Buoy and satellite data show pronounced subseasonal oscillations of sea surface temperature (SST) in the summertime Bay of Bengal. The SST oscillations are forced mainly by surface heat flux associated with the active break cycle of the south Asian summer monsoon. The input of freshwater (FW) from summer rain and rivers to the bay is large, but not much is known about subseasonal salinity variability. We use 2002–2007 observations from three Argo floats with 5 day repeat cycle to study the subseasonal response of temperature and salinity to surface heat and freshwater flux in the central Bay of Bengal. About 95% of Argo profiles show a shallow halocline, with substantial variability of mixed layer salinity. Estimates of surface heat and freshwater flux are based on daily satellite data sampled along the float trajectory. We find that intraseasonal variability of mixed layer temperature is mainly a response to net surface heat flux minus penetrative radiation during the summer monsoon season. In winter and spring, however, temperature variability appears to be mainly due to lateral advection rather than local heat flux. Variability of mixed layer freshwater content is generally independent of local surface flux (precipitation minus evaporation) in all seasons. There are occasions when intense monsoon rainfall leads to local freshening, but these are rare. Large fluctuations in FW appear to be due to advection, suggesting that freshwater from rivers and rain moves in eddies or filaments.
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 Organized atmospheric convection associated with intraseasonal oscillations (ISO) of the South Asian summer monsoon generally moves north to the Indian subcontinent and the Bay of Bengal [Webster et al., 1998; Wang et al., 2005; Jiang et al., 2005] from the equatorial Indian Ocean. Spatially coherent ISO of deep convection, surface heat fluxes and sea surface temperature (SST) attain their largest amplitudes over the Bay of Bengal and South China Sea [Sengupta et al., 2001; Han et al., 2006; Sobel et al., 2008]. Episodes of active monsoon convection (cloudy skies and strong surface winds) alternate with suppressed convection (clear skies and weak winds); net surface heat flux into the ocean (Qnet) is alternately negative and positive, cooling and warming SST by upto 2°C. A few 2–3 week records of ship-based observations during the Monsoon Experiments of 1979 and 1999 show that subseasonal variations of SST can be large, particularly in the north bay where freshwater (FW) from river runoff and rain leads to shallow surface mixed layers [Moshonkin and Harenduprakash, 1991; Bhat, 2002; Webster et al., 2002]. Subseasonal variability of Bay of Bengal SST in summer appears to be closely determined by net surface heat flux [Sengupta and Ravichandran, 2001], provided the effect of penetrative solar radiation below the shallow, fresh mixed layer are taken into account. However, previous studies of Bay of Bengal SST ISO have used mainly surface observations from buoys and satellites, due to the nonavailability of sufficiently long records of in situ subsurface data.
 Ocean models also show that summer ISO of Bay of Bengal SST are forced mainly by heat flux, with occasional contribution from vertical mixing/entrainment at the base of the mixed layer [Schiller and Godfrey, 2003; Waliser et al., 2004]. Both observations and models suggest that ISO of north Indian Ocean SST in turn influences the large-scale wind field, atmospheric temperature and humidity, and the active break cycle of monsoon convection [Vecchi and Harrison, 2002; Waliser, 2006; Yang et al., 2008]. The presence of SST feedback in coupled models improves the simulation of organized convection, making it more realistic in many respects and increasing predictability on intraseasonal time scales [Fu et al., 2007]. Therefore we need deeper understanding of the physical mechanisms responsible for the enhanced SST response of the Bay of Bengal to monsoon ISO.
 Most observational studies of near-surface salinity in the north Indian Ocean examine the seasonal cycle. The variability of upper ocean salinity is determined by ocean circulation, in addition to rainfall, evaporation and river runoff. Five of the world's 50 largest rivers discharge into the Bay of Bengal, with total annual runoff exceeding half the river runoff to the entire tropical Indian Ocean. Both rainfall and river runoff to the bay have pronounced seasonality; rainfall peaks in June–August, and runoff in July–September. The lowest near-surface salinity is found in the north bay in October–November, after the monsoon season. Ship-based climatology shows a pronounced seasonal cycle of salinity along the eastern and western boundaries of the Bay of Bengal, likely due to advection of freshwater from rainfall and river runoff [Rao and Sivakumar, 2003; Sengupta et al., 2006]. This deduction is consistent with studies of salinity in the equatorial West Pacific, where the seasonal cycle of rain and surface salinity are uncorrelated [Delcroix et al., 1996]. Even though the west Pacific is a region of heavy rain, salt balance suggests that advection, rather than surface freshwater flux (Precipitation minus Evaporation, P − E), is the most important forcing [Cronin and McPhaden, 1998; Feng et al., 1998].
