1. Introduction
It is well known that oceanic vertical mixing plays a prominent role in regulating the sea surface temperature (SST), a critical oceanic parameter in controlling the exchanges of energy and momentum between the ocean and atmosphere. Climate models with an aim to represent realistic ocean dynamics have to properly describe the vertical-mixing processes. The vertical mixing, because of the small-scale turbulent processes involved, usually cannot be explicitly resolved in ocean general circulation models (OGCMs) and has to be parameterized.
The conventional parameterization of the vertical mixing is to use an eddy diffusion model (the so-called K theory), which assumes a local relationship between eddy fluxes and model prognostic variables. The simplest example is to use a constant mixing coefficient everywhere (Bryan and Lewis 1979; Sarmiento and Bryan 1982). Although the constant mixing coefficient can be optimized for some specific regions, its application to models of basin to global scales is often problematic. One alternative is to relate the mixing coefficients to the local Richardson number (Ri) based on stability theory (Robinson 1966). The Ri number–dependent mixing scheme was demonstrated to have a reasonable skill in simulating the tropical circulation in three-dimensional OGCMs (Pacanowski and Philander 1981, hereafter as PP; Philander et al. 1987). Simulations with the PP scheme provide a good representation of the shear instability process in the tropical oceans. Therefore, they are significantly better in the Tropics than those with constant mixing coefficients. However, the PP scheme is still deficient in simulating several important aspects of the tropical circulation (Stockdale et al. 1993; Niiler et al. 1995). Comparison with turbulence measurements has shown that the PP scheme underestimates the turbulent mixing at low Ri, while overestimating the turbulence mixing at high Ri (Peters et al. 1988). As a result, the thermocline simulated by the PP scheme is much too diffused as compared to observations. The surface current simulated by the PP scheme is too strong, while the equatorial undercurrent is too shallow due to insufficient momentum penetration in the surface boundary layer (Niiler et al. 1995; Halpern et al. 1995). Furthermore, the performance of the PP scheme in the extratropics is rather poor (Stammer et al. 1996) due to the lack of explicit specification of other turbulence mixing processes (e.g., wind stirring and convective overturning).
One alternative is to use higher-order turbulence closure schemes; for example, the second-order closure scheme of level-1.5 (Blanke and Delecluse 1993), level-2.5 (Mellor and Yamada 1982; Rosati and Miyakoda 1988), or a modified second-order closure mixed layer scheme (Kantha and Clayson 1994). However, most of these higher-order closure schemes require high vertical resolution and/or high-frequency forcings and are, therefore, computationally costly for climate studies. These turbulence closure schemes attempt to parameterize small-scale motions with local prognostic variables in the model such as turbulence length scales, which are small in comparison to the boundary layer. Gnanadesikan and Weller (1995) and McWilliams et al. (1997) have argued that such schemes are unstable to large eddies, such as those in the Langmuir circulation. Meanwhile, the lack of explicit nonlocal turbulence transport in these turbulence closure schemes strongly limits their representation of the subgrid-scale mixing processes due to the difficulty in reproducing the entrainment flux at the bottom of the boundary layer (Ayotte et al. 1996).
Another alternative is to employ a vertically homogeneous mixed layer model (e.g., Kraus and Turner 1967; Garwood 1977) to simulate the near-surface processes. Using a layered model, Chen et al. (1994) recently developed a hybrid scheme by combining a homogeneous mixed layer model with Price’s (Price et al. 1986) dynamical instability model. However, the coupling of such a bulk mixed layer model to a discrete level model is far from straightforward (Haidvogel and Beckmann 1999).
Recently a nonlocal vertical-mixing scheme called K-Profile Parameterization (KPP) has been proposed (Large et al. 1994). The KPP scheme does not assume a priori that the boundary layer is well mixed and explicitly predicts an ocean boundary layer depth. Within this boundary layer, the turbulent mixing is parameterized using a nonlocal bulk Richardson number and the similarity theory of turbulence. Below the boundary layer, the vertical mixing is parameterized through the local gradient Richardson number and a background mixing similar to the PP scheme.
