A Spatially Distributed, Physically-Based Modeling Approach for Estimating Agricultural Nitrate Leaching to Groundwater
Abstract
:1. Introduction
- the sub-cycle occurring in the atmosphere;
- the sub-cycle occurring in the unsaturated zone;
- the sub-cycle occurring in the plants, which involves NO3− uptake by roots.
2. Materials and Methods
2.1. Overview of the Nitrogen Cycle Module
- a conservation term, which expresses the variation of nitrogen concentration in time;
- the conservation term for NH4+ includes also sorption by soil ;
- a vertical, unidimensional transport term, which is driven by unsaturated zone flow;
- a term related to lateral movement of nitrogen in the unsaturated zone (lateral outflow term). However, in our approach, we assume that vertical transport of nitrogen is the predominant process. As such, lateral movement of nitrogen is not simulated;
- a crop uptake term for NO3− and NH4+. Such term is estimated for NO3− only, adopting the EPIC model approach (Sharpley 1990) [27], taking into account the phenological phases of crops. We assume, indeed, that NO3− is the predominant form of available nitrogen uptaken by roots (Nadelhoffer et al., 1984; Xu et al., 2012) [45,46];
- a decomposition term, i.e., mineralization for NH2−, nitrification for NH4+, denitrification for NO3−;
- a production/loss term, which includes source/sink terms for each pool and the decomposition term from the above pool (i.e., NH2− represents the pool above NH4+, and NH4+ represents the pool above NO3−).
- (a)
- (b)
- -
- the mathematical approach adopted, based on the mass conservation and the solution of transport Equation (1);
- -
- the mathematical approach adopted is relatively frugal, in the sense that it requires few input parameters;
- -
- the integration between Equation (1) and the unsaturated zone flow term calculated by means of distributed models integrated within the FREEWAT platform was pretty straightforward with respect to the space and time dimension of the involved processes.
2.2. Overview of the FREEWAT Platform
2.3. Coupling the Nitrogen Cycle and the Hydrological One
- -
- if crop NO3− demand is simulated over the cropping season (Option 1), the following is needed:
- running a MODFLOW-2005 model, including the UZF Package, to simulate water flow through the unsaturated zone. This is needed for the calculation of the thickness of the unsaturated zone, the water content, the runoff rate and the leaching rate in space and time;
- running an FMP-CGM scenario. This is needed for the calculation of crop transpiration flux and cumulated above-ground biomass;
- -
- if crop NO3− demand is not simulated, but the User inputs crop NO3− requirement parameters over the cropping season (Option 2). In such case, only running a MODFLOW-2005 model, including the UZF Package, is needed to simulate water flow through the unsaturated zone as above-mentioned.
- -
- if Option 1 occurs, all of the processes involved in the nitrogen cycle are simulated taking steps from the ANIMO model approach, except for the NO3− crop uptake process, which is simulated through a sub-routine based on the EPIC model approach;
- -
- if Option 2 occurs, all the processes involved in the nitrogen cycle are simulated taking steps from the ANIMO model approach. In such case, the sub-routine based on the EPIC model approach is not executed, and the NO3− crop uptake process is simulated by comparing the crop NO3− requirement defined by the User with the NO3− availability in the unsaturated zone.
2.4. Model Testing Using a Synthetic Case Study
3. Results and Discussion
- -
- the unsaturated zone is discretized in only one layer. It is then considered as a unique layer extending from the ground surface to the water table. This representation may not be suitable in case of non-homogeneous soil sediments, with different physical and chemical properties. Furthermore, NO3− uptake at different depths according to the root distribution in the vertical domain may not be adequately reproduced;
- -
- purely advective transport of nitrogen through the unsaturated zone is simulated (dispersion is neglected);
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- the biological fixation process is not simulated. This can lead to underestimation of mineral nitrogen available in the soil;
- -
- volatilization of NH4+ is taken into account through a volatilization coefficient (fv) only, which is difficult to quantify;
- -
- NH4+ uptake by plants’ roots is not simulated (we assume, indeed, that NO3− is the predominant form of available nitrogen uptaken by roots);
- -
- taking steps from the UZF MODFLOW package approach, we assume that vertical movement of nitrogen is the predominant process. As such, lateral movement of nitrogen across neighboring cells is not simulated;
- -
- when the thickness of the unsaturated zone varies, according to water level fluctuations, the mass of nitrogen stored in the soil is simply redistributed over the whole unsaturated thickness.
