Introduction to Sea Ice Modelingby Clara Deal
Focus: Ecosystem and biogeochemical modeling
Lecture Outline
I. Introduction 1. Why model? 2. Some challenges of modelingII. Upper-ocean mixed layer ecosystem model 1. Eslinger model in Prince William Sound i. Schematic, summary, equations ii. Bering Sea iii. With DMS biogeochemistry 2. Physical-Ecosystem Model (PhEcoM) for Bering
and Chukchi SeasIII. Adding sea ice and sea ice algae 1. Bering Sea 2. Chukchi shelf 3. Larger-scale
Why model?
A numerical simulation (model) is a tool to help:
• ask better questions
• identify important processes or factors
• link data intensive process study and time series measurement sites, to larger spatial and temporal scales
• synthesize and interpret data
• guide field campaigns and laboratory studies
Some Challenges of Modeling
• Balancing complexity and simplicity
• Do assumptions about food web extend beyond the local scale?
• Site-specific nature of parameter determinations in the field
• Inadequate observational data to test or constrain model
Approach based on previous work:Eslinger, D. L. and R.L. Iverson, The effects of convective and wind-driven mixing on spring phytoplankton dynamics in the Southeastern Bering Sea middle shelf domain, Cont. Shelf. Res. 21, 627-650, 2001.
Eslinger, D.L., R.T. Cooney, C.P. McRoy, A. Ward, T.C. Kline, P. Simpson, J. Wang and J.R. Allen, Plankton dynamics: observed and modelled responses to physical conditions in Prince William Sound, Alaska, Fish. Oceanogr., 10, 81-96, 2001.
Jodwalis (Deal), C.M., R.L. Benner and D.L. Eslinger, Modeling of dimethylsulfide ocean mixing, biological production, and sea-to-air flux at high latitudes, J. Geophys. Res., 2000.
Wang, J., C.J. Deal, and Z. Wan, USER'S GUDIE for A Physical-Ecosystem Model (PhEcoM) In the Subpolar and Polar Oceans, Version 1, IARC-FRSCG Technical Report 02-01 May 2002.
Mechanical (wind), convective mixingTemperature
PhytoplanktonTwo compartments:DiatomsFlagellates
ZooplanktonThree compartments:Large, Small, Other
Detritus
Nitrate-Nitrite
Silicon(diatoms only)
Ammonium
Light
Interactions among variables in 1-D model.
Eslinger, D.L., R.T. Cooney, C.P. McRoy, A. Ward, T.C. Kline, P. Simpson, J. Wang and J.R. Allen, Plankton dynamics: observed and modeled responses to physical conditions in Prince William Sound, Alaska, Fish. Oceanogr., 10, 81-96, 2001.
Summary of 1-D Model• Nitrogen based: all biomasses and uptakes are in mmol/m3 N
• Phytoplankton: diatoms, flagellates
Zooplankton: small copepods, large copepods, other large zooplankton
Nutrients: nitrate-nitrite, ammonium, silicon
Other: detritus
• Vertical mixing controlled by balancing of wind stress,
convective mixing, and stratification; turbulent mixing also included
• One spatial dimension: Depth = 100 m
• Temporal: March - January
• Resolution
Vertical: 2 m
Time: 1 hrs
Forcing Data – Wind Velocity, Air Temperature, Sea Surface Temperature, Relative Humidity, Cloud Cover, Light
Governing Equations
2
2)()(
z
DK
z
DSZPZLZSRgRGD
t
D DDPDLDSDDD
2
2)()(
z
FK
z
FSZPZLZSRgRGF
t
F FFPFLFSFFF
2
2
))1)(((z
ZSKMExAZS
t
ZS SSFSDSS
23
2
33 ))()((
z
NOKRGFRGDf
t
NO FFDDNO
2
42
3
4
))()((1
)()()(
z
NHKRGFRGDfRgDet
RgFRgDExAZPExAZLExAZSt
NH
FFDDNO
Det
FDPFPDPPLFLDLLSFSDSS
2
2
)(z
SiKRGDk
t
Si DDSi
DetPFPDPP
LFLDLLSFSDSS
RgDetMAZP
MAZLMAZSt
Det
)))(1((
)))(1(()))(1((
LegendF = FlagellatesD = DiatomsZ = ZooplanktonG = growthR = respirationRg = regeneration= grazingM = mortalityA = assimulationEx = egestion
Maximum temperature-dependent phytoplankton X growth rate:
where m is the growth rate at 0C,rx is the temperature coefficient, and Nfrac, Sifrac and Ifrac are unitless ratios
expressing nutrient and light limitation.
