Sea Surface Energy Fluxes' Response to the Quasi‐Biweekly Oscillation: A Case Study in the South China Sea

The South China Sea (SCS) owns the world's strongest quasi‐biweekly oscillation (QBWO) in boreal summer, but the mechanism is still unclear. This case study summarizes two modes of QBWO over the summer SCS in 2019 by using empirical orthogonal function on the 10–20‐day bandpass‐filtered outgoing longwave radiation fields. The maximum positive irradiance anomalies for the two modes are 90 W m−2. The upward solar and downward longwave radiation anomalies own about 4%–8% of the irradiance magnitude, and the surface upward longwave radiation shows a weak response. Sea surface turbulent heat fluxes' responses to QBWO display different spatial patterns compared to radiation fluxes. Their changes are mainly ascribed to the surface wind in Mode1 and the air‐sea thermal contrast in Mode2. We also discuss the cause and impact of sea surface turbulent heat fluxes on QBWO.

Information S1). The observed radiation fluxes include downward/upward shortwave radiation (R sd /R su ) and downward/upward longwave radiation (R ld /R lu ). Turbulent heat fluxes, including sensible heat flux (Q s ) and latent heat flux (Q l ), are estimated from a bulk algorithm of Coupled Ocean-Atmosphere Response Experiment (COARE 3.0) with observed meteorological variables as input (Edson et al., 2013;Fairall et al., 2003). Wind speed data is discarded when the angle between the wind and the ship's sailing direction exceeds 90°. All energy fluxes were averaged every hour. R sd and R ld are positive downward, and other fluxes are positive upward. We also use the underway observation in the SCS in 2021 summer (for details, see Liu et al., 2023).

Gridded Data
Daily surface energy fluxes and meteorological variables fields from the fifth-generation ECMWF reanalysis (ERA5; Hersbach et al., 2020): the solar and thermal radiation fluxes, the two turbulent heat fluxes, sea surface temperature (SST), 2 m air temperature and dewpoint, 10 m and 950-hPa wind, and precipitation. Caution is needed when using sea surface energy flux in an atmosphere reanalysis, although some recent studies confirmed the reliability of ERA5 over the ocean (Pokhrel et al., 2020;Renfrew et al., 2021). Therefore, despite the different spatial-temporal coverage, we try to assess the ERA5 with the underway observation before analysis in this study.

Regression Analysis
The regression analysis is widely used in this study to show the variable's anomaly corresponding to QBWO. For the statistical significance test, we estimate the p-value based on a two-tailed Student's t-test with the effective degree of freedom calculated referring to Bretherton et al. (1999).

Turbulent Heat Flux Diagnosing
In ERA5 reanalysis, the sensible and latent heat flux on the ocean surface is given by (ECMWF, 2016): with ρ a the air density; C p the heat capacity of moist air; C H the turbulent exchange coefficient; V the wind speed at 10 m above the surface; g the gravitational acceleration; z the height of 2 m; T sk (T a ) the temperature of skin (2 m air); q sk the 98% saturated specific humidity at an air temperature equal to T sk (assuming that water vapor pressure near the sea surface is always saturated, and the salinity of the sea surface is 34 PSU); q a the specific humidity in the 2 m air calculated by dewpoint.
For the convenience of analysis, we simplified Equations 1 and 2 as follows: (a) the geopotential term gz/C p , which is two orders of magnitude smaller than T a -T sk , is neglected; (b) SST is substituted for the T sk ; (c) The sign of Q s and Q l reverses for expressing an intuitive physical process.
With these considerations, Q s and Q l can be given as follows: Here, the T s-a (q s-a ) represents the temperature (specific humidity) difference between the sea surface and 2 m air. To keep the consistency among fluxes and sea surface variables from ERA5 at each grid, we calculated the ρ a C p C H and ρ a C H by regressing VT s-a and Vq s-a onto Q s and Q l in Equations 3 and 4, respectively.
Next, we performed Reynolds decomposition onto V, T s-a , and q s-a to separate the contribution from dynamic (wind speed) and thermal (air-sea temperature or specific humidity) processes to surface turbulent heat flux anomalies: The overbar denotes the mean in MJJ, and the prime denotes the anomalies. The three terms on the righthand side of Equation 5 are the dynamic, thermodynamic, and second-order terms, and we named them Q sD , Q sT , and Q sS , respectively. Similarly, the three terms on the right-hand side of Equation 6 are Q lD , Q lT , and Q lS .

