Empirical Approach

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NOAA NESDIS Algorithm Theory Based Document, July 2012 [ PDF]

Based on the initial approach by Shay et al. (2000) and Mainelli et al. (2008), the method of calculating ocean heat content (OHC) was expanded in the North Atlantic, and North and South Pacific, eventually forming a global OHC product suite. Basin-specific ocean climatologies were developed to estimate ocean heat content (OHC) variability.  Each climatology is a blend of temperature and salinity fields from the World Ocean Atlas 2001 (WOA) and Generalized Digital Environmental Model v.2.1 (GDEM) at 1/4° resolution.  Monthly mean isotherm depths of the 20°C (D20) and 26°C (D26) (and their mean ratios), reduced gravities, and mixed layer depth (MLD) were estimated for both GDEM and WOA climatologies.  Daily fields were created by applying a 15-day running average to the monthly fields to eliminate discontinuities when transitioning between months.  To blend the two climatologies and create each new climatology, a weighting scheme was developed by minimizing the residual covariances between in-situ and satellite-derived fields.

Using a 2.5 layer model approach together with the new climatology, and satellite-derived sea surface height anomaly (SHA) and sea surface temperature fields, daily D20, D26, MLD, and OHC were estimated.  In addition, the SHA product includes mapping errors given the different repeat tracks from the altimeters and sensor accuracy.  This is especially important across the eddy-rich regions in the western Pacific Ocean and the complex equatorial wave guide.  To assess uncertainties in the daily fields, ship-deployed probes, TAO moorings, and Argo profiling floats provided more than 240,000 quality controlled in-situ thermal profiles.  This carefully constructed climatology creates an accurate estimate of OHC from satellite based measurements to build realistic ocean products globally for multiple applications, including model assimilation, hurricane intensity forecasting, and climate research.

Two-Layer Model:

The two-layer model used here is based on reduced gravity where the upper and lower layers are separated by the depth of the 20°C isotherm:

  g'  =   g    ( ρ 2  -  ρ 1 )  
ρ 2

where g is the acceleration of gravity (9.81 m s -2 ), ρ 2 represents the density of the lower layer and ρ 1 represents the density of the upper layer (O’Brien and Reid 1967; Kundu 1991; Goni et al. 1996). The depth of the 20°C isotherm is given by:

   g' η'   
  H 20   =  H 20   +   (2)

where H 20 represents the average depth the 20°C isotherm from climatology and η' is the SHA from the blended and objectively analyzed altimetry measurements from multiple platforms. Each day the SHA field is updated with new tracks of data in the domain from the various radar altimeters, which implies that the 20°C isotherm depth is also updated. The key issue is then the relationship of this depth to the 26°C isotherm depth (Palmen 1948). The updated depth of the 26°C isotherm is determined from the relationship:

  H 26     =       H 26   · H 20   (3)
    H 20  

where H 26 is the average depth of the 26°C isotherm from climatology. Now that we have this depth based on satellite altimetry and the SST from satellite measurements, the OHC relative to the 26°C isotherm is given by:

  Q = ρ1  c p ( T z - 26°C ) dz   (4)
        H 26      

where T(z) is upper ocean temperature structure that includes the SST, c p is the specific heat of seawater at constant pressure which has a value of 1 cal g m -1 °C -1 and ρ 1 is 1.026 g cm -3 (Leipper and Volgenau 1972). Note that we use the 26°C isotherm here since it is the temperature assumed for tropical cyclogenesis (Palmen 1948)

Empirical Representation:

To estimate the OHC from space-based measurements, we use the climatological OML (h) and assume that the SST from TMI is a proxy for the OML temperature. From the surface to this depth, the OHC in the mixed layer is proportional to the product [(SST-26°C) x h]. The second contribution to this estimate is underneath this layer from h to the depth of the 26° C isotherm using the SST given by 0.5 [H 26-h][SST-26°C]. The total OHC is the addition of the OML contribution plus the contribution from the layer depth to the isotherm depth. There are few underlying assumptions involved with this crude empirical approach:

1.   Seasonal climatological OML has its own density that sits on top of a two-layer fluid;  


2.   The OML depth is time invariant since we do not have surface heat fluxes, wind stress or current shear at the base of the OML to determine its’ evolution.

Variations in the SHA field have maximum impact in the seasonal thermocline (i.e. 20°C isotherm) depth and have a minimal impact on h. This approach has been tested in the Atlantic Ocean basin to assess whether there is an improvement in the OHC estimates. Based on extensive comparisons to in-situ data and the satellite-derived OHC have indicated good agreement between satellite-inferred and observed OHC estimates in the Gulf of Mexico given its weaker thermal structure and vertical density changes compared to that observed in the EPAC and the Gulf of Mexico Common Water (Shay 2008).

