1. Introduction
Ocean mixed layer models play an important role in simulated air–sea interactions and are required to explain upper-ocean characteristics (e.g., Martin 1985; Sterl and Kattenberg 1994; Schopf and Loughe 1995). The major difficulty in parameterizing the ocean mixed layer is that the ocean boundary layer is not as fully observed as the atmospheric boundary layer (e.g., Smith et al. 1996). Thus, specific attention must be given to the atmospheric forcing that drives the upper ocean.
Sensible and latent heat fluxes, longwave and shortwave radiation, wind stress, and ocean surface temperature constitute the principal means for coupling between the atmosphere and ocean. Among these variables, the vertical distribution of shortwave radiation within the ocean is significant for upper-ocean studies because radiation can penetrate below the mixed layer and destabilize the stratification (e.g., Austin and Petzold 1986; Morel and Antonie 1994; Morel and Maritonera 2001), thereby affecting SST during upwelling/downwelling events (Nakamoto et al. 2000). Knowledge of the shortwave radiation within the ocean is particularly critical for understanding dynamical and thermodynamical processes occurring in the ocean surface mixed layer. For example, the amount of solar irradiance affects sea surface temperature (SST) and ocean surface mixed layer depth (MLD) by changing the surface energy budget of the water (e.g., Gallimore and Houghton 1987; Lewis et al. 1990), and it controls the rates of photosynthetic processes (e.g., Frouin et al. 1989; Brock and McClain 1992; Brock et al. 1993). We note here that unlike the atmospheric boundary layer, which is nearly transparent, the ocean boundary layer strongly absorbs solar radiation. Thus, changes in upper-ocean characteristics are closely tied to variations in solar radiation within the ocean and its attenuation within the water column, which need to be taken into account in numerical ocean modeling studies. Radiation attenuation might also be significant for long-term climate variability if the attenuation depth scale is greater than the MLD. For example, a fraction of the solar radiation heating might be absorbed below the thermocline during the onset of an El Niño event (e.g., Woods 1994). This heating may not be redistributed easily by the mixed layer and could be significant on interannual time scales.
Bulk mixed layer models (e.g., Garwood 1977; Niller and Kraus 1977; Price et al. 1986) and diffusion-based mixed layer models (e.g., Mellor and Yamada 1982) have different responses to solar heating as reviewed by Kantha and Clayson (1994). The sensitivity to the distribution of the solar radiation (Simpson and Dickey 1981; Dickey 1983; Le Treut et al. 1985) is primarily because vertical stratification plays a controlling role in the vertical turbulent mixing. As was shown in Simonot and Le Treut (1986), part of the solar radiation can be absorbed below the MLD at low latitudes. Therefore, the modification of the water optical properties can change the density field of the ocean and the dynamical response of the oceanic layers to surface wind stress forcing (e.g., Kara et al. 2000a). High turbidity also raises the temperature in a shallow mixed layer, thus changing the SST and stratification. This implies that a good representation of optical properties of seawater is necessary for accurate modeling of SST and MLD. The importance of solar extinction in the upper ocean in relation to the diurnal cycle was discussed using a mixed layer model based on second-moment closure of turbulence (Kantha and Clayson 1994). They explained that the rise in SST for a very shallow MLD is highly sensitive to the parameterization of the solar extinction that includes different Jerlov (1976, 1977) water types. When using a clear water type instead of a variable water type in their simulations, the diurnal cycle of SST essentially disappeared. Other studies (e.g., Woods et al. 1984; Lewis et al. 1990) have also discussed the effects of optical water types on the ocean surface mixed layer. They indicated the need to consider the penetration of solar irradiance in developing simulations of tropical Pacific SST.
The sensitivity of SST and MLD evolution to solar transmission in large-scale ocean general circulation model (OGCM) studies has also been investigated. For example, Schneider and Zhu (1998) showed with a coupled atmosphere–ocean GCM that inclusion of sunlight penetration was essential to correctly simulate the strong semiannual SST cycle in the eastern equatorial Pacific. This was achieved using a constant penetration depth of 15 m and did not use any satellite-based ocean color data to account for water turbidity. Murtugudde et al. (2002) illustrated the importance of a realistic treatment of penetrating radiation in climate models by using spatially varying annual-mean attenuation depths that were estimated from remotely sensed chlorophyll concentrations provided by the Coastal Zone Color Scanner (CZCS). While their OGCM study was limited to the Tropics because of the available coverage of CZCS, the study did show significant improvement in model SST simulations when using annual-mean attenuation depths versus a constant value of 17 m. The study by Nakamoto et al. (2001) examined the effects of including space- and time-varying solar attenuation with depth by using monthly CZCS chlorophyll concentrations where available over the World Ocean. Their analysis of the model simulations focused on the equatorial Pacific. Ohlmann et al. (1996) used monthly CZCS data with a fully spectral radiation model to show that solar radiation penetration can be a significant term in the mixed layer heat budget for the tropical regions. Rochford et al. (2001) constructed a global monthly mean climatology for the attenuation of photosynthetically available radiation (PAR), denoted as kPAR, using a diffusive attenuation coefficient at 490 nm (k490). They showed that the inclusion of solar subsurface heating is important for improving the global OGCM simulation of SST in the equatorial regions, while subsurface heating is not important for MLD simulations. Although these studies indicate the importance of including a penetrating radiation scheme to improve model SST and MLD simulations, none examined the effects of water turbidity on SST and MLD simulations on short time scales (e.g., daily).
