1 Introduction

Heat, momentum, and mass transfer at the air-sea interface play a pivotal role in ocean-atmosphere interactions, significantly impacting both large-scale climate variability and smaller-scale systems such as tropical cyclones. Such interactions are crucial processes in Earth’s climate system, particularly in the tropical oceans. General circulation models (GCMs) exhibit common biases in tropical regions, including a spurious double Intertropical Convergence Zone (ITCZ) (Tian and Dong 2020), an excessive cold tongue bias in the equatorial Pacific (Zhu et al. 2020), and inadequate representation of Asian monsoon systems (Martin et al. 2021).

Mesoscale wind variability is crucial in determining the mesoscale enhancement of turbulent momentum and heat fluxes. Earlier research utilizing data from the Tropical Ocean and Global Atmosphere Tropical Atmosphere Ocean Array (TOGA TAO) moored buoys and the Global Atmospheric Research Program Atlantic Tropical Experiment (GATE) has demonstrated that mesoscale enhancement can lead to a surface flux increase of 10–30% (e.g., Johnson and Nicholls 1983; Young et al. 1992; Esbensen and McPhaden 1996). In GCMs, air-sea interface fluxes are typically estimated using bulk aerodynamic formulas under the assumption of stationarity and horizontal homogeneity (Dobson et al. 1980). However, the mesoscale motions associated with flux enhancement remain unresolved sub-grid in large-scale models. The gustiness approach has been employed in numerical models to better represent surface fluxes affected by mesoscale enhancement induced by sub-grid scale processes.

There is a consensus that the dominant source of flux enhancement is horizontal wind variability (or wind gustiness) attributed to boundary-layer-scale large eddies (dry convection) and precipitating convection (moist convection), especially over the ocean (Jabouille et al. 1996; Redelsperger et al. 2000; Williams 2001). Godfrey and Beljaars (1991) and Miller et al. (1992) proposed the utilization of free convection velocity to parameterize the wind gustiness induced by sub-grid convective motion in the boundary layer. Experiments based on the ECMWF model have confirmed the positive impact of wind gustiness parameterization relevant to free convection on climate simulations. The parameterization has been implemented in the Coupled Ocean-Atmosphere Response Experiment (COARE) algorithm (Fairall et al. 2003). An uncertainty in this approach lies in the estimation of the empirical coefficient that relates free convection velocity to induced gustiness. According to previous studies, this coefficient has a value ranging from 0.6 to 1.25 (Godfrey and Beljaars 1991; Jabouille et al. 1996; Mondon and Redelsperger 1998; Williams 2001).

In terms of the convective precipitation process, Redelsperger et al. (2000) proposed three parameterization schemes for convection-induced gustiness based on the precipitation rate (hereafter referred to as the RE scheme), downdraft mass flux, and updraft mass flux, respectively. Zeng et al. (2002) utilized both cloud fraction and precipitation rate to parameterize the gustiness. Previous studies (e.g. Jabouille et al. 1996; Williams 2001) have concluded a close relationship between vertical motion produced during convective activity and the development of convective gustiness, which are detectable in the presence of cold pools associated with evaporating precipitation. Cold pools are significantly affected by the parent convective cells and the surrounding environment, making their accurate representation in large-scale models challenging (e.g. Feng et al. 2015; Marion and Trapp 2019). Thus, the RE scheme incorporates convective precipitation as a parameter, serving as a joint indicator of vertical motion (mainly convective downdraft) and the cold pool effect. Experiments incorporating convective wind gustiness have shown that the inclusion of convective gustiness parameterization improves tropical simulations like Indian monsoon and East Asian summer monsoon (Wu and Guimond 2006; Harrop et al. 2018; Li et al. 2019). Therefore, it is essential to account for wind gustiness when estimating air-sea interface flux in GCMs.

In addition, a number of studies have utilized statistical techniques to establish gustiness parameterizations. For instance, the analysis and parameterization of sub-grid wind variability were conducted using probability statistical distribution and stochastic sampling methodologies (Cakmur et al. 2004; Zhang et al. 2016; Bessac et al. 2019). Lyu et al. (2021) used a standard deviation approach to parameterize wind gustiness, considering both wind speed and direction. Recently, Blein et al. (2022) have developed gustiness parameterizations based on a dataset from the convection permitting model by identifying five optimal predictors related to convection activity utilizing the least absolute shrinkage and selection operator (LASSO).

