  Cosmic Microwave Background (CMB) full-sky temperature data show a
hemispherical asymmetry in power nearly aligned with the Ecliptic. In real
space, this anomaly can be quantified by the temperature variance in the
northern and southern Ecliptic hemispheres. In this context, the northern
hemisphere displays an anomalously low variance while the southern hemisphere
appears unremarkable (consistent with expectations from the best-fitting
theory, $\Lambda$CDM). While this is a well established result in temperature,
the low signal-to-noise ratio in current polarization data prevents a similar
comparison. This will change with a proposed ground-based CMB experiment,
CMB-S4. With that in mind, we generate realizations of polarization maps
constrained by the temperature data and predict the distribution of the
hemispherical variance in polarization considering two different sky coverage
scenarios possible in CMB-S4: full Ecliptic north coverage and just the portion
of the North that can be observed from a ground based telescope at the high
Chilean Atacama plateau. We find that even in the set of realizations
constrained by the temperature data, the low northern hemisphere variance
observed in temperature is not expected in polarization. Therefore, an
anomalously low variance detection in polarization would provide strong
evidence against the hypothesis that the temperature anomaly is simply a
statistical fluke. We show, within $\Lambda$CDM, how variance measurements in
both sky coverage scenarios are related. We find that the variance makes for a
good statistic in cases where the sky coverage is limited, however a full
northern coverage is still preferable.
