As the availability of spatially distributed data sets for distributed
rainfall-runoff modelling is strongly increasing, more attention should be paid
to the influence of the quality of the data on the calibration. While a lot
of progress has been made on using distributed data in simulations of
hydrological models, sensitivity of spatial data with respect to model
results is not well understood. In this paper we develop a spatial
sensitivity analysis method for spatial input data (snow cover fraction –
SCF) for a distributed rainfall-runoff model to investigate when the model is
differently subjected to SCF uncertainty in different zones of the model. The
analysis was focussed on the relation between the SCF sensitivity and the
physical and spatial parameters and processes of a distributed rainfall-runoff
model. The methodology is tested for the Biebrza River catchment, Poland, for
which a distributed WetSpa model is set up to simulate 2 years of daily
runoff. The sensitivity analysis uses the Latin-Hypercube
One-factor-At-a-Time (LH-OAT) algorithm, which employs different response
functions for each spatial parameter representing a 4

Distributed hydrological models are developed to improve the simulation
and analysis of physically based, spatially distributed hydrological
processes. While more spatially distributed parameters and input data
are becoming available for modelling, most attention is paid to the
influence of the data on the quality of the calibration and to the
capacity of models to reproduce measured output time series. Several
researchers focussed on the effect of using distributed precipitation
data in hydrological models.

Several studies address classical sensitivity and uncertainty analysis methods
to spatial data and parameters. An interesting stochastic uncertainty approach
for spatial rainfall
fields in the dynamic TOPMODEL

Another study is presented by

Another spatial approach for sensitivity analysis was
presented by

In this study, the various approaches of spatial sensitivity (or uncertainty)
analysis presented above are compiled and extended in order to propose a
method that would be generally applicable and thus would give a framework for
inter-comparison of different models. Such a method would use a regular grid
to quantify the spatial pattern of sensitivity as in

The main purpose of the application of spatial sensitivity analysis proposed in
this study would be, after the

An important issue in this study is the selection of the hydrological model used
to conduct the spatial sensitivity analysis. An option is the Water
and Energy Transfer between Soil, Plants and Atmosphere (WetSpa) model

Another issue is the selection of the input data used to conduct the spatial
sensitivity analysis. A spatial data set that is frequently tested and easy to
obtain is snow cover. Snow cover fraction (SCF [-]) or snow water equivalent
remote sensing products are widely available from a number of sensors. The
different available products vary widely in spatial resolution (500 m to
25 km), temporal resolution (sub-daily to monthly) and temporal coverage
(the oldest time series starts in 1966, while new products are regularly
announced). One of the most frequently used remote sensing snow products
comes from the MODIS instrument

The aim of this paper is to provide and test a methodology for a global spatial sensitivity analysis of SCF in a distributed rainfall-runoff model. The purpose of this analysis is to show whether the WetSpa model is spatially sensitive to SCF, i.e. to identify zones where the model output is most vulnerable to input uncertainty. An important point of the analysis is to explain the existing patterns of spatial sensitivity in function of physical and spatial parameters used and hydrological processes in the study area. For the remainder of the paper, the section “Methods” presents the spatially distributed rainfall-runoff model WetSpa, the study area, data and spatial sensitivity analysis. In “Results” the output of the spatial sensitivity analysis of SCF for the Biebrza River catchment is presented and described. The “Discussion” section presents the results in light of the hydrological processes occurring in the study area, but further applicability of the spatial sensitivity analysis method and the limitation of the method (e.g. computation time) are also provided. The final section “Conclusions” recaps the main findings of the study.

The hydrological simulations in this study were conducted using the WetSpa model (

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

Surface water routing is based on a geomorphological instantaneous
unit hydrograph (IUH)

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.

Topography of the study area and location of meteorological stations.

Slope map of the study area.

The study area is the Biebrza River catchment upstream from the discharge
station at Burzyn. The total catchment area comprises 6845 km

Land use in the study area. Land-use classes are the same as used in the WetSpa model, defined by International Geosphere–Biosphere Programme classification system.

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

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.

Daily SCF was obtained from MODIS/TERRA snow product MOD10A1

Soil texture map of the study area. Soil textures are the same as used in the WetSpa model, defined by the US Department of Agriculture.

Spatial data (elevation, land use and soil) used to calculate distributed
model parameters were obtained from variable GIS sources. The elevation
map (Fig.

Usually a sensitivity analysis is performed for global parameters of a model (i.e. a
set of parameters valid for the whole model area). The sensitivity analysis presented
in this paper, however, follows a spatial approach, i.e. parameters (

Major landscape features of the Biebrza River catchment. The Biebrza River valley runs NE–SW through the catchment with at the upstream part of the valley a large forest complex. Catchment area outside the river valley is upland/plateau with mineral soils.

Graph illustrating the spatial LH-OAT SCF sampling for calculating
the sensitivity analysis. The top row presents a spatially averaged observed SCF
for an example catchment (top left panel) and the example catchment with highlighted
snow zones

LH-OAT

The experimental
set-up for the spatial sensitivity was as follows. The values of the
global parameters of the WetSpa model were the same as those obtained from
the model calibration. To be able to achieve convergence, a relatively
large number of LH samples was selected (

Descriptions and abbreviations of the 15 response functions (RF) which were used in the sensitivity analysis.