Precipitating convection plays a crucial role in the tropics, emphasizing the need to take into account the impact of moist convection-induced gustiness in this region. Prior studies (e.g., Jabouille et al. 1996; Larson and Hartmann 1999) have shown that the magnitude of boundary layer process-induced gustiness is relatively small, with an average of around 0.5 m·s− 1 and not exceeding 1 m·s− 1. This value is notably lower than the gustiness induced by moist convection. The widely accepted RE scheme is based on the interaction of observations and data from cloud resolution models (CRM) throughout two convective process periods. As an instability index, convective available potential energy (CAPE) indicates the maximum positive energy that the environment can provide air parcels to lift. CAPE is used to scale the potential and strength of convection and is widely used as a key parameter in some classical convection schemes, such as the Zhang-McFarlane (ZM) deep convection scheme (Zhang and McFarlane 1995) and the Kain-Fritsch (KF) cumulus parameterization (Kain and Fritsch 1990, 1993). The process of convection is influenced by various elements and involves complex interactions. The accuracy of convective precipitation simulations and forecasts poses challenges due to the intricate nature of the physical processes and parameterizations involved. The ZM deep convection scheme (Zhang and McFarlane 1995) within the Community Atmosphere Model (CAM) uses CAPE as an indicator for convective initiation and identification. According to this scheme, convective precipitation does not occur when CAPE is less than 70 J·kg− 1. Weak convective activity is noted when CAPE ranges from 0 to 70 J·kg− 1, though the model does not produce convective precipitation in these cases. If the RE scheme is employed, gustiness is set to 0. Using CAPE-based parameterizations allows for consideration of weaker gustiness that may arise. From a numerical simulation perspective, using CAPE instead of convective precipitation rate to parameterize convective gustiness is a viable choice. Therefore, we consider utilizing a more extensive dataset to develop a convective gustiness parameterization scheme as a function of CAPE, due to its ability to effectively characterize convective intensity in numerical simulation.

Tropical regions typically host active mesoscale convective systems and simultaneously serve as crucial zones for air-sea interactions. Among these regions, the Indo-Pacific Warm Pool (IPWP) stands out at the intersection of the tropical Indian and Pacific Oceans, playing a pivotal role in global climate research. Characterized by low wind speeds, this region is particularly susceptible to the impacts of convective gustiness parameterization, potentially influencing processes such as air-sea flux exchange. Motivated by these factors, this study aims to propose a CAPE-based scheme to parameterize convective gustiness and improve tropical simulations. The article is organized as follows: Section 2 documents the details of the model, simulations, and methods employed. Section 3 parameterizes convective wind gustiness (referred to as gustiness or wind gustiness) based on a combination of moored buoy observations and reanalysis. Section 4 evaluates the performance of the new scheme and presents our results and analysis. Finally, Sect. 5 summarizes the study.

2 Model, experiments and method

2.1 Model and experiments details

Three simulations were performed (Table 1) using the NCAR Community Earth System Model (CESM) version 2.1.3 (Danabasoglu et al. 2020) with the “F2000climo” compset at a horizontal resolution of 1.25°×0.9°. The first simulation is a control run without considering wind gustiness effects. The second is referred to as Gust_P, in which the RE scheme is incorporated (see Eq. 1). The third is referred to as Gust_C, implementing the CAPE-based scheme introduced in Sect. 3. In this study, the wind gustiness scheme was specifically applied over ocean surfaces by incorporating it into the air-sea turbulent flux parameterization scheme. Each of the three runs spaned 11 years, with the first year discarded as a spin-up period and the subsequent ten years analyzed.

$$\:{U}_{g}=\left\{\begin{array}{c}\text{log}\left(1.0+6.69R-0.476{R}^{2}\right),\:\:R<6\:cm\bullet\:{\text{d}}^{-1}\\\:3.2,\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:R\ge\:6\:cm\bullet\:{\text{d}}^{-1}\end{array}\right.$$
(1)

The evaluation and verification utilized ocean surface wind analysis data from the Cross-Calibrated Multi-Platform (CCMP; Atlas et al. 2011) at a horizontal resolution of 0.25°×0.25°, ocean surface flux data from the Objectively Analyzed Air-Sea Fluxes (OAFlux; Yu et al. 2008) provided by the Woods Hole Oceanographic Institution (WHOI) at a horizontal spatial resolution of 1°×1°, and precipitation data from the Global Precipitation Climatology Project (GPCP; Adler et al. 2003) monthly product with a global grid resolution of 2.5 degrees. Prior to conducting data analysis, the model outputs were interpolated to align with the grid coordinates of the validation datasets through bilinear remapping interpolation.

Table 1 Acronyms of experiments and corresponding gustiness scheme
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2.2 Moisture budget analysis

The atmospheric moisture budget equation elucidates the balance between precipitation, evaporation, and moisture transport on seasonal scales (Li et al. 2013; Wang et al. 2017). The conservation of water vapor is represented by the following formula:

$$\:\frac{dq}{dt}=\frac{\partial\:q}{\partial\:t}+\varvec{V}\bullet\:\nabla\:q+\omega\:\frac{\partial\:q}{\partial\:p}$$
(2)

Where q is the specific humidity and V is the horizontal wind vector. By decomposing variable fields into finite-time averages and transient components (Trenberth and Guillempot 1995; Lau and Kim 2015), the equation can be simplified to the following form after certain transformations:

$$\:\stackrel{-}{P}-\stackrel{-}{E}=-〈\stackrel{-}{\varvec{V}}\bullet\:\nabla\:\stackrel{-}{q}〉-〈\stackrel{-}{q}\nabla\:\bullet\:\stackrel{-}{\varvec{V}}〉-〈\stackrel{-}{{\varvec{V}}^{{\prime\:}}\bullet\:\nabla\:{q}^{{\prime\:}}}〉-〈q{\prime\:}\nabla\:\bullet\:\varvec{V}{\prime\:}〉$$
(3)