 Model studies of the seasonal cycle of salinity of the north Indian Ocean are broadly in accord with climatology [e.g., Han and McCreary, 2001; Diansky et al., 2006; Wu et al., 2007]. They suggest that river runoff, and not surface freshwater forcing, is the dominant factor in salinity variability in the bay. On intraseasonal scales, the model study of Schiller and Godfrey  suggests that the influence of advection and entrainment could be important. It has been suggested that salinity could be indirectly influenced by the high variability of rainfall [Illig and Periguad, 2007]: In the north Indian Ocean, most of the rainfall variance is at submonthly periods; the breaks in rain lead to net increase of surface salinity via entrainment of salty water. As far as we know, there is no observational study of subseasonal variability of Bay of Bengal salinity, with the exception of Riser et al.  (see below).
 The paucity of subsurface observations has been partially resolved by Argo floats, which measure profiles of temperature (T) and salinity (S) as they drift in the ocean. The floats provide an unprecedented view of the subsurface ocean, and Argo data is being widely used for basic science as well as applications [e.g., Ravichandran et al., 2004; Iwasaka et al., 2006; Mathews et al., 2007; Krishnamurti et al., 2007]. Riser et al.  studied the variability of near-surface salinity in the southwestern Bay of Bengal using 14 months (November 2004 to December 2005) of data from an Argo float equipped with additional passive acoustic sensors to estimate rainfall and surface winds. Their main finding is that upper ocean freshening can occur both in the presence and absence of rain: For instance, episodes of surface freshening coincide with rain events in October–December 2005, but freshening occurs also in the absence of rain (i.e., during January 2005), suggesting that salinity variability can be due to lateral advection.
 The aim of the present work is to understand the response of the upper ocean in the central Bay of Bengal to surface heat and freshwater fluxes on intraseasonal time scales (i.e., period ∼10–90 days). We use observations from Argo floats to study intraseasonal variability (ISV) of mixed layer T and S in relation to satellite-derived heat and freshwater fluxes sampled along the float trajectories. In section 2, we discuss the Argo data, the mixed layer heat and freshwater balance, and the estimation of fluxes. Results of the intraseasonal heat and freshwater balance, and the sources of uncertainty in our calculations, are discussed in section 3. We summarize the main results and their implications in section 4.
2. Data and Methods
 We use data from three Argo floats (WMO identifiers 2900093, 4900671 and 4900673; 093, 671 and 673 for brevity) which report T and S profiles every 5 days. The selected floats are from the central Bay of Bengal (10°N–18°N and 81°E–94°E) with parking depths of 650 m (093) and 1500 m (671 and 673). The longest stretch of data comes from float 093, covering August 2002 to January 2007 with a 6 month gap from mid-January to mid-July 2005. We use two full years of data from float 671 and 673, covering the period January 2006 to December 2007. All data are from the open ocean except for 093, which is in the western boundary region from August 2002 to May 2003 (Figure 1). The shallowest depth of observation for 093 is 10 m from August 2002 to January 2004. All other data are at depths of 5 m, 10 meters, and every 10 m thereafter down to 500 m. Since our interest is in the near-surface layer, we linearly extrapolate T and S to the surface using the 10 m and 5 m observations in most of our calculations. Surface flux estimates at the float location are based on daily satellite fields sampled along the float trajectories (see below); 5 day Argo locations and profiles are linearly interpolated to daily values. Note that the basic 5 day T and S observations can only resolve variability with period 10 days and longer.
2.1. Near-Surface Heat and Freshwater Balance
 As mentioned earlier, our main aim is to investigate whether surface heat and freshwater flux force subseasonal variability in the mixed layer. Previous observational studies use (1) short time series of surface fluxes and profiles of T and S from research ships [Moshonkin and Harenduprakash, 1991; Bhat, 2002] or (2) observations of SST and other surface parameters from moored buoys or satellites [Sengupta and Ravichandran, 2001; Sengupta et al., 2001], to study heat balance in the summer monsoon season. As far as we know, this is the first study of ISV of upper ocean temperature and freshwater to use long time series of subsurface observations from the north Indian Ocean.
