  We investigate whether the current Hubble parameter $H(z)$ measurements could
help improve the constraints on dark energy on the basis of the mainstream
cosmological probes including the type Ia supernovae (SN) observation, the
cosmic microwave background anisotropies (CMB) observation, and the baryon
acoustic oscillations (BAO) observation. For the current $H(z)$ data, we use 30
data points measured by using a differential age method. Furthermore, we also
consider the future $H(z)$ measurements based on the Sandage-Loeb (SL) test by
means of the E-ELT in construction, and thus we also use 30 simulated $H(z)$
data according to a 10-year SL test observation. In this work, we choose four
typical dark energy models as examples, i.e., the $\Lambda$CDM model, the
$w$CDM model, the $\alpha$DE model, and the GCG model, to complete the
analysis. We find that, when only the current $H(z)$ data are added, the
constraints on these models are not improved compared to the cases using the
SN+CMB+BAO data; but when further adding the 10-year SL test data, the
constraint results are tremendously improved for all the four models.
Therefore, we conclude that, although the current $H(z)$ measurements could not
provide an evident improvement on the basis of the current mainstream
cosmological probes, the future $H(z)$ measurements from the SL test would have
enormous potential to change the status of the Hubble parameter measurements in
constraining dark energy.