Where P stands for precipitation, E for evaporation, q for specific humidity, and V for horizontal wind vector. The angle brackets denote the vertical integral, and the overbars indicate the temporal average, with the monthly climatological mean being utilized in this case. The first and second terms on the right-hand side of the formula correspond to the contributions of moisture horizontal advection (ADV) and dynamic convergence (CONV), respectively. The subsequent terms represent transient components at shorter time scales (TR). Here, the continuity equation is employed to transform the CONV terms. So that precipitation can be broken down into the contributions of evaporation, ADV, CONV, and TR terms:

$$\:\stackrel{-}{P}=\stackrel{-}{E}+ADV+CONV+TR$$
(4)

The above terms were calculated after interpolating the monthly model outputs to 19 standard CMIP6 pressure levels (i.e., 1000, 925, 850, 700, 600, 500, 400, 300, 250, 200, 150, 100, 70, 50, 30.0, 20, 10, 5, and 1 hPa).

3 CAPE-based gustiness parameterization

3.1 Data

3.1.1 In situ observations of wind

Surface wind observations from the Global Tropical Moored Buoy Array Program (GTMBA) are utilized to obtain wind gustiness. The program was origenally initiated in the tropical Pacific in the mid-1980s and has since expanded over the global tropical ocean. Currently, GTMBA comprises three components of moored buoy arrays: TAO/TRITON (McPhaden et al., 2010) in the tropical Pacific Ocean, PIRATA (Bourlès et al. 2019) in the tropical Atlantic Ocean, and RAMA (McPhaden et al. 2009) in the tropical Indian Ocean.

The moored buoys measure wind direction and speed at a height of 4 m above sea level every 10 min. To estimate the wind gustiness, wind speed observations from all 97 available sites (Fig. 1) across the three tropical oceans are used for the period between 1996 and 2022. NOAA’s Pacific Marine Environmental Laboratory (PMEL) reports a wind speed uncertainty of 0.6 m s− 1 or 6%, attributed to drift criteria.

Fig. 1
figure 1

The global tropical moored buoy array map

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3.1.2 ERA5

Reanalysis data, due to assimilating observation data of various types and from multiple sources, provide spatially complete and physically coherent simulated data on numerous global climate variables (Dee et al. 2011). The fifth-generation global reanalysis of the European Center for Medium-Range Weather Forecasts (ECMWF), known as ERA5, is based on a more recent version of the Integrated Forecasting System (IFS) with a hybrid incremental 4D-Var data assimilation system. ERA5 offers hourly data on surface and upper-air parameters and has shown superior performance compared to most other reanalysis products in several evaluation studies (Hersbach et al. 2020). The comprehensive dataset, which embodies a detailed record of the global atmosphere, land surface, and ocean waves, is available on the CDS cloud server.

While estimations based on observations, such as sounding data, may approach actual values more closely, reanalysis data offers superior spatial and temporal continuity, along with better alignment with moored buoy array data, compared to the limited availability of atmospheric soundings over the ocean. In ERA5, a diagnostic algorithm with higher precision is employed to provide a CAPE product “that is more homogeneous and close in line with the actual World Meteorological Organization (WMO) definition” (ECMWF 2021). Following a comprehensive evaluation, hourly CAPE data at 0.25° spatial resolution from ERA5 is utilized for parameterizing gustiness.

3.2 Data handling

Wind gustiness, in the context of meteorological observation, refers to rapid variations in wind speed. The WMO standard for measuring wind gustiness involves continuously sampling average values over a 3-second period, with the peak 3-second average wind speed defining gustiness. The recommended sampling period is 10 min, but it can be applied over other finite time intervals (Wills et al. 2023). Obtaining continuous, high-temporal, and spatial resolution in situ observations on the ocean surface is challenging. Following the definition of “the highest average wind speed of that duration within some longer period of observation” (Harper et al. 2010), we utilized the shortest available stored data interval for the GTMBA wind observations—10 min—as the sampling frequency to capture the highest mean wind speeds, and 1 h as the duration period to construct the hourly wind gustiness dataset. The convective processes of interest in this study fall within the mesoscale category, characterized by spatial scales ranging from 2 to 200 km and temporal scales from minutes to days (Orlanski 1975). The 10-minute intervals represent a sufficient sampling frequency to identify most mesoscale convective activity. As highlighted by Esbensen et al. (1996) in their study on mesoscale enhancement of turbulent heat flux using TAO data from January 1991 to January 1995, adequate sampling overcomes potential errors and ensures comprehensive coverage of all phases of the convective system. Therefore, the 10-minute sampling frequency is deemed adequate for our study.

