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Modelling the Variability in the Somali Current
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MODELLING THE VARIABILITY J NTHE SOMALI C U R R E " Mark E. Luther and James J. O'Brien The Florida State University Mesoscale Air-Sea Interaction Group, Tallahassee, FL 32306-3041
ABSTRACT A numerical model of the wind driven circulation in the Indian Ocean is used to study the variability of the circulation on seasonal and interannual time scales. The model is a nonlinear reduced gravity model driven by observed winds. Model simulations use a monthly mean climatology of ships' winds a s forcing and the 23 year long monthly mean Cadet and Diehl winds a s forcing, The model is very successful in simulating the observed features of the circulation in this region, such a s the formation and decay of the two-gyre system in the Somali Current during the southwest monsoon and the formation of the eddies off the coasts of Oman and Yemen. Examination of model statistics from many years of simulation using climatological monthly mean winds shows that the model fields are exactly repeating from one year to the next over most of the basin, even in the highly nonlinear eddies like the great whirl. Exceptions occur in the smaller scale eddies that form in the strong shear zones around the great whirl and in the southern gyre recirculation region, where the flow field exhibits a more chaotic nature, but even these features are nearly repeating from one year to the next. When observed, interannually varying winds are used to drive the model, the variability from year to year increases dramatically. This indicates that interannual variability in the model fields is due solely to variability in the winds and not due to inherent variability in the model physics, a s is seen in mid-latitude models of the oceanic general circulation.
WCKGROUND Numerous modelling efforts have sought to explain the observed flows in the tropical Indian Ocean, with particular attention given to the semi-annual reversals in the Somali Current along the east coast of Africa (e. g. Cox, 1970, 1976, 1979; Hurlburt and Thompson, 1976; Lin and Hurlburt, 1981; Luther and O'Brien, 1985; Luther et al., 1985; see Luther (1987) or Knox (1987) for a review). While the Somali Current is similar to mid-latitude western boundary currents in some respects, it is unique in many others. The most striking feature of this current is its reversal with the changing monsoon winds (see Schott, 1983; Knox, 1987). During boreal summer, the boundary current flows toward the north and northeast from the coast of Mozambique (11's)to the island of Socotra at 12"N, driven by the southwest monsoon winds. A "two-gyre" system is often observed in this current (Swallow and Fieux, 19821, with a southern gyre that straddles the equator, flowing offshore a t 3-4"N, and a northern gyre, called the great whirl, between 5 ' N and 9"N. Wedgeshaped areas of cold, upwelled water are found along the coast t o the north of these gyres. Late in the summer, the southern gyre and its cold wedge migrate rapidly
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northward and coalesce with the great whirl (Brown et al., 1980; Evans and Brown, 1981; Swallow et al., 1983). This appears to be the case in most years; however, there is evidence of some years when the two-gyre system does not form (Swallow and Fieux, 1982). The summer Somali Current to the north of 2-3"s gradually breaks up during the fall transition period, and is replaced by the southwestward winter Somali Current with the onset of the northeast monsoon in December. The boundary current to the south of 3"sflows to the north throughout the year and is called the East African Coastal Current (EACC). During the summer, the EACC feeds the northward Somali Current; during winter, i t meets the southwestward Somali Current and both flow offshore into the South Equatorial Counter Current (SECC). Woodberry et al. (1989) show that this region of the EACC is a tropical analog to a mid-latitude western boundary current recirculation region that is strongly modified by the presence of the equatorial wave guide and by the seasonal reversals in the wind. It closes the circulation in a tropical Sverdrup-like gyre in the southern hemisphere, consisting of the eastward SECC that meanders between the equator and 8"s and the westward South Equatorial Current (SEC) between 10 and 20"s. We use "Sverdrup-like" to describe this gyre because it is far from steady state; indeed, it has large seasonal variability (Schott et al., 1988; Swallow et al., 1988; Woodberryet al., 1989). In this paper, we will show that the model response to observed winds is largely deterministic, with only limited regions where the response appears to be chaotic. It then follows that interannual variability in ocean fields seen in the model is due to variability in the wind fields, rather than to inherent variability contained in the dynamics of the ocean itself. We begin by briefly describing the model and then summarizing some results from recent calculations. We describe the interannual variability in the summer Somali Current from a 23 year simulation and its relationship to Indian monsoon rainfall. Next, we describe results from a n 18 year simulation using climatological monthly mean winds. We then present statistical fields from these two simulations and identify regions where the ocean's response is largely deterministic and where it exhibits a chaotic nature. 2 "HEMODEL
The model used here is that of Luther and O'Brien (1985). It is a nonlinear reduced gravity model forced by observed winds. The advantage to such a model is ite inherent simplicity. As demonstrated by Lin and HurIburt (1981),this is the simplest model that contains the necessary physics to reproduce the observed eddy patterns in the Somali Current. Luther and O'Brien (1985) and Luther et al. (1985) show that the model faithfully reproduces most of the observed features of the
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seasonal cycle of the northwest Indian Ocean circulation, such as the formation and coalescence of the two-gyre system during the southwest monsoon, the formation and decay of the energetic eddy field off the Arabian Peninsula during the fall transition and the formation of the southwestward Somali Current with the onset of the northeast monsoon. Simmons et al. (1988) show that the model can accurately simulate the features observed in a particular year by comparing model fields driven by the observed winds for 1985 with extensive observations taken off the coasts of northern Somalia and the Arabian Peninsula during the fall of that year. Because the model physics are well known and the model fields are more easily analyzed, and because it reproduces many of the important features of the observed flows in this region, this model is ideal for use in long term, multi-year integrations, to assess the importance of interannual and seasonal variability in the region. Results from two versions of the model will be discussed here. The first is a limited area version that covers the northwest portion of the Indian Ocean from 10"sto 26"N and from 40"E to 74"E at a resolution of 118 degree zonally and 114 degree meridionally. The second version covers the entire Indian Ocean basin from 35"E t o 120"E and from 25"s to 26"N at a resolution of 0.1 degree in both directions (Fig. 1). We will call these the limited area model and the full basin model, respectively. Both versions employ open boundaries along the south and along a portion of the east boundaries. The free parameters in the model are the initial upper layer thickness, Ho, the wind stress drag coefficient, Cd, and the
Fig. 1: Model Geometry. The land boundaries are closed, no-slip boundaries. The southern boundary and a portion of the eastern boundary are open boundaries. The shallow banks located along the Seychelles-Mauritius Ridge, around Socotra, the Maldives and the Chagos Archipelago that are less than 40m deep are land boundaries in the model.
