Water and Nutrient Balance Model J2000-S
The water and nutrient balance model J2000-S offers a simulation of the water and nitrogen balance of meso scale catchment areas. The model is an extension to the J2000 model with which it shares most of the components for the description of the hydrologic cycle. The additional components, soil temperature, soil nitrogen balance, land use management, plant growth as well as ground water nitrogen balance, are described for the specification of the nitrogen balance. Further modules are adapted for the demands of the nitrogen balance.
Contents |
Soil Nitrogen Module
The description of the soil nitrogen balance is carried out similarly to the SWAT model (Arnold et al. 1998). Within the individual soil horizons the five nitrogen pools for nitrate, ammonium, stable organic substances, active organic substance and fresh plant remains as biomass are distinguished. The fluxes and transformations between the pools and outside the soil, like nitrification, denitrification, mineralization, volatilation, Pflanzenaufnahme and eluviation, are calculated via the empirical relations against the soil humidity and soil temperature. The nitrogen flux is passed as well as the water transport via a routing method between the subareas to the receiving stream (see figure 1).
The nitrogen input caused by fertilization and Bestandesabfall as well as the removal through the plants is provided by the plant growth module and the land use management module. The mineral inputs are allocated to the ammonium pool or directly to the nitrate pool. The organic nitrogen is either allocated to the Bestandesabfall pool or the active organic pool. The latter is poised with the stable organic pool. The nitrate pool is the central allocation section for the discharge as eluviation, Pflanzenaufnahme and denitrification. The processes described in the module take place in free parameterizable soil horizons. Here, the delivery of organic substances and fertilizer as well as the removal of nitrogen with the surface runoff are limited to the top horizon.
Figure 1: Structure of the soil nitrogen module
The here applied nitrogen module contains some simplifications. Thus, no Pflanzenaufnahme from the ammonium pool is offered. Furthermore, the decomposition of organic substances is directly simulated to nitrate without any detour via ammonium. The N immobilization from mineral to organic nitrogen in the soil zone is neglected completely. The water transport of nitrogen is shown very generalized. Thus, a complete mixing of nitrogen in the individual storages takes place instead of advection and dispersion. The individual processes are described in the model as follows:
Pflanzenaufnahme
At first, the plant’s demands (potential Pflanzenaufnahme) which shall be met by the soil nitrogen storage per day t0 are generated:
[1]
with:
= potential Pflanzenaufnahme [kgN/ha]
= optimal biomass [kgN/ha]
= actual biomass [kgN/ha]
Afterwards, the proportions of the soil horizons which lie within the effective root zone are generated. At this, the horizons which lie completely within the root zone are taken into account completely (partroot = 1). However, the horizon which lies only partly in the root zone is only considered partly:
![partroot[i] = \frac {rootdepth - layerdepth[i - 1]}{layerdepth[i] - layerdepth[i - 1]} \!](/ilmswiki/uploads/math/9/4/9/94988578303bd534638cb5e0651802fb.png)
[2]
with:
= horizon [-]
= proportion of the horizon at the root zone [-]
= lower threshold of soil horizon [-]
The allocation of the n-uptake to the individual horizons is carried out against a calibration parameter (
). At this, the potential uptake for the individual horizons is calculated:
![potNup_z[i] = \frac {potNup} {1 - \exp(-\beta_{Ndist})} \cdot \left(1 - \exp\left(-\beta_{Ndist} * \frac {layerdepth[i]} {rootdepth}\right)\right) - uptake[i-1]](/ilmswiki/uploads/math/3/7/0/3707f7d3586df91bd005046e7176d435.png)
[3]
with:
= Horizont [-]
= proportion of the horizon at the root zone [-]
= lower threshold of the soil horizon [-]
= potential Pflanzenaufnahme [kgN/ha]
= potential Pflanzenaufnahme in the individual horizons [kgN/ha]
= potential Pflanzenaufnahme which has been taken from upper horizons already [kgN/ha]
= distribution parameter of the Pflanzenaufnahme; default value = 1.0; possible values 1 - 15 [-]
For the calculation of the potential Pflanzenaufnahme which is covered by upper horizons already, the following connection is applied:
![uptake = uptake + potNup_z[i] \!](/ilmswiki/uploads/math/c/9/7/c9702b635f7c1db449196a0c17994b7a.png)
[4]
= potential Pflanzenaufnahme in the individual horizons [kgN/ha]
= potential Pflanzenaufnahme which has been taken from upper horizons already [kgN/ha]
The calculation of a demand is carried out according to the following equation:
