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  • View in gallery

    Flowchart for STA (e.g., 300-m depth) estimation using SOM neural network: SSTAI, SSSAI, and SSHAI are datasets for training—large datasets from long time series and large coverage of space. SSTAE, SSSAE, and SSHAE are the datasets for estimation—it can be single spot, cruise transaction, or horizontal 2D maps. SSP is another possible sea surface parameter.

  • View in gallery

    Comparison of STA at 300-m depth from (left) Argo and (right) SOM neural network estimation, January, April, July, and October 2006.

  • View in gallery

    (left) SSTA and (right) SSHA from Argo, in the North Atlantic for January, April, July, and October 2006. Absolute dynamic depth anomaly (ADDEP; equal SSHA at the sea surface) was used as SSHA here.

  • View in gallery

    Maximum correlation coefficient (γ) between estimated STA by SOM neural network (STASOM) and STA from Argo (STAArgo) from ~30- to 2000-m depth in the North Atlantic. The solid contour line is for γ = 0.8; the dashed contour line is for γ = 0.6. Areas noted as a, b, c, and d are for the labeling and testing in discussed in section 3d—a: western part of the North Atlantic subtropical gyre, 32°–37°N, 65°–70°W; b: central part of the midlatitude North Atlantic, 35°–40°N, 40°–45°W; c: eastern part of the midlatitude North Atlantic, 35°–40°N, 15°–20°W; and d: the subpolar gyre of the North Atlantic, 45°–50°N, 40°–45°W.

  • View in gallery

    Depth determined from the maximum correlation coefficient (γ) between STASOM and STAArgo through the water column from ~30 to 2000 m in the North Atlantic.

  • View in gallery

    Argo STA profiles from January 2005 to December 2010 [Figs. 6a–e in areas a, b, c, d, and e; the geolocation is indicated in panel (f); the bold green line shows the depth determined from maximum STA variance, while the red dashed line is the depth determined from the maximum correlation coefficient (γ) between STASOM and STAArgo], and depth determined from maximum STA variance from ~30 to 2000 m in the North Atlantic [see panel (f)].

  • View in gallery

    Typical subsurface temperature profiles in (a),(c) western (at 35°N, 60°W) and (b),(d) eastern (at 38°N, 20°W) basins in the midlatitude North Atlantic during the months of (a),(b) April and (c),(d) December 2005. The variables plotted are monthly climatology temperature (STClimat), temperature from Argo (STArgo), and temperature estimated by SOM neural network (STSOM) as labeled in (b). RMSE between STAs profiles from Argo and SOM estimation, and RMS of Argo STA was noted.

  • View in gallery

    Cross section of correlation coefficient (γ) between STA estimated from SOM neural network and STA from Argo from the surface (30 m) to 1100 m at 35°N in the North Atlantic.

  • View in gallery

    Time series of monthly STAs at 300-m depth in the North Atlantic 2005–10 [(a)–(d) areas a, b, c, and d in Fig. 4, respectively]. Colored lines: red solid line = STA estimated from SOM (STASOM), blue solid line = STA from labeling data (STALaboratory), and green starred line = STA for independent Argo data (STAInd). Here γ is correlation coefficient between STASOM and STAInd, and RMSE is the root-mean-square error between STASOM and STAInd.

  • View in gallery

    Sensitivity of correlation coefficient (γ) between STA estimated from SOM neural network and STA from Argo to the different input for SOM: (left) changes in γ and (right) the depth for the changes. (top)–(bottom) Training inputs are (a),(b) γ(SSTA, SSHA, climatology)–γ(SSTA, SSHA); (c),(d) γ(SSTA, SSHA, SSSA, climatology)–γ(SSTA, SSHA, SSSA); (e),(f) γ(SSTA, SSHA, SSSA, climatology)–γ(SSTA, SSHA, climatology); (g),(h) γ(SSTA, SSHA, SSSA) – (SSTA, SSHA). Grids where Δγ < 0.1 were masked.

  • View in gallery

    Remote sensing data of January 1994 [(a) SSTA and (b) SSHA] and (c) STA at 300 m from SOM estimation with remote sensing data as inputs in the North Atlantic.

  • View in gallery

    Time series of stability of SOM-reconstructed ocean in area a (32°N, 65°W) at depths of (a) 100, 300, and (b) 500 m.

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Estimation of Subsurface Temperature Anomaly in the North Atlantic Using a Self-Organizing Map Neural Network

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  • 1 State Key Laboratory of Marine Environmental Science, Xiamen University, Xiamen, China, and Center for Remote Sensing, and Joint Institute for Coastal Research and Management, University of Delaware, Newark, Delaware
  • | 2 Center for Remote Sensing, and Joint Institute for Coastal Research and Management, University of Delaware, Newark, Delaware
  • | 3 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California
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Abstract