 The variability of mixed layer temperature is governed by
where H0 is the mixed layer depth (MLD). Since all floats have data at 10 m, we define MLD as the depth where potential density exceeds density at 10 m depth by 0.05 kgm−3; this criterion is similar to that used by de Boyer Montégut et al.  to construct mixed layer depth from Argo profiles. The mixed layer temperature, or equivalently, SST = T(z)dz. The heat flux absorbed in the mixed layer, i.e., the ‘effective’ heat flux (Qeff) is equal to net surface heat flux (Qnet) minus penetrative shortwave radiation (Qpen) below depth H0; ρ and Cp are density and specific heat of seawater.
 The mixed layer freshwater balance is
where the freshwater content of the mixed layer is defined as FW = dz; the reference salinity Sref = 34 psu, and P − E is Precipitation minus Evaporation. We have no estimates of advection or mixing across the base of the mixed layer, except as residuals from equations (1) and (2) (see the discussion in section 4).
2.2. Heat and Freshwater Fluxes
 The net surface heat flux Qnet = Qsw + Qlw + Qlat + Qsens is estimated from daily satellite data. 2.5° × 2.5° NOAA outgoing longwave radiation (OLR) is used to estimate the net surface insolation (Qsw) and longwave (Qlw) radiation, following Shinoda et al. . Shinoda's original empirical relation between daily Qsw and OLR was based on insolation data from the equatorial oceans. In order to extend it to include the strong seasonal cycle in the Bay of Bengal [see Sengupta et al., 2001], we estimate daily net surface insolation from
where QERBE is the climatological monthly mean net surface insolation from the Earth Radiation Budget Experiment (ERBE [Li and Leighton, 1993]) and OLRa is the OLR anomaly, i.e., daily OLR minus the seasonal OLR.
where ε is the emissivity of the sea surface, σ the Stefan-Boltzmann constant and C the cloudiness derived empirically from OLR: C = 166.39 − 1.38OLR + 9.1 × 0.001 × OLR2 − 20.87 × 10−6 × OLR3. Ts and Ta are sea surface temperature and air temperature.
 Turbulent fluxes of latent heat Qlat and sensible heat Qsens are based on bulk formulae according to the algorithm of Zeng et al. , where the exchange coefficients are functions of surface wind speed and stability. Wind speed is from daily vector winds from the scatterometer on QuikSCAT [Liu, 2002] optimally interpolated onto a 1° × 1° grid [Pegion et al., 2000]. Computation of Qlat and Qsens requires knowledge of sea surface temperature, air temperature (AT) and relative humidity (RH). Since AT and RH are not easily obtained from satellite data, we use ΔT (sea surface temperature minus AT), and RH, from monthly climatology [da Silva et al., 1994]. We take the 1 m temperature from the (extrapolated) Argo T profiles to be the sea surface temperature; AT is then SST − ΔT, linearly interpolated to daily values.
 The daily net downward shortwave radiative flux across H0, is estimated as Qpen = Qsw (1 − α) exp() where α = 0.58 is the fraction of incident sunlight (mainly red and infrared) absorbed in the upper ∼2 m; ζ is the attenuation depth, i.e., the 1/e-folding depth for subsurface radiation [Paulson and Simpson, 1977]. ζ is calculated from a spatially varying, monthly blended product of satellite and in situ chlorophyll [Gregg and Conkright, 2001] following Morel . H0 is MLD, as in equations (1) and (2).
 Like the heat flux, daily freshwater flux P − E is estimated following the trajectories of the individual Argo floats. Rainfall is from the daily 0.25° × 0.25° TRMM 3B42 version 6 product, which is a multisatellite estimate from the precipitation radar and microwave sensors on board the Tropical Rainfall Measuring Mission (TRMM) satellite, merged with infrared observations from other satellites and calibrated against rain gauges [Huffman et al., 2007]. Comparison with the Indian meteorological Department's daily gridded rain gauge data over central India shows that the TRMM daily rainfall estimate accurately captures the phase of monsoon ISV, but amplitudes are underestimated by about 15% [Rahman and Sengupta, 2007]. Evaporation E = where Lv is latent heat of vaporization. Comparison with buoy data suggests that on intraseasonal scales, the root mean square (RMS) error of daily Qsw and Qlat is about 20 and 10 Wm−2, while the RMS difference between daily buoy and satellite rainfall is about 4 mm/d (see section 4).
