LMs are the most commonly used tool to describe concentration–discharge (C–Q) relationships (Hirsch et al., 2010). Typically, a log transformation is often applied to C and Q data (Crowder et al., 2007; Meybeck and Moatar, 2012; Herndon et al., 2015), with the linear model then described as 2log⁡C=β0+β1log⁡(Q), where C is nutrient concentration and Q is total flow. In this study, the linear model was used as a benchmark for other models. The fitted slope β0 can represent the base nutrient concentration in a stream, while β1 can describe relationships between hydrological and biogeochemical data. The WRTDS model was also used (Hirsch et al., 2010) and can be described as log⁡C=β0+β1log⁡Q+β2JD+β3sin⁡JD3+β4cos⁡JD+ε, where JD is the Julian day and ε is unexplained variation. β2JD is used to represent the long-term trend from year to year, while β3cos⁡(JD) and β4sin⁡(JD) are used to describe the seasonal variation in stream nutrient concentrations. To calculate the Julian Day for use in Eq. (3), the days since 1 January 1970 were first calculated and then multiplied by 2π. WRTDS advances the simpler linear model in two aspects. Firstly, the additional components in the equation allow a consideration of seasonal and long-term patterns and make the WRTDS model more able to describe stream nutrient concentrations across the year. Secondly, unlike the linear model, whose parameters are constant in time, WRTDS adjusts the parameters in a gradual manner throughout Q, JD space. This is accomplished by applying a weighted regression for the estimation of log⁡(C), where the weights on each observation are based on three distances between the observation (Qo, JDo) and the estimation point (Qi, JDi), which are (1) the time distance between JDo and JDi, (2) the seasonal distance between the time of year at JDo and the time of year at JDi, and (3) the discharge distance between log⁡(Qo) and log⁡(Qi) (Hirsch et al., 2010; Green et al., 2014). Thus, log⁡(C) is considered to be locally linearly related to log⁡(Q), JD, sin⁡(JD) and cos⁡(JD).

RF and GBMs are ensemble models that combine multiple base learners inside the model to improve the prediction performance (Ishwaran and Kogalur, 2010; Singh et al., 2014). The ensemble methods are the main difference between RF and GBM. In RF, bootstrap aggregating is used to resample the original dataset with replacement. Hence, datasets with partial data are generated and then used to build individual base learners. Unlike bootstrap aggregating, GBM iteratively generates a sequence of base learners, where each successive base learner is built for the residual prediction of the preceding base learner (Friedman, 2001, 2002). The probability with which data points are selected for the next training set is not constant and equal for all data points. The selection probability increases for data points that have been misestimated in the previous iteration; data points that are difficult to classify would receive higher selection probabilities than easily classified data points (Yang et al., 2010; Erdal and Karakurt, 2013).

For RF and GBM, the most commonly used base learner is a classification and regression tree (CART). A CART model is built to split the dataset into different nodes (Breiman et al., 1984): X1,xia<v and X2,xja≥v for numeric variables or X1,xid=c and X2,xjd≠c for categorised variables, where i and j are the sample indices, a is a numerical variable, v is one of the values of a variable, d is a categorised variable, and c is one of the values of d variable. To split the dataset at a or d, the sum of least-square error of the two nodes is calculated for a regression task as 4error=∑l=0L(yl-y‾L)2+∑r=0R(yr-y‾R)2, where yl and yr are observations in two split nodes and y‾L and y‾R are the average y in that node. The split is chosen among all candidate variables and values to minimise this error. This splitting process is applied from the root to the terminal node, which creates a tree structure for the model (Erdal and Karakurt, 2013). A CART can be used both for classification and regression problems due to this tree structure (Coops et al., 2011). However, a single CART can sometimes oversimplify variable interactions and may lead to low prediction performance (McBratney et al., 2000; Cutler et al., 2007; Coopersmith et al., 2010). This drawback can be overcome by the ensemble method that generates many resampled datasets and creates various CARTs to achieve higher accuracy (Breiman, 2001) and more stable results when facing slight variations in input data (Martínez-Rojas et al., 2015). New data input is thus evaluated against all trees created in the ensemble model, and each tree votes using the main class or the averaged values in the terminal node. The class with the maximum votes will be used for a classification model, and the averaged predicted value from all trees is used for a regression model (Singh et al., 2014; Belgiu and Drăgu, 2016). It is found that ensemble methods in RF and GBM can significantly improve the prediction accuracy of CART (Ismail and Mutanga, 2010; Erdal and Karakurt, 2013).

