Assessing impacts of climate change on hydrologic systems
is critical for developing adaptation and mitigation strategies for water
resource management, risk control, and ecosystem conservation practices. Such
assessments are commonly accomplished using outputs from a hydrologic model
forced with future precipitation and temperature projections. The algorithms
used for the hydrologic model components (e.g., runoff generation) can
introduce significant uncertainties into the simulated hydrologic variables.
Here, a modeling framework was developed that integrates multiple runoff
generation algorithms with a routing model and associated parameter
optimizations. This framework is able to identify uncertainties from both
hydrologic model components and climate forcings as well as associated
parameterization. Three fundamentally different runoff generation
approaches, runoff coefficient method (RCM, conceptual), variable
infiltration capacity (VIC, physically based, infiltration excess), and
simple-TOPMODEL (STP, physically based, saturation excess), were coupled
with the Hillslope River Routing model to simulate surface/subsurface runoff
and streamflow. A case study conducted in Santa Barbara County, California,
reveals increased surface runoff in February and March but decreased
runoff in other months, a delayed (3 d, median) and shortened (6 d,
median) wet season, and increased daily discharge especially for the
extremes (e.g., 100-year flood discharge,
Streamflow is essential to humans and ecosystems, supporting human life and
economic activities, providing habitat for aquatic creatures, and exporting
sediment/nutrients to coastal ecosystems (Feng et al., 2016; Barnett et
al., 2005; Milly et al., 2005). Understanding streamflow characteristics is
important for water-resource management, civil infrastructure design and
making adaptation strategies for economic and ecological practices
(Feng et al., 2019). With economic development and population growth,
the emission of greenhouse gas is likely to increase during the 21st
century (IPCC, 2014). The increase in global surface temperature is
projected to exceed 2
The integration of climate projections and hydrologic models enables the investigation of hydrologic dynamics under the future climate conditions. However, the simulated hydrologic fluxes contain uncertainties from various sources. Due to the epistemic limitations (e.g., humans' lack of knowledge about hydrologic processes and boundary conditions) and the complexities in nature (e.g., temporal and spatial heterogeneity), hydrologic models are simplified representations of natural hydrologic processes (Beven and Cloke, 2012). Generally, hydrologic models have modules simulating water partitioning at land surface (named runoff generation process in this study), evapotranspiration (ET), and water transportation along terrestrial hillslopes and channels (named the routing process here). Each process can be represented in different ways, which thus results in uncertainties in simulated variables. For the runoff generation process, surface runoff is mainly represented as infiltration excess overland flow (or Hortonian flow, Horton, 1933) or saturation excess overland flow. Infiltration excess overland flow occurs when water falls on the soil surface at a rate higher than that which the soil can absorb. Saturation excess overland flow occurs when precipitation falls on completely saturated soils. Surface runoff can also be quantified conceptually; for example, a runoff coefficient can be used to generate surface runoff as a proportion of precipitation rate. Subsurface runoff is generally represented as functions of soil characteristics and topographic features. The complexity of these functions varies significantly, from simple linear to combinations of multiple nonlinear. Parameterization can be another uncertainty source. Due to the nonlinearity of hydrologic processes, different combinations of model parameters can achieve similar, if not identical, model performance. Model parameter selections based on calibration metrics can result in different optimal parameter values (i.e., parameter equifinality). When it comes to hydrologic impact assessments, the climate forcings, which differ among general circulation models (GCMs) due to the model discrepancy and the uncertainty of future emission scenarios, also contribute to the uncertainties in hydrologic simulations. Without appropriate assessment of these uncertainties, standalone studies on the climate change impacts can be difficult to interpret. Systematic assessments of the relevant uncertainties associated with simulated hydrologic fluxes are needed.
