An assessment of climate change impacts on stream phosphorus using a climate model ensemble and Bayesian Belief Networks

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Wade, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5165980/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract Climate-induced changes in precipitation will lead to greater frequency of high and low-flow events, causing further phosphorus losses due to increased mobilisation and delivery and decreased dilution. The uncertainty associated with climate-induced changes to water quality is rarely represented in water quality models. Bayesian Belief Networks (BBNs) are probabilistic graphical models incorporating uncertainty, making them useful frameworks for communicating risk. This study presents a set of catchment-specific BBNs to simulate total reactive phosphorus (TRP) concentrations in four agricultural catchments under projected climate change. Downscaled discharge time series from six climate models (five models plus their mean), for two Representative Concentration Pathways (RCP 4.5 and 8.5) and three time periods (the 2020s, the 2040s, and the 2080s), were used to create discharge scenarios for the catchment-specific BBNs. The BBN-simulated monthly mean TRP concentrations showed no obvious trends over time or differences between the RCP scenarios, with the ensemble-driven future TRP essentially replicating the results obtained for the baseline period. We found that in four small (7–12 km 2 ) catchments farmed for livestock or arable crops with one or no wastewater treatment plants, the projected effects of climate change alone were not a significant driver of monthly TRP concentrations. However, the TRP concentration distributions simulated using the outputs from just the HadGEM2-ES model, showed differences from the baseline in the drier months. This difference occurred because the catchment-specific BBNs were sensitive to changes in the mean monthly discharge simulated using in the HadGEM2-ES projections but not by the other ensemble members. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1 Introduction Phosphorus (P) over-enrichment from intensive farming in Ireland has led to freshwater eutrophication and harmful algal blooms (HAB) [ 1 ]. P losses in rural catchments are complex, resultant from multiple sources, including manure and mineral fertilizer applications and effluent discharges, and multiple flow-pathways such as overland flow, farm drains, and groundwater flow; all of which vary with location [ 2 – 4 ]. Phosphorus bound to soil and stream sediment, known as legacy P, can also be later released, further confounding P reduction efforts. For these reasons, whilst reducing P losses from land to water is expected to reduce freshwater eutrophication overall, determining the focus and priorities for effective policy and catchment management to achieve such reductions is difficult. Climate change further complicates this management challenge [ 5 ], with projections for Ireland suggesting increased winter, and reduced summer, precipitation [ 6 ]. Against this backdrop, P models have been applied to quantify P sources, transport, in-stream concentrations and loads to identify appropriate management strategies to continue recent progress in the reduction of stream water P concentrations and loads [ 7 – 9 ]. Increased and more intense winter storms have been shown to result in greater mobilisation and delivery of P loads to surface waters in small UK river catchments, whilst summer reductions in precipitation were shown to reduce the dilution of point source and groundwater inputs [ 8 ]. While studies have shown increased P loads from agricultural diffuse sources under climate change [ 8 , 10 , 11 ], water quality standards for freshwaters are typically specified as annual concentrations, for example, under the European Water Framework Directive [ 12 ]. Given this background, determining the effect of climate change on the distribution of P concentrations remains important to understand future eutrophication risk and to design mitigation measures [ 7 , 13 , 14 ]. Catchment area, inputs from diffuse and point sources and land use are important factors that determine how stream water P concentrations will respond to future climate change and must be accounted for when modelling P under climate change [ 9 ]. Furthermore, the associated changes in chlorophyll-a concentrations, a measure of algal production in response to stream water phosphate alterations, are complex, with growing evidence that stream water residence-time, prevailing light conditions and nitrogen are equally, if not more, important than P concentrations or loadings as controls of algal bloom initiation and development [ 15 – 17 ]. However, inadequate data resolution to describe flow and phosphorus dynamics, particularly under extreme high and low flow conditions, and the lack of uncertainty analysis in model applications have been cited as current limitations when simulating these future changes in P concentrations and loadings [ 8 ]. While the lack of suitable data means that the testing of the assumptions to construct P models is limited, representing uncertainty is critical to help decision-makers assess models and make informed decisions about water quality management [ 18 , 19 ]. Bayesian Belief Networks (BBNs) are probabilistic graphical models that can help to bridge uncertainty knowledge gaps as they provide robust quantitative uncertainty estimates, including epistemic and aleatoric uncertainty [ 20 , 21 ], and can facilitate the identification of uncertainty sources within the model [ 22 ]. Given that incorporating both uncertainty and stakeholder knowledge in water quality research is becoming increasingly relevant [ 23 – 25 ], BBNs are an alternative to the widely-used process-informed catchment P models such as HYPE, SWAT, and INCA-P, and are advantageous because they incorporate P sources, processes, and delivery pathways, as well as the socio-economic aspects, in a way that is interpretable and accessible to wider audiences [ 26 – 28 ]. Furthermore, uncertainty estimation is also inherent to BBNs, through the specification of prior probability distributions, equations or conditional probabilities (CPTs) describing P processes and transport pathways, based on either measurements, expert and stakeholder elicitation, or literature. Taking these issues into consideration, new catchment-specific BBNs have been developed and applied in four Irish catchments representative of contrasting land cover and hydrological regimes [ 29 ]. The networks performed well when simulating total reactive P concentrations (TRP) [ 29 ]. Here, we take the science further and present the application of these BBNs to simulate future phosphorus losses in these four catchments under climate change scenarios, using an ensemble approach for the first time. All four catchments have extensive datasets of discharge (Q), in-stream TRP concentrations, and turbidity measured sub-hourly since 2009. These stream water measurements are supplemented by 400 to 500 soil P test measurements, described in detail elsewhere [ 4 , 30 ]. These data have been combined previously to construct and test catchment-specific BBNs which incorporate septic tank inputs, in-stream P processes, and groundwater pathways [ 26 , 29 ]. The aim of this study was to quantify stream TRP concentrations under future projections of climate change. To achieve this overall aim, we followed three research objectives: To evaluate the sensitivity of the BBN outputs to changes in flow inputs as a precursor to help interpret and understand the model sensitivity to climate change effects. To use projected future flows as input to the previously developed BBN models to determine TRP concentrations based on flow simulations from five climate models and their ensemble, two RCPs (4.5 and 8.5) and present day (2020s), near (2040s) and far future (2080s) time periods. To use the sensitivity analysis results to interpret the simulated response of future TRP concentrations in the BBN models to altered flow and the relative importance of flow as a driver of future change. 2 Study Areas This study focusses on four agricultural catchments located in the Republic of Ireland. These have contrasting agricultural land use and hydrology and have been described in more detail elsewhere [ 31 ]. The catchments included are Ballycanew (1191 ha, poorly-drained, 78% grassland) and Castledockrell (1117 ha, well-drained, 54% tillage) in County Wexford, Timoleague (758 ha, well-drained, 85% grassland) in County Cork, and Dunleer (948 ha, moderately-drained, 33% tillage) in County Louth. Point P sources include rural septic tanks, and a single wastewater treatment plant in the Castledockrell catchment. The catchments have been monitored since 2009 by the Agricultural Catchments Programme (ACP) to oversee the environmental and economic effectiveness of the Programme of Measures and derogation under the Nitrates Direction National Action Programmes (NAPs) of the European Union [ 32 ]. Specifically, the monitoring included high-frequency (sub-hourly) measurements of hydro-chemo-metrics at the catchment outlet such as discharge (Q, m 3 ), turbidity (NTU), and total reactive P (TRP, mg l − 1 ) concentrations aggregated at the daily time step [ 26 ] and field-scale soil sampling including agronomic soil P [ 33 ]. Murphy et al., [ 6 ] have simulated future flows under climate change scenarios in twenty-six Irish catchments, including those in this study, by using the Irish Centre for High-End Computing (ICHEC) ensemble [ 34 ] to drive the Soil Moisture Accounting and Routing for Transport (SMART) hydrological model [ 35 , 36 ]. Annual mean flows were projected to increase across Irish catchments under RCP 8.5 (a fossil fuel-intensive emissions pathway), and the largest increase was expected in Castledockrell by the 2080s (23.8%) [ 6 ]. Under RCP 8.5 in the 2080s, Timoleague, Ballycanew, and Castledockrell showed increased winter mean flow (> 30%). Large summer flow decreases were predicted for Ballycanew and Dunleer (up to -50%) and, in the Castledockrell catchment, a 114% increase in autumn mean flow occurred under the RCP 8.5 scenario [ 6 ]. Changes to the mean seasonal and annual flows were also found under RCP 4.5 (an intermediate pathway with emissions peaking around the year 2040), albeit less marked. In Murphy et al., [ 6 ], small catchments such as those considered here (with areas of 7–12 km 2 ) showed the widest flow changes, especially in the summer, compared to larger catchments (48-2460 km 2 ). Therefore, these catchments are to be considered vulnerable to climate-induced changes. 3 Methods 3.1 Bayesian Belief Network development The hybrid BBNs (comprised of both discrete and continuous variables) used in this study were developed in the software GeNIe, version 2.4 [ 37 ] for the four catchments [ 29 ]. The development and testing of the BBNs are described in detail elsewhere [ 26 , 29 ]. In short, a BBN was developed to simulate monthly P losses at the outlet of a surface flow-dominated Irish grassland catchment, including point P sources such as farmyards and septic tanks. This BBN was adapted for application in three further catchments by including groundwater P concentrations and in-stream P cycling by both biotic and abiotic processes, on the basis of high-frequency piezometer P data and expert elicitation. The four BBNs quantify the monthly in-stream TRP concentration at the catchment outlet by integrating the P loads from different compartments (soils, sediments, septic tanks, farmyards, groundwater, and a wastewater treatment plant) and then converting the loads into concentrations by dividing by the monthly discharge. Catchment-specific datasets were used wherever possible, including the quantification of the different discharge (Q) components, namely quick-flow, interflow, and baseflow [ 38 ]. The finalized BBNs achieved good performance in all four catchments in terms of percentage bias (-5% ≤ PBIAS ≤ 49%) when compared to the observed TRP concentrations (2009–2016) [ 29 ]. The BBNs reproduced the observed mean monthly TRP concentration relatively well in Castledockrell and Timoleague, though less accurately in Ballycanew and Dunleer, where the model predicted the mean concentration better in winter than in summer; however, model performance was still sufficiently good to warrant further application to explore the response of discharge and TRP concentration to climate change projections. A summary of the BBNs’ performance is given in Table 1 , whilst further detail, including the monthly performance, is reported in [ 29 ]. Table 1 Summary performance of the BBNs developed in [ 24 ] for the four agricultural catchments, including 68%, 94% credible intervals, and percentage bias (PBIAS, %), alongside with the observed 68% (µ ± 1 ơ) and 95% (µ ± 2 ơ) confidence interval. Both observed and predicted TRP concentrations were log-transformed before calculating the intervals, and then converted back to linear space (geometric mean). The marginal distribution mean can reproduce the observed mean TRP concentration in the reference period (2009–2016). PBIAS TRP TRP % mg l − 1 mg l − 1 predicted marginal (68% credible interval) observed mean (68% confidence interval) predicted marginal (95% credible interval) observed mean (95% confidence interval) TIMOLEAGUE -5 \(\:{0.05}_{0.08}^{0.03}\) \(\:{0.05}_{0.09}^{0.03}\) \(\:{0.05}_{0.12}^{0.02}\) \(\:{0.05}_{0.16}^{0.01}\) BALLYCANEW 49 \(\:{0.07}_{0.17}^{0.03}\) \(\:{0.06}_{0.11}^{0.06}\) \(\:{0.07}_{0.41}^{0.02}\) \(\:{0.06}_{0.19}^{0.02}\) CASTLEDOCKRELL 18 \(\:{0.02}_{0.05}^{0.01}\) \(\:{0.02}_{0.04}^{0.01}\) \(\:{0.02}_{0.09}^{0.00}\) \(\:{0.02}_{0.07}^{0.00}\) DUNLEER 45 \(\:{0.09}_{0.28}^{0.03}\) \(\:{0.10}_{0.16}^{0.06}\) \(\:{0.09}_{0.85}^{0.00}\) \(\:{0.10}_{0.27}^{0.03}\) 3.2 Sensitivity to discharge To help interpret the results, a sensitivity analysis was done on the model parameters for discharge (Q) by adapting the code developed in rSMILE 2.0.1 by Negri et al., [ 29 ], using rSMILE version 2.2.1. rSMILE is an API engine available in R which can perform the same operations as GeNIe Modeler [ 37 ], the software used to develop the BBN model structures used in this study. The “Mean total monthly Q (discharge) [m 3 ]” was defined as a series of monthly Lognormal (µ, ơ) distributions. For each catchment, we tested varying the mean (9 ≤ µ ≤ 17) and standard deviation (0.1 ≤ ơ ≤ 1) of the Lognormal discharge on the median log 10 (TRP) posterior concentration (mg l − 1 ) by applying a stepwise variation on the mean (increments of 1) and on the standard deviation (0.1 increments). This variation in the log space is equivalent to varying the mean total discharge between 8000 and 2.4*10 7 m 3 month − 1 . 