A self-organizing map (SOM) neural network was developed from Argo gridded datasets in order to estimate a subsurface temperature anomaly (STA) from remote sensing data. The SOM maps were trained using anomalies of sea surface temperature (SST), height (SSH), and salinity (SSS) data from Argo gridded monthly anomaly datasets, labeled with Argo STA data from 2005 through 2010, which were then used to estimate the STAs at different depths in the North Atlantic from the sea surface data. The estimated STA maps and time series were compared with Argo STAs including independent datasets for validation. In the Gulf Stream path areas, the STA estimations from the SOM algorithm show good agreement with in situ measurements taken from the surface down to 700-m depth, with a correlation coefficient larger than 0.8. Sensitivity of the SOM, when including salinity, shows that with SSS anomaly data in the SOM training process reveal the importance of SSS information, which can improve the estimation of STA in the subtropical ocean by up to 30%. In subpolar basins, the monthly climatology SST and SSH can also help to improve the estimation by as much as 40%. The STA time series for 1993–2004 in the midlatitude North Atlantic were estimated from remote sensing SST and altimetry time series using the SOM algorithm. Limitations for the SOM algorithm and possible error sources in the estimation are briefly discussed.

Corresponding author address: Xiao-Hai Yan, Center for Remote Sensing, College of Earth, Ocean and Environment, University of Delaware, 209 Robinson Hall, Newark, DE 19716. E-mail: xiaohai@udel.edu

Abstract

A self-organizing map (SOM) neural network was developed from Argo gridded datasets in order to estimate a subsurface temperature anomaly (STA) from remote sensing data. The SOM maps were trained using anomalies of sea surface temperature (SST), height (SSH), and salinity (SSS) data from Argo gridded monthly anomaly datasets, labeled with Argo STA data from 2005 through 2010, which were then used to estimate the STAs at different depths in the North Atlantic from the sea surface data. The estimated STA maps and time series were compared with Argo STAs including independent datasets for validation. In the Gulf Stream path areas, the STA estimations from the SOM algorithm show good agreement with in situ measurements taken from the surface down to 700-m depth, with a correlation coefficient larger than 0.8. Sensitivity of the SOM, when including salinity, shows that with SSS anomaly data in the SOM training process reveal the importance of SSS information, which can improve the estimation of STA in the subtropical ocean by up to 30%. In subpolar basins, the monthly climatology SST and SSH can also help to improve the estimation by as much as 40%. The STA time series for 1993–2004 in the midlatitude North Atlantic were estimated from remote sensing SST and altimetry time series using the SOM algorithm. Limitations for the SOM algorithm and possible error sources in the estimation are briefly discussed.

Corresponding author address: Xiao-Hai Yan, Center for Remote Sensing, College of Earth, Ocean and Environment, University of Delaware, 209 Robinson Hall, Newark, DE 19716. E-mail: xiaohai@udel.edu

1. Introduction

Since the 1970s, remote sensing has provided much data of high spatial and temporal resolution, large overall coverage, and long time series of sea surface data, allowing for unprecedented progress and notable discoveries in the atmosphere, ocean, and climate sciences. While remote sensing is the most cost-efficient tool, its observations are confined to the sea surface phenomena. Therefore, our knowledge of the sea surface greatly exceeds what is known below the surface. Subsurface data, however, are critical to understand the mechanisms and processes in the ocean as a whole, as well as for the entire earth climate system (e.g., Meehl et al. 2011). Despite the large subsurface in situ measurement projects such as Integrated Ocean Observing System (IOOS) and Global Ocean Observing System (GOOS) with over 8000 platforms including drift buoys, moored buoys, Argo floats, gliders, and expendable bathythermographs (XBTs), the subsurface observations available are still too scarce in most parts of the ocean.

The ocean surface is dynamically influenced at the sea surface by waves, wind shear, heat exchange, and from the interior ocean by thermal expansion, ocean circulation, and turbulent mixing. Variation in the subsurface layer will very likely leave traces on the sea surface through sea surface height changes, which make the estimation of parameters from the subsurface form to the sea surface possible. The relation between sea surface parameters and subsurface parameters has been studied (Khedouri et al. 1983; Yan et al. 1990; Chu et al. 2000; Ali et al. 2004). On the one hand, sensors that could measure subsurface parameters directly are under development (Leonard et al. 1977). On the other hand, studies have been carried out to estimate subsurface parameters from sea surface information based on either the combination of dynamical models (Yan et al. 1990, 1991b; Yan and Okubo 1992), in situ observations (Chu et al. 2000), or model-based data assimilation (Robinson and Lermusiaux 2000). Numerical model-based data assimilation became a powerful methodology for parameter estimation in the ocean (Ghil and Malanotte-Rizzoli 1991) with the development of computational technology. It combines the in situ measurements and the dynamic principles that govern the ocean, giving the most efficient, accurate, and realistic estimation for parameter of interest, though it has several aspects that may introduce uncertainty (Robinson and Lermusiaux 2000). The statistical approach for parameter estimation, which has been used for decades, is not constrained by the dynamical equations and the predicted parameter may be limited to the range of the available data. However, this approach is relatively easy to establish and has reasonable accuracy. In the subsurface ocean where the in situ data are limited, statistical estimation is a necessary and useful supplement to the model-based parameter estimation.

