Ocean Sci., 4, 183–198, 2008 www.ocean-sci.net/4/183/2008/ Ocean Science © Author(s) 2008. This work is distributed under the Creative Commons Attribution 3.0 License.

On the Indonesian Throughflow in the OCCAM 1/4 degree ocean model

U. W. Humphries1 and D. J. Webb2 1King Monghut’s Institute of Technology, Thailand 2National Oceanography Centre, Southampton SO14 3ZH, UK Received: 5 March 2007 – Published in Ocean Sci. Discuss.: 21 March 2007 Revised: 24 June 2008 – Accepted: 9 July 2008 – Published: 28 July 2008

Abstract. The Indonesian Throughflow is analysed in two 1 Introduction runs of the OCCAM 1/4 degree global ocean model, one us- ing monthly climatological winds and one using ECMWF This paper is concerned with the ocean currents and trans- analysed six-hourly winds for the period 1993 to 1998. The ports between the Pacific and Indian Oceans, via the Indone- long-term model throughflow agrees with observations and sian Archipelago, making use of results from a 1/4◦ version the value predicted by Godfrey’s Island Rule. The Island of the OCCAM global ocean model. Oceanographically the Rule has some skill in predicting the annual signal each year Indonesian Region is important. It connects the equatorial but is poor at predicting year to year and shorter term varia- wave guides of the Indian and Pacific Oceans, it is the major tions in the total flow, especially in El Nino˜ years. route for water exchanges between the two oceans and, re- The spectra of transports in individual passages show lated to this, it is a major link in the thermohaline circulation significant differences between those connecting the region of the global ocean. to the Pacific Ocean and those connecting with the Indian The topography of the area is complex. Between the is- Ocean. On investigation we found that changes in the north- lands there are many deep basins connected by a multitude ern transports were strongly correlated with changes in the of channels with a large range of sill depths. Field measure- position of currents in the Celebes Sea and off Halmahera. ment programmes are usually forced to concentrate on just Vertical profiles of transport are in reasonable agreement one or two of the channels so, even when such experiments with observations but the model overestimates the near sur- can be mounted, it is difficult to build up a full quantitative face transport through the Lombok Strait and the dense over- description of the flow (Godfrey, 1996; Gordon, 2005). As flow from the Pacific through the Lifamatola Strait into the a result there are still major uncertainties in our estimates of deep Banda Sea. In both cases the crude representation of the transports between the two oceans and many questions the passages by the model appears responsible. remain concerning the role of the different basins, seas and In the north the model shows, as expected, that the largest channels in these exchanges. transport is via the Makassar Strait. However this is less than Under these conditions, insights that come from ocean expected and instead there is significant flow via the Halma- model studies should be valuable. Ocean models are not hera Sea. If Godfrey’s Island Rule is correct and the through- perfect. Quantitatively they contain errors but qualitatively flow is forced by the northward flow between Australia and our experience is that the high resolution ocean models are South America, then the Halmahers Sea route should be im- usually good at representing the major features of the cir- portant. It is the most southerly route around New Guinea culation. Because they represent most of the key physical to the Indian Ocean and there is no apparent reason why processes, they can also provide useful insights into the in- the flow should go further north in order to pass through the teractions between different components of the circulation. Makassar Strait. The model result thus raises the question of For similar reasons they can also be extremely helpful when why in reality the Makassar Strait route appears to dominate planning the next round of field experiments. the throughflow. With these ideas in mind, in this paper we briefly review some of the results from a 1/4◦ version of the OCCAM model. We report on the transports through the different channels, their variations with time and their variations with Correspondence to: D. J. Webb depth. Comparisons between a run using repeating monthly ([email protected]) wind forcing and one forced by the analysed six-hourly wind

Published by Copernicus Publications on behalf of the European Geosciences Union. 184 U. W. Humphries and D. J. Webb: The Indonesian Throughflow in OCCAM

field from the 1990s, gives insight into the effect on the ocean mixing scheme for the tracer fields and vertical Laplacian of both short wind events and interannual variations in the mixing, with a coefficient of 1×10 cm2 s−1, for the velocity wind field. fields. The surface fluxes of heat and fresh water are ob- As part of the analysis we compare the model transports tained by relaxing the 20 m thick surface layer of the model with those predicted by Godfrey’s Island Rule (Godfrey, to the Levitus monthly average values (Levitus and Boyer, 1989; Wajsowicz, 1993; Godfrey, 1996). The Rule was de- 1994a; Levitus et al., 1994b). The scheme uses a relaxation veloped to give an estimate of the mean long term trans- time scale of 30 days and linear interpolation to transform port between the Pacific and Indian Oceans. Godfrey’s Rule the Levitus values to the model grid. Further details about shows good agreement with the model transports at long pe- the model configuration are given in Webb et al. (1998b). riods and at a period of one year. It is less good at predicting The model has a horizontal resolution of 1/4◦×1/4◦ (i.e. year to year variations in the transport and it also fails at short approximately 28 km by 28 km at the equator) and has 36 periods. levels in the vertical. The latter have thicknesses increasing We also compare the model results with hydrographic from 20 m, near the surface of the ocean, to 250 m at the data from the region and with the few transport measure- maximum depth of 5500 m. Note that because of the free sea ments available from individual straits. The results highlight surface boundary condition, the thickness of the top layer is model weaknesses in representing narrow straits and over- not fixed. This is allowed for in the model equations. flows, which need to be addressed, but they also raise other The model bathymetry is derived from the DBDB5 dataset questions. (US Naval Oceanographic Office, 1983), which provides ocean depths every 50 of latitude and longitude. The depths of 1.1 The OCCAM Model key sills and channels were checked manually and adjusted where necessary (Thompson, 1995)2. In the Indonesian Re- The OCCAM model was originally developed as part of the gion, discussed here, topography is particularly important be- Ocean Circulation and Climate Advanced Modelling Project cause of the sills and deep basins which block and trap dif- (OCCAM). It is a primitive equation model, using level sur- ferent water masses. This is discussed further later in the faces in the vertical and an Arakawa-B grid in the horizontal paper. (Arakawa, 1966). The underlying code is based on that of The model is initialised with potential temperature and the Bryan, Cox and Semtner models (Bryan, 1969; Semtner, salinity fields derived from the Levitus (1982) annual mean 1974; Cox, 1984; Griffies et al., 2005) but there have been a dataset. The initial velocity is set to zero everywhere, as is large number of changes. In particular the rigid lid surface the sea surface height. boundary condition of the earlier codes has been replaced by a free surface. This has also meant replacing the barotropic In this paper, we analyse data from two OCCAM model stream function equation by a barotropic tidal equation which runs. In the first, denoted by CMW, the model is forced with is solved explicitly. an annually repeating climatological monthly wind field. The primary model variables are two tracer fields, poten- This wind field was derived by Siefridt and Barnier (1993) tial temperature and salinity, the two horizontal components from the European Centre for Medium Range Weather Fore- of velocity1, the sea-surface height and the two components casting (ECMWF) analyses for the years 1986 to 1988. The of barotropic velocity. In the Arakawa B-grid, the tracer vari- second run, denoted by E6W, starts from the model state at ables and sea-surface height are placed at the centre of each the end of the eighth year of the first run. The second run model grid box and the velocities are placed at the corners, is then forced with the ECMWF analysed six-hourly wind an arrangement which is much better at representing small field for the period between the 1 January 1992 and the 31 frontal regions than other standard grids. In the version of December 1998. the OCCAM code used here, the model advects both tracers Analysis of the model results was carried out using archive and momentum horizontally using the Split-Quick scheme data from six years of each of the two model runs. The anal- (Webb et al., 1998a). In the vertical a revised version of the ysis period starts on the 1st January in the ninth year of the momentum advection term is also used (Webb, 1995). Split- climatological wind run (CMW) and on the 1st January 1993 Quick is not used in the vertical because of the increased for the ECMWF analysed wind field run (E6W). During the diffusion it produces in the presence of strong internal waves analysis period, archive data was available at intervals of two – such as those generated when using realistic surface wind days for the CMW run and five days for the E6W run. forcing. Sub-grid scale horizontal mixing is represented using a 2In the Arakawa B-grid, the grids for velocity variables is offset 2 −1 Laplacian operator, with coefficients of 1×10 m s for dif- from those for tracer variables. Unfortunately although the tracer − fusion and 2×10 m2 s 1 for kinematic viscosity. In the ver- (T-point) depths were adjusted correctly, the velocity offset was not tical, the model uses the Pacanowski and Philander (1981) allowed for. Thus advection across some sills is only possible at much shallower depths. Table 1, shows the advective sill depths 1Vertical velocity is derived from the horizontal velocities. and also the T-grid depth where diffusion can occur.

Ocean Sci., 4, 183–198, 2008 www.ocean-sci.net/4/183/2008/ U. W. Humphries and D. J. Webb: The Indonesian Throughflow in OCCAM 185

15 0

500 South China Sea PACIFIC 1000 10 OCEAN D e p t h ( m )

1500 Halmahera Sea South China Sea 2000 L a t i u d e 5 Malacca Strait Sulawesi Sea 2500 Molucca Sea

3000 0 Molucca (a) Makassar Strait Makassar Strait Halmahera 3500 Strait Sea 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 Distance (km) 5 Banda Sea 0 Sunda Strait 500 Malacca Strait Sunda 10 Lombok Ombai Torres 1000 Strait Strait Strait Strait Lombok Timor D e p t h ( m ) Strait Passage 1500 15 Timor Passage INDIAN 2000 OCEAN AUSTRALIA 2500 Ombai Strait

20 3000 90 95 100 105 110 115 120 125 130 135 140 (b) Longitude 3500 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 Distance (km)

Fig. 1. The Indonesian Throughflow region. The passages of the northern section used in the paper are marked in red; those of the Fig. 2. Depth profiles through (a) the northern and (b) the southern southern section are in green. sections. The sill depth of each passage in the model is shown in green. Blue indicates the sill for diffusion where this is different.

