Site characteristics
This study concretizes, exemplifies, and compares results for soil moisture in the two climatically different basins of Norrström and Piteälven (Fig.
1). In Norrström (22 650 km
2), which has been hydrologically well investigated and described in more detail in previous studies (Destouni et al.
2013; Jaramillo et al.
2013; Destouni and Verrot
2014), the long-term average annual temperature is 5.8 °C, the average annual precipitation is 600 mm, and the average annual runoff is 225 mm over the entire present study period of 1950–2009.
The Piteälven basin (10 817 km
2) has also been investigated and described in previous studies (Humborg et al.
2004; Aldahan et al.
2006), including comparisons with Norrström with regard to their hydro-climatic conditions and changes (Destouni et al.
2013), however, not before with specific regard to soil moisture. The long-term average annual temperature is here −0.8 °C, the average annual precipitation is 584 mm, and the average runoff is 468 mm for the whole period 1950–2009.
The Piteälven basin is thus subject to considerably colder conditions than Norrström. This difference may play an important role in winter, when the precipitation falls mainly as snow in Piteälven, whereas in Norrström, it may still largely fall as rain. In Piteälven, the winter precipitation is then to a larger degree than in Norrström stored as snow at the surface and does not contribute to soil moisture before it melts when the weather gets warmer in spring. The present extension of analytical soil moisture modeling to also include snow storage and melting dynamics, as described in the following section, may thus be necessary for direct comparison of soil moisture variability and change in such different climatic conditions as in these two basin examples.
Modeling approach
We follow the previously developed analytical modeling framework by Destouni and Verrot (
2014). For calculation of water content
θ
uz
[–] in the unsaturated zone, average water content
θ
z
[–] over a fixed soil depth
z [L] from the surface, and groundwater level
z
gw [L] within
z, novel extensions are made here from the basic framework of Destouni and Verrot (
2014) in order to account for a wider range of hydro-climatic conditions, including snow dynamics.
One main model extension made for the calculation of
θ
uz
[Electronic Supplementary Material (ESM) section Methods] is in order to account for the fact that not the whole observed runoff
R [LT
−1], but only some fraction of it (denoted
γ [–]), actually flows through the soil-groundwater system where it can contribute to soil moisture. An effective runoff measure
R
eff [LT
−1] is here used to approximate average vertical soil water flux through the unsaturated zone (
q [LT
−1]) in equation
S2 of ESM—Methods, and the fraction
γ relates effective runoff
R
eff [LT
−1] to measured runoff
R as
R
eff =
γR with 0 ≤
γ≤1.
Previous studies have shown that the soil water flux
q and its temporal variability can successfully be estimated for such
θ
uz
estimation from available time series of the contribution of water flow through the soil to runoff
R (Destouni
1991,
1993). Use of
R
eff in this estimation implies averaging over the (basin, watershed, catchment, field) area that is integrated by the flow that feeds into
R through the soil-groundwater system. Such simplified area-depth-averaged expression of soil water content
θ
uz
in the unsaturated zone has been tested and found practically useful by both numerical experimentation (Destouni
1991) and field experimentation (Graham et al.
1998) over different soil depths and different time scales of averaging
q ≈
R
eff.
On annual average basis,
γ is typically above 0.5 and in many cases close to 1 for a wide range of investigated temperate, through cold, to permafrost region conditions (Bosson. et al.
2012). However, differences in relevant
γ values between basins may still be important and can then readily be accounted for when comparing different hydro-climatic conditions, as in the present study.
The approach to estimating unsaturated water content
θ
uz
by use of
q ≈
R
eff also implicitly (through actual
R observation data) and explicitly (through
γ dependence on temperature) accounts for snow storage-melting dynamics effects. Specifically, for a given month in a cold period, the precipitation that falls and is stored as snow does not contribute to the observed
R, whereas the water added to the soil by snow melting during warmer months does contribute to the observed
R, in addition to the water amount that comes directly from liquid precipitation minus evapotranspiration. By expressing the unsaturated water content
θ
uz
as a function of
q ≈
R
eff and relevant depth-averaged soil parameters (equation
S2 in ESM—Methods; see also ESM section Data regarding soil data used to evaluate these parameters), the need for model extension in order to account for snow-ice dynamics effects is limited to modeling of the fraction
γ dynamics, since the measured
R dynamics already reflect such effects.
