Improved historical reconstruction of daily flows and annual maxima in gauged and ungauged basins

In the wake of the events of spring 2017, the government of Quebec initiated a broad-based reflection on the management of flood risks across the province in the context of climate change. This reflection gave rise to several major observations, including the need for up-to-date and complete mapping of flood-prone areas in Quebec, allowing for sufficient evaluation of this risk in land use planning and in the implementation of adaptation solutions. To achieve this, the frequency of high recurrence events must be estimated, as well as the associated uncertainty.

As the mapping of flood hazards will cover gauged and ungauged locations, the calculation chain must adapt to both types. For ungauged areas, it is a major challenge to perform a historical reconstruction of daily flows and annual maxima.

• To develop methods to combine flows from several different historical hydrological simulations (calibrations, meteorological forcing, choice of sub-models) with data from gauging stations, in order to produce the best reconstruction of past hydrology in gauged and non-gauged areas.

• To identify the optimal way to produce series of annual maxima and/or their distribution, taking uncertainty into account.

• Creation of 144 new simulations using the HYDROTEL hydrological model, by varying the inputs and the parameters

• Application of historical hydrological simulation weighting algorithms to gauged sites with windows of varying length

• Regionalization of historical hydrological simulation weights to ungauged sites

• Leave-one-out cross-validation

• Quantification of uncertainty by means of an error modelling approach

• Comparison of the results with the optimal interpolation method used by the hydrologic expertise unit

• Simulation of future flows using the 50 members of ClimEx post-processed with the ensemble of 144 HYDROTEL models to create a database that will be explored in subsequent projects

Figure 1. Results of the leave-one-out cross-validation for the KGE of flows (a, b, c) and for the NRMSE of the annual maximum discharge (d, e, f), according to the optimal interpolation (a, d), the simple average of the models (b, e) and the GRA technique in which the weights are regenerated each year (c, f).

Several regionalization techniques were explored during the project and were compared to the optimal interpolation used operationally at the Direction principale des prévisions hydriques et de la cartographie, the hydrologic forecasting and cartography division of the Ministère de l’Environnement et de la Lutte contre les changements climatiques. The regionalization techniques consist of evaluating the performance of hydrological simulations at gauged sites and applying a weighting algorithm to these simulations then extrapolating the weights to the rest of the ungauged areas, taking the distance and physiographic characteristics of each site into account. The main advantage of these regionalization techniques is that they maintain the spatio-temporal consistency of the simulations and thereby provide a higher level of realism and a consistent water balance in the reconstructed time series. In comparison, the optimal interpolation performs very well because it extrapolates the errors of the hydrological model at each time step, to the detriment of the spatio-temporal consistency and the water balance.

Among the regionalization techniques explored for the project, a variant of the methodology developed by Granger and Ramanathan (1984), called GRA, proved to be the most promising. However, it was not possible to beat or equal the optimal interpolation by weighting the six HYDROTEL platforms used operationally at the Direction principale des prévisions hydriques et de la cartographie, because the regionalization techniques require a wide diversity of hydrological responses, which it was not possible to achieve with six versions of the same model. To obtain performance similar to the optimal interpolation using the GRA technique, it was necessary to produce 144 additional simulations by varying the meteorological inputs and parameters of the model. These simulations were combined with the six HYDROTEL platforms for a total of 150 hydrological simulations. With this set, the performance of GRA became comparable to the optimal interpolation, but without the previously mentioned compromises of the optimal interpolation. Additionally, in a slightly more exploratory step, it was shown that historical flow rate reconstruction with GRA can be further improved and can even beat the optimal interpolation by reassessing year-by-year weights (Figure 1), or even the month-by-month ones. Unlike the optimal interpolation, this technique also has a great deal of potential to integrate information from hydrological simulations coming from different models. The ensemble approach used for the historical reconstruction in this project also made it possible provide an error model with the results.

Lastly, with a view to exploring alternatives that are completely external to the classic regionalization techniques, the reconstructions performed using the optimal interpolation and GRA were compared to a long short-term memory (LSTM) deep learning model. A model with three layers (excluding inputs and outputs) and 500,000 parameters was therefore built, using the characteristics of the watersheds and meteorological data for the previous 365 days as inputs. The results are still very preliminary but demonstrate similar performance in cross-validation for the KGE of the flows compared to the optimal interpolation and the GRA. Apart from the spatio-temporal consistency aspects, which have not been validated, the main weakness seems to be in the ability to simulate peak flows, which are particularly difficult due to the (relatively) low number of extreme flow values in the training dataset. As artificial intelligence is advancing extremely rapidly, continued research is planned on the potential of LSTM-type methods, for example by using more gauged watersheds located outside Quebec or exploring oversampling/undersampling approaches.