Modeling The Physical and Biogeochemical Processes in Lake Superior Using Lake2K
Modeling The Physical and Biogeochemical Processes in Lake Superior Using Lake2K
Modeling The Physical and Biogeochemical Processes in Lake Superior Using Lake2K
2016
Recommended Citation
Mccarthy, Sheelagh M., "MODELING THE PHYSICAL AND BIOGEOCHEMICAL PROCESSES IN LAKE SUPERIOR USING
LAKE2K", Open Access Master's Thesis, Michigan Technological University, 2016.
http://digitalcommons.mtu.edu/etdr/102
By
Sheelagh M. McCarthy
A THESIS
Submitted in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
In Geology
Acknowledgements ........................................................................................................... 5
Abstract .............................................................................................................................. 6
References ........................................................................................................................ 45
3
List of Figures
4
Acknowledgements
My journey to this Master’s degree would not have been possible without the
unrelenting support and love from my parents and family. I have my parents to thank for
instilling my love and passion for the Great Lakes, which has led me down an educational
and professional journey to study and protect the lakes I grew up loving.
I sincerely thank Dr. Martin Auer for his guidance and support throughout our time
working together. From our first meeting going over the basics of modeling to the final
stages of this research project, I am so grateful for his helpfulness and willingness to work
with me. I would also like to thank Dr. John Gierke for his support and mentoring
throughout my entire graduate school journey, and to Dr. Colleen Mouw for her valuable
I would like to thank Marcel Dijkstra and Rasika Gawde for providing the
foundation for this research project. I would also like to thank my fellow students,
particularly my officemate Varsha Raman for our discussions, along with Anika
I owe a large, heartfelt thank you to Brody. Thank you for your encouragement,
enthusiasm, and belief in me from the beginning. Thanks for your support throughout this
graduate school adventure, by asking the right questions, listening to me, and sharing a
love and excitement for this project. Finally, I would like to thank Dillon, for being my
5
Abstract
Modeling lake processes and dynamics improves understanding of the system and
supports predictions of the response of the lake to perturbations, such as climate change.
LAKE2K, a 3-layer surface water quality model, uses a mass balance approach to simulate
the physical and biogeochemical cycles in Lake Superior. The model is successfully
calibrated with data from offshore Lake Superior in 2011, a year with average
trends in this dimictic system. The calibrated model is confirmed with an application for
include expanding the model to a more finely segmented multi-layered version and
partitioning the particulate phosphorus variable. The model serves as a test bed to simulate
6
1.0 Introduction
1.1 Background
The Great Lakes are an invaluable resource not only for their provision of
ecosystem services, but culturally and aesthetically as well. Among the Great Lakes, Lake
Superior has the largest volume and the smallest population density in its basin, resulting
in limited impacts to its watershed (Matheson and Munawar, 1978). The expansive surface
area of Lake Superior provides heightened opportunity for atmospheric input, and human
influence to the system is primarily due to this source of pollutants (Eisenreich et al., 1998).
Understanding the processes driving Lake Superior is critical when working to predict
the world (Adrian et al., 2009; Vincent, 2009). Lakes are particularly vulnerable to the
than the surrounding land (Williamson et al., 2009). The Great Lakes are all displaying the
effects of climate change in their water temperatures, with an increase in average water
temperature of 2.5°C in Lake Superior since 1976 (Magnuson et al., 1997; Austin and
Lake Superior, the response to potential changes due to increased human activity induced
the system, including nutrient cycling, primary production, and the thermal regime
(Magnuson et al., 1997; Mortsh and Quinn, 1996). Biogeochemical cycling is dependent
7
on the annual thermal regime of the system, and increases in lake temperatures could have
strong ecosystem impacts (Zepp et al., 2007). In particular, as phosphorus is the limiting
nutrient for Lake Superior, temperature-driven changes to phosphorus cycling can have
models represent an idealized system, e.g., a lake, and simulate the response of that system
approach to model and understand a system (Chapra, 2008). The ability to simulate the
results in a greater understanding of the factors that not only drive the system, but also in
predicting how the lake will change in response to climate change or other anthropogenic
influences.
Lake Superior provides a unique opportunity for research due to its large volume
and depth, with an average depth of 147 meters and maximum of 400 meters. Lake Superior
is a temperate, dimictic system that displays thermal stratification during summer and
inverse stratification in winter (Bennet, 1978). The system undergoes two periods of
mixing throughout the spring and fall (Hutchinson, 1957). The period of thermal
stratification in Lake Superior lasts an average of 170 days (Austin and Coleman, 2008).