The KPP formulation and its performance in one-dimensional models have been described in Large et al. (1994) and Large and Gent (1999). The annual-mean climatology from a three-dimensional coarse-resolution global ocean model with the KPP scheme can be found in Large et al. (1997), where numerical experiments are designed for comparsion with a baseline experiment with constant vertical-mixing coefficients.
What is the performance of the KPP scheme in a higher-resolution ocean general circulation model? Besides the annual-mean climatology, what kind of systematic impact does the KPP scheme have on simulating the important annual cycle and interannual-to-interdecadal variability? How significant are those improvements of the KPP scheme, if any, in simulating the thermal and current structures when compared with those conventional schemes? This paper describes the performance of the KPP scheme in simulating the three-dimensional thermal and current structures in a Pacific OGCM with enhanced resolutions in the Tropics. Systematic comparisons are made between the KPP and PP schemes in terms of the annual-mean climatology, annual cycle, and interannual-to-interdecadal variability. The description of the ocean model and model experiments is given in section 2. In section 3, both mixing schemes are described briefly. In section 4, the comparisons between the simulations and available observations are made. Finally, discussion and summary are presented in section 5.
2. Model description and experiment design
a. The model
The numerical model used in this study is based upon the National Center for Atmospheric Research’s (NCAR) Climate System Modeling (CSM) Ocean Model (NCOM; Gent et al. 1998) that evolved from the version 1.0 of the Modular Ocean Model (Pacanowski et al. 1991) developed at the Geophysical Fluid Dynamical Laboratory. Among several new features implemented in NCOM, we want to emphasize the eddy-induced isopycnal transport parameterization (Gent and McWilliams 1990, hereinafter GM) and the KPP vertical-mixing scheme that will be explained in detail in section 3. The governing equations are the primitive equations in spherical coordinates, with hydrostatic, Boussinesq, and rigid-lid approximations (Bryan 1969;Cox 1984). The model domain covers the Pacific basin from 45°S to 65°N in latitude and from 100°E and 70°W in longitude. The longitudinal resolution is 2° uniformly. The latitudinal resolution is 0.5° within 10°S and 10°N and gradually increases poleward to 2° at and beyond 20°S and 20°N. There are 25 levels throughout the water column, with 5 uniform levels in the upper 50 m and 10 additional levels between 50 and 277 m (see Table 1). Because of the use of the GM parameterization, the horizontal diffusivity is set to zero and a relatively small value of 5 × 105 cm2 s−1 is used for horizontal viscosity, isopycnal diffusivity, and thickness diffusivity. The vertical-mixing terms are treated implicitly. The time step is 1 h.
b. Surface forcing
c. Experiment design
The annual-mean climatological temperature and salinity distributions of Levitus et al. (1994) and Levitus and Boyer (1994) are used for model initial conditions. The model ocean was spun up for 30 yr from rest using the COADS monthly mean climatological wind stress, heat, and freshwater fluxes (da Silva et al. 1994). The shortwave radiation is allowed to penetrate below the model ocean surface, leading to subsurface bulk heating using the formula of Paulson and Simpson (1977). For this spinup experiment, as in Barnier et al. (1995), the model heat flux has two components: a prescribed COADS net flux and a correction term proportional to the difference between the COADS climatological SST and the model SST. The correction coefficient is computed based on air–sea variables and is a function of space and time. The COADS monthly mean climatological evaporation and precipitation rates are used to calculate the model freshwater flux. In order to compensate errors in the freshwater flux, the surface salinity is restored toward the Levitus monthly mean climatology with a restoring timescale of 30 days. After 30 yr of model integration, the upper ocean reaches a quasi-equilibrium state. Then, the monthly mean COADS wind stress from January 1945 to December 1993 is used to force the model ocean. Two 49-yr (1945–93) solutions have been obtained. The two simulations differ from each other only by the vertical-mixing schemes: that is, PP versus KPP, which is explained in the following section.
3. The vertical-mixing schemes
a. The Pacanowski and Philander (PP) scheme
b. The K-Profile Parameterization (KPP) scheme
The nonlocal transport term γx in Eq. (15) represents the nonlocal impact of the large-scale turbulence mixing and is nonzero only in the boundary layer for tracers under unstable forcing for our present simulations. The detailed description of γx can be found in appendix C. Below the boundary layer h, the vertical mixing is parameterized through the local gradient Richardson number and a background mixing coefficient similar as in the PP scheme. Several model sensitivity experiments have been conducted using different KPP parameters. The major results from these sensitivity experiments are summarized in appendix D.