Based on a mixed layer thermal inertia model, one-dimensional (Yan et al. 1990, 1991b, 1991a) and three-dimensional (Yan and Okubo 1992) models were developed to determine oceanic mixed layer depth (MLD), which is much simpler than the Kraus and Turner (1967) mixed layer model and can be conducted directly from satellite observations. With the help of in situ measurements, phenomena occurring even deeper than MLD can be revealed from the signal at sea surface. A unique method has been developed by Yan et al. (2006) using satellite altimetry, wind scatterometers, infrared satellite imagery, and XBT datasets that successfully detected the Mediterranean outflow and “Meddies” at a depth of about 1000 m in the Atlantic Ocean. Chu et al. (2000) developed a parametric model for determining the subsurface thermal structure of the ocean from satellite sea surface temperature (SST) observations in the South China Sea. Willis et al. (2003) combined altimetric height and SST with in situ data with a linear regression technique and improved estimates of 0–800-m steric height, heat content, and temperature variability. Ali et al. (2004) used a neural network to determine subsurface thermal structure from SST, sea surface height (SSH), wind stress, net radiation, and net heat flux obtained from a mooring system deployed in the Arabian Sea. Guinehut et al. (2004) derived a large-scale, monthly mean temperature at 200-m depth from altimetry and SST data through a multiple linear regression method, combining high-spatial-resolution satellite altimetry data with sparse high-accuracy Argo temperature. Takano et al. (2009) developed an empirical method to estimate mesoscale three-dimensional thermal structure from near-real-time satellite altimetry data based on a two-layer model hypothesis.

SST and SSH have been monitored by remote sensing since the late 1970s and 1992, respectively. Two salinity sensors, Soil Moisture and Ocean Salinity (SMOS) mission by the European Space Agency and Aquarius by National Aeronautics and Space Administration (NASA) and Argentina, were launched in 2009 and 2011. Cross validation for the sensors will make the global sea surface salinity (SSS) data more reliable than before. Since SST anomaly (SSTA), SSH anomaly (SSHA), and SSS anomaly (SSSA) can now be obtained through remote sensing platforms, in this paper a self-organizing map neural network is adopted to estimate the subsurface temperature structure from these datasets with the help of Argo in situ data. A SOM neural network is trained and labeled from Argo gridded data. Validations are carried out by comparing the horizontal maps, vertical profiles, and time series of SOM-estimated subsurface temperature anomaly (STA) with Argo STA data. The method is applied in the midlatitude North Atlantic to estimate the subsurface thermal structure from remote sensing SST and altimetry. Sensitivity of this method to input parameters are discussed, followed by conclusions on the capability of the method in estimating subsurface thermo structure in the North Atlantic.

2. Data and method

Datasets used in this study are monthly global gridded Argo data provided by the International Pacific Research Center (IPRC; http://iprc.soest.hawaii.edu) at the School of Ocean and Earth Science and Technology, University of Hawaii at Manoa. The temperature, salinity, and absolute dynamic topography datasets have 1° × 1° horizontal spatial resolution and global coverage, and were interpolated to 27 standard depth levels in the upper 2000 m from January 2005 to December 2010. The absolute dynamic height (ADH) in the IPRC gridded Argo data is defined as SSH minus dynamic height (DH), where the SSH is obtained from altimeter products. At the sea surface, ADH is equal to SSH. ADH data are calculated using Archiving Validation and Interpretation on Satellite Data in Oceanography (AVISO) altimetry referred to as MDT_CNES-CLS09 (MDT_CNES-CLS09 was produced by Collecte Localisation Satellites (CLS) Space Oceanography Division and distributed by AVISO, with support from Centre National d’Études Spatiales (CNES) (http://www.aviso.oceanobs.com/).

In the section for application of the SOM algorithm, NOAA Optimum Interpolation Sea Surface (NOAA_OI_SST_V2; http://www.emc.ncep.noaa.gov/research/cmb/sst_analysis/), temperature anomaly monthly data, and monthly maps of sea level anomalies (MSLA) from altimetry distributed from AVISO (http://www.aviso.oceanobs.com/es/data/products/sea-surface-height-products/global/msla/index.html) were used as input data to estimate the STA. The MLD extends from about a few tens of meters to 200-m depth in most of the tropical and midlatitude ocean (de Boyer Montégut et al. 2004). Considering the MLD for high latitudes, 300 m is chosen to reasonably represent the subsurface-layer depth. The datasets have a 1° × 1° (Mercator grid) spatial resolution, which is the same as that of Argo datasets that were used in training and labeling processes. The SST data are a combination of in situ and satellite SSTs.

A SOM neural network is a computational method for the visualization and analysis of high-dimensional data. It was first introduced by Kohonen (1982, 2001) as an unsupervised neural network to study empirical relationships between variables of which the physical relationships are not clear and has turned out to be very useful tool in feature extraction and classification. It has been widely applied in meteorology and ocean science (Liu et al. 2006; Telszewski et al. 2009; Liu and Weisberg 2011).

