Offshore Migration of Summer Monsoon Low‐Level Jet on a Diurnal Scale

This study investigates the diurnal migration of the low‐level jet (LLJ) over the Bay of Bengal in the summer monsoon, which remains understudied despite the well‐documented diurnal offshore propagation of rainfall worldwide. The southwesterly LLJ exhibits maximum strength during the night and morning. The LLJ undergoes a substantial eastward migration of approximately 600 km from the eastern offshore of India at midnight to the center of the Bay of Bengal by afternoon. A linear land‐sea breeze model is effective in capturing the diurnal migration with similar speed and phase. Including background wind offshore extends the migration, rather than confining it to the coast. This migration is driven by inertia‐gravity waves arising from the diurnal land‐sea thermal contrast and is influenced by the westerly upstream wind from the Indian subcontinent. Our results have important implications for understanding diurnal monsoon circulations and their associated precipitation.


Introduction
Diurnal variation in rainfall and wind is a widespread and well-documented phenomenon that is primarily driven by solar radiation.Typically, rainfall reaches its maximum in the afternoon on land and at night over the ocean (Johnson, 2011).Coastal regions experience alternating sea breeze and land breeze that also exhibit diurnal variation (Rotunno, 1983).Intense low-level winds near coasts, known as coastal low-level jets (LLJs), also have diurnal variations (Du et al., 2015(Du et al., , 2022;;Kong et al., 2020;Lima et al., 2022;Stensrud, 1996).
A notable diurnal phenomenon is the offshore propagation of rainfall and winds observed off coasts globally (Du & Rotunno, 2015;Fang & Du, 2022;Mapes et al., 2003;Peng & Chen, 2023;Yang & Slingo, 2001;Yang & Smith, 2006;Yokoi et al., 2017).Yang and Slingo (2001) identified strong diurnal signals spreading out from the land to sea in the Bay of Bengal, New Guinea and Mexico.Fang and Du (2022) found this offshore propagation primarily occurs at low latitudes, and is explained by inertia-gravity waves resulting from diurnally varying thermal contrast near tropical or subtropical coasts.This theoretical examination of this mechanism uses a linear theory of land and sea breezes (Drobinski et al., 2011;Jiang, 2012;Qian et al., 2009;Rotunno, 1983).The land-sea breezes manifest as either inertia-gravity waves at low latitude or trapped circulations at high latitude, determining whether diurnal signals propagate offshore or are in phase (Du & Rotunno, 2015).Background winds can also impact offshore propagation by changing inertia-gravity wave patterns (Du & Rotunno, 2018).
In the South Asian monsoon region, satellite observations in the Bay of Bengal have revealed the offshore co-propagation of winds and diurnal rainfall signals from the east coast of India into the Bay of Bengal at a speed of around 18 m s −1 , and the maximum convergence of surface wind precedes the maximum rainfall by 1-2 hr, indicating the presence of inertia-gravity waves driven by diurnal thermal contrast between Indian subcontinent and the Bay of Bengal (Kilpatrick et al., 2017).Li and Carbone (2015) found that mid-tropospheric westerlies facilitate eastward propagation from India but hinder westward propagation from Burma because strong onshore winds make the inertia-gravity wave dissipate owing to Doppler effect.
During the summer, the Bay of Bengal experiences low-level monsoon flows that come from India and turn northeastward (Fujinami et al., 2020(Fujinami et al., , 2022)), forming a strong southwesterly coastal LLJ (Figure 1a).Previous studies have documented that the LLJs over the Indian subcontinent exhibit a pronounced diurnal cycle with a nocturnal maximum, due to reduced frictional force and inertia oscillation of the winds (Blackadar, 1957;Chen, 2020).However, the control mechanism of diurnal variation of the marine LLJ over the Bay of Bengal remain unclear.This study hypothesizes that diurnal heating over India may influence the coastal LLJ via inertia-gravity waves, and the core location of the coastal LLJ may be modulated on the diurnal scale by such waves.This study aims to address the yet-to-be-documented question of whether the diurnal migration of LLJ over the Bay of Bengal exists and what factors affect this migration.

