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.