The subsurface temperature estimation was carried out using a SOM Toolbox for Matlab, which is developed by the Laboratory of Information and Computer Science at the Helsinki University of Technology and available online at http://www.cis.hut.fi/projects/somtoolbox. General SOM procedures contain unsupervised training of available datasets to a 2D network, labeling the trained network and estimation (Fig. 1). For detailed descriptions, consult Liu et al. (2006) and Telszewski et al. (2009).

Fig. 1.
Fig. 1.

Flowchart for STA (e.g., 300-m depth) estimation using SOM neural network: SSTAI, SSSAI, and SSHAI are datasets for training—large datasets from long time series and large coverage of space. SSTAE, SSSAE, and SSHAE are the datasets for estimation—it can be single spot, cruise transaction, or horizontal 2D maps. SSP is another possible sea surface parameter.

Citation: Journal of Atmospheric and Oceanic Technology 29, 11; 10.1175/JTECH-D-12-00013.1

The SOM map adopted in this study consists of 1600 (40 × 40) neurons with rectangular grids on a flat sheet map and a “Gaussian” neighborhood function with a radius of 2. This network is to be trained using sea surface information and labeled with STA data before it can be used to estimate the subsurface temperature anomaly. Telszewski et al. (2009) suggested reducing the datasets into a moderate-sized map, not only for consideration of calculation efficiency, but also to provide sufficient representation of patterns to extract all characteristic patterns. To find out the most suitable map size, several tests were carried out: map sizes of 100 × 100, 80 × 80, 64 × 64, 40 × 40, and 30 × 30 were tested. The best one was the 40 × 40 with high calculating efficiency, good estimation, and low root-mean-square error (RMSE) level.

For the SOM training process, the data inputs are SSTA, SSSA, and SSHA in the North Atlantic Ocean (25°–63°N, 80°–0°W). In this paper, the SSTA, SSSA, and SSHA were calculated from the monthly climatology field so as to avoid the climatology seasonal variation signal; this would improve the sensitivity of the SOM method to temperature anomaly.

Variation of each parameter was normalized to one by the standard deviation, and the mean value was set to zero before training: x′ = (xxm)/σx, where x is the parameter to be normalized, x′ is the normalized parameter, σx is the standard deviation of x, and xm is the mean value of x (Vesanto et al. 2000). The SOM map was trained every year, and 48 000 data triplets were used to train one map. In the trained map, each neuron has three components representing all the combinations of input variables (SSTA, SSHA, and SSSA). The relationship between these three training parameters, with similar patterns mapped to neighboring regions and dissimilar patterns mapped to separate locations, then became the foundation for the labeling and estimation processes.

For each layer, Argo subsurface temperature anomaly data at that depth was used to label the trained neural network: 70% for labeling and 30% for testing. According to the SSTA, SSHA, and SSSA, the STA values were labeled onto the nearest neurons by a definition of Euclidean distance (Telszewski et al. 2009). For the neurons that have more than one STA value labeled, the averaged STA value was the final labeling value. Estimation of STA was carried out using the labeled SOM map and sea surface information. Input vectors of arbitrary position and time had one neuron in the labeled SOM map according the Euclidean distance; the STA of that neuron became the estimation of the input vectors. The estimations were implemented every month from the surface down to 2000-m depth from January 2005 to December 2010 with Argo sea surface data as input and from January 1993 to December 2009 with remote sensing data as input.

3. STA estimation using Argo and remote sensing sea surface data

a. Horizontal maps of STA

A total of 72 monthly-averaged STA datasets at all depth levels in the North Atlantic were estimated using a SOM neural network, which is trained using Argo sea surface data and is labeled using Argo STA data. Comparison between the estimated STA and Argo gridded data shows that the basic patterns of STA have been retained by the SOM method (Fig. 2). The STA variation at 300-m depth near the western boundary is from −3° to 3°C. From the Gulf Stream separation area to the Irminger Sea, the variation is 5–6 times larger than other areas, where the STA range varies from −0.5° to 0.5°C. The in situ and estimated STA maps show a similar spatial structure as the SSTA and SSHA: large anomaly values located along the Gulf Stream path, with the negative anomalies having considerably larger magnitude than the smaller positive anomalies (Fig. 3). The sensitivity tests also indicate that SSTA and SSHA are the two major driving forces for the STA in the western boundary area (Fig. 11; this will be discussed in detail in section 3e).

Fig. 2.
Fig. 2.

Comparison of STA at 300-m depth from (left) Argo and (right) SOM neural network estimation, January, April, July, and October 2006.

Citation: Journal of Atmospheric and Oceanic Technology 29, 11; 10.1175/JTECH-D-12-00013.1

Fig. 3.
Fig. 3.

(left) SSTA and (right) SSHA from Argo, in the North Atlantic for January, April, July, and October 2006. Absolute dynamic depth anomaly (ADDEP; equal SSHA at the sea surface) was used as SSHA here.

