Streamflow predictions play a key role in water and environmental management, especially in the water-stressed Western United States (WUS). In the short term, these predictions provide early warnings for impending flood events, thereby enabling timely preparation and response to mitigate immediate flood risk and damages (Raff et al., 2013; Maidment, 2017). In the longer term, streamflow predictions enable water utilities and agencies to plan water distribution within and across multiple uses – urban, agricultural, and industrial (Anghileri et al., 2016). Streamflow predictions also aid in understanding and foreseeing the impacts of climate change on water systems, thereby informing adaptive strategies for water resource management.

Streamflow predictions are derived via a synthesis of hydrometeorological data, statistical methodologies, and computational modeling. Direct measurement of runoff is an important element of this process; however it is only possible in river basins with well-developed observational infrastructure (Sharma and Machiwal, 2021). This limitation leaves vast areas, often critical to water resource management and climatology, without direct runoff observations on which to base streamflow predictions. As an alternative, land surface models (LSMs) can be used to simulate streamflow. LSMs typically are forced with air temperature, precipitation, and other surface meteorological variables. By integrating climatic, topographic, and land-use information, they can fill streamflow observation gaps and provide comprehensive, spatially distributed runoff predictions (Fisher and Koven, 2020). The capabilities of LSMs equip us with the necessary tools to produce streamflow predictions that can be used to prepare for severe weather conditions, form the basis for water resource management, and inform water management associated with our evolving climate.

One of the key challenges in hydrological modeling is the reliable representation of the spatiotemporal variability of natural processes (Dembélé et al., 2020). Enhanced spatial resolution and improved estimates of surface meteorological variables have empowered LSMs to predict diverse processes with greater detail. However, a recurrent issue is that the parameters embedded in LSMs often inadequately capture fine-scale variations in land surface processes, as illustrated in Figs. S7 and S8 in the Supplement. Accurate prediction of land surface processes, particularly over large areas, requires accurate parameter estimation, which remains a significant bottleneck. Errors in parameter estimates affect LSMs' ability to forecast runoff at continental or subcontinental scales. Fisher and Koven (2020) identify LSM parameter estimation as one of three grand challenges in land surface modeling.

To deal with this challenge, we describe methods and resulting high-resolution parameter datasets for two widely used LSMs across the WUS. We base our estimates on a strategy of minimizing metrics of differences in observed and model-predicted streamflow, following many previous studies (Arsenault and Brissette, 2014; Poissant et al., 2017; Razavi and Coulibaly, 2017; Gochis et al., 2019; Qi et al., 2021; Bass et al., 2023). We do so because streamflow observations are more readily available than other model prognostic variables like soil moisture or evapotranspiration (Demaria et al., 2007; Gao et al., 2019; Troy et al., 2008; Yadav et al., 2007), although the methods we use could be generalized to incorporate other observed and model-predicted fluxes and state variables. Although previous studies have mostly focused on a single hydrologic model (e.g., Mascaro et al., 2023; Sofokleous et al., 2023; Gou et al., 2020), here we utilize two models to address structural model uncertainty and to ensure broader applicability of the calibration methods we employ.

The variable infiltration capacity (VIC; Liang et al., 1994) model and the Noah LSM with multiparameterization options (Noah-MP; Niu et al.. 2011), which we use here, are widely used hydrologic models both in the United States and globally, as highlighted by Mendoza et al. (2015) and Tangdamrongsub (2023). Many previous implementations of VIC for the Western United States (WUS) have been based on the Livneh et al. (2013) dataset, and its predecessor, Maurer et al. (2002), which performed initial calibrations across the region. In the case of Noah-MP, Bass et al. (2023) performed manual calibration across the region. Neither of these implementations, however, employs globally optimized calibration, as we do here.

