between 1985 and 2020. These datasets are divided into two parts : one is used to better characterize and set up the initial state of the system, and the other is used to evaluate model outputs.&lt;/p&gt;&lt;p&gt;Uncertainties in the model comes from different sources: (i) the model parameters, (ii) the initial topography as the surface elevation in 1985 is only partially known, and (iii) the forcings (i.e. the surface mass balance, the ice front position).&lt;br&gt;For the model parameters we take into account uncertainties in the ice rheology by perturbing the Glen&amp;#8217;s enhancement factor and by generating an ensemble of friction coefficients for different friction laws using a set of inversions that has been performed for the whole Greenland using present day observations. Using these perturbed parameters and a set of surface mass balance representative of the period we generate and evaluate an ensemble of initial topographies for 1985.&lt;/p&gt;&lt;p&gt;&lt;br&gt;With this ensemble of initial states, we perform transient simulations where the position of glacier terminus and a set of perturbed SMB are prescribed each year. Each simulation is scored with specifically designed metrics in terms of dynamics and geometry using the observations described previously. This analysis allows to evaluate the impact of different sources of uncertainty on the transient simulation. Using the results of this study, we will discuss the capacity of Elmer/Ice to reconstruct the trend of the evolution of Upernavik Isstr&amp;#248;m and the possibility to perform transient data assimilation.&lt;/p&gt;