In the Kuroshio Extension System Study (KESS) east of Japan, bottom pressure observations over the 2 year study period exhibit strong high-frequency variability near 13 days. The first cyclostationary empirical orthogonal function mode for the band-pass-filtered KESS bottom pressure explains about 57% of the near 13 day variance and exhibits almost in-phase variability in space with a hint of westward propagation. The 13 day variability is strong during the winter and is driven by the large-scale wind stress curl over a broad region of the North Pacific. Modeling results over the North Pacific closely follow the observations and indicate that topography confines the barotropic response to the west of Emperor Seamount Chain and slows the westward propagation of the near 13 day bottom pressure variability.
 High-frequency (periods shorter than about 60 days) bottom pressure variability has not been well understood, mainly due to the sparse distribution of observations in both space and time. During the North Pacific Barotropic Electromagnetic and Pressure Experiment (BEMPEX) [Luther et al., 1987], the barotropic response observed by ocean bottom pressure recorders was shown to be related to the large-scale atmospheric forcing for time scales longer than about 10 days [Luther et al., 1990; Chave et al., 1991]. BEMPEX provided insight into bottom pressure variability using a well-sampled data set in time, but not in space.
 More recently, analysis of Gravity Recovery and Climate Experiment (GRACE) mission data has lead to an increasingly global view of bottom pressure variability. Yet, GRACE is limited in the time domain due to the monthly mapping interval, which restricts the Nyquist period to 60 days [Condi and Wunsch, 2004; Park et al., 2008; Quinn and Ponte, 2011; Quinn and Ponte, 2012]. Furthermore, Quinn and Ponte have noted that high-frequency (<60 days) bottom pressure variability is underestimated in the Ocean Model for Circulation and Tides (OMCT) that has been used to de-alias the nontidal bottom pressure variability measured by GRACE, and underestimated as well in the data-constrained solutions produced by the Estimating the Circulation and Climate of the Ocean (ECCO) project. Better understanding of high-frequency bottom pressure variability is needed to reduce these aliasing errors.
 In the Kuroshio Extension System Study (KESS) east of Japan [Donohue et al., 2008], 2 year long hourly records of bottom pressure were measured at 15 sites (Figure 1a). The barotropic signal exhibited strong high-frequency variability near 13 and 21 days contributing nearly two thirds of the deep subtidal pressure variance [Donohue et al., 2010], however, previous studies have focused on the mesoscale circulation in the KESS region after removing a site-averaged pressure signal [Jayne et al., 2009; Tracey et al., 2012].
 Local wind stress curl variability has been reported as a major factor driving the bottom pressure variability at periods shorter than about 7–10 days, whereas remote large-scale wind stress curl can be important at some periods longer than about 7–10 days [Willebrand et al., 1980; Müller and Frankignoul, 1981; Luther et al., 1990]. The focus of this study, the near 13 day bottom pressure signals, might therefore arise from a combination of local and large-scale forcing. The objective of this study is to understand what drives the strong near 13 day bottom pressure variability in the Kuroshio Extension and in particular to distinguish between local and large-scale atmospheric forcing. Notably the 13 day period is close to that of the fortnightly lunar tide (Mf), however, the amplitude of Mf in the KESS region is about 4 mm [Schwiderski, 1982; Egbert and Ray, 2003], an order of magnitude smaller than the observed near 13 day variability.
 To interpret the contextual relationship of the KESS measurements, which are restricted within the western edge of the North Pacific (Figure 1a), to the broader regional ocean's response to atmospheric forcing, a basinwide (Figure 1b) barotropic model is employed which is shown to closely replicate the observations. The KESS data, atmospheric data, barotropic model and the analytical tools used in this study are described in section 2. The near 13 day bottom pressure variability in the KESS measurements is examined, and its relationship with the atmospheric variability in the North Pacific is investigated in sections 3 and 4. A comparison with the results from the barotropic model in the North Pacific and discussion and conclusions follow in sections 5 and 6.
