www.sciencemag.org/cgi/content/full/science.1188703/DC1
Supporting Online Material for Simulated Rapid Warming of Abyssal North Pacific Waters Shuhei Masuda,* Toshiyuki Awaji, Nozomi Sugiura, John Philip Matthews, Takahiro Toyoda,Yoshimi Kawai, Toshimasa Doi, Shinya Kouketsu, Hiromichi Igarashi, Katsuro Katsumata, Hiroshi Uchida, Takeshi Kawano, Masao Fukasawa *To whom correspondence should be addressed. E-mail:
[email protected] Published 24 June 2010 on Science Express DOI: 10.1126/science.1188703
This PDF file includes: Materials and Methods Figs. S1 to S3 References
Materials and Methods
4D-VAR data assimilation system. The 4-dimensional variational (4D-VAR) data assimilation approach is a strategy for deriving an optimal synthesis of observational data and model results for better descriptions of the time trajectory of the ocean state (S1, S2). A model is defined by an algorithm and its independent variables (e.g., initial conditions and boundary conditions). A “performance index” or “cost function” measures how well a model realization matches observations, while the optimization determines the independent (control) variables such that the cost function is minimized (S3). The method of Lagrange multipliers is used in this approach. An adjoint code of the ocean general circulation model is applied in an iterative procedure to seek the best possible time trajectory of model variables on the basis of the observational data. The result is a dynamically self-consistent estimate of the evolving ocean circulation (S4).
Our ocean-data assimilation system is based on a global oceanic general circulation model (OGCM), version 3 of the GFDL Modular Ocean Model (MOM) (S5). The OGCM was developed, in particular, for a higher-level representation of the deep ocean state. For this purpose, we incorporate sophisticated parameterization schemes for the bottom boundary layer (S6) and a Noh mixed layer scheme (S7) with major physical parameter values determined through a variational optimization procedure (S8). The OGCM is forced by the surface fluxes. The geothermal heating effect is represented as vertical diffusion and is implicitly incorporated by the optimization of the diffusive coefficient through the variational procedure. The horizontal resolution is 1o in both latitude and longitude, and there are 46 vertical levels for the global ocean basin. The adjoint code of the OGCM was obtained using the Transformation of Algorithms in Fortran (TAF) (S9).
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Adjoint sensitivity analysis. The Lagrange multiplier or adjoint method used in a 4D-VAR data assimilation system offers a straightforward method of determining the sensitivity of various objective functions to perturbations in oceanic state or elements governing the oceanic state (e.g., surface fluxes as external disturbances) (S10).
Consider any objective function, J, e.g., water temperature in the abyssal North Pacific. The adjoint to the state estimate can be used to calculate the sensitivities, ∂J / ∂X (r, t), where X is any variable of concern at location r at time t. We are interested in determining how a shift of model variables would affect J. Hence we consider the normalized form of δJ in the form
δJ =
∂J 1 δX (r, t ) , dz ∂X (r, t )
where δX is an estimate of the uncertainty (variance of the variable X), and non-dimensional length of dz is introduced for variables such as water temperatures that are best evaluated per unit depth.
In the adjoint formulation of the coarse-grained modeling, a linear approximation is used for nonlinear terms such as the advection term because of difficulties arising in the exact formulation, which sometimes cause computational instability (S11). In this study, in particular, we assume that the tangent linear assumption holds for the relatively slow abyssal current system and also that the practical transactions involved in the sub-grid scale parameterizations are valid in the modeled processes related to the variations in dense water formation. A model climatology of the seasonal evolution is used as the background ocean state for the determination of δJ.
Earth Simulator. Earth Simulator is a highly parallel vector supercomputer system of the distributed-memory type, and consisted of 160 processor nodes connected by Fat-Tree Network with a theoretical peak performance of 131 Tera-FLOPS. -3-
Kelvin wave propagation in the southern hemisphere. The evidence of the Kelvin waves travel throughout the southern hemisphere in our adjoint sensitivity analysis is clearly seen in the distribution of the temporal rate of change of bottom-water temperature (as Fig. 2), when the “oceanic velocity” is changed (Fig. S2). We can identify features that are typical of topographic Kelvin waves, that is, exponential diminution in wave amplitudes from the maximum at the lateral boundary and a length scale corresponds to the Rossby radius of deformation.
The Kelvin wave propagation speed. The Kelvin waves travel in a direction for which the lateral boundary is always on the left (in the Southern Hemisphere) and they propagate on a density interface with the internal-wave speed
c = ( gH
Δρ
ρ0
) = g ′H ,
where g is the acceleration due to gravity, ∆ρ the density difference through the density interface, ρ0 the mean water density, H the depth of the relevant isopycnal layer. The parameter g’ represents the reduced gravity: g′ = g
Δρ
ρ0
.
