The amplitude of the frequency response function between coastal alongshore wind stress and adjusted sea level anomalies along the west coast of the United States increases linearly as a function of the logarithm (log10) of the period for time scales up to at least 60, and possibly 100, days. The amplitude of the frequency response function increases even more rapidly at longer periods out to at least 5 yr. At the shortest periods, the amplitude of the frequency response function is small because sea level is forced only by the local component of the wind field. The regional wind field, which controls the wind-forced response in sea level for periods between 20 and 100 days, not only has much broader spatial scales than the local wind, but also propagates along the coast in the same direction as continental shelf waves. Hence, it has a stronger coupling to and an increased frequency response for sea level. At periods of a year or more, observed coastal sea level fluctuations are not only forced by the regional winds, but also by joint correlations among the larger-scale climatic patterns associated with El Niño. Therefore, the amplitude of the frequency response function is large, despite the fact that the energy in the coastal wind field is relatively small. These data show that the coastal sea level response to wind stress forcing along the west coast of the United States changes in a consistent and predictable pattern over a very broad range of frequencies with time scales from a few days to several years.
Tide gauges, which monitor changes in sea level at the coast, record both local and remote effects of wind, temperature, and atmospheric pressure on sea level at frequencies ranging from the synoptic band to seasonal and interannual events (e.g., Gill and Niiler 1973). A major difficulty in determining how individual mechanisms force sea level is that most mechanisms are not independent of each other, especially at the longer periods (e.g., Chelton and Davis 1982; Ponte 1994). In particular, examining the response of coastal sea level to both local and remote atmospheric forcing is increasingly important in light of long-term rises in sea level (e.g., Douglas 1995), which can impact millions of people living along and near low-lying coastal areas. Understanding the forcing of sea level by wind stress at the longer periods (greater than the synoptic wind band) is necessary so that we will be able to better determine changes in rates of sea level rise by removing this effect from tide gauge records (Sturges and Hong 2001).
In this paper, we examine 18 or more years of adjusted sea level anomalies (SLA) and alongshore wind stress anomalies (WSA) recorded primarily near three stations located along the west coast of the United States. These records show a strong positive correlation between the wind stress and sea level anomaly frequency response function (FRF) and the period of the signal. The longest periods have the highest FRF. This relationship holds despite the fact that the coastal wind properties differ along the West Coast in the main areas we investigated: the southern California bight, central California, and Oregon–Washington (Dorman and Winant 1995). We show that the primary driving mechanisms that account for the increase in FRF differ as a function of frequency. At higher frequencies (periods <6–10 days), sea level is directly forced by local winds. Regional large-scale winds drive the sea level signal for periods of about 2–14 weeks (e.g., Chelton and Davis 1982). At annual and longer periods, the FRF between wind stress and sea level is even larger, primarily because observed coastal sea level fluctuations are not only forced by the regional winds, but also by joint correlations among the larger-scale climatic patterns associated with El Niño.
There are only a few places along the west coast of the United States that have long (18 yr or more) relatively complete records of wind, atmospheric pressure, and sea level. We obtained hourly records of these variables at three sites along the coast—Neah Bay, Washington (NB), San Francisco, California (SF), and Los Angeles, California (LA) (Fig. 1, Table 1). Los Angeles is about 600 km south of San Francisco; Neah Bay is about twice that distance north of San Francisco. The wind records from near Los Angeles and San Francisco were from offshore National Oceanic and Atmospheric Administration (NOAA) wind buoys (46025 and 46012). The wind station near Neah Bay was a Coastal-Marine Automated Network (C-MAN) station DESW1 located on the shore. An additional C-MAN wind record was obtained near Point Conception, California (PTGC1). All of these stations had relatively complete datasets for the time period from August 1984 through December 2002 (Fig. 2). The sea level records from San Diego and San Francisco were considerably longer; these records began in the early 1900s (Table 1).