3.3 Climate Scenarios and their implementation in the BBN Nolan and Flanagan [ 34 ], developed high-resolution climate scenarios for Ireland by downscaling the outputs of five Global Climate Models: CNRM-CM5 [ 39 ], EC-Earth [ 40 ], HadGEM2-ES [ 41 ], MIROC5 [ 42 ], and MPI-ES-LR [ 43 ]. Future climate was simulated under Representative Concentration Pathway 2.6, 4.5, 6.0, and 8.5, of which RCP 4.5 and 8.5 are included in this study to represent an intermediate (RCP 4.5) and an extreme scenario (RCP 8.5). Murphy et al., [ 6 ], used these climate scenarios to drive the SMART hydrological model, calibrated independently with both the Nash-Sutcliffe Efficiency (NSE) and the log Nash-Sutcliffe Efficiency (log NSE) as objective functions. These simulated river flows (discharge, Q) up to the year 2100 obtained through the SMART model [ 6 ] are used in the present study. The available daily discharge (Q, mm) timeseries were summed into total monthly Q (m 3 ) for each climate model, concentration pathway, and reference period. A bootstrapping procedure was implemented to fit a Lognormal distribution to the monthly Q using the R package fitdistrplus [ 44 ]. The monthly lognormal parameters (mean, µ, standard deviation, ơ) per each scenario were then used to specify the distributions for the BBN node “Mean total monthly Q (discharge) [m 3 ]” using the same procedure used to parametrize the BBN baseline in [ 26 ]. A scenario for the ensemble was also included, whereby monthly discharge was averaged between the five climate models prior to distribution fitting. This was done because of the recommendation to use a multi-model ensemble approach to address model formulation and climate variability-related uncertainties when using the dataset [ 34 ]. The combination of two emission pathways, three reference periods: the 2020s (2010–2039), the 2050s (2040–2069), and the 2080s (2070–2099), six model outputs (five models plus the ensemble), and two calibration functions gave seventy-two scenarios of monthly discharge per catchment. These were used as input to the catchment-specific BBNs to simulate monthly TRP concentrations at the catchment outlet. The posterior probability for the target node “In-stream P concentration [mg l − 1 ]” was simulated using rSMILE version 2.2.1 [ 45 ]. To visually inspect the results, mean monthly TRP concentrations and 68% credible intervals (µ ± 1 ơ, mg l − 1 ) derived from the posterior TRP distribution for each scenario were plotted alongside mean total precipitation (µ ± ơ, mm), observed TRP (µ ± ơ, mg l − 1 ) as well as the same credible interval predicted by the BBN in baseline period (2009–2016) [ 29 ]. A schematic of this workflow in context with the work of Nolan and Flanagan, [ 34 ] and Murphy et al., [ 6 ] is shown in Fig. 1 . 4 Results and Discussion 4.1 Sensitivity to discharge The sensitivity analysis showed that the BBNs developed for the four catchments are sensitive to a variation in the monthly mean discharge. Specifically, the model was significantly sensitive to variations in mean (µ) of the Lognormal discharge in the range 9 ≤ µ ≤ 12 (these are specified in the log e scale in the BBNs), which is equivalent to a variation between 8000 and 1.6*10 5 m 3 month − 1 , beyond which (Lognormal µ ≥ 12) median log 10 (TRP) concentrations (mg l − 1 ) tended to an asymptote (e.g., 0.02 mg l − 1 in Castledockrell, shown in Figure S1 in the log scale). Variations in discharge standard deviation (ơ: 0.1-1) had a negligible impact, indicating that mean flow – not its variability – drives the monthly median TRP response under climate change in these BBNs. The Supplementary Information contains the validation figures for this analysis (Figure S1). Table 2 68% credible interval (µ ± 1 ơ) of the ensemble discharge prior (total monthly Q, m 3 ) in the month of January across the two climate scenarios (RCP 4.5 and RCP 8.5) against the same for the BBN baseline [ 29 ] for each of the four catchments. Here, only results derived from the NSE calibration driving the SMART model are shown. Monthly discharge is represented in the model with a Lognormal(µ, ơ) distribution (base e). Timoleague RCP 4.5 RCP 8.5 BBN baseline [ 29 ] µ-ơ µ µ+ơ µ-ơ µ µ+ơ µ-ơ µ µ+ơ m 3 *10 6 month −1 2009–2016 - - - - - - 0.89 0.98 1.09 2010–2039 0.81 0.84 0.88 0.75 0.78 0.81 - - - 2040–2069 0.85 0.89 0.93 0.85 0.88 0.92 - - - 2070–2099 0.89 0.92 0.96 0.98 1.02 1.07 - - - Ballycanew RCP 4.5 RCP 8.5 BBN baseline [ 29 ] µ-ơ µ µ+ơ µ-ơ µ µ+ơ µ-ơ µ µ+ơ m 3 *10 6 month −1 2009–2016 - - - - - - 0.83 0.98 1.17 2010–2039 0.84 0.89 0.96 0.85 0.91 1.88 - - - 2040–2069 0.88 0.94 1.01 0.87 0.93 1.00 - - - 2070–2099 0.91 0.97 1.04 1.03 1.11 1.20 - - - Castledockrell RCP 4.5 RCP 8.5 BBN baseline [ 29 ] µ-ơ µ µ+ơ µ-ơ µ µ+ơ µ-ơ µ µ+ơ m 3 *10 6 month −1 2009–2016 - - - - - - 0.97 1.09 1.21 2010–2039 0.61 0.63 0.66 0.60 0.63 0.65 - - - 2040–2069 0.63 0.66 0.69 0.66 0.69 1.02 - - - 2070–2099 0.67 0.70 0.73 0.76 0.79 0.82 - - - Dunleer RCP 4.5 RCP 8.5 BBN baseline [ 29 ] µ-ơ µ µ+ơ µ-ơ µ µ+ơ µ-ơ µ µ+ơ m 3 *10 6 month −1 2009–2016 - - - - - - 0.60 0.66 0.73 2010–2039 0.71 0.75 0.79 0.71 0.74 0.78 - - - 2040–2069 0.73 0.77 0.81 0.76 0.81 0.85 - - - 2070–2099 0.78 0.83 0.88 0.84 0.89 0.95 - - - A comparison of the discharge (Q) for the month of January between the model ensemble scenarios (NSE calibration only) and the BBN baseline [ 29 ] is shown in Table 2 . Here, all Lognormal Q distributions have a mean of 13.36 ≤ µ ≤ 13.92, and a standard deviation of 0.04 ≤ ơ ≤ 0.17, a range for which the model is insensitive (Figure S1). The ensemble-driven total monthly discharge in the scenarios was comparable to that in the BBN baseline (Table 2 ). Further, the ensemble underestimates the discharge in in Timoleague and Castledockrell in the 2020s. The BBNs showed sensitivity only to mean (µ) Lognormal discharge in the range 9 ≤ µ ≤ 12 also when testing for a drier month (e.g., August, data not shown), which would indicate that the sensitivity is the same across the months. However, there were some differences when looking at discharge driven by the individual ensemble members rather than their mean. For example, the HadGEM2-ES model predicts total monthly Q in ranges that the BBN is sensitive to (Lognormal µ ≤ 12), especially in the warmer months (Table S1 shows this for the Timoleague catchment). The analysis suggests low sensitivity of the target node (TRP concentrations at the catchment outlet) to parents (discharge, Q) distant from the target node. In these BBNs, discharge is used to calculate both the concentrations at the catchment outlet and the loads from different model compartments, therefore it’s considered to be distant from the target node because there is an increased number of variables between input (parent nodes) and output (target child node). This supports the finding that increased model complexity weakens the relationship between input and output [ 46 ]. 4.2 Phosphorus concentrations under future climate Each catchment BBN predicts the marginal TRP concentration probability distribution (the posterior distribution without setting any evidence) using the model ensemble across the three reference periods: the 2020s (2010–2039), the 2050s (2040–2069), and the 2080s (2070–2099). We compared the marginal posterior distribution to the Environmental Quality Standard (EQS) of 0.035 mg l − 1 [ 12 ]. This comparison showed that the ensemble-driven BBNs do not predict EQS exceedance marginal probabilities that differ from the baseline, although admittedly these models are not recommended for such purpose, but rather perform better when looking at the full posterior distributions, due to the predicted posterior distributions being wider and more skewed than those observed [ 26 , 29 ]. Marginal probabilities of exceeding the Environmental Quality Standard (EQS) of 0.035 mg l − 1 [ 12 ] under the ensemble are shown in Table S2 of the Supplementary Information. Furthermore, the means of the marginal TRP distributions show no clear differences against the observed reference period (2009–2016), no obvious trend over time, nor differences when using the two different SMART model calibrations (log NSE vs NSE) (shown Table S3, Supplementary Information, as log 10 (TRP)). This agrees with previously conducted research which demonstrated that climate change alone has a small effect on mean phosphate concentrations in north-west Europe in larger (50–12 000 km 2 ) catchments [ 9 ]. Additionally, here we applied a model ensemble consisting of the mean discharge simulated by five climate models which progresses previous works using a single climate scenario in a BBN [ 47 , 48 ]. The response of the BBNs under climate change showed TRP concentrations similar to those shown in the baseline when using the model ensemble were explained by the low sensitivity of the BBNs to discharge, and the fact that the ensemble-driven mean discharge simulations are within the model insensitivity range in most cases. These parsimonious BBNs only represent changes in runoff as the key process impacting P transport under future climate, disregarding other processes that may have an effect, such as soil temperature changes affecting P dynamics [ 49 ], changes in rainfall intensity that will impact P mobilization and consequently dissolved P losses [ 50 ], and P source change due to land use alteration [ 49 ]. However, some of these processes might be negligible (i.e., temperature) compared to precipitation and runoff [ 8 , 51 ], or are outside the scope of the present research. This could also explain why the marginal mean TRP was not affected under future climate. We would expect changes in P sources due to future land use and/ or land cover changes to have an effect on P loads (as shown in [ 8 ]) and potentially P concentrations and recommend that these additional scenarios are explored in future research. The marginal mean TRP concentrations driven by the ensemble could mask seasonal variation, therefore, monthly mean TRP (µ, mg l − 1 ) predictions are shown for the Castledockrell catchment in Fig. 2 . The figure shows that the mean monthly TRP driven by the ensemble (grey dot-dashed lines, in both top and bottom plot) replicates the trends simulated by the BBN baseline (dark green, in both top and bottom plot), but there are considerable differences in mean TRP when looking at the concentrations driven by each climate model (ensemble member- driven TRP concentrations are shown in the bottom plot of Fig. 2 ). Future TRP concentrations for the Ballycanew (top plots) and Castledockrell (bottom plots) catchments are shown in Fig. 3 , and Fig. 4 shows the same for Timoleague (top plots) and Dunleer (bottom plots); both plots include the uncertainty around the mean in the form of error bars (µ ± 1 ơ). Simulated future TRP concentrations are plotted against the total monthly precipitation (mm) predicted by the different models (on the left-hand side) and against the observed and predicted TRP for the baseline period (2009–2016), as