1. Introduction
The westward-flowing North Equatorial Current (NEC) is an important component of the tropical Pacific circulation system. East of the Philippine coast, the NEC bifurcates to form the northward-flowing Kuroshio and the southward-flowing Mindanao Current. The bifurcation of the NEC plays an important role in the heat and water mass exchanges between the tropical and subtropical gyres (e.g., Qu et al. 1999; Toole et al. 1990).
The Sverdrup balance (Sverdrup 1947) predicts that the mean bifurcation latitude of the NEC should occur where the zonally integrated wind stress curl is zero, around 12°–14°N (e.g., Qu and Lukas 2003). The NEC bifurcation latitude also experiences seasonal variations (Qu and Lukas 2003; Yaremchuk and Qu 2004; Kim et al. 2004; Chen and Wu 2011), with its northernmost position in November/December and southernmost position in June/July (Qu and Lukas 2003; Jensen 2011). On interannual time scales, there are also meridional migrations of the NEC bifurcation (Kim et al. 2004; Qiu and Chen 2010, hereafter QC10), with connection to El Niño–Southern Oscillation (ENSO) events. The NEC bifurcation tends toward higher (lower) latitude during El Niño (La Niña) events (Qiu and Lukas 1996; Kim et al. 2004; QC10). The annual excursion of the NEC bifurcation is about 2° latitude, much smaller than its interannual excursion of 5°–6° latitude (QC10). The smaller annual excursion may be due to the along-path cancellation of annually forced Rossby waves, while such cancellation is not significant on interannual and longer time scales (QC10).
The NEC bifurcation latitude is not uniform vertically, but rather tends poleward with increasing depth, as noted in hydrographic data (Qu 2002) and numerical modeling (e.g., Kim et al. 2004; Jensen 2011).
Several previous studies have noted the relationship between the NEC bifurcation variations and basin-scale circulation changes, especially their connection with surface wind stress (Qiu and Lukas 1996; Kim et al. 2004; QC10; Jensen 2011). In particular, QC10 recently investigated interannual-to-decadal variations of NEC bifurcation and found that the bifurcation latitude is highly correlated with and thus can be estimated by the sea surface height (SSH) variations in an adjacent region (12°–14°N, 127°–130°E). They further demonstrated that SSH variations in this region (and thus the NEC bifurcation) can be explained well by the wind forcing in the western tropical North Pacific through wind-forced long Rossby wave dynamics.
In this study, inspired by QC10, we aim to study the western boundary transport (WBT) variability at the mean NEC bifurcation latitude and its relationship to wind forcing, in a dynamically realistic way by running an ocean general circulation model (OGCM) and its adjoint. Rather than directly examine the NEC bifurcation variations, here we choose to examine the WBT variations at the mean NEC bifurcation latitude because the WBT is a well-defined physical variable that can be measured with currently available in situ observational techniques. In contrast, the NEC bifurcation latitude cannot be easily measured and can be defined with different criteria. Nonetheless, our current study can still be connected with NEC bifurcation latitude variations, since the WBT at the mean NEC bifurcation latitude is highly anticorrelated with the NEC bifurcation latitude. In particular, we try to quantify the role of atmospheric forcing on the WBT variability, using adjoint sensitivity analysis as a useful dynamical tool, similar to Zhang et al. (2011, hereafter ZCR) who carried out adjoint sensitivity analysis of the Niño-3 surface temperature to surface wind stress in the tropical Pacific. We also carried out forward perturbation experiments to verify the adjoint solution and examine sensitivity fields. Furthermore, we performed hindcast experiments, as a good application of adjoint sensitivity analysis, to estimate the WBT by multiplying adjoint sensitivity with historical wind stress changes.
The paper is organized as follows. In section 2, we introduce the OGCM and its adjoint model. Main results are shown in section 3, including an examination of the adjoint sensitivity field, and description of forward perturbation and hindcast experiments. Finally, discussion and conclusions are given in section 4.
2. Model and numerical experiment design
The OGCM used in this study is the MIT general circulation model (MITgcm), which is developed at Massachusetts Institute of Technology (Marshall et al. 1997; more information can be found online at http://mitgcm.org). The MITgcm and its adjoint model have been applied to the tropical Pacific basin to hindcast the ocean state (Hoteit et al. 2005, 2008, 2010). Recently a tropical Pacific basin model similar to Hoteit et al’s previous work has also been applied by ZCR to study the sensitivity of the Niño-3 surface temperature to atmospheric forcing. Our current model setup is essentially the same as ZCR, so only key attributes and differences are discussed here. The model domain covers the tropical Pacific basin (26°S–26°N, 104°E–68°W), with constant ⅓° resolution in both zonal and meridional directions. The model topography is derived from the 5-min gridded elevations/bathymetry for the world (ETOPO5, see online at http://www.ngdc.noaa.gov/mgg/global/etopo5.HTML). The model has realistic open boundaries at 26°S, 26°N, and 104°W, except that an artificial island has been added at the southwest corner for ease of implementation of open boundary conditions (Fig. 1a). There are 51 vertical layers with fine resolution for the upper ocean (10 uniform layers for the upper 100 m). The surface forcing fields (including heat flux, wind stress, and freshwater flux) are all derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) Interim Reanalysis, which are available daily at 1.5° × 1.5° horizontal resolution (Dee et al. 2011; see online at http://data-portal.ecmwf.int/data/d/interim_daily). Initial and open boundary conditions (temperature, salinity, horizontal velocity) are derived from the combination of two global 1° × 1° data assimilation products based on the MITgcm: estimating the Circulation and Climate of the Ocean–Global Ocean Data Assimilation Experiment (ECCO-GODAE) version 2 (Köhl et al. 2007) is used for the period 1993–2003, while Ocean Comprehensive Atlas (OCCA) product (Forget 2010) is used for the period 2004–07.
