Supplementary Material
Temperature-index Snowpack model
A simple snowpack model (Fig. S1) based on the degree-day snowmelt approach, applied as a
part of water balance model by Okkonen and Kløve (2010), was used for estimating main
variables related to wintertime precipitation forms and snowpack fluxes (ID nos. 5-20 in
Table 2). The input parameters to the temperature-index snowpack model were observed daily
precipitation (P0) and air temperature (T0) and the main model outputs were daily rainfall and
snowfall proportions, daily snowpack meltout, refreezing, and snow water equivalent (SWE).
Precipitation sub-model (Fig. S1) calculated, the proportion of precipitation falling as snow
(Ps) and rain (Pr) as (Vehviläinen, 1992):
𝑃𝑟 = 𝐶𝑟 𝐹𝑟 𝑃0
(S.1)
𝑃𝑠 = 𝐶𝑠 𝐹𝑠 𝑃0
(S.2)
where Cr and Cs are the correction coefficients for rainfall and snowfall, respectively, Fr is
fraction of rainfall and Fs is fraction of snowfall, calculated as follows (Vehviläinen, 1992):
𝐹𝑟 =
0
𝑖𝑓 𝑇0 < 𝑇𝑚𝑖𝑛
𝑇0 − 𝑇𝑚𝑖𝑛
𝑇𝑚𝑎𝑥 − 𝑇𝑚𝑖𝑛
𝑖𝑓 𝑇𝑚𝑖𝑛 ≤ 𝑇0 ≤ 𝑇𝑚𝑎𝑥
1
𝑖𝑓 𝑇0 > 𝑇𝑚𝑎𝑥
{
𝐹𝑠 = 1 − 𝐹𝑟
(S.3)
(S.4)
1
Snowpack sub-model (Fig. S1) was used to calculate snowpack main fluxes. The degree-day
model (Kuusisto, 1984) was used to estimate daily snowmelt (Md). The refreezing of liquid
water (Fd) inside snowpack was also considered. According to Vehviläinen (1992), Md and Fd
are calculated as:
𝑀𝑑 = {
𝐾𝑑 (𝑇0 − 𝑇𝑚𝑒𝑙𝑡 )
(S.5)
0
𝐹𝑑 = {
𝑖𝑓 𝑇0 > 𝑇𝑚𝑒𝑙𝑡
𝐾𝑓 (𝑇𝑓 − 𝑇0 )
𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
𝑒
0
𝑖𝑓 𝑇0 > 𝑇𝑓
(S.6)
𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
where Kd is the degree-day factor, Tmelt is snowmelt base temperature, Kf is degree-day
freezing factor, Tf is freezing base temperature, and e is a coefficient indicating a non-linear
relationship between refreezing and temperature (Bengtsson, 1982). Meltout is the melt water
that leaves snowpack when the maximum liquid water retention capacity of snowpack
(Retmax) is exceeded (Kuusisto, 1984). Retmax is controlled by liquid water of ice inside
snowpack (WIP) and computed as (Vehviläinen, 1992):
𝑅𝑒𝑡𝑚𝑎𝑥 = 𝑅 × 𝑊𝐼𝑃
(S.7)
𝑀𝑒𝑙𝑡𝑜𝑢𝑡 = 𝑀𝑑 − 𝐹𝑑 − (𝑅 × 𝑊𝐼𝑃)
(S.8)
where R is a retention parameter. The mass balance of snowpack is calculated as follows:
𝑑𝑅𝑒𝑡⁄ = 𝑃 + 𝑀 + 𝐹 𝑅𝑒𝑡 ≤ 𝑅𝑒𝑡
𝑟
𝑑
𝑑
𝑚𝑎𝑥
𝑑𝑡
(S.9)
𝑑𝑊𝐼𝑃⁄ = 𝑃 − 𝑀 + 𝐹
𝑟
𝑑
𝑑
𝑑𝑡
(S.10)
𝑆𝑊𝐸 = 𝑅𝑒𝑡 + 𝑊𝐼𝑃
(S.11)
2
where SWE is snow water equivalent.