Respiration rate of phytoplankton X, set to 5% of growth rate
Mortality and extracellular excretion of phytoplankton X and fecal material (from data in Harrison 1980, see Eslinger and Iverson 2001)
Fraction of phytoplankton growth due to nitrate uptake over that due to ammonium uptake.
),,min( fracfracfracTrx
ox ISiNemG
x
xoo
Txrgxo
x eRgRg
]exp[(
exp
433
3
44
4
433
3
NHNOKS
NO
NHKS
NH
NHNOKS
NON
NONH
NOfrac
SiKS
SiSi
Sifrac
ba
af
4NHKS
4NHb
4NHexp3NOKS
3NOa
3NO
4NH
3NO
B
sB
s PbI
PaI expexp1I frac
Biological equations
(after Wroblewski, 1977)
(after Dugdale, 1967)
(after Platt et al. 1980)
Map showing R/V Mirai, T/S Oshoro-Maru, PMEL surface buoy and PROBES observation locations in Bering Sea
x station 12X PMEL buoy
PROBES transect
Eslinger model resultsvs. field observations
(April 10 – July 10)
Processes included in 1-D DMS model.
DMS loss and production in Jodwalis, C., R. Benner, and D. Eslinger, 2000, J. Geophys. Res., 105, D11, 14,387-14,399.
Physical processes included in the original model by Eslinger et al., (2001).
Sensitivity study indicates which parameters are most important.
Mixed-layer dynamics important factor
Mechanical (wind), convective and turbulent mixingTemperature
PhytoplanktonTwo compartments:DiatomsFlagellates
ZooplanktonThree compartments:Small, Large, Other
Detritus
Nitrate-Nitrite
Silicon(diatoms only)
Ammonium
Light
Wang, J., C. Jodwalis Deal, Z. Wan, M. Jin, N. Tanaka and M. Ikeda, USER’S GUIDE for a Physical-Ecosystem Model (PhEcoM) in the Subpolar and Polar Oceans (Version 1), IARC/FRSGC/UAF, 2003.
Interactions among variables in Bering Sea 1-D model.
Sinking/export
Sinking/export
Time series of sea water temperatureand fluorescence at ~ 12 m (yellow trace) from Mooring M-2 in southeastern Bering Sea.
Year 2000 data and model results at ~12 m depth
Month of year
May June July August September
De
pth
(m
)
0
10
20
30
40
50
60
70
2
22
2
4
4
4
4
3
3
3
3 6
6
6
5
5
5
7
7
778
8
8
99
10108
8
89 99
10
1
1
1
1
15
3
Year 2000 temperature (oC) model resultsMonth of year
May June July August September
Flu
ores
cenc
e (v
olts
)
0
1
2
3
4
Ph
yto
plan
kto
n bi
omas
s (u
g ch
l /L)
0
2
4
6
8
10
12
14 fluorescence datachlorophyll model results
chlorophyll data (diatoms only)
Time series of sea water temperatureand fluorescence at ~ 12 m (yellow trace) from Mooring M-2 in southeastern Bering Sea.
Year 1999 data and model results at ~12 m depth
Year 1999 temperature (oC) model results
Month of year
May June July August September
Flu
ores
cenc
e (v
olts
)
0
1
2
3
4
Phy
topl
ankt
on b
iom
ass
(ug
chl L
-1)
0
2
4
6
8
10
12
14 fluorescence datachlorophyll model results
chlorophyll model results (diatoms only)
Month of year
May June July August September
De
pth
(m
)
0
10
20
30
40
50
60
70
0
00
0
1
11
77
7 7
6
6
65
5
54
4
43
33
2
2
2
8
8
9
9 9
9
8 88 88 89
6
-1
-1
-1
-1
11
12
2
3-1
-1
-1
-1
0
Is SST important factor in the initiation and maintenance of coccolithophore boom in the Bering Sea?