Compared to LM and WRTDS models, one drawback of RF and GBM, as well as many ML methods in general, is that there is no specific equation in GBM or RF to directly demonstrate model structures. However, GBM and RF do provide the relative importance of each variable, which is based on the empirical improvement in the loss function due to the split on the specific variable in a tree (Povak et al., 2014; Puissant et al., 2014). The improvement of a certain variable was averaged over all trees and used as the relative importance of that variable for the final model. This relative importance serves as the key index to understand the model structure of RF and GBM (Makler-Pick et al., 2011).

Total flow is commonly conceptualised as including baseflow and quickflow components (Meshgi et al., 2015). Baseflow separation techniques use the time-series record of streamflow to extract the baseflow and quickflow signatures from the total flow. This can be done by using graphical methods to identify the intersection between baseflow and the rising and falling limbs of the quickflow response (Szilagyi and Parlange, 1998) or by filtered methods which process the entire stream hydrograph to derive a baseflow hydrograph (Furey and Gupta, 2001). In this study, the three-pass filtered method was applied for baseflow separation; the quickflow was first estimated as described below (Lyne and Hollick, 1979; Nathan and McMahon, 1990), and then baseflow was calculated: 5QFi=αQFi-1+(Qi-Qi-1)1+α2, where QFi is the filtered quickflow for the ith sampling instant, QFi-1 is the filtered quickflow for the previous sampling instant to i and α is the filter parameter with a value of 0.925 for daily flow as recommended by Nathan and McMahon (1990). Baseflow is then calculated as BF=Q-QF.

In this study, the root mean squared error (RMSE) and the Nash–Sutcliffe model efficiency coefficient (MEF) were used to compare model performance. The RMSE is a measure of overall error between the predicted and measured data and returns an error value with the same units as the data, which is given by the following equation: 6RMSE=∑(yi-y^i)2n, where n is the number of data samples. RMSE varies from 0 to +∞, and a perfect model would have RMSE of 0. The MEF is a dimensionless “goodness-of-fit” measure which can vary from -∞ to 1, with a value of 1 indicating a perfect fit and 0 indicating that the mean of the measured values performs as well as the model. The MEF can be calculated as 7MEF=1-∑(yi-y^i)2∑(yi-y‾i)2, where y‾i is the mean of the measured values. Note that the predicted and measured nutrient values were normalised to [0, 1] in this study to compare model performance across different nutrient species.

The main aims of this research is to test the hybrid model, rebuild the historical nutrient data, and explore the short- and long-term nutrient changes. The first step is verifying the model performance. In this case, the data were randomly divided into 80:20. Different models were built and tuned on the training dataset (80 %) and tested on the testing dataset (20 %). To further test model uncertainty and stability, the divided and tested processes were repeated 30 times except for WRTDS. After this, all data points including the testing data were then used to rebuild the historical nutrient data. Five-fold cross validation (CV) was done on the training dataset to tune the model parameters. Leave-one-out cross validation (LOOCV) was used in WRTDS to predict daily nutrient concentrations; LOOCV is the default cross-validation method in the EGRET (Exploration and Graphics for RivEr Trends) package. In that method, one data point was excluded at a time from the whole dataset, all other data points were used to build the model, and the excluded point was used for testing the model performance. This process was repeated for all data points. The performance of all six methods (LM, WRTDS, RF, GBM, hybrid RF and hybrid GBM) was evaluated on the testing dataset. WRTDS was run through the EGRET package (Hirsch and De Cicco, 2015) in R to produce daily concentrations for six nutrient species (TP, TN, DON, DOC, NH4 and FRP). The default settings specified by the user guide (Hirsch and De Cicco, 2015) were used. RF and GBM models were built through the H2O package in R.