2. Data and Methods
 Fifteen sites within the KESS array spanned the 2 year period from 1 June 2004 to 8 June 2006 (Figure 1c). The 12 hourly detided KESS bottom pressure signal ranges ±0.3 dbar, which is equivalent to ±30 cm in height of the ocean water column, without considering variations in sea level (atmospheric) pressure. To focus upon the near 13 day signal, each time series is band-pass filtered with cut off periods of 11 and 15 days. A fourth-order Butterworth filter is run forward and backward to eliminate phase shifts.Figure 1dshows the band-pass-filtered data; all sites exhibit nearly in-phase fluctuations with highest amplitude (up to 0.06 dbar) in winter. After band-pass filtering, the near 13 day signal remains without a loss of energy (Figure 1e).
 The relationship between the near 13 day signal and large-scale atmospheric variability is investigated using wind and sea level pressure over the North Pacific (Figure 1b) from the ERA-Interim (European Centre for Medium-range Weather Forecasts Re-Analysis) data set [Uppala et al., 2005] for the same period as the KESS bottom pressure data. These data are also band-pass filtered for the 11–15 day period.Figure 2shows the 12 hourly wind stress curl and band-pass-filtered wind stress curl, averaged near the Emperor Seamount Chain (ESC, blue box inFigure 1b). The region near the ESC is where wind stress curl and KESS bottom pressure signal show the highest covariability near 13 day periods in section 4. It is interesting that the wind stress curl near the ESC shows a broad spectral peak near 13 day period (Figure 2c), considering the stochastic nature of atmospheric fluctuations (white noise at periods longer than synoptic time scales).
2.2. North Pacific Barotropic Model
 The ocean barotropic model used in this study is the ROMS (Regional Ocean Modeling System) version 3.1, which is a free-surface, terrain-following, primitive equations ocean model (http://www.myroms.org). We focus on the barotropic component of ROMS that solves the vertically integrated momentum equation neglecting density variations. The model bathymetry is setup with ETOPO5, which is a digital bathymetry data set with resolution 5 min (http://www.ngdc.noaa.gov/mgg/global/etopo5.html). The model area covers the region 100°E–70°W, 35°S–65°N with grid resolution of 1/2° in latitude and longitude. The eastern boundary of the model domain (close to the western coast of the Americas) is closed, while Flather boundary condition [Flather, 1976] is employed at the open boundaries (southern, northern and western) for barotropic normal velocity components. For the surface elevation, a gradient boundary condition is applied by setting the surface elevation at the open boundary to be equal to the closest interior value. Model results over the region and subregions of the North Pacific shown in Figure 1b are analyzed in this study.
 To calculate momentum at the sea surface, wind stress from ERA-Interim data with 1.5° resolution and 12 h intervals are used from January 2004 to December 2006; the barotropic model does not require a long spin-up time because of a rapid adjustment to the wind stress forcing. Atmospheric forcing was only by wind stress; to have included atmospheric pressure forcing would have required a global model. The wind-only forced barotropic model (North Pacific Barotropic Model, NPBM hereafter) results agree well with the KESS observational data (Figure 3). The bold and light lines in Figure 3 are the time series of NPBM results averaged over the KESS_box (region defined by the red box in Figure 1b) and averaged bottom pressure of the KESS sites, respectively. Correlation coefficient between them is 0.71 for the 2 year period. After band-pass filtering, it decreases to 0.57. Nevertheless, the records match well during the winter when the near 13 day variability is relatively strong.
 Two additional experiments were performed with different conditions of bottom topography (Table 1). One experiment uses a 5000 m deep flat bottom over the entire model domain (NPBM_flat) and the other uses real topography, but with the ESC removed (NPBM_noESC). Other conditions, including the wind forcing, are unchanged from the real topography case. A comparison between the results from NPBM with real topography (NPBM_realtopo), NPBM_flat, and NPBM_noESC helps to distinguish the effect of bottom topography on bottom pressure variability.
Table 1. List of the North Pacific Barotropic Model (NPBM) Experiments With Different Conditions of Topographya
All other conditions are the same for all three experiments.