1999: relatively low SST and small coccolithophore bloom2000: relatively high SST and large, extensive coccolithophore bloom
2000/07/26 2000/08/25 2000/09/17
Flagellates (g Chl L-1)year 1999 weather data used
Month of year
May June July
De
pth
(m
)
0
10
20
30
40
50
60
70
0.50.50.5
0.5
0.5
0.5
0.5
0.5
2.5
2.5
2.54.5
4.5
4.5
6.56.5
0.5
0.5
0.5
0.5
0.5
Flagellates (g Chl L-1)year 2000 weather data used
Month of year
May June July
Dep
th (
m)
0
10
20
30
40
50
60
70
0.50.50.5
0.50.5
0.5
0.5
2.52.5
2.54.5
4.54.56.5 6.5
8.58.56.5 6.5
0.5
0.5
0.5
Flagellates(coccolithophore)1999
Sea Surface Temperaturesyears 1999 and 2000
Time (hours)
0 500 1000 1500 2000 2500 3000 3500 4000
SS
T (C
)
-2
0
2
4
6
8
10
12
year 1999year 2000
April26
Model results. Flagellate
(coccolithophore) biomass profiles for model runs 1999 and 2000.
Observations. 1999 and 2000 NOAA/ PMEL buoy data. Wind speed, air temperature, and SST.
July 26
Flagellates(coccolithopore)2000
1999: relatively low SST and small coccolithophore bloom
2000: relatively high SST and large, extensive coccolithophore bloom
Initial Zooplankton Biomass (mg C m-3)
024681012
Du
ratio
n o
f F
lag
ella
te B
loo
m in
Mo
de
l (d
ays
> 4
ug
ch
l L-1)
20
30
40
50
60
70
80
90
Threshold Grazing Rate (hr-1)
0.0030.0040.0050.0060.0070.0080.0090.0100.0110.0120.013
Initial Zooplankton Biomass Threshold Grazing Rate
Sensitivity analysis results showing increasing flagellate (coccolithophore) bloom duration with decreasing zooplankton initial biomass or threshold grazing rate (year 2000).
Surface currents of the North Pacific are reproduced by the global MITgcm model with the coarse (~22km) resolution.
Map showing major currentsfor comparison with model results.
The Ocean Model (MITgcm):• horizontal spherical grid with resolution 1/20x1/30 degrees (eddy permitting)• 48 z-levels in the veritcal, 3m resolution in upper 50m and
6m from 50-100m•Atmospheric forcing using NCEP/NCAR reanalysis: heat flux, mass (moisture) flux, daily,monthly wind stress, freshwater runoff
We are working on including sea ice in the 1-D model, starting with the “under ice bloom”.
nutrientupwelling
nutrient upwelling
temperature-basedstratification
“open-water bloom”
salinity-basedstratification
nutrientupwelling
nutrient upwelling
“ice-edge bloom”
Sea Ice
nutrientupwelling
nutrient upwelling
Sea Ice
“under ice bloom”
Spring Bloom in the Bering-Chukchi Seas
Modeling Objectives
What are the consequences of marine ecosystem responses to climate variability and climate change? Specifically,
1) How do different sea ice conditions and external forcing (i.e. solar radiation) control local rates of primary production?
2) How will projected retreat of sea ice change the production, transport and fate of primary production in the Arctic? The release of climate relevant trace gases?
3) Will a warming climate result in higher primary productivity (or changes in the boom timing and dominant species) in the water column in the Arctic?
4) How is regional atmospheric CO2 variability linked to changing sea ice conditions?
Year 2002 measurements near Barrow. Sea ice began to melt between May 1 and 22. Chl.a maximum in ice bottom (2 cm layer) was observed on May 1 with the value of 0.6 mg/l. That in seawater was observed on Apr. 17 with the value of 3.6 u(micro)g/l.
Sea ice algal biomass is greatest in the bottom few cm of sea ice.
