ON CARBON / NUTRIENT PROCESSESIN A TIDAL LAGOON TO DIRECT FUTURE RESEARCH
• ABSTRACT
• INTRODUCTION
• MODEL DESCRIPTION
• INCLUDED STATE VARIABLES AND PROCESSES
• MODEL RESULTS
• CRITICAL EVALUATION AND DISCUSSION
• REFERENCES
Abstract
A mathematical box-model is introduced, that focuses on pelagic carbon and nutrient processes in the List tidal basin, including parameters from field measurements. Benthic processes, the exchange of matter between pelagic and benthic compartments, and the exchange of water volume with the adjacent North Sea are incorporated under simplifying assumptions. Model runs still diverge from observed patterns. At its current state, the model reflects the annual cycle of Chlorophyll a and nitrogen in a realistic range, but quantitative and temporal discrepancies are apparent. Sources of error are discussed.
The model is a helpful tool for analysing pelagic carbon/nutrient pathways and their responding to changing parameters/variables (e.g. sinking velocity, zooplankton grazing). The simulation of benthic processes and the benthopelagic coupling has to be improved. Since information on this coupling is scarce, this would be a scope for future field research in the Wadden Sea.
Introduction
For the List tidal basin, time series data on phytoplankton biomass, dissolved and particulate organic and inorganic nutrients and data on the processes of primary production, respiration and zooplankton grazing (this study) are available. For the benthic ecosystem data are available on pore-water concentrations, and in preparation on benthic respiration and primary production (HEDTKAMP 2005, HEDTKAMP IN PREP).
All data are available for the same period in high temporal resolution. For combining these data, a mathematical model is a useful tool and vice versa data from measurements are necessary for validation. Two ecosystem models for the List tidal basin exist. The SRB-Model of FAST ET AL. (1999) including a complex hydrology.
HOHN (2005) developed a model for the List tidal basin on the basis of the ecosystem system model ReCoM.
The model of the present study is mainly based on investigated processes of the pelagic carbon-nutrient cycle and in a simple forms the benthic system and the exchange with the adjacent North Sea. Hydrological processes, atmospheric and riverine nutrient imports are not incorporated. In future steps, benthic processes have to be incorporated in more detail.
Model description
For the List tidal basin a NPZD - box-model (nutrient-phytoplankton-zooplankton-detritus) was developed. The main focus of this model are pelagic processes, but since a strong coupling between benthic and pelagic ecosystem exist, the benthic ecosystem was included as one further state variable (= sediment). The model is programmed in MATLAB 6.1. The model is a box-model (waterdepth = 2 m) and based on hourly time steps. The model currency is nitrogen, units of all state variables are µmol N L-1. The model is forced by solar irradiance. Solar irradiance can be inserted into the model in two ways: Calculating irradiance from date and geographical range or as data from hourly measurements of the Deutsche Wetter Station List. The water column is divided into 20 layers. Irradiance decrease is calculated according to suspended matter concentrations and their linear relation to measured light attenuation coefficients.
Primary production was calculated according to PLATT ET AL. (1980) and follows in each layer the respective irradiance. Phytoplankton growth is calculated by a fixed Chla:
C ratio and a minimum-function of light and nutrients (Liebig’s law).
Nutrient uptake follows the Michaelis-Menten Kinetik. Conversions between nitrogen and carbon were made according to the Redfield ratio (106:16). A homogenous water column was defined after each time step for concentrations of all ‘pelagic’ state variables. The state variable ‘sediment’ is defined as one extra layer.
Changes of state variables over time were calculated numerically (Euler-Method).
Variables (e.g. P/I-parameters, grazing rates) were incorporated from measured data and interpolated to hourly values. A second box model (NoS) was developed to describe a water exchange of the List tidal basin with the adjacent North Sea. This model is similar to the LTB-model, assuming a mean waterdepth of 27 m. Calculated state variables of NoS (PBM, N, Z) were in inserted for each time step (1hour) into the List tidal basin-model (LTB) on the assumption of 10% exchange of water volume with the North Sea per tidal cycle (=12 hours). An impact Wadden Sea concentrations on North Sea concentrations was not included. Also hydrographical processes were not included.