 We define ISV as variability with periods from ∼10–90 days. Harmonic analysis is used to remove all periods longer than 90 days from and Qeff. A 10 day running mean is applied to the filtered and Qeff to smooth short periods that are not resolved in the original 5 day Argo data. Since daily rainfall as well as is highly variable at short subseasonal periods, filtering the forcing P − E or the ocean response can give rise to spurious Gibbs oscillations [Emery and Thomson, 2001]. Therefore we use the unfiltered, full fields for the study of freshwater balance. Note that although the freshwater content in the mixed layer FW depends on the choice of reference salinity, the term in the freshwater balance (equation (2)) does not.
3. Results and Discussion
 Temperature from float 093 (Figure 1) shows seasonal warming in spring (January–May), cooling during the summer monsoon (June–September), secondary warming in October and winter cooling (November–January). The seasonal warming extends down to 60–80 m depth, but seasonal cooling is shallower (Figure 1). Salinity is lower than 33 in the upper 50 m, except during December 2003 to February 2004, and in May 2006; it falls below 31 during January and October 2003, September 2004, and December 2006. The fresh layer generally extends deeper (∼80 m) in 2005–2006 compared to 2003–2004. Vertical displacement of the thermocline (the 22 and 24°C isotherms in Figure 1) occurs mainly on seasonal time scales, but it can be large and rapid at times, for instance, the 22°C isotherm moves from 70 m to 140 m in 15 days in March 2003. Interestingly, displacement of the 34.7 and 34.8 isohalines is almost identical to that of the thermocline.
 Mixed layer depth from float 093 lies in a range from just over 10 m, to about 22 m (Figure 2a). The difference between T, S and density at 10 m and 30 m depth shows that most of the time, the density stratification across 10 m and 30 m depth is due to the vertical gradient of salinity; at float 093 in 2004, for example, S at 30 m minus S at 10 m (δS) is zero or negative (Figures 2b and 2c) in only 3% of all spring and winter profiles, and less than 5% of summer profiles. Similarly, T at 10 m minus T at 30 m (δT) is zero or negative in about 20% of spring and winter profiles, and 25% of summer profiles, corresponding to inversions(Figure 2b). At least 95% of all profiles have either positive δS or positive δT or both. Temperature inversions of 0.5–1.5°C [Thadathil et al., 2002] occur only in association with substantial salinity differences (e.g., δS at 093 is 0.5–1.5 in January–February 2003, and December 2004; Figure 2b). Occasionally the upper ocean is strongly stratified by temperature, e.g., δT exceeds 0.5°C in April and August 2004 at 093 (Figure 2), or April 2007 at 671 (not shown), note that δS can be negative at these times. The data show that the isothermal layer depth (say, the depth at which the temperature is 0.2°C lower than 10m temperature) is almost always larger than the mixed layer depth, i.e., a barrier layer is present. At float 093 the barrier layer thickness can exceed 80 m in winter; the August 2002 to December 2004 mean barrier layer thickness is about 30 m.
 The time variability of temperature is largest in the thermocline (Figure 3a); there is a secondary maximum in the near-surface ocean (∼15 m depth in float 093; Figure 3a), with low values at about 30 to 60 m depth. Salinity variability is largest within the upper 25 m or so, with a maximum standard deviation of about 1 (Figure 3b). There is a minimum between 30–40 m, followed by a secondary maximum at 60–70 m probably associated with thermocline displacement; variability at deeper depths is smaller because vertical gradients of S are relatively weak. The structure of temperature variability in the frequency domain is illustrated by variance-preserving spectra of T, computed using data from three summer seasons (2003, 2004 and 2006) from float 093 (Figure 3). The spectra of average temperature at 35–50 m and 85–100 m depth are similar, with peaks at about 25 day and 40–50 day periods, and relative minima at 20, 30, and 60 days. SST (i.e., mixed layer T) has a distinctly different spectral signature, with a peak at 30 days (Figure 3c). The implication is that while 35–50 m temperature is influenced by thermocline displacements, the variability in the mixed layer is probably not significantly affected by vertical movement of the subsurface ocean.
