The hydrological simulations in this study were conducted using the WetSpa model (). The model divides a catchment into a regular grid with a specified dimension. In each grid cell, the water balance is simulated and the surface, interflow and groundwater discharge components are routed to the catchment outlet . Spatial parameters used to calculate the hydrological processes are obtained from land-use, soil and elevation input maps. Attribute tables based on literature data are linked to the maps and transformed to distributed physical values via a GIS preprocessing step . Several studies have demonstrated that WetSpa and its steady-state version WetSpass are suited to integrate distributed remote sensing input data in the simulation of the hydrological processes .

The model consists of the following storages: interception, depression, root zone, interflow and groundwater. Water transport between the storages is based on physical and empirical equations. Rainfall, temperature and potential evapotranspiration based on data from meteorological stations are made spatially explicit by use of Thiessen polygons, but a spatially distributed input form is also possible.

In the standard WetSpa version, snow accumulation is calculated based on precipitation and a threshold temperature t0 (∘C). When the temperature in a grid cell is t (∘C) and falls below t0, precipitation is assumed to be snow. Snowmelt is calculated based on t0, a degree-day coefficient ksnow (mm ∘C-1 day-1) and coefficient krain (mm mm-1 ∘C-1 day-1), reflecting the amount of snowmelt caused by rainfall vrain (mm). In this study SCF was obtained from MODIS snow products and used as input data. Thus, snow accumulation was not calculated but replaced with the input SCF, while the snowmelt amount (vsm) (mm) per model time step δt (day) is calculated as vsm=SCFksnow(t-t0)+krainvrain(t-t0)δt. This approach of calculating snowmelt based on SCF and snowmelt rate was proposed by . It allows us to obtain distributed vsm values weighted by SCF from grid cells where SCF > 0. WetSpa is also capable of using an energy balance model for snowmelt calculation ; however, because of the higher demand on input data, this approach was not used.

Surface water routing is based on a geomorphological instantaneous unit hydrograph (IUH) . The IUH is calculated for a flow path starting in a grid cell and ending at the catchment outlet, i.e. each grid cell has its own IUH. Groundwater flow and interflow are calculated on a sub-catchment level based on a linear reservoir method and routed to the catchment outlet with the IUH. Comparison of the WetSpa performance with other distributed hydrological models can be found in the results of the DMIP2 project .

The model was set up with a daily time step and 250 by 250 m grid cells. The calibration period was 1 September 2008 to 31 August 2009, while validation was from 1 September 2007 to 31 August 2008. The length of the calibration and validation was selected to optimize the model for snow conditions occurring in the period selected for sensitivity analysis (Sect. ). The global WetSpa parameters were calibrated using the Shuffled Complex Evolution algorithm . The calibration was conducted with the R software and package “hydromad”. The model was optimized to maximize the efficiency (NSE): NSE=1-∑x=1τQx-Q^x2∑x=1τQx-Q‾2, where Qx and Q^x are observed and simulated discharges at time x, Q‾ is the mean observed discharge and τ is the total number of time steps. Sensitivity of the WetSpa model to the global parameters is presented in .

The study area is the Biebrza River catchment upstream from the discharge station at Burzyn. The total catchment area comprises 6845 km2 (Fig. ). Biebrza is a lowland catchment consisting of moraine plateaus and post-glacial valleys with low slopes (average 1.03 %, Fig. ) and an elevation ranging from 102 m a.s.l. at the catchment outlet to 298 m a.s.l. at the northern water divide. Land use is composed of agriculture (54 %), forests (26 %), wetlands and grasslands (17 %), water (2 %) and urban (1 %) (Fig. ). The area is considered semi-natural, especially because of its large area of well-preserved wetlands and forests and is therefore used as a reference area in wetlands research . Several lakes in the northern part of the catchment are controlled by management schemes, which usually discharge into Biebrza tributaries after the accumulation period. Lakes in WetSpa are modelled by setting appropriate values of the hydraulic parameters in the model, e.g. by a high runoff coefficient and low friction. The simulation of water management schemes in the controlled lakes is, however, not implemented. Dominant soil textures in the study area are sand (34 %), loamy sand (26 %) and sandy loam (18 %), whereas minor parts are covered by sandy clay (4 %) and silt (2 %) and other soils cover less than 1 % of the area. In the river valley, organic soils are frequent and cover in total 16 % of the study area (Fig. ). The dominating landscape features that certainly have influence on the functioning of the Biebrza hydrological system are the river valley and the large forest complex located in the north-eastern part of the catchment (Fig. ).

