Identification of climatic state with limited proxy data

We investigate the identifiability of the climate by limited proxy data. We test a data assimilation approach through perfect model pseudoproxy experiments, using a simple likelihood-based weighting based on the particle filtering process. Our experimental set-up enables us to create a massive 10 000-member ensemble at modest computational cost, thus enabling us to generate statistically robust results. We find that the method works well when data are sparse and imprecise, but in this case the reconstruction has a rather low accuracy as indicated by residual RMS errors. Conversely, when data are relatively plentiful and accurate, the estimate tracks the target closely, at least when considering the hemispheric mean. However, in this case, our prior ensemble size of 10 000 appears to be inadequate to correctly represent the true posterior, and the regional performance is poor. Using correlations to assess performance gives a more encouraging picture, with significant correlations ranging from about 0.3 when data are sparse to values over 0.7 when data are plentiful, but the residual RMS errors are substantial in all cases. Our results imply that caution is required in interpreting climate reconstructions, especially when considering the regional scale, as skill on this basis is markedly lower than on the large scale of hemispheric mean temperature.