Biannually, turnover occurs during the spring and fall in Lake Superior (Croley et al.,
8
1998). At the point of turnover, the lake has reached uniform temperature and density, and
the system cycles nutrients and heat within the lake profile. Recognizing the influence of
the thermal regime of Lake Superior on its nutrient cycling and algal growth processes is
the layers of the lake (Chapra, 2008). The mixing strength is dependent on the exposed,
unobstructed lake surface, or fetch, water temperature, and wind speed (Bennington et al.,
2010). Increased lake surface area allows for stronger vertical mixing, and thus the
expansiveness of Lake Superior allows for high mixing rates, particularly during fall and
spring mixing (Bennington, 2010). In the early summer months, as the lake begins to
thermally stratify, there are progressively lower rates of mixing between the layer
minimum during the period of strongest stratification, occurring in late August in Lake
between phosphorus cycling and algal growth is particularly important (Auer et al., 1986;
Baehr and McManus, 2003). Modeling of algal populations utilizes a mass balance
approach, where growth (a function of light, temperature, phosphorus) is the source term
and zooplankton grazing, death, and settling are sinks (Chapra, 2008).
1
“Vertical diffusion” is used to represent solute mass moved by large-scale eddies in water within a lake
profile. Vertical diffusion coefficients representative vertical mixing caused by water density changes
rusting from changes in heat at the surface (Chapra, 2008)
9
The phosphorus cycle is critical in biogeochemical processes within Lake Superior
due to the role of phosphorus as the limiting nutrient (Auer et al., 1986; Baehr and
McManus, 2003; Sterner, 2010). In oligotrophic systems, such as Lake Superior, inputs of
phosphorus are relatively small compared to the lake volume (Reynolds and Davies, 2001;
Sterner, 2010). The offshore waters of Lake Superior are largely isolated from the direct
and immediate impacts of tributary and point-source inputs, and phosphorus dynamics
typically depend on the cycling of the nutrient (Sterner, 2010). Phosphorus levels are low
in Lake Superior, due not only to the small load:volume ratio, but also because the nutrient
is rapidly taken up by phytoplankton and removed from the water column by settling.
Therefore, the presence of phosphorus in Lake Superior plays a significant role for algal
The phosphorus cycle within Lake Superior includes three pools (soluble reactive-
in sustaining algal growth and ecosystem stability (Baehr and McManus, 2003; Sterner,
2010). Soluble reactive phosphorus (SRP) is fully and freely bioavailable for
phytoplankton uptake and is then converted into particulate phosphorus (PP), where it is
(DOP). Dissolved organic phosphorus is then mineralized into SRP form. The rates of
phosphorus may have significant repercussions for the rest of the system (Scavia, 1976).
10
Recent studies demonstrate the relationship between phosphorus availability and
temperature in Lake Superior (Dijkstra, 2015). The phenomenon of the “summer desert” is
apparent in average and warm summers in Lake Superior (Dijkstra, 2015). The “summer
during early summer, and in late summer, the phosphorus quantities are exhausted. The
lack of phosphorus within the lake creates a “summer [phosphorus] desert”, resulting in
extreme nutrient limitation. The occurrence of the “summer desert” is noted in average and
warm summers and is nonexistent during the cold years, which are historically
characteristic for Lake Superior (Dijkstra, 2015). The duration of the summer desert in
warms years and its absence in cold years is due to the timing and duration of temperature
11
2.0 Objectives & Approach
Superior are described above; modeling provides a framework for developing a better
through the use of a model? How do these dynamics change between years, e.g.
The research questions are addressed within this study to model and better understand the
kinetic processes within Lake Superior by utilizing LAKE2K, a 3-layer surface water
quality model. The model results are calibrated and confirmed with data collected from
illustrate annual heat flux, vertical mixing, and the thermal regime
Following the calibration of the model for temperature, phytoplankton growth, and
phosphorus cycling, the foundation for the use of LAKE2K is set. The calibrated model is
then used for simulating the same physical and biogeochemical trends for a different year
with extreme weather conditions, 2012, to assess the validity of the model.
within Lake Superior, and it provides a basis for examining changes to its thermal regime,
12
biogeochemistry, and plankton dynamics. The calibrated surface water quality for Lake
Superior can be used as a test bed for future applications. LAKE2K will serve as a useful
tool for those interested in the response of Lake Superior to changes to physical and
13
3.0 Methods
LAKE2K, a model created by Chapra and Martin (2004) is used to simulate the
and biogeochemical conditions. The model was written and executed in Microsoft Visual
Basic, and it utilizes Microsoft Excel as its graphical user interface (GUI). The LAKE2K
GUI includes worksheets for model inputs (e.g., system volume, inflow/outflow, mass
transport/kinetic coefficients and initial conditions) and output (field measurements and
results for all state variables trends), in both tabular and graphical form.
