Since the air–sea exchanges in the TC affected regions within 0–3 days of the storm passage are dominated by TCs effects, which is several times larger than the background air–sea heat exchanges, it is reasonable to assume that the net ocean heat change within the TC-affected regions during this period is totally induced by TCs. Our choice of 3 days is to, at least partially, average out any float drift caused by inertial oscillations (see part I for more discussion).

This strategy is based on the notion that the ocean must be the energy source of a storm, so the total heat loss in the ocean during the storm is transported to the air as air–sea heat flux during the storm passage (0–3 days). The averaged OHC change is calculated as follows (in W): QATSTD=Ltrack-TSTD∫dist=-8dist=81T3days∫δt=0δt=3∫depth=0depth=1200ρcpFTSTD(dist,depth,δt)ddepthdδtddist/TyearQAHur=Ltrack-Hur∫dist=-8dist=81T3days∫δt=0δt=3∫depth=0depth=1200ρcpFHur(dist,depth,δt)ddepthdδtddist/Tyear whereFTSTD, FHur – footprints of the track-averaged ocean responses obtained in part I of this studycp – heat capacity of sea water ∼4186 J (kg ∘C)-1ρ – density of sea water, which are calculated by using Argo salinity, pressure and temperature measurements before the stormδt- elapsed time after the storm passage, which is averaged from 0 to 3 days after storm passagedist – cross-track distance from the location of the Argo pair to the track, which is set to 8∘ across the trackdepth – vertical position of the measurement which is integrated from 0 to 1200 mTyear – duration of one calendar year in seconds, to calculate an annual meanLtrack-TSTD, Ltrack-Hur – averaged track length within one year, about 1.4 × 108 m, 8.3 × 107 m for TS/TD and Hurricanes respectively, which are obtained by averaging the track length from 2004 to 2012.

We choose the time period between 0–3 days, because it likely captures the majority of the air–sea heat exchange during storm passage. However, other mechanisms may also influence air–sea heat flux in this time period, such as storm induced cooling via mixing and wave generation. TC-induced surface cooling can cause a reversal of surface fluxes in the days following storm passage, which marks the transition between the forcing stage and the recovery stage. Some studies suggest fluxes may reverse sign around 2 days after TC passage (Dare and McBride, 2011; Lloyd and Vecchi, 2011), The exact timing of this reversal depends on many factors, such as storm intensity, translation speed and regional conditions, and the best choice is unclear in a global context. Thus, we use 3 days as conservative estimate. We performed sensitivity tests of the TC response to different choices of the time length (0–2, 0–2.5, 0–3.5 and 0–4 days), but the results (not shown), and the results and interpretations are generally consistent for all time scales.

We examine the air–sea heat transfer rate in the TC-affected regions, by averaging air–sea heat flux as follows (in Wm-2): HTSTD=QATSTD/(Ltrack-TSTD×R)HHur=QAHur/(Ltrack-Hur×R) where R is the cross-track size of the TC-affected region which is set to be 16∘ (±8∘ across the track). The other variables are consistent with QATSTD and QAHur.

To calculate the geographical distribution of the TC-induced air–sea heat fluxes, we bin the global ocean using 1∘ by 1∘ grid boxes. From 2004 to 2012, the air–sea heat flux from each TC is calculated in each grid box (denoted as i and j for latitude and longitude respectively): Hi,j=∑ID1(i,j)ID2(i,j)HTSTD+∑ID1(i,j)ID2(i,j)HHur/T9years where T9years is the duration of 9 years in years. If a grid box is affected by two or more individual storms at the same time, only the heat flux due to the stronger storm is included. This avoids potential double-counting of storm effects. Annual air–sea heat flux is calculated by calculating the 9 year average (2004–2012). In this calculation, we assume that the heat exchange is uniform over the TC-affected region.

We estimate the net OHC changes by examining the average temperature response between 4 to 20 after storm passage, referenced to pre-storm conditions. We choose 20 days as the maximum duration, because sea surface temperatures are typically restored by this time, and it is difficult to separate TC effects from seasonal signals on timescales greater than 3 weeks. Tests on the different choices of the time length are also conducted (4–18, 4–19 and 4–21 days). The results of these tests (not shown) suggest the magnitude of the TC signal is relatively insensitive to the choice of timescales.

We calculate OHC changes using (in W): QNTSTD=Ltrack-TSTD∫dist=-8dist=81T17days∫δt=4δt=20∫depth=0depth=1200ρcpFTSTD(dist,depth,δt)ddepthdδtddist/TyearQNHur=Ltrack-Hur∫dist=-8dist=81T17days∫δt=4δt=20∫depth=0depth=1200ρcpFHur(dist,depth,δt)ddepthdδtddist/Tyear where δt is the elapsed time after storm averaged from 4 to 20 days, T17days is the duration of 17 days in seconds. The other variables are the same to those in calculating QATSTD and QAHur.

