A probability prediction using conditional distribution function derived
from copula provides a great deal of flexibility in the suspended
sediment concentration as well as other hydrological variable
estimations, but the influencing variables of the probability prediction
model capability are necessary to be investigated. The bivariate
conditional distribution function of suspended sediment concentration
with runoff as its only influencing variable is firstly derived to
assess the sensitivity of the probability prediction to the choice of
copula and marginal distribution, and the probability prediction is
further extended to the trivariate conditional distribution function
with runoff and precipitation as its influencing variables. The approach
is exemplified using stationary mean daily precipitation, runoff and
suspended sediment concentration data sets from six hydrological
stations in the central Yellow River located in the Loess Plateau, which
is characterized by heavy sediment transport. The results of the
bivariate conditional distribution functions indicate that the
probability prediction is mainly influenced by the choice of copula
function, and the tail dependence of the copula function determines the
shape of the estimated suspended sediment concentration curve. The
comparison between the bivariate conditional distribution function,
trivariate conditional distribution function, and traditional sediment
rating curve demonstrates the uncertainty bands from trivariate
conditional distribution function are always smallest, and those from
the sediment rating curve are usually largest, while the difference
between different models become larger at hydrological stations with
smaller sample size.