4.0 Equation Notation

English

B = width of stream channel (cm)
C = dissolved instream contaminant concentration (g mL^-1 or Ci mL^-1)
C_i = decayed concentration of the i-th member of the decay chain (i = 1 for the parent, i = 2 for the first decay product, etc.) (Ci mL^-1)
C_n = contaminant concentration for the current receptor (g mL^-1 or Ci mL^-1)
C_n-1 = contaminant concentration for the previous receptor (g mL^-1 or Ci mL^-1)
C_p = undecayed parent concentration (Ci mL^-1)
D_x,D_y,D_z = dispersion coefficients in the x-, y-, and z-directions, respectively (cm² s^-1)
f = fraction of the source term upstream of the receptor (dimensionless)
f_n = fraction of the source term upstream of the current receptor (dimensionless)
f_n-1 = fraction of the source term upstream of the previous receptor (dimensionless)
h = depth of stream (cm)
l_m = lateral distance over which the contaminant is assumed to be uniformly distributed (equivalent to one-half the standard deviation) (cm)
l'_m = alternative lateral distance over which the contaminant is assumed to be uniformly distributed (cm)
l_m(n) = lateral mixing length at the current receptor location (cm)
l_m(n-1) = lateral mixing length at the previous receptor location (cm)
l_s = total length of the source term (cm)+
l_ur = length of the source term upstream of the receptor (cm)
M = contaminant mass or activity per unit area (g cm^-2 or Ci cm^-2)
M_T = total mass or activity being released from the waste site (g or Ci)
Qc = contaminant flux at the source (g s^-1 or Ci s^-1)
Q_r = river discharge at the receptor location (cm³/s)
Q_ratio = dilution ratio (dimensionless)
Q_r(n) = river discharge at the current receptor location (mL s^-1)
Q_r(n-1) = river discharge at the previous receptor location (mL s^-1)
Q_s = river discharge at the source location (cm³/s)
t_t = representative contaminant travel time (s)
t_m = time to achieve the fully mixed condition (i.e., representative contaminant travel time) (s)
u = average instream flow velocity (cm s^-1)
u^* = shear velocity (cm s^-1)
x = downstream distance to receptor (cm)
y = lateral distance to receptor (cm)

Greek

b = proportionality constant used to calculate the lateral dispersion coefficient (dimensionless)
l = degradation/decay constant [= (ln 2)/(half-life)] (s^-1)
l_{1 =} radiological decay coefficient of the parent (s^-1)
l_{i =} radiological decay coefficient of the i-th member of the decay chain (s^-1)
x = proportionality constant in the alternative mixing length equation (dimensionless)
s_{l =} standard deviation of the Gaussian distribution of the one-dimensional advective-dispersive equation in the lateral direction (cm)
t = time at which the release from the waste site ends (s)
f = proportionality constant in the alternative mixing length equation (reciprocal of x) (dimensionless)