Table 1. Model parameters and error model parameters with initial values and prior distributions. The implementation of the HBV model is based on Heistermann & Kneis (2011).

Parameter name	Definition	Initial value through deterministic calibration a	Prior distribution of parameter b
Model parameters
CFMAX	Degree day factor for snow melt [mm/°C/d]	0.324	Beta[3, 5, 0, 10]
TT	Temperature threshold below which precipitation falls as snow [°C]	0.387	Beta[3, 2, −3, 3]
FC	Field capacity [mm]	106.4	Beta[1, 4, 50, 200]
MINSM	Minimum soil moisture for storage [mm]	44.66	Beta[1, 4, 0, 200]
BETA	Parameter to control the fraction of rain and snow melt partitioned for groundwater recharge [–]	1.888	Beta[1, 1, 1, 5]
LP	Fraction of soil moisture-field capacity-ratio above which actual evapotranspiration equals potential evapotranspiration [–]	0.845	Beta[1, 1, 0, 1]
CET	Correction factor for potential evapotranspiration [–]	0.570	Beta[1, 1, 0, 20]
KPERC	Percolation coefficient [1/d]	2.670	Beta[1, 1, 0, 5]
K0	Fast storage coefficient of soil upper zone [1/d]	0.498	Beta[1, 1, 0, 0.5]
UZL	Threshold above which soil upper zone storage empties at rate computed by storage coefficient K0 [mm]	1.226	Beta[3, 4, 0, 60]
K1	Slow storage coefficient of soil upper zone [1/d]	0.356	Beta[1, 4, 0, 0.5]
K2	Storage coefficient of soil lower zone [1/d]	9.7 × 10−4	Beta[1, 4, 0, 0.1]
MAXBAS	Length of (triangular) unit hydrograph [d]	3.887	Beta[1, 4, 0, 6]
etpmean	Mean evaporation [mm/d]	4.446	Beta[1, 3, 0, 50]
tmean	Mean temperature [°C]	4.549	Beta[4, 4, −20, 30]
n	(Real) number of storages in linear storage cascade	1.901	Beta[1, 2, 0, 7.5]
k	Decay constant for linear storage cascade	1.481	Beta[1, 2, 0, 5]
Initial state parameters
snow	Snow storage [mm]	178	Beta[1, 3, 0, 200]
sm	Soil moisture storage [mm]	369	Beta[1, 3, 0, 200]
suz	Soil upper zone storage [mm]	117	Beta[1, 3, 0, 200]
slz	Soil lower zone storage [mm]	44	Beta[1, 3, 0, 200]
Error model parameters
β1	Coefficient for the AR(1) in Eq. (2)	–	U[0,1]
${\sigma }_{\delta }^2$	Variance for the AR(1), Eq. (2)	–	U[0,1]
${\sigma }_{\eta }^2$	Measurement error variance, Eq. (1)	–	U[0,1]
$\overline{\mathbf{z}}$	Vector of length T + W for the rainfall parameters	–	$F_{\overline{\mathbf{z}}}$, see Eq. (7)

Notes.

^aA deterministic calibration is performed prior to the Bayesian calibration. The parameters are optimized with differential evolution. The objective function is the MSE between the predicted and measured discharge.

^bBeta [a,b,c,d] represents a beta distribution in the interval [c,d] with shape parameters a and b. U[a,b] is a uniform distribution over the interval [a, b].