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Laplacian eddy viscosity coefficient, A,. For the results presented here, the limited area model uses Ho = 200 m, cd = 1.25 x 10-3, and A, = 750 m2s-1; the full basin model uses HO= 200 m, Cd = 1.5 x 10-3, and A, = 750 m2s-I. These models have been run for over 200 years of integration using various wind data sets as forcing, including interannual simulations using ship observed winds from 1954 to 1986 and long, multi-year simulations using climatological winds. Earlier model simulations have used a monthly mean climatology of ships' winds as forcing (Luther and O'Brien, 1985) and a monthly mean of the FGGE 1000 mbar winds as forcing (Luther et al., 1985). Our longest continuous interannual simulation covers the period 1954 through 1976 using the ship winds analyzed by Cadet and Diehl(1984).
3.1 Interannual Variability in the Somali Cumnt A great deal of interannual variability is seen in the model fields from the 23 year simulation using the Cadet and Diehl (1984) ships' winds as forcing. This variability can be attributed directly to variability in the wind fields. The two-gyre system is clearly present in all but two of the 23 years (Fig. 2), but the strength, location and timing of formation and collapse of the gyres vanes from year to year. In the two years when the two-gyre system is apparently absent ('72 and '731, the northern gyre, or great whirl, is present but the southern gyre is absent or at least very weak. Of the 21 years when there was clearly a two-gyre pattern, the northern and southern gyres coalesced in July-August in 14 years ('55, '56, '58, '60, '61, '62, '63, '64, '66, '68, '69, '70, '71, '74). In the other 7 years, a blocking flow formed to the north of the southern gyre a t about 2"N and prevented it from migrating northward. In these years, the along-shore winds near the equator were anomalously strong. In 5 of these years ('54, '57, '59, '65, '75) smaller eddies formed between the southern gyre and the great whirl and then coalesced with the great whirl. In 1967 and 1968 the great whirl was anomalously weak while the southern gyre was anomalously strong, and no coalescence was observed in the model fields. 3.2 Indian Monsoon Rainfall In a cooperative study with S. K. Dube of the Indian Institute of Technology, Delhi, we investigated the relationship between the interannual Variability in the model fields and variability in Indian monsoon rainfall (Dube et al., 1989). We found that the period 1954 to 1966 is a period during which the southern gyre of the Somali Current is generally stronger, the cross-equatorial winds are stronger and the upper layer is thinner (the thermocline is shallower) in the central Arabian
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Upper Layer Velocity
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August 16. 1958
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Fig. 2: Two very different circulation patterns for mid-August from the Somali Current region of the model. (a) In 1958, there was a pronounced two-gyre system, that collapsed in late August. In this image, the southern gyre is just beginning to coalesce with the great whirl, while another clockwise eddy has formed a t the equator. This was also a year of very good Indian monsoon rainfall. (b) In contrast, the circulation pattern for the same period in 1972 shows no evidence for a southern gyre, although there is some smaller scale eddy activity to the south of the great whirl. This year was one of the worst Indian monsoons in recent decades.
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Sea, implying that sea surface temperatures are lower. This period was identified by Cadet and Diehl (1984) as one of generally higher Indian monsoon rainfall. In contrast, the period 1967 to 1975 was one of generally lower Indian monsoon rainfall and also was a period during which the southern gyre was weaker, the cross-equatorial winds were weaker and the model upper layer was thicker (deeper thermocline) implying higher SST. A pronounced quasi-biennial oscillation (QBO) was found in the model fields and in the wind stress curl fields during the period of higher rainfall but was absent during the period of lower rainfall. The significance of the presence o r absence of this QBO signal is not yet clear, but is certainly suggestive.
3.3 Southern Hemisphere Circulation The full basin model is integrated for 20 years using the Hellerman and Rosenstein (1983) monthly mean climatological winds. A steady seasonal cycle is achieved throughout the basin by the tenth year of integration (Fig. 3). The southern hemisphere circulation from the 10th year of this simulation has been investigated i n detail (Woodberry et al., 1989). The primary feature of this circulation is a basin wide tropical gyre between the equator and approximately 20"S, consisting of the South Equatorial Current (SEC) in the south, the South Equatorial Counter Current (SECC) t o the north and the East African Coastal Current (EACC) closing the circulation in the west. A strong recirculation region exists in the EACC between 10"s and 2% during most of the year, with numerous eddies forming and being reabsorbed into the EACC. During the boreal summer, the separation point of the EACC moves northward across the equator, and the recirculation region becomes the southern gyre of the two gyre system in the Somali Current. Late in the summer monsoon, a n eddy separates from this region and migrates northward to coalesce with the great whirl. Due to the annual cycle in the wind stress curl, the Sverdrup-like interior consists of a series of first baroclinic mode nonlinear Rossby waves that propagate slowly westward. The required poleward Sverdrup flow from the SECC t o the SEC thus occurs in meridional bands in the lee of the minima in model upper layer thickness associated with these nonlinear waves. The model reproduces the SEC and its branches a s it splits around the Nazareth Bank and Cargados Carajos Shoals along the Seychelles-Mauritius Ridge at 60°E,14%, and again a t the east coast of Madagascar. The transport in the current around the northern tip of Madagascar shows a prominent 40 to 50 day oscillation during the months of February through April (Fig. 4), even though there is no forcing in that period band in the winds, but shows little annual cycle, as observed by Schott et al. (1988) and Swallow et al. (1988). This is due to the blocking effect of the very shallow banks
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Fig. 3: Model upper layer thickness (ULT) and velocity from the standard case (with islands) for August after 10 years of spin-up with the Hellerman winds. Colors denote ULT, with red being deeper ULT and higher heat content of the upper ocean, and blue being shallower ULT and lower heat content. Brown shading denotes land points. Arrows indicate upper layer velocity, with arrows shown only once per 1.6 degree in each direction. No arrows are shown for velocities less than 5 em s-l and velocities greater than 1m are truncated for clarity of display.
