Unrealistic M2 tide amplitude in Sulu Sea, Indonesian Sea

[hezhiwei]

Dear all:
I'm setting up a model to simulate Indonesian throughfow with explicit tidal forcing. The model configuration is simlar to the work of Liang et. al (2019) except that I have added explicit tidal forcing and potential tide. The tidal forcing is from the TPXO 7.2. The resolution of the model is 1/12 degree. The topography is interpolated from the SRTM data and smoothed with the Linear Program script in the the package of pyroms. This method minimizes the modification to bathymetry while satisfying the rx0<=0.2 requirement. The simulated mean flow and seasonal variaiton generally agrees with INSTANT observation.

The problem is that the tidal amplitude of M2 in Sulu Sea is unrealistic, much larger than observations and previous studies, as shown in the figure below.

Fig. (a) and (b) are the simulated M2 tide by me, while Fig. (c) and (d) are the simulated M2 tides by Castruccio et. al (2013).
As can be seen from the figure, the pattern of tidal amplitude and phase generally agree with Castruccio et. al (2013) except in Sulu Sea, but the M2 amplitude is larger.

I checked the tidal forcing file. It seems there is no problem in the TPXO M2 amplitude, which is shown in figure 2.

Ways I have tried to solve this problem:
(1) Change the mask of several islands around the Sulu Sea. Some straits were closed and some islands were removed to see if there is any difference. The bathymetry was smoothed after modification
(2) Change the bottom drag scheme with spatially varying drag coefficient to increase the tidal dissipation in shallow water.
(3) Change the vertical mixing scheme and horizontal mixing coeffients.
(4) Remove potential tide.

However, none of the ways work, and currently I have no idea how to solve this problem.
At the end of the posts I have shown the configurations of my model.
Any suggestion is welcome. Thanks in advance.


Zhiwei

Reference:
Castruccio, F. S., E. N. Curchitser, and J. A. Kleypas (2013), A model for quantifying oceanic transport and mesoscale variability in the Coral Triangle of the Indonesian/Philippines Archipelago, J. Geophys. Res. Oceans, 118, 6123–6144, doi:10.1002/2013JC009196.
Liang, L., Xue, H., & Shu, Y. (2019). The Indonesian throughflow and the circulation in the Banda Sea: A modeling study. Journal of Geophysical Research: Oceans, 124, 3089–3106. https://doi.org/10.1029/2018JC014926


Model configuration :