(a) The domain for the tropical Pacific regional model. Active ocean grids are indicated by the cyan shading. The red rectangle shows the region for (b), while the black rectangle indicates the wind perturbation region (section 3b). (b) Mean sea surface height (m) simulated by the tropical Pacific regional model. Mean velocity (m s−1) at 15-m depth is also overlaid as vectors with scale shown in the top-left corner. The zonal range (125.33°–126.67°E) for the meridional transport definition is indicated by the blue solid line at 12°N.
Citation: Journal of Physical Oceanography 42, 11; 10.1175/JPO-D-11-0229.1
Horizontal diffusivity and viscosity are both parameterized by laplacian and biharmonic schemes, with coefficients 3 × 103 m2 s−1 and 1 × 1012 m4 s−1, respectively. Laplacian diffusivity and viscosity are used in the vertical with values 2 × 10−5 m2 s−1 and 1 × 10−4 m2 s−1, respectively. These diffusivity and viscosity schemes in both horizontal and vertical are kept the same for all numerical experiments in this study. Relatively high horizontal viscosity was chosen to damp mesoscale eddies in the forward runs, smoothing and simplifying the background fields for the adjoint calculation. Identical viscosity magnitudes are also used in the adjoint run to suppress high small-scale sensitivities while preserving the large-scale patterns in the adjoint run (about this point, refer to detailed discussion in section 2d of Hoteit et al. 2005). Forward simulations with 1 × 103 m2 s−1 horizontal Laplacian viscosity had more high-wavenumber variability but were similar at the larger scales. Because the adjoint is linearized, horizontal viscosity in the adjoint acts as a linear filter, attenuating high-wavenumber structure.
As shown by ZCR, the tropical Pacific regional model has been tuned and validated using in situ observations and other modeling results, as the current regional model is based on previous works published in Hoteit et al. (2005, 2008, 2010). Those validations are not repeated here and readers are referred to the references above for details. Here we show the features most relevant to our current study: mean SSH and surface current at 15 m (Fig. 1b). Major ocean surface currents and structures, that is, the NEC and its bifurcation, the Kuroshio, the Mindanao Current, and the North Equatorial Counter Current (NECC), have all been realistically simulated. The Mindanao Dome with its center around 7.5°N, 130°E (indicated by lower SSH values in Fig. 1b) is also represented well by the model.
Compared with historical studies mentioned in the introduction, the model simulates the meridional migrations of the NEC bifurcation with correct amplitude and phase of seasonality, as well as on interannual time scales with higher (lower) latitude during El Niño (La Niña) events.
The tropical Pacific regional model also reproduces ocean variability patterns well. As an important dynamical variable, SSH integrates ocean interior variability, thus its variability can be regarded as an effective parameter for checking model performance in representing ocean variability. Compared with the merged Ocean Topography Experiment (TOPEX)/Poseidon and Jason altimeter measurements (data source http://www.aviso.oceanobs.com/), the model simulates interannual SSH variations well for the period 1993–2007. The spatial patterns of interannual SSH standard deviation simulated by the model, that is, high standard deviation values in the eastern equatorial Pacific centered along the equator and two off-equatorial high standard deviation regions in the western basin near the boundary, are very similar to that observed by altimeter, although the model has slightly weaker standard deviation values (Figs. 2a,b). The temporal correlation of SSH between model simulation and altimeter measurements is generally high (0.8–1.0) for most areas in the tropical Pacific (Fig. 2c), with small 2–3 cm root-mean-square (RMS) differences (Fig. 2d). Since no observational data are assimilated into the model run, good matching of SSH variability suggests that the model can capture large-scale ocean variability well despite suppressed small-scale variability, and is adequate for the current study of the WBT transport at the mean NEC bifurcation on monthly and longer time scales.
(a) Interannual standard deviation of sea surface height (SSH) anomalies simulated by the model. (b) As in (a), but for SSH anomalies based on altimeter measurements. Also shown are (c) correlation and (d) RMS differences between model and altimeter SSH anomalies.
Citation: Journal of Physical Oceanography 42, 11; 10.1175/JPO-D-11-0229.1
Adjoint models are widely used in meteorology and dynamical oceanography. Errico (1997) gave an excellent overview and heuristic explanation of adjoint model application. Marotzke et al. (1999) provided a comprehensive mathematical derivation of adjoint sensitivity (see their section 2) in their study of Atlantic heat transport sensitivity with the MITgcm and its adjoint model. The reader is referred to the references cited above for details about adjoint model derivation and construction. The adjoint model of the MITgcm is generated by automatic differentiation of numerical models with the Transformation of Algorithms in FORTRAN (TAF) compiler (Giering and Kaminski 1998; Heimbach et al. 2005). An OGCM can be treated as a sequence of operations with each code line representing a compositional element. The TAF, as a transformation tool, applies the chain rule to the code, line by line, to generate the tangent linear and adjoint model (Heimbach et al. 2005). The adjoint model calculates the sensitivity (i.e., the partial derivative) of the cost function J with respect to the control variable υ, which is simply 
For the current study, we are interested in the variability of the meridional boundary transport east of the Philippine coast at the mean bifurcation latitude of the NEC, and its relationship to atmospheric forcing. As a consequence, the cost function is defined as the monthly mean meridional transport over the last month of a two-year forward model run in the upper 400 m immediately east of the Philippine coast from 125.33° to 126.67°E across 12°N (refer to Fig. 1b). The choice of this section for transport definition is guided by the vertical structure of meridional velocity along 12°N (Fig. 3). High standard deviation of meridional velocity occupies the upper layer near the western boundary (Fig. 3a). Meridional velocity in the upper 500 m within ~2° of the western boundary varies coherently, and such coherence tends to extend deeper to at least 2000 m (Fig. 3b). Farther east, the meridional velocity is generally anticorrelated with the western boundary transport. Therefore, there is a dipole-like structure in the region within 5° of the western boundary. Unfortunately there is no in situ data to verify such a vertical structure of meridional velocity variability. Nonetheless, very similar vertical structure can also be identified with an ocean reanalysis product—Simple Ocean Data Assimilation (SODA; Carton et al. 2000; see online at http://soda.tamu.edu/opendap/SODA_2.2.4/). This motivated the transport definition, which is meant to encompass upper ocean transport in the narrow western boundary current region at the mean NEC bifurcation latitude.