Fig. 4: Time-longitude contours of meridional transport across 12"S,from 50"E to 60"E. Westward propagation of the 40-50 day waves from the Seychelles-Mauritius Ridge toward Madagascar can be seen in February - April as sloped contours . These waves are excited by an annual Rossby wave that is blocked by the shallow Saya de Malha and Nazareth banks along the Ridge at 60"E. Units are in Sverdrups (1 Sv = 106 m3s-l). Contour interval is 0.2 Sv.
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along the Seychelles-Mauritius Ridge a t 60"E (see below). The annual Rossby wave that is generated in the interior farther to the east is trapped on the east side of these banks where it then sheds smaller scale, higher frequency waves through the gap between these banks. These higher frequency waves are the source of the 40 to 50 day oscillations to the north of Madagascar. 3.4 Equatorial Waves
The model also reproduces the 26 to 28 day waves seen along the equator in current meter records (O'Neill, 1984;Luyten and Roemmich, 1982)and in similar ocean models (Kindle and Thompson, 1989). These waves are identified as mixed Rossby-gravity waves, and are generated a t the western boundary when strongly nonlinear eddies in the East African Coastal Current or the Somali Current cross the equator. These waves have a n eastward group speed, but a westward phase speed, as seen in Fig. 5 . The existence of these waves constitutes the primary difference between this region and a mid-latitude western boundary current. The presence of the equatorial wave guide allows energy to be carried away from the western boundary a s either mixed Rossby-gravity waves or a s equatorial Kelvin waves. A t midlatitudes, there are no long waves available to carry energy eastward.
Fig. 5: Time-longitude contours of meridional transport along the equator between the coast of Africa and Gan (43-73"E). Solid (dashed) contours show northward (southward) transport. East of 50"E the presence of mixed Rossby-gravity waves, with eastward group speed and westward phase propagation, is apparent in the sloping contour lines. These waves are generated at the western boundary several times a year by the abrupt changes that occur in the western boundary current, seen in the convoluted contours west of 50'E.
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3.6 Island Effects The standard version of the model considers as land boundaries any bathymetry less than 200 m deep. This results in large islands along the Seychelles-Mauritius Ridge (around the Seychelles, the Saya de Malha Bank, the Nazareth Bank and the Cargados Carajos Shoals), along the Maldives, around Socotra and around the Chagos Archipelago, as well as numerous smaller islands. These land boundaries are shown in dark shading in Fig. 1. This is a realistic geometry, as these banks are extremely shallow, typically 10 to 40 m deep, are dotted with tiny islands and reefs, and therefore present substantial barriers to flow. Models of the Indian Ocean circulation presently in use by others omit these islands in their model geometry. Fig. 6 shows the flow field in the model for August after 10 years of integration using the Hellerman climatological winds as in Fig. 3; however, in Fig. 6, all the islands have been removed at the beginning of the integration. There are substantial differences between the two cases, particularly in the South Equatorial Current (SEC) between Madagascar and 60"E, in the equatorial wave guide and in the Somali Current. In the standard case (Fig. 3), the great whirl of the summer Somali Current is blocked t o the south of Socotra in August. The SEC splits at the Ridge at 60"E, with the northern branch flowing around the tip of Madagascar at about 12"s and the southern branch splitting again at the coast of Madagascar at 18%. There is almost no annual variation in the flow around the northern tip of Madagascar, which is consistent with observations of Swallow et al. (1988) and Schott el al. (1988). In the no islands case (Fig. 6) the great whirl continues t o migrate northward in the absence of the blocking effects of Socotra. The SEC impinges on the coast of Madagascar as a single broad current at about 15"S, with a pronounced annual signal, due to the absence of the blocking effect of the Ridge on the annual Rossby wave generated by the wind stress curl in the east. There is higher eddy energy in the East African Coastal Current (EACC) in the no islands case, again due to the absence of blocking of Rossby wave 'energy from the interior by the islands. The inclusion of these islands therefore appears to be crucial for an accurate simulation of the Indian Ocean circulation. 4 INHERENT vs. lN!CJ3RA"uAL VARIABILITY
From the last ten years of the 20 year full basin simulation, we compute the mean and standard deviation of the model upper layer thickness (ULT) field for the 16th of each month of the year, i.e., we compute the mean and standard deviation of ULT at each grid point from all January 16ths, from all February 16th's, etc. The standard deviation fields, expressed as meters of deviation about the mean, are thus a measure of the inherent variability in the model physics, since the wind
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Fig. 6: Same as in Fig. 3, for the no islands case. Flow in the SEC, in the EACC and in the great whirl are changed appreciably.
Fig. 7: ULT standard deviation for all August 16th'~from years 11 through 20 of model integration using the Hellerman climatological monthly mean winds.
