Sea-Level Change (1990)

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1 ~ Sea Level and the Thermal Variability of the Ocean DEAN ROEMMICH Scripps Institution of Oceanography ABSTRACT The time variability of deep-ocean temperature and the relationship of temperature changes to changes in steric height and sea level are addressed using data from the subtropical North Atlantic and the eastern North Pacific spanning several decades. This is the longest period for which high- quality hydrographic time-series measurements are currently available. In the Atlantic, data con- sisted of 27 yr of repeated deep hydrographic stations near Bermuda, sea level at Bermuda, and two large spatial-scale hydrographic surveys of the subtropical North Atlantic Ocean that were separated in time by 23 yr. In the Pacific, a number of coastal sea-level stations were considered together with a grid of hydrographic stations sampled to 500 m depth in the period 1950 to 1978. By concentrating on these data-rich regions, the intention was to obtain a non-aliased view of the scales of time variability that should be applicable elsewhere in the oceans. The following conclusions were reached. 1. Although seasonal and interannual temperature fluctuations are concentrated in the upper ocean, decadal time-scale variations are not, at least in the Atlantic. Rather, they extend deep into the ocean. In the Atlantic study area, the upper 1000 m cools hv fin t~ n cow ~^,1 the ;~ ] ~_~ 1000 to 3000 m warmed by as much as 0.2°C. ~ The 1~ +; ~1~ ~ ~ ~ w._ at, Alla alla 1llt~lVal llU111 a. '11~1~11~ `1111~-~1c remperalUre changes resulted in steric height change that was closely related to sea-level variability. The estimated power spectra of steric height near Bermuda and of sea level at Bermuda are indistinguishable and equally red at long periods. Coherence between steric height and sea level is very high at longer periods. In the eastern North Pacific, the areally averaged interannual sea-level and steric height changes were also indistinguishable within the limits of sampling errors. 3. The trends in sea-level records are typically 1 to 2 cm/decade, whereas the coherent oscilla- tions of sea level and steric height at 10- to 20-yr periods have amplitudes of the order of 5 cm. A time series of about 50-yr length of sea level and steric height is required to determine whether the sea-level trend is accompanied by a similar trend in steric height. 4. Long time-scale temperature changes are spatially variable on the scale of the oceanic gyres, particularly for depths in and above the main thermocline. In terms of sea level, this means that fluctuations in mid-ocean sea level may be quite independent of those at coastal stations, even over a period of 20 yr. 208

SEA LEVEL AND THE THERMAL VARIABILITY OF THE OCEAN INTRODUCTION This study focuses on changes in the steric height of the ocean surface on time scales of 10 yr or longer and the relationship of steric height changes to changes in sea level. (The steric height of the sea surface is defined as the integral of the specific volume from a specified pressure level to the ocean surface.) Global sea-level fluctuations may be due to steric height change (e.g., temperature or salinity variation), to changes in the total mass of water in the ocean because of melting or freezing of ice caps, or to changes in the volume or shape of the ocean basin. It has been shown in regional studies that steric height changes account very well for the sea-level variations (on the order of 10 cm) observed on seasonal and interannual time scales (e.g., Shaw and Donn, 1964; Schroeder and Stommel, 1969; Reid and Mantayla, 1976~. On the other hand, sea- level fluctuations over periods of thousands of years ap- pear to be so large for example, the 150-m increase of the past 15,000 yr (Moore, 1982)-that steric expansion can be ruled out as a major contributor. A warming of the entire ocean from 0°C to the currently observed tempera- tures would involve a thermal expansion of only a few meters. What then of the intermediate range of time scales from tens to hundreds of years? Can the secular trends currently observed in many sea-level records be attributed to steric expansion and contraction of the water column? Is there some residual sea-level rise that cannot be due to steric expansion? For the reader's convenience, some values of the ther- mal expansion coefficient of seawater at a level of 35 practical salinity units are listed in Table 13.1. These are based on the 1980 equation of state (UNESCO, 1981~. A point of interest is that the expansion coefficient increases significantly both with increasing temperature and with increasing pressure. The steep increase with increasing temperature has sometimes been used as an argument that deep cold water may be ignored in steric height calcula- tions relative to warm surface water. This is not so; a parcel of water at 4°C at 2000 dbar has a thermal expan TABLE 13.1 Thermal Expansion Coefficient (1~7/K) of Sea Water at Salinity of 35 Practical Salinity Units for Different Temperatures and Pressures Pressure (dbar) Temperature 20°C 10°C 4°C o 2000 4000 2572 2784 2978 1669 2012 2323 1022 1470 1872  209 sion coefficient that is 60 percent as large as that of a parcel at the ocean surface at 20°C. Barnett (1983) found that the global hydrographic data base is inadequate for determining long-term trends in steric height. He considered pairs of stations from nearly the same location and the same month of the year, but separated in time by more than 30 yr. In each of 11 regions of the world ocean, between 1 and 68 pairs were found. But the standard deviation of the difference in steric height of the sea surface relative to 1000 dbar was very large (20 dynamic centimeters in several regions) and none of the areas had a statistically significant trend. This is because the "noise" consisting of mesoscale eddies and other energetic low-frequency phenomena is very large compared to a hypothetical signal of the order of 1 dy- namic centimeter per 10 yr. Thus, the sampling problem is formidable. The approach used here is to concentrate