The Biebrza River is characterized by a spring flood regime; the discharge of the spring flood is mostly related to the volume of snowmelt in the catchment . Based on the meteorological record from 25 stations and the flow record at the Burzyn profile (Fig. ) managed by the Polish Institute of Meteorology and Water Management National Research Institute (IMGW), the study area can be characterized by the following figures. Mean yearly discharge (1951–2012) at Burzyn is 34.9 m3 s-1, while summer and winter averages are respectively 26.0 and 43.9 m3 s-1. Recorded extreme low and high discharges (1951–2012) are 4.33 and 517 m3 s-1 respectively. The climate in this area is transitional between continental and Atlantic with relatively cold winters and warm summers, effectively making this area the coldest region in lowland Poland. The mean air temperature (1979–2009) is 7.0 ∘C; in the winter half-year it is 0.3 ∘C and in the summer half-year 13.7 ∘C. The mean monthly temperature (1979–2009) has a maximum in July (17.6 ∘C) and minimum in January (-3.3 ∘C). The yearly precipitation (1979–2009) is 587 mm (375 mm in the summer half-year, 212 mm in the winter half-year). The yearly average number of days with temperature below 0 ∘C (1979–2009) is 79 and with snow cover (1975–2012) is 93 (average snow depth is 12 cm). Based on the meteorological maps , the mean yearly evaporation from free water surface (1951–2000) is 550 mm, 465 mm in summer and 85 mm in winter (1951–1970).

Hydrometeorological data (precipitation, air temperature and discharge) were obtained from IMGW. Daily precipitation was obtained for 25 rain gauge stations, whereas air temperature was available for 5 stations (Fig. ). Temperature was recorded as minimum and maximum daily temperature; an average from these values was calculated to obtain the mean daily temperature for each station. Daily discharge was obtained for Burzyn. Potential evapotranspiration was estimated based on mean monthly evaporation from free water surface and uniformly disaggregated into daily values.

Daily SCF was obtained from MODIS/TERRA snow product MOD10A1 datasets used: IX 2007 to X 2009 with a 500 m resolution. The SCF values in MOD10A1 are calculated based on the Normalized Difference Snow Index (NDSI): NDSI=rvis-rirrvis+rir, where rvis and rir are the reflectance visible and in near-infrared bands, which for the MODIS sensor are respectively bands 4 (545–565 nm) and 6 (1628–1652 nm). In general, NDSI gives higher values when a larger part of a pixel is covered by snow. However, it may be affected by noise from many sources and has to be corrected for bias in forest areas . The MOD10A1 SCF input data were aggregated into 524 4 km by 4 km snow zones, while zones close to the catchment boundary are fractions of a 4 km square. The purpose of the aggregation was to decrease computation time of the sensitivity analysis and reduce noise in the MOD10A1 data while keeping enough variability to obtain meaningful spatial results. In order to remove missing data related to cloud cover occurrence the SCF in snow zones was linearly interpolated over time. Finally, SCF was set to 0 in months when there was no snow recorded in lowland Poland, i.e. from May to September. The aggregated MOD10A1 SCF data in snow zones were used to calibrate the WetSpa model. For the spatial sensitivity analysis, however, the daily time series of catchment averages of MOD10A1 SCFs were used; i.e. the spatial pattern of SCF in snow zones was obtained by perturbing the catchment averages by random factors (Sect. ).

Spatial data (elevation, land use and soil) used to calculate distributed model parameters were obtained from variable GIS sources. The elevation map (Fig. ) was compiled from three sources: the digital elevation model of Poland on a scale of 1:26,000, digitized contours from the topographical map of Poland on a scale of 1 : 25 000 and from field surveys in the Biebrza valley . The land-use map (Fig. ) was obtained from the Corine Land Cover 2006 project . In the catchment area outside the Polish border (56 km2), agricultural land-use was assigned. The soil map (Fig. ) was obtained from the soil map of Poland with a scale of 1 : 50 000 for agricultural areas and 1 : 500 000 in forests and cities. Outside the Polish border the most frequent in the neighbourhood, sandy soil, was assigned. All the spatial data were interpolated to 250 m grid cells using the nearest-neighbourhood (soil, land use) and the bilinear (elevation) algorithms.

The calibrated model shows high efficiencies: NSE = 0.86 for the calibration period, NSE = 0.73 for the validation period and NSE = 0.79 for the whole period. The snow-related global WetSpa parameters were estimated during the calibration as: ksnow = 5.03 mm ∘C-1 day-1, krain=0.02 mm mm-1 ∘C-1 day-1. The comparison of observed and simulated discharge is presented in Fig. . Of the simulated discharge at the catchment outlet, 90 % has a groundwater origin, while surface runoff (5.3 %) and interflow (4.7 %) contribute mostly to the highest peaks (Fig. ).

The maps presenting global model output sensitivities s⋆i to variations of spatial SCF are presented in Fig. . The use of different response function results in different patterns of spatial sensitivity, although some similarities can be distinguished as well. The minimum, maximum and mean values are indicated on each map (Fig. ). When the minimum is equal to 0, the model is completely insensitive in at least one snow zone for this response function. The values presented in the first four rows can be compared within a row; however, comparison between the rows is more difficult as in different rows the response functions concern discharge components of different magnitude. Note that the grey scale is different for all maps in the lowest row. This is because, unlike in the upper rows, the s⋆i calculated from these response functions are not intended to be compared within this row as they concern different processes.

