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Extreme Learning Machine Predicts High-Frequency Stream flow and Nitrate-N Concentrations in a Karst Agricultural Watershed
Timothy McGill2, William Isaac Ford1,*
Published in Journal of the ASABE 67(2): 305-319 (doi: 10.13031/ja.15747). Copyright 2024 American Society of Agricultural and Biological Engineers.
1 Biosystems and Agricultural Engineering, University of Kentucky, Kentucky, USA.
2 Geosyntec Consultants, Jacksonville, Florida, USA.
* Correspondence: bill.ford@uky.edu
Submitted for review on 24 July 2023 as manuscript number NRES 15747; approved for publication as a Research Article and as part of the “Digital Water: Computing Tools, Technologies, and Trends” Collection by Associate Editor Dr. Debabrata Sahoo and Community Editor Dr. Kati Migliaccio of the Natural Resources & Environmental Systems Community of ASABE on 8 December 2023.
Highlights
Abstract. Efforts to reduce nitrogen contributions from karst agroecosystems have had variable success, in part due to an incomplete understanding of nitrogen source, fate, and transport dynamics in karst watersheds. Recent advancements in environmental sensors and data-driven artificial intelligence models may be useful in improving our understanding of system behavior and the linkages between soil hydrologic processes and karst nitrate loading dynamics. We collected 35 months of high-resolution streamflow, nitrate-N concentration, soil moisture and temperature (from 10-100 cm depths), and meteorological data in a karst agricultural watershed in the Inner-Bluegrass region of Central Kentucky. Two-layer extreme learning machine (TELM) models were developed to predict nitrate-N concentrations and flow rates as a function of meteorological and soil parameter inputs. Results suggest tight linkages between soil moisture gradients at different depths and nitrate-N concentrations at the watershed outlet. TELM modeling results supported visual observations from the high-frequency data and suggest that inclusion of both soil moisture and temperature parameters at all soil depths improved predictions of both flow rate and nitrate-N concentration (with optimal NSE values of 0.93 and 0.94, respectively, when all inputs were considered). Hysteresis analysis suggested that inclusion of the deepest soil layer (100 cm) was necessary to predict hysteresis observed during storm events. The findings of the study highlight the importance of variable activation of matrix waters in preferential flows throughout events and seasons and its subsequent impacts on nitrate-N concentrations. Results suggest that management models should incorporate vertical variability in soil hydrology to accurately characterize nitrate source and transport dynamics. Further, the results of hysteresis analysis underscore the importance of inclusion of hysteresis indices, in addition to typical model evaluation statistics, to ensure accurate representation of nutrient flow pathways.
The hydrologic and biogeochemical drivers of nitrate loading from karst agricultural watersheds remain poorly understood despite the recognized impact of these landscapes on eutrophication of receiving waters (Weary and Doctor, 2014; Robertson and Saad, 2021). Recent studies have demonstrated that nitrogen transiently stored in the vadose zone is often the primary source of nitrate in watersheds without high rates of chemical fertilizer, manure, or sewage inputs (e.g., Husic et al., 2019; Chang et al., 2022). Nevertheless, current process-based and conceptual modeling frameworks in karst agroecosystems have limitations in simulating nitrate loading dynamics due to an oversimplification of soil hydrological and biogeochemical processes and to the high parametric uncertainty associated with equifinality (Hartmann, 2016; Husic et al., 2019). A need exists to advance our understanding of the impact of soil hydrologic and biogeochemical drivers on nitrate loadings in karst landscapes to improve management tools. Recent influxes in high-frequency sensing data have led researchers to increasingly utilize AI-based modeling approaches as predictive and inference tools in water quality assessment, yet their utility for predicting nitrate dynamics in karst agroecosystems remains unclear and is the focus of this study.
Karst landscapes are characterized by dissolution conduits and caves in the subsurface bedrock that have high hydrologic connectivity to surface and soil water. Karst soils that develop on carbonate rock are fine textured with a high clay content (Hartmann et al., 2014). As a result, transmission of waters to the subsurface through the soil matrix (micro porosity) is often low, and subsurface connectivity to dissolution conduits generally occurs through preferential flow paths (e.g., sinkholes and swallets). However, studies have demonstrated that hydrological and biogeochemical processes in the soil matrix are the most important drivers of nitrate concentration dynamics to subsurface springs (Husic et al., 2019). More recently, preferential flow dynamics from soil have been identified as a primary factor impacting nitrate delivery to subsurface springs in cultivated landscapes (Yan et al., 2023), cumulatively suggesting that variable connectivity of soil matrix waters to subsurface conduits via preferential flow paths is an important driver. Preferential flows are now recognized to be comprised of both waters stored in the bulk soil matrix prior to the event (old-water) and event water in the form of precipitation or irrigation inputs (new-water) (Nazari et al., 2022). Exchange between the bulk soil matrix and macropore domains is bi-directional depending on antecedent conditions (Klaus et al., 2013; Germer and Braun, 2015; Chen et al., 2021). During precipitation events with low antecedent moisture, preferential flows from overland flow may be transported directly to the subsurface or may infiltrate into soils; however, under saturated soil conditions, pre-event matrix water can be mobilized to groundwater springs via preferential flow paths and can occur at variable depths throughout the soil column (Klaus et al., 2013; Ford et al., 2018; Wang et al., 2018). Variable connectivity of different soil layers during storm events is likely important for predicting nitrate concentrations and loadings in karst agroecosystems.
Additionally, vertical and temporal variability in soil biochemical processes influence the nitrate composition of porewaters that are transiently stored in the soil matrix. For example, coupled evapotranspiration and mineralization of soil organic matter can result in nitrate buildup in porewaters between flushing events, leading to seasonal variations in nitrate concentrations in both karst and non-karst agroecosystems (Donner et al., 2004; Yevenes and Mannaerts, 2011; Tian et al., 2015; Yang et al., 2017; Seybold et al., 2019; Yue et al., 2019). As a result, studies have demonstrated asymmetric profiles of nitrate-N concentrations with depth in the soil column (Igbal and Krothe, 1995; Green et al., 2018). Nevertheless, existing conceptual and physically based models simulating karst hydrology and water quality often neglect vertical soil profile variability (e.g., Hartmann et al., 2014; Husic et al., 2019), due in part to limited databases that capture nitrate dynamics at high frequencies.