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cycle is exactly repeating from year to year. These fields are shown in Fig. 7 for representative months. Over most of the basin, on a particular day of the year, ULT varies by less than l m from one year t o the next; for instance, the ULT field for August 16, year 15, is within l m of the value it had on August '16, year 14, over most of the basin, indicating that the model solution is a nonlinear periodic response t o the seasonal winds. Exceptions to this occur only in limited regions such as the East African Coastal Current recirculation region, which is a tropical analog of a mid-latitude western boundary current recirculation region. High values of ULT standard deviation are also found in the intense shear zone around the great whirl during the summer monsoon, but this is confined to very small scale motions around the periphery of the great whirl; the center of the great whirl is found in the same position with the same intensity from one year to the next. The highest values of ULT standard deviation in these regions are in the range of 12-15m, indicating a more chaotic nature in the model response. In the EACC recirculation region and around the great whirl, the chaotic nature of the flow stems from horizontal shearing (barotropic) instabilities; still, the solution over much of these regions is repeating to a high degree. The situation is much different when real-time, interannual winds are used to drive the model. Fig. 8 shows the same standard deviation calculation from a version of the model driven by 23 years of real-time, interannually varying ship winds from Cadet and Diehl (1984). Fig. 8a shows the ULT standard deviation, expressed in meters of deviation about the mean, from 10 years of simulation driven by the climatological monthly mean of the 23 years of winds, while Fig. 8b shows the the same quantity from the 23 year simulation using the interannually varying winds. The ULT standard deviation for the interannual case is everywhere an order of magnitude larger than for the climatological case, except in the highly nonlinear shear zones around the great whirl, indicating that interannual variability in the model response is solely due to variability in the winds, rather than to inherent variability contained in the model physics. 5 CONCLUSION
The variability seen in this model is in stark contrast to that seen in midlatitude ocean models, where the flow field approaches chaotic motion and agreement between model fields and observations is found only in a statistical sense (eg. Schmitz and Holland, 1982; Holland and Schmitz, 1985). One reason for
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Fig. 8: (a) ULT standard deviation, expressed as departure from the mean in meters, for all August 1 6 t h ’ ~from a 10 year integration driven by the climatological monthly mean winds compiled from ship observations from 1954 through 1976. 6)Same for all August 1 6 t h from ~ the 23 year simulation using the interannual winds from 1954 through 1976.
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this disparity is that baroclinic instability is more important in mid-latitudes than in the tropics, giving rise to more random eddy production. This mechanism is absent in the reduced gravity formulation; however, a t low latitudes, barotropic instability, which is contained in our model physics, is the dominant instability mechanism. A more likely reason is that the mid-latitude models use steady, idealized winds in an idealized basin, while our model uses a realistic basin geometry with observed winds as forcing. It may be possible that a more deterministic solution would arise from the use of realistic, time varying winds with realistic basin geometry in mid-latitude oceans as well.
6 ACKNOWLEIIGE3lENTS This research was supported by the Office of Naval Research through the Secretary of the Navy Chair in Oceanography, by the Naval Ocean Research and Development Activity and by the Institute for Naval Oceanography. Additional support was provided by the Florida State University through time granted on their Cyber 205 supercomputer. This is contribution number 272 of the Geophysical Fluid Dynamics Institute and contribution number 89-09 of the Supercomputer Computations Research Institute at Florida State University.
Brown, 0. B., J. G. Bruce and R. H.Evans, 1980. Evolution of sea surface temperature in the Somali Basin during the southwest monsoon of 1979. Science, 209:595-597. Cadet, D. L. and B. C. Diehl, 1984. Inter-annual variability of surface fields over the Indian Ocean in recent decades. Mon. Wea. Rev., 112: 1921-1935. Cox, M. D., 1970. A mathematical model of the Indian Ocean. Deep-sea Res., 17:47-75. Cox, M. D.,1976. Equatorially trapped waves and the generation of the Somali Current. Deep-sea Res., 23: 1139-1152. Cox, M. D., 1979. A numerical study of Somali Current eddies. J. Phys. Oceamgr., 9:311-326. Dube, S. K, M. E. Luther and J. J. OBrien, 1989. Relationships between interannual variability in the Arabian Sea and Indian monsoon rainfall. J. Geophys. Res. - Oceans, 94 (to appear). Evans, R. H. and 0. B. Brown, 1981. Propagation of thermal fronts in the Somali Current system. Deep-sea Res., 28: 521-527. Holland, W. R. and W. J. Schmitz, 1985. Zonal penetration scale of model midlatitude jets. J. Phys. Oceanogr., 15: 1859-1875. Hurlburt, H. E. and J. D. Thompson, 1976. A numerical model of the Somali Current. J. Phys. Oceanogr.,6: 646-664. Kindle, J. C. and J. D. Thompson, 1989. The 26 and 50 day oscillations in the western Indian Ocean: Model results. J. Geophys. Res. - Oceans, 94 (in press).
386 Knox, R. A,, 1987. The Indian Ocean: Interaction with the monsoon. In: J. S. Fein and P. S. Stephens (Editors), Monsoons, John Wiley, New York, pp. 365-397. Lin, L. B. and H. E. Hurlburt, 1981. Maximum simplification of nonlinear Somali Current dynamics. In: M. J. Lighthill and R. P. Pearce (Editors), Monsoon Dynamics, Cambridge University Press, pp. 541-555. Luther, M. E., 1987. Indian Ocean modelling. In: E. Katz and J. Witte, (Editors), Further Progress in Equatorial Oceanography, Nova Univ. Press, Dania, FL, pp. 303-316. Luther, M. E., and J. J. OBrien, 1985. A model of the seasonal circulation in the Arabian Sea forced by observed winds. Prog. Oceanogr., 14:353-385. Luther, M. E., J. J. O'Brien and A H. Meng, 1985. Morphology of the Somali Current System during the southwest monsoon. In: J. C. J. Nihoul (Editor), Coupled Ocean-Atmosphere Models, Elsevier, Amsterdam, pp. 405-437. Luyten, J. R., and D. H. Roemmich, 1982. Equatorial currents at semi-annual period in the Indian Ocean. J. Phys. Oceanogr., 12: 406-413. O'Neill, K., 1984. Equatorial velocity profiles: I. Meridional component. J. Phys. Oceanogr., 14: 1829-1841. Schmitz, W. J. and W. R. Holland, 1982. A preliminary comparison of selected numerical eddyresolving general circulation experiments with observations. J. Mar. Res., 40: 75-117. Schott, F., 1983. Monsoon response of the Somali Current and associated upwelling. Prog. Oceanogr., 12:357-382. Schott, F., M. Fieux, J. Kindle, J. Swallow and R. Zantopp, 1988. The boundary currents east and north of Madagascar, 2, Direct measurements and model comparisons. J. Geophys. Res.Oceans, 93:4963-4974. Simmons, R. C., M. E. Luther, J. J. O'Brien and D. M. Legler, 1988. Verification of a numerical model of the Arabian Sea. J. Geophys. Res. - Oceans, 93:15 437-15455. Swallow, J. C., and M. Fieux, 1982. Historical evidence for two gyres in the Somali Current. J. Mar. Res., 4O(Suppl.): 747-755. Swallow J. C., M. Fieux and F. Schott, 1988. The boundary currents east and north of Madagascar, 1, Geostrophic currents and transports. J. Geophys. Res.-Oceans, 93:4951-4962. Woodberry, K. E., M. E. Luther and J. J. O'Brien, 1989. The wind driven seasonal circulation in the southern tropical Indian Ocean. J. Geophys. Res.-Oceans, 94 (in press).
