A new approach to paleoclimatic research using linear programming

One of the most frequently attempted correlations in Quaternary research is between insolation and paleoclimatic data. Yet there are a large number of insolation time series that could potentially explain a Quaternary dataset, individually or in combination. We computed 342 insolation time series (varying by latitude, time of year and time of day) for fitting to four different paleoclimatic records: foraminiferal δ¹⁸O from SPECMAP; temperatures inferred from Vostok, Antarctica ice cores; marine accumulation rates of a freshwater diatom, Melosira, originating from tropical Africa lakebeds: and δ¹⁸O variations in calcite at Devil's Hole, Nevada. We developed two 'inductive' linear programming models that solve for the weighted combination of insolation curves that minimize either the average or maximum residual from the proxy curve. Each of the four proxy records, lagged and unlagged, was solved by both model types. On average, our composite insolation curves fit the proxy records 48-76% better than does June daily insolation at 60°N, the key insolation curve of the Milankovitch paradigm. Globally, high latitude insolation (60°-70°N and S) and insolation at specific times of day (noon or non-noon, as opposed to daily) dominated the results. Regionally, the model tended to select insolation curves from absolute latitudes similar to those of the proxy records. The fact that these results are plausible given known biophysical processes, combined with the fact that a small number of curves repeatedly accounted for a disproportionate share of the explanation, suggest strongly that the correlations found are not happenstance, despite the inductive method used.