## 1 Introduction  
Simulation of hydrological processes using computer models has a long and rich history [1; 2]. Hydrological models are merely a mathematical approximation of a variety of dynamic processes in highly heterogeneous conditions in nature. A model's variables are spatially heterogeneously distributed, while we have limited datasets available. The same is true for data on how water moves over and below the surface [3; 4; 5; 6]. Different hydrological processes dominate different river catchments due to natural conditions. Therefore, various models were developed to simulate these hydrological processes more or less successfully [1; 2; 7; 8]. More than 60 different hydrological models are available for rainfall-runoff simulations [1]. Due to noise, the discrepancies between simulation results and measurements are still significant and challenging for many researchers [9; 10; 11; 12; 13; 14; 15; 16]. One of the reasons for the discrepancy between measurements and results of simulations can also be attributed to a lack of knowledge [17]. Discrepancies between observed data and simulated values, i.e., noise, can be produced by many sources. First, the data we use in the model alone is a source of the so-called primary noise resulting from measurements and observations [18; 19; 20; 21; 22; 23; 24; 6; 10; 25]. Second, the source of noise is the structure of the model itself, i.e., structural noise. The structural noise of modeling is the fact that the model is not a duplicate of the real state of nature. The structural noise of the modeling can be further divided into conceptual noise [26], model design noise, and model calibration noise. Conceptual noise is caused by a set of selected equations of complex hydrological processes that simulate natural phenomena [25; 27]. For example, when highly nonlinear phenomena are modeled using linear equations, or due to the lack of data, certain parts of the hydrological cycle can be easily extracted from the model producing structural noise [25; 26]. The design noise of the model is conditioned by the spatial and temporal discretization of the model when preparing the input data, i.e., with the same concept, the same river catchment can be designed differently. A model's calibration noise is conditioned by the choice of the calibration method by which the model parameters are calibrated. In practice, hydrological modeling involves various models, stochastic or deterministic and conceptual or empirical. Hydrological models contain many parameters that are integral to the model's equations and cannot be determined directly by field measurements. At best, only the limits, within which the parameters take value according to their physical meaning or practical experience, can be defined. The parameters are determined in the calibration procedure when the calculated results are compared with the measurements [28; 29; 30]. The question of model calibration is as old as modeling itself, and several different calibration methods have evolved. The oldest procedure for model calibration is the trial-and-error method, where the modeler manually changes the parameter values and visually analyzes the results. This approach was also used in the original design of the HBV (Hydrologiska Byrans Vattenavdelning) hydrological model [31; 32]. The process is entirely subjective and conditioned by the knowledge and experience of the modeler and is mainly time-consuming. However, the modeler gets a direct sense of the sensitivity of the model and the importance of the individual parameters. Over time, many computer-based methods for model calibration have evolved which can otherwise be used for a variety of purposes and in different scientific areas: the Monte Carlo method [33; 34], the general probability of estimation uncertainty [35], the artificial neural network [36], the genetic algorithm (GAP) [18], the hybrid harmony search algorithm [37], the covariance matrix adaptation evolution strategy (CMA-ES) global optimization scheme [38; 39; 40], and the generalized reduced gradient [41].