 Band-pass-filtered KESS bottom pressure data are analyzed using a cyclostationary empirical orthogonal function (CSEOF) technique [Kim et al., 1996; Kim and North, 1997]. Space-time data,P(r, t), are decomposed into cyclostationary loading vectors (CSLVs), CSLVn(r, t), and their corresponding principal component (PC) time series, PCn(t):
where n, r, and t denote the mode number, space and time, respectively. CSLVs are orthogonal to each other and PC time series are mutually uncorrelated. Each CSLV represents a temporally evolving spatial pattern, and the corresponding PC time series shows the amplitude modulation of that pattern. The CSLVs are periodic with a nested period, d, which is set to be 13 days in this study:
The CSEOF technique is useful for extracting physically evolving spatial patterns. The physical evolution within the nested period, which is the near 13 day bottom pressure variability in this study, is captured in the resulting spatial patterns (CSLVn). The long-term evolution of the physical process is reflected in the corresponding PC time series (PCn).
 A multiple regression analysis is applied to understand the relationship between KESS bottom pressure (a target variable) and wind stress curl or sea level pressure (a predictor variable). After a predictor variable is also decomposed into CSLVs of the same 13 day nested period, its PC time series are regressed onto the PC time series of the target variable:
where PCn(P)(t) is the target PC time series for mode i, PCn(P)(t) is the predictor time series for mode n, an is the regression coefficient for mode n, and ε(t) is the regression error. In this study, 10 predictor PC time series are used for the regressions (N = 10); the first 10 PC time series explain about 79% and 96% of the wind stress curl and sea level pressure variability in the North Pacific, respectively. Last, the regression patterns of the predictor variable, CSLVn(R)(r, t), are obtained using the regression coefficients:
where CSLVn(P)(r, t) are the CSLVs of the predictor variable. The resulting spatial patterns represent the cyclic evolution of the predictor variable, which is physically consistent with the evolution of the target variable based on the regression analysis as in (3). Further details of the regression analysis based on the CSEOF PC time series are presented by Kim et al. [2012, section 2]. The relationship between the target mode and predictor variables is investigated by comparing the spatial patterns of the target mode, CSLVi(r, t), and the regressed anomalies of the predictor variables, CSLVi(R)(r, t).
3. Near 13 Day Ocean Bottom Pressure Variability
Figure 4 shows the first CSEOF mode of the KESS bottom pressure (CSLV1(r, t) and PC1(t)). The 13 daily maps show spatial patterns of the first mode and the site versus time plot (middle) replots these bottom pressures over 13 days (x axis) at the 15 sites (yaxis). The sites are arranged as in a Hovmöller plot with the site number increasing from east to west, and they exhibit almost in-phase fluctuations with a slight hint of westward propagation. This mode explains 57% of the near 13 day KESS bottom pressure variance. The second CSEOF mode explains 28% and shows a similar spatial pattern as the first mode, but with 90° (about 3 days) offset (figures not shown here). The 13 daily maps show relatively larger amplitude in the northeastern region and smaller amplitude in the southwestern region. The spatial pattern suggests that strong near 13 day variability may extend farther to the northeast than the KESS array.
 The corresponding PC time series (Figure 4, bottom) shows the lower-frequency modulation of the 13 day cyclic spatial pattern over the time period from June 2004 to June 2006. Positive (or negative) amplitude in the PC time series indicates that positive (negative) phase in the spatial patterns arrives first (equivalent to 13/2 = 6.5 days of offset). The near 13 day bottom pressure variability is strongest in the 2004–2005 winter, which is consistent with what is inferred from the band-pass-filtered time series inFigure 1d.
 It has been known that westward propagating barotropic ocean waves are induced at periods between a week and a month by large-scale atmospheric variability (larger than order of 100 km) [Willebrand et al., 1980; Gill, 1982]. Although the westward propagating signal is not very notable in Figure 4, the responsible atmospheric forcing for the near 13 day variability needs to be investigated over a larger domain than the Kuroshio Extension region, as in section 4.