2400 ntimes Number of timesteps for 3-D equations.
180.000 dt Timestep size (s) for 3-D equations.
60 ndtfast Number of timesteps for 2-D equations between
each 3D timestep.
1 ERstr Starting ensemble/perturbation run number.
1 ERend Ending ensemble/perturbation run number.
-1 nrrec Number of restart records to read from disk.
T LcycleRST Switch to recycle time-records in restart file.
4800 nRST Number of timesteps between the writing of data
into restart fields.
60 ninfo Number of timesteps between print of information
to standard output.
T ldefout Switch to create a new output NetCDF file(s).
0 nHIS Number of timesteps between the writing fields
into history file.
20 nQCK Number of timesteps between the writing fields
into quicksave file.
1 ntsAVG Starting timestep for the accumulation of output
time-averaged data.
0 nAVG Number of timesteps between the writing of
time-averaged data into averages file.
2.0000E+01 nl_tnu2(01) NLM Horizontal, harmonic mixing coefficient
(m2/s) for tracer 01: temp
2.0000E+01 nl_tnu2(02) NLM Horizontal, harmonic mixing coefficient
(m2/s) for tracer 02: salt
2.0000E+02 nl_visc2 NLM Horizontal, harmonic mixing coefficient
(m2/s) for momentum.
T LuvSponge Turning ON sponge on horizontal momentum.
T LtracerSponge(01) Turning ON sponge on tracer 01: temp
T LtracerSponge(02) Turning ON sponge on tracer 02: salt
1.0000E-05 Akt_bak(01) Background vertical mixing coefficient (m2/s)
for tracer 01: temp
1.0000E-05 Akt_bak(02) Background vertical mixing coefficient (m2/s)
for tracer 02: salt
1.0000E-05 Akv_bak Background vertical mixing coefficient (m2/s)
for momentum.
5.0000E-06 Akk_bak Background vertical mixing coefficient (m2/s)
for turbulent energy.
5.0000E-06 Akp_bak Background vertical mixing coefficient (m2/s)
for turbulent generic statistical field.
3.0000E-04 rdrg Linear bottom drag coefficient (m/s).
3.0000E-03 rdrg2 Quadratic bottom drag coefficient.
1.0000E-03 Zob Bottom roughness (m).
2.0000E+00 blk_ZQ Height (m) of surface air humidity measurement.
2.0000E+00 blk_ZT Height (m) of surface air temperature measurement.
1.0000E+01 blk_ZW Height (m) of surface winds measurement.
1 lmd_Jwt Jerlov water type.
2 Vtransform S-coordinate transformation equation.
4 Vstretching S-coordinate stretching function.
5.0000E+00 theta_s S-coordinate surface control parameter.
4.0000E-01 theta_b S-coordinate bottom control parameter.
10.000 Tcline S-coordinate surface/bottom layer width (m) used
in vertical coordinate stretching.
1025.000 rho0 Mean density (kg/m3) for Boussinesq approximation.
0.000 dstart Time-stamp assigned to model initialization (days).
0.000 tide_start Reference time origin for tidal forcing (days).
-1.00 time_ref Reference time for units attribute (yyyymmdd.dd)
1.0000E+01 Tnudg(01) Nudging/relaxation time scale (days)
for tracer 01: temp
1.0000E+01 Tnudg(02) Nudging/relaxation time scale (days)
for tracer 02: salt
1.0000E+01 Znudg Nudging/relaxation time scale (days)
for free-surface.
1.0000E+01 M2nudg Nudging/relaxation time scale (days)
for 2D momentum.
1.0000E+01 M3nudg Nudging/relaxation time scale (days)
for 3D momentum.
2.0000E+01 obcfac Factor between passive and active
open boundary conditions.
F VolCons(1) NLM western edge boundary volume conservation.
F VolCons(2) NLM southern edge boundary volume conservation.
F VolCons(3) NLM eastern edge boundary volume conservation.
F VolCons(4) NLM northern edge boundary volume conservation.
10.000 T0 Background potential temperature (C) constant.
35.000 S0 Background salinity (PSU) constant.
-1.000 gamma2 Slipperiness variable: free-slip (1.0) or
no-slip (-1.0).


Tracer Advection Scheme: NLM
========================

Variable Grid Horizontal Vertical
--------- ---- ------------ ------------

temp 1 Akima4 Akima4

salt 1 Akima4 Akima4

Akima4 Fourth-order Akima advection
Centered2 Second-order centered differences advection
Centered4 Fourth-order centered differences advection
HSIMT Third High-order Spatial Inteporlation at Middle Time Advection with TVD limiter
MPDATA Multidimensional Positive Definite Advection Algorithm, recursive method
Splines Conservative Parabolic Splines Reconstruction Advection (only vertical; not recommended)
Split_U3 Split third-order Upstream Advection
Upstream3 Third-order Upstream-biased Advection (only horizontal)


Lateral Boundary Conditions: NLM
============================

Variable Grid West Edge South Edge East Edge North Edge
--------- ---- ---------- ---------- ---------- ----------

zeta 1 Chapman Imp Chapman Imp Chapman Imp Chapman Imp

ubar 1 Flather Flather Flather Flather

vbar 1 Flather Flather Flather Flather

u 1 Rad + Nud Rad + Nud Rad + Nud Rad + Nud

v 1 Rad + Nud Rad + Nud Rad + Nud Rad + Nud

temp 1 Rad + Nud Rad + Nud Rad + Nud Rad + Nud

salt 1 Rad + Nud Rad + Nud Rad + Nud Rad + Nud

tke 1 Radiation Radiation Radiation Radiation

Activated C-preprocessing Options:

ADD_FSOBC Adding tidal elevation to processed OBC data
ADD_M2OBC Adding tidal currents to processed OBC data
ANA_BSFLUX Analytical kinematic bottom salinity flux
ANA_BTFLUX Analytical kinematic bottom temperature flux
ANA_DRAG_GRID Analytical spatially varying linear drag coefficient
ASSUMED_SHAPE Using assumed-shape arrays
AVERAGES Writing out time-averaged nonlinear model fields
!BOUNDARY_ALLGATHER Using mpi_allreduce in mp_boundary routine
BULK_FLUXES Surface bulk fluxes parameterization
!COLLECT_ALL... Using mpi_isend/mpi_recv in mp_collect routine
CURVGRID Orthogonal curvilinear grid
DIFF_3DCOEF Horizontal, time-dependent 3D diffusion coefficient
DIFF_GRID Horizontal diffusion coefficient scaled by grid size
DIURNAL_SRFLUX Modulate shortwave radiation by the local diurnal cycle
DJ_GRADPS Parabolic Splines density Jacobian (Shchepetkin, 2002)
DOUBLE_PRECISION Double precision arithmetic numerical kernel.
EMINUSP Compute Salt Flux using E-P
MASKING Land/Sea masking
MIX_GEO_TS Mixing of tracers along geopotential surfaces
MIX_GEO_UV Mixing of momentum along geopotential surfaces
MPI MPI distributed-memory configuration
MY25_MIXING Mellor/Yamada Level-2.5 mixing closure
NONLINEAR Nonlinear Model
NONLIN_EOS Nonlinear Equation of State for seawater
N2S2_HORAVG Horizontal smoothing of buoyancy and shear
POWER_LAW Power-law shape time-averaging barotropic filter
PROFILE Time profiling activated
QCORRECTION Surface net heat flux correction
K_C2ADVECTION Second-order centered differences advection of TKE fields
RAMP_TIDES Ramping tidal forcing for one day
REDUCE_ALLREDUCE Using mpi_allreduce in mp_reduce routine
RI_SPLINES Parabolic Spline Reconstruction for Richardson Number
!RST_SINGLE Double precision fields in restart NetCDF file
SALINITY Using salinity
SOLAR_SOURCE Solar Radiation Source Term
SOLVE3D Solving 3D Primitive Equations
SPLINES_VDIFF Parabolic Spline Reconstruction for Vertical Diffusion
SPLINES_VVISC Parabolic Spline Reconstruction for Vertical Viscosity
SSH_TIDES Add tidal elevation to SSH climatology
TS_DIF2 Harmonic mixing of tracers
TS_SMAGORINSKY Smagorinksy-like time-dependent diffusion coefficients
UV_ADV Advection of momentum
UV_COR Coriolis term
UV_U3HADVECTION Third-order upstream horizontal advection of 3D momentum
UV_C4VADVECTION Fourth-order centered vertical advection of momentum
UV_DRAG_GRID Spatially varying linear drag coefficient
UV_LDRAG Linear bottom stress
UV_TIDES Add tidal currents to 2D momentum climatologies
UV_VIS2 Harmonic mixing of momentum
UV_SMAGORINSKY Smagorinksy-like time-dependent viscosity coefficients
VAR_RHO_2D Variable density barotropic mode
VISC_GRID Horizontal viscosity coefficient scaled by grid size
VISC_3DCOEF Horizontal, time-dependent 3D viscosity coefficient
WIND_MINUS_CURRENT Compute effective wind by removing surface ocean current

Metrics information for Grid 01:
===============================

Minimum X-grid spacing, DXmin = 8.02461129E+00 km Water points = 8.02461129E+00 km
Maximum X-grid spacing, DXmax = 9.26670119E+00 km Water points = 9.26670119E+00 km
Minimum Y-grid spacing, DYmin = 8.03041326E+00 km Water points = 8.03041326E+00 km
Maximum Y-grid spacing, DYmax = 9.26665997E+00 km Water points = 9.26665997E+00 km
Minimum Z-grid spacing, DZmin = 1.43704112E-01 m Water points = 1.43704112E-01 m
Maximum Z-grid spacing, DZmax = 6.19292121E+02 m Water points = 6.19292121E+02 m