 Mixed layer temperature from float 093, and effective heat flux Qeff along the trajectory of this float are shown in Figures 4a and 4b. Qeff is generally positive in spring (about +100 Wm−2) and negative in winter (about −50 Wm−2). Note that Qeff is alternately positive and negative (generally in the range −50 to +50 Wm−2) during the summer monsoon season. Mixed layer salinity from float 093 (Figure 4c) and precipitation along the float trajectory (Figure 4d) show substantial variability on subseasonal scales; note the episodic occurrence of low salinity and freshening in the absence of rain, consistent with the findings of Riser et al. .
3.1. Intraseasonal Heat Balance
 Intraseasonal variability of SST and Qeff at all three floats (Figure 5) is substantial, with the standard deviation of 2 year time series being 0.21–0.23°C and 22–26 Wm−2. Comparison of SST and Qeff suggests that there are periods when the phase and amplitude of ocean response matches that of the forcing. We examine ISV in the ocean response and heat flux forcing for different seasons, summer (June–September, JJAS), winter (November–January, NDJ) and spring (February–April, FMA). All three floats have at least two consecutive years of data for each season. The amplitude response is measured by R, the ratio of root mean square (RMS) ρ CpH0 to Qeff
(For brevity we sometimes refer to ρ CpH0 as with units of Wm−2, this usage should be clear from the context.) If were entirely forced by Qeff, the correlation coefficient and R would both be 1. The magnitude of ISV of Qeff and at float 093 is distinctly smaller in 2003 than in 2004; at float 671, it is smaller in 2006 than 2007, suggesting substantial year-to-year changes in ISV.
 During the summer monsoon season, the amplitude of ISV in the central bay (where the floats reside; Figure 6), is smaller than in the north bay [Sengupta and Ravichandran, 2001; Sengupta et al., 2001]. The correlation between intraseasonal and Qeff for floats 093, 671 and 673 is 0.69–0.75, while R is 0.86–1.03 (Table 1). Most intraseasonal oscillations are clearly forced by Qeff, but the amplitude of some oscillations of are larger than Qeff (Figure 6). This could be because of (1) errors in heat flux estimates, (2) offset between the two time series arising from the original 5 day Argo sampling versus daily fluxes, or (3) advection/entrainment acting in phase with atmospheric forcing to warm and cool SST (e.g., 1 August to 10 September 2004 in 093; 5–20 August 2007 in 673). The situation where the amplitude of the ocean response is weaker than the forcing is more common. For example, during 15 July to 15 August 2007 at float 671, both warming and cooling of the near-surface ocean is small relative to the forcing. In principle, the reduced warming could be due to vertical mixing/entrainment of cooler subsurface water. The magnitude of SST cooling is smaller than the forcing, but this is unlikely to be due to mixing. Since there is no evidence of sustained mixing across the mixed layer base (Figure 2), advection is the likely reason for the somewhat muted response of the ocean to forcing.
Table 1. Correlation Between and Qeff and R From Floats 093, 671, and 673 for Different Seasonsa
Here R = RMS()/RMS(Qeff). Also shown are RMS of Qeff and in Wm−2.
 Advection appears to enhance a 30 day intraseasonal oscillation in summer at float 093 during 20 July to 20 August 2006 (Figure 7): The mixed layer cools by 2°C from 20 July to 3 August, and then warms by 1.5°C. The amplitude of is 90 Wm−2 but that of Qeff is about 30 Wm−2 (Figure 7a). Anomalously cool water extends to at least 100 m during the cooling phase of SST (Figure 7b). Individual Argo profiles show that the upper 50 m on 5 August is 2°C cooler than on 31 July or 10 August. The 27°C isotherm shoals from about 70 m to the surface and the 34.8 isohaline from 120 m to 60 m (Figure 7c), between 25 July and 5 August. Maps of daily 0.25° × 0.25° optimally interpolated (OI) SST from the Tropical rainfall Measuring Mission TRMM Microwave Imager (TMI) [Gentemann et al., 2004] show a cooling of the central and northwestern bay from 30 July; on 5 August the float is in a 200 by 300 km region of SST cooler than 27°C centered at 17°N,90°E (not shown). Examination of the surface winds and sea surface height anomalies suggests that this is a cold core eddy generated by a monsoon deep depression [Jayanthi et al., 2006].