MODELLING THE VARIABILITY J NTHE SOMALI C U R R E " Mark E. Luther and James J. O'Brien The Florida State University Mesoscale Air-Sea Interaction Group, Tallahassee, FL 32306-3041
ABSTRACT A numerical model of the wind driven circulation in the Indian Ocean is used to study the variability of the circulation on seasonal and interannual time scales. The model is a nonlinear reduced gravity model driven by observed winds. Model simulations use a monthly mean climatology of ships' winds a s forcing and the 23 year long monthly mean Cadet and Diehl winds a s forcing, The model is very successful in simulating the observed features of the circulation in this region, such a s the formation and decay of the two-gyre system in the Somali Current during the southwest monsoon and the formation of the eddies off the coasts of Oman and Yemen. Examination of model statistics from many years of simulation using climatological monthly mean winds shows that the model fields are exactly repeating from one year to the next over most of the basin, even in the highly nonlinear eddies like the great whirl. Exceptions occur in the smaller scale eddies that form in the strong shear zones around the great whirl and in the southern gyre recirculation region, where the flow field exhibits a more chaotic nature, but even these features are nearly repeating from one year to the next. When observed, interannually varying winds are used to drive the model, the variability from year to year increases dramatically. This indicates that interannual variability in the model fields is due solely to variability in the winds and not due to inherent variability in the model physics, a s is seen in mid-latitude models of the oceanic general circulation.
WCKGROUND Numerous modelling efforts have sought to explain the observed flows in the tropical Indian Ocean, with particular attention given to the semi-annual reversals in the Somali Current along the east coast of Africa (e. g. Cox, 1970, 1976, 1979; Hurlburt and Thompson, 1976; Lin and Hurlburt, 1981; Luther and O'Brien, 1985; Luther et al., 1985; see Luther (1987) or Knox (1987) for a review). While the Somali Current is similar to mid-latitude western boundary currents in some respects, it is unique in many others. The most striking feature of this current is its reversal with the changing monsoon winds (see Schott, 1983; Knox, 1987). During boreal summer, the boundary current flows toward the north and northeast from the coast of Mozambique (11's)to the island of Socotra at 12"N, driven by the southwest monsoon winds. A "two-gyre" system is often observed in this current (Swallow and Fieux, 19821, with a southern gyre that straddles the equator, flowing offshore a t 3-4"N, and a northern gyre, called the great whirl, between 5 ' N and 9"N. Wedgeshaped areas of cold, upwelled water are found along the coast t o the north of these gyres. Late in the summer, the southern gyre and its cold wedge migrate rapidly
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northward and coalesce with the great whirl (Brown et al., 1980; Evans and Brown, 1981; Swallow et al., 1983). This appears to be the case in most years; however, there is evidence of some years when the two-gyre system does not form (Swallow and Fieux, 1982). The summer Somali Current to the north of 2-3"s gradually breaks up during the fall transition period, and is replaced by the southwestward winter Somali Current with the onset of the northeast monsoon in December. The boundary current to the south of 3"sflows to the north throughout the year and is called the East African Coastal Current (EACC). During the summer, the EACC feeds the northward Somali Current; during winter, i t meets the southwestward Somali Current and both flow offshore into the South Equatorial Counter Current (SECC). Woodberry et al. (1989) show that this region of the EACC is a tropical analog to a mid-latitude western boundary current recirculation region that is strongly modified by the presence of the equatorial wave guide and by the seasonal reversals in the wind. It closes the circulation in a tropical Sverdrup-like gyre in the southern hemisphere, consisting of the eastward SECC that meanders between the equator and 8"s and the westward South Equatorial Current (SEC) between 10 and 20"s. We use "Sverdrup-like" to describe this gyre because it is far from steady state; indeed, it has large seasonal variability (Schott et al., 1988; Swallow et al., 1988; Woodberryet al., 1989). In this paper, we will show that the model response to observed winds is largely deterministic, with only limited regions where the response appears to be chaotic. It then follows that interannual variability in ocean fields seen in the model is due to variability in the wind fields, rather than to inherent variability contained in the dynamics of the ocean itself. We begin by briefly describing the model and then summarizing some results from recent calculations. We describe the interannual variability in the summer Somali Current from a 23 year simulation and its relationship to Indian monsoon rainfall. Next, we describe results from a n 18 year simulation using climatological monthly mean winds. We then present statistical fields from these two simulations and identify regions where the ocean's response is largely deterministic and where it exhibits a chaotic nature. 2 "HEMODEL
The model used here is that of Luther and O'Brien (1985). It is a nonlinear reduced gravity model forced by observed winds. The advantage to such a model is ite inherent simplicity. As demonstrated by Lin and HurIburt (1981),this is the simplest model that contains the necessary physics to reproduce the observed eddy patterns in the Somali Current. Luther and O'Brien (1985) and Luther et al. (1985) show that the model faithfully reproduces most of the observed features of the
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seasonal cycle of the northwest Indian Ocean circulation, such as the formation and coalescence of the two-gyre system during the southwest monsoon, the formation and decay of the energetic eddy field off the Arabian Peninsula during the fall transition and the formation of the southwestward Somali Current with the onset of the northeast monsoon. Simmons et al. (1988) show that the model can accurately simulate the features observed in a particular year by comparing model fields driven by the observed winds for 1985 with extensive observations taken off the coasts of northern Somalia and the Arabian Peninsula during the fall of that year. Because the model physics are well known and the model fields are more easily analyzed, and because it reproduces many of the important features of the observed flows in this region, this model is ideal for use in long term, multi-year integrations, to assess the importance of interannual and seasonal variability in the region. Results from two versions of the model will be discussed here. The first is a limited area version that covers the northwest portion of the Indian Ocean from 10"sto 26"N and from 40"E to 74"E at a resolution of 118 degree zonally and 114 degree meridionally. The second version covers the entire Indian Ocean basin from 35"E t o 120"E and from 25"s to 26"N at a resolution of 0.1 degree in both directions (Fig. 1). We will call these the limited area model and the full basin model, respectively. Both versions employ open boundaries along the south and along a portion of the east boundaries. The free parameters in the model are the initial upper layer thickness, Ho, the wind stress drag coefficient, Cd, and the
Fig. 1: Model Geometry. The land boundaries are closed, no-slip boundaries. The southern boundary and a portion of the eastern boundary are open boundaries. The shallow banks located along the Seychelles-Mauritius Ridge, around Socotra, the Maldives and the Chagos Archipelago that are less than 40m deep are land boundaries in the model.
