Evaluation of conditional non-linear optimal perturbation obtained by an ensemble-based approach using the Lorenz-63 model

Abstract

A B S T R A C TThe authors propose to implement conditional non-linear optimal perturbation related to model parameters (CNOP-P) through an ensemble-based approach. The approach was first used in our earlier study and is improved to be suitable for calculating CNOP-P. Idealised experiments using the Lorenz-63 model are conducted to evaluate the performance of the improved ensemble-based approach. The results show that the maximum prediction error after optimisation has been multiplied manifold compared with the initial-guess prediction error, and is extremely close to, or greater than, the maximum value of the exhaustive attack method (a million random samples). The calculation of CNOP-P by the ensemble-based approach is capable of maintaining a high accuracy over a long prediction time under different constraints and initial conditions. Further, the CNOP-P obtained by the approach is applied to sensitivity analysis of the Lorenz-63 model. The sensitivity analysis indicates that when the prediction time is set to 0.2 time units, the Lorenz-63 model becomes extremely insensitive to one parameter, which leaves the other two parameters to affect the uncertainty of the model. Finally, a serial of parameter estimation experiments are performed to verify sensitivity analysis. It is found that when the three parameters are estimated simultaneously, the insensitive parameter is estimated much worse, but the Lorenz-63 model can still generate a very good simulation thanks to the relatively accurate values of the other two parameters. When only two sensitive parameters are estimated simultaneously and the insensitive parameter is left to be non-optimised, the outcome is better than the case when the three parameters are estimated simultaneously. With the increase of prediction time and observation, however, the model sensitivity to the insensitive parameter increases accordingly and the insensitive parameter can also be estimated successfully.

Sensitivity and resilience of the climate system: A conditional nonlinear optimization approach

“…However, it is still a computational challenge to determine a CNOP for a global climate model. Recently, an ensemble method has been proposed to determine CNOPs [28] which can be promising to address this challenge. 2.…”

A New Scheme for Capturing Global Conditional Nonlinear Optimal Perturbation

“…The PAIG-CNOP method uses the settings P = 4 and N = 15. Set the number of ensemble members n = 3 [37,48] of the initial perturbation matrix in the EN-CNOP method. Notice that in Equation ( 13) the sampling errors of B T0 , B 0T and B 00 have no determinant influence since only n = 3 non-colinear perturbation directions are needed to estimate the cost function gradient.…”

A new application of conditional nonlinear optimal perturbation approach to boundary condition uncertainty

“…To obtain the CNOP, we have to solve the optimization problem (3). Optimization algorithms such as Sequential Quadratic Programming (SQP) [ Powell , ] and Spectral Projected Gradient (SPG) [ Birgin et al ., ] are useful, and have been frequently employed to obtain CNOP‐I and CNOP‐P [ Mu et al ., ; Mu and Zhang , ; Yin et al ., ]. In these algorithms, the knowledge of the gradient of the objective function is necessary for identifying the maximal value.…”