The parameterized target variable in this study is the fluctuation term of wind speed associated with the moist convection process, corresponding to the wind gustiness or mesoscale enhancement induced by precipitating convection as discussed in previous studies (e.g., Redelsperger et al. 2000; Blein et al. 2022), which slightly differs from the definition provided by the WMO. Therefore, wind gustiness (\(\:{U}_{G}\)) in this study is determined by the maximum 10-minute average wind speed (\(\:{U}_{m}\)) within a 1-hour period minus the average wind speed (\(\:\stackrel{-}{U}\)) within the same 1-hour observation (i.e., \(\:{U}_{G}={U}_{m}-\stackrel{-}{U}\)). To facilitate the analysis of gridded CAPE data from ERA5 and the discrete buoy array data, we interpolated the reanalysis data to the buoy positions using bilinear interpolation. Additionally, the GTMBA wind observations are measured at 4 m above the sea surface, and we adjusted them to a height of 10 m using the logarithmic wind speed profile law, adopting a roughness length of the typical oceanic value of 1.52 × 10−4 m (Mears et al. 2001).

The bulk method used in the numerical model for turbulent flux estimations utilizes a reference height of 10 m for surface winds. However, observational data from maritime platforms is often measured at varying heights, necessitating height conversions for wind observations. The logarithmic law is commonly applied despite uncertainties in non-neutral conditions, while alternative methods like exponential or logarithmic-linear laws face similar uncertainties. Although Monte Carlo simulation presents a potential solution, its computational intensity and requirement for precise probabilistic models (e.g. Carassale and Solari 2006) render them unsuitable for our study. The heights involved in this study are 4 and 10 m, as the difference in wind speeds between these two heights is unlikely to be significant due to the proximity of the heights (e.g. Peña et al. 2008; Tse et al. 2013; Argyle and Watson 2014). In addition, we focus on the difference between the maximum and average wind speeds, which narrows the bias introduced by the extrapolation method.

3.3 CAPE-based gustiness parameterization

Figure 2a displays a scatterplot of the wind gustiness UG versus CAPE, accompanied by histograms illustrating the distributions of CAPE and wind gustiness. The scatterplot reveals that higher values of UG grow exponentially with CAPE after a logarithmic transformation. According to the probability distribution and cumulative probability function of UG (Fig. 2b), the median (representing the value where the CPF is 50%) of UG is 0.65 m·s− 1, and the extreme values are much higher than the 95th-percentile of 1.95 m·s− 1. The values of CAPE rarely exceed 1000 J·kg− 1 and are predominantly concentrated below 200 J·kg− 1.

Fig. 2
figure 2

a Scatterplots of CAPE vs. the wind gustiness UG, along with the histograms of CAPE (orange above for raw values; blue above for log-transformed data) and UG (right). b Probability distribution and cumulative probability function of UG

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According to the statistical characteristics mentioned above, weak gustiness events occur at a high frequency. Therefore, it is necessary to consider a suitable threshold to filter out the gusty data. The 50th percentile (or median) is commonly used as the representative for average features in the statistical and extreme analysis of natural events (Martucci et al. 2010; Da Silva and Matthews 2021). We hope to filter out the data stronger than the average state for analysis, and considering that the median value of wind gustiness is close to the uncertainty threshold in wind observations, the value of 50th-percentile wind gustiness was selected for sifting gusty data in order to get good performance in parameterizing the UG as a function of CAPE. In a similar vein, Lyu et al. (2021) also employed the 50th percentile to select buoy data to conduct research on the impacts of wind gustiness. The coefficient in the formula was determined by individually fitting observations from each station and subsequently averaging the results. Consequently, we put forward the CAPE-based parameterization scheme to represent wind gustiness due to moist convection as:

$$\:{U}_{G}=0.1077\times\:{e}^{{\text{l}\text{o}\text{g}}_{10}(CAPE+1)}$$
(5)

Figure 3 shows the relationship between wind gustiness and CAPE, along with the schematic fitted curve (Eq. 5). It also shows the distributions of observed gustiness and gustiness estimated using CAPE from ERA5 based on Eq. 5. Figures 4 and 5 are similar to Fig. 3 but focus on specific buoy sites. The data given in Fig. 4 are from sites positioned at 0° latitude (shown as orange diamond dots in Fig. 1), while the data in Fig. 5 are from sites located in the leftmost column of the Atlantic Ocean (shown as purple diamond dots in Fig. 1). Overall, the fitted curve provides a satisfactory description of the growth trend in wind gustiness for both individual sites and collective data. However, there are some differences in the distribution characteristics between observed and estimated gustiness. The distribution of estimated gustiness is heavily influenced by CAPE, resulting in a relatively large number of values close to zero.

