TY - JOUR
T1 - Ensemble-type Kalman filter algorithm conserving mass, total energy and enstrophy
AU - Zeng, Yuefei
AU - Janjic, Tijana
AU - Ruckstuhl, Yvonne
AU - Verlaan, Martin
PY - 2017
Y1 - 2017
N2 - For numerical discretization schemes, the violation of enstrophy conservation causes a systematic and unrealistic energy cascade towards high wave numbers. The same occurs in data assimilation schemes, where the total energy, enstrophy and divergence could be strongly affected. In this article, we construct an ensemble data assimilation algorithm that conserves mass, total energy and enstrophy. The algorithm uses B-spline functions for localization and sequential quadratic programming to solve nonlinear constrained minimization problem. Idealized experiments are performed using a 2D shallow-water model, with selected contraints derived from the nature run. It is found that all experiments exhibit comparable root-mean-square errors, with a slight advantage for those that include the conservation constraint on the globally integrated enstrophy. However, the kinetic energy and enstrophy spectra in experiments with the enstrophy constraint are considerably closer to the true spectra, in particular at the smallest resolvable scales. Therefore, imposing conservation of enstrophy within the data assimilation algorithm effectively avoids the spurious energy cascade of the rotational part and thereby successfully suppresses the noise generated by the data assimilation algorithm. The 14 day deterministic free forecast, starting from the initial condition enforced by both total energy and enstrophy constraints, produces the best prediction. The same holds for the ensemble free forecasts.
AB - For numerical discretization schemes, the violation of enstrophy conservation causes a systematic and unrealistic energy cascade towards high wave numbers. The same occurs in data assimilation schemes, where the total energy, enstrophy and divergence could be strongly affected. In this article, we construct an ensemble data assimilation algorithm that conserves mass, total energy and enstrophy. The algorithm uses B-spline functions for localization and sequential quadratic programming to solve nonlinear constrained minimization problem. Idealized experiments are performed using a 2D shallow-water model, with selected contraints derived from the nature run. It is found that all experiments exhibit comparable root-mean-square errors, with a slight advantage for those that include the conservation constraint on the globally integrated enstrophy. However, the kinetic energy and enstrophy spectra in experiments with the enstrophy constraint are considerably closer to the true spectra, in particular at the smallest resolvable scales. Therefore, imposing conservation of enstrophy within the data assimilation algorithm effectively avoids the spurious energy cascade of the rotational part and thereby successfully suppresses the noise generated by the data assimilation algorithm. The 14 day deterministic free forecast, starting from the initial condition enforced by both total energy and enstrophy constraints, produces the best prediction. The same holds for the ensemble free forecasts.
KW - B-spline
KW - conservation laws
KW - enstrophy
KW - kinetic energy spectrum
KW - localization
KW - noise
KW - SQP
KW - total energy
UR - http://www.scopus.com/inward/record.url?scp=85034646942&partnerID=8YFLogxK
U2 - 10.1002/qj.3142
DO - 10.1002/qj.3142
M3 - Article
AN - SCOPUS:85034646942
SN - 0035-9009
VL - 143
SP - 2902
EP - 2914
JO - Royal Meteorological Society. Quarterly Journal (online)
JF - Royal Meteorological Society. Quarterly Journal (online)
IS - 708 Part A
ER -