4. Results
In order to distinguish the difference between the KPP and PP simulations, a detailed comparison is made in this section by separating the simulated 49-yr time series into the annual mean state, annual cycle, and interannual-to-interdecadal variability. All the mean states are calculated within the period from 1961 to 1990 unless specifically mentioned otherwise.
a. The mean state
1) Tropics
The coefficients of vertical eddy viscosity Km and eddy diffusivity Kt vary considerably in the global oceans. They usually have large values in the surface mixed layer, but have very small values below the thermocline. Figure 1 shows the vertical profile of the mean Km simulated by both PP (dash) and KPP (solid) schemes at 165°E, 140°W, and 110°W on the equator. As a remarkable difference in the surface of 50–100 m, Km from the KPP scheme is much larger than Km from the PP scheme. For the KPP scheme, as observed by Crawford and Osborn (1979), Km varies from 10 to 100 cm2 s−1 in the top 50-m water column in both the central and eastern equatorial Pacific Ocean. In the western warm pool region, Km can be even larger, with a value of 250 cm2 s−1 at the surface. As expected, the simulated value of Km in and below the thermocline is substantially smaller.
Figure 2 shows the vertical distribution of simulated mean zonal velocity on the equator for comparison with the mean Tropical Atmosphere Ocean (TAO) array observation (Yu and McPhaden 1999) at 165°E, 140°W, and 110°W, respectively. Note that the Equatorial Undercurrent (EUC) at 140°W in the KPP solution is much deeper and the depth of the maximum EUC is about 20 m closer to the observation than that in the PP solution. This can be explained as follows: a larger vertical eddy viscosity is parameterized in the KPP scheme and, therefore, more surface kinetic energy can penetrate into the deeper ocean interior across the sharp thermocline through the resolved surface boundary layer. The improvement in the western equatorial Pacific is also evident, even though the Indonesian passages have been closed in the model. At 110°W, the amplitude of the EUC simulated by both schemes is weaker than observations, probably due to the coarse vertical resolution in the thermocline out-cropped region.
In addition to the improvement in simulating the mean tropical current structure, the KPP scheme also produces more realistic thermal structure than the PP scheme. Figure 3 shows the annual-mean temperature along the equator and the differences between the two simulations and the Levitus climatology (Levitus and Boyer 1994). Although both solutions are colder than the Levitus annual-mean climatology, the KPP solution has a stronger vertical temperature gradient than the PP solution, and agrees more with observations. Figure 4 shows the annual-mean SST and the differences between the simulations from both the KPP and PP schemes and the Levitus climatology. When the PP scheme is used, the simulated temperature in the eastern equatorial Pacific Ocean can be more than two degrees colder than the observed (Fig. 4e). This cold bias as described in Stockdale et al. (1993) and Niiler et al. (1995) in the eastern equatorial Pacific is significantly reduced to less than one degree when the KPP scheme is used (Fig. 4d).
2) Extratropics
b. The annual cycle
In addition to the mean state, the difference of Km also results in a different annual cycle of both current and thermal structures.
1) Current
Figure 7 shows the vertical distribution of mean annual cycle of equatorial zonal currents taken at 140° and 110°W during 1980–91 from both observation (Yu and Schopf 1997) and the twin 49-yr (1945–93) simulations. In general, both the phase and amplitude are comparable in both KPP and PP schemes. However, the depth of the maximum current amplitude in spring from the KPP scheme is closer to the TAO observation than the PP scheme. In the extratropical region, the current structure also exhibits strong seasonal variability as shown in Fig. 6d. In winter (January–March) when the wind is strongest, the zonal component of modeled Ekman Current can reach 4 cm s−1, while it is only about 1 cm s−1 in summer (July–September).