on two rela- tively data-rich regions, the subtropical North Atlantic and the eastern North Pacific, rather than to seek a global solution. The objective is to discover how much variabil- ity in steric height is contained in time scales of decades or longer and to detains what vertical and horizontal scales of variability correspond to these long-term changes. These essential questions must be answered before we can ask how long the ocean must be sampled at a single location, how many locations must be sampled, and to what depths the sampling should extend to determine the relationship of steric height to the long-term trend in sea level. BERMUDA SEA LEVEL AND THE PANULIRUS DATA The longest regular time-series of deep (>1000 m) hydrographic stations is the Panulirus series (32°10'N, 64°30'W) near Bermuda (Figure 13.1~. This program of measurements was initiated by Henry Stommel and was carried out by the Bermuda Biological Station beginning in 1954. Weather permitting, and barring occasional other problems, two casts per month were made at a location where the water depth is about 3000 m. Nearly all casts extend to 2000 m and many to 2500 m or deeper. From 1954 to 1981, 392 casts were made to depths greater than 2000 m. The time series is not very long for our pu~poses, and its limited depth precludes a study of the abyssal water, but it is all we have. A number of investigators have studied the Panulirus data, sometimes in combination with Bermuda sea level. Shaw and Donn (1964) compared monthly means of sea level data (corrected for atmospheric pressure variations) with monthly means of the steric height of the sea surface relative to 2000 dbar and found them to be indistinguish- able. Schroeder and Stommel (1969) noted that this sea

210 4oo N 20° ~D1 ~1 1 ~ BERMUDA ~1 1 ' 80°W . . 4oo Do FIGURE 13.1 Map of the North Atlantic, showing Bermuda and ship tracks of IGY and 1981 transatlantic hydrographic sections. sonal signal was mainly confined to the upper 200 dbar and was due to local buoyancy fluxes across the sea sur- face. In addition, they found that year-to-year variations in steric height were mirrored in the sea-level record; they attributed these variations to vertical motion of the main thermocline. Wunsch (1972) considered 8 yr of Bermuda sea-level data and 13 yr of Panulirus station data. He found that the steric height spectrum tapered off at periods longer than a year, an inference that we will contradict (Figure 13.8) after considering the longer records now available. Pocklington (1972) constructed time series of temperature at a number of standard depths using data from 1955 to 1969. He observed a trend of decreasing temperature down to 400 m with a suggestion that it con- tinued to decrease as deep as 800 m. Below this there was no apparent trend. Frankignoul (1981) compared tempera- ture at 10 standard levels in the first 12 yr of Panulirus data with temperature in the next 12 yr. He too found a tem- perature decrease down to 1000 m with a slight increase at 1600 and 2000 m. fThe text and Table 1 of Frankignoul (1981) appear to reverse the sign of the changes, but they are given correctly in his Figure 23. Here, 27 yr of Panulirus data will be used for two purposes. First, it will be shown that in contrast to sea- sonal and interannual variations, which are confined to the upper 1000 m, a significant 27-yr trend in the data extends down to the level of the deepest observations. Then this trend in time will be compared to a large space-scale temperature difference between two deep hydrographic surveys, each of which covered the subtropical North Atlantic at the same two latitudes (Figure 13.11. All of the Panulirus casts were sorted by month and year and interpolated to 24 standard depths that were 50 m apart down to 300 m and then 100 m apart down to 2000 m. Casts in a given month were averaged over all years to estimate a mean annual cycle. Then, for each cast the mean for that month (over all years) was subtracted to DEAN ROEMMICH  remove the annual cycle and then all casts in a year were averaged to estimate a mean anomaly for the year. We are interested in seeing how, on different time scales, the variability extends to different depths. Figure 13.2 shows steric depth for each of the 12 mean monthly profiles. By steric depth, we mean that the specific volume anomaly is integrated downward from the ocean surface to the pres- sure level indicated by the ordinate. Since the slope of each curve is the specific volume anomaly, it can be seen that the month-to-month changes in specific volume are large in the upper 200 m and small below this level. Fig- ure 13.3 is of steric depth for the 26 yearly anomalies. The year-to-year changes in steric depth are slightly larger in magnitude than the annual cycle and clearly are distnb- uted over a much greater depth range. This depth differ- ence is summarized by examining empirical orthogonal functions (EOFs) of the specific volume profiles. The first EOF is, by definition, a best fitting shape, in a least squares sense, to all of the profiles in a group. Figure 13.4 shows the first EOF based on the 12 mean monthly profiles and the first EOF based on the 26 profiles of yearly anomalies. The much greater depth range of the yearly anomalies is apparent. The secondary maximum in the yearly anoma- lies at 800 m is in the main thermocline. These EOFs describe 90 percent and 62 percent of the total variance in the profiles of the annual cycle and the yearly anomalies in specific volume, respectively. But our main interest is in longer time scales. The yearly temperature anomalies are smoothed with a 5-yr running mean filter (Figure 13.5~. Successive standard levels are offset from one another by 0.25°C. In and above o L`J cr 1000 ~n ~n I1J C~ 1500 ,~ 2000 1 1 1 . . . . 1 1 1 1 1 1 1 1 1 -0.06 0 0.06 STERIC DEPTH (dyn m) FIGURE 13.2 Mean monthly values of steric depth at the Panu- lirus station, averaged over 1954 through 1981, with the average over all months removed. Steric depth is the integral of specific volume from the ocean surface down to the pressure level indi- cated on the ordinate.

