Influences of the inflation factors generation in the main parameters of the ensemble smoother with multiple data assimilation

Evaluating the Impact of the Inflation Factors Generation for the Ensemble Smoother With Multiple Data Assimilation

“…From Equation (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13), we obtain a value of m such that ∇O(m) = 0. This vector corresponds to the maximum a posteriori estimate of the vector of model parameters and is denoted as m map .…”

“…Opposite to the left-hand side of Equation (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15), the right-hand side of the same equation displays a matrix problem of size N d × N d , which is more feasible when N d N m , as explained before. Therefore, one may compute m map as follows:…”

“…Figure 3.7 Computed coefficients t (Equation (3)(4)(5)(6)) for v i for N e = 50 in linear and semi-log scales. Figure 3.8 Computed coefficients t (Equation (3)(4)(5)(6)) for v i for N e = 100 in linear and semi-log scales. Figure 3.9 Computed coefficients t (Equation (3)(4)(5)(6)) for v i for N e = 500 in linear and semi-log scales.…”

“…Figure 3.8 Computed coefficients t (Equation (3)(4)(5)(6)) for v i for N e = 100 in linear and semi-log scales. Figure 3.9 Computed coefficients t (Equation (3)(4)(5)(6)) for v i for N e = 500 in linear and semi-log scales. Figure 3.10 Update vector δm 1 for each inflation factor selection for the case N e = 25 and comparison with a low-order parametrization.…”

“…5. (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21) and (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22) for different ensembles.…”