A second main extension made here to the model of Destouni and Verrot (
2014) is to explicitly consider effects of snow storage-melting dynamics on the change in soil water storage (Δ
S [LT
−1] expressed as volume of water per unit area and unit time). This extension introduces an effective precipitation of liquid water
P
eff [LT
−1], which relates to measured precipitation
P [LT
−1] as described further below. The storage change is then at any point in time given by the water balance expression Δ
S =
P
eff –
ET −
R
eff, with
ET [LT
−1] being evapotranspiration, with resulting net cumulative change in water storage
S(
t;
t
0) from some initial time
t
0 to time
t becoming
$$ S(t;t_{0} ) = \int\limits_{{t_{0} }}^{t} {\{ \gamma [P_{\text{eff}} (\tau ) - ET(\tau )] - R_{\text{eff}} (\tau )\} } \,{\text{d}}\tau, $$
(1)
where
τ is a dummy integration variable, and the factor
γ comes in also here to distribute to the soil a proportional fraction of water from total
P
eff −
ET as the fraction
γ of total
R flowing through the soil-groundwater system. The associated change in the depth of the groundwater table can further be estimated by distributing the storage change Δ
S at each time point over the available unsaturated pore space per unit area (
θ
s −
θ
uz
) and integrating the result from initial time
t
0 to time
t as
$$ z_{\text{gw}} (t;t_{0} ) = z_{{{\text{gw}} - 0}} (t_{0} ) + \int\limits_{{t_{0} }}^{t} {\frac{{\gamma [P_{\text{eff}} (\tau ) - ET(\tau )] - R_{\text{eff}} (\tau )}}{{\theta_{\text{s}} - \theta_{uz} (\tau )}}} \,{\text{d}}\tau, $$
(2)
where
z
gw−0 is the initial groundwater level position at time
t
0. The average water content
θ
z
over the whole considered soil depth
z can thus finally be obtained as
$$ \theta_{z} (t) = \frac{{z_{\text{gw}} (t)\theta_{uz} (\tau ) + \left( {z - z_{\text{gw}} (t)} \right)\theta_{\text{s}} }}{z} $$
(3)
The effective precipitation
P
eff is used in Eqs.
1 and
2 because only the liquid water part of
P,
P
water [LT
−1], in addition to a snow-melt contribution,
S
M [LT
−1], can effectively contribute to changes in water storage and in the depth of the groundwater table. The
P
eff value is then obtained from a simple snowpack model proposed by Rankinen et al. (
2004a), based on a degree-day conceptualization. Such models have been developed (Vehviläinen
1992; Tobin et al.
2013) and widely used for different regional conditions (Braithwaite and Zhang
2000; Tobin et al.
2011), including for Scandinavia (Mörth et al.
2007; Juston et al.
2009).
The modeling approach of Rankinen et al. (
2004a) was developed within the frame of the Integrated Nitrogen Model for Catchments (INCA) model and tested for conditions in Finland (Limbrick et al.
2000; Granlund et al.
2004; Rankinen et al.
2004b). Following this approach, the manifestation of measured precipitation
P as snow (
P
snow) or liquid water rainfall (
P
water =
P −
P
snow) is at any point in time first determined on the basis of mean air temperature
T
A [Θ] as
$$ P_{\text{snow}} = 0;\quad {\text{for}}\;T_{\text{A}} \ge T_{\text{U}} $$
(4a)
$$ P_{\text{snow}} = \frac{{P(T_{\text{U}} - T_{\text{A}} )}}{{T_{\text{U}} - T_{\text{L}} }};\quad {\text{for}}\;T_{\text{L}} \le T_{\text{A}} \le T_{\text{U}} $$
(4b)
$$ P_{\text{snow}} = P;\quad {\text{for}}\;T_{\text{A}} \le T_{\text{L}} $$
(4c)
with
T
U [Θ] and
T
L [Θ] being temperature thresholds, above and below which precipitation is considered to fall entirely as water (Eq.
4a) or as snow (Eq.
4c), respectively. Furthermore, Eq.
4b states that when the air temperature is between
T
L and
T
U, the precipitation falls partly as water and partly as snow. If
T
A is greater than
T
M [Θ], with the latter being the temperature at which the snow starts to melt, the associated flux of meltwater
S
M is determined as
$$ S_{\text{M}} = (T_{\text{A}} - T_{\text{M}} )F_{\text{M}},$$
(5)
where
F
M [LT
−1 Θ
−1] is a degree-day factor for snow melt.
From the above temperature conditions,
P
eff in Eqs.
1 and
2 can be calculated as
$$ P_{\text{eff}} = P_{\text{water}} + S_{\text{M}} $$
(6)
The original model presented by Rankinen et al. (
2004a) accounts also for evaporation from the snow. Here, however, the effects of basin-scale evapotranspiration, which includes evaporation in addition to transpiration, are explicitly accounted for in Eqs.
1 and
2 based on actual observed hydro-climatic data along with basin-scale water balance constraints, as described further in the next section.