SEA LEVEL AND THE THERMAL VARIABILITY OF THE OCEAN the thermocline, down to 1000 m, one can see decreasing temperature between 1957 and 1970, as described by Pocklington (1972~. However, the temperature then began to rise again, reaching a maximum in 1975 to 1977 that was still generally cooler than the initial values. Below 1000 m, the pattern is qualitatively different. In the deep levels, the 20-yr oscillation seen above is not apparent. Rather, there is a more regular rise amounting to between 0.1 and 0.2°C. The long time-scale variations below 1500 m appear not to be coupled to those in the thermocline. In order to extract the longest time scale in the Panu- lirus data, a linear trend in specific volume over 26 yr was computed at each standard depth. For comparison pur- poses, the trends were normalized in the same way as the EOFs and are plotted in Figure 13.4. The pattern is similar to the EOF of yearly anomalies in that it has a maximum in the main thermocline. An important difference though is that the trend does not become negligibly small below 1000 m. Rather it extends to the deepest levels sampled and to some undetermined depth beyond, with a change in sign at about 1000 m. In viewing the trends in relation to the running mean values in Figure 13.5, it is clear that the oscillations are as large or larger than the apparent trend and that the apparent trend in another 25 yr of data could be quite different. So far we have mentioned only temperature change although the density of seawater depends on salinity as well. On the time scales of interest here, tens to hundreds of years, the effect of salinity changes on global sea-level changes are slight. The total salt content of the oceans remains approximately constant and sea-level changes due to vertical redistribution of salt in the water column are likely to be small. Heat, unlike salt, is freely exchanged with the atmosphere and even the combined heat content 0 Coo - ~ 1000 llJ 2000 // i} L\\\ ~ . -0.10 STERIC DEPTH (dyn m) 010 FIGURE 13.3 Yearly anomalies in steric depth at the Panulirus station for the years from l9S5 to 1981. TREND / LL  2000 211 ! ', _ l 11 ( l i -0.8 -0.4 0 FIGURE 13.4 The first empirical orthogonal function of the mean monthly profiles of steric depth and the first EOF of the yearly anomaly profiles, normalized to have unit length. The third profile is of the linear trend in time of steno depth over the period 1955 to 1981, also normalized to unit length. Of the ocean-atmosphere system may change significantly over a few decades or centuries. Thus we would argue that global expansion or contraction of ocean waters must be dominated by temperature change rather than by salinity change. Of course, this may not be true in any particular region, so a word about salinity changes in the Panulirus data is in order. In general, temperature changes are ac- complished by salinity changes such that a fairly tight temperature-salinity correlation is maintained. A tem- perature increase of 1°C in the thermocline at the Panu- lirus station is accompanied by a salinity change of ap- proximately 0.1 practical salinity units. This temperature change produces a decrease in specific volume whose magnitude is more than three times the corresponding increase in specific volume caused by the salinity change. Thus the effects are of opposite sign, and although salinity is not negligible, the temperature effects dominate. Talley and Raymer (1982) studied temporal changes in the tem- perature-salinity relation at the Panulirus station and found that the slope of the relation changed very little between 1954 and 1971. There was a slope change between 1972 and 1975 in waters at the top of the thermocline, but the effect on steric height of the observed temperature-salinity shift is much less than that due to the observed tempera- ture changes. The trends observed at the Panulirus station are pre- sumably not strictly local, and one would like to know the spatial extent of the signal. For this purpose, we compare the Panulirus trends to two large space-scale surveys sepa- rated in time by 22 yr. As part of the International Geo- physical Year (IGY) hydrographic survey, transatlantic sections were occupied along latitudes 36°l5'N from the

212 o ~ -2 o by: l`, _ 3 cr LLJ - 4 :: 190 m 1500m 1960 1970 1980 YEAR FIGURE 13.5 The 5-yr running mean of temperature anomaly at the Panulirus station at 24 standard depths. Standard depths are offset from one another by 0.25°C. United States to Spain in 1959 and 24°30'N from Morocco to the Bahamas in 1957. With similar ship tracks, these sections were repeated by the R/V Atlantis II in 1981, as shown in Figure 13.1. The two IGY sections have a total of 99 hydrographic stations while the 1981 sections, made with a continuously profiling conductivity-temperature- depth (CTD) recorder, have 191 stations to the ocean bottom. Large-scale differences in water mass volumes were discussed by Roemmich and Wunsch (1984~. Con- toured profiles of temperature and salinity are displayed for the IGY data by Fuglister (1960) and for the 1981 data by Roemmich and Wunsch (19851. Here, we examine the average temperature difference as a function of depth along that part of the 36°N section that is east of the Gulf Stream