Citation: Journal of Atmospheric and Oceanic Technology 29, 11; 10.1175/JTECH-D-12-00013.1

b. Time series

For each pixel and subsurface layer (23 layers, from 30 to 2000 m), the relationship between the time series of SOM-estimated STA and Argo STA were investigated using correlation coefficient (γ), RMSE, and regression coefficients. The highest correlation through the water column from 30- to 2000-m depth, the depth of the layer that has highest correlation (Fig. 4), and the RMSE between the two datasets at that depth was calculated. In most of the areas between 25° and 55°N, the correlation is over 0.8 with only two exceptions where correlation is low: the center of the North Atlantic gyre and the western part of the central Labrador Sea. The depths determined by maximum γ are larger in the western part of the basin (Fig. 5), extending as far as about 700- to 800-m depth, while in the eastern part and the northern part the depth is much smaller and is comparable to the MLD (less than 100 m, de Boyer Montégut et al. 2004; Chu and Fan 2010).

Fig. 4.
Fig. 4.

Maximum correlation coefficient (γ) between estimated STA by SOM neural network (STASOM) and STA from Argo (STAArgo) from ~30- to 2000-m depth in the North Atlantic. The solid contour line is for γ = 0.8; the dashed contour line is for γ = 0.6. Areas noted as a, b, c, and d are for the labeling and testing in discussed in section 3d—a: western part of the North Atlantic subtropical gyre, 32°–37°N, 65°–70°W; b: central part of the midlatitude North Atlantic, 35°–40°N, 40°–45°W; c: eastern part of the midlatitude North Atlantic, 35°–40°N, 15°–20°W; and d: the subpolar gyre of the North Atlantic, 45°–50°N, 40°–45°W.

Citation: Journal of Atmospheric and Oceanic Technology 29, 11; 10.1175/JTECH-D-12-00013.1

Fig. 5.
Fig. 5.

Depth determined from the maximum correlation coefficient (γ) between STASOM and STAArgo through the water column from ~30 to 2000 m in the North Atlantic.

Citation: Journal of Atmospheric and Oceanic Technology 29, 11; 10.1175/JTECH-D-12-00013.1

The thermal and dynamic mechanisms of the eastern/western parts of the North Atlantic are completely different. In the western part, the major driving force is the Gulf Stream through strong advection and mixing. The seasonal thermocline can reach up to 1000-m depth (Figs. 6a and 7a,c), inducing large variations of STA along the Gulf Stream, where the magnitude is about 4°C (−2.4°–1.9°C). However, in the eastern part of the ocean, especially east of the mid-Atlantic Ridge (Fig. 6c), there are two depths where the temperature variation is relatively large: the mixed layer, extending within less than 100 m from the surface, and an “undercurrent” of warm, high-salinity water outflowing from the Mediterranean Sea (Bozec et al. 2011), located at about 800~1200-m depth. The temperature anomaly ranges between −0.6° and 0.6°C, and its variation is about one-third to one-fourth of that in the western basin.

Fig. 6.
Fig. 6.

Argo STA profiles from January 2005 to December 2010 [Figs. 6a–e in areas a, b, c, d, and e; the geolocation is indicated in panel (f); the bold green line shows the depth determined from maximum STA variance, while the red dashed line is the depth determined from the maximum correlation coefficient (γ) between STASOM and STAArgo], and depth determined from maximum STA variance from ~30 to 2000 m in the North Atlantic [see panel (f)].

Citation: Journal of Atmospheric and Oceanic Technology 29, 11; 10.1175/JTECH-D-12-00013.1

Fig. 7.
Fig. 7.

Typical subsurface temperature profiles in (a),(c) western (at 35°N, 60°W) and (b),(d) eastern (at 38°N, 20°W) basins in the midlatitude North Atlantic during the months of (a),(b) April and (c),(d) December 2005. The variables plotted are monthly climatology temperature (STClimat), temperature from Argo (STArgo), and temperature estimated by SOM neural network (STSOM) as labeled in (b). RMSE between STAs profiles from Argo and SOM estimation, and RMS of Argo STA was noted.

Citation: Journal of Atmospheric and Oceanic Technology 29, 11; 10.1175/JTECH-D-12-00013.1

The correlation coefficients at 300-m depth were chosen to show the quality of the method. The estimation based on the SOM neural network has a relatively better performance in the Gulf Stream and in the North Atlantic Current path, with the correlation coefficient being about between 0.8 and 1.0. Low correlation coefficient values were found near the center of the Atlantic subtropical gyre, Bay of Biscay, and North Atlantic Ocean off the coast of Portugal and in the Labrador Sea. The latter two areas have unique thermal dynamic processes that contribute to the change in thermal structure: the Mediterranean outflow (Rahmstorf 1998; Bozec et al. 2011) and deep convection, which is the source of Labrador Seawater (Marshall et al. 1998). The ratio of RMSE between Argo STA and SOM-estimated STA to the total variation of Argo were obtained. The areas of relatively smaller ratio (<0.4) almost overlap the areas of high correlation coefficients (>0.8). The areas defined by these two parameters are those where the SOM algorithm has highest confidence level for the STA estimation at 300 m or deeper.

