Hydrological models are useful tools for exploring the impact of climate change. To prioritize parameters for calibration and to evaluate hydrological
model functioning, sensitivity analysis can be conducted. Parameter
sensitivity, however, varies over climate, and therefore climate change could
influence parameter sensitivity. In this study we explore the change in
parameter sensitivity for the mean discharge and the timing of the discharge,
within a plausible climate change rate. We investigate whether changes in sensitivity propagate into the calibration strategy and diagnostically compare three hydrological models based on the sensitivity results. We
employed three frequently used hydrological models (SAC, VIC, and HBV) and explored parameter sensitivity changes across 605 catchments in the United
States by comparing GCM(RCP8.5)-forced historical and future
periods. Consistent among all hydrological models and both for the mean
discharge and the timing of the discharge is that the sensitivity of snow parameters decreases in the future. Which other parameters increase in
sensitivity is less consistent among the hydrological models. In 45
Earth and environmental computer models are indispensable tools to explore an
uncertain future. Whereas observational studies report on historical changes
in streamflow patterns across the contiguous United States (CONUS) that might
be attributed to climate change
Given the relevant role of models in supporting decision making, model functioning should be thoroughly scrutinized. A frequently used tool to
evaluate hydrological model functioning is sensitivity analysis
However, parameter sensitivity also differs across climate, as for instance
shown by
Many hydrological models that are used for long-term projections have parameters that require calibration to identify their values for the catchment under study. Hydrological model parameters are generally calibrated on discharge time series. However, discharge is a lumped catchment response and therefore only provides limited catchment information “With four parameters I can fit an elephant, with five I can make him wiggle his trunk”, John von Neumann (1903–1957)
Besides the potential consequence for calibration, evaluating the relation
between change in parameter sensitivity and climate change also provides the
opportunity to diagnostically evaluate model functioning during long-term
projections. Several studies already investigated the change in parameter
sensitivity over time, focusing on specific events or relatively short timescales
In this study we investigate how parameter sensitivity changes as a consequence of climate change. We evaluate whether and how this has consequences for parameter prioritization for calibration and whether systemic changes are robust across different hydrological model structures. To this end, we apply a hybrid local–global sensitivity analysis method to three frequently used hydrological models in 605 basins across the US. We evaluate two signatures (mean discharge and timing of the discharge) and link changes in sensitivity to changes in climate. To sample plausible climate change space, we employ forcings from three different GCMs. Finally, we evaluate the impact on the top-5 most sensitive parameters in each basin and investigate the transmission of sensitivity from one parameter to the other. We end with a recommendation on how to account for changes in sensitivity in the calibration strategy of models used for long-term projections and an evaluation of the robustness of systemic changes across different models.
To investigate changes in parameter sensitivity, we employed three frequently
used hydrological models. The models were run for a historical period and a future period over 605 catchments, forced with three bias-corrected and statistically
downscaled global circulation models. A hybrid local–global sensitivity analysis method was applied to the simulations of both periods, evaluating two target variables: the mean discharge and the day of the year on which half of
the yearly discharge has passed (discharge timing). Then, the differences in
parameter sensitivity between the historical and future periods were explored in several ways: first, per parameter to investigate which parameters change and over different climate indicators to investigate how climate and climate
change explain changes in sensitivity. Then, we assessed how the top-5 most
sensitive parameters would change in the future period, thereby impacting the
calibration strategy. Finally, we conduct a diagnostic model evaluation,
amongst others by investigating the transmission of sensitivity from one
parameter to the other. An overview of the procedure is shown in
Fig.
Summary of the methodological approach, to be read from left to right. The first three panels are the calculations, and the other four panels are the actual analyses.
We investigated for three models whether parameter sensitivity changes within
a plausible climate change range: the TUWmodel following the structure of HBV
Simplified representation of the model structure of the three models employed in this study. All the parameters that are displayed are included in the sensitivity analysis. Parameters are coloured according to the flux or state they influence (evapotranspiration (ET), snow, soil moisture and shallow layer, percolation, deep layer). The colours are used consistently throughout all the figures in this study. Parameter boundaries can be found in Appendix Tables
A simplified representation of the model structures, including a description
of the parameters that were accounted for in the sensitivity analysis, are
displayed in Fig.