Data
To obtain concrete regional evaluation results from the above quantification framework, daily values of
R from 1901 until 2010 were used, as downloaded from the Swedish Meteorological and Hydrological Institute (SMHI) website (SMHI
2010), for the Övre station in the Norrström basin. For the Piteälven basin, only monthly
R values were available from 1928 until 2013 and these were similarly used and downloaded for the Sikfors station. We further used as model inputs the time series of observed daily
P and
T from the E-OBS dataset of the EU-FP6 project ENSEMBLES (Haylock et al.
2008) with a 0.25° × 0.25° resolution from 1950 until 2013.
Effective runoff
R
eff was further calculated by use of reported simulated
γ factors for different hydro-climatic and landscape conditions in typical Swedish soils (Bosson et al.
2012). Specifically,
γ was here calculated based on the Bosson et al. simulation results for the ratio of groundwater recharge (
R
gw in Bosson et al.
2012) to measured total runoff
R. On average, this ratio was found to be 0.73 for temperate and 0.53 for cold (but without permafrost) conditions. We used then here, for exemplification of
γ dynamics effects, a
γ value of 0.53 for months with negative average temperature (when both
R and
γ are relatively small due to snow storage and frozen ground conditions) and a
γ value of 0.73 for months with positive average temperature (when both
R and
γ are relatively large due to snow melt and unfrozen ground conditions).
The parameter values of
T
U,
T
L,
T
M, and
F
M, required for calculation of
P
eff, were taken from Rankinen et al. (
2004b). Based on comparable climate characteristics, the parameters for the Norrström basin and the Piteälven basin were assumed to be similar to those used in Rankinen et al. (
2004b) for the observation station 1201 and the observation station 7501, respectively. Both stations are located in Finland, one in the southern and one in the northern part. The coordinates of the station 1201 are (60°49, 23°30). The mean annual precipitation is 607 mm per year, and the mean annual temperature is 4.3 °C. For the station 7501, the coordinates are (67°22, 26°37), the precipitation is 507 mm per year on average, and the mean annual temperature is −0.8 °C. The values for
T
L and
T
U were chosen as the mean values of the ranges presented by Rankinen et al. (
2004b). The used values for the present two study basins are listed in Table
1.
Table 1
Values of the parameters
T
M (temperature threshold for snow melt),
T
L (temperature threshold, below which the precipitation is considered to fall entirely as snow),
T
U (temperature threshold, above which the precipitation is considered to fall entirely as water), and
F
M (degree-day factor for snow melt) for Norrström and for Piteälven (selected values from Rankinen et al.
2004b)
T
M (°C) | 0.30 | 0.15 |
T
L (°C) | −2.02 | −4.00 |
T
U (°C) | 3.70 | 0.00 |
F
M (mm day−1 °C−1) | 3.34 | 2.85 |
Calculated daily values of
P
eff were further aggregated on a monthly basis, in order to be comparable and used together with the available monthly values of
R
eff in the calculations of water contents
θ
uz
and
θ
z
, according to equations
S2 in ESM—Methods and Eq.
3, respectively. With regard to time scales,
P and
P
eff differ at both daily and monthly resolutions. Annually aggregated values of
P and
P
eff, however, are essentially the same over a hydrological year, i.e., from September to August, as the snow during 1 year commonly also melts during the same year.
Estimation of monthly
ET values, corresponding to the monthly
P
eff and
R
eff values, is further required in Eq.
2. These monthly
ET values were estimated for the whole investigation period 1950–2009 based on annual values of directly observed
ET over the time period 2000–2010 (ORNL DAAC
2011), as described further in the Data section of ESM. In general, however, the present modeling approach neither requires nor relies on this particular
ET estimation method. If and where reliable data are directly available for
ET over a whole long-term investigation period, then such time series both can and should be used in Eq.
2.
Soil parameter values used to evaluate
θ
uz
from equation
S2 in ESM-Methods are listed in Table
2 with further details given in ESM-Data. Two scenarios of initial groundwater table
z
gw−0 = −1 m and
z
gw−0 = −2 m were used for realistic result exemplification (see ESM—Data for choice motivation), and a total soil depth of
z = −2.5 m was used for the
θ
z
quantification (Eq.
3), similarly to conditions considered in Destouni and Verrot (
2014).
Table 2
Soil parameter values used to evaluate equation
S2 in Supplementary Material—Methods section for two contrasting soil types (selected values from Destouni
1991)
K
s (m/s) | 9.30 × 10−5
| 1.20 × 10−5
|
θ
ir (–) | 0.02 | 0.15 |
θ
s (–) | 0.45 | 0.40 |
β (–) | 0.18 | 0.11 |