The sediment transport functions are, to varying degrees, combinations of theoretical and empirical science. Even the most theoretically detailed equations were fit to data using empirical coefficients. These coefficients represent the central tendencies of the data considered but will not likely reflect the transport of a specific site precisely, even if an appropriate transport function is selected. Therefore, HEC-RAS provides opportunities to "Calibrate" the transport function. This should be the last stop in calibration, after the user has selected the most appropriate (theoretically and based on initial performance) transport function, carefully checked all data and parameters, and considered calibrating by adjusting data within the observed range. To use calibration parameters first click the box labeled Modify Transport Functions with Factors or Parameters Defined in This Editor. If the box is not checked, variables can be edited and changed but they will not be used for transport calculations.

Transport Function Calibration and Modification Editor.

Scaling Factors:

Scaling Factors are (new in 5.1) are the preferred method for calibrating transport equations. Most transport functions are built around an excess shear or stream power function, where the shear or stream power is compared to a critical mobility factor ( $\begin{array}{l}\tau_c^*\end{array}$ , SV_c) raised to some power. So a simplified version of the MPM equation is often written:

$\begin{array}{l}\displaystyle q_b^* = 8 \left( \tau^* - \tau^*_c \right) ^{3/2}\end{array}$

where q_b^* is a dimensionless measure of transport (the Einstein number), $\begin{array}{l}\tau^*\end{array}$ is the dimensionless shear stress (the Shields number) and $\begin{array}{l}\tau_c^*\end{array}$ is the critical dimensionless shear.
The Scaling Factor calibration method provides users two opportunities to scale results. So, the simplified MPM function could be re-written with the two scaling factors:

$\begin{array}{l}\displaystyle q_b^* = \alpha \times 8 \left( \tau^* - \epsilon \times \tau^*_c \right) ^{3/2}\end{array}$

where is the Transport Function Scaling Factor and is the Critical Mobility Scaling Factor.

The transport function scaling factor is a simple linear multiplier on the capacity equation (e.g. 1.1 increases capacity 10% and 0.9 decreases capacity by 10%). The Critical Mobility Factor is a little more complicated, but also easier to justify physically. The Critical Mobility Scaling Factor affects the competence (the minimum flow at which water can move a grain class) as well as the capacity. It is inversely related to flow (a factor of 1.1 will make the sediment less mobile and will decrease transport). Additionally, because it is usually inside of the power, the effects are non-linear. Finally, not all transport functions use an excess shear/power/mobility form, so some (Engelund Hansen and Toffaleti) do not have a Critical Mobility Scaling Factor.

However, Buffington and Montgomery (1997) - among others - point out that the original critical shear data from Shields research had significant scatter and studies that have back-calculated critical Shields' parameters have found a wide range of values. So some modelers find mobility to be an appropriate, and more physically defensible parameter to adjust.

Table: List of the critical mobility factor adjusted with the scaling factor in each transport function (where applicable).

	Transport Scaling Factor	Critical Mobility Scaling Factor
Ackers-White	X	A
Engelund-Hansen	X
Laursen (Copeland)	X
Meyer-Peter Muller	X
Toffaleti	X
MPM-Toffaleti	X	in MPM
Yang	X	SV_c
Wilcock-Crowe	X

Warning: Be Careful Calibrating the Transport Function

These variables should only be adjusted within reasonable ranges in response to a hypothesis based on observed physical processes. Only change the critical shields parameter within a reasonable range, with physical justification. Changing coefficients no longer honors the form of the transport function.

Define Transport Function Parameters and Coefficients:

The second calibration option exposes parameters in four of the HEC-RAS transport functions. This feature is not recommended. The scaling factors are preferred, and the second method is mainly maintained for backward compatibility.
Each of the four transport functions has a variable that quantifies the force or energy required to mobilize the particle. In Laursen-Copeland and MPM it is the critical shear stress, $\begin{array}{l}\tau_c^*\end{array}$ (also known as the Shields number), in Ackers-White it is the Threshold Mobility (A) and in Wilcock it is the reference Shear Stress $\begin{array}{l}\tau_{rm}^*\end{array}$ . When calibrating a sediment transport function using this feature, these mobility factors should be the main parameters adjusted, since they can be related to physical phenomena. For example, imbricated or vegetated particles will be harder to move than the critical Shields parameter would suggest, so a physical case could be made for a higher $\begin{array}{l}\tau_c^*\end{array}$ , which would decrease transport. Conversely, the presence of substantial fine particles could make it easier for the flow field to entrain coarser particles, resulting in a lower $\begin{array}{l}\tau_c^*\end{array}$ .
Consider, again, the simplified form of MPM:

$\begin{array}{l}\displaystyle q_b^* = 8 \left( \tau^* - \tau^*_c \right) ^{3/2} , \space \tau^*_c = 0.047\end{array}$

where q_b^* is a dimensionless measure of transport (the Einstein number), $\begin{array}{l}\tau^*\end{array}$ is the dimensionless shear stress (the Shields number) and $\begin{array}{l}\tau_c^*\end{array}$ is the critical dimensionless shear. 8 and 3/2 are coefficients fit to the simple excess shear relationship in the original formulation. Exposing the critical shear stress, the coefficient and the power of the MPM relationship turns it into a generic excess shear formula that can be used to customize a site-specific excess shear, power function. In fact, Wong and Parker (2006) recently reanalyzed the data set initially used to develop the MPM equation and found that the relationship

$\begin{array}{l}\displaystyle q_b^* = 4.93 \left( \tau^* - \tau^*_c \right) ^{1.6} , \space \tau^*_c = 0.047\end{array}$

fit the original MPM data better than the MPM equation. Pressing the Use Wong and Parker Correction to MPM button, will automatically set the coefficient and power to the corrected values.

The transport function calibration menu offers the opportunity to use the Wong and Parker correction to the MPM equation, based on their 2006 paper. This reduces the MPM coefficient from 8 to 4.93, maintains the critical Shield's number of 0.047, and increases the power (MPM exponent) from 1.5 to 1.6. Wong and Parker's function was developed based only on reanalysis of data sets used by MPM without bed forms. Wong and Parker (2006) argued that the form drag correction embedded in many versions of MPM (including the one used in HEC-RAS) is not justified for lower-regime plane-bed conditions, and that MPM over-predicts bed load transport without it. Therefore, if the Wong Parker coefficients (a=4.93, =0.047, b=1.6) are used with MPM, whether entered manually or selected with the interface button, HEC-RAS will set the form drag correction to 1, which implies plane-bed conditions (i.e. no bed forms).

Warning: Be Careful Overwriting Dynamic Parameters

Several of the parameters exposed in this editor are actually functions that can have different values in different hydrodynamic and sediment settings. You may notice that selecting this method but leaving the parameters default may change the result because the default does not reflect the model conditions. This is why the scaling factors calibration method should be preferred (the direct parameterization may disappear in future versions). For example, the critical mobility scaling factor can adjust the reference shear in Wilcock and Crowe - as recommend–d - (Wilcock, personal communication) without over-writing the sand dependency built into the reference shear that is the main feature of the transport function.

Toffaleti Limiter

Yaw et al., (2019) Yaw, M., Pizzi, D., AuBuchon, J., Gronewold, R., Gibson, S. (2019) Middle Rio Grande and Tributaries Numerical Sediment Routing Study, Cochiti Dam to Elephant Butte Reservoir, Proceedings, SedHyd Interagency Sediment Conference. demonstrated that the Toffaleti equation (and the combined Toffaleti-MPM equation) include a discontinuity in high energy conditions for high energy conditions. This can lead to unrealistic transport under certain conditions. The issue emerges when the suspended zone equations try to compute transport for materials that are not suspended.

The Toffaleti Limiter (which is included in the Transport Function Calibration editor) uses a shear velocity-to-fall velocity ratio (u*/w≤0.4) to determine if the grain class is likely to be suspended by the hydraulics. The feature limits suspended transport to grain classes under that threshold and only includes the larger particles in the bed load (near bed) portion of the equation.

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Transport Function and Calibration

Scaling Factors:

Table: List of the critical mobility factor adjusted with the scaling factor in each transport function (where applicable).

Define Transport Function Parameters and Coefficients:

Toffaleti Limiter