c. Vertical profiles

The depth at which the SOM STAs have the largest correlation with the Argo STA measurements varies tremendously by location. For example, in the western midlatitude North Atlantic, the depth of largest correlation can be as high as 500–700-m depth, while in most other areas, it is only about 100 m deep (Fig. 5). To aid in understanding the physical meaning of this depth, Fig. 6 illustrates the Argo monthly STA and temperature profiles in selected areas with a different dynamic characteristic. The depths of the maximum STA variation and maximum correlation coefficient show a general agreement, especially in the western basin of the North Atlantic, where this depth is near the bottom of the thermocline. Although the depth at the maximum correlation coefficient in area d (Fig. 6d) is very close to the sea surface, the STA variance is about 4°C, and the SOM algorithm has good STA estimation at 500-m depth. Fig. 7 shows the typical temperature profiles in the eastern and western basins of midlatitude North Atlantic (35°N). In the western basin, the SOM algorithm has good agreement from the surface to about 1000 m, while in the eastern part, the SOM algorithm tends to underestimate the STA, which means that the temperature profile has less variation and more closely resembles the climatology (Fig. 8). Along the Gulf Stream path, the STA profiles have large variance near the surface, through the mixed layer, and in the middle of the thermocline (about 800-m depth).Variance is instead rather small at a depth of 350 m. The STAs are in opposite phase at those two depths. The contribution from these two depths may compensate each other. In this situation, it would be more difficult to predict STA from sea surface signal. The maximum STA is between −0.7° and 0.7°C, and this relatively small variation is due to the sustained strength of the Gulf Stream. Moreover, in those areas where the Gulf Stream meanders considerably and produces many eddies, the magnitude of STA variance can be as high as 4°C (areas a, b, and d shown in Figs. 4 and 6a) and 2–3 times larger than in the Gulf Stream before the separation.

Fig. 8.
Fig. 8.

Cross section of correlation coefficient (γ) between STA estimated from SOM neural network and STA from Argo from the surface (30 m) to 1100 m at 35°N in the North Atlantic.

Citation: Journal of Atmospheric and Oceanic Technology 29, 11; 10.1175/JTECH-D-12-00013.1

d. Validation: Comparing labeling and independent data

The gridded Argo STA datasets were randomly divided into two parts during the labeling process of the SOM estimation. About 70% of the data was used for labeling the SOM map and the remaining 30% was used as independent data to test the SOM estimation. Four regions (shown in Fig. 4) were selected for the following comparisons: SOM-estimated STA, labeling Argo STA data, and independent Argo STA data (data that is not used for labeling). The results are shown in Fig. 9 (for 300-m depth). The coefficients of the results for comparison between the time series of SOM STAs and Argo STAs are listed in Table 1 (also at 100-, 500-, and 700-m depths).

Fig. 9.
Fig. 9.

Time series of monthly STAs at 300-m depth in the North Atlantic 2005–10 [(a)–(d) areas a, b, c, and d in Fig. 4, respectively]. Colored lines: red solid line = STA estimated from SOM (STASOM), blue solid line = STA from labeling data (STALaboratory), and green starred line = STA for independent Argo data (STAInd). Here γ is correlation coefficient between STASOM and STAInd, and RMSE is the root-mean-square error between STASOM and STAInd.

Citation: Journal of Atmospheric and Oceanic Technology 29, 11; 10.1175/JTECH-D-12-00013.1

Table 1.

Comparisons of the SOM STA and Argo STA at different locations and depths.

Table 1.

There is good consistency as expected between the labeling datasets and the testing datasets, which were randomly sampled from the same data collection. The relationship between SOM STA and Argo STA varies with time and location. Generally speaking, the SOM-based STA is tending to underestimate the STA. The RMSE between them is about 20% of the total variance of Argo STA. The correlation coefficient at 100-m depth is at the level of between 0.7 and 0.9 (Table 1) with the coefficient for linear regression between 0.7 and 0.9. On the eastern side of the North Atlantic (area c in Figs. 4 and 8), which is not included in the high-confidence area, the SOM estimations have some difficulties reproducing the in situ STA variations. The RMSE level is comparable to the in situ STA variation as well as to the accuracy of the SOM estimation method. Along the Gulf Stream path (areas a, b, and d), where many eddies are generated and thermal structure variation is high, the SOM estimation has good performance between the depths of 100 and 700 m; the γ remains around 0.8–0.91 (especially in area d, where γ lies between 0.88 and 0.9) because of the large variation of STA.

The significance of correlation between STA estimated by SOM and Argo gridded STA at 100- and 300-m depth in the regions of the Labrador Sea, Bay of Biscay, and off the Portugal coast highlights that the STA derived by the SOM method is not significantly correlated to the measured Argo STA at 300-m depth, indicating primarily that the SOM method does not work well for that depth in that area. It is consistent with the results from the time series comparison of area c (position shown in Figs. 4 and 6f): the correlation coefficient reduces to 0.5 at the depth of 300 m and 0.28 at a depth of 700 m (Figs. 8 and 9c).

e. Sensitivity of salinity and climatology in SOM estimation

Dhomps et al. (2011) used Argo salinity profiles instead of salinity climatology in calculating sea level anomalies and DHA and obtained an improvement of 35% in the comparison of these two datasets. Comparisons of the SOM estimations were carried out with different training inputs to test the sensitivity of the SOM network to salinity (Fig. 10). The four input groups are 1) SSTA and SSHA; 2) SSTA, SSHA, and SSSA; 3) SSTA, SSHA, SST climatology (SSTC), and SSH climatology (SSHC); and 4) SSTA, SSHA, SSSA, SSTC, and SSHC. With the SST and SSH climatology, the estimation was improved up to 30% in the Labrador Sea. In the Irminger Sea, however, the improvement of SSS was reduced.