Limitations of this methodology include:

To create the geographical distribution of air–sea heat fluxes, we assume that ocean response to a storm is the same everywhere (based on the composite analysis of the footprints). This assumption neglects the regional differences in the ocean response due to differences in the background state and seasonal effects.

Here we calculate a global estimate of air–sea heat exchange during TCs by integrating the ocean heat differences within storm-affected regions during a 3 day interval surrounding storm passage. We assume that during this period, the net column-integrated ocean heat loss is caused by heat transfer from the ocean to the atmosphere. We use the footprint methodology described in part I, which has two spatial dimensions: vertical depth and cross-track distance relative to the storm's direction of motion. The footprint averages over the along-track direction. Thus the footprint represents a 2-dimensional insulated box that is ±8∘ across the storm track relative to the storm center and 1200 m deep, with an opening at the air–sea interface. The heat exchange between the box and its surroundings occurs only at the surface.

To test whether assumptions about the footprint hold, particularly related to insulation from horizontal advection at the sides of the box and vertical heat exchange at the base, we calculate the box-averaged air–sea heat flux at different horizontal and vertical spatial scales, ranging from dx=±1 to ±15∘ (with 0.5∘ increment) and dz=100 to 1900 m (with 200 m increment). As shown in Fig. 1, the averaged air–sea heat flux stabilizes for dx>∼6∘. The decreasing trend for dx>∼7∘ is a “dilution” effect, which is caused by enlarging the box size while the OHC change within TC-affected region remains unchanged. Note this effect is generally linear for large dx, which is expected since the depth is held constant. In the vertical direction, the air–sea flux estimates are unchanged for dz greater than 700 m (corresponding to dx >∼5∘). This result suggests the method requires at least ±7∘ and 700 m in order for the insulated box assumption to be considered valid. Thus, we use a terminal depth dz=1200 m based on the availability of data in the upper ocean (a large portion of Argos stop near 1200 m), and dx=8∘.

The annual contribution of TCs to the air–sea heat fluxes for dx=8∘ and dz=1200 m is about ∼4.80 and ∼6.25 Wm-2 for TS/TD and Hurricanes, respectively. The positive heat flux represents the net ocean heat loss. We calculate the total global air–sea heat exchange in Fig. 2. Given the methodology described previously, the integrated heat transport should converge to the total TC contribution as we increase the domain size. Consistent with Fig. 1, this convergence occurs for dx >∼6∘. For TS/TD, heat exchange continues to increase to dx >9. However, this increase is probably not caused by TCs given the large spatial scale. Therefore, we estimate the global annual air–sea heat exchange during TCs to be 1.05 and 0.82 PW for TS/TD and hurricanes, respectively. The total heat transfer is 1.87 PW annually, which represents the total heat loss from ocean to atmosphere during the forced stage (0–3 days).

The global air–sea fluxes derived in Fig. 1 correspond to 584 Wm-2 for TS/TD and 761 Wm-2 for hurricanes, when averaging fluxes within storm-affected regions (±8∘ across the track) These values are consistent with previously published case study estimates, such as the mooring observations during the category-4 hurricane Nargis (Lin et al., 2009; Mcphaden et al., 2009), which estimated storm-induced air–sea fluxes of ∼400–900 Wm-2. Furthermore, our global estimates are consistent to first order with the estimated heat required to bring the troposphere into thermodynamic equilibrium (Emanuel, 1991) with the ocean ∼108 Jm-2, which is equivalent to ∼3 Wm-2 annually over the global ocean basin. This estimate generally agrees with our results (4.80 and 6.25 Wm-2 for weak and strong storm categories respectively). A recent observational study (Bell et al., 2012) shows that the mean TC enthalpy fluxes from CBLAST field program increases from 764 Wm-2 at wind speeds of 52 ms-1 (category 3) to 2189 Wm-2 at wind speeds of 72 ms-1 (category 5) near the storm center. The result of the category 3 conditions is similar to our estimate averaging over all hurricanes (category 1 to 5). In addition, Braun, (2006) estimates a 1.34 PW heat loss from the ocean caused by hurricanes, which is ∼0.52 PW larger than our estimates. Trenberth and Fasullo, (2007) estimates the TC-induced enthalpy exchange caused by hurricanes is about 0.58 PW in total for 1990–2005, ranging from 628, 703, 783 and 895 to 1019 Wm-2 for categories 1 to 5 respectively, where the category-3 estimate is similar to our estimates averaged over all hurricane conditions. In total, their result is about 0.24 PW smaller than our result for similar conditions. As noted previously, the three day averaging period used here may capture some of the recovery stage associated with a reversal of air–sea fluxes and the reheating of anomalously cold surface waters after storm passage, thus these results may be considered slightly conservative compared to previous estimates (e.g. Braun, 2006).