Data
The fifth generation of the European Centre for Medium-Range Forecasts (ECMWF) global climate atmospheric reanalysis, ERA5, is employed to examine the diurnal variability of the monsoon LLJ and its associated atmospheric processes.The high spatial and temporal resolution of ERA5, with a horizontal grid spacing of 0.25° × 0.25° and a time interval of 1 hr, makes it a widely used tool for detecting LLJs (Chen et al., 2021;Du & Chen, 2019;Lima et al., 2022;Luo & Du, 2023).The ERA5 data is averaged over the summer months of June-August for the years 1979-2018 to generate hourly mean climatologies.This approach allowed us specifically target the diurnal components.

Identification of the LLJ
The presence of LLJs is identified using two criteria: (a) a wind maximum exceeding 10 m s −1 below 700 hPa, and (b) a substantial vertical wind shear defined as a reduction in wind speed of over 3 m s −1 from the wind speed maximum upward to the subsequent wind speed minimum at or below the 600 hPa (Du & Chen, 2019;Whiteman et al., 1997).

A Linear Land-Sea Breeze Model
The linear equations of motion in two dimensions, incorporating a background wind and friction, can be described under the Boussinesq and hydrostatic approximation: Here, the variables u,v,w represent the wind components in the x, y, and z directions, respectively, U is a constant zonal background wind, ϕ is the geopotential, N is the Brunt-väisälä frequency, f is the Coriolis parameter, b is the buoyancy and the friction force is represented by (αu,αv) with a linear frictional coefficient α.The heating function is specified as x 0 and z 0 being the horizontal and vertical scale of heating, respectively, ω being 2π day −1 , and Q 0 representing the maximum heating rate at noon (t = 0) (Du & Rotunno, 2018;Rotunno, 1983).The coastline is located at x = 0 and separates land to the west and ocean to the east.
Equations 1-5 are combined into a single equation for the streamfunction ψ with  =   and  = −   , resulting in By assuming that ψ = Re(Ψe −iωt ), Equation 6becomes The Fourier transform of Equation 7 in the x direction,    = ∫ ∞ −∞ Ψ − is given by: where σ = ω−kU + iα.With the constraints of lower boundary condition    = 0 at z = 0 and upper boundary condition    finite and satisfying the radiation condition when z = ∞, the solution of Equation 8 is given by By utilizing the inverse Fourier transform, we obtain In accordance with Du andRotunno (2015, 2018), we set f = 3.77 × 10 −5 s −1 at 15°N, α = 0.2ω, Q 0 = 1 × 10 −5 m s −3 , z 0 = 1.5 km, x 0 = 50 km, N = 0.01 s −1 in solution of Equations 10 and 11.The numerical calculations for ψ, u, and v were performed using MATLAB.

Diurnal Variation of the Monsoon Low-Level Jet
During the summer, strong southwesterly low-level winds occur over the Bay of Bengal, with a core centered approximately 15°N, 87°E (Figure 1a) and a maximum intensity at 925 hPa (Figure 1c).These winds meet the criteria for a LLJ (Du & Chen, 2019), as the wind maximum (∼12.5 m s −1 ) exceeds the 10 m s −1 below 700 hPa, and the wind speed decreases by 6.5 m s −1 below 600 hPa.The LLJ is formed by the confluence of two monsoon flows from the west (westerlies over India subcontinent) and south (southwesterlies surrounding the south of India).A low-pressure vortex can be observed at 925 hPa over the northeastern region of India (indicated by "L" in Figure 1b), causing southwesterly winds to prevail on the southeastern side of the vortex.
An evident diurnal variation of the monsoon LLJ in the center of Bay of Bengal is observed, with a morning maximum between 09 and 12 local standard time (LST) (Figure 1d).This contrasts with the nocturnal peak of LLJ over India or near its eastