Model calibration for ice sheets and glaciers dynamics: a general theory of inverse problems in glaciology

摘要: Abstract. Numerical modelling of the dynamic evolution ice sheets and glaciers requires solution discrete equations which are based on physical principles (e.g. conservation mass, linear momentum energy) phenomenological constitutive laws Glen's Fourier's laws). These must be accompanied by information forcing term initial boundary conditions (IBCs) velocity, stress temperature; other hand involve many parameters, some depend thermodynamical state. The proper forecast dynamics a precise knowledge several quantities appear in IBCs, terms laws. As these cannot easily measured at study scale field, they often obtained through model calibration solving an inverse problem (IP). objective this paper is to provide thorough rigorous conceptual framework for IPs cryospheric studies particular: clarify role experimental monitoring data determine targets values parameters that can considered fixed; define characterise identifiability, property related forward problem; well-posedness correct way, without confusing instability with ill-conditioning or properties method applied compute solution; cast sensitivity analysis general differentiate between computation local indicators one-at-a-time approach first-order consider whole possible variability parameters. relevant illustrated means simple numerical example isothermal flow, shallow-ice approximation.