# Qom--A New Hydroologic Prediction Model Enhanced with Multi-Objective Optimization
## 4 Hydrologic Calibration Strategy
### Qom Model  
The Qom model considers moisture, evapotranspiration, surface stored water and infiltration, and percolation processes, that is, those actions that cause water storage in the soil. It is applicable to permeable and impermeable soils and it determines the runoff in three layers, two of them superficial (permeable and impervious soils) and one another of underground flow. In order to determine the outlet flows in a given place in the basin in response to rainfall, we separate the total volumes of rainfall into volumes of losses and excesses discretly over time, simulating for excess water the way in which runoff occurs, considering the transit and delay in the basin. Therefore, besides the rainfall data and morphometric characteristics of the basin, the model needs three initial tuning parameters, namely the maximum storage water volume on surface \(Rmax\), the maximum storage volume in the soil \(Smax\) and the volumetric conductivity coefficient \(VC\), which represents the volume of water that would move in three-dimensions in the soil towards the exit per unit of surface in a certain time, expressed in volume of water sheet per unit of time. These variables are emphasized in red color in the flow chart of Figure 2, which represents the mathematical model that corresponds to the equations commented in lines (1) to (12) of the this figure, involving the hydrologic natural processes of Qom. The computation cycle starts obtaining those required data from the problem specification given from the scenario instance, as well as the parameters (decision variables), to calculate the soil moisture states. A part of the rainfall defined with the variable \(P\) in the unity of the volume of the water sheet. Retentions in the basin are produced by surface depressions of the soil \(R\), by the infiltration of water in the porosity of the soil \(S\) and percolates in permeable soils \(D\). Another part of the volume is lost in the atmosphere through evaporation and plant transpiration \(EVT\). The rest of the volumes would leave the basin superficially by a portion of impermeable areas \(Vi\) and permeable ones \(Vp\). In addition, another part \(Vg\) of the volume can be percolated into deep layers remaining in the basin as soil moisture or as a mass of water that will be added to the underground outflow of the river. Figure 2: Flowchart of the Qom model. When the Qom process is finished, the \(Vi\), \(Vp\) and \(Vg\) volumes are passed to model the hydrograms. [PERSON]'s model is then used for modeling direct runoff of watershed rainfall response. It is based on the concept that instantaneous unit hydrograph can be derived by routing the unit excess rainfall in the form of a time-area histogram (translation) through a single linear reservoir (attenuation). As a consequence of the application of this model, a new set of decision variables is taken into account for the calibration of the model, comprising: \(Ki\), \(Kp\), \(Kg\) (emphasized in blue in Figure 3) and additionally the variables \(CT\), \(SC\) and \(Eq\) can be enabled and considered (emphasized in grey); which leads to obtaining the solution vector \(Qe\) that includes the estimated water flow as formalized in Equation (4). \[Qe_{i}=Qi_{i}+Qp_{i}+Qg_{i}\,,\;1\leq\;i\;\leq N. \tag{4}\]  
A description of all the terms and factors used in equations of Qom model can be found in Table 1. The coding of the solution consists of a real value vector that includes each decision variable as a parameter for calibration, three decision variables namely: \(Rmax\), \(Smax\) and \(VC\), which represent the soil moisture estimated by \(Qom\). Finally, in order to estimate the output flow \(Qe\) through Clark, we need 3 other decision variables: \(Ki\), \(Kp\), \(Kg\), alternatively \(CT\), \(Shape\), \(Eq\). Actual data values \(Qo\) and those estimated by the computation of \(Qe\) are used to calculate prediction errors in the two objective functions that will be optimized, as explained next.