Some studies have been performed to investigate uncertainties mentioned above at both variable scales (for example, Wilby and Harris, 2006; Vetter et al., 2015; Valentina et al., 2017; Kay et al., 2009; Eisner et al., 2017; Su et al., 2017; Schewe et al., 2014; Hagemann et al., 2013; Asadieh and Krakauer, 2017; Chegwidden et al., 2019; Hattermann et al., 2018; Addor et al., 2014; Vidal et al., 2016; Giuntoli et al., 2018; Alder and Hostetler, 2019). Most previous studies treated hydrologic models as a whole package. However, hydrologic models consist of multiple components (e.g., runoff generation, ET, and routing). These components can be significantly different among models. When considering the hydrologic model as a whole, it is difficult to quantify relative uncertainty contributions from different components. Troin et al. (2018) tested the uncertainties from hydrologic model components for snow and potential ET. In this study, a consistent hydrologic modeling framework that integrates multiple runoff generation process models with surface, subsurface, and channel routing processes and associated parameter uncertainties was developed. This framework enables uncertainties from different components representing hydrologic processes and associated model parameters as well as model forcings (e.g., precipitation and temperature) to be quantified and compared in a consistent manner. In this framework, three runoff generation process models which represent three fundamentally different approaches mentioned above were used. The conceptual frameworks were adapted from the Variable Infiltration Capacity model (Wood et al., 1992; Liang et al., 1996) (infiltration excess), simple-TOPMODEL (Niu et al., 2005; Beven et al., 1995; Beven, 2000) (saturation excess), and the runoff coefficient method (Feng et al., 2019) (conceptual). Each approach was coupled within one routing model (i.e., Hillslope River Routing model, HRR (Beighley et al., 2009)) to simulate the terrestrial hydrological processes. This modeling framework was also integrated with a Bayesian model averaging (BMA) analysis to assess the performance of different model–forcing–parameter combinations and to provide actionable information (e.g., probability of estimated changes) for associated practices, such as water resource management and ecology conservation.
A case study was presented for Santa Barbara County (SBC), CA, a biodiverse region under a Mediterranean climate with a mix of highly developed and natural watersheds. Previous studies (e.g., Feng et al., 2019) showed that the intensified storm events concentrated in a shorter and delayed wet season in SBC under future climate conditions will cause significant increase in discharge, especially the extremes (e.g., 100-year discharge). The climate change impacts on the path and quantity of surface/subsurface runoff and discharge will impact the soil erosion and sediment/nutrient transport and subsequently affect the coastal ecosystems (Myers et al., 2019; Feng et al., 2019). The longer dry season may also contribute to the increased occurrence of droughts and wildfires (Myers et al., 2019). Therefore, changes in these hydrologic variables (e.g., runoff, discharge, and seasonality) under future climate conditions and associated uncertainties are essential to assess the vulnerability of coastal regions in CA and make adaptation strategies to accommodate climate change. In this study, we simulated future hydrologic variables using three hydrologic models forced with climate outputs from 10 GCMs that were selected for their good performance in representing historical meteorological characteristics in the study region, under two emission scenarios (RCP 4.5 and RCP 8.5) (Feng et al., 2019). The main objectives of this study were to (1) evaluate and compare the performance of hydrologic models with different approaches representing runoff generation process using a consistent modeling framework; (2) quantify the relative contributions of different sources (including hydrologic process models, parameterizations, GCM forcings, and emission scenarios) to the total uncertainty in simulated surface/subsurface runoff, streamflow, and seasonality; and (3) provide actionable information and suggestions for studies and practices associated with hydrologic impacts of climate change.
The study region is located in coastal Santa Barbara County (SBC),
California, where watersheds drain into the Santa Barbara Channel from just
west of the Ventura River to just east of Point Conception (Fig. 1). The
combined land area is roughly 750 km
Study region with USGS streamflow gauges. The inset figure indicates the location of SBC in the state of California (CA).
Daily precipitation and temperature with a spatial resolution of
For the historical (1986–2005) and future climate simulations (2081–2100), downscaled precipitation and temperature from 10 climate models (please refer to Pierce et al., 2014, and Pierce et al. ,2015, for model details) in the Coupled Model Inter-Comparison Project, Phase 5, (CMIP5) (Taylor et al., 2012) for two emission scenarios, RCP 4.5 and RCP 8.5 (Moss et al., 2010), were used. These 10 GCMs were selected because they have the best performance in representing historical climate dynamics at southwest U.S. and California state scales (Pierce et al., 2018).