The year 2011 is chosen for model simulations as it displays average seasonal
conditions for Lake Superior. Data obtained from field sampling is used to calibrate the
model results. Offshore sampling of Lake Superior occurred aboard the R/V Agassiz from
May through November of 2011 (Dijkstra, 2015). Data was collected monthly or bimonthly
at station, HN260, located 26 km offshore the western coast of the Keweenaw Peninsula
with a depth of ~190 meters. Field data is used to establish initial conditions within
LAKE2K and is used as a comparison with the model output in the calibration process.
LAKE2K models lakes by creating a water balance, heat balance, and mass balance
metalimnion, and hypolimnion of a system (Chapra and Martin, 2004). The water balance
the vertical turbulent diffusion coefficients specified as a user-defined time series. The
inflows set equal to outflows for the lake (as opposed to reservoirs).
LAKE2K models the heat balance of the system through analyzing the surface heat
exchange at the air-water interface of the lake. Daily and seasonal variability in the
meteorological conditions driving the heat balance are inputted by the user. The sources
and sinks for surface heat exchange include solar shortwave radiation, atmospheric
longwave radiation, water longwave radiation, conduction and convection, and evaporation
and condensation (Chapra, 2008). Solar shortwave, atmospheric longwave, and water
longwave radiation all contribute to net absorbed radiation, whereas the other processes are
water dependent2 terms (Figure 3.1; Chapra, 2008). Heat is transferred within the system
based on the turbulent diffusion coefficients used for vertical mixing. Model output from
the heat balance includes layer specific temperature trends for the study duration. The
goodness of fit compared to temperature data confirms the utility of the model for the
thermal regime and simulating the mixing of other constituents for mass balance processes.
2
Water dependent terms refer to surface heat exchange components that are dependent on water
temperature variability, whereas the other non-water dependent terms are independent forcing
functions (Chapra, 2008)
15
Figure 3.1 Conceptual physical model of Lake Superior in LAKE2K segmented into 3
vertical layers (epilimnion, metalimnion, and hypolimnion). Top arrows (shaded) represent
surface heat exchange sources and sinks that determine the heat balance of the system.
White arrows represent turbulent diffusion, or mixing, between layers.
16
LAKE2K includes as state variables: carbon, nitrogen, oxygen, phosphorus, silica,
and phytoplankton and zooplankton biomass. This current application of LAKE2K focuses
on phosphorus and plankton with the latter represented as organic carbon. A mass balance
for each constituent is performed for the epilimnion, metalimnion, and hypolimnion. The
mass balances account for the sources and sinks of dissolved and particulate carbon and
balance equations include algorithms describing kinetic and mass transfer processes and
detrital C (Figure 3.2a). The total phosphorus analysis is represented in three forms (DOP,
detrital-PP, and SRP) in LAKE2K (Figure 3.2b). Algal growth and phosphorus cycling are
interdependent processes, and perturbations of one state variable (e.g., through a kinetic
coefficient) may have a strong reaction on the entire system. For example, SRP can be
transferred up the food chain through grazing, transferred to the detrital particulate
phosphorus through death and settling (Chapra and Martin, 2004). Therefore, it is
necessary to determine and use the correct kinetic or coefficient in this model, otherwise a
process or pool within the cycle could be accelerated or limited, resulting in an inability of
17
Figure 3.2a Carbon cycle
components of the lake. The model includes worksheets for numerical inputs of the system:
coefficients, initial conditions, and model execution specifications. Other data worksheets
accept field data (Lake Superior station HN260) for the epilimnion, metalimnion, and
factor, precipitation rate, and average daily solar radiation. Photosynthetically active
Martin, 2004). Meteorological data is used from a previous study that acquired and
analyzed from sources including multiple NOAA offshore buoys and EPA open lake
stations (Gawde, 2015). Hydrodynamic simulations using this data set proved an accurate
offshore waters in Lake Superior (Gawde, 2015). LAKE2K utilizes the meteorological data
inputs to create a heat balance for the thermal layers based on surface heat exchange
processes.
