  Rising concerns about the impact of space weather-related disruptions demand
modelling and reliable forecasting of coronal mass ejection (CME) impacts. In
this study, we demonstrate the application of the modified Miller-Turner (mMT)
model implemented in EUropean Heliospheric FORecasting Information Asset
(EUHFORIA), to forecast the geo-effectiveness of observed coronal mass ejection
(CME) events in the heliosphere. The goal is to develop a model that not only
has a global geometry to improve overall forecasting but is also fast enough
for operational space weather forecasting. We test the original full torus
implementation and introduce a new three-fourth Torus version called the
Horseshoe CME model. This new model has a more realistic CME geometry, and it
overcomes the inaccuracies of the full torus geometry. We constrain the torus
geometrical and magnetic field parameters using observed signatures of the CMEs
before, during, and after the eruption. The assessment of the model's
capability to predict the most important Bz component is performed using the
advanced Dynamic Time Warping technique. The Horseshoe model prediction of CME
arrival time and geo-effectiveness for both validation events compare well to
the observations and are weighed with the results obtained with the spheromak
and FRi3D models that were already available in EUHFORIA. The runtime of the
Horseshoe model simulations is close to that of the spheromak model, which is
suitable for operational space weather forecasting. Yet, the capability of the
magnetic field prediction at 1~AU of the Horseshoe model is close to that of
the FRi3D model. In addition, we demonstrate that the Horseshoe CME model can
be used for simulating successive CMEs in EUHFORIA, overcoming a limitation of
the FRi3D model.