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Laplacian eddy viscosity coefficient, A,. For the results presented here, the limited area model uses Ho = 200 m, cd = 1.25 x 10-3, and A, = 750 m2s-1; the full basin model uses HO= 200 m, Cd = 1.5 x 10-3, and A, = 750 m2s-I. These models have been run for over 200 years of integration using various wind data sets as forcing, including interannual simulations using ship observed winds from 1954 to 1986 and long, multi-year simulations using climatological winds. Earlier model simulations have used a monthly mean climatology of ships' winds as forcing (Luther and O'Brien, 1985) and a monthly mean of the FGGE 1000 mbar winds as forcing (Luther et al., 1985). Our longest continuous interannual simulation covers the period 1954 through 1976 using the ship winds analyzed by Cadet and Diehl(1984).
3.1 Interannual Variability in the Somali Cumnt A great deal of interannual variability is seen in the model fields from the 23 year simulation using the Cadet and Diehl (1984) ships' winds as forcing. This variability can be attributed directly to variability in the wind fields. The two-gyre system is clearly present in all but two of the 23 years (Fig. 2), but the strength, location and timing of formation and collapse of the gyres vanes from year to year. In the two years when the two-gyre system is apparently absent ('72 and '731, the northern gyre, or great whirl, is present but the southern gyre is absent or at least very weak. Of the 21 years when there was clearly a two-gyre pattern, the northern and southern gyres coalesced in July-August in 14 years ('55, '56, '58, '60, '61, '62, '63, '64, '66, '68, '69, '70, '71, '74). In the other 7 years, a blocking flow formed to the north of the southern gyre a t about 2"N and prevented it from migrating northward. In these years, the along-shore winds near the equator were anomalously strong. In 5 of these years ('54, '57, '59, '65, '75) smaller eddies formed between the southern gyre and the great whirl and then coalesced with the great whirl. In 1967 and 1968 the great whirl was anomalously weak while the southern gyre was anomalously strong, and no coalescence was observed in the model fields. 3.2 Indian Monsoon Rainfall In a cooperative study with S. K. Dube of the Indian Institute of Technology, Delhi, we investigated the relationship between the interannual Variability in the model fields and variability in Indian monsoon rainfall (Dube et al., 1989). We found that the period 1954 to 1966 is a period during which the southern gyre of the Somali Current is generally stronger, the cross-equatorial winds are stronger and the upper layer is thinner (the thermocline is shallower) in the central Arabian
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Upper Layer Velocity
Upper Layer Thickness
10 N
ION
5N
5N
EQ
EQ
August 16. 1958
a
4; E
5iE
5SE
45 E
Upper Layer Thickness
WE
55E
Upper Layer Velocity
August 16. 1972
b
rJ
I
45 E
I
WE
I
I
55E
Fig. 2: Two very different circulation patterns for mid-August from the Somali Current region of the model. (a) In 1958, there was a pronounced two-gyre system, that collapsed in late August. In this image, the southern gyre is just beginning to coalesce with the great whirl, while another clockwise eddy has formed a t the equator. This was also a year of very good Indian monsoon rainfall. (b) In contrast, the circulation pattern for the same period in 1972 shows no evidence for a southern gyre, although there is some smaller scale eddy activity to the south of the great whirl. This year was one of the worst Indian monsoons in recent decades.
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Sea, implying that sea surface temperatures are lower. This period was identified by Cadet and Diehl (1984) as one of generally higher Indian monsoon rainfall. In contrast, the period 1967 to 1975 was one of generally lower Indian monsoon rainfall and also was a period during which the southern gyre was weaker, the cross-equatorial winds were weaker and the model upper layer was thicker (deeper thermocline) implying higher SST. A pronounced quasi-biennial oscillation (QBO) was found in the model fields and in the wind stress curl fields during the period of higher rainfall but was absent during the period of lower rainfall. The significance of the presence o r absence of this QBO signal is not yet clear, but is certainly suggestive.
