Piston-shock model is an analytic description of the momentum interchange between the coronal mass ejection (CME) and the ambient solar wind. The piston-shock model's equations express the trajectories of both, CME leading edge and shock front as functions of time. In order to calculate the trajecotries of CME leading edge and shock front, the model requires data available, in principle, since the detection time of the CME.
In the middle of 2015, the SCiESMEX Board decided to implement the Piston-Shock model as an experimental tool for arrival-forecasting of CME/shocks. Since then, the model's predictions have been regularly used in SCiESMEX's space weather reports (weekly and special issues).
SCiESMEX team explored the forecasting capabilities of the model, the test period finished by January 2016. Since January 2016, SCiESMEX began the development of SPArToS, which is an experimental tool for arrival-forecasting of CMEs based on the Piston-Shock model. In the near future, we expect to implement the model to arrival-recasting of shock waves.
The model allows the user to calculate:
The data inputs required by the model are:
Corona-Romero & Gonzalez-Esparza  used hydrodinamic numerical simulations to study the dynamic relations between fast CMEs (driver) and their associated shocks. They found that the relation between the drivers and the shocks could be addressed by an analytic approach by Canto et.al. . The analytic approach solves the mass center trajectory of two interacting fluid parcels through interchange of linear momentum and conservation of mass. According the numerical simulations, the masscenter corresponded to the leading edge of the driver (CME).
The numerical simulations pointed out that the trajectories of shocks have two dynamic phases: the first where the shock is driven by the CME, followed by a decaying phase. Although the shock is a non-adiabatic process, during the driving phase a shock wave has a constant speed, due to the driver replaces the energy and momentum spent by the shock wave. In contrast, in the decaying phase the shock evolves as a blast wave because the driver's energy is exausted.
By comparing the results from numerical simulations and analytic model, Corona-Romero & Gonzalez-Esparza  were able to use the analytic model and initial conditions of events to reproduce in-situ arrivals of CMEs and associated shocks. They also found systematic differences between calculated arrivals of shocks, which were provoke by the geometrical assumptions on analytic shock's shape.
Corona-Romero & Gonzalez-Esparza  changed the geometry of the associated shock wave from a spherical shock to a bow-shock. This extended version of the piston-shock model solved the systematic errors in calculated arrivals of shocks. Corona-Romero et.al.  validated this extended version by approximate the trajectories, in-situ arrivals, and type II radio bursts of a number of radio-loudly CME/shock events.
Corona-Romero & Gonzalez-Esparza  probed that piston-shock model is capable to approximate the in-situ transit profiles of shocks and plasma sheaths associated with the arrival of CMEs. Recently, Corona-Romero et.al. , have probed that piston shock model is capable to forecast in-situ arrivals of CMEs.
We have not finished to develop all the capabillities of piston-shock model. We are still working in finding new ways to use our model to describe solar storms.
Piston-shock model assumes that CMEs are fast and blunt ostacles that interact with ambient solar wind. The initial mass and energy of CMEs are set at the initiation of the event and remain constant along the interplanetary propagation of CMEs. The initial speed of CMEs need to be larger than the local super-magnetosonic speed. Thus, CMEs initially drive shock waves which geometry needs to resemble bow-waves. The ambient solar wind is thought stationary polytropic plasma, which expands at a constant rate.
Perhaps, the main assumption of the model is that CMEs drive for a short period (tens of minutes) their associated shocks. After this driving phase the CME and shock evolve independently each other. On one hand, the shock waves evolve as blast waves, until they discipate into compression waves. On the other hand, the CMEs decelerate due to the interaction with the shocked solar wind (plasma sheath material). This interaction provokes an inertial drag, leading CME speeds to asymptotically equilize solar wind expansion speed.
Piston-shock model is an hydrodynamic approach to a full MHD phenomenon. The validity of piston-shock model is linked to the local values of sonic (solar wind), alfvenic (solar wind), and magnetosonic (CME-speed) Mach numbers. As long these numbers be shorter than 1, the piston-shock model is reliable.
Piston-shock model obtains the best results for isolated events propagating during periods of quite solar activity. It is preferably that the events source region (associated solar flare's active region) be as near as possible from the solar disk center (Sun-Earth line of sight).
Piston-Shock model fails when analzing complex events (CME-CME or CME-streams interactions), save very special cases listed in Corona-Romero et.al. 
Peer-review published papers:
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