well as BBN predictions when using the ensemble. Figures 3 and 4 also better represent the full distribution of TRP, because, for each month and scenario, they include the 68% credible intervals (µ ± 1 ơ) calculated from ten-thousand simulated BBN realizations. In all catchments, the modelled extremes are wider than the observed ones due to the inherently wider distributions typical of the BBN approach [ 26 ], but are better constrained in Castledockrell and Timoleague than in Ballycanew and Dunleer [ 29 ]. In Ballycanew (Fig. 3 ) and Castledockrell (Figs. 2 and 3 ), the HadGEM2-ES driven BBN predicts higher TRP concentrations under future scenarios, likely due to lower predicted precipitation (Figs. 3 and 4 , left hand-side) and therefore discharge, and a subsequent reduction in dilution by HadGEM2-ES. This concurs with [ 9 ], whereby the change in future SRP concentrations depended on the choice of climate model. However, the HadGEM2-ES model also shows higher uncertainty, made evident by the wider intervals (µ ± 1 ơ) compared to the other models, shown in Figs. 3 and 4 . Except for some HadGEM2-ES model simulations, the predicted TRP concentrations remained at levels similar to those simulated during the baseline period in all catchments. Differences in climate-driven mean concentrations were negligible, especially when accounting for uncertainty by considering the upper and lower simulated concentrations (see for example, the differences between Figs. 2 and 3 in this paper, or the difference between Fig. 3 and Figure S2, Supplementary Information). No simulations showed increased TRP in the wintertime due to an increased magnitude of storms. An exception to these trends was found in Castledockrell, a groundwater-dominated catchment [ 3 ], with a higher mean TRP in August, September, and October for HadGEM2-ES RCP 8.5, irrespective of time period (Table S3 and Figure S2 in Supplementary). It should be noted that the uncertainty in the Ballycanew catchment was larger, due to a poorer fit of the BBN to the data in the reference period than in the other catchments [ 29 ]. Similarly, the uncertainty in the Timoleague and Dunleer catchments shows a larger variance in predicted stream TRP concentrations. The precipitation plots (Figs. 3 and 4 ) show differences and therefore large uncertainty between climate models, which could probably explain some of the uncertainty in TRP predictions. In Castledockrell, the least P-vulnerable catchment [ 4 , 52 ], the uncertainty in the observed and baseline TRP concentrations is smaller than the range of TRP concentrations predicted under the climate change scenarios. This is because the climate model ensemble performance, evaluated by Murphy et al. [ 6 ] with Nash-Sutcliffe Efficiency, NSE, during calibration (NSE cal 0.87) and validation (NSE val 0.83) of the SMART model was best in Castledockrell compared to the other three catchments. Further, the BBN specified for the Castledockrell catchment most closely represented the mean TRP concentration at the catchment outlet during the baseline period (Table 1 ), therefore, the predictions for this catchment are considered more robust than those for the other three. While all the BBNs achieved good performance in predicting the marginal posterior mean TRP concentrations across the four catchments during the baseline period (Table 1 ), the BBNs did not represent seasonal TRP concentrations well in Ballycanew and Dunleer, likely due to a lack of seasonality in P sources and discharge underestimation [ 26 , 29 ]. However, the ability to correctly reproduce seasonal variation in discharge - and therefore dilution - during ecological sensitive periods is important, for example, to determine algal bloom development and persistence [ 16 , 53 ], which is relevant to developing mitigation strategies under anticipated climate change impacts. The results outlined here are consistent with similar research conducted using process-based models [ 9 ] and Load Apportionment Models [ 7 ], whereby the effects of climate change alone may not be significant when evaluating annual mean P concentrations in rivers and streams, with land use changes having a bigger impact on P concentrations [ 9 ]. However, the effects of climate may become apparent elsewhere, for example in terms of total loads entering lakes, which will need to be reduced to achieve WFD standards [ 54 , 55 ]. Further, studies done at small-scales have highlighted enhanced phosphorus losses under increased precipitation frequency and intensity, with incidental losses from point sources playing an important role during summer low flows [ 11 , 56 ]. Meanwhile, at larger scales (> 50 km 2 ), the phosphorus response to climate change alone has been generally small [ 57 – 59 ]. Contrast between small-scale catchment studies and the findings reported here highlights the need to reconcile differences in catchment phosphorus dynamics, both observed and simulated, from small (10 km 2 ) to large (> 10 000 km 2 ) catchments and from minutes to decades - to better understand and quantify phosphorus loss in response to climate change. One of the advantages of using the Bayesian Network approach adopted in this study was that of representing the uncertainties associated with both data and models when modelling future TRP concentrations in the ACP catchments. Specifically, these included: the epistemic and data uncertainty represented by the catchment-specific BBNs, the accuracy of each catchment-specific BBN, the uncertainty of the climate models (represented by the ensemble) and of the climate-driven SMART model to derive the discharge. Furthermore, this approach allowed us to partially disentangle these uncertainties. An example of this is given in Fig. 5 , where TRP concentrations with 68% credible intervals (µ ± 1 ơ, mg l − 1 ) for an extreme scenario (a warmer month, September, under the more intensive RCP 8.5) are shown across the four catchments for the climate models vs the ensemble. This clearly shows the power of the modelling tool, with the distributions of the two best-performing BBNs (Castledockrell and Timoleague catchments, [ 29 ]) being more constrained than that of the other two (Ballycanew and Dunleer). Further, it is apparent from Fig. 5 that even when the uncertainty around the BBN’s predictive ability is decreased (as in Castledockrell), the HadGEM2-ES has a notable impact on TRP compared to the other four models, underlining the need for careful consideration when choosing ensemble members. By developing scenarios based on the individual climate models, we showed an example application whereby the networks (BBNs) were used as diagnostic tools: whilst the simulated means showed apparent significant changes in future TRP concentrations, plotting the uncertainty indicated that our present understanding and representation of P processes are not yet accurate enough to detect real change, except when the HadGEM2-ES drove the BBNs. The derived information can be used by modelers to inform future modelling decisions. 5 Conclusions and further research Downscaled climate-driven discharge (Q) time series up to the year 2099 were used as input to the catchment-specific Bayesian Belief Networks, to quantify future TRP concentrations in the four study catchments for the first time. The present study constitutes an advancement in Bayesian Network modelling of climate change impacts in that it used an ensemble comprised of five climate models to drive predictions of future water quality. The results driven by the ensemble showed no evident trends in stream TRP concentration in the four catchments, regardless of concentration pathway (RCP 4.5 vs RCP 8.5) and future time periods. This outcome is consistent with similar research conducted using process-based models in large catchments and suggests that the impacts of climate change alone might not be significant when evaluating TRP concentrations in rivers and streams; however, effects may become apparent elsewhere, for example in terms of total loads in standing waters. Given that the present study focusses on smaller catchments, there is a need to reconcile these findings with evidence from event-based studies in smaller catchments. The sensitivity analysis explained why the simulated changes in monthly Q driven by an ensemble of climate models are insufficient to drive stream TRP concentration changes in the studied catchments. As the ensemble-driven projected Q distributions were similar to those for the present day, no significant reductions in dilution were apparent in most simulations. Thus, the sensitivity analysis demonstrated that in-depth understanding of the model response is necessary to interpret the results of future scenario simulations. Further, due to their parsimonious nature, these BBNs are limited in the number of processes related to the P transfer continuum [ 60 ] that could be impacted by climate change, only representing runoff impacts on P transport. Designing scenarios where the discharge was driven by the individual climate models rather than the ensemble proved to be an effective tool into understanding the individual ensemble members, with the HadGEM2-ES model showing higher TRP concentrations than the other ensemble members under extreme scenarios. This also suggested that future research should focus on testing different climate ensemble sets. This study evaluated the hydrological effects of climate on future stream water phosphorus concentrations. Future research needs to integrate water quality models with socioeconomic and ecosystems responses to climate [ 61 ], and since networks such as BBNs facilitate the representation of relationships among climate factors and their interaction with local “subjective” knowledge [ 62 ], the present BBNs could be integrated with bespoke mitigation scenarios. Further, given the role of land use in driving future P concentrations and loads [ 58 , 63 , 64 ], investigating the combined effects of climate and land use changes in the ACP catchments will give insight into the controls of future TRP changes in these catchments, and these BBNs are particularly suited to integrate land use change scenarios co-constructed with stakeholders. Declarations Conflict of interest The Authors declare no conflict of interest. Consent to Publish : not applicable. Consent to Participate : not applicable. Ethics Declaration not applicable. Authors contribution Camilla Negri : Conceptualization, Methodology, Formal analysis, Data Curation, Writing - Original Draft, Visualization, Writing - Review & Editing. Elizabeth Cowdery : Methodology. Nicholas J. Schurch : Conceptualization, Methodology, Writing - Review & Editing, Supervision. Andrew: J. Wade : Conceptualization, Methodology, Funding acquisition, Writing - Review & Editing, Supervision. Per-Erik Mellander : Conceptualization, Funding acquisition, Data Curation, Writing - Review & Editing, Supervision. Miriam Glendell : Conceptualization, Funding acquisition, Methodology, Writing - Review & Editing, Resources, Project Administration, Supervision. Acknowledgments: We acknowledge the Teagasc Walsh Fellowship Programme for providing the funding (Reference Number Teagasc). We wish to thank the team at BayesFusion ( https://www.bayesfusion.com/ ) for providing us with the necessary academic licensing and software support. Data availability The reader is referred to the Murphy et al., (2023) [ 6 ] data availability statement. Code availability The models used in this research paper have been published on GitHub ( https://github.com/CamillaNegri/Transferability_Ptool ) and in Negri et al., (2024) [ 29 ]. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5165980","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":368863578,"identity":"614cda5a-c6a6-4100-9117-f28766f17d9e","order_by":0,"name":"Camilla Negri","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEElEQVRIiWNgGAWjYPACCTkYi7ENLkZAizHJWhgSG2BaYAycWvgbeA8+/LrHIn07/9oHzBUVdrJ90u0XGH7UMCTObMCuReIAX7KxzDOJ3J0znhswnjmTbNwmc6aAsecYQ+JsHLYYMPCYSUsckMjdcOMYA2NjG3Nim0ROAgNvA0PiPNxazH8DtaQbgLX8qwdrYfyLX4sZ44cDEgkG59uAWhoOA7WkH2AG2YLLYRKHeYylGQ5IGO6cwcZwsOHYcWOgLQyHZY5JGOPyPn97j+HHHwfq5M35jzE+bKiplp0/I/3hwzc1NrIzDuCwhhmIeEAulEhggKrhMThAKCIZf4C08MMNZX+AV/koGAWjYBSMOAAAfhpX0zhhCX8AAAAASUVORK5CYII=","orcid":"","institution":"University of Reading","correspondingAuthor":true,"prefix":"","firstName":"Camilla","middleName":"","lastName":"Negri","suffix":""},{"id":368863579,"identity":"32c1dd5c-76b0-457c-b07c-302d7e4f4270","order_by":1,"name":"Elizabeth Cowdery","email":"","orcid":"","institution":"James Hutton Institute","correspondingAuthor":false,"prefix":"","firstName":"Elizabeth","middleName":"","lastName":"Cowdery","suffix":""},{"id":368863580,"identity":"45387d85-dd11-4d7e-a627-20b4ccfe0575","order_by":2,"name":"Nicholas Schurch","email":"","orcid":"","institution":"Biomathematics and Statistics Scotland","correspondingAuthor":false,"prefix":"","firstName":"Nicholas","middleName":"","lastName":"Schurch","suffix":""},{"id":368863581,"identity":"9bb45d2f-db60-4056-a05e-e08193587860","order_by":3,"name":"Andrew J. 