Volume 54, Issue 8 p. 5856-5877
Research Article
Free Access

A New Fully Distributed Model of Nitrate Transport and Removal at Catchment Scale

Xiaoqiang Yang

Corresponding Author

Xiaoqiang Yang

Department of Aquatic Ecosystem Analysis and Management, Helmholtz Centre for Environmental Research – UFZ, Brueckstrasse 3a, Magdeburg, Germany

Correspondence to: M. Rode and X. Yang,

[email protected];

[email protected]

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Seifeddine Jomaa

Seifeddine Jomaa

Department of Aquatic Ecosystem Analysis and Management, Helmholtz Centre for Environmental Research – UFZ, Brueckstrasse 3a, Magdeburg, Germany

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Matthias Zink

Matthias Zink

Department of Computational Hydrosystems, Helmholtz Centre for Environmental Research – UFZ, Permoserstrasse 15, Leipzig, Germany

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Jan H. Fleckenstein

Jan H. Fleckenstein

Department of Hydrogeology, Helmholtz Centre for Environmental Research – UFZ, Permoserstrasse 15, Leipzig, Germany

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Dietrich Borchardt

Dietrich Borchardt

Department of Aquatic Ecosystem Analysis and Management, Helmholtz Centre for Environmental Research – UFZ, Brueckstrasse 3a, Magdeburg, Germany

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Michael Rode

Corresponding Author

Michael Rode

Department of Aquatic Ecosystem Analysis and Management, Helmholtz Centre for Environmental Research – UFZ, Brueckstrasse 3a, Magdeburg, Germany

Correspondence to: M. Rode and X. Yang,

[email protected];

[email protected]

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First published: 14 May 2018
Citations: 37


Hydrological water quality models have gained wide acceptance from environmental scientists and water managers to address deterioration of surface water quality. Higher spatiotemporal accuracy of such models is increasingly required for better understanding the functional heterogeneity of catchments and improving management decisions at different governance levels. However, balancing spatial representation and model complexity remains challenging. We present a new flexibly designed, fully distributed nitrate transport and removal model (mHM-Nitrate) at catchment scale. The model was developed mainly based on the mesoscale Hydrological Model (mHM) and the Hydrological Predictions for the Environment (HYPE) model. The mHM-Nitrate model was tested in the Selke catchment (Central Germany), which is characterized by heterogeneous physiographic and land-use conditions, using adequate observed hydrological and nitrate data at three nested gauging stations. Long term (1997–2015) daily simulations showed that the model well reproduced the seasonal dynamics of biweekly nitrate observations in forested, agricultural and urban areas. High-frequency measurements (2010-2015) were additionally used to validate model performance of simulating short-term changes in stream-water concentrations that reflect changes in runoff partitioning and event-based dilution effects. Uncertainty analysis confirmed the model's robustness. Moreover, model calculations showed that mean terrestrial nitrate input/output (in total 105 kg ha−1 yr−1) and in-stream removal (8% of mean nitrate load) were in comparable ranges with literature, respectively. The new mHM-Nitrate model is capable of providing detailed spatial information on nitrate concentrations and fluxes, which can motivate more specific catchment investigations on nitrate transport processes and provide guidance on spatially differentiated agricultural practices and measures.

Key Points

  • New grid-based catchment nitrate model (mHM-Nitrate) with a flexible multi-resolution structure
  • Spatiotemporal validation with uncertainty analysis is conducted in a nested heterogeneous catchment using multi-frequency observations
  • The mHM-Nitrate model provides detailed and reliable catchment-wide spatial information of nitrate concentrations and fluxes

1 Introduction

Water quality in river systems is of growing concern due to rising anthropogenic pressures and climate change. Current understanding of the mechanisms and dynamics of nutrient leaching and transport from in-situ monitoring has significantly improved (Rode et al., 2016b; Rozemeijer et al., 2016). Mathematical modeling is one way to formalize this knowledge (Jackson-Blake et al., 2016) and transfer it to sub-areas that are not covered by monitoring schemes. Models can enhance our understanding of the natural behavior of environmental systems (Kirchner, 2006); for instance, they can test alternative explanations of observed phenomena to suggest the most plausible ones. Catchment models can also scientifically support decision-making (e.g., guiding optimization of monitoring strategies and analyzing different future climate and agricultural scenarios (Rode et al., 2016b)).

Spatially distributed, process-based models are recommended to adequately represent the heterogeneity of catchment characteristics. Wellen et al. (2015) evaluated the current state of distributed catchment water quality models and summarized the five models mostly used worldwide: Soil Water Assessment Tool (SWAT) (Arnold et al., 1998), Integrated Catchment model (INCA) (Whitehead et al., 1998a), Agricultural Nonpoint Source Pollution Model (AGNPS/AnnAGNPS) (Young et al., 1989), Hydrological Simulation Program-Fortran (HSPF) (Bicknell et al., 1997) and HBV-NP (now revised as Hydrological Predictions for the Environment (HYPE) (Lindström et al., 2010)). Four of them, except AGNPS/AnnAGNPS, are semi-distributed and most studies use this type of model (e.g., SWAT, INCA, HSPF and HYPE account for more than 70% of 257 studies investigated by Wellen et al. (2015)). These models usually disaggregate a catchment into sub-catchments based on surface topography and then define homogenous classes (e.g., Hydrological Response Units (HRUs) in SWAT and Soil and Land-use Classes in HYPE) within each sub-catchment based on land-use and soil type combinations. Consequently, information on class locations and interactions with neighboring classes is lost (Rathjens & Oppelt, 2012). Although these models simulate terrestrial processes for each class, they aggregate outputs from each class to the whole sub-catchment. Detailed spatial information, such as nutrient status (e.g., soil moisture concentration) and dynamics (e.g., leaching and percolation) in specific locations is missing (Rathjens et al., 2015). This kind of information, however, is increasingly asked for by researchers and stakeholders. For instance, the information can help to identify critical source areas of non-point source pollution and to place agricultural mitigation measures at the field scale (Bieger et al., 2017). Moreover, in-stream processes in such semi-distributed models are usually simulated in a river network represented by the total length of rivers within each sub-catchment and the connections between all sub-catchments. Terrestrial outputs are routed along this conceptual river network, neglecting the variability of nutrient transport processes within sub-catchments. However, the river network must be represented in detail to reflect the variability of in-stream residence time and stream morphological characteristics, which are essential factors driving in-stream processes (Alexander et al., 2000). Additionally, locations where point-source inputs may enter the river network can significantly influence in-stream processes and corresponding spatial distribution of stream water quality.