2 The total volume transports tion, over the full six year analysis period. The transport time As stated above, water from the Pacific flows through the series are plotted in Figs. 3 to 5, 7 and 8 and the six year and Indonesian Archipelago into the eastern Indian Ocean via a annual averages tabulated in Tables 1 and 2. complex series of passages (Fig. 1). In the north there are connections with the North Pacific via the shallow southern 2.1 Transports with climatological forcing portion of the South China Sea, the Makassar Strait, the deep Molucca Sea (1600 m) and the Halmahera Sea. In the east When forced by the monthly climatological winds, the mean there is an additional connection with the South Pacific via transport through the northern section during the analy- the shallow Torres Strait. sis period is 11.7 Sv. (Unless otherwise stated all trans- In the south and west, there are connections with the In- ports quoted are from the Pacific towards the Indian Ocean, dian Ocean via the Malacca and Sunda Straits, both of which 1 Sv=106 m3 s−1). The mean transport through the southern are shallow, the Lombok Strait, and the deeper Ombai Strait section is 11.8 Sv, the slight difference being due to evapora- and the Timor Passage. To investigate the flow we have there- tion and precipitation in the region between the two sections. fore defined two sections, shown in Fig. 1, which stretch River flow was not included in OCCAM but if included it from Asia to Australia, and together include all of the above would also contribute to the difference. passages. The profiles and model sill depths of each passage The transport time series (Fig. 3a) shows that the through- are shown in Fig. 2. flow is highly variable, with both high frequency and year Transports are calculated from the model velocity field us- to year variations. Maximum transports occur around June ing the equation, and July and minimum transports around December and Jan- Z h Z B uary, the total range varying from 5 Sv to 6 Sv depending on M = dz ds ∧ v, (1) the year. The time series also shows that transport dropped z1 A slightly during the analysis period, probably due to changing where M is the volume transport, z is the vertical coordinate model stratification in the Indian and Pacific Oceans. and s the horizontal coordinate running between the two ends Table 1 shows that, in the north, the Makassar Strait is the of the section A and B. The vector v is the velocity, h is the primary route for the model throughflow, the average trans- sea surface elevation and z1 is the ocean bottom (which is port being 5.7 Sv. There is also a significant annual variation negative). In order to ensure that the result is fully consis- (see Fig. 4) with a maximum of 8 Sv to 9 Sv occurring in tent with the model conservation equations, the sections are July and August. Because it is the westernmost deep pas- chosen to follow the edges of the model tracer boxes. sage, the transport through the Makassar Strait is expected to Using the above equation, we calculated the ocean model be the largest. However the model results indicate that there transports through each passage, and the total for each sec- are also significant transports via the Molucca Sea (2.1 Sv), www.ocean-sci.net/4/183/2008/ Ocean Sci., 4, 183–198, 2008 186 U. W. Humphries and D. J. Webb: The Indonesian Throughflow in OCCAM

Table 1. The transports through the northern and the southern sections. Positive transports correspond to flow from the Pacific Ocean to the Indian Ocean. (1 Sv=106 m3 s−1). The sill depth is that for advective transport. Where indicated, the Arakawa B-grid allows diffusion between T-grid points at a deeper level.

Mean Transport (Sv) Section Width Depth Sill T-grid Monthly ECMWF (km) (m) Depth Depth Winds Winds (m) (m) Years 9-14 93-98 S. China Sea 1,000 240 40 1.7 1.2 Makassar Strait 160 2,800 269 (555) 5.7 5.9 Molucca Sea 250 2,200 1,600 2.1 1.8 Halmahera Sea 230 1,150 269 (555) 1.6 3.4 Torres Strait 140 20 20 0.6 0.6 Total 11.6 12.9 Malacca Strait 350 100 20 0.2 0.1 Sunda Strait 100 350 20 0.3 0.2 Lombok Strait 80 430 389 5.7 5.6 Ombai Strait 80 3,400 779 (1068) 4.5 4.9 Timor Passage 520 1,800 659 (1419) 1.1 2.2 Total 11.7 13.0

Table 2. Average transports for each strait and for each year when the model is forced by analysed ECMWF winds. Positive transports correspond to flow from the Pacific Ocean to the Indian Ocean. Transports in Sverdrups (1 Sv=106 m3 s−1).

YEAR 1993 1994 1995 1996 1997 1998 1993–1998 S. China Sea 1.5 1.5 1.2 0.8 1.2 0.9 1.2 Makassar Strait 5.4 6.0 6.3 7.2 5.0 5.5 5.9 Molucca Sea 2.1 0.8 1.9 1.4 0.2 4.4 1.8 Halmahera Sea 1.9 5.9 5.0 4.9 3.2 -0.4 3.4 Torres Strait 0.75 0.67 0.43 0.43 0.66 0.56 0.58 Total 11.7 14.9 14.9 14.7 10.2 10.9 12.9 Malacca Strait 0.16 0.19 0.12 0.09 0.18 0.06 0.13 Sunda Strait 0.24 0.29 0.18 0.15 0.28 0.11 0.21 Lombok Strait 5.4 6.7 6.1 7.2 4.8 3.4 5.6 Ombai Strait 4.8 5.2 5.9 4.9 3.3 5.1 4.9 Timor Passage 1.2 2.6 2.7 2.5 1.8 2.2 2.2 Total 11.8 15.0 15.0 14.8 10.3 10.9 13.0 the Halmahera Sea (1.6 Sv), and the shallow South China Sea The South China Sea route is very shallow, many regions (1.7 Sv). having depths of less than 40 m, so the effect of bottom fric- The transport time series (Fig. 4) also show a wide range tion can be significant. In summer sea levels remain rela- of behaviour. In the South China Sea, the transport follows a tively constant throughout the region and currents are weak. regular pattern, repeating each year with a maximum flow of As an example the sea level difference between the Gulf of 4 Sv to the south in January and a small, ∼0.2 Sv, northward Thailand (10 N, 101 E) and the Java Sea (6 S, 110 E) is only flow in June. When Fourier transformed, the data shows an 3 cm (July of year 9). In winter much higher sea levels are r.m.s. amplitude3 of 1.6 Sv near 1 cy/year. There are ad- found in the Gulf of Thailand and adjacent regions, the sea ditional contributions at 2 and 4 cy/year resulting from the level difference increasing to 40 cm (January of year 9) under underlying saw-tooth signal. the influence of the north-east monsoon.

3Quoted r.m.s. values are the square root of the total variance in At this time sea level drops 20 cm along the Malasian neighbouring frequency bands Coast, where there is a narrow boundary current, and it

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25 Transport (a) 20 15 10.0 10

T r a n s p o t ( S v ) 5.0 5

0 0.0 -5

T r a n s p o t ( S v ) South China Sea 8 9 10 11 12 13 10.0 Years 5.0

25 (b) 0.0 20 Makassar Strait 15 10.0 10 5.0 T r a n s p o t ( S v ) 5 0 0.0

-5 Molucca Strait 1993 1994 1995 1996 1997 1998 10.0 Years 5.0

0.0

Fig. 3. Total transport from the model when using (a) monthly Halmahera Sea climatological winds and (b) ECMWF analysed six-hourly winds. 10.0 Positive values correspond to a net flow from the Pacific to the In- 5.0 dian Ocean. The figure shows the transports through the northern section. The transports through the southern section are similar. 0.0 Torres Strait -5.0 9 10 11 12 13 14 Years drops a further 20 cm at the Karimata Strait (Selat Karimata: 2 S, 109 E) where there is another region of strong currents through the deepest channel. In both cases the along-stream Fig. 4. Transport time series for passages in the northern section pressure gradient in the model is balanced primarily by the when the model is forced with monthly climatological winds. bottom friction term. From these results we conclude that the strong repeating annual signal seen in the model is a result of the balance between sea level changes produced by the mon- later, the annual average flow in the Makassar Strait is south- soons and bottomF friction opposing the resulting currents. A wards at all depths). similar behaviour is also seen in the transport through Torres Amongst the Southern sections (Fig. 5), the largest mean Strait, the small annual signal reflecting the fact that the straitData file: ../Orirun/CMW_home.dat Program: data/otransportsccam/usa/prog/fig3 ina.F the model occur through the Lombok Strait is both narrow and shallow. (5.7 Sv) and the deeper Ombai Strait (4.5 Sv). The fluctu- A more complicated pattern is seen in the three deep sec- ations in the transport through the Lombok Strait are domi- tions. Here the regular annual signal is still present but nated by a two cycle per year signal (amplitude 1.2 Sv). In it is largely masked by an irregular fluctuations with peri- the Ombai and Timor passages there are strong annual and ods near 6 cy/year. If the six-year Makassar Strait time se- semi-annual signals, Timor having spectral peaks of 1.1 Sv at ries is Fourier transformed, the spectra shows a peak with 1 cy/year and 0.9 Sv at 2 cy/year and Ombai peaks of 0.8 Sv r.m.s. amplitude of 0.9 Sv at 1 cy/year, a similar peak with at 1 cy/year and 0.6 Sv at 2 cy/year. All three passages also r.m.s. amplitude also of 0.9 Sv at 2 cy/year, and then a large show irregular fluctuations at shorter periods but the ampli- group of lines with variances of order 0.5 Sv between 5 and tude is much smaller than for the northern sections. Thus for 7 cy/year. The spectra for the Halmahera and Molucca pas- Lombok Strait the fluctuations near 6 cy/year have an r.m.s sages, show annual (and for Halmahera a semi-annual peak) amplitude of 0.5 Sv and Ombai and Timor Straits both have of comparable amplitudes but the peaks around 6 cy/year are values near 0.3 Sv. much larger, 1.1 Sv for Halmahera and 1.3 Sv for Molucca. As discussed by Qu et al. (2005) and Tozuka et al. (2007), 2.2 The source of variability part of the reduced winter transport in the Makassar Strait is due to the increased Karimata Strait transport. In the clima- The fact that the fluctuations with periods near 6 cpy are tological run this reached 4 Sv in winter, of which just over irregular implies that they are not due to the local repeat- 1 Sv turned northwards into the Makassar Strait, for a time ing winds. We investigated the source of the variability by reversing the mean flow there in the top 60 m (as discussed fourier transforming the model SSH and barotropic velocity www.ocean-sci.net/4/183/2008/ Ocean Sci., 4, 183–198, 2008 188 U. W. Humphries and D. J. Webb: The Indonesian Throughflow in OCCAM

