Towards the assimilation of treeringwidth record

Authors: Walter Acevedo Sebastian Reich Ulrich Cubasch

Publish Date: 2015/06/10

Volume: 46, Issue: 5-6, Pages: 1909-1920

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Abstract

This paper investigates the applicability of the Vaganov–Shashkin–Lite VSL forward model for treeringwidth chronologies as observation operator within a proxy data assimilation DA setting Based on the principle of limiting factors VSL combines temperature and moisture time series in a nonlinear fashion to obtain simulated TRW chronologies When used as observation operator this modelling approach implies three compounding challenging features 1 time averaging 2 “switching recording” of 2 variables and 3 bounded response windows leading to “thresholded response” We generate pseudoTRW observations from a chaotic 2scale dynamical system used as a cartoon of the atmosphereland system and attempt to assimilate them via ensemble Kalman filtering techniques Results within our simplified setting reveal that VSL’s nonlinearities may lead to considerable loss of assimilation skill as compared to the utilization of a timeaveraged TA linear observation operator In order to understand this undesired effect we embed VSL’s formulation into the framework of fuzzy logic FL theory which thereby exposes multiple representations of the principle of limiting factors DA experiments employing three alternative growth rate functions disclose a strong link between the lack of smoothness of the growth rate function and the loss of optimality in the estimate of the TA state Accordingly VSL’s performance as observation operator can be enhanced by resorting to smoother FL representations of the principle of limiting factors This finding fosters new interpretations of treeringgrowth limitation processesIn recent years the assimilation of proxy data into climate models has emerged as a very promising way to bring physical consistency to paleoclimate reconstructions as well as to reduce their uncertainty levels “High resolution” proxy records Hughes and Ammann 2009 offer information about interannual and slower internal climate variabilities which in principle could be constrained by a suitable DA scheme As a result several research groups have been actively working with the purpose of paving the way towards an eventual paleoreanalysis Hughes et al 2010 Guiot et al 2009 Brönnimann 2011To date several very diverse DA schemes have been tested on climate models—such as pattern nudging von Storch et al 2000 forcing singular vectors Barkmeijer et al 2003 adjoint method KurahashiNakamura et al 2014 particle filter Dubinkina and Goosse 2013 Mathiot et al 2013 and ensemble Kalman filter Bhend et al 2012 Pendergrass et al 2012—providing very encouraging results regarding the potential constraint of the interannual internal variability As for the observations employed in these experiments the dominant approach has been to use either pseudoproxies or statistically reconstructed climate time series both considering a univariate linear relationship between climate state and climatedriven proxy signalsNowadays the many developments in the booming field of highresolution paleoclimatology Hughes and Ammann 2009 have made evident the complexity of climate proxy systems The formation of a proxy record might comprise biological physical and chemical mechanisms each of these able to introduce nonlinear processes Accordingly there is a growing interest in adopting more realistic approaches regarding the relation between proxy data and climate forcing Evans et al 2013 One of the most promising approaches in this direction is “Proxy Forward Modeling” Hughes et al 2010 Evans et al 2013 which takes climate forcing as input data and generate artificial proxy records that can be directly compared to actual proxy records This strategy is diametrically opposed to the traditional inverse approach where climate conditions are directly inverted from proxy dataProxy forward models can be used for different purposes such as modelpaleodata comparison in the proxy space Evans et al 2013 and prediction of future evolution of proxy archives Vaganov et al 2006 On the other hand despite its forth direction forward models can also be used for reconstruction purposes by resorting to probabilistic inversion strategies such as Bayesian hierarchical modeling TolwinskiWard et al 2014 Markov Chain Monte Carlo method Boucher et al 2014 and DA Hughes et al 2010 Contributing to the development of the latter approach is the objective of the present paperDifferent proxy data kinds react in distinctive ways to specific sets of climate variables Accordingly the assimilation of a given proxy type should be pursued on its own merits using a forward model able to simulate the climate recording processes specific to that particular kind of proxy record Nowadays there exist forward models for many different proxy types most notably TRW Vaganov et al 2006 Evans et al 2006 TolwinskiWard et al 2011 treering isotopes Roden et al 2000 Danis et al 2012 Evans 2007 coral isotopes Thompson et al 2011 ocean sediments Heinze 2001 Schmidt 1999 and stalagmite isotopes Baker et al 2012 There are also initiatives to model the transport of isotopes within the atmosphere Sturm et al 2010 Depending on the particular application and the availability of data proxy forward models assume different complexity levels which go from the minimalistic linear pseudoproxies to comprehensive models that simulate the proxy generation process as realistically as possible

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