A52A-01 INVITED
State and Parameter Estimation for a Coupled Ocean--Atmosphere Model
The El-Nino/Southern-Oscillation (ENSO) dominates interannual climate variability and plays, therefore, a key role in seasonal-to-interannual prediction. Much is known by now about the main physical mechanisms that give rise to and modulate ENSO, but the values of several parameters that enter these mechanisms are an important unknown. We apply Extended Kalman Filtering (EKF) for both model state and parameter estimation in an intermediate, nonlinear, coupled ocean--atmosphere model of ENSO. The coupled model consists of an upper- ocean, reduced-gravity model of the Tropical Pacific and a steady-state atmospheric response to the sea surface temperature (SST). The model errors are assumed to be mainly in the atmospheric wind stress, and assimilated data are equatorial Pacific SSTs. Model behavior is very sensitive to two key parameters: (i) $\mu$, the ocean- atmosphere coupling coefficient between SST and wind stress anomalies; and (ii) $\delta_{s}$, the surface-layer coefficient. Previous work has shown that $\delta_{s}$ determines the period of the model's self-sustained oscillation, while $\mu$ measures the degree of nonlinearity. Depending on the values of these parameters, the spatio-temporal pattern of model solutions is either that of a delayed oscillator or of a westward propagating mode. Estimation of these parameters is tested first on synthetic data and allows us to recover the delayed- oscillator mode starting from model parameter values that correspond to the westward-propagating case. Assimilation of SST data from the NCEP-NCAR Reanalysis-2 shows that the parameters can vary on fairly short time scales and switch between values that approximate the two distinct modes of ENSO behavior. Rapid adjustments of these parameters occur, in particular, during strong ENSO events. Ways to apply EKF parameter estimation efficiently to state-of-the-art coupled ocean--atmosphere GCMs will be discussed.
A52A-02 INVITED
A Fixed-lag Ensemble Kalman Smoother to Estimate Surface Carbon Dioxide Exchange
The NOAA ESRL carbon cycle group uses an ensemble data assimilation system to estimate multiple years of emissions and uptake (fluxes) of carbon dioxide at the Earth's surface. Thereto, atmospheric observations of carbon dioxide mixing ratios are assimilated in a weekly cycle, constraining five weeks of past surface fluxes. This five week smoother window is needed because the time between the release of carbon dioxide at the surface and downwind sampling of the resulting signal at our relatively sparse observation network (~100 per cycle) is determined by slow atmospheric mixing processes. The �observation operator' for our problem thus links surface flux variations to atmospheric mixing ratios, and is a full tracer transport model of the global atmosphere with nested grids to focus on regions of special interest. We optimize a set of linear parameters (~1000 per cycle) that control the behavior of simplified �flux modules'. These contain physical descriptions of surface exchange from the oceans, biosphere, fires, and fossil fuel burning. The optimal set of parameters estimated in the assimilation, combined with the flux modules, yields a high resolution multiyear reanalysis of surface exchange for scientific studies. In addition to showing results from our assimilations, we will discuss some particularities of our system such as the lack of an appropriate dynamical model, the impracticality of geographical localization, and the resulting need for many (>100) ensemble members.
http://www.esrl.noaa.gov
A52A-03
A New Approximate Solution of the Optimal Nonlinear Filter for Data Assimilation with High Dimensional Systems
We introduce a new approximate solution of the optimal nonlinear filter suitable for high dimensional nonlinear data assimilation problems. The method is based on a local linearization in a low-rank kernel representation of the state's probability density function. In the resulting ``Low-Rank Kernel Particle Kalman'' (LRKPK) filter, the standard (weight-type) particle filter correction is complemented by a Kalman-type correction for each particle using the covariance matrix of the kernel mixture. The LRKPK filter's solution is then obtained as the weighted average of several low-rank square-root Kalman filters operating in parallel. The Kalman-type correction reduces the risk of ensemble degeneracy, which enables the filter to efficiently operate with fewer particles than the particle filter. Combined with the low-rank approximation, it allows the implementation of the LRKPK filter with highly dimensional systems. The new filter is described and its relevance tested using a realistic configuration of the Princeton Ocean Model (POM) in the Mediterranean Sea.
A52A-04
Exploiting multi-phase measurements for constraining aerosol simulations using the adjoint of GEOS-Chem
Simultaneous observations of gas and particle-phase concentrations from surface, satellite and aircraft measurements present an exciting yet challenging opportunity for constraining predictions of aerosol concentrations and enhancing our understanding of their influence on the chemical state of the atmosphere. Using a recently derived adjoint of the global chemical transport model GEOS-Chem, we examine the potential for exploiting such measurements in a data assimilation framework. This adjoint model is the first to include treatment of aerosol equilibrium thermodynamics, providing us with a new tool for exploring the ways in which secondary formation of inorganic aerosol is governed by coupling of aerosol thermodynamics, gas-phase chemistry and heterogeneous reactions. We show that these feedbacks increase our ability to constrain aerosol precursor emissions by affording assimilation of multi-phase measurements. General challenges inherent in the variational inverse modeling procedure are also addressed for this specific type of application, such as estimation of covariance matrices and conditioning of the cost function.