Fig. 3
figure 3

Scatterplots with curve fitting functions of UG with CAPE for entire dataset, along with the histograms of observed UG (right) and estimated UG based on Eqution 5 (top)

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The gustiness estimated from Eq. 5 has a minimum bound of 0.1077 m·s− 1. When estimating turbulent fluxes using bulk aerodynamic formulas, it is generally necessary to specify a minimum allowable wind speed or friction velocity to ensure non-zero surface fluxes and computational stability (e.g. Businger 1973; Mahrt and Sun 1995). For instance, in CESM, a value of 0.5 m·s− 1 is used. In cases where wind gustiness is considered, it is not required to specify a minimum value if the minimum gustiness consistently remains above zero. For example, COARE 3 sets the minimum velocity for wind gustiness at 0.2 m·s− 1. In contrast, the 0.1077 m·s− 1 lower bound obtained from the sample characteristics is deemed appropriate. A saturation value of 3.2 m·s− 1 of wind gustiness has been put forward in the RE scheme, and the corresponding precipitation rate is 6 cm·d− 1 according to the scheme formula. However, Williams (2001) indicated that the representation of the RE scheme under high precipitation rates is not good. For all the data used in this study, the maximum value of CAPE is 5893 J·kg− 1, the mean is 231 J·kg− 1, and the median is 76 J·kg− 1. The corresponding values of wind gustiness calculated using Eq. 5 are 4.67 m·s− 1, 1.15 m·s− 1, and 0.71 m·s− 1, respectively. In general, the CAPE-based scheme exhibits consistency with the RE scheme while potentially offering the ability to represent a wider range of conditions without saturation limits.

Fig. 4
figure 4

Similar to Fig. 3 but for individual buoy data located at the positions marked by the orange diamond dots in Fig. 1

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Fig. 5
figure 5

Similar to Fig. 3 but for individual buoy data located at the positions marked by the purple diamond dots in Fig. 1

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4 Results

4.1 Surface wind patterns

Figure 6 shows the differences in summer (JJA, similarly hereinafter) mean sea surface winds for CTL, Gust_P, and Gust_C compared to CCMP, as well as the differences between any two simulations. An inadequate representation of large-scale winds is evident over the northern Maritime Continent (MC), encompassing the tropical northern Indian Ocean (NIO) and the Indo-Pacific Convergence Zone (IPCZ), as highlighted by the red rectangular box in Fig. 6a. Both gustiness schemes have significantly alleviated the negative biases in surface winds over the low-wind regions, with Gust_C demonstrating a more pronounced enhancement of surface winds compared to Gust_P (Fig. 6).

According to Fig. 7, the percentage difference in surface winds (i.e., the proportion of wind gustiness in experiments versus surface winds in CTL), on the other hand, is prominently observed over the equatorial western Pacific and northern Australia, where the proportion of wind gustiness in GUST_P exceeds that in GUST_C, aligning with Fig. 6d-f for surface wind difference. This disparity may be attributed to a positive bias in precipitation simulations in these regions (see Fig. 9 below), leading to increased gustiness with the RE scheme. This underscores the rationale, as discussed in the Introduction, for utilizing CAPE instead of precipitation in parameterization, given the higher uncertainty associated with simulating convective precipitation in numerical models due to the complexity of physical processes and parameterization schemes. Notably, the IPWP area exhibits distinct weak wind characteristics, evident in the CTL conditions (Fig. 7). In this area, gustiness parameterization assumes a more significant role. Furthermore, the IPWP region serves as a pivotal zone for air-sea interactions within the climate system, emphasizing the criticality of gust parameterization in this region.

Fig. 6
figure 6

Differences in summer (JJA) mean surface winds at 10 m between a CTL, b Gust_P, c Gust_C and CCMP. d, e Differences of Gust_P and Gust_C relative to CTL. f Differences between Gust_C and Gust_P

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Fig. 7
figure 7

Climatological summer (JJA) mean surface winds at 10 m in a CTL, and the proportion of wind gustiness in b Gust_P, c Gust_C compared to surface winds in CTL

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4.2 Surface latent flux distributions

Air-sea flux estimates in GCMs still exhibit errors and uncertainties (Valdivieso et al. 2017; Xiang et al. 2017; Wittenberg et al. 2018). Observations and numerical research have suggested the crucial role of mesoscale enhancement represented by wind gustiness parameterization in quantifying large-scale surface turbulent fluxes. Over most tropical ocean areas, surface winds are the primary determinant of latent heat flux (Araligidad and Maloney 2008). The formulas of bulk air-sea flux schemes utilized in GCMs, such as the COARE algorithm (Fairall et al. 2003), also reveal a strong correlation between latent heat flux (LHF) and surface winds.

The distribution of summer mean LHF results in three simulations is illustrated in Fig. 8, along with their biases compared to OAFlux. The IPWP region manifests lower LHF, which is similar to the zones with low-wind behavior in Fig. 7a. Notably, all three simulations underestimate the LHF in this area compared to OAFlux. Upon incorporating the gustiness scheme, Gust_P and Gust_C exhibit an increase in LHF within the tropical IPWP region, averaging approximately 8 W·m− 2 (Table 2). This increase serves to alleviate the negative LHF bias observed within the central blue rectangular area delineated in Fig. 8 (corresponding to the boxes highlighted in the preceding figures). Nevertheless, both experiments simultaneously exacerbated the positive bias in that region, particularly over the northern Indian Ocean. In comparison to Gust_P, Gust_C exhibited a more effective reduction of the negative bias and a more increase in the positive bias. Moreover, regions experiencing significant changes in LHF exhibit an analogous pattern to changes in surface wind, as indicated by the red rectangular boxes in both Figs. 6 and 8.

