Nitrate in Polar Ice: A New Tracer of Solar Variability

Abstract

Knowledge of the long-term variability of solar activity is of both astrophysical and geoscientific interest. Reconstructions of solar activity over multiple millennia are traditionally based on cosmogenic isotopes ¹⁴C or ¹⁰Be measured in natural terrestrial archives, but the two isotopes exhibit significant differences on millennial time scales, so that our knowledge of solar activity at this time scale remains somewhat uncertain. Here we present a new potential proxy of solar activity on the centennial-millennial time scale, based on a chemical tracer, viz. nitrate content in an ice core drilled at Talos Dome (Antarctica). We argue that this location is optimal for preserving the solar signal in the nitrate content during the Holocene. By using the firn core from the same location we show that the 11-year and Gleissberg cycles are present with the variability of 10 – 25 % in nitrate content in the pre-industrial epoch. This is consistent with the results of independent efforts of modeling HNO₃ and NO _y in Antarctic near surface air. However, meteorological noise on the interannual scale makes it impossible to resolve individual solar cycles. Based on different processes of formation and transport compared to cosmogenic isotopes, it provides new, independent insight into long-term solar activity and helps resolve the uncertainties related to cosmogenic isotopes as diagnostics of solar activity.

Appendix: Non-parametric Random Phase Method to Estimate the Significance of Coherence

When discussing any statistical measures of agreement between time series, such as correlation or coherence, not only the magnitude but also the significance should be calculated, which evaluates the probability that the correlation/coherence is caused by a random coincidence. This is particularly important for pre-processed (e.g., smoothed, filtered, or de-trended) series where the standard formulas of error propagation are not directly applicable. In addition, standard significance estimates are usually based on the assumption that the data are subject to normally distributed additive random white noise. However, this assumption is often violated because of significant autocorrelation within the actual data series. This is of particular relevance for the long-term changes studied here. In such a situation, a Monte-Carlo test can be applied to estimate the significance of the calculated coherence.

A simple random shuffling of the real data series, which is sometimes applied, typically leads to a serious overestimate of the significance because it destroys the serial correlation (Usoskin et al., 2006a). Here we applied a non-parametric random-phase method, as described below, suggested by Ebisuzaki (1997) and successfully applied in many studies of various physical systems.

Let us denote the two analyzed time series as x and y, with the coherence being C _xy . The significance estimate is performed as follows.

• i) The x series is randomized by the random-phase method: first, the FFT-transform f of the original x series is computed, $x\xrightarrow{(\mathrm{FFT})}f$; in a second step, a new FFT f′ series is produced which has the same amplitude as the f-series but whose phase sequence is randomized, $f\xrightarrow{(\mathrm{rand.phase})}f'$; thirdly, the new phase-randomized x′ series is obtained by an inverse FFT-transform of the f′ series, $f'\xrightarrow{(\mathrm{FFT}^{-1})}x'$.

• ii) The new value of the coherence is calculated between the phase-randomized x′ and the original y series, C _x′y .

• iii) A phase-randomized y′ series of the y series is produced in the same way as described in item 1 above, and the coherence C _xy′ is calculated.

• iv) The maximum of C _x′y and C _xy′ is considered as C ^∗.

• v) Steps 1 – 4 are repeated N times to obtain a sequences of C ^∗ values. Then the number N ^∗ is calculated, which is the number of cases (within the total of N simulations) when C ^∗ exceeds C _xy in the absolute value, within the defined relative phase range.

Finally, the significance is defined as

$$ s = N^{*}/N $$

(2)

and gives an estimate of the chance that the observed coherence level is not due to a causal relationship but is rather produced by a random coincidence. Here we used the number of random realizations N=10⁵. An example in Figure 7 shows the calculated integral coherence between NO₃(C) and CR(¹⁴C) series, as a function of the time scale, and its 95 % confidence level. This method, called the non-parametric random-phase test, preserves the autocorrelation function of the original series. Moreover, this method may tend to underestimate the confidence level (i.e., overestimate the probability of a random coincidence) if one of the time series is dominated by a periodic signal (Usoskin et al., 2006a). Thus, we consider this significance estimate as conservative.