The newly developed DynQual model builds on the modelling framework of DynWat, a global water temperature model that solves the energy–water balance to simulate daily water temperature (Tw) and ice thickness (Van Beek et al., 2012; Wanders et al., 2019). A full model description including the energy balance equations and the representation of ice cover, floodplains, channel roughness and lakes and reservoirs within DynWat is available in published literature (Wanders et al., 2019). DynQual further includes the impact of heat dumps produced in thermo-electric powerplants (Van Vliet et al., 2012a, 2021) on water temperature. In addition to water temperature, DynQual simulates daily in-stream concentrations of three water quality constituents, namely, total dissolved solids (TDS), biological organic matter (BOD) and fecal coliform (FC), which are of key social and environmental relevance (Van Vliet et al., 2021) (Fig. 1).

We also offer two options for running DynQual: (1) in a stand-alone configuration with specific discharge (i.e. baseflow, interflow and direct runoff in m d-1) fed from any land surface or hydrological model or (2) coupled with the global hydrological and water resources model PCR-GLOBWB2 (Sutanudjaja et al., 2018). The routine for surface water (and pollutant) routing follows an eight-point steepest-gradient algorithm across the terrain surface (local drainage direction) in a convergent drainage network with the lowermost cell connected to either the ocean or an endorheic basin as per PCR-GLOBWB2 (Sutanudjaja et al., 2018) and DynWat (Van Beek et al., 2012; Wanders et al., 2019). Routing within DynQual uses the kinematic wave approximation of the Saint-Venant equations with flow described by Manning's equation, solved using a time-explicit variable sub-time-stepping scheme based on the minimum Courant number (Sutanudjaja et al., 2018). In the coupled configuration, surface waters are subject to water withdrawals and return flows from the domestic, industrial, livestock and irrigation sectors calculated within the water use module of PCR-GLOBWB2. A complete model description of PCR-GLOBWB2 including detailed information on the model structure, individual modules (meteorology, land surface, groundwater, surface water routing and water use) and validation of hydrological output is available in published literature (Sutanudjaja et al., 2018). In both configurations of DynQual, pollutant loadings can be prescribed directly (akin to a forcing). Alternatively, when running DynQual coupled with PCR-GLOBWB2 pollutant loadings can be simulated within the model runs by providing only simple input data (Sect. S1 in the Supplement). An overview of DynQual, which details the input data required for the different model configurations, is displayed (Fig. 1). By providing these options, we allow for flexibility – allowing pollutant loadings to be directly imposed on the model enables users to estimate loadings using their preferred methodology and assumptions, whereas the option to estimate pollutant loadings within the model run enables users to simulate water quality without any pre-processing requirements but still provides flexibility to use their preferred input datasets. Parameter values related to pollutant emissions can be adjusted by the user as desired. When simulating pollutant loadings within model runs, it is also possible to quantify the contribution and relative importance of different water use sectors to the spatial patterns and temporal trends in surface water quality.

As per PCR-GLOBWB2 (Sutanudjaja et al., 2018) and DynWat (Wanders et al., 2019), DynQual is written in Python 3 and is run using an initialization (.ini) file in which key aspects of the model run are defined (e.g. spatial extent, simulation period, paths to parameter and forcing files). Most input files required and all output files are in NetCDF format. Global 5 arcmin DynQual runs that are coupled with PCR-GLOBWB2 have a wall-clock time of approximately 6 h yr-1 when run with parallelization due to the requirement to use the kinematic wave routing option for higher-accuracy discharge and water temperature simulations. This is approximately equivalent to the PCR-GLOBWB2 run times given by Sutanudjaja et al. (2018). DynQual runs performed in the stand-alone configuration are faster (∼ 20 %).

In both model configurations (stand-alone or coupled to PCR-GLOBWB2), user-defined pollutant loadings can be directly imposed on the model (akin to a forcing). Users can estimate pollutant loadings using their preferred methodology, and subsequently route these through the global stream network, account for in-stream decay processes and calculate in-stream pollutant concentrations using the DynQual model framework. Pollutant loadings that are prescribed to DynQual directly should have a daily temporal resolution (e.g. g d-1 or 106 cfu d-1; note that “cfu” indicates “colony forming units”.).