A synthesized dataset for the global ocean. Under the JAMSTEC-Kyoto-University
collaborative program, we have conducted a global ocean synthesis on the basis of in situ temperature and salinity observations, satellite altimetry and a global ocean general circulation model through a 4D-VAR data assimilation to obtain a comprehensive 4-dimensional integrated dataset from the sea surface to the ocean bottom for all the major ocean basins for the period of 1967-2006. The assimilated elements are historical hydrographic data of temperature and salinity from the
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ENSEMBLES (EN3) data set which was quality controlled using a comprehensive set of objective checks developed at the Hadley Centre of the UK Meteorological Office (S12). This dataset is largely composed of observations from the World Ocean Database 2005 (S13) and is supplemented by data from the GTSPP (Global Temperature and Salinity Profile Program) and Argo autonomous profiling floats (S14). As such, the dataset includes all available hydrographic observations, including those from
shipboard
Expendable
Bathythermographs
(XBTs)
and
Conductivity-Temperature-Depth (CTD) measurements, as well as observations from mooring arrays (such as TAO and PIRATA). NOAA Optimum Interpolation SST (NOAA_OI_SST_V2) values (S15) provided by the NOAA/OAR/ESRL (Office of Oceanic and Atmospheric Research/Earth System Research Laboratory) Physical Sciences Division, and sea level anomaly data derived from the high-precision multi-satellite
altimetry
products
multimissions
d'ALTimétrie,
produced
by
Ssalto/Duacs
d'Orbitographie
et
de
(Segment
localisation
Sol
précise/Data
Unification and Altimeter Combination System) are also assimilated. The latter were distributed by Aviso (Archiving, Validation and Interpretation of Satellite Oceanographic data), with support from CNES (Centre National d'Études Spatiales).
The assimilation is based on a 4D-VAR adjoint approach which can precisely determine the time-trajectory of the ocean states, and thus can provide analysis fields in superb quality through 4-dimensional dynamical interpolation of in-situ observations for water temperature, salinity and sea surface height anomaly, as obtained from various instrumental sources. In order to enhance the representation of the deep ocean where in-situ observations are spatially and temporally sporadic, the assimilated observations are compiled into 5o x 5o bins below 2000-m depth (Fig. S1a) and weighted at the equivalent level as those for the upper ocean.
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The analysis fields successfully capture the observed patterns of ocean circulation and surface air-sea heat fluxes. They have been extensively inter-compared with important abyssal hydrographic data around the Wake Island passage (S16), direct ocean velocity records for the subsurface layers by the Tropical Atmosphere-Ocean (TAO) mooring array (S17, S18), satellite products from Japanese Ocean Flux Data Sets based on remote sensing observations (J-OFURO) (S19), and atmospheric operational analyses by the National Centers for Environmental Prediction, Department of Energy Atmospheric Model Intercomparison Project (NCEP-DOE AMIP-Ⅱ). In particular, the bottom-water warming in the North Pacific is reproduced as a positive temperature trend of 0.005-0.002 degree Kelvin per 10-year during the recent decade (Fig. S1b), with values that are by and large consistent with the hydrographic observations recorded during the World Ocean Circulation Experiment (WOCE) and the WOCE Revisit (WOCE_rev).
Term balance diagnosis by using the synthesized dataset. A dynamically
self-consistent dataset can enable us to estimate the precise term balance of the temperature equation, thus heat budget, in the ocean because it requires no artificial sources or sinks for the temperature field (S4). The primitive equation governing the temporal change of the water temperature is ∂T ∂T ∂T = uh ⋅ ∇hT + w + Ah∇hT + κh +F, ∂t ∂z ∂z where uh is 2-dimensional velocity, w vertical velocity, ∇h 2-dimensional differential operator, Ah horizontal diffusivity, κh vertical diffusivity, F external forcing. The calculation using the synthesized field is in line with this equation, since it matches the observations through a sophisticated optimization by a 4D-VAR adjoint approach. Thus, the term balance is precisely diagnosed by examining each term. The geothermal heating effect incorporated in vertical diffusive term does not explicitly
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appear in this term balance. The combined effect including the geothermal heating is evaluated as a "vertical diffusion" in this balance. In this paper it was examined by averaging the value during 1984-2000 including WOCE and WOCE_rev observational periods, since we focus on long-term changes in abyssal water.
Quantitative diagnosis for the work performed by oceanic waves. The power
density for the oceanic waves, the rate at which work is performed by the wave passage, is defined as the temporal change in the total energy density (the sum of the potential energy and the kinetic energy per unit area) in this study. The power density for the topographic Kelvin waves across the deep trench in the Southern hemisphere (173-180oW, 50oS, 3800-5200 m-depth) in the synthesized field, which is assumed to be associated with the bottom-water warming, is roughly 2.3 x 10-1 W m-2. These signals trigger a downward reconfiguration of the abyssal isopycnal surfaces by some 50-100 meters per decade and thereby reduce the deep water current by a factor of 0.74, in line with the notion that local changes in the abyssal circulation due to the wave propagations cause the observed bottom-water warming.
Possible link between the changes in the Antarctic surface conditions and the supply of Antarctic Bottom Water. Figure S3 shows the time series of the sea level
anomaly derived from high-precision multi-satellite altimetry products produced by Ssalto/Duacs (Segment Sol multimissions d'ALTimétrie, d'Orbitographie et de localisation précise/Data Unification and Altimeter Combination System) (black curve) together with that of the net surface heat flux form the synthesized ocean dataset (green curve) during 1992-2006. The correlation coefficient value between these curves is 0.42 (p