Efforts are in place to improve the spatial representation of semi-distributed models. For instance, the landscape unit (LSU) version of SWAT was developed to increase its description of connections between spatial objects (i.e., HRUs, LSUs and sub-catchments) (Arnold et al., 2010); however, detailed connection information for each object (e.g., accurate proportions of runoff assigned to receiving objects) is difficult to determine. Ultimately, a grid-based model structure, with high spatial representation of catchment heterogeneity (Rathjens et al., 2015), facilitates mechanistic analyses of variable flow and matter flux processes (Schulz et al., 2006). Some grid-based water quality models have been developed. One of them is AGNPS/AnnAGNPS (for event-based modeling of sediment bound compounds (Rode & Frede, 1997; Young et al., 1989)) and for continuous simulations (Yuan et al., 2001), respectively). Studies have verified advantages of the grid-based structure of AGNPS (Emili & Greene, 2013; Liu et al., 2008), but among other limits (Edsel et al., 2011), most of the studies are limited to catchments smaller than 200 km2 (see arguments by Krysanova et al., 1998) and the grid size normally does not exceed 1 km2. Similar scale limitations have also been observed in other grid-based water quality modeling studies, such as the integrations of physically based Water Flow and Balance Simulation Model (WaSiM-ETH) with nutrient routines (Rode & Lindenschmidt, 2001; Shrestha et al., 2007), the STREAM-N model (Dunn et al., 2013) and a nitrate transport model development based on the J2000 model (Hesser et al., 2010). This is probably due to the imbalance between spatial representation and model complexity, resulting in high computational demand as catchment size increases. This dilemma can be reflected in the development of the grid-based version of SWAT (Rathjens et al., 2015; Rathjens & Oppelt, 2012), which takes each Digital Elevation Model (DEM) cell as a sub-catchment with one HRU defined. Meanwhile, a high DEM resolution (e.g., 100 m) is strongly recommended to minimize uncertainties (Chaubey et al., 2005). This leads to long run-times of the code in larger catchments (e.g., nearly 1 hour per simulated year for Rathjens et al. (2015) in a 334 km2 catchment) and practically limits applications of the model to relative small catchments (Pignotti et al., 2017). Overall, grid-based catchment water quality model developments need to find a compromise between accurate spatial representation and a flexible and manageable structure.

In addition to catchment discretization, adequate descriptions of flow and matter flux processes along different flow paths is one of the core challenges in water quality modeling. Most process-based catchment models focus on describing processes at the surface and in the shallow subsurface (i.e., the upper 2 m of soil depth) because they are the most active response zones for stream flow and nutrient concentrations. The dynamics of deeper groundwater are largely simplified or even excluded in some models. However, groundwater and its nutrient dynamics become more essential during low-flow conditions, when baseflow contributes most to total stream flow. Studies have been conducted to couple catchment models with groundwater models (e.g., MODFLOW) (Bailey et al., 2016; Wriedt & Rode, 2006); but doing so greatly increases model complexity and data requirements, which constrains applicability of the coupled models, although such complexity is needed in many cases (Fatichi et al., 2016). It is believed that hydrological processes are only sensitive to the dynamic part of groundwater storage (Kirchner, 2009), thus deep groundwater storage in hydrological models is typically considered to be of minor importance for stream flow simulation. In contrast, the dynamics of deep groundwater storage are much more important for nutrient models, due to the long residence time of groundwater and the associated impacts on nutrient concentrations (Benettin et al., 2015; Wriedt & Rode, 2006). This subject still needs further consideration in process-based catchment water quality models.

A model's capability to support decision-making is largely based on how it represents anthropogenic pressures, such as impacts of agricultural practices and of point-source pollution. Non-point sources from agricultural land are identified to be a major cause of high nutrient concentrations in surface water(EEA, 2005). Effects of agricultural management practices and mitigation measures on improving water quality have been intensively evaluated (Hashemi et al., 2016; Rode et al., 2009). However, studies targeting effects of spatially differentiated agricultural management are still not well covered (Hansen et al., 2017; Hashemi et al., 2016), partly due to the few models that can do this at catchment scale and their inability to provide the necessary cropping information at the field scale. For instance, current catchment models insufficiently represent crop rotations since cropping patterns are difficult to be identified from commonly used land-use map, where agricultural fields are always classified as one “arable land” type. Similarly, model limitations exist in studying effects of spatially distributed point sources on water quality in river networks.

Overall, the need exists to develop a flexibly structured catchment water quality model with comprehensive descriptions of flow and matter flux dynamics and greater ability under changing anthropogenic conditions. In this study, we present a new grid-based nitrate model (mHM-Nitrate) at catchment scale, which is able to balance model complexity and representation of nitrate transport and removal processes. The model is mainly based on the advanced implementations of the mesoscale Hydrological Model (mHM) (Samaniego et al., 2010) and the HYPE model (Lindström et al., 2010). Since mHM has been evaluated in catchments with a wide range of sizes (Kumar et al., 2013), it is a promising hydrological platform to further extend to a water quality model. The main objectives of this study are 1) to develop the new mHM-Nitrate model, 2) to validate the model's ability to reproduce dynamics of long-term and high-frequency observations in a heterogeneous catchment at nested locations, 3) to evaluate model parameter sensitivity and model uncertainty, and 4) to provide detailed spatial information on nitrate concentrations and fluxes.

2 Methodology

2.1 Model Description

2.1.1 Hydrological Submodel

The mHM model (www.ufz.de/mhm) has a flexible reservoirs based structure, in which users can specify multiple spatial resolutions: From input data perspective, resolutions of geographic and meteorological data levels can be defined independently; According to specific research objectives, resolutions of modeling levels (i.e., terrestrial hydrological process and in-stream routing levels) can be specified individually. Cell size of all specified resolutions must be multiples of each other. All geographic and meteorological information is aggregated or disaggregated to the modeling levels and the scaling operations are done automatically according to the resolutions specified by users. For each cell of the terrestrial modeling level, the conceptual HBV model (Bergström, 1995) is used to represent the most important hydrological processes: evapotranspiration, canopy interception, snowpack and snowmelt, soil moisture dynamics and percolation, and runoff generation (Figure 1). Three conceptual reservoirs are defined to represent water storage in impervious areas, the unsaturated soil zone and the deep saturated subsurface zone, which generate direct flow, interflow (fast near surface flow and slow interflow) and baseflow, respectively. Total runoff from each terrestrial modeling cell is disaggregated or aggregated to the routing level and then routed along the river network. The river network is generated according to the main flow direction of each cell of routing level, which is upscaled from flow direction data at geographic data level.

Details are in the caption following the image

Structure of the mHM-Nitrate model, adapted from mHM and HYPE concepts (Lindström et al., 2010; Samaniego et al., 2010). In the terrestrial phase, four different nitrogen forms are defined (i.e., dissolved inorganic (DIN) and organic (DON) nitrogen, active (SONA) and inactive (SONI) solid organic nitrogen); in the in-stream phase, two forms are defined (i.e., dissolved inorganic (DINw) and organic (DONw) nitrogen in stream water).

The mHM model also integrates the multiscale parameter regionalization (MPR) technique for hydrological parameters (Samaniego et al., 2010), which overcomes common parameterization problems in distributed models while maintaining spatial variability in hydrological parameters and state variables (Samaniego et al., 2010). Unlike a standard regionalization scheme (Pokhrel & Gupta, 2010), MPR uses different transfer functions to regionalize most hydrological model parameters at geographic data level. For instance, using pedotransfer functions, soil moisture contents are calculated from soil properties provided by the soil map at geographic data level. Parameters introduced in these transfer functions, along with parameters that have not been regionalized (e.g., baseflow recession rate which varies by geological unit), must be upscaled (the second phase of MPR) to model levels and calibrated against observations. Noticeably, the parameters of transfer functions are denoted as “global parameters”, indicating greater transferability across locations and scales (Rakovec et al., 2016; Zink et al., 2017). Detailed descriptions of the technique and mHM model parameters are given by Samaniego et al. (2010) and Kumar et al. (2013).

2.1.2 Nitrate Submodel

We considered nitrate-nitrogen ( urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0001) as equivalent to dissolved inorganic nitrogen (DIN). Other forms of DIN, namely ammonium ( urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0002) and nitrite, typically account for less than 15% and 1%, respectively, at natural levels (Meybeck, 1982), and both compounds are rapidly transformed into urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0003 during their downstream transport. Moreover, improved waste water treatment has substantially decreased urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0004 concentrations (EEA, 2012), which remain at a low level as in natural rivers (Meybeck, 1982). It is theoretically possible to calculate dissolved organic nitrogen (DON) concentrations, but they are generally low and rarely measured.

