Model

Reservoir/

Component

Water Balance or State Equations

Constitutive Relations

State Variables

Model Fluxes

Model Parameters

HyMod

Soil Moisture (S_m)

Ÿ S_m is the soil moisture in the upper soil layer [mm].

Ÿ S_q1 is the total water content in tank 1 [mm].

Ÿ S_q2 is the total water content in tank 2 [mm].

Ÿ S_q3 is the total water content in tank 3 [mm].

Ÿ S_s is the total water content in the lower soil layer [mm].

Ÿ S_m = 0; at t = 0 is the initial basin storage [mm].

Ÿ S_q = 0; at t = 0 is the initial storage of quick-flow tanks [mm].

Ÿ S_s = 0; at t = 0 is the initial storage of slow = flow tanks [mm].

Ÿ P is the Precipitation [mm∙d⁻¹].

Ÿ Pe is the effective Precipitation [mm∙d⁻¹].

Ÿ ET is the Evapo-transpiration from the soil [mm∙d⁻¹].

Ÿ PET is the Potential Evapotranspiration [mm∙d⁻¹].

Ÿ Q_qi is the quick surface runoff in S_qi [mm∙d⁻¹].

Ÿ Q_S is the slow groundwater runoff in S_s [mm∙d⁻¹].

Ÿ is the maximum storage capacity in the basin [5 - 600 mm].

Ÿ b is the shape parameter of the distribution of storage capacities within the basin [0.05 - 1.95].

Ÿ α is the routing ratio quick to slow pathway [0.01 - 1].

Ÿ Kq is the conductivity of the quick-flow routing tanks [0.001 - 0.1 day⁻¹].

Ÿ Ks is the conductivity of the slow-routing tanks [0.001-0.95 day⁻¹]

Ÿ Nq is the number of quick flow linear tanks [1] - [5] . In this description Nq = 3.

Quick Routing Reservoir 1 (S_q1)

Quick Routing Reservoir 2 (S_q2)

Quick Routing Reservoir 3 (S_q3)

Slow Routing

Reservoir (S_S)

ARX

Autoregressive Component

Ÿ is streamflow forecast in time t + 1 [m³∙s⁻¹].

Ÿ is streamflow observed in time t − i­ [m³∙s⁻¹].

Ÿ is rainfall observed in time t − j [mm].

Ÿ is the error for the streamflow forecast in time t + 1

Ÿ α is a parameter calculated from the autoregressive component applied to streamflow.

Ÿ β is a parameter calculated from the autoregressive component applied to rainfall.

Ÿ na is the lag number for streamflow.

Ÿ nb is the lag number for rainfall.

DKF

Discrete

Kalman Filter Component

Ÿ is a vector containing the present streamflow (not observed).

Ÿ is a vector containing the streamflow in the time k.

Ÿ is a vector containing the rainfall in the time k.

Ÿ and are vectors containing the Gaussian noise for the process and measurements. and

Ÿ is a vector containing the streamflow measurement.

Ÿ A and B are matrices containing α and β parameters from the series of streamflow and rainfall data in the ARX model.

Ÿ H is a transformed matrix that contains the states of the measurements.

Ÿ Q and R are matrices containing the covariance for the noise in the process and the measurements.