2) Temperature
Figure 8 shows the vertical distribution of zonally averaged mean seasonal temperature anomalies in the whole Pacific basin for March and September. The seasonal temperature anomalies were calculated from the mean seasonal cycle of the last 5 yr of the 30-yr spinup model integration. It can be seen that in the PP solution the mean seasonal temperature anomalies are mostly trapped near the surface. In contrast, in the KPP solution, the mean seasonal temperature anomalies are more realistically distributed in the upper-ocean water column. A layer of 30–50 m deep with a uniform temperature can be found in the subtropics in both hemispheres. The improvement is significant, although it is still shallower in the KPP solution than in the Levitus climatology. It requires more extensive studies to ascertain to what extent the KPP scheme can be further improved, by adjusting the KPP parameters, using alternative surface forcing or interplaying the interaction between the KPP and GM schemes.
Figure 9 shows the zonally averaged mean seasonal temperature anomalies in the midlatitude (40°N) as a function of depth and month from the Levitus climatology and the differences between the two simulations and the Levitus climatology. For the KPP simulation, the difference is less than 1 degree most of the time except for the summer transition period when the monthly variation has the largest value (Fig. 9d). For the PP simulation, the seasonality is overestimated in the thin surface layer (about 20 m) while underestimated in the interior and sandwiched in between with a thin layer of strong gradient, which is obviously unrealistic (Fig. 9e).
Inaccurate simulations of sea surface temperature due to improper mixed layer physics can lead to wrong sensible and latent heat fluxes that will subsequently affect the upper-ocean heat storage. Figure 10 shows the seasonal anomalies of the heat storage (defined as the vertically averaged temperature in the upper 300 m) against the sea surface temperature averaged in the central North Pacific (30°–40°N, 160°E–160°W). It is interesting to note that the KPP solution is significantly better than the PP solution when compared with the Levitus climatology. The PP scheme underestimates the seasonal change of heat storage while overestimating the seasonal change of SST in this midlatitude ocean region, which is consistent with a recent study of Stammer et al. (1996). In particular, the March temperature in the PP solution is 2 degrees colder than the Levitus observation, while the September temperature is over 1 degree warmer. The KPP scheme has resulted in a much larger heat storage capacity in the upper ocean than the PP scheme.
3) Boundary layer depth (h)
Based on the turbulence similarity theory, the surface buoyancy and momentum fluxes should be able to penetrate into a depth where they first become stable relative to the local buoyancy and velocity. In the KPP formulation, this boundary layer depth (h) is determined explicitly by calculating the bulk Richardson number relative to the surface according to Eq. (18). Figure 11 shows the monthly mean distribution of h for March. The distribution of h is strongly inhomogeneous, ranging from 10 to more than 100 m. In the central tropical Pacific Ocean, h can change in the range of 30 < h < 100 m. There is a distinct seasonal cycle for h, mainly due to the seasonal cycle of surface fluxes of buoyancy and momentum. In the Northern Hemisphere spring, h in the Northern Hemisphere is much deeper than that in the Southern Hemisphere. Especially in the Kuroshio Current and its extension region and the central tropical Pacific region, the value of h can be as high as 100 m, implying that the surface momentum and buoyancy fluxes can penetrate as deep as 100 m before they reach stable condition.
For comparison, the distribution of the mixed layer depth (MLD) is also shown in Fig. 11. Following Levitus et al. (1994) and Levitus and Boyer (1994), the MLD is defined as the depth where the density (σt) first exceeds its surface value by 0.125 kg m−3. The MLD depends on the integrated performance of wind and also depends on the stability of the underlying water and on the heat and freshwater balance through the surface. To understand the time-dependent process of mixed layer dynamics is still an active area of research (e.g., Lukas and Lindstrom 1991; Large et al. 1994; Kantha and Clayson 1994). Overall, the distribution pattern of h is similar to that of MLD although MLD is generally deeper than h, mostly due to the Ekman pumping, which is a nonlocal process. This is particularly true in the Kuroshio Current and its extension region and in the central Northeast Pacific region.