and west of the mid-Atlantic ridge (this is about half of the total section and is roughly 3000 km in length). This difference is shown in Figure 13.6 together with the linear trend in temperature in the Panulirus data scaled to the same time frame. The stan- dard error of the linear trend is shown by the error bars. Although there are differences in detail, these two profiles of temperature difference are remarkably similar consider- ing that one is the difference between two large space- scale surveys and the other is a trend in time at a single point. They show a cooling trend, or uplifting of iso- therms, down to the base of the therrnocline at about 1000 m and a warming or downward displacement below. In the large space-scale surveys, the warming extended down DEAN ROEMMICH to a depth of about 3000 m. Moreover, a similar pattern existed along 36°N, east of the mid-Atlantic ridge, and along 24°N for the width of the ocean. At 24°N, the cooling was in a more restricted layer down to only 500 m with warming from 500 to 3000 m (Roemmich and Wunsch, 1984~. Just as the thermocline showed more structure than the deep water in the time domain, there also appears to be greater spatial variability in the 22-yr difference above 1000 m than in the deep water (see Roemmich and Wunsch,  1984, for temperature difference sections). The existence of both the Panulirus time series and the two large space- scale surveys allows us to confirm that the secular trends in the Panulirus data are indicative of change over much of the subtropical gyre. Of central importance here is the relationship between the apparent trends in specific volume and sea level. In Figure 13.7, the 5-yr running mean of Bermuda sea level is shown together with that of the Panulirus steric height of the sea surface relative to 2000 dbar. For reference, we also show sea level at Charleston, South Carolina. It is at nearly the same latitude as Bermuda, and the record there is typical of the east coast of the United States. The correlation of Bermuda sea level and Panulirus steno height is very high the correlation coefficient is about 0.9 for the unsmoothed yearly values. Charleston sea level, on the other hand, does not show the fall and rise that is associated with the thermocline variations at Bermuda (Figure 13.5) but rather has a more steady rise. If the Charleston record is detrended, then the residual has sub- stantially less variance than the Bermuda record. A plau - ~ I 000 1500 2000 - 1 1 1 -1.0 o TREND (°C per 22 years) 1.0 FIGURE 13.6 The smooth curve expresses the temperature difference between the IGY (1959) and 1981 surveys along 36°N west of the mid-Atlantic ridge and east of the Gulf Stream. A positive value indicates that the ocean was warmer in 1981. The horizontal bars show the linear trend of temperature in time, with the standard error of the estimate, at the Panulirus station.

SEA LEVEL AND THE THERMAL VARIABILITY OF THE OCEAN sible explanation is as follows. The base of the thermocline slopes sharply upward across the Gulf Stream shoreward from the Sargasso Sea. The 7°C isotherm, found at about 1000 m in the Sargasso Sea, is at around 200 m shoreward of the Gulf Stream. Thus, if all water above 7°C was cooled by a uniform amount, the effect on sea level would be 5 times as great on the offshore side of the Gulf Stream. Thus, because of the greater thickness of the warm layer on the offshore side, the lower sea-level variance at the coast could be explained by lower sensitivity to tempera- ture fluctuations in and above the thermocline. An inter- esting question, which requires a long time series of deep hydrographic data near the coast, is whether all or part of the sea-level rise observed along the eastern United States can be attributed to the subthermocline warming seen throughout the subtropical North Atlantic. A power-density spectrum of Bermuda sea level was computed using monthly mean values from 1955 to 1978. The high-frequency end is undoubtedly affected by ali- asing, but here we are concerned only with the longest periods. A comparable series of monthly steric height of the sea surface relative to 2000 dbar was obtained from the monthly means of the Panulirus data, also from 1955 to 1978. Missing months were filled in by linear interpola- tion. The two spectra are displayed together in Figure 13.8. They are indistinguishable at periods of a year and longer. Indeed the only appearance of a difference is in a band from about 3 to 5 months, where the sea-level spec- trum appears elevated. A prominent annual signal is seen in both records. In the lowest frequency bands, the spectra slope more steeply than (frequency)-~, indicating that the - ~ ~ 0.10 ~ _ _' ~ ~ I llJ ~ _ - llJ I (a LLJ En o - 0.,0 _ _ -_ 7~L 940 1960 1980 YEAR FIGURE 13.7 From top to bottom, S-yr running means of Char- leston sea level, Bermuda sea level, Panulirus steric height (O to 2000 dbar), and the residual of steric height subtracted from sea level. The height of each curve is arbitrary. The straight line drawn through the bottom curve has an upward slope of 1 dy- namic centimeter per decade. 