The main goal of this paper is to indicate the regions where water turbidity variability can affect SST and MLD simulations over the global ocean on daily time scales. For this purpose we examine daily SST and MLD sensitivity to subsurface heating using interannual simulations from the Naval Research Laboratory (NRL) Layered Ocean Model (NLOM) with an embedded mixed layer. All model simulations presented in this paper use atmospheric forcing with high temporal (6 hourly) resolution. Model–data comparisons are performed using daily moored buoy observations.
This paper is organized as follows. In section 2, a brief description is given of the NLOM mixed layer implementation, surface forcing, turbulence model, and model parameterizations. In section 3, the effects of ocean turbidity on the model simulations are explained by comparing the daily model SST time series with daily buoy SST time series over the different regions of the global ocean. Some comparisons are also made between the findings obtained from NLOM and the findings of similar studies that used different OGCMs. A summary and conclusions of this paper are presented in section 4.
2. Mixed layer model description
The numerical ocean model used is a primitive equation layered formulation in which the equations have been vertically integrated through each layer. The NLOM is a descendent of the model by Hurlburt and Thompson (1980) with enhancements by Wallcraft (1991), Wallcraft and Moore (1997), and Moore and Wallcraft (1998). It can be run in reduced-gravity mode, in which the lowest layer is infinitely deep and at rest, or in finite-depth mode, which allows realistic bottom topography. In addition, NLOM can be run in hydrodynamic mode (spatially and temporally constant density within each layer; e.g., Hurlburt et al. 1996) or in thermodynamic mode (spatially and temporally varying density within each layer—i.e., density is a prognostic variable; e.g., Metzger and Hurlburt 2001). The model boundary conditions are kinematic and no slip. Prognostic variables are layer density, layer thickness, and layer volume transport. The model includes entrainment (detrainment) processes by allowing the exchange of mass, momentum, and heat between the layers.
The model domain used for this study covers the global ocean from 72°S to 65°N, gridded to a resolution of 0.5° in latitude and 0.703 125° in longitude. The lateral boundaries follow the 200-m isobath. One of the major advantages of NLOM over other types of OGCMs such as z-level and sigma-coordinate models is its lower computational cost for the same model domain and horizontal resolution. One reason is that we can use lower vertical resolution to realistically represent the ocean circulation. For example, in the (½°) model there are only six dynamical layers plus a semipassive mixed layer in the vertical with layer thickness that varies in both time and space. NLOM is also a single efficient portable and scalable computer code that can run any of the model configurations on a variety of computing platforms (Wallcraft and Moore 1997).
In this paper, we give only a brief description of the embedded mixed layer parameterizations. See Wallcraft et al. (2003) for a full description of the model formulations and the ½° global model used here. See Kara et al. (2000b, 2002a) for the parameterizations used in calculating atmospheric forcing fields.
a. Mixed layer equations
The NLOM has typically been run without an explicit mixed layer, which is equivalent to assuming the mixed layer is always inside the upper layer, but now the model has been extended with an “almost passive” embedded well-mixed surface turbulent boundary layer. A schematic illustration of the global NLOM with an embedded mixed layer is shown in Fig. 1.
In the model simulations, the Laplacian temperature diffusion in Eq. (1) is typically turned off (i.e., KH = 0) because the van Leer monotonic scheme (Lin et al. 1994) used for advection contributes sufficient nonlinear diffusion for stability. This scheme allows NLOM to be run using a very small minimum imposed MLD (e.g., 10 m).
b. Surface energy balance
The net surface heat flux that has been absorbed (or lost) by the upper ocean to depth z, Q(z), is parameterized as the sum of the downward surface solar irradiance (QSOL), upward longwave radiation (QLW), and the downward latent and sensible heat fluxes (QL and QS, respectively). The solar irradiance at the ocean surface ranges in wavelength from about 300 to 2800 nm and is composed of three general regions: the ultraviolet (UV) below 400 nm, the visible at 400–700 nm, and the infrared (IR) above 700 nm. The light available for photosynthesis by photoplankton is the PAR and is defined as the 350–700-nm range of the spectrum (e.g., Liu et al. 1994). It accounts for 43%–50% of the solar irradiance at the sea surface (Rochford et al. 2001).