3.3 Southern Hemisphere Circulation The full basin model is integrated for 20 years using the Hellerman and Rosenstein (1983) monthly mean climatological winds. A steady seasonal cycle is achieved throughout the basin by the tenth year of integration (Fig. 3). The southern hemisphere circulation from the 10th year of this simulation has been investigated i n detail (Woodberry et al., 1989). The primary feature of this circulation is a basin wide tropical gyre between the equator and approximately 20"S, consisting of the South Equatorial Current (SEC) in the south, the South Equatorial Counter Current (SECC) t o the north and the East African Coastal Current (EACC) closing the circulation in the west. A strong recirculation region exists in the EACC between 10"s and 2% during most of the year, with numerous eddies forming and being reabsorbed into the EACC. During the boreal summer, the separation point of the EACC moves northward across the equator, and the recirculation region becomes the southern gyre of the two gyre system in the Somali Current. Late in the summer monsoon, a n eddy separates from this region and migrates northward to coalesce with the great whirl. Due to the annual cycle in the wind stress curl, the Sverdrup-like interior consists of a series of first baroclinic mode nonlinear Rossby waves that propagate slowly westward. The required poleward Sverdrup flow from the SECC t o the SEC thus occurs in meridional bands in the lee of the minima in model upper layer thickness associated with these nonlinear waves. The model reproduces the SEC and its branches a s it splits around the Nazareth Bank and Cargados Carajos Shoals along the Seychelles-Mauritius Ridge at 60°E,14%, and again a t the east coast of Madagascar. The transport in the current around the northern tip of Madagascar shows a prominent 40 to 50 day oscillation during the months of February through April (Fig. 4), even though there is no forcing in that period band in the winds, but shows little annual cycle, as observed by Schott et al. (1988) and Swallow et al. (1988). This is due to the blocking effect of the very shallow banks
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Fig. 3: Model upper layer thickness (ULT) and velocity from the standard case (with islands) for August after 10 years of spin-up with the Hellerman winds. Colors denote ULT, with red being deeper ULT and higher heat content of the upper ocean, and blue being shallower ULT and lower heat content. Brown shading denotes land points. Arrows indicate upper layer velocity, with arrows shown only once per 1.6 degree in each direction. No arrows are shown for velocities less than 5 em s-l and velocities greater than 1m are truncated for clarity of display.
Fig. 4: Time-longitude contours of meridional transport across 12"S,from 50"E to 60"E. Westward propagation of the 40-50 day waves from the Seychelles-Mauritius Ridge toward Madagascar can be seen in February - April as sloped contours . These waves are excited by an annual Rossby wave that is blocked by the shallow Saya de Malha and Nazareth banks along the Ridge at 60"E. Units are in Sverdrups (1 Sv = 106 m3s-l). Contour interval is 0.2 Sv.
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along the Seychelles-Mauritius Ridge a t 60"E (see below). The annual Rossby wave that is generated in the interior farther to the east is trapped on the east side of these banks where it then sheds smaller scale, higher frequency waves through the gap between these banks. These higher frequency waves are the source of the 40 to 50 day oscillations to the north of Madagascar. 3.4 Equatorial Waves
The model also reproduces the 26 to 28 day waves seen along the equator in current meter records (O'Neill, 1984;Luyten and Roemmich, 1982)and in similar ocean models (Kindle and Thompson, 1989). These waves are identified as mixed Rossby-gravity waves, and are generated a t the western boundary when strongly nonlinear eddies in the East African Coastal Current or the Somali Current cross the equator. These waves have a n eastward group speed, but a westward phase speed, as seen in Fig. 5 . The existence of these waves constitutes the primary difference between this region and a mid-latitude western boundary current. The presence of the equatorial wave guide allows energy to be carried away from the western boundary a s either mixed Rossby-gravity waves or a s equatorial Kelvin waves. A t midlatitudes, there are no long waves available to carry energy eastward.
Fig. 5: Time-longitude contours of meridional transport along the equator between the coast of Africa and Gan (43-73"E). Solid (dashed) contours show northward (southward) transport. East of 50"E the presence of mixed Rossby-gravity waves, with eastward group speed and westward phase propagation, is apparent in the sloping contour lines. These waves are generated at the western boundary several times a year by the abrupt changes that occur in the western boundary current, seen in the convoluted contours west of 50'E.
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3.6 Island Effects The standard version of the model considers as land boundaries any bathymetry less than 200 m deep. This results in large islands along the Seychelles-Mauritius Ridge (around the Seychelles, the Saya de Malha Bank, the Nazareth Bank and the Cargados Carajos Shoals), along the Maldives, around Socotra and around the Chagos Archipelago, as well as numerous smaller islands. These land boundaries are shown in dark shading in Fig. 1. This is a realistic geometry, as these banks are extremely shallow, typically 10 to 40 m deep, are dotted with tiny islands and reefs, and therefore present substantial barriers to flow. Models of the Indian Ocean circulation presently in use by others omit these islands in their model geometry. Fig. 6 shows the flow field in the model for August after 10 years of integration using the Hellerman climatological winds as in Fig. 3; however, in Fig. 6, all the islands have been removed at the beginning of the integration. There are substantial differences between the two cases, particularly in the South Equatorial Current (SEC) between Madagascar and 60"E, in the equatorial wave guide and in the Somali Current. In the standard case (Fig. 3), the great whirl of the summer Somali Current is blocked t o the south of Socotra in August. The SEC splits at the Ridge at 60"E, with the northern branch flowing around the tip of Madagascar at about 12"s and the southern branch splitting again at the coast of Madagascar at 18%. There is almost no annual variation in the flow around the northern tip of Madagascar, which is consistent with observations of Swallow et al. (1988) and Schott el al. (1988). In the no islands case (Fig. 6) the great whirl continues t o migrate northward in the absence of the blocking effects of Socotra. The SEC impinges on the coast of Madagascar as a single broad current at about 15"S, with a pronounced annual signal, due to the absence of the blocking effect of the Ridge on the annual Rossby wave generated by the wind stress curl in the east. There is higher eddy energy in the East African Coastal Current (EACC) in the no islands case, again due to the absence of blocking of Rossby wave 'energy from the interior by the islands. The inclusion of these islands therefore appears to be crucial for an accurate simulation of the Indian Ocean circulation. 4 INHERENT vs. lN!CJ3RA"uAL VARIABILITY
From the last ten years of the 20 year full basin simulation, we compute the mean and standard deviation of the model upper layer thickness (ULT) field for the 16th of each month of the year, i.e., we compute the mean and standard deviation of ULT at each grid point from all January 16ths, from all February 16th's, etc. The standard deviation fields, expressed as meters of deviation about the mean, are thus a measure of the inherent variability in the model physics, since the wind
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Fig. 6: Same as in Fig. 3, for the no islands case. Flow in the SEC, in the EACC and in the great whirl are changed appreciably.
Fig. 7: ULT standard deviation for all August 16th'~from years 11 through 20 of model integration using the Hellerman climatological monthly mean winds.
