A segmentation algorithm for characterizing rise and fall segments in seasonal cycles: an application to XCO₂ to estimate benchmarks and assess model bias

There is more useful information in the time series of satellite-derived column-averaged carbon dioxide (XCO2) than is typically characterized. Often, the entire time series is treated at once without considering detailed features at shorter timescales, such as nonstationary changes in signal characteristics – amplitude, period and phase. In many instances, signals are visually and analytically differentiable from other portions in a time series. Each rise (increasing) and fall (decreasing) segment in the seasonal cycle is visually discernable in a graph of the time series. The rise and fall segments largely result from seasonal differences in terrestrial ecosystem production, which means that the segment's signal characteristics can be used to establish observational benchmarks because the signal characteristics are driven by similar underlying processes. We developed an analytical segmentation algorithm to characterize the rise and fall segments in XCO2 seasonal cycles. We present the algorithm for general application of the segmentation analysis and emphasize here that the segmentation analysis is more generally applicable to cyclic time series. We demonstrate the utility of the algorithm with specific results related to the comparison between satellite- and model-derived XCO2 seasonal cycles (2009–2012) for large bioregions across the globe. We found a seasonal amplitude gradient of 0.74–0.77 ppm for every 10∘ of latitude in the satellite data, with similar gradients for rise and fall segments. This translates to a south–north seasonal amplitude gradient of 8 ppm for XCO2, about half the gradient in seasonal amplitude based on surface site in situ CO2 data (∼19 ppm). The latitudinal gradients in the period of the satellite-derived seasonal cycles were of opposing sign and magnitude (−9 d per 10∘ latitude for fall segments and 10 d per 10∘ latitude for rise segments) and suggest that a specific latitude (∼2∘ N) exists that defines an inversion point for the period asymmetry. Before (after) the point of asymmetry inversion, the periods of rise segments are lesser (greater) than the periods of fall segments; only a single model could reproduce this emergent pattern. The asymmetry in amplitude and the period between rise and fall segments introduces a novel pattern in seasonal cycle analyses, but, while we show these emergent patterns exist in the data, we are still breaking ground in applying the information for science applications. Maybe the most useful application is that the segmentation analysis allowed us to decompose the model biases into their correlated parts of biases in amplitude, period and phase independently for rise and fall segments. We offer an extended discussion on how such information about model biases and the emergent patterns in satellite-derived seasonal cycles can be used to guide future inquiry and model development.