Advances in sensing technology over the last decade have enabled the collection of in situ hydrologic and water quality data at sub-hourly frequencies via UV spectroscopy-based sensors (Pellerin et al., 2013; Carey et al., 2014; Jensen and Ford, 2019). These high-frequency datasets have enabled analysis of concentration versus discharge patterns at the event-scale, which can inform source and pathway connectivity dynamics (Blaen et al., 2017; Liu et al., 2021). In karst agroecosystems, watershed nitrate concentrations during storm events initially become diluted with low nitrate concentrations from new-water on the rising limb of the hydrograph, increase following peak flows as soil and epikarst connectivity of old-water increases, and then decrease towards pre-event levels as phreatic connectivity becomes prominent during the receding limb of the hydrograph (Baran et al., 2008; Rusjan et al., 2008; Buda and DeWalle, 2009; Ford et al., 2019; Husic et al., 2019). Quantitative hysteresis index (HI) values have been used to evaluate the direction and magnitude of hysteretic behavior and therefore may be useful in numerical model evaluations to ensure models can accurately capture nitrate source and pathway variability (Liu et al., 2021; Mehdi et al., 2021; Husic et al., 2023). Given the variability in connectivity of waters throughout the soil profile during events and variable nitrate concentrations in pore waters with depth, we hypothesize that the hysteretic behavior of watershed nitrate concentrations is tightly linked with the hysteretic behavior of soil hydrology.
Given the limitations of current numerical models to simulate karst hydrology and water quality, data-driven artificial intelligence models may be useful in informing important processes that impact nitrate concentrations. The influx of large databases associated with in situ sensor advancements has led to an increase in AI applications in hydrologic and water quality studies in recent years (Krishnan et al., 2022). Several studies have applied Extreme Learning Machines (ELMs), which are feedforward neural networks that achieve similar or better generalization performance, scalability, and faster learning times than other AI-modeling approaches such as support vector machines (Huang et al., 2012). Recent studies have demonstrated the effectiveness of ELM models to predict stream and river flow rates (Deo and Sahin, 2016; Yaseen et al., 2016; Roushanger et al., 2017; Rezaie-Balf and Kisi, 2017; Yaseen et al., 2019), as well as ground and surface water quality (Barzegar et al., 2018a,b; Fijani et al., 2019). Therefore, ELM models may also be effective at simulating nitrate loading dynamics in karst agroecosystems.
The objective of this study was to assess the impact of soil hydrologic connectivity dynamics on nitrate loadings in karst agroecosystems, utilizing an AI-based modeling approach to inform important processes. To meet the overarching objective, the specific objectives were to: (1) collect and analyze a novel high-frequency in situ dataset of surface water nitrate-N concentrations and flow rates and compare with high-frequency soil sensing data in a karst agricultural watershed, (2) assess the utility of ELM models to predict nitrate-N concentrations and flow rates in the karst agroecosystem and quantify the relative importance of meteorological, soil moisture, and soil temperature inputs on model response variables, and (3) assess the utility of ELM models to account for storm-event hysteresis impacting nitrate-N concentration and loadings.
Study Site
To meet the objectives of this study, data collection and analysis efforts were conducted in the Camden Creek watershed in Kentucky, U.S.A. (fig. 1). This watershed has a drainage area of 1,069 ha (including surface and spring drainage areas) and drains much of the University of Kentucky 600 ha C. Oran Little Research Center (LRC). The watershed is located within the Inner-Bluegrass physiographic region of central Kentucky, which is characterized by a temperate Midwestern United States climate (Ford et al., 2019). Over the past decade, the region has received an average annual rainfall of 1322 mm with an average temperature of 13.14°C. The surface tributaries in the watershed are shallow and emanate from springs. Streams flow over limestone bedrock and are mostly unshaded through grazed pasture with riparian vegetation, with low streambed sediment storage on the exposed bedrock (Ford et al., 2019).
The watershed was selected for study because: (1) extensive hydrologic and water quality research has been conducted in the watershed (Ford et al., 2019; Bunnell et al., 2020; Radcliffe et al., 2021), (2) a U.S. Climate Reference Network meteorological and soil gauging station is located on the research farm, (3) the watershed is impacted by complex heterogeneity in karst maturity with flow pathways ranging from seeps activated during high-intensity rainfalls to large regional perennial springs (Reed et al., 2010), and (4) the land use is typical of agriculture across the state of Kentucky, as well as much of the food producing Midwest encompassing cropland, animal husbandry operations including beef, swine and sheep facilities, and pasture lands for horse and cattle. Inorganic nitrogen application rates and the volume of manure slurry applied to the fields were provided by farm managers. Based on reported fertilization rates, organic fertilizer application (injected liquid swine manure) occurred on approximately 4% of the watershed area, while inorganic fertilizer application (primarily 32-0-0 urea ammonium nitrate and 46-0-0 urea) occurred on approximately 16% of the watershed area. In our preliminary analysis, we considered application rate and timing as model input variables but found them to be insensitive predictors, likely because of the limited drainage area impacted by fertilization (McGill, 2022). We therefore excluded fertilization as an input variable for this study.
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| Figure 1. (a) University of Kentucky ARC property lines in Kentucky, USA, noting fields, basin watershed boundaries, and locations of the ST1 surface water monitoring site and the NOAA weather station. (b) Aerial image of the NOAA meteorological and soil moisture sensing station. (c) Sensors, housing, and v-notch weir located at the watershed outlet. |
Methodology
Data Collection and Analysis
Data collection efforts included surface water, meteorological, and soil monitoring. Surface water measurements were collected at the watershed outlet (ST1) and included flow depth and nitrate-nitrite-N concentrations obtained from in situ water quality sondes that were validated via grab sample analysis. Meteorological and soil variables, including precipitation, wind speed, air temperature, solar radiation, soil moisture, and temperature at depths of 10, 20, 50, and 100 cm were obtained from the National Centers of Environmental Information’s climate reference network, which is operated through the National Oceanic and Atmospheric Administration (NOAA).