A52A-05
Geomagnetic Data Assimilation
Geomagnetic data assimilation is a new application of traditional data assimilation techniques in which surface geomagnetic observations are combined with a dynamo model to get an improved estimate of the state of the Earth's core. An optimal estimate can potentially be obtained using Bayesian techniques, provided that good estimates of observation and model error statistics are available. Geomagnetic field observations have well understood error characteristics. we have begun to develop the means to estimate the error statistics of the MoSST core dynamics model, a geodynamo model that uses spherical harmonics (zonal and meridional) and finite differences (radial) for spatial derivative approximation. However, only a limited part of the poloidal magnetic field (up to degree L = 13 in spherical harmonic expansion) is observable at the Earth's surface, and we need to apply the estimated error statistics of MoSST core dynamics model correctly into a data assimilation system. We have developed a geomagnetic data assimilation system, in which the error covariances are estimated using an ensemble of model solutions. By analyzing the error covariances, we know not only how the poloidal magnetic field deep inside the core should be corrected by the surface observations, but also other physical variables, i.e. the remaining poloidal field, the toroidal magnetic field, the velocity field and the density perturbation should be corrected. This "balanced" approach to correcting the core state will also correct the non-observed state variables more rapidly, which is important considering the short duration of the surface magnetic field record. As our first step, we use the error covariances with correlation length to correct part of these variables in order to determine the impact of each correction. In a set of simulated experiments in which true states are known we can determine under what conditions (e.g., assimilation frequency) the model solutions converge to the true states. These tests will give us more confidence that assimilation using real observations has made dynamically consistent corrections.
A52A-06
Towards the Assimilation of Remote Sensing Products by Climate Models with Updated Land Surface Process Schemes
The most advanced representation of terrestrial surface processes in climate models is confined to simplistic modules implementing one-dimensional (1-D) vertical exchange models. In particular, the radiation component of these 1-D modules relies on solutions derived from the so-called two-stream approaches applied notably to the case of vegetation canopies. The latter are, however, characterized by strong three dimensional (3-D) effects implied by the internal spatial variability of, for instance, the leaf area density, at all scales and resolutions involved (typically from 1 to 100 kilometers). This internal variability itself controls the radiation fluxes such as the fraction of radiation scattered, transmitted and finally absorbed by the vegetation canopy. Some of these fluxes estimated from remote sensing measurements, are becoming nowadays operationally available from space agencies. Such remote sensing products can be ingested or assimilated by climate models to the extent that the latter can explicitly and accurately represent these radiation quantities. In order to avoid the discrepancies and biases generated by 1-D radiation transfer models when representing 3-D effects, we propose a comprehensive 1-D scheme which introduces a parameterization of the internal variability of the vegetation canopies through a domain-averaged vegetation structure factor. We then present a computer efficient software package enabling us to assimilate operational remote sensing products into this updated two-steam radiation transfer scheme suitable for climate models. This package implements the adjoint code, generated using automatic differentiation techniques, of the cost function. This cost function itself balances two main contributions reflecting 1) the a priori knowledge on the model parameter values and, 2) the remote sensing flux uncertainties together with the requirement to minimize the mismatch between these measurements and the 2-stream model simulations. The individual weights of these contributions are specified notably via covariance matrices of the uncertainties in the a priori knowledge on the model parameters and the observations. This package also reports on the probability density functions of the retrieved model parameter values that thus permit the user to evaluate the a posteriori uncertainties on these retrievals. This is achieved by evaluating the Hessian of the cost function at its minimum. We will discuss results from applications conducted using MODIS and MISR operational surface albedo products over selected EOS validation sites where some ground-based estimates are available.
http://fapar.jrc.it/WWW/Data/Pages/FAPAR_Software/FAPAR_Software_RTModels_two- stream.php
A52A-07
Development of a Reduced Order Control Strategy in 4D-Var Data Assimilation
The practical implementation of 4D-Var data assimilation for atmospheric and oceanographic models is hampered by the large dimensionality of the discrete model initial conditions, typically in the range $10^6-10^7$. Order reduction strategies aim to alleviate the computational burden of the 4D-Var procedure by formulating the optimal control problem in a low-order control space. In this study a proper orthogonal decomposition method (POD) is used to identify a low dimensional space that captures most of the energy and the main directions of variability of the model. Data assimilation experiments are setup with a 2D global shallow- water model using the Lin-Rood flux-form semi-Lagrangian discretization with initial conditions specified from the ECMWF 500mb ERA-40 dataset. Qualitative and quantitative aspects of the reduced-order control strategy are analyzed in a twin experiments 4D-Var framework by comparison with results in the full model space. Numerical results show that with an appropriate selection of the basis vectors the optimization in the low-order POD space is able to significantly reduce the computational cost while preserving the quality of the solution. Issues related to the generation of the ensemble of snapshots and optimal selection of the basis vectors in the context of optimal control are addressed. A second order adjoint model implemented in the reduced space is used to provide a Hessian condition number analysis and to assess the efficiency of the POD-based optimization. Further applications in numerical weather prediction to estimation of information content of data and to identification of observational data of most benefit to the analysis and data assimilation procedure are presented.
A52A-08
Lognormal Data Assimilation: Theory and applications
One of the fundamental assumptions made in both variational and ensemble data assimilation is that the errors and hence the variables involved are all Gaussian distributed. Although for larger scales in the atmosphere this may thought to be true there is a synoptic variable, humidity, which does not meet this criteria. With the continued increase in model resolution then we have meso-scale variables which now have to be considered in the state vector and hence this assumption may not be as valid. In other geophysical model and data assimilation applications we have different variables which may also not adhere to these assumptions. However, it is not just with the state variables we have this problem. With the introduction of more sophisticated satellites which do not measure the state variables directly we have observations which do not conform to the Normal assumption. This is however not just a problem with numerical weather prediction and is true for most geophysical models. In this paper we introduce the theory of lognormal data assimilation for the 3D variational case and show the impact of incorrectly assuming Normality when the variables are lognormally distributed. We present some results with the Lorenz 1963 model where we use a set of mixed Normal and lognormal observations and show how to assimilated these simultaneously.