![demand = (NO_3Pool[i] \cdot partroot[i]) - potNup_z[i] \!](/ilmswiki/uploads/math/3/b/e/3beb853670497bc45c37498ec5baed42.png)
[5]
with:
= horizon [-]
t = proportion of the horizon of the root zone [-]
= demand that can be met by the soil nitrogen pool [kgN/ha]
= soil nitrogen pool [kgN/ha]
= potential Pflanzenaufnahme in the individual horizons [kgN/ha]
If this demand is greater than 0, it can be met by the existing nitrogen storage with:
![NO_3Pool2[i] =
\begin{cases}
NO_3Pool1[i] - potNup_z[i] & \mathrm{f\ddot{u}r} \; \; demand >= 0 \\
NO_3Pool1[i] - (NO_3Pool1[i] \cdot partroot[i])& \mathrm{f\ddot{u}r} \; \; demand < 0
\end{cases}](/ilmswiki/uploads/math/a/3/1/a312b06a7c8f2e01cd7b524cde87eb2b.png)
and
![demand =
\begin{cases}
demand[i] = 0 & \mathrm{f\ddot{u}r}\; \; demand >= 0 \\
demand[i] = demand &\mathrm{f\ddot{u}r} \; \; demand < 0
\end{cases}](/ilmswiki/uploads/math/a/9/2/a92440f6c49c729de089ed8e1ea21283.png)
with
= horizon [-]
= demand that can be met by the soil nitrogen pool [kgN/ha]
= soil nitrate pool before the time step [kgN/ha]
= soil nitrate pool after the time step [kgN/ha]
= potential Pflanzenaufnahme in the individual horizons [kgN/ha]
= proportion of the horizon of the root zone [-]
Anschließend berechnet sich die aktuelle Pflanzenaufnahme aus der potentiellen Pflanzenaufnahme und dem über die Horizonte summierten Bedarf:
![N_{uptake} = potNup + \sum^{n}_{i=1}{demand[i]} \!](/ilmswiki/uploads/math/e/c/d/ecd12f7c1e2fb802760d78eb62419a0b.png)
[10]
with
= horizon [-]
= proportion of the horizon of the root zone [-]
= demand which can be met by the soil nitrogen pool [kgN/ha]
= potential Pflanzenaufnahme [kgN/ha]
= actual Pflanzenaufnahme [kgN/ha]
Nitrate Rising by Evaporation
Soil water from deeper layers is transported into upper horizons via the evaporation flux. This happens for each horizon according to the SWAT method:
[1]
with
= amount of nitrogen from the individual horizon which is transported by evaporation [kgN/ha]
= soil nitrogen pool [kgN/ha]
= actual evapotranspiration of the horizon [l]
= actual large pore storage of the horizon [l]
= actual middle pore storage of the horizon [l]
= fine pore storage of the horizon [l]
Transformation Processes in the Soil
Nitrification and Ammonium Volatilation
The transformation processes of the ammonium pool in this model are the nitrification from ammonium to nitrate and the ammonium volatilation. The calculation of the total transformation of the ammonium pool is carried out for both processes together. Afterwards, the rates for both processes are separated. In order to represent the influence of the temperature, the following coefficient needs to be calculated:
[1]
with
= soil temperature coefficient [-]
= temperatur of the soil layer [°C]
The influence of the soil humidity on the nitrification is described via the coefficient eta_water:
for 
[2]
for 
[3]
with
= soil humidity coefficient[-]
= maximum large pore storage of the horizon [l]
= maximum middle pore storage of the horizon [l]
= maximum fine pore storage of the horizon [l]
= actual large pore storage of the horizon [l]
= actual middle pore storage of the horizon [l]
The dependency of the ammonium volatilation on the soil depth is calculated with the following equation:
= soil depth coefficient [-]
= layer depth of the horizon [cm]
The total Gesamtumsatz of the ammonium pool can be calculated as follows:
This Gesamtumsatz is then distributed into:
with
= soil humidity coefficient [-]
= soil temperature coefficient [-]
= soil depth coefficient [-]
= soil humidity coefficient [kgN/ha]
= Gesamtumsatz of the ammonium pool [kgN/ha]
= fraction nitrification [-]
= fraction ammonium volatilation [-]
= amount of nitrifikation [kgN/ha]
= amount of ammoniumvolatilation [kgN/ha]
Pre-calculation for the Influence of the Environmental Conditions
In order to show the influence of the soil temperature and the soil humidity in the different transformation processes, the following coefficients are calculated beforehand: U
[1]
with
= soil temperature coefficient [-]
= temperature of the soil layer [°C]
[2]
with
= soil humidity coefficient [-]
= maximum large pore storage of the horizon [l]
= maximum middle pore storage of the horizon [l]
= maximum fine pore storage of the horizon [l]
= actual large pore storage of the horizon [l]
= actual middle pore storage of the horizon [l]
Transfer between the Organic Pools
The transfer between the active and the stable organic pool can be calculated with the following equation:
with
= transfer rate between the active and the stable organic pool [kgN/ha]
= transfer constant between the active and the stable organic pool; default value= 0.00001 [-]
= active organic pool [kgN/ha]
= stable organic pool [kgN/ha]
= fraction of the organic nitrogen in the active organic pool = 0.02 [-]
The transfer rate is here subtracted from the active pool whereas it is added to the stable pool.