The overall processes of ML-SWAN can be divided into three stages (Fig. 1). The first stage was baseflow separation using the EcoHydRology package (Fuka et al., 2018). The generated baseflow, quickflow, total flow and rainfall were further transformed into lagged data (the averaged values over the previous 3, 7 and 15 days) to capture any short-term impacts of different water pathways and rainfall on stream nutrients. JD, cos⁡(JD) and sin⁡(JD) were also calculated for RF and GBM to include seasonal and long-term impacts. A description of all the variables used is given in Table 1.

The second stage of ML-SWAN was to build intermediate RF and GBM models that generated daily nutrient concentrations. For the intermediate RF and GBM models, only lagged hydrological data (including total flow, baseflow and quickflow), lagged rainfall and seasonal components on the training dataset were used. Nutrients were not used as a predictor in the intermediate model. Note that, in this study TP, TN, DOC and DON were selected to be generated in the second step. If one nutrient was considered as the final target, the other three nutrients were used to generate daily data. For instance, daily TP, DOC and DON were generated as additional variables to predict TN. In that case, the missing TP, DOC and DON were generated by the intermediate model for the training dataset and the testing dataset. Daily TN, TP, DOC and DON data were generated and used for the final predictions. These nutrients were selected since they may be generated from similar sources or are important components of the total nutrient load. For instance, DOC and DON may both be generated from dissolved organic matter (DOM) (Seitzinger et al., 2002; Bernal et al., 2005; Filep and Rékási, 2011). In the catchments studied here, DON can be a dominant component of TN (Nice et al., 2009; Petrone, 2010; Bourke et al., 2015). The selection of DOC and DON for pre-generation may not necessarily be appropriate for other catchments. The selection of nutrients for pre-generation depends on data availability in the dataset. The use of different species of the same nutrients (N or P) can generally improve model performance.

The third stage of ML-SWAN built an additional hybrid model using the training data, which has generated nutrient data by the intermediate models, lagged hydrological data, lagged rainfall data and seasonal components. Note that at this stage, the only difference between stand-alone ML and hybrid ML methods was that stand-alone ML did not use pre-generated daily nutrient data.

Overall, the scaled RMSE reduced from LM, WRTDS, stand-alone ML and hybrid ML for all nutrients except NH4, and the same pattern was found for MEF in both Ellen Brook and Murray River (Fig. 3). The linear model had the worst performance: the scaled RMSE was significantly higher and MEF was significantly lower than the other models, for all six nutrients and across both sites. WRTDS generally had higher RMSE and lower MEF than the stand-alone ML, although it achieved similar results to stand-alone ML for FRP and NH4 at both sites. LOOCV was used in WRTDS, and only one set of results was generated, compared to 30 RMSE and MEF values for other methods. This results in a shortened line for WRTDS in Fig. 3, instead of the interquartile ranges (IQR=75th percentile - 25th percentile) presented for the other methods. LOOCV can sometimes overestimate the model performance as only one sample was tested at a time; in contrast, 20 % of the independent testing data were tested in the other five models. LOOCV can also have a higher variance than other CV methods (Li, 2016). As such, the WRTDS results are not directly comparable to the other methods.

Stand-alone ML achieved results that placed it between WRTDS and hybrid ML. Stand-alone GBM achieved the highest accuracy for NH4 prediction in Murray River. Hybrid RF and hybrid GBM had the lowest RSME and highest MEF for all nutrients except NH4, in Ellen Brook and Murray River (Fig. 3). Compared to the stand-alone ML, the hybrid ML also had much lower prediction uncertainty, in that the RMSE and MEF had narrower IQR than that of the stand-alone ML, especially for DON and FRP prediction in Ellen Brook and DOC prediction in Murray River. The use of pre-generated daily nutrient data was the only difference between hybrid ML and stand-alone ML. This means that the generated nutrients provided additional information for the hybrid model that allowed more stable results. Interestingly, while the hybrid ML had better performance than the stand-alone ML, there was no significant difference in performance between the hybrid RF and hybrid GBM, though they showed differences between different nutrient species. For instance, hybrid RF achieved slightly better performance for DOC in Ellen Brook, while hybrid GBM had lower RMSE for DOC in Murray River. There was no significant performance difference between stand-alone RF and GBM.