213 for  z ~o2 I3J C) o lot 10° STERIC '-HEIGHT _ \^ \ \ A-I FVFI FREQUENCY (cycles per month) FIGURE 13.8 Power-density spectra, band averaged over three frequency bands, of Bermuda sea level and Panulirus steric height (0 to 2000 dbar). contribution per unit frequency to the total record variance increases with increasing period. Estimates of coherence amplitude and phase from the cross spectra of the sea-level and steric height series are displayed in Figure 13.9. The estimates have been band- averaged over 5 adjacent frequency bands. The ampli- tudes are high at low frequencies, well above the 95 per- cent confidence limit, with corresponding phases near zero. At higher frequencies, the coherence drops. This is likely to be due to the sampling noise in the Panulirus steric height series, that is, in forming monthly averages from pairs of hydrographic stations. Another way of illustrating the strong similarity of the sea-level and steric height series at low frequency is show- ing the difference of steric height (O to 2000 dbar) sub- tracted from sea level. That is shown, again as a 5-yr running mean, in the bottom line of Figure 13.7. Time variations in this difference amount to a few centimeters. For reference, a line sloping upward at 1 cm/decade is also shown. There may be a trend in the difference, a rise in sea level relative to steric height, but the ~10-yr variations are larger than the apparent trend. Clearly a longer time series is required to resolve the question of whether the difference between sea level and steric height is growing. Further, data from the 1981 and ICY surveys of the sub- tropical Atlantic suggest that if the warming from 2000 to 3000 dbar were considered, the apparent trend in the sea- level residual would be reduced. Another point to note in Figure 13.7 is that whereas there is an upward trend in the overall sea-level record at Bermuda (1933 to 1980), there is no trend in the period overlapping the Panulirus observations (1954 to 1980~. Thus, several decades more of sea-level data together with

214 100 1 0.0 ~ 1 95o/o ~2 10 FREQUENCY (cycles per month) FIGURE 13.9 Coherence amplitude and phase from cross spec- tra of monthly mean sea level at Bermuda and monthly interpo- lated Panulirus steric height (0 to 2000 dbar) from 1955 to 1978, band averaged over five frequency bands. static height are required in order to see whether the upward trend in sea level is reestablished, and if so, whether it is accompanied by a similar rise in steric height. An addi- tional valuable piece of information would be direct mea- surement of the time rate of change in the geopotential height of the Bermuda benchmark used for reference for the sea-level station. Only then could we separately esti- mate the three possible contributions to change in relative sea level, i.e., steric height change, change in the mass of seawater per unit area, and change in the height of the land in relation to the geoid. THE EASTERN NORTH PACIFIC On a global basis, the great majority of sea-level sta- tions are located along continental coastlines, as opposed to the mid-ocean island station discussed in the previous section. It is anticipated that direct comparisons of steric height with sea level near continental boundaries are sub- ject to additional difficulties not encountered in mid-ocean. These difficulties include the presence of time-dependent boundary currents that have a substantial effect on sea- surface height and the presence of continental shelves that dictate that deep water for stereo height calculations is located some significant distance away from shore and the sea-level station. We elected to look at the California DEAN ROEMMICH Cooperative Fisheries (CALCOFI) hydrographic data, which has some unique advantages and some unfortunate disadvantages for our purposes. The principle drawback is that the maximum depth of routine sampling is only 500 m. We can say nothing about changes below this level. The great advantage is that the data consist of a grid of  stations extending about 2000 km along the west coast of the United States and Baja California and from very near the coast to several hundred kilometers offshore. The same basic grid has been occupied at irregular intervals since 1950. For statistical reasons, we decided to use only those stations occupied more than 50 times. The resulting subset of stations is shown in Figure 13.10. The first problem is in deciding what sea-level record or records should be compared with the CALCOFI steric height. Sea-level stations in the area of interest and their trends and standard eITors (in parentheses) are at San Diego (1.6 + 0.4), La Jolla (1.5 + 0.4), Los Angeles (-0.1 + 0.4), San Francisco (1.5 i 0.4), and Alameda (0.1 ~ 0.5~(Hicks et al., 19831. Thus, even nearby stations such as San Francisco and Alameda, and also Los Angeles and Santa Monica, have very different trends. The average trend for the region is not well estimated. We will make an arbi- trary choice of San Diego, Los Angeles, and San Francisco .. CALCOFI BASIC STATION PLAN SINCE 1950 ~; <: '. \ 3 . ):F9ANC'SCO 3P\\ · 9> '\ N: \~ ~ Fount \Q · \e~) ~ /CONC{PTION as  I ~1 1 , , , , 1 1 125- 120. 115° 110. as FIGURE 13.10 Map of the eastern North Pacific showing CALCOFI stations occupied on more than 50 occasions between 1950 and 1978. The trend in steric height (0 to 500 dbar) is indicated for each station (see text).