The process of calibration can be computationally demanding, and prior research typically has focused on obtaining parameters appropriate to facilitating model simulations that match observations as closely as possible at stream gauge locations (Duan et al., 1992; Tolson and Shoemaker, 2007). Most previous studies have concentrated on a limited number of gauges/river basins (e.g., Mascaro et al., 2023; Sofokleous et al., 2023; Gou et al., 2020). Here, we aim to establish parameterizations for VIC and Noah-MP across the entire WUS. In doing so, we apply global optimization methods at 263 river basins, followed by a second stage regionalization to the whole of WUS.

Specifically, the work we report here aims to develop calibration parameters for the VIC and Noah-MP models that can be implemented at the catchment (hydrologic unit code or HUC) 10 level across the region. We explore and elucidate (i) the choice of physical parameterizations and calibration of land surface parameters, (ii) extension of these calibrated parameters to areas without gauges, and (iii) factors that influence calibration efficiency and LSM performance using regional parameter estimates. Following this introduction, Sect.  describes our calibration basins, the hydrologic models used, and the forcing dataset. The framework of our procedures is illustrated in Fig. . Section  provides an in-depth exploration of the calibration process. In the case of Noah-MP, which offers multiple runoff generation (physics) options, our initial step involves choosing the most effective runoff parameterization option. Following this, we perform the calibration of land surface parameters. In the case of the VIC model, the runoff parameterization scheme is predetermined, so we commence immediately with calibration at 263 river basins across our region. Our second stage regionalization (Sect. ) extends the calibrated parameters to ungauged basins using the technique known as the donor-basin method, as implemented by Bass et al. (2023). In Sect. , we evaluate both flood and low flow simulation skills both pre- and post-calibration and following regionalization. Finally, following discussion and interpretation (Sect. 6), Sect. 7 presents conclusions, encapsulating the insights and implications of our study.

To distribute parameters from the calibration basins to the entire region, we used the donor-basin method as implemented in numerous previous studies (e.g., Arsenault and Brissette, 2014; Poissant et al., 2017; Razavi and Coulibaly, 2017; Gochis et al., 2019; Qi et al., 2021; Bass et al., 2023). Following the calibration process, we regionalized the parameters from gauged to ungauged basins based on a mathematical assessment of the spatial and physical proximity between the gauged and ungauged basins. We considered two primary methods for implementing the donor-basin approach. The first uses models calibrated to spatially continuous gridded runoff metrics (Beck et al., 2015; Yang et al., 2019). The second approach, which we ultimately adopted, calibrates models to individual gauges and then extends these parameters to ungauged basins, based either on a statistical or mathematical similarity measures (e.g., Arsenault and Brissette, 2014; Razavi and Coulibaly, 2017). Our preference for the second method was guided by a key limitation of the first approach; specifically it is limited to calibrating against runoff metrics, such as long-term mean flow and flow percentiles, rather than streamflow time series.

In the donor-basin method, an ungauged basin inherits its land surface parameters from the most similar gauged basin(s) (or the n most similar gauged basins). Here, we evaluated the similarity or proximity between gauged and ungauged basins based on the similarity index SI as defined and used by Burn and Boorman (1993) and Poissant et al. (2017): 1SI=∑i=1k|XiG-XiU|ΔXi.

In Eq. , k stands for the total number of features considered; XiG represents the ith feature of the gauged basin G; XiU is the ith feature of a specific ungauged basin; and ΔXi is the range of potential values for the ith feature, grounded in the data from the gauged basins. This yields a unique value of SI for each gauged basin, contingent on the specific ungauged basin it is compared with. Typically, gauged basins that exhibit greater resemblance to the ungauged basin will have a smaller SI.

We assessed the donor-basin method's efficacy using a cross-validation approach, where each gauged basin was treated as ungauged one at a time. The pseudo-ungauged basin inherits its hydrological parameters from its three most similar gauged basins, determined by SI. The parameters inherited are a weighted average from the three donor basins. After testing one to five donor basins, we found that using three donors yielded the best results. Thus, every basin inherits parameters from the three most similar gauged basins in each simulation, offering a concise evaluation of the donor-basin method's regionalization performance.

