# DimensionlessDischarge: Testing thresholds of debris flows in stream segments following Tang et al.#

Code author: S Lundell

Section author: S Lundell

class DimensionlessDischarge(*args, **kwds)[source]#

Bases: Component

Component that calculates dimensionless discharge of stream

segments.

The dimensionless discharge model calculates the unitless discharge value of streams and can be used to help determine locations of debris flows. It uses an equation from Tang et al. (2019) to calculate the dimensionless discharge as well as the threshold for whether a debris flow will occur for a specified location.

\begin{align}\begin{aligned} q* = \frac{q}{\sqrt{\frac{\rho_s-\rho}{\rho}*g*D_{50}^3}}\\where :math:q* is the dimensionless discharge value for a stream segment, :math:q is flux in a stream segment, :math:\rho_s is soil density, :math:\rho is water density, :math:g is the gravitational constant, and :math:D_50 is the average sediment partical size in the stream segment area.\\Constants C and N are coefficients used in the slope-dependent equation\\.. math::\\ q*_{thresold} = \frac{C}{(tan(\theta))^N}\\to determine whether the dimensionless discharge calculated exceeds thresholds for a sediment-laden (Upper Limit) or water-producing only (Lower Limit) debris flow. C and N are empirically-derived by comparing dimensionless discharge estimates against previous debris flow events. The values will vary based on local geology and soil type. In southern California values of C=12 and N=0.85 (upper limits, Tang et al, 2019) and C=4.29, N=0.78 (lower limits, Tang et al, 2019) have been used, while values of C=0.195 and N=1.27 have been in used in the Italian Dolomites (Gregoretti and Fontana, 2008). Default values are C=12 and N=0.85.\\Examples -------- >>> from landlab.components import DimensionlessDischarge >>> from landlab import RasterModelGrid >>> import random >>> watershed_grid = RasterModelGrid((3, 3)) >>> surface_water__unit_discharge = watershed_grid.add_ones( ... "surface_water__unit_discharge", at="node" ... ) >>> d50 = watershed_grid.add_ones( ... "channel_bottom_sediment_grain__d50_diameter", at="node" ... ) >>> watershed_grid.at_node["topographic__elevation"] = np.array( ... [[1.1, 2, 3, 4, 2, 3, 4, 5, 3]] ... ) >>> dd = DimensionlessDischarge(watershed_grid, gravity=9.8) >>> dd.run_one_step() >>> watershed_grid.at_node["dimensionless_discharge"] array([0.55372743, 0.55372743, 0.55372743, 0.55372743, 0.55372743, 0.55372743, 0.55372743, 0.55372743, 0.55372743])\\References ---------- Tang, H., McGuire, L. A., Rengers, F. K., Kean, J. W., Staley, D. M., & Smith, J. B. (2019). Developing and Testing Physically Based Triggering Thresholds for Runoff-Generated Debris Flows. Geophysical Research Letters, 46(15), 8830–8839. https://doi.org/10.1029/2019GL083623\end{aligned}\end{align}

Initialize the DimensionlessDischarge.

Parameters:
• soil_density (float, field name, or array, optional) – density of soil (kg/m^3) (defaults to 1330)

• water_density (float, optional) – density of water (kg/m^3) (defaults to 997.9)

• C (float, optional) – Numerator of the debris flow threshold equation; Empirically derived constant (See Tang et al. 2019). (defaults to 12.0)

• N (float, optional) – Exponent for slope in the denominator of the debris flow threshold equation; Empirically derived constant (See Tang et al. 2019). (defaults to 0.85)

• gravity (float, optional) – (defaults to scipy’s standard acceleration of gravity)

• channel_bottom_sediment_grain__d50_diameter (float, field_name, or array) – defaults to the field name “channel_bottom_sediment_grain__d50_diameter”

__init__(grid, soil_density=1330, water_density=997.9, C=12.0, N=0.85, gravity=9.80665, channel_bottom_sediment_grain__d50_diameter='channel_bottom_sediment_grain__d50_diameter')[source]#

Initialize the DimensionlessDischarge.

Parameters:
• soil_density (float, field name, or array, optional) – density of soil (kg/m^3) (defaults to 1330)

• water_density (float, optional) – density of water (kg/m^3) (defaults to 997.9)

• C (float, optional) – Numerator of the debris flow threshold equation; Empirically derived constant (See Tang et al. 2019). (defaults to 12.0)

• N (float, optional) – Exponent for slope in the denominator of the debris flow threshold equation; Empirically derived constant (See Tang et al. 2019). (defaults to 0.85)

• gravity (float, optional) – (defaults to scipy’s standard acceleration of gravity)

• channel_bottom_sediment_grain__d50_diameter (float, field_name, or array) – defaults to the field name “channel_bottom_sediment_grain__d50_diameter”

run_one_step()[source]#