The study area is the 0.6 km2 Houay Pano headwater catchment, located 10 km south of the city of Luang Prabang, Lao PDR (Boithias et al., 2021a) (Fig. 1). This catchment is representative of montane agroecosystems in Southeast Asia and is part of the long-term critical zone observatory network called multiscale TROPIcal CatchmentS (M-TROPICS), which is affiliated with the French research infrastructure OZCAR (Gaillardet et al., 2018). This site had undergone rapid land-use changes from 2011 to 2018 (Fig. S1a). The characteristics of this area, including land-use information, are provided in the Supplement (Sect. S1). We collected weather, hydrological, E. coli concentration, and electrical conductivity data at 6 min time steps from 2011 to 2018. Rainfall, relative humidity, solar radiation, wind speed, and air temperature were measured with an automatic weather station Campbell Scientific BWS200, which was equipped with ARG100 (a 0.2 mm capacity tipping bucket). The potential evapotranspiration was calculated using the Penman–Monteith method. We measured the stream water level at the monitoring station using a V-notch and water-level recorder (OTT Thalimedes). The discharge was estimated based on the rating curve relating discharge to water levels. The surface flow and subsurface flow were calculated using the electrical conductivity method (Ribolzi et al., 2018). A detailed description of this method is provided in the Supplement (Sect. S2). E. coli concentration was measured based on the standardized microplate method (ISO 9308–3). A detailed explanation of the E. coli experiment can be found in the Supplement (Sect. S3). In this study, we carried out biweekly grab sampling of E. coli from 2011 to 2018. Over the same period, we also monitored 11 flood events to assess E. coli dynamics during flood events using an automated sampler (ICRISAT) triggered by the water-level recorder to collect water after every 2 cm water-level change during flood rising and every 5 cm water-level change during flood recession. The total number of E. coli samples collected over the 2011–2018 period was 255. In addition, we collected the monthly numbers of poultry, swine, goats, and the number of people who visited the study area. These data were used to quantify the source of E. coli in this catchment (Rochelle-Newall et al., 2016) (Fig. S1b).

HSPF and LSTM models were used to simulate in-stream surface flow, subsurface flow, and E. coli concentration. HSPF and LSTM are popular models (Bicknell et al., 1997; Ahmadisharaf and Benham, 2020; Kratzert et al., 2019). Both models have been used for hydrological and water quality simulations (Peterson et al., 2020; Isikdogan et al., 2017; Ahmed et al., 2014). In the HSPF, the simulation of surface and subsurface flow and of E. coli concentration was carried out in three steps: (1) building the model, (2) conducting sensitivity analysis based on Latin hypercube–one factor at a time (LH-OAT), and (3) calibrating the model using the Newton algorithm (Nash, 1984). The schematic of the LSTM simulation is shown in Fig. 2. The first step in building this model was data preparation (Fig. 2a). LSTM then simulated surface and subsurface flow with weather data (Fig. 2b). Finally, we estimated the E. coli concentration at 6 min intervals using rainfall, bacteria source, land-use change, and surface and subsurface flow (Fig. 2c). The fecal matter from the E. coli sources was assumed to be evenly distributed in the catchment. The monthly E. coli source data are presented in Fig. S1b. The time-series data of the E. coli source were used as input for the E. coli simulation.

Evaluations to assess the performance of the HSPF and LSTM were conducted using MSE, Nash–Sutcliffe efficiency (NSE), and percent bias (PBIAS) (Nash and Sutcliffe, 1970; Gupta et al., 1999). NSE is useful for interpreting the model performance by generating a dimensionless value as the performance index (Lin et al., 2017). The PBIAS measures the average tendency of the simulated data to be overestimated or underestimated than observed values (Moriasi et al., 2015). The MSE, NSE, and PBIAS were calculated using the following equations: 7MSE=∑i=1moi-pi2m,8NSE=1-∑(oi-pi)2∑(oi-o‾)2,9PBIAS=1-∑i=1m(oi-pi)∑i=1moi, where pi is the simulated data, oi is the observed data, and m is the number of points in the data.