(a) Standard deviation (cm s−1) of meridional velocity during 1993–2007 along the mean NEC bifurcation latitude 12°N. (b) Correlation between western boundary transport (125.33°–126.67°E, 0–400 m, indicated by the rectangle) and meridional velocity everywhere along 12°N during 1993–2007. Only regions with high correlation (>0.6 or <−0.6) are shaded. (c) As in (b), but based on SODA reanalysis dataset. Please note there are some slight differences in the bathymetry between our model and SODA.
Citation: Journal of Physical Oceanography 42, 11; 10.1175/JPO-D-11-0229.1
For ease of explanation, we set t = 0 as the end of a forward run. Thus a two-year forward model runs from −24 months to 0 month. Then the adjoint model generates the adjoint sensitivity of this WBT to control variables going from 0 to −24 months backward in time. The definition of the meridional transport, especially the depth range, is somewhat arbitrary. However, we tried different depths (e.g., 300 m) to represent the upper-ocean WBT, and found our main conclusions still hold well.
Two adjoint experiments are carried out: one is for the period 2005/06 with reanalysis atmospheric forcing and open boundary conditions; the other is a climatological two-year run with climatological atmospheric forcing and open boundary conditions to generate the adjoint sensitivity under climatological conditions.
3. Results
a. Analysis of adjoint sensitivity field
The adjoint model provides an alternative perspective for understanding how the WBT east of the Philippines is sensitive to control variables in the past, including atmospheric forcing fields (especially wind stress), over the whole model domain. As discussed by our previous study ZCR, there is similarity between the adjoint sensitivity and regression coefficient (see mathematical derivation in section 4 of ZCR). Nonetheless there is one fundamental difference between adjoint sensitivity analysis and regression analysis (or some similar statistical analysis): statistical analysis usually does not guarantee any causality and underlying mechanisms (could be due to coincidence), while the adjoint sensitivity cannot only indicate the relationship but also reveal the underlying mechanism since full ocean dynamics are kept in the process of derivation of adjoint sensitivity. In other words, the adjoint model is dynamics based, therefore its solution is determined by the dynamics contained in the OGCM and model states in the forward run, not by other factors such as atmospheric forcing structure or coincidence. The adjoint model can also explore variability in the linearized dependence with different background ocean conditions, as ZCR examined the event-to-event difference of adjoint sensitivity of Niño-3 surface temperature to surface wind stress during different ENSO events.
The 2005/06 adjoint run reveals the evolution of the adjoint sensitivity of the monthly mean WBT in Decemeber 2006 to wind stress in previous months over the whole model domain (Fig. 4). The physical interpretation of this sensitivity field is that, if the wind stress at some time lead (e.g., three-month lead) is perturbed over a single grid box (⅓° × ⅓°) for one month with one standard unit of wind stress (i.e., 1 N m−2), the monthly average WBT east of the Philippines in Decemeber 2006 will change by the given number of Sverdrups (1 Sv ≡ 106 m3 s−1).
Adjoint sensitivity (10−2 Sv N−1 m2) of monthly mean meridional transport in the upper 400 m immediately east of the Philippine coast from 125.33° to 126.67°E across 12°N in December 2006 to monthly wind stress in previous months during 2006. Colors show sensitivity to zonal wind stress, while vectors show sensitivity to both zonal and meridional wind stress.
Citation: Journal of Physical Oceanography 42, 11; 10.1175/JPO-D-11-0229.1
At −1 month, east of the Philippine coast, there is a dipolar structure with strong positive (negative) sensitivity to zonal wind stress north (south) of 12°N latitude. Sensitivity to both zonal and meridional wind stress reveals a strong anticyclonic structure (as indicated by vectors in Fig. 4a). This anticyclonic sensitivity structure is offset farther eastward and southward with increasing time lags and can still be easily recognized at −11 months (Fig. 4f). Zonal phase speed can be derived from the evolution of the adjoint sensitivity field, and is about 0.23 m s−1. The propagation phase speed is faster than the theoretical first baroclinic mode’s phase speed, but in good agreement with altimeter observations (e.g., Chelton and Schlax 1996; Killworth et al. 1997). Thus both the evolution of the adjoint sensitivity field and the propagation phase speed imply that wind-forced baroclinic Rossby wave dynamics are the underlying mechanism. The southward back-propagation shows the refraction of the waves by the planetary waveguide, showing the generalization from long Rossby waves assumed in QC10.
Interestingly, in the first two months significant sensitivity can also be seen around the archipelago, especially along the west coast of the Philippines (Fig. 4a), where topographic Rossby waves carry the influence of alongshore winds.
Furthermore, the sensitivity of the WBT to annual mean wind stress in the past year can be derived by temporal integration of instantaneous adjoint sensitivity field (Fig. 5). Physically it means that a one-year duration unit wind stress anomaly at a particular grid point would produce a perturbation in the WBT by the given number of Sverdrups. A broad anticyclonic structure emerges, mainly significant in the western subtropical Pacific basin north of the equator. Such anticyclonic distribution of wind stress curl and its relationship with the WBT east of the Philippines is close to the well-known Sverdrup Balance (Sverdrup 1947), which relates steady-state large-scale ocean circulation to surface wind stress curl forcing and can explain much of the large-scale circulation in the Pacific (e.g., Deser et al. 1999; Hautala et al. 1994). Note that enhanced sensitivity in the tropical instability wave (e.g., Contreras 2002) region north of the equator from 140° to 120°W. This is a result of amplification of wind stress perturbations by the instability, even with the relatively high viscosity.
Adjoint sensitivity (10−1 Sv N−1 m2) of monthly mean meridional transport in the upper 400 m immediately east of the Philippine coast from 125.33° to 126.67°E across 12°N in December 2006 to annual mean wind stress during 2006. Colors show sensitivity to zonal wind stress, while vectors show sensitivity to both zonal and meridional wind stress.