To look at the coupling between wind stress and sea level for even longer time periods, we obtained surrogate records of winds by using the downwelling (negative upwelling) index (DWI) off of Neah Bay, San Francisco, and Los Angeles from 1967 to 2002 (Fig. 1, Table 1; PFEL 2003). As shown by Halliwell and Allen (1984, 1987), and corroborated by our analyses, the DWI does a reasonable job of representing fluctuations in the wind field at periods longer than 10–15 days. However, it should be noted that the DWI does not represent the actual amplitude of wind stress over the coastal ocean; it does not even have the same units. Data from C-MAN stations at the shore are also highly coherent with and representative of wind fluctuations over the coastal ocean, but they tend to have smaller amplitudes. Hence, our analysis will focus on patterns among wind and sea level stations that change with frequency. Relations that involve a change in the amplitude of the response with location are not statistically reliable.
A few additional long records of oceanic parameters were obtained for this study (Table 1). These include an 18-yr record of sea surface temperature (SST) in the coastal ocean recorded at wind buoy 46012 off of San Francisco and a 10-yr record of temperature at 100 m in Monterey Bay, 200 km south of San Francisco, collected by the Monterey Bay Aquarium Research Institute (MBARI). Records of atmospheric pressure for Neah Bay, San Francisco, and Los Angeles for the time periods coincident with the sea level records were obtained either from the nearby ocean buoys or from the Fleet Numerical Oceanography Center (FNOC) locations. We also obtained monthly multivariate ENSO indexes (MEI) (Wolter and Timlin 1998) for the time period from 1950 to 2003 in order to determine if the energetic longer period sea level fluctuations were associated with Pacific-wide climatic fluctuations.
There were temporal gaps in the wind, temperature, and sea level datasets that ranged from 1 day to as long as 3 months. In general, these gaps made up only a small fraction of the dataset. Small gaps of less than 4 days were filled linearly. When nearby stations were available, gaps in the records were filled with scaled data (Fig. 1) or with values generated by the spectra calculated using data from both sides of the gap (Anderson 1974). A large gap of about 3 months in the Neah Bay wind and sea level records during 1992 could not be filled with nearby stations. It was filled spectrally, but this filled gap should not affect the statistical properties of the 18-yr record because it makes up less than 2% of the dataset. The 100-m MBARI temperature record had three large gaps that ranged in size from 24 to 160 days, making up about 8% of the data. By necessity, these data were also filled spectrally in order to calculate the statistics.
Wind records were rotated into the alongshore and cross-shore components, then converted to wind stress (Wu 1980). Atmospheric pressure was added to the sea level records at Neah Bay, San Francisco, and Los Angeles. Hence, these records, designated sea level records in this paper, are adjusted records that actually represent synthetic subsurface pressure (SSP). Both the wind and sea level records were low-pass filtered (PL33; Limeberner 1985) and then averaged to daily values.
An annual cycle is prominent in most records. Because the annual cycle is large, it tends to dominate statistical relations between datasets. Therefore, the annual cycle was removed from wind, sea level, and sea surface temperature records. Monthly mean values calculated for each dataset were used to create an annual cycle for each variable. A spline interpolation of the monthly mean values was used to calculate daily values. These daily values were then removed from each dataset to create alongshore WSA, sea level adjusted by atmospheric pressure anomalies (SLA), sea surface temperature anomalies (SSTA), and down-welling index anomalies (DWIA).
3. Analysis methods
The main statistical analyses reported in this paper are calculations of the coherence, phase, and the FRF between the various datasets as a function of frequency. For the 18.3-yr datasets, the analyses usually use a piece length of 60 days in order to keep the error bars on these quantities small. A Hanning window was applied to each 60-day length of record. Each 60-day piece overlapped the previous one by 50%. Usually, the highest frequencies were also averaged together to reduce noise. Hence, the 60-day statistics had a minimum of 220 degrees of freedom for the coherence statistic. The analyses of datasets with records longer than 18.3 yr used methods similar to those described above. The major difference for the longer datasets was that the lengths of the basic section of record were commonly increased to one year or more.
4. Frequency domain relationships among the wind stress and sea level anomaly datasets
a. Characteristics of the wind stress and sea level datasets
The dominant energy in the alongshore WSA records generally has periods between 5 and 20 days (Fig. 3). The apparent increase in energy to the north is probably real, because the most energetic station (Neah Bay) is a coastal C-MAN station. Hence, the measured wind stress energy at Neah Bay is either similar to or weaker than the wind stress that would be observed at an offshore station.