Benthic carbon processes (primary production, grazing, and remineralisation) are not calculated in detail. Organic matter and phytoplankton is ‘trapped’ in the sediment and released as nitrogen after a defined time. The yielded results of LTB were compared /validated by data of Phytoplankton biomass (Chl a) and DIN (NO3) from the Sylt long term time series.
State variables (defined scalar as start value from field measurements):
• Phytoplankton biomass (PBM)
• Nitrate (N)
• Zooplankton pool (Z)
• Sediment (S)
• Pelagic organic matter pool (OM)
Data included from field measurements/experiments (interpolated to hourly values):
• Light (I)
• Temperature (T)
• Pmax
• Alpha
• Suspended matter (SPM)
• Pelagic grazing rate (graz)
Simulated results:
• Nitrate (N)
• Phytoplankton biomass (PBM)
• Primary production rates (PP)
Sediment (S)
org. matter pool (OM) dis. inorg.
nutrients (N)
Phytopl.-biomass (PBM) ZooPlankton (Z)
North-Sea (NoS-model)
ex
ex
ex
sr bi
fc
mort* 1-r graz
benflux mort* r
rg
-PP (uptake)
Figure 1. Schematic diagram of state variable and fluxes between stat variables in the Box Model for the List tidal basin
Table 1. Included state variable, parameters and variables of the model.
Phytoplankton
PBM mmol
N L-1
Phytoplankton-Biomass (pool of biomass)
state variable
simulated result
PP primary production variable calculated acc.
Platt et all (1980)
mort h-1 mortality of PBM parameter defined
dependent to N and PBM Zooplankton
Z mmol
N L-1
Zooplankton (pool of biomass)
state variable
simulated result graz h-1 grazing rate of Zooplankton variable measured data rg h-1 proportion of PBM directly
remineralised due to ingestion losses (sloppy feeding)
parameter defined
fc h-1 loss of N from Z as faeces parameter defined Nitrogen
N mmol
N L-1
Nitrogen state
variable
simulated result
r(t) mmol
N L-1
proportion of dead PBM that is directly remineralized
function of temperature
calculated from a defined value Organic matter
OM mmol
N L-1
pelagic organic matter state variable
simulated result sr h-1 sinking-velocity of OM parameter defined
Sediment
S mmol
N L-1
Sediment
(pool of biomass/nutrients)
state variable
simulated result bi h-1 filtering-volume of the benthic
layer
parameter defined br h-1 N-release of the benthic parameter defined b_flux h-1 rate of N coming out of the
benthic
dependent of susp matter
function of suspended matter
br*SPM(T)
North Sea
PBM_NoS mmol N L-1
Phytoplankton-Biomass state variable
simulated result
Z_NoS mmol
N L-1
Zooplankton(pool) state variable
simulated result
N_NoS mmol
N L-1
Nitrogen state
variable
simulated result ex h-1 exchange-rate between LTB
and North Sea
parameter defined
Included state variables and processes
Irradiance
Irradiance was calculated for each layer. Surface irradiance was incorporated from hourly measurements of the Deutsche Wetterdienst Station List/Sylt. The decrease of irradiance throughout the water column was linear to suspended matter (SPM) concentrations and followed a measured linear regression model. SPM-concentrations were incorporated from measurements (twice a week) after an interpolation to hourly values.
)
* _
0 exp( k SPM d
I
I
d = − [1]k_SPM= 0.6+ (SPM.*0.045) [2]
Photosynthesis
Photosynthesis in relation to irradiance was calculated according to (PLATT ET AL. 1980). A term for light limitation is not included. P/I-parameters were included from measured data.
Photosynthesis in relation to nitrogen followed the Michaelis-Menten-Kinetik. The model chooses the respective minimum value of both calculations for each layer and time step. This value is multiplied by the amount of Chlorophyll a to calculate the community production.