Alternatively, when running DynQual coupled with PCR-GLOBWB2, pollutant loadings (with a daily temporal resolution) can be simulated within the model runs, requiring only simple input data (Fig. 1 and Sect. S1). This option is beneficial for users that do not have pre-calculated pollutant loadings. Furthermore, this option may be useful for those interested in scenario modelling, as input files related to different scenarios can be altered to reflect alternative climate and socio-economic conditions.

In this set-up, DynQual estimates and routes pollutant loadings individually and combined for the main water use sectors (domestic, manufacturing, livestock and irrigation) and from urban surface runoff at 5 arcmin spatial resolution. Loadings from the domestic sector are estimated by multiplying the gridded population with region-specific per capita excretion rates (Sect. S1.1, Table S1 in the Supplement). For the manufacturing sector, a mean effluent concentration is multiplied by location-specific gridded estimates of return flows from the manufacturing sector (Sect. S1.2, Table S2). Urban surface return flows are approximated by multiplying surface runoff (simulated by PCR-GLOBWB2) with the gridded urban fraction, which are multiplied by a region-specific mean urban surface runoff effluent concentration (Sect. S1.3; Table S3). The livestock sector is sub-divided into “intensive” and “extensive” production systems based on livestock densities to better account for differences in the paths by which waste enters the stream network (Sect. S1.4, Table S4). Gridded livestock numbers for buffalo, chickens, cows, ducks, goats, horses, pigs and sheep are multiplied by pollutant excretion rates per livestock type and by region (Sect. S1.4, Tables S5–S7). TDS loadings from the irrigation sector are estimated by multiplying irrigation return flows simulated by PCR-GLOBWB2 with spatially explicit mean irrigation drainage concentrations based on salinity (as indicated by electrical conductivity) over the topsoil and sub-soil (Sect. S1.5). Thermal effluents (heat dumps) from thermoelectric powerplants are included as point sources of advected heat by considering the temperature difference between the flows and ambient surface water temperature conditions (Sect. S1.6). Pollutant loadings from the domestic, manufacturing and intensive livestock sectors and from urban surface runoff are abated based on grid-cell-specific wastewater practices. The proportion of pollutant loadings removed by wastewater treatment practices is estimated by multiplying the fraction of each treatment level occurring in a grid cell by the pollutant removal efficiency associated with that treatment level, as described in detail in previous work (Jones et al., 2021, 2022a).

A detailed explanation of how pollutant loadings are estimated within DynQual is provided in Sect. S1, including equations (Eqs. S1–S8), data sources and all parameter estimates (Tables S1–S7).

DynQual is run for the time period 1980–2019 using W5E5 forcing data (Cucchi et al., 2020; Stefan et al., 2021) in the configuration coupled with PCR-GLOBWB2. We used the standard parameterization of PCR-GLOBWB2 for hydrological simulations, as described in previous work (Sutanudjaja et al., 2018). The focus of our model demonstration is on TDS, BOD and FC, as results for Tw have been displayed extensively in previous work (Wanders et al., 2019). Pollutant loadings of TDS, BOD and FC are estimated within the model run at the daily time step using input data summarized in Table 2 and as detailed in Sects. 2.3 and S1. Both the meteorological forcing data and input data used for simulating pollutant loadings used in this study are accessible through links provided. We also provide the model code and full input data required for running an example catchment (Rhine basin) in the “Code and data availability statement”.

As per PCR-GLOBWB2 (Sutanudjaja et al., 2018), in addition to the original water temperature model DynWat (Wanders et al., 2019), no calibration was performed. The process-based nature and global scale of DynQual, combined with strong spatial biases in observations (Fig. S2) and the large number of parameters that need to be estimated, complicate meaningful calibration. In addition, uncalibrated physical models can theoretically be applied in ungauged basins without loss of performance and are more preferable for global change assessments with different climatic and socio-economic scenarios (Hrachowitz et al., 2013; Wanders et al., 2019).