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This flow chart shows the sequential steps described in section 3.3 of this paper. The steps are shown in context with the previous research that was used as input for this study [6,34].\u003c/p\u003e","description":"","filename":"f1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5165980/v2/1cb9d8bb3517ba0a5edf1dac.jpg"},{"id":88046036,"identity":"0cb1db6c-6b82-49ba-8693-0bbdbe00fa9d","added_by":"auto","created_at":"2025-07-31 18:21:09","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":112620,"visible":true,"origin":"","legend":"\u003cp\u003eMonthly mean TRP concentrations under future climate for the Castledockrell catchment. Predicted monthly mean TRP concentrations (mg l\u003csup\u003e-1\u003c/sup\u003e) driven by the ensemble of climate models are shown alone in dot-dashed grey in the top plots, while the bottom plots show TRP concentration driven by both the ensemble and the ensemble members. Observations (2009-2016) are shown in dark green dashed lines and the TRP predicted by the BBN baseline is shown in black. All concentrations were log-transformed before calculating the mean, and then converted back to linear space (geometric mean). Results are shown for the NSE calibration of the SMART model only. Fig. S2 of Supplementary Information shows the same as the bottom panel, but includes the other three catchments as well.\u0026nbsp;\u003c/p\u003e","description":"","filename":"f2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5165980/v2/4619b52a01f7f41815840b0d.jpg"},{"id":88046043,"identity":"c17d56cf-61e5-4dd2-a466-82cb0f4a8497","added_by":"auto","created_at":"2025-07-31 18:21:09","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":136719,"visible":true,"origin":"","legend":"\u003cp\u003eMean monthly predicted precipitation (left-hand side) in Ballycanew (top left) and Castledockrell (bottom left) driven by five climate models and the ensemble. The predicted and observed TRP monthly means (mg l\u003csup\u003e-1\u003c/sup\u003e) with the 68% credible interval (µ ± 1 ơ) are shown on the right-hand side to demonstrate the full range of uncertainty in the predictions and observations. Predicted TRP concentrations were log-transformed before calculating the statistics, and then converted back then converted back to linear space (geometric mean). Results are shown for the NSE calibration of the SMART model only.\u003c/p\u003e","description":"","filename":"f3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5165980/v2/c665b179bc1f4f1ae999cabf.jpg"},{"id":88046047,"identity":"4ba3f5b2-5787-411e-ba7f-3cf74cb9a30d","added_by":"auto","created_at":"2025-07-31 18:21:09","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":137837,"visible":true,"origin":"","legend":"\u003cp\u003eMean monthly predicted precipitation (left-hand side) in Timoleague (top left) and Dunleer (bottom left) driven by five climate models and the ensemble. The predicted and observed TRP monthly means (mg l\u003csup\u003e-1\u003c/sup\u003e) with the 68% credible interval (µ ± 1 ơ) are shown on the right-hand side to demonstrate the full range of uncertainty in the predictions and observations. Predicted TRP concentrations were log-transformed before calculating the statistics, and then converted back to linear space (geometric mean). Results are shown for the NSE calibration of the SMART model only.\u003c/p\u003e","description":"","filename":"f4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5165980/v2/f671b0cc2ed359fd8c4c9550.jpg"},{"id":88046042,"identity":"be25a23c-8109-4ecc-8504-82c2d8284616","added_by":"auto","created_at":"2025-07-31 18:21:09","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":81953,"visible":true,"origin":"","legend":"\u003cp\u003eTRP concentrations (mg l\u003csup\u003e-1\u003c/sup\u003e) in the month of September under RCP 8.5 across the four catchments and three time periods as predicted by the BBN using both the individual climate models and the ensemble are shown as 68% credible intervals (µ ± 1 ơ). Predicted TRP concentrations were log-transformed before calculating the statistics, and then converted back to linear space (geometric mean). Results are shown for the NSE calibration of the SMART model only.\u003c/p\u003e","description":"","filename":"f5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5165980/v2/dc53820e6ba70b998b8893c5.jpg"},{"id":89096746,"identity":"ea9a18e9-b80f-4921-b9cd-ea6e6691b14f","added_by":"auto","created_at":"2025-08-14 15:36:56","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1688984,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5165980/v2/7fd29298-0758-4a78-a7e1-208190ba162c.pdf"},{"id":88046039,"identity":"a49ef570-bcbd-459b-a46c-7e368e28f836","added_by":"auto","created_at":"2025-07-31 18:21:09","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":687137,"visible":true,"origin":"","legend":"\u003cp\u003eSupplementary Information\u003c/p\u003e","description":"","filename":"SupplementaryInformationrevised.docx","url":"https://assets-eu.researchsquare.com/files/rs-5165980/v2/bc22f671c0a0a1015c1c932b.docx"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"An assessment of climate change impacts on stream phosphorus using a climate model ensemble and Bayesian Belief Networks","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003ePhosphorus (P) over-enrichment from intensive farming in Ireland has led to freshwater eutrophication and harmful algal blooms (HAB) [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. P losses in rural catchments are complex, resultant from multiple sources, including manure and mineral fertilizer applications and effluent discharges, and multiple flow-pathways such as overland flow, farm drains, and groundwater flow; all of which vary with location [\u003cspan additionalcitationids=\"CR3\" citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Phosphorus bound to soil and stream sediment, known as legacy P, can also be later released, further confounding P reduction efforts. For these reasons, whilst reducing P losses from land to water is expected to reduce freshwater eutrophication overall, determining the focus and priorities for effective policy and catchment management to achieve such reductions is difficult.\u003c/p\u003e\u003cp\u003eClimate change further complicates this management challenge [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e], with projections for Ireland suggesting increased winter, and reduced summer, precipitation [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Against this backdrop, P models have been applied to quantify P sources, transport, in-stream concentrations and loads to identify appropriate management strategies to continue recent progress in the reduction of stream water P concentrations and loads [\u003cspan additionalcitationids=\"CR8\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Increased and more intense winter storms have been shown to result in greater mobilisation and delivery of P loads to surface waters in small UK river catchments, whilst summer reductions in precipitation were shown to reduce the dilution of point source and groundwater inputs [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. While studies have shown increased P loads from agricultural diffuse sources under climate change [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], water quality standards for freshwaters are typically specified as annual concentrations, for example, under the European Water Framework Directive [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Given this background, determining the effect of climate change on the distribution of P concentrations remains important to understand future eutrophication risk and to design mitigation measures [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eCatchment area, inputs from diffuse and point sources and land use are important factors that determine how stream water P concentrations will respond to future climate change and must be accounted for when modelling P under climate change [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Furthermore, the associated changes in chlorophyll-a concentrations, a measure of algal production in response to stream water phosphate alterations, are complex, with growing evidence that stream water residence-time, prevailing light conditions and nitrogen are equally, if not more, important than P concentrations or loadings as controls of algal bloom initiation and development [\u003cspan additionalcitationids=\"CR16\" citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. However, inadequate data resolution to describe flow and phosphorus dynamics, particularly under extreme high and low flow conditions, and the lack of uncertainty analysis in model applications have been cited as current limitations when simulating these future changes in P concentrations and loadings [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. While the lack of suitable data means that the testing of the assumptions to construct P models is limited, representing uncertainty is critical to help decision-makers assess models and make informed decisions about water quality management [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eBayesian Belief Networks (BBNs) are probabilistic graphical models that can help to bridge uncertainty knowledge gaps as they provide robust quantitative uncertainty estimates, including epistemic and aleatoric uncertainty [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], and can facilitate the identification of uncertainty sources within the model [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Given that incorporating both uncertainty and stakeholder knowledge in water quality research is becoming increasingly relevant [\u003cspan additionalcitationids=\"CR24\" citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], BBNs are an alternative to the widely-used process-informed catchment P models such as HYPE, SWAT, and INCA-P, and are advantageous because they incorporate P sources, processes, and delivery pathways, as well as the socio-economic aspects, in a way that is interpretable and accessible to wider audiences [\u003cspan additionalcitationids=\"CR27\" citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. Furthermore, uncertainty estimation is also inherent to BBNs, through the specification of prior probability distributions, equations or conditional probabilities (CPTs) describing P processes and transport pathways, based on either measurements, expert and stakeholder elicitation, or literature.\u003c/p\u003e\u003cp\u003eTaking these issues into consideration, new catchment-specific BBNs have been developed and applied in four Irish catchments representative of contrasting land cover and hydrological regimes [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. The networks performed well when simulating total reactive P concentrations (TRP) [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Here, we take the science further and present the application of these BBNs to simulate future phosphorus losses in these four catchments under climate change scenarios, using an ensemble approach for the first time. All four catchments have extensive datasets of discharge (Q), in-stream TRP concentrations, and turbidity measured sub-hourly since 2009. These stream water measurements are supplemented by 400 to 500 soil P test measurements, described in detail elsewhere [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. These data have been combined previously to construct and test catchment-specific BBNs which incorporate septic tank inputs, in-stream P processes, and groundwater pathways [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. The aim of this study was to quantify stream TRP concentrations under future projections of climate change. To achieve this overall aim, we followed three research objectives:\u003c/p\u003e\u003cp\u003e\u003col\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eTo evaluate the sensitivity of the BBN outputs to changes in flow inputs as a precursor to help interpret and understand the model sensitivity to climate change effects.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eTo use projected future flows as input to the previously developed BBN models to determine TRP concentrations based on flow simulations from five climate models and their ensemble, two RCPs (4.5 and 8.5) and present day (2020s), near (2040s) and far future (2080s) time periods.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eTo use the sensitivity analysis results to interpret the simulated response of future TRP concentrations in the BBN models to altered flow and the relative importance of flow as a driver of future change.