Minimum barotropic Courant Number = 4.53468013E-03
Maximum barotropic Courant Number = 1.22764050E-01
Maximum Coriolis Courant Number = 1.31284790E-02

Horizontal mixing scaled by grid area squared root, MAXVAL(grdscl) = 9.26667856E+00 km (Water points)

Minimum horizontal diffusion coefficient = 6.68959313E+01 m2/s
Maximum horizontal diffusion coefficient = 7.72223214E+01 m2/s

Minimum horizontal viscosity coefficient = 6.68959313E+01 m2/s
Maximum horizontal viscosity coefficient = 7.72223214E+01 m2/s

Basin information for Grid 01:
Maximum grid stiffness ratios: rx0 = 2.000000E-01 (Beckmann and Haidvogel)
rx1 = 5.029797E+00 (Haney)

[johnluick]

I suggest you focus on the South China Sea. Fix that and the Sulu Sea might be OK. Sulu Sea tide is just the tail; SCS is the dog. Note you have no phase progression across SCS. Could it be too deep?

[stef]

You integrate for 5 days

Code: Select all

2400 ntimes Number of timesteps for 3-D equations.
180.000 dt Timestep size (s) for 3-D equations.

I would check if the cotide/corange plots are sensitive to the integration period. Depending on how many constituents you are solving for in the LSQR routine, 5 days may be too little.

[hezhiwei]

I suggest you focus on the South China Sea. Fix that and the Sulu Sea might be OK. Sulu Sea tide is just the tail; SCS is the dog. Note you have no phase progression across SCS. Could it be too deep?

Dear johnluick, thanks for your kindly suggestion, that might be the reason, I'll have a try.

You integrate for 5 days, I would check if the cotide/corange plots are sensitive to the integration period. Depending on how many constituents you are solving for in the LSQR routine, 5 days may be too little.

Dear stef, I'm very sorry I didn't make it clear. The hamonic analysis was done using the model output of a 90-day run, and the first 15 days were excluded. When I found the problem, I made some short runs to see how the tidal waves propogate with different model configuration, and this is the log of last 5-day run, which was not used for hamonic analysis. Thank you for your kindly reply, you must have checked my model configuration very carefully.

[jzavala]

I think you should review the straits that communicate with the Sulu Sea. At 1/12 resolution and rx0 max of 0.2 I suspect you are strongly reducing the sectional area of the straits (and hence the tidal transports). The DT you are using suggests to me that you have an extremely smooth bathymetry.
And the problem might not be just at the Sulu Sea, it is just more obvious there, but I can see you also have problems in the South China Sea and the Banda Sea. BTW, it makes more sense to compare your solution with your forcing file from TPXO 7.2, the tidal solution from Castruccio et. al (2013) has some errors too. I suggest that you relax rx0 to say a max value of 0.4 (but you might have to decrease DT) in order to better resolve the straits, and you might need to do some hand editing of your bathymetry, focusing of preserving the sectional area at the main straits.

Good luck!
Javier

[hezhiwei]

I think you should review the straits that communicate with the Sulu Sea. At 1/12 resolution and rx0 max of 0.2 I suspect you are strongly reducing the sectional area of the straits (and hence the tidal transports). The DT you are using suggests to me that you have an extremely smooth bathymetry.
And the problem might not be just at the Sulu Sea, it is just more obvious there, but I can see you also have problems in the South China Sea and the Banda Sea. BTW, it makes more sense to compare your solution with your forcing file from TPXO 7.2, the tidal solution from Castruccio et. al (2013) has some errors too. I suggest that you relax rx0 to say a max value of 0.4 (but you might have to decrease DT) in order to better resolve the straits, and you might need to do some hand editing of your bathymetry, focusing of preserving the sectional area at the main straits.

Dear Javier, that's very nice suggestion. I'll have a try. Thank you very much.

Now I realize that in the Indonesian Sea, it is very hard to have a good simulation of both tides and mean flow. Because we need to spin up the model for a long time to simulate the mean flow well, reducing the time step will greatly increase the computational costs. Anyway, according to your suggestion, now I know how to improve it, the bathymetry may be the main problem.