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
Code | References | Modelling Approach (lumped/Spatially Distributed) | Scale of Application | Spatial Discretization | Time Discretization | Hydrological Component | Nitrogen Cycling Component |
---|---|---|---|---|---|---|---|
EPIC | Sharpley 1990 | Lumped | Field scale | Watershed divided into smaller drainage areas; Soil profile divided into layers | Daily | Based on algebraic mass balance equation involving rainfall, runoff and evapotranspiration | Organic/inorganic transformations based on first-order decay functions involving soil water content, temperature, mineral nitrogen availability, and the amount of soluble carbon associated with soil organic matter; Nitrogen leaching estimated by an exponential decay weighting function |
APEX | Williams et al., 2015 | Lumped | Farms and small watersheds scales | Watershed divided into hydrologically connected landscape units; Soil profile divided into layers | Daily | Based on algebraic mass balance equation involving rainfall, runoff and evapotranspiration | Organic/inorganic transformations based on first-order decay functions involving soil water content, temperature, mineral nitrogen availability, and the amount of soluble carbon associated with soil organic matter; Nitrogen leaching estimated by an exponential decay weighting function |
SWAT | Neitsch et al., 2002 | Lumped | Watershed scale | Watershed divided into Hydrologic Response Units; Soil profile divided into layers | Daily | Based on algebraic mass balance equation involving rainfall, runoff and evapotranspiration | Organic/inorganic transformations based on algebraic equations involving soil water content, temperature, and soil organic matter availability; Nitrogen leaching estimated by multiplying the leaching rate by a decay coefficient |
ANIMO | Groenendijk and Kroes 1999 | Lumped | Field and regional scales | Watershed divided into sub-regions; Soil profile divided into layers | Any (not sub-daily) | Water fluxes and moisture contents are computed by external models, and then algebraically summed to get the change in water volume over time | Conservation and transport equation solved for dissolved organic nitrogen, nitrate and ammonium; Nitrogen leaching estimated by means of a 1D transport equation in the unsaturated zone |
DAISY | Hansen et al., 1990 | Lumped | Field and regional scales | Watershed divided into sub-regions; Soil profile divided into layers | Daily | Based on Richards’ equation for soil water dynamics, and on Darcy’s law for vertical flow rate | The organic nitrogen pool is represented in a very detailed way, with further sub-pools; Inorganic transformations based on algebraic equations involving soil water content, temperature, and carbon availability; Nitrogen leaching estimated by means of a 1D transport equation in the unsaturated zone |
PRZM-3 | Suárez 2005 | Lumped | Field and regional scales | Watershed divided into sub-regions; Soil profile divided into two layers (root zone and unsaturated zone) | Daily | Evapotranspiration from the root zone estimated directly from pan evaporation data, or based on an empirical formula; Water leaching through the root zone simulated using generalized soil parameters, and saturation water content; Flow in the unsaturated zone simulated by Richards’ equation | The organic nitrogen pool is represented in a very detailed way, with further sub-pools; Inorganic transformations based on first-order kinetics involving soil water content and temperature; Nitrogen leaching estimated by means of a 1D transport equation in the unsaturated zone |
