Maximum Likelihood Ensemble Filter application to carbon problems

Maximum Likelihood Ensemble Filter: application to carbon problems Prepared by Dusanka Zupanski and ……

Maximum Likelihood Ensemble Filter (MLEF) (Zupanski 2005; Zupanski and Zupanski 2005) Developed using ideas from: ØVariational data assimilation (3 DVAR, 4 DVAR) ØIterated Kalman Filters ØEnsemble Transform Kalman Filter (ETKF, Bishop et al. 2001) Characteristics of the MLEF ØCalculates optimal estimates of: - model state variables (e. g. , carbon fluxes, sources, sinks) - empirical parameters (e. g. , light response, allocation, drought stress) - model error (bias) - boundary conditions error (lateral, top, bottom boundaries) ØCalculates ØFully uncertainty of all estimates non-linear approach. Adjoint models are not needed. ØProvides more information about PDF (higher order moments could be calculated from ensemble perturbations) ØNon-derivative minimization (first variation instead of first derivative is used). Dusanka Zupanski, CIRA/CSU Zupanski@CIRA. colostate. edu

MLEF APPROACH Minimize cost function J Change of variable (preconditioning) - model state vector of dim Nstate >>Nens - control vector in ensemble space of dim Nens - information matrix of dim Nens Dusanka Zupanski, CIRA/CSU Zupanski@CIRA. colostate. edu

MLEF APPROACH (continued) Analysis error covariance Forecast model M essential for propagating in time (updating) Dusanka Zupanski, columns of Pf. CIRA/CSU Zupanski@CIRA. colostate. edu

Ideal Hessian Preconditioning VARIATIONAL MLEF Milija Zupanski, CIRA/CSU Zupanski. M@CIRA. colostate. edu

STATE AUGMENTATION APPROACH as a part of the MLEF Example: parameter estimation - augmented state variable - augmented forecast model Parameters are randomly perturbed only in the first cycle. In later cycles, the MLEF updates ensemble perturbations. Assumption: parameter remains constant, or changes slowly with time SAME FRAMEWORK IS USED FOR MODEL BIAS ESTIMATION (use bias instead of a parameter to augment state variable)

Applications of the MLEF to carbon studies ØTRANSCOM - …. -…. (Ravi, perhaps you can include a couple of bullets for Transcom) ØSi. B Parameter estimation - Estimate control parameters on the fluxes - MLEF calculates uncertainties of all parameters (in terms of Pa and Pf) ØLPDM - Estimate monthly mean carbon fluxes, empirical parameters - Estimate uncertainties of the mean fluxes and empirical parameters ØSi. B-CASA-RAMS - Use various observations of weather, eddy-covariance fluxes, CO 2 - Estimate carbon fluxes, empirical parameters (e. g. , light response, allocation, drought stress, phonological triggers) - Time evolution of state variables, provided by the coupled model, is critical for updating Pf Dusanka Zupanski, CIRA/CSU Zupanski@CIRA. colostate. edu

TRANSCOM Ravi, you might want to add more detail about TRANSCOM Dusanka Zupanski, CIRA/CSU Zupanski@CIRA. colostate. edu

Preliminary results using RAMS ØHurricane Lili case Ø 35 1 -h DA cycles: 13 UTC 1 Oct 2002 – 00 UTC 3 Oct Ø 30 x 21 grid points, 15 km grid distance (in the Gulf of Mexico) ØControl variable: u, v, w, theta, Exner, r_total (dim=54000) ØModel simulated observations with random noise (7200 obs per DA cycle) ØNens=50 ØIterative minimization of J (1 iteration only) RMS errors of the analysis (control experiment without assimilation) Hurricane entered the model domain. Impact of assimilation more pronounced. Dusanka Zupanski, CIRA/CSU Zupanski@CIRA. colostate. edu

Example: Total humidity mixing ratio, level=200 m, cycle 31 TRUTH NO ASSIMILATION Locations of min and max centers are much improved in the experiment with assimilation.

SUMMARY The MLEF is currently being evaluated in various atmospheric science applications, showing encouraging results. Ø The MLEF is suitable for assimilation of numerous new carbon observations, employing complex non-linear coupled models. Ø Work in carbon applications has just started. Results will be presented in the future. Ø Dusanka Zupanski, CIRA/CSU Zupanski@CIRA. colostate. edu