General Ocean Turbulence Model: Recent advances and future plans

Transcription

1 General Ocean Turbulence Model: Recent advances and future plans Hans Burchard 1,3, Lars Umlauf 1 Andreas Meister 2, Thomas Neumann 1, and Karsten Bolding 3 hans.burchard@io-warnemuende.de 1. Baltic Sea Research Institute Warnemünde, Germany; 2. University of Kassel, Germany; 3. Bolding & Burchard Hydrodynamics, Asperup, Denmark; Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 1/33

2 Contents Motivation Basic structure of GOTM Predictability for turbulent quantities in the field Rationale for using stiff solvers Neumann et al. [2002] model implemented into GOTM-BIO Application of GOTM-BIO to Gotland Basin ecosystem Description of GOTM Lagrangian test environment Some first test of Lagrangian model environment Conclusions Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 2/33

3 Motivation To create an environment within which any biogeochemical model can be implemented without technical problems. To provide an environment in which various biogeochemical models can be compared under the same physical forcing conditions. To create a test environment for Lagrangian studies for ecosystem modelling. To allow for direct plug-in of the GOTM-BIO module into three-dimensional models. To offer a wide choice of advection schemes (for vertical motions) and solvers for the ODE (sources and sinks) part. Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 3/33

4 GOTM, Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 4/33

5 Turbulence modelling principles Two-equation models with TKE-equation and length scale related equation (e.g. dissipation rate, turbulence frequency, generic equation). Algebraic second-moment closure for e.g. w 2, ũ w Calibration of empirical parameters by physical considerations (e.g. freely decaying turbulence, steady-state Richardson number of 1/4,... ). Boundary conditions from law of the wall or from turbulence injection (breaking surface waves). Turbulence module used by GETM is from the water column model GOTM (General Ocean Turbulence Model, see See Umlauf and Burchard (CSR 2005) for details and references. Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 5/33

6 Structure of GOTM-BIO Second Warnemu nde Turbulence Days, Warnemu nde, Germany, September 28-30, p. 6/33

7 Stiff versus explicit solvers Surface nutrient content in Northern North Sea seen with numerical different solvers (from Burchard et al. [2005]): th-order Runge-Kutta RK4, t = 2 h RK4, t = 1/2 h RK4, t = 20 s 10 Modified Patankar-Runge-Kutta MPRK2, t = 2 h MPRK2, t = 1/2 h RK4, t = 20 s nut(z = 0) [mmol N m 3 ] nut(z = 0) [mmol N m 3 ] Julian Day Julian Day 1998 Explicit solver at long time steps (left) does not obey nutrient limitation. Stiff solver (right, Burchard et al. [2003]) is stable and accurate. Note the different scales. Note the new Extended Modified Patankar scheme by Bruggeman et al., Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 7/33

8 Neumann et al model Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 8/33

9 Gotland Basin setups 1. Basic experiment 2. Experiment with no feedback of bio-turbidity to Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 9/33

10 Base run: temperature Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 10/33

11 Base run: Chl-a Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 11/33

12 Base run: DIN Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 12/33

13 Base run: DIP Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 13/33

14 Base run no feedback run: Temp. Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 14/33

15 Random walk Random walk consistent with diffusion equation: t C z (ν t z C) = 0. (1) z n+1 i = z n i + zν t (z n i ) t + R { 2r 1 ν t (z n i zν t (z n i ) t) t} 1/2 (2) R: random process with R = 0 and R 2 = r. zi n : vertical position of particle i at time step n. Reference: Visser [1997] Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 15/33

16 Rouse profile Analytical Problem Constant settling velocity w c Parabolic eddy diffusivity ν t Reflective bottom and surface Steady-state solution t C + z (w c C ν t z C) = 0, (3) with ν t = κu ( z) D + z 0 + z D + z 0. (4) Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 16/33

17 Rouse profile Analytical Solution C C 0 = ( z D + z 0 + z ) wc /(κu ) (5) Rouse number: R = w c u. (6) Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 17/33

18 Rouse profile Analytical Solution Concentration: linear Concentration: logarithmic z / m -5 z / m C / (kg m 3 ) C / (kg m 3 ) Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 18/33

19 Rouse profile Numerical Solution for N = 1000 Particles Concentration: linear Concentration: logarithmic 0-1 Analytical Eulerian Lagrangian 0-1 Analytical Eulerian Lagrangian z / m -5 z / m C / (kg m 3 ) C / (kg m 3 ) Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 19/33