Fig. 10.
Fig. 10.

Sensitivity of correlation coefficient (γ) between STA estimated from SOM neural network and STA from Argo to the different input for SOM: (left) changes in γ and (right) the depth for the changes. (top)–(bottom) Training inputs are (a),(b) γ(SSTA, SSHA, climatology)–γ(SSTA, SSHA); (c),(d) γ(SSTA, SSHA, SSSA, climatology)–γ(SSTA, SSHA, SSSA); (e),(f) γ(SSTA, SSHA, SSSA, climatology)–γ(SSTA, SSHA, climatology); (g),(h) γ(SSTA, SSHA, SSSA) – (SSTA, SSHA). Grids where Δγ < 0.1 were masked.

Citation: Journal of Atmospheric and Oceanic Technology 29, 11; 10.1175/JTECH-D-12-00013.1

By comparing the results with SSSA as one of the inputs in training SOM network, the estimations in the (subtropical) eastern basin of North Atlantic and in the Labrador Sea are improved significantly (up to 30% in the subtropical North Atlantic, where strongest evaporation takes place) while it is less (10%) elsewhere. With the SST and SSH climatology, the estimation was improved up to 30% in the Labrador Sea and Irminger Sea. Along the Gulf Stream path, the improvement is quite limited (less than 5% improvement) when using the SSSA, SST, and SSH climatology. Furthermore, as previous results already show, even the STA estimations with only SSTA and SSHA have a very low RMSE with high correlations (about 0.8~1.0 and p value is 0.01).

The sensitivity of the salinity in the subtropical ocean (eastern basin) is increased by about 20% when the SST and SSH monthly climatology is included in the training process, indicating that the seasonal variation of SST and SSH plays an important role in the development of subsurface thermal structures. The depths at which the SOM method is sensitive to climatology inputs are from about 1600 to 2000 m at high latitudes and from 1000 to 1500 m in the subtropical North Atlantic. The highest sensitivities of salinity are found near the surface, while with SST and SSH climatology, the depth of highest sensitivity in the subpolar ocean reaches down to 1200-m depth.

f. STA estimation from remote sensing data for the pre-Argo era

Since the SSS data in the 1990s is not available from remote sensing, in this application, the datasets used for neural network training contain Argo SSTA and SSHA only (from 2005 to 2009). With NOAA optimum interpolation SST V2 data (derived from remote sensing and in situ measurements) and altimetry MSLA data since 1993, the STA at 300-m depth was extrapolated backward to January 1993. The STAs at 300 m in January 1994 in the midlatitude North Atlantic, as an example, show reasonable agreement with the SSTA and SSHA measurements (Fig. 11), including the basic horizontal extension and locations of extreme values of SSTA.

Fig. 11.
Fig. 11.

Remote sensing data of January 1994 [(a) SSTA and (b) SSHA] and (c) STA at 300 m from SOM estimation with remote sensing data as inputs in the North Atlantic.

Citation: Journal of Atmospheric and Oceanic Technology 29, 11; 10.1175/JTECH-D-12-00013.1

4. Discussion and conclusions

The SOM neural network approach is good for visualization and analysis of multidimensional data (Liu and Weisberg 2011). However, there is the possibility that the information of the training data is overly compacted so as to introduce errors during the estimation. The training datasets with certain temporal and spatial resolution (1° × 1° and monthly data in this study) contain information about physical processes of equal or lower resolutions and frequencies. It is not reasonable to expect the SOM method to have high accuracy in the estimation of processes occurring at higher temporal and spatial resolutions and frequencies when compared to that of training datasets. However, by using gridded monthly Argo float data as training datasets, this study can correctly interpret phenomena that vary at seasonal-to-annual time scales.

The results from SOM algorithm are not constrained by the dynamical equations, which may lead to various instabilities. We checked the static stability of the reconstructed ocean. Stability is defined as (McDougall 1987). The time series of stability for Gulf Stream area at 100, 300, and 500 m (Fig. 12) is greater than 0 (which means the reconstructed ocean is stable) all the time and changed smoothly.

Fig. 12.
Fig. 12.

Time series of stability of SOM-reconstructed ocean in area a (32°N, 65°W) at depths of (a) 100, 300, and (b) 500 m.

