1. Introduction
Wind stress at the sea surface is the main driver of global ocean circulation, redistributing mass, momentum, and energy in the ocean (e.g., Gill 1982; Wunsch and Ferrari 2004). Moreover, representing the momentum flux between the atmosphere and the ocean, surface wind stress is one of the key factors controlling oceanic turbulent mixing and therefore exerts significant impacts on ocean temperature and salinity (e.g., Ouni et al. 2021; Zhou et al. 2018). Due to the nonlinear dependence of wind stress on wind, the high-frequency variability of winds has a large influence on low-frequency wind stress (e.g., Ponte and Rosen 2004; Zhai et al. 2012). Many studies have shown that the synoptic variability in surface winds makes a significant contribution to the mean wind stress, with far-reaching implications for ocean circulation and turbulent mixing (e.g., Duteil 2019; Lin et al. 2018, 2020; Ponte and Rosen 2004; Wu et al. 2016, 2020; Zhai 2013; Zhai and Wunsch 2013; Zhai et al. 2012). For example, Duteil (2019) found that removing synoptic winds (from 2 days to 1 month) in the tropical Pacific decreased the mean wind stress by up to 20%, weakening the wind-driven ocean circulation by 20%.
Likewise, neglecting subdaily wind variability may have severe effects on mean wind stress estimates (e.g., Eymard et al. 2003; Ledvina et al. 1993; Ouni et al. 2021; Zhai et al. 2012; Zhou et al. 2018). Based on ship/buoy measurements during March and April 1998 in the northwestern Mediterranean Sea, Eymard et al. (2003) evaluated the impact of the subdaily variability of air–sea parameters on air–sea flux estimates. They found a strong underestimation of the mean momentum flux when the vector-averaged winds were employed; the mean friction velocity decreased by 22% (Table 3 in their paper). Due to the nonlinear effect, subdaily winds exert significant impacts on wind power input to the ocean and ocean temperature and salinity at longer time scales (e.g., Lee and Liu 2005; Ouni et al. 2021; Zhai et al. 2012; Zhou et al. 2018). Zhai et al. (2012) showed that including subdaily winds in analyses led to a one-third increase in the estimated total wind power input to the ocean through an increased mean wind stress (Table 1 in their paper). Zhou et al. (2018) conducted sensitivity experiments using a one-dimensional ocean model at 15.5°N, 61.5°E and found that including subdaily signals in the wind field lowered the daily mean sea surface temperature (SST) by 0.8°C on average, primarily due to intensified wind stress magnitude and turbulent heat fluxes.
To date, however, the contribution of subdaily winds to the mean wind stress has not been quantified on a global scale. The Global Tropical Moored Buoy Array (GTMBA) provides long-term high-frequency (10 min and hourly) measurements of air–sea variables across the entirety of the tropical oceans (McPhaden et al. 2010), allowing us to address this problem. Buoy observations have been used to investigate some of the characteristics of subdaily winds, such as diurnal and semidiurnal cycles and wind gusts (e.g., Christophersen et al. 2020; Deser and Smith 1998; Giglio et al. 2017, 2022; Joseph et al. 2021; Serra et al. 2007; Turk et al. 2021; Ueyama and Deser 2008). Here, these data are used to investigate the relation between subdaily winds and the mean wind stress. Thus, the first objective of this paper is to systematically quantify the effects of subdaily winds on the mean wind stress magnitude across the entirety of the tropical oceans using GTMBA observations.
Given the importance of subdaily winds, their effect on the ocean has been taken into account in numerical simulations by employing wind forcing with subdaily variability (e.g., Ouni et al. 2021; Thushara and Vinayachandran 2014; Yu et al. 2020). Wind forcing with subdaily variability is largely available from the most recent atmospheric reanalysis products with hourly temporal resolutions, such as the fifth-generation ECMWF reanalysis product (ERA5; Hersbach et al. 2020) and the Modern-Era Retrospective analysis for Research and Applications product, Version 2 (MERRA2; Gelaro et al. 2017). However, the accuracy of subdaily winds in these reanalysis products is still unknown. Thus, the second objective of this paper is to evaluate the effect of subdaily winds on the mean wind stress magnitude in the ERA5 and MERRA2 reanalysis products.