The nitrogen mass balance and transformation equations were mainly adopted and modified from HYPE, which is revised from HBV-NP (Andersson et al., 2005; Lindström et al., 2010) and widely verified in many catchment water quality modeling studies (Arheimer et al., 2012; Jiang et al., 2014; Jomaa et al., 2016). In the terrestrial phase (Figure 1), four different nitrogen pools (i.e., active solid organic nitrogen (SONA), inactive solid organic nitrogen (SONI), DON and DIN) were defined in each soil layer for each cell of terrestrial modeling level. Sources (i.e., atmospheric deposition, fertilizer and manure application and plant residues), sinks (i.e., denitrification and plant uptake) and transformations between the pools (i.e., degradation, dissolution and mineralization) for nitrogen mass balance and dynamics were included. DIN and DON fluxes (i.e., infiltration into deeper soil layers, percolation into groundwater and leaching into the stream) were calculated with flow dynamics, with the assumption of full mixing in each reservoir. In the in-stream phase (Figure 1), dissolved inorganic (DINw) and organic (DONw) pools were defined in each reach at the routing level. We assumed that all inputs (i.e., transport from upstream, exports from associated terrestrial grids and potential point-source inputs) of each reach fully mixed with the pre-stored volume in the reach. For in-stream processes, we considered denitrification and transformations between the DINw and DONw pools (inverse processes of primary production and mineralization). Initial pool sizes and transformation parameters were mainly land use dependent. More detailed descriptions of nitrate-related processes can be found in supporting information (Text S1) and Lindström et al. (2010).

2.1.3 Additional Implementations

In order to further improve the model representation of nitrate dynamics and model ability of considering anthropogenic impacts, we added three major improvements in the mHM-Nitrate model development.

First, we divided deep groundwater storage into two parts. The hydrological submodel considers only a relatively small storage, which actively contributes to baseflow generation. Additional retention groundwater storage, which can be as large as tens of meters, was added to the nitrate submodel. The mass conservative equation for calculating baseflow urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0005 concentration was modified from the INCA-N model (Wade et al., 2002; Whitehead et al., 1998a):
where urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0007 denotes baseflow urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0008 concentration ( urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0009); urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0010 and urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0011 denote retention storage and hydrologically active storage of deep groundwater, respectively ( urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0012); and urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0013 and urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0014 denote percolated mass per unit area and baseflow export load, respectively ( urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0015). This ordinary differential equation was solved using the fourth order Runge-Kutta technique. Initial values of urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0016 and urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0017 were set as land-use type dependent (supporting information, Table S1).

Second, we added an input map of “crop rotation” to provide the spatial distribution of crop rotation types and a corresponding look-up table to define the crop sequence of each rotation type. Technically, the crop rotation map can be easily modified from the land-use map by separating arable land into different rotation regions. Forest and pasture can be treated as individual rotation types in this map, so that their nitrogen supply (e.g., plant/grass residues and animal wastes) and uptake can be defined in the look-up table to estimate the terrestrial nitrogen mass balance.

Third, we added the ability to consider time series inputs of waste water treatment plants (WWTPs) based on their exact geographic locations. In mHM-Nitrate, point sources can be added to nearby streams and be routed along the spatially explicit river network. In other words, the model facilitates the assessment of impacts of spatially differentiated point-source pollution. Furthermore, time-series data of point source inputs enabled long-term continuous simulations under changing point-source conditions.

2.2 Model Parameters and Sensitivity Analysis

We parsimoniously parameterized the nitrate submodel using only six parameters for rates of soil denitrification (denis), degradation (degdr), dissolution (dislr), mineralization (minlr), in-stream denitrification (deniw) and in-stream primary production (pprt). All parameters represent individual or combined biogeochemical reaction(s) in nitrate transport and removal processes. These reactions, which depend greatly on specific physical, chemical and biological characteristics, have not been fully understood and conceptualized in catchment modeling. Therefore, parameters were defined as land-use dependent at the geographic data level, except for in-stream denitrification rate (deniw) which is a general parameter. These parameters, along with state variables in the nitrate sub-model, were upscaled to the terrestrial and in-stream modeling levels, following the second phase of MPR. Among the upscaling operators that can be chosen to maintain spatial variability (Samaniego et al., 2010), we chose the area-weighted mean method in this study.

Although some of mHM parameters are potentially transferable (Kumar et al., 2013) and hydrological simulations are insensitive to some parameters (Cuntz et al., 2015), the total number of mHM-Nitrate parameters is still too large to be calibrated directly. Therefore, parameter sensitivity analysis is needed. We used the SAFE (Sensitivity Analysis For Everybody) tool developed by Pianosi et al. (2015).The Elementary Effects (EE) (Morris, 1991) method was selected for the sensitivity analysis, based on the screening and ranking purpose (Pianosi et al., 2016). It is a multiple-starts perturbation method and each trajectory allows for evaluating one EE per factor. The elementary effect of the urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0018th parameter ( urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0019) is based on a sample generated from the radial one-factor-at-a-time sampling strategy (Campolongo et al., 2011). The urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0020 and absolute mean urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0021 and standard deviation urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0022 of urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0023 in urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0024 trajectories are calculated:

Where urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0027 denotes the objective function used for sensitivity analysis (here we selected the Root-Mean-Square-Error, RMSE); urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0028 denotes the value of the urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0029th parameter; urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0030 denotes the sampling step; urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0031 denotes urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0032 in the urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0033th trajectory; and urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0034 denotes the number of sampled trajectories. By plotting urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0035 versus urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0036 of all parameters, the sensitivity ranking is obtained, with the more to the right-up section the point, the more influential and interdependent, respectively, the parameter becomes.

We first separately analyzed sensitivity ranking of hydrological and nitrate submodel parameters for discharge and nitrate simulation, respectively. Then, we simultaneously analyzed all parameter sensitivities for nitrate simulation, to take account interactions between hydrological and nitrate processes.

2.3 Model Calibration and Uncertainty Analysis

Based on sensitivity analysis, the most sensitive parameters have to be carefully calibrated against observations. Due to the complexity of grid-based parameterization approach, it is necessary to use an effective and efficient automatic optimization method. We used the Dynamically Dimensioned Search (DDS) method (Tolson & Shoemaker, 2007), which is developed for identifying approximation of global optimal solutions of computationally demanding models in limited evaluations (Behrangi et al., 2008).

Apart from a powerful optimization method, selection and construction of an objective function, which reflects the goodness-of-fit between observations and simulated results, is also critical for successful model calibration. We used a multi-objective calibration approach with multi-criteria, multi-site and multi-variable.

First, we used the Nash-Sutcliffe Efficiency (NSE) coefficient (Nash & Sutcliffe, 1970) as one of the criteria. Given the equivalent importance of high- and low-value periods in nitrate simulations, we also combined the logarithmic transformation of NSE ( urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0037), which flattens high values to a comparable level with low values (Krause et al., 2005). Thus, the multi-criteria objective function was:
where urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0041 and urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0042 denote simulated and observed variables (discharge or urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0043concentration), respectively, at time step urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0044; urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0045 and urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0046 denote the mean of observed values and of their log-transformation, respectively; urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0047 denotes the number of time steps. Second, multi-site calibration has been proofed outperforming single-site approaches in heterogeneously characterized catchments (Jiang et al., 2015; Li et al., 2010). Thus, the multi-site objective function (for both discharge and urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0048concentration) was adapted as follows:
where urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0050 and urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0051 denotes the number of gauging stations. Third, nitrate transport processes are mostly driven by hydrological processes. While in model calibration, nitrate observations can help to constrain hydrological processes (e.g., indicating runoff partitioning which cannot be reflected in discharge observations (Zhang et al., 2016)). Thus a weight-aggregated multi-variable function was constructed as follows:
where urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0053 and urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0054 denote weights for discharge and urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0055concentration objectives, respectively. The weight for each variable can be optimized, or using Pareto multi-objective optimization, but it is not within the scope of this study.