Surface Water Measurements
Volumetric flow rates (Q) at the watershed outlet were calculated based on flow depth over a 120° V-notch with an invert 0.5 feet from the channel bed with a YSI EXO2 sonde (Bunnell et al., 2020). The YSI EXO2 Sonde required monthly calibration, battery replacement, and general maintenance consistent with manufacturer specifications. The sonde’s pressure measurements were collected at 15-minute intervals, beginning on 29 August 2018 through 4 August 2021 (1070 days), with some periodic gaps in the record due to sensor failures and research restrictions associated with the Covid-19 pandemic. Flow depths measured with the sonde were compared with manual flow depth measurements to ensure accuracy.
High-frequency nitrate/nitrite-N measurements at the watershed outlet were obtained using a SUNA V2 sensor manufactured by Sea-Bird Scientific. Data were collected from 7 September 2018 to 4 August 2021 at 15-minute intervals. Like flow rate, data gaps existed due to sensor errors, restrictions to research from Covid-19 precautions, and data that failed QC protocols. The longest period of missing data occurred from 20 November 2019 until 20 July 2020. Reference spectrum updates were completed every four to twelve weeks, although most updates were carried out every four to five weeks. The sensor was checked for debris or other possible fouling during site visits. The SUNA was powered externally, and a data logger was used to store and offload data. The software used to communicate with the SUNA V2 was Sea-Bird Scientific’s UCI 2.0.3 version software. Grab samples were used to validate SUNA measurements and ensure flagged values were accurate. At least two samples were collected each month and delivered to the Kentucky Geological Survey for analysis of nitrate-N with EPA method 9056A-Determination of Inorganic Anions by Ion Chromatography (EPA, 2007). Concentrations of nitrite-N are generally more than an order of magnitude lower than nitrate-N at the site, and hence were not measured explicitly. Linear regression was performed between measured nitrate-N values and SUNA measurements to ensure the accuracy and precision of in situ measurements.
Meteorological and Soil Moisture Data
Soil and meteorological data were obtained from the Midwestern Regional Climate Center cli-MATE database and the U.S. Climate Reference Network (Diamond et al., 2013) and collected by the automated weather observation system located on the LRC property (ID:63838, latitude 38.0944 N, longitude -84.7464 W, fig. 1). This station contains a Geonor T-200B series precipitation gauge and three sets of HydraProbe II sensors using SDI-12 connections mounted 120° off from each other (fig. 1), based on NOAA standards (Geonor, 2016; NOAA, 2021). The station is in a pasture field, containing Bluegrass-Maury and McAfee silt loam-soil along a hillslope that is characteristic of the broader Camden Creek watershed. Soil moisture and temperature sensors were located at 10, 20, 50, and 100-cm depths. Data were collected hourly and interpolated to 15-minute results using linear interpolation to align with nutrient and flow rate measurement frequency. Meteorological variables including precipitation, 1.5m windspeed, air and surface temperature, relative humidity, and solar radiation data were obtained at 5-minute intervals and were aggregated to 15-minute intervals. The meteorological and soil data were obtained from 29 August 2018 to 4 August 2021. While we feel the meteorological and soil data were characteristic of the watershed, we note that the soil and meteorological data was limited to this single monitoring station.
There were several periods with missing or erroneous soil data. The largest data gap was associated with the 100-cm data from 29 August 2018 to 30 June 2019. Following quality control analysis, 100 cm soil depth data were only analyzed from July 2020 to August 2021. Further, during manual inspection of the 50 cm soil data, periodic short-term erroneous increases in soil moisture data were removed and interpolated based on measurements before and after the erroneous readings. Data gaps also existed from 31 December 2018 until 12 January 2019 for air temperature, precipitation, surface temperature, and 1.5 m wind speed.
Modeling Nitrate-N Concentrations in Karst Agroecosystem Watershed
Model Scenarios and Approach
Data-driven AI modeling was performed to assess: (1) ‘How does representation of soil hydrologic variability impact watershed nitrate-N concentration and flow predictions in karst watersheds?’, and (2) ‘What degree of vertical discretization of the soil profile is needed to represent within-event hysteresis dynamics?’. The response variable in the model was nitrate-N concentrations or flow rate at the watershed outlet. Variables used as inputs for the nitrate-N concentration and flow rate predictions were based on available long-term meteorological and soil data, which were perceived to impact hydrologic and N cycles in the karst agroecosystem watershed. Model inputs included precipitation, air temperature, ground surface temperature, soil moisture and soil temperature at depths of 10, 20, 50, and 100 cm, solar radiation, wind speed at 1.5 m, and relative humidity. We ran three model scenarios to address our research questions. Scenario 1 included all meteorological parameters and soil moisture and temperature variables from 10 to 50 cm for the full 3-year monitoring period. Scenario 2 included only meteorological parameters for the full 3-year monitoring period. Scenario 3 included all meteorological parameters and soil moisture parameters from 10 to 100 cm for the one-year period in July 2020 to August 2021, in which all datasets were available.
We selected a two-hidden-layer ELM (TELM) model to predict the nitrate-N concentration and flow rate response variables at the watershed outlet. For each of the three modeling scenarios, the input and response variable datasets were randomly divided into fifths, in which four of the divided sets were used to train the model in batches and the last fifth was retained for model validation. Each scenario was trained at least three times to account for training equifinality. We used the Rectified Linear Unit activation function (Agostinelli et al., 2014; Banerjee et al., 2020; Jin et al., 2015). We tested the sensitivity of the number of hidden layers and the number of neurons in each hidden layer and found that 50 neurons in each hidden layer provided the lowest mean squared (MSE) for outputs. To check for TELM model overfitting due to redundant inputs, a variable pruning analysis (Bishop, 1995) was performed, and the results showed a limited impact on model fit and calibration statistics. An optimized tensor computation package known as PyTorch was employed to assist in model generation in Python (Steppa and Holch, 2019).