19
hypolimnion boundaries (Chapra and Martin, 2004). The magnitude of the diffusion
and stratification. Values for the diffusion coefficients are found by calibration to measure
layer temperatures throughout the model duration. LAKE2K uses linear interpolation to
Kinetic algorithms and coefficients are used to quantify energy and mass transfer
processes for state variables. LAKE2K simulates net phytoplankton growth (gCm-3d-1) as
the difference between the gross maximum specific growth rate (a function of temperature,
light and phosphorus availability) and losses to algal populations (respiration, death,
settling, and zooplankton grazing) times the phytoplankton standing crop. Death is
combined with the grazing term, as both deliver phytoplankton biomass to the detrital-
phosphorus pool and the processes are not separable experimentally. This yields,
𝑑𝐶𝑝ℎ𝑦𝑡𝑜
= [𝜇𝑚𝑎𝑥,𝑔𝑟𝑜𝑠𝑠 ∙ 𝑓(𝑇) ∙ 𝑓(𝐼) ∙ 𝑓(𝑃) − (𝑅 + 𝑆 + 𝐺)] ∙ 𝐶𝑝ℎ𝑦𝑡𝑜
𝑑𝑡
where dCphyto/dt is the net rate of change in phytoplankton carbon concentration (gCm-
3
d1), µmax,gross (1.30 d-1) is the gross specific growth rate coefficient. f(T,I,P) are
temperature, light and phosphorus. R, S, and G are the rate constants for respiration (0.02
d-1), settling (0.03 m d-1) and grazing (0.20 d-1 for herbivorous zooplankton; Chapra, 2008;
20
specifically for the warm water phytoplankton assemblage within Lake Superior, has an
describing the slope of the growth response above and below the optimal temperature
(Dijkstra, 2015). Light limitation for phytoplankton growth is found through a sub-model
using the Beer-Lambert law, which utilizes photosynthetically active radiation (47%) and
light extinction coefficients (Chapra and Martin, 2004; Di Toro, 1978). These values are
phytoplankton growth attenuation and light parameter (Baly, 1935). Nutrient growth
limitation also uses a sub-model that includes a Michaelis-Menten equation for SRP, which
depends on both the concentration of the limiting nutrient, SRP, and the phosphorus half-
saturation constant (Chapra and Martin, 2004). The half-saturation constant represents the
nutrient concentration of SRP when growth is half the maximum rate (Chapra, 2008). The
phosphorus half-saturation constant used in this study is 2.0 µgPL-1 and is consistent with
Phosphorus kinetics support the tracking of the dynamics of the SRP, DOP and PP
pools. The phosphorus cycle in offshore Lake Superior is essentially a closed loop with
phosphorus lost to the sediments and replaced by phosphorus transported offshore from
nearshore waters that are impacted by river discharge. In a closed loop system of the
phosphorus cycle, phosphorus enters the SRP pool through mineralization of DOP
(0.03day-1; Imboden, 1974; Lung et al., 1976) and phytoplankton respiration (0.02 d-1) and
is lost through the SRP pool through phytoplankton uptake (Figure 3.2). Uptake of SRP
21
𝑑𝐶
𝑑𝑆𝑅𝑃
= − 𝐶:𝑃
𝑑𝑡
[2]
𝑑𝑡
constant throughout modeling as 260:1 (molar basis). C:P ratios vary from 101:1 to 474:1
throughout the algal growing season in Lake Superior as phosphorus rich spring
phytoplankton grow and distribute their stored phosphorus among new biomass in the
phosphorus deficient lake (Dijkstra, 2015). However, the model does not accommodate
seasonal C:P ratios, so an average is used. Limitations to this modeling method and its
influence on algal- PP, measurements are discussed within the recommendations section.
Table 3.1: Comparison of LAKE2K plankton kinetics for Lake Superior with previous
studies. **Settling velocity for Lake Superior (Chapra and Dolan, 2012)
LAKE2K Chapra Fillingham
Phytoplankton Kinetics L.Superior L. Ontario L. Michigan Units
Max. Growth Rate 1.3 2.0 1.4 d-1
Respiration rate 0.015 0.025 0.05 d-1
Settling Velocity 0.027 0.04** 0.5 md-1
Death Rate 0 0 0.01 d-1
Phosphorus Half Saturation 2 2 3.1 µgPL-1
Selected system characteristics, e.g., latitude (47.7° N) and maximum depth at the
sampling station (190 m) are set as a primary step in performing model runs. Inflows and
outflows are zeroed for this 1D, offshore application to the essentially homogenous open
22
lake conditions of Lake Superior (Russ et al., 2004). Inflows and outflows may be included
for future applications involving the nearshore influence, i.e. with riverine inputs. Initial
consistent with data from the first day of sampling (HN260 on May 5, 2011). The
epilimnion, metalimnion, and hypolimnion thicknesses are set at annual averages for the
study period of 20.0 m, 15.0 m and 155.0 m, respectively, and remain at these positions for
the entire simulation. An ability to accommodate time variable layer thickness may be
desirable in some applications (see subsequent discussion). The model is run for the ice
free season on Lake Superior with a time step of 0.1 day, for model run-time and calculating
efficiency. Model results are generated on LAKE2K worksheets with model output (lines)
23
4.0 Model Calibration
The adoption of a conceptual model and input of model coefficients and parameters
sets the foundation for calibrating LAKE2K for Lake Superior in 2011. The calibration
examines both physical (heat balance and thermal regime) and biogeochemical
(phosphorus cycling and algal growth) features of ecosystem function in Lake Superior.
