Twin experiments with the equivalent weights particle filter and HadCM3

This paper investigates the use of a particle filter for data assimilation with a full scale coupled ocean–atmosphere general circulation model. Synthetic twin experiments are performed to assess the performance of the equivalent weights filter in such a high-dimensional system. Artificial 2-dimensional sea surface temperature fields are used as observational data every day. Results are presented for different values of the free parameters in the method. Measures of the performance of the filter are root mean square errors, trajectories of individual variables in the model and rank histograms. Filter degeneracy is not observed and the performance of the filter is shown to depend on the ability to keep maximum spread in the ensemble.

Evaluation of the realism of climate reconstruction using the Coexistence Approach with modern pollen samples from the Tibetan Plateau

We apply the Coexistence Approach (CoA) to reconstruct mean annual precipitation (MAP), mean annual temperature (MAT), mean temperature of thewarmestmonth (MTWA) and mean temperature of the coldest month (MTCO) at 44 pollen sites on the Qinghai–Tibetan Plateau. The modern climate ranges of the taxa are obtained (1) from county-level presence/absence data and (2) from data on the optimum and range of each taxon from Lu et al. (2011). The CoA based on the optimumand range data yields better predictions of observed climate parameters at the pollen sites than that based on the county-level data. The presence of arboreal pollen, most of which is derived fromoutside the region, distorts the reconstructions. More reliable reconstructions are obtained using only the non-arboreal component of the pollen assemblages. The root mean-squared error (RMSE) of the MAP reconstructions are smaller than the RMSE of MAT, MTWA and MTCO, suggesting that precipitation gradients are the most important control of vegetation distribution on the Qinghai–Tibetan Plateau. Our results show that CoA could be used to reconstruct past climates in this region, although in areas characterized by open vegetation the most reliable estimates will be obtained by excluding possible arboreal contaminants.

Improvement and sensitivity analysis of thermal thin-ice thickness retrievals

Considering the sea ice decline in the Arctic during the last decades, polynyas are of high research interest since these features are core areas of new ice formation. The determination of ice formation requires accurate retrieval of polynya area and thin-ice thickness (TIT) distribution within the polynya.We use an established energy balance model to derive TITs with MODIS ice surface temperatures (Ts) and NCEP/DOE Reanalysis II in the Laptev Sea for two winter seasons. Improvements of the algorithm mainly concern the implementation of an iterative approach to calculate the atmospheric flux components taking the atmospheric stratification into account. Furthermore, a sensitivity study is performed to analyze the errors of the ice thickness. The results are the following: 1) 2-m air temperatures (Ta) and Ts have the highest impact on the retrieved ice thickness; 2) an overestimation of Ta yields smaller ice thickness errors as an underestimation of Ta; 3) NCEP Ta shows often a warm bias; and 4) the mean absolute error for ice thicknesses up to 20 cm is ±4.7 cm. Based on these results, we conclude that, despite the shortcomings of the NCEP data (coarse spatial resolution and no polynyas), this data set is appropriate in combination with MODIS Ts for the retrieval of TITs up to 20 cm in the Laptev Sea region. The TIT algorithm can be applied to other polynya regions and to past and future time periods. Our TIT product is a valuable data set for verification of other model and remote sensing ice thickness data.

Sparse density estimator with tunable kernels

A new sparse kernel density estimator with tunable kernels is introduced within a forward constrained regression framework whereby the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Based on the minimum integrated square error criterion, a recursive algorithm is developed to select significant kernels one at time, and the kernel width of the selected kernel is then tuned using the gradient descent algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing very sparse kernel density estimators with competitive accuracy to existing kernel density estimators.

Sparse density estimation on multinomial manifold combining local component analysis

A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion combining local component analysis for the finite mixture model. We start with a Parzen window estimator which has the Gaussian kernels with a common covariance matrix, the local component analysis is initially applied to find the covariance matrix using expectation maximization algorithm. Since the constraint on the mixing coefficients of a finite mixture model is on the multinomial manifold, we then use the well-known Riemannian trust-region algorithm to find the set of sparse mixing coefficients. The first and second order Riemannian geometry of the multinomial manifold are utilized in the Riemannian trust-region algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with competitive accuracy to existing kernel density estimators.