In summary, the hybrid ML had the best performance amongst the six methods, followed by stand-alone RF and GBM. WRTDS was better than the linear model but could only achieve results similar to stand-alone RF and GBM for NH4 prediction in Ellen Brook and for NH4 and FRP prediction in Murray River.

Model performance for six nutrients was compared in the last section. To make this section more concise, these six models were then compared in their ability to generate daily TN in Ellen Brook from 1 January 1989 to 16 July 2018 (Fig. 4). The daily TN in Murray River and daily TP in both sites were also generated (see results in the Supplement). TN was selected because TN is the most important and most frequently measured nutrient in many places. This hybrid method can also be used for other nutrients. Note that all data points (not just the 80 % training dataset) were used to generate daily TN.

The LM performed very poorly for TN prediction; low-concentration samples (TN<1.9mgL-1) were all underestimated, and some extremely high concentrations were incorrectly generated due to the high flow (Fig. 4a). There were some seasonal patterns in the generated TN which come from the flow data. LM only used total flow to predict nutrient concentrations, while other important hydrological processes were ignored. Thus the oversimplified LM had high errors in nutrient prediction (Fig. 4), and this method might be more suitable for solutes that are not substantially bioactive (e.g. SiO2, Ca2+, Mg2+, Cl-) (Stallard and Murphy, 2014). The WRTDS captured some seasonal patterns of TN (from 2008 to 2018) but still had problems predicting TN between 1989 and 1996; some extremely high values were generated, and TN<1.0mgL-1 were overestimated. Some high values (e.g. TN in 2008) were underestimated (Fig. 4b). Stand-alone ML and hybrid ML generated similar daily TN data but varied in the detail. These models successfully captured the low-concentration data and the seasonal pattern of TN. Unlike results by WRTDS, the generated TN by stand-alone ML and hybrid ML have a more consistent seasonal pattern from 1989 to 2018. The RF and hybrid RF both underestimated a few high-concentration data (TN<4.0mgL-1), compared to GBM and hybrid GBM, although hybrid RF still showed better performance than RF. For instance, high-concentration data in 2007 and again from 2014 to 2017 were successfully predicted by hybrid RF but underestimated by RF. Compared to stand-alone GBM, the hybrid GBM achieved lower errors for high-concentration data.

Apart from the better performance for high-concentration data, another difference between stand-alone ML and hybrid ML was that the long-term trend in TN was consistent in stand-alone ML, but this trend fluctuated in hybrid ML. For instance, hybrid GBM results fluctuated from 1989 to 1999 and then showed an increasing long-term trend from 2005 to 2018, in addition to the seasonal fluctuation. The pre-generated nutrient is the only difference between stand-alone model and hybrid model. If there are long-term trends in nutrient concentrations (e.g. TN), similar trends should also exist in the components of TN (either DON or dissolved inorganic nitrogen). The pre-generated nutrients emphasise this impact on the hybrid model. This suggests that the generated nutrient data could provide additional information that allowed the hybrid ML to capture long-term trends; this information was not included in the seasonal components but existed in the generated nutrient data.

The distribution of the TN data generated by the six models was compared to the distribution of the measured TN data (Fig. 5). Similar to the results shown in Fig. 4, hybrid GBM had the most similar distribution to the measured TN data. Only a few low- and high-concentration data were incorrectly predicted by the hybrid GBM. Hybrid RF also achieved a distribution similar to the measured data, but more extreme-value data were underestimated compared to the hybrid GBM. Stand-alone GBM and RF showed a similar distribution to the hybrid GBM and RF with less accuracy in the extreme data. Overall, GBM (either stand-alone model or hybrid model) could have a better distribution than RF. WRTDS generated some extremely high data and underestimated many low-concentration data, which is also seen in Fig. 4b. The linear model incorrectly predicted most of the TN data. The results in both Figs. 4 and 5 showed that hybrid GBM achieved the best simulated daily TN data, followed by hybrid RF, stand-alone GBM and RF. WRTDS and LM generated large biases in TN prediction.