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e"},{"header":"2 Study Areas","content":"\u003cp\u003eThis study focusses on four agricultural catchments located in the Republic of Ireland. These have contrasting agricultural land use and hydrology and have been described in more detail elsewhere [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. The catchments included are Ballycanew (1191 ha, poorly-drained, 78% grassland) and Castledockrell (1117 ha, well-drained, 54% tillage) in County Wexford, Timoleague (758 ha, well-drained, 85% grassland) in County Cork, and Dunleer (948 ha, moderately-drained, 33% tillage) in County Louth. Point P sources include rural septic tanks, and a single wastewater treatment plant in the Castledockrell catchment. The catchments have been monitored since 2009 by the Agricultural Catchments Programme (ACP) to oversee the environmental and economic effectiveness of the Programme of Measures and derogation under the Nitrates Direction National Action Programmes (NAPs) of the European Union [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. Specifically, the monitoring included high-frequency (sub-hourly) measurements of hydro-chemo-metrics at the catchment outlet such as discharge (Q, m\u003csup\u003e3\u003c/sup\u003e), turbidity (NTU), and total reactive P (TRP, mg l\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) concentrations aggregated at the daily time step [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] and field-scale soil sampling including agronomic soil P [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eMurphy et al., [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] have simulated future flows under climate change scenarios in twenty-six Irish catchments, including those in this study, by using the Irish Centre for High-End Computing (ICHEC) ensemble [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e] to drive the Soil Moisture Accounting and Routing for Transport (SMART) hydrological model [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. Annual mean flows were projected to increase across Irish catchments under RCP 8.5 (a fossil fuel-intensive emissions pathway), and the largest increase was expected in Castledockrell by the 2080s (23.8%) [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Under RCP 8.5 in the 2080s, Timoleague, Ballycanew, and Castledockrell showed increased winter mean flow (\u0026gt;\u0026thinsp;30%). Large summer flow decreases were predicted for Ballycanew and Dunleer (up to -50%) and, in the Castledockrell catchment, a 114% increase in autumn mean flow occurred under the RCP 8.5 scenario [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Changes to the mean seasonal and annual flows were also found under RCP 4.5 (an intermediate pathway with emissions peaking around the year 2040), albeit less marked. In Murphy et al., [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], small catchments such as those considered here (with areas of 7\u0026ndash;12 km\u003csup\u003e2\u003c/sup\u003e) showed the widest flow changes, especially in the summer, compared to larger catchments (48-2460 km\u003csup\u003e2\u003c/sup\u003e). Therefore, these catchments are to be considered vulnerable to climate-induced changes.\u003c/p\u003e"},{"header":"3 Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e3.1 Bayesian Belief Network development\u003c/h2\u003e\u003cp\u003eThe hybrid BBNs (comprised of both discrete and continuous variables) used in this study were developed in the software GeNIe, version 2.4 [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e] for the four catchments [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. The development and testing of the BBNs are described in detail elsewhere [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. In short, a BBN was developed to simulate monthly P losses at the outlet of a surface flow-dominated Irish grassland catchment, including point P sources such as farmyards and septic tanks. This BBN was adapted for application in three further catchments by including groundwater P concentrations and in-stream P cycling by both biotic and abiotic processes, on the basis of high-frequency piezometer P data and expert elicitation. The four BBNs quantify the monthly in-stream TRP concentration at the catchment outlet by integrating the P loads from different compartments (soils, sediments, septic tanks, farmyards, groundwater, and a wastewater treatment plant) and then converting the loads into concentrations by dividing by the monthly discharge. Catchment-specific datasets were used wherever possible, including the quantification of the different discharge (Q) components, namely quick-flow, interflow, and baseflow [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. The finalized BBNs achieved good performance in all four catchments in terms of percentage bias (-5% \u0026le; PBIAS\u0026thinsp;\u0026le;\u0026thinsp;49%) when compared to the observed TRP concentrations (2009\u0026ndash;2016) [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. The BBNs reproduced the observed mean monthly TRP concentration relatively well in Castledockrell and Timoleague, though less accurately in Ballycanew and Dunleer, where the model predicted the mean concentration better in winter than in summer; however, model performance was still sufficiently good to warrant further application to explore the response of discharge and TRP concentration to climate change projections. A summary of the BBNs\u0026rsquo; performance is given in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, whilst further detail, including the monthly performance, is reported in [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e].\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eSummary performance of the BBNs developed in [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] for the four agricultural catchments, including 68%, 94% credible intervals, and percentage bias (PBIAS, %), alongside with the observed 68% (\u0026micro;\u0026thinsp;\u0026plusmn;\u0026thinsp;1 ơ) and 95% (\u0026micro;\u0026thinsp;\u0026plusmn;\u0026thinsp;2 ơ) confidence interval. Both observed and predicted TRP concentrations were log-transformed before calculating the intervals, and then converted back to linear space (geometric mean). The marginal distribution mean can reproduce the observed mean TRP concentration in the reference period (2009\u0026ndash;2016).\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePBIAS\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003eTRP\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003eTRP\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e%\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003emg l\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003emg l\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003epredicted marginal\u003c/p\u003e\u003cp\u003e(68% credible interval)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eobserved mean (68% confidence interval)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003epredicted marginal\u003c/p\u003e\u003cp\u003e(95% credible interval)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eobserved mean (95% confidence interval)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eTIMOLEAGUE\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{0.05}_{0.08}^{0.03}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{0.05}_{0.09}^{0.03}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{0.05}_{0.12}^{0.02}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{0.05}_{0.16}^{0.01}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eBALLYCANEW\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e49\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{0.07}_{0.17}^{0.03}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{0.06}_{0.11}^{0.06}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{0.07}_{0.41}^{0.02}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{0.06}_{0.19}^{0.02}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eCASTLEDOCKRELL\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e18\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{0.02}_{0.05}^{0.01}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{0.02}_{0.04}^{0.01}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{0.02}_{0.09}^{0.00}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{0.02}_{0.07}^{0.00}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eDUNLEER\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e45\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{0.09}_{0.28}^{0.03}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{0.10}_{0.16}^{0.06}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{0.09}_{0.85}^{0.00}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{0.10}_{0.27}^{0.03}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Sensitivity to discharge\u003c/h2\u003e\u003cp\u003eTo help interpret the results, a sensitivity analysis was done on the model parameters for discharge (Q) by adapting the code developed in \u003cem\u003erSMILE\u003c/em\u003e 2.0.1 by Negri et al., [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], using \u003cem\u003erSMILE\u003c/em\u003e version 2.2.1. \u003cem\u003erSMILE\u003c/em\u003e is an API engine available in R which can perform the same operations as GeNIe Modeler [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e], the software used to develop the BBN model structures used in this study. The \u0026ldquo;Mean total monthly Q (discharge) [m\u003csup\u003e3\u003c/sup\u003e]\u0026rdquo; was defined as a series of monthly Lognormal (\u0026micro;, ơ) distributions. For each catchment, we tested varying the mean (9\u0026thinsp;\u0026le;\u0026thinsp;\u0026micro;\u0026thinsp;\u0026le;\u0026thinsp;17) and standard deviation (0.1 \u0026le; ơ \u0026le; 1) of the Lognormal discharge on the median log\u003csub\u003e10\u003c/sub\u003e(TRP) posterior concentration (mg l\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) by applying a stepwise variation on the mean (increments of 1) and on the standard deviation (0.1 increments). This variation in the log space is equivalent to varying the mean total discharge between 8000 and 2.4*10\u003csup\u003e7\u003c/sup\u003e m\u003csup\u003e3\u003c/sup\u003e month\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e3.3 Climate Scenarios and their implementation in the BBN\u003c/h2\u003e\u003cp\u003eNolan and Flanagan [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e], developed high-resolution climate scenarios for Ireland by downscaling the outputs of five Global Climate Models: CNRM-CM5 [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e], EC-Earth [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e], HadGEM2-ES [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e], MIROC5 [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e], and MPI-ES-LR [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e]. Future climate was simulated under Representative Concentration Pathway 2.6, 4.5, 6.0, and 8.5, of which RCP 4.5 and 8.5 are included in this study to represent an intermediate (RCP 4.5) and an extreme scenario (RCP 8.5). Murphy et al., [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], used these climate scenarios to drive the SMART hydrological model, calibrated independently with both the Nash-Sutcliffe Efficiency (NSE) and the log Nash-Sutcliffe Efficiency (log NSE) as objective functions. These simulated river flows (discharge, Q) up to the year 2100 obtained through the SMART model [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] are used in the present study. The available daily discharge (Q, mm) timeseries were summed into total monthly Q (m\u003csup\u003e3\u003c/sup\u003e) for each climate model, concentration pathway, and reference period. A bootstrapping procedure was implemented to fit a Lognormal distribution to the monthly Q using the R package \u003cem\u003efitdistrplus\u003c/em\u003e [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e]. The monthly lognormal parameters (mean, \u0026micro;, standard deviation, ơ) per each scenario were then used to specify the distributions for the BBN node \u0026ldquo;Mean total monthly Q (discharge) [m\u003csup\u003e3\u003c/sup\u003e]\u0026rdquo; using the same procedure used to parametrize the BBN baseline in [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. A scenario for the ensemble was also included, whereby monthly discharge was averaged between the five climate models prior to distribution fitting. This was done because of the recommendation to use a multi-model ensemble approach to address model formulation and climate variability-related uncertainties when using the dataset [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. The combination of two emission