NTT-Watershed | Heng and Nikolaidis 1998 | Spatially distributed | Watershed scale | Watershed discretized into square cells; Soil profile divided into layers | Any | Green-Ampt equation used to determine the infiltration capacity of the soil; Richards’ equation used to simulate the vertical movement of water in the unsaturated zone | Organic/inorganic transformations based on first-order kinetics involving soil water content and temperature; Nitrogen leaching estimated by means of a 1D transport equation in the unsaturated zone |
Appendix B
Symbol | Description | Dimensions | Note |
---|---|---|---|
Time instant referring to the beginning of a stress period | [T] | Retrieved from the groundwater flow model setup | |
Time instant referring to the end of a stress period | [T] | Retrieved from the groundwater flow model setup | |
Cartesian coordinate along the vertical direction | [L] | ||
Time derivative | [T−1] | ||
Spatial derivative along the vertical direction | [L−1] | ||
Length of the stress period | [T] | Retrieved from the groundwater flow model setup | |
Column width of the grid cell | [L] | Retrieved from the groundwater flow model setup | |
Row width of the grid cell | [L] | Retrieved from the groundwater flow model setup | |
Thickness of the unsaturated zone | [L] | Estimated by UZF package | |
Stress period number | Retrieved from the groundwater flow model setup | ||
Number of stress periods | Retrieved from the groundwater flow model setup | ||
Plant available water | User-defined | ||
Cumulated biomass | [M/L2] | Estimated by CGM and converted into kg/ha | |
Crop parameter expressing NO3− concentration in the crop at emergence | User-defined | ||
Crop parameter expressing NO3− concentration in the crop at emergence at 0.5 maturity | User-defined | ||
Crop parameter expressing NO3− concentration in the crop at emergence at maturity | User-defined | ||
Cation Exchange Capacity of the soil | [meq/M] | User-defined | |
Concentration of NH2− | [M/L3] | Derived variable | |
Concentration of NH4+ | [M/L3] | Derived variable | |
Concentration of NO3− | [M/L3] | Derived variable | |
Nitrogen concentration | [M/L3] | Derived variable | |
Initial nitrogen concentration (initial condition) | [M/L3] | Derived variable | |
Nitrogen concentration in the rain water | [M/L3] | User-defined | |
Optimal NO3− content in the crop | Derived variable | ||
Dose of fertilizer application of the applied material | [M/L2] | User-defined | |
Field capacity of the soil | User-defined | ||
Volatilization fraction for NH4+ | User-defined | ||
Fraction of NH2−, NH4+, or NO3− of the applied material | User-defined | ||
Heat Unit Index () | Derived variable | ||
Daily Heat Unit accumulation in the sp-th stress period | [Θ] | Estimated by CGM and expressed in °C | |
Sorption coefficient | [L3/M] | Derived variable | |
NO3− uptake term | [T−1] | Derived variable | |
NO3− mass flux in the unsaturated grid cell | [M/L2] | Derived variable and converted into kg/ha | |
Total content of nitrogen in the soil | [M of nitrogen/M of soil] | User-defined | |
Potential Heat Units required for crop maturity | [Θ] | User-defined and expressed in °C | |
NO3− mass which could be potentially adsorbed by the crop | [M/(L2*T)] | Derived variable and converted into kg/(ha*day) | |
Rainfall flux | [L/T] | User-defined | |
Leaching rate | [L3/T] | Estimated by UZF package | |
Runoff rate | [L3/T] | Estimated by UZF package | |
Vertical flow term for NH2− | [M/(L2*T)] | Derived variable | |
Vertical flow term for NH4+ | [M/(L2*T)] | Derived variable | |
Vertical flow term for NO3− | [M/(L2*T)] | Derived variable | |
Lateral outflow term for NH2− | [M/(L3*T)] | Derived variable | |
Lateral outflow term for NH4+ | [M/(L3*T)] | Derived variable | |
Lateral outflow term for NO3− | [M/(L3*T)] | Derived variable | |
NH4+ uptake term | [M/(L3*T)] | Derived variable | |
NO3− uptake term | [M/(L3*T)] | Derived variable | |
Decomposition term for NH2− | [M/(L3*T)] | Derived variable | |
Decomposition term for NH4+ | [M/(L3*T)] | Derived variable | |
Decomposition term for NO3− | [M/(L3*T)] | Derived variable | |
