  $^{37}$Ar is a promising candidate for complementing radioxenon isotopes as
indicators of underground nuclear explosions. This study evaluates its
potential anthropogenic background caused by emissions from commercial
pressurised water reactors. Various $^{37}$Ar production pathways, which result
from activation of $^{36}$Ar and of $^{40}$Ca, respectively, are identified and
their emissions quantified. In-core processes include (1) the restart of
operation and degassing of the primary cooling water after maintenance and
refueling shutdown, (2) the replacement of primary coolant water for limiting
its tritium concentrations, and (3) the leakage of $^{37}$Ar produced from
calcium impurities in UO$_{2}$ after fuel rod failures. Activation of air and
of calcium in concrete within the biological shield are major out-of-core
production pathways. Whereas emissions from in-core processes are transient, a
rather constant $^{37}$Ar source term results from its out-of-core production.
Generic atmospheric dispersion simulations indicate that already at moderate
distances from the emitter, concentrations of $^{37}$Ar caused by routine
reactor operations are far below its cosmogenic background in air. The only
exception results from an inadvertent reactor re-start without operation of the
primary cooling water degassing system for prolonged time. Such an event also
causes high emissions of $^{41}$Ar which can be used for discriminating its
$^{37}$Ar signal from an underground nuclear explosion.