The QBWO Cases
The SCS summer monsoon in 2019 was established around the pentad 25-26, and the background wind was southwesterly in our research. In contrast, the spatial pattern of EOF2 shows northeast-southwest dipole patterns with variance concentrated 20°N, 117.5°E, marked as region B (Mode2), which refers to the meridional movement of the WPSH (Bi, 1989;Qian et al., 2020). Moreover, after checking the power spectral density of the original OLR series, we find the biweekly peak is statistically significant (95%) in regions A and B. From their time series, Mode1 was active from May to July except for late May, while Mode2 was inactive until June.
The two modes also appear in other years regardless of little differences, like in 2021 ( Figure S2 in Supporting Information S1). To show the representativeness of the 2019 case, we calculated the explained variance of the two modes in each summer's OLR field from 1979 to 2022, following the method of Thomson and Emery (2014).
The median values for the two modes are 17% and 10% regardless of the orthogonality in each year (Figures 1e and 1f). Besides, a slight change in the domain area or extending the period (e.g., from May to September) will not significantly alter the EOF results. Therefore, we suggested that the case in 2019 has at least partly captured the fundamental features of QBWO in summer SCS.

The Responses of Sea Surface Energy Fluxes
First, we assessed ERA5 referring to the underway observation and confirmed their reliability in the sea surface energy fluxes (Text S2 and Figure S3 in Supporting Information S1). In a positive (negative) phase of QBWO, the atmospheric column is more (less) transparent for solar radiation and emits less (more) thermal radiation back to the sea surface. Positive R sd anomaly occupied most SCS, with its maximum of about 90 W m −2 at region A and along the west coast of the Philippines (Figure 2a). R su anomalies own similar spatial patterns as R sd (Figure 2b). Sea surface albedo shows a significant but minor negative response (about 0.003, not shown). As a result, ocean-absorbed solar radiation responds significantly in QBWO. However, such input energy flux didn't alter the R lu significantly, which will be discussed later. R ld shows negative anomalies with a center around 115°E, 12.5°N (about −4 W m −2 ). Therefore, the spatial patterns of all radiation flux anomalies, except for R lu , are similar in Mode1 because they are all closely related to the thermal structure of the air column.
In contrast, the response of surface turbulent heat fluxes to QBWO is quite complicated. Being regressed by PC1, Q s shows evident negative anomalies of about −6 W m −2 within the region of 10-17.5°N, 115-120°E, and scattered positive ones (about 1 W m −2 ) along the coast of East Malaysia. Q s anomalies, with a max magnitude of about −30 W m −2 , are mainly concentrated along the west coast of the Philippines. We also calculated the explained variance of Mode1 for all sea surface fluxes. The results for R sd , R su , R ld , R lu , Q s and Q l are 9.1%, 4.4%, 3.5%, 1.4%, 3.2%, and 6.8%, being comparable to the ensemble of 1979-2022 summer, whose medians are 6.7%, 4.4%, 4.1%, 2.4%, 4.3%, and 6.9%, respectively.  The linkage between OLR and sea surface energy fluxes can also be confirmed in Mode2 (Figure 3). According to PC2, the regressed R sd displays positive loadings in the north and negative in the south with separation along 15°N, with its northern center around 122°E, 22°N, about 90 W m −2 . Anomalies of R su are similar, but those for R ld are opposite to R sd . R lu (and so for SST in Figure S5b in Supporting Information S1) anomalies under Mode2 are more significant and identical to R sd 's pattern than Mode1. However, because a positive SST anomaly and a negative Q s anomaly (about −7 W m −2 ) appear together, the SST anomaly in Mode2 will not destroy the anticyclone circulation anomaly. Q l anomalies in Mode2 are scattered, with negative ones concentrating around the Taiwan Strait and Bashi Strait (about −30 W m −2 ) and positive ones near some coastal seas.
Compared to Mode1, Mode2 caused a comparable response in sea surface energy fluxes, with explained variances of 7.4%, 5.8%, 5.1%, 5.1%, 3.6%, 3.5% for R sd , R su , R ld , R lu , Q s, and Q l in 2019 and similar results in other years (not shown). Since Mode1 represent a more predominant variation of OLR than Mode2 (Figure 1e), we suggested that sea surface fluxes will significantly impact the QBWO at a specific area of SCS (e.g., Region A seems more critical than Region B in 2019). Oceanic processes might have produced such spatial dependence, but we haven't found any evidence yet.
The imperfections of the assimilation system can bias the surface energy fluxes over the SCS in ERA5. Therefore, we need to check whether the sea surface energy flux's response can also be confirmed from observation. We focus on the difference in observational sea surface energy fluxes between positive and negative periods under Mode1. Two periods are picked when the magnitude of PC1 is beyond half of its standard deviation. The positive-phase period includes June 9 and 19-24 June, and the negative-phase one contains June 13-16 and June 27-July 3 ( Figure 1c).
All ERA5's radiation fluxes (except for the unresponsive R lu ) are relatively identical to observation. The observed R sd , R su , and R ld show equivalent comparisons between the positive and negative periods with ERA5, with median differences of 167, 11, and −5 W m −2 , respectively (Insets of Figure 2). Nevertheless, the median differences for sensible and latent heat fluxes are −2 and −11 W m −2 , smaller than ERA5's results, partly because the observation region is far from the turbulent heat fluxes anomalies center. The observation in 2021 (Text S3 and Figure S4 in Supporting Information S1) also gives similar results.