Model simulations were compared to observations from surface water quality monitoring stations worldwide at daily temporal resolution. Observed data were obtained from various state-of-the-art databases (Sect. S3.1). Water quality monitoring data cover the entire modelled time period (1980–2019) and include a far greater number of observations than in previous surface water quality modelling validation procedures (Table S8). However, monitoring stations are unevenly distributed across space, with a strong bias towards North America and western Europe for all water quality constituents (Fig. S2). Furthermore, observations at monitoring stations are highly fragmented across time, particularly for BOD and FC.

The overarching purpose and applications of a model, including large-scale water quality models (Beusen et al., 2015; UNEP, 2016), must be considered both for determining suitable metrics for model evaluation and for judging model performance. Given the approximations in the model, uncertainties in input data and the overall complexity in the drivers of pollutant loadings, the purpose of global water quality models is not to compute daily concentrations exactly (UNEP, 2016). The modelling strategy is thus to focus on the main spatial and temporal drivers of pollution in river networks globally to facilitate first-order approximations of in-stream concentrations. A key reason for implementing DynQual at 5 arcmin spatial resolution is due to the marked improvement of the performance of both PCR-GLOBWB2 (e.g. discharge) (Sutanudjaja et al., 2018) and DynWat (e.g. water temperature) (Wanders et al., 2019) at finer spatial extents. These two factors have an important influence on simulated in-stream concentrations due to dilution and in-stream decay processes, respectively.

Given these factors, combined with limitations in the observational records of surface water quality (Sect. S3.1), global water quality models have typically not been evaluated with metrics commonly used for hydrological modelling such as coefficients of determination, Nash–Sutcliffe efficiency (NSE) and Kling–Gupta efficiency (KGE) (Voß et al., 2012; Beusen et al., 2015; UNEP, 2016; Wen et al., 2017; Van Vliet et al., 2021), with the exception of water temperature simulations (Van Vliet et al., 2012b; Wanders et al., 2019). The model evaluation approach adopted for DynQual combines methods applied for the evaluation of other global water quality modelling efforts. Simulated TDS, BOD and FC concentrations are evaluated with respect to pollutant classes linked to key sectoral water quality thresholds (UNEP, 2016; Wen et al., 2017) (Sect. S3.2.1; Table S9) and statistically using normalized root-mean-square error (nRMSE) (Beusen et al., 2015; Van Vliet et al., 2021) (Sect. S3.2.2; Eq. S11). This provides an indication of prediction errors across the different water quality constituents comparable with previous large-scale water quality assessments. Conversely, the quality of water temperature simulations is evaluated using KGE (Sect. S3.2.2; Eq. S10). All four water quality constituents are also evaluated by considering long-term time series and multi-year annual cycles at individual monitoring stations (Sect. S3.2.3), which we present for the station with the most data availability across all four constituents (see Fig. 5 for a station in the Mattaponi River in the USA) and for a selection of additional monitoring stations per water quality constituent (Figs. S5–S8).

Overall, a strong correspondence between simulated and observed concentrations classes is found, indicating that the model is (largely) able to simulate concentrations within the correct concentration range (Fig. 3). The simulated concentration class matches the observed concentration class exactly in 69 %, 51 % and 44 % of instances for TDS, BOD and FC, respectively. When considering ±1 pollutant class, these percentages rise to 92 %, 79 % and 79 %. Of the mismatches in simulated and observed concentration classes, DynQual tends to under-estimate TDS and BOD concentrations relative to observed in-stream concentrations (i.e. difference in classification level ≥ 1). This occurs for 75 % of mismatches in simulated TDS classes and 69 % of mismatches in BOD classes. Conversely, FC mismatches occur both for under-estimates (57 % of cases) and over-estimates (43 % of cases) in more equal proportions.

