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Development of nitrate response curves using MODFLOW-MODPATH, MODFLOW-MT3DMS, and lumped parameter model

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MODPATH, MT3DMS, and lumped parameter models (LPMs) allow us to estimate transit times of nitrate to streams while only LPMs can be applied over a large regional scale with minimal time or cost investment, albeit in an approximate manner. In New Zealand, all three models have been calibrated to tritium measurements in streams, allowing us an evaluation of different methodologies to obtain nitrate concentrations. In this talk, we discuss some of the issues inherent in using LPMs to assess subsurface transport of nitrate to streams. We demonstrate that LPMs cannot account for spatially variable nitrate inputs; in particular when high nitrate concentrations are exclusive to a specific band of transit times of groundwater (i.e. only short or only long). Therefore, by estimating isochrones, the spatial application of nitrate can be simulated more effectively with LPMs. We also highlight the importance of tritium when investigating the delivery of nitrate to streams. Tritium, which is a component of meteoric water, decays with a half-life of 12.32 years, is inert in the subsurface and streams, and can provide information on transit time of the water through the subsurface, which will reduce the degrees of freedom when calibrating to nitrate levels in a stream.
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Development of nitrate response curves using MODFLOW-MODPATH,
MODFLOW-MT3DMS, and lumped parameter model
Maksym A. Gusyev
1,3
, Daniel Abrams
2
, Uwe Morgenstern
3
and Mike Stewart
3,4
1
National Graduate Institute for Policy Studies (GRIPS), maksymgusyev@gmail.com, Tokyo, Japan
2
Illinois State Water Survey, dbabrams@illinois.edu, Champaign, IL, USA
3
GNS Science, U.Morgenstern@gns.cri.nz, Lower Hutt, NZ
4
Aquifer Dynamics, M.Stewart@gns.cri.nz, Lower Hutt, NZ
ABSTRACT
MODPATH, MT3DMS, and lumped parameter models (LPMs) allow us to estimate transit times of nitrate
to streams while only LPMs can be applied over a large regional scale with minimal time or cost
investment, albeit in an approximate manner. In New Zealand, all three models have been calibrated to
tritium measurements in streams, allowing us an evaluation of different methodologies to obtain nitrate
concentrations. In this talk, we discuss some of the issues inherent in using LPMs to assess subsurface
transport of nitrate to streams. We demonstrate that LPMs cannot account for spatially variable nitrate
inputs; in particular when high nitrate concentrations are exclusive to a specific band of transit times of
groundwater (i.e. only short or only long). Therefore, by estimating isochrones, the spatial application of
nitrate can be simulated more effectively with LPMs. We also highlight the importance of tritium when
investigating the delivery of nitrate to streams. Tritium, which is a component of meteoric water, decays
with a half-life of 12.32 years, is inert in the subsurface and streams, and can provide information on
transit time of the water through the subsurface, which will reduce the degrees of freedom when
calibrating to nitrate levels in a stream.
INTRODUCTION
The numerical models such as lumped parameter model (LPM), MODPATH and MT3DMS provide
groundwater arrival times and pathways to surface water features such as streams and lakes. In New
Zealand, these estimated arrival times are commonly utilized by Regional Council authorities, who are in
charge of implementing land-use change policies and monitoring water quality, especially planning for
future nitrate loading concentrations. The importance of this information and policies is visible for general
public as illustrated by an example of water quality deterioration in Lake Rotorua located on the North
Island. In the Lake Rotorua watershed, the nitrate input from agricultural activities such as piggery and
dairy farming have been contributing nitrate to the lake via groundwater since 1960s and deteriorated
water quality beyond the acceptable standards (Morgenstern et al. 2015). Currently, this is a concern that
Lake Taupo, which is located nearby Lake Rotorua and is famous for its pristine water quality, may have
a similar fate in the near future unless appropriate measures are taken now.