The hybrid ML models predicted most of the extreme concentrations (Figs. 4 and 5), and only a few points were under-predicted. The limited number of extreme data and the model structure that tried to balance the overall trend prediction with extreme data prediction can cause under-prediction. For example, higher weights can be set up for extreme data during the model training process to force model to over-predict the value for extreme concentrations, which may reduce the accuracy for overall trend prediction. In this study, our target is to understand the long-term nutrient trend. Therefore, we did not use this technique during the model training process.

The daily data generated by the hybrid GBM showed a lower RMSE and better distribution than stand-alone ML, WRTDS and LM (Figs. 4 and 5). Compared to LM, WRTDS and simple CART models, one drawback of RF and GBM, as well as many ML methods in general, is that there is no specific equation in GBM or RF to directly demonstrate model structures. However, GBM and RF do provide the relative importance of each variable, which is based on the empirical improvement in the loss function due to the split on the specific variable in a tree (Povak et al., 2014; Puissant et al., 2014). The improvement of a certain variable was averaged over all trees as the relative importance for the final model. This relative importance serves as the key index to understanding the model structure of RF and GBM (Makler-Pick et al., 2011).

The variable importance for TN prediction by hybrid GBM in Ellen Brook and Murray River is presented in Fig. 6. The variable importance in the intermediate models is also included, and the length of coloured sections represents the importance of those variables in the hybrid GBM or intermediate GBM. The importance was scaled according to the most important variable. The generated DON and TP ranked as the first two critical variables in Ellen Brook, while all three generated nutrients were listed as the most important variables in Murray River. This suggests that the generated nutrients do provide critical information to the model and improve model performance. The quickflow was most important for the generated DON and TP, as well as the TN itself in Ellen Brook. The impacts of quickflow decreased, and baseflow, seasonal components and rainfall data become more important for TN prediction in Murray River. This difference in variable importance reflects different catchment characteristics across the two sites and therefore different hydrological and hydrochemical processes controlling TN concentrations. The total flow was not of high importance at either site, which suggests that baseflow or quickflow had more impact on surface water TN. Moreover, TN concentrations were affected by more variables in Murray River than in Ellen Brook.

Hydrological conditions, specific sub-catchment characteristics and the chemical properties of nutrients can all impact surface water nutrient concentrations (Barron et al., 2009; Moatar et al., 2016), nutrient partitioning (Ruibal-Conti et al., 2013) and nutrient transport (Burt and Pinay, 2005; Tesoriero et al., 2009). TN prediction in Murray River was impacted by more variables than in Ellen Brook (Fig. 6), suggesting more complex relationships in Murray River.

Quick flow is composed of runoff, interflow and direct precipitation (Brodie and Hostetler, 2005) and was shown to be important for TN prediction in Ellen Brook. Direct precipitation, however, did not have a large impact on TN (the green bars in Fig. 6); this suggests that runoff and interflow were important for TN concentrations. Baseflow can account for (on average) 53 % of annual stream discharge in Ellen Brook, but baseflow was not of high importance for TN prediction in this study. This may occur due to low TN concentrations in the baseflow (Barron et al., 2009), large areas of low nutrient-retaining sandy soils in the Ellen Brook catchment, and high nutrient transport efficiency in quickflow and first flush. Mellander et al. (2012) quantified nutrient transport pathways in agricultural catchments and found that quickflow was only 2 %–8 % of total flow, but it can transport up to 50 % of TP. Gunaratne et al. (2017) found that the seasonal first flush was only 30 % of runoff volume but contained 40 %–70 % of the nutrient load.

