Gartner 2014 Models¶

The gartner2014 (or g14) module provides two functions that implement the potential sediment volume models of Gartner et al., 2014. In brief, these are a long-term and emergency assessment model.

Emergency Assessment Model¶

This model is given by:

\[lnV = 4.22 + 0.39\ \mathrm{sqrt}(i15) + 0.36\ \mathrm{ln}(Bmh) + 0.13\ \mathrm{sqrt}(R)\]

\[V = \mathrm{exp}(lnV)\]

\[\mathrm{95\%} \ \mathrm{CI} = \mathrm{exp}[lnV ± (1.96 \times 1.04)]\]

where:

Variable	Description	Units
V	Potential sediment volume	m³
lnV	Natural log of potential sediment volume
i15	Peak 15-minute rainfall intensity	mm/hour
Bmh	Catchment area burned at moderate or high intensity	km²
R	Watershed relief	meters
1.96	Normal distribution percentile multiplier for 95% confidence interval
1.04	Residual standard error of the model

You can run this model using the emergency function. This function returns the estimated potential sediment volumes (V), the lower bound of the 95% confidence interval (Vmin), and the upper bound of the 95% confidence interval (Vmax). For example, assuming you have already built a stream segment network:

from pfdf.models import g14
from pfdf import severity, watershed

# Compute model inputs
i15 = 0.24
moderate_high = severity.mask(barc4, ["moderate","high"])
Bmh = segments.burned_area(moderate_high)
relief = watershed.relief(dem, flow)
R = segments.relief(relief)

# Estimate debris-flow volume
V, Vmin, Vmax = g14.emergency(i15, Bmh, R)

You can also use the Ci, Cb, Cr, and B options to change the values of the model coefficients and intercept:

# Estimate volume using custom parameters
V, Vmin, Vmax = g14.emergency(i15, Bmh, R, B=4.23, Ci=0.38, Cb=0.35, Cr=0.12)

And the CI and RSE options to calculate custom confidence intervals:

# Estimate the 90% CI using a custom RSE
V, Vmin, Vmax = g14.emergency(i15, Bmh, R, CI=0.9, RSE=1.13)

Long-term Model¶

This model is given by:

\[lnV = 6.07 + 0.71\ \mathrm{ln}(i60) + 0.22\ \mathrm{ln}(B_t) - 0.24\ \mathrm{ln}(T) + 0.49\ \mathrm{ln}(A) + 0.03\ \mathrm{sqrt}(R)\]

\[V = \mathrm{exp}(lnV)\]

\[\mathrm{95\%} \ \mathrm{CI} = \mathrm{exp}[lnV ± (1.96 \times 1.25)]\]

where:

Variable	Description	Units
V	Potential sediment volume	m³
lnV	Natural log of potential sediment volume
i60	Peak 60-minute rainfall intensity	mm/hour
Bt	Total burned catchment area	km²
T	Time elapsed since fire	years
A	Total catchment area	km²
R	Watershed relief	meters
1.96	Normal distribution percentile multiplier for 95% confidence interval
1.25	Residual standard error of the model

You can run this model using the longterm function. This function returns the estimated potential sediment volumes (V), the lower bound of the 95% confidence interval (Vmin), and the upper bound of the 95% confidence interval (Vmax). For example, assuming you have already built a stream segment network:

from pfdf.models import g14
from pfdf import severity

# Compute model inputs
i60 = 0.96
burned = severity.mask(barc4, "burned")
Bt = segments.burned_area(burned)
T = 2
A = segments.area()
R = segments.relief(relief)

# Estimate debris-flow volume
V, Vmin, Vmax = g14.longterm(i60, Bt, T, A, R)

You can also use the Ci, Cb, Ct, Ca, Cr, and B options to change the values of the model coefficients and intercept:

# Estimate volume using custom parameters
V, Vmin, Vmax = g14.longterm(i60, Bt, T, A, R, B=6.08, Ci=0.72, Cb=0.21, Ct=0.25, Ca=0.48, Cr=0.04)

And the CI and RSE options to calculate custom confidence intervals:

# Estimate the 90% CI using a custom RSE
V, Vmin, Vmax = g14.longterm(i60, Bt, T, A, R, CI=0.9, RSE=1.13)