All three models have a different structure, but HBV and SAC are more alike in
terms of structure and conceptualization than VIC. A difference is that for
HBV and SAC, potential evapotranspiration was obtained with the
Priestley–Taylor equation
All three models were run for a historical and future period of 28 years, of
which the first 5 years were omitted from both periods for spin-up. As such, the historical period that is analyzed covers 1985–2008 and the future period 2070–2093, 23 years each. The forcing for both periods was obtained
from statistically downscaled and bias-corrected output from three GCMs: the Max Planck Institute for Meteorology Earth System Model MR
Our study is an investigation of the potential that a plausible climate change
rate might impact hydrological model parameter sensitivity. As such, we only
selected a subset of three GCMs to sample plausible climate change rates. The
three selected GCMs represent different climate model families as identified
by
Finally, the GCM forcing was lumped over the CAMELS basins. The CAMELS data
set contains forcing, discharge observations, and catchment characteristics
for 671 catchments throughout the contiguous United States with limited human
impact
The hydrological models were not calibrated, since we employed global
sensitivity analysis across the full parameter range. Therefore, the 605
simulated catchments should be perceived as 605 different climate instances
with an individual level of climate change rather than as catchment-representative models. Given that each catchment was forced with the three
GCMs, in total,
The goal of this study is to investigate how climate might impact parameter sensitivity within a plausible climate change range. We are thus particularly interested in the extent to which we can expect changes in the sensitivities of model parameters as a consequence of changes in the climate. As such, it is of second-order importance whether the climate model gives highly accurate predictions or whether the hydrological model can exactly capture catchment behavior. It is, however, important to note that we employed the highest emission scenario (RCP8.5), thereby investigating the effect of the higher ranges of plausible climate change. It can be expected that the impact of climate change on parameter sensitivity will be lower for lower emission scenarios. However, RCP 8.5 is often used to provide an upper boundary for long-term projections, thereby demonstrating the relevance of choosing this scenario.
In the selection of the sensitivity analysis method, a few points were
considered. First, it had to be a global method, because global sensitivity
analysis methods are used to identify the most sensitive parameters for
calibration (whereas local methods are generally applied after
calibration). Secondly, we had to account for a high number of runs (605 basins, three GCMs, two periods, three hydrological models). Therefore, we
selected the hybrid local–global method DELSA
DELSA evaluates local sensitivity at several places throughout parameter
space, as such mimicking global sensitivity analysis. First, 100 parameter
samples called base runs were created based on a space-filling sampling strategy. The models were run for all 100 samples. Secondly, the parameters
are one-at-a-time perturbed with 1
We used the average sensitivity from the 100 samples per parameter per basin
as a measure of parameter sensitivity. Each parameter that is displayed in
Fig.
Besides the selection of a sensitivity analysis method
The sensitivity analysis was conducted for both the historical and future periods, for all 605 basins forced with three different plausible climate change rates (based on the three GCMs). The first analysis of the calculations was a simple exploration of which parameters increase and which parameters decrease in sensitivity in the future over all 605 basins to achieve a first insight into potential changes in parameter sensitivity in future and to see which parameters are mainly affected.
The 605 climate instances from the 605 basins are not a representative sample since certain climates might be over- or under-represented. Therefore, the difference in sensitivity was also related to climate indicators. This also allows us to combine the results obtained with the three different GCMs: if there is a relation between a climate indicator and parameter sensitivity, this should be visible regardless of which GCM was used. Basically, the three GCMs were used to sample the plausible climate change space.
Given their relevance for discharge, we employed the Knoben climate indicators
To determine the aridity index, first Thorntwaite's moisture index
To evaluate the impact of change in parameter sensitivity on calibration
strategy, we determined the top-5 most sensitive parameters for each basin,
both for the historical and future periods. We analyzed which parameters left and entered the top-5 in the future compared to the historical period, as a
consequence of a change in sensitivity. This was again related to the climate
indicators of Sect.
To diagnose how the results from the different models have come about, we relate the direct model output (several states and fluxes) to changes in sensitivity. Furthermore, we introduce the concept of “parameter sensitivity transmission”: we evaluate whether any negative correlations exist between parameters with increasing and decreasing sensitivity. Strong negative correlations can be an indication that sensitivity is transmitted from one parameter to the other, so we define transmission as a clear negative correlation in change in sensitivity between two parameters. However, since we evaluate correlation, transmission does not refer to absolute sensitivity values.
The goal of this analysis is to investigate to what extent sensitivity is transmitted directly from the decreasing parameter to the increasing parameter. When there is no direct relation, it can indicate that sensitivity changes at several places within the model structure. The transmission of sensitivity can give insights into which processes become more relevant in the future, at the expense of processes that become less relevant – a systemic change as a result of climate change. A comparison among the different model structures will indicate their (dis)agreement on the change in relevant processes.