Mineralization of the Active Pool
The active pool is mineralized to nitrate directly without taking the nitrification into account. The rate is calculated as follows:
with
= transfer rate between the active organic and the nitrate pool [kgN/ha]
= transfer constant between the active organic and the nitrate pool; default value = 0.002 [-]
= active organic pool [kgN/ha]
= soil humidity coefficient [-]
= soil temperature coefficient [-]
The transfer rate is substracted from the active pool whereas it is added to the nitrate pool.
Dynamics of the Residue Pools
The dynamics of the decomposition of fresh organic substances (residue) from plant remains and organic fertilizer is carried out only in the top horizon. the residue are divided in two pools: the first one represents the biomass as a whole, the second represents the residue's amount of nitrogen. The supply to the residue pools is carried out via plant remains after the harvest and via the organic fertilization with the help of the following equation:
with
= residue pool [kg/ha]
= input biomass [kg/ha]
= input nitrogen via organic fertilization [kgN/ha]
= residue pool's amount of nitrogen [kgN/ha]
The decomposition of the residue pool is carried out against the carbon-nitrogen relation (C/N-relation). The calculation of the C/N-relation is carried out according to the following equation.
with
= C/N-relation [-]
= residue decomposition factor [-]
= residue pool [kg/ha]
= nitrate pool [kgN/ha]
= residue pool's amount of nitrogen [kgN/ha]
The decomposition constant of the residue pool is calculated with γntr, γwater, γtemp:
with
= constant of the residue decomposition’s rate [-]
= residue decomposition factor [-]
= residue decomposition coefficient; default value = 0.05 [-]
= soil humidity coefficient [-]
= soil temperature coefficient [-]
The decomposition of the residue pools is carried out with the decomposition constant of the residue pool. At this, the nitrogen part is allocated to the active organic pool, in terms of humification, and the nitrate pool, in terms of mineralization, in a ratio of 20%:80%:
with
= constant of the residue decomposition’s rate [-]
= residue pool before the time step [kgN/ha]
= residue pool after the time step [kgN/ha]
= active organic pool before the time step [kgN/ha]
= active organic pool after the time step [kgN/ha]
= soil nitrate pool before the time step [kgN/ha]
= soil nitrate pool before the time step [kgN/ha]
= amount of nitrogen of the residue pool before the time step [kgN/ha]
= amount of nitrogen of the residue pool after the time step [kgN/ha]
Denitrification
Denitrification occurs when the soil is nearly water-saturated. The rate depends on the amount of organic carbon in the soil as well as on the soil temperature. In comparison to SWAT (0,95), the degree of water saturation is lower (0.91) when denitrification occurs. This is because SWAT - in contrast to J2000 - does not consider the soil's air capacity. Thus, the underlying pore volume for the calculation of water saturation is higher in J2000. Furthermore, it is ensured that the rate is at the most 1 kgN/ha*d since higher rates are not expected in open land.