It is noted that we use Eq. (4) although fully spectral representations are available (e.g., Morel and Maritorena 2001). In general, OGCMs that have few layers near the surface (e.g., Schneider and Zhu 1998), with a minimum MLD, for example, 10 m, use simple solar irradiance approximations, such as single or bimodal exponential parameterizations (Paulson and Simpson 1977; Zaneveld and Spinrad 1980). This is because, for depths greater than 10 m, the penetrative solar flux can be accurately determined by resolving just the 300–745-nm spectral region, which is well represented by a single exponential below 10 m.
As explained in detail in Kara et al. (2003, unpublished manuscript, hereinafter KHR), the attenuation depth for PAR differs depending on water type (Simonot and Le Treut 1986) and is quite variable over the global ocean. The extent to which PAR penetrates into and below the mixed layer has been quantified using remotely sensed satellite color data and used in other OGCM studies (e.g., Schneider and Zhu 1998; Murtugudde et al. 2002; Kara et al. 2003b). To properly include effects of turbidity, the model therefore reads in monthly kPAR fields (KHR) based on Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) data (McClain et al. 1998). Thus, our approach amounts to a one-band versus two-band approach, where the red and near-infrared radiation is completely absorbed within the minimum MLD of 10 m imposed by the NLOM, and the penetrating radiation portion is allowed to have space and time variations.
Latent and sensible heat fluxes at the air–sea interface are calculated using efficient and computationally inexpensive simple bulk formulas that include the effects of dynamic stability (Kara et al. 2002a). The combination of accuracy and ease of computation of this method makes it the one preferred for computing air–sea fluxes in the NLOM. Note that both sensible and latent heat fluxes are calculated using mixed layer temperature (Tm) at the model time step. Radiation flux (shortwave and longwave fluxes) is so dependent on cloudiness that this is taken directly from European Centre for Medium-Range Weather Forecasts (ECMWF) data (ECMWF 1995; Gibson et al. 1997) for use in the model. Basing fluxes on the model SST automatically provides a physically realistic tendency toward the “correct” SST. If the model SST is too high or low, the flux is reduced or increased relative to that from the correct SST. In NLOM, the accuracy of the SST is also enhanced by relaxing the dynamic layer densities below the mixed layer back toward climatology (monthly in layer 1, annually otherwise), in addition to applying the heat flux (Kara et al. 2003b). There is no direct SST relaxation term in the equation, but entrainment at the base of the mixed layer allows the dynamical layer density relaxation to influence SST.
c. Turbulence model
d. Model spinup
The six-layered thermodynamic model without the mixed layer is spun up to statistical energy equilibrium and then continued for 5 years with a mixed layer and climatological forcing. Climatological monthly means of the thermal forcing are obtained from the Comprehensive Ocean–Atmosphere Data Set (COADS) (da Silva et al. 1994). Thermal forcing includes shortwave (incoming solar) plus longwave radiation (QR), air temperature (Ta) at 10 m, and the air mixing ratio (qa) at 10 m. Scalar wind speed (υa) is obtained from the input wind stress, which has 6-hourly variability. All climatological model simulations with a mixed layer are performed using climatological 6-hourly hybrid winds. These consist of monthly Hellerman and Rosenstein (1983) wind stresses (HR) plus ECMWF wind anomalies (Wallcraft et al. 2003). We add a high-frequency component to the climatological forcing because of its impact on the mixed layer and because the model is targeted at simulations forced by high-frequency interannual atmospheric fields from operational weather centers. After reaching statistical energy equilibrium, the climatological model simulation with a mixed layer is extended using interannual surface forcing from 1996 and 1997. In this case, the 6-hourly thermal forcing from ECMWF includes the shortwave plus longwave radiation (QR), air temperature (Ta) at 10 m, and air mixing ratio (qa) at 10 m. None of the model simulations presented in this paper include assimilation of any SST data.
3. Turbidity effects on NLOM simulations
In this section, sensitivity of model results to water turbidity is examined with a particular focus on SST and MLD simulations. The model results are then compared with daily SST and MLD time series obtained from buoys located in different regions of the global ocean.
a. Global turbidity effects
Before analyzing the model results, we first examine where turbidity might be important to the annual mean and seasonal cycle of the mixed layer. Our purpose is to indicate the regions where kPAR variability can affect the SST simulation over the global ocean. The greatest interest is in those situations where subsurface heating can occur below the mixed layer, thereby resulting in a cooler SST than is obtained by assuming complete absorption of solar irradiance within the bulk mixed layer. This is expected to occur in regions of small kPAR values. The reverse situation of large kPAR values is expected to produce complete (or almost complete) absorption of the solar radiation within the mixed layer because a minimum MLD of 10 m is imposed by the NLOM. It is noted that, based on a single exponential approach [100–49.0 exp(−hkPAR)] as shown in Fig. 2, all large kPAR values (i.e., kPAR > 0.20 m−1) are essentially uniform.
