ECOSMO an ECOSystem Model coupled physics-lower trophic level dynamics

General Overview

Basic equations Towards model equations: vertical integration Model equations and approximations Air-sea and air-ice-ocean fluxes Lower trophic level dynamics Numerical schemes Grid- and slab information Model flow, main program Literature Additional features New set-up Irina

Basic equations

Reynolds equations, hydrostatic approximation, conservation equation: mass (volume), salt mass, heat and tracer mass (nutrients, biomass etc…)

Vertical integration and boundary conditions results in model equations

Basic equations:

Approximations

Transport model equations : subroutines motmit, druxav, konv

Transport model equations: boundary conditions

Model equations for T and S(and other tracers) subroutine strom3

More model equations

subroutine konti

subroutine sor, sorcof

subroutine estate

Turbulence closure

Stationarity

local production and local dissipation of turbulent kinetic energy balance,

advection and diffusion of turbulent kinetic energy can be neglected

Vertical integration for one model layer k from zk-zk-1:Horizontal transport

Turbulence closure

Turbulence closure

Turbulence closure

subroutine druxav

Dynamic sea ice model: subroutine icemod, icevel

• 3 state variables:

-Ice compactness Ai,

-level ice thickness hi

- ridging ice thickness hr

• continuum approach, conservation equations for open water area, level ice thickness, ridging ice thickness

• Hibler type ice dynamics: viscous-plastic, elliptical yield curve, normal flow rule

Ice transports

Conservation equation for ice stages: compactness (open water and thin ice), level ice, ridged ice

Mechanic deformation functions

1. Ai<1 and convergent or divergent flow field, or divergent flow field ice transport change only ice concentration

2. Ai=1, ice thickness below critical value (0.1m), convergent flow field ice transport results in rafting: level ice thickness change

3. Ai=1, ice thickness above critical value, convergent flow field

ice transport results in ridging: level ice thickness change

3 cases:

Fluxes

Air sea fluxes : subroutine fluxes

Based on Monin-Obukhov similarity theory:

- MONIN and OBUKHOV, 1954

- LAUNIAINEN and VIHMA, 1990

•2m Tair, spec. humidity are up-scaled to 10m-ref heights

•Upscaling, cd exchange coefficients and fluxes depend on

atmospheric stability

Ice thermo-dynamics: subroutine trmice

Ice thermodynamics

Lower trophic level dynamics: coupling vs. transport equations subroutine strom3 calls subroutine bio

12 biological and chemical variables:

Phytoplankton: Pd - diatoms; Pf - flagellates;

Zooplankton: Zs, Z l – micro and macro-zooplankton;

Nitrogen: NH4 - ammonium; NO2 - nitrite; NO3 - nitrate;

Phosphorus: PO4 - phosphate;

Silica: SiO2 - silicate; SiO2•2H2O - biogenic opal;

O2 – Oxygen, D - detritus

NO3

Pf Z s

Z l Pd

NH4

D

O2

SiO2 PO4

NO2

N2

SiO2•2H2O

Nitrification Denitrification

Lower trophic level dynamics: subroutine bio

Biological state variables

parameter (nbio=14) dimension Tc(ndrei,nbio)

ibio=1,nbio

ibio = 1,2 reserved for T,S

ibio = 3,nbio: 3 4Phytoplankton: Ps – flagellates; Pl - diatoms;

5 6Zooplankton: Zs, Z l – micro and macro-zooplankton;

7 D - detritus;

8 9 10Nitrogen: NH4 - ammonium; NO2 - nitrite; NO3 - nitrate;

11 Phosphorus: PO4 - phosphate;

12 14Silica: SiO2 - silicate; SiO2•2H2O - biogenic opal;

13 O2 – Oxygen.

Biological reactionssPlssssPsPs PmZPGZPGPФR

ss )()( 21

lPllsllPlPl PmZPG)Z(PGPΦσRll

)(21

ssZsslssslsZs ZmZμ)Z(ZG(D)ZGZ)(PG)(PGγR 2111 ][

lZllllsls ZmZ(D)ZGZ)(ZG)(PG)(PGγRl

2222 ][Zl

DZmZmPmPm

(D)ZGZ)(ZG)(PG)(PG

(D)ZGZ)(PG)(PGR

lZsZlPsP

llsls

sslsD

lsls

2222

111

1

1

])[(

][)(

44

4

1(z)NHΩZμZμεD

β

βPΦPΦ

REDFR allss

N

NHlPlsPs

NCNH ls

:

2324 NOzNOzNOzNHzR drna )()()()(2NO

323

3

1(z)NOΩ(z)NOΩ

β

βPΦPΦ

REDFR rn

N

NO

lPlsPsNC

NO ls

:

llsslPlsPsPC

PO ZμZμεDPΦPΦREDF

Rls

:

14

Biological reactions in the model : term RC is Dxbi(ndrei,nbio)

*------------------BIOLOGICAL SOURCES------------------------------------ *Ps DXbi(ll,3)= ( BioC(2)*Ps_prod-BioC(10) )*Tc(ll,3) !1 prod & - ZsonPs*Tc(ll,5) ! & - ZlonPs*Tc(ll,6) ! *Pl DXbi(ll,4)= ( BioC(1)*Pl_prod-BioC(9 ) )*Tc(ll,4) !2 prod, c & - ZsonPl*Tc(ll,5) ! & - ZlonPl*Tc(ll,6) ! *Zs DXbi(ll,5)= ( BioC(20)*(ZsonPs+ZsonPl) !3,4,5 & + BioC(21)*ZsonD & - BioC(16) !c & - BioC(18)) *Tc(ll,5) !c & - ZlonZs*Tc(ll,6) ! *Zl DXbi(ll,6)= ( BioC(19)*(ZlonPs+ZlonPl+ZlonZs) !6,7,8,9 & + BioC(21)*ZlonD & - BioC(15) !c & - BioC(17) ) *Tc(ll,6) !c *D DXbi(ll,7)= ( (1.-BioC(20))*(ZsonPs+ZsonPl) !3,4,5 & + (1.-BioC(21))*ZsonD & + BioC(16) )*Tc(ll,5) !c & +( (1.-BioC(19))*(ZlonPs+ZlonPl+ZlonZs) !6,7,8,9 & + (1.-BioC(21))*ZlonD & + BioC(15) )*Tc(ll,6) !c & + BioC(10)*Tc(ll,3) !c & + BioC(9)*Tc(ll,4) !c & - ZsonD*Tc(ll,5) !5 & - ZlonD*Tc(ll,6) !9 & - BioC(22)*Tc(ll,7) !reminiralization !10 *NH4 DXbi(ll,8)= - UP_NH4/UP_N*Prod !11 & + BioC(18)*Tc(ll,5)+BioC(17)*Tc(ll,6) !c,c & + BioC(22)*Tc(ll,7) !reminiralization !c & - BioOM1*Tc(ll,8) !oxydation !13 BioOM1 *NO2 DXbi(ll,9)= BioOM1*Tc(ll,8)-(BioOM2+BioOM4)* !14, 16 BioOM2,BioOM4 & Tc(ll,9)+BioOM3*Tc(ll,10) !15 BioOM3 *NO3 DXbi(ll,10)=- UP_NO3/UP_N*Prod !NO3 !12 & + BioOM2*Tc(ll,9)-BioOM3*Tc(ll,10) !14,15 *PO4 DXbi(ll,11)=(-Prod !1+2 & + BioC(18)*Tc(ll,5)+BioC(17)*Tc(ll,6) & + BioC(22)*Tc(ll,7) ) !reminiralization !10 *SiO2 DXbi(ll,12)=- BioC(1)*Pl_prod *Tc(ll,4) & + BioC(27)*Tc(ll,14) !regeneration SiO2 !17 *O2 DXbi(ll,13)= ((6.625*UP_NH4+8.125*UP_NO3)/UP_N*Prod !O2 !18 O2 from production & - 6.625*(BioC(18)*Tc(ll,5)+BioC(17)*Tc(ll,6)) !zoo exctrition ! & - 6.625*BioC(22)*Tc(ll,7) !detritus mineralization ! & - BioOM1*Tc(ll, 8) !NH4-NO2 ! & -0.5*BioOM2*Tc(ll, 9) !NO2-NO3 ! & +0.5*BioOM3*Tc(ll,10) !NO3-NO2 ! & + BioOM4*Tc(ll, 9))*REDF(11) !NO2-N2 !29 DXbi(ll,14)= + BioC(9 )*Tc(ll,4) & + ZsonPl*Tc(ll,5) & + ZlonPl*Tc(ll,6) & - BioC(27)*Tc(ll,14) !regeneration SiO2

do ibio=3,nbio Tc(ll,ibio) = Tc(ll,ibio)+DXbi(ll,ibio)*dt end do

Subroutine bio (Tc,dd,dz,sh_wave,sh_depth)

