  High-precision pulsar timing requires accurate corrections for dispersive
delays of radio waves, parametrized by the dispersion measure (DM),
particularly if these delays are variable in time. In a previous paper we
studied the Solar-wind (SW) models used in pulsar timing to mitigate the excess
of DM annually induced by the SW, and found these to be insufficient for
high-precision pulsar timing. Here we analyze additional pulsar datasets to
further investigate which aspects of the SW models currently used in pulsar
timing can be readily improved, and at what levels of timing precision SW
mitigation is possible. Our goals are to verify: a) whether the data are better
described by a spherical model of the SW with a time-variable amplitude rather
than a time-invariant one as suggested in literature, b) whether a temporal
trend of such a model's amplitudes can be detected. We use the pulsar-timing
technique on low-frequency pulsar observations to estimate the DM and quantify
how this value changes as the Earth moves around the Sun. Specifically, we
monitor the DM in weekly to monthly observations of 14 pulsars taken with LOFAR
across time spans of up to 6 years. We develop an informed algorithm to
separate the interstellar variations in DM from those caused by the SW and
demonstrate the functionality of this algorithm with extensive simulations.
Assuming a spherically symmetric model for the SW density, we derive the
amplitude of this model for each year of observations. We show that a spherical
model with time-variable amplitude models the observations better than a
spherical model with constant amplitude, but that both approaches leave
significant SW induced delays uncorrected in a number of pulsars in the sample.
The amplitude of the spherical model is found to be variable in time, as
opposed to what has been previously suggested.
