  Reflectance losses on solar mirrors due to soiling are a significant
challenge for Concentrating Solar Power (CSP) plants. Soiling losses can vary
significantly from site to site -- with (absolute) reflectance losses varying
from fractions of a percentage point up to several percentage points per day
(pp/day), a fact that has motivated several studies in soiling predictive
modelling. Yet, existing studies have so far neglected the characterization of
statistical uncertainty in their parameters and predictions. In this paper, two
reflectance loss models are proposed that model uncertainty: an extension of a
previously developed physical model and a simplified model. A novel uncertainty
characterization enables Maximum Likelihood Estimation techniques for parameter
estimation for both models, and permits the estimation of parameter (and
prediction) confidence intervals.
  The models are applied to data from ten soiling campaigns conducted at three
Australian sites (Brisbane, Mount Isa, Wodonga). The simplified model produces
high-quality predictions of soiling losses on novel data, while the
semi-physical model performance is mixed. The statistical distributions of
daily losses were estimated for different dust loadings. Under median
conditions, the daily soiling losses for Brisbane, Mount Isa, and Wodonga are
estimated as $0.53 \pm 0.66$, $0.08 \pm 0.08$, and $0.58 \pm 0.15$ pp/day,
respectively. Yet, higher observed dust loadings can drive average losses as
high as $2$ pp/day.
  Overall, the results suggest a relatively simple approach characterizing the
statistical distributions of soiling losses using airborne dust measurements
and short reflectance monitoring campaigns.
