Regionalization methods for PUB: a comprehensive review of progress after the PUB decade

Streamflow is a fundamental component of the water cycle, and achieving reliable and continuous streamflow simulation is considered an essential objective within the hydrological community (Boughton & Droop 2003; Brocca et al. 2011; Cislaghi et al. 2020). The scientific and practical importance of reliable and continuous streamflow simulation cannot be overstated as it helps solve various engineering and water resource problems, such as reservoir design and management, predicting climatic and anthropogenic impacts on water resources, and risk assessment for extreme hydrological events (Parajka et al. 2013). Over decades of development and improvement, hydrological models, particularly rainfall-runoff models, have become the most common and useful tools for streamflow/runoff prediction and the estimation of water balance (Beven 2012). These models provide a visual representation of water systems using a set of equations that estimate the amount of runoff from rainfall based on various parameters (Devi et al. 2015). For practical applications, these models are calibrated to achieve optimal parameter values through the comparison of observations and simulations.

However, many catchments around the world are ungauged or poorly gauged, which presents a significant challenge (Sivapalan et al. 2003; Gorgoglione et al. 2019; Narbondo et al. 2020), especially in developing countries (Mulligan 2012). Even more concerning is that global efforts to collect streamflow data are decreasing, particularly in headwater basins (Kirchner 2006; Davids et al. 2019). Without the necessary information to drive hydrological models, the calibration process cannot be performed (Oudin et al. 2008; He et al. 2011). As a result, simulating runoff in ungauged or poorly gauged basins becomes exceedingly difficult. To address this fundamental challenge in hydrological science that has persisted for decades, the International Association of Hydrological Sciences (IAHS) launched the ‘Decade on Predictions in Ungauged Basins (PUB): 2003–2012’ (Cislaghi et al. 2020). The PUB decade aimed to improve the capacity for reliable predictions in basins lacking observations (Sivapalan et al. 2003).

Regionalization is the most commonly used method for predicting ungauged streams in PUB studies (Hrachowitz et al. 2013; Arsenault et al. 2021). Blöschl & Sivapalan (1995) define regionalization as the process of transferring model parameters (MP) from similar catchments to the ungauged one of interest. Egbuniwe & Todd (1976) tested the transferability of MP between neighboring Kontagora and Malendo watersheds even before this definition was established. In recent years, with increased attention on PUB studies, the definition of regionalization has expanded. Tarek et al. (2021) describe how regionalization can be used to estimate MP for generating continuous streamflow in ungauged basins. Xu (1999) estimates MP in ungauged basins by relating them to catchment descriptors (CDs). In PUB research, various approaches have been proposed to estimate MP in ungauged basins, which fall into two categories: distance-based methods and regression-based methods (e.g., He et al. 2011; Pool et al. 2021). Distance-based methods transfer information, including MP, from hydrologically similar catchments using a similarity metric based on spatial location or catchment attributes (e.g., Parajka et al. 2005; Oudin et al. 2008; Yang et al. 2018). Regression-based methods relate individual MP to selected catchment properties (e.g., Skaugen et al. 2015; Yang et al. 2018) and use this relationship to estimate the MP in ungauged basins.

In order to determine the most suitable regionalization method for PUB research applications, a regional evaluation of various methods has been conducted. Arsenault et al. (2019) evaluated both physical catchment descriptor-based and spatial-proximity (distance-based) regionalization methods on 30 catchments in Mexico's semi-arid and humid regions. They concluded that the distance-based method provides more robust results compared to methods relying on physical CDs. Yang et al. (2020) compared both types of regionalization methods using four hydrological models on 86 basins in different climate sub-regions in Norway. They found that the physical similarity (distance-based) method consistently outperformed other methods across all models and sub-regions. A study conducted on 264 catchments in Canada by Arsenault & Brissette (2016) revealed that the preference for distance-based regionalization method depends on the number of donor catchments applied. The regression-based method was found to be more effective than the distance-based method with only one similar donor, but the distance-based method with multiple donors performed better.