Radiation Fluxes
The circulation anomaly that emerges in the region of QBWO signal causes the local response of R sd , R su , and R ld . An anticyclonic circulation and subsidence cover the positive OLR anomaly regions, corresponding to sunny days with low cloud cover, weak R ld , and strong R sd . The air temperature anomalies on the Indochina Peninsula and the Philippines exceed 0.7°C under the positive phase of Mode1; in South China, they increase to 1.7°C under Mode2 (Figures S5c and S5d in Supporting Information S1). In contrast, cyclonic circulation appears in the negative phase, causing opposite responses of these radiation fluxes, cooling of land, and rain (2 mm/day) along the west coast of the Philippines under Mode1(not shown).
R lu anomalies in Mode2 (Figure 3d) are more significant and show more identities as R sd than in Mode1. The weak response in SST is beneficial for sustaining the atmospheric circulation anomaly because a positive SST anomaly will stimulate convective circulation and weaken the anticyclone circulation in a positive phase of QBWO (Bjerknes, 1966;Sabin et al., 2013;Waliser et al., 1993). In Mode1, the additional irradiance due to QBWO is stored in the deep ocean rather than near the sea surface. The SST responds more significantly under Mode2, especially around Taiwan Island, probably due to the more intensive ocean dynamics (Qiu et al., 2019) and the shallower mixing layer around Region B (Qu et al., 2007).

