Method of frequency dependent correlations: investigating the variability of total solar irradiance

TL;DR

This paper introduces a frequency-dependent correlation method to analyze and hindcast total solar irradiance (TSI) using proxy data, revealing insights into the variability and modeling of solar irradiance over time.

Contribution

A novel frequency-dependent correlation technique for analyzing TSI proxies and targets, optimizing parameters, and improving hindcasting accuracy of historical solar irradiance.

Findings

Detected large variance in low-frequency TSI target components.

Identified the rotational signal in FDC spectrum despite its weak presence in proxies.

Provided insights into the capabilities of TSI modeling procedures for historical data.

Abstract

This paper contributes to the field of modeling and hindcasting of the total solar irradiance (TSI) based on different proxy data that extend further back in time than the TSI that is measured from satellites. We introduce a simple method to analyze persistent frequency-dependent correlations (FDCs) between the time series and use these correlations to hindcast missing historical TSI values. We try to avoid arbitrary choices of the free parameters of the model by computing them using an optimization procedure. The method can be regarded as a general tool for pairs of data sets, where correlating and anticorrelating components can be separated into non-overlapping regions in frequency domain. Our method is based on low-pass and band-pass filtering with a Gaussian transfer function combined with de-trending and computation of envelope curves. We find a major controversy between the historical proxies and satellite-measured targets: a large variance is detected between the low-frequency parts of targets, while the low-frequency proxy behavior of different measurement series is consistent with high precision. We also show that even though the rotational signal is not strongly manifested in the targets and proxies, it becomes clearly visible in FDC spectrum. The application of the new method to solar data allows us to obtain important insights into the different TSI modeling procedures and their capabilities for hindcasting based on the directly observed time intervals.