To place the results in context, we first briefly discuss the change in climate between the historical and future periods and the changes in several simulated water balance terms for both periods for the three employed hydrological models. Subsequently, we discuss the change in sensitivity between the historical and future periods, the relation between changes in sensitivity and climate, the impact of sensitivity changes on calibration strategy, and finally the model diagnostic evaluation.
Figure
Changes between the historical (1985–2008) and future (2070–2093) periods. The left two panels depict the change in temperature (
Figure
Figures
The distribution of change in parameter sensitivity (
Consistent over all three hydrological models when evaluating the mean discharge as a target variable is a decrease in the sensitivity of snow parameters in the future. The parameters that show increasing sensitivity cannot consistently be associated with one specific process. Whereas a strong decrease in sensitivity requires high sensitivity in the historical period, this is not required for a strong increase in sensitivity. It can be observed, however, that model parameters that display an increase in sensitivity were also already sensitive in the historical period.
In the HBV model, the snow correction factor (SCF) especially displays a large decrease. This is also the parameter with the highest sensitivity in the historical period, thereby having the highest potential to decrease. The other three snow parameters in HBV displayed lower sensitivity in the historical period and also show a less consistent decrease in the future. Also in the SAC and VIC models, the snow parameter that displayed the highest sensitivity in the historical period (SCF in SAC and Snowrough in VIC, respectively) show the strongest decrease.
Among the three hydrological models, different parameters related to different processes display an increase in sensitivity in the future. In HBV, evapotranspiration and soil parameters increase in sensitivity in the future, with the largest increase in the evapotranspiration parameter PT, while there is hardly any observable change in sensitivity in percolation and deep layer parameters. In the SAC and VIC models, there are parameters associated with all processes except snow that tend to mainly increase in sensitivity in the future. Like for HBV, also in SAC the evapotranspiration parameter PT has the highest increase. In the VIC model, the depth of the second soil layer (Depth2) shows the largest positive change in sensitivity. Consistent with the results in the previous section on water balance terms, it can be seen that changes in sensitivity are quite consistent among the three different GCMs when it considers snow-related parameters, whereas more differences can be observed in parameters related to soil moisture and evapotranspiration processes.
Figure
Since the 605 basins employed in the previous section are not a
representative, balanced sample over climates and climate changes, the results
are split out over the three Knoben climate
indicators. Figure
Change in parameter sensitivity vs. historical climate indicators and change in climate indicators for 605 basins. The climate indicators are determined for all three GCMs. Displayed are aridity index (
From Fig.
In most cases, the patterns that can be identified relate to the projected change in climate. For instance, soil moisture/shallow layer parameter Depth2 (VIC) and percolation parameter Expt2 (VIC) demonstrate a more pronounced increase in regions with decreasing aridity index. Sometimes also the historical climate, combined with the projected change, can show organization. For example, the sensitivity of the evapotranspiration parameter PT in both SAC and HBV is particularly increasing in regions with a high historical aridity index, and the direction of change relates to the change in aridity index.
Given that no clear patterns were revealed based on the Knoben indicators, we
also explored patterns related directly to climate: the mean temperature and
mean precipitation and their projected changes. These results for mean
discharge as a target variable can be found in Fig.
With discharge timing as a target variable, we found overall similar sensitivity patterns (Figs.
In this section we explore to what extent the changes in parameter sensitivity that were observed in the previous sections propagate into the calibration procedure. To this end, we evaluate the top-5 most sensitive parameters and how this top-5 changes between the historical and future periods.
Impact of change in parameter sensitivity on top-5 position for the mean discharge, where top-5 refers to the five most sensitive parameters per basin – generally the parameters that are calibrated. The pie charts show which parameters leave the top-5 (left) and which parameters enter the top-5 (right). The right panels relate the number of changes in the parameter top-5 to climate and climate change indicators.
Figure
For HBV, snow parameters SCF and TR especially exit the top-5 in the future runs. The largest increase in top-5 notations for HBV is found for evapotranspiration parameter LP. Remarkably, snow parameter TR (threshold temperature where precipitation falls as rain) also appears as a parameter that enters the top-5: this parameter leaves the top-5 in many basins but also enters the top-5 in many other basins. In SAC, snow parameter PXTEMP loses the most top-5 notations. Lower-zone parameter LZTWM shows the strongest increase in top-5 notations. In VIC, mainly the snow parameter Snowrough decreases in top-5 notations. Deep layer parameters gain the most notations, especially DS.
The results of the pie charts in Fig.
The same results are displayed in Fig.