The energy in SLA records at the two sites in California tends to increase out to periods of nearly a year (Fig. 3). The dominant energy is at periods much longer than that found in the wind stress anomaly records. The very energetic sea level fluctuations off of Neah Bay are dominated by periods between 10 and 50 days. This range encompasses, but shows longer periods than, those observed in the local wind stress anomaly spectra. The energy in SLA spectra increases from south to north.
For periods longer than 15 days, the coherence and phase between adjacent WSA stations have relatively constant amplitude with frequency out to periods of 60 days (Fig. 4). The coherences are significant at the 95% confidence level, although the amplitudes are not high. They explain less than 20% of the joint variances in the signals. The negative phases at periods longer than 10 days show that winds to the south lead those to the north. The coherences between WSA at San Francisco and Los Angeles are slightly stronger than those between San Francisco and Neah Bay, but these small amplitude differences do not suggest that there is a definite change in the WSA field at these spatial scales over this section of the coast. The spatial scale of the WSA field is shorter than the spatial scale for the entire domain at these periods, because WSA are not coherent between Los Angeles and Neah Bay. At the higher frequencies, the spatial scales of WSA change. The coherence amplitudes between adjacent sites tend to drop for periods near 8 days. The winds at Neah Bay lead those at San Francisco for periods of less than 8 days. Los Angeles and San Francisco winds are approximately in phase at these short periods.
The coherences between SLA records (not shown) are generally low (<0.3), although they are significant at the 95% confidence level. The only exception is that the coherence between SLA at San Francisco and Los Angeles approaches 0.6 for periods greater than 20 days. The phase relationships between SLA stations are similar to WSA; the southern stations generally lead the northern stations. Again, for periods less than 8 days, SLA at Neah Bay leads the stations to the south, similar to the relationships found for WSA.
b. Relationships between alongshore wind stress and adjusted sea level anomalies
WSA and SLA along the west coast of the United States are significantly coherent at almost all periods between 4 and 60 days (Fig. 5). Wind stress anomalies lead sea level anomalies. The coherence amplitudes between these two fields are highest near Neah Bay and lowest in the southern California bight. About 50% of the variance in fluctuations of SLA at the northern two stations can be explained by wind forcing. The coherence amplitudes are usually less than 0.5 in southern California, as might be expected owing to the overall weaker wind forcing in the region (Halliwell and Allen 1987; Dorman and Winant 1995). The coherence amplitudes tend to decrease at the highest frequencies (periods less than 6–10 days).
The FRF between WSA and SLA increases markedly with period (Fig. 5). The FRF doubles between periods of about 10 and 30 days. It is largest at the lowest frequency at all three sites. A strong linear relationship exists between the FRF and the logarithm (log10) of the period (Fig. 6). The squared linear correlation ranges between 0.97 and 0.99 at the three coastal stations. The FRF near Neah Bay is higher than the other stations, particularly at longer periods. However, these higher values may not be real, but an artifact of the dataset because Neah Bay WSA were measured by a C-MAN station on land. Hence, the lower wind speeds relative to those measured from an oceanic buoy would artificially increase the FRF in this region (Halliwell and Allen 1987).
To determine if the FRF between wind stress and sea level anomalies continues to increase at El Niño time scales of 2–5 yr, we use the much longer records of wind stress, as represented by DWIA and SLA off of San Francisco. These records are at least 35 yr long. The FRF clearly increases with period (Fig. 7). At periods up to 20 days, the increase is linear with the logarithm of the period, with very small error bars, similar to the pattern found for measured WSA at San Francisco (Fig. 5b). The FRF continues to increase with approximately the same slope out to periods of 100 days or more, though error bars around the FRF are larger. The data suggest that the slope of the linear response changes at the longer periods. The slope for periods between 200 days and 5 yr is more than double that measured for periods less than 100 days. At periods greater than 2 yr, the calculated FRF is about 6 times greater than that observed for a period of 20 days.