Turbulent Heat Fluxes
The response of turbulent heat flux to QBWO is opposite to OLR and shows more complicated spatial patterns.
To estimate the relative contributions of atmospheric thermal and dynamic processes to turbulent fluxes' perturbations, we regress the dynamic (Q lD and Q sD ) and thermodynamic (Q lT and Q sT ) terms from Equations 5 and 6 onto the OLR's PCs (Figure 4). We neglect the second-order terms because of their minor variation.
In Mode1, the change in surface wind mainly determines the spatial patterns of Q s and Q l anomalies. Negative Q sD and Q lD cover the region from the west coast of the Philippines to the latitudinal band around 10°N. The 10.1029/2023GL104288 8 of 11 superimposition of the QBWO-induced wind anomaly on background wind might determine surface wind speed, further affecting Q sD and Q lD (Figure 1a). For example, the direction of the QBWO-induced surface wind anomaly is opposite to the background southwesterly in the western coastal area of the Philippines, which produces an obvious negative Q sD and Q lD . In contrast, over the ocean east of the Indo-China peninsula, the negative Q lT largely cancels the contribution of Q lD , making Q l show little response to QBWO.
The discrepancy in underlying heating or cooling between ocean and land could also impact the surface wind through the thermal wind. Over the east of the Indo-China peninsula, the surface wind has experienced significant acceleration. In a positive phase of QBWO, the 2 m temperature anomalies are about 0.5 K in the east of the peninsula, while it barely changes over the neighboring coastal seas ( Figure S5c in Supporting Information S1). As a result, the ocean-continent thermal contrast generates a thermal wind against the wind anomaly from QBWO's Mode1 (Figure 1a), generating weak Q sD and Q lD . In contrast, on the west coast of the Philippines, the surface air temperature anomalies are about 0.5 and 0.3 K over the islands and the nearby seas, respectively, producing weak thermal wind there.
In Mode2, both Q s anomaly and Q sT show a northeast-negative and southwest-positive dipole pattern, indicating that the change in air-sea temperature difference mainly controls the Q s (Figure 4b). Q sT is always opposite to . The top and bottom panels are for Q s and Q l , respectively. The black, red, and blue contours denote the zero, positive, and negative values, respectively (intervals: 0.5 for Q sD ; 5 for Q lD ). Dotted and Bubbled areas are statistically significant for Q sD /Q lD anomalies (95%) and Q s /Q l (99%) anomalies.
OLR anomaly, especially for Mode2. The surface air warmed (cooled) more quickly than its capping sea surface within SCS under a negative (positive) phase period of QBWO ( Figure S5 in Supporting Information S1). For instance, the amplitudes of air temperature and SST variations are 0.19 K (0.36 K) and 0.06 K (0.18 K) under Mode1 (Mode2) averaged in region A (B), respectively. One potential cause might be the ocean's great thermal inertia.
The wind anomaly in Mode2 is much smaller and contributes less to the surface turbulent heat flux anomaly than in Mode1. However, compared with Q s , the spatial pattern of Q l in both modes is quite identical with Q lD , even in Mode2, indicating that surface wind might be a determinant for surface evaporation on a quasi-biweekly scale over the SCS.
When the ocean is heating and moistening (cooling and drying) its capping atmosphere, the atmosphere becomes unstable (stable) and intends to trigger (depress) convective circulation, corresponding to a negative (positive) anomaly of OLR. The sea surface turbulent heat fluxes, rather than SST, represent the ocean's heating/cooling and moistening/drying (Sobel et al., 2008). Since they both show opposite patterns to the OLR on the quasi-biweekly scale, their responses might be essential for the outstanding QBWO signal over summer SCS ). According to Krishnamurti and Bhalme (1976) and Webster (1983), the heavy summer rainfall around the SCS might be crucial for the strong QBWO there. From the discussions above, the summer SCS at least owns the other three advantages for QBWO: first, the unified strong northward background wind after the SCS monsoon onset, making the southward/northward surface wind anomaly most critical for surface wind speed ( Figure 1a); second, different continent-ocean thermal contrast between the east and west boundary of SCS ( Figure S5c in Supporting Information S1), making the wind anomaly to the west of Philippine most intensive and significant; third, in the oceans without significant surface wind responses, the thermal contrast between ocean and atmosphere is opposite to OLR's anomaly on a quasi-biweekly scale ( Figure S5 in Supporting Information S1). Among the three factors, the first and second contributes to half of the meridional water vapor transport (not shown) through modulating wind field in the lower troposphere, further affecting the associated condensation and radiation process within the air column. Therefore, the sea surface turbulent heat flux induced by QBWO helps maintain a surface wind anomaly, favoring the water vapor supply of QBWO-related condensation in return. Such a positive feedback loop might be essential for the QBWO in the SCS.

Summaries
Using daily OLR, we diagnose two modes of QBWO over the SCS during MJJ 2019: Mode1 with variance concentrated in 112.5-117.5°E, 10-15°N, and Mode2 with dipole patterns. Then, after evaluating the representativeness of ERA5 by underway observations, we examine the sea surface energy fluxes' responses to these modes and discuss the mechanism behind them.
R sd and R su share a similar spatial pattern with OLR in both modes and the sign of R ld anomaly reverse. The magnitude of R su and R ld anomaly is about 4%-8% of the irradiance, and R lu anomaly is insignificant in Mode1 but significant in Mode2, especially around Taiwan Island. In other words, although the main change of irradiance due to QBWO is stored in the ocean, the SST shows an insignificant response.
The response of Q s and Q l own peak magnitudes of about 6 and 30 W m −2 , respectively. Their patterns seem opposite to OLR, despite the spatial difference. Under Mode1, Q s and Q l are mainly controlled by surface wind, especially within 10-15°N, 115-120°E. In Mode2, the surface wind is less critical than the sea-air thermal contrast for Q s , and a dipole pattern of the Q s anomaly, with a negative center around Taiwan and positive one south of 15°N, can be found. Although Q l shows weak and scattered responses within SCS in Mode2, its spatial patterns seem to be determined by the surface wind.
The response in the sea surface turbulent heat fluxes to QBWO from Yang et al. (2021) is comparable to this study. Zhu et al. (2020) revealed a weaker R sd anomaly (60 W m −2 ) and a stronger Q l anomaly (−45 W m −2 ). The interannual variation of QBWO might have caused the differences (Mao & Chan, 2005). Meanwhile, SST evolution leads the convection cycle by a near-quadrature phase in these two studies, partly explaining the insignificant in-phase relationship between SST (and so for R lu ) and OLR in this study. From this study, sea surface turbulent heat fluxes' spatial patterns are essential to modulate the water vapor transportation and condensation associated with QBWO. To better understand the air-sea interaction within SCS, besides the sea surface, the physical process within the ocean (Roman-Stork et al., 2019), at least within the oceanic mixed layer, needs more concerns.