Nonlinearity in the trend of GRACE time series: improving understanding of global total water storage changes over two decades

Abstract

The Gravity Recovery and Climate Experiment (GRACE) mission and its successor, the GRACE Follow-On mission, have been continuously observing changes in Total Water Storage (TWS) since 2002. These global, monthly, two-decade changes are conventionally modelled using a harmonic regression function, assuming a linear trend and seasonal signals; the former is extremely important because it indicates the long-term loss or gain of water masses. However, current climate change, sudden, unpredictable floods, or prolonged droughts, increased human water withdrawals due to increased demand in drought-affected areas or excessive population growth, make the actual long-term changes occurring in the TWS time series significantly different from the linear trend. For the first time, we parameterize these deviations globally, supplementing the conventional model with a polynomial function of the third, fourth and fifth degree; the optimal degree is chosen separately for each region. We demonstrate that the new parameterized augmented deterministic model of the TWS has advantages, as the previously unparameterized nonlinearities lead to improvements in the root-mean-square (RMS) values of up to 50%, especially for areas where nonlinearity is most pronounced. Furthermore, it allows for the assessment of the nature of the residuals of the TWS series, previously considered white noise, and leads to more reliable interpretations of short-term events such as droughts or floods.