c. Alongshore wind stress, sea level, and SST cross spectra
WSA, SLA, and SSTA are all correlated at some level. We examined the relationships among SSTA, WSA, and SLA in the San Francisco region to determine whether temperature was independently contributing to the observed increase with the period of the FRF between WSA and SLA. Wind stress anomalies were coherent with SSTA, although at lower levels than found between WSA and SLA. The coherence amplitudes between SSTA and SLA were also lower than observed between WSA and SLA. The coherence amplitudes between SLA and SSTA can be explained by hypothesizing that fluctuations in both SLA and SSTA are forced by the same wind stress. The observed coherence between SSTA and SLA is nearly the same as one would predict if one assumed that 1) a portion of the energy in SSTA and SLA is independently forced by wind stress, and 2) the remaining energy in these two fields is independent of each other. Hence, SSTA and SLA are coherent only because they share a driving force, not because one forces the other. The SST signal does not appear to be independently contributing to the higher FRF between wind and sea level at periods of up to at least 60 days.
5. Local versus remote wind forcing of SLA
The observed changes in the relationships between wind stress and sea level anomalies as a function of frequency suggests that different components of the wind field, such as the local and regional wind systems, force sea level at different portions of the frequency band. To examine this hypothesis, we ran a principal component analysis between WSA near San Francisco and near PTGC1 (Fig. 1) to separate the local from the regional component of the WSA field in central California. The Point Conception station is 370 km southeast of the San Francisco site and just northwest of the unique wind field characteristic of the southern California bight. This station was more coherent with the San Francisco than the Los Angeles winds. The first mode for the regional WSA in central California contained 76% of the variance at both stations. The first mode was scaled to the amplitude of the observed WSA near San Francisco. “Local” WSA was created by subtracting the regional from the observed WSA off of San Francisco.
The coherences between SLA and the local wind field are largest at the higher frequencies and are similar to that seen between SLA and the measured wind field (Fig. 8). The coherence amplitudes for the local wind field decrease with increasing period. At periods longer than 10 days, it decreases to below 0.2. Only a very small percent of the SLA signal at San Francisco can be explained by local winds at the longer periods.
The frequency response functions for local winds and sea level have amplitudes of less than 4 cm dyne−1 cm−2 at the highest frequencies. These amplitudes are similar to those that were observed for the direct wind stress set up of sea level near San Francisco for periods less than 16 days (Noble and Ramp 2000).
The coherence amplitudes between SLA and the regional winds off of central California, as represented by the first mode in wind stress, increase with period and, at the lower frequencies, are much larger than observed between SLA and local wind forcing. Clearly, SLA in central California is responding primarily to the large-scale regional wind field at the longer periods. It is the regional, not the local, wind field that is responsible for the increasing amplitudes of the FRF between wind stress and sea level at the longer periods.
6. SLA forcing at ENSO time scales
ENSO is one of the more important coupled ocean–atmosphere processes that control climate variability in the Pacific Ocean at interannual time scales. The measured FRF between wind stress and sea level on the West Coast is largest at these ENSO time scales. To examine the possible relationships between ENSO processes, SLA, and WSA at periods longer than 1 yr, we obtained monthly MEI (Wolter and Timlin 1998) for the time period from 1950 to 2003. The MEI is a weighted average of the following six variables measured over the tropical Pacific: SST, the east–west and north–south components of the surface winds, sea level pressure, surface air temperature, and total amount of cloudiness. We used these data to determine if the energetic longer period sea level fluctuations that have a large FRF to WSA were also associated with Pacific-wide climatic fluctuations.
The first principal component of SLA fluctuations at San Diego and at San Francisco was used to represent a regional West Coast SLA field. Monthly means of this signal were calculated in order to compare the SLA with the MEI. Monthly values for the DWIA wind field were calculated over the same time period. For periods of 2–8 yr, the regional SLA oscillations were highly coherent (amplitudes from 0.7 to 0.8) and in phase with fluctuations in the MEI (Fig. 9). A significant coherence was also observed between the MEI and DWIA at these periods, although the amplitudes were lower for wind stress than for sea level. Clearly, both SLA and WSA were affected by ENSO processes at these long periods.
