Segmented linear integral correlation Kernel ensemble reconstruction: A new method for climate reconstructions with applications to Holocene era proxies from an East Antarctic ice core

Abstract

Understanding past climate is essential to our knowledge of how our current climate system operates, and how it might respond to future change. Techniques to reconstruct climate history are challenging, and both accuracy and certainty are hampered by the quality of the datasets used. Here we both develop a new reconstruction tool and apply it to four ice core proxy based multi-millennial Holocene climate reconstructions, chosen because of their potential influence on East Antarctic climate. The new multi-proxy reconstruction method is called Segmented Linear Integral Correlation Kernel Ensemble Reconstruction (SLICKER). This method employs a segmented linear rather than Gaussian correlation approach and builds an ensemble of reconstructions with a best fit and spread related to the best estimate of uncertainty. This method is robust for non-linear, uneven or differently sampled data and produces high-fidelity reconstructions and associated uncertainty estimates. This new method has the potential to produce more realistic reconstructions, with associated uncertainty estimates based on robust statistical measures that are insensitive to outliers. The main findings from these new reconstructions are: Antarctica temperature shows multi-decadal variability over the last twelve thousand years with increased frequency over the last two thousand years; Zonal Wave 3 index and the Southern Annular Mode both show limited trends over the last two thousand years, but an increase since the 1970s CE; and the Indian Ocean Dipole Moment index has a twentieth century CE upward trend, and a thirteenth to sixteenth century CE below average period which may be related to volcanic activity.

Fig 1. Ensemble center uncertainty calibration. To estimate the uncertainty in ensemble center calculation, the standard deviation of a resample is calculated and then scaled by a calibration factor to convert this to a 95% confidence interval, based on the assumption of a normally distributed ensemble.

Fig 2. 20th century annual average continental USA 2m air temperature TCONUS from the 20CRv3 reanalysis [29] reconstruction target (light cray line with open circles). IID noise pseudo-proxies P1 (solid black line), P2 (dotted black line) and P3 (dashed black line). Location of missing data also shown at bottom of plot (gray filled circles), upper row for P1, middle row for P2 and lower row for P3.

Fig 3. 20th century annual average continental USA 2m air temperature TCONUS from the 20CRv3 reanalysis [29] using pseudo-proxies. SLICKER reconstruction (black line), uncertainty (dark shading) and ensemble spread (light shading) for the target (grey circles). Also shown is the median and standard deviation of the Gaussian kernel correlation reconstruction of [16] (grey dashed). a) blue noise, b) IID (white) noise, c) red noise.

Fig 4. AR1 test case using pseudo-proxies. SLICKER reconstruction (black line), uncertainty (dark shading) and ensemble spread (light shading) for the target (grey circles). Also shown is the median and standard deviation of the Gaussian kernel correlation reconstruction of [16] (grey dashed).

Fig 5. 60 °S–90 °S mean temperature reconstruction. Gaussian smoothed (100 year half power) M-Estimator SLICKER reconstruction (solid lines), uncertainty (colored shading) and ensemble spread (dotted lines) for the 60°S–90°S mean temperature, 100 year (half power) for three calibration targets: ERA-20C (black), HadCRUT (red) and ModE-RA (blue). The HadCRUT and ModE-RA reconsturctions are for a temperature anomaly based target, and have had a constant offset added to have the same median value as the ERA-20C based reconstruction. Also shown is multi-method median result of [12] renormalised to have the same 1800–1900 CE mean value (long dashed line) and inter-quartiles (short dashed lines).

Fig 6. Indian Ocean Dipole Moment Index reconstruction. SLICKER reconstruction (black line), uncertainty (dark grey shading) and ensemble spread (light shading) for the Indian Ocean Dipole Moment Index. a) 3 year (half power) Gaussian smoothed M-Estimator. b) 10 year (half power) Gaussian smoothed M-Estimator, also shown 50 year (half power) Gaussian smoothed M-Estimator (dotted line), linear breakfit analysis (dashed line) showing break in linear tread at 1907 CE ± 30 years, and timing of DMI positive years (black dots) defined from 10 year Gaussian smoothed M-Estimator. c) 30-year moving windowed standard deviation of Indian Ocean Dipole Moment Index reconstruction.

Fig 7. Zonal Wave 3 Index reconstruction. SLICKER reconstruction (black line), uncertainty (dark grey shading) and ensemble spread (light shading) for the Zonal Wave 3 Index. a) 3 year (half power) Gaussian smoothed M-Estimator. b) 10 year (half power) Gaussian smoothed M-Estimator, also shown linear breakfit analysis (dashed line) showing break in linear tread at 1979 CE ± 7 years.

Fig 8. Southern Annular Mode Index reconstruction. Gaussian smoothed M-Estimator SLICKER reconstruction (black line), uncertainty (dark grey shading) and ensemble spread (light shading) for the Southern Annular Mode Index. a) 3 year (half power) Gaussian smoothed M-Estimator. b) 10 year (half power) Gaussian smoothed M-Estimator, also shown linear breakfit analysis (dashed line) showing break in linear tread at 1979 CE ± 9 years.

Fig 9. 60 °S–90 °S 2m air temperature power spectrum. a) Local wavelet power spectrum of the 60 °S–90 °S mean HadCRUT temperature reconstruction using Morlet wavelets. 95% significance level for a 0.902 lag-one correlation red-noise process is shown (black lines). The cone-of-influence where edge-effects may impact the results is shown in gray hatching. b) Average combined proxy sampling density for running 256 year windows.