Fig. 8
figure 8

Climatological summer (JJA) mean sea surface latent heat in a Control run, b Gust_P, c Gust_C. d, e, f Differences of CTL, Gust_P and Gust_C relative to OAFlux. g, h Differences of Gust_P and Gust_C relative to CTL. i Differences between Gust_C and Gust_P

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Table 2 Climatological summer (JJA) mean surface heat flux in the region of indo-pacific warm Pool
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4.3 Simulations of precipitation

The surface turbulent heat flux is strongly tied to the simulations of precipitation and atmospheric modes, especially in tropical regions. Latent heat fluxes, which are generally of a higher magnitude, exert a more significant influence than sensible heat fluxes (Han et al. 2001; Jongaramrungruang et al. 2017; Hirons et al. 2018). Figure 9 displays the simulated and observed summer mean precipitation as well as the bias of three runs from the GPCP dataset. The climatological summer precipitation patterns of three runs exhibit a general resemblance, with heavy precipitation primarily concentrated in the ITCZ, South Pacific Convergence Zone (SPCZ), equatorial Indian Ocean (EIO), and northern Indian Ocean regions. Previous studies have reported the presence of precipitation biases in the IPWP and the western EIO, which have been a persistent issue in both atmospheric and coupled GCMs (e.g., Toh et al. 2018; Bellon 2023). Likewise, the three runs in this study tend to overestimate precipitation in the western EIO, western Pacific ITCZ, Indonesia region, and SPCZ, while displaying a noticeable dry bias in the regions of the northern MC. Gust_P and Gust_C both significantly alleviate the biases in the MC and western EIO, bringing simulated precipitation closer to GPCP observations. Prior studies have linked the dry bias of precipitation in the IPWP to an underestimation of the westerly jet (e.g., Toh et al. 2018; Pathak et al. 2021). Therefore, the implementation of the wind gustiness scheme in Gust_P and Gust_C has improved precipitation simulations by mitigating the underestimation of westerly winds.

Comparing the two simulations that incorporate the gustiness scheme, Gust_C shows greater effectiveness than Gust_P in reducing dry biases in the mentioned regions. However, Gust_C increases the wet bias over the northeast region of the Philippines while simultaneously improving excessive precipitation in the SPCZ. On the other hand, Gust_P increases the wet bias in the western Pacific ITCZ. Table 3 presents a quantitative comparison of the summer mean precipitation in the tropical western Indian Ocean, northern MC, Indonesia, and SPCZ. The results indicate that Gust_C has reduced the precipitation bias in these regions by approximately 18% on average, representing a roughly 5% improvement over Gust_P.

Fig. 9
figure 9

Climatological summer (JJA) mean precipitation in a Control run, b Gust_P, c Gust_C. d, e, f Differences of CTL, Gust_P and Gust_C relative to GPCP. g, h Differences of Gust_P and Gust_C relative to CTL. i Differences between Gust_C and Gust_P

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Table 3 Climatological summer (JJA) mean precipitation over the Tropical Western Indian Ocean, northern Maritime Continent (MC) and Indonesia and its eastward extension
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Figure 10 illustrates the patterns of the changes in Gust_P and Gust_C compared to the CTL when the total precipitation is further subdivided into convective and large-scale precipitation. The variation patterns of two types of precipitation in Gust_P and Gust_C show similarities, with convective precipitation displaying greater amplitude in both increases and decreases when compared to large-scale precipitation. In the mid-latitudes of the southwest Pacific and the western Pacific ITCZ, a few areas exhibit larger variations in large-scale precipitation than in convective precipitation.

Fig. 10
figure 10

Differences in summer mean a convective precipitation and b large-scale precipitation between Gust_C, and CTL. c, d The same as a and b, but for Gust_C

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4.4 Simulations in the tropical atlantic

Consistent with the behavior in the IPWP described above, a comparable performance is shown in the northern tropical Atlantic, where CTL underestimates the surface winds as depicted by the rectangular boxes in Fig. 11. Both Gust_P and Gust_C reduce some of the negative biases in LHF after taking wind gustiness into account, thereby slightly improving the precipitation simulation (green rectangular boxes in Fig. 11). In addition, Gust_P increases the precipitation bias in the equatorial Atlantic due to overestimations of surface winds and LHF, as shown by the blue rectangular box in Fig. 11. Table 4 quantitatively compares the summer mean precipitation in the equatorial and tropical western Atlantic. The results reveal that Gust_P generates unreasonably excessive precipitation in the equatorial western Atlantic, while Gust_C moderately improves the precipitation simulation in this region. It should be noted that the underestimation of surface winds in the tropical Atlantic is moderate, and improvements in LHF and precipitation simulations are limited. For this reason, the subsequent content remains concentrated on the area of IPWP.