We used 18 basin-specific features in the donor-basin method, detailed in Table S1 in the Supplement, calculated based on the forcings and parameters used in the study. For feature selection in the donor-basin method, we adopted an iterative approach, explained in detail in the following paragraph. Only basins with a KGE exceeding 0.3 were considered, following previous studies suggesting that inclusion of poorly performing basins can lower regionalization performance. We found that a KGE threshold of 0.3 resulted in a median performance improvement of 0.08 larger than a KGE threshold of 0 did; hence it was chosen. After screening, 223 basins were utilized in VIC regionalization and 194 in Noah-MP regionalization. We note that the parameters used for calibration and the features used to determine the similarity index in the regionalization process are different. The physics that control the key hydrological processes of the two models are different, so we explored their best regionalization features separately.

To determine the most effective regionalization features from the 18 basin characteristics listed in Table S1, we employed a systematic iterative approach. The first iteration includes 18 simulations, each of which incorporates one of the 18 features. The feature that yielded the greatest increase in the median KGE across all basins, based on leave-one-out cross validation, was then retained. In the second iteration, we conducted 17 simulations, each combining the retained feature from the first iteration with one of the remaining 17 features. This process was repeated iteratively, reducing the number of features considered in each subsequent round, until the addition of new features no longer resulted in an appreciable increase in median KGE. The sequence of features shown in Fig.  (also shown in Table S1) indicated the importance of the features. This iterative approach ensured that each feature's individual and combined contribution to model performance was thoroughly assessed. It allowed us to identify a subset of features that, when used together, optimally improved model accuracy. We recognize the potential existence of inter-feature correlations that may exert a discernible influence on their collective efficacy when utilized in combination.

This procedure resulted in five features that generated the best regionalization performance for VIC (longitude centroid, latitude centroid, maximum elevation, fall mean precipitation, and fall mean temperature). Three features were found to be best for Noah-MP (latitude centroid, longitude centroid, and drainage area) (see Fig. ). Among them, latitude and longitude are the common features that contribute the most to regionalization when using the similarity index method. This suggests that geographical similarities are the most important factor in parameter information transfer from gauged to ungauged basins.

Upon evaluating the performance of baseline, calibrated, and regionalized simulations, the respective median daily KGEs for the VIC model were found to be 0.41, 0.71, and 0.49. For the Noah-MP, these values were 0.38, 0.60, and 0.49 (refer to Figs.  and S4). These metrics are for basins that have a calibrated KGE greater than 0.3 only, resulting in higher median KGEs than for all 263 basins (see Fig. ). The KGE distribution also improved overall. It is noteworthy that the regionalization improvement relative to baseline is higher for Noah-MP than for VIC. While VIC's baseline and calibrated KGE skill distributions outperform Noah-MP's, the differences between regionalized skills of Noah-MP and VIC are decreasing. We will explore more on this in the following section.

After optimizing the features and specific design of the donor-basin method, parameters were regionalized to 4816 ungauged USGS hydrologic unit code (HUC)-10 basins across the WUS. HUCs are delineated and quality-controlled by USGS using high-resolution DEMs. For each of the 4816 HUC-10 basins, we calculated a similarity index with the calibrated basins using the selected features. The three most similar basins were identified as donor basins, and their weighted average parameters were then adopted by the target HUC-10 basin. The final hydrologic parameters for both VIC and Noah-MP for all WUS HUC-10 basins are shown in Figs. S5 and S6. The baseline HUC-10 parameters are shown in Figs. S7 and S8.

Comparison of Figs. S5 and S6 to S7 and S8 makes it clear that the baseline model parameters lack accuracy and exhibit significant spatial uniformity where large geographical regions share identical parameter values. For example, parameters such as Ds and Soil_Depth1 in VIC show this uniformity. Furthermore, certain parameters, such as SLOPE and REFKDT in Noah-MP, remain invariant across all spatial domains and do not reflect real-world conditions. Regionalization improved the parameters, leading to increased accuracy and strengthening of region-specific characteristics.