The coherence and frequency response patterns between sea level and wind stress anomalies suggest that the energetic portion of the SLA at the higher frequencies (periods less than 100 days) reacts to two different wind forcings. Sea level responds dominantly to the local portion of the wind field at periods less than about 6–10 days. It responds to the regional wind field at the longer periods. These results are consistent with and expand the time scales of Wang and Mooers (1977), who found that 4-day fluctuations in the coastal ocean were local, whereas fluctuations at 10 days were related to nonlocal large-scale winds.
At periods less than about 6–10 days, the FRF between the primarily local wind field and sea level is relatively small (Fig. 5). One possibility for the small amplitude of the FRF at short periods is that the local wind field has relatively small along-shelf spatial scales (Fig. 4). In addition, the local winds do not have a strong tendency to propagate northwestward along the coast, the direction for a possible resonance with a poleward-propagating continental shelf wave. The high-frequency local winds at Neah Bay actually led the local wind field at sites to the south. It is possible, given the higher frequencies in the local wind field, that there is not enough time for sea level to fully respond to the wind field. All of these properties of the local, or higher frequency, wind field, reduce the potential for a large FRF between winds and sea level. However, because the wind field is energetic at these frequencies, the wind forcing of sea level at these frequencies is not negligible, even though the FRF is relatively small.
The modal structure of the regional winds shows that the measured winds at sites along the west coast of the United States are transitioning from the local to the regional winds at periods of less than 20 days. The structure for the wind field at these middle frequencies is consistent with the well-known phenomenon that locally measured winds are highly correlated with sea level response for the commonly studied synoptic wind band.
Sea level is driven more by the regional, rather than by the local, wind field for the longer periods out to at least 60 days, and probably 100 days. Sea level is not only driven by the regional winds, but it responds with increasingly stronger amplitudes to a unit wind stress at these longer periods. The periods associated with the higher FRF are commonly found in coastally trapped waves (CTW). Both the CTW and the regional wind systems propagate in a poleward direction along the west coast of the United States (Fig. 4; Halliwell and Allen 1987). Consequently, these regional wind systems can force sea level fluctuations associated with CTW for relatively long time periods over a broad range of frequency bands. If the phase speed of a poleward-propagating CTW at a given frequency is similar to that of a propagating atmospheric system, a near resonance occurs in the coastal ocean (Wang and Mooers 1977; Chapman 1987). Because a decrease in friction at longer periods will allow a CTW to travel longer distances, a CTW will contribute to the wind-forced SLA over much broader spatial scales. These processes could be some of the causes for the observed increase in FRF between wind stress and sea level with period.
On the west coast of the United States with its attendant narrow shelf, wind-driven currents have been observed to extend into the deeper waters over the slope (e.g., Noble and Ramp 2000; Noble et al. 2002, Ryan and Noble 2005). The poleward wind-driven currents over the slope cause sea level to rise at the shelf break, which, in turn, causes sea level to rise at the coast. Given that along-shelf current fluctuations over the slope tend to have longer periods than currents over the shelf, this process could potentially contribute to the observed increase in FRF between wind stress and frequency at longer periods. In a study of wind-forced sea level along the Great Barrier Reef shelf at periods of 5–30 days, Cahill and Middleton (1993) also observed an increase in the FRF between alongshore wind stress and sea level with period. An increase in FRF was not observed between the alongshore wind stress and currents on the shelf. They attribute the larger sea level response to the wind stress to wind-forced sea level changes over the slope that are generally enhanced at lower frequencies and along narrower shelves.
Fluctuations in sea surface temperature do not appear to contribute to the increasing FRF between winds and sea level with period. However, this does not preclude the possibility that temperature fluctuations associated with wind stress do act to increase the FRF at the longer periods. It is probable that the longer period upwelling (downwelling) wind stress fluctuations cause the thermocline to rise higher (sink deeper) into the water column. Hence, water below the sea surface, but above the thermocline, is cooler (warmer) and will cause a steric decrease (increase) in sea level. There is some evidence for this effect in that the water temperature measured 100 m below the sea surface in Monterey Bay is coherent with wind forcing for periods longer than 50 days. At periods greater than 5 months, a steric affect associated with wind forcing is contributing to the sea level signal (Fig. 10), and is responsible for the increase in the slope of the FRF at the longer periods (Fig. 7).