After model calibration, we used three evaluation criteria, namely NSE, RMSE and percent bias (PBIAS), to evaluate the model performance in discharge and urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0056concentration simulations.

We also integrated a widely used Markov Chain Monte Carlo (MCMC) approach - DREAMZS (Differential Evolution Adaptive Metropolis algorithm) (ter Braak & Vrugt, 2008; Vrugt et al., 2009; Wilusz et al., 2017) to evaluate model uncertainties. Model parameter inferences were based on the log-likelihood function:
where urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0058 and urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0059 denote the number of discharge and nitrate measurements, respectively; urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0060 denotes the model error at urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0061th measurement; and urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0062 denotes the error standard deviation. Following the work of Vrugt et al. (2005), the discharge urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0063 was tested as heteroscedastic ( urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0064), while nitrate urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0065 was homoscedastic ( urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0066−1, see details in supporting information, figure S1). We also assumed the errors independently follow the Gaussian distribution. The 95% confidence band of parameter uncertainty was generated from 10,000 MCMC evaluations in this study, and that of total uncertainty was calculated from model simulations with random errors (normal distribution urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0067).

3 Test Catchment and Data Analysis

3.1 Catchment Description

The mHM-Nitrate model was tested in the Selke catchment, a sub-catchment of the Bode catchment in Central Germany (the TERENO Harz/Central German Lowland Observatory (Wollschläger et al., 2016)). The drainage area of the Selke catchment is approximately 456 km2. Mean annual precipitation is 660 mm, ranging from 792 mm in the upper mountainous areas to 450 mm in the lower agricultural lands. Mean monthly temperature is 9 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0068 (ranging from −1.8 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0069 in winter to 15.5 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0070 in summer) and a considerable amount of snowmelt from the upper mountains contributes to stream discharge according to our field experience. Three nested gauging stations (Silberhütte, Meisdorf and Hausneindorf, with area of 99, 184 and 456 km2, respectively) and five WWTPs were considered in this study (Figure 2a). The station Meisdorf, above which 72% of the area is occupied by forest, measures discharge and nutrient exports from the upper forest area. Agricultural land dominates the lower part of the catchment (almost 80% of the area between the station Meisdorf and the outlet station Hausneindorf), with considerable urban areas (Figure 2b). The main crops planted on agricultural land are winter wheat, winter barley, triticale, rye, rapeseed, maize and sugar beet. The amount of fertilizer applied each year ranges from 130 to 190 kg N ha−1 (Kistner, 2007). Soil and geological characteristics also differ in areas upstream and downstream of the station Meisdorf. Upstream of the station Meisdorf, cambisols and schist/claystone form the soils and geology, respectively, while chernozems and tertiary sediments with loess dominate the lower parts of the catchment (Figures 2c and 2d). Due to this heterogeneity of physiographic condition, the Selke catchment was selected to test the new mHM-Nitrate model.

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Geographic data of the Selke catchment, Central Germany: (a) Digital Elevation Model (DEM), river network and station locations, (b) land use types, (c) soil types, and (d) geological map.

Geographic data were resampled from original sources into a user-defined resolution (100 m in this study, Table 1). Resolution of the crop rotation map was set equal to that of the land-use map for technical simplification since it is modified from the land-use map and unique rotation type was assigned in all arable lands in this study. Meteorological data were collected from the German Weather Service. The number of precipitation stations within and around the Selke catchment has decreased from 16 to 8 after 2004 and another station was dismantled in 2013. There is no reservoir constructed in the catchment. Evaluation data (discharge and concentration observations) were collected from the State Agency for Flood Protection and Water Management of Saxony-Anhalt -LHW (daily discharge data for 1993–2015 and biweekly urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0071 concentration data for 1997–2009, with a one-year gap) and the Helmholtz Center for Environmental Research - UFZ (biweekly and 15-minute urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0072 concentrations for 2010–2015). In the years 1998–2004, about 18% of annual stream flow was abstracted from the downstream part for flooding of a mining pit. Resolutions of terrestrial modeling and in-stream routing levels were set as 1km and 8 km, respectively. Daily discharge and nitrate data were averaged values from high-frequency measurements, and biweekly nitrate data were grab sample measurements.

Table 1. Data used to Set-Up and Evaluate the mHM-Nitrate Model in the Selke catchment, Germany
Data catalog Data type Resolution Period Source
Geographic data Digital Elevation Model SR (All resampled to 100 m): 30 m, State Survey Office/ BGR
Land-use 30m,
Soil-type 1:1 000 000,
Geological map 1:1 000 000
Agricultural practices

Application of fertilizer/manure

Dates of farming practices

Field survey/


Map & look-up table of crop rotations

SR: 100 m

(based on the land-use map)

Point source data Discharge and water quality Daily 2002–2010 Five waste water treatment plants
Meteorological data Precipitation


SR: 1 km

1993–2015 (warming period: 1993–1996) DWD
Potential evapotranspiration
Atmospheric nitrogen deposition 9–15 kg ha−1 yr−1 State agricultural authority

Evaluation data

(three gauging stations)

Discharge Daily 1997–2015 LHW
Nitrate concentration Biweekly 1997–2015 LHW/UFZ
Daily 2010–2015 UFZ
  • Note. Data source: BGR - Federal Institute for Geosciences and Natural Resources, Germany; DWD - German Weather Service; LHW - State Agency for Flood Protection and Water Management of Saxony-Anhalt; UFZ - Helmholtz Center for Environmental Research. SR: spatial resolution

3.2 Time-Series Data Analysis and Preprocessing

Long-term dynamics of observed biweekly urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0073 concentrations showed notable differences between dominant land-use types. Mean concentration at the outlet (3.61 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0074 at Hausneindorf) was much higher than that from the upper forest-dominant area (1.60 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0075 at Meisdorf). Seasonal Mann-Kendall Test (Hirsch et al., 1982) for 1997–2015 (results not shown) indicated no significant trend at Silberhütte, while at Meisdorf, a negative trend was only observed in July ( urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0076 value equaled to 0.019) when the lowest flow occurred. At Hausneindorf, however, a strong negative trend was detected throughout the year, except in February and March which are the main high flow months. Seasonal patterns of concentration also differed largely. At the two upper stations (Silberhütte and Meisdorf), the pattern was clear and consistent with the discharge pattern, showing high concentrations (ca. 4 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0077) in high-flow periods and low concentrations (as low as 0.5 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0078) in low-flow periods. However, the pattern at Hausneindorf changed during the periods studied. After 2007, concentrations in high-flow periods were higher than those in low-flow periods, but amplitudes of seasonal variability were much lower than those of the two upper stations, primarily due to much higher minimum values (ca. 2 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0079). In the previous period (1997–2006), concentrations slightly decreased (from ca. 4 to 2 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0080) in the recession phases of the main high-flow period of the year, but greatly increased during subsequent low-flow periods (up to 8 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0081).

Five WWTPs have been constructed since 2002, but they only started to properly operate in 2007, identified by annual mean outflow discharge (supporting information Figures S2–S4). We assumed that the unrecorded waste water was put directly into streams at the plant sites. Therefore, we estimated the unknown point-source inputs before 2007 according to available measurements (WWTP Harzgerode, for which inflow measurements were collected) and urban populations (WWTPs Ballenstedt and Hoym, for which inflow measurements were missing). The estimation of daily point-source data were given in supporting information Figures S2–S4. We excluded WWTPs Straßberg and Alexisbad in this study since the outflow discharge and city population were much less than the other ones.