Three different kPAR values are considered: 1) a monthly kPAR dataset to account for the seasonal and spatial variation of subsurface heating, 2) a global constant value of kPAR = 0.06 m−1 that is representative of most open-ocean conditions, and 3) an unrealistically large value of kPAR = 99 m−1 to ensure the complete absorption of solar radiation within the mixed layer. Case 2 corresponds to an e-folding penetration depth of hP =
For all three cases the monthly mean radiation absorbed below the mixed layer is calculated using QP exp(−z/hP), with hP [cf. Eq. (5)] defined as a temporally interpolated monthly global field. These calculations use global climatologies of monthly kPAR and monthly optimal MLD based on observations (Kara et al. 2003a). Then, the differences of cases 1 − 2 and cases 1 − 3 are calculated month by month and presented as a percentage relative to the net surface heat flux at the ocean surface Qa. Note here that case 1 − case 2 represents the percentage difference absorbed from using monthly versus kPAR = 0.06 m−1, and case 1 − case 3 is just case 1 because QP is assumed to be zero for case 3. Last, global maps of the annual mean and the maximum value over the 12 months are formed. The reason for using a worst-month approach is the root-mean-square error (rmse) would not be a useful measure of turbidity impact because the error is likely to be near zero whenever the MLD is deep. The annual-mean climatological MLD is as shallow as 10 m in some regions where absorption is greater, such as parts of the equatorial region and the North Pacific (see KHR). This is especially evident in summer months. For example, strong solar heating occurs in conjunction with optical depths on the order of 10–15 m throughout the year in the equatorial Pacific.
The impact of a space- and time-varying kPAR can be most easily determined from the ratio of PAR below the MLD relative to the PAR at the air–sea interface. An examination of the annual mean difference between experiments for this PAR fraction expressed as a percentage (Figs. 3a and 3b) reveals that kPAR has essentially no effect over most of the global ocean (regions displayed as white). This occurs where PAR penetration below the MLD is low because of a relatively deep mixed layer most of the time. The relatively deep annual mean MLD, as shown in KHR, tends to correlate well with Fig. 3a and/or high turbidity, especially in relation to Fig. 3c. Using a monthly kPAR makes a large difference (in at least one month) at high latitudes and in the equatorial ocean (Fig. 3c). The sensitivity to solar attenuation in the Tropics agrees with earlier studies (Murtugudde et al. 2002; Nakamoto et al. 2001; Schneider and Zhu 1998). Note that the absorption anomaly only indicates when solar heating within the mixed layer is significantly affected by turbidity and does not indicate its influence on SST.
Based on the observational results presented above, interannual model simulations that use three different kPAR values are performed to investigate the effects of ocean turbidity for the model SST and MLD simulations in 1996 and 1997 (see Table 1 for a brief explanation of each experiment performed). The model spinup and forcing were already described in section 3. For experiment 1, spatially and monthly varying kPAR values interpolated to the global NLOM grid are used. For experiment 2, the global ocean turbidity is set to a constant, kPAR = 0.06 m−1. In experiment 3, all of the solar radiation is absorbed in the mixed layer by using a very large kPAR value. Differences between experiments 1 and 2 are only expected near the equator and in coastal regions where larger space- and time-varying kPAR values occur (Fig. 3). Differences in SST between these two simulations only occur in regions where a shallow MLD coincides with a monthly varying kPAR that differs substantially from 0.06 m−1.
b. NLOM model–data comparisons
Table 2 statistically compares the daily averaged NLOM SSTs from the three experiments with TAO buoy SSTs in 1997, and Table 3 shows the same for NODC buoy SSTs outside the equatorial region. Overall, the ME values are small between the NLOM and buoy SSTs for all locations. The NLOM is able to capture SST variability well because correlation coefficients are close to R = 1 in most of the cases. Large and positive SS values show that the NLOM is able to simulate SST with skill. This is especially true when turbidity effects (i.e., variable kPAR) are taken into account (expt 1). Using a constant kPAR (expt 2) rather than variable kPAR did not significantly affect the results for the locations used in this study. However, we clearly see that absorption of all solar radiation into the mixed layer (expt 3) simulates the SST less accurately. This is not surprising because this choice can affect SST in two ways: 1) by allowing too much solar radiation to be absorbed in the mixed layer and 2) by influencing the stability of the upper ocean and thus SST.
To further examine the effects of turbidity the observed SSTs from two moorings are compared with those obtained from the three NLOM experiments (Fig. 4): one located in the central equatorial Pacific (0°, 155°W), and the other off the U.S. northwest coast (46°N, 131°W). Recall that experiment 1 is performed using turbidity at each buoy location as represented by the monthly SeaWiFS kPAR values. For the buoy at (0°, 155°W), it is obvious that complete absorption of solar radiation within the mixed layer (expt 3) produces the highest SST from February through April and from October through November. Note that kPAR values at this location are greater than 0.06 m−1 for February–April but not October–November (Fig. 5). Clearly, absorption of all solar radiation (expt 3) in the mixed layer causes a relatively large warm bias between the NLOM SST and buoy SST at this location. A similar warm bias was found in the annual mean SST by Schneider and Zhu (1998) between simulations assuming no solar penetration and a constant attenuation depth for solar penetration. As for (46°N, 131°W), the SST differences between experiment 1 (the standard simulation) and experiment 2 are again small. These results agree with other studies (e.g., Murtugudde et al. 2002) that find larger SST changes occurring at low latitudes. Experiment 3 produces the highest SST, and the difference with respect to experiments 1 and 2 is largest for June–September.
To determine how the differences between the SST simulations may be due to differences in MLD, we used daily averaged subsurface temperature measurements from (0°, 155°W) to determine the daily MLD. Subsurface parameters from the buoys include daily water temperatures at 10 discrete depths between 25 and 500 m. For this buoy they are 25, 50, 75, 100, 125, 150, 200, 250, 300, and 500 m. Subsurface temperature accuracy is about 0.01°–0.05°C for the different sensors used (Freitag et al. 1994). Salinity measurements from the buoys were not available for the location. Thus, an isothermal layer depth (ILD) definition is used with a ΔT value of 0.5°C. The ILD can be summarized in its simplest form as being the depth at the base of an isothermal layer where the temperature has changed by a fixed amount of ΔT = 0.5°C from the temperature at a reference depth of 10 m. A layer depth obtained using the ILD with this ΔT value is approximately equal to true mixed MLD in the equatorial ocean (Kara et al. 2000c). Figure 6 shows the daily buoy MLD as well as those from the three NLOM simulations. There are very small differences in MLDs from the three experiments.
Overall the model MLD is shallow. As expected based on turbulence considerations (cf. section 3c), the MLD in general deepened when subsurface heating was permitted within the OGCM. However, the changes at this particular location were not significant. For example, the ME values between the buoy MLD and those obtained from the three experiments are close to each other with values of −15.1, −14.8, and −14.8 m, respectively. Large SST differences do not occur during winter at (46°N, 131°W) because of the deep MLD (not shown). When heat storage is distributed over a thicker ocean layer, the amplitude of the SST variations decreases (Schneider and Zhu 1998). Since subsurface temperatures were unavailable for this buoy, a monthly MLD climatology (Kara et al. 2003a) based on temperature and salinity profiles from the World Ocean Atlas 1994 (Levitus et al. 1994; Levitus and Boyer 1994) was used as a proxy for the observed MLD. The MLD climatology has been previously shown to be in good agreement with hydrographic profiles taken at (49°N, 131°W) giving confidence in its use as a proxy for the mooring at (46°N, 131°W).
c. Comparisons with other OGCM studies
With regard to other studies, we note here that Murtugudde et al. (2002) report annual-mean SST differences as large as −0.5°C between their variable and constant-attenuation-depth simulations in the Tropics by using a primitive equation OGCM that has 19 sigma layers beneath a surface mixed layer. They found that warming of the water column below the mixed layer led to an SST warming in the Tropics despite penetrating solar radiation below the mixed layer. In contrast, we find the SST decreases when permitting penetration of solar radiation. These different outcomes are likely due to the different data sources and methods used for calculating the penetration of solar radiation. Murtugudde et al. (2002) obtain penetration depths from the CZCS data that are from 10–20 m greater than those obtained here using the SeaWiFS data. The larger penetration depths lead to solar heating being distributed over a greater depth of the upper ocean, thereby producing a weaker and deeper thermocline. As a consequence, wind-deepening events more easily erode the thermocline than when solar penetration is neglected. This leads to larger amounts of appreciably warmer water being entrained into the mixed layer and, thus, a warmer SST and deeper MLD. The lesser penetration depths used in this study result in a stronger and shallower thermocline. This permits colder water to be entrained during wind-deepening events and sustains a shallower mixed layer. This combines to produce an SST that is colder than when solar penetration is neglected. The opposing results from these two studies point to the sensitivity of SST in the Tropics to the parameterization of the penetration depths.
Earlier studies consistently find much larger differences in the mean MLD error between simulations performed when excluding and including sunlight penetration below the ocean surface than those reported here. For example, using a Richardson-number-dependent vertical mixing scheme of heat and momentum, Schneider and Zhu (1998) found mean MLD errors increased by 30 m off the equator in the Pacific, while the mean MLD error increased by 10–30 m at the equator. Murtugudde et al. (2002) obtained annual-mean MLD differences of up to 12 m between their variable and constant-attenuation-depth simulations in the Tropics. This is a threefold increase over the annual mean MLD difference of 2–4 m that we obtained between our corresponding simulations. Nakamoto et al. (2001) report mean MLD errors of 20–40 m in the western and central equatorial Pacific. These larger differences relative to our findings can be related to the greater penetration depths obtained using the CZCS versus SeaWiFS data. The greater depth penetration obtained from the CZCS data permits a larger value for the radiation contribution Brad in the ATKE equation [see Eq. (7)] and thus a deeper MLD.
Kantha and Clayson (1994) performed a one-dimensional ocean model study to examine turbidity effects on SST. The model was based on second-order closure of turbulence. They noted that the SST rise for a very shallow MLD is highly sensitive to the parameterization of solar extinction. However, their results were limited because they used the Secchi depth approach (Gordon and Wouters 1978) to determine ocean turbidity in the simulations and used it for only one location. They concluded that there could be as large as 1°C differences in SST when using different turbidity in model simulations. This is confirmed by the variety of buoys used in this study. Results presented in this paper support the conclusion of Kantha and Clayson (1994) that, if available, a model simulation should include turbidity to account for variations in solar radiation extinction in the mixed layer. However, a constant turbidity (i.e., kPAR = 0.06 m−1) assumption is also adequate to obtain reliable SSTs in global ocean simulations. Although there can be differences in SST for some months when using a variable ocean turbidity rather than using constant kPAR, overall there are no significant differences between SSTs obtained from experiment 1 and experiment 2 over annual time scales. This is true for the two buoy locations that we examined in detail and statistically for a large number of buoys (see Tables 2 and 3). Assuming a constant kPAR = 0.06 m−1 instead of using a spatially and temporally varying kPAR does not change the SST simulation very much.
4. Summary and conclusions
In this paper, the impact of solar subsurface heating using space- and time-varying turbidity on SST and MLD simulations have been examined using the global Naval Research Laboratory Layered Ocean Model with an embedded bulk-type mixed layer model. The model used 6-hourly wind and thermal forcings from the European Centre for Medium-Range Weather Forecasts during 1996 and 1997. However, it develops its own sensible and latent heat fluxes from this forcing input and model SST. In the model, the attenuation of solar radiation with depth was included by using a global monthly attenuation of photosynthetically available radiation, denoted as kPAR, climatology. These global fields of kPAR are derived from the Sea-Viewing Wide Field-of-View Sensor data on the spectral diffuse attenuation coefficient at 490 nm (k490). This study showed that differences in SST and MLD values simulated using a spatially and temporally varying attenuation parameter versus a constant attenuation value of 0.06 m−1 were small when averaged over the course of a year but were significant on shorter time scales.
To determine the impacts of ocean turbidity on SST simulations and find an indication of where to use a monthly kPAR climatology over the global ocean, the percentage of PAR absorbed below the mixed layer was calculated using global monthly mixed layer depth (MLD) and kPAR climatologies. In addition, three different ocean model experiments were used. The first experiment used a spatially and temporally varying global monthly kPAR climatology, the second experiment used a constant kPAR value of 0.06 m−1, and the last experiment assumed all radiation was completely absorbed within the mixed layer. For the present application, the greatest interest is in two situations: 1) where subsurface heating occurs below the mixed layer (Fig. 3), thereby resulting in a cooler SST than obtained by assuming complete absorption of solar irradiance within the ocean general circulation model (OGCM) mixed layer (expts 1 and 2 vs expt 3) or 2) where sub–mixed layer heating is substantially reduced by high turbidity (expt 1 vs expt 2). Comparisons of daily SSTs obtained from the three NLOM simulations with buoy SSTs showed that using monthly varying water type rather than using the constant kPAR approach in all months usually yields the best SST simulation from the model at low latitudes. The SST differences can vary from one month to another depending on kPAR and are larger when the kPAR value is large. However, considering one yearlong daily SST time series, statistical analysis revealed that the differences between experiments 1 and 2 are small, at least for the buoy locations examined here. It was also found that allowing absorption of all solar radiation entering the mixed layer (expt 3) yields degraded SST simulations.
Last, we have also shown the sensitivity of a six-layer OGCM to water turbidity and compared it with other studies using OGCMs with different vertical resolutions and physical parameterizations: a coupled atmosphere–ocean general circulation model and a reduced-gravity, primitive equation OGCM having 19 sigma layers beneath a surface mixed layer. As noted, the effects of water turbidity on SST and MLD prediction can vary substantially when using different types of OGCMs because of differences in physical parameterization, forcing, and turbidity product used.
Acknowledgments
We extend our special thanks to E. J. Metzger of the Naval Research Laboratory at the Stennis Space Center for processing and providing surface forcing fields for the model runs. Alan J. Wallcraft of the NRL is acknowledged for his helpful discussions. Appreciation is extended to the reviewers, whose helpful comments improved the quality of this paper. Additional thanks go to M. McPhaden of the TAO project office for making the daily SST mooring data available. Use of the ocean color dataset is in accord with the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) Research Data Use Terms and Conditions Agreement. The numerical simulations were performed under the Department of Defense High Performance Computing Modernization Program on an SGI Origin 2000 and a Cray T3E at the Naval Oceanographic Office, Stennis Space Center, Mississippi, and on a Cray T3E at the Arctic Region Supercomputer Center, Fairbanks, Alaska. This work is a contribution of the 6.2 Basin-Scale Prediction System project, the 6.1 Coupled Bio-Physical Dynamics Across the Littoral Transition project, and the 6.1 Thermodynamic and Topographic Forcing of Global Ocean Models project, all funded by the Office of Naval Research (ONR) under Program Elements 602435N for the 6.2 project and 601153N for the 6.1 project. This is contribution NRL/JA/7304/02/0002 and has been approved for public release.
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APPENDIX
List of Symbols
b∗w∗ Buoyancy (m2 s−3)
Brad Contribution due to attenuation of solar radiation (W m−2)
Cpa Specific heat of air (1004.5 J kg−1 K−1)
Cpw Specific heat of water (3993 J kg−1 K−1)
DC Maximum depth of solar heating of the upper ocean
e f+ Coriolis parameter at 5° latitude (2.5 × 10−5 s−1)
hm Mixed layer depth (m)
h+m h*m hP Radiation absorption e-folding length scale (m)
k490 Diffusive attenuation coefficient at 490 nm (m−1)
kPAR Attenuation coefficient for photosynthetically available radiation (m−1)
KH Coefficient of horizontal temperature diffusivity (0 m2 s−1)
mi Kraus–Turner constants (m1 = 6.25, m3 = 7.5, m5 = 6.3, m6 = 0.3)
ME Mean error (°C)
nc Kraus–Turner constant (nc = 1)
N Number of cases in the time series
nrmse Normalized root-mean-square difference
P Net rate of ATKE generation (m3 s−3)
PAR Photosynthetically available radiation (W m−2)
Qa Net heat flux at the ocean surface (W m−2)
QIR Infrared radiation (W m−2)
QL Latent heat flux (W m−2)
QLW Net longwave radiation at sea surface (W m−2)
QP(z) Penetrating solar radiation at depth z (W m−2)
QS Sensible heat flux (W m−2)
QSOL Solar irradiance at the sea surface (W m−2)
Q(z) Net surface heat flux at depth z (W m−2)
R Linear correlation coefficient
rmse Root-mean-square difference (°C)
SS Skill score
t Time (s)
Tb Temperature just below the mixed layer (°C)
Tm Sea surface temperature (°C)
u∗ Friction velocity (m s−1)
v1 Layer-1 velocity (m s−1)
α(Tm) Coefficient of thermal expansion of seawater (°C−1)
ΔTb Temperature shear (°C)
Δ
T+b ΔTm Temperature change across the mixed layer (°C)
ωm Vertical mixing velocity (m s−1)
Ω Rotation rate of the earth (7.292 × 10−5 s−1)
ϕ Latitude (°)
ρ0 Reference density for seawater (1000 kg m−3)
σe Standard deviation of NLOM SST time series (°C)
συ Standard deviation of buoy SST time series (°C)
σ−1ω υ τa Wind stress (N m−2)
Schematic illustration of mixed layer structure in the NLOM adapted from Wallcraft et al. (2003). For simplicity, only three thermodynamic layers and the mixed layer are shown, although six layers plus the mixed layer are used in this study. Prognostic variables are layer density (ρk), layer thickness (hk), layer transport per unit width (hkvk), mixed layer temperature (Tm), and MLD (hm). Atmospheric forcing is wind stress (τ), air temperature (Ta), mixing ratio at 10 m above the sea surface (qa), longwave radiation (QLW), and downward solar irradiance at the sea surface (QSOL)
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
Schematic illustration of mixed layer structure in the NLOM adapted from Wallcraft et al. (2003). For simplicity, only three thermodynamic layers and the mixed layer are shown, although six layers plus the mixed layer are used in this study. Prognostic variables are layer density (ρk), layer thickness (hk), layer transport per unit width (hkvk), mixed layer temperature (Tm), and MLD (hm). Atmospheric forcing is wind stress (τ), air temperature (Ta), mixing ratio at 10 m above the sea surface (qa), longwave radiation (QLW), and downward solar irradiance at the sea surface (QSOL)
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
Schematic illustration of mixed layer structure in the NLOM adapted from Wallcraft et al. (2003). For simplicity, only three thermodynamic layers and the mixed layer are shown, although six layers plus the mixed layer are used in this study. Prognostic variables are layer density (ρk), layer thickness (hk), layer transport per unit width (hkvk), mixed layer temperature (Tm), and MLD (hm). Atmospheric forcing is wind stress (τ), air temperature (Ta), mixing ratio at 10 m above the sea surface (qa), longwave radiation (QLW), and downward solar irradiance at the sea surface (QSOL)
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
Percentage absorption of solar radiation with depth (h) calculated using a single exponential decay formula. These profiles are good representatives of solar transmission in the visible band within the mixed layer below 10 m. The same approach is also used in NLOM
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
Percentage absorption of solar radiation with depth (h) calculated using a single exponential decay formula. These profiles are good representatives of solar transmission in the visible band within the mixed layer below 10 m. The same approach is also used in NLOM
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
Percentage absorption of solar radiation with depth (h) calculated using a single exponential decay formula. These profiles are good representatives of solar transmission in the visible band within the mixed layer below 10 m. The same approach is also used in NLOM
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
Changes in PAR below the MLD as percentage of PAR at the surface: (a) annual-mean difference when using a monthly varying kPAR relative to complete PAR absorption within the mixed layer (i.e., the effect of ignoring kPAR), (b) annual-mean difference when using a monthly varying kPAR relative to kPAR = 0.06 m−1, and (c) largest difference of all 12 months for case (b), indicating where using a monthly kPAR can make a large difference in model simulations.
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
Changes in PAR below the MLD as percentage of PAR at the surface: (a) annual-mean difference when using a monthly varying kPAR relative to complete PAR absorption within the mixed layer (i.e., the effect of ignoring kPAR), (b) annual-mean difference when using a monthly varying kPAR relative to kPAR = 0.06 m−1, and (c) largest difference of all 12 months for case (b), indicating where using a monthly kPAR can make a large difference in model simulations.
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
Changes in PAR below the MLD as percentage of PAR at the surface: (a) annual-mean difference when using a monthly varying kPAR relative to complete PAR absorption within the mixed layer (i.e., the effect of ignoring kPAR), (b) annual-mean difference when using a monthly varying kPAR relative to kPAR = 0.06 m−1, and (c) largest difference of all 12 months for case (b), indicating where using a monthly kPAR can make a large difference in model simulations.
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
Daily averaged SST time series comparisons between two buoys and three NLOM experiments (see Table 1). Two different buoy locations are used in two different years: (a) equatorial ocean (0°, 155°W) in 1997 and (b) off the northwest coast of the United States (46°N, 131°W) in 1996. See Fig. 5 for monthly kPAR values at these locations
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
Daily averaged SST time series comparisons between two buoys and three NLOM experiments (see Table 1). Two different buoy locations are used in two different years: (a) equatorial ocean (0°, 155°W) in 1997 and (b) off the northwest coast of the United States (46°N, 131°W) in 1996. See Fig. 5 for monthly kPAR values at these locations
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
Daily averaged SST time series comparisons between two buoys and three NLOM experiments (see Table 1). Two different buoy locations are used in two different years: (a) equatorial ocean (0°, 155°W) in 1997 and (b) off the northwest coast of the United States (46°N, 131°W) in 1996. See Fig. 5 for monthly kPAR values at these locations
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
Climatological monthly mean of kPAR at the locations given in Tables 2 and 3. Note that x-axis labels are written for every other month
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
Climatological monthly mean of kPAR at the locations given in Tables 2 and 3. Note that x-axis labels are written for every other month
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
Climatological monthly mean of kPAR at the locations given in Tables 2 and 3. Note that x-axis labels are written for every other month
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
Daily averaged MLD time series comparisons between values calculated from buoy subsurface temperatures and those from the three NLOM experiments at (0°, 155°W) in 1997. See Fig. 5 for monthly kPAR values at this location
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
Daily averaged MLD time series comparisons between values calculated from buoy subsurface temperatures and those from the three NLOM experiments at (0°, 155°W) in 1997. See Fig. 5 for monthly kPAR values at this location
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
Daily averaged MLD time series comparisons between values calculated from buoy subsurface temperatures and those from the three NLOM experiments at (0°, 155°W) in 1997. See Fig. 5 for monthly kPAR values at this location
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
Compensation depths computed from kPAR for the two mooring locations shown in Fig. 4. Also shown are daily time series of model MLD from experiment 1
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
Compensation depths computed from kPAR for the two mooring locations shown in Fig. 4. Also shown are daily time series of model MLD from experiment 1
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
Compensation depths computed from kPAR for the two mooring locations shown in Fig. 4. Also shown are daily time series of model MLD from experiment 1
Citation: Journal of Physical Oceanography 34, 2; 10.1175/1520-0485(2004)034<0345:TIOWTO>2.0.CO;2
The three interannual NLOM simulations for 1996 and 1997. The model has an embedded bulk-type mixed layer. It used wind and thermal forcings (i.e., air temperature at 10 m, air mixing ratio at 10 m, shortwave and longwave radiation) from the 6-hourly ECMWF data
Statistical verification of daily SST time series between NLOM and TAO buoys at different locations in the equatorial ocean. Comparisons are made during a 1-yr period (1997). All statistical calculations are based on 365 daily SST values
As in Table 2 but for 1996 and with statistical verification performed using NODC buoys outside the equatorial ocean
Naval Research Laboratory Contribution Number NRL/JA/7304/02/0002.