Statistical evaluation of the water temperature simulations using the KGE coefficient demonstrates the strong performance of DynQual (Fig. 4a) across all world regions (Fig. S3). Across all observation stations, a median KGE of 0.72 is found (25th percentile is 0.52, 75th percentile is 0.83), with 32 % of stations with KGE > 0.8, 83 % of stations with KGE > 0.4 and 99 % of stations with KGE values exceeding the performance threshold of >-0.41 (Knoben et al., 2019). Detailed time series of individual rivers also demonstrate the ability of DynQual to closely replicate observed water temperature at the daily time step, in addition to seasonal patterns, across different world regions (Figs. 5a, S5). A detailed evaluation of water temperature simulations is available in previous work (Wanders et al., 2019).

The distribution of nRMSE values, sub-divided by annual average river discharge, for TDS, BOD and FC is displayed in Fig. 4b–d. Statistical evaluation of the simulations using nRMSE shows mixed results. A median nRMSE value of 0.76 is found for TDS across all observation stations, with a 25th percentile of 0.79 and a 75th percentile of 1.83 (Fig. 4b). For BOD simulations, a median nRMSE of 0.98, 25th percentile of 0.76 and 75th percentile of 1.25 is found (Fig. 4c). A large spread is found for nRMSE values for FC simulations, with a median of 1.89, a 25th percentile of 1.16 and a 75th percentile of 3.53 (Fig. 4d). Simulated TDS concentrations are typically lower than observations in many locations that are proximate to the coastline, presumably due to a combination of background TDS concentrations based upon minimum observations (and applied constantly) and DynQual not accounting for the influence of saltwater intrusion. This may somewhat explain the long tail (nRMSE > 10) in the histogram for TDS (Fig. 4b) and the disproportionate tendency of DynQual to simulate TDS concentrations that are lower than observed concentrations (Fig. 3). Overall, no strong spatial patterns are found in the distribution of nRMSE values of BOD (Fig. S4b) and FC (Fig. S4c). For these water quality constituents, model simulations tend to represent the observed data better in larger streams (> 100 m3 s-1). This is likely due to the influence of spatial mismatches between monitoring station locations and model simulations being especially important in smaller streams, where concentrations are more sensitive to natural dilution capacity (i.e. water availability) and variabilities in pollutant source contributions.

Long-term time series and average annual cycle plots for TDS (Figs. 5b, S6), BOD (Figs. 5c, S7) and FC (Figs. 5d, S8) show that DynQual can generally simulate in-stream concentrations within the correct range (e.g. min–max daily concentrations, 10th and 90th percentile average annual cycles). Simulated concentrations at the example monitoring station (Fig. 5) display that TDS, BOD and FC concentrations are largely simulated within plausible limits with strong overlaps in the average annual cycles, but the exact correspondence between observed and simulated concentrations at the daily time step is relatively poor. For this observation station, simulated peaks in daily TDS, BOD and FC concentrations tend to exceed those in the observational record. However, given the incomplete nature of the observed records, it is problematic to draw conclusions on whether these concentrations are plausible but unrecorded or if DynQual is simulating unrealistic peak concentrations. For example, while DynQual captures some of the peaks in observed daily BOD concentrations, simulated BOD concentrations exceed those in the observational record while simultaneously under-predicting average annual cycles in BOD concentrations (Fig. 5). This pattern is also observable in TDS concentrations in the Mersey River (Fig. S6) and FC concentrations in the Exe River (Fig. S8).

While strong seasonality is present in the Tw observations, which is well captured by DynQual (Figs. 5a, S5), and in TDS concentrations to a lesser extent (e.g. Mersey and Komati rivers in Fig. S6), there is an overall lack of strong seasonal patterns in the observed records of BOD and FC concentrations. This, combined with large variability in the observed concentrations, results in large uncertainty in average annual cycles of observed concentrations across all months, as indicated by 10th and 90th percentiles (Figs. 5c–d, S7–S8). Annual average cycles in observed and simulated concentrations tend to strongly overlap for both BOD and FC. However, seasonal patterns are more evident in BOD simulations than observations (e.g. Mersey, Periyar in Fig. S7), and the large variability in observed FC concentrations is not replicated by DynQual daily simulations (e.g. Cauvery, Rhine in Fig. S8). In the case of FC concentrations, for example, this could suggest that DynQual misses or under-represents the importance of pulse disturbances (e.g. high rainfall events causing sewer overflows) on the transport of pollutants to surface waters.