pathways, three reference periods: the 2020s (2010\u0026ndash;2039), the 2050s (2040\u0026ndash;2069), and the 2080s (2070\u0026ndash;2099), six model outputs (five models plus the ensemble), and two calibration functions gave seventy-two scenarios of monthly discharge per catchment. These were used as input to the catchment-specific BBNs to simulate monthly TRP concentrations at the catchment outlet. The posterior probability for the target node \u0026ldquo;In-stream P concentration [mg l\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e]\u0026rdquo; was simulated using \u003cem\u003erSMILE\u003c/em\u003e version 2.2.1 [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. To visually inspect the results, mean monthly TRP concentrations and 68% credible intervals (\u0026micro;\u0026thinsp;\u0026plusmn;\u0026thinsp;1 ơ, mg l\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) derived from the posterior TRP distribution for each scenario were plotted alongside mean total precipitation (\u0026micro; \u0026plusmn; ơ, mm), observed TRP (\u0026micro; \u0026plusmn; ơ, mg l\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) as well as the same credible interval predicted by the BBN in baseline period (2009\u0026ndash;2016) [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. A schematic of this workflow in context with the work of Nolan and Flanagan, [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e] and Murphy et al., [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"4 Results and Discussion","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e4.1 Sensitivity to discharge\u003c/h2\u003e\u003cp\u003eThe sensitivity analysis showed that the BBNs developed for the four catchments are sensitive to a variation in the monthly mean discharge. Specifically, the model was significantly sensitive to variations in mean (\u0026micro;) of the Lognormal discharge in the range 9\u0026thinsp;\u0026le;\u0026thinsp;\u0026micro;\u0026thinsp;\u0026le;\u0026thinsp;12 (these are specified in the log\u003csub\u003ee\u003c/sub\u003e scale in the BBNs), which is equivalent to a variation between 8000 and 1.6*10\u003csup\u003e5\u003c/sup\u003e m\u003csup\u003e3\u003c/sup\u003e month\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, beyond which (Lognormal \u0026micro;\u0026thinsp;\u0026ge;\u0026thinsp;12) median log\u003csub\u003e10\u003c/sub\u003e(TRP) concentrations (mg l\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) tended to an asymptote (e.g., 0.02 mg l\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e in Castledockrell, shown in Figure S1 in the log scale). Variations in discharge standard deviation (ơ: 0.1-1) had a negligible impact, indicating that mean flow \u0026ndash; not its variability \u0026ndash; drives the monthly median TRP response under climate change in these BBNs. The Supplementary Information contains the validation figures for this analysis (Figure S1).\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003e68% credible interval (\u0026micro;\u0026thinsp;\u0026plusmn;\u0026thinsp;1 ơ) of the ensemble discharge prior (total monthly Q, m\u003csup\u003e3\u003c/sup\u003e) in the month of January across the two climate scenarios (RCP 4.5 and RCP 8.5) against the same for the BBN baseline [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] for each of the four catchments. Here, only results derived from the NSE calibration driving the SMART model are shown. Monthly discharge is represented in the model with a Lognormal(\u0026micro;, ơ) distribution (base e).\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"10\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"10\" nameend=\"c10\" namest=\"c1\"\u003e\u003cp\u003eTimoleague\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eRCP 4.5\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e\u003cp\u003e\u003cb\u003eRCP 8.5\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e\u003cp\u003e\u003cb\u003eBBN baseline\u003c/b\u003e [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;-ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;+ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;-ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;+ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;-ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;+ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"9\" nameend=\"c10\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003em\u003c/b\u003e\u003csup\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sup\u003e\u003cb\u003e*10\u003c/b\u003e\u003csup\u003e\u003cb\u003e6\u003c/b\u003e\u003c/sup\u003e\u003cb\u003emonth\u003c/b\u003e\u003csup\u003e\u003cb\u003e\u0026minus;1\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003e2009\u0026ndash;2016\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.89\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.98\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.09\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003e2010\u0026ndash;2039\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.81\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.84\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.75\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.78\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.81\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003e2040\u0026ndash;2069\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.85\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.89\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.85\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003e2070\u0026ndash;2099\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.89\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.98\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.02\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"10\" nameend=\"c10\" namest=\"c1\"\u003e\u003cp\u003e\u003cb\u003eBallycanew\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eRCP 4.5\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e\u003cp\u003e\u003cb\u003eRCP 8.5\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e\u003cp\u003e\u003cb\u003eBBN baseline\u003c/b\u003e [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;-ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;+ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;-ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;+ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;-ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;+ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"9\" nameend=\"c10\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003em\u003c/b\u003e\u003csup\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sup\u003e\u003cb\u003e*10\u003c/b\u003e\u003csup\u003e\u003cb\u003e6\u003c/b\u003e\u003c/sup\u003e\u003cb\u003emonth\u003c/b\u003e\u003csup\u003e\u003cb\u003e\u0026minus;1\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003e2009\u0026ndash;2016\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.83\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.98\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.17\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003e2010\u0026ndash;2039\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.84\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.89\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.85\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003e2040\u0026ndash;2069\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.01\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.87\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003e2070\u0026ndash;2099\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.04\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.03\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.20\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"10\" nameend=\"c10\" namest=\"c1\"\u003e\u003cp\u003e\u003cb\u003eCastledockrell\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eRCP 4.5\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e\u003cp\u003e\u003cb\u003eRCP 8.5\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e\u003cp\u003e\u003cb\u003eBBN baseline\u003c/b\u003e [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;-ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;+ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;-ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;+ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;-ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;+ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"9\" nameend=\"c10\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003em\u003c/b\u003e\u003csup\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sup\u003e\u003cb\u003e*10\u003c/b\u003e\u003csup\u003e\u003cb\u003e6\u003c/b\u003e\u003c/sup\u003e\u003cb\u003emonth\u003c/b\u003e\u003csup\u003e\u003cb\u003e\u0026minus;1\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003e2009\u0026ndash;2016\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e1.09\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.21\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003e2010\u0026ndash;2039\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.61\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.63\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.66\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.63\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.65\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003e2040\u0026ndash;2069\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.63\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.66\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.69\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.66\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.69\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.02\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003e2070\u0026ndash;2099\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.67\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.70\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.73\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.76\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.79\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.82\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"10\" nameend=\"c10\" namest=\"c1\"\u003e\u003cp\u003e\u003cb\u003eDunleer\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003eRCP 4.5\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e\u003cp\u003e\u003cb\u003eRCP 8.5\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e\u003cp\u003e\u003cb\u003eBBN baseline\u003c/b\u003e [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;-ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;+ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;-ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;+ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;-ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e\u003cb\u003e\u0026micro;+ơ\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"9\" nameend=\"c10\" namest=\"c2\"\u003e\u003cp\u003e\u003cb\u003em\u003c/b\u003e\u003csup\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sup\u003e\u003cb\u003e*10\u003c/b\u003e\u003csup\u003e\u003cb\u003e6\u003c/b\u003e\u003c/sup\u003e\u003cb\u003emonth\u003c/b\u003e\u003csup\u003e\u003cb\u003e\u0026minus;1\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003e2009\u0026ndash;2016\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.66\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.73\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003e2010\u0026ndash;2039\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.71\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.75\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.79\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.71\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.74\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.78\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003e2040\u0026ndash;2069\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.73\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.77\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.81\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.76\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.81\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.85\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003e2070\u0026ndash;2099\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.78\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.83\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.84\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.89\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.95\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eA comparison of the discharge (Q) for the month of January between the