## Materials and Methods
### Hydrological Model and Data  
The hydrological model HBV in the version of HBV-light software [71] was selected for the study because of the possibility of its direct connection with external calibration programs. The HBV model is a widely used conceptual precipitation-runoff model that simulates catchment runoff based on precipitation, temperature, and long-term potential evaporation at a daily time step [72]. The HBV model was developed in the early 1970s to assist hydropower operations by the Hydrology Department of the Swedish Meteorological and Hydrological Institute [31]. The model is partially distributed since it allows the river catchment to be divided into smaller subcatchment units. Each subcatchment can be further subdivided into smaller areas based on land use and altitude. The model includes computational procedures that describe hydrological processes: snow accumulation and melting, evapotranspiration assessment and soil moisture calculation, subsoil runoff, and water flow transformation in a riverbed [73]. A version of the HBV-light model developed at Uppsala University was used and further refined at various universities around the world. The latest version of HBV-light was coded in the VB6 programming language in VB.NET [54]. In principle, the HBV-light routines correspond to the HBV model. However, some simplifications were made. Additional information on the HBV model is described in the articles [31; 54; 73]. An analysis based on a synthetic model was selected for the study, where the calibration procedure is performed based on the calculated catchment runoffs and taking into account known parameters. The process for creating the ideal model is relatively simple. The calibrated model is calculated once with known parameters. Then, the observed flow measurement (\(Q_{obs}\)) is replaced by the simulated flow (\(Q_{sim}\)) results. The model knows the simulated flow at known parameters, which is equal to the observed flow. The synthetic model eliminates measurement noise, conceptual noise, and model design noise from the calibration process. Therefore, only the calibration noise can be analyzed in this way. When calibrating such a model, a perfect match of the measured discharges with the simulated discharges can be expected [18; 47]. However, when calibrated under ideal conditions, it is often not possible to re-establish (history match or to restore) the unique values of all parameters. In the synthetic model, deviations from perfect parameter matching are due to the noise generated by a particular calibration procedure and some nonunique parameters. This problem can be at least partially solved by appropriately parameterizing the relevant model equations [74]. For the calibration of parameters, the GLM calibration method, together with SVD and Tikhonov regularization, was used. Also, other calibration procedures, namely CMA-ES and GAP, were applied, expecting to result in a perfect goodness-of-fit measure as well. We selected these two additional procedures because they are already included in the software used for this study. CMA-ES is included in the PEST tool package, whereas GAP is integrated into the HBV-light program for calibration purposes. The GAP algorithm produces reasonably good results in finding a global solution to the observed function [18]. The existing hydrological test case included in the HBV-light model was selected for the analysis. For the test, Exercise 1 \"HBV-Land\" catchment case [54; 55] was used. This hydrological test model needs 16 parameters to calibrate (Table 1). The model has more than enough parameters to test. The selected time step is one day in the period for ten years. The measured data on precipitation, temperature, and discharges are available for the period from 1 January 1981 to 31 December 1991. More details about HBV-Land catchment and the overall scenario of how to prepare and run a model are described in the article [54; 55] in section A1 Exercise 1.