with
= soil nitrate pool [kgN/ha]
= denitrification rate [kgN/ha]
= soil humidity coefficient [-]
= soil temperature coefficient [-]
= denitrification coefficient; defaul value = 0.91 [-]
Mass Transport with Water Movement in the Soil
Nitrogen Concentration of Mobile Water
For the simulation of the mass transport with water movement, the nitrogen concentration of the mobile water is defined. Here, it is simplified assumed that only the nitrogen of the nitrat pool is mobile and therefore is taken into account for the calculation. The amount of water is determined on the basis of the soil storages and the water streams that leave the horizon.
with
= soil nitrate pool [kgN/ha]
= soil water [mm]
= amount of mobile water [mm]
= percolation coefficient; default value = 0.2 [-]
= surface runoff [mm]
= interflow [mm]
= percolation in deeper horizons or ground water [mm]
= infiltration water that goes into deeper layers in a time step and therefore passes by the actual horizon [mm]
= water that leaves the horizon via diffusion [mm]
= fraction of the pore volume from which anions are excluded (due to positive charge preponder of the clay mineral); default value = 0.05 [-]
= nitrogen concentration of the mobile water [kgN/ha*mm]
The influence of the water that expands into deeper horizons in a time step is determined with a parameter (
). At this, the parameter represents to what extend the bypass water interacts with the soil matrix or bypasses in macro pores at the layers that are flown through.
![hor_{by_{infilt}}[i-1] = \sum^{n}_{i}{hor_{by_{infilt}}} * infil_{conc_{factor}} \!](/ilmswiki/uploads/math/2/9/5/29521387268f9a1f06a8919346e9fc41.png)
with
= infiltration water that goes into deeper layers in a time step and therefore passes by the actual horizon [mm]
= bypass parameter [mm]
= actual horizon [-]
= number of horizons [-]
Nitrogen Transport in the Runoff Components
For the individual horizons the nitrogen loads for the runoff components are calculated on the basis of the mobile water's nitrogen concentration. At this, the interflow is considered in all horizons whereas the surface runoff is only considered in the top horizon. The percolation occurs in the deeper horizons or in the ground-water reservoir.
with
= nitrogen concentration of the mobile water [kgN/ha*mm]
= infiltration water that goes in deeper layers and thus bypasses the actual horizon in a time step dass [mm]
= nitrogen in the surface runoff [kgN/ha]
= nitrogen in the interflow [kgN/ha]
= nitrogen in the percolation water [kgN/ha]
= surface runoff [mm]
= interflow [mm]
= percolation [mm]
= percolation coefficient [-]
The percolation coefficient represents a measurement for the interaction of the surface runoff and the soil matrix of the top horizon and therefore determines the surface runoff's amount of nitrogen.
The material that leaves the horizon with the diffusion water can be calculated as follows: the water movement that occurs above the field capacity due to potential gradients is called diffusion. A negative value for the diffusion water means here a downward water movement whereas a positive value represents an upward water movement.
![diffoutN =
\begin{cases}
w_{l_{diff}}[i] * ConcN_{mobile}[i] & \mathrm{f\ddot{u}r} \; \; w_{l_{diff}} < 0 \\
w_{l_{diff}}[i] * ConcN_{mobile}[i+1] & \mathrm{f\ddot{u}r} \; \; w_{l_{diff}} < 0
\end{cases}](/ilmswiki/uploads/math/5/2/d/52d8953e30a1b04c6d9dd799c9a047e4.png)
and
![NO_3Pool[i] = NO_3Pool[i] + diffoutN \!](/ilmswiki/uploads/math/7/b/5/7b57cb1ca33cde9ac1002c2b7af7788c.png)
and
![NO_3Pool[i+1] = NO_3Pool[i+1] - diffoutN \!](/ilmswiki/uploads/math/8/d/a/8da310efcecc92e2ec1b314ec8d885d8.png)
with
= nitrogen concentration of the mobile water [kgN/ha*mm]
= nitrogen in the diffusion water [kgN/ha]
= soil nitrat pool [kgN/ha]
= diffussion water [mm]
= soil horizon [kgN/ha]
Soil Temperature Module
The soil temperature is an important measurement for the matter regime modeling. Especially mcorbiological processes like nitrification, denitrification and the transformation of organic nitrogen in the soil-zone is strongly influenced by the prevailing temperature. In the here developed model J2K-S the soil temperature also plays an important role for the calculation of the following processes (see Soil Nitrogen Module):
• nitrification
• volatilation
• transformation of organic substance
• decomposition of plant remains
• denitrification
Structure of the Module
The soil temperature is simulated according to the empirical routines of SWAT (Arnold et al. 1998) and EPIC (Williams et al. 1984). At first, a surface soil temperature is generated for bare ground on the basis of the air temperature and insolation.This surface temperature is modified by attenuation factors that describe the effect of biomass and snow. The temperature of the different soil horizons is generated as upper boundary condition between the surface soil temperature and the long lasting mean temperature as lower boundary condition. At this, the attenuation effect of the soil is defined in consideration of the soil humidity and the bulk density. The equations of the individual processes can be found in Neitsch et al. (2002).