accepted bounds, seeking an appropriate fit of model output to field data over the May
LAKE2K utilizes the meteorological data provided for 2011 to account for the
various sources and sinks of heat within the lake and create a heat balance (Gawde, 2015).
The model results, depicted in Figure 4.1, illustrate the losses and gains of heat throughout
the system from May through November 2011. Heat gains during the spring and summer
and conduction. Heat is typically transferred to the lake through evaporation, although a
small quantity of heat is also lost through evaporation during May, due to the cooler lake
temperature that is only beginning to warm. The lake is consistently heated throughout the
summer months through August. Heat is lost from the lake during late summer and
continues throughout the fall season. Heat is primarily lost through evaporation, and to a
lesser extent, conduction. The lake experiences its maximum heat loss through evaporation
24
The LAKE2K results are consistent with the anticipated response of heat flux in
the spring, summer, and fall in Lake Superior. The lake is experiencing a net gain of heat
during spring and early summer. However, as summer progresses and the amount of solar
radiation decreases, the lake experiences a net loss of heat and consequentially cools. The
loss of heat is also evident in conduction and evaporation, both water dependent terms.
Evaporation is a particularly significant heat loss term for a lake during fall and winter
months (Blanken et al., 2011). The heat flux modeled by LAKE2K for 2011 represents a
base for predicting the heat losses and gains within Lake Superior in response to changes,
for example, climate anomalies (e.g., the Big Heat and Big Chill years of 2012 and 2014;
Dijkstra, 2015).
1000
Heat (calcm-2d-1)
500
-500
-1000
-1500
May-11 Jun-11 Jul-11 Aug-11 Sep-11 Oct-11 Nov-11
Figure 4.1 LAKE2K modeled heat flux of Lake Superior 2011. Positive values indicate
net gain of heat, negative values indicate net loss of heat in the system.
25
4.2 Modeling the Thermal Regime
Lake Superior as well as those for 2011 with little difference between the data and model
predicted results (Bennett, 1978; Dijkstra, 2015). Additionally, the duration of thermal
stratification for Lake Superior (typically four months) is well simulated (Austin and
Coleman, 2008). This feature of the thermal regime plays an important role in evaluating
While the thermal regime of Lake Superior is well represented, conditions in the
the 3-layer model where LAKE2K uses set thicknesses for the epilimnion, metalimnion
and hypolimnion for the entire study duration, i.e., it does not account for variability in the
metalimnion thickness over the stratified period. It is well known and evident in data for
Lake Superior in 2011 that the epilimnion undergoes thickening (migrates downward) over
waters (Barbiero and McNair, 1996; Dijkstra, 2015). With the position of the epilimnion-
metalimnion boundary held constant (deepening not simulated), averaging of field data
does not accurately represent conditions in the metalimnion for the entire modeled
duration, i.e., epilimnetic water is included in the metalimnion average. Addition of layers
to the model (e.g., n = 100) would better represent gradients in temperature within the
metalimnion throughout the stratified period and yield a better fit to the data.