Production term for NH2− | [M/(L3*T)] | Derived variable | |
Production term for NH4+ | [M/(L3*T)] | Derived variable | |
Production term for NO3− | [M/(L3*T)] | Derived variable | |
Fertilizer term | [M/(L3*T)] | Derived variable | |
Nitrogen production term | [M/(L3*T)] | Derived variable | |
Surface runoff term | [M/(L3*T)] | Derived variable | |
Ammonium volatilization term | [M/(L3*T)] | Derived variable | |
Residual NO3− mass available in the grid cell | [M/(L2*T)] | Derived variable and converted into kg/(ha*day) | |
Crop transpiration flux | [L/T] | Estimated by FMP and converted into mm/day | |
NO3− crop demand | [M/(L2*T)] | Derived variable and converted into kg/(ha*day) | |
Rate of NO3− supplied by the soil to the crop | [M/(L2*T)] | Derived variable and converted into kg/(ha*day) | |
Rate of NO3− supplied by the soil to the crop in the sp-th stress period | [M/(L2*T)] | Derived variable and converted into kg/(ha*day) | |
Wilting point of the soil | User-defined | ||
Sorbed ammonium content | Derived variable | ||
Water content in the unsaturated zone | [L3/L3] | Estimated by UZF package | |
Water content change with time | [T−1] | Derived variable | |
First order decay rate constant | [T−1] | User-defined | |
Dry bulk density of the soil | [M/L3] | User-defined | |
Apparent density of the soil | [M/L3] | User-defined |
Appendix C. Conceptualization of the Nitrogen Cycle Module
- -
- the thickness of the unsaturated zone (Δz(t) in the following);
- -
- the water content ( in the following);
- -
- the runoff rate (qrunoff(t) in the following);
- -
- the flow rate towards the saturated zone (qperc(t) in the following).
- -
- if the optimal, User-defined, NO3− concentration is higher or equal to the concentration of NO3− available in the soil for crop uptake, then POT(t) equals the concentration of NO3− available in the soil for crop uptake;
- -
- if the optimal, User-defined, NO3− concentration is lower than the concentration of NO3− available in the soil for crop uptake, then POT(t) equals the optimal NO3− concentration.
- -
- the decomposition term from the above pool (source term to be summed to the current pool), as detailed in the above lines;
- -
- surface runoff (sink term to be subtracted), calculated as
- -
- ammonium volatilization (sink term to be subtracted from the NH4+ pool), calculated as
- -
- fertilizers (source term to be summed), calculated as
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Nitrogen Pool | Conservation Term | Vertical Flow Term | Lateral Outflow Term | Crop Uptake Term | Decomposition Term | Production Term | |
---|---|---|---|---|---|---|---|
NH2− | = | ||||||
NH4+ | = | ||||||
NO3− | = |
Parameter | Units of Measurements | Value |
---|---|---|
NT | kg/kg | 10−3 |
ρa and ρd | kg/m3 | 1360 (silt) 1440 (sandy loam) 1200 (silty clay) |
λ1 | day−1 | 10−2 |
fv | 10−3 | |
CEC | meq/kg | 148 (silt) 110 (sandy loam) 146 (silty clay) |
bn1 | 0.05 | |
bn2 | 0.023 | |
bn3 | 0.0146 | |
PHU | 1600 | |
D | kg/m2 | 1.856 × 10−2 (silt) 1.788 × 10−2 (sandy loam) |
1 | ||
0 | ||
0 |
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De Filippis, G.; Ercoli, L.; Rossetto, R. A Spatially Distributed, Physically-Based Modeling Approach for Estimating Agricultural Nitrate Leaching to Groundwater. Hydrology 2021, 8, 8. https://doi.org/10.3390/hydrology8010008
De Filippis G, Ercoli L, Rossetto R. A Spatially Distributed, Physically-Based Modeling Approach for Estimating Agricultural Nitrate Leaching to Groundwater. Hydrology. 2021; 8(1):8. https://doi.org/10.3390/hydrology8010008
Chicago/Turabian StyleDe Filippis, Giovanna, Laura Ercoli, and Rudy Rossetto. 2021. "A Spatially Distributed, Physically-Based Modeling Approach for Estimating Agricultural Nitrate Leaching to Groundwater" Hydrology 8, no. 1: 8. https://doi.org/10.3390/hydrology8010008