Citation: Journal of Physical Oceanography 42, 11; 10.1175/JPO-D-11-0229.1
b. Forward perturbation experiments
As mentioned in section 2, the adjoint model is an efficient tool for finding the sensitivity of one output (i.e., the cost function) to all inputs (e.g., wind forcing). There is also a traditional way to derive sensitivity in the forward manner, by trial perturbation, which has been widely used in numerical modeling (e.g., Rüdiger et al. 2006; Zhang and McPhaden 2008). By applying a sufficiently small perturbation to the forcing (e.g., wind forcing), we can derive the sensitivity of all outputs to one input, by comparing the perturbed model trajectory with the control (unperturbed) one. So in this subsection, forward perturbation experiments are discussed for two purposes: (i) verification of the adjoint sensitivity to see whether it can be matched with the solution from forward perturbation experiments, and (ii) examination of the physical processes to see how inputs (e.g., wind forcing) in the perturbation region can affect the output (i.e., the cost function—the WBT as defined here).
For the current study, we carried out perturbation experiments in which the zonal wind stress was perturbed uniformly with magnitude 0.05 N m−2 for one week over a 6° × 1.5° box centered at 12°N, 162.5°W. The box size and location was chosen by considering the resolution and grid location of zonal wind forcing from the 1.5° × 1.5° ECMWF Interim Reanalysis (see the black rectangle box in Fig. 1a). The only difference between the perturbed and control runs is a zonal wind stress perturbation for one week over that region. The sensitivity, in this case the partial derivative of the cost function (the WBT) with respect to the control variable (the zonal wind stress), can be approximated by the ratio of the change in the monthly mean WBT at 12°N in December 2006 to the zonal wind stress perturbation (Fig. 6).
Comparison of adjoint sensitivity (Sv N−1 m2) and forward perturbation-based sensitivity of the western boundary transport at 12°N to weekly wind stress over a 6° × 1.5° box centered at 12°N, 162.5°W. The adjoint sensitivity over the region (solid line) is obtained by spatial summation of the adjoint sensitivity covering grid points within that box. Crosses are obtained from perturbation experiments (see section 3b for details).
Citation: Journal of Physical Oceanography 42, 11; 10.1175/JPO-D-11-0229.1
To obtain a spatial map of such a perturbation-derived sensitivity at that time lead, one must repeat the perturbation experiment for each grid box of the model domain (or at least for each subregion at coarser horizontal resolution). By repeating the wind perturbation for one week for every four week period in 2006 for the above 6° × 1.5° region centered at 12°N, 162.5°W we can derive a time-dependent perturbation-based sensitivity for that perturbation region, which matches the adjoint sensitivity well (Fig. 6). We also repeated the same perturbation experiments but with different latitudinal locations of wind stress perturbation (one is centered at 6°N, another is centered at 0°), and found good agreement between the adjoint sensitivity and the perturbation-derived sensitivity fields (not shown). Obviously such a forward perturbation-based sensitivity is very computationally expensive, so a grid-by-grid (or region-by-region) comparison between forward sensitivity and adjoint sensitivity both spatially and temporally is impractical. So, similarly to Bugnion and Hill (2006), Hill et al. (2004), and ZCR, we are only able to compare the adjoint with forward sensitivity fields for some representative locations for validation purposes, and find that they agree with each other reasonably well (Fig. 6 as an example).
The adjoint model calculates the sensitivity (i.e., partial derivative) around a time-dependent but unperturbed model trajectory. In contrast, the forward perturbation method estimates the partial derivative by comparing the perturbed and unperturbed model trajectory. For a nonlinear system (which is generally true for most geophysical problems), solutions from these two methods can be different. This is the reason why slightly better agreement of the sensitivity between these two methods can be found at shorter time lags, that is, in late calendar months during 2006 in Fig. 6.
To test nonlinearity, both positive and negative wind stress perturbations can be applied. The former is referred to here as the “positive perturbation” experiment, and the latter as the “negative perturbation” experiment. Using SSH as an example, the SSH perturbation field from the positive perturbation (
The spatiotemporal evolution of the model state perturbation fields contains propagating features which provide some clues about underlying mechanisms. How does the wind stress perturbation in the middle of the northern equatorial Pacific affect the WBT east of Philippines about one year later? The propagating features can be clearly identified in the perturbation fields, and those originating from the perturbation region are especially helpful for understanding the physical mechanisms. The westerly wind stress anomalies in the 6° × 1.5° perturbation region centered at 12°N, 162°W create a dipolar wind stress curl structure initially: cyclonic (anticyclonic) north (south) of 12°N latitude. The dipolar wind stress curl structure can excite a dipolar SSH structure (Fig. 7a), which propagates westward from the wind stress perturbation region with varying phase speeds (Fig. 7). The equatorward positive SSH patterns move faster, while the poleward negative SSH patterns move more slowly, as expected from the planetary beta effect (e.g., Cushman-Roisin 1994). The arrival of SSH perturbations induces changes in zonal SSH gradient and the WBT accordingly, with positive (negative) zonal SSH gradient perturbations associated with northward (southward) WBT perturbations. Similarly, a Hovmöller diagram of the SSH perturbation field (
Bimonthly sea surface height perturbation 
Citation: Journal of Physical Oceanography 42, 11; 10.1175/JPO-D-11-0229.1
(a) Hovmöller diagram of sea surface height perturbation 
Citation: Journal of Physical Oceanography 42, 11; 10.1175/JPO-D-11-0229.1
Thus the above perturbation experiment clearly indicates that the excitation and propagation of Rossby waves are the main underlying mechanism for the connection between historical wind stress in the “remote” region and the WBT east of the Philippines, and that wind stress at other areas can also contribute to the transport by various processes such as refraction of the waves by the planetary waveguide, and coastal wave propagation near the Philippines. The essential job of the adjoint model is to find the transpose of the Jacobian matrix of the forward OGCM numerically. Therefore whatever dynamics and processes are kept in the Jacobian matrix will also be kept in the adjoint model (e.g., Errico 1997). Detailed examination of those possible processes is worth exploring, but it’s beyond the scope of current paper.
