Model Reservoir/ Component Water Balance or State Equations Constitutive Relations State Variables Model Fluxes Model Parameters HyMod Soil Moisture (Sm)  Sm is the soil moisture in the upper soil layer [mm].  Sq1 is the total water content in tank 1 [mm].  Sq2 is the total water content in tank 2 [mm].  Sq3 is the total water content in tank 3 [mm].  Ss is the total water content in the lower soil layer [mm].  Sm = 0; at t = 0 is the initial basin storage [mm].  Sq = 0; at t = 0 is the initial storage of quick-flow tanks [mm].  Ss = 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 Evapo-transpiration from the soil [mm∙d−1].  PET is the Potential Evapotranspiration [mm∙d−1].  Qqi is the quick surface runoff in Sqi [mm∙d−1].  QS is the slow groundwater runoff in Ss [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 quick-flow routing tanks [0.001 - 0.1 day−1].  Ks is the conductivity of the slow-routing tanks [0.001-0.95 day−1]  Nq is the number of quick flow linear tanks [1] - [5] . In this description Nq = 3. Quick Routing Reservoir 1 (Sq1) Quick Routing Reservoir 2 (Sq2) Quick Routing Reservoir 3 (Sq3) Slow Routing Reservoir (SS) ARX Autoregressive Component  is streamflow forecast in time t + 1 [m3∙s−1].  is streamflow observed in time t − i­ [m3∙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.