The PUB decade has seen significant progress in improving regionalization methods while also identifying their limitations. For example, McIntyre et al. (2005) suggested using the entire model parameter set for distance-based regionalization methods, which preserves the integrity of the parameters as a set (e.g., Oudin et al. 2010; He et al. 2011). Livneh & Lettenmaier (2013) proposed replacing local parameters with zonal parameters when building a regression model with local CDs. Their approach was validated in experiments over 220 catchments in the United States.

In studies conducted in regions with high diversity and heterogeneity, there are significant differences in performance among different regionalization methods. Petheram et al. (2012) investigated the performance of regionalization methods in tropical and arid regions in Australia and found that the regionalization methods performed better in the tropical region than in the arid region. Bao et al. (2012) evaluated the performance of regionalization methods in three different types of hydro-climatic regions (i.e., humid, semi-humid, and arid regions). The results showed that the accuracy of the regression-based method decreased more significantly than the similarity-based method from humid to arid regions. Yang et al. (2020) assessed the performance of regionalization methods using 86 catchments over three climatic regions in Norway and found that regionalization performance declined from oceanic to continental and polar tundra regions. Qi et al. (2021) explored the performance dependence of different regionalization methods on climatic regions by using thousands of catchments under varying hydro-climatic conditions in North America. The results displayed that the regionalization performance was worst in the arid region, and the performance differences among methods were larger in the arid region than in others. Additionally, some studies investigated the relationship between the regionalization performance and the aridity index (i.e., an index that presents the degree of dryness of the climate of a site) and concluded that the regionalization performance decreases as the aridity index increases for all regionalization methods (Viglione et al. 2013; Guo et al. 2020).

As mentioned previously, regionalization involves deriving model parameters in ungauged catchments from hydrological MP calibrated in gauged catchments. There are several regionalization methods, which can be broadly categorized into two classes: (1) distance-based methods (including both spatial-proximity and physical similarity (PS) methods); and (2) regression-based methods (which involve two steps). A more detailed description of each regionalization method is provided below.

The first step in the regionalization process is to determine the ‘donor catchment(s).’ These are assessed based on hydrological MP that can be achieved through the calibration process and then transferred to ungauged basins for regionalization applications (Blöschl & Merz 2005). Different catchment attributes are considered in this step using both SP and PS methods. Geographical location information of catchments is used for the SP method, which is consistent across all studies, but the measure of distance can vary depending on whether the centroid or outlet location is used (Cislaghi et al. 2020). For the PS method, more catchment attributes are included, but these can differ between studies due to data availability and subjective experience (He et al. 2011). Land cover, area, mean annual precipitation, and mean elevation are the four most frequently applied catchment attributes identified through reviewed studies. However, similarity indices used to assess the similarity between gauged and ungauged basins, like Euclidean distance, can be the same for both SP and PS methods. Catchment similarity is crucial for distance-based regionalization methods, with smaller distances indicating higher similarity. Various similarity indicators for PS methods are presented by Guo et al. (2020). Based on similarity evaluation, gauged catchments with higher similarity are preferred as donor catchments, but the number of donor catchments selected is highly dependent on researchers' experience, which plays an essential role in performance during PUB regionalization (Guo et al. 2020; Qi et al. 2021). For instance, Yang et al. (2020) observed that the NSE (Nash–Sutcliffe Efficiency) difference between different numbers of donor catchments could be larger than 0.1.

The second step in the regionalization process involves transferring information from gauged basins to ungauged basins (see Figure 2). Based on previous studies and Figure 2, using multiple donor catchments is preferred for achieving good performance in PUB. When there are multiple donor catchments, two averaging options can be used to obtain final simulations for the target catchment (McIntyre et al. 2005). The first option is to average parameter values from the donor catchments, referred to as the parameter option (par). The second option is to average discharges simulated using an individual parameter set from each donor catchment, called the output option (out). Thus, four approaches are obtained by combining distance-based regionalization methods (SP and PS) with the two averaging options. After completing these two steps, streamflow simulation can be performed for ungauged basins.

