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tokens: into the ring current, which extends the recovery phase of the storm (Gonzalez et al. 1994 ; Fok et al. 1995 ; Jordanova et al. 1997 ; Miyoshi et al. 2003 ; Søraas et al. 2004 ; Tsurutani et al. 2006a ; Kasahara et al. 2009 ). The prediction of time corresponding to the minimum value that the Dst index will reach is the main goal of geomagnetic storm forecasting research. However, many technological applications rely on the expected time of the disturbed magnetosphere returning to quiet time conditions. These predictions are even more important for extreme/severe geomagnetic storms (Cid et al. 2014 ). In the literature, a linear proportional relation is expected between the decay rate of the ring current and the Dst index through the Dessler–Parker–Sckopke relationship (Olbert, Siscoe Vasyliunas 1968 ; Greenspan Hamilton 2000 ). Therefore, an exponential function was accepted to fit the recovery phase Dst index data to find the decay time of the storm (e.g. Burton, McPherron Russell 1975 ; Hamilton et al. 1988 ; Ebihara Ejiri 1998 ; O’Brien McPherron 2000 ; Dasso, Gómez Mandrini 2002 ; Kozyra et al. 2002 ; Wang, Chao Lin 2003 ; Weygand McPherron 2006 ; Monreal MacMahon Llop-Romero 2008 ). In a few cases, the decay time was expected to be a constant value (Burton et al. 1975 ). Moreover, in some cases, this was dependent on the convective electric field E y (O’Brien McPherron 2000 ), or also dependent on the dynamic pressure (Wang et al. 2003 ). However, the intense and/or extreme storms show a two-phase recovery profile, i.e. an early fast recovery phase followed by slow recovery. Therefore, it was difficult to model the observational data assuming a unique exponential function (Akasofu, Chapman Venkatesan 1963 ; Hamilton et al. 1988 ; Gonzalez et al. 1989 ; Prigancová Feldstein 1992 ; Liemohn et al. 1999 ; Monreal MacMahon Llop-Romero 2008 ). This issue was resolved by assuming a hyperbolic decay function (Aguado et al. 2010 ; Cid et al. 2014 ). In this model the entire recovery phase is dependent on two parameters, i.e. the minimum Dst value ( Dst 0 , the intensity of the storm or the value of the Dst index when the recovery phase starts) and the recovery time (τ h , the time to get the value of Dst 0 /2). A superposed epoch analysis of recovery phases of intense storms from 1963 to 2003 suggests that the hyperbolic decay function reproduces the experimental data better than the exponential function for any type of storm, which indicates a non-linear coupling between the decay rates of Dst and Dst (Aguado et al. 2010 ; Cid et al. 2014 ). Generally, the recovery phase takes one to two days or sometimes more than two days, depending on the source of the magnetic storm (Dessler Parker 1959 ; Gonzalez et al. 1994 ; Kozyra et al. 1997 ; Tsurutani et al. 2006a ). ICMEs generate extreme storms with an exponential/hyperbolic recovery phase profile of one or two days whereas the CIR- and high-speed stream (HSS)-driven magnetic storms can last from