4. Relationship With Atmospheric Variability
 The relationship between the near 13 day KESS bottom pressure variability and atmospheric variability in the North Pacific is examined using the regression analysis described in section 2.3. Figure 5 shows the regressed wind stress curl anomalies, CSLV1(R)(r, t), targeting the first mode of the KESS bottom pressure variability in Figure 4. The r-squared value of the multiple regression is 0.80, which means that low-frequency variability of the wind stress curl spatial patterns inFigure 5closely follows the low-frequency variability of the KESS bottom pressure (the PC time series inFigure 4) during the time period June 2004 to June 2006. The first mode of KESS bottom pressure variability is large (corresponding to the PC time series in Figure 4) when there are regions of large wind stress curl anomalies as in Figure 5. The interpretation is that the spatial patterns of wind stress curl shown in Figure 5 drive the bottom pressure anomalies shown in Figure 4.
 Interestingly, the regressed wind stress curl anomalies in Figure 5 have largest amplitude near the Emperor Seamount Chain (ESC), which is relatively far from the KESS measurements. Note how the positive and negative wind stress curl anomalies propagate eastward and show the largest amplitude near the ESC in Figure 5. The spatial scale of the regressed anomalies is so large as to cover most of the North Pacific. The puzzle of how eastward propagating wind forcing can generate westward propagating oceanic Rossby waves in the 10–30 day band was discussed by Willebrand et al. , and observations by Luther et al.  reconfirmed that their bottom pressure signals responded to wind stress curl forcing to the east of the site. Gill  simply states that barotropic waves in the ocean can be produced by the wind and estimates a westward propagating Rossby wave speed based upon the meridional scale of forcing, as discussed in section 5.
 The area-averaged time series of wind stress curl anomaly over the ESC box exhibit positive maximum in days 4–6 and negative maximum in days 11–13 (Figure 5, bottom right). The positive phase of the wind stress curl anomalies near the ESC in days 4–6 corresponds to the negative phase of the KESS bottom pressure variability in days 6–8. This 2 day time lag between the wind stress curl near the ESC and KESS bottom pressure is considered in section 5. The negative relationship between wind stress curl and bottom pressure is consistent with Ekman divergence/convergence, e.g., positive wind stress curl induces mass divergence in the ocean and consequently decreases ocean bottom pressure.
 North Pacific sea level pressure and KESS bottom pressure exhibit a strong relationship (r-squared value of the regression: 0.74).Figure 6 shows the regressed sea level pressure anomalies in the North Pacific, CSLV1(R)(r, t), targeting the first mode of the KESS bottom pressure variability. If the response of sea surface height to atmospheric pressure was exactly isostatic (“inverted barometer”), bottom pressure would remain unchanged and there would be no correlation between sea level pressure and bottom pressure. If a correlation between them is observed, it could be explained in two ways. The response of sea surface height is not fully inverted-barometric. Alternatively, the response of sea surface height is related to wind stress curl which itself is related to the atmospheric pressure [Ponte, 1994; Wunsch and Stammer, 1997].
 The inverted barometric assumption is generally considered to be applicable for time scales longer than 3–4 days and spatial scales larger than 500 km, the dominant atmospheric forcing scales in the North Pacific [Philander, 1978; Chave et al., 1992; Ponte, 1994]. One notable exception is the near 5 day Rossby-Haurwitz wave [Luther, 1982; Ponte, 1997; Hirose et al., 2001; Mathers and Woodworth, 2004; Park and Watts, 2006; Stepanov and Hughes, 2006]. Here it is suggested that the significant correlation observed between atmospheric pressure and bottom pressure arises because the sea level pressure anomalies shown in Figure 6 are related geostrophically to the wind stress curl anomalies in Figure 5and not directly related to the bottom pressure variability. This assertion is supported by the wind-only forced NPBM which reproduces well the bottom pressure variability without including atmospheric pressure forcing (Figure 3).