The seasonal cycle of h is primarily determined by the seasonal cycle of the surface fluxes, including both wind stirring and radiation fluxes. Figure 12 shows the monthly mean value of the zonally averaged bulk Richardson number around the date line for March and September. The monthly mean values
c. Interannual-to-interdecadal variability
While the tropical interannual variability associated with ENSO in the Pacific Ocean can be simulated reasonably well by the PP scheme (Philander et al. 1987;Chao and Philander 1993), the extratropical interannual-to-interdecadal variability has not been well simulated with an OGCM (Stammer et al. 1996). A number of recent studies have reported the pronounced interannual-to-interdecadal variability in the extratropical Pacifc Ocean (for recent reviews, see Mantua et al. 1997 and Nakamura et al. 1997). Although the cause of this variability is still a matter of debate, the spatial pattern of the decadal-to-interdecadal variability in the ocean has proven to be strongly three-dimensional by analyzing both SST and subsurface ocean thermal data (Zhang and Levitus 1997). In particular, Deser et al. (1996) presented a detailed analysis of the vertical structure of seasonal thermal anomalies in the upper North Pacific Ocean during 1970–91, emphasizing the role of local interactions between the surface mixed layer and the thermocline in producing subsurface thermal anomalies.
Figure 14 shows the time–depth structures of the seasonal temperature anomalies in the Kuroshio extension region as observed by Deser et al. (1996) and simulated by both the KPP and the PP experiments. Same as Deser et al. (1996), the seasonal temperature anomalies were calculated by removing the monthly mean climatology from 1970 to 1991. The residuals were then averaged seasonally within the Kuroshio extension region (34°–42°N, 140°–180°E). It is interesting to note that the KPP scheme realistically simulates those interannual temperature anomalies with comparable amplitudes and similar phases. As observed, the surface-initiated interannual anomalies occurs nearly simultaneously within the upper 400 m and shows very little attenuation with depth. The −0.6°C contour line can reach as deep as 400 m. In contrast, the PP scheme only generates the near-surface interannual anomalies. The vertical penetration of these interannual temperature anomalies simulated by PP is significantly shallower than KPP and observations.
5. Discussions and summary
In this paper we have studied the impact of two different vertical-mixing schemes on the solution of a Pacific OGCM. In the conventional PP scheme, the vertical eddy viscosity and diffusivity are determined based on local vertical gradients of density and velocity. In contrast, the KPP scheme includes nonlocal processes and determines the vertical profiles of eddy viscosity and diffusivity based on a diagnosed boundary layer depth and a turbulent velocity scale. The boundary layer depth is determined through the requirement that surface momentum and buoyancy fluxes should penetrate to a depth where they become stable relative to the local velocity and buoyancy. The turbulent velocity scale is a function of surface wind forcing, buoyancy forcing, and the boundary layer depth. It also incorporates a smooth transition to the parameterization of interior vertical mixing.
The PP and KPP schemes have been compared using two 49-yr (1945–93) simulation experiments forced by monthly mean wind stresses and heat fluxes derived from COADS. The comparison is made in both tropical and extratropical regions for the annual-mean state, annual cycle, and interannual-to-interdecadal variability. Overall, the KPP scheme has produced more realistic simulations of the upper-ocean thermal structures. In the Tropics, the KPP vertical-mixing scheme produces more realistic thermal structures than the PP scheme. For example, the cold bias in the eastern equatorial Pacific has been significantly reduced when KPP is used. In the extratropics, the KPP scheme is significantly better in simulating the temperature anomalies and the upper-ocean heat storage when compared with observations.
Both the mean state and the seasonal cycle of current structures have also been analyzed. It is found that the core of Equatorial Undercurrent in the KPP solution has comparable amplitude but about 20 m deeper than in the PP solution and closer to TAO observations. In the midlatitude, the Ekman spiral depth in the KPP solution is about 20–30 m deep by investigating the current structures in the central North Pacific Ocean region. For the PP solution, the Ekman layer either is too shallow or almost does not exist. The improvement in both the Tropics and the extratropics by KPP can be understood by more realistic vertical profiles of vertical eddy viscosity and diffusivity.
In summary, the KPP scheme works better than the PP scheme in both the Tropics and the extratropics. The PP scheme appears to be applicable only in the Tropics where the shear-dependent instability dominates in the turbulent mixing. In comparison to the high-order turbulence closure schemes, the advantage of the KPP scheme is its relative insensitivity to vertical resolution. Given the correct surface forcing and advective transports, it will properly distribute properties in the vertical according to the empirical functions determined from measurements. From a computational point of view, the addition of the KPP scheme increases only about 10% of the computing time. It is therefore more efficient than high-order turbulence closure schemes, which requires 50% or more computational time (Rosati and Miyakoda 1988).