SEA LEVEL AND THE THERMAL VARIABILITY OF THE OCEAN as representative, bearing in mind that the average of these is a poor estimate of the true average sea-level change. Yearly mean sea level for each of these stations, and the yearly mean of the three-station average, are shown in Figure 13.1 1. Year-to-year changes in sea level are clearly well correlated along the coast, and the trend of the three- station average is 1.0 cm/decade. The CALCOFI grid yielded 90 stations where hydro- graphic casts were made to a depth of 500 m on 50 or more occasions between 1950 and 1978. For each cast, we computed the steric height of the sea surface relative to the 500-dbar surface. Casts were sorted by month and year. At each station, an annual cycle was estimated by averag- ing all casts in each month, regardless of year. This annual cycle in steric height was then removed by subtraction and yearly anomalies were computed by averaging all casts at a given station in a given year. We then computed a trend for each station based on the yearly anomalies. The trends, in centimeters per decade, are shown on the station map, Figure 13.10. There is considerable variability in the trends from station to station and from line to line of the grid. This small-scale variability is interpreted as noise due to under- sampling in time. There are no apparent large-scale vari- ations in the trend. That is, if the California Current had strengthened in the period 1950 to 1978, we would see steric height at the offshore stations increasing relative to the nearshore stations. This is not the case. Similarly, there is no apparent difference in the steric height trends in the northern half of the grid as compared to the southern half, indicating that the alongshore pressure gradient did not change greatly. The station-to-station changes in trend - ~ 005 - J 111 > J 015 0.1u ~ i -005 ~ SWAN I -0.10 - 0.15 _ . . . DIEGO /~ ~ ~ 3 STATION 950 1960 1970 1980 YEAR FIGURE 13.11 Annual mean sea level at San Francisco, Los Angeles, and San Diego and the average of the three stations. The vertical offset is arbitrary, for display purposes. o ~ -002  - 0.04 006 0.04 LLJ I Lo SEA LEVEL · STERIC HEIGHT I ~n Al 1 1 1 1 1 1 950 1960 1970 1980 YEAR 215 FIGURE 13.12 Averaged annual anomalies in sea level and steric height (O to 500 dbar) using hydrographic stations of Fig- ure 13.10 and the sea-level stations of Figure 13.11. are as random as can be expected given the fact that the grid is occupied on a line-by-line basis, that is, adjacent stations in a given line are usually very close together in time. If there are no strong spatial patterns, what about the overall trend? We averaged the yearly anomalies for all 90 stations, and these yearly averages are shown in Figure 13.12 together with the average sea level. The zero level for each set of data is arbitrary and has been adjusted so that they approximately coincide. In general, the interan- nual variations in sea level are well reproduced by the steric height series. The large sea-level oscillation of the 1950s and the rise in the mid-1970s are examples. There are also some notable disagreements, for example, 1972. Examination of the records reveals that whereas the 1972 CALCOFI data were collected early in the year, the large sea-level rise associated with the 1972 E1 Nino episode occurred late in the year. Thus, the undersampling in time can generate large errors in estimating annual mean steric height. The linear trend in steric height (0 to 500 dbar) for the averaged data of Figure 13.12 is 0.5 cm/decade, compared to 1.0 cm/decade for the averaged sea-level data. Within the error bounds established by the sampling noise, these are indistinguishable, but also, the steric height rise is not statistically different from zero. Once again, it appears from Figure 13.12 that a time series of about twice the length of the present CALCOFI data is required to over- come the sampling noise. Unfortunately, the ambiguity of the result is severalfold: 1. Because of the large station-to-station changes in the coastal sea-level trend, the areally averaged coastal sea-level trend is not well determined.

