radiation. Where the atmosphere is in contact with land, the incoming shortwave radiation is absorbed by the land and reemitted as longwave radiation into the atmosphere. For a detailed derivation of heat fluxes between layers we refer to Hogg et al. (2003a,b).
The model is initialised from rest, driven by latitudinally varying solar forcing. The atmospheric stress over the ocean is computed, from which the oceanic mixed layer temperature is derived. Then, the oceanic QGPVs are found and from these the atmospheric mixed layer temperature. Finally the atmospheric QGPVs are stepped and the procedure is repeated for each time step.
For every experiment the Q-GCM is initially run for 20 years, during which the ocean spins up and reaches a steady state. Then, the run is continued for a total of 200 model years.
3.3
Experimental design and basic state solutions
Next, we describe the different parameters and configurations used in this study; modifications of any of these will be clearly stated in the next chapters. While the ocean response will be studied under different parameters, the atmospheric channel component of the model will remain constant throughout the study. The oceanic and atmospheric parameters used in the standard 3-layer basin ocean configuration are listed in Table 3.1. We opted for a relatively coarse resolution in the ocean (∆x=40 km), as we aim to identify large scale coupled ocean atmosphere interactions.
0 5000 10000 0 2000 4000 τx (× 10−5m2/s2) Y (km ) 0 5000 10000 0 2000 4000 τy (× 10−5m2/s2) 5000 10000 2000 4000 SST (K) Y (km ) X (km) 5000 10000 2000 4000
OceanEkmanvelocity (× 10−6W/m2)
X (km)
0 0
Figure 3.2: Average of τx (Contour Interval=20), τy (CI=3), SST (CI=3) and
3.3 Experimental design and basic state solutions 46 0 2000 4000 6000 8000 10000 0 500 1000 1500 2000 2500 3000 3500 4000 4500 ψ1 (SV) X (km) Y (km ) −36 −30 −24 −18 −12 −6 0 4 10 16 22 28 34 40 46
Figure 3.3: Time-averaged ψ1 of a 200 year run.
We explore the response of the model at two different central latitudes, corres- ponding to 300 and 400; for the two cases, our model is barely resolving the first Rossby radius of deformation but not the second one. The basin dimensions are fairly large and, in particular, the ocean is very wide in order to study the zonal propagation of planetary waves under the effect of atmospheric coupling. This has the advantage of using a quasi-channel configuration but retaining the effects of me- ridional boundaries. In fact, Rossby waves are dissipated at the western boundary and any coupled Rossby mode will be affected by this interaction (Goodman and Marshall, 2003). Viscosities are set to their minimum value ensuring stability and no-slip boundary conditions are enforced.
The averaged ocean forcing fields, τ = (τx, τy), and relative Ekman pumping,
woek, are shown in Fig.3.2, together with the oceanic sea surface temperature (SST).
The flow responds to the wind stress in a symmetrical double-gyre solution, a sub- polar and a subtropical gyre, and the gyres shrink moving down towards lower layers.
In Fig.3.3 we show the time-averaged stream function in the first layer. The Q- GCM actually computes the layer pressures and, in geostrophic balance, the oceanic stream functions are estimated from the layer pressures pi via
ψi(x, y, z, t) = hi{pi(x, y, z, t)−pi(xe, y, z, t)}/f0,
where xe is the eastern longitude of the eastern coast.
We also note the presence of a strong boundary current, separating at the centre of the meridional extension of the basin, which will play a major role in damping the incident planetary waves in the model.
3.3 Experimental design and basic state solutions 47 0 2000 4000 6000 8000 10000 0 2000 4000 PV1 (s−1) Y (km) 0 2000 4000 6000 8000 10000 0 2000 4000 PV2 (s−1) Y (km) 0 2000 4000 6000 8000 10000 0 2000 4000 PV3 (s−1) X (km) Y (km) 0 2000 4000 6000 8000 10000 0 2000 4000 ψ1(Sv) 0 2000 4000 6000 8000 10000 0 2000 4000 ψ2(Sv) 0 2000 4000 6000 8000 10000 0 2000 4000 ψ3(Sv) X (km)
Figure 3.4: Snapshots of PV fields (left panels) and stream functions (right panels) for each layer at the end of the run. Bluish colours are for lower values and reddish colours for higher values; contour interval is arbitrary.