 The area-averaged time series of sea level pressure anomalies over the ESC box exhibit negative maximum in days 4–6 and positive maximum in days 11–13 (Figure 6, bottom right), coinciding with the timing of the regressed wind stress curl anomalies in Figure 5 but with opposite sign. The negative relationship between sea level pressure and wind stress curl is consistent with atmospheric geostrophic balance, e.g., negative sea level pressure is associated with positive wind stress curl. The location and size of the positive and negative anomalies of sea level pressure in Figure 6 match well with those of wind stress curl in Figure 5. This consistency is noteworthy because those anomalies are independently derived from the regression analysis targeting the near 13 day bottom pressure variability in the KESS array in Figure 4.
5. North Pacific Barotropic Model Results
 Spatial patterns of the regressed wind stress curl anomalies in Figure 5(wind forcing responsible for the KESS bottom pressure variability) suggest that the bottom pressure response would occur widely over the North Pacific and not be confined to the region of KESS measurements. To investigate the bottom pressure variability in the wider North Pacific, a wind-forced barotropic model is applied over the North Pacific (NPBM) as described insection 2.2. The NPBM experiments with different conditions of topography are listed in Table 1. The model results with real topography (NPBM_realtopo) agree fairly well with the KESS measurements as seen in Figure 3 (correlation coefficient 0.71) and they are analyzed in the same way as the KESS bottom pressures described in section 2.3.
Figure 7 shows the first CSEOF mode of the bottom pressure variability from NPBM_realtopo. This mode explains about 34% of the near 13 day variance. Spatial patterns of days 1–13 show positive and negative anomalies with westward propagating signals. The corresponding PC time series exhibit largest amplitude during the 2004–2005 winter, consistent with the KESS bottom pressure variability PC time series (Figure 4). The correlation coefficient between the KESS and NPBM_realtopo PC time series is 0.74; this statistically significant correlation suggests that the NPBM_realtopo first mode in Figure 7 is closely related to the KESS bottom pressure first mode in Figure 4.
 The significant correlation coefficient (0.74) between the PC time series of the KESS bottom pressure and NPBM_realtopo also implies that regressed wind stress curl and sea level pressure anomalies targeting the NPBM_realtopo first mode for its broad region of the North Pacific would not be very different from those targeting the KESS bottom pressure first mode (Figures 5 and 6); this is confirmed later (Figure 9b). Thus, comparison of spatial patterns in Figures 5, 6, and 7 shows relationship between the bottom pressure variability from NPBM_realtopo and the atmospheric variability. For example, relatively large negative anomalies of the bottom pressure in days 4–6 (Figure 7) match well in time with the relatively large positive regressed wind stress curl anomalies in days 4–6 (Figure 5) and negative sea level pressure anomalies in days 4–6 (Figure 6).
 One interesting point is that the large NPBM_realtopo bottom pressure anomalies (Figure 7) are confined in the western region of the North Pacific. Largest amplitudes of the anomalies occur west of the ESC. The area-averaged time series over the W_ESC box shows a negative maximum in days 4–6 and a positive maximum in days 11–13. The area-averaged time series over the KESS_box shows about 2 days delay compared to that over the W_ESC (Figure 7). This 2 day time lag is consistent with the time lag between the wind stress curl anomalies near the ESC and KESS bottom pressure (Figure 5). The interpretation is that the wind stress curl anomalies near the ESC induce bottom pressure anomalies over the W_ESC with no time delay (shorter than resolvable in the daily maps) and the bottom pressure anomalies propagate westward and are observed over the KESS box after 2 days.
 Westward propagating phase speed of the barotropic oceanic waves induced by wind forcing can be estimated as β/l2, where l−1is north-south scale; it is of order 20 m/s withl−1 of about 1000 km [Gill, 1982]. The propagation speed of the bottom pressure variability in the NPBM_realtopo (Figure 7) can be roughly estimated as 6.6 m/s (determined by dividing the distance between the middle of the W_ESC box (40°N, 160°E) and that of the KESS_box (36°N, 148°E) by 2 days). The north-south scale suggested byFigures 5 and 7 is 600 to 700 km, i.e., shorter than 1000 km, and the corresponding β/l2 would be about 7 to 10 m/s.