−
=
exp
max*
max* 1 P
Iz alpha
L
P
P
[3]
=
N kn
P
NP
N max* * [4]( P P )
P
=min L, N [5]chl
P
C =P* [6]Synthesis of Phytoplankton biomass
The synthesis of biomass in this model is following a constant Chl a: Carbon ratio.
PBM = PC * Chla_C [7]
Grazing of Zooplankton
Hourly grazing rates were incorporated from measured field data. The ingestion of phytoplankton biomass by zooplankton was assumed to be dependent on phytoplankton concentrations.
graz
Z
ing = PBM* [8]Pelagic remineralisation
Pelagic remineralisation was assumed to be fuelled by two processes: Loss of biomass due to grazing (‘sloppy feeding’) and degradation of decaying phytoplankton biomass.
Decaying phytoplankton biomass was divided into two fractions: one fraction that is immediately remineralised and one fraction that is remaining in the ‘organic matter pool’, transported to the benthic and remineralised there.
r
*
*rg decay
Z
rem =
ing + [9]Benthic assimilation/ sinking of phytoplankton and organic matter
Sinking of organic matter and benthic filtering of phytoplankton biomass is a similar rate in the model.
bi PBM bi
OM ass
b_ = * + * [10]
Benthic remineralisation /primary production/ nutrient release
All three processes were included in a simplifying assumption: After benthic assimilation of organic matter and phytoplankton biomass, nutrients were released as a function of time and measured suspended matter concentrations. It was assumed that the release of nutrients is indirectly related to wind and to resuspension of benthic material.
SPM br flux
b_ = * [11]
Phytoplankton biomass
Phytoplankton biomass was a result of phytoplankton growth, dependent on the availability of light and nutrients. A defined percentage of phytoplankton was assumed die and to be remineralised after a defined time. Grazing is a further factor reducing phytoplankton biomass. Another percentage of phytoplankton biomass was assumed to be assimilated by the benthic layer due to benthic filter feeders and sediment percolation. A start value of biomass concentration was given in the first time step of the model run from measured field data.
lay Pbm bi T
graz Pbm mort
Pbm T
PP dT Pbm
dPbm = * ( )− * − * ( )− * [12]
Nitrogen
Nitrogen is reduced by uptake during phytoplankton growth. Nitrogen sources were remineralisation after sloppy feeding on phytoplankton biomass, remineralisation of decaying cells and the release of nitrogen from the benthic layer. A start value of nitrogen concentration was given in the first time step of the model run from measured field data.
lay benflux t S
r T mort Pbm t
rg graz Pbm T
PP dT Pbm
dN *
) (
* ) (
* )
(
*
* )
(
* + + +
−
=
[13]
Organic matter pool
The organic matter pool is a result of decaying phytoplankton biomass and zooplankton faeces, which is not immediately remineralised. This organic matter is assumed to sink with a defined speed to the benthic layer.
sr OM fc Z t r T
mort dT Pbm
dOM =+ * ( )*(1− ( ))+ * − * [14]
Zooplankton
Zooplankton biomass increases by grazing on phytoplankton. Losses of phytoplankton biomass due to sloppy feeding are inserted. Zooplankton biomass is lost due to faeces excretion. A closing term for higher trophic levels is not included until now.
fc Z t rg T
graz dT Pbm
dZ =+ * ( )*(1− ( ))− * [15]
Sediment biomass
Organic biomass is transported into the sediment by sinking of detritus (organic matter) and benthic ingestion of phytoplankton biomass. Export of nutrients from the sediment layer is defined as a fixed hourly rate.
benflux S
bi Pbm sum sr OM dT sum
dS =+ ( )* + ( )* − * [16]
Equitations for including NoS into LTB
The exchange of seawater with the North Sea is assumed for phytoplankton biomass, zooplankton and nutrients (nitrogen). An exchange of organic matter was not included.
The Wadden Sea acts as particle trap and particles are imported rather than exported from the North Sea. In the model, the organic matter pool of the Wadden Sea exceeds the one for the North Sea. Since the model is a box-model and does not include hydrological processes (tidal currents), the exchange of organic matter would result in a loss of organic matter to the North Sea.
