Verhoff et al. [1980] (also see
Thomas and Lewis [1995])
describes a stratified sampling method to estimate nutrient and chemical
transport.
Each sample is assigned to one of 
strata according to discharge.
The weight corresponding to each
observation is proportional to the probability associated with its stratum
(in this case, the amount of time that discharge was within the bounds of
the stratum)
and inversely proportional to the number of samples in the stratum.
Approximate confidence intervals for resulting estimates are derived.
To implement stratified sampling one first divides the target population,
usually next year's sediment load, into strata corresponding to ranges of
water discharge
or to some other explanatory variable.
The load in the h-th stratum, denoted 
, can be expressed as the sum of the
loads corresponding to each of 
equal-sized intervals in that stratum:
where
The true total load is the sum of the loads in each stratum:
where
Equations (9) and (10) can be combined to yield:
which provides the basis for the stratified estimators. Having collected at least one sample (i.e. one observation of concentration, and therefore also of load) in each stratum, total load can be estimated by:
where
sampled intervals represent the 
intervals
in the h-th stratum;
The variance of 
can be estimated by:
where