 Spatial patterns of the NPBM_realtopo CSEOF mode (Figure 7) suggest that the bottom topography may play an important role in controlling the bottom pressure variability in the North Pacific. In order to investigate the effects of bottom topography, the North Pacific Barotropic Model with 5000 m deep flat bottom (NPBM_flat) is examined. The first mode of the NPBM_flat bottom pressure variability is shown in Figure 8. This mode explains about 31% of the near 13 day variance.
 The most notable difference between the NPBM_flat (Figure 8) and NPBM_realtopo (Figure 7) results is that the locations of large anomalies in NPBM_flat are not confined in the western region of the North Pacific, but rather closely located to the large anomalies of wind stress curl (Figure 5). From the NPBM_flat results, the area-averaged time series over the KESS_box inFigure 8 shows about a 2.5 days delay compared to that over the ESC box. Note that the 2.5 days of delay is obtained from the ESC box based on the location of largest anomalies in Figure 8, not from the W_ESC box as in Figure 7. The propagation speed of the bottom pressure variability in the NPBM_flat of 10.6 m/s is roughly estimated by dividing the distance between the middle of the ESC box (45°N, 172.5°E) and that of the KESS_box (36°N, 148°E) by 2.5 days. This propagation speed appears to be as much as 60% faster than that in case of the NPBM_realtopo and is close to the above β/l2 ∼ 10 m/s estimate for l−1 ∼ 700 km [Gill, 1982], which is based on a flat bottom ocean. An intriguing question remains of how bottom topography affects the propagation speed, because the large-scale topographic slopes in this region would tend to increase the effective beta, which would not account for the modeled decrease in propagation speed for real versus flat topography.
6. Discussion and Conclusions
 The westward propagation signal in the North Pacific was barely detected in the KESS measurements (Figure 4) because of the relatively small longitudinal extent of KESS measurements, which would produce only a half-day lag for the propagation speed indicated by the NPBM_realtopo (Figure 7). This study shows that the near 13 day variability that was observed in the KESS region is a part of the larger-scale bottom pressure variability and is driven by large-scale wind stress curl in the North Pacific. Comparison between the barotropic model results with real topography (NPBM_realtopo) and flat bottom (NPBM_flat) reveals that the bottom topography strongly confines the near 13 day bottom pressure variability to the western North Pacific and slows its westward propagation.
 Slower propagation in the NPBM_realtopo compared to the NPBM_flat may be intuitively apparent, considering that wave propagation is constrained by ridges and seamounts and may depend strongly on the shape of bottom topography [Matano and Palma, 2005]. However, the limited barotropic response to the east of ESC in the NPBM_realtopo (Figure 7) is not easily explained. Figure 9 summarizes the NPBM results with different conditions of bottom topography (Table 1). An additional experiment with real topography, but removing only the ESC (NPBM_noESC, Figure 9c) shows similar spatial patterns to NPBM_realtopo (Figure 9a). It suggests that the overall bottom topography (f/H contours are shown in Figure 9), not particularly the ESC, controls the western confinement of the barotropic ocean response to atmospheric forcing in the North Pacific. This, however, does not mean that there is little near 13 day variability in the eastern North Pacific. What we showed in Figure 7 is the first mode of the NPBM_realtopo results. Some regions in the east show approximately 80% as high standard deviation as in the west and the variability in the east is captured in the higher modes (not shown). The main point is that the most dominant mode of NPBM_realtopo shows western confinement in the North Pacific and it is coherent with the variability in the KESS measurements.
 The comparison between the NPBM with and without realistic topography (Figures 7, 8 and 9) highlights the effect of bottom topography on the near 13 day barotropic ocean response to atmospheric forcing in the North Pacific. The NPBM results provide insight on the near 13 day bottom pressure variability in the broader region of the North Pacific. However, the NPBM results also raise a lot of questions beyond the scope of this study. Further analysis of the NPBM results in future studies would be helpful to understand more about the topographic effects on barotropic ocean variability in the North Pacific and how they are different for time scales other than the near 13 day period.
 This work was supported by the National Science Foundation as part of the Kuroshio Extension System Study (OCE-0221008, 0827280, and 0851246). J.H.P. was supported by KIOST grants PE98822 and PE98731.