Note that the median TN in Ellen Brook (2.1 mgL-1) is significantly higher than that in Murray River (0.67 mgL-1) which can be explained to some extent by the large area of grazing lands in Ellen Brook. Previous investigations in south-eastern Australia (Adams et al., 2014), New Zealand (Davies-Colley et al., 2004) and north-western Europe (Conroy et al., 2016) all suggested that livestock can increase TN discharge to the receiving water bodies. Most of the piggeries and poultry farms in the Swan–Canning catchment are located in Ellen Brook catchment (Kelsey et al., 2010), which has the highest TN and TP discharge loads. Thus the large grazing areas, piggeries and poultry farms and low nutrient-retaining sandy soils may explain the importance of quickflow for TN prediction and high TN concentrations in Ellen Brook.

Baseflow is derived from groundwater discharge to streams and the slow drainage of water stored in local wetlands (Kelsey et al., 2010). Baseflow is highlighted as an important variable for TN prediction in Murray River. The Murray River catchment has large areas with high nutrient-retaining soils (high PRI) (Kelsey et al., 2011) and relatively low TN concentrations, and it is likely that groundwater makes significant contributions to TN in Murray River. Ruibal-Conti et al. (2013) previously found that variability in TN is strongly associated with variability in flows in Murray River. Our results extend this finding, in that both baseflow and quickflow likely impact TN in the river.

It is noted that seasonal components including sin⁡(JD), and cos⁡(JD) showed significantly higher importance in Murray River. This may because seasonal information is captured in other inputs in Ellen Brook (e.g. quickflow and baseflow). But the main reason is the stronger seasonal TN signals in Murray River compared to Ellen Brook. This finding is supported by the generated daily TN data for Murray River (see results in Supplement S2). Natural reserves occupy large areas of the Murray River catchment, and this may increase seasonal signals. Additionally, the lagged quickflow, baseflow and rainfall were generated (for the previous 3, 7 and 15 days), but only the lagged 15 d baseflow and quickflow were ranked as important variables for both Ellen Brook and Murray River. This suggests a timescale of nutrient transport in the sub-catchments and likely reflects soil permeability and geology; long hydrochemical recessions from storm events may prolong their impact on the ecological status of receiving rivers (Mellander et al., 2012).

Six models were compared for nutrient predictions and the hybrid GBM model achieved the highest accuracy (Figs. 3 and 5). The long-term changes in TN have been discussed in previous sections. To understand the long-term changes in other nitrogen species across the year, the hybrid GBM was then applied to generate daily DON, NH4 and NOx in Ellen Brook from 1 January 1989 to 16 July 2018 (Fig. 7). The generated DON has much higher concentration than NH4 and NOx. This is consistent with previous investigations in this study area that DON was the dominant form of TN in both surface water and groundwater (Nice et al., 2009; Petrone, 2010; Bourke et al., 2015). There is no clear long-term patterns in generated NH4 and NOx; however, an increasing long-term trend in generated DON can be found from 2006 to 2018. There is also an increasing trend in TN from 2005 (Fig. 4), suggesting DON was the main reason for the increasing TN concentrations. DON is often assumed to be relatively slow to react, but depending on the source of DON, it can turnover rapidly, thereby constituting an active contributor to the eutrophication of surface waters (Petrone et al., 2009).

The generated nutrient data provided additional information to enhance the hybrid model performance (Figs. 3 and 5). To assess the individual impact of a generated nutrient, we did a simple test that sequentially added generated TP, DOC and DON data to the base GBM (only seasonal components and lagged hydrological data) and evaluated RMSE and MEF for TN prediction. This process was repeated 30 times and the results are presented in Fig. 8.

The RMSE significantly decreased when generated TP was added as an additional variable. DOC and DON only have 297 and 129 data, respectively, and were only measured in recent years, while TP has more than 1000 data and has been measured since 1990 (Table 3). However, DOC and DON could still improve model performance (Fig. 8), and the generated DON was ranked as the most important variable across both sites (Fig. 6). The medium RMSE slightly decreased when both generated DOC and DON were added. Moreover, the generated DOC and DON also reduced the model uncertainty, such that the IQRs became narrower than model results without the generated nutrients.

Our results suggest that the recent DON and DOC data improved understanding of historical TN. It is not uncommon to have a similar data structure when several datasets are combined or new measurements are added to a project. While there were no DON data prior to 2006 in Ellen Brook, daily DON can be generated back to 1990 with the help of generated TN, DOC and TP data; DON had the highest MEF among the six nutrients (Fig. 3). This hybrid method provides a feasible process to fully utilise all available nutrient data to accurately fill gaps in either historical or recent nutrient datasets.