Citation: Journal of Atmospheric and Oceanic Technology 29, 11; 10.1175/JTECH-D-12-00013.1

The relationship between sea surface signal and the subsurface temperature could vary widely because of different dynamic processes. In this paper, data from the entire North Atlantic Ocean were used to train and label the SOM, and the empirical relationship of all these areas was extracted. However, the Gulf Stream and North Atlantic Current are by far the most dominant phenomena in this area with their horizontal extent and SSTA and SSHA magnitude. In the center of subtropical gyre in the North Atlantic Ocean, warm waters build up at the top layer and there is downwelling due to the convergence of surface flow (McClain et al. 2004). In the subpolar gyre, the situation is slightly the opposite. In the Labrador Sea, warm water from the Gulf Stream cooled down and became denser, leading to deep ocean convection (Lazier et al. 2002). To predict the STA in the Gulf Stream area, the input should include data from that area. At the presence of large anomaly values, the capability of a SOM map to resolve the small temperature variation was weakened. This may be responsible for the weak correlation coefficient in the center of subtropical gyre and the Labrador Sea (Fig. 4). Figure 8 shows a cross section of correlation coefficient (γ) between STASOM and STAArgo at 35°N in the North Atlantic. The low correlation around 900-m depth between 30° and 10°W may related to the high-salinity and -temperature Mediterranean outflow, which spread at the depth of about 800–1400 m (Reid 1979; Prince et al. 1986; Arhan 1987). This is an outstanding feature in the North Atlantic, but the overlaid water will dampen the salinity and temperature variation, which leads to the difficulty of reconstruction of the STA at 700–1100 m from the SSTA and SSHA. With a SOM map trained within the eastern basin of the midlatitude North Atlantic instead of the whole North Atlantic, the estimation would improve.

SOM, as a statistical approach for parameter estimate, enables us to predict STA within the “ranges” of input data; this may underestimate and miss the signal of some large anomaly events. In the SOM map obtained in the labeling process, the STAs of the neurons are in the range of input data for labeling. For any inputs of sea surface parameter combination, one neuron will be singled out as the winning neuron, and the STA value of that neuron will be the output STA for the input data. So the SOM algorithm can only predict the STA that lies in the range of labeling data. For those large anomaly events with STA outside of the range of labeling datasets, SOM will underestimate the anomaly.

de Boyer Montégut et al. (2004) showed that, for a 0.2°C criterion, the MLD estimated from spatially averaged profiles was 25% more shallow than the MLD estimated from individual profiles. The gridded Argo data were generated from the irregularly sampled profiles with the interpolated two- and three-dimensional data with variational analysis method. (IPRC Argo gridded documentation: http://apdrc.soest.hawaii.edu/projects/Argo/data/Documentation/gridded-var.pdf.) This may be partially responsible for the errors of the SOM estimation, especially where the Argo profiler density is low.

Using the SOM map trained from anomalies defined from 2005 to 2010 climatology to estimate the STA in 1990s may introduce errors. In this study, the anomaly is defined relative to the monthly mean climatology from 2005 to 2010 Argo data rather than the annual or longer-term mean climatology (Ivchenko et al. 2011). This makes the SOM algorithm unaffected by the seasonal variations. In this study, we assumed the climatology did not change over the decades. However, there is long-term variation in the North Atlantic with multidecadal period, such as the Atlantic multidecadal oscillation (Andronova and Schlesinger 2000; Enfield et al. 2001; Dima and Lohmann 2007), which would change the seasonal climatology and as well as the spatial patterns of the physical parameters.

This paper presented an approach for estimating the subsurface thermal structures of the ocean from remote sensing data recorded at the sea surface, with the help of Argo in situ datasets. The method was validated by the Argo STA data, and applied to the western midlatitude North Atlantic with remote sensing SST and altimetry data. A SOM neural network was trained using SSTA, SSHA, and SSSA data from IPRC Argo gridded monthly sea surface datasets, and was then labeled with Argo STA data. The labeled SOM maps, together with the SSTA, SSHA, and SSSA, were then used to estimate the STA at different depths in the North Atlantic. The estimated STA maps and time series were then compared with Argo STAs, including independent datasets that were not used in the labeling processes.

Results showed that along the Gulf Stream path, the SOM STA estimation has good performance from 30- to 700-m depth, with a correlation coefficient larger than 0.8. The depths of maximum correlation coefficient show a general agreement with the maximum STA variation in this area. The labeled SOM maps were used to estimate the STA with remote sensing SST and altimetry SSH data from January 1992 to December 2004. Sensitivity tests revealed the importance of SSS information, which can significantly improve the estimation in the subtropical ocean by as much as 30%. In areas where the seasonal variation of SST and SSH is relatively large (such as high-latitude subpolar basins, the Irminger Sea, and the Labrador Sea), the monthly climatology SST and SSH can also help to improve the estimation by as much as 40%.

Acknowledgments

This research was partially supported by the NASA Physical Oceanography Program, NASA EPSCoR Program, NASA Space Grant, and NOAA Sea Grant. The authors thank Weiwei Zhang and Feili Li for the help in data analysis. We also thank Federico Ienna for editorial assistance with the English language. Argo gridded data used in this study provided by IPRC, University of Hawaii. NOAA_OI_SST_V2 data provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, from their website at http://www.esrl.noaa.gov/psd/. The altimeter products (MSLA data) were produced by Ssalto/Duacs and distributed by AVISO with support from CNES. We thank two anonymous reviewers whose comments have helped improve the manuscript.

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