Although the KPP scheme has made significant improvement in simulating the vertical distrubution of thermal and kinetic energy, there is still room for improvement. It is expected that the KPP solutions can be further improved by adjusting the KPP interior mixing parameters (W. G. Large 1999, personal communication). One of the future studies with the nonlocal KPP scheme should focus on using synoptic forcing (with a high-frequency component, such as diurnal cycle) to drive the ocean boundary layer. In this case, the turbulence will be developed fully inside the boundary layer and the physics of turbulence similarity theory might be more effective in explaining the real situation. The sensitivity of the KPP scheme to salinity and freshwater flux and its potential impact on simulating the low-frequency thermal variability also require further investigation.
The research described in this paper was carried out, in part, by the Jet Propulsion Laboratory (JPL), California Institute of Technology, under contract with National Aeronautics and Space Administration. Support from the JPL Director’s Research and Development Fund is acknowledged. We’d like to thank Dr. Clara Deser and Michael S. Timlin for providing us the XBTs data used in Fig. 14, the TAO project office and Margie McCarty at NOAA PMEL for providing the observed current data used in Fig. 7, and Arlindo M. da Silva at Goddard Space Flight Center for providing the COADS data. Computations were performed on the Cray J90 through the JPL Supercomputing Project.
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APPENDIX A
The Turbulent Velocity Scales in the Nonlocal KPP Scheme
The turbulent velocity scale of Eq. (17) depends primarily on the relative height d/h (h is the OBL depth) and the stability within the OBL (Högström 1988; Holtslag and Boville 1993; Large et al. 1994). Here, stability is defined with respect to the surface active heat flux
APPENDIX B
Turbulent Velocity Shear
APPENDIX C
Nonlocal Transport Term γx
APPENDIX D
Model Sensitivity Experiments to KPP Parameters
Before conducting our 45-yr OGCM simulation, we have conducted several sensitivity experiments forced with climatological air–sea fluxes with regard to various KPP parameters. We have compared our simulated annual-mean zonal current amplitude at 140°W on the equator against the observed value from TAO observations (100 cm2 s−1).
Table D1 shows the sensitivity of model-simulated EUC amplitude with various values of critical Richardson number (Ric) used in the KPP formulation. The boundary layer depth (h) is determined at a depth where the bulk Richardson number (Rib), as defined in the Eq. (18), equals to the critical Richardson number (Ric). Based on these sensitivity experiments, we have selected a critical Richardson number of 0.3 in the present study that yields the best agreement with the available observations.
Table D2 shows the model sensitivity to the background viscosity νb and diffusivity κb used in Eqs. (13) and (14), respectively. Clearly, the amplitude of the EUC is sensitive to the background viscosity and diffusivity being used. The original NCOM formulation, with the background viscosity and diffusivity of 10.0 and 0.3, significantly underestimated the amplitude of the EUC. It is interesting to note that there is very little sensitivity when the background viscosity/diffusivity goes below 1.0/0.1, which is the value used in our final calculation.
