Colored noise in GRACE total water storage time series: Its impact on trend significance in the Türkiye region and major world river basins.

• Temporal correlations exist in the GRACE TWS time series, resulting in the presence of colored noise. • To show the impact of these correlations, we apply autoregressive noise model and variance component estimation model. • Neglecting these correlations leads to underestimation of trend uncertainty, misinterpreting its significance. Temporal correlations are prevalent in most geophysical time series data, leading to what is known as colored noise, which become more apparent in the frequency domain rather than time domain. Neglecting this type of noise in modeling can result in underestimated standard errors for the parameters of the model used to analyze the time series. As a result, statistical tests misinterpret the significance of these parameters, such as the overall trend rate, because the "signal to noise" ratio becomes incorrectly larger than it should be. In this study, we investigate the temporal correlations in the time series data from the Gravity Recovery and Climate Experiment (GRACE) mission. GRACE and its successor mission GRACE Follow-On (GRACE-FO) have been successfully employed to monitor global total water storage anomalies over two decades since its initial launch in 2002. We primarily utilize monthly GRACE mascon (mass concentration) solutions provided by NASA Goddard Space Flight Center (GSFC), examining both regional and global scales. The power spectrum density of the residuals, calculated after applying standard harmonic regression to each mascon time series on Earth's land, reveals an average spectral index of κ = −1. This indicates the predominance of flicker noise, one of the most common forms of colored noise in geodetic time series. Notably, the noise becomes more Brownian (κ < −1) in regions with intense hydrological events, while it tends to be more white noise (κ → 0) in areas with less water circulation compared to other land regions. This observation suggests that unmodelled hydrological events, such as droughts, floods, and ones associated with ice-melting, contribute to the residuals as colored noise in the time series. To account for this noise in our time series modeling, we primarily consider autoregressive (AR) moving average (MA) process, commonly known as ARMA, in addition to the standard variance component estimation for noise amplitudes. We focus on individual mascon blocks in the Türkiye Region and mascon solutions for 24 world's major river basins. Our findings demonstrate that an ARMA(1,1) model is sufficient for describing the noise in these regions. The results underscore the importance of considering colored noise, as it leads to approximately three times larger standard errors for the overall trend rate. This substantially impacts the significance of the trend rates. [ABSTRACT FROM AUTHOR]