Ensemble Data Assimilation (EnsDA) with Maximum Likelihood Ensemble Filter (MLEF)

Purpose of this Documentation:

This documentation is prepared to give some introductory information for the MLEF program. It includes:

• Make files
• Scripts
• Fortran Code

What is Data Assimilation:

1. Method of defining optimal initial conditions (classic definition)
2. Model error estimation method
3. Model development tool (estimate and correct model errors during the model development phase)
4. PDF estimation

Note that there are many data assimilation techniques. Some of them are - Optimal Interpolation, 3D Variational, 4D Variational. For the details of these methods consider reference [1].

What is Ensemble Data Assimilation (EnsDA):

Probabilistic approach to data assimilation and forecasting.

MLEF Provides the following:

• Optimal solution or state estimate (e. g., optimal CO₂ analysis)
• Optimal estimates of model error and empirical parameters
• Uncertainty of the analysis (a component of the analysis error covariance Pa)
• Uncertainty of the estimated model error and parameters (components of the analysis error covariance Pa
• Estimate of forecast uncertainty (the forecast error covariance Pf)

4D Variational Method versus EnsDA

There are two approaches for Ensemble Data Assimilation (EnsDA)

1. Maximum likelihood approach (involves an iterative minimization of a functional) (Zupanski 2005, MWR)
2. Minimum variance approach (calculates ensemble mean)

Some of the Critical Issues are:

• Uses only non-linear models (tangent-linear, adjoint models are not needed)
• Iterative minimization is beneficial for non-linear processes
• Estimate and correct all major sources of uncertainty: initial conditions, model error, boundary conditions, empirical parameters
• Unified algorithm: MLEF+state augmentation approach (Zupanski and Zupanski 2006, MWR)

Maximum Likelihood Ensemble Filter (MLEF) is developed using ideas from:

• Variational data assimilation (3DVAR, 4DVAR)
• Iterated Kalman Filters
• Ensemble Transform Kalman Filter (ETKF, Bishop et al. 2001)

What the MLEF can do:

• Calculate 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)
• Calculate uncertainty of all estimates
• Calculate information content of observations (observability in ensemble subspace)
• Calculate sensitivity, defined in calculus of variations
  • Find the most likely sources/sinks of carbon
• Define targeted observations strategies, based on the forecast uncertainty
  • The system knows where, when and which observations are needed in order to reduce forecast uncertainty
• Acquire new knowledge about atmospheric and carbon processes
  • the system learns from the past about the state variables, model errors, empirical parameters, etc.
  • the system is adaptive (updates error covariance matrices in each data assimilation cycle)

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