A more efficient and less expensive approach to account for subdaily winds is to parameterize them by using a gustiness correction for the daily vector-averaged wind speed (e.g., Cronin et al. 2006; Praveen Kumar et al. 2012, 2013). For example, Praveen Kumar et al. (2012) proposed a climatological gustiness parameterization scheme related to SST and applied the gustiness correction to account for unresolved subdaily winds in the TropFLUX reanalysis product. An evaluation showed that including the gustiness correction increased the mean wind stress magnitude by ∼5% (Fig. 2d in Praveen Kumar et al. 2013). In this study, we relate gustiness to the precipitation rate, which has a close relation to the momentum flux associated with subdaily winds (see section 3). Two new gustiness parameterization schemes are proposed: one is time independent, similar to that of Praveen Kumar et al. (2012), and the other is time dependent. This is the third objective of this study.
This paper is structured as follows: after a short description of the data and methods in section 2, section 3 will present the major results of this study. First, the contribution of subdaily winds to the mean wind stress magnitude is estimated from the GTMBA observations, and then the effects of subdaily winds in the ERA5 and MERRA2 products are evaluated. Finally, two new parameterization schemes to represent unresolved subdaily winds are developed. Conclusions are drawn in section 4.
2. Data and methods
To estimate air–sea fluxes, the GTMBA observations are used as inputs for the Coupled Ocean–Atmosphere Response Experiment (COARE) 3.5 bulk flux algorithm (Edson et al. 2013). The GTMBA observations provide long-term, high-frequency measurements (10 min and hourly) of air–sea variables, including surface vector winds, surface air temperature and relative humidity, and water temperature near the surface (McPhaden et al. 2010). The 10-min measurements were averaged into hourly means before the flux estimate. For surface winds, we used vector averaging. More information about the GTMBA observations was provided in Yan et al. (2021, 2022).
Next, the wind stress magnitude induced by the mean daily wind vector is calculated using the COARE 3.5 algorithm [
Likewise, all the terms in Eq. (3) are estimated using the hourly ERA5 and MERRA2 reanalysis wind values to evaluate their performance. Note that the wind stresses estimated from ERA5 and MERRA2 are based on the COARE algorithm for the convenience of comparison with those derived from the GTMBA observations. However, wind stresses directly downloaded from these two reanalyses are estimated using their own algorithms. For example, the ERA5 air–sea fluxes are calculated using the ECMWF algorithm (ECMWF 2021). Therefore, the wind stress magnitudes of the reanalysis products in this study refer to our calculated wind stresses via the COARE algorithm.
Finally, we develop two new parameterization schemes to account for the effect of subdaily winds: one is time dependent, and the other is not. We use the gustiness approach, which has been widely applied to parameterize unresolved wind variability at different spatial and temporal scales (e.g., Bessac et al. 2019, 2021; Blein et al. 2020, 2022; Godfrey and Beljaars 1991; Hourdin et al. 2020; Redelsperger et al. 2000; Zeng et al. 2002). To establish the time-independent scheme, the climatological gustiness value (Gclim) is first calculated from the GTMBA observations per the methods of Cronin et al. (2006):
3. Results
We start by examining the mean surface wind stress magnitude obtained from the GTMBA observations (Fig. 1a). Spatially, the wind stress magnitude is relatively small in the calm equatorial belt, especially in the equatorial Indian Ocean, western Pacific, and equatorial cold tongue region of the Pacific and Atlantic, reaching amplitudes of less than 4 × 10−2 N m−2. In contrast, the wind stress magnitude is larger in areas farther from the equator, such as the trade winds region, where it reaches amplitudes of over 8 × 10−2 N m−2. Subdaily winds make a positive contribution to the mean wind stress magnitude (Figs. 1b,c), with an average contribution of 6.5 × 10−3 N m−2 (12.4%) in the tropics. The contribution is particularly large over the intertropical convergence zone (ITCZ), a region characterized by strong precipitation, and it increases to 8.4 × 10−3 N m−2 (17.4%) in regions with a surface precipitation rate greater than 5 mm day−1. The maximum percentage contribution from subdaily winds reaches 28.5% in the equatorial western Pacific, where the mean wind stress magnitude is small. The estimates from buoy observations suggest that subdaily winds have a nonnegligible effect on the mean surface wind stress magnitude over the tropics, especially over the ITCZ.