model ensemble scenarios (NSE calibration only) and the BBN baseline [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] is shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Here, all Lognormal Q distributions have a mean of 13.36\u0026thinsp;\u0026le;\u0026thinsp;\u0026micro;\u0026thinsp;\u0026le;\u0026thinsp;13.92, and a standard deviation of 0.04 \u0026le; ơ \u0026le; 0.17, a range for which the model is insensitive (Figure S1). The ensemble-driven total monthly discharge in the scenarios was comparable to that in the BBN baseline (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Further, the ensemble underestimates the discharge in in Timoleague and Castledockrell in the 2020s. The BBNs showed sensitivity only to mean (\u0026micro;) Lognormal discharge in the range 9\u0026thinsp;\u0026le;\u0026thinsp;\u0026micro;\u0026thinsp;\u0026le;\u0026thinsp;12 also when testing for a drier month (e.g., August, data not shown), which would indicate that the sensitivity is the same across the months. However, there were some differences when looking at discharge driven by the individual ensemble members rather than their mean. For example, the HadGEM2-ES model predicts total monthly Q in ranges that the BBN is sensitive to (Lognormal \u0026micro;\u0026thinsp;\u0026le;\u0026thinsp;12), especially in the warmer months (Table S1 shows this for the Timoleague catchment). The analysis suggests low sensitivity of the target node (TRP concentrations at the catchment outlet) to parents (discharge, Q) distant from the target node. In these BBNs, discharge is used to calculate both the concentrations at the catchment outlet and the loads from different model compartments, therefore it\u0026rsquo;s considered to be distant from the target node because there is an increased number of variables between input (parent nodes) and output (target child node). This supports the finding that increased model complexity weakens the relationship between input and output [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e].\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e4.2 Phosphorus concentrations under future climate\u003c/h2\u003e\u003cp\u003eEach catchment BBN predicts the marginal TRP concentration probability distribution (the posterior distribution without setting any evidence) using the model ensemble across the three reference periods: the 2020s (2010\u0026ndash;2039), the 2050s (2040\u0026ndash;2069), and the 2080s (2070\u0026ndash;2099). We compared the marginal posterior distribution to the Environmental Quality Standard (EQS) of 0.035 mg l\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. This comparison showed that the ensemble-driven BBNs do not predict EQS exceedance marginal probabilities that differ from the baseline, although admittedly these models are not recommended for such purpose, but rather perform better when looking at the full posterior distributions, due to the predicted posterior distributions being wider and more skewed than those observed [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Marginal probabilities of exceeding the Environmental Quality Standard (EQS) of 0.035 mg l\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] under the ensemble are shown in Table S2 of the Supplementary Information. Furthermore, the means of the marginal TRP distributions show no clear differences against the observed reference period (2009\u0026ndash;2016), no obvious trend over time, nor differences when using the two different SMART model calibrations (log NSE vs NSE) (shown Table S3, Supplementary Information, as log\u003csub\u003e10\u003c/sub\u003e(TRP)). This agrees with previously conducted research which demonstrated that climate change alone has a small effect on mean phosphate concentrations in north-west Europe in larger (50\u0026ndash;12 000 km\u003csup\u003e2\u003c/sup\u003e) catchments [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Additionally, here we applied a model ensemble consisting of the mean discharge simulated by five climate models which progresses previous works using a single climate scenario in a BBN [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e]. The response of the BBNs under climate change showed TRP concentrations similar to those shown in the baseline when using the model ensemble were explained by the low sensitivity of the BBNs to discharge, and the fact that the ensemble-driven mean discharge simulations are within the model insensitivity range in most cases. These parsimonious BBNs only represent changes in runoff as the key process impacting P transport under future climate, disregarding other processes that may have an effect, such as soil temperature changes affecting P dynamics [\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e], changes in rainfall intensity that will impact P mobilization and consequently dissolved P losses [\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e], and P source change due to land use alteration [\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e]. However, some of these processes might be negligible (i.e., temperature) compared to precipitation and runoff [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e], or are outside the scope of the present research. This could also explain why the marginal mean TRP was not affected under future climate. We would expect changes in P sources due to future land use and/ or land cover changes to have an effect on P loads (as shown in [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]) and potentially P concentrations and recommend that these additional scenarios are explored in future research.\u003c/p\u003e\u003cp\u003eThe marginal mean TRP concentrations driven by the ensemble could mask seasonal variation, therefore, monthly mean TRP (\u0026micro;, mg l\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) predictions are shown for the Castledockrell catchment in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The figure shows that the mean monthly TRP driven by the ensemble (grey dot-dashed lines, in both top and bottom plot) replicates the trends simulated by the BBN baseline (dark green, in both top and bottom plot), but there are considerable differences in mean TRP when looking at the concentrations driven by each climate model (ensemble member- driven TRP concentrations are shown in the bottom plot of Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFuture TRP concentrations for the Ballycanew (top plots) and Castledockrell (bottom plots) catchments are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, and Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the same for Timoleague (top plots) and Dunleer (bottom plots); both plots include the uncertainty around the mean in the form of error bars (\u0026micro;\u0026thinsp;\u0026plusmn;\u0026thinsp;1 ơ). Simulated future TRP concentrations are plotted against the total monthly precipitation (mm) predicted by the different models (on the left-hand side) and against the observed and predicted TRP for the baseline period (2009\u0026ndash;2016), as well as BBN predictions when using the ensemble. Figures\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e also better represent the full distribution of TRP, because, for each month and scenario, they include the 68% credible intervals (\u0026micro;\u0026thinsp;\u0026plusmn;\u0026thinsp;1 ơ) calculated from ten-thousand simulated BBN realizations. In all catchments, the modelled extremes are wider than the observed ones due to the inherently wider distributions typical of the BBN approach [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], but are better constrained in Castledockrell and Timoleague than in Ballycanew and Dunleer [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. In Ballycanew (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) and Castledockrell (Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), the HadGEM2-ES driven BBN predicts higher TRP concentrations under future scenarios, likely due to lower predicted precipitation (Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, left hand-side) and therefore discharge, and a subsequent reduction in dilution by HadGEM2-ES. This concurs with [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], whereby the change in future SRP concentrations depended on the choice of climate model. However, the HadGEM2-ES model also shows higher uncertainty, made evident by the wider intervals (\u0026micro;\u0026thinsp;\u0026plusmn;\u0026thinsp;1 ơ) compared to the other models, shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eExcept for some HadGEM2-ES model simulations, the predicted TRP concentrations remained at levels similar to those simulated during the baseline period in all catchments. Differences in climate-driven mean concentrations were negligible, especially when accounting for uncertainty by considering the upper and lower simulated concentrations (see for example, the differences between Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e in this paper, or the difference between Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and Figure S2, Supplementary Information). No simulations showed increased TRP in the wintertime due to an increased magnitude of storms. An exception to these trends was found in Castledockrell, a groundwater-dominated catchment [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], with a higher mean TRP in August, September, and October for HadGEM2-ES RCP 8.5, irrespective of time period (Table S3 and Figure S2 in Supplementary). It should be noted that the uncertainty in the Ballycanew catchment was larger, due to a poorer fit of the BBN to the data in the reference period than in the other catchments [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Similarly, the uncertainty in the Timoleague and Dunleer catchments shows a larger variance in predicted stream TRP concentrations. The precipitation plots (Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) show differences and therefore large uncertainty between climate models, which could probably explain some of the uncertainty in TRP predictions. In Castledockrell, the least P-vulnerable catchment [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e], the uncertainty in the observed and baseline TRP concentrations is smaller than the range of TRP concentrations predicted under the climate change scenarios. This is because the climate model ensemble performance, evaluated by Murphy et al. [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] with Nash-Sutcliffe Efficiency, NSE, during calibration (NSE\u003csub\u003ecal\u003c/sub\u003e 0.87) and validation (NSE\u003csub\u003eval\u003c/sub\u003e 0.83) of the SMART model was best in Castledockrell compared to the other three catchments. Further, the BBN specified for the Castledockrell catchment most closely represented the mean TRP concentration at the catchment outlet during the baseline period (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), therefore, the predictions for this catchment are considered more robust than those for the other three.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eWhile all the BBNs achieved good performance in predicting the marginal posterior mean TRP concentrations across the four catchments during the baseline period (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), the BBNs did not represent seasonal TRP concentrations well in Ballycanew and Dunleer, likely due to a lack of seasonality in P sources and discharge underestimation [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. However, the ability to correctly reproduce seasonal variation in discharge - and therefore dilution - during ecological sensitive periods is important, for example, to determine algal bloom development and persistence [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e], which is relevant to developing mitigation strategies under anticipated climate change impacts.\u003c/p\u003e\u003cp\u003eThe results outlined here are consistent with similar research conducted using process-based models [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] and Load Apportionment Models [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], whereby the effects of climate change alone may not be significant when evaluating annual mean P concentrations in rivers and streams, with land use changes having a bigger impact on P concentrations [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. However, the effects of climate may become apparent elsewhere, for example in terms of total loads entering lakes, which will need to be reduced to achieve WFD standards [\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e, \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e]. Further, studies done at small-scales have highlighted enhanced phosphorus losses under increased precipitation frequency and intensity, with incidental losses from point sources playing an important role during summer low flows [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e]. Meanwhile, at larger scales (\u0026gt;\u0026thinsp;50 km\u003csup\u003e2\u003c/sup\u003e), the phosphorus response to climate change alone has been generally small [\u003cspan additionalcitationids=\"CR58\" citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e]. Contrast between small-scale catchment studies and the findings reported here highlights the need to reconcile differences in catchment phosphorus dynamics, both observed and simulated, from small (10 km\u003csup\u003e2\u003c/sup\u003e) to large (\u0026gt;\u0026thinsp;10 000 km\u003csup\u003e2\u003c/sup\u003e) catchments and from minutes to decades - to better understand and quantify phosphorus loss in response to climate change.