Statistical Evaluation of Model Performance
The output of the TELM model for each scenario was compared using statistical and visual model evaluation approaches. Timeseries of measured and modeled data were plotted to visualize goodness-of-fit both globally and at finer-resolution time scales. Nash-Sutcliffe Efficiency (NSE) was used as a quantitative model evaluation statistic (McCuen et al., 2006; Moriasi et al., 2007) and was calculated as follows:
(1)
where
= ith observation of nitrate-N concentration or flow rate
= ith value of nitrate-N concentration or flow rate from the model
ymean = mean of the observed nitrate-N concentration or flow rate for the entire modeling period
N = total number of observations.
Integrated Gradients Analysis of Input Variables
Integrated gradients (IG) analysis was performed to determine the impact of input variables on model training. Gradients of the output with respect to the model input are a natural analog of the model coefficients for a deep network, meaning they are a good starting point for defining the attribution, or relevance, of inputs to the output (Sundararajan et al., 2017). The IG algorithm within the Captum module recognizes these gradients within the trained model and integrates them across the entire sample to determine the average importance each variable carried during the training process (see Sundararajan et al., 2017 for full explanation). By using these integrated gradients, each variable’s perceived effect on the system can be represented. Values were reported as a fraction and sum to one. This attribution function was run three times for each model run to ensure an accurate estimate was made due to the use of the Riemann Sum to determine the IG. Once generated from each model run, the IG were averaged, giving a composite IG for each run. The composite IGs from each run were then averaged to give an IG for each scenario.
Concentration-Discharge Hysteresis Analysis
To evaluate the ability of the TELM model to predict nitrate hysteresis, we performed quantitative hysteresis index (HI) and qualitative concentration-discharge plot analysis (Lloyd et al., 2016). A small, medium, and large (except for summer) event was obtained from each season, and we compared the observed hysteresis using the measured nitrate-N concentration and observed discharge with the modeled hysteresis using the predicted nitrate-N concentration and observed discharge. We operationally defined event size based on peak flow rate (small < 0.3 cms, medium 0.3 to 0.9 cms, and large > 0.9 cms). The seasons were defined as winter (21 December to 19 March), spring (20 March to 20 June), summer (21 June to 21 September), and fall (22 September to 20 December). In total, eleven storm events were selected for analysis (table 2). The hysteresis index was determined by first normalizing the flow and concentration data for each storm event as follows:
(2)
where
Qi = measured flow at the ith time step
Qmin = minimum flow measured during the event period
Qmax = maximum flow measured during the event period.
(3)
where
Ci = nitrate-N concentration at time step i
Cmin = minimum nitrate-N concentration during the event period
Cmax = maximum nitrate-N concentration during the event period.
With data normalized, the HI can be determined by calculating the difference in normalized concentration values on rising and falling limb at 5% and averaging intervals throughout the event.
(4)
where
k = index representing percentile of peak flow in 5% increments
HIevent = hysteresis index for each event
Ck,RL = normalized concentration at kthpercentile of flow on the rising limb
Ck,FL = normalized concentration at kthpercentile of flow on the falling limb
M = number of flow intervals analyzed.
Results and Discussion
Surface Water and Soil Data Results
Results showed that the SUNA V2 in situ measurements produce accurate and unbiased results under low and high flow conditions relative to laboratory analysis of the 80 grab samples (figs. 2 and 3a). The best-fit linear regression equation between laboratory and SUNA V2 measurements had a slope of 0.96 and an intercept of 0.07 (R2 = 0.98) (fig. 2).
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| Figure 2. Linear regression comparing laboratory analysis of grab samples (Laboratory Nitrate-N concentration) and the SUNA V2 Nitrate-N measurements. Linear regression results and coefficient of determination are included. |
Timeseries of the nitrate-N and discharge data highlighted the impacts of flow dynamics and seasonality on nitrate-N concentrations (fig. 3). On average, summer concentrations were least, often dropping below 2 mg/L, coinciding with lower flow rates for the season. Conversely, during elevated baseflow conditions of late fall and winter, nitrate-N concentrations were greater, often exceeding 4 mg/L. Regarding storm events (figs. 3b-e), a dilution in the nitrate-N concentration was commonly observed on the rising limb of the hydrograph, although this dilution is much more prominent in the winter months, reflecting the gradients observed in pre-event concentrations between seasons. On the falling limb of the hydrograph, nitrate-N concentrations increased and often met or exceeded pre-event levels.
Findings from our study site are reflective of dynamics commonly observed for contaminants in karst and agricultural watersheds, excluding findings from heavily fertilized agricultural landscapes (Liu et al., 2007; Baran et al., 2008; Buda and DeWalle, 2009; Blaen et al., 2017; Husic et al., 2019; Yue et al., 2019; Jackson and Polk, 2020). Storm event hysteresis patterns reflect hydrologic connectivity pathways that have been commonly described. Lui et al. (2007) and Jackson and Polk (2020) showed similar seasonal trends and storm event dilution and recharge characteristics in karst study sites when analyzing specific conductance and dissolved inorganic carbon. Likewise, numerous studies have highlighted increased nitrate-N concentration and loading during the wet season, which has been attributed to enhanced hydrologic connectivity of nitrate rich pore waters in the soil to the watershed outlet (Basu et al., 2010; Yang et al., 2017; Husic et al., 2019; Yue et al., 2019). Contrary to findings from heavily fertilized agricultural fields and watersheds (e.g., Rusjan et al., 2008; Kennedy et al., 2012; Ford et al., 2018), we did not find flushing of nitrate-rich waters during the rising limb or peak of the hydrograph, which is demonstrated quantitatively in our hysteresis analysis (table 4; fig. 6).Collectively, the findings suggest the study site is a representative testbed to evaluate the ability of machine learning algorithms to represent hydrologic connectivity processes of N sources, although its inability to reflect fluvial fertilizer losses is a limitation.