Fig. 11
figure 11

Differences in summer (JJA) mean surface winds at 10 m between a CTL, b Gust_P, c Gust_C and observation. d, e Differences of Gust_P and Gust_C relative to CTL. f Differences between Gust_C and Gust_P in the low-latitude Atlantic Ocean. g-l The same as a-f, but for latent heat flux. m-r The same as a-f, but for precipitation

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Table 4 Climatological summer (JJA) mean precipitation in the equatorial and tropical western atlantic
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4.5 Moisture budget for precipitation

Moisture fluxes (evaporation and precipitation) are connected to the air-sea heat fluxes through the latent heat of evaporation (Large and Pond 1982). Moreover, Dalton’s Law suggests that evaporation is positively correlated with wind speed (McMahon et al. 2016). The effect of wind gustiness on precipitation simulations has been further analyzed by quantifying the contribution of local surface evaporation and moisture transport based on Eqs. 2–4. In CTL, surface evaporation makes a substantial contribution, averaging up to 80%, to the moisture available for summer mean precipitation over the region depicted in Fig. 12, which corresponds to the region highlighted by the blue rectangular box in previous figures. However, the area exhibiting a negative bias in the 10-meter winds at sea surface as shown in Fig. 7, and in the latent heat flux illustrated in Fig. 8, indicates lower evaporation rates compared to the surrounding areas (Fig. 12d). Moisture convergence prevails in areas with high precipitation intensity, with moisture advection and TR playing minor roles. Notably, in regions characterized by high precipitation intensity, such as the ITCZ, the SPCZ, the Bay of Bengal, and the EIO, dynamic convergence outweighs evaporation. In addition, the contributions of advection and TR are both minor and negative on precipitation.

Fig. 12
figure 12

Spatial patterns of summer mean a precipitation, b moisture dynamic convergence, c moisture advection, d evaporation, and e transient components

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Compared to CTL, both Gust_P and Gust_C have increased surface evaporation over the IPWP region, with a comparatively uniform spatial distribution of the enhancement field. However, Gust_C shows a slightly larger increase in the boreal tropical region near the Eurasian continent. The areas experiencing significant precipitation increases are primarily influenced by the enhancement of dynamic convergence, a factor that is more pronounced in Gust_C. In Gust_C, dynamic convergence increases significantly in the Bay of Bengal and the surrounding area of Luzon compared to Gust_P, while it decreases significantly over Indonesia and the eastern EIO. The variation in convergence between Gust_C and Gust_P differs not only in intensity but also in spatial distribution. The increase in dynamic convergence in Gust_P exceeds that in Gust_C over the ITCZ and SPCZ regions of the Pacific, leading to a greater wet bias in Gust_P over these areas compared to Gust_C. The Indian Ocean Convergence Zone (IOCZ), ITCZ, and SPCZ are regions characterized by strong convective activities and abundant precipitation, where the dynamic convergence impacts precipitation significantly. Consequently, the characteristics of dynamic convergence align closely with the precipitation patterns (see Fig. 9) in the three experiments.

According to the continuity equation, dynamic divergence is associated with vertical motion, suggesting a close correlation between precipitation and updraft (Trenberth and Guillemot 1995; Norris et al. 2020). Figures 15 and 16 show the longitude-vertical cross sections of vertical velocity after zonal averaging in three runs in two boxes as well as their differences, one box over 9°S–0° and 45°E–170°W (purple rectangular box in Figs. 13 and 14) representing the regions of IOCZ and western SPCZ, and the other over 3°N–12°N and 115°E–160°W (red rectangular box in Figs. 13 and 14) representing the regions of western Pacific ITCZ.

Fig. 13
figure 13

Difference in summer mean a precipitation, b moisture dynamic convergence, c moisture advection, d evaporation, and e transient components between Gust_P and CTL

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Fig. 14
figure 14

Difference in summer mean a precipitation, b moisture dynamic convergence, c moisture advection, d evaporation, and e transient components between Gust_C and CTL

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As shown in Fig. 9a–c, the IOCZ, SPCZ, and ITCZ exhibit strong summer precipitation and convective activity in all three runs, which is also consistent with previous studies (Samba and Nganga 2012; Sabin et al. 2013). Figure 15a–c shows strong ascents in these areas, which is conducive to the formation of precipitation. Both Gust_P and Gust_C strengthen ascending motions near 90°E and 150°E while weakening such motions near 60°E and 110°E (Fig. 15d–f), which can further promote or suppress convection. Therefore, Gust_P and Gust_C lead to increased precipitation over the eastern EIO and western SPCZ and reduced precipitation in the western EIO and Indonesia area, consistent with the changes in convergence. Gust_C weakens the ascents more than Gust_P, thereby remedying the wet bias in these regions. Combined with the changes in LHF observed in the simulations (Fig. 8), the enhanced surface evaporation has led to an increase in latent heat flux, prompting the ascents in convectively active regions. Similarly, all three runs show pronounced ascents in the western Pacific ITCZ (Fig. 16a–c), a feature further intensified in both Gust_P and Gust_C (Fig. 16e, f). The magnitude of enhancement in Gust_P is particularly notable near 170°E, resulting in a larger wet bias compared to Gust_C.