Figure 1: Structure of the soil temperature model
Figure 2: Results of the soil temperature modeling for the surface area and at 40 cm depth at an investigated slope near Zeulenroda (Thuringia).
This figure shows the measured and modeled temperature at the surface (upper figure) as well as at 40 cm depth (lower figure) for an investigated area near the dam Zeulenroda. It can be seen that the temperature curve can be followed quite well in spite of certain deviations. This is emphasized by the high coefficient of determination of about 0.95.
Pflanzenwachstumsmodul
Die Beschreibung zur Simulation des Pflanzenwachstums ist für eine Vielzahl von hydrologischen und Stofftransport-Prozessen wichtig, wie z.B. für die Interzeption oder die Stickstoffaufnahme durch den Pflanzenbestand. Das Pflanzenwachstum wird prinzipiell über die Simulation der Blattflächenentwicklung (LAI), der Lichtinterzeption und der Transformation in Biomasse gesteuert und erfolgt in Anlehnung an SWAT (Arnold et al. 1998). Dabei wird zunächst von einem potenziellen, d.h. unter optimalen Bedingungen vorliegenden, Pflanzenwachstum ausgegangen, welches unter Einbeziehung von Stressfaktoren modifiziert wird.
Temperaturentwicklung und Wärmesummen
Wichtigster Faktor für die Entwicklung des Pflanzenbestandes ist die Temperatur, deren Kennwerte für jede Pflanze unterschiedlich sind. Daher verfügt jede Pflanze über eine eigene Basistemperatur, die erreicht werden muss, um ein entsprechendes Wachstum auszulösen. Das Wachstum erhöht sich über die Optimumtemperatur bis es beim Überschreiten der Maximaltemperatur deutlich eingeschränkt wird.
Der pflanzenspezifische Wachstumsverlauf erfolgt über die Generierung der Wärmesummen (‚heat units = HU’). Die zugrunde liegende Hypothese hierfür beruht auf der Annahme, dass Pflanzen einen spezifischen Wärmebedarf haben, der bis zum Erreichen des Erntezustands quantifizierbar ist. Eine ‚HU’ ist als eine phänologisch wirksame Temperatureinheit definiert. Sie ergibt sich aus der täglich akkumulierten Tagesdurchschnittstemperatur, die oberhalb der pflanzenspezifischen Basistemperatur liegt. Besitzt eine Maispflanze z.B. eine Basistemperatur von 7° C und unterliegt einer Tagestemperatur von 15° C, so ergeben sich für diesen Fall 15 – 7 = 8 HU's. Auf diese Weise werden, unter Bekanntgabe der Aussaat- und Erntezeitpunkte sowie der täglichen Mittelwertstemperaturen, die individuellen Wärmesummenentwicklungen für jede Landnutzungsart simuliert. Anhand der Wärmesummenentwicklung wird der Entwicklungsverlauf des Wurzelwachstums und des Blattflächenindex gesteuert. Hierbei wird vereinfachend davon ausgegangen, dass die Pflanzen zunächst ihre Enregie in die Blattentwicklung und das Wurzelwachstum investieren. Diese Vereinfachung bedeutet auch, dass die Entwicklung von Blättern und Wurzeln unabhängig von der Wasser- und Nährstoffversorgung simuliert wird. Weiterhin wird der Reifegrad der Pflanze, der den maximalen Stickstoffgehalt in der Biomasse beeinflusst, ausschließlich über die Temperatursumme gesteuert.
Biomasseentwicklung
Die Biomasseentwicklung selbst wird zunächst als potenzielle Biomasse simuliert. Steuernde Größe für die Biomasseentwicklung ist hierbei die photosyntetisch wirksame Strahlung. So wird für jeden Tag anhand der Strahlung und der Blattfläche ein potenzieller Biomassezuwachs ermittelt (vgl. Abbildung 1).