Numerics: basic information

Semi-implicit:

-implicit: barotropic pressure gradients, turbulent vertical exchange

-explicit: convective terms, baroclinic pressure gradients, horizontal

turbulent diffusion

Convective or nonlinear terms: energy and enstrophy conserving

scheme Arakawa J7

Rotation of corriolis term (C-grid)

Upstream advection scheme (2d) for T,S and bio-parameter

Free surface and bottom depth resolving coordinates application of

kinematic boundary conditions necessary

Model grid: Arakawa C-grid horizontal

•TC(i,j) •TC(i,j+1)

•TC(i+1,j) •TC(i+1,j+1)

X U(i,j)

+V(i,j)

X U(i,j+1)

X U(i+1,j+1)X U(i+1,j)

+V(i+1,j+1)

+V(i,j+1)

+V(i+1,j)

NW=(1,1) Columns n (j)

Rows

m (i)

Model grid: vertical grid

•TC(k)

•TC(k+1)

+w (k+1) Av(k+1)

Surface layer: 1

ilo (k)

+w (k) Av(k)

•Av and w are not defined at the lower boundary of the bottom layer

•Av(1)=0, i.e. at the sea surface

•w(1) is the first guess for solving the equation system for the sea surface elevation

Organisation of slabs: Counting wet grid points

c----------------------------------------------------------------------- c set grid index arrays c----------------------------------------------------------------------- lwe = 0 nwet=0 do k=1,n lwa = lwe+1 lwe = indend(k) do lw=lwa,lwe i = iwet(lw) lump = lazc(lw) jjc(i,k) = 1 iindex(i,k) = nwet id3sur(lw) = nwet+1 do jj=1,lump nwet = nwet+1 enddo izet(i,k) = lw enddo enddo

•Start with NW grid point, at the sea surface

•2-d arrays: outer loop columns, inner loop rows

•3-d arrays: outer loop, columns, than rows, inner loop depth layers

Relevant arrays and dimensions

•compressed 3-d arrays of dimension ndrei UC(ndrei)

•compressed 2-d arrays of dimension khor zac(khor)

•iindex(i,j) help array to address wet grid from i,j,k arrays i,j,k

known respective uc=uc(iindex(i,j)+k)

•jjc(i,k) mask array, =1 if wet, =0 if land point

•lazc(khor): number of layers for compressed 2-d arrays

•iwet (khor): i-index(row) for compressed 2-d arrays

•indend(k): end index of compressed arrays for

Literature model description

Backhaus J. O. (1983) A semi-implicit scheme for the shallow water equations for application to shelf sea modelling. Continental Shelf Research, 3,243-254.

Backhaus J. O. (1985) A three-dimensional model for the simulation of shelf sea dynamics. Deutsche Hydrographische Zeitschrifi, 38, 165-187.

Schrum, C. (1997): Thermohaline stratification and instabilities at tidal mixing fronts. Results of an eddy resolving model for the German Bight. Cont. Shelf. Res., 17(6), 689-716.

Schrum, C, Backhaus, J. O. (1999): Sensitivity of atmosphere-ocean heat exchange and heat content in North Sea and Baltic Sea. A comparitive assessment. Tellus 51A. 526-549.

Schrum, C, Alekseeva, I, St. John, M (2006): Development of a coupled physical–biological ecosystem model ECOSMO Part I: Model description and validation for the North Sea, Journal of Marine Systems, doi:10.1016/j.jmarsys.2006.01.005.

Access to model code and literature

ftp://ftp.uib.no/

path: /var/ftp/pub/gfi/corinna/ECOSMO

Additional features (not in basic version)

3-d wetting and drying, mass conserving

Groundwater runoff module

Particle tracking module (online)

IBM parameterized for larvae fish growing (temperature based

and food consumption)

Setting up a new configuration

Attention required:

•ngro array size to be set in C_model.f, it needs to be

ngro=max((m*(ilo*20+10),(kasor*8)), for current configuration set to

m*(ilo*20+10)

•consider exclusion of boundary points for iteration in kotief!

currently weak programming

•3 frame lines are necessary in the west and north, only 2 frame lines

in the south and east

•consider 3 equal boundary lines at the open boundaries