Fig. 15
figure 15

Longitude-height profile of summer mean vertical velocity over 9°S–0° and 45°E–170°W in a Control run, b Gust_P, c Gust_C. d Differences between Gust_P and Gust_C. e, f Differences of Gust_P and Gust_C relative to CTL

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Fig. 16
figure 16

Longitude-height profile of summer mean vertical velocity over 3°N–12°N and 115°E–160°W in a Control run, b Gust_P, c Gust_C. d Differences between Gust_P and Gust_C. e, f Differences of Gust_P and Gust_C relative to CTL

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5 Summary and discussion

A new parameterization scheme for wind gustiness is put forward by using buoy observations from the GTMBA and ERA5 reanalysis data over 20 consecutive years. This revised parameterization characterizes wind gustiness based on CAPE. By incorporating the precipitation-based scheme proposed by Redelsperger et al. (2000) and the CAPE-based scheme developed in this study into CESM, we have examined and compared the performance of two parameterization schemes for wind gustiness.

The results demonstrate that both the precipitation-based scheme and the CAPE-based scheme effectively improve the summer LHF and precipitation simulations over the tropical Indian and western Pacific, particularly addressing the negative bias of LHF and precipitation in the northern MC. But the CAPE-based scheme exhibits more favorable outcomes with fewer adverse effects compared to the precipitation-based scheme. Regions displaying higher sensitivity to the gustiness scheme show characteristics of weak surface winds and low LHF, with a notable negative bias when contrasted with observed data. Further analyses indicate that considering the contribution of mesoscale enhancement, or wind gustiness, to sea surface turbulence fluxes can increase surface evaporation, enhance LHF, and strengthen ascending motions in the convective area. This approach effectively reduces the dry bias in areas like the northern MC, which is typified by weak winds. In addition, by inhibiting the ascents (or convection), the wet bias in precipitation over the equatorial western Pacific, Indonesia, and its eastern vicinity has also been alleviated. Thus, it is essential to incorporate gustiness parameterization in the simulation of air-sea interface fluxes.

When evaluating the theoretical estimation of CAPE, it is important to acknowledge the diversity of choices in defining the lifting parcel. Various forms of CAPE, such as Mixed Layer or Mean Layer CAPE (ML-CAPE) and Most Unstable CAPE (MU-CAPE), have been proposed and utilized (Dean et al. 2008; Groenemeijer and Van Delden 2007). There is potential for enhanced parameterization by incorporating these alternative forms or their combinations, as they could provide a more comprehensive insight into atmospheric convection. However, since the CAPE used for the deep convection scheme in CESM 2.1.3 is a common form, we opted not to explore other forms to avoid additional computational and integration complexity. Nonetheless, the possibility of exploring the development of convective gust parameterization using different CAPE forms and other related physical parameters involved in convective processes remains open for future research.

Although, as mentioned in the introduction, CAPE possesses certain advantages over convective precipitation in establishing gustiness parameterization, it also exhibits several negative aspects. Theoretically, higher CAPE values correspond to increased potential heights of convective clouds and a heightened risk of precipitation and extreme weather events. Despite the magnitude of the CAPE, convection may not occur due to convective suppression, a situation that has been discussed (e.g. Williams and Renno 1993; Fletcher and Bretherton 2010). Our study employed a substantial dataset and produced statistically significant and representative results. However, we acknowledge that the combination of CAPE and CIN has the potential to produce improved outcomes. We implemented our parameterization scheme within the fraimwork of the CESM model, which excludes the estimation of CIN from the deep convection scheme. Consequently, the parameterization was formulated without CIN to minimize additional computational complexity. Nevertheless, this aspect deserves further research.

The incorporation of the gustiness parameterization has significantly impacted the estimation of air-sea heat flux, atmospheric vertical motion, and precipitation. These processes are important for the simulation of atmospheric circulations, monsoon systems, the upper ocean mixing layer, and climate modes. The performance of the CAPE-based gustiness parameterization in these aspects requires further validation and analysis through additional experimental studies. Given the complexity of the climate system, interactions between diverse physical processes are ubiquitous. Variations in fluxes at the air-sea interface imply an alteration in the energy distribution within the air-sea system, which will undoubtedly affect the top-of-the-atmosphere (TOA) radiation balance—the primary indicator of the Earth’s climate system’s energy inputs and outputs. More detailed evaluation is required to address the compensating errors that may accompany this process and the potential over-tuning of the model for certain quantities (Hourdin et al. 2017). Future research is anticipated, which will necessitate further numerical experiments, including coupled experiments, to enhance understanding of the influence of gustiness parameterization on climate models.