(a) Mean surface wind stress magnitude estimated from GTMBA observations. (b),(c) Contribution from subdaily winds to the mean wind stress magnitude and the corresponding percentage. Gray arrows and contours denote the satellite-derived mean surface wind stress in (a) and precipitation rate (mm day−1) in (b) and (c), respectively. The satellite-derived mean wind stress was calculated from the Scatterometer Climatology of Ocean Winds (SCOW; Risien and Chelton 2008).
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0156.1
The contribution from subdaily winds to the mean wind stress magnitude arises from four aspects, which are associated with the mean wind speed change, mean drag coefficient change, wind speed variance, and covariance between wind speed and the drag coefficient [see Eq. (3)]. The MWSC, MDCC, WSV, and CV terms are all estimated from the GTMBA observations and amount to 3.5 × 10−3, 0.8 × 10−3, 2.1 × 10−3, and 0.4 × 10−3 N m−2 (51.9%, 12.3%, 31.2%, and 7.8%), respectively, on average, using all buoy sites (Fig. 2). The two largest contributors are associated with the MWSC and WSV terms, which account for approximately 80% of the overall contribution. The other two terms, which are related to the variable drag coefficient, make an approximately 20% total contribution. Moreover, the MWSC and WSV terms exhibit significant spatial variations, with large values located over the ITCZ, while the spatial distributions of the other two terms are relatively uniform (see also Fig. S1 in the online supplemental material). The enhanced MWSC and WSV terms over the ITCZ are thus the main contributors to the increased wind stress magnitude in these regions. The spatial correlation coefficient between the MWSC (WSV) term and the total contribution is 0.98 (0.93). This result implies that the contribution from subdaily winds to the mean wind stress magnitude largely results from the MWSC and WSV terms, which are related to the change in the mean wind speed due to subdaily winds and the variance in subdaily wind speed variability.
All the terms in Eq. (3) estimated from the GTMBA observations: The total contribution (black curve, representing the values at all buoy sites as shown in Fig. 1b but ordered from west to the east and from south to north; the order is listed in Table S1; black dots on the x axis denote the buoys, and the corresponding labels are their longitudes), mean wind speed change term (red curve), mean drag coefficient change term (cyan curve), wind speed variance term (blue curve), and covariance term (green curve).
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0156.1
Having calculated the contribution of subdaily winds to the mean wind stress, we next investigate the total change in wind speed, averaged over the full record, that results from the subdaily winds (
(a) Change in the mean wind speed due to subdaily winds (
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0156.1
Linear relationship between the mean wind stress magnitude from subdaily winds and the kinetic energy of subdaily winds.
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0156.1
To evaluate the role of the subdaily winds in the most recent atmospheric reanalysis products, the contribution from the subdaily winds to the mean wind stress magnitude is calculated from ERA5 and MERRA2 data. Notably, both products underestimate the contribution of subdaily winds (Fig. 5a). The mean absolute percentage error (MAE) in the tropics is 51% and 63% for ERA5 and MERRA2, respectively, where MAE = |(reanalysis − observation)/observation| × 100%. The value of the error in the contribution corresponds to the errors for the MWSC and WSV terms (the two largest contributors), which are underestimated by 50% and 49% (61% and 64%) in the ERA5 (MERRA2) product (Figs. 5b,c). The underestimated MWSC and WSV terms in these two products arise from the underestimations of the mean wind speed change due to subdaily winds (the MAEs are 47% and 59%) and the variance in subdaily wind speed variability (the MAEs are 56% and 71%), which are associated with the underestimation of the (strength) kinetic energy of subdaily winds (the MAEs are 59% and 72%, Fig. 5d).