Comparison of the nitrate-N measurements with soil moisture data illustrates that the magnitude and variable response of soil moisture layers with depth correspond with nitrate-N concentration dynamics at the watershed outlet (fig. 4). The measured nitrate-N concentrations were typically low during periods of low soil moisture, and concentrations were elevated during periods of high soil moisture (fig. 4a). Generally, greater changes in soil moisture levels corresponded with greater shifts in nitrate-N concentrations. In events during seasonal transitions from dry to wet periods, particularly summer to late fall (fig. 4b), the variable soil moisture responses within different layers of the soil profile corresponded with a variable response in nitrate-N concentration fluctuations. When the shallower depths of the soil profile (10 and 20-cm depths) had increasing soil moisture contents without a response in deeper soil layers (e.g., 25 to 26 August 2019), modest increases in nitrate-N concentration were observed (1.26 to 1.86 mg/L). Conversely, as deeper soil layers (e.g., 50-cm) had increasing soil moisture content, larger shifts were observed in nitrate-N concentrations. For instance, the 6 October 2019 event impacted the 50-cm soil depth with an increase in volumetric water content from 0.13 to 0.19, and a subsequent increase in nitrate-N concentration from 0.36 to 2.53 mg/L was measured (fig. 4b). We also observed a lag in response time between the layers of the soil profile when all measured layers are dynamic during an event (fig. 4c). This shows the deeper layers begin to activate and reach their peak moisture content later in the event than the shallower layers, with the 100-cm layers showing activation following all other layer’s peak activation. Given the variable response of nitrate dynamics to the variable soil depths and the variable timing of soil moisture response during storm events, we anticipate that representation of soil moisture variability would be an important component to accurately represent event-hysteresis dynamics.
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| Figure 3. (a) Timeseries for measured nitrate-N concentrations and discharge at the watershed outlet from 29 August 2018 through 4 August 2021. Storm events and subsequent recessions are provided for typical events in winter on (b) 10 to 11 February 2021, and (c) 23 to 24 January 2019. Storm events and subsequent recessions are also provided for typical events in summer on (d) 2 to 3 September 2020 and (e) 21 to 22 July 2019. |
TELM Modeling of Flow Rate and Nitrate-N Concentrations
Comparison of the predicted nitrate-N concentration for Scenarios 1 and 2 highlighted the importance of accounting for soil moisture variability in predicting dynamics in the karst agroecosystem watershed (table 1; figs. 5a-c). For the nitrate-N concentration models, the best fit models for Scenario 1 and 2 had NSE averaging 0.89 and 0.38, respectively. While the criterion is not available for sub-daily NSE values, the daily criterion for N modeling (Moriasi et al., 2015) suggests our results would fall in the “Very good” and “Satisfactory” categories for Scenario 1 and 2, respectively. Visually, the results show the TELM models in both Scenario 1 and 2 represented the seasonality of the data, with an average increase during the wetter winter months and an average decrease during the summer months (figs. 5a and 5b). Where the models differed was in predicting variability in nitrate-N concentrations at shorter timescales, particularly when there were major shifts in both the nitrate-N concentrations and soil moisture contents in deeper soil layers (e.g., October 2020). Results of within-event variability are compared for Scenarios 1 and 3 using the hysteresis analysis (table 4; figure 6).
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| Figure 4. (a) Measured nitrate-N concentrations are plotted against the volumetric water content measured at four different depths within the soil profile (10, 20, 50, and 100-cm) throughout the monitoring period of 29 August 2018 through 4 August 2021. (b) Period from 7 August to 20 November 2019 is emphasized to demonstrate varied temporal response of soil moisture with depth and the associated impacts on nitrate-N concentrations. (c) Rain event on 25 to 26 January 2021 showing the activation of the various layers within the soil profile and the time lag associated with this activation during a rain event. |
Similarly, flow rate modeling improved when including soil moisture data but highlighted the importance of representing the 100 cm soil layer dynamics to accurately predict hydrographs (table 1; figs. 5d and 5e). Best fit models for Scenario 1 and Scenario 2 had NSE values of 0.65 and 0.16, respectively, which would fall in the “Satisfactory” and “Not Satisfactory” categories for daily flow model evaluations outlined in Moriasi et al. (2015). Both models captured baseflow variability seasonally; however, Scenario 2 was not able to capture event-scale hydrograph dynamics (figs. 5d and 5e). Scenario 1 improved capturing general trends of hydrographs during events but often missed peak flow predictions. When including 100 cm soil depth data in Scenario 3, visual and statistical results improved markedly over Scenario 1, with NSE values increasing to 0.93 and an improved representation of peak flows and hydrograph recessions (fig. 5f).
Comparing results from the integrated gradients analysis supports the importance of both soil moisture and temperature for predicting stream nitrate-N concentrations and flow rates (table 3). The soil moisture and temperatures at various depths within the soil profile received the highest attribution scores for both nitrate-N concentration and flow rate predictions. For nitrate-N modeling, soil parameters had attribution scores summing to 0.82 (0.39 for soil moisture, 0.43 for soil temperature) and 0.80 (0.42 for soil moisture and 0.38 for soil temperature) for Scenarios 1 and 3, respectively. Similarly, soil parameters had attribution scores summing to 0.81 (0.52 soil moisture and 0.29 soil temperature) and 0.80 (0.41 soil moisture and 0.39 soil temperature) for Scenarios 1 and 3 of the flow rate models. This finding suggests similar importance of both soil moisture and temperature in both hydrologic and nitrate-N concentration simulations and marginal contributions <0.2 of all other variables. Surprisingly, precipitation was the least important parameter in modeling, likely reflecting the lag time between precipitation occurrences and the subsequent hydrologic response at the watershed outlet.