216 2. For the 29-yr period over which data were available, the sampling noise in the steric height record was of the same order as the signal. 3. Even if the sea-level and steric height records were long and error free, the lack of data below 500 m would still be troubling. Unlike the Atlantic Ocean, there is no deep water formed at high latitudes in the North Pacific. Therefore, one might suspect that the deep North Pacific is less sensitive to climatic fluctuations than the Atlantic. But without supporting data, this is pure conjecture. DISCUSSION A principal lesson of the extensive North Atlantic and eastern North Pacific data sets is that steric height vari- ations occur over such a variety of space and time scales that possible trends cannot be identified in the approxi- mately 30-yr time series, no matter how dense the sam- pling. In the 27 yr of overlapping steric height and sea- level data at Bermuda, there was no evidence of a "spec- tral gap" that would allow separation of the time scale spanned by the data from a much longer time scale that would appear as a trend. Rather, the sea-level and steric height spectra were equally red in the lowest frequency bands. But the news is not all bad. Many longer sea-level records, such as the Charleston record in Figure 13.7 (for which there is no accompanying steric height time series), do show evidence of such a gap. That is, the 15-cm trend over 50 yr is greater than the 5-cm fluctuations over 10 to 20 yr at that location. The expectation then is that about 50 yr of sea-level data together with steric height data at Bermuda and off the California coast would be sufficient to resolve the question of whether the sea-level trend is accompanied by a trend in steric height (at those loca- tions). Steric changes in the water column on time scales of a decade and longer are not confined to or concentrated in the upper ocean. In the subtropical North Atlantic such changes extend to depths of at least 3000 m. Maxima in temperature change appeared in the thermocline at depths of from 300 to 700 m and below the thermocline at about 1800 m. For observational programs the large vertical extent of the signal means that the entire depth of the ocean should be sampled. The Panulirus data are not sufficiently deep, though this deficiency can be made up by a few ancillary deep measurements elsewhere. For climate modeling studies, it is clear that the commonly used one-dimensional vertical advection-diffusion models not only miss the essential physics of the problem but also do not reproduce the observed patterns of change. Critical processes are air-sea interactions at middle and high lati- tudes, which determine volume and composition of the DEAN ROEMMICH mid-depth and deep water masses, and the spreading of those waters to lower latitudes. Temperature variations had a somewhat different char- acter in and above the thermocline than in the deep water in the subtropical North Atlantic. The therrnocline fluc- tuations had greater variance in the time domain than the deeper changes and also more variability around the sub- tropical gyre. Over 27 yr, the thermocline fluctuations made a greater contribution to steric height change than to the deep changes, but on a longer time scale, it is not clear  whether mid-depth or deep variations would dominate. The thermocline comes to the surface along the northern rim of the subtropical gyre, and these waters are therefore subject to atmospheric forcing relatively near to the area of our study. The deep water is farther removed from contact with the atmosphere, which can account for the more gradual changes and larger spatial scale of the deep signal. In combination, the Atlantic and Pacific data sets high- light several problems. If we are to unambiguously deter- mine the relationship between sea-level rise, steric height change, and changes in the mass of water in the ocean the following are necessary. 1. Density measurements in the ocean should extend to the ocean bottom at least occasionally. 2. Sampling in the time domain should be sufficient, at least in selected locations, so that variations with periods of months to years are not aliased into much longer peri- ods. 3. At key sea-level stations, the rate of change of the height of reference benchmarks relative to the geoid needs to be determined. ACKNOWLEDGMENTS I thank Walter Munk and S. Tabata for making helpful comments. The work was supported by the National Sci- ence Foundation through grants OCE-8121262 and OCE- 8317389 to UCSD. REFERENCES Barnett, T. (1983~. Long-term changes in dynamic height, J. Geophys. Res. 88, 9547-9552. Frankignoul, C. (1981~. Low-frequency temperature fluctua tions off Bermuda, J. Geophys. Res. 86, 6522-6528. Fuglister, F. (19604. Atlantic Ocean Atlas of Temperature and Salinity Profiles and Data from the International Geophysical Year of 1957-1958, Woods Hole Oceanographic Institution Atlas Series 1, Woods Hole, Mass., 209 pp. Hicks, S., H. Debaugh, Jr., and L. Hickman, Jr. (1983J. Sea Level Variations for the United States 1855-1980, U.S. De partment of Commerce, National Ocean Survey, 170 pp.

SEA LEVEL AND TTIE THERMAL VARIABILITY OF THE OCEAN Moore, W. (19821. Late Pleistocene sea level history, in Ura- nium Series Disequilibrium: Applications to Environmental Problems, M. Ivanovich and R. Harmon, eds., Clarendon, Oxford. Pocklington, R. ~ 1972~. Secular changes in the ocean off Bermuda, J. Geophys. Res. 77, 6604 6607. Reid, J., and A. Mantayla (1976~. The effect of geostrophic flow upon coastal sea elevations in the northern North Pacific Ocean, J. Geophys. Res. 81, 3100-3110. Roemmich, D., and C. Wunsch (1984). Apparent changes in the climatic state of the deep North Atlantic Ocean, Nature 307, 447~50. Roemmich, D., and C. Wunsch (19851. Two transatlantic sec 2l7 lions: Meridional circulation and heat flux in the subtropical North Atlantic Ocean, Deep-Sea Res. 32, 619~64. Schroeder, E., and H. Stommel (1969). How representative is the series of monthly mean conditions off Bermuda? Prog. Oceanogr. 5, 31~0. Shaw, D., and W. Donn (1964~. Sea level variations at Iceland and Bermuda, J. Marine Res. 22, 111-122. Talley, L., and M. Raymer (1982~. Eighteen degree water variability, J. Marine Res. 40, 757-775. UNESCO (1981). Tenth report of the joint panel on oceano- graphic tables and standards, UNESCO Technical Papers in Marine Science 36, UNESCO, Paris. Wunsch, C. (1972~. Bermuda sea level in relation to tides, weather, and baroclinic fluctuations, Rev. Geophys. Space Phys. 10, 1~9.