Model calibration, validation and performance
For all three stations, Kisaniemi, Kajaani and Sodankylä, the snowpack dynamics model used
long-term daily precipitation and temperature datasets (> 100 years) as mentioned in Section
2.1 (Table 1), and was calibrated with the observed daily snow water equivalent (SWE0) at
very close stations (Section 2.1) based on non-linear least-squares errors using 11 different
selected parameters (Table S1) recommended by the literature (e.g. Male and Gray, 1981;
Kuusisto, 1984; Vehviläinen, 1992; Førland et al., 1996). The study periods, datasets
considered and model goodness indicators for both calibration and validation procedures at
each station are given in Table S2. Performance of the model for both the calibration and
validation phases was examined by five different indicators: Nash-Sutcliffe coefficient (NSE)
(Nash and Sutcliffe, 1970); percentage deviation from observed SWE (PBIAS); root mean
squared error (RMSE), determination coefficient (R2); and regression line slope (S). The
temperature-index snowpack model showed acceptable and very good performance (R2 =
0.64-0.85) at all stations (Table S2). The model performance at Kajaani is shown in Fig. S2.
References
Bengtsson L. 1982. The importance of refreezing on the diurnal snowmelt cycle with
application to a northern Swedish catchment. Nordic Hydrology 13: 1–12.
Førland EJ, Allerup P, Dahlström B, Elomaa E, Jónsson T, Madsen H, Perälä J, Rissanen P,
Vedin H, Vejen F. 1996. Manual for operational correction of Nordic precipitation data.
Report 24/96, Norwegian Meteorological Institute, 66pp.
Kuusisto E. 1984. Snow accumulation and snowmelt in Finland. Publication of Water
Research Institute, National Boards of Waters, Helsinki, 149 pp.
3
Male DH, Gray DM. 1981. Snow cover ablation and runoff. In: Gray DM, Male DH (Eds.),
Handbook of Snow Principles, Processes, Management and Use. Pergamon Press, Toronto,
pp. 360–436.
Nash JE, Sutcliffe JV. 1970. River flow forecasting through conceptual model Part І – A
discussion of principles. Journal of Hydrology 10: 282-290.
Okkonen J, Kløve B. 2010. A conceptual and statistical approach for the analysis of climate
impact on ground water table fluctuation patterns in cold conditions. Journal of Hydrology
388: 1-12.
Vehviläinen B. 1992. Snow Cover Models in Operational Watershed Forecasting.
Publications of the Water Research, Institute, vol. 11, National Board of Waters, 149 pp.
4
Table S1. Selected parameters used to calibrate the temperature-index snowpack model
Parameter
Description
* Range
Calibrated Values
Initial
value
Kaisaniemi
Kajaani
Sodankylä
(15.09.1980-15.09.2000)●
(15.09.1960-15.09.1993)●
(15.09.1948-15.09.1995)●
Tmin
Snowfall base temperature (°C)
-6.10 to 0.00
-0.830
-4.826
-0.597
-1.396
Tmax
Rainfall base temperature (°C)
-0.10 to 3.5
-0.100
3.380
1.084
0.050
Cs
Snowfall correction coefficient
1.01 to 1.80
1.100
1.057
1.349
1.052
Cr
Rainfall correction coefficient
1.01to 1.40
1.030
1.387
1.025
1.022
Kd
Degree-day factor (mm °C-1 day-1)
0.80 to 14.0
1.410
2.384
1.618
2.714
Tmelt
Snowmelt base temperature (°C)
-0.50 to 2.10
0.000
1.400
0.119
1.573
R
Liquid water retention capacity
0.02 to 0.52
0.029
0.031
0.087
0.045
-e
-1
Kf
Degree-day freezing (mm °C day )
0.02 to 5.1
3.500
0.027
4.417
3.100
Tf
Freezing base temperature
-5.0 to -0.001
0.000
-4.414
-0.601
-0.021
e
Exponent
0.001 to 1.0
0.000
0.013
0.016
0.600
E
Evaporation from snow
0.01 to 0.50
0.000
0.012
0.059
0.493
* From literature
●
Calibration period
5
Table S2. Statistical analysis of the temperature-index model performance at the Kajaani, Kaisaniemi and Sodankylä stations for both calibration
and validation periods.
Station
Study period
Simulation type
Number of
PBIAS (%)
RMSE
R2
Slope
observed SWE
data
15.09.1980-15.09.2000
Calibration
84
6.29
20.50
0.74
0.93
15.09.2000-15.09.2008
Validation
32
-1.88
22.87
0.76
1.02
15.09.1960-15.09.1993
Calibration
196
1.89
30.71
0.76
0.81
15.09.1993-15.09.2008
Validation
99
10.39
37.51
0.68
0.74
15.09.1948 – 15.09.1995
Calibration
269
-1.44
41.27
0.64
1.04
15.09.1995– 15.09.2008
Validation
92
2.29
24.54
0.85
0.98
Kaisaniemi
Kajaani
Sodankylä
PBIAS = Percentage deviation from observed SWE; RMSE = Root Mean Square Error; R 2 = Coefficient of determination; Slope = Slope of the regression line.
6