The regression-based method is one of the most commonly used regionalization methods in hydrology (Beck et al. 2016; Guo et al. 2020), particularly two-step regression. This study focuses on discussing only two-step regression methods that utilize the established relationship between CDs and MP to derive parameter values for ungauged basins (Xu 1999, 2003; Timilsena & Piechota 2007; Beck et al. 2016). Many hydrological models have been found to be suitable for application across various climatic and physiographic conditions (Strömqvist et al. 2012; Hrachowitz et al. 2013) and have been widely used in PUB studies.

To maximize the benefits and reduce the drawbacks of traditional methods in regionalization, researchers have proposed the concept of ensemble prediction as an alternative option for ungauged basins. For example, Waseem et al. (2015) introduced ensemble hydrological prediction (EHP) as an improved regionalization method to predict hydrological variables in ungauged basins. The basic idea of EHP is to give weights to traditional regionalization simulations based on their performance, which has been proven to be more robust in certain Pakistan catchments. Similarly, Razavi & Coulibaly (2016) proposed a multi-modelling approach to improve streamflow estimation in ungauged basins. Based on evaluations conducted on 90 Canadian watersheds, ensemble regionalization was found to perform better.

In regionalization research, similar hydrological responses are assumed within homogeneous groups (e.g., Hailegeorgis et al. 2015; Swain & Patra 2019). Recently, some studies have pre-classified catchments into groups to assess the impact. For example, Yang et al. (2018) grouped 118 Norwegian catchments, which were widely distributed, into five groups based on climatic indices but found no distinct effect. In contrast, Swain & Patra (2019) observed an improvement in regionalization performance in India when catchments were pre-classified, and they recommended this practice for future PUB studies. However, Pool et al. (2021) found that prior classification led to lower performance based on estimations across 671 U.S. catchments. This difference may be due to differences in classification methods or factors used in prior classification, and further exploration is needed to determine the reason behind this discrepancy.

Hydrological signatures, which describe the statistical or dynamical properties of hydrologic characteristics of catchments on different time scales, have recently received increased attention for regionalizing these signatures from donor catchments to ungauged basins. Atieh et al. (2017) proposed gene expression programming (GEP) and artificial neural networks (ANN) models to predict flow duration curves (FDCs) at ungauged basins across North America. Choubin et al. (2019) applied a comprehensive set of signatures to estimate streamflow in ungauged basins, which proved to be an efficient method.

To investigate whether poorly calibrated donor catchments could impair the performance of PUB simulations or not, some studies introduced threshold values of model efficiency during the calibration stage to filter donor selection (e.g., Arsenault & Brissette 2014; Qi et al. 2021). Arsenault & Brissette (2014) used a threshold of calibrated NSE values larger than 0.7 for donor selection over 268 Canadian catchments and found that well-calibrated donors would not guarantee good performance in PUB. Garambois et al. (2015) observed that poorly modeled catchments could also produce good performances when transferred to the ungauged catchment. Tarek et al. (2021) compared two thresholds (KGE (Kling Gupta Efficiency) values above 0.6 and 0.8 in the calibration, KGE is a widely used metric for evaluating the goodness of-fit of model simulations and corresponding observations proposed by Gupta et al. (2009)) as the threshold for donor catchments over 314 catchments in Africa. They detected decreased regionalization performance when applying the threshold 0.8, but no clear change when applying the threshold 0.6. Qi et al. (2021) set five thresholds for KGE (all, 0.6, 0.7, 0.8, 0.9) when evaluating the influence on the regionalization performance over 3,444 catchments in Canada and the US. The result showed deteriorated regionalization performance for higher thresholds (0.8 and 0.9) and no clear difference in regionalization performance for lower thresholds (0.6 and 0.7). In summary, setting too high a threshold value results in the use of too few donor catchments, which in turn causes a clear deterioration in regionalization performance.

The main concept behind regionalization involves utilizing information from donor catchments, which are selected from a ‘donor pool’. Thus, the analysis of donor influence is conducted from two perspectives: (1) the size of the ‘donor pool’ (which equals the total number of basins included minus one), defined as data availability by Parajka et al. (2013), and (2) the quantity and quality aspects of the applied donor basins.