 In the spring season, the correlation between forcing and response is generally smaller than in summer. The correlation is about 0.1 at float 093 and 0.4 at 673, but a single 45 day intraseasonal oscillation at 671 forced by heat flux (not shown) raises it to 0.66; R is significantly larger than one at all floats (Figure 8a and Table 1). In general, SST variability is not forced mainly by Qeff. Since the upper ocean can be stratified by temperature as well as salinity in this season (Figure 2), the results suggest that ISV of spring SST is influenced by advection rather than mixing/entrainment. The lowest correlations between and Qeff are found in winter, ranging from 0.11 to 0.39, while R is between 0.89 and 1.07 (Figure 8b and Table 1). As in spring, examination of Argo profiles shows no evidence of vertical mixing across the mixed layer base. Therefore ISV of winter SST is probably dominated by advection.
 To illustrate the relation between ISV of SST and surface flux in an alternate form, we define predicted SST as SSTp = (Qeff/ρCpH0)dt; the seasonal cycle (i.e., periods exceeding 90 days) of SST and SSTp are removed. Figure S3 shows the subseasonal variability of SST and SSTp for float 093 in different seasons. In the two summer seasons of 2003 and 2004, observed and predicted SST match reasonably well, whereas there is substantial mismatch between the two in winter and in spring.
 Variance-preserving spectra of and Qeff averaged over two consecutive summer seasons are shown in Figure 9. Since the time series is relatively short, the spectral estimates can have large error, particularly at 90 day period. Note that almost all intraseasonal power is in the 10–60 day range. Han et al.  find from TRMM data that submonthly variability of Bay of Bengal SST (period <30 days and standard deviation of ∼0.2°C), which can account for 30–50% of the total ISV, is forced mainly by surface heat flux. We see that in general, 30–60 day variance of Qeff is larger than that of , with the exception of float 673, where ‘response’ is comparable to forcing. It may be that advection is responsible for the muted response of the near-surface ocean to heat flux at 30–60 day periods (Figures 9a and 9b).
3.2. Freshwater Balance
 In summer, the east and north bay receive the highest rainfall in the global tropical ocean. Apart from pronounced seasonal and diurnal cycles, monsoon rainfall over the bay has significant subseasonal variability, with distinct peaks at about 10 and 30 days [Hoyos and Webster, 2007]. We investigate whether near-surface salinity in the central bay away from coasts (Figure 1a) is a response to local freshwater flux. As mentioned before, we do not filter the freshwater forcing and response (see equation (2)). In any case, it is clear from the full P − E and that there is no one-dimensional balance between the two at any float (Figures 10a–10c). It has been suggested that during the summer monsoon, the dominance of advection is due to lateral salinity gradients [Schiller and Godfrey, 2003; Diansky et al., 2006].
 There are large fluctuations (−60 to +90 mm/d) of in January–April, when there is no rain and P − E is negative (about −5 mm/d, Figure 10 [Riser et al., 2008]). However, even in May–October, when P − E reaches large positive values (up to 100 mm/d), is uncorrelated with the forcing. As noted earlier, the difference of S between 30 m and 10 m is positive most of the time, and vertical mixing/entrainment across the mixed layer base is not significant. The implication is that lateral advection is the dominant term in the freshwater balance. Occasionally, intense rain events do lead to local freshening, two examples are shown in Figures 10d and 10e (note that the rate of change of freshwater is estimated from the basic 5 day Argo data). However, such correspondence is rare; in general, variability of mixed layer freshwater is not due to local P − E.
 Variance-preserving spectra of and P − E averaged over two consecutive JJAS seasons show that ISV of rate of change of freshwater is several times larger than ISV of surface flux at floats 093 and 671 at all time scales (Figures 11a and 11c) except at float 673, where P − E has substantial 30–60 day variability. However, all floats show that the ‘response’ of the near-surface ocean is preferentially at 10–30 day periods (Figures 11a and 11c). We define the ratio of freshwater variability to flux as Rf = RMS()/RMS(P − E); the average of Rf for all floats and all seasons is 3.04.