Transport

10.0

5.0

0.0

T r a n s p o t ( S v ) Malacca Strait 10.0

5.0

0.0

Sunda Strait 10.0

5.0

0.0

Lombok Strait 10.0

5.0

0.0 0 1000 2000 Ombai Strait 10.0

5.0 Fig. 6. Variance of barotropic transport near six cycles per year. 4 −2 3 −1 2 0.0 (Units are m s , i.e. (m s per meter) ) Timor Passage -5.0 9 10 11 12 13 14 Years tion just north of the Makassar Strait. (The Makassar Eddy also tended to be further south than normal at such times.) Fig. 5. Transport time series for passages in the southern section From these results we conclude that the 6 cy/year fluctuations when the model is forced with monthly climatological winds. in transport arises, because first, there is some relatively peri- odic behaviour of the eddies during this run of the model, and because secondly, the Mindinao and Celebes Sea eddies can fields and comparing the properties near 6 cpy with those at have a significant effect on the transport though the different other periods. straits. Figure 6 shows the variance of the barotropic transport

Data file: ../Orirnearun/MW_ 6ho cpy.me.dat The largest values are found south-east of Min- 2.3 Transports with high-frequency forcing Program: data/odanaoccam/usa/p inrog/f theig3b.F region normally associated with the Mindanao Eddy (or more accurately the Mindinao Retroflection). This In the second run, when the model is forced by the more real- is also a region of large SSH variance and where the fourier istic ECMWF analysed winds, there are significant changes components indicate that the features are propagating. Sim- in both the mean transports and their variability. The to- ilar behaviour is also found in the Celebes Sea where the tal mean throughflow, averaged over the six years, increases model shows eddies spawned by the retroflection region. from 11.7 and 11.8 Sv to 12.9 Sv and 13.0 Sv through the Correlations of the northern strait transport time series northern and southern sections respectively. The time series with the sea surface height and velocity fields show connec- (Fig. 3b and Table 2), shows that the largest values of the tions between the strait transports and the Mindinao Eddy throughflow occurred between 1994 and 1996, the annual av- region, but the correlation values (up to 0.55) are only just erage reaching 14.9 Sv through the northern section in both above the large background value (typically 0.3). This may 1994 and 1995. This is followed by a sharp drop to 10.2 Sv be because such a correlation includes all frequencies. The in 1997 and 10.9 Sv 1998. Both years were partly affected by high background value may also be a result of the regular an El Nino.˜ The SOI index was large and negative between forcing of the ocean during this run of the model. April 1997 and April 1998, but the model indicates that the However a study of periods when the transport time series throughflow was reduced over a much longer period of time. was changing rapidly, showed that the Molucca Sea trans- In the north, the Makassar Strait is the primary route for port fell when the Mindinao Eddy moved furthest south, such the throughflow with a mean transport over the six year pe- that the retroflecting current swept past the northern entrance riod of 5.9 Sv. The maximum flows, up to 10 Sv, occur in to the Molucca Sea. The Makassar transport also dropped July and August and the minimum, as low as 2 Sv, in Jan- when the eddy in the Celebes Sea moved to a similar posi- uary and February.

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15.0 15.0

10.0 South China Sea 10.0

5.0 5.0

0.0 0.0 T r a n s p o t ( S v ) T r a n s p o t ( S v ) Malacca Strait 15.0 15.0

10.0 Makassar Strait 10.0

5.0 5.0

0.0 0.0 Sunda Strait 15.0 15.0

10.0 Molucca Strait 10.0

5.0 5.0

0.0 0.0 Lombok Strait 15.0 15.0 Halmahera Sea 10.0 10.0

5.0 5.0

0.0 0.0 Ombai Strait 15.0 15.0 Torres Strait 10.0 10.0

5.0 5.0

0.0 0.0 Timor Passage -5.0 -5.0 1993 1994 1995 1996 1997 1998 1993 1994 1995 1996 1997 1998 Years Years

Fig. 7. Transport time series for passages in the northern section Fig. 8. Transport time series for passages in the southern section when the model is forced with ECMWF analysed six-hourly winds. when the model is forced with ECMWF analysed six-hourly winds.

Amongst the southern sections, the largest mean transports The next most important route in the model is via the occur through the Lombok Strait (5.6 Sv) and the Ombai Halmahera Sea, where the mean transport is 3.4 Sv. This is Strait (4.9 Sv). Next most important is the Timor Passage, 1.8 Sv more than that found with monthly averaged winds. its average transport, (2.2 Sv), being almost twice that found Maximum southward flows, around 6 Sv, occur in October with the monthly wind forcing run. All three passages also and November during the Northwest Monsoon. Minimum show significant short term variability, but the amplitude is flows can in practice be northward flows, the northward less than that seen in the deep northern passages. transport during January and February 1997 averaging 2 Sv. There are also significant transports via the shallow South China Sea (average of 1.2 Sv) and the Molucca Sea (1.8 Sv). 3 Vertical structure Year to year variability is significant (Table. 2), the Halma- hera Sea transport ranging from 5.9 Sv in 1994 to −0.44 Sv The vertical distribution of transport was calculated from the (i.e. northwards) in 1998. OCCAM model velocity field using the equation, There is also a large increase in variability at shorter pe- Z B1 riods although the annual signal (Fig. 3) still appears cou- T1 = ds ∧ u1(δz1 + h0)/δz1, (2) pled to the monsoon. Between 1993 and 1996 maximum A1 maximum monthly values, up to 21 Sv, occur in June, July and August and minimum values around 10 Sv in Decem- for the shallowest model level, and, ber and January. The El Nino˜ years of 1997 and 1998 have Z Bi lower transports, the monthly average throughflow being be- Ti = ds ∧ ui, (3) low 5 Sv in January 1998. Ai

Amongst the northern sections, the largest amount of short for the deeper levels, where Ti is the transport per unit depth term variability is found in the Molucca Sea. The Makassar at level i, ui the mean velocity, δzi the level thickness, h0 the and Halmahera passages also show significant variability but sea surface elevation and s is the horizontal coordinate along in the two shallow sections, the South China Sea and Torres the section. The resulting vertical distribution of the mean Strait, short term variability is small. (six-year average) transports are show in Figs. 9 to 12. www.ocean-sci.net/4/183/2008/ Ocean Sci., 4, 183–198, 2008 190 U. W. Humphries and D. J. Webb: The Indonesian Throughflow in OCCAM

Mass Transport through the Northern Sections Mass Transport Through the Southern Sections with Climatological Monthly Wind Forcing with Climatological Monthly Wind Forcing 0 0 100 100 200 200 300 300 400 400 500 500 D e p t h ( m ) D e p t h ( m )

1000 1000

1500 1500

2000 2000

Malacca 2500 2500 Sunda S. China Sea Lombok Makassa Ombai Molucca Timor Halmahera Total 3000 Total 3000

-0.01 0.0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 -0.01 0.0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Transport (Sv/m) Transport (Sv/m)

Fig. 9. Vertical profile of mean transports through the northern Fig. 10. Vertical profile of mean transports through the southern section when forced by monthly climatological winds (average of section when forced by monthly climatological winds (average of years 8 to 13 inclusive). years 8 to 13 inclusive).

3.1 Monthly climatological wind run However the model also shows significant flow through the Halmahera Sea. This extends down to at least 200 m, is un- The total transports per unit depth for the northern section of expected, and indicates that other factors are involved. the monthly climatology wind forced run is shown in Fig. 9 The corresponding transports for the southern sections are together with the transport through the individual passages. shown in Fig. 10. The total transport shows two important The total transport is concentrated mainly in the top 500 m changes. First the sub-surface maximum has disappeared and and it has a sub-surface maxima at approximately 100 m instead the maximum transport per unit depth occurs at the depth. Below 500 m the transport per unit depth remains surface. Secondly there is a weak deep circulation, with flow fairly uniform down to 1100 m. There is then a weak flow out of the Indian Ocean between 1200 m and 2100 m and a reversal, down to 1700 m, followed by a weak flow out of the return flow below that down to 3200 m. Pacific down to 2000 m. Above 300 m the bulk of the flow is through the Lombok The data for the individual passages shows that the most Strait. (This is a fault of the model which is discussed later). of the flow above 400 m is through the Makassar Strait. This The flow has a maximum at the surface and then drops off has a sub-surface maximum (around 120 m) and then drops rapidly with depth. Next in importance is the Ombai Strait. off rapidly, with little flow below 400 m and none below This has a slight near surface maximum, but otherwise the 600 m. Below 400 m, largest transports are found through the flow is relatively constant down to 1100 m. Below 300 m al- Molucca Sea, and this is responsible for all of the transports most all the transport goes via this route. It is also responsible below 600 m. This is to be expected as it is the only passage for all of the weak deep circulation below 1200 m. with a sill below 550 m. Above 500 m the flows through the Molucca Sea are negligible, except for a slight flow reversal 3.2 High frequency forcing in the top 100 m. Near the surface the flows through other sections in the The vertical distribution of transport with actual six-hourly north also become significant. In the case of the South China wind forcing is shown in Fig. 11 and 12. The gross fea- Sea, this may be expected because of the effect of the mon- tures are the same as for monthly forcing – except for the soon on the shallow waters of the region. The beta effect surface layer where there are significantly increased trans- may also be involved, steering any steady current from the ports through the Halmahera Strait in the north and through North Pacific into the Indian Ocean as far west as possible. the Ombai and Timor Straits in the south. The six-hourly

Ocean Sci., 4, 183–198, 2008 www.ocean-sci.net/4/183/2008/ 8 U. W. Humphries and D. J. Webb: The Indonesian Throughflow in OCCAM Mass Transport Through the Southern Sections Mass Transport through the Southern Sections with Climatological Monthly Wind Forcing with Six-hourly Wind Forcing 0 0 100 100 200 200 300 300 400 400 500 500 D e p t h ( m ) D e p t h ( m )

1000 1000

1500 1500

2000 2000

Malacca Malacca 2500 Sunda 2500 Sunda Lombok Lombok Ombai Ombai Timor Timor Total Total 3000 3000

-0.01 0.0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 -0.01 0.0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Transport (Sv/m) Transport (Sv/m)