STRATEGY FOR FUTURE MEASUREMENTS OF VERY-LOW-FREQUENCY SEA-LEVEL CHANGE nificant baroclinic component. However, even at 100 m, corresponding to 1-mm precision for a stability of 1 x 10-5, one would expect the baroclinic component to be substan- tially attenuated relative to that measured by a surface tide gauge (since the largest ocean temperature changes occur in the upper ocean). If lower drift could be achieved at pressures corresponding to a few hundred meters depth, one might be able to move the sensor somewhat deeper. But this is clearly not the most desirable approach. If one were to pursue the use of piston gauges on the seafloor for long time periods, a number of practical prob- lems would need to be addressed. Some of the less obvi- ous ones include the following: 1. Although NIST is of the opinion that a high-quality, oil-operated piston gauge would function continuously for a year, there is no evidence of anyone that has done it for longer than two weeks (D. R. Johnson and C. Tilford, NIST, personal communication). 2. The axis of the gauge must be aligned to the vertical to better than 1 milliradian. 3. The gauge would have to be installed on the seafloor in such a way that it would settle by less than 1 mm/yr. 4. The external pressure applied to the piston by the gas in the pressure vessel used to house it must either be measured or eliminated by housing it in a vacuum. 5. The temperature of the piston and cylinder must be monitored to allow compensation for the approximately 9 ppm/°C temperature coefficient of the effective area. Many other detailed considerations would be required for making high-precision measurements; the ones given above are only examples. Success with this approach would prompt the desire to construct instruments to be deployed for multiyear periods, with real time data readouts on shore. Fiber-optic technology currently under active de- velopment should make it economically feasible to con- nect the instruments via cables to shore-based data record ers. INVERTED FATHOMETER Consider a fathometer looking upwards from the seafloor. The one-way acoustic travel time is Sh, where S = 1/C is the sound slowness and h is the total water thick- ness. In a homogenous ocean, the departure in travel time iS lit = S(Z - z ~ as a result of departures z and z surface c ' surface c in the surface and crustal elevations, respectively. We define z - t/S SO that z = z - z . IF IF surface c For an external contribution to the water budget OF = z - z . The effect of steric disturbances is twofold: it leads b c to an additional component, Is, in the surface elevation, and it changes the sound speed in the water column. In considering the effect of a long baroclinic wave in a 225 two-layer ocean, the upper ocean is characterized by a thickness hi, density pi, temperature 0~, and salinity so, with a corresponding h2, P2, 02, and s2 for the lower ocean. With a change in layer thickness from h. to (h. + ah. ), j = 1,2, but leaving Hi and si unchanged, the condition of  constant mass per unit area requires that piths + p2bh2 = 0, or Gh2 = -(P1/P2)6h1 (14.3) The steric change in sea levels equals z = Gh + Oh = 2 1 ah . s 1 2 P2 ~ This can be written The change in acoustic travel time (one-way) is fit = Sldhi + S26h2 - SOZF- (14.5) St = S2 dh lo- 5 A. (14.6) The first term is S2ZS' which is very nearly the increase in travel time associated with the steric rise in sea level. Typical values are (P2 - P1~/P2 = 0.001 and (S2 - S14/S2 = 0.01 so that the second term dominates. In terms of the temperature differential be, we have bp/p =-a~p and bS/ S = -ocCp, with a _ 0.13 x 10-3/°C and a = 3 x 10-3/°C. Thus the ratio of the second to the first term in brackets is p = a/a _ 23. (14.7) The result is that the second (negative) term dominates. A thickening of the upper layer (positive Chic raises the sea level by zs = t(P2 - p~/P23Gh~ and thus increases the one- way travel time by Szs; but the relative thickening of the warm (high speed) upper layer decreases travel time, and the latter effect dominates. We can write the result of a purely steric disturbance in the form ZIF Zs(l 2), p >> 1. (14.8) TOMOGRAPHY The inverted fathometer method is associated with a steep acoustic path and by its nature depends on a combi- nation of surface elevation and the variable interior field of sound speed. Tomography depends on near-horizontal refracted paths that do not intersect the surface and so can be used to estimate Is directly. An advantage of the method is that it provides a spatial average (order 1000 km). This reduces the mesoscale noise (100 km, month scale) in the estimate of the decadal fluctuations (104 km, decade scale). Munk and Wunsch (1985) estimated an rms