U.S. Navy Generalized Digital Environmental Model:

Central to this vertical structure issue is its’ representation in climatology and in situ data. In comparing the two climatologies ( V2.1 and V3 GDEM) on monthly and seasonal time scales, an important issue is determining the OML depth (Teague et al. 1990). For example, the ocean mixed layer (h) by definition is well mixed in properties such as temperature and salinity. Close inspection of the salinity profiles for September reveal differences between salinity in the upper 10 to 15 m of the water column (not shown) That is, the salinity structure in V2.1 reveals no constant salinity in this near-surface layer, by contrast, the salinity is relatively constant in the layer from 15 m to the surface. While these vertical salinity changes affect the density structure, the thermal structure dominates the density in the upper ocean, which seems to be more realistic in GDEM V2.1 than V3.0. For example, the well-mixed OML (temperature only) depth decreases from a maximum in May of 35 to 40 m to a minimum of about 15 m in October. Such thermal structure behavior is generally more in line with observed thermal structure variations during from the EPIC CTD profiles. That is, this layer shallowing from the EPIC data suggests that the OML is about 20 to 25 m deep in the warm pool or about 5 to 10 m deeper than the September climatology. Of equal importance is the vertical temperature structure beneath the layer is more in line with the CTD profile as well in GDEM V2.1. However, averaged over the EPAC hurricane season (May to October) at 10°N and 95°W, climatologies suggest a general shallowing of the OML depth.

This approach uses this earlier version of GDEM climatology for the analysis contained herein. This is also the same version used for the Atlantic Ocean basin to ensure consistency between the two basins. Climatologically, the SSTs exceed 28°C in the EPAC as shown in Fig. 8a. The spatial variations in the surface OML depth are shown in Figure 6b based on an average from May through November. Notice how the OML shoals towards the east where mean values range between 15 to 20 m as compared to OML of more than 80 m west of 120°W. These spatial changes in h are now reflected in the approach. As shown in Figure 8c,d, the seasonal mean depths of the 20°C and 26°C isotherms are based on an average over a hurricane season using GDEM profiles objectively analyzed to 0.25° resolution. Notice the general shoaling of the isotherm depths from west to east that forces tighter vertical gradients in the warm pool’s upper ocean thermal structure (and shallower ocean mixed layer depths). Generally, the 20°C isotherm depths range from 30 to 50 m compared to more than 100 m west of 140°W. The corresponding 26°C mean isotherm depth ranges between 15 to 25 m in the warm pool (12°N, 95°W) and north of 20°N, the 26°C isotherm shoals to the surface.

This surface shoaling, known as ventilating of the 26°C isotherm, implies that once a TC reaches that area, they will begin to lose their oceanic heat source and begin to weaken. A second aspect of this area is that the buoyancy frequencies at the base of the OML exceed 20 cph as suggested in Figure 6.

The reduced gravity (g’) distribution (from (1)) and the ratio between the 26°C and 20°C isotherm depths are shown in Fig. 8e,f. East of 120°W, reduced gravities are about 5 x 10 -2 m s -2, which is indicative of the strong stratification of the EPAC. West of this longitude, g’ decreases to about 3.5 x 10 -2 m s -2 whereas towards the northern part of the domain, reduced gravities decrease to about 2 x 10 -2 m s -2. For example, in the area of hurricane Norbert experiment in 1984 (Sanford et al. 1987), the observed buoyancy frequency was 11 to 12 cycles per hour (cph) compared to more than 20 cph in the warm pool (Raymond et al. 2004). Such spatial variations have a pronounced impact on cooling and the generation of a cold wake, or trail left behind by a hurricane. In general, the strong stratification in the EPAC often precludes a strong internal wave wake left behind by hurricanes at these low latitudes. During Juliette in 2001, the cold wake of SSTs exceeding 4°C only began towards the north and west of the warm pool (Shay and Jacob 2006).