The land-use change from 2011 to 2018 is shown in Fig. S1a. The area of Fallow land use increased from 2011 to 2016, whereas Annual crop area decreased. Teak tree plantations were expanded until 2013 and were retained. Forest land use accounted for about 10 % of the study area from 2011 to 2018. In general, the land-use change was dynamic from 2011 to 2013, whereas its variation diminished from 2016 to 2018. Previous studies have demonstrated that the expansion of Teak trees might increase the surface flow (Ribolzi et al., 2017; Song et al., 2020). Higher runoff at the soil surface may cause a higher inflow of E. coli with surface flow. The monthly E. coli source in the catchment decreased from 2×1015 in 2011 to 3×1014 in 2018 (Fig. S1b). This decrease in the E. coli source is caused by the decrease in manpower needed in Teak tree plantations and in Fallow plots compared to the Annual crop (Fig. S1a) (Boithias et al., 2021b).

The sensitivity results for the flow simulation are shown in Fig. S3, and the most sensitive parameters are listed in Table S2. The interflow and infiltration-related parameters were the most sensitive parameters for surface and subsurface flows. Manning's “n” value (NSUR) for Teak and Fallow land uses was among the 10 most sensitive parameters. Kim et al. (2017) suggested that Manning's coefficient value is the most sensitive parameter in the hydrological simulation of tropical headwater catchments, such as the Houay Pano catchment in the northern Lao PDR. The groundwater recession rate (AGWRC) and soil infiltration capacity (INFILD) were sensitive to subsurface flow. In Annual crop land use, infiltration capacity (INFILT) and upper zone storage (UZSN) were the most sensitive parameters. Abbas et al. (2020) demonstrated that INFILT is the most sensitive parameter for subsurface flow in tropical subcatchments.

The sensitivity analysis results for E. coli are shown in Fig. S4 and Table S3. The parameters related to the transport of E. coli on the land surface (e.g., WSQOP, SQOLIM_MF) were more sensitive than other parameters. IOQC and AOQC were the least sensitive parameters. These parameters are related to E. coli transport in interflow and baseflow (Bicknell et al., 1997). This implies that the in-stream E. coli concentration at the study site is mainly driven by surface flow (Boithias et al., 2021b). A previous study also demonstrated that 89 % of in-stream E. coli concentrations were driven by surface flow (Boithias et al., 2021b). Figure 3 shows the model performance dependent on different objective functions. We found that the model performance was better when the NSE was selected as the objective function. The NSE of the surface and subsurface flow was positive by optimizing with NSE. However, the NSE value for surface flow was negative when the objective function was MSE during the optimization. Negative NSE indicated an “unsatisfactory” performance range (Moriasi et al., 2015).

The simulated surface and subsurface flows using the HSPF are plotted in Fig. 4. We found that the simulated subsurface flow was underestimated compared to the observations. Although surface flow from the HSPF followed the trend and peaks of observations, this model yielded a negative NSE value, indicating that the model simulation was unacceptable (Moriasi et al., 2015) (Table 3). The NSE values for subsurface flow from HSPF were 0.49 and 0.59 for calibration and validation, respectively. Hence, the HSPF model was better at simulating subsurface flow than surface flow. In particular, the simulated surface flow was underestimated compared to the observations. The average values of INFILT and UZSN were 0.36 and 1.22, respectively, which were larger than those reported in previous studies (Lee et al., 2020). INIFILT controls the overall division of available moisture into the surface and subsurface (Bicknell et al., 1997). The parameter UZSN influences the evapotranspiration process (Bicknell et al., 1997). This underestimation of surface flow using HSPF is consistent with a previous study (Kim et al., 2017). We also investigated the impact of underestimation and overestimation of the flow by plotting flow duration curves (Fig. S5). Although both flows can capture the peak flow, the simulated subsurface flow was still underestimated compared to the observed subsurface flow.

