Assessing statistical features of time series through Trend Detection Time method

Robust detection of climate change is crucial to assess the influence of anthropogenic forcing on the status of the marine biogeochemical system. The sparse and varied quality of time series data can hinder long-term trend detection. The traditional linear regression to estimate trend assumes that the series consist of a stationary random noise. However, time series are data collected sequentially over time, so the assumption of noise independence is not guaranteed. This noise consists of red noise, linked to fluctuations due to internal processes or recurring natural cycles, and white noise, indicating random noise which may include data quality. Thus, accurate trend analysis requires to establish the effect of the autocorrelation of the noise (serial correlation between each sequential sampling) on the detectability of the trend.

In the framework of EuroGO-SHIP project, the Trend Detection Time (TDT) method was used to determine years required for detecting statistically significant trends, considering the signal-to-noise ratio and noise autocorrelation. High autocorrelation indicates red noise, while near zero suggests white noise. This method was performed using complete temporal and spatial reanalysis data to assess how data quality and coverage affect TDT of the seawater carbonate system, dissolved inorganic nutrients, and dissolved oxygen, in the Mediterranean, Black and Baltic Seas; regions with a high anthropogenic footprint. In addition, subsampling three random months and each season yearly, with and without adding varying levels of noise based on GLODAPv2 (Global Data Analysis Project version 2) adjustment limits, simulate noncontinuous data conditions and best-to-worst expected data quality, respectively. This approach advances a key application of understanding noise nature to gauge trend uncertainty.

TDT averages well over 20 years varying greatly with seawater properties and regions included in this study, as well as local factors like meso-scale eddies, which are responsible for high variability and may even double the TDT. Random subsampling provides knowledge on the nature of the noise. It may increase the randomness by less capturing the cyclic record of the noise, which reduces its magnitude, thus shortening TDT. Mimic the data quality changes is even more enlightening. Adding perturbations increases noise magnitude, combining with inherent white and red noise, which lengthens TDT despite raised randomness. However, in case of large magnitude and high autocorrelation of the inherent noise, the additional perturbation fails to mask the inherent cyclicity of the noise and TDT is unchanged. Exception remains when this perturbation yields decrease in the autocorrelation which lead to underestimate the overall magnitude of the noise.

In general, original high noise’s autocorrelation or lowering it due to data strategy and quality would engender an erroneous sens of confidence in the ability to detect a trend. Consequently, failing to consider noise characteristics and magnitude may mislead trend precision, and its standard deviation shall understate true uncertainty. This study provides concrete examples that underpin the falsely accurate estimation of trends due to misestimating the autocorrelation of the noise.