---
title: "Parker (1990) Bedload Equation | Sediment Transport"
slug: "parker-1990-bedload-equation"
description: "Find the Parker (1990) bedload equation and its suggested application."
tags: ["1D river modelling"]
updated: 2022-09-23T15:02:01Z
published: 2022-09-23T15:02:01Z
canonical: "help.floodmodeller.com/parker-1990-bedload-equation"
stale: true
---

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# Parker (1990) Bedload Equation

The Parker bedload equation was developed from field measurements of graded sediment transport in gravel-bed Oak Creek, Oregon, U.S.A. (bed surface $D_{50} = 54$mm, $\sqrt{D_{84}/D_{16}}=2.09$, $S=0.0097-0.0108$, $h=0.31-0.45$m, $V=0.84-1.16$m/s). The Parker equation is based on the use of a so-called 'hiding function', which is a correction of the mobility of different size fractions in graded sediments for intergranular effects. These effects reduce the mobility of fine fractions (due to sheltering from larger grains) and increase the mobility of coarse fractions (due to increased exposure) in graded sediments compared to uniform sediments. The form of the equation used is:

![image048(1).gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image048%281%29.gif) (A11)

where ![image050(1).gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image050%281%29.gif) is the transport parameter for i-th size fraction (of proportion Fi), defined as

![image052(1).gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image052%281%29.gif)

![image054.gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image054.gif) is the function given by

![image056.gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image056.gif)

![image058.gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image058.gif)is the normalized dimensionless bed shear stress,

![image060.gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image060.gif)

![image062.gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image062.gif) is the straining parameter,

![image064.gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image064.gif)

![image066.gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image066.gif)is the arithmetic standard deviation of the surface size distribution,

![image068.gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image068.gif)

![image070.gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image070.gif) is the bed surface geometric mean size,

![image072.gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image072.gif)

![image074.gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image074.gif)

![image076.gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image076.gif)

![image078.gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image078.gif)

![image080.gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image080.gif)

The parameters ![image082 (1).gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image082%20%281%29.gif) and ![image084 (1).gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image084%20%281%29.gif) are functionally related ![image086.gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image086.gif) to as given below.

![SedimentTransportimagesimage088.gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/SedimentTransportimagesimage088.gif)

**Plots of ![image082 (1).gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image082%20%281%29.gif) and ![image084 (1).gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image084%20%281%29.gif) versus ![image086.gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image086.gif).**

The reduced hiding function ![image093.gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image093.gif) is defined as

![image095.gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image095.gif)

The suggested applicability of the Parker equation is for gravel-bed streams with ![image066.gif](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/image066.gif) <2 and negligible suspended load.