The simulated surface and subsurface flows using the LSTM model are plotted in Fig. 4. The NSE values for the calibration period were 0.56 and 0.69 for surface and subsurface flow, respectively. The corresponding validation NSE values of the surface and subsurface flows were 0.51 and 0.64, respectively. These results indicate that the LSTM had a satisfactory performance for both the calibration and validation periods according to the criteria of Moriasi et al. (2015). LSTM overcame the problem of the HSPF model underestimating subsurface flow. In addition, the peak surface flows from the LSTM were similar to observations. The observed and simulated flows in storm events are presented in Figs. S6–S11. The simulated surface flow by HSPF followed the rainfall events more closely as compared to that of LSTM. The peaks in surface flow in Fig. S8 are completely missed by LSTM but captured by the HSPF model. We also noted that LSTM can follow the observed trends in surface and subsurface flow more closely than the HSPF (Figs. S6, S9, S10). The falling limb from the predicted subsurface flow of LSTM is gentle and follows the observed pattern (Figs. S9–S11). This leads to increased NSE values for both surface flow as well as for subsurface flow. The hyperparameters of the LSTM are described in Table 2. The rectified linear unit (ReLU) was chosen as the activation function for the LSTM output. Because the simulated E. coli should be positive, we chose ReLU, which cannot produce negative values from the model (Nair and Hinton, 2010). The optimal batch size and LSTM units were 128 and 64, respectively. The optimal value of the lookback steps was 50, which is equal to 5 h of input data.

We analyzed the model performance for surface and subsurface flows during storm events (Fig. 5). The events were selected in which the peak flow exceeded 0.2 m3 s-1. The performance of LSTM is considerably better than that of HSPF for most storm events. In surface flow, the average MSE of LSTM and HSPF was 1.1×10-4 and 6.1×10-4 (m3 s-1), respectively. The NSE values from LSTM varied from 0.2 to 0.6, whereas those of HSPF ranged from -1.0 to 0.4. We found that the NSE values from the HSPF vary considerably depending on storm events. On 11 June 2015, the NSE value of HSPF was as high as 0.4, whereas for some other dates it was below 0. Although the subsurface flow of the HSPF provided better model performance than surface flow simulation, this model still presented an unacceptable result, with a negative NSE value.

Figure 6 shows the temporal distribution of E. coli concentration using HSPF and LSTM. The E. coli concentration from HSPF was overestimated. The performance matrices of the HSPF were also worse than those of the LSTM (Table 4). In particular, the HSPF simulation presented a PBIAS value of 73, indicating an overestimation of E. coli concentration (Moriasi et al., 2015). Ackerman and Weisman (2014) reported that the E. coli from HPSF was overestimated compared to observation. The overestimation of simulated E. coli at tropical sites has also been observed by Kim et al. (2017). E. coli simulation from LSTM is satisfactory in both calibration and validation periods according to the criteria set by Moriasi et al. (2015). In contrast, the HSPF result can be regarded as “unsatisfactory” in both the calibration and validation periods. These results implied that LSTM could generate acceptable performances and had good agreement between the observed and simulated E. coli.

The simulation results during the storm events using both the HSPF and LSTM models are shown in Figs. 7 and S6–S11. Figure 8 shows two storm events from the validation data during July and August 2017, whereas the other figures show the storm events from the calibration data. In general, the simulated E. coli by HPSF and LSTM were overestimated and underestimated, respectively. This difference might be caused by the fact that E. coli from HSPF is more responsive to surface flow, whereas E. coli from LSTM is more influenced by subsurface flow (Ackerman and Weisman, 2014). The sensitivity analysis of HSPF also demonstrated that the influence of interflow and baseflow on E. coli is weaker than that of surface flow because the parameters IOQC and AOQC are the least sensitive parameters for E. coli simulation. Both parameters affect the E. coli concentration in interflow and baseflow (Bicknell et al., 1997). The simulated E. coli of LSTM rose sharply and dropped slowly, similarly to the observations, whereas that of the HSPF decreased steeply (Figs. S6–S11). Although both models simulated the peak time of the E. coli correctly, the HSPF was limited in its ability to simulate the slope of the falling limb. This performance difference between models was caused by the extent of the influence from hydrological variables (e.g., rainfall, surface flow, and subsurface flow) on model output. LSTM was effective in reflecting the response of the output to hydrologic variables (Kratzert et al., 2019).

We observed that both HSPF and LSTM simulated peaks even when the observed data did show corresponding peaks (Figs. S8 and S11). The peaks predicted in Fig. S8 are solely from HSPF, while the peak event in Fig. S11 is predicted by both HSPF and LSTM models. This shows the efficacy of both calibrated models. We could conclude from Fig. S11 that the lack of an observed peak is more likely because of missing observation. However, a similar conclusion cannot be drawn for all the predicted E. coli peaks in Fig. S8 because of contradicting results of LSTM and HSPF.