As a part of the TERENO Harz/central German lowland observatory, high-frequency monitoring has been performed in the Selke catchment since 2010. We aggregated daily mean urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0082 concentrations from newly available 15-minute sensor data at the three gauging stations. Given the quantity and quality of urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0083 observations, daily discharge and biweekly concentration data in the period 2010–2015 were used for daily model calibration and data in the period 1997–2009 were used for long-term model validation. Also, daily concentration observations in the period 2010–2015 were used for additional high-resolution validation. The period 1993–1996 was used as a spin-up period for hydrological simulation and the initial conditions for the nitrate simulation are provided in the supporting information Table S1.

4 Results

4.1 Parameter Analysis

We identified nine land use types and ten geological units in the Selke catchment (Figures 2b and 2d). Consequently, the total number of parameters reached up to 99 (53 and 46 in hydrological and nitrate submodels, respectively), making a parameter sensitivity analysis necessary.

Separate parameter sensitivity ranking (PSR) results showed that parameters related to soil moisture (soil) influenced hydrological simulations the most, followed by those related to evapotranspiration (pet) and interflow generation (intfl) (Figure 3a), which highlights the importance of soil moisture dynamics, evapotranspiration and interflow generation processes in simulating discharge. Results also showed that denitrification rates in stream water (deniw) and for land-use types (denis) influenced nitrate simulation the most (Figure 3b). Simultaneous PSR results showed that hydrological parameters dominated the upper-right section, with one nitrate parameter ranked in the third place (Figure 3c), demonstrating that nitrate simulation was mainly driven by hydrological processes. Specifically, the most influential processes were also soil moisture dynamics, interflow generation and evapotranspiration. Comparing the separate and simultaneous analyses of nitrate submodel parameters (Figure 3b and c), the top ten parameters differed in both rank and number, with a decrease in denitrification process parameters and an increase in in-stream primary production process parameters (pprt). This indicates that hydrological processes also influenced the sensitivity of nitrate sub-model parameters.

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mHM-Nitrate parameter sensitivity ranking (PSR) using the Elementary Effect method. Graphs (a) and (b) show the top 30 parameters, with the top 10 labeled; graph (c) shows the top 60 parameters, with 20 labeled (the top 10 of hydrological and nitrate parameters, respectively). Labeled parameters are related to soil moisture (soil), evapotranspiration (pet), interflow generation (infl), geological units (geo), soil denitrification rates (denis), dissolution rate (dislr), mineralization rate (minlr), in-stream denitrification rates (deniw) and in-stream primary production rate (pprt). Numbers after nitrate parameter refer to land-use types numbered in Figure 2b. The more to the right-up section the point, the more influential and interdependent, respectively, the parameter becomes. Note the log-log scales.

Results of simultaneous analysis also showed large variance in sensitivity among all parameters (i.e., wide range and dramatic decrease in values of urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0084 and urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0085) (Figure 3c). We selected the top ten and top six hydrological and nitrate submodel parameters, respectively, for model calibration and uncertainty analysis. We further grouped the land-use dependent nitrate parameters into an agricultural group (parameters in intensive orchard, pasture and arable lands) and a non-agricultural group. The DDS calibration method was used and 50,000 iterations were set as the terminal criterion. The calibrated optimal values were given in Table 2.

Table 2. Description of the Calibrated Model Parameters
Parameter Brief description Parameter range Optimal value
soil3 Correction factor of hydraulic conductivity considering organic matter content [0.00E+0;4.00E+0] 3.99E+0
soil4 Pedotransfer function parameter for calculating soil moisture content (Zacharias & Wessolek, 2007) [6.46E-1; 9.51E-1] 9.50E-1
soil7 Pedotransfer function parameter for calculating soil moisture content (Zacharias & Wessolek, 2007) [5.36E-1; 1.12E+0] 9.21E-1
soil10 Transfer function parameter for calculating saturated hydraulic conductivity (Cosby et al., 1984) [-1.20E+0; -2.85E-1] -9.02E-1
soil13 Transfer function parameter for calculating saturated hydraulic conductivity (Cosby et al., 1984) [1.00E+0; 1.50E+2] 6.23E+1
soil14 Fraction of roots for calculating actual evapotranspiration in forest areas [9.00E-1; 9.99E-1] 9.62E-1
intfl4 Transfer function parameter for recession rate in slow interflow generation process [1.00E+0; 3.00E+1] 1.42E+1
intfl5 Transfer function parameter for exponent coefficient (alpha) in slow interflow generation process [5.00E-2; 3.00E-1] 1.20E-1
pet1 Parameter for aspect correction of input potential evapotranspiration data [7.00E-1; 1.30E+0] 1.02E+0
geo12 Baseflow recession rate under geological unit number 12 [1.00E+0; 1.00E+3] 2.10E+2
denisna Soil denitrification rate in non-agricultural land (d−1) [1.00E-4; 1.00E-1] 1.87E-2
denisa Soil denitrification rate in agricultural land (d−1) [1.00E-4; 1.00E-1] 3.98E-3
deniw In-stream denitrification rate (kg m−2 d−1) [1.00E-8; 5.00E-2] 3.94E-4
pprtna Primary production rate in non-agricultural stream (kg m−3 d−1) [1.00E-8; 1.00E+0] 6.73E-2
pprta Primary production rate in agricultural stream (kg m−3 d−1) [1.00E-8; 1.00E+0] 5.40E-4
dislra Soil dissolution rate in agricultural land (d−1) [1.00E-1; 2.00E+2] 2.00E+2
  • Note. More detailed descriptions of hydrological submodel parameters are given by Samaniego et al. (2010). Shaded rows indicate nitrate submodel parameters, with subscripts “na” and “a” denote non-agricultural group and agricultural group, respectively,

4.2 Model Performance

Long-term discharge simulation results (Figure 4) and corresponding evaluation criteria (Table 3) showed that the model performed well for both calibration (2010–2015) and validation (1997–2009) periods. For the two upper stations, Silberhütte and Meisdorf, the model adequately captured seasonal dynamics of discharge, covering both the high- and low-flow periods. NSE values were above 0.81 and 0.76 for discharge simulations in the calibration and validation periods, respectively. NSE values at Meisdorf (0.81 and 0.76 for calibration and validation, respectively) were slightly lower than those at Silberhütte (0.85 and 0.82, respectively). This could be attributed to the underestimation of several flow peaks at Meisdorf after 2006, since NSE is strongly influenced by high values. The amount of precipitation recorded during these events seems to be too low to generate such high flows compared to those of previous flood events (Figure 4a and b). This insufficient precipitation is probably due to the reduced number of precipitation stations in the Selke catchment after 2004 (see section 3.1). However, the water balance at Meisdorf (discharge PBIAS within ±10%) was better than that at Silberhütte (discharge PBIAS exceeded −10% in the validation period). Underestimation of the discharge balance in mountainous areas (e.g., station Silberhütte) is frequently reported in hydrological modeling studies. This is probably due to the large uncertainties in meteorological input data in these areas. Weather conditions change rapidly due to the high geographic heterogeneity, which leads to decreased spatial representation of weather stations. Moreover, simplifying snowmelt processes likely worsened model performance in the mountainous areas.

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Model performances of discharge and urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0086 concentrations in calibration (2010–2015) and long-term validation (1997–2009) periods at the three gauging stations.