The instantaneous PV fields are shown on the left panels of Fig.3.4. In the first layer, where the wind forcing provides a source of PV, a sharp region denotes the separation of the two gyres, while in the inner layers a region of homogenised PV is formed, caused by the intense eddy activity driving an enstrophy cascade. This is clearly visible in the second layer but is shrinking in size in the deeper layers.
Snapshots of the layer stream functions can be found on the right panels of Fig.3.4. They reveal an intense eddy activity, a westward intensification of mesoscale structures in all three layers and the ability of resolving mesoscale eddies.
A 3-layer ocean model is able to better represent baroclinic instability, which is the source of these eddies on the scale of the first Rossby radius, enhancing the turbulent structure even in a coarse resolution simulation.
In order to reproduce the intense eddy activity and the dynamics of long wave- mean flow interaction, one can either increase the ocean resolution or the strati- fication of the layered model (Dewar and Morris, 2000). This will be discussed in Chapter 5, where the Q-GCM will be run with a 20 km resolution 6-layer ocean and the results compared with the standard configuration.
3.3 Experimental design and basic state solutions 48
Parameters Value Description
Ocean
Zi 3 No of layers
∆x 40 [km] Horizontal grid spacing
(X, Y) (11520,4800) [km] Domain size
Hi (300, 1100, 2600) [m] Mean layer thicknesses
Hm 100 [m] Mixed layer thickness
Ti (278, 268, 258) [K] Layer’s potential temperature
gi0 (0.05, 0.025) [m s−2] Reduced gravities
ρo 1×103 [kg m−3] Density
Cpo 4×103 [J(kg K)−1] Specific heat capacity
K2 5.7×102 [m2 s−1] ∇2 diffusion coefficient
K4 8×1010 [m4 s−1] ∇4 diffusion coefficient A4 4×1010 [m4 s−1] ∇4 viscosity coefficient
δek 2 [m] Bottom Ekman layer
f0 7.292×10−5 [s−1] Coriolis parameter,φ=30o β 1.982×10−11 [(m s)−1] df/dy (30o) ai (53.1, 35.6) [km] Rossby radii (30o) f0 9.374×10−5 [s−1] Coriolis parameter,φ=40o β 1.753×10−11 [(m s)−1] df/dy (40o) ai (41.3, 27.9) [km] Rossby radii (40o) Atmosphere Zi 3 No of layers
∆x 120 [km] Horizontal grid spacing
(X, Y) (15360,7680) [km] Domain size
Hi (2000, 3000, 4000) [m] Mean layer thicknesses
Hm 100 [m] Minimum mixed layer thickness
Ti (330, 340, 350) [K] Layer’s potential temperature
gi0 (1.2, 0.4) [m s−2] Reduced gravities
ρa 1 [kg m−3] Density
Cpa 1×103 [J(kg K)−1] Specific heat capacity
K2 2.7×104 [m2 s−1] ∇2 diffusion coefficient
K4 3×1014[m4 s−1] ∇4 diffusion coefficient A4 2×1014 [m4 s−1] ∇4, viscosity coefficient
λ 35 [W m−2 K−1] Sensible and latent heat flux coefficient
ai (496, 259) [km] Rossby radii
Table 3.1: List of the standard oceanic and atmospheric parameters of the Q-GCM used in this study.
Chapter 4
Coupled Rossby waves in the
Q-GCM
Rossby wave propagation is investigated in the framework of an idealised middle- latitude coupled ocean-atmosphere model. Rossby waves are observed to be unstable according to a latitude-dependent instability process but also show resistance to this mechanism. A clear coupled Rossby wave mode is identified between a baroclinic oceanic Rossby wave and an equivalent barotropic atmospheric wave. The spatial phase relationship of the coupled wave is similar to the one predicted by Goodman and Marshall (1999) suggesting a positive ocean-atmosphere feedback. It is argued in this chapter that Rossby waves can be efficiently coupled to the overlying atmo- sphere allowing the waves to partially maintain themselves against dissipation and instability mechanisms so that the waves travel longer distances than those predicted by the unforced problem considered in LaCasce and Pedlosky (2004). Furthermore, evidence for a coupling speed-up is found and comparisons with previous theoretical and observational studies are given.