26
LAKE2K Temperature 2011
20
18
16
14
Temperature (°C)
12
10
0
May-11 Jun-11 Jul-11 Aug-11 Sep-11 Oct-11 Nov-11
Figure 4.2 LAKE2K modeled thermal regime with data for Lake Superior 2011
100
(cm2sec-1)
10
0.1
May-11 Jun-11 Jul-11 Aug-11 Sep-11 Oct-11 Nov-11
Figure 4.3 Vertical diffusion coefficients at epi-meta and meta-hypo boundaries 2011
27
4.3 Modeling Algal Growth
LAKE2K can either model distinct classes of phytoplankton (e.g., diatoms, green algae) or
can represent the whole natural plankton assemblage of Lake Superior, which is used in
due to the absence of other sources of POC found in Lake Superior offshore (Sterner, 2010;
Urban et al., 2005). The use of measuring POC, rather than chlorophyll, avoids
complications related to shade adaptation where POC remains constant, but algal-
light, and phosphorus availability (see LAKE2K Conceptual Model above). For
temperature, kinetic coefficients are representative of the Lake Superior warm water
particularly for the epilimnion and hypolimnion (Figure 4.4). The less satisfactory fit in the
layer from depth-variable settling velocities. The layers initially have uniform
28
concentrations of phytoplankton-carbon due to the high mixed state of the system during
the pre-stratified period (May through the end of June). Phytoplankton growth is limited
during this time due to lack of available sunlight (extensive mixing depth) and low lake
temperatures (Nalwajko et al., 1981, Nalwajko and Voltino, 1986). Algal populations have
sufficient levels of phosphorus at this time, because light and temperature conditions are
limiting growth. With the onset of thermal stratification in July, epilimnetic temperatures
warm (Figure 4.2) and the mixing depth is significantly reduced. Phytoplankton retained
in the metalimnion and hypolimnion at the onset of stratification settle to the lake bottom
stratification, reaching a maximum in August (Figure 4.4). While light availability remains
favorable throughout the stratified period, temperatures eventually exceed the optimum
(13.3 C) and phosphorus resources are depleted through uptake and settling during the
growth season. Model output predicts a gentle decline in phytoplankton biomass with the
period, as populations increase following stratification and as growth slows in mid and late
summer (the “summer desert”). The model performs less well at turnover, represented at
the outlier epilimnion data point in October, failing to capture elevated observed POC level,
likely evolving from resuspension of plankton trapped in the deep chlorophyll maximum
29
chlorophyll; Barbiero and Tuchman, 2004) and benthic nepheloid layer (found directly
heavily of organic carbon; Urban et al., 2004); two features not accommodated in this 3-
0.15
Phytoplankton (mgCL-1)
0.1
0.05
0
May-11 Jun-11 Jul-11 Aug-11 Sep-11 Oct-11 Nov-11
Figure 4.4 LAKE2K modeled phytoplankton growth and Lake Superior data 2011
30
4.4 Modeling Phosphorus Cycling
Phosphorus cycling in LAKE2K is modeled for each of the three layers over the
May through November interval of 2011 as total phosphorus and its components (SRP,
DOP, and PP). SRP is the targeted phosphorus form, due to its role as the limiting nutrient
in Lake Superior and its strong connection with algal populations. Because it is the
bioavailable form of phosphorus that is necessary for growth, SRP trends are representative
of phytoplankton growth.
SRP levels are similarly low (near the limit of detection) in the three layers during
the mixed pre-stratification period (Figure 4.5). SRP levels increase in all three layers as
but less similar than during pre-stratification. Summer SRP depletion is a striking feature
of the phosphorus cycle in Lake Superior (Figure 4.5). SRP depletion coincides with
phytoplankton growth as uptake of SRP increases in the relatively warm, well-lit waters of
phosphorus from the surface layer, and limited vertical mixing (thermal stratification) and
phosphorus. Juxtaposition of model results for phytoplankton carbon with those for SRP
(Figure 4.6) confirms the ability of this application of LAKE2K to simulate the
1994).
31
LAKE2K SRP 2011
2.5
2
SRP (µgPL-1)
1.5
0.5
0
May-11 Jun-11 Jul-11 Aug-11 Sep-11 Oct-11 Nov-11
Figure 4.5 LAKE2K modeled SRP and data from Lake Superior 2011
0.18
2 0.16
Phytoplankton (mgCL-1)
0.14
SRP (µgPL-1)
1.5 0.12
0.1
1 0.08
0.06
0.5 0.04
0.02
0 0
Jun-11 Jul-11 Aug-11 Sep-11 Oct-11 Nov-11
plankton. The model illustrates PP at uniform concentration during the mixed period
(Figure 4.7). With a limited amount of phosphorus in the water column, data exhibit a
parabolic shape reflecting a decrease throughout the summer season from settling and, in
the epilimnion, an increase during late summer and early fall due to resuspension and
mixing of phosphorus from the deep chlorophyll and benthic nepheloid layers. LAKE2K
model results for PP are low, compared with data from Lake Superior throughout 2011.