Fig. 10. Vertical profile of mean transports through the southern Fig. 12. Vertical profile of mean transports through the southern section when forced by monthly climatological winds (average of section when forced by ECMWF six-hourly winds (average of years 8yearsU. W. 8 Humphries to 13 inclusive). and D. J. Webb: The Indonesian U. W. Throughflow Humphries in OCCAMand D.1993 J. Webb:to 1998 The inclusive). Indonesian Throughflow in 191 OCCAM Mass TraMnasspso rTt rTahnrsopuogrht tthhreo uSgohu ther Nn oSrethcetironn Ss ections Mass Transport through the Southern Sections with Climwaittohl oSgixic-ahlo Murolyn tWhliyn dW Finodr cFinogrcing with Six-hourly Wind Forcing 0 0 0 100 100 100 200 200 200 of the flow above 400 m is through the Makassar Strait. This 300 300 300 400 400 400 has a sub-surface maximum (around 120 m) and then drops 500 500 500 off rapidly, with little flow below 400 m and none below D e p t h ( m ) D e p t h ( m ) D e p t h ( m ) 600 m. Below 400 m, largest transports are found through 1000 1000 1000 the Molucca Sea, and this is responsible for all of the trans- ports below 600 m. This is to be expected as it is the only 1500 1500 1500 passage with a sill below 550 m. Above 500 m the flows through the Molucca Sea are negligible, except for a slight 2000 2000 2000 flow reversal in the top 100 m. Near the surface the flows through other sections in the Malacca Malacca 2500 2500 Sunda 2500 north also become significant. In theSunda case of the South China LombSo. kChina Sea Lombok OmbMaiakassa Sea, this may be expected becauseOm ofbai the effect of the mon- TimoMr olucca Timor TotalHalmahera soon on the shallow waters of theTotal region. The beta effect 3000 3000 Total 3000 may also be involved, steering any steady current from the North Pacific into the Indian Ocean as far west as possible. -0.01 0.-00.01 0.001.0 0.0.201 0.03.02 0.04.03 0.05.04 0.0.605 0.07.06 0.07 -0.However01 0.0 the0.01 model0.02 also0.03 shows0.04 significant0.05 0.06 flow0.07 through the Transport (STvra/mns)port (Sv/m) Halmahera Sea. This extends downTransp toort at(Sv/m least) 200m, is un- expected, and indicates that other factors are involved. Fig. 11. Vertical profile of mean transports through the northern Fig. 12. Vertical profile of mean transports through the southern Fig. 10.Fig.Vertical 11. Vertical profile of profile mean of transports mean transports through through the southern the northernFig. 12. VerticalThe corresponding profile of mean transports transports for through the southern the southern sections are section when forced by six-hourly winds (average of years 1993 to section whenshown forced in byFig. ECMWF 10. The six-hourly total winds transport (average shows of years two important sectionsection when1998 inclusive). forced when byforced monthly by six-hourly climatological winds winds (average (average of years of 1993section to1993 to when 1998 inclusive). forced by ECMWF six-hourly winds (average of years years 81998 to 13 inclusive). 1993 tochanges. 1998 inclusive). First the sub-surface maximum has disappeared and Mass Transport through the Northern Sections instead the maximum transport per unit depth occurs at the with Six-hourly Wind Forcing surface. Secondly there is a weak deep circulation, with flow 0 wind run also produces a reduction of the deep flows through where To is the total depth-integrated mass transport, τ is 100 200 togetherthe Ombai with Strait. the transport through the individual passages.ofthe the time flowout average of above the wind Indian 400 stress, m Oceanis throughs is between the the locus Makassar 1200 of the m path andStrait. of 2100 This m and a 300 400 TheIt istotal not transport obvious why isconcentrated the vertical profiles mainly differ in in the the top two 500 mhasintegration, a sub-surfacereturnρo flowis the maximum below mean water that (around down density, to and120 3200f m)N m.− andfS are then the drops 500 andruns. it The has monthly a sub-surface climatological maxima run at was approximately based on winds 100 moffvalues rapidly, ofAbove the with Coriolis 300 little parameterm flowthe bulk below at of the the 400 latitudes flow m and is of through the none two below the Lombok D e p t h ( m ) depth.for the period Below 1986–1988, 500 m the whereas transport the per analysis unit period depth for remains600east-west m.Strait. Below crossings. (This 400 is m, a fault largest of transportsthe model arewhich found is discussed through later). 1000 fairlythe actual uniform six-hourly down wind to 1100 run covers m. There the period is then 1993–1998. a weak flowtheIf Molucca theThe Island flow Sea, Rule has and is a this maximumvalid is then responsible it at should the surface for equal all ofthe and the In- then trans- drops off Thus the differences in the mean winds over these periods reversal, down to 1700 m, followed by a weak flow out of theportsdonesian belowrapidly Throughflow 600 with m. depth. plusThis any is Next to transport be in expected importance through as the itis Bering is the the Ombai only Strait. may be responsible. However the actual winds may vary Strait and the effect of evaporation, precipitation and river 1500 Pacific down to 2000 m. passageThis with has a sill a slight below near 550 surface m. Above maximum, 500 m but the otherwise flows the very rapidly, so it is possible that non-linearities acting on inflow in the North Pacific. In practice the mean northward theThe short data term for wind the driven individual fluctuations passages may also shows produce that the mostthroughtransportflow the through is Molucca relatively the Bering Sea constant are Strait negligible, is down about to except 11100 Sv and form. pre- a Below slight 300 m 2000 observed changes in the averaged current. flowcipitation, reversal evaporation in the top and 100 river m. inflow also contribute about 1 Sv.Near In the the following surface wethe assume flows that through these otherterms cancel sections out. in the 2500 northPirani also(1999 become) used significant. results from In the the climatological case of the South wind China 4 Godfrey’s Island Rule S. China Sea Makassa Sea,run to this carry may out be a expected preliminary because comparison of the ofeffect the of model the mon- Molucca Halmahera soonthroughflow on the with shallow the value waters predicted of the byregion. Godfrey’s The Island beta effect 3000 In his study of the Global OceanT Circulation,otal Godfrey (1989, Rule. The integral path was approximated by a rectangle 1996) developed a new method for estimating the average to- may also be involved, steering any steady current from the with boundaries at the equator, 115◦ E, 40◦ S and 85◦ W and tal northward transport of the South Pacific Ocean between North Pacific into the Indian Ocean as far west as possible. comparisons were made for model years nine to twelve inclu- -0.0Australia1 0.0 and0.01 South0.02 America.0.03 0.04 The0 method.05 0.06 involves0.07 an in- However the model also shows significant flow through the sive of the run. Godfrey’s Rule is based on Sverdrup trans- tegral of the time average wind stressTrans alongport (Sv/m a) path which Halmaheraport ideas, which Sea. This are really extends concerned down towith at the least long 200m, term is un- includes two east-west crossings of the South Pacific, at the expected,mean transport and indicates of the ocean that after other all factors transient are waves involved. have northern and southern extremities of the Australian and New diedThe out. corresponding However Pirani’s transports results for showed the southern that there sections was are Fig. 11.GuineaVertical continental profile of shelf. mean These transports two through east-west the sections northern are showngood agreement in Fig. 10. forboth The thetotal mean transport transport shows each two year important and section whenthen joined forced by by paths six-hourly along windsthe shelf (average edges of of South years1993 America to the annual cycle. This implies that there may be more to be 1998 inclusive).and West Australia. changes. First the sub-surface maximum has disappeared and gained from the integral, for example as an analogue of the Godfrey’s estimate of the transport, which has become instead the maximum transport per unit depth occurs at the time varying Indonesian Throughflow. known as Godfrey’s Island Rule, is given by the equation: surface. Secondly there is a weak deep circulation, with flow together with the transport through the individual passages. outFor of the the present Indian study Ocean we calculatedbetween 1200 the integral m and in 2100(4) using m and a I the more accurate path shown in Fig. 13. The path is simi- The total transport is concentrated mainly in the top 500 m return flow below that down to 3200 m. To = τ · ds/ρo(fN − fS), (4) lar to the one used by Godfrey but, to the west of Australia and it has a sub-surface maxima at approximately 100 m Above 300 m the bulk of the flow is through the Lombok depth. Below 500 m the transport per unit depth remains Strait. (This is a fault of the model which is discussed later). fairly uniformwww.ocean-sci.net/4/183/2008/ down to 1100 m. There is then a weak flow The flow has a maximum at Ocean the surface Sci., 4, 183– and198 then, 2008 drops off reversal, down to 1700 m, followed by a weak flow out of the rapidly with depth. Next in importance is the Ombai Strait. Pacific down to 2000 m. This has a slight near surface maximum, but otherwise the The data for the individual passages shows that the most flow is relatively constant down to 1100 m. Below 300 m U. W. Humphries and D. J. Webb: The Indonesian Throughflow in OCCAM 9

4 Godfrey’s Island Rule 0 In his study of the Global Ocean Circulation, Godfrey (1989, -20

L a t i u d e ( N ) 1996) developed a new method for estimating the average to- tal northward transport of the South Pacific Ocean between -40 Australia and South America. The method involves an in- tegral of the time average wind stress along a path which -60 includes two east-west crossings of the South Pacific, at the 100 150 200 250 300 Longitude (E) northern and southern extremities of the Australian and New Guinea continental shelf. These two east-west sections are then joined by paths along the shelf edges of South America Fig. 13. Path, in red, used for the Godfrey Integral of the wind and West Australia. 192U. W. Humphries and D. J. Webb: The Indonesian U. Throughflow W. Humphries instress. OCCAM and D. J. Webb: The Indonesian Throughflow in OCCAM 9 Godfrey’s estimate of the transport, which has become known as Godfrey’s Island Rule, is given by the equation:

4 Godfrey’s30 Island Rule I 0 To = τ · ds/ρo(fN − fS), (4) In his study of the Global Ocean Circulation, Godfrey (1989, -20 L a t i u d e ( N ) 1996)20 developed a new method for estimating the average to- where To is the total depth-integrated mass transport, τ is

talT r a n s p o t ( S v ) northward transport of the South Pacific Ocean between the time average wind stress, s is the locus of the path of -40 Australia and South America. The method involves an in- integration, ρo is the mean water density, and fN − fS are tegral10 of the time average wind stress along a path which -60 the values of the Coriolis parameter at the latitudes of the includes two east-west crossings of the South Pacific, at the 100 150 200 250 300 two east-west crossings. Longitude (E) northern and southern extremities of the Australian and New If the Island Rule is valid then it should equal the In- Guinea0 continental shelf. These two east-west sections are donesian Throughflow plus any transport through the Bering then joined19 by93 paths199 along4 the1995 shelf edges1996 of1 South997 America1998 Strait and the effect of evaporation, precipitation and river Fig.Fig. 13. 13. Path, in red, red, used used for for the the Godfrey Godfrey Integral Integral of the wind wind Years and West Australia. inflow in the North Pacific. In practice the mean northward stress.stress. Godfrey’s estimate of the transport, which has become transport through the Bering Strait is about 1 Sv and precip- Fig.known 14. asThirty-fiveThirty-five Godfrey’s day day Island average average Rule, of of (blue)is (blue) given model model by the throughflow throughflow equation: and itation, evaporation and river inflow also contribute about 1 and South30 America, it follows the continental shelf edge at (green)(green)I throughflow throughflow calculated calculated from from Godfrey’s Godfrey’s Island Island Rule. Rule. The The Sv. In the following we assume that these terms cancel out. PacificTo = wasτ affected· ds/ρo by(f anN − Elf NinoNiSno)˜, in 1997 and 1998. (4) a depth of 100 m. No correction has been made for New Pirani (1999) used results from the climatological wind Zealand as Godfrey found that its effect was negligible. run to carry out a preliminary comparison of the model 20 where To is the total depth-integrated mass transport, τ is throughflow with the value predicted by Godfrey’s Island Comparisons were made for years nine to fourteen for run T r a n s p o t ( S v ) gatethe time thorough average the wind system stress, thans theis normal the locus annual of the variations path of Rule. The integral path was approximated by a rectangle CMW and years 1993 to 1998 for run E6W. For each year we almost all the transport goes via this route. It is also respon- seenintegration, earlier. ρo is the mean water density, and fN − fS are with boundaries at the equator, 115◦E, 40◦S and 85◦W and calculated the mean transports and the amplitude of the an- sible for all of the weak deep circulation below 1200 m. 10 theWhen values calculating of the Coriolis the response parameter values, at the we latitudes hopedto of find the comparisons were made for model years nine to twelve inclu- nual, semi annual and higher frequency signals. The results evidencetwo east-west that crossings. propagation delays were responsible for the sive of the run. Godfrey’s Rule is based on Sverdrup trans- are given in Tables 3 and 4, together with the response, that 3.2 High frequency forcing differencesIf the Island between Rule the is two valid time then series. it should However equal we the could In- port ideas, which are really concerned with the long term is the ratio of the actual transport to the value predicted by 0 finddonesian no evidence Throughflow for this, plus either any transport in the analysis through theof individ- Bering mean transport of the ocean after all transient waves have the Island Rule1993 and1 the994 phase1995 delay1 between996 19 the97 maximum1998 TheualStrait years vertical and (Table the distribution effect4) or of in evaporation, of a combinedtransport precipitation with analysis actual of six-hourly the and whole river died out. However Pirani’s results showed that there was in the wind forcing and the maximum in the transport.Years windsix-years.inflow forcing in the North is shown Pacific. in Fig. In practice 11 and the 12. mean The northward gross fea- good agreement for both the mean transport each year and The results from the climatological forcing run agree with turestransport are the through same the as for Bering monthly Strait forcing is about - except 1 Sv and for theprecip- sur- the annual cycle. This implies that there may be more to be those of Pirani. The mean value of the throughflow each year Fig. 14. Thirty-five day average of (blue) model throughflow and faceitation, layer evaporation where there and are river significantly inflow also increased contribute transports about 1 gained from the integral, for example as an analogue of the is given to a good approximation by the Godfrey Island rule. (green) throughflow calculated from Godfrey’s Island Rule. The through5Sv. ComparisonIn the the following Halmahera with we observations assume Strait in that the these north terms and cancel through out. the time varying Indonesian Throughflow. ThePacific annual was affected signal, by which an El Ninocan be in 1997 seen and in Fig.1998.3, is also in OmbaiPirani and (1999) Timor used Straits results in the from south. the Theclimatological six-hourly wind wind For the present study we calculated the integral in (4) using good agreement for both the amplitude and phase. At higher runTherun also analysisto carry produces so out far a has reduction preliminary concentrated ofthe comparison ondeep the flows behaviour of through the model of the the more accurate path shown in Fig. 13. The path is simi- frequencies the agreement is poor, the actual variation being Ombaimodelthroughflow ocean Strait. withunder the the value two forcing predicted regimes. by Godfrey’s In this final Island sec- lar to the one used by Godfrey but, to the west of Australia much smaller than the value predicted by the Godfrey for- almost all the transport goes via this route. It is also respon- tionRule.It is on not The the obvious analysis, integral why path the the focus was vertical approximated is on profiles how well differ by the a in modelrectangle the two re- and South America, it follows the continental shelf edge at mula. ◦ ◦ ◦ sible for all of the weak deep circulation below 1200 m. runs.produceswith boundariesTheknow monthly aspects at climatological the equator, of the real 115 run ocean.E, was 40 The basedS and best on 85 set windsW of dataand for a depth of 100 m. No correction has been made for New comparisons were made for model years nine to twelve inclu- With the six-hourly winds there is much more variability theavailable period for 1986-88, the region whereas is hydrographic the analysis data period and this for the is con- ac- Zealand as Godfrey found that its effect was negligible. sive of the run. Godfrey’s Rule is based on Sverdrup trans- in3.2 both High the frequency observed transportsforcing and the Godfrey predicted tualsidered six-hourly first. There wind is run also covers an important the period set 1993-1998. of current meter Thus Comparisons were made for years nine to fourteen for run port ideas, which are really concerned with the long term value. Averaged over the six years, the model throughflow themeasurements differences which in the have mean been winds used over to estimatethese periods transports may CMW and years 1993 to 1998 for run E6W. For each year we mean transport of the ocean after all transient waves have agrees well with the Godfrey prediction. However in indi- bethrough responsible. some of theHowever straits. the actual winds may vary very calculated the mean transports and the amplitude of the an- The vertical distribution of transport with actual six-hourly died out. However Pirani’s results showed that there was vidual years (Table 4), both the mean transports and the ratio rapidly,The comparisons so it is possible show that up a non-linearities number of apparent acting failings on the nual, semi annual and higher frequency signals. The results wind forcing is shown in Fig. 11 and 12. The gross fea- good agreement for both the mean transport each year and vary significantly, indicating that the Island Rule by itself is shortof the term model. wind Most driven seem fluctuations to be the may result also ofproduce errors the in ob- the are given in Tables 3 and 4, together with the response, that nottures suitable are the as same an analogue as for monthly of the forcingannual mean - except transports. for the sur- the annual cycle. This implies that there may be more to be face layer where there are significantly increased transports servedmodel changesphysicsbut in the there averaged are some current. where the model may be is the ratio of the actual transport to the value predicted by Figure 3 indicates that the annual signal is larger in the six- gained from the integral, for example as an analogue of the through the Halmahera Strait in the north and through the partially correct. In any case the results are a stimulus – both hourly run than in the climatological run, but its peak occurs time varying Indonesian Throughflow. Ombai and Timor Straits in the south. The six-hourly wind to improve the model and to improve our limited physical at about the same time during the year. This is confirmed For the present study we calculated the integral in (4) using run also produces a reduction of the deep flows through the understanding of the flows. by Fourier analysis (see Table 4) which also shows that the the more accurate path shown in Fig. 13. The path is simi- Ombai Strait. lar to the one used by Godfrey but, to the west of Australia Godfrey Island Rule has some skill in predicting the ampli- 5.1 The water masses tudeIt and is not phase obvious of the why transport the vertical especially profiles between differ in 1993 the andtwo and South America, it follows the continental shelf edge at runs. The monthly climatological run was based on winds for a depth of 100 m. No correction has been made for New 1996. The Indonesian Throughflow transports an important group the period 1986-88, whereas the analysis period for the ac- Zealand as Godfrey found that its effect was negligible. Smoothed versions of the two timeseries (Fig. 14) also of water masses from the North Pacific into the Indian Ocean. tual six-hourly wind run covers the period 1993-1998. Thus Comparisons were made for years nine to fourteen for run show better agreement between between 1993 and 1996 than Within the region, the deep basins also give rise to a series of the differences in the mean winds over these periods may CMW and years 1993 to 1998 for run E6W. For each year we for the two El Nino˜ years, 1997 and 1998. The Island Rule remarkably uniform water masses. In order to illustrate how be responsible. However the actual winds may vary very calculated the mean transports and the amplitude of the an- is based on the steady state solution after all gravity and well the model represents such features, Fig. 15 shows the rapidly, so it is possible that non-linearities acting on the nual, semi annual and higher frequency signals. The results Rossby waves have propagated around the system and died average summer temperatures during years nine to fourteen short term wind driven fluctuations may also produce the ob- are given in Tables 3 and 4, together with the response, that away. The present results thus indicate that the energetic of the monthly climatological wind forced run along a sec- served changes in the averaged current. is the ratio of the actual transport to the value predicted by waves generated by the El Nino˜ may take longer to propa- tion through the eastern side of the Indonesian Archipelago.

