## 2 Background of Soft Computing Methods
### Equilibrium Optimizer (EO)
## 3 Methodology

### Study Area and Dataset Used

The daily rainfall and runoff data (15 years (2000-2015)) from two different benchmark stations of two catchments in the UK were obtained from the UK national river flow archive website ([[https://nrfa.ceh.ac.uk/](https://nrfa.ceh.ac.uk/)]([https://nrfa.ceh.ac.uk/](https://nrfa.ceh.ac.uk/)) (accessed on 5 August 2019)). These two stations are part of the UK benchmark network (UKBN2) which are most suitable for interpretation and identification of long-term hydrological variability and change. The UK benchmarkstations have all the full flow regime called low, medium and high flows. These catchments are sensibly free from disturbances of human like river engineering, urbanization, and water abstractions. Therefore, these are near-natural catchments and have climate-driven alterations in river flows. The catchment of the river Teifi at Glanteifi from a wetter, cloudy, and windy region south-west Wales where the values of potential evapotranspiration are low relative to rainfall [70]. The winter months are wetter than the warm summer months. The monthly rainfall pattern increases from August, to peak in November-December, to January, then the pattern begins falling from February. The outlet of the basin is 893.6 km\({}^{2}\) and the river gauge at 5.2 m AOD (mean above ordnance datum). The primary river flow data measuring authority is Natural Resources Wales. The catchment has minor flow abstractions due to upland reservoirs and negligible agricultural demands. Therefore, the flow regime is natural. The factor affecting runoff are (i) reservoirs, and (ii) public water supply. The major portions of the catchment land cover are grassland (79%), woodland (12%), horticulture (4.74%), mountain (1.80%) and urban extent (2.83%). Catchment is mainly impermeable Ordovician and Silurian deposits. Over the land, dairy farming predominates in the south and hill farming in the upper catchment. Some forest with peaty soils on hills and is seasonally wet. The most of the lower areas have soils with permeable substrate. The catchment of the river Fal at Tregony from dry, sunniest, mild winter, and cool summer region Cornwall country of south-west England where the values of potential evapotranspiration are higher relative to rainfall [70]. The monthly rainfall patterns increase from September to January [30]. The outlet of the basin is 87 km\({}^{2}\) and the river gauge at 6.9 m AOD. The primary river flow data measuring authority is the Environment Agency. Due to steep topography, the catchment has fast responses to the water events. The runoff coefficient is at a daily time step. The factor affecting runoff are (i) increased by effluent return, and (ii) reduced by industrial/agriculture use. The major portions of the catchment land cover are grassland (41.43%), horticulture (21.52%) with woodland (16.22%), mountain (0.18%) and urban extents (4.98%). The land use is low-grade agriculture and pasturage with some woodland. The catchment has no major changes. The statistics of catchments data is given in Table 2.

The daily precipitation (mm per day) dataset was obtained from the center for ecology and hydrology-gridded estimates of areal rainfall (CEH-GEAR) [71; 72]) which was interpolated to 1 km from the rain gauge data using the natural neighbor interpolation approach [71]. The uncertainty degree of the associated rainfall value depends on the mean distance to the nearest rain gauge station and the spatial variability of the rainfall. More details about the rainfall data can be found in [71]. Figure 3 shows daily discharge and rainfall data of the two basins. A partial autocorrelation function (PACF) was used to select the number of preceding days runoff data for number of input features along with a previous day rainfall value. The proposed models predict the next day runoff value. Furthermore, the highest correlated preceding runoff series and previous day rainfall series are pre-processed using discrete wavelet transform technique.