The spatial patterns in TDS (Fig. 6), BOD (Fig. 7) and FC (Fig. 8) concentrations show substantial variations both within and across world regions, driven by different sectoral activities (Fig. 9). The dilution capacity of rivers is also a major determinant of in-stream concentrations. Averaged at the annual timescale this is particularly evident for BOD and FC, where the large dilution capacity of some major rivers is sufficient to dilute concentrations to relatively low levels, despite often being fed by more polluted tributaries. However, it should also be noted that both river discharges and in-stream concentrations can exhibit substantial intra-annual variability, thus pollutant hotspots and the magnitude of pollutant levels must also be considered at finer temporal scales than presented here. Intra-annual variability can occur in the model due to temporal variations in (1) pollutant loadings, (2) water availability (i.e. dilution capacity) and (3) in-stream decay processes.

TDS concentrations show strongly regional patterns, with key hotspots of salinity pollution located in South Asia (Pakistan and northern India) and eastern China and to a lesser degree across the United States and Europe (Fig. 6). High TDS concentrations in South-East Asia are predominantly driven by the irrigation sector and the presence of saline soils (Fig. 9a). While the irrigation sector is also an important driver of TDS pollution in eastern China, the contribution from manufacturing activities is also substantial (Fig. 9a). The manufacturing sector is the dominant contributor of TDS pollution across most of North America and western Europe, accounting for > 75 % of in-stream pollutant loadings in almost all major river segments in these regions (Fig. 9a). Aside from the lower Nile, where salinity pollution is predominantly from the manufacturing sector, the domestic sector is the key source of (non-natural) TDS loadings in Africa. However, it should be noted that, aside from in the lower Nile, TDS concentrations are simulated to be relatively low across most of Africa (Fig. 6).

While BOD concentrations show considerable diversity across the major world regions, a substantial proportion of river segments across populated areas of all continents experience moderate-to-high organic pollution (Fig. 7). There are clear spatial patterns in the dominant sectoral activities contributing BOD loadings worldwide, and it also evident that BOD pollution in most world regions is driven by a combination of multiple sectors opposed to from an individual dominant activity (Fig. 9b). Across Europe in particular, which sector is dominant varies both spatially and temporally, and the contribution from the dominant sector is typically < 50 % (Fig. 9b). The manufacturing sector is the most significant source of BOD pollution across rivers in the United States; however, the relative contribution commonly falls in the 20 %–50 % or 50 %–75 % categories (Fig. 9b). In the most polluted world regions, South Asia and South-East Asia, the domestic sector is typically dominant. However, there are also significant contributions from manufacturing and extensive livestock activities (Figs. 7, 9b). Lastly, while its influence is highly localized, urban surface runoff can also represent an important source of BOD pollution in heavily urbanized grid cells across all world regions.

FC pollution is particularly high across South Asia and South-East Asia, with more localized hotspots found in parts of western Latin America, southern Europe, Middle East and eastern Africa (Fig. 8). Similar to BOD pollution, a large proportion of stream segments in South Asia and South-East Asia are heavily polluted, with typically only rivers with extremely high dilution capacities appearing in the lower concentration classes. In this region, the domestic sector is predominantly responsible for FC pollution (commonly > 75 %), attributed to large urban populations coupled with a large proportion of domestic wastewater being inadequately treated (Fig. 9c). In countries with high municipal wastewater collection and treatment rates, such as in Europe, the relative influence of livestock activities tends to be larger. While manufacturing activities remain the dominant source of FC pollution in North America, despite relatively high wastewater treatment rates, the percentage contribution is typically < 50 % and livestock activities also represent an important source of FC loadings (Fig. 9c). Despite variable municipal wastewater collection and treatment rates across Latin America, livestock activities appear to dominate FC loadings outside of the Amazon basin (Fig. 9c). This can be attributed to very high livestock numbers (particularly cattle), combined with the fact that the most of the large urban settlements (and thus domestic FC pollutant loadings) in South America are located in the coastal zone. As such, pollution from the domestic and manufacturing sectors typically enter the river network at downstream locations causing localized pollution before outflow to the ocean.