20 Rouse profile Numerical Solution for N = Particles Concentration: linear Concentration: logarithmic 0-1 Analytical Eulerian Lagrangian 0-1 Analytical Eulerian Lagrangian z / m -5 z / m C / (kg m 3 ) C / (kg m 3 ) Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 20/33

21 Rouse profile Numerical Solution for N = Particles Concentration: linear Concentration: logarithmic 0-1 Analytical Eulerian Lagrangian 0-1 Analytical Eulerian Lagrangian z / m -5 z / m C / (kg m 3 ) C / (kg m 3 ) Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 21/33

22 Rouse profile Error with respect to analytical solution (standard deviation) Lagrangian scheme N σ Eulerian scheme Advection scheme upwind TVD σ Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 22/33

23 Mussel filtration Benthic filter feeders as sinks for suspended particulate matter Eulerian formulation of boundary condition: ν t z C z= H = w f C z= H, w f = N m V f (7) w f : filtration velocity N m : number of mussels per m 2 (e.g. 1000) V f : filtration volume per mussel (e.g. 18 l per hour) Lagrangian formulation of boundary condition: At each time step take out all particles which are below z = H + tw f. Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 23/33

24 Mussel filtration Profiles of suspended matter: Euler (x-axis: 0h t 12 h, z-axis: -10 m z 0 m, contours: 0 C 1) Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 24/33

25 Mussel filtration Profiles of suspended matter: Lagrange (x-axis: 0h t 12 h, z-axis: -10 m z 0 m, contours: 0 C 1) Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 25/33

26 Mussel filtration Profiles of suspended matter: Euler vs. Lagrange Profiles at t = 3 1/3; 6 2/3; 10 h z / m C / (kg m 3 ) Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 26/33

27 Photo adaptation Let any Lagrangian particle represent a phytoplankton cell. Then the photosynthetic production rates may be calculated according to Nagai et al. [2003] as P = P d + Y (P l P d ) (8) with production rates for uninhibited and inhibited cells, ( P d = P dm (1 exp PAR )), E d P l = P lm (1 exp ( PAR )), E l (9) with P dm, P lm, E d and E l being constants. Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 27/33

28 Photo adaptation, cont d Y is the inhibition parameter defined by dy dt = 1 (X Y ), (10) γ with the adaptation time scale γ and the instantaneous inhibition parameter ( ( ) ) 2 max{par,eb } E X = 1 exp b E b. (11) PAR is the photosynthetically available radiation. Some experiments with variations in surface forcing (W = 0, 5, 10 m s 1 ) and turbidity (Jerlov I and III, coastal) have been carried out, see the following slides. Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 28/33

29 Photo adaptation W = 10 m s 1, turbidity: Jerlov I (left), coastal (right) Eddy diffusivity x-axis: 6:00 h t 19:00 h, z-axis: -100 m z 0 m Contours: 0 ν t 0.04 m 2 s 1 Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 29/33

30 Photo adaptation W = 0 m s 1, turbidity: Jerlov I Inhibition parameter Photosynthetic production rate x-axis: 6:00 h t 19:00 h, z-axis: -100 m z 0 m Contours left: 0 Y 1; right: 0 P pg-at O 2 cell 1 h 1 Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 30/33

31 Photo adaptation W = 5 m s 1, turbidity: Jerlov I Inhibition parameter Photosynthetic production rate x-axis: 6:00 h t 19:00 h, z-axis: -100 m z 0 m Contours left: 0 Y 1; right: 0 P pg-at O 2 cell 1 h 1 Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 31/33

32 Photo adaptation W = 10 m s 1, turbidity: Jerlov I Inhibition parameter Photosynthetic production rate x-axis: 6:00 h t 19:00 h, z-axis: -100 m z 0 m Contours left: 0 Y 1; right: 0 P pg-at O 2 cell 1 h 1 Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 32/33

33 Conclusions GOTM is a Public Domain model tool which may be downloaded and used by anybody interested in statistical turbulence modelling and bulk turbulence implications on the marine ecosystem. Please register to the GOTM mailing list before you start to implement your chnages into GOTM, and ask the list whether anybody has done a similar job before (that may save you a lot of head ache). Report your changes back to the GOTM developers. Have a look into and tell us what you think. Second Warnemünde Turbulence Days, Warnemünde, Germany, September 28-30, p. 33/33