The low concentration of PP is due to a modeling parameter that LAKE2K employs and is
LAKE2K PP 2011
2.5
2
PP (µgPL-1)
1.5
0.5
0
May-11 Jun-11 Jul-11 Aug-11 Sep-11 Oct-11 Nov-11
Figure 4.7 LAKE2K modeled PP and data from Lake Superior 2011
33
TDOP represents the non-reactive form of phosphorus within Lake Superior (Baehr
and McManus, 2003). The data illustrates similar concentrations of TDOP within the
epilimnion and hypolimnion (Figure 4.8). The modeled results for TDOP display uniform
concentrations throughout the lake profile, with a slight increase in concentration within
the epilimnion and a small decrease within the hypolimnion during the height of
stratification. Increases in TDOP are a result of increased solubilization from the PP pool.
Although the model results do not implicitly follow the increasing and decreasing periods
of TDOP, the overall trend of DOP in offshore Lake Superior is consistent with previous
studies from Baehr and McManus (2003), showing little variation both over the summer
The final phosphorus cycle component modeled with LAKE2K for Lake Superior
is TP and includes the phosphorus components of the previously modeled SRP, PP, and
TDOP (Figure 4.9). LAKE2K models the average concentrations of TP within the
throughout the study duration. The only distinction between the model results layers is
stratification in Lake Superior. Variation within the TP modeled results and data is due to
34
LAKE2K TDOP 2011
2.5
2
TDOP (µgPL-1)
1.5
0.5
0
May-11 Jun-11 Jul-11 Aug-11 Sep-11 Oct-11 Nov-11
Figure 4.8 LAKE2K modeled TDOP and data from Lake Superior 2011
LAKE2K TP 2011
4
3.5
2.5
TP (µgPL-1)
1.5
0.5
0
May-11 Jun-11 Jul-11 Aug-11 Sep-11 Oct-11 Nov-11
Figure 4.9 LAKE2K modeled TP and data from Lake Superior 2011
35
5.0 Model Confirmation
Following modeling Lake Superior within LAKE2K for 2011, the model can be
adapted and applied for another year to confirm the modeled results. Here, LAKE2K is
used for modeling phosphorus cycling and phytoplankton carbon in Lake Superior in 2012,
considered an extremely warm year (Dijkstra, 2015). Adapting LAKE2K for 2012 begins
with adding field data from the same station, HN260, for the new study period. In 2012,
field sampling occurred from April 4, 2012 through October 13, 2012; the model is set to
run for this study period, and uses the data for initial conditions. The meteorological data
used for LAKE2K in the 2011 application is a portion of a larger dataset that includes
information for 2012 (Gawde, 2015). Vertical diffusion coefficients are adjusted to fit the
2012 thermal regime for model confirmation (Figure 5.1 and Figure 5.2). LAKE2K then
models Lake Superior for 2012, using the same volume, inflows/outflows, light and heat
parameters, and kinetics as 2011. In doing so, the modeled results can be confirmed for a
year with different forcing conditions than the one used for calibration, but with no change
in kinetics. Confirmation focuses on algal-growth (carbon) and SRP, two features well
LAKE2K modeled results regarding the thermal regime for 2012 display an earlier
onset of thermal stratification during the summer season than in the average seasonal
conditions year (2011), with stratification beginning in in June as opposed to July (Figure
4.2 and Figure 5.1). The influence of an earlier stratification period, as expected in a year
36
LAKE2K Temperature 2012
20
18
16
14
Temperature (°C)
12
10
8
6
4
2
0
Apr-12 May-12 Jun-12 Jul-12 Aug-12 Sep-12 Oct-12 Nov-12
Figure 5.1 LAKE2K modeled thermal regime and data for Lake Superior confirmation
2012
100.000
(cm2sec-1)
10.000
1.000
0.100
Apr-12 May-12 Jun-12 Jul-12 Aug-12 Sep-12 Oct-12
Figure 5.2 Vertical diffusion coefficients at epi-meta and meta-hypo boundaries for 2012
37
LAKE2K model results for both phytoplankton-carbon and SRP are depicted in
Figures 5.3 and 5.4. Figure 5.3 displays model results for phytoplankton-carbon
measurements, compared with data collected from the epilimnion of Lake Superior during
2012. The model results illustrates the lake as mixed, with uniform concentrations of
phytoplankton throughout the mixing period. The lake begins to display disassociation of
model then over predicts the concentration of phytoplankton throughout July and August,
before trending to a mixed period at the end of the modeled duration. Although the model
results are not entirely similar with field data from 2012, the initial concentration of
LAKE2K model results for SRP in Lake Superior during 2012 are illustrated in
Figure 5.4. Similar to phytoplankton populations, the model indicates a mixed period
within the system from the beginning of the model duration through May. In June, the lake
begins to thermally stratify, signaling phytoplankton populations to uptake SRP for growth.