The geographical patterns of the TC-induced air–sea heat fluxes are presented in Fig. 3, using spatial and temporal averaging consistent with our global estimates. We find significant spatial variability in the flux estimates, with the largest fluxes occurring in regions with the most TC activity (e.g. northwestern Pacific). These results indicate the zonally averaged TC contribution to the total annual air–sea enthalpy flux budget may be as large as ∼9.1 Wm-2, with peak value of 20 Wm-2 at latitudes experiencing the most TCs. These fluxes could account for as much as ∼10 % of the total annual ocean latent heat flux (90–110 Wm-2) (Trenberth et al., 2009) derived using NCAR/NCEP reanalysis (Kalnay et al., 1996), shown as the black curve in Fig. 3b.

As a simple check of the TC contributions of net surface fluxes, we compare the results from Argo data to the background surface fluxes using the NCEP/NCAR reanalysis. Specifically, we calculate the net climatological air–sea heat fluxes along TC tracks using NCEP/NCAR reanalysis for the same Argo sampling criteria (dx=8∘, dt=0–3 days). However, these climatological fluxes represent the daily averages over a 20 year period (1990–2012), rather than from specific TC days. In other words, the plot shows the surface fluxes along storm tracks for non-TC conditions. The NCEP/NCAR reanalysis product generally predicts a net oceanic heat uptake in background climatological conditions during TC seasons (Fig. 3c). In the absence of TCs, typical conditions would favor a net ocean heat uptake, on the order of 1 Wm-2 zonally averaged across the global ocean. This background warming signal is of opposite sign to the TC effect, which tends to cool the ocean through enhanced surface fluxes during the forcing stage.

Figure 3a shows a prominent peak in air–sea heat flux in the Western Pacific Ocean, reaching values as large as 65 Wm-2. Because this region experiences the most TC activity, this peak is probably due to more TCs occurrences relative to other regions. In Fig. 4a and b, we present the frequency at each 1∘ by 1∘ grid box which is affected by TCs per year, given the affected regions (cross-track distance) defined to be ±1 and ±8∘ relative to storm center. As expected, the figure shows a higher frequency of TC occurrences in grid boxes as we increase the size of the affected region. For example, in the western and eastern Pacific Ocean, between 1 and 1.5 storms pass directly through a single 1∘ by 1∘ grid box annually, but this activity can contribute to as much as 12∼14 storms affecting the same grid boxes when we increase the TC-affected region to ±8∘.

To check whether the peak in heat flux is caused by increased frequency of TCs, we assume that one grid box can be affected by only one storm within 20 days. The annual air–sea heat fluxes for this method are presented in Fig. 5, showing the peak fluxes in the northwestern Pacific decrease to 30 Wm-2 while the overall fluxes in the other basins are relatively unaffected (to within ∼5–10 Wm-2). Since the nature of air–sea heat exchanges is complicated by the close proximity of storms in active TC regions, such as in northwestern and northeastern Pacific, our geographical map of air–sea heat flux should be regarded as a first-order approximation.

Net OHC changes are estimated by calculating the difference between the average post-storm temperature during wake recovery (between 4 and 20 days after storm passage) and the pre-storm conditions. We choose 20 days as the upper limit of the post-storm temperature, because it represents the time scale of SST recovery after storm passage. Temperature anomalies are plotted in Fig. 6 as a function of the spatial and vertical extents of the TC footprint. Within 3∘ of the storm center, both TS/TD and Hurricanes induce column-averaged cooling at all depths. The cooling effect decreases for increasing footprint size, approaching zero for TS/TD and a net warming for Hurricanes. This result suggests that upwelling and heat loss to the atmosphere near the storm center are partly (for TS/TD) or fully (for Hurricane) compensated by post-storm surface fluxes. Furthermore, when the footprint size is larger than 8–9∘, the absolute value of the average temperature anomalies decreases, which is again attributable to the “dilution” effect as discussed in the previous section. The temperature anomalies also converge for increasing depth, when the footprint is greater than 3∘. Thus, we use a cross-track length scale of ∼8∘ and depth scale of 1200 m to quantify the TC-induced upper ocean thermal response. The average temperature anomalies for these footprint length scales are +0.039 ∘C for Hurricanes and -0.0125 ∘C for TS/TD.