Monitoring, modelling and forecasting water quality inputs are essential to support the management of the quality of receiving waters while responding to current anthropogenic stressors (Holguin-Gonzalez et al., 2013; Schnoor, 2014). The performances of six models were comprehensively compared, in an exploration of historical and contemporary nutrient data across two study sites. LM had the highest error while stand-alone RF and GBM had similar error. This agrees with previous findings by Erdal and Karakurt (2013) that RF and GBM models achieved similar correlation coefficients (R) for streamflow forecasting. Ismail and Mutanga (2010) also reported that RF and GBM increased the R of a single CART by 10.01 % and 9.59 %, respectively.

The performance of WRTDS, as well as many conceptual models, is often reliant on a prescribed set of input information, which can account for variance in nutrient concentrations but may miss some important processes for certain rivers (e.g. baseflow in this study). This can compromise the performance of WRTDS for nutrient prediction. Moreover, hydrological and chemical processes within the systems are typically ignored by many conceptual models, which may exclude important hydrochemical information. By contrast, some complex conceptual models may include these hydrochemical processes but are often constrained by insufficient nutrient data to calibrate and validate the models. Some simplifications may be made to account for lack of data, but the simplifications may often weaken model performance. The hybrid framework presented in this study has overcome the challenge caused by data paucity by building intermediate models to generate missing nutrient data and then using this additional hydrochemical information to improve final model performance.

The hybrid models developed in this study were able to take advantage of the complementary strengths of both hydrochemical (additionally generated nutrient data) and hydrological (lagged data) information. This was particularly the case for the prediction of high nutrient concentrations, where the hybrid models were shown to outperform the stand-alone RF and GBM, in terms of accuracy, reliability and value distribution. Improved accuracy in the hybrid model was achieved by using intermediate models, although these intermediate models may also have a relatively high error (similar to stand-alone RF and GBM). However, if the improved model performance is higher than the introduced error, the results are manageable. Similar results were also found in Hunter et al. (2018), who compared a hybrid process-driven and ANN model with the stand-alone ANN model and the process-driven model. In their study, the hybrid also achieved the best performance followed by stand-alone ANN. The process-driven benchmark model had a significantly lower accuracy than the other two models.

A limitation of the hybrid modelling approach, however, is that it requires the time and expertise to develop intermediate models for generating additional nutrient data. Prior knowledge also plays an important role in identifying the variables for pre-generation. Some statistical methods (e.g. the correlation test, simple linear model) can be helpful to identify these variables if there is no clear theoretical or conceptual understanding on which to base the selection of the important variables.

In this study, we tested the generalised performance of the hybrid model across six nutrient species and two tributaries. We also note that nutrients may not always be the critical variables targeted for pre-generation; the pre-generated DOC was ranked as having low importance for Ellen Brook and produced only a slight improvement in the performance of the hybrid model for NH4.

There were constraints in the nutrient datasets in this research, and similar constraints commonly exist in other study areas. Many nutrient datasets contain important information, but sometimes it can be challenging to directly combine or utilise them. ML methods provide a feasible approach to preprocess these datasets or combine them. In this study, the concentrations of missing nutrient species were first predicted by the intermediate ML method and then used as inputs for another ML method for final predictions. The pre-generation of missing data and pre-modelling hydrological analysis were critical components of the hybrid model and allowed the identification of the impact of different hydrological transport pathways for TN export from the two tributary catchments. The hybrid ML methods were further applied to generate nutrient data for eight tributaries, and the generated data have since been used as inputs to an estuary prediction model, which simulates and forecasts nutrient concentrations in the previous and next 5 d in the Swan–Canning Estuary (Huang et al., 2019). The modelling methods and strategies developed in the work presented here can be easily applied to other study areas. Overall, ML methods provide a flexible and feasible solution to explore the underlying relationships, reconstruct spatial and temporal datasets, and combine different models.