[17]
[18]
[19]
ex NoS Z ex dT Z
dZ
ex NoS N ex dT N
dN
ex NoS Pbm ex dT Pbm
dPbm
* _
*
* _
*
* _
*
+
−
=
+
−
=
+
−
=
Model results
0 10 20 30 40 50 60 70 80
01-0402 -0403
-0404 -0405
-0406 -0407
-0408 -0409
-0410 -0411
-0412 -04 month Nitrate (µmol L-1 )
Figure 2 a & b. Nitrogen, a comparison of – a) simulated data x-axis: time (one year in hours);
y-axis µmol N L-1 b) measured data.
a)
b)
0 5 10 15 20 25 30 35 40 45
01 -0 4 02 -0 4
03 -0 4 04 -0 4
05 -0 4 06 -0 4
07 -0 4 08 -0 4
09 -0 4 10 -0 4
11 -0 4 12 -0 4 month
Chlorophyll a (µg L-1 )
Figure 3 a & b. Chlorophyll a, the comparison of a) simulated data x-axis: time (one year in hours); y-axis µg Chla L-1 and b) measured data
a)
b)
Critical evaluation and discussion
The courses of chlorophyll a and nitrogen (Figure 2 & 3) show, that the model in general reflects the quality of annual matter cycling as it was measured in the List tidal basin. However, large differences exist in the quantity between model results and in-situ measured data:
Nitrogen: The model starts in January with a given nitrogen concentration for the first time step. The measured increase of nitrogen concentration from January until March is reflected in the model, but the range is lower compared to measured data. Nutrient depletion after a spring bloom is reflected. The increase of nitrogen in the model occurs approximately 8 weeks too early and the increase is steeper than measured in the field.
Chlorophyll a: As for nitrogen, the model starts in January with a given concentration for the first time step. In the field a diatom spring bloom from the end of March until the mid of April and the Phaeocystis globosa bloom from the end of April until the mid of May occurred. The model simulates a bloom situation, but calculates higher biomass concentrations and did not reflect the ‘gap’ of species succession in the End of April.
During summer the model calculates phytoplankton biomass concentrations in lower range than measured in the field.
The present model includes 4 ecological compartments: Pelagic processes, benthic processes, benthopelagic coupling, and North Sea exchange. Differences in model output and measured data result mainly from a) missing processes b) wrong parametrisation c) oversimplified assumptions (SOETAERT & HERMAN 2001).
The differences between model output and measured data may result from uncertainties within all compartments, but mainly the benthic system and exchange between benthic and pelagic system are –at the moment- simulated under simplified assumptions, missing processes and possibly wrong parametrisation:
Several processes of the benthic system have to be included, such as remineralisation and primary production. Secondly, the parametrisation of exchange rates between pelagic and benthic compartments has to be improved. Since literature provides data mainly for single species investigations (e.g. blue mussels Mytilus edulis & lugworm Arenicola marina) or from investigations on exchange processes on a small spatial and temporal scale, this quantification of exchange processes on a larger scale would be a scope of future field research.
References
HOHN S (2005) Entwicklung und Analyse eines Ökosystemmodells für die Sylt-Römö-Bucht. Diplomarbeit, Universität Bremen, Germany.
HEDTKAMP SIC (2005) Shallow subtidal sand: Permeability, nutrient dynamics, microphytobenthos and organic matter. PhD-Thesis, University of Kiel, Germany.
FAST T, MÜLLER A, WILHELM A (1999) The Sylt-Römö Bight Ecosystem Model (SRB Model) an Introduction, GKSS 99/E/28.
PLATT T, GALLEGOS CL, HARRISON, WG (1980) Photoinhibition of photosynthesis in natural assemblages of marine phytoplankton. J Mar Res 38:587-701.
REDFIELD AC, KETCHUM BH, RICHARDS FA (1963) The influence of organisms on the composition of sea-water. In: Hill MN (ed) The Sea, Vol 2, Wiley New York: 26-77 SOETART, K HERMAN P (2001). Ecological modelling. Netherlands Institute of Ecology – Centre for Estuarine and Coastal ecology, Yerseke, the Netherlands.