This modeling framework was developed on the basis of the Hillslope River
Routing model (HRR) (Beighley et al., 2009). The
watersheds were delineated using the digital elevation model (DEM) data with
a resolution of 3
The water movement between soil layers in the soil matrix was similar to
that in the modified VIC-2L model (Liang et al., 1996). The soil
was divided into two layers: upper layer (0.6 m) and lower layer (1.2 m). The
soil thickness data were from the Soil Survey Geographic (SSURGO) Data Base
for Santa Barbara County (NRCS, 1995). After the surface runoff was
determined, the infiltrated water was added to the upper soil layer, and the
soil moisture was updated. If the upper soil was oversaturated, the excess
water was returned to the surface. The evapotranspiration was estimated using
Eq. (S15) in the Supplement. The interaction between the upper and lower soil layers was simulated
using the Clapper–Hornberger equation (Eqs. S16–S17). Subsurface runoff was
generated from the bottom of the lower soil layer. After the water fluxes
(runoff, ET, and water movement between soil layers) were determined, the
soil moisture was updated, which would be used for the water balance
calculation in the next time step. After water excess for surface and
subsurface runoff was quantified, the kinematic wave approach was applied to
simulate the transport of runoff from the planes (surface and subsurface),
and the Muskingum–Cunge method was used for channel routing following the
conservation equations (Eqs. S18–S20) (Beighley et al.,
2009). Two conceptual parameters,
The conceptual framework of the hydrologic models used in this
study. Portions of this figure were adapted from the work of Beighley et al. (2009).
After the models were set up, a state-of-the-art optimization algorithm, the Borg
Multiobjective Evolutionary Algorithm (Borg MOEA) (Hadka and Reed, 2013),
was adopted to optimize the model parameters (Table 1). The models were spun up
for 1 year to ensure the equilibrium status. For each model, there were four
parameters calibrated for runoff generation processes and two parameters
calibrated for routing processes.
Calibrated parameters for hydrologic models.
To quantify the uncertainties from model parameters, we selected 10 parameter sets using the following criteria: (1) select 4 parameter sets with the highest NSE based on the calibration results; (2) rank the remaining parameter sets based on their performance (i.e., NSE) and randomly select 6 sets from the top 20 % candidates. This parameter selection process enabled us to take both parameter dominance and variability into account while maintaining the high model performance, which is important for the uncertainty analysis. These 10 parameter sets were then used for uncertainty analysis.
The uncertainty was quantified by running each of the 30 hydrologic
model-parameter sets (i.e., 3 hydrologic models and 10 parameter sets,
To avoid bias from the difference in sample sizes of uncertainty sources
(i.e., 3 hydrologic models, 3 parameter sets, 10 GCMs and 2 RCPs), a
subsampling step was performed by following Vetter et al. (2015). In the
subsampling step, 2 samples (i.e., the minimum number of uncertainty sources,
here RCPs) from each source were randomly selected, that is, 2
hydrologic models, 2 parameter sets, 2 GCMs, and 2 RCPs, which indicates that
In addition to quantifying uncertainties and associated contributions from
different sources, an evaluation of the probability of uncertain changes in
discharge can be useful to provide actionable information for the
stakeholders such as water-resource managers. In this study, Bayesian
model averaging (BMA) (Duan et al., 2007) was used to evaluate
the model performance in reproducing historical hydrologic conditions, and
then weights were assigned to each of them based on their performance. A
model with better performance was assigned a higher weight, assuming it has
a higher probability of representing the truth. Note that there is no RCP for
the historical period, so only combinations of hydrologic models, parameter sets
and GCMs (
To quantify the onset and duration of hydrologic seasons, we calculated the accumulative discharge in the whole basin for each water year. Then the day showing the 10 % of accumulative annual discharge was defined as the onset of the wet season, and the number of days between 10 % and 90 % of the accumulated discharge series was defined as the duration of the wet season.