Ocean Sci., 4, 183–198, 2008 www.ocean-sci.net/4/183/2008/ U. W. Humphries and D. J. Webb: The Indonesian Throughflow in OCCAM 193

Table 3. The mean value of the Indonesian Throughflow in the model, when forced by monthly climatological winds, and its amplitude at one, two and three cycles per year compared with the value predicted by Godfrey’s Island Rule, during years nine to thirteen of the model run. Also shown is the ratio of the two values and the number of degrees that the model transport delays the wind contribution to the Godfrey integral. Small differences in the Godfrey term arise because the model data is archived on different days each year

Year Transport (Sv) Response Transport (Sv) Response Model Godfrey Amp. Phase Model Godfrey Amp. Phase Mean 1 cy/yr 9 12.43 11.64 1.07 – 2.26 1.98 1.14 0 10 12.08 11.64 1.04 – 1.62 1.98 0.82 0 11 11.62 11.64 1.00 – 1.80 1.99 0.90 −10 12 11.43 11.64 0.98 – 1.85 1.98 0.93 −14 13 11.13 11.64 0.96 – 1.97 1.98 1.00 15 14 11.15 11.64 0.96 – 2.07 1.99 1.04 14 2 cy/yr 3 cy/yr 9 0.79 2.02 0.39 −167 0.79 1.75 0.45 −116 10 0.43 2.02 0.21 126 0.43 1.75 0.25 −157 11 0.45 2.05 0.22 124 0.28 1.69 0.17 −122 12 0.77 2.01 0.38 137 0.48 1.75 0.27 −83 13 0.58 2.01 0.29 −140 0.23 1.75 0.13 −47 14 0.44 2.05 0.21 −111 0.55 1.69 0.32 −112

Table 4. The mean value of the Indonesian Throughflow in the model, when forced by ECMWF analysed six-hourly winds, and its amplitude at one, two and three cycles per year compared with the value predicted by Godfrey’s Island Rule, during model years 1993 to 1998. Also shown is the response, the ratio of the two values and the number of degrees that the model transport delays the wind contribution to the Godfrey integral.

Year Transport (Sv) Response Transport (Sv) Response Model Godfrey Amp. Phase Model Godfrey Amp. Phase Mean 1 cy/yr 93 11.652 10.618 1.097 – 2.85 4.01 0.71 −20 94 14.883 12.332 1.207 – 1.98 2.51 0.79 −24 95 14.867 14.107 1.054 – 4.51 3.90 1.16 3 96 14.686 14.313 1.026 – 2.58 2.98 0.86 8 97 10.187 9.019 1.129 – 4.06 1.10 3.70 −128 98 10.857 14.946 0.726 – 3.54 5.95 0.60 −58 93–98 12.858 12.561 1.024 – 2 cy/yr 4 cy/yr 93 1.14 2.27 0.50 −18 0.29 0.58 0.50 15 94 1.19 2.34 0.51 −43 1.48 1.38 1.07 −22 95 0.26 1.18 0.22 64 1.48 1.30 1.14 73 96 1.05 2.53 0.41 135 0.53 1.61 0.33 128 97 0.96 2.83 0.34 2 1.11 1.72 0.64 96 98 1.63 0.53 3.05 53 1.14 1.91 0.59 74

The section is similar to that used by Wyrtki (1961) in re- Comparison of the different figures shows that above porting observations from the region (see his Fig. 6.25, also 1200 m, at the levels with the largest transports, there is rea- based on summer data), and by van Aken et al. (1988) in sonable agreement between the model and observations. Be- their report on later measurements. The Levitus and Boyer low 1200 m the flow is blocked by sills. The resulting water (1994a) summer temperatures, plotted for the same section in properties therefore reflect the actual water mass overflow- Fig. 16, lie close to the values given in the two observational ing each sill and the mixing processes occurring within the papers. sill regions and the deep basins. www.ocean-sci.net/4/183/2008/ Ocean Sci., 4, 183–198, 2008 U. W. Humphries and D. J. Webb: The Indonesian Throughflow in OCCAM 11

the Island Rule and the phase delay between the maximum 0 25 25 25 20 20 15 15 15 in the wind forcing and the maximum in the transport. 10 10 10 500 INDIAN SAWU BANDA MOLUCCA PACIFIC The results from the climatological forcing run agree with OCEAN SEA SEA SEA OCEAN 5 1000 5 5 those of Pirani. The mean value of the throughflow each year 4 4 4 4 3.5 3.3 3.5 3.5 3.4 3.5 3.5 3.2 3.2 3.3 3.3 3.2 3.2 3.3 D e p t h ( m ) 3.4 3.1 is given to a good approximation by the Godfrey Island rule. 1500 3.3 3.1 3.2 2.9 3 3 3 2.9 2.7 2.7 2.7 2.8 2.9 2.5 2.5 2.6 3 2.4 2.4 2.4 2.5 2.8 2.2 2.2 2.3 The annual signal, which can be seen in 3, is also in good 2.3 2.1 2.1 2000 2.2 2 2 2.1 1.9 2 agreement for both the amplitude and phase. At higher fre- 1.9 1.8 2.8 1.7 1.8 2.9 2.8 2500 1.7 1.6 quencies the agreement is poor, the actual variation being 1.6 1.5 1.5 3000 1.4 2.78 1.4 much smaller than the value predicted by the Godfrey for- 1.3 1.2 mula. 3500 1.1 2.77 1.3 1 With the six-hourly winds there is much more variability 0.9 4000 a b c d e f g in both the observed transports and the Godfrey predicted 0.8 value. Averaged over the six years, the model throughflow 4500 0.77 agrees well with the Godfrey prediction. However in indi- 5000 0.73 vidual years (Table 4), both the mean transports and the ratio 0 500 1000 1500 2000 2500 3000 3500 4000 4500 vary significantly, indicating that the Island Rule by itself is Distance(Km) not suitable as an analogue of the annual mean transports. Fig. 3 indicates that the annual signal is larger in the six- hourly run than in the climatological run, but its peak occurs Fig. 15. Pacific to Indian Ocean section, showing model potential at about the same time during the year. This is confirmed temperature in summer from the run with monthly wind forcing. by Fourier analysis (see Table 4) which also shows that the The deep basins are (a) Sawu, (b) Wetar, (c) South Banda, (d) North Banda, (e) Buru, (f) Bacan and (g) Morotai Basin. U. W. Humphries and D. J. Webb: The Indonesian ThroughflowGodfrey in194 OCCAM Island Rule has some skill in predicting the U. W. ampli- Humphries 11 and D. J. Webb: The Indonesian Throughflow in OCCAM tude and phase of the transport especially between 1993 and the Island Rule and the phase delay between the maximum 1996. 0 25 25 0 25 20 20 25 25 25 15 15 15 20 15 20 15 in the wind forcing and the maximum in the transport. 10 15 Smoothed10 versions of the two10 timeseries (Fig. 14) also 10 10 10 500 MOLUCCA PACIFIC INDIAN SAWU BANDA 500 INDIAN SAWU BANDA MOLUCCA PACIFIC SEA OCEAN The results from the climatological forcing run agree with show betterOCE agreementAN SE betweenA betweenSEA 1993 and 1996 than OCEAN SEA SEA SEA OCEAN 5 5 5 5 1000 1000 5 5 those of Pirani. The mean value of the throughflow each year 4 4 4 4 for the two4 El Nino years,3.5 1997 and 1998. The Island Rule 3.3 3.5 3.5 3.4 3.5 D e p t h ( m ) 4 4 3.5 3.5 3.2 3.2 3.3 3.3 3.2 3.2 3.3 3.4 3.2 3.3 D e p t h ( m ) 3.3 3.4 3 3.1 3.5 3.4 3.1 is given to a good approximation by the Godfrey Island rule. 1500 3.1 3.2 2.9 3 1500 3.4 3.2 3.3 3.5 3.5 3.5 3 2.8 2.9 is based on3 the steady state solution2 after.9 all2.7 gravity2.7 and 3.1 3.4 3.3 3.4 2.7 2. 2.8 2.9 2.5 2.5 3 2.9 3.2 3.4 7 2.6 2.7 3 2.4 2.8 3.3 2.5 2.5 2.5 2.6 2.8 2.4 2.3 2.7 3.3 2. The annual signal, which can be seen in 3, is also in good 2.4 2.12.2 2.2 2.5 2.6 3.2 3.2 2.3 4 2.3 2000 2.3 2.1 2.4 3.1 2.2 Rossby waves2.2 have propagated around the system2 and2 died 2000 2.3 2 2.1 1.9 2.2 3.1 3.1 2.1 .1 2 2 2.1 agreement for both the amplitude and phase. At higher fre- 1.9 1.8 2 2 1.9 2.8 1.7 1.9 3 3 1.8 away. The1.8 present results2.9 2.8 thus indicate that the energetic 1.7 2500 1.7 1.6 1.8 1.9 2500 1.7 2.9 1.6 quencies the agreement is poor, the actual variation being 1.6 1.5 waves generated1.5 by the El Nino may take longer to propa- 1.6 1.5 1.5 3.1 3000 1.4 2.78 1.4 much smaller than the value predicted by the Godfrey for- 3000 1.4 1.4 gate thorough1.3 the system than the normal annual variations 1.3 1.2 1.2 mula. 3500 1.1 2.77 1.3 2.8 3500 1.1 seen earlier.1 1 1.3 With the six-hourly winds there is much more variability 0.9 0.9