The performance metrics for the LSTM and HSPF models during storm events are shown in Fig. 8. In general, we observed better LSTM performance than HSPF in terms of NSE and MSE values. The HSPF model performed better than the LSTM for only two storm events: on 15 June 2014 and 11 June 2015. For the remaining storm events, the NSE values from LSTM are higher than those of the HSPF – an NSE range from 0.20 to 0.65. Similarly, for MSE values, the LSTM was superior to the HSPF for all storm events except for the storm events on 15 June 2014 and 11 June 2015.

We observed the impact of logarithmic and min–max transformations on the model performance (Fig. 9). The results of the logarithmic transformation were closer to the observations than the min–max transformation by showing an NSE of 0.57. A negative PBIAS value was obtained in logarithmic transformation. This indicated that the simulated E. coli from logarithmic transformation was underestimated, whereas the result of the min–max transformation was overestimated. This behavior can be attributed to the ability of min–max scaling to be more sensitive to outliers (Chuang et al., 2010). As a result, if a better accuracy during storm events is required, the target variable can be transformed on a logarithmic scale prior to calibration. This is because log transformation can reduce the effect of outliers (Singh and Kingsbury, 2017). It has been reported that log transformation can improve the performance of data-driven models when the data contain outliers (Zheng and Casari, 2018).

We investigated the impact of land-use change and bacterial sources on the in-stream E. coli concentration simulation (Fig. 10). In scenario 1, we used land-use change time-series information (Fig. S1a) and bacterial source information (Fig. S1b). In scenario 2, we divided the bacterial source by the fraction of each land use (Fig. S2c). In scenario 1, we observed a larger variation in E. coli concentration from 2014 to 2018 (Fig. 10a), whereas in scenario 2, the variation in E. coli was smaller than that in scenario 1 (Fig. 10b). This variation in E. coli was due to land-use change in scenario 1. In particular, E. coli in 2016 was less than in other years because the Annual crop land use decreased. On the other hand, the variation in E. coli was not observed in scenario 2 from 2015 to 2017. Neither scenario showed a significant response from 2011 to 2014. During these years, the rise in Fallow land use was complemented by a decrease in Annual crop land use.

Transport of soil particles by surface flow and suspended sediments within the stream plays a crucial role in the fate and transport of E. coli (Thupaki et al., 2013). Several studies have emphasized the importance of particle size (Cho et al., 2010), adsorption to soil and sediment particles (Palmateer et al., 1993), and resuspension of E. coli (Kim et al., 2017) with streambed sediments for modeling the fate and transport of E. coli at the catchment scale. In this study, we considered neither sediment transport nor the attachment/detachment of E. coli on/from soil particles and suspended sediments. Several studies have been conducted on the monitoring and modeling of E. coli without considering sediment transport (Ahmadisharaf and Benham, 2020; Mishra et al., 2018). However, the need for its inclusion has been indicated elsewhere (Pandey and Soupir, 2013). To model sediment transport, additional data on suspended sediment concentration are required to build both the HSPF and deep-learning-based models. Therefore, this modeling can be further improved by collecting sediment-related data and modeling sediment transport along with E. coli concentration.

The deep-learning-based approach can yield high model performance, but it has the limitation in terms of explainability and interpretability (Molnar, 2020). The neural networks are generally considered black boxes, and the question of interpreting them is still an open research problem (Mitchell, 2021; Tiddi, 2020). Several methods have been proposed to interpret the behavior of neural networks (Molnar et al., 2020). Explaining the output of neural networks can enhance the confidence of decision makers (Lipton, 2018). Therefore, we propose future research involving deep-learning models will benefit if the questions of interpretability and explainability are considered along with a model's prediction performance.

Deep-learning models are based upon the independent and identically distributed (IID) assumption, which means that the validation data are expected to have the same distribution as that of the training data (Kawaguchi et al., 2017). However, this is not a realistic assumption, and it is considered one of the challenges for researchers in machine learning (Bengio et al., 2021). Thus, in order to build regional or global hydrological models, the deep-learning model should be trained on catchment data from diverse catchments. Several researchers have adopted this approach to build regional models for streamflow prediction (Anderson and Radic, 2021; Kratzert et al., 2019; Xiang et al., 2021). However, a similar approach for building regional water quality models will be more challenging due to the scarcity of water quality data. We hope that the lessons from this study can be used as a guideline to train neural networks on regional water quality data.