In conclusion, changes in parameter sensitivity as a consequence of climate
change can propagate into the calibration strategy. For the mean discharge,
one change in the parameter top-5 is common and can occur across all climates
and climate changes, whereas about 4
The evaluated changes in parameter sensitivity in response to climate change
can be perceived as a way to evaluate models diagnostically, especially since
we can compare the results for three different hydrological models. The
parameter sensitivity in the historical period (the top panels in
Fig.
There are a few points where all three hydrological models agree: all models
simulate a decrease in snow in the future across all basins and an increase in ET across most basins (Fig.
Indication of parameter sensitivity transmission.
However, many other changes in sensitivity for mean discharge can be observed
where the models disagree, for instance the role of percolation and soil
moisture/the shallow layer. To further explore how the models respond to
climate change in terms of parameter sensitivity, the transmission of
sensitivity is explored by means of the negative correlation between change in
sensitivity among two parameters. An example is Fig.
Figure
Whereas the models agree on the decline in snow water equivalent and decreased sensitivity of snow parameters despite employing different snow formulations, the models disagree on changes related to many other processes. Since the three models differ in many aspects in their model structure, the difference in response to changing forcing cannot directly be related to specifics of the model structure. The results, however, do show that the internal functionings of the models differ when used for long-term simulations, and this might impact the results and subsequently the conclusions of the model study.
A first evaluation of the different states and fluxes that are simulated by the hydrological models for the future period demonstrates that the three models agree that in general, snow water equivalent will decrease under RCP 8.5 using three different GCMs. This same signal is propagated into the sensitivity of the parameters related to this process: in all three models, the sensitivity of snow parameters tends to decrease for the mean discharge. All models also agree on the tendency that evapotranspiration will increase in the future, although this varies across GCM forcing. Also, this signal is reflected in the sensitivity of evapotranspiration parameters for mean discharge: their sensitivity tends to increase (although the models disagree on the magnitude of change). These results imply that the impact of snow on mean discharge will decrease, while the impact of evapotranspiration on mean discharge will increase. The results for discharge timing are much more variable across the models.
For other states and fluxes simulated by the models, such as soil moisture and
percolation, the models agree less on the change in sensitivity when using
mean discharge as a target variable (Fig.
We evaluated change in sensitivity against three climate indicators: aridity index, seasonality, and fraction precipitation falling as snow. We were not
able to identify a clear, robust relation between climate indicator, change in
climate indicator, and change in parameter sensitivity. In our approach, we
investigated whether any temporal relations exist. Another way to evaluate change in sensitivity would be to evaluate spatial relations.
We investigated how parameter sensitivity changes as a consequence of climate
change. We also explored the use of sensitivity analysis to provide the most
relevant parameters (factor prioritization) for an effective model calibration
The implication of our result is that the more the parameter sensitivity changes, the more parameter identifiability decreases for long-term
projections. Accordingly, we can expect that in particular the parameters that
will enter the top-5 in the future are probably not well identified in the
historical period. Therefore, we provide suggestions to account for changing
sensitivities in the calibration strategy of hydrological models for long-term
projections. A first strategy, related to methods that have been suggested for
changing parameters over time
In the previous sub-section we provide suggestions to further validate the
calibration procedure of models employed for long-term projections. It seems a
valid question, however, whether our models are fit for this purpose at
all. The results of the sensitivity analysis indicate a change in relevant
processes in the future which is captured differently among the three
investigated models. This emphasizes the need to improve model structure for
long-term projections, as suggested by
Assuming that a sensitivity analysis conducted over 23 years of daily data is
robust and thus that the observed changes in sensitivity can be attributed to
a changing climate rather than to noise, our results demonstrate that
parameter sensitivity is nonstationary
A decrease in sensitivity of snow parameters and an increase in the sensitivity of evapotranspiration parameters in a warming climate (considering enough moisture being available) could be expected based on expert judgement, and at least the three models agree on those signals despite employing different formulations to compute these processes. However, the models disagree on the other processes that will become more or less relevant in the future, while changes in these processes are not straightforward to estimate based on expert judgement. It is, for instance, not easy to judge whether the relatively higher amount of rain in the future (due to a decrease in snow) goes on average more to higher evaporation or to higher infiltration. As such, we have to acknowledge that the models differ in the processes they use to simulate future changes and that we cannot easily differentiate the right from the wrong models. This calls for a more process-based evaluation of historical changes to evaluate their plausibility for future changes to guide model selection.
In this study we investigated whether hydrological model parameter sensitivity changes within a plausible climate change rate. This is relevant for parameter prioritization in the calibration procedure for long-term projections and can be insightful for model diagnostic evaluation to investigate how the models simulate systemic changes as a consequence of climate change.