Long-term trends in TDS, BOD and FC concentrations over the simulated period (1980–2019) are also presented (Fig. 10). TDS concentrations in most world regions are either relatively constant or show relatively upward gradual trends (Fig. 10a). Typically, where TDS concentrations are increasing, the trend has been driven mainly by expansions in manufacturing or irrigation activities. Comparatively, trends in BOD (Fig. 10b) and FC (Fig. 10c) concentrations are larger in magnitude and exhibit substantially more spatial variation across the major world regions. Regionally, the strongest increases in BOD and FC concentrations are found in sub-Saharan Africa, where wastewater treatment rates are low, and South Asia, where the rate of population growth and economic development has significantly outstripped the expansion of wastewater treatment infrastructure. Strong increasing trends are also found across most of Latin America, where a significant proportion of collected wastewater does not undergo wastewater treatment (UNEP, 2016; Jones et al., 2021). BOD and FC concentrations across North American rivers have typically remained relatively constant or exhibit small decreasing trends. Strong decreasing trends are found across Europe, including the Danube and Rhine basins. In all world regions, the influence of reservoirs on BOD and FC concentrations is also evident, with increased water volumes (i.e. dilution) coupled with longer residence times (i.e. greater decay) reducing BOD and FC concentrations at these specific locations.

Complementary to the spatial analysis, we considered the proportion of the population that inhabits grid cells exhibiting different trends in pollutant concentrations, aggregated by geographical region and economic classification (Fig. 11). It should be noted that trends (Figs. 10 and 11) are not indicative of the degree of pollution directly and thus should also be considered with respect to in-stream concentrations (Figs. 6–8). Changes in TDS concentrations in the most populated areas worldwide are typically low, with increases of 0 %–1 % most common across all geographical regions (Fig. 11a). Conversely, strong regional patterns are evident for BOD (Fig. 11b) and FC (Fig. 11c) concentrations. Particularly in sub-Saharan Africa and South Asia, BOD and FC concentrations in populated locations have been almost exclusively increasing. Over half of the population of sub-Saharan Africa live in areas where BOD and FC concentrations have increased (on average) by > 2 % yr-1 from 1980–2019. Conversely, in western Europe, trends in BOD and FC have been negative for areas where 60 % of the population lives.

When aggregating trends by country-specific economic classifications, trends in TDS, BOD and FC pollutant concentrations all display a clear correlation with level of economic development (Fig. 11). For the water quality constituents considered, the strongest and most widespread decreases in pollutant concentrations have been experienced by “high-income” countries, while “low-income” countries have experienced the greatest and most widespread degree of water quality degradation. These patterns are particularly clear for FC, where approximately 60 % of the population in high-income countries live in grid cells displaying negative trends in FC concentrations, compared to 50 %, 25 % and 10 % in “upper-middle-income”, “lower-middle-income” and low-income countries, respectively. Furthermore, in the low-income countries, 50 % of the population lives in areas where FC concentrations have increased (on average) by > 2 % each year from 1980 to 2019.

Lastly, we present time series of in-stream TDS, BOD and FC concentrations delineated by sector-specific contributions at three selected locations (Fig. 12) for which validation plots are also presented (Figs. S6–S9). While it is not our intention to explain the patterns in concentrations and sectoral drivers for the Mersey, Cauvery and Kiso rivers specifically, these plots are illustrative of the capabilities of DynQual. For example, these plots demonstrate the relative importance of different water use activities on in-stream concentrations dynamically, and also display changes over longer time periods. This is particularly evident in FC concentrations in the Mersey River, where decreasing loadings from the domestic and manufacturing sectors, primarily due to increases in wastewater treatment capacities, have driven an overall trend towards water quality improvements. Conversely, the manufacturing sector is simulated to have had an increasing influence on TDS concentrations in the Kiso River since ∼ 2004, replacing the irrigation sector as the dominant driver of salinity pollution.