The analysis of ρ2 values (Table ) explains the spatial relations between SCF sensitivity with different response function and the spatial parameters. Most of the pairs in Table  have low ρ2, suggesting that a parameter was not relevant for sensitivity with this response function. However, for most of the response functions at least one ρ2⩾0.40 was found, indicating that the SCF sensitivity with these response functions can be partially explained by the values of the parameter maps. The values of ρ2 show influential and unimportant spatial parameters for the SCF sensitivity, i.e. for the snow-related processes. Detailed analysis of Fig.  and Table  is provided in the subsequent subsections.

The groundwater-dominated discharge composition obtained with the calibrated model is in conceptual agreement with . The model performed well during snowmelt-supplied spring floods. However, the peaks were underestimated by 8 % of the observed value on average. The underestimations of peak discharges are possibly determined by the uncertainty of the rating curve. During the yearly spring floods, the measurement profile near the gauging station widens outside the riverbed and extends into the densely vegetated floodplain, where proper hydraulic measurements are very difficult. Nonetheless, the shape of the events resembled well the observed values, which can be an advantage of using observed SCF data instead of predicting snow cover in the model. This is supported by the comparison of the hydrograph (upper part of Fig. ) with the timing of snowmelt and temperature rise above 0 ∘C (lower part of Fig. ), which shows a rapid discharge rise at the beginning of spring floods. Good results of using MODIS snow products in other hydrological models have also been shown by , , , , and . The model performed worse during periods of intensive summer storms. For these storms, a rapid discharge rise was simulated, which was not observed in reality. A possible reason for this low performance is the positively biased soil moisture prediction of the model during these periods.

The global model output sensitivities (s⋆i) are calculated for a regular-structured grid (Fig. ). This approach may be considered imperfect, as irregular, homogenous zonation could more directly reference the sensitivity to spatial features of the model. Regular zonation used in this study was similar as in . This approach implies that the borders of spatial features do not resemble the zonation and the results are somewhat aggregated. An advantage of the structured grid lies, however, in broad comparability of different models; e.g. spatial sensitivity analysis in a study area modelled with different spatial discretization like hydrological response unit (SWAT) or grid cell (WetSpa) could be easily compared when using the structured grid. Moreover, an irregular approach would require much more zones if very fine spatial features were to be analyzed. This would require additional computational time, as the number of zones determines the number of parameters for the sensitivity analysis (see Sect.  for further discussion on this topic).

Computational time could be decreased if methods other than LH-OAT were used. Spatial sensitivity calculated based on a gradient method was presented by . Their results, although showing the importance of spatial sensitivity analysis, were calculated using a local method. Local methods do not properly handle the non-linear models . On the contrary, the method presented in this study results in a global sensitivity; i.e. it covers the whole parameter space and thus gives more insight into the model behaviour than a local method. There is still room for selecting other method for spatial sensitivity. Interesting results could be obtained when a variance-based method, like Sobol's would be used. Such an analysis would give additional information to LH-OAT on interactions between the model parameters.

The total computation time, a product of simulation time and number of required runs, is a limitation of the applicability of this method and is similar to in all methods requiring a large number of model runs to achieve the desired output. This was also the case in this study; as WetSpa required about 1 min for a single run, the total time for 52 500 simulations was about 36.5 days. The advantage of any random-sampling-based sensitivity analysis method (including LH-OAT) is that it is easily parallelized, i.e. the LH-OAT samples are obtained before the simulations and the model runs are divided over a number of processors or computers.

One could, however, consider decreasing the number of zones (n) in which the input data are perturbed or the number of LH samples (p) to receive the results faster. The latter implies that the LH-OAT method may not converge . Thus, it seems more reasonable to decrease the number of zones and be satisfied with results at lower spatial resolution.

The analyses conducted in this case study are both a validation and an example application of the spatial sensitivity analysis method. The further potential use of this method could be twofold: for generic sensitivity analysis and for a catchment change scenario analysis.

The generic sensitivity analysis would be similar to the presented approach in this paper. The maps (e.g. Fig. ) would show zones of the catchment with high or low sensitivity. The correlation analysis as in Table  would show the parameters explaining the sensitivity pattern which thus require more attention during the parametrization. This would require possibly denser field sampling of the correlated parameters additional to the data subjected to sensitivity analysis or obtaining the data from a source with less uncertainty; as a result, the prediction uncertainty should be decreased. Additionally, the detailed scatter plots of parameters against response functions (e.g. Fig. ) would show which data ranges of the parameters are the most responsible for the spatial sensitivity pattern. In contrast, the “standard” sensitivity analysis is performed for global parameters which usually are not spatially distributed or are semi-distributed (i.e. grouped to few categories with the same values; e.g. ).

The catchment change scenario analysis was not investigated in this paper but is a possible application of the presented spatial sensitivity analysis method. In such an analysis instead of SCF input time series the LH-OAT sampling would be done for e.g. different land covers proportions in the catchment zones. The output of such an analysis would be sensitivity of the zones to changes in land cover and could be used as e.g. a decision support for urban development.