By applying both positive and negative wind stress perturbations, we can also quantify the nonlinearity. 
c. Hindcast experiment
The adjoint sensitivity can also be treated as an “impulse response function” or “Green’s function,” which describes the relationship between inputs (control variables) and output (cost function). ZCR performed a detailed mathematical derivation to show the correspondence between adjoint sensitivity, response functions, and linear regression coefficients (see their section 4).
The adjoint model calculates the partial derivatives of the cost function to previous fields around a time-dependent model trajectory. Consequently, the adjoint model solution depends on the chosen period of the forward run that defines the model trajectory. For example, ZCR explicitly discussed the event-to-event differences of adjoint solutions for their Niño-3 surface temperature experiments and explained the differences and similarities of the adjoint sensitivity among different ENSO events (refer to their section 3b). Consequently, 
For the period 1993–2007, the WBT east of the Philippines directly simulated by the forward model run compares well with the hindcast based on Eqs. (1) and (2) (Fig. 9a). When the adjoint sensitivity field from the 2005/06 adjoint run is used, the temporal correlation between the two monthly time series is 0.89 (exceeding 95% significance level, see Fig. 9a), and increases to 0.93 (exceeding 95% significance level) if they are low-pass filtered with a 5-month running-mean filter (Fig. 9d). The success of this hindcast experiment, that is, the fact that most of the variability of the WBT east of the Philippines can be recovered by considering just surface wind stress variability, indicates that surface wind stress forcing has a dominant impact on the WBT east of the Philippines at the mean NEC bifurcation latitude 12°N. Using adjoint sensitivity from the climatological run for the hindcast [Eq. (1)] does not change the hindcast very much, and the temporal correlation between the directly simulated and the hindcast WBT is 0.90 (exceeding 95% significance level) (not shown, refer to Fig. 9a). This supports the aforementioned assumption of time-independent adjoint sensitivity. Nonetheless, we want to point out that the assumption of time-independent adjoint sensitivity, as in the current hindcast experiment, may not be applicable to other investigations when the adjoint solution is very sensitive to the forward model state.
(a) Meridional transport (Sv) over 0–400 m east of the Philippines across 12°N from a forward model run for the period 1993–2007 (solid black line). Also plotted is the hindcast meridional transport by multiplying the adjoint sensitivity and the time-lagged wind stress over the model domain [solid red line; refer to Eq. (2)], and hindcast with only zonal wind stress in the western tropical Pacific indicated by the dashed rectangle box in Fig. 10a. (b) Hindcast meridional transports with summation over different ranges of lag. (c) Correlation between hindcast transport from each time lag and total hindcast (black line), and cumulative variance (red line). (d) As in (a), but for interannual anomalies which are derived by low-pass filtering with 5-month running-mean filter. Also over plotted are monthly Niño-3.4 SST anomalies (×2, blue line), the western boundary transport derived by Sverdrup Balance with annual wind stress curl (pink line), and the NEC bifurcation latitude derived from model meridional velocity field (green line).
Citation: Journal of Physical Oceanography 42, 11; 10.1175/JPO-D-11-0229.1
In Eq. (2), the summation over lag is for the past 1–12 months. Summations over different lag ranges were also carried out for the previous month and the previous 1–3 seasons (Fig. 9b). The correlation between the WBT due to wind forcing in the previous one month and the total hindcast over the previous one year is 0.31, while it is 0.61 (0.89) for the previous one (two) seasons. We further calculated the WBT hindcast from each time lag, that is, 
The WBT at the mean NEC bifurcation latitude 12°N is highly anticorrelated with the NEC bifurcation latitude (correlation coefficient −0.80, exceeding 95% significance; Fig. 9d). This is simply because when the NEC bifurcation is north (south) of its mean latitudinal position, the transport at the mean bifurcation latitude will be negative (positive). Further the WBT at the mean NEC bifurcation latitude is also found to be highly anticorrelated (correlation coefficient −0.90, exceeding 95% significance) with the Niño-3.4 SST index on interannual time scales, that is, warmer Niño-3.4 SST anomalies correspond with larger negative (i.e., southward) WBT anomalies at 12°N (Fig. 9d). This agrees with earlier findings that the NEC bifurcation tends to occur at higher (lower) latitude during El Niño (La Niña) events (Qiu and Lukas 1996; Kim et al. 2004; QC10). The close connection between the NEC bifurcation (or equivalently the WBT at the mean NEC bifurcation latitude) and ENSO events is due to the fact that a broad anomalous cyclonic (anticyclonic) curl pattern tends to appear mainly in the western tropical Pacific and thus push the zero zonally integrated wind stress curl line northward (southward) during El Niño (La Niña) events (QC10; Lee and Fukumori 2003).
(a) Temporal standard deviation of 
Citation: Journal of Physical Oceanography 42, 11; 10.1175/JPO-D-11-0229.1
The temporal standard deviation of 
Since the wind stress curl is directly relevant to the vorticity and Rossby wave dynamics, it would be interesting to transform the WBT sensitivity from the two components of wind stress to wind stress curl, divergence, and a planar component (A. Moore 2000, personal communication). However, this transformation is complicated and could obscure some of the simple physics highlighted here, particularly the alongshore winds, which are dynamically important but are not well-represented by a curl. Ideally we would like to discuss the footprint for the source region of wind forcing (like Fig. 10a) in terms of adjoint sensitivity of the WBT to wind stress curl and wind stress curl variability. Thus, if we could repeat the WBT hindcast in Eq. (1) using the adjoint sensitivity to wind stress curl and wind stress curl variability instead, we may get a different footprint from Fig. 10a, though the time series of total wind-driven WBT hindcast (Fig. 9a) should stay unchanged. So standard deviations of meridional wind stress and wind stress curl are also shown in Fig. 10 to give a full picture of wind forcing variability in the tropical and subtropical Pacific.