Our primary calibration objective was to enhance the accuracy of daily streamflow simulations. However, to ensure the versatility of our parameter sets for research related to both floods and dry conditions, we also evaluated the models' capabilities in reproducing high and low streamflow. To understand the capabilities of the two models in reconstructing high and low streamflow, we assessed their performance across baseline, calibrated, and regionalized settings. a.

Evaluation of high flow performance.

We used the peaks-over-threshold (POT) method (Lang et al., 1999) to identify extreme streamflow events as in Su et al. (2023a) and Cao et al. (2019, 2020). We first applied the event independence criteria from USWRC (1982) to daily streamflow data to identify independent events. We set thresholds at each basin that resulted in three extreme events per year on average (denoted as POT3). After selecting the flood events over the study period based on the observation, we sorted the floods based on the return period and then calculated the KGE of baseline, calibrated, and regionalized floods. Figure S9 displays the associated CDF plots. The median KGE for baseline floods in Noah-MP was 0.14, which rose to 0.37 post-calibration and receded to 0.22 after regionalization. For VIC, the flood KGE started at 0.11, increased to 0.41 after calibration, and declined to 0.20 post-regionalization. As anticipated, these numbers are lower than (all) daily streamflow skill due to our calibration target being daily streamflow. Still, flood competencies experienced considerable enhancement, surpassing the Noah-MP KGE benchmark of -0.41 found by Knoben et al. (2019).

We summarize our key accomplishments in calibrating the two hydrological models, we examine our approach to choosing calibration objective functions and metrics, and we consider lessons learned in model regionalization.

a.

Improved parameter sets.

We generated calibrated parameter sets for the VIC and Noah-MP hydrological models at 1/16° latitude–longitude scale across WUS. These calibrated parameter sets are intended to facilitate the use of the two models for climate change and water investigations across the region, among other applications. Our focus on calibrating daily streamflow aligns with common practice in hydrology, providing a comprehensive representation of catchment hydrology dynamics which should enhance future understanding of hydrological phenomena and their spatial variations across the region.

Our intent was to develop a regional parameter estimation strategy for the VIC and Noah-MP land surface schemes and to apply it across the WUS region at the HUC-10 catchment scale. We have described what we believe is a robust framework that can be applied in future hydrological and climate change studies across the WUS and is applicable to other regions as well. Our key findings and conclusions are given in the following.

Our catchment-scale calibration of the two models to 263 sites across WUS resulted in major improvements in the performance of both models relative to a priori parameters, but performance improvement was the greatest for Noah-MP – although this may be in part because VIC a priori parameters benefitted from prior calibration and hence resulted in better baseline performance than the a priori Noah-MP did.

Both models performed best in more humid basins, mainly in the Pacific Northwest and central to northern CA where runoff ratios are high. This is consistent with previous results (e.g., Bass et al.,2023).

Post-calibration regional model performance improved for both models in most areas, especially where the baseline KGE was low, such as southern CA and the southeastern part of the study region.

VIC performance across all calibration basins was mostly better than for Noah-MP. However, Noah-MP performance benefitted more from regionalization than VIC did, and ultimately post-regionalization VIC performance was only slightly superior to that of Noah-MP. When partitioned into hydroclimatic categories, VIC outperforms Noah-MP in all but interior dry basins following regionalization, where Noah-MP is better.

Post-regionalization, both VIC and Noah-MP performance declines in comparison with the calibrated run, with declines more pronounced for VIC. The performance degradation is greatest in interior dry basins for both models.

VIC outperforms Noah-MP in simulating annual mean streamflow and flood simulations in most cases. Conversely, Noah-MP performs better for low flows. These results should provide guidance for selecting the most appropriate model depending on the hydrological condition being analyzed.