The sensitivity of the parameters in the three investigated hydrological models changes within a plausible changing climate. The three models agree that especially the snow parameters decline in sensitivity, while evapotranspiration parameters show a tendency to increase (dependent on the employed GCM). Which other parameters increase in sensitivity is, however, less consistent among the models: sometimes mainly ET and soil moisture/shallow layer parameters, sometimes mainly percolation and/or deep layer parameters. These differences occur due to differences in the three hydrological model structures. We did not identify a clear pattern that relates climate and climate change to changes in parameter sensitivity.
The change in parameter sensitivity propagates into the calibration
strategy. Typically, a global sensitivity analysis is conducted to determine
the most sensitive parameters, and based on that, the top-5 most sensitive
parameters are selected for calibration. Dependent on the model, 45
Some parameters become sensitive in the future but are currently not sensitive. Therefore, their value cannot be obtained through calibration based on current data. One way to account for changes in sensitivity is to identify a historical period that mimics the future projected sensitivity. Another approach is to sample the parameter that becomes sensitive in the future to account for predictive uncertainty as a consequence of the uncertainty in this parameter value. A third approach is to invert the value of this parameter based on observations specifically related to the process that the parameter is related to.
Besides implications for the calibration strategy when using models for long-term projections, our results also have implications for model selection for this purpose. The results demonstrate that the three employed models consider different processes to be more or less relevant in the future: they simulate different systemic changes. Whereas the models agree on systemic changes that can be excepted based on expert judgement (decreased relevance of snow and increased relevance of evapotranspiration in a warming climate), the models disagree on other processes that are more difficult to judge. These results not only stress the need, but also the challenge in carefully assessing model structure adequacy when applying models for long-term projections.
Selected parameters, their classification, and their boundaries for the HBV model. The parameters and their boundaries are based on
Selected parameters and their boundaries for the SAC model. The parameter boundaries are based on
Selected parameters and their boundaries for the VIC model based on
Change vs. historical values in mean temperature and mean precipitation over 605 basins, with change in parameter sensitivity indicated using mean discharge as the target variable. All three climate scenarios are shown together in each subplot. Parameter sensitivity for the historical period is expressed as dot size. Change in parameter sensitivity in colour. Red colours indicate an increase in sensitivity, blue a decrease.
The distribution of change in parameter sensitivity (
Change in parameter sensitivity vs. historical climate indicators and change in climate indicators for 605 basins using discharge timing as the target variable. All three climate scenarios are shown in the plots. The climate indicators are aridity index (
Change vs. historical values in mean temperature and mean precipitation over 605 basins, with change in parameter sensitivity indicated using discharge timing as the target variable. All three climate scenarios are shown together in each subplot. Parameter sensitivity for the historical period is expressed as dot size. Change in parameter sensitivity in colour. Red colours indicate an increase in sensitivity, blue a decrease.
Impact of change in parameter sensitivity to top-5 position for the discharge timing, where top-5 refers to the five most sensitive parameters per basin – generally the parameters that are calibrated. The pie charts show which parameters leave the top-5 (left) and which parameters enter the top-5 (right). The right panels relate the number of changes in the parameter top-5 to climate and climate change indicators.
Indication of parameter sensitivity transmission for the discharge timing – the day of the year that half of the discharge has passed. The chord (circle) diagrams display transmission of sensitivity, indicated with a band from the parameter that decreases in sensitivity to the parameter that increases in sensitivity. The width of the band indicates the strength of the negative correlation. The white number indicates the strength of the correlation. In all three chord diagrams, the lower part shows the parameters that decrease in sensitivity and the upper part the parameters that increase in sensitivity, with the white number indicating the strength of the correlation (for clarity, lower negative correlations are not displayed). Colours are according to the process they represent (with different shades of blue used for snow parameters for clarity). The chord diagrams are focused around the most relevant parameters based on Fig.
The model output will be made available on the 4TU website.
LM and BG designed the study together. LM conducted the calculations and wrote the first draft of the paper. LM and BG processed the data together and finalized the manuscript together.
There are no competing interests.
The authors would like to thank three anonymous reviewers for their constructive feedback and Thorsten Wagener for his suggestions.
Björn Guse is grateful for financial support from the German Research Foundation (“Deutsche Forschungsgemeinschaft”, DFG) via the FOR 2416 “Space-Time Dynamics of Extreme Floods (SPATE)” research group.
This paper was edited by Xing Yuan and reviewed by three anonymous referees.