Hydrological models are being applied for impact assessment across a wide range of resolutions.
In this study, we quantify the effect of model resolution on the simulated hydrological response
in five mesoscale basins in the Swiss Alps using the distributed hydrological model Spatial
Processes in Hydrology (SPHY). We introduce a new metric to compare a range of values resulting
from a distributed model with a single value: the density-weighted distance (DWD). Model simulations
are performed at two different spatial resolutions, matching common practices in hydrology:
500 m
In current distributed hydrological modeling, we identify two approaches at
opposite ends of the scale of application. On the one hand studies are performed
at global scale, and on the other hand studies are performed at regional or
basin scales. The modeling approach generally affects the choice of spatial
resolution, one of the key modeling decisions in hydrological modeling
Another type of hydrological study are those at basin or regional scales.
These studies mostly use distributed hydrological models to simulate the
hydrological response under climate change or climatic extremes
Both global and regional studies focus on reaching similar goals, yet with
different methodologies. So far, no study has investigated how these two
methodologies connect and how the modeling approach affects the results. The
effect of model resolution on the simulated response has been investigated by
numerous studies, either for regional climate models or for hydrological
models
Statistics for each catchment
In this study, we aim to bridge the large-scale (climatological) and
regional-scale (hydrological) approaches by quantifying how the simulated
hydrological response depends on spatial resolution, including within-basin
complexity. Despite the large body of literature addressing the problem of
scaling in hydrology
For this study, we selected five mesoscale basins in the Swiss Alps. Not only
is the response of these basins relevant at regional scale, these basins also
contribute considerable amounts to large rivers in Europe. For example, the
discharge of the Rhine consisted of almost 40 % meltwater from the
Swiss Alps during the warm and dry summer of 2003
Overview of the location
The model is forced with daily precipitation and temperature from MeteoSwiss
The SPHY model was used to simulate each
basin at both resolutions. SPHY is a spatially distributed conceptual
hydrological model, including representations of rainfall–runoff, cryosphere,
evapotranspiration and soil moisture processes, as well as their
nonlinearities and thresholds
Schematic overview of the conceptualization in SPHY.
Blue arrows represent fluxes contributing to total runoff generated in
each model cell and small grey arrows represent fluxes between the different
reservoirs. Overview is based on the more detailed concept by
SPHY was applied to each basin at two different resolutions: at
In this study, we only focus on the runoff and actual evaporation responses.
We averaged all model output over 3 months, grouping the hydrological
response according to season: December, January and February for winter (DJF); March,
April and May for spring (MAM); June, July and August for summer (JJA); and
September, October and November for autumn (SON). Standardized anomalies are
used to quantify the magnitude of the deviation within each season and are
calculated for each individual model cell, using the following equation:
The concept behind density-weighted distance
Since the goal of this paper is to compare results from a high-resolution
model with results from a low-resolution model, we require a suitable metric
to quantitatively evaluate the difference between those results. Based on the
previously discussed methodology, the high-resolution model outputs a
distribution of values, which needs to be evaluated against a single value
from the low-resolution model. Ideally, the metric provides robust
information regardless of the shape of the distribution of the results from
the high-resolution model. A common option would be to calculate the
percentile score of the low-resolution model result within the high-resolution model results. However, the percentile score does not provide
information about the size of the error between the high- and low-resolution
models. Another option would be the root mean square error (RMSE). The
Therefore we propose a new metric, which provides a measure of the distance
between a single point and a distribution of values, regardless of the shape
of the distribution. This metric includes information not only on the
difference in mean or median, but also on the width of the underlying
distribution that the single value tries to represent. We call this new
metric the density-weighted distance.
Relation between climate anomalies and observed discharge anomalies. Each dot represents a single season and is colored with the corresponding standardized observed discharge anomaly. Dots with a black outline represent the selected extreme seasons (winter of 1995, spring of 2007, summer of 2003 and autumn of 2002).
The DWD can be interpreted as the difference in terms of number of
standardized anomalies. DWD is zero when the high-resolution data have zero
variability, and when the difference with the low-resolution model results is
also zero. If the high-resolution data have zero variability, but the result
from the low-resolution model is outside of this range, DWD will give the
distance between the low- and high-resolution data, measured in the number of
standardized anomalies (see the “Flat” subplot in Fig.
In order to illustrate the concept behind DWD and compare it to the
previously mentioned metrics, Fig.
The key focus of this work is the catchment response to extreme seasons. To
identify those extreme seasons, standardized precipitation and temperature
anomalies are calculated for each season and basin (see
Fig.
Discharge observations compared with discharge simulations for
The highlighted dots in Fig.
The colors of the circles indicate the discharge anomalies. Discharge anomalies in the pre-Alpine basin seem to follow a distinct pattern, where high precipitation values often coincide with high positive discharge anomalies, and vice versa. Temperature also seems to influence discharge anomalies in the pre-Alpine basin, but this relation is less evident. The Alpine basin shows a much more random pattern, without any clear relation between temperature and/or precipitation. This indicates that the runoff-generating processes are not consistently driven by either precipitation or temperature, but by a combination of both.
Comparison between anomalies simulated with SPHY and observed anomalies in the Rietholzbach, anomalies are based on the entire simulation period. Winter and autumn values for evaporation are in italic type, since they are not the focus of this study due to the fact that SPHY does not allow for evaporation during snow-covered periods.
Spatial distribution of anomalies of actual evapotranspiration
The calibration results for each basin are presented in
Fig.
