Uncertainty bands in thresh

[ernesto561]

Some of the differences in the implementation of the frequentist method of Rossi et al (2017) compared to Peruccacci et al (2012), are that in the bootstrapping procedure the median of the alpha and gamma values are selected instead of the mean, and the q5 and q95 are used as the uncertainty bands instead of plus and minus the standard deviation.

In Peruccacci et al (2012), the measures of the uncertainty Δα and Δγ, taken individually, identify two minimum and two maximum curves:

To evaluate the combined effect of the uncertainty associated with the intercept α and the scaling exponent γ, for each given rainfall duration D, they took the lowest and highest values of the two minimum and maximum curves:

In Rossi et al (2017) this is not mentioned explicitly, but because it's based on Peruccacci et al (2012), probably it's the same case, using the q5 and q95.

It seems that in RainSlide::thresh the uncertainty bands are calculated only considering the uncertainty in alpha, but not in gamma, as shown in the code for the lower band (not completely sure) thresh.R#L202. The bands plotted with the plot method of thresh are constant for all the values of D, compared to the ones shown in Rossi et al (2017), where the width is variable.

[raff-k]

your point is right. However, you can extract the boot$gamma uncertainty values and simply re-fit the function.

[ernesto561]

Thanks for your answer. For anyone else reading this, I have to take the boot$alpha$q5_sigma and boot$gamma$q5 values for the minimum curve and the boot$alpha$q95_sigma and boot$gamma$q95 for the maximum curve. Then, for each value of D, calculate the minimum of the minimum curves and the maximum of the maximum curves. The fitted values should be the boot$alpha$q50_sigma and the boot$gamma$q50. I'll give it a try.