Selected model parameters and their values.Parameters Value Units Reference , Initial slope of PB vs. I curve 0.174 mg C (mg Chla h W m-2)–1 Eslinger & Iverson, 2001(from data), Photoinhibition coefficient 0.0058 for diatoms mg C (mg Chla h W m-2)–1 Eslinger & Iverson, 2001(from data)
no photoinhibition for coccos Nanninga & Tyrell, 1996k(P), Diffuse attenuation coefficient k(P) = k0 + kp(P/kchl) (m-1) k0, kp from Magley, 1990 (PROBES data)KS,nitrate-nitrite, KS,ammonium 2.5 for diatoms M N Eppley et al., 1969 Nutrient half-saturation constant (0.5-2.75) Sambrotto & Goering, 1980
0.1 for E. hux M N Tyrell & Taylor, 1996 (Eppley et al., 1969)KS,silicon 3.0 for diatoms M N Eslinger et al., 2001kchl,, Carbon:chlorophyll mass ratio 40 g C (g Chl)-1 Eslinger & Iverson, 2001kN, Carbon:nitrogen mass ratio 5.69 g C (g N)-1 Eslinger & Iverson, 2001µ0, Growth rate at 0oC 0.06 h-1 Eslinger & Iverson, 2001(Durbin 1974;
PROBES data; within Olson & Strom, 2002)r, temperature coefficient 0.0633 deg –1 Eppley et al., 1969 Ro, Respiration rate at 0oC 0.05µ0 h-1 Yentsch, 1981 (w/in 10% of daily 1o prod.)PBs, Maximum photosynthesis rate 3.25 mg C (mg Chl h)-1 Eslinger & Iverson, 2001
Rg0, Regeneration rate at 0oC 9.23 x 10-4 h-1 Eslinger & Iverson, 2001 (Harrison, 1980)rg, Regeneration constant 3.0 x 10-2 oC-1 Eslinger & Iverson, 2001 (Harrison, 1980)Sk, Sinking rate constant 0.22 i.e. tanh[SkKs]=0.5 m d-1 Eslinger & Iverson, 2001 (Harrison, 1980)Smax, Maximum sinking rate 4.0 for diatoms m d-1 Eslinger & Iverson, 2001 (PROBES data)Zooplankton and phytoplankton growth limitation parameters to be included (see manual).Parameters specifically for sea ice algae Value Range Units Reference /PB
s, Initial slope of PB vs. I curve/ 0.22 (0.22 - 0.028) W m-2 Lee et al., unpublished data estimates maximum photosynthesis rate (~15 x larger than for phytoplankton) Arrigo, 2003 (and references therein)/PB
s, Photoinhibition coefficient/ 0.019 (0.013 - 0.031) W m-2 Lee et al., unpublished data estimates maximum photosynthesis rate (~10 x larger than for phytoplankton) Arrigo, 2003 (and references therein)KS,nitrate-nitrite, KS,ammonium 1.0 M N Arrigo, 2003 (and references therein)
(4 or 5)Whitledge, personal communications
KS,silicon 3.0 M N Eslinger et al., 2001kchl,, Carbon:chlorophyll mass ratio 57 (43 - 66) g C (g Chl)-1 Lee et al., unpublished data estimateskN, Carbon:nitrogen mass ratio 8.88 (7.2 - 11.1) g C (g N)-1 Lee et al., unpublished data estimatesµ0, Growth rate at 0oC 0.06 h-1 Arrigo, 2003 (and references therein)
(0.040 - 0.053) Hegseth, 1992 (Arctic ice algae)r, temperature coefficient 0.0633 deg –1 Arrigo, 2003 (and references therein)Sk, Sinking rate ? m d-1
Note: Median potential grazing rates in Central Arctic are at least 1 order of magnitude less than the mean primary production estimates of Arctic sea-ice associated algae (Gradinger, R., 1999). Grazing impact at ice underside in summer is low [1.1%Laptev, 2.6% Greenland Seas] (Werner, 1997).
Large-scale model of sea ice primary production
“Little is presently known about either the large-scale horizontal distribution of sea ice algae or their contribution to total regional productivity due to the difficulty inherent in sampling ice covered systems” (course text, p. 159).
It is also difficult to sample over a seasonal cycle.
Antarctic sea ice model during 1989-90 (Arrigo et al., 1997, 1998b).
General take home message
A fundamental difficulty in developing marine biogeochemical models is the absence of equations of state for biological processes.
As a consequence, biological or chemical formulations may be different for models of the same processes within and between environments.
However, the most important feature responsible for biogeochemical model accuracy is the fidelity with which physical models replicate the major physical factors controlling biogeochemical cycling.