To address this issue of groundwater and contaminant lag times, LPM, MODPATH and MT3DMS models
were developed in the western Lake Taupo catchment (WLTC) and utilized tritium river water samples
data for the model calibration (Morgenstern and Taylor 2009; Gusyev et al. 2013; 2014). Tritium, which is
a component of meteoric water, decays with a half-life of 12.32 years, and is inert in the subsurface and
streams, can provide information on transit time of the water through the subsurface, which will reduce
the degrees of freedom when calibrating to nitrate levels in a stream. In New Zealand, the tritium input
concentrations were obtained from tritium measurements in precipitation at Kaitoke station (Morgenstern
and Taylor, 2009). For the WLTC, only Kuratau River catchment has a long term tritium time series data
from 1960 to 2009 (Morgenstern and Taylor, 2009). These tritium data were utilized by Morgenstern and
Taylor (2009) to obtain a good fit with a binary LPM model and the selected binary LPM was used for the
synthetic nitrate loading estimation. For the distributed models, the tritium data in surface water was used
by Gusyev et al. (2013) to calibrate MODFLOW/MT3DMS and by Gusyev et al. (2014) to calibrate
MODPATH model groundwater transit times. Therefore, the Kuratau river catchment is uniquely
positioned to investigate three models in terms of simulated transit times and nitrate concentrations in
Kuratau streams.
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In this paper, tritium-calibrated MT3DMS, MODPATH and LPM models developed for the Kuratau River
catchment are utilized for a comparison of simulated transit time and tritium concentration to investigate
the limitations of LPMs and their effect on future nitrate concentrations. The MT3DMS model, which is
the most data demanding approach, simulates tritium and nitrate concentrations directly but it is not
suitable to generate detailed transit time distributions (Gusyev et al., 2014). LPMs generate a transit time
distribution which is selected based on a general understanding of the study area. This distribution is to
be incorporated with temporally variable nitrate inputs in a convolution integral; this procedure cannot
include a spatial distribution of nitrate input concentrations. The MODPATH model falls between
MT3DMS and LPMs by being able to represent spatial variability of nitrate input on a cell by cell basis or
directly generating a transit time distribution to be utilized with a convolution integral (practical if there is
no knowledge of spatial variability of an input).
METHODOLOGY
In our analysis, the Kuratau river basin of the WLTC was selected for a comparison of tritium-calibrated
LPM, MODPATH and MT3DMS model outputs in terms of tritium concentrations and transit times. It also
allowed a comparison of LPM and MODPATH simulated nitrate concentrations. In the Kuratau river basin,
tritium in river waters has been measured in the river basin outlet in 1964-1965 (bomb-peak tritium in
precipitation), 1970s (tritium decline) and 2001-2009 (tritium natural levels) in the Southern Hemisphere
(Morgenstern and Taylor, 2009). For the tritium calibrated LPM, Morgenstern and Taylor (2009) selected
a binary mixing model with Mean Transit Time (MTT) of 11.81 years that was estimated from 67% of an
exponential ELPM (ELPM) with MTT of 1 year and 33% of exponential-piston model (EPM) with MTT of
30 years. In both MT3DMS and MODPATH models, a steady-state MODFLOW model that represented
subsurface hydrogeology and was calibrated with groundwater levels and river discharges was utilized to
produce transit times and tritium concentrations (Gusyev et al., 2013; 2014). For transit time distribution
comparison, we utilize a transit time distribution generated with TracerLPM (Jurgens et al. 2012) and
Mean Transit Times (MTTs) obtained from the tritium calibrated MT3DMS and MODPATH models
(Gusyev et al. 2014). From these calibrated MT3DMS transit times results, we selected MTT of 7.05
years and plotted ELPM and the binary mixing LPM. This comparison allows us to illustrate differences
between LPM and distributed model setups.
For the nitrate concentrations, we simulated nitrate concentrations in streams using LPMs and
MODPATH models. The MT3DMS model allows us to simulate distributed nitrogen sources and was not
included in this comparison. For the LPM and MODPATH models, the nitrate concentrations in streams
were computed with a convolution integral using transit times and a synthetic nitrate input concentrations.
This synthetic nitrate input concentration represents agricultural activities that intensified from 1955 to
2015. In our assessment, we investigated two cases of nitrate input in the Kuratau catchment: a spatial
average of nitrate input and a zone of higher nitrate input near streams. For the latter case, we applied a
higher nitrate input concentration band in the MODPATH model to an area that was representative of
water that would have a transit time of less than 2 years. These nitrate concentrations assigned to the
short transit times (<2 years) represent a more realistic distribution of agricultural activities that are
situated nearby rivers. Since the LPM could not explicitly account for a spatial component, we divided the
convolution integral up into two, calculating it from 0 to 2 years with a high nitrate input concentration and
from 2 years to infinity with a zero nitrate input concentration. We assumed no denitrification processes in
the sub-surface. As a result of these simulated nitrate concentrations we indicate the importance of
evaluating a spatially distributed nitrate input concentration.