Based on the scatter plot, it appears that many studies apply hydrological models with fewer parameters for regression methods, and most of them perform relatively well (with NSE values higher than 0.5). Along with the subplot (b), this result suggests that models with fewer parameters provide better performance based on the higher mean NSE value. This finding is in line with the distance-based method and some previous studies (e.g., Xu 2003; Clark et al. 2017). However, there are still 7 studies that yield NSE values higher than 0.6 using models with more than 12 parameters. Thus, we must accept the notion that there is no inherent incentive to prefer a parsimonious hydrological model over a model with adequate complexity for regionalization studies (Arsenault et al. 2015, 2019; Poissant et al. 2017). Concerning the difference between studies, hydrological models with more than 12 parameters yield the largest statistically significant uncertainty. This result is consistent with the finding of Arsenault et al. (2019), which suggests that using a more complicated model may result in larger uncertainty. Therefore, simple hydrological models are suggested for application when there is a lack of pre-knowledge. However, models with adequate complexity are encouraged for application to improve regionalization performance in PUB.

The x-axis of the scatter plot displays the size of the ‘donor pool.’ There is no clear pattern observed in general, indicating that the performance is not dependent on the number of catchments, which is consistent with the findings of Yang et al. (2018) and Parajka et al. (2013). However, slightly higher NSE values appear when the ‘donor pool’ size is greater than 30 and parameters are less than 7. This improved performance with a larger ‘donor pool’ is related to a stronger regression relationship.

Regarding subplot (a), models with parameters higher than 12 for climatic classes A, B, and C yielded all the low NSE values, whereas averaged NSE values were visibly higher for the group of models with parameters less than 7 in classes D and E. This result tends to suggest using parsimonious models for relatively humid regions. When hydrological models include 7–12 parameters, the performance in class A is generally better than in other classes, whose NSE values are mostly higher than 0.5. Connecting the Köppen–Geiger climate classification with the map of FAO (Food and Agriculture Organization of the United Nations) aridity index (Spinoni et al. 2014) suggests using models with adequate complexity in relatively arid regions. In subplot (b), there are only five values for the regression-based method in Class A and E, which are statistically meaningless, and these results are excluded from the following comparison. According to the general performance assessed by mean NSE values (the dashed lines), the distance-based method is considered to outperform the regression-based method across all climate groups, especially for class C. This is consistent with global results and many regional evaluation studies (Yang et al. 2018; Zhu et al. 2021) but to a more pronounced extent. Comparing the difference in general performance between climate classes and between two regionalization methods, the former is larger, which confirms the statement that climatic influence is stronger than regionalization methods for PUB performance (Parajka et al. 2013; Yang et al. 2020). When assessing the distributions of NSE values over studies across all climate classes, the regression-based method displays a relatively larger spread. This means that the performance is more unpredictable or the prediction is in larger uncertainty if applying the regression-based method in these regions. Taking the interquartile range as the uncertainty measure, distinct differences exist between climate groups for both methods. Therefore, climatic impact is not ignorable in regionalization performance (Haaf et al. 2020; Qi et al. 2021; Xu 2021).

The subplots (c) and (d) present a comparison of mean NSE values with the corresponding number of MP used to represent model complexity (e.g., Parajka et al. 2013; Jehn et al. 2019). For distance-based methods, the performance decreases from class E to class A, with a corresponding decrease in aridity. This supports the finding that higher accuracy is generally achieved in humid rather than arid regions (e.g., Guo et al. 2020; Xu 2021), and that hydrological model capacity is considered a negative factor (e.g., Parajka et al. 2013; Gao et al. 2016). Regarding performance differences between studies across climatic classes, class C displays the largest difference, and very low performance appears for models with more than 15 parameters. Taking this difference as uncertainty, it means that randomly selecting a hydrological model for runoff simulation might produce a larger difference in runoff simulation for class C than for other classes. For regression-based methods, classes A and E are excluded from the discussion due to the few values, while more studies are encouraged in these classes. For the remaining classes, there is no distinct dependence between climatic classes and MP, but the chance of low accuracy for models with more than seven parameters is greater. However, several studies have obtained high NSE values (possibly over 0.83) when applying models with 16 parameters, which may be due to stronger physically relevant applied hydrological models that are clearly identifiable (Xu 2021). In comparing the performance between methods, model complexity seems to affect regression-based methods more than distance-based methods. This is considered mainly due to the influence of model parameter interaction on regression-based methods (e.g., Zhang & Chiew 2009; Yang et al. 2018).