 An alternative depiction of the relation between monsoon P − E and is obtained by integrating the terms in time from June to October. Both FW and (P − E)dt are prescribed to be zero on 1 June. The accumulated freshwater content and (P − E)dt (Figure 12) shows that in general, surface flux does not determine freshwater variability even in the monsoon season [Wu et al., 2007]. Of the six monsoon seasons covered by the floats, only one (2003, 093) shows freshwater content responding to seasonal rain, accumulated P − E and freshwater increase by about 0.6 m from early June to early October (Figure 12a). Floats 671 and 673, for instance, show a decrease in FW in spite of near-monotonic increase of (P − E)dt by about 0.8 m through the summer of 2007 (Figures 12b and 12c). This is consistent with findings from the west Pacific (see Introduction), where the seasonal evolution of upper ocean salinity is not correlated with surface freshwater forcing [Cronin and McPhaden, 1998; Feng et al., 1998].
 Step-like changes in (P − E)dt, for instance the large increments in June 2006, September 2006, and June 2007 at 673 (Figure 12c), are due to subseasonal rainfall events. FW has distinct ISV, with the period of most oscillations lying in the 10–30 day range; these include one or two events with giant amplitude (about 1 m), such as in October 2003 and September 2004 at 093 (Figure 12a). It is clear that the ISV of FW are not forced by surface flux. Float data sometimes shows a steep fall in FW during periods of intense rainfall, e.g., in June 2006 and June 2007 at 673 (Figure 12c). In principle, these episodes could be due to entrainment of saltier subsurface water, but the salinity gradient across the mixed layer base is stable. Further, if the salinity rise were influenced by vertical advection, it would be accompanied by cooling that is not forced by negative heat flux, we find no evidence for this (Figure 6). We therefore conclude that abrupt changes or subseasonal oscillations of FW are mainly due to lateral advection.
3.3. Error Estimates
 The shallowest depth at which the Argo floats report T and S throughout the record is 10 m. The absence of observations at shallower depths leads to uncertainty in the estimates of mixed layer depth. If data were available from, say, 1 m depth, it is possible that we might occasionally obtain MLD shallower than 10 m; the deepest MLD might also be different (see Figure 2). We have done a test calculation of heat and freshwater balance for all floats used here with a constant MLD of 15 m: All our results remain qualitatively the same (although the values of correlation and R change slightly from those in Table 1), suggesting that the exact value of MLD is not critical.
 The drift of the Argo float between successive profiles can lead to ‘spurious advection’. Unlike moored observations, float drift could lead to errors in the heat balance terms (equation (1)). We estimate spurious advection QSpAdv using lateral gradients of sea surface temperature (, ) from (1) daily TMI OI SST and (2) the 5 day Objectively Analysed (OA) Argo gridded product [Gaillard et al., 2009]; velocity (ufloat, vfloat) is estimated from the location of successive float profiles
TMI SST has a cool bias of 0.13°C relative to 5 m temperature from 093, and the RMS difference between TMI SST and Argo temperature is about 0.4°C (not shown). This suggests that there could be considerable uncertainty in SST gradients estimated from TMI. On the other hand, 5 day OA gridded Argo data underestimates the variability of T and S in relation to individual floats (see Figure S1 in Auxiliary material). The ratio of RMS from 093 and from the gridded product is 2.4; the corresponding ratio for () is 13.6. We estimate spurious advection QSpAdv at 093 based on (1) TMI SST and (2) gridded Argo SST; RMS QSpAdv is about 9 Wm−2 for TMI and 3 Wm−2 for gridded Argo SST, for the period April 2003 to December 2006 (Figure 13). The mean speed of float movement is about 0.05 m/s, and the mean distance between successive 5 day profiles is thus about 20 km; SST differences across this distance are generally not large. Therefore spurious advection is generally within the uncertainty of heat flux estimates (see below). Since the gridded Argo data is likely to underestimate spatial gradients of near-surface salinity (Figure S1), we cannot evaluate the influence of spurious advection on salinity evolution. However, since and P − E are uncorrelated, the broad conclusions from the freshwater balance probably remain valid.