RESULTS AND DISCUSSION
In Figure 1, the simulated transit times are shown on the left hand side and the tritium concentrations on
the right hand side. In the Kuratau river basin, the transit time distributions of the tritium-calibrated
MT3MS, MODPATH and LPM models have very different shape while similar MTTs. For example, the
MTT of MT3DMS transit times is 7.05 years and MODPATH MTT is 7.51 years. The MTT of the binary
mixing LPM is 11.81 years, which is slightly different from the other transit times. The simulated transit
times with MT3DMS model fit the shape of ELPM with MTT of 7.05 and MODPATH transit times a
binary LPM with MTT of 7.05 years. For the binary LPM, transit times represent a mixture of a large
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135
volume of young water, which is similar to MODPATH transit times and a lesser portion of the old water
compared to MODPATH transit times. For the tritium concentrations, tritium-calibrated MT3DMS,
MODPATH and LPM models simulate comparable tritium time-series data. The binary LPM with MTT of
11.81 years and the ELPM with 7.51 years match one tritium measurement in 1970s. The binary LPM
transit times with the MTT of 7.05 years follows MODPATH tritium concentrations with a slight variation
during the tritium peak. In the next step, we illustrate an effect of the shape of CFD on nitrate
concentrations in river waters.
For nitrate concentrations, a synthetic input to groundwater and simulated nitrate in the Kuratau river
waters are demonstrated in Figure 2a. The MODPATH transit times and MODFLOW stream network
setup of the WLTC are shown in Figure 2b and 2c, respectively. For the Kuratau river basin, out of 30185
MODPATH particles, which were released in Layer 1 with one particle per 80 m MODFLOW grid, 3997
particles were collected at the drain cells with zero transit times, 11746 particles had 0.01-2 years, 11856
particles - 2.01-20 years, 1089 particles - 20.01 30 years, and 1497 particles - above 30.01 years. Zero
transit times represent rainfall that fell on the Kuratau river network implemented in the MODLFOW model
and the long transit time (>50 years) occur at the groundwater divides. The distribution of MODPATH
particles is consistent with the shape of MODPATH CFD and indicates the importance of spatially
distributed nitrate concentrations for <2 year transit times, which is about 30% of particles distributed in
the Kuratau river basin.
For the uniform nitrate input, the nitrate output concentrations have a similar shape for the binary mixing
LPM, ELPM and MODPATH transit time while ELPM with MTT of 7.01 yrs produces the largest deviation
from the other two curves. This is in stark contrast to the discrepancy observed in Figure 1, where the
tritium curve with the ELPM did not simulate reasonable results. This is likely because the tritium input is
a sharp spike in which the discrepancy in short times between the ELPM and other approaches was
noticeable. For nitrate, where the input concentration is increasing slowly over time (albeit in a stepwise
manner), it appears that the discrepancy in short transit times is much less important.
In contrast to the above case, the nitrate output concentrations are very different when the nitrate input
concentration is located only in the zone of short transit times (<2 years). The delivery of nitrate to
surface waters was much faster compared to the average nitrate input concentration uniformly applied
over the entire watershed (the dashed black line). This example illustrates the importance of being able to
identify isochrones in a watershed and integrating those into the convolution integral to best develop
water resources management plans on a river basin scale.
Figure 1. Simulated transit times (left) and tritium (right) in the Kuratau river basin.
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136
SUMMARY
In this study, we presented a comparison of tritium-calibrated LPM, MODPATH and MT3DMS model
outputs in surface waters in terms of simulated transit times, tritium concentrations and nitrate
concentrations. The Kuratau river basin situated in the WLTC, New Zealand, was uniquely situated for
such analysis due to availability tritium time-series data in river water for model calibration. For the nitrate
simulations, we utilized a synthetic nitrate input curve that may represent a land-use change and
intensification of agricultural activities in the WLTC. All approaches yielded reasonable results for the
nitrate simulation, even the ELPM (which was unable to accurately simulate the more spiky tritium input).
In the future study, a link between LPM and distributed models will be investigated to provide guidance on
the distributed model setup.
REFERENCES
Gusyev, M. A., Abrams D., Toews, M., Morgenstern, U., Stewart, M.K., 2014. A comparison of particle-
tracking and solute transport methods for simulation of tritium concentrations and groundwater
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3109-2014, http://www.hydrol-earth-syst-sci.net/18/3109/2014/
Gusyev, M. A., Toews, M., Morgenstern, U., Stewart, M., White, P., Daughney, C., Hadfield, J., 2013.
