This collaborative interdisciplinary research project aims to reconstruct past climates on Earth from sparse and noisy paleo-proxy measurements using novel techniques in state estimation ("data assimilation"). The technique involves the optimal fusion of independent estimates of the state of the climate system from a numerical model and from proxy measurements. Our goal is to reconstruct a dynamically consistent record of Earth's climate.
Steiger. N. J., G. J. Hakim, E. J. Steig, D. S. Battisti, and G. H. Roe, 2013: Climate field reconstruction via data assimilation. J. Climate, 26, submitted. (pdf)
Pendergrass, A. G., G. J. Hakim, D. S. Battisti, and G. Roe, 2012:Coupled air--mixed-layer temperature predictability for climate reconstruction. J. Climate, 25, 459-472. (pdf) DOI: 10.1175/2011JCLI4094.1
Huntley, H. S., and G. J. Hakim, 2009: Assimilation of time-averaged observations in a quasi-geostrophic atmospheric jet model. Climate Dyn., 32, DOI: 10.1007/s00382-009-0714-5
Dirren, S., and G. J. Hakim, 2005: Toward the assimilation of time-averaged observations. Geophys. Res. Lett., 32, L04804. (pdf) DOI: 10.1029/2004GL021444
Knowledge of the long-term historical behavior of Earth's climate provides a critical benchmark for comparing potential future changes. An accurate historical record also provides the basis for theories that attempt to explain the dynamics of variability on, for example, decadal and centential time scales. Since the instrumented record only extends about 150 years into the past, proxy measurements must be considered. These measurements present challenges to analysis methods compared to methods of analysis for instrumented weather observations.
A substantial challenge to paleo-climate assimilation is the fact that the proxy measurements represent long integrals in time as compared to nearly instantaneous values as for weather measurements. Our research for the past eight years has addressed this problem by a novel extension of the traditional Kalman filter to deal with time integrals. The method has been tested on low-order dynamical systems (Dirren and Hakim, 2005), idealized models of midlatitude storm tracks (Huntley and Hakim, 2009; Pendergrass et al. 2012) and in pseudo-proxy experiments for GCM and reanalysis data (Steiger et al., 2013).
Results show that the method performs well in recovering the low-frequency part of the state resolved by time-averaged observations. An example from Dirren and Hakim (2005) is shown below.
A surprising finding of this research is that the observations improve estimates of the state on timescales shorter than the observation averaging period. The reason for this is that the dynamics of the model couple different timescales, such that the observational information "cascades" to shorter timescales than were actually measured! An example from the research described in Huntley and Hakim (2009) is shown below.
Normally the prior estimate for data assimilation comes from a model, such as a six-hour weather forecast, but for the paleoclimate problem, the timescales of the proxy measurements are long enough that they may approach or exceed the model predictability limit. In that case, a tremendous cost savings is realized, since the model does need to be integrated, and one may use "offline" datasets for the prior. This issue was explored in Huntley and Hakim (2009), Pendergrass et al. (2012), and most completely in Steiger et al. (2013). Steiger et al. (2013) also compare the method with a common climate reconstruction technique using empirical orthogonal functions (e.g. Mann et al. 1998; Mann and Jones 2003), which we call "PCA." In this paper we show that: (1) our data assimilation technique consistently outperforms PCA, (2) data assimilation captures not only the global mean, but also regional spatial patterns, and (3) reconstructions of climate simulations give a false sense of accuracy compared to a reconstruction of the 20th Century Reanalysis dataset. An example is shown in the figures below, which compares reconstructions of surface temperature for the 20th Century Reanalysis dataset using data assimilation (left) and PCA (right). The colors show the correlation of time series reconstructed from pseudo-proxy data at sparse location (squares) with the true value in the reanalysis data.The difference is most dramatic near Tasmania and southeast Asia, where the local fields do not project well on the EOFs used in the PCA method.
Current work involves using this technique on real proxy measyurements. An unpublished example (do not quote---subject to change!) shows a reconstruction of the past 500 years using our data assimilation technique based only tree-ring data.
Another exciting aspect of this research is the potential for providing objective quantitative guidance for siting new proxy measurements. Huntley and Hakim (2009) employ the ensemble sensitivity theory described in Torn and Hakim (2008) and Ancell and Hakim (2007) to determine the optimal locations for observations to constrain the leading mode of variability in the idealized climate model. The results, shown below, show that the first few observations are located where one might expect: near the "centers of action" for the EOF. However, the fourth and subsequent observation locations are not intuitively located because they are conditional on the information contained in the previously identified locations.
Results also indicate that four optimally placed observations capture about 50% of the error reduction of a randomly distributed network of 100 observations. A real-world application of these ideas is currently being explored in collaboration with Philip Mote (UW Climate Impacts Group) to optimally redesign the Washington state network of climate observation stations.