4000 2.8 When calculatinga the responseb c values,d wee f hopedg to find 4000 in both the observed transports and the Godfrey predicted 0.8 2.8 evidence that0.8 propagation delays were responsible for the 4500 value. Averaged over the six years, the model throughflow 4500 differences0.77 between the two time series. However we could 5000 agrees well with the Godfrey prediction. However in indi- 5000 find no evidence0.73 for this, either in the analysis of individ- vidual years (Table 4), both the mean transports and the ratio 0 500 1000 1500 2000 2500 3000 3500 4000 4500 ual years (Table 4) or in a combined analysis of the whole 0 500 1000 1500 2000 2500 3000 3500 4000 4500 vary significantly, indicating that the Island Rule by itself is Distance(Km) six-years. Distance(Km) not suitable as an analogue of the annual mean transports. Fig. 3 indicates that the annual signal is larger in the six- Fig. 15. Pacific to Indian Ocean section, showing model potential hourly run than in the climatological run, but its peak occurs Fig. 15. Pacific to Indian Ocean section, showing model potential Fig.Fig. 16. 16. PacificPacific to to Indian Indian Ocean Ocean section, showing in-situ in-situ potential potential 5temperature Comparison in summer with observations from the run with monthly wind forcing. at about the same time during the year. This is confirmed temperature in summer from the run with monthly wind forcing. temperaturetemperature in in summer summer from from the Levitus (1994a) (1994a) dataset. dataset The deep basins are (a) Sawu, (b) Wetar, (c) South Banda, (d) North by Fourier analysis (see Table 4) which also shows that the The deep basins are (a) Sawu, (b) Wetar, (c) South Banda, (d) North TheBanda, analysis(e) Buru, so far(f) hasBacan concentrated and and(g) (g)Morotai Morotai on theBasin. Basin. behaviour of the Godfrey Island Rule has some skill in predicting the ampli- model ocean under the two forcing regimes. In this final sec- files downstream showed that the overflow forms a “quasi- tude and phase of the transport especially between 1993 and tion on the analysis, the focus is on how well the model re- to improve the model and to improve our limited physical homogeneous layer” with a thickness of about 500 m, which 1996. 0 understanding of the flows. producesIn the know deep20 25 aspects Pacific and of the Indian realocean. Oceans20 The the modelbest set25 tempera- of data25 15 15 15 continues downslope to depths near 3000 m (van Aken et al., Smoothed versions of the two timeseries (Fig. 14) also 10 10 10 availableture profiles500 for the are region little changed is hydrographic from the initialdata and state this and is so con- are INDIAN SAWU BANDA MOLUCCA PACIFIC 1991). show better agreement between between 1993 and 1996 than OCEAN SEA SEA SEA OCEAN sideredin reasonable first. There agreement is also with an important observations. set of In current the deep meter5 In- 5.1 The water masses 1000 5 5 In the model, the Lifamatola Strait is represented with a for the two El Nino years, 1997 and 1998. The Island Rule 4 D e p t h ( m ) 4 measurementsdonesian Basins, which the have bottom been4 temperatures used to estimate in the modeltransports3.4 3.5 also3.3 3.5 3.4 3.1 3.2 1500 3.4 3.2 3.3 3.5 3.5 3.5 3 2.8 2.9 sill at 1823 m. During the analysis period all the southward is based on the steady state solution after all gravity and 3.1 3.4 3.3 3.4 2.7 2. through some3 2 of.9 the3. straits.2 3.4 7 2.6 compare well2.8 with observations,3.3 warming3.3 slowly2.5 in2.5 going The Indonesian Throughflow transports an important group 2.7 2.6 2.4 2.3 2.4 2.5 3.2 3.2 2.3 2.2 flow was confined to the bottom layer (extending upwards Rossby waves have propagated around the system and died 2000 2.3 3.1 2 fromThe thecomparisons Pacific2.2 to the show Indian3. up1 a Ocean. number3.1 However of apparent2.1 in thefailings vertical,.1 2 of water masses from the North Pacific into the Indian Ocean. 2.1 1.9 2 3 3 2 1.8 from 1823 m to 1615 m). The transport in the layer was away. The present results thus indicate that the energetic 1.9 1. ofthe the temperature model.1.8 Most gradient seem is to much be the weaker result than of1.9 errors it should in7 the be. Within the region, the deep basins also give rise to a◦ series of 2500 1.7 2.9 1.6 0.8 Sv and the temperature was approximately 2.5 C. The waves generated by the El Nino may take longer to propa- 1.6 1.5 modelAs a physics result,1.5 the but deep there3.1 basins are some are capped where by the a model much maystronger be remarkably uniform water masses. In order to illustrate how 3000 1.4 1.4 transport is less that that observed but the temperature is ap- gate thorough the system than the normal annual variations 1.3 partiallythermal correct.1. gradient2 In than any is case observed the results in the are real a stimulusocean. - both well the model represents such features, Fig. 15 shows the 2.8 proximately equal to the average temperature of the overflow seen earlier. 3500 1.1 This result1 was unexpected. Ocean models like OCCAM,1.3 0.9 observed by van Aken et al. (1988). It is also similar to the When calculating the response values, we hoped to find 4000 2.8 which use0.8 level surfaces, tend2.8 to produce too much verti- temperature in the offshore Pacific at this depth. evidence that propagation delays were responsible for the cal mixing in the open ocean, because of numerical effects 4500 Near the sill, at a depth of 1950 m, van Aken et al. (1988) differences between the two time series. However we could and because of internal waves which mix water up and down observed temperatures of 2.3◦C but bottom temperatures find no evidence for this, either in the analysis of individ- 5000 between model layers. These effects should mix down ad- rose to 2.4◦C only a few kilometers downstream. Further ual years (Table 4) or in a combined analysis of the whole ditional0 heat500 from1000 the1 surface500 2000 layers,2500 weakening3000 3500 the4000 thermo-4500 downstream, the minimum temperature in the Baru Basin is six-years. Distance(Km) cline and warming the deep basins. Mixing in the poorly approximately 2.6◦C and in the Banda Sea itself the mini- represented overflows would also tend to increase the model mum observed temperatures lie near 2.78◦C(Wyrtki, 1961). temperatures at depth. 5 Comparison with observations Fig. 16. Pacific to Indian Ocean section, showing in-situ potential Both the observations and the model are thus consistent temperatureWe investigated in summer the from Banda the SeaLevitus region (1994a) and dataset concluded that with the inflow of Pacific waters in a layer, possibly a few the error there arose primarily because of model errors at the ◦ The analysis so far has concentrated on the behaviour of the hundred metres thick, with average temperatures near 2.5 C. Lifamatola Strait (1◦100 S, 126◦490 E). This lies at the south- model ocean under the two forcing regimes. In this final sec- There is then some turbulent mixing in the overflow which ern end of the Molucca Sea. It is the deepest sill connecting tion on the analysis, the focus is on how well the model re- to improve the model and to improve our limited physical produces warmer temperatures at the bottom of the Baru the Banda Sea to the Pacific Ocean and is deeper than any of produces know aspects of the real ocean. The best set of data understanding of the flows. Basin and the Banda Sea. the routes connecting the Banda Sea with the Indian Ocean. available for the region is hydrographic data and this is con- This does not explain why, during the analysis period, both sidered first. There is also an important set of current meter 5.1A detailed The water survey masses of the strait (van Aken et al., 1988), the transport in the overflow and the density profile in the measurements which have been used to estimate transports showed that the overflow region is roughly V-shaped in pro- deep basins are so weak. However further study indicates file and that it has a sill depth that lies between 1950 m and that both effects arise because the model sill is far too wide. through some of the straits. The Indonesian Throughflow transports an important group 2000 m. Below 1900 m the strait is less than 2 km wide, As the model uses a grid spacing of 1/4◦, the sill has a width The comparisons show up a number of apparent failings of water masses from the North Pacific into the Indian Ocean. at 1700 m it is approximately 5 km wide and at 1500 m ap- of one velocity grid box (27.8) km and two tracer grid boxes of the model. Most seem to be the result of errors in the Within the region, the deep basins also give rise to a series of proximately 20 km wide. Current measurements in the strait (55.6 km). The increased number of tracer boxes arises from model physics but there are some where the model may be remarkably uniform water masses. In order to illustrate how showed that the transport was 1.5 Sv and temperature pro- the staggered grid used by the Arakawa-B scheme. As a partially correct. In any case the results are a stimulus - both well the model represents such features, Fig. 15 shows the

Ocean Sci., 4, 183–198, 2008 www.ocean-sci.net/4/183/2008/ U. W. Humphries and D. J. Webb: The Indonesian Throughflow in OCCAM 195 result the overflow is best thought of as having a velocity have been moorings in the Makassar Strait from December profile in the horizontal which is triangular in shape, with a 1997 to July 1998 (Gordon et al., 1999; Susanto and Gordon, maximum in the centre and a width of 55.6 km. 2005) and the Lifamatola Passage overflow, at the southern If we assume that the average width of the actual sill end of the Molucca Sea, from January to March 1985 (van is given by the value at 1700 m, then the model sill has a Aken et al., 1988, 1991). cross sectional area which is eleven times too large. During In the south there have been measurements in the Lom- the analysis period the transport in model is low but this is bok Strait from January 1985 to January 1986 (Murray and only after the presure difference between the Pacific and the Arief, 1988; Murray et al., 1990; Arief and Murray, 1996), Banda Basin has almost equalised (it is then equivalent to a in the Timor Passage from August 1989 to September 1990 dynamic height difference of 0.25 cm). During year 4 of the and from March 1992 to April 1993 (Cresswell et al., 1993; run, the earliest available for analysis, the transport was much Molcard et al., 1994, 1996), and in the Ombai Strait from higher (3.6 Sv). The dynamic height difference (1.0 cm) was November 1995 to November 1996 (Molcard et al., 2001). also higher and presumably more realistic. There have also been some indirect estimates of transports. The large width of the model sill also means that the vis- Meyers (1996) used XBT sections and Fieux et al. (1996) hy- cous terms are underestimated. The horizontal viscosity term drographic data from sections between Australia and Indone- is proportional to the width squared, so even after allowing sia. Transports depended strongly on season and varied be- for the excess length of the channel (two velocity boxes, so tween 2.6±9 Sv and 18±7 Sv. Qu (2000) used hydrographic possibly a factor of three too long), the viscosity term in the data to estimate the flow through the Luzon Strait (3 Sv), model is still likely to be a factor of 40 too small. Analy- most of which will have turned south through the shallow sis of the momentum balance in the sill regions showed that S China Sea. Wolanski et al. (1988) studied the flow through both at year 4 and during the main analysis period, the vis- Torres Strait and found a transport of order 0.01 Sv. cosity term was a factor of 10 smaller than the along channel In his review of the transport estimates, Gordon (2005) pressure gradient4. With a realistic channel width the total concluded that the mean value for the total transport lies in transport would be reduced and the viscous term could thus the range of 8 to 14 Sv, his preferred value being about 10 Sv. become significant. The OCCAM model transports reported here (11.7 Sv for run In their analysis of their results, van Aken et al. (1991) CMW and 12.9 Sv for E6W) are thus within the overall limits concluded that the vertical structure of the Banda Sea re- but on the high side of his preferred value. sulted from the balance between vertical mixing within the basin and the influx of the bottom waters by the inflow If we compare individual straits the agreement is not so through the Lifamatola Strait. A flow of 1.5 Sv gives a flush- good. In the north the most striking difference is in the ing time of about 27 years, so if this is increased to 3.6 Sv Makassar Channel, where the model gives values of 5.7 and or more, as occurred early in the model run, it would signifi- 5.9 Sv for the two runs. These are lower than Susanto and cantly affect the stratification after only a few years. Gordon’s (2005) estimate of 7 to 11 Sv. There is also a We conclude that the wide model sill resulted in a large marked difference in the Halmahera Sea where the model inflow of dense water from the Pacific which filled the deep shows transports of 1.6 and 3.4 Sv. Gordon (2005) assumed Banda Sea Basin early in the run. This produced a more the transport here was negligible but Cresswell and Luick uniform water mass in the deep basin. As the basin filled (2001) using a single mooring found a transport of 1.5 Sv with denser water it also reduced the pressure gradient across at depths between 350 m and 700 m. Unfortunately, in the the sill, reducing the inflow until the model transport was less model this channel is blocked at these depths so flow only than that observed. occurs above 300 m. However both observations and model In future models, a better representation of sills is required. indicate this may be a significant pathway. This could be done by using a finer horizontal grid. An al- Between the two straits lies the Malacca Strait with its sill ternative is to use partial box widths, in the same way that at the Lifamatola Strait. van Aken et al. (1991) estimated a partial box depths are presently used to obtain a better mean transport of 1.5 Sv in the overflow and implied that after mix- ocean topography. The channel width also affects the vis- ing and upwelling this continued as part of the throughflow. cosity terms in the momentum equation. Thus the viscosity In the model there is an overflow, as discussed in the previ- terms will also need correcting. ous section, but the upwelled water returns to the Pacific (see Fig. 15). This is because the sill to the Indian Ocean lies at 5.2 Current meter observations and transports a much shallower depth (1420 m). Above 1000 m the model shows a second region of inflow through the Malacca Strait A further check on the model comes from transports esti- which continues through to the Indian Ocean. mated from the limited current meter data. In the north there In the south, the most striking difference between the 4The horizontal pressure gradient is balanced primarily by the model and observations occurs in the Lombok Strait. Murray inertial terms in the along-channel momentum equation. This is as and Arief (1988) found a transport of of 1.7 Sv concentrated expected when a control point is involved. in the upper 200 m. The model finds much larger values, www.ocean-sci.net/4/183/2008/ Ocean Sci., 4, 183–198, 2008 196 U. W. Humphries and D. J. Webb: The Indonesian Throughflow in OCCAM