Impacts of other forcing terms (such as surface heat and freshwater fluxes) on the WBT are also examined using the same hindcasting technique [refer to Eqs. (1) and (2)], though their roles are found to be insignificant. The variance of WBT east of the Philippines, as hindcast by surface heat and freshwater fluxes only, is less than 1% of that hindcast by the wind stress only. Thus including surface heat and freshwater fluxes doesn’t change the hindcast skill. It also demonstrates the dominant effect of wind stress on the WBT east of the Philippines.
4. Discussion and conclusions
In this study, we examine the variability of the WBT at the mean NEC bifurcation latitude (12°N) and its relationship with surface wind forcing in the Pacific basin, using a new dynamical tool based on an OGCM and its adjoint model. The adjoint model provides a novel perspective for understanding how the WBT is sensitive to previous wind stress forcing. The WBT is found to be largely determined by surface wind forcing, especially in the western subtropical Pacific. Based on the analyses of both the adjoint solution and the forward perturbation experiment, we conclude that wind-forced Rossby waves are the dominant underlying mechanism for the connection between the WBT and surface wind forcing, although other physical processes can also affect the WBT as discussed below.
QC10 identified the close relationship between the NEC bifurcation latitude and SSH in the adjacent region (12°–14°N, 127°–130°E). They further successfully simulated the SSH variations in this region by considering a forced Rossby wave model under the long-wave approximation. We repeated QC10’s analysis and derived SSH variations along 12°N by integrating time-lagged wind stress curl along this latitudinal band. In the Rossby wave model, the westward phase speed is set as 0.22 m s−1, which is very close to what we derived from the adjoint sensitivity field (section 3a) and forward perturbation experiment (section 3b). We further used this long-wave-model-derived SSH at (12°N, 127°E) to hindcast the WBT east of the Philippines and found the correlation between the directly simulated and the hindcast WBT is 0.80 (exceeding 95% significance; figure not shown). The adjoint-based hindcast, as discussed in section 3c, includes impacts from wind stress across the whole model domain (i.e., the tropical and subtropical Pacific basin), while the hindcast based on the Rossby wave model only considers wind stress in the narrow latitudinal band. Though the long-wave hindcast recovers a large portion (64%) of variance in the WBT, the adjoint-based hindcast recovers about 15% more variance by including impacts of wind stress out of the narrow 12°N latitudinal band. In other words, physical processes other than the long Rossby waves, driven by wind stress outside of the narrow 12°N latitudinal band, can also affect the WBT east of the Philippines (refer to Fig. 5). Broad spatial distributions of the adjoint sensitivity field (Fig. 5) also imply that long Rossby waves are not the only possible dynamical processes to affect the WBT. Detailed examination of these physical processes is beyond the scope of current paper.
We carried out an additional adjoint model run by setting the monthly mean SSH in the region (12°–14°N, 127°–130°E) as the cost function, following QC10’s finding that the average SSH in this adjacent region can be treated as a proxy for the NEC bifurcation latitude. The adjoint sensitivity field of SSH to surface wind stress indicates similar features located farther to the east with increasing time lag (not shown, refer to Fig. 4). The hindcast experiment (section 3c) is repeated and high hindcasting skill is also found (Fig. 11). The correlation between the directly simulated and the hindcast SSHs in this region is 0.95 (exceeding 95% significance). Note that the correlation between observed and simulated SSHs is also quite high at 0.89 (exceeding 95% significance), which serves as another good validation for the model performance (note that there is no data assimilation in this model run). This additional adjoint experiment supports the finding that wind stress is the dominant factor for SSH variability in the adjacent region (12°–14°N, 127°–130°E) as QC10 identified.
The mean sea surface height (SSH, in meters) in the adjacent region (12°–14°N, 127°–130°E) east of the Philippines from a forward model run for the period 1993–2007 (solid black line). Also plotted is the hindcast SSH by multiplying the adjoint sensitivity and the time-lagged wind stress over the model domain (solid red line), and observed SSH by altimeters (dotted blue line).
Citation: Journal of Physical Oceanography 42, 11; 10.1175/JPO-D-11-0229.1
Andres et al. (2011) recently reported that large-scale wind stress forcing can affect the Kuroshio in the East China Sea (around 27°N) at two time scales: one is a fast response via barotropic Rossby waves; the other is a slow response via baroclinic Rossby waves. However, in the current study, the barotropic Rossby wave propagation is obscured for the following reasons: first, the cost function is defined as a monthly average of the WBT over the last month; and second, we focus on sensitivity to monthly wind stress. As a result, the temporal resolution is too coarse to show the propagation of barotropic waves, though they are included in the forward and adjoint sensitivity calculations.
As mentioned in section 2, higher than normal horizontal viscosity was applied in both forward and adjoint runs. Higher viscosity tends to damp mesoscale eddies, which provides a smoother background for the adjoint calculation. One impact of horizontal viscosity is the decay of Rossby waves in the forward run (or similarly the decay of adjoint sensitivity in the adjoint run), with higher viscosity associated with faster decay. Qiu et al. (1997) pointed out the decay scale of the long baroclinic Rossby wave is function of 
Sverdrup Balance reveals a simple relationship between meridional current and wind stress curl for steady-state or at low-frequencies (Sverdrup 1947). For a closed basin, the total meridional transport in the interior should be balanced by the WBT along the same latitude, therefore the WBT can be derived by the integral of wind stress curl along that latitude. This relationship between the WBT and zonal integral of wind stress curl should generally not hold for short time scales since it takes time for the ocean to adjust to varying wind forcing. The oceanic adjustment process mainly involves westward propagation of baroclinic Rossby waves, with adjustment time scale determined by the transit time for Rossby waves to cross the basin which is about two years along 12°N in the Pacific (Anderson and Gill 1975; Anderson and Killworth 1977). By integrating annual average ECMWF wind stress curl along 12°N, the total WBT implied by Sverdrup Balance is derived, which is generally consistent with the low-frequency variability of the WBT defined for the upper 400 m from 125.33° to 126.67°E (Fig. 9d). However the low-frequency variability for the model-defined WBT is weaker, which is likely because the transport integration is only for the upper 400 m. The WBT transport in the upper 2000 m from the model is in better agreement with the total WBT derived by Sverdrup Balance on periods longer than one year (not shown; refer to Fig. 3b for vertical structure of meridional velocity variability). Of course, just as with the WBT hindcast (section 3c), there are some cases where strong local wind stress curl makes the Sverdrup theory work on shorter time scales.