The mean vertical profiles of Km calculated from Eq. (13) in PP (dotted line) and Eq. (17) in KPP schemes (solid line) on the equator at (a) 165°E, (b) 140°W, and (c) 110°W, respectively. Unit is in cm2 s−1
Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1377:ACOTVM>2.0.CO;2
The vertical profiles of long-term mean zonal current from the Tropical Ocean and Global Atmosphere (+), KPP (solid lines), and PP (dotted lines) along the equator at 165°E, 140°W, and 110°W, respectively. Unit is in cm s−1
Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1377:ACOTVM>2.0.CO;2
Annual-mean temperature along the equator from (a) Levitus climatology, (b) KPP simulation, (c) PP simulation, and the difference between Levitus climatology and (d) KPP and (e) PP simulations. Unit is in °C
Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1377:ACOTVM>2.0.CO;2
(Continued)
Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1377:ACOTVM>2.0.CO;2
Annual-mean SST from (a) Levitus climatology, (b) KPP simulation, (c) PP simulation, and the differences between Levitus climatology and (d) KPP and (e) PP simulations. Unit is in °C
Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1377:ACOTVM>2.0.CO;2
(Continued)
Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1377:ACOTVM>2.0.CO;2
The mean vertical profile of Km calculated from Eq. (13) in PP (dotted line) and Eq. (17) in KPP schemes (solid line) in the central North Pacific Ocean region from 176°E to 176°W in long and from 34° to 36°N in lat. Unit is in cm2 s−1
Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1377:ACOTVM>2.0.CO;2
The vertical profiles of the (a) annual-mean total zonal velocity, (b) the annual-mean geostrophic zonal velocity, (c) the annual-mean zonal Ekman velocity, and (d), (e), two different seasonal mean Ekman velocities averaged in the same region as in Fig. 5. The geostrophic velocity is computed by calculating the geopotential anomalies between 34 and 36°N and is relative to level-19 that is between 768- and 1092-m depth. Unit is in cm s−1. Same as in Fig. 4, PP (dotted) and KPP (solid). Note the different vertical scale in (b)
Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1377:ACOTVM>2.0.CO;2
Annual cycles of equatorial zonal currents from TAO observations taken at upper 140° and 110°W and (middle) from KPP and (lower) PP simulations. TAO observation is from Yu and Schopf (1997). Unit is in cm s−1
Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1377:ACOTVM>2.0.CO;2
Zonally averaged temperature anomalies (with annual-mean values removed) (top) as a function of depth and latitude from Levitus climatology, (middle) KPP solution, and (bottom) PP solution for Mar and Sep. Contour interval is 0.5°C
Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1377:ACOTVM>2.0.CO;2
Zonally averaged temperature anomalies as in Fig. 8 at 40°N as a function of time and depth from (a) Levitus climatology, (b) KPP, and (c) (PP). (d) and (e) The differences between the simulations and Levitus climatology are also shown. Contour interval is 0.5°C
Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1377:ACOTVM>2.0.CO;2
Heat content anomalies as a function of sea surface temperature from Levitus climatology (solid line), KPP solution (dashed line), and PP solution (dotted line) averaged over a box region from 160°E to 160°W in long and from 25° to 40°N in lat. The heat content anomaly is integrated up to 277 m and averaged over the box region with a unit of °C m. The numbers (1, 2, . . . , 12) represent the months of Jan, Feb, . . . , Dec
Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1377:ACOTVM>2.0.CO;2
The distribution of monthly mean boundary layer depth h (above) and monthly mean mixed layer depth (below) from the KPP solution in Mar averaged between 1971 and 1990. Contour interval is 20 m. The mixed layer depth is defined as the depth where σt first exceeds its surface value by 0.125 k gm−3. The rectangular box region (below) is defined as the Kuroshio Current Extension (KCE) region used in Fig. 14
Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1377:ACOTVM>2.0.CO;2
Monthly mean bulk Richardson number as a function of depth and latitude for Mar and Sep. The bold solid lines represent monthly mean boundary layer depth and the bold dotted lines represent the monthly mean mixed layer depth
Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1377:ACOTVM>2.0.CO;2
Monthly mean vertical eddy viscosity calculated from KPP scheme and averaged between 1971 and 1990 as a function of depth and latitude for Mar and Sep at the date line. The bold solid lines represent the monthly mean boundary layer depth and the bold dotted lines represent the monthly mean mixed layer depth
Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1377:ACOTVM>2.0.CO;2
Monthly mean temperature anomalies as a function of depth and time from (top) Deser et al. (1996), (middle) KPP simulation, and (bottom) PP simulation. The monthly mean temperature anomalies are calculated by averaging the value in the Kuroshio Current Extension (KCE) region (34°–42°N, 140°–180°E, see Fig. 11). Contour interval is 0.2°C. For Deser et al. (1996) observation data, there is a gap in the mid-1970s
Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1377:ACOTVM>2.0.CO;2
Vertical grid size and depth used in the NCOM
Ekman spiral depth against vertical viscosity (lat 35°N)
Table D1. Sensitivity of zonal velocity amplitude at 140°W on the equator to the critical Richardson number Ric in the NCOM climatology run with KPP
Table D2. Sensitivity of zonal velocity amplitude at 140°W on the equator to the background νb and κb in the NCOM climatology run with KPP