The three hydrologic models performed well in representing streamflow dynamics in the study region. The NSE varies within 0.56–0.67 and 0.53–0.62 for the calibration and validation periods, respectively, in Mission Creek (USGS gauge no. 11119750) (Fig. 3). At other calibrated watersheds, the models perform similarly well, with NSE varying between 0.45 and 0.60 for the calibration period and between 0.42 and 0.62 for the validation period (Figs. S1–S3 in the Supplement). Simulated streamflow from the three models matches the in situ measurements in both magnitudes and timing of hydrographs at event scales (Fig. 3b). At annual scale, simulated annual peak flows are comparable to the observations in most years. However, in some years with extreme events, for example in January 1995, February 1998, and January 2005 (highlighted in Fig. 3c), the simulated peaks are much lower than the gauge records. This disparity can be attributed to the input bias (e.g., precipitation or streamflow measurements). This was identified using an “extreme scenario” simulation, which assumed 100 % precipitation is transformed to surface runoff (i.e., without any loss due to, for example, infiltration or evapotranspiration) and transported immediately to river channels and represents the maximum streamflow considering groundwater is minimal in the study region (Beighley et al., 2003). Even in this extreme scenario, the simulated peaks were still lower (events highlighted in red in Fig. 3c) or slightly higher (event highlighted in blue in Fig. 3c) than the gauge observations. This is likely because model forcings are biased low for these events. One possible source of this bias can be the grid-based precipitation dataset which averages the precipitation rates over the grid masking spatial heterogeneity and thus reducing precipitation rates at some locations. The uncertainties in gauge measurements can also be a bias source. For example, in typical conditions the uncertainty in streamflow measurements ranges between 6 % and 19 % in small watersheds, but it can be higher during large storm events when accurate stage measurements are more difficult (Harmel et al., 2006). Beighley et al. (2003) also identified the overestimation of gauge records for the 1995 January event at gauge 11119940. As for mean annual discharge, all three models tend to overestimate it for the study period, mainly due to the overestimation of subsurface flow during dry seasons (Fig. 3d). This highlights challenges in simulating hydrologic processes in semiarid regions under a Mediterranean climate.
Model performance for calibration and validation periods:
Among the three hydrologic models, STP-HRR has the best overall performance
(i.e., highest average NSE), mainly due to its better ability to capture
flood peaks than the other two models (Figs. 3, S1–S3). The peak
performance is likely a result of the STP-HRR representing the runoff
generation process as an exponential relationship between soil moisture and
runoff rates, which makes runoff generation more sensitive to soil moisture
dynamics as compared to the other two models. This algorithm is well suited
to representing the significant nonlinearity of hydrologic response to rainfall
in the study region. RCM-HRR and VIC-HRR have similar overall performance
(i.e., similar average NSE); however, they represent hydrologic dynamics
differently. VIC-HRR tends to perform better in representing small peak
flows than RCM-HRR but worse in simulating mean flow (or total discharge
volume) (Figs. 3, S1–S3). This is because as the wet season proceeds, the
lower soil layer is close to saturation (i.e., relative soil moisture is
higher than the threshold
Simulated monthly surface and subsurface runoff for the Mission Creek watershed (USGS gauge no. 11119750) by three models for the calibration period (water year 1985–2005). Surface runoff is denoted by “SR” and subsurface runoff is denoted by “SS” in this figure. Monthly surface and subsurface runoff from National Land Data Assimilation Systems (NLDAS) VIC model simulation for the same period are shown here for comparison purposes.
These results may suggest that STP-HRR is more suitable than VIC-HRR in
representing hydrologic processes in Mediterranean regions, where 80 % of
annual precipitation is concentrated in a short period (roughly 3 months).