A prerequisite condition for applying the adjoint sensitivity analysis is to check that linearity holds well for the problem of interest, due to the general nonlinear nature of ocean dynamics. The good match between the adjoint sensitivity and perturbation-derived sensitivity (section 3b), and the high skill from the hindcast experiment which is linear in nature (section 3c), and the nonlinearity check in perturbation experiments (Fig. 8b), all imply that linearity can be assumed for our current study of the WBT east of the Philippines. Nonetheless, nonlinearity in general should be cautiously considered in any application of an adjoint model, and testing and validation are necessary before any useful conclusions can be confidently drawn (e.g., Errico 1997; Hill et al. 2004; ZCR).
The current study period 1993–2007 is constrained by the global data assimilation products which provide open boundary conditions for the current region model (section 2), and current adjoint method should also be applicable for longer periods, thus it has the potential to be applied for climate change related study. In fact, the MITgcm and its adjoint have been applied to climate change related studies by several groups: the meridional overturning circulation (MOC) on centurial time scale by Bugnion and Hill (2006), the carbon cycle by Hill et al. (2004), Indonesian Throughflow by Lee et al. (2001), and tropical water mass exchange and circulation by Fukumori et al. (2004). It is worthwhile to explore applying the adjoint method for many climate change related studies in the future, such as ocean heat content change (Masuda et al. 2010), and regional sea level change (Feng et al. 2004; Merrifield 2011).
Acknowledgments
The authors would like thank Bo Qiu and Daniel Rudnick for helpful discussions. Detailed comments on early draft by Gary Meyers and Chaojiao Sun helped to improve the manuscript significantly. We also want thank the MITgcm developers and the ECCO project for providing source codes. We also thank Matthew Mazloff, Ganesh Gopalakrishnan, Ibrahim Hoteit, and Caroline Papadopoulos for helping with implementing adjoint sensitivity numerical experiments. Critical reviews from two anonymous reviewers and the editor greatly improved the manuscript. The authors also wish to acknowledge use of the Ferret program for analysis and graphics in this paper. Ferret is a product of NOAA’s Pacific Marine Environmental Laboratory (information is available at http://ferret.pmel.noaa.gov/Ferret/). D. Roemmich and X. Zhang were supported through NOAA Grant NA17RJ1231 (SIO Joint Institute for Marine Observations). B. Cornuelle was supported by ONR Contract N00014-10-1-0273. X. Zhang was also supported by the Pacific Climate Change Science Program (PCCSP) and follow-up Pacific-Australia Climate Change Science and Adaptation Program (PACCSAP) administered by the Australian Department of Climate Change and Energy Efficiency (DCCEE) in collaboration with AusAID.
REFERENCES
Anderson, D. L., and A. E. Gill, 1975: Spin-up of a stratified ocean, with applications to upwelling. Deep-Sea Res., 22, 583–596.
Anderson, D. L., and P. D. Killworth, 1977: Spin-up of a stratified ocean, with topography. Deep-Sea Res., 24, 709–732.
Andres, M., Y.-O. Kwon, and J. Yang, 2011: Observations of the Kuroshio’s barotropic and baroclinic response to basin-wide wind forcing. J. Geophys. Res., 116, C04011, doi:10.1029/2010JC006863.
Bugnion, V., and C. Hill, 2006: Equilibration mechanisms in an adjoint ocean general circulation model. Ocean Dyn., 56, 51–61.
Carton, J. A., G. Chepurin, X. Cao, and B. Giese, 2000: A simple ocean data assimilation analysis of the global upper ocean 1950–95. Part I: Methodology. J. Phys. Oceanogr., 30, 294–309.
Chelton, D. B., and M. G. Schlax, 1996: Global observations of oceanic Rossby waves. Science, 272, 234–238.
Chen, Z., and L. Wu, 2011: Dynamics of the seasonal variation of the North Equatorial Current bifurcation. J. Geophys. Res., 116, C02018, doi:10.1029/2010JC006664.
Contreras, R. F., 2002: Long-term observations of tropical instability waves. J. Phys. Oceanogr., 32, 2715–2722.
Cushman-Roisin, B., 1994: Introduction to Geophysical Fluid Dynamics. Prentice Hall, 320 pp.
Dee, D. P., and Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553–597.
Deser, C., M. A. Alexander, and M. S. Timlin, 1999: Evidence for a wind-driven intensification of the Kuroshio current extension form the 1970s to the 1980s. J. Climate, 12, 1697–1706.
Errico, R. M., 1997: What is an adjoint model? Bull. Amer. Meteor. Soc., 78, 2577–2591.
Feng, M., Y. Li, and G. Meyers, 2004: Multidecadal variations of Fremantle sea level: Footprint of climate variability in the tropical Pacific. Geophys. Res. Lett., 31, L16302, doi:10.1029/2004GL019947.
Forget, G., 2010: Mapping ocean observations in a dynamical framework: A 2004–06 ocean atlas. J. Phys. Oceanogr., 40, 1201–1221.
Fukumori, I., T. Lee, B. Cheng, and D. Menemenlis, 2004: The origin, pathway, and destination of Niño-3 water estimated by a simulated passive tracer and its adjoint. J. Phys. Oceanogr., 34, 582–604.
Giering, R., and T. Kaminski, 1998: Recipes for adjoint code construction. ACM Trans. Math. Software, 24, 437–474.
