Algorithm
From EFAS v4.0 and GloFAS version 2.0, an Evolutionary Algorithm (EA) was used for the calibration of the LISFLOOD model parameters on the relevant spatial domain. EA is a population-based optimisation algorithm in which each individual (e.g, a vector of model parameters) in a large population represents a candidate solution for the optimisation problem. The goodness of fit for each individual is evaluated based on selected objective functions, which are designed as either maximisation (e.g, Kling-Gupta efficiency) or minimisation (e.g., root mean square error) equations constrained by physically meaningful model parameter ranges. The basic principle of the EA is to modify and improve the population through evolution over a range of generations, from one generation (parent) to the next (offspring), and ultimately identify the best performing individual.
The EA developed by Hirpa et al., 2018 for the calibration of GloFAS and DEAP - Distributed Evolutionary Algorithm in Python (Fortin et al., 2012, De Rainville et al., 2014; https://github.com/deap/deap) were used, adapted to 6-hourly computation steps whilst minimising the number of iterations. The offspring generation is followed by offspring evaluation, which is performed through model simulation (LISFLOOD run) with the newly generated parameters. A Non-dominated Sorting Genetic Algorithm (NSGA-II; Deb et al., 2002) was used to select the best performing parameters from a mixed set of parents and offspring (µ+λ). The evolutionary loop continues until a stopping criterion is met.
The modified Kling-Gupta efficiency KGE' (Gupta et al., 2009; Kling et al., 2012) was selected as the objective function for the calibration. A combination of improvement based criteria (i.e., improvements in the objective functions) and exhaustion-based criteria (fixed number of generations) was employed for stopping the calibration algorithm.
Implementation for sub-daily application
A specific calibration implementation was introduced from EFAS version 4.0 to cope with observational river discharge time series being available at 6 hourly (time step of the operational system) but also at the reduced temporal resolution of daily. Multiple calibration points are generally available in one catchment, often with a mix of 6-hourly and daily data. LISFLOOD simulations are performed with 6-hourly steps for all calibration catchments, for calibration points with daily observations, 6-hourly LISFLOOD time series are aggregated at daily steps to allow comparison with daily observed discharge data. Each calibration station uses a different calibration period, depending on length of available discharge observations, but a minimum of 4 years is always used for calibration. If a longer record was available, the discharge record was split in two for calibration and validation purposes. If the record was shorter than eight years, four years were used for calibration and the remaining days were used for validation. If the record was equal to or longer than eight years, half was used for calibration and half for validation. The most recent period was used for the calibration because the earlier forcing data and discharge observations have greater uncertainty. An additional spin up period of three year is added to each model run to ensure that model's variable are correctly initialised.
Regionalised parameters
From GloFAS version 4 and EFAS version 5, a parameter regionalization approach was implemented to estimate the parameters that control snow melt, infiltration, runoff, groundwater, and routing for catchments without available river discharge observation time series. In the implemented regionalization approach, calibrated parameter set were transferred from calibrated catchments (donors) to uncalibrated catchments. For each uncalibrated catchment, the donor catchment was identified according to a proximity criterion accounting for both climatic similarity and the geographical proximity (Parajka et al 2005, Beck et al. 2016).
Reference
, , , , , , and (2016), Global-scale regionalization of hydrologic model parameters, Water Resour. Res., 52, 3599– 3622, doi:10.1002/2015WR018247.
Parajka, J., Merz, R., and Blöschl, G.: A comparison of regionalisation methods for catchment model parameters, Hydrol. Earth Syst. Sci., 9, 157–171, https://doi.org/10.5194/hess-9-157-2005, 2005