3.5. Static modelling with point operations: forest fire¶
3.5.1. Introduction and gradient calculation¶
In a static model, we can calculate the time that the front of a forest fire reaches a certain cell location using weighted (relative) distance calculation, assuming the fire spreading is restricted to neighbouring cells in uphill direction only. This approach, further explained in the next section, requires a map with cell values representing the velocity of the forest fire spreading at that cell, given in hours per metre distance. The value of this velocity (h/m) is calculated as:
h = bes/a
with, b, a parameter, s, the gradient of the topographical surface (m/m), a a parameter, and h velocity of forest fire spreading at the cell. The value of b is known, b = 0.002, and it is assumed here that the gradient can be calculated from the digitial elevation model (assumed to have zero uncertainty). The value of a is known with a certain uncertainty, and thus a is modelled as a stochastic parameter (constant over the whole area) with a probability distribution, defined by a mean of 0.5 and a variance of 0.01.
Go to the folder fire
and display all maps in the folder, including dem.map
, the digital elevation model that can be used to calculate the gradient. Open the script stochStaticMod.py
. Add statements to calculate a variable gradient
containing the slope of the topographical surface, write to disk under the file name gradient
. Save and run the script, and display gradient
.
Question: Where did you type the statements?
- In the premcloop.
- In the initial.
- In the postmcloop.
- At the top of the script, below the from.. statements.
3.5.2. Point operation to calculate fire front velocity¶
In stochStaticMod.py
, add a statement that calculates realizations of a. Use the variable name a
written to disk with a file name a
. You will need to use the function mapnormal
. Save the script and run. Check the output.
Calculate the mean, variance, and percentiles of a
in the postmcloop. Save the script and run. Display the output. Be sure to check whether the mean and variance of a
are correct.
Calculate h, save the variable as hpm
(i.e., hours per minute) and calculate mean, variance, and percentiles. Display the output.
Question: What is the probability density distribution of the velocity of the forest fire, i.e. what is the shape? Explain the shape using the equation used to calculate it.
- The probability density distribution has a zero standard deviation, due to the exponent, reducing the variation.
- The shape of the probability density distribution is normal, because the equation uses a normally distributed variable in the exponent of a natural logarithm.
- The shape of the probability density distribution is log-normal, because the equation uses a normally distributed variable in the exponent of a natural logarithm.
- The shape of the probability density distribution is uniform, which is due to the exponent.
Question: What is the variance and the standard deviation of the velocity of forest fire (h/m) at the gridcell location indicated on house.map
? Write down and store, you will need it later on.
- average = 0.045, variance = 0.43·10-9, standard deviation = 2·10-10
- average = 0.45, variance = 4.3·10-9, standard deviation = 2·10-9
- average = 0.0045, variance = 7.58·10-7, standard deviation = 8.71·10-4
- average = 0.0045, variance = 4.3·10-9, standard deviation = 2·10-9
Question: Display hpm
together with the slope map gradient
. Plot the 95% confidence interval for a (threshold) value of 0.005. A velocity below 0.005 is considered a high forest fire front spreading velocity. For what areas in terms of slope values is it not distinguishable whether the value is above or below the threshold?
- For areas with a slope of about 0.1.
- For areas with a slope of about 0.2.
- For areas with a slope of about 0.5.
- For areas with a slope of about 0.7.