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cycle is exactly repeating from year to year. These fields are shown in Fig. 7 for representative months. Over most of the basin, on a particular day of the year, ULT varies by less than l m from one year t o the next; for instance, the ULT field for August 16, year 15, is within l m of the value it had on August '16, year 14, over most of the basin, indicating that the model solution is a nonlinear periodic response t o the seasonal winds. Exceptions to this occur only in limited regions such as the East African Coastal Current recirculation region, which is a tropical analog of a mid-latitude western boundary current recirculation region. High values of ULT standard deviation are also found in the intense shear zone around the great whirl during the summer monsoon, but this is confined to very small scale motions around the periphery of the great whirl; the center of the great whirl is found in the same position with the same intensity from one year to the next. The highest values of ULT standard deviation in these regions are in the range of 12-15m, indicating a more chaotic nature in the model response. In the EACC recirculation region and around the great whirl, the chaotic nature of the flow stems from horizontal shearing (barotropic) instabilities; still, the solution over much of these regions is repeating to a high degree. The situation is much different when real-time, interannual winds are used to drive the model. Fig. 8 shows the same standard deviation calculation from a version of the model driven by 23 years of real-time, interannually varying ship winds from Cadet and Diehl (1984). Fig. 8a shows the ULT standard deviation, expressed in meters of deviation about the mean, from 10 years of simulation driven by the climatological monthly mean of the 23 years of winds, while Fig. 8b shows the the same quantity from the 23 year simulation using the interannually varying winds. The ULT standard deviation for the interannual case is everywhere an order of magnitude larger than for the climatological case, except in the highly nonlinear shear zones around the great whirl, indicating that interannual variability in the model response is solely due to variability in the winds, rather than to inherent variability contained in the model physics. 5 CONCLUSION
The variability seen in this model is in stark contrast to that seen in midlatitude ocean models, where the flow field approaches chaotic motion and agreement between model fields and observations is found only in a statistical sense (eg. Schmitz and Holland, 1982; Holland and Schmitz, 1985). One reason for
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Fig. 8: (a) ULT standard deviation, expressed as departure from the mean in meters, for all August 1 6 t h ’ ~from a 10 year integration driven by the climatological monthly mean winds compiled from ship observations from 1954 through 1976. 6)Same for all August 1 6 t h from ~ the 23 year simulation using the interannual winds from 1954 through 1976.
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this disparity is that baroclinic instability is more important in mid-latitudes than in the tropics, giving rise to more random eddy production. This mechanism is absent in the reduced gravity formulation; however, a t low latitudes, barotropic instability, which is contained in our model physics, is the dominant instability mechanism. A more likely reason is that the mid-latitude models use steady, idealized winds in an idealized basin, while our model uses a realistic basin geometry with observed winds as forcing. It may be possible that a more deterministic solution would arise from the use of realistic, time varying winds with realistic basin geometry in mid-latitude oceans as well.
6 ACKNOWLEIIGE3lENTS This research was supported by the Office of Naval Research through the Secretary of the Navy Chair in Oceanography, by the Naval Ocean Research and Development Activity and by the Institute for Naval Oceanography. Additional support was provided by the Florida State University through time granted on their Cyber 205 supercomputer. This is contribution number 272 of the Geophysical Fluid Dynamics Institute and contribution number 89-09 of the Supercomputer Computations Research Institute at Florida State University.
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386 Knox, R. A,, 1987. The Indian Ocean: Interaction with the monsoon. In: J. S. Fein and P. S. Stephens (Editors), Monsoons, John Wiley, New York, pp. 365-397. Lin, L. B. and H. E. Hurlburt, 1981. Maximum simplification of nonlinear Somali Current dynamics. In: M. J. Lighthill and R. P. Pearce (Editors), Monsoon Dynamics, Cambridge University Press, pp. 541-555. Luther, M. E., 1987. Indian Ocean modelling. In: E. Katz and J. Witte, (Editors), Further Progress in Equatorial Oceanography, Nova Univ. Press, Dania, FL, pp. 303-316. Luther, M. E., and J. J. OBrien, 1985. A model of the seasonal circulation in the Arabian Sea forced by observed winds. Prog. Oceanogr., 14:353-385. Luther, M. E., J. J. O'Brien and A H. Meng, 1985. Morphology of the Somali Current System during the southwest monsoon. In: J. C. J. Nihoul (Editor), Coupled Ocean-Atmosphere Models, Elsevier, Amsterdam, pp. 405-437. Luyten, J. R., and D. H. Roemmich, 1982. Equatorial currents at semi-annual period in the Indian Ocean. J. Phys. Oceanogr., 12: 406-413. O'Neill, K., 1984. Equatorial velocity profiles: I. Meridional component. J. Phys. Oceanogr., 14: 1829-1841. Schmitz, W. J. and W. R. Holland, 1982. A preliminary comparison of selected numerical eddyresolving general circulation experiments with observations. J. Mar. Res., 40: 75-117. Schott, F., 1983. Monsoon response of the Somali Current and associated upwelling. Prog. Oceanogr., 12:357-382. Schott, F., M. Fieux, J. Kindle, J. Swallow and R. Zantopp, 1988. The boundary currents east and north of Madagascar, 2, Direct measurements and model comparisons. J. Geophys. Res.Oceans, 93:4963-4974. Simmons, R. C., M. E. Luther, J. J. O'Brien and D. M. Legler, 1988. Verification of a numerical model of the Arabian Sea. J. Geophys. Res. - Oceans, 93:15 437-15455. Swallow, J. C., and M. Fieux, 1982. Historical evidence for two gyres in the Somali Current. J. Mar. Res., 4O(Suppl.): 747-755. Swallow J. C., M. Fieux and F. Schott, 1988. The boundary currents east and north of Madagascar, 1, Geostrophic currents and transports. J. Geophys. Res.-Oceans, 93:4951-4962. Woodberry, K. E., M. E. Luther and J. J. O'Brien, 1989. The wind driven seasonal circulation in the southern tropical Indian Ocean. J. Geophys. Res.-Oceans, 94 (in press).