As the wet season proceeds, the soil is close to saturation conditions,
under which the saturation excess overland flow is dominant. That explains
why STP-HRR performs best in this study region. VIC-HRR is probably more
suitable to the regions where precipitation events are sparsely distributed
where soil is not easy to get saturated. Although RCM is an empirical
method, it performs fairly well in this study, mainly because it captures
the nonlinearity of hydrologic processes through a switch between dry and
wet surface runoff coefficients (
Ten sets of parameters were selected for each model (Fig. 5). Most optimal
parameter sets (red circles in Fig. 5) are very close, except for
Parameters (black circles) sampled during the calibration process and
their corresponding performance (assessed by NSE). The red circles indicate
the four parameter sets with the highest NSE values, and the green circles indicate
six randomly selected parameter sets from the top 20 % samples (ranked by
NSE). These 10 parameter sets were used for uncertainty analysis. In this
figure, the parameter values are normalized by their ranges (shown in Table 1), so the range of the
The projected changes in monthly runoff (surface, subsurface, and total)
during 2081–2100 compared to the 1986–2005 range between
For the 28 major watersheds in SBC, the projected changes in
Changes in
Probability of changes in
Consistent with the work of Feng et al. (2019), this study suggests a
delayed onset and shorter duration of the wet season (Fig. 9a). The median
changes show that the wet season will start later by 3 d and become
shorter by
As the major carrier of nutrients/sediment, surface runoff and discharge are crucial for beach ecosystems in the study region (Myers et al., 2019; Aguilera and Melack, 2018). Nutrients and sediment build up over land surface and in channels during the dry season and get flushed with the initiation of the wet season (Scott and Williams, 1978; Keller and Capelli, 1992; Bende-Michl et al., 2013; Aguilera and Melack, 2018). The nutrients/sediment fluxes are positively correlated with hydrologic variability, and the majority of them occurs at the beginning of the wet season (Aguilera and Melack, 2018; Homyak et al., 2014). Therefore, both timing and magnitude of runoff and discharge will impact the nutrients/sediment export to the coastal ecosystems. The findings in this study reveal that the surface runoff and river discharge (especially the extremes) will increase but get delayed during the wet season (Figs. 6 and 9), implying that the nutrients/sediment fluxes will likely increase and occur in a shorter and delayed period. The decrease in runoff (both surface and subsurface) during the dry season suggests that the soil moisture will be lower under future climate conditions in the study region. The longer and drier dry season will probably increase the occurrence of severe droughts and wildfires.
Compared to previous studies (e.g., Vetter et al., 2015, Schewe et al., 2014; Hagemann et al., 2013; Troin et al., 2018; and Asadieh and Krakauer, 2017), this work identifies relatively low uncertainty contributions from hydrologic models. The main reason for this is probably that the hydrologic model uncertainty in this study was only from runoff generation algorithms and associated parameters. As is, the three hydrologic models share common algorithms for ET and plane/channel routing and the same model configuration (e.g., soil matrix and model unit definition). These similarities among models likely reduced the differences in simulated runoff and discharge. In addition, the uniform calibration approach and parameter selection criteria were also likely to eliminate user/method bias, which is common in studies that consider more than one hydrologic model. In contrast, the hydrologic models used in previous studies have their own model component algorithms (e.g., ET and routing algorithms) and model configurations. For example, the VIC model (here VIC refers to the original VIC model and is different from the model used in this study; to clarify, in the following text, VIC refers to the original VIC model, while VIC-HRR refers to the model used in this study) applies an ET algorithm different from the one used in this study (Raoufi and Beighley, 2017), uses the grid-based model units, ignoring the spatial arrangement, and has its own routing scheme which adopts the synthetic unit hydrograph concept. When comparing models owning their own component algorithms, the differences between models likely resulted in larger uncertainties in the simulation from hydrologic models in previous studies.
