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 km2 with 135 watersheds ranging from 0.1 to 123 km2. The local climate is Mediterranean, with an average annual precipitation of roughly 600 mm (Feng et al., 2019). Most of the annual precipitation occurs in fall/winter with 85 % of rainfall occurring in the November–March period. Thus, it is characterized by the intense and flashy floods in winter time. More than 80 % of annual discharge occurs in only a low number of large events during January–March, and a large fraction of annual discharge happens within 1 d (Beighley et al., 2003). River channels are typically filled with sediment during the dry season (April–October) and are scoured with the initiation of wet season floods (Scott and Williams, 1978; Keller and Capelli, 1992). River flow is the major source of sediment exported to the coastal sandy beaches in SBC. Therefore, the timing of seasonality, path of runoff, and magnitudes of flood events are critical to both local community and coastal ecosystems.

Daily precipitation and temperature with a spatial resolution of 0.0625∘×0.0625∘ (roughly 6 by 6 km) (Livneh et al., 2015), and daily streamflow from four USGS gauges for the period 1984–2013 were used to calibrate and validate the hydrologic models. The Global Soil Dataset for use in Earth system models (GSDE) was used to estimate saturated hydraulic conductivity and saturated moisture content. The 16 d composite albedo product (MCD43C3) with a spatial resolution of 0.05∘×0.05∘ and the monthly aerosol optical depth product (MOD08M3) with a spatial resolution of 1.0∘×1.0∘, both derived from NASA's Moderate Resolution Imaging Spectroradiometer (MODIS), were used to determine net radiation for evapotranspiration (PET) estimation. The aerosol optical depth product was downscaled to 0.05∘×0.05∘ (Raoufi and Beighley, 2017).

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).

The uncertainty was quantified by running each of the 30 hydrologic model-parameter sets (i.e., 3 hydrologic models and 10 parameter sets, 3×10=30) with each of the 20 forcing sets (i.e., 10 GCMs and 2 emission scenarios, 10×2=20) for a total of 600 simulations. Here, we used GCM outputs as the forcings of hydrologic models for both historical (1986–2005) and future (2081–2100) periods. For each simulation scenario (i.e., the combination of hydrologic model, parameter set, GCM, and RCP), the historical and future daily streamflow and runoff were simulated and the relative changes (%) were quantified. Note that there is no RCP for the historical period, and we used the same historical simulation for RCP 4.5 and 8.5. To evaluate the uncertainty sources and their relative significance in these simulated changes in runoff, discharge, and seasonality for the future period, the analysis of variance (ANOVA) (Vetter et al., 2015; Addor et al., 2014; Hattermann et al., 2018; Chegwidden et al., 2019) was used. The contribution of each uncertainty source for a variable of interest (e.g., monthly runoff, 100-year flood discharge, or the duration of the wet season) was defined as the fraction of its variance to the total variance. The total variance was quantified as the total sum of squares (SStotal) of differences between the simulations and the mean of all simulations (Eq. 2): 2SSTotal=∑i=1NHyd∑j=1Npara∑k=1NGCM∑l=1NRCP(qijkl-qoooo)2, where qijkl is the simulated value of the variable of interest by the ith hydrologic model with the jth parameter set, forced by the kth GCM projection under the lth RCP scenario; qoooo is the overall average of the simulated variable. Next, the SSTotal can be divided into 15 parts representing the four main effects (or first-order effects) and six second-order, four third-order, and one fourth-order interaction effects. For clarity, the third and fourth orders of interaction effects were combined and represented as SS3.4 in Eq. (3). 3SSTotal=SSHyd+SSpara+SSGCM+SSRCP+SSHyd.para+SSHyd.GCM+SSHyd.RCP+SSpara.GCM+SSpara.RCP+SSGCM.RCP+SS3.4, where SSHyd, SSpara, SSGCM, and SSRCP are the main effects (i.e., uncertainties or variance) from hydrologic models, hydrologic model parameters, GCMs and RCPs, respectively; SSHyd.para, SSHyd.GCM,SSHyd.RCP, SSpara.GCM, SSpara.RCP, and SSGCM.RCP are uncertainties from interactions between the hydrologic models and parameterization, hydrologic models and GCMs, hydrologic models and RCPs, parameterization and GCMs, parametrization and RCPs, and GCMs and RCPs, respectively. The calculation of each order is illustrated in Eqs. (S21)–(S23).

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 NHyd, Npara, NGCM, and NRCP in Eqs. (2) and (S21)–(S22) are all equal to 2. This generated C32×C102×C102×C22=6075 subsamples. For each subsample, the fractional sum of squares was calculated for each effect using Eqs. (S21)–(S23), and then the average of variance fractions of each source is used as the uncertainty contribution from that source using Eq. (S24).

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 (3×10×10=300) were evaluated. Here the models' performance in representing annual mean discharge (Qm) and annual maximum daily discharge (Qp) is evaluated. Here, the annual mean discharge was defined as the average of daily streamflow in a year. In this study region, there is typically no rain for most times of a year, and it is not uncommon in such a Mediterranean climate region that the annual runoff is mainly generated from one major storm event. Therefore, the annual mean/max series are representative of the characteristics of the discharge dynamics. The details of this procedure can be found in the Supplement. After the weights of model ensemble were obtained using the BMA method, the statistics of posterior probability distribution (here it was assumed to be normal distribution) of estimated changes in Qm, Qp, and Q100 in the future (2081–2100) relative to the historical period 1986–2005 were calculated using Eqs. (S29)–(S34).

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.

