U. of Delaware College of Earth, Ocean, and Environment


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Helga S. Huntley's Research

Data Assimilation

Assimilation of Time-Averaged Data for Paleoclimate Applications

(In collaboration with Greg Hakim.)

I have been studying data assimilation methods for treating observations of averaged quantities to capture low frequency variability. Since the climate system is chaotic, any model forecast is at best one of many possibilities. The idea behind data assimilation (or state estimation) is to produce a more accurate and more certain (i.e. with smaller variance) estimate of the actual state of the system by combining knowledge about the dynamics implemented in a model with information from observations.

The methods of state estimation in use today fall into three main categories: variational methods, optimal interpolation and Kalman filter techniques. All of these are implementations of a least squares (or best linear unbiased) estimate, based on the statistics of the background forecast (i.e., the model output) and the observations. The difference lies in how the correction to the initial forecast is calculated to produce an analysis (i.e. the final estimate). Variational methods, as the name implies, rely on the minimization of a cost function. These are currently used in operational weather forecasting centers, such as NOAA (National Oceanic and Atmospheric Administration) and ECMWF (European Centre for Medium-Range Weather Forecasts). Optimal interpolation instead uses an explicit expression for the correction factor. The Kalman filter is similar in this regard, but is especially designed to handle sequential assimilation. Generally, optimal interpolation also assimilates only a few observations at each point, whereas the Kalman filter can work with a large number of them. Bouttier and Courtier, 2002, gives a comprehensive overview of these methods.

Crucial for the success of any state estimation is the use of the correct statistics for both the background forecast and the observations. Unfortunately, it is often difficult to estimate the former. One method is to use an ensemble to generate a mean, variances, and covariances of the variables of interest. Running an ensemble also conveniently advances error statistics in time. It is thus possible to capture the dependence of the error on the flow itself. The use of such Monte Carlo methods in conjunction with a Kalman filter was first proposed by Evensen, 1994, and is known as the ensemble Kalman filter.

In the context of paleoclimate reconstruction, an additional problem stems from the fact that the available data typically comes at a low temporal resolution, thus capturing only low-frequency signals. The goal of my work is to develop, and demonstrate the feasibility of, a method for assimilating such observations into a higher resolution model to create a more complete picture of what past climate likely looked like. When spatially averaged data is assimilated, the covariance of the averaged quantity with non-averaged quantities is used to update the forecast. However, when low-frequency and high-frequency variability is mostly decoupled, it is logical to update only the temporal average with a temporally averaged observation. Dirren and Hakim, 2005, illustrated this idea on a simple Lorenz model. In my recent work, I have implemented this state estimation algorithm with a quasi-geostrophic atmospheric model for a jet over a mountain, in order to test it with a system of intermediate complexity. Perfect model experiments, assimilating "data" from a truth run of the model, with a wide range of averaging times, show that it is indeed possible to constrain the low-frequency variability, leading to a significant reduction (about 50%) of the root-mean-square error in the analysis versus an ensemble run without assimilation. In fact, for relatively short averaging times, the root-mean-square error of the instantaneous variable is also improved. These results are robust to modest changes in observation error, number, and location. In the limit of very few observations, the error reduction is small except for optimally designed networks. Even when model error is introduced by lowering the resolution or the damping timescale for perturbations from a prescribed climate, significant error reductions are realized. These findings indicate that our method for state estimation may enable us to describe paleoclimate with a better temporal and spatial resolution than based on observations alone and with a higher accuracy than based on model runs only.

While this is promising, the practical situation of assimilating real data into a climate model presents several additional layers of complexity, including among others increased and less systematic model error, limited control over the observation network, and observations in the form of tracers rather than controlling variables. Further work is needed to address these issues -- and ultimately to achieve the paleoclimate reconstruction that initially motivated this work.

References

Bouttier, F. and P. Courtier, Data Assimilation and Methods, Meteorological Training Course Lecture Series, ECMWF, 59 pp., 2002.

Dirren, S. and G.J. Hakim, Toward the assimilation of time-averaged observations, Geophysi. Res. Lett., 26, 23, L04804, doi: 10.1029/2004GL021444, 2005.

Evensen, G., Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res., 99, C5, 10,143-10,162, 1994.

Related publication

Muscarelli, P., M. Carrier, H. Ngodock, S. Smith, B.L. Lipphardt, Jr., A.D. Kirwan, Jr., and H.S. Huntley, 2015: Do assimilated drifter velocities improve Lagrangian predictability in an operational ocean model?, Mon. Weather Rev., doi: 10.1175/MWR-D-14-00164.1, 143, 1822--1832.

Jacobs, G., B. Bartels, D. Bogucki, F.J. Beron-Vera, S. Chen, E.F. Coelho, M. Curcic, A. Griffa, M. Gough, B.K. Haus, A.C. Haza, R.W. Helber, P.J. Hogan, H.S. Huntley, M. Iskandarani, F. Judt, A.D. Kirwan, Jr., N. Laxague, A. Valle-Levinson, B.L. Lipphardt, Jr., A.J. Mariano, H.E. Ngodock, G. Novelli, M.J. Olascoaga, T.M. Özgökme, A.C. Poje, A.J.H.M. Reniers, C.D. Rowley, E.H. Ryan, S.R. Smith, P.L. Spence, P.G. Thoppil, and M. Wei, 2014: Data assimilation considerations for improved ocean predictability during the Gulf of Mexico Grand Lagrangian Deployment (GLAD), Ocean Model., doi: 10.1016/j.ocemod.2014.09.003, 83, 98--117.

Chang, Y., D. Hammond, A.C. Haza, P. Hogan, H.S. Huntley, A.D. Kirwan, Jr., B.L. Lipphardt, Jr., V. Taillandier, A. Griffa, and T.M. Özgökmen, 2011: Enhanced estimation of sonobuoy trajectories by velocity reconstruction with near-surface drifters, Ocean Model., doi: 10.1016/j.ocemod.2010.11.002, 36, 179-197.

Huntley, H.S. and G.J.Hakim, 2010: Assimilation of time-averaged observations in a quasi-geostrophic atmospheric jet model, Climate Dynamics, doi: 10.1007/s00382-009-0714-5, 35, 995-1009.


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