Abbildung 1: Aufbau des Pflanzenwachstumsmoduls
Dieser tägliche Biomassezuwachs wird anhand von Stressfaktoren auf den aktuellen Biomassezuwachs reduziert. Die Stressfaktoren sind hierbei Stickstoffversorgung, Temperatur und Wasserversorgung (vgl. Abbildung 2).
Abbildung 2: Aufbau des Wachstumsstresses
Der zu einem Punkt in Raum und Zeit am stärksten wirkende Stressfaktor bestimmt, nach dem Prinzip der limitierenden Faktoren, die aktuelle Biomasseentwicklung. Dies hat wiederum eine Rückwirkung auf den Stickstoffbedarf.
Landnutzungsmanagementmodul
Die Beschreibung des Landnutzungsmanagements erfolgt in Anlehnung an die Methodik im Modell SWAT (Arnold et al. 1998). Das Landnutzungsmanagementmodul realisiert die Möglichkeit komplexe Fruchtfolgen in J2k-S darzustellen. Ausgehend von Managementoperationen wie Aussaat, Düngung und Ernte werden einzele Feldfrüchte charakterisiert. Wie in Abbildung 1 dargestellt, bezieht sich die Fruchtfolge auf eine aktuelle Pflanze, die sich wiederum aus den Pflanzenparametern und den einzelnen Managementoptionen zusammensetzt.
Bild:Pflanzenmanagementmodul1.jpg
Abbildung 1: Funktionsschema des Landnutzungsmanagementmoduls
Die grundlegenden Bausteine (Basisobjekte) zur Beschreibung des Landnutzungsmanagements sind Bodenbearbeitung (bisher noch ohne Funktion), Düngung, Pflanzeneigenschaften und die Fruchtfolge selbst. Während die Managementoptionen Bodenbearbeitung und Düngung mit einfachen Parametern wie Durchmischungseffizienz, Bearbeitungstiefe, Düngemenge, Ammonium- und Nitratanteil auskommen, ist das Pflanzenobjekt mit zahlreichen Parametern versehen. Die Fruchtfolge ist dann nur noch eine einfache Liste mit der Reihenfolge der einzelnen Feldfrüchte (vgl. Abbildung 2).
Bild:Pflanzenmanagementmodul2.jpg
Abbildung 2: Grundlegenden Bausteine (Basisobjekte)
Zur Erläuterung ist in Abbildung 3 ein Ausschnitt einer Managementparameterdatei dargestellt. In der ersten Zeile findet sich eine Bodenbearbeitungsmaßnahme. Darauf folgt die Aussaat des im Beispiel verwendeten Maises. Es finden weiterhin 3 Düngemaßnahmen mit verschiedenen Düngern statt. Weiterhin ist die Ernte mit dem geernteten Anteil der Biomasse angegeben. Der Rest verbleibt auf dem Feld und wird dem Residuen-Pool im Bodenstickstoffmodul zugeführt. Zum Abschluss findet in diesem Beispiel noch eine Bodenbearbeitung statt.
Bild:Pflanzenwaschtumsmodul4.jpg
Abbildung 3: Aufbau einer Managementparameterdatei
Mit diesem Modul ist es möglich, die wesentlichen Tätigkeiten des pflanzenbaulichen Management flexibel abzubilden und Managementalternativen darzustellen.
Grundwasserstickstoffmodul
Die Beschreibung der Dynamik des Stickstoffes im Grundwasser wird in Anlehnung an die in J2k verwendete Grundwasserdynamik durchgeführt. Hierbei wird die Stofffracht entsprechend der Verteilung des Wassers auf die beiden Grundwasserspeicher RG1 und RG2 aufgeteilt. Es werden für beide Grundwasserspeicher getrennt die Wasser- und Stoffgehalte ermittelt. Die Abgabe erfolgt analog zum Wasser und den ermittelten Gehalten. Es ist möglich eine Anfangsstickstoffkonzentration vorzugeben.
Auserdem wurde noch ein Dämpfungsfaktor implementiert, der die Änderung der Stickstoffgehalte im Speicher verzögert. Dieser, zur Kalibration verwendbare Faktor, ist für beide Grundwasserspeicher getrennt einstellbar. Er repräsentiert Durchmischungs- und Diffusionseffekte im Grundwasserleiter.
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