Table 3. Statistical Criteria (Nash-Sutcliffe Efficiency – NSE, Root-Mean-Square Error –RMSE and Percent Bias - PBIAS) of Model Calibration and Validation for Hausneindorf (Haus), Meisdorf (Meis) and Silberhütte (Silber) in the Selke Catchment, Germany
Variable Criterion Calibration Validation
2010–2015 1997–2009 2010–2015
Haus Meis Silber Haus Meis Silber Haus Meis Silber
Discharge NSE 0.68 0.81 0.85 0.65 0.76 0.82
RMSE 0.02 0.02 0.01 0.01 0.01 0.01
PBIAS (%) −4.61 −9.02 −8.86 24.36 10.63 −17.50
urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0087 concentration Frequency Bi-weekly Bi-weekly Daily
NSE 0.37 0.59 0.70 −0.07 0.47 0.72 0.43 0.66 0.66
RMSE 0.07 0.07 0.07 0.07 0.07 0.06 0.02 0.02 0.01
PBIAS (%) −3.38 −2.88 2.48 3.34 −3.35 −0.45 2.75 −7.38 −8.83

For discharge simulation at station Hausneindorf, the model had a somewhat worse performance than that for the upper stations, but still reproduced the observed discharge reasonably well (NSEs were 0.68 and 0.65 in calibration and validation periods, respectively, Table 3). Underestimation of peak flows probably propagated from the upper part of the catchment where most of the flow is generated. The lower spatial density of precipitation stations in the lower catchment probably exacerbated the problem of insufficient precipitation data. The water balance in the model was most accurate in the calibration period (PBIAS was −4.6%), and least accurate in the validation period (PBIAS reached up to 24.4%). Jiang et al. (2014) reported that approximately 18% of mean annual stream flow was abstracted in the downstream part of the Selke catchment during 1998–2004. However, water balance was still slightly overestimated after considering the abstraction. A similar slight overestimation also occurred at Meisdorf (10%) in the validation period. Due to the sparser precipitation stations in the calibration period, the model was likely forced to increase the runoff generation to fit the observed discharge more accurately. Consequently, during the validation period when precipitation data differed, water balance (PBIAS) was slightly overestimated. Additionally, the RMSE for all stations (not exceeding 0.02) indicated reasonable simulation of discharge (Table 3).

For nitrate simulations at the two upper stations, the model adequately reproduced the observed concentrations covering both high and low values (Figure 4a and b). NSE values of urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0088 concentration at Silberhütte were even higher than 0.70, presumably due to the clear seasonal concentration pattern. urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0089 concentrations under low-flow conditions were slightly higher at Meisdorf than Silberhütte in the validation period, probably due to unknown point sources from the city of Harzgerode. By estimating the unknown point-source inputs, the model adequately simulated the increased concentration in low flow conditions (NSE was 0.47). Biweekly RMSE and PBIAS values also indicated adequate nitrate simulations at the two upper stations (Table 3). At Hausneindorf, urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0090 concentrations were obviously higher than those at the two upper stations (Figure 4c), due to strong impacts from intensive agricultural activities on arable lands and from point sources in urban areas. The model simulated nitrate concentration well in the calibration period, when point sources were clearly controlled by two large WWTPs in the lower part (plants Hoym and Ballenstedt, Figure 2a). Statistical performance in the calibration period illustrated a good simulation accuracy (NSE = 0.37, RMSE = 0.07 and PBIAS = −3.38%). In the validation period, long-term nitrate dynamics were acceptably reproduced by estimating the changing unknown point sources in lower urban areas, although the NSE value was slightly less than zero (-0.07). The largely increased concentrations in low-flow conditions were not captured well. RMSE (0.07) and PBIAS (3.34%) were similar with that in the calibration period, and were acceptable. The Quantile-Quantile plots of observations vesus simulations were shown in supporting information Figure S8.

Regarding the additional validation using daily observations of urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0091 concentration (2010–2015), the model adequately reproduced seasonal patterns and fluctuations during high value periods at the two upper stations (Figure 5a and 5b). NSE values were both 0.66 and RMSE were below as low as 0.02 and 0.01, respectively (Table 3). The complex dynamics of concentration at Hausneindorf were reproduced well. Peaks and drops in simulated results were reasonably validated by daily observations (Figure 5c). Statistically, NSE was high and RMSE and PBIAS values were relatively low, confirming the model performance of daily validation (Table 3).

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Model validation using daily urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0092 concentration observations at the three gauging stations.

We used the daily discharge and biweekly urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0093 concentration data (2010–2015) for the uncertainty analysis. The discharge uncertainty results showed that the uncertainty in high-flow periods was much higher than that in low-flow periods and differences between total uncertainty and parameter uncertainty in high-flow periods were also larger than those in low-flow periods (Figure 6a and supporting information Figures S4 to S6), demonstrating that higher uncertainty from input data and model structure occurs in high-flow periods. This, to some extent, corroborates the above explanations for reduced model performance of the flow peaks. The 95% total uncertainty band of urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0094 concentration covered most of grab-sampling observations (ca. 98%) and most of them were also within or around the parameter uncertainty band (Figure 6b and supporting information Figures S4 to S6).

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The 95% confidence bands of (a) discharge and (b) urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0095 concentration at station Hausneindorf using DREAMZS. Graph (a) shows only results of two-year period (2010–2011) for a better visibility. Complete results of uncertainty analysis at all three gauging stations were provided in supporting information (Figures S5 to S7).

4.3 Spatial Information

We calculated the spatial distributions of mean interflow and baseflow urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0096 concentrations for the period of 2010–2015 (Figure 7), representing nitrate statuses in soil moisture and groundwater, respectively. Interflow concentrations of agricultural land were much higher than those in forested areas (Figure 7a), which reflects the strong environmental impacts of agricultural practices (e.g., fertilizer and manure applications). Also, variability for agricultural land was high and most critical source areas were located near the catchment outlet. Baseflow concentrations of the lower agricultural land were higher than interflow concentrations (Figure 7b), indicating the impacts of long-term agricultural fertilizer application on groundwater nitrate concentration (Musolff et al., 2016).

Details are in the caption following the image

Spatial distributions of nitrate concentration ((a) interflow and (b) baseflow concentrations, representing nitrate statuses in soil moisture and groundwater, respectively) provided by the mHM-Nitrate model (cell size: 1 km urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0097 1 km) in period 2010–2015.

Nitrate terrestrial inputs/outputs and internal transformation processes can also be provided by the model spatially. All results (Figure 8) were averaged from model calculations in period 2010–2015. Main biogeochemical processes (i.e., mineralization, uptake and denitrification) showed high spatial variability across the heterogeneous landscapes in the Selke catchment (Figure 8b, d and e). Compared to results in forested areas, these processes were generally more active in agricultural areas. The variability within agricultural areas was also higher than that within forested areas, especially for the denitrification process which is strongly influenced by soil moisture. The calculated terrestrial export loads, which are predominated by annual runoff generation, showed even higher variability in agricultural lands (annual load ranges from 0.1 to 18 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0098, Figure 8f). Nitrate external supply through fertilizer and manure application and nitrate soil uptake by crops and plants, accounted for the largest fractions of nitrate input and output, respectively (Figure 8a and d). The overall terrestrial mean balance was nearly closed in the Selke catchment, with a mean total input amount of 106 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0099 (the sum of nitrate external supply, mineralization and atmospheric wet deposition) equivalent to a mean total output amount of 105 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0100 (the sum of crop/plant uptake, denitrification and terrestrial export).

Details are in the caption following the image

Spatial distributions of terrestrial nitrate inputs/outputs and internal transformation processes provided by the mHM-Nitrate model (cell size: 1 km urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0101 1 km) in period 2010–2015.