The annual contribution of the net TC-induced changes in global OHC is calculated by multiplying the net ocean temperature changes with yearly averaged track lengths. This method is based on our results that the averaged ocean thermal change over all storms between post-storm (after recovery) and pre-storm conditions is 0.039 ∘C and -0.0125 ∘C for Hurricanes and TS/TD, respectively. The positive values indicate heat gained by the ocean. These estimates correspond to global annual flux contribution of ∼5.98 Wm-2 (0.75 PW) for Hurricanes and ∼-1.90 Wm-2 (-0.41 PW) for TS/TDs, where the positive values represent oceanic heat convergence and negative flux represents the net oceanic heat loss. This implies that after hurricanes, the ocean keeps on warming, and recovers the storm-induced enthalpy flux during the storm passage.

These findings indicate the total TC contribution to the global ocean heat convergence is estimated to be 0.34 PW annually in 2004–2012 periods, which reflects a net ocean heat gain from the atmosphere due to all storms.

Our results suggest that weak storms (TS/TD) tend to cool the ocean, while hurricanes tend to warm the ocean, when considering both storm-induced and post-storm fluxes. The difference in the ocean response may be due to the relatively weak vertical ocean mixing and surface cooling induced by TS/TD compared to hurricanes. For TS/TD, the OHC change is likely driven by the storm-induced enthalpy fluxes during passage. Because weaker storms typically cause less vertical mixing and thus less significant cold wakes following storms, there will be less post-storm heat flux into the ocean during the wake recovery stage. Conversely, strong events (hurricanes) induce more vertical mixing and surface cooling, which leads to more heat flux into the ocean during the recovery stage and thus net oceanic heat convergence. This finding is generally remarkably consistent with recent results analyzing satellite altimetry (Mei et al., 2013), who show positive oceanic heat convergence for hurricanes (∼0.37 PW globally). And also this result is consistent with those presented in Sriver and Huber (2007) and Jansen et al. (2010).

It is important to note that this estimate averages the post-storm temperature between 4 and 20 days after storm passage. As a test of this assumption, we can also define the post-storm restoration period to be when the OHC change is to zero. In other words, post-storm warming balances the storm-induced enthalpy flux. Our estimates suggest that the OHC restoring period for hurricanes is less than 20 days but more than 20 days for TS/TD.

In the previous two sections, we estimate the annual air–sea heat fluxes during 0–3 days after storm passage and OHC changes during 4–20 days after storm passage relative to pre-storm conditions. Here we use a bootstrap technique to constrain the error bars and characterize the uncertainties of our heat flux and OHC estimates. Beginning with the total number of Argo float samples (4410 pairs), we randomly choose 90 % of pairs and repeat our air–sea heat flux and anomalous OHC calculations, as described in the previous sections. We repeat the calculation 200 times.

In Fig. 7b and d, 200 estimates of air–sea heat fluxes presented as function of horizontal footprint size of the TC-affected regions (distance to the storm center). Most of these bootstrap estimates exhibit similar patterns with those shown in Fig. 1, supporting the robustness of our estimates. We choose an error bar of one standard deviation near 8∘ to quantify the uncertainty of our estimate. This uncertainty measure is equal to ±0.85 Wm-2 for TS/TD and ±1.50 Wm-2 for Hurricanes, which is equivalent to ∼20 and ∼25 % of the fluxes for TS/TD and hurricanes, respectively. Or, in terms of global annual heat flux, this uncertainty equates to ±0.20 PW for TS/TD and ±0.21 PW for Hurricanes, which is equivalent to ∼20 and ∼25 % of the total estimates for TS/TD and Hurricanes, respectively. Including these uncertainties, our estimates of air–sea heat flux during the TC forcing stage (0–3 days relative to storm passage) are: 1.05±0.20 PW (4.8±0.85 Wm-2) for TS/TD and 0.82±0.21 PW (6.25±1.5 Wm-2) for hurricanes.

Similarly, the 200 estimates of TC-induced OHC changes are shown in Fig. 8. We choose the uncertainty to be equivalent to the standard deviation of the average temperature change for spatial extent of 8∘ and 1200 m, consistent with the heat flux estimate. This uncertainty equates to ±0.0063 ∘C for TS/TD and ±0.0143 ∘C for hurricanes, which represents ∼50 and 36 % of the estimated OHC changes for TS/TD and hurricanes, respectively. Considering this uncertainty, our estimates of TC-induced thermal changes are: -0.0125±0.0063 ∘C for TS/TD and 0.0390±0.0143 ∘C for hurricanes. Equivalently, these estimates correspond to global annual heat flux of -0.41±0.21 PW (-1.90±0.96 Wm-2) for all TS/TDs, and 0.75±0.25 PW (5.98±2.1 Wm-2) for all hurricanes, where the positive values denote a net oceanic heat convergence.