Hydrological response maps for the two main hydrological fluxes (actual
evapotranspiration, ET, and generated runoff) during each extreme season are
presented in Fig.
Relation between spatial standard deviation (
In Fig.
Anomalies in the generated runoff also show a contrasting within-basin
response, in particular in the Alpine basins. Here, cells with low elevations
show a different anomaly than the cells at high elevations. This dependency
between anomaly and elevation is not visible in the pre-Alpine basins, where
all model cells show roughly the same response. The cause of this difference
between the two basin types will be further investigated below in
Fig.
Relation between elevation and hydrological response colored
by land cover type, presented for the Reuss
The spatial variability (as expressed by the standard deviation,
Spread in the actual evapotranspiration response seems related to temperature
(Fig.
Standard deviation of generated runoff seems most sensitive to temperature
during summer and autumn; see Fig.
The influence of average precipitation on the runoff
To gain a better understanding of the hydrological behavior within each
basin, the standardized anomalies of each individual grid cell are plotted
against elevation in Fig.
The hydrological responses can be grouped according to land cover class: “forest” and
“glaciers” nearly always show a different response within the same basin
and season, where “grass” and “other” are covering a gradual transition
between the two groups. This grouping can be explained by the runoff-generating processes. Areas at high elevation generate runoff by melting ice
and snow (if present), while areas at low altitudes rely on root zone and/or
groundwater processes. The latter are mostly driven by the amount of
available water (water-limited), while runoff from ice and snow is mostly
dependent on the incoming energy (energy-limited). This dependency is most
visible in Fig.
Our results may be influenced by parameterizations defined within the model.
For example, the limited evapotranspiration of snow-covered cells is a choice
made by the developer of SPHY. One could argue whether this is realistic.
Furthermore, the glaciers in SPHY are fixed in location and extent. The
importance of dynamical glaciers is investigated by
With improved understanding of the hydrological response to extreme seasons
when simulated at high resolution (matching the regional-scale studies), we
can now compare those results to the model output when the basins are
simulated on a
Comparison between the average high-resolution model response
and the low-resolution model response, for the generated runoff. Colors
indicate the different extreme seasons, and the dotted line represents the
Model response to extreme seasons for both generated runoff
Scale mismatch between the high- and low-resolution models as measured by DWD, for both hydrological fluxes during the four extreme seasons.
Next, we compare how the range of values from the high-resolution model
compare to the low-resolution model in Fig.
For each hydrological flux, basin and extreme season, the DWD is calculated and presented in Table
The summer of 2003 in the Rhone basins shows a very high DWD value for the
generated runoff. This is due to a combination of a relatively low percentile
score (
Another high DWD value is found for actual evapotranspiration during the
summer of 2003 in the Emme basin (see Fig.
Actual evapotranspiration is not only dependent on the amount of available water, but snow cover is also an important factor. For example. the high DWD value for evaporation in the Inn basin during the spring of 2007 can be attributed to this response. In the low-resolution model, the cell was free of snow, allowing the model to evaporate, while in the high-resolution model only half the cells were free of snow. The cells covered with snow were not able to evaporate water, resulting in a large variation in anomalies and thus a large 5 %–95 % range.
Our results are in line with numerous studies either investigating effects of
model resolution or comparing the performance of lumped models with
(semi-)distributed models. For example,
The results may be influenced by the fact that the model did not allow for subgrid variability in land use or soil types, something other models might have included. When subgrid variability is taken into account, we expect the low-resolution model results to become less extreme. However, the low-resolution model will not be able to capture the full dynamics simulated with the high-resolution model, since landscape characteristics still need to be aggregated to a coarser resolution.
In this study, we investigated the hydrological response anomalies in five
catchments in the Swiss Alps at two different spatial resolutions. The
catchments were selected based on topography and land cover. Three out of
five catchments are situated at high elevations and contain glaciers
(referred to as Alpine catchments), and the two other catchments are situated
at lower elevations and do not contain glaciers (referred to as pre-Alpine
basins). We ran the distributed hydrological model Spatial Processes in
Hydrology (SPHY) at two different spatial resolutions to match two common
hydrological modeling approaches: at a high resolution of
Results from the high-resolution model show that the intra-basin response
covers a large range of anomalies during the selected seasons, where
contrasting anomaly signs within a single catchment are often occurring.
Within-basin complexity of hydrological response was found to generally
increase with the magnitude of the forcing anomaly. The low-resolution model
failed to capture this diverse and contrasting response, since the entire
region was covered by a single grid cell. The newly introduced density-weighted distance (
The variability in simulated response was associated with the different land
cover classes. We found that runoff anomalies matched the temperature
anomalies when the dominant runoff-generating processes are energy-limited
(snow/glaciers), and runoff anomalies matched precipitation anomalies
when the dominant runoff-generating processes are water-limited
(grass/forest). The two pre-Alpine basins generally showed a different
response than the Alpine basins, which can be attributed to the smaller
variation in elevation and land cover in these basins. The grouping of
responses in our study matches the elevation classes as defined by
The SPHY model code (version 2.1) is available at
The supplement related to this article is available online at:
JB, AJT and RH designed the research. JB performed the research, analyzed the data and wrote the first draft; all authors contributed to interpreting results, discussing findings and improving the paper.
The authors declare that they have no conflict of interest.
The authors would like to thank the editor Nadav Peleg, and Davide Zoccatelli, Staffan Druid and the anonymous reviewer for their constructive comments, which helped to improve the quality of this paper.
This paper was edited by Nadav Peleg and reviewed by Davide Zoccatelli and one anonymous referee.