Modelling dNBR
Predicting dNBR based on elevation and northness
In MATLAB 2014a I used the group statistics [grpstats()] to calculate the average dNBR by elevation (10m bin sizes) and northness (0.1 bins). Next I used Matlab's CurveFittingTool to fit the distributions using least-squares regression. A Gaussian model was fit to a function of the average dNBR (from MTBS) and elevation. There was a strong correlation between dNBR and elevation
Increasing northness showed a positive correlation with
dNBR versus elevation Gaussian model
MEDIAN
General model Gauss1:
f(x) = a1*exp(-((x-b1)/c1)^2)
Coefficients (with 95% confidence bounds):
a1 = 258.7 (252.4, 265)
b1 = 1974 (1950, 1999)
c1 = 957 (912.3, 1002)
Goodness of fit:
SSE: 1.233e+05
R-square: 0.8319
Adjusted R-square: 0.83
RMSE: 26.1
MAXIMUM
General model Gauss1:
f(x) = a1*exp(-((x-b1)/c1)^2)
Coefficients (with 95% confidence bounds):
a1 = 1146 (1123, 1169)
b1 = 2099 (2073, 2125)
c1 = 967.8 (926, 1010)
Goodness of fit:
SSE: 1.726e+06
R-square: 0.9089
Adjusted R-square: 0.9079
RMSE: 97.65
STANDARD DEVIATION
General model Gauss1:
f(x) = a1*exp(-((x-b1)/c1)^2)
Coefficients (with 95% confidence bounds):
a1 = 257.8 (252.1, 263.6)
b1 = 2183 (2158, 2209)
c1 = 830.2 (793.1, 867.3)
Goodness of fit:
SSE: 9.43e+04
R-square: 0.9292
Adjusted R-square: 0.9284
RMSE: 22.83
dNBR versus Northness Gaussian model
MEDIAN
General model Gauss1:
f(x) = a1*exp(-((x-b1)/c1)^2)
Coefficients (with 95% confidence bounds):
a1 = 189.3 (164.6, 213.9)
b1 = 1.55 (-0.9604, 4.061)
c1 = 5.156 (0.9536, 9.359)
Goodness of fit:
SSE: 984.7
R-square: 0.7558
Adjusted R-square: 0.7286
RMSE: 7.396
MAXIMUM
General model Gauss1:
f(x) = a1*exp(-((x-b1)/c1)^2)
Coefficients (with 95% confidence bounds):
a1 = 1177 (1157, 1197)
b1 = 0.01042 (-0.1668, 0.1876)
c1 = 4.312 (2.904, 5.72)
Goodness of fit:
SSE: 1.471e+04
R-square: 0.3692
Adjusted R-square: 0.2991
RMSE: 28.58
STANDARD DEVIATION
General model Gauss1:
f(x) = a1*exp(-((x-b1)/c1)^2)
Coefficients (with 95% confidence bounds):
a1 = 190.8 (185.4, 196.3)
b1 = 0.3672 (0.1814, 0.553)
c1 = 2.497 (1.958, 3.037)
Goodness of fit:
SSE: 1274
R-square: 0.7897
Adjusted R-square: 0.7664
RMSE: 8.413
Incorporating existing vegetation into future dNBR predictions
The predicted models of dNBR (shown above) do not take into account the influence existing vegetation on the likely dNBR should it burn in a future fire.
In order to account for the impact of vegetation on dNBR I suggest using one of the Gridmetric layers for vegetation - either mean height above ground or max height above ground