online_modified_einstein: Total sediment discharge by the Modified Einstein Procedure

References
 Einstein, H. A., 1950. The bedload function for sediment transportation in open channel flows. USDA Soil Conservation Service, Technical Bulletin
No. 1026, Washington, D.C., September.
 Colby, B. R. and C. H. Hembree, 1955. Computations of total sediment discharge, Niobrara river, near Cody, Nebraska. U.S. Geological
Survey Water Supply Paper 1357, Washington, D.C.
 U.S. Bureau of Reclamation, 1955. Step method for computing total sediment load by the Modified Einstein Procedure. Sedimentation Section,
Hydrology Branch, Project Investigations Division, July.
 U.S. Bureau of Reclamation, 1966. Computation of "Z's" for use in the Modified Einstein Procedure. Sedimentation Section,
Hydrology Branch, Project Investigations Division, June.

FEATURES
[Main Page]
[Sample input]
[Rationale]
[Procedure]
 The fall velocities to calculate the multipliers of Col. 13 are calculated using Rubey's formula.
 In SI units, input is metric, and the data is converted to U.S. units for internal execution.
Output from Columns 1 to 24 is the same for both systems of units.
Column 24 is the computed load in tons/day, and Column 25 is the equivalent in Metric tons/day.
 The program can take either of two sets of size fractions: Normal (9 sizes) and Long (10 sizes).
 The viscosity vs temperature table used is that given by Linsley (Linsley, R. K., 1982. Hydrology for Engineers, 3rd Edition, McGrawHill,
New York). This table is essentially the same as Plate 2 of USBR (1955).
 The reference size fraction is chosen as the diameter that has the largest percentage of suspended load (Column 11).
 The USBR (1955) Z' computational mode states that the ratio of Z' for each size fraction to Z' for the reference size fraction is equal to
the ratio of their respective fall velocities to the 0.7 power. The fall velocities are calculated by Rubey's formula. The multipliers of Col. 13 are the
ratios of fall velocities to the 0.7 power. Given a Z' for the reference size, estimated by trial and error, the remaining Z's (Col. 14)
are calculated using the multipliers (Col. 13).
The USBR (1966) Z' computation is implemented in the following way:  A value of Z'_{r} for the reference size fraction is found by trial and error, as
described in USBR (1955).
 A value of Z'_{r+1} for the next greater size fraction is found in the same way.
 These two values of Z' are plotted
against their respective fall velocities, to find: Z' = α V^{ β}.
 This latter relation is used to calculate Z' for all other size fractions
(Col. 14).
 The multipliers of Col. 13 are not used in the USBR (1966) method.
The results of computations using the UBSR (1966) Z' method may differ from those calculated with the USBR (1955) method.
While the Z's calculated with the USBR (1955) method are based on only one size fraction (the reference size), the Z's calculated with the 1966 method are based
on more than one size fraction (USBR, 1966).
 Caution:
 For the USBR (1955) Z' method, the reference size fraction is that with the largest percentage in Col. 11.
This requires that Columns 7 and 11 be greater than zero (0) for the reference size fraction. This is typically the case. Otherwise, the problem is undefined.

For the USBR (1966) Z' method, the two size fractions considered are the reference size fraction and the next larger size fraction.
This requires that Columns 7 and 11 be greater than zero (0) for these two size fractions. Otherwise, the problem is undefined.
In other words, for the USBR (1955) option to work, there should be at least one size fraction for which there is both [sampled] bed material (Col. 7)
and [sampled] suspended material (Col. 11). It is also desirable that the chosen reference size fraction (Item 5) have a substantial [sample]
bed material in Col. 7.
Likewise, for the USBR (1966) option to work, there should be at least two size fractions for which there is
both [sampled] bed material (Col. 7)
and [sampled] suspended material (Col. 11).
 The default unit system is U.S. Customary.
 Please report errors or omissions to vponce@sdsu.edu