| Table 1. Summary of the variables included in each set of model training scenarios for both nitrate-N and discharge. Each scenario was trained three times to develop an average. The highlighted cells indicate which variables were included in each set of runs. Average Nash Sutcliffe Efficiency results for both nitrate-N concentrations and discharge are provided for each scenario. | ||||
| Variables | Scenario 1 (Aug 2018- Aug 2021) | Scenario 2 (Aug 2018- Aug 2021) | Scenario 3 (Aug 2020- Aug 2021) | |
| Atmospheric variables | Precipitation, wind speed, solar radiation, air temp, surface temp, relative humidity | |||
| Soil Profile | 10 cm | |||
| 20 cm | ||||
| 50 cm | ||||
| 100 cm | ||||
| Nash Sutcliffe Efficiency (NSE) | Nitrate-N Model | 0.89 | 0.38 | 0.94 |
| Flow rate Model | 0.65 | 0.16 | 0.93 | |
| Table 2. Summary of the rain events chosen to perform the hysteresis analysis. Three events of varying sizes were chosen from each season to evaluate the TELM model’s ability to capture storm event dynamics. Captured events during the summer months in our monitoring duration did not meet the criteria for a large event. | ||||
| Season | Size | Start Date | End Date | Max Q (cms) |
| Summer | Small | 29 July 2020 | 9 August 2020 | 0.18 |
| Med | 3 July 2019 | 13 July 2019 | 0.40 | |
| Large | None | None | None | |
| Fall | Small | 19 December 2020 | 23 December 2020 | 0.14 |
| Med | 28 October 2020 | 10 November 2020 | 0.36 | |
| Large | 30 October 2019 | 7 November 2019 | 1.85 | |
| Winter | Small | 10 February 2021 | 21 February 2021 | 0.28 |
| Med | 30 January 2021 | 10 February 2021 | 0.84 | |
| Large | 27 February 2021 | 14 March 2021 | 2.76 | |
| Spring | Small | 23 April 2021 | 29 April 2021 | 0.08 |
| Med | 2 May 2021 | 22 May 2021 | 0.76 | |
| Large | 6 June 2021 | 13 June 2021 | 1.53 | |
The results of the model evaluation and integrated gradients analysis suggest the importance of soil moisture and temperature dynamics to regulate both hydrologic and biochemical processes impacting watershed nitrate loadings. Regarding nitrate-N concentrations, soil temperature and moisture were expected to be important predictors of nitrate-N concentrations, given that they are well recognized to impact a variety of N transformations such as mineralization, nitrification, and denitrification (De Neve et al., 2003; Guntinas et al., 2012; Miller and Geisseler, 2018). However, the sensitivity of flow rate predictions to both moisture and temperature of the different soil layers also likely reflects the ability of the model to capture variable hydrologic connectivity throughout an event. The importance of soil moisture variables likely reflects that stored matrix water becomes hydrologically connected to the watershed outlet via matrix-macropore interaction, conveying the water and constituents to subsurface conduits and springs (Donner et al., 2004; Yevenes and Mannaerts, 2011; Tian et al., 2015; Husic et al., 2019).
The importance of soil temperature parameters in flow modeling is less intuitive. One possible explanation is that soil temperature variability reflects infiltration of influent rainfall and preferential flows, which will impact the extent of transport to the monitored surface channel and hence enable improved understanding of water attenuation by the soil layers. Similarly, for nitrate-N concentrations, soil moisture temperature is a non-conservative tracer (e.g., Chi et al., 2020) and will reflect the extent of mixing of pre-event matrix waters and new water from the event. Therefore, it may have aided in accounting for the time-varying concentration dynamics of the pore waters that are then transported to preferential flow paths during events. While the exact reasons for the sensitivity of these variables remain uncertain, and are outside the scope of our study, our results highlight the importance of representing soil profile variability when simulating karst watershed hydrology and nitrate-N concentrations and provide avenues for future investigation.
Hysteresis Analysis
Qualitative concentration versus discharge plots for measured and modeled (Scenario 1 and 3) nitrate-N concentrations demonstrated improvements when including the 100 cm soil depth measurements (fig. 6). Scenario 3 displayed an improved representation of measured hysteresis dynamics in most events. As an example, for the event from 20 to 21 December, Scenario 1 (fig. 6e) predicts a clockwise hysteresis pattern with concentration increases early in the event, leveling off during most of the rising limb, and slowly decreasing during the falling limb of the hydrograph. Scenario 3 more closely tracks the observed trends for most of the rising limb. It also predicts increased concentrations on the falling limb, resulting in an anti-clockwise looping pattern. Further, for the event from 4 to 5 May (fig. 6j), both scenarios predicted anti-clockwise hysteresis patterns, and the rising limbs of both scenario predictions showcased similar magnitudes and trends. However, Scenario 3 more accurately predicted concentrations on the falling limb, which aligns with the lag-time associated with deeper portions of the soil profile.
(c)  |
| Figure 5. Timeseries of the measured vs. predicted nitrate-N concentrations (a-c) and discharge (d-f) for Scenario 1 (a,d), Scenario 2 (b,e), and Scenario 3 (c,f). Note Scenario 3 has a different timeframe (29 July 2020 through 4 August 2021) from Scenarios 1 and 2. |
The hysteresis index provided further quantitative evidence that Scenario 3 improved the simulation of within-event dynamics as compared to Scenario 1 (table 4). For the eleven observed events, all hysteresis indices were negative, indicating anti-clockwise patterns, and fell between -0.20 and -0.63 (average HI = -0.39). Regarding model results, Scenario 1 predicted that the small events in fall and spring had positive HI values, indicating clockwise hysteresis patterns, and the nine other events had negative HI values, ranging from -0.52 to 0.32 (table 4a). For the events simulated in Scenario 3, the HI values were all negative and fell between -0.57 and -0.19, with an average of -0.33 (table 4b). As a result, the difference between the observed HI and predicted HI for scenario 1 was 0.29, and it was 0.08 for scenario 3 on average. These findings indicate that inclusion of the deepest soil layer (100 cm) was important in capturing the counterclockwise hysteresis behavior across all events and reflects the delay in saturation for the deepest soil layer observed later in the precipitation event (fig. 4c). Collectively, these findings underscore the importance of including vertical soil variability dynamics in accurately representing within-event nitrate-N concentration dynamics.