This paper compares the performance of two classes of regionalization methods in predicting runoff hydrographs in ungauged basins using the assessment method proposed by Parajka et al. (2013). However, the study is based on a completely different set of regionalization studies published after 2013. The review revealed that the accuracy of the regionalized PUB performance is affected by various factors, including hydrological models, climate characteristics, data availability, and regionalization approaches (e.g., Pool et al. 2021; Xu 2021). Nevertheless, based on comparative assessments and previous regionalization studies, some meaningful, consensus knowledge has been obtained.

• The distance-based regionalization method, with an output averaging option from multiple donor catchments, is statistically the most effective method. If the donor pool is larger than 20, it is not recommended to use one donor catchment.

• If prior knowledge is limited, the parsimonious hydrological model is a robust choice for future regionalization studies.

• The ensemble concept is the most attractive modification, and prior classification does not necessarily improve the performance of the study.

• Adding a low threshold (less than 0.5) to the donor selection has a limited impact, but using a threshold that is too high (larger than 0.8) results in performance deterioration.

• The total number of included catchments could affect the ranking of the two regionalization methods, and a larger performance difference may be observed with an increased number of total basins.

• The general performance difference between climatic classes is larger than between the two methods. Large uncertainties might exist if applying the regression-based method in tropical climatic regions.

Despite over two decades of development and numerous regionalization studies in public urban basin (PUB) research, there remain several challenges that must be addressed for future studies of regionalization in PUB:

• (1)

  There are too few studies on the impact of station density on regionalization methods to summarize its global pattern. Until now, this objective has only been explored in some European regions located in relatively humid areas. As such, it is imperative to conduct studies in different regions to provide new insights and assess the differences among varying climatic and geographic regions.

• (2)

  A comprehensive understanding of hydrological processes and regionalization methods is essential, especially in relatively arid areas. Many studies have found worse performance and high uncertainties in these regions. However, not enough research has been conducted to identify the factors that influence the final result. Answering this question is central to further improving regionalization methods, and it should be considered a meaningful future direction of research.

• (3)

  Techniques that widen the availability of data for PUB science should be prioritized. The development of remote sensing has led to the emergence of various new data sets, and understanding how to apply these data to improve regionalization performance is an area that needs further research. Additionally, as big data and machine learning science continue to grow, it becomes more attractive to explore how to extract better value from limited observation data.

• (4)

  Climate change has made it essential to predict streamflow in ungauged basins under non-stationary climates, and this requires more investigation. In recent years, a large number of hydrologic variable products, such as evaporation, soil moisture, and terrestrial water storage change, have been generated. These products provide diverse hydrologic data sets at finer spatial and temporal resolutions. Therefore, exploring how to use these data sets to carry out real-time correction on hydrological process variables to overcome the shortcomings of traditional regionalization methods under changing environmental conditions needs further investigation.

The National Natural Science Foundation of China (Grant No. 52209035), the Education Department of Shaanxi Provincial Government (Project No. 21JT032), the Science and Technology Program of Gansu Province (22JR11RA143), and the Research Council of Norway (FRINATEK Project 274310) supported this work.

Xue Yang conceptualized the whole article, developed the methodology, conducted funding acquisition, and wrote the original draft. Fengnian Li and Wenyan Qi rendered support in data curation, analysis, investigation, and wrote the review and edited the article. Mengyuan Zhang and Chengxi Yu brought resources, rendered support in data curation, analysis, and reviewed and edited the article. Chong-Yu Xu rendered support in the initiation of the study, funding acquisition, and review and editing.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.