  The cold dark matter (CDM) scenario generically predicts the existence of
triaxial dark matter haloes which contain notable amounts of substructure.
However, analytical halo models with smooth, spherically symmetric density
profiles are routinely adopted in the modelling of light propagation effects
through such objects. In this paper, we address the biases introduced by this
procedure by comparing the surface mass densities of actual N-body haloes
against the widely used analytical model suggested by Navarro, Frenk and White
(1996) (NFW).
  We conduct our analysis in the redshift range of 0.0 - 1.5. In cluster sized
haloes, we find that triaxiality can cause scatter in the surface mass density
of the haloes up to sigma_+ = +60% and sigma_- = -70%, where the 1-sigma limits
are relative to the analytical NFW model given value. Subhaloes can increase
this scatter to sigma_+ = +70% and sigma_- = -80%. In galaxy sized haloes, the
triaxial scatter can be as high as sigma_+ = +80% and sigma_- = -70%, and with
subhaloes the values can change to sigma_+ = +40% and sigma_- = -80%.
  We present an analytical model for the surface mass density scatter as a
function of distance to the halo centre, halo redshift and halo mass. The
analytical description enables one to investigate the reliability of results
obtained with simplified halo models. Additionally, it provides the means to
add simulated surface density scatter to analytical density profiles. As an
example, we discuss the impact of our results on the calculation of
microlensing optical depths for MACHOs in CDM haloes.
