Event selection for dynamical downscaling: a neural network approach for physically-constrained precipitation events

Abstract

This study presents a new dynamical downscaling strategy for extreme events. It is based on a combination of statistical downscaling of coarsely resolved global model simulations and dynamical downscaling of specific extreme events constrained by the statistical downscaling part. The method is applied to precipitation extremes over the upper Aare catchment, an area in Switzerland which is characterized by complex terrain. The statistical downscaling part consists of an Artificial Neural Network (ANN) framework trained in a reference period. Thereby, dynamically downscaled precipitation over the target area serve as predictands and large-scale variables, received from the global model simulation, as predictors. Applying the ANN to long term global simulations produces a precipitation series that acts as a surrogate of the dynamically downscaled precipitation for a longer climate period, and therefore are used in the selection of events. These events are then dynamically downscaled with a regional climate model to 2 km. The results show that this strategy is suitable to constraint extreme precipitation events, although some limitations remain, e.g., the method has lower efficiency in identifying extreme events in summer and the sensitivity of extreme events to climate change is underestimated.

Appendix: Skill metrics

1.1 Correlation

We use Pearson correlation. This metric evaluates the co-variability of two series disregarding possible systematic biases, therefore being especially suitable for the evaluation of the ANN to predict the right timing of extreme events. We repeated the calculation with Spearman correlation and the results are similar (not shown).

As we are especially interested in the performance towards the most extreme events, correlations are successively calculated after the daily series are filtered out to retain only the values of precipitation above a given quantile q that corresponds to percentiles p between 1 and 99. In detail, all days in which precipitation in the dynamically downscaled series above q are selected, and the correlation coefficient between the latter and the series for the ANN within this subset of dates is calculated. This process of successive recalculation of the statistics filtering out the data towards higher percentiles is repeated for all skill metrics described here. Note that as we move towards higher percentiles, the length of the series becomes shorter, which leads to larger uncertainty in the estimation of the skill metrics. This uncertainty is estimated by jointly bootstra** the series with repetition (shadings in Fig. 6 represent the confidence interval at $\alpha =0.1$, while solid lines represent the median). Further, the value that rejects the null hypothesis of no skill at $\alpha =0.05$ is obtained by independently bootstrap** both series with repetition (dashed curves in Fig. 6).

1.2 Hit rate F

In the evaluation of the skill of predicting rare events, it is common to use contingency tables (Skamarock 2000; Ferro and Stephenson 2011). Thereby, each event can fall in one out of four categories: either it is correctly predicted (hit), incorrectly predicted when it did not happen (false alarm), incorrectly non predicted with it actually happened (missed event) or it can be correctly rejected (most common situation). It is customary to name the number of the events within these disjoint sets as a, b, c and d, respectively. Given this notation, the Hit Rate is defined as (e.g. Skamarock 2000):

$$\begin{aligned} H=\frac{a}{a+c}={\hat{p}}(f|o), \end{aligned}$$

(1)

which can be interpreted as the probability of predicting a situation (event f, where f stands for “predicted”) given that it actually happened (event o, where o stands for “observed”). In a similar fashion, we can define the false alarm rate F as:

$$\begin{aligned} F=\frac{b}{b+d}={\hat{p}}(f|{\bar{o}}), \end{aligned}$$

(2)

representing the probability of incorrectly having predicted a situation that did not happen.

A detail to be determined is how to define whether an event happened or not in either the observations or the predicted dataset. For instance, if a given threshold of precipitation is fixed for both datasets, it might be that the total number of events above such threshold differs between the two datasets, leading to a systematic bias, defined as:

$$\begin{aligned} B=\frac{a+b}{a+c}. \end{aligned}$$

(3)

Values of B other than 1 indicate a systematic bias between the observations and the predicted dataset. However, this bias is meaningless to us, as we are not interested in the given values of precipitation provided directly by the ANN, but in their ranking of most extreme values, which will be ultimately used to select the events to be downscaled dynamically. Therefore, we carry out a form of hedging to the data that consists of working with quantiles. This is, for a given a percentile p, we obtain the corresponding quantiles separately for the statistical and dynamical downscaling series (as they are in general different if the ANN is biased). Then, we define that an event happened in one of the series when the precipitation in a given day is above its respective quantile. Summing the number of events, leads to the numbers a, b, c and d of the contingency table, which ultimately determines H for a given percentile p. As describe above, this calculation is repeated for p ranging between 1 and 99.

1.3 Symmetric Extremal Dependence Index

The Symmetric Extremal Dependence Index (SEDI) was proposed by Ferro and Stephenson (2011) as an alternative metric to evaluate the skill in predicting rare events that supersedes a number of drawbacks of more simple metrics, such as H. It is still based on the calculation of a contingency table, and as such it is defined as a function of a, b, c and d:

$$\begin{aligned} \text {SEDI}=\frac{\log F -\log H-\log (1-F) + \log (1-H)}{\log F + \log H +\log (1-F)+\log (1-H)}. \end{aligned}$$

(4)

SEDI has the advantage of being base rate independent, non degenerate and asymptotically equitable (Ferro and Stephenson 2011). The calculation of SEDI for different percentiles p has been performed following the same procedure as for H.