Information of in-stream removal (i.e., net removal by primary production and denitrification processes) showed high variability both temporally and spatially (Table 4). Nitrate loads were much higher in wet-winter seasons than in dry-summer seasons due to the hydrological seasonal pattern. Loads at Meisdorf accounted for 35% and 59% of the loads at the outlet (station Hausneindorf) in summer and winter, respectively. Nitrate removal was highest in summer and lowest in winter. Removal in the upper forested reaches was 26–54% of the amount removed from the whole river network. Generally, more nitrates were removed from the lower agricultural reaches than the upper reaches, except spring when they were equivalent. The proportion of nitrate removal to load (percentage) showed high seasonal variability. The highest percentage occurred in summer (e.g., 76% and 54% in the upper forested reaches and the whole river network, respectively, in July) and the lowest removal occurred in winter (e.g., only ca. 0.1% and 0.3%, respectively, in February). Spatial variability of the percentage was not pronounced throughout the whole year, except in summer when nitrate load at Meisdorf was very low (with 83.4 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0102 vs. 234 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0103 at the outlet).

Table 4. Seasonal and Annual Mean Values of the In-Stream Balance at Station Meisdorf and Hausneindorf
Mean(kg N d−1) Spring Summer Autumn Winter Annual
Meis Haus Meis Haus Meis Haus Meis Haus Meis Haus
Load 279 555 83.4 234 144 332 487 826 248 486
Removal 28.3 52.5 36.3 79.4 9.60 27.9 1.77 6.73 19.0 41.6
Percentage (%) 10.1 9.46 43.5 33.9 6.67 8.40 0.36 0.81 7.64 8.55
  • Note. The loads were calculated based on model simulated discharge and concentrations at two stations and the removal (primary production and denitrification) values were amount from all reaches above each station.

5 Discussion

5.1 Model Evaluation

Dynamics of urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0104 concentrations depend largely on the spatial distribution of non-point sources (Musolff et al., 2017). Due to heterogeneous land-use types, soil types and geological characteristics in the contributing areas upstream of the three nested gauging stations, the validation results demonstrates that the model can represent different nitrate behaviors well. Seasonal variability in urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0105 concentrations at the two upper stations represents mainly the nitrate behavior in natural forest-dominated areas, which has high interflow concentrations and extremely low baseflow concentrations. Due to the impermeable geological property, a shallow and flashier flow pathway is developed in the upper Selke (Dupas et al., 2017). The fertilizers and plant residues added to the upper arable lands and forests, respectively, increased urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0106 concentrations of soil moisture, but not of deeper groundwater. The model reasonably captured the processes under these conditions and performed well throughout the whole simulation period. At the catchment outlet, urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0107 concentrations combine exports from the upper natural forested areas and intensive agricultural and considerable urban areas in the lower parts of the catchment. The lowland agricultural area is dominated by sedimentary materials and loess, which leads to a deeper and slower groundwater dominant hydrological behavior (Musolff et al., 2016). Due to long-term fertilizer application, concentrations were much higher in soil moisture and also in deeper groundwater (ca. 25 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0108, from field measurements). Point sources from lower urban areas were clearly controlled by WWTPs in the calibration period (2010–2015), and exports from upper areas were captured well at Meisdorf. Therefore, model performance at Hausneindorf can reflect the model ability to simulate agricultural exports. The adequate results validate the applicability of mHM-Nitrate in typical intensive agricultural areas.

Although point sources contributed to a small proportion of nitrate load, they strongly influenced the pattern of observed concentrations. For instance, in the validation period (1997–2009), the change points of observed urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0109 concentration pattern at Hausneindorf (i.e., the years 2002 and 2007, Figure 4c) were correspondent to the change points of waste water treatments (see Section 3.2 and supporting information). After reconstructing the point-source time series according to WWTP measurements, the changes of seasonal patterns were reasonably captured by simulations, although the NSE was slightly less than zero. This is probably due to large uncertainties which might be involved in estimating unknown point-source inputs in the validation period. Overall, by considering the exact locations of WWTPs and time series of point source inputs, mHM-Nitrate facilitates the use for long-term continuous simulation under changing anthropogenic conditions.

Benefiting from currently available high-frequency monitoring, the daily data (2010–2015) were used to validate short-term nitrate behavior that is rarely observed in regular grab sampling. At the two upper stations, the fluctuations of urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0110 concentrations in high-flow periods are presumably due to shifting runoff partitioning among runoff components (surface direct flow with relatively low concentrations, interflow with high concentrations and baseflow with extremely low concentrations). Outlet concentrations frequently decreased during small storm events in low-flow periods, reflecting dilution by small events from upper forested areas or direct runoff from paved urban areas. The model captures general dynamics accurately and mimics peaks and drops reasonably well. Even though the daily model was calibrated using biweekly nitrate data, simulations reasonably captured the short-term dynamics (i.e., the concentration fluctuations, peaks and drops) that can only be observed in higher frequency observations. Moreover, during spring and summer 2011, the discharge contribution from the lower part (below the station Meisdorf) was abnormally higher than in other years. The model successfully captured the discharge and concentration changes, indicating its ability to represent variable spatial contributions of runoff and nitrate.

The uncertainty results were consistent with above model calibration and validations, although the evaluation criteria are different (log-likelihood function and multi-objective function, respectively). This indicated the model's robustness and reduced the risk of over-optimization. The mHM-Nitrate model can be a suitable tool to explicitly present spatial distributions of catchment nitrate concentrations and fluxes. Nitrate statuses of soil moisture and groundwater were represented by nitrate concentrations in interflow and baseflow, respectively, due to the basic fully mixing assumption and the lack of precise information of soil DIN pool size, of which initial value was also assigned in form of concentration. The nitrate concentration appeared to be generally stable in different seasons, consistently with the almost closed mean terrestrial balance in the catchment. Moreover, the spatial variabilities of soil nitrate concentrations and fluxes were also correspondent. For instance, in the north-west part of the Selke catchment, the relatively lower nitrate outputs (i.e., soil denitrification and terrestrial exports, Figure 8e and f) resulted in nitrate enrichment in the soil moisture and urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0111 concentration reached up to 45 mg l−1 in recent years (Figure 7a).

Although the model was validated at the three gauging stations, nitrate distributions of concentrations and fluxes were in reasonable ranges that suggested by literature (Hofstra & Bouwman, 2005; Wade et al., 2002; Whitehead et al., 1998b) and field measurements. Hofstra and Bouwman (2005) summarized 336 denitrification experiments in agricultural soils and reported mean values ranged 8–51 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0112, comparing with our modeling mean value 24.5 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0113. Wade et al. (2002) reported INCA-N model results of crop/plant uptake, denitrification, mineralization and N-leaching (i.e., terrestrial export in this study) in an England catchment and provided literature ranges respectively. Calculations from local authority (LLFG, 2012) showed that N mineralization is 30–45 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0114 in the arable lands of the study area. Jiang et al. (2014) calculated the N terrestrial export (0–10.6 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0115) of the Selke catchment using the HYPE model. These findings are compatible with our results. This rationalizes the use of spatial information provided in each model cell to support spatially differentiated N balance investigations. We recognized that a more theoretical and comprehensive scale analysis should be conducted to assess the predictive capability at model grid scale. The representative elementary scale concept, suggested by Refsgaard et al. (2016), can be a potential approach for further study. Calculated in-stream nitrate removal reflected high seasonal variability of the in-stream processes. The annual mean percentage of nitrate removal was about 8%. This value is comparable to values from other in-stream nitrate retention studies, given a wide range of values that has been reported (Alexander et al., 2009; Covino et al., 2010). Rode et al. (2016a) calculated the in-stream assimilatory uptake based on high-frequency sensor measurements in the Selke catchment. They reported nitrate gross assimilatory uptake of 12.4 and 45.2 urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0116 in upper forest reaches and lower agricultural reaches, respectively. The order of magnitude is in line with our modeling results of net removal (Table 4). Given model uncertainty and “equifinality” effects, internal terrestrial and in-stream information provided by mHM-Nitrate only gives a coarse estimation on catchment-wide nitrate status. For a more comprehensive simulation, more in-situ knowledge benefiting from newly available monitoring data should be integrated in future catchment model development (Rode et al., 2016b).