Climatic signals such as ENSO result in a Pacific basin-wide response to large-scale wind forcing at intraseasonal and longer periods (e.g., Davis 1978; Chelton and Davis 1982). Schwing et al. (2002) show atmospheric teleconnection patterns during ENSO events that affect sea surface height anomalies along the entire west coast of North America. The strong coherence between the MEI and SLA for annual and longer periods suggests that SLA fluctuations at these frequencies are associated with large-scale climatic patterns. At ENSO time scales, the MEI and the regional winds represented by the DWIA are significantly coherent. At these periods, the slope of the FRF between wind stress and sea level as a function of period also increases markedly (Fig. 7). Climatic patterns associated with ENSO on the West Coast impact both the wind signal and subsurface temperature, which, in turn, contribute to the very large FRF observed at periods of 1 yr or more.
ENSO processes could have an additional effect on the FRF between wind stress and sea level. The poleward propagation of coastally trapped waves from lower latitudes coincident with local poleward WSA would enhance the SLA. This pattern was observed during the 1997/98 El Niño (Strub and James 2002; Ryan and Noble 2002).
Power et al. (1990) show that alongshore wind stress can force a near-resonant response in the alongshore pressure gradient at subinertial frequencies along a continental margin where bottom friction is important. However, the resonance as described in their model requires a phase shift of 180° in the pressure gradient response. That phase shift was not observed at any of the sites we studied. In addition, the shelf width along the entire West Coast is narrow (generally <50 km wide). The resonant response of sea level to wind forcing would be at periods on the order of a few days, which is much too short to be relevant in this study. Hence, it is unlikely that a resonant response on the shelf to wind forcing is responsible for the increase in the FRF with period.
At three locations along the west coast of the United States we observed a strong increase in the amplitude of the FRF between wind stress and sea level anomalies for periods from a few days to periods of several years. At the shortest periods, the low FRF is the result of the sea level being forced only by the local (nonregional) wind field, which has fairly short spatial scales. The increasing FRF with a period at longer periods (10–100 days) is the result of the forcing of sea level by the regional wind field, and is possibly associated with the consequent generation of coastally trapped waves by these winds. Interannual changes in Pacific basin–wide winds related to climatic events such as ENSO result in changes in overall basin circulation, which in turn modifies the geostrophic boundary transport and thus sea level at annual and longer periods. The observation that the response of coastal sea level to wind stress forcing changes in a consistent pattern over very long periods is interesting, and may be an important parameter for models used to predict sea level response to long-term wind forcing along the west coast of the United States.
Although it is beyond the scope of this paper, we speculated on whether the response of sea level to wind forcing on the east coast shows a similar increase in the FRF with period. We examined a long set of data at one location on the east coast of the United States near Atlantic City, New Jersey. These datasets did not show an increase in the FRF between WSA and SLA with period. This may be because CTW and the regional wind fields do not propagate in the same directions on the east coast. At this location on the Atlantic coast, CTW propagate equatorward, whereas the dominant winds systems propagate poleward (Noble and Butman 1979). Hence, the wind and CTW systems interact only for short periods of time, in contrast to the West Coast systems. It is also possible that the East Coast may respond differently to wind forcing because the East Coast atmospheric disturbances primarily propagate across landmasses, while winds that force the West Coast propagate across the Pacific Ocean. This is an interesting problem for future research programs.
We are grateful to NOAA for allowing easy access to wind buoy (NODC), tidal gauge data (NOS), and upwelling indices (PFEL) on their Web sites. MBARI kindly granted permission for use of the 100-m temperature data. We thank Frank Schwing and Jon Warrick for their reviews of an early version of this manuscript, and two anonymous reviewers who helped us to greatly improve the manuscript.
Corresponding author address: H. F. Ryan, USGS, 345 Middlefield Road, MS 999, Menlo Park, CA 94025. Email: email@example.com