Implications for Modeling Nitrate Dynamics in Karst Agroecosystems
The availability of novel datasets, including soil moisture, hydrology, and nitrate measurements enabled a highly accurate TELM model of flow and nitrate-N concentrations in a heterogenous karst agroecosystem in this study, but the model may have limitations in broad-scale applicability given that long-term soil moisture and temperature data at different depths are scarcely available. In the absence of soil moisture data, recent innovations have suggested time lags between input and response variables can be represented using transformations and decomposition of input and response variable signals, including approaches such as wavelet transforms (Barzegar et al., 2018a), particle swarm optimization (Zhu et al., 2020), or empirical mode decomposition (Prasad et al., 2018). For instance, Prasad et al. (2018) employed a hybrid ELM model integrated with ensemble empirical mode decomposition to forecast upper and lower layer soil moisture using meteorological data (solar radiation, precipitation, minimum and maximum daily temperatures) along with continental parameter maps (albedo, soil characteristics, and seasonality of vegetation), reporting an R2 of 0.97 between the observed and predicted soil moisture. An adaptation to the ELM model that incorporates one of these methods could prove to be an effective tool in developing models that can accurately represent and predict nitrate exports when soil data are lacking or sparse.
 |
| Figure 6. Concentration vs. discharge hysteresis loops for observed and predicted results for the eleven rain events (a-k) selected for the hysteresis comparison (table 2). Note that only nine events occurred during the period simulated for Scenario 3. |
Regarding process-based and conceptual models, the findings of this study underscore the importance of inclusion of vertical soil variability when quantifying nitrate exports. Existing modeling approaches for water quality simulations in karst utilize reservoir-style models that often lump the entire soil matrix or the soil matrix and epikarst into a single reservoir (e.g., Husic et al., 2019). Our findings suggest that root zone, and deeper soil moisture dynamics (and subsequent matrix-macropore exchange), should be more robustly represented given the gradients observed in nitrate-N concentrations between these zones throughout the year and within events. One approach to accomplishing this is coupling process-based models of soil hydrologic and biochemical processes at the watershed-scale with reservoir models often used to represent epikarst and phreatic zones. Some studies have applied modified versions of the Soil Water Assessment Tool (SWAT) (e.g., Amin et al., 2017) but have had varying success due to high epistemic and parametric uncertainties. Alternatively, better discretization of the soil layer in parsimonious reservoir models (e.g., surface, root zone, and deeper layer) may be sufficient, would significantly reduce parameterization requirements over models such as SWAT, and will be an important area for further investigation.
The results of the hysteresis analysis illustrate the importance of integrating quantitative hysteresis indices into model evaluation to ensure accurate representation of event-scale dynamics and reduce prediction uncertainty. Previous studies suggested the importance of incorporating hysteresis metrics into numerical model evaluation (Liu et al., 2021). A recent study by Husic et al. (2023) integrated nitrate hysteresis metrics into a cascading linear reservoir model simulating flow and nitrate at a daily timestep in a mature karst watershed. The authors found that including hysteresis indices as a model evaluation metric reduced uncertainty associated with both model parameterization and nitrate loading. Our results build on the findings of their study, highlighting the importance of soil profile variability on nitrate hysteresis dynamics, particularly when anti-clockwise loops are
| Table 3. Results of the integrated gradients analysis showing average attribution values assigned to each of the variables used in the tested scenarios. Each set represents the averaged results from at least three runs of the specified scenario for the nitrate-N concentration and discharge models. | |||||||||||||||||||
| Attributions for Nitrate Models from IG analysis | Attributions for Flow rate Models from IG analysis | ||||||||||||||||||
| Scenario 1 | Avg Soil Mstr 50-cm | 0.23 | Avg Soil Mstr 50-cm | 0.33 | |||||||||||||||
| 20-cm Temp | 0.21 | 50-cm Temp | 0.14 | ||||||||||||||||
| 50-cm Temp | 0.17 | Avg Soil Mstr 10-cm | 0.11 | ||||||||||||||||
| Avg Soil Mstr 10-cm | 0.08 | 20-cm Temp | 0.10 | ||||||||||||||||
| Air Temp | 0.07 | Avg Soil Mstr 20-cm | 0.09 | ||||||||||||||||
| Avg Soil Mstr 20-cm | 0.07 | Air Temp | 0.08 | ||||||||||||||||
| Sur Temp | 0.06 | 10-cm Temp | 0.06 | ||||||||||||||||
| 10-cm Temp | 0.06 | Sur Temp | 0.04 | ||||||||||||||||
| Avg Rel Hum | 0.03 | Avg Rel Hum | 0.04 | ||||||||||||||||
| 1.5m Wind Speed | 0.01 | 1.5m Wind Speed | 0.02 | ||||||||||||||||
| Sol Rad | <0.01 | Sol Rad | 0.01 | ||||||||||||||||
| Precip | <0.01 | Precip | <0.01 | ||||||||||||||||
| Scenario 2 | Sur Temp | 0.49 | Sur Temp | 0.52 | |||||||||||||||
| Avg Rel Hum | 0.24 | 1.5m Wind Speed | 0.22 | ||||||||||||||||
| Air Temp | 0.17 | Avg Rel Hum | 0.14 | ||||||||||||||||
| Sol Rad | 0.08 | Air Temp | 0.08 | ||||||||||||||||
| 1.5m Wind Speed | 0.02 | Sol Rad | 0.04 | ||||||||||||||||
| Precip | <0.01 | Precip | <0.01 | ||||||||||||||||
| Scenario 3 | Avg Soil Mstr 20-cm | 0.16 | Avg Soil Mstr 50-cm | 0.20 | |||||||||||||||