5.2 Remarks on Model Representation

Balancing accurate representation and complexity remains a major challenge in model development (Clark et al., 2017). The grid-based mHM-Nitrate model was developed to address issues related to model representation.

5.2.1 Representing Spatial Variability

Most current hydrological water quality models adopt the semi-distributed structure, mainly because 1) sub-catchments and basic modeling units are delineated based on natural geographic information (topography, land use and soil types) that, to some extent, ensures a close relationship between model parameters and catchment characteristics, and 2) the hierarchical structure greatly decreases the number of basic units and increases computing efficiency (Krysanova et al., 1998). However, the spatial representation of these models has been criticized for their lack of location and connecting information for spatial objects (Bieger et al., 2017). In mHM-Nitrate, catchment characteristics and model parameters are assigned at the basic input-data level and then upscaled to model levels, for which users can specify the resolutions. Representation of variability in catchment characteristics and model parameters becomes more accurate if a finer model resolution is specified; however, the computational demand will increase accordingly. By simply changing settings in the model configuration file, users can test different modeling resolutions to obtain the optimal catchment discretization scheme.

5.2.2 Representing Subsurface Water Storage and Nitrate Concentration

Studies have shown the significance of nitrate retention in subsurface water (Højberg et al., 2017; Wriedt & Rode, 2006). However, there are different options on how to conceptualize the subsurface water storage (e.g., the general “groundwater” storage or separated “soil moisture” and “deep groundwater” storages), and how to estimate nitrate concentration therein considering its vertical distribution (Dupas et al., 2016; Musolff et al., 2016). In the reservoirs based mHM-Nitrate model, subsurface storage is represented by a sequence of conceptual reservoirs (i.e., multi-layer soil moisture and beneath deep groundwater). Regarding water storage, the active water volumes for hydrological and nutrient calculations need to be different because the retention storage is critical only for chemical response in the catchment (Benettin et al., 2015). This difference is more pronounced in lower deep groundwater, where the hydrologically active volume only accounts for a small proportion of total storage. Therefore, groundwater storage was subdivided in the new model and relatively large retention storage was assigned. Water and nitrate dynamics are considered separately and interactively between each reservoir to represent the vertical variability. Currently, nitrate retention (e.g., denitrification and transformation) is considered only in soil layers, not in deep groundwater (Figure 1). First, potential denitrification in groundwater is somehow considered in soil layer (with a depth of around 2 m), part of which can be below groundwater table. Second, denitrification in deeper groundwater is not pronounced in the study region, especially given the large storage assigned in the model. For aquifers where nitrate reduction is significant, an additional reaction term and corresponding parameter have to be added to the Eq. 1. Due to the vertical variability of nitrate concentration in deep groundwater, the assumption of full mixing is probably not appropriate. Therefore, we modified the equation from the INCA-N model (Wade et al., 2002), which still follows the full mixing assumption but avoids calculating the nitrate concentration in the retention storage. Based on the equation, the initial baseflow concentration reflects long-term N percolation from upper soil layers and the large retention storage (e.g., tens of meters) keeps baseflow concentration stable to represent the long-delayed deep groundwater nitrate transport.

5.2.3 Representing Crop Rotation and Point Source Pollution

In most existing models, crop rotation, if being considered, is represented by assigning crop sequences to homogeneous units (e.g., HYPE) or to land-use/cover types (e.g., SWAT). However, the former usually lacks spatial information, while the latter ignores other influential factors (e.g., climate conditions, soil types and choices of farmers). In mHM-Nitrate, spatial variability in agricultural crop rotations is explicitly defined using crop rotation maps, which also ensures an easy setup for further analysis of agricultural scenarios.

Catchment water quality models are mainly oriented to address environmental problems from non-point sources, but point sources strongly and directly influence stream water quality. Due to the relatively long residence time for natural nutrient transport processes, especially in lowland areas (Wriedt & Rode, 2006), it can take years to decades to observe the impacts of agricultural practices on stream water concentrations. Thus, modelers prefer to have long-term monitoring data and conduct continuous modeling. Therefore, changes in point sources (e.g., new pollution sources or improved waste water treatments) require careful consideration before using long-term stream water observations to calibrate catchment model for natural processes. In mHM-Nitrate, time-series point-source input is allowed and can be added in the exact location within the river network. This feature enables the model to assess their impacts on nutrient transport more reasonably and can provide a better evaluation of changing point sources within the river network (e.g., in the context of restoration measures).

6 Conclusions

The new grid-based mHM-Nitrate model was developed mainly based on implementations of the mHM and HYPE models. Benefiting from the multi-resolution discretization scheme, spatial representation of catchment characteristics and model parameters were flexibly designed based on the user-specified modeling resolution. Major improvements were added to represent more accurately nitrate dynamics in deep groundwater, crop rotation practices in agricultural land and point-source impacts. The mHM-Nitrate model successfully simulated nitrate transport and removal processes in the highly heterogeneous Selke catchment, Germany. It well reproduced seasonal dynamics of biweekly urn:x-wiley:00431397:media:wrcr23375:wrcr23375-math-0117 observations in forested and agricultural areas. Additionally, daily observations from high-frequency monitoring confirmed its general ability to reproduce short-term changes that reflect runoff partitioning changes and event-based dilution effects. Moreover, uncertainty analysis results confirmed the model robustness and reduced the risk of over-optimization.

The mHM-Nitrate model provided detailed spatial information (e.g., spatially resolved nitrate terrestrial concentrations and fluxes) that is within reasonable ranges. Therefore, it offers promising opportunities for further evaluation of nutrient transport and removal processes spatiotemporally, for instance, to support future studies that target spatial agricultural mitigation measures (Hashemi et al., 2016)and interactions between terrestrial and in-stream processes (Dupas et al., 2017). Further validation of the new model needs to be done by cross validating for catchments that differ in natural conditions and scales. An internal scale analysis also can help to assess the model predictive capability at grid scale (Refsgaard et al., 2016). Furthermore, we consider the model as a starting point and new platform for investigations of new parameter regionalization and upscaling procedures, and for further model development to consider other water quality compounds (e.g., phosphorus, organic carbon), and their interactions.


Xiaoqiang Yang is funded by the Chinese Scholarship Council (CSC). We would like to thank Dr. Luis Samaniego, Dr. Andreas Musolff and Prof. Sabine Attinger for their constructive comments. We highly appreciate the comments from the Editor Martyn Clark, Riccardo Rigon and three anonymous Reviewers, which helped us to improve the manuscript significantly. The high-frequency data are provided by TERENO (Terrestrial Environment Observatories) project. We thank the German Weather Service (DWD), Federal Institute for Geosciences and Natural Resources (BGR), State Agency for Flood Protection and Water Management of Saxony-Anhalt (LHW) for providing meteorological, geological and discharge and water quality data, respectively. The data used are presented in the tables, figures and supplements. The model is developed based on the GNU General Public License. Source codes and relevant data to rebuild the work are available under request to X. Yang and M. Rode, and are on-line accessible under https://git.ufz.de/yangx/mHM-Nitrate.