How long a river remembers its past is still an open question. Perturbations
occurring in large catchments may impact the flow regime for several weeks
and months, therefore providing a physical explanation for the occasional
tendency of floods to occur in clusters. The research question explored in
this paper may be stated as follows: can higher than usual river discharges
in the low flow season be associated to a higher probability of floods in the
subsequent high flow season? The physical explanation for such association
may be related to the presence of higher soil moisture storage at the
beginning of the high flow season, which may induce lower infiltration rates
and therefore higher river runoff. Another possible explanation is
persistence of climate, due to presence of long-term properties in
atmospheric circulation. We focus on the Po River at Pontelagoscuro, whose
catchment area amounts to 71 000

Perturbations occurring in large catchments may impact the flow regime for several weeks and months, therefore providing a physical explanation for the occasional tendency of floods to occur in clusters (Montanari, 2012). In the Po river, for instance, it has been observed that some flood events have been preceded by long lasting average flows. The physical explanation for such association may be related to the presence of higher than usual soil moisture storage, which may induce lower infiltration rates and therefore higher river runoff. Another possible explanation is persistence of climate, due to presence of long-term properties in atmospheric circulation.

It is well known that river flows are affected by forms of persistence that are not fully understood yet (O'Connell et al., 2015). These are referred to as the “Hurst Phenomenon”, or the “Hurst Effect”. The Hurst Effect has been physically explained as an implication of the principle of maximum entropy (Koutsoyiannis et al., 2011; Koutsoyiannis, 2014) and implies the presence of long-term cycles over a multitude of time scales. Therefore, the presence of long memory is connected to the possible occurrence of long-term cycles that imply the persistence of high and extreme flows.

Po River Basin. Location (left), drainage network and closure section at Pontelagoscuro (right).

With the idea that extreme floods may be induced by long term stress, rather than a short sequence of extreme rainfall, this paper explores the following research question: can higher than usual river discharges in the low flow season be associated to a higher probability of floods in the subsequent high flow season? An application in the Po River is carried out in order to set up a methodology to update the uncertainty associated to the estimation of flood occurrence probability.

The Po River whose catchment has an area of about 71 000

Daily discharge time series for the Po River Basin in Pontelagoscuro were analyzed in this study. The observation period of the complete series was 1920–2009. The discharge pattern shows a typical pluvial regime and thus a strong seasonality with two flood seasons in spring and autumn (Fig. 2).

In order to look at the stochastic connection between the average river flows
in the pre-flood season and the peak flows in the flood season a bivariate
probability distribution function is fitted to observed data sets. In what
follows, random variables and their outcomes are identified with bold and
un-bold characters, respectively. The yearly random variables included in the
analysis were:

Monthly mean flow in the pre-flood season,

Peak flow in the flood season,

Daily mean value

Probability distribution functions of the normalized dependent
variable (NQ

Finally, a bivariate Gaussian distribution function between both canonical
Gaussian random variables is fitted. The parameters of the distribution are
the mean

The following two main assumptions are applied in this study. (1) The peak flows season covers the months of October and November in the Po River. Thus, the low flow season is assessed in the previous months to the peak flows season (July–September). Nevertheless, the methodology allows the user to select the seasons arbitrarily so that it can be applied to any other study site or hydrological regime. (2) For the sake of comparison, peak flows can be adequately modeled through the EV1 distribution.

In order to infer the actual impact of the dependence between peak flows and average flow in the low flow season, the unconditioned flood frequency distribution and the updated distributions inferred for several levels higher-than-average values of mean flow (e.g. 70, 80, and 95 % quantiles) in the pre-flood season were compared.

Correlation coefficient between NQ

The correlation coefficient between NQ

The effect of the identified dependence on peak flow estimation, for an
assigned return period, is shown in Fig. 3 for three different levels of mean
flow (70, 80, and 95 % quantiles) in the considered pre-flood season. The
probability distribution functions (pdf) of the normalized observed variable,
NQ

Once a pre-flood season was identified it is possible to update the flood
frequency distribution after the observation of

Peak flows in the flood season (October–November) vs return period modeled through the EV1 distribution function.

We found that the peak flow of the Po River is dependent on the average flow of the pre-flood season. Thus, we conclude that it is possible to update the flood frequency distribution basing on discharge observations during the low flow season. To this end, we use a bivariate Gaussian distribution function to model the above dependence. The methodology herein proposed can be applied to any other study site once the flood season is identified and the parameters of the bivariate distribution confirm the presence of the above stochastic dependence.

Several possible physical explanation can be postulated for the sensitivity of the peak flow to the mean discharge in the preceding low flow season, such as the impact of the catchment storage or soil moisture, which in turn impact the formation of net rainfall, and the existence of memory in the weather. Current research is focusing on gaining a better understanding of the processes leading to the formation of the flood flows and in particular the related weather dynamics. Furthermore, we are carrying out experiments on several other rivers in the attempt to relate the above dependence to catchment properties.

Cristina Aguilar acknowledges funding by the Jose Castillejo Programme (Grant number CAS14/00432) and Juan de la Cierva Fellowship Programme (Grant number JCI-2012-12802) of the Spanish Ministry of Economy and Competitiveness. The present work was (partially) developed within the framework of the Panta Rhei Research Initiative of the International Association of Hydrological Sciences (IAHS).