| 20-cm Temp | 0.13 | 20-cm Temp | 0.19 | ||||||||||||||||
| Avg Soil Mstr 10-cm | 0.12 | Avg Soil Mstr 100-cm | 0.12 | ||||||||||||||||
| 100-cm Temp | 0.11 | 50-cm Temp | 0.10 | ||||||||||||||||
| 10-cm Temp | 0.10 | 10-cm Temp | 0.09 | ||||||||||||||||
| Avg Soil Mstr 100-cm | 0.08 | Sur Temp | 0.07 | ||||||||||||||||
| Avg Soil Mstr 50-cm | 0.06 | Avg Soil Mstr 20-cm | 0.06 | ||||||||||||||||
| Sur Temp | 0.06 | Rel Hum | 0.05 | ||||||||||||||||
| Air Temp | 0.05 | Air Temp | 0.04 | ||||||||||||||||
| Avg Rel Hum | 0.05 | Avg Soil Mstr 10-cm | 0.03 | ||||||||||||||||
| 50-cm Temp | 0.03 | 100-cm Temp | 0.03 | ||||||||||||||||
| Sol Rad | 0.02 | Sol Rad | 0.02 | ||||||||||||||||
| 1.5m Wind Speed | 0.02 | 1.5m Wind Speed | 0.01 | ||||||||||||||||
| Precip | <0.01 | Precip | <0.01 | ||||||||||||||||
Table 4. The results for the hysteresis index (HI) analysis for Scenario 1 and Scenario 3 included TELM model predicted HI, observed HI, and the difference in hysteresis index between predicted and observed HI. | |||||||||||||||||||
| Season | Size | Start Date | End Date | Max Q (cms) | Predicted HI | Observed HI | Difference | ||||||||||||
| Rain Event Hysteresis Scenario 1 | Summer | Small | 29 July 2020 | 9 August 2020 | 0.18 | -0.12 | -0.63 | 0.51 | |||||||||||
| Med | 3 July 2019 | 13 July 2019 | 0.40 | -0.05 | -0.38 | 0.34 | |||||||||||||
| Large | None | None | None | None | None | None | |||||||||||||
| Fall | Small | 19 December 2020 | 23 December 2020 | 0.14 | 0.32 | -0.55 | 0.87 | ||||||||||||
| Med | 28 October 2020 | 10 November 2020 | 0.36 | -0.52 | -0.26 | 0.26 | |||||||||||||
| Large | 30 October 2019 | 7 November 2019 | 1.85 | -0.20 | -0.20 | <0.01 | |||||||||||||
| Winter | Small | 10 February 2021 | 21 February 2021 | 0.28 | -0.15 | -0.23 | 0.07 | ||||||||||||
| Med | 30 January 2021 | 10 February 2021 | 0.84 | -0.19 | -0.41 | 0.22 | |||||||||||||
| Large | 27 February 2021 | 14 March 2021 | 2.76 | -0.01 | -0.31 | 0.30 | |||||||||||||
| Spring | Small | 23 April 2021 | 29 April 2021 | 0.08 | 0.12 | -0.33 | 0.45 | ||||||||||||
| Med | 2 May 2021 | 22 May 2021 | 0.76 | -0.16 | -0.40 | 0.24 | |||||||||||||
| Large | 6 June 2021 | 13 June 2021 | 1.53 | -0.16 | -0.59 | 0.43 | |||||||||||||
| Average | -0.10 | -0.39 | 0.29 | ||||||||||||||||
| Rain Event Hysteresis Scenario 3 | Summer | Small | 29 July 2020 | 9 August 2020 | 0.18 | -0.26 | -0.63 | 0.37 | |||||||||||
| Med | 3 July 2019 | 13 July 2019 | 0.40 | None | None | None | |||||||||||||
| Large | None | None | None | None | None | None | |||||||||||||
| Fall | Small | 19 December 2020 | 23 December 2020 | 0.14 | -0.46 | -0.55 | 0.09 | ||||||||||||
| Med | 28 October 2020 | 10 November 2020 | 0.36 | -0.57 | -0.26 | 0.31 | |||||||||||||
| Large | 30 October 2019 | 7 November 2019 | 1.85 | None | None | None | |||||||||||||
| Winter | Small | 10 February 2021 | 21 February 2021 | 0.28 | -0.31 | -0.23 | 0.08 | ||||||||||||
| Med | 30 January 2021 | 10 February 2021 | 0.84 | -0.40 | -0.41 | 0.01 | |||||||||||||
| Large | 27 February 2021 | 14 March 2021 | 2.76 | -0.35 | -0.31 | 0.04 | |||||||||||||
| Spring | Small | 23 April 2021 | 29 April 2021 | 0.08 | -0.21 | -0.33 | 0.12 | ||||||||||||
| Med | 2 May 2021 | 22 May 2021 | 0.76 | -0.25 | -0.40 | 0.14 | |||||||||||||
| Large | 6 June 2021 | 13 June 2021 | 1.53 | -0.19 | -0.59 | 0.41 | |||||||||||||
| Average | -0.33 | -0.41 | 0.08 | ||||||||||||||||
prominent. Our findings illustrate that strong NSE values can be achieved with or without 100 cm soil moisture data; however, errors in HI values were three-fold greater when the 100 cm data were excluded, despite both modeling approaches generally capturing anti-clockwise hysteresis patterns. The synthesis of studies that integrate hysteresis metrics into model evaluation will be important to developing criteria for HI indices.
Conclusions
TELM models were developed in this study to assess the impact of soil hydrological processes on flow rate and nitrate-N concentrations exported from a heterogenous karst agroecosystem watershed. The conclusions are summarized as follows:
- A novel high-frequency dataset of streamflow, nitrate-N concentration, and soil moisture (at depths throughout and below the root zone) highlighted tight connectivity between soil moisture dynamics and nitrate-N concentrations spanning event to seasonal timescales.
- A TELM model successfully predicted both flow rate and nitrate exports from these complex systems because the time lag associated with the soil conditions was represented in model training.
- The inclusion of soil moisture and temperature data well below the effective root zone was important to accurately capture the storm event hysteresis dynamics observed in the exported nitrate signals.
- The findings have implications for revising physically based and conceptual modeling frameworks as well as model evaluation procedures for karst hydrology and water quality modeling studies.
Acknowledgments
We thank the three anonymous reviewers and the Associate Editor for their valuable comments and suggestions. We gratefully acknowledge funding support for this research from the National Science Foundation (NSF-1632888) and support from the USDA National Institute of Food and Agriculture, Multistate Project S-1089. The authors also thank the Department of Biosystems and Agricultural Engineering for partial funding support for the graduate research assistant. The authors thank Alex Fogle and the graduate and undergraduate research assistants at the University of Kentucky who assisted with sensor installation, maintenance, data collection, and analysis.
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