20
P. Muñoz et al.
Ideally, when producing ML algorithms for extreme discharge forecasting, it is
recommended to use target functions specifically designed for extreme flows (e.g.,
mean peak difference, see (Peleg and Gvirtzman 2010)). However, this demands
extensive data for properly training and testing models (enough independent flood
and drought events). In our case, less than 4 years of hourly information was not
sufficient for using target functions. To overcome this issue, our approach consisted
firstly in using the RF algorithm, which is capable to deal with small size samples
and has been already tested in a previous flood forecasting study using 2.5 years of
hourly information (Muñoz et al. 2018). Secondly, we proposed to train the model
for all flows, and to enrich model’s input with additional information specifically
aimed to improve the prediction of extreme high and low flows.
2.4 Graphical Techniques
We encountered two main issues when performing graphical analyses to the observed
and forecasted timeseries. The first one is known as homoscedasticity problem,
where the M SE and S
2
E Q increase with higher flows. To overcome this issue, we
employed a Box-Cox (BC) transformation to the discharge timeseries, according to
the recommendations of Willems (2009).
BC(q) =
q
λ
− 1
λ
,
where q is discharge and the parameter λ can be calibrated graphically until
reaching homoscedasticity in the residuals (constant standard deviation). We set λ
= 0.25, following the indications of Willems (2009) for runoff transformation.
The second problem is the serial dependence of flow magnitudes to the timescale
selected. The graphical evaluation of flows occurring at all hourly timesteps will
imply a higher representation of low flows. Moreover, the serial dependence for
extreme high flows (floods) is stronger for shorter timesteps (hourly or smaller than
the recession constant of the quickest subflow component). Here, the solution relies
on selecting nearly independent observations obtained by splitting the discharge
timeseries in events and using one value per event (peak-over-the-threshold approach,
see Willems (2009)).
Once both problems have been solved, we complemented model assessment with
a graphical inspection of the flow frequency distribution plots for extreme high and
low flows (observations vs. forecasts). This is aimed to evaluate the overall model
performance for both extreme flow conditions, floods, and droughts. It consists on
analyzing the behavior of the distribution curve toward its tail (higher values for
high frequency distribution and lower values for low flows frequency distribution).
Underestimation or overestimation of the tail toward more extreme values unmask
the weaknesses of a model for extreme flow forecasting.
P. Muñoz et al.
Ideally, when producing ML algorithms for extreme discharge forecasting, it is
recommended to use target functions specifically designed for extreme flows (e.g.,
mean peak difference, see (Peleg and Gvirtzman 2010)). However, this demands
extensive data for properly training and testing models (enough independent flood
and drought events). In our case, less than 4 years of hourly information was not
sufficient for using target functions. To overcome this issue, our approach consisted
firstly in using the RF algorithm, which is capable to deal with small size samples
and has been already tested in a previous flood forecasting study using 2.5 years of
hourly information (Muñoz et al. 2018). Secondly, we proposed to train the model
for all flows, and to enrich model’s input with additional information specifically
aimed to improve the prediction of extreme high and low flows.
2.4 Graphical Techniques
We encountered two main issues when performing graphical analyses to the observed
and forecasted timeseries. The first one is known as homoscedasticity problem,
where the M SE and S
2
E Q increase with higher flows. To overcome this issue, we
employed a Box-Cox (BC) transformation to the discharge timeseries, according to
the recommendations of Willems (2009).
BC(q) =
q
λ
− 1
λ
,
where q is discharge and the parameter λ can be calibrated graphically until
reaching homoscedasticity in the residuals (constant standard deviation). We set λ
= 0.25, following the indications of Willems (2009) for runoff transformation.
The second problem is the serial dependence of flow magnitudes to the timescale
selected. The graphical evaluation of flows occurring at all hourly timesteps will
imply a higher representation of low flows. Moreover, the serial dependence for
extreme high flows (floods) is stronger for shorter timesteps (hourly or smaller than
the recession constant of the quickest subflow component). Here, the solution relies
on selecting nearly independent observations obtained by splitting the discharge
timeseries in events and using one value per event (peak-over-the-threshold approach,
see Willems (2009)).
Once both problems have been solved, we complemented model assessment with
a graphical inspection of the flow frequency distribution plots for extreme high and
low flows (observations vs. forecasts). This is aimed to evaluate the overall model
performance for both extreme flow conditions, floods, and droughts. It consists on
analyzing the behavior of the distribution curve toward its tail (higher values for
high frequency distribution and lower values for low flows frequency distribution).
Underestimation or overestimation of the tail toward more extreme values unmask
the weaknesses of a model for extreme flow forecasting.