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 Ws for VIC-HRR), which initiates the quadratic relationship between soil moisture and subsurface runoff in VIC-HRR. This quadratic response to soil moisture conditions can lead to much higher subsurface runoff (1–2 orders of magnitude higher than that of RCM-HRR), which contributes to the lower performance in reproducing the total volume of discharge. This also explains that VIC-HRR generates the highest subsurface runoff during the wet season (Fig. 4). In addition, VIC-HRR also generates the most surface runoff during the wet season (Fig. 4). This is because when soil is almost saturated, surface runoff in VIC-HRR is almost a linear function of precipitation with a coefficient of 1 (much larger than RCM-HRR, which is 0.2 (C2), and STP-HRR, which is around 0.5 depending on the watershed topography). The higher surface and subsurface runoff generated by VIC-HRR lead to the overestimation of mean annual flow (Fig. 3d). However, there are no in situ measurements of surface and subsurface runoff fluxes, and it is difficult to evaluate model performance for these quantities. In Fig. 4, the simulated surface and subsurface runoff from National Land Data Assimilation Systems VIC model (NLDAS-VIC) (Xia et al., 2012) outputs are shown for the purpose of comparison. The NLDAS-VIC runoff simulations are from the same runoff generation model (i.e., VIC) as used in this work and have similar spatial/temporal resolutions to those in this study, which makes it a suitable reference for comparison. A similar pattern, i.e., a very high subsurface runoff, even higher than surface runoff, during the wet season, can be found from NLDAS-VIC simulations. The surface runoff of NLDAS-VIC is lower than those generated by the models in this study, which is probably because of the difference in precipitation inputs. The NLDAS precipitation input is lower during the wet season than that used in this study for the study region. In addition, the difference in spatial resolutions of precipitation (0.125∘ for NLDAS vs. 0.0625∘ for this study) can also contribute to the difference in simulated runoff.

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 (C1 and C2) based on the soil moisture conditions.

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 C1, Ks_all in RCM-HRR and Ks_all, Ds in VIC-HRR, suggesting that most parameters are important factors controlling model performance. For the randomly selected parameters (green circles in Fig. 5), most of them spread over the whole range, suggesting sufficient space for uncertainty analysis.

The projected changes in monthly runoff (surface, subsurface, and total) during 2081–2100 compared to the 1986–2005 range between -100 % and 300 % (Fig. 6a). The median changes indicate that surface runoff will probably increase in February and March and decrease in other months (Fig. 6a). This is because in the future, the onset of the wet season will be delayed and more severe storm events will occur during the shorter wet season (mainly during February and March) (Feng et al., 2019). The decrease in subsurface runoff in all months is probably because of the decrease in the frequency (or total number) of storm events (Feng et al., 2019). The changes in monthly total runoff show a similar pattern to the surface runoff, suggesting the more pronounced changes in surface runoff as compared to subsurface runoff. The major uncertainty sources are GCM and RCP, which account for ∼45 % of the total uncertainty (Fig. 6b). Hydrologic models contribute ∼10 % of the total uncertainty (Fig. 6b). This suggests that the climate patterns (e.g., storm event frequency and intensity) are more important factors controlling the runoff generation than the hydrologic model algorithms.

For the 28 major watersheds in SBC, the projected changes in Qm during 2081–2100 as compared to the historical period 1986–2005 range from -100 % to 220 % (Fig. S4). The median changes for each of these major watersheds are slightly above 0 %, varying between 1 % and 8 %. The major uncertainty sources are GCM and RCP, which account for ∼54 % of the total uncertainty. Among the first-order factors (i.e., GCM, RCP, hydrologic model, and parameterization), hydrologic model ranks third after GCM and RCP, accounting for 10 %–15 % of total uncertainty. In contrast, parameterization only induces less than 2 % of the total uncertainty. The remaining 25 %–35 % uncertainty is from the second-, third-, and fourth-order interactions between the four major sources. The projected relative changes in Qp and Q100 are similar in magnitude, both varying from -90 % to 250 % (Figs. S5 and 7). The median changes in Qp and Q100 for each watershed are higher than those of Qm, ranging between 10 % and 40 %. For most of the watersheds, GCM and RCP are the two major uncertainty contributors for Qp and Q100, accounting for ∼45 % of total uncertainties. The hydrologic model contributes ∼14 % of total uncertainties in Qp and Q100. Compared to Qm, Qp and Q100 get more uncertainty from the hydrologic models, which is likely due to highly nonlinear rainfall–runoff behavior and larger differences between runoff generation methods in generating peak flows as compared to average flow conditions.

Changes in Qm, Qp, and Q100 are higher under RCP 8.5, but the uncertainties are also higher (Fig. 8), which suggests the higher contribution of RCP 8.5 in the uncertainties of higher-order interactions between RCP and other factors (i.e., GCM, hydrologic model, and parameters). In Mission Creek watershed (USGS gauge no. 11119750), the probability of increase in Qm under RCP 4.5 is only 51 %. However, this probability increases to 64 % under RCP 8.5. For the less frequent events (Qp and Q100), the probabilities of positive changes are higher: 78 % and 85 % for Qp and Q100, respectively, under RCP 8.5. This implies that if RCP 8.5 happens in the future, the extreme events will probably get intensified.

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 ∼6 d. The major uncertainty sources for both onset and duration of the wet season are GCM (∼20 %) and hydrologic models (∼15 %). Different from discharge and runoff, the seasonality shows more uncertainty from hydrological models (15 % vs. 12 %) and model parameters (∼6 % vs. 2 %) (Fig. 9b). This is because the seasonality integrates the runoff generation, paths, and transport processes for both surface and subsurface runoff, which are important for the timing and quantity of simulated discharge.

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.