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Jurgens, B.C., Böhlke, J.K., and Eberts, S.M., 2012. TracerLPM (Version 1): An Excel® workbook for
interpreting groundwater age distributions from environmental tracer data: U.S. Geological Survey
Techniques and Methods Report 4-F3, 60 p.
Morgenstern, U., 2007. Lake Taupo Streams Water age distribution, fraction of landuse impacted water
and future nitrogen load. GNS Science consultancy report 2007/150, 25 p.
Morgenstern, U., Taylor, C.B., 2009. Ultra Low-level tritium measurement using electrolytic enrichment
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contamination through the catchment into Lake Rotorua, New Zealand, Hydrol. Earth Syst. Sci.,
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Figure 2. Simulated nitrate concentrations in the Kuratau (Kur) river basin a). MODPATH
simulated transit times b) and MODFLOW stream network setup c) of the WLTC.
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Technical Report
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TracerLPM is an interactive Excel® (2007 or later) workbook program for evaluating groundwater age distributions from environmental tracer data by using lumped parameter models (LPMs). Lumped parameter models are mathematical models of transport based on simplified aquifer geometry and flow configurations that account for effects of hydrodynamic dispersion or mixing within the aquifer, well bore, or discharge area. Five primary LPMs are included in the workbook: piston-flow model (PFM), exponential mixing model (EMM), exponential piston-flow model (EPM), partial exponential model (PEM), and dispersion model (DM). Binary mixing models (BMM) can be created by combining primary LPMs in various combinations. Travel time through the unsaturated zone can be included as an additional parameter. TracerLPM also allows users to enter age distributions determined from other methods, such as particle tracking results from numerical groundwater-flow models or from other LPMs not included in this program. Tracers of both young groundwater (anthropogenic atmospheric gases and isotopic substances indicating post-1940s recharge) and much older groundwater (carbon-14 and helium-4) can be interpreted simultaneously so that estimates of the groundwater age distribution for samples with a wide range of ages can be constrained. TracerLPM is organized to permit a comprehensive interpretive approach consisting of hydrogeologic conceptualization, visual examination of data and models, and best-fit parameter estimation. Groundwater age distributions can be evaluated by comparing measured and modeled tracer concentrations in two ways: (1) multiple tracers analyzed simultaneously can be evaluated against each other for concordance with modeled concentrations (tracer-tracer application) or (2) tracer time-series data can be evaluated for concordance with modeled trends (tracer-time application). Groundwater-age estimates can also be obtained for samples with a single tracer measurement at one point in time; however, prior knowledge of an appropriate LPM is required because the mean age is often non-unique. LPM output concentrations depend on model parameters and sample date. All of the LPMs have a parameter for mean age. The EPM, PEM, and DM have an additional parameter that characterizes the degree of age mixing in the sample. BMMs have a parameter for the fraction of the first component in the mixture. An LPM, together with its parameter values, provides a description of the age distribution or the fractional contribution of water for every age of recharge contained within a sample. For the PFM, the age distribution is a unit pulse at one distinct age. For the other LPMs, the age distribution can be much broader and span decades, centuries, millennia, or more. For a sample with a mixture of groundwater ages, the reported interpretation of tracer data includes the LPM name, the mean age, and the values of any other independent model parameters. TracerLPM also can be used for simulating the responses of wells, springs, streams, or other groundwater discharge receptors to nonpoint-source contaminants that are introduced in recharge, such as nitrate. This is done by combining an LPM or user-defined age distribution with information on contaminant loading at the water table. Information on historic contaminant loading can be used to help evaluate a model’s ability to match real world conditions and understand observed contaminant trends, while information on future contaminant loading scenarios can be used to forecast potential contaminant trends.
Article
We describe an advanced methodology for low-level tritium measurement in regard to calibration, electrolytic tritium enrichment, liquid scintillation counting (LSC) measurement, and prevention of sample contamination. Details are given on enrichment parameters and electrode processes for optimisation of enrichment reproducibility and on optimisation of LSC stability. Intercomparison results demonstrate high accuracy of the tritium measurement system. The use of accurate tritium data for groundwater dating in the southern hemisphere is demonstrated with data from several groundwater systems of New Zealand.
Lake Taupo Streams -Water age distribution, fraction of landuse impacted water and future nitrogen load
  • U Morgenstern
Morgenstern, U., 2007. Lake Taupo Streams -Water age distribution, fraction of landuse impacted water and future nitrogen load. GNS Science consultancy report 2007/150, 25 p.