In order to investigate the relationship between parameters and different
model processes, the sensitivity analysis was performed for a set of response
functions

WetSpa parameter maps used to analyze the sensitivity analysis results: the generic
input maps used to derive the parameters maps are marked with

The spatial approach followed in this study gives a large output data
set, i.e. sensitivity maps based on different response functions. Each sensitivity
map was analyzed in light of 15 WetSpa parameter maps presented in
Table

In order to prepare the data set for statistical analysis, each of
the 15 parameter maps was spatially aggregated to fit the spatial
extent of the sensitivity analysis results (

Observed and simulated daily discharge from the calibrated WetSpa for the period in which the sensitivity analysis was conducted (upper panel). Also presented is WetSpa simulated groundwater and interflow discharge as well as only groundwater discharge. Catchment average daily temperature and SCF in the same period is presented in the lower panel. The ticks on the time axis indicate the 1st day of a month.

The calibrated model shows high efficiencies: NSE

The SCF sensitivity maps showing

The maps presenting global model output sensitivities

The analysis of

The last column of Table

Relation between the slope and spatial sensitivity analysis results
(

The scatter plots of the slope versus different response functions
(Fig.

Using

Some differences between

When comparing

The SCF sensitivity for

The SCF sensitivity for the interflow response function differs from the
groundwater and surface water response function results. The spatial pattern
of SCF sensitivity for

The SCF sensitivity for

The pattern of

The groundwater-dominated discharge composition obtained with the
calibrated model is in
conceptual agreement with

The global model output sensitivities (

Computational time could be decreased if methods other than LH-OAT were used.
Spatial sensitivity calculated based on a gradient method was presented by

The reason why most sensitivity maps calculated
for different response functions (Fig.

A number of sensitivity maps were correlated with soil-texture-related parameters.
These parameters have an influence on directing water that is stored
as soil moisture and thus have general impact on groundwater, interflow
and infiltrability. The soil-texture-related parameters have higher
frequencies than the land-use-related parameters (cf. Tables

Some of the WetSpa parameter maps have a

Parameters responsible for generating surface runoff also did not have

The frequency analyzed here is obviously dependent on
the value of the

The analysis of correlation between slope and sensitivity
maps provided in more details in Fig.

All the sensitivity maps calculated for the winter half-year response
functions resemble the full-year response functions, both in the

This surface runoff response functions (

The opposite pattern to

No

Similarly, no

The pattern of

A completely different pattern than for the other response functions is
presented by SCF sensitivity for

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 (

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.

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.

With increasing spatial data availability for distributed hydrological modelling a need appears for a methodology for sensitivity analysis of the spatial data. Such a methodology should point to zones of the study area where the sensitivity of a model spatial input to output is higher or lower and should relate these patterns to the processes simulated by the model. In order to answer these needs this paper presents an application of the LH-OAT sensitivity analysis to the WetSpa model of the Biebrza River catchment. Unlike a standard sensitivity analysis of global model parameters, a spatial approach is presented in this study. The catchment is divided into regular snow grid cells or zones in which sensitivity of SCF as input data was evaluated. The aim of this study was to present an approach for using sensitivity analysis for spatial input data and to show that the WetSpa model is sensitive to spatial input data. Moreover, it was intended to show that the spatial sensitivity results are related to physical parameters used in the model.

The spatial approach of the LH-OAT sensitivity analysis results in spatial maps presenting areas of relatively higher and lower sensitivity. In order to extend the analysis, the sensitivity analysis was repeated with different response functions. Most of the sensitivity analysis results were similar for the whole year and winter half-year response functions. Moreover, the sensitivity obtained for the mean discharge response function was very similar to the sensitivity analysis for the mean groundwater discharge response function. Hence, the model behaviour related to snow processes is dominated by winter half-year and groundwater processes, which is in agreement with the Biebrza River spring flood regime with a dominant share of groundwater discharge. Another important finding was that SCF sensitivity was high in snow zones in the river valley under the winter half-year surface runoff response function. This is in agreement with the observation that the snowmelt in the river valley is a considerable surface runoff source to spring floods.

In this case study, the spatial patterns of SCF sensitivity could, for most of the response functions, easily be interpreted by co-occurrence of different landscape features like upland and river valley. However, for some of the response functions a straightforward interpretation was impossible. A successful approach to interpreting the patterns was performed by analysing the values of coefficients of determination between the physical model parameters and the SCF sensitivity. The spatial pattern of the sensitivity for different response functions, obtained from these results, is related to different spatial parameters and to different physical processes simulated by the model. The parameters which had a strong correlation with the SCF sensitivity for most of the response functions were slope and soil-related parameters. The potential runoff coefficient and depression storage were important for only a few response functions, because the catchment is not urbanized. Temperature, which directly influences the snowmelt generation in the WetSpa model, shows a strong correlation only with the mean snowmelt response function. It is important to mention that the spatial sensitivity quantified with several response functions was correlated to more than one spatial parameter. This shows the importance of the links between the parameters which were revealed by this spatially distributed analysis.

In summary, a spatial approach of sensitivity analysis can be performed with the LH-OAT algorithm, as presented in the results of this paper, and the SCF is spatially sensitive in the WetSpa model. The pattern of spatial sensitivity is related to spatially distributed physical parameters, and the results are confirmed by a priori scientific understanding of the Biebrza River catchment functioning. The spatial sensitivity maps can by used to highlight areas which require better attention during the parametrization and to show which spatial parameters have influence on the analyzed phenomena: in this case, the snow-related processes.

In future work, other input time series or input parameters should be evaluated in a spatial analysis. It would also be interesting to compare spatial sensitivity of the same input data with other models, e.g. TOPMODEL or SWAT. Finally, since spatial SCF is sensitive in WetSpa, other sources of these input data should be tested in the model.

We wish to thank two anonymous reviewers for their comments and suggestions that improved this work. We also acknowledge Ignacy Kardel for sharing the sources for the soil map used in this study. The first author acknowledges the Flemish government for supporting his research visit to the Vrije Universiteit Brussel. The hydrometeorological data were provided by Institute of Meteorology and Water Management National Research Institute (IMGW). Edited by: A. Gelfan