(a) Contribution from subdaily winds to the mean wind stress magnitude at all buoy sites. (b) Change in the mean wind speed due to subdaily winds (dashed curve) and the associated contribution (solid curve). (c) Variance in subdaily wind speed variability (dashed curve) and the associated contribution (solid curve). (d) Kinetic energy of subdaily winds. Black, red, and blue curves denote values estimated from the GTMBA observations, ERA5 product, and MERRA2 product, respectively. The x axes in (a)–(d) are the same as those in Fig. 2.
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0156.1
To assess in more detail the extent to which ERA5 and MERRA2 products underestimate the effects of subdaily winds relative to the GTMBA observations, we next examine the kinetic energy spectrum of winds. The kinetic energy spectrum is calculated by averaging the zonal and meridional wind power spectra, which are obtained using Welch’s overlapped segment averaging estimator with a 60-day Hamming window and 0% overlap. The results include peaks at diurnal (24-h) and semidiurnal (12-h) time scales (Fig. 6), which have been reported in previous studies (Deser and Smith 1998; Ueyama and Deser 2008). The corresponding diurnal and semidiurnal winds are induced by atmospheric tides and/or land–sea breezes (Christophersen et al. 2020; Takahashi 2012; Ueyama and Deser 2008). ERA5 and MERRA2 are capable of reproducing diurnal (84% and 77%) and semidiurnal (111% and 91%) winds. However, at other subdaily time scales, these two reanalysis products underestimate wind variability, and the estimation performance decreases as the time scale becomes shorter. For example, the MAE of kinetic energy is 48% (55%) between the 24- and 23-h time scales and increases to approximately 94% (100%) between the 3- and 2-h time scales in the ERA5 (MERRA2) product. The underestimation of the kinetic energy at these time scales results in underestimated subdaily winds in the ERA5 and MERRA2 products. A reason for the underestimated kinetic energy in atmospheric reanalyses is that, in numerical models, the energy in the highest resolved wavenumbers is damped due to the nature of numerical solutions and parameterizations (Abdalla et al. 2013; Bolgiani et al. 2022; Klaver et al. 2020; Skamarock 2004). The model’s effective resolution is typically 7 times the model grid spacing (Skamarock 2004). Recently, Bolgiani et al. (2022) showed that ERA5 has an effective resolution from 1300 to 1100 km in the tropical band and hence does not adequately capture mesoscale variability. In contrast, the buoy observations at fixed points reflect the contributions due to mesoscale spatial variability.
Kinetic energy spectrum of surface winds (variance-preserving plots, solid curve) and the ratio between the reanalysis estimates and observations (percentage, dashed curve). Black, red, and blue curves denote values estimated from the GTMBA observations, ERA5 product, and MERRA2 product, respectively.
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0156.1
Importantly, the underestimated contribution from the ERA5 (MERRA2) subdaily winds results in a 7% (8%) error in the mean wind stress magnitude, on average, in the tropics (black curve in Fig. 7). The error increases to 12% (14%) in the tropical western Pacific. The total underestimation of the mean wind stress magnitude is 11% (18%) in the ERA5 (MERRA2) product based on GTMBA observations (red curve in Fig. 7). The underestimation of the subdaily wind contribution accounts for 60% (44%) of the total error in the mean ERA5 (MERRA2) wind stress magnitude. This percentage ratio rises to 73% (88%) in the tropical western Pacific, implying that accurate simulations of subdaily winds in ERA5 and MERRA2 will greatly improve estimates of the mean wind stress magnitude in the tropics, especially in the tropical western Pacific.
Percentage error (red curve) of the mean wind stress magnitude in the (a) ERA5 and (b) MERRA2 products based on the GTMBA observations. The black curve denotes the percentage relative error associated with inaccurate subdaily winds. The x axes are the same as those in Fig. 2.
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0156.1
Regression model between the square of the gustiness value (G2) and precipitation rate (P) for the (left) time-independent and (right) time-dependent schemes.
