Landscape Processes

Input Rasters

All clipped to study area and coregistered

Name	Description	units
`dem`	elevation	m
`precip`	precipitation 30 year norm	m/day
`T`	transmissivity of soil (Ksat * depth)	m^2/day
$p_{s}$	particle bulk density of the soil	kg/m^3
`loss_factor`	ET and land use coeffictient	(dimensionless)

Derived Rasters:

Input	Description	Source	units
$a$	contributing area	dem	m^2
$b$	contour width	dem pixel resolution	m
$\theta$	slope	dem	degrees
$M$	slope: sine(theta)	dem	(dimensionless)
$q$	runoff	precip * loss factor (ET, land use raster)	m/day

Parameters:

Symbol	Description	Default Value	units
$\tau$	critical sheer stress for channelization	16	Pa
$\phi$	internal friction angle	45	degrees
$k$	surface roughness	10000	(dimensionless)

Constants:

Symbol	Description	Value	Units
$p_{w}$	water density	1000	kg/m^3
$g$	gravity constant	9.81	m/s^2
$v$	kinematic viscosity	$1.31 * 10 ^(-6)$	m^2/s
	seconds per day	86400	s/d

Saturated:

$\frac{a}{b}> \frac{T }{q}M$

Channelization:

$\frac{a}{b}> \frac{2\tau^3 }{p_{w}^{3}kvg^2M^2q} + \frac{T}{q}M$

Shallow Landsliding:

$\frac{a}{b}> \frac{p_{s}}{p_{w}} \left [ 1 - \frac{tan\theta}{tan\phi} \right ]\frac{T}{q}M$

Unconditionally stable:

$tan\theta < 0.5 tan\phi$

Unconditionally unstable

$tan\theta > tan\phi$