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eOne of the advantages of using the Bayesian Network approach adopted in this study was that of representing the uncertainties associated with both data and models when modelling future TRP concentrations in the ACP catchments. Specifically, these included: the epistemic and data uncertainty represented by the catchment-specific BBNs, the accuracy of each catchment-specific BBN, the uncertainty of the climate models (represented by the ensemble) and of the climate-driven SMART model to derive the discharge. Furthermore, this approach allowed us to partially disentangle these uncertainties. An example of this is given in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, where TRP concentrations with 68% credible intervals (\u0026micro;\u0026thinsp;\u0026plusmn;\u0026thinsp;1 ơ, mg l\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) for an extreme scenario (a warmer month, September, under the more intensive RCP 8.5) are shown across the four catchments for the climate models vs the ensemble. This clearly shows the power of the modelling tool, with the distributions of the two best-performing BBNs (Castledockrell and Timoleague catchments, [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]) being more constrained than that of the other two (Ballycanew and Dunleer). Further, it is apparent from Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e that even when the uncertainty around the BBN\u0026rsquo;s predictive ability is decreased (as in Castledockrell), the HadGEM2-ES has a notable impact on TRP compared to the other four models, underlining the need for careful consideration when choosing ensemble members. By developing scenarios based on the individual climate models, we showed an example application whereby the networks (BBNs) were used as diagnostic tools: whilst the simulated means showed apparent significant changes in future TRP concentrations, plotting the uncertainty indicated that our present understanding and representation of P processes are not yet accurate enough to detect real change, except when the HadGEM2-ES drove the BBNs. The derived information can be used by modelers to inform future modelling decisions.\u003c/p\u003e\u003c/div\u003e"},{"header":"5 Conclusions and further research","content":"\u003cp\u003eDownscaled climate-driven discharge (Q) time series up to the year 2099 were used as input to the catchment-specific Bayesian Belief Networks, to quantify future TRP concentrations in the four study catchments for the first time. The present study constitutes an advancement in Bayesian Network modelling of climate change impacts in that it used an ensemble comprised of five climate models to drive predictions of future water quality. The results driven by the ensemble showed no evident trends in stream TRP concentration in the four catchments, regardless of concentration pathway (RCP 4.5 vs RCP 8.5) and future time periods. This outcome is consistent with similar research conducted using process-based models in large catchments and suggests that the impacts of climate change alone might not be significant when evaluating TRP concentrations in rivers and streams; however, effects may become apparent elsewhere, for example in terms of total loads in standing waters. Given that the present study focusses on smaller catchments, there is a need to reconcile these findings with evidence from event-based studies in smaller catchments.\u003c/p\u003e\u003cp\u003eThe sensitivity analysis explained why the simulated changes in monthly Q driven by an ensemble of climate models are insufficient to drive stream TRP concentration changes in the studied catchments. As the ensemble-driven projected Q distributions were similar to those for the present day, no significant reductions in dilution were apparent in most simulations. Thus, the sensitivity analysis demonstrated that in-depth understanding of the model response is necessary to interpret the results of future scenario simulations. Further, due to their parsimonious nature, these BBNs are limited in the number of processes related to the P transfer continuum [\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e] that could be impacted by climate change, only representing runoff impacts on P transport.\u003c/p\u003e\u003cp\u003eDesigning scenarios where the discharge was driven by the individual climate models rather than the ensemble proved to be an effective tool into understanding the individual ensemble members, with the HadGEM2-ES model showing higher TRP concentrations than the other ensemble members under extreme scenarios. This also suggested that future research should focus on testing different climate ensemble sets.\u003c/p\u003e\u003cp\u003eThis study evaluated the hydrological effects of climate on future stream water phosphorus concentrations. Future research needs to integrate water quality models with socioeconomic and ecosystems responses to climate [\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e], and since networks such as BBNs facilitate the representation of relationships among climate factors and their interaction with local \u0026ldquo;subjective\u0026rdquo; knowledge [\u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e], the present BBNs could be integrated with bespoke mitigation scenarios. Further, given the role of land use in driving future P concentrations and loads [\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e, \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e63\u003c/span\u003e, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e64\u003c/span\u003e], investigating the combined effects of climate and land use changes in the ACP catchments will give insight into the controls of future TRP changes in these catchments, and these BBNs are particularly suited to integrate land use change scenarios co-constructed with stakeholders.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003ch2\u003eConflict of interest\u003c/h2\u003e\u003cp\u003eThe Authors declare no conflict of interest.\u003c/p\u003e\u003c/p\u003e\u003cp\u003e\u003cstrong\u003e\u003cb\u003eConsent to Publish\u003c/b\u003e:\u003c/strong\u003e\u003cp\u003enot applicable.\u003c/p\u003e\u003c/p\u003e\u003cp\u003e\u003cstrong\u003e\u003cb\u003eConsent to Participate\u003c/b\u003e:\u003c/strong\u003e\u003cp\u003enot applicable.\u003c/p\u003e\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eEthics Declaration\u003c/strong\u003e\u003cp\u003enot applicable.\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eAuthors contribution\u003c/h2\u003e\u003cp\u003e\u003cb\u003eCamilla Negri\u003c/b\u003e: Conceptualization, Methodology, Formal analysis, Data Curation, Writing - Original Draft, Visualization, Writing - Review \u0026amp; Editing. \u003cb\u003eElizabeth Cowdery\u003c/b\u003e: Methodology. \u003cb\u003eNicholas J. Schurch\u003c/b\u003e: Conceptualization, Methodology, Writing - Review \u0026amp; Editing, Supervision. \u003cb\u003eAndrew: J. Wade\u003c/b\u003e: Conceptualization, Methodology, Funding acquisition, Writing - Review \u0026amp; Editing, Supervision. \u003cb\u003ePer-Erik Mellander\u003c/b\u003e: Conceptualization, Funding acquisition, Data Curation, Writing - Review \u0026amp; Editing, Supervision. \u003cb\u003eMiriam Glendell\u003c/b\u003e: Conceptualization, Funding acquisition, Methodology, Writing - Review \u0026amp; Editing, Resources, Project Administration, Supervision.\u003c/p\u003e\u003ch2\u003eAcknowledgments:\u003c/h2\u003e\u003cp\u003eWe acknowledge the Teagasc Walsh Fellowship Programme for providing the funding (Reference Number Teagasc). We wish to thank the team at BayesFusion (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.bayesfusion.com/\u003c/span\u003e\u003cspan address=\"https://www.bayesfusion.com/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e) for providing us with the necessary academic licensing and software support.\u003c/p\u003e\u003ch2\u003eData availability\u003c/h2\u003e\u003cp\u003eThe reader is referred to the Murphy et al., (2023) [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] data availability statement.\u003c/p\u003e\u003ch2\u003eCode availability\u003c/h2\u003e\u003cp\u003eThe models used in this research paper have been published on GitHub (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/CamillaNegri/Transferability_Ptool\u003c/span\u003e\u003cspan address=\"https://github.com/CamillaNegri/Transferability_Ptool\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e) and in Negri et al., (2024) [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e].\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eReid N, Reyne MI, O\u0026rsquo;Neill W, Greer B, He Q, Burdekin O et al (2024) Unprecedented Harmful algal bloom in the UK and Ireland\u0026rsquo;s largest lake associated with gastrointestinal bacteria, microcystins and anabaenopeptins presenting an environmental and public health risk. 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Sci Total Environ 668:470\u0026ndash;484. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.scitotenv.2019.02.251\u003c/span\u003e\u003cspan address=\"10.1016/j.scitotenv.2019.02.251\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-5165980/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5165980/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eClimate-induced changes in precipitation will lead to greater frequency of high and low-flow events, causing further phosphorus losses due to increased mobilisation and delivery and decreased dilution. The uncertainty associated with climate-induced changes to water quality is rarely represented in water quality models. Bayesian Belief Networks (BBNs) are probabilistic graphical models incorporating uncertainty, making them useful frameworks for communicating risk. This study presents a set of catchment-specific BBNs to simulate total reactive phosphorus (TRP) concentrations in four agricultural catchments under projected climate change. Downscaled discharge time series from six climate models (five models plus their mean), for two Representative Concentration Pathways (RCP 4.5 and 8.5) and three time periods (the 2020s, the 2040s, and the 2080s), were used to create discharge scenarios for the catchment-specific BBNs. The BBN-simulated monthly mean TRP concentrations showed no obvious trends over time or differences between the RCP scenarios, with the ensemble-driven future TRP essentially replicating the results obtained for the baseline period. We found that in four small (7\u0026ndash;12 km\u003csup\u003e2\u003c/sup\u003e) catchments farmed for livestock or arable crops with one or no wastewater treatment plants, the projected effects of climate change alone were not a significant driver of monthly TRP concentrations. However, the TRP concentration distributions simulated using the outputs from just the HadGEM2-ES model, showed differences from the baseline in the drier months. This difference occurred because the catchment-specific BBNs were sensitive to changes in the mean monthly discharge simulated using in the HadGEM2-ES projections but not by the other ensemble members.\u003c/p\u003e","manuscriptTitle":"An assessment of climate change impacts on stream phosphorus using a climate model ensemble and Bayesian Belief Networks","msid":"","msnumber":"","nonDraftVersions":[{"code":2,"date":"2025-07-31 18:21:04","doi":"10.21203/rs.3.rs-5165980/v2","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}},{"code":1,"date":"2024-10-22 05:37:26","doi":"10.21203/rs.3.rs-5165980/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"42af5c27-20bd-4199-a96c-435560e619cf","owner":[],"postedDate":"July 31st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-08-17T12:38:25+00:00","versionOfRecord":[],"versionCreatedAt":"2025-07-31 18:21:04","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v2","identity":"rs-5165980","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5165980","identity":"rs-5165980","version":["v2"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}