Griffies, S. M., and R. W. Hallberg, 2000: Biharmonic friction with a Smagorinsky-like viscosity for use in large-scale eddy-permitting ocean models. Mon. Wea. Rev., 128, 2935–2946.
Hautala, S. L., D. Roemmich, and W. J. Schmitz, 1994: Is the North Pacific in Sverdrup balance along 24°N? J. Geophys. Res., 99, 16 041–16 052.
Heimbach, P., C. Hill, and R. Giering, 2005: An efficient exact adjoint of the parallel MIT general circulation model, generated via automatic differentiation. Future Gener. Comput. Syst., 21, 1356–1371.
Hill, C., V. Bugnion, M. Follows, and J. Marshall, 2004: Evaluating carbon sequestration efficiency in an ocean circulation model by adjoint sensitivity analysis. J. Geophys. Res., 109, C11005, doi:10.1029/2002JC001598.
Hoteit, I., B. Cornuelle, A. Kohl, and D. Stammer, 2005: Treating strong adjoint sensitivities in tropical eddy-permitting variational data assimilation. Quart. J. Roy. Meteor. Soc., 131, 3659–3682.
Hoteit, I., B. Cornuelle, V. Thierry, and D. Stammer, 2008: Impact of resolution and optimized ECCO forcing on simulation of the tropical Pacific. J. Atmos. Oceanic Technol., 25, 131–147.
Hoteit, I., B. Cornuelle, and P. Heimbach, 2010: An eddy-permitting, dynamically consistent hindcast of the tropical Pacific in 2000 using and adjoint-based assimilation system. J. Geophys. Res., 115, C03001, doi:10.1029/2009JC005437.
Jensen, T. G., 2011: Bifurcation of the Pacific North Equatorial Current in a wind-driven model: Response to climatological winds. Ocean Dyn., 61, 1329–1344, doi:10.1007/s10236-011-0427-2.
Killworth, P. D., D. B. Chelton, and R. A. De Szoeke, 1997: The speed of observed and theoretical long extratropical planetary waves. J. Phys. Oceanogr., 27, 1946–1966.
Kim, Y. Y., T. Qu, T. Jensen, T. Miyama, H. Mitsudera, H.-W. Kang, and A. Ishida, 2004: Seasonal and interannual variations of the North Equatorial Current bifurcation in a high-resolution OGCM. J. Geophys. Res., 109, C03040, doi:10.1029/2003JC002013.
Köhl, A., D. Stammer, and B. Cornuelle, 2007: Interannual to decadal changes in the ECCO global synthesis. J. Phys. Oceanogr., 37, 313–337.
Lee, T., and I. Fukumori, 2003: Interannual-to-decadal variations of tropical–subtropical exchange in the Pacific Ocean: Boundary versus interior pycnocline transports. J. Climate, 16, 4022–4042.
Lee, T., B. Cheng, and R. Giering, 2001: Adjoint sensitivity of Indonesian throughflow transport to wind stress: Application to interannual variability. Jet Propulsion Laboratory Publ. 01-11, 34 pp.
Marotzke, J., R. Giering, K. Q. Zhang, D. Stammer, C. Hill, and T. Lee, 1999: Construction of the adjoint MIT ocean general circulation model and application to Atlantic heat transport variability. J. Geophys. Res., 104, 29 529–29 547.
Marshall, J., A. Adcroft, C. Hill, L. Perelman, and C. Heisey, 1997: A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. J. Geophys. Res., 102, 5753–5766.
Masuda, S., and Coauthors, 2010: Simulated rapid warming of Abyssal North Pacific Waters. Science, 329, 319–322.
Merrifield, M. A., 2011: A shift in western tropical Pacific sea-level trends during the 1990s. J. Climate, 24, 4126–4138.
Qiu, B., and R. Lukas, 1996: Seasonal and interannual variability of the North Equatorial Current, the Mindanao Current, and the Kuroshio along the Pacific western boundary. J. Geophys. Res., 101, 12 315–12 330.
Qiu, B., and S. Chen, 2010: Interannual-to-decadal variability in the bifurcation of the North Equatorial Current off the Philippines. J. Phys. Oceanogr., 40, 2525–2538.
Qiu, B., W. Miao, and P. Muller, 1997: Propagation and decay of forced and free baroclinic Rossby waves in off-equatorial Oceans. J. Phys. Oceanogr., 27, 2405–2417.
Qu, T., 2002: Depth distribution of the subtropical Gyre in the North Pacific. J. Oceanogr., 58, 525–529.
Qu, T., and R. Lukas, 2003: The birfurcation of the North Equatorial Current in the Pacific. J. Phys. Oceanogr., 33, 5–18.
Qu, T., H. Mitsudera, and T. Yamagata, 1999: A climatology of the circulation and water mass distribution near the Philippine Coast. J. Phys. Oceanogr., 29, 1488–1505.
Rüdiger, G., W. Hurlin, and S. M. Griffies, 2006: Sensitivity of a global ocean model to increased run-off from Greenland. Ocean Modell., 12, 416–435.
Sverdrup, H. U., 1947: Wind-driven currents in a baroclinic ocean: With application to the equatorial currents in the eastern Pacific. Proc. Natl. Acad. Sci. USA, 33, 318–326.
Toole, J. M., R. C. Millard, Z. Wang, and S. Pu, 1990: Observations of the Pacific north equatorial current bifurcation at the Philippine Coast. J. Phys. Oceanogr., 20, 307–318.
Yaremchuk, M., and T. Qu, 2004: Seasonal variability of the large-scale currents near the coast of the Philippines. J. Phys. Oceanogr., 34, 844–855.
Zhang, X., and M. J. McPhaden, 2008: Eastern equatorial Pacific forcing of ENSO sea surface temperature anomalies. J. Climate, 21, 6070–6079.
Zhang, X., B. Cornuelle, and D. Roemmich, 2011: Adjoint sensitivity of the Niño-3 surface temperature to wind forcing. J. Climate, 24, 4480–4493.