populations in Figures 5.3 and 5.4, indicating the relationship between phosphorus and
algal growth. The SRP pool is depleted throughout thermal stratification, with a sharp
decrease from June 26 – July 19, 2012. SRP concentrations begin to reach similar
concentrations at the end of the model duration, indicating the system approaching a mixed
2012 in Lake Superior is referred to as the “big heat” (Dijkstra, 2015). Comparing
LAKE2K model results for 2011, a year with average temperature conditions, with 2012,
38
a year with above average temperatures, gives insight to the model application for further
studies, particularly in regards to climate change scenarios. The model results displays an
earlier thermal stratification period in Lake Superior, which is consistent with expected
results with warm weather conditions. The earlier onset of thermal stratification influences
both the phytoplankton population and phosphorus pools, particularly SRP. Because
phytoplankton populations grow earlier in the summer season compared to a typical Lake
Superior year, the phosphorus pool is depleted earlier in the growing season. The depletion
of SRP creates a “summer desert” effect, consistent with the modeled and expected results
39
LAKE2K Phytoplankton 2012
0.25
0.2
Phytoplankton (mgCL-1)
0.15
0.1
0.05
0
Apr-12 May-12 Jun-12 Jul-12 Aug-12 Sep-12 Oct-12 Nov-12
2
SRP (µgPL-1)
1.5
0.5
0
Apr-12 May-12 Jun-12 Jul-12 Aug-12 Sep-12 Oct-12 Nov-12
40
6.0 Modeling Limitations
LAKE2K provides a user friendly modeling system suitable for application to lakes
that thermally stratify. The model is successfully adopted here to represent trends in
temperature, phosphorus, and algal carbon in Lake Superior. In its present form the model
of a more finely segmented multi-layered version of LAKE2K that would provide greater
insight regarding phosphorus and plankton variability in the water column. The expansion
of LAKE2K into an increased number of layers, e.g. n=100, may include variations of layer
41
Presently, LAKE2K underestimates PP concentrations, and consequentially TP,
due to not accounting for seasonal variation in stored algal-phosphorus within Lake
Superior. Separating the PP state variable into two parts, one including terrigenous and
detrital PP and the other algal-PP would permit better simulation of particulate phosphorus
by,
in the nearshore of lakes where riverine inputs are received, and detrital
phosphorus, a form important in P-cycling but not available for driving growth
seasonal C:P ratios better reflect algal-PP and potential for algal growth. Significant
differences in C:P ratios reflect elevated stored-PP abundance in spring and early summer,
and lower quantities in late summer leading to the summer desert phenomenon in Lake
Superior (Dijkstra, 2015). Although all models contain some error, improving LAKE2K
with the aforementioned suggestions would increase model accuracy and consistency for
future applications and would reduce modeling limitations discovered during this study.
42
7.0 Conclusion
Among the global climate change impacts currently facing the world and its many
changes in atmospheric and lake temperatures (Austin and Colman, 2007; Williamson et
al., 2009). Therefore, having a calibrated and confirmed model to simulate perturbations
to the system will allow for a greater understanding for scientists, policy makers, and the
Lake Superior utilizing LAKE2K, a 3-layer surface water quality model. The foundation
for modeling Lake Superior is set through the simulation of the annual thermal regime.
cycling (SRP, DOP, PP) and algal growth (carbon) seeking consistency with observations.
The use of model inputs, forcing conditions, and kinetic coefficients, results in output that
represents the magnitude and timing of dynamics in the thermal regime and
biogeochemical cycles.
The research questions are addressed and answered through the successful
calibration of LAKE2K during 2011, a year with average climatic conditions, and is
confirmed for 2012, a year representing a warm climatic anomaly. Additionally, the
calibrated model, to model trends in algal growth and phosphorus cycling. Calibration and
confirmation were performed for the thermal regime, phytoplankton growth and SRP in
offshore Lake Superior. Although the target phosphorus component (SRP) was modeled
successfully for 2011 and 2012, limitations when simulating other forms of phosphorus
43
(PP, DOP). Improvements to modeling these forms of phosphorus are discussed with the
recommendations and include expanding LAKE2K into a more finely segmented multi-
layered model, along with adopting the Droop function to accommodate changes in stored
algal-phosphorus and their impact on growth. These suggestions for LAKE2K will
improve accuracy and consistency of modeled results. The calibrated model can then be
used efficiently as a test bed in further studies regarding the response of Lake Superior to
44
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