This study can also provide useful information for hydrologic model evaluation and selection. As discussed in Sect. 3.1, the STP-HRR model is more suitable than the other two models for the study region, mainly due to its ability to represent the highly nonlinear hydrological response to precipitation forcings. This implies hydrologic models adopting the saturation excess runoff generation algorithms may be more suitable for areas with a Mediterranean climate. The uncertainties from hydrologic models are larger than those from the hydrologic model parameters for all variables (i.e., discharge, runoff and seasonality), suggesting the inter-model variability is larger than the intra-model variability (from model parameters). This implies that model selection is more important than the parameter selection and that the parameter equifinality (or non-uniqueness) is less of a concern when quantifying climate change impacts on hydrologic fluxes using an ensemble of GCM forcings. In this study, only the runoff generation algorithm was investigated. Other hydrologic model components, such as ET algorithms and routing methods, also have variants. The choice of these components may also make a difference in the total uncertainties in simulated runoff and streamflow. In addition, the methods for GCM downscaling can also contribute to the uncertainty in predicted changes in hydrology. Further study integrating different algorithms for hydrologic model components as well as GCM downscaling methods can be conducted in the future. Such analysis can be useful to guide stakeholders to select appropriate hydrologic algorithms and to develop actionable adaptation and mitigation strategies to accommodate climate change.
This is the first study investigating hydrologic model uncertainty solely from runoff generation algorithms for a region with a Mediterranean climate. The framework developed in this study can be potentially used to identify the internal uncertainties of hydrologic models, i.e., uncertainties from hydrologic model components (e.g., runoff generation algorithms, ET algorithms, and routing models), which is particularly important for assessing model performance and quantifying the relative roles of different components in the uncertainty of simulations. This study region is a representative Mediterranean area characterized by dry summers and wet winters. This climate pattern and the highly nonlinear relationship between climate and hydrology significantly impact local society, agriculture, and ecosystems, as discussed before. The findings in this study, including the favorability of the STP algorithm, the important role of GCM selection, and the negligible role of hydrologic model parameters in the uncertainty, can be useful for studies associated with hydrologic model evaluation and climate change impact analysis for other Mediterranean regions.
A modeling framework which integrates multiple runoff generation algorithms
(VIC, STP, and RCM) with the HRR routing model was developed. Forced with an
ensemble of GCM outputs under different emission scenarios, this framework
is able to quantify the climate change impacts on surface and subsurface
runoff, streamflow, and hydrologic seasonality and evaluate the associated
uncertainties from different sources (i.e., RCPs, GCMs, hydrologic process
models and parameterization). The results show that the surface runoff will
likely increase in February and March while decrease in other months, and
the subsurface runoff will likely decrease due to changes in the patterns of
storm events. The median changes in mean annual discharge for the major
watersheds in SBC are 1 %–8 %, with an uncertainty of 320 % (here,
uncertainty refers to the range of predicted relative changes among models,
that is, from
Unique to the framework in this study, the uncertainties from different hydrologic model components (e.g., runoff generation process) and associated model parameterizations can be identified and quantified. The results can be useful for practices and studies in many fields, e.g., water resources, risk controls, and ecosystem conservation, for the study region as well as other Mediterranean regions.
The source code and dataset supporting this work are available on Github:
The supplement related to this article is available online at:
DF designed the experiments, developed the models, performed the simulations, and prepared the manuscript. EB conceptualized the project and reviewed and edited the manuscript.
The authors declare that they have no conflict of interest.
This research was supported by the Santa Barbara Area Coastal Ecosystem Vulnerability Assessment (SBA CEVA) with funding from the NOAA Climate Program Office Coastal and Ocean Climate Applications (COCA) and Sea Grant Community Climate Adaptation Initiative (CCAI) and the National Science Foundation's Long-Term Ecological Research (LTER) program (Santa Barbara Coastal LTER – OCE9982105, OCE-0620276 and OCE-123277). The authors thank David Hadka at Pennsylvania State University and Chinedum Eluwa at University of Massachusetts, Amherst, for their help with setting up the Borg MOEA. The authors acknowledge editor Hilary McMillan, Konstantinos Andreadis and two anonymous reviewers for their valuable comments that significantly improved the manuscript.
This research has been supported by the National Science Foundation (grant nos. OCE9982105, OCE-0620276, and OCE-123277).
This paper was edited by Hilary McMillan and reviewed by two anonymous referees.