 Another source of uncertainty is errors in surface fluxes of heat, precipitation and evaporation. We estimate these errors from a comparison with moored buoy observations. Long-term data on shortwave radiation and relative humidity from the Bay of Bengal are available only from late 2007 [McPhaden et al., 2009], so we use the 2003–2004 data from the TRITON buoy [Kuroda and Amitani, 2000] at 1.5°S,90°E; concurrent buoy wind and humidity is available for the 11 month period of July 2003 to May 2004. The OLR-based relation generally underestimates variability of Qsw [see Zhang and McPhaden, 2000]. Although the daily RMS difference between 10 day smoothed subseasonal variations of buoy and satellite estimates is about 16 Wm−2, the phase of ISV is accurate (the correlation is about 0.8 for two years of data; Figure S2a). Our estimates of Qlat use relative humidity RH and ΔT (sea surface temperature minus AT) from climatology, and daily QuikSCAT wind speed (section 2). Yet, the daily RMS difference between buoy and satellite Qlat is only 11 Wm−2 (Figure S2b). It appears that ISV of RH or AT does not have a major influence on Qlat: AT cools rapidly during convective rain events, but increase of evaporation due to enhanced ΔT tends to be countered by a decrease due to higher RH (not shown). The phase of satellite rainfall variability is realistic (correlation 0.76); the daily RMS difference with buoy rainfall is substantial (about 4 mm/d), but the satellite does not systematically underestimate subseasonal rainfall amplitude (Figure S2c).
 We have examined intraseasonal mixed layer heat and freshwater balance in the central Bay of Bengal using a few years of data from 5 day Argo floats and daily satellite-based fluxes. About 95% of all Argo profiles have lower salinity at 10 m than at 20 m depth (not shown) or 30 m depth (Figure 2), suggesting that the influence of vertical mixing/entrainment across MLD is small or short-lived. Previous modeling work suggests that entrainment across the base of the mixed layer can be significant in the heat and freshwater balance [Waliser et al., 2004; Schiller and Godfrey, 2003; Illig and Periguad, 2007]. Although the Argo data suggest that vertical mixing is generally insignificant, we cannot obtain quantitative estimates of mixing or advection except as residuals from the balance equations.
 Total surface heat flux minus penetrative flux is alternately positive and negative in summer (Figure 5), in association with the active break cycle of the monsoon; the amplitude of intraseasonal Qeff is about 30 Wm−2 (Table 1). The correlation between intraseasonal and Qeff is high, and the ratio of ocean response to forcing (R) is close to one, suggesting that the ISV of SST is mainly forced by heat flux during the summer monsoon. However, this is not true in winter (November–January) or spring (February–April), in these seasons either the correlation is small or R is larger than one (i.e., the ISV of rate of change of SST is larger than the heat flux). Our analysis suggests that advection is important for the heat balance in winter and spring. Examination of spatial gradients of TMI SST show that averaged over our study region (84°E–94°E, 11°N–16°N), the typical magnitude of SST gradients in spring and winter is twice as large as in summer. In addition to seasonal differences in surface forcing, this is a possible reason why advection may play a more important role in spring and winter relative to summer.
 Freshwater forcing P − E has large subseasonal variability in the summer monsoon season, while the mixed layer ‘response’ is highly variable in all seasons. In general, near-surface freshwater content is not a response to local P − E, although there are one or two instances when FW responds to P − E on seasonal or subseasonal scales. Advection appears to dominate subseasonal freshwater balance in all seasons, implying that lateral gradients of near-surface salinity are large. Mixing must be sufficiently weak that freshwater from river runoff or rainfall can move large distances in eddies and/or filaments. It is likely that stable near-surface salinity stratification suppresses mixing in the Bay of Bengal [Sengupta et al., 2007; Bhat, 2002], and in other regions of the Indian Ocean [Sengupta et al., 2008, 2006].
 We note that the frequency dependence of mixed layer T, S, and surface fluxes (Figures 9 and 11) has possible implications for the summer monsoon. Monsoon heat flux has prominent 30–60 day variability, with a peak at about 40 days (Figures 9a and 9b); the 30–60 day SST response is comparable to, or somewhat smaller than the forcing (Figure 9). In contrast, the advection-dominated freshwater variability is primarily at 10–30 day periods, and several times larger than the forcing (Figure 11). If lateral gradients of temperature were effectively as large as salinity gradients, SST variability would be advection dominated. The observed large-scale spatial pattern of SST ISO is coherent with atmospheric convection [Sengupta et al., 2001; Vecchi and Harrison, 2002] because SST is forced by surface heat flux. Several models suggest that coupling with the ocean helps to organize monsoon ISO on the observed 30–60 day time scales [e.g., Waliser et al., 1999; Zhang et al., 2006]. If SST were determined by advection rather than surface flux, the pattern of SST ISO would not match convection, and the ocean might not then be able to influence the monsoon active break cycle.