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0156.1
4. Conclusions and discussion
Previous studies suggested that subdaily winds may contribute significantly to the mean surface wind stress, but direct estimates over the open ocean are lacking, and to date, there is no quantification of this contribution on a global scale. Here, the effects of subdaily winds on the mean surface wind stress magnitude were systematically quantified in the entirety of the tropical oceans using high-frequency measurements of air–sea variables from the GTMBA. We found that subdaily winds contribute 12.4% to the mean wind stress magnitude on average, and the contribution is large over the ITCZ. The magnitude of the contribution is primarily determined by the kinetic energy of subdaily winds. We also estimated the effect of subdaily winds on the mean wind stress vector (Fig. 9). The inclusion of subdaily winds clearly significantly enhances the mean stress vector. The zonal and meridional components increase by 3.2% and 9.4%, respectively. This suggests that including subdaily winds in climate models would improve their simulations of the equatorial current regime and the resultant simulated ocean variability.
Effect of subdaily winds on wind stress vector (red arrows). Black arrows denote the long-term mean wind stress vector. Red arrows are amplified by 10.
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0156.1
Thus, our study highlights the importance of subdaily winds for the total air–sea momentum flux in the tropics. Two state-of-the-art and widely used reanalyses, ERA5 and MERRA2, largely underestimate this effect by 51% and 63%, leading to 7% and 8% underestimations in the mean wind stress magnitude. Considering the importance of accurate wind stress estimates for simulating air–sea interactions, the identified biases are expected to have far-reaching implications for the simulated ocean and climate variability in models. Notably, the wind stresses derived from ERA5 and MERRA2 use the COARE algorithm, rather than their own bulk algorithms. To investigate the sensitivity to different algorithms, we also employ the ERA5 own algorithm (ECMWF algorithm) to estimate the effect of ERA5 subdaily winds. The estimated contribution of subdaily winds using the ECMWF algorithm is almost the same as that using the COARE algorithm (Fig. 10a). This finding suggests that our main conclusions are insensitive to the bulk algorithm. It is worth mentioning that the ECMWF algorithm slightly overestimates the contribution of the ERA5 subdaily winds with respect to the COARE algorithm (Fig. 10). The bulk formula [Eq. (1)] shows that the discrepancy between different bulk algorithms for estimating wind stress mainly relies on the parameterizations for drag coefficient and convective gustiness. The parameterizations for convective gustiness are the same in the COARE and ECWMF algorithms (Brodeau et al. 2017; also see black curve in Fig. 10b). Therefore, the discrepancy results from the different parameterizations for drag coefficient typically differ by approximately 15% between the bulk algorithms (blue curve in Fig. 10b; Bonino et al. 2022; Brodeau et al. 2017).
(a) Contribution from subdaily winds to the mean wind stress magnitude estimated from the GTMBA observation using the COARE algorithm (black curve) and from the ERA5 reanalysis using the COARE (red curve) and ECMWF (blue curve) algorithms. (b) Mean absolute percentage errors of the subdaily wind contribution (red curve), convective gustiness (black curve) and drag coefficient (blue curve) calculated using the ECMWF algorithm with respect to those calculated using the COARE algorithm.
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0156.1
To improve the representation of subdaily winds, two parameterization schemes related to precipitation were developed in this study: one is time dependent, and the other is not. These two new schemes have almost the same performance regarding the effect of subdaily winds, explaining ∼80% of the mean wind stress magnitude associated with subdaily winds. The inclusion of these parameterization schemes in climate models is expected to substantially improve simulations of large-scale climate variability. Note that there still exists an ∼20% underestimation of the subdaily wind contribution when using these two schemes. Further improvements may potentially be achieved by future analyses that develop schemes based on different variables and techniques, for instance, using machine learning approaches. However, these analyses are beyond the scope of this study.
Acknowledgments.
This work is supported by the National Natural Science Foundation of China (41976028, 42122040, and 42076016).
Data availability statement.
The GTMBA measurements are available at https://www.pmel.noaa.gov/tao/drupal/disdel/, the ERA5 reanalysis at https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5, the MERRA2 reanalysis at https://disc.gsfc.nasa.gov/datasets?project=MERRA-2, and the IMERG products at https://gpm.nasa.gov/data/directory.
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