5.7 Sv and 5.6 Sv for the two runs but agrees that these are to this conclusion. If so, it is possible that the model is pro- concentrated in the top 200 m. viding too much control on the flow in the Labani Channel. Further east observations in the Timor Passage (Cresswell This may be due to finite-difference effects in the model but, et al., 1993; Molcard et al., 1994, 1996) give transports of 3 whatever the explanation, the effect must be subtle in order to 6 Sv, the model much lower values of 1.1 and 2.1 Sv. For to explain why similar constrictions produce too much flow the Ombai Strait, Molcard et al. (2001) estimate 4 to 6 Sv, the in the Lombok Strait and too little in the Makassar Strait. model 4.5 and 4.9 Sv. The model thus seems to increasing the Having failed to explain the behaviour in terms of small near surface flows in the Lombok Strait at the expense of the scale model physics, we also looked at the larger scale. If Timor Passage. Godfrey’s theory is correct and the throughflow is primarily generated by the northward flow in the South Pacific, then 5.3 The deep western channels the shortest route to the Indian Ocean is via the Halmahera Sea. In order to follow the “deep western boundary current” In studying these discrepancies we have concentrated on the route via the Makassar Strait, the flow would have to go a two deep western channels, the Makassar Strait where the few degrees further north. At mid-latitudes any blockage like model transport appears to be too low and the Lombok Strait this normally causes the current to split (Webb, 1993). So where it appears to be too high. At the surface, the Makassar if Godfrey is correct, the throughflow should generate flows Strait appears to be very much wider than the Timor Strait, through both the Halmahera Sea and the Makassar Strait - as but it is blocked by sediments at its southern end, so that seen in the model. below 30 m the width is reduced to about 25 km. The Timor Strait has a similar width over most of its length, but around 115◦450 E, 8◦460 S, near the island of 6 Discussion Paula Penida, it narrows to 13 km for a distance of under 20 km. As with the Lifamatola Sill, the width at the narrows The Indonesian region has an important role in the large scale is less than the model grid, so the extra model transport may circulation of the ocean. It therefore needs to be accurately be partially explained by the differing cross-sectional area at represented in many types of ocean model, ranging from the the narrowest point. high resolution ocean physics models, to the medium resolu- The model is also likely to be underestimating the effect of tion biological models and the low resolution ocean models viscosity in the strait. In the model, the magnitude of the hor- used in climate change research. Over the next ten years, izontal viscous forces acting on the top 200 m is equivalent most ocean models are likely to use a resolution similar to or to a pressure difference of approximately 0.4 cm between the lower than the one used here. The results of the present work ends of the strait. In comparison, the average dynamic height should thus be relevant to all such models. difference along the western boundary at this depth is 3 cm. The present analysis has shown a number of areas where Thus in the model, viscosity appears to have little effect on the model agrees roughly with expectations. Rather more in- the flow. However if it were increased by a factor of four or teresting are the areas where the model fails and areas where more, its effect should become significant. This would hap- it throws up questions whose solution seems to require better pen if the width of the strait was correctly represented in the observations and the development of better theories. model. Internal tides and other features of the flow may also We have shown that after nine years with climatological increase the viscosity in the region. winds, the total throughflow agrees with observations and, The low model transport in the Makassar Strait is not so to within a few percent, with the value predicted by God- easily understood. The narrowest section, the Labani Chan- frey’s Island Rule. Using the more realistic ECMWF winds nel (3◦00 S, 118◦400 E) is about 28 km wide5 and 70 km long, we found that the model and Godfrey’s Island Rule roughly so it is reasonably well represented by the model. The vis- agree at a period of one cycle per year. They disagree at cous terms, at year 10.0 in run CMW, correspond to a dy- shorter periods, which one might expect, but they also give namic height difference of 0.6 cm. This is much smaller than different values for the year to year variations in transport. the actual difference in dynamic height between the ends of To us it seems odd that both the long term and annual wind the Labani Channel (3 cm at a depth of 100 m). fields give agreement between the model and Godfrey’s Is- Both here and in the Lombok Strait, the difference is con- land Rule but that at intermediate frequencies the agreement sistant with a horizontal control point acting on the surface breaks down. The results invite further study. layers of the channel. Such control points have been dis- One promising approach is that of Lee et al. (2001). He cussed by Armi and Williams (1993). The strong accelera- used an adjoint model to show that at periods of a year, the tions at the entrance to the channel and the shallowing of the throughflow is affected by winds in the western equatorial density surfaces in passing through the channel give support Pacific and by winds south of Australia. Both regions lie near the path of the Godfrey Integral and so help to explain the 5Wajsowicz at al. (2003), Fig. 9, show that the channel is just correlation seen here. It would be interesting to use an adjoint under 50 km wide at their mooring position. model to investigate the relationships at other frequencies.

Ocean Sci., 4, 183–198, 2008 www.ocean-sci.net/4/183/2008/ U. W. Humphries and D. J. Webb: The Indonesian Throughflow in OCCAM 197

When we investigated the spectra, we found that the spec- of New Guinea which, on approaching Halmahera, is likely tra of the flows through the individual northern straits dif- to split. Part would turn south into the Halmahera Sea and fer significantly from the spectra through the southern straits part turn north to eventually join the Makassar Strait current. (although the spectra for the total flows are similar). Fur- It is possible that this is what happens. If so then the ob- ther investigation indicated that the difference was due to servations of Cresswell and Luick (2001) may be significant changes in the offshore current field which affected indi- but why are the Makassar transport estimates so large? If the vidual northern straits. Thus the flow through the Makassar theory is not correct then why not? In either case some key Strait was significantly reduced when an eddy in the Celebes part of the observations or the theory appears to be missing. Sea moved close to the northern end of the strait. The flow Further research is required. via the Molucca Sea was similarly affected when the Halma- hera Eddy (or Retroflection) extended close to its northern Acknowledgements. We wish to thank Beverly de Cuevas and boundary. Andrew Coward for their valuable work with the OCCAM model In the deep basins we found that although the deep tem- and for their technical support and helpful comments during the peratures were reasonable, the vertical stratification was too period of this research. weak. This was traced to errors in the sills, especially the Lifamatola Sill which was far too wide. Part of the prob- Edited by: K. Do¨os¨ lem could be solved by introducing partial box widths, as well as the partial bottom box depths that are used in current ocean models. However the V-shaped sill region is much References more complex than is usually allowed for in ocean models and raises the question of what improvements are needed be- Arakawa, A.: Computational design for long-term numerical inte- fore the models can accurately represent the effect of critical gration of the equations of fluid motion: Two-dimensional in- points, mixing and other aspects of the overflows. compressible flow, J. Comput. Phys., 1, 119–143, 1966. The model also raised the question of what happens to Arief, D. and Murray, S. P: Low-frequency fluctuations in the In- the deep water upwelled in the Banda Sea and surrounding donesian Throughflow through Lombok Strait, J. Geophys. Res., basins. Usually it is assumed that this continues upwelling 101(C5), 12 455–12 464, 1996. Armi, L. and Williams, R.: The hydraulics of a stratified fluid flow- within the region until it is shallow enough to continue on ing through a contraction, J. Fluid Mech., 251, 355–375, 1993. into the Indian Ocean. However the model results suggest Bryan, K.: A numerical method for the study of the circulation of that the upwelled water returns to the Pacific. If in reality the world ocean, J. Comput. Phys., 4, 347–376, 1969. this does not happen, we need to understand why. Bryden, H. L. and Beal, L. M.: Role of the Agulhas current in In- The model flow through the Lombok Strait was much dian ocean circulation and associated heat and freshwater fluxes, larger than the observations. The reason is again probably Deep-Sea Res., 48, 1821–1845, 2001. due to the channel width being too large in the model. The Cox, M. D.: A primitive equation 3-dimensional model of the representation of viscosity in the model and the extra effects ocean. Tech.Rep. 1, Geophysical Fluid Dyn. Lab, Natl. Oceanic of locally generated turbulence in the strait could also be in- and Atmos. Admin., Princeton Uni. Press, Princeton, N.J., 1984. volved. 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