Ocean Heat Content Estimation:

As shown in Figure 10, the OHC is estimated using GDEM V2.1 climatology (Fig. 9) using the surface height anomaly (SHA) and TMI-derived SST fields for mid-September 2001 to coincide with EPIC experiment. The approach uses SHA from TOPEX, GFO, and ERS-2 altimetry data (not the blended AVISO in Figure 1) where repeat tracks are 9.9, 17 and 35 days, respectively. These fields are blended and objectively analyzed to a 0.25° grid from the coast to 180°W and from the equator to 30°N and are then combined to estimate isotherm depths and OHC. As shown in Fig. 10a, the warm SSTs exceeded 27.5°C north of the equatorial cold tongue and extended longitudinally from the coast to 180°W. Cooler SSTs are observed north of 20°N, and decrease to below 26°C at about 24°N. The mean 20°C isotherm depths suggest a general shoaling from west to east to a relative minimum of about 40 m in the EPIC domain. Notice the general shape of this minimum that apparently was affected by a warmer feature between the two cold cells (Fig. 10b). This may be a manifestation of the Costa Rica Dome, which is a semi-permanent feature of the EPAC due to the cyclonic mean wind stress curl (Hofmann et al. 1981). The 26°C isotherm depths also show a similar pattern except that the relative minimum is about 20 to 25 m. Finally, the resultant OHC distribution shows values of ~50 kJ cm-2 at ~14°N and 95°W.

Sea Surface Temperatures:

The surface boundary condition is central to these satellite retrievals as suggested in Figure 6. As shown in Figure 11, SSTs from Reynolds, TMI and TAO mooring data are compared using regression techniques. For example, TAO mooring derived data suggest warmer SSTs than those derived from Reynolds analysis (slope of the least squares fit is 0.63) with RMS differences of about 0.6°C. The better comparison is between TAO and TMI data where the RMS difference is 0.5°C. Note that in this comparison, the slope of the regression curve is 0.93, which is indicative of a better fit with a bias of 1.7°C. Finally, the Reynolds analysis is compared to the TMI SSTs. The RMS differences are 0.54°C and the slope of the regression curve is 0.71 with a bias of 0.2. In general, Reynolds-derived SSTs tend to be higher than the TMI SST. Note the TMI data are corrected for diunal cycling (Gentemann 2007). Thus, not all SST products are equal, and when it represents the surface boundary condition, care must be afforded to the optimal SST choice in the data stream for OHC estimation for input into forecasting models.

Data Resources

In this section, data resources are described for developing a hurricane season climatology for the EPAC as in the Atlantic Ocean Basin (Mainelli 2000; Mainelli et al. 2008). As shown in Figure 2, Tropical Atmosphere Ocean (TAO) moorings relative to the EPIC domain are superposed on a Sept 2001 SST image. These TAO moorings were originally deployed as part of the Tropical Ocean Global Atmosphere Program in the 90’s to monitor equatorial wave guide and were enhanced at 95° W during EPIC (Cronin et al. 2002).

2.1 Radar Altimetry:

TOPEX/Poseidon (T/P) and Jason-1 radar altimeters measure sea level every 9.9 days along repeat ground-track spaced 3° longitudinally at the Equator. ERS-2 mission and U. S. Navy Geosat Follow-On-Missions (GFO) have repeat tracks of 35 and 17 days, respectively. More recently, Envisat data has been added since ERS-2 mission is no longer providing data. The availability of such altimetry measurements is shown in Figure 3 for several satellites that carry altimetry sensors. For example, NASA TOPEX mission began in 1992 (Cheney et al. 1994; Ali et al. 1998) followed by Jason-1 in 2000 as the follow on to TOPEX. As noted in Figure 1, altimetry data are useful in tracking oceanic mesoscale features such as warm and cold features as observed from Aug through Oct 2001 using an AVISO blended product during the EPIC field program. The ring pathway, tracked over a three-month period based successive SHA images, suggests that the warm feature moved at speeds of 13 to 15 km d-1 towards the west southwest as its diameter decreased during its spin-down process in the EPIC domain. Tracking of oceanic features has been done in other regions such as the Gulf of Mexico to study warm core ring shedding processes from the Loop Current (Leben 2005).

Although the 10- and 17-d repeat cycles utilized in the OHC estimates are long compared with the hurricane lifecycles usually, they are reasonable compared to the time scales of upper ocean variability (Shay et al. 2000), such as the ocean rings being analyzed. Moreover, this analysis system is designed to be updated daily to incorporate latest altimetry measurements from all sensors including Envisat, which has further improved the OHC estimates, particularly in areas where the signal to noise (SNR) ratios are large.

2.2 Objective Analysis:

In the forthcoming analysis, only periods when there are at least two sets of radar altimeter data available are used here. These SHA data are objectively mapped to a 0.25° grid using the approach of Mariano and Brown (1992). The oceanic analysis decomposes a scalar observation into three components using parameters derived from the hurricane Gilbert data set (Shay et al. 1992). Based on this approach, the first part of this scalar field is the large scale or trend field. The second component is represented by the synoptic time scale or the field variability on the mesoscale. The composite SHA field from the 10- and 17-days of altimeter tracks from the various platforms is considered synoptic in time as each day this field is updated with the latest tracks of SHA data. The last component represents unresolved scales, ie. noise and errors. Each day, final field estimates of the SHA data are a sum of the trend field and the objectively mapped deviation field in space (Mainelli et al. 2001). In this procedure, the mapping noise is significantly reduced by adding additional platforms. Two and three sets of altimeter data decrease the mapping error of the objectively analyzed field. This analysis procedure allows the SHA data to accurately depict mesoscale features as well as delineate areas of strong horizontal thermal gradients each day when the latest data are ingested into the scheme.

2.3 EPIC Data

To understand this EPAC upper ocean variability, the EPIC field program, was conducted in and over the warm pool and along the 95° W transect to improve our understanding of these upper ocean processes and determine their relationship to the atmospheric boundary layer. During the field program (Weller et al. 1999; Raymond et al. 2004), oceanic current, temperature and salinity measurements from Airborne expendable Current Profilers (AXCP), Airborne eXpendable Conductivity Temperature and Depth

(AXCTD) profilers and Airborne eXpendable Bathythermographs (AXBT) were acquired from NOAA WP-3D and NCAR WC-130 research aircraft (see Table 1). Profilers were deployed from 19 research flights encompassing the warm pool and ITCZ and along the 95° W equatorial transects in Sept and Oct 2001. Oceanic profilers were complemented with flight-level winds and atmospheric profiler data from GPS sondes. Flight tracks were located on adjacent sides of the R/V Brown and R/V New Horizon centered on the 10° N TAO mooring (Wijesekera et al. 2005).

Objectively mapping the thermal structure from the grid measurements revealed the warm eddy structure (Figure 4) is consistent with SHA measurements shown in Figure 1. The OHC values estimated from these snapshots range between 50 to 55 kJ cm -2 compared to more than 100 kJ cm -2 in the Loop Current (Shay 2008). The depth of the 26° C isotherm depth exceeds 45 m in the warm ring (consistent with Figure 1 for the 20°C), and decreases to 20 m outside of it. As the warm ring propagated southwestward in Oct, the isotherm depth decreased to about 15 m in the approximate region of the Costa Rica Dome along the eastern portion of the domain (Hofmann et al. 1981) This spatial variability in the warm ring structure has a pronounced impact on the OHC distributions.

2.4 TAO Mooring Data:

NOAA TAO moorings in the EPAC are part of the long-term monitoring efforts by Pacific Marine Environmental Laboratory (PMEL). These moorings provide time series of thermal structure at various depths and during the EPIC program, these TAO moorings were enhanced to acquire temperature measurements at 1, 5, 10, 20, 40, 60, 80, 100, 120, 140, 180, 300 and 500 m, and salinity at 1, 5, 10, 20, 40, 80 and 120 m at 8, 10 and 12°N, 95°W (Cronin et al. 2002). TAO temperature structure data from moorings at 95°W, 110°W and 140°W will be used here to assess the OHC climatology based on satellite sensing.

As shown in Figure 5, the thermocline is depressed (i.e. 20°C isotherm depth) during the passage of a warm core ring at the TAO mooring located at 10° N and 95°W as suggested by the higher SHA values in Figure 1b. That is, the warm ring has warmer water at depth which causes a positive SHA detected by radar altimeters. At this position, the OHC values exceeded 40 kJ cm -2 as the warm feature began to spin down and weaken, consistent with Figures 1 and 4. Over several years of measurements, TAO time series from May through November are used to evaluate remotely sensed isotherm depths and OHC values.

2.5 VOS XBT Transects:

Ship-based expendable bathythermographs (XBT) are acquired through Volunteer Observing System (VOS), Ship of Opportunity Program (SOOP) and on NOAA, UNOLS, and Coast Guard vessels. These data are routinely provided to AOML through the AMVER SEAS 2K, a Windows based real-time ship and environmental data acquisition and transmission system. This software creates a series of reports, which describe point of departure, route and arrival of a ship. These reports are transmitted using Standard-C and include ships in a real-time search and rescue database. These data are subsequently transmitted in real-time via the Global Telecommunication System (GTS) to operational data bases to be used by scientists. Specifically, XBT profiles from from the ships involved in the SOOP are transmitted to receiving stations onshore via satellite. These data are placed in the GTS and are made publicly available. The global spatial data are available since 1999. Here we accessed data from the website at NOAA AOML and processed the data from the Eastern Pacific Ocean from 2000- 2008 (see Figure 6). Since minimal quality control is applied to the data, we reprocessed these data and checked for bad data in the profiles.