Model  Reservoir/ Component  Water Balance or State Equations  Constitutive Relations  State Variables  Model Fluxes  Model Parameters  
HyMod  Soil Moisture (S_{m}) 

 S_{m} is the soil moisture in the upper soil layer [mm]. S_{q}_{1} is the total water content in tank 1 [mm]. S_{q}_{2} is the total water content in tank 2 [mm]. S_{q}_{3} is the total water content in tank 3 [mm]. S_{s} is the total water content in the lower soil layer [mm]. S_{m} = 0; at t = 0 is the initial basin storage [mm]. S_{q} = 0; at t = 0 is the initial storage of quickflow tanks [mm]. S_{s} = 0; at t = 0 is the initial storage of slow = flow tanks [mm].  P is the Precipitation [mm∙d^{−1}]. Pe is the effective Precipitation [mm∙d^{−1}]. ET is the Evapotranspiration from the soil [mm∙d^{−1}]. PET is the Potential Evapotranspiration [mm∙d^{−1}]. Q_{qi} is the quick surface runoff in S_{qi} [mm∙d^{−1}]. Q_{S} is the slow groundwater runoff in S_{s} [mm∙d^{−1}].  is the maximum storage capacity in the basin [5  600 mm]. b is the shape parameter of the distribution of storage capacities within the basin [0.05  1.95]. α is the routing ratio quick to slow pathway [0.01  1]. Kq is the conductivity of the quickflow routing tanks [0.001  0.1 day^{−1}]. Ks is the conductivity of the slowrouting tanks [0.0010.95 day^{−1}] Nq is the number of quick flow linear tanks [1]  [5] . In this description Nq = 3.  
Quick Routing Reservoir 1 (S_{q}_{1}) 

 
Quick Routing Reservoir 2 (S_{q}_{2}) 

 
Quick Routing Reservoir 3 (S_{q}_{3}) 

 
Slow Routing Reservoir (S_{S}) 

 
ARX  Autoregressive Component 
 is streamflow forecast in time t + 1 [m^{3}∙s^{−1}]. is streamflow observed in time t − i [m^{3}∙s^{−1}]. is rainfall observed in time t − j [mm]. is the error for the streamflow forecast in time t + 1  α is a parameter calculated from the autoregressive component applied to streamflow. β is a parameter calculated from the autoregressive component applied to rainfall. na is the lag number for streamflow. nb is the lag number for rainfall.  
DKF  Discrete Kalman Filter Component 
 is a vector containing the present streamflow (not observed). is a vector containing the streamflow in the time k. is a vector containing the rainfall in the time k. and are vectors containing the Gaussian noise for the process and measurements. and is a vector containing the streamflow measurement.  A and B are matrices containing α and β parameters from the series of streamflow and rainfall data in the ARX model. H is a transformed matrix that contains the states of the measurements. Q and R are matrices containing the covariance for the noise in the process and the measurements.  