BINCOR: An r package for estimating the correlation between two unevenly spaced time series

This paper presents a computational program named BINCOR (BINned CORrelation) for estimating the correlation between two unevenly spaced time series. This program is also applicable to the situation of two evenly spaced time series not on the same time grid. BINCOR is based on a novel estimation approach proposed by Mudelsee (2010) for estimating the correlation between two climate time series with different timescales. The idea is that autocorrelation (e.g. an AR1 process) means that memory enables values obtained on different time points to be correlated. Binned correlation is performed by resampling the time series under study into time bins on a regular grid, assigning the mean values of the variable under scrutiny within those bins. We present two examples of our BINCOR package with real data: instrumental and paleoclimatic time series. In both applications BINCOR works properly in detecting well-established relationships between the climate records compared. © Technische Universitaet Wien

Reconciling unevenly sampled paleoclimate proxies: a Gaussian kernel correlation multiproxy reconstruction

Reconstructing past hydroclimatic variability using climate-sensitive paleoclimate proxies provides context to our relatively short instrumental climate records and a baseline from which to assess the impacts of human-induced climate change. However, many approaches to reconstructing climate are limited in their ability to address sampling variability inherent in different climate proxies. We iteratively optimise an ensemble of possible reconstruction data series to maximise the Gaussian kernel correlation of Rehfeld et al. (2011) which reconciles differences in the temporal resolution of both the target variable and proxies or covariates. The reconstruction method is evaluated using synthetic data with different degrees of sampling variability and noise. Two examples using paleoclimate proxy records and a third using instrumental rainfall data with missing values are used to demonstrate the utility of the method. While the Gaussian kernel correlation method is relatively computationally expensive, it is shown to be robust under a range of data characteristics and will therefore be valuable in analyses seeking to employ multiple input proxies or covariates

Correlation confidence limits for unevenly sampled data

Estimation of correlation with appropriate uncertainty limits for scientific data that are potentially serially correlated is a common problem made seriously challenging especially when data are sampled unevenly in space and/or time. Here we present a new, robust method for estimating correlation with uncertainty limits between autocorrelated series that does not require either resampling or interpolation. The technique employs the Gaussian kernel method with a bootstrapping resampling approach to derive the probability density function and resulting uncertainties. The method is validated using an example from radar geophysics. Autocorrelation and error bounds are estimated for an airborne radio-echo profile of ice sheet thickness. The computed limits are robust when withholding 10%, 20%, and 50% of data. As a further example, the method is applied to two time-series of methanesulphonic acid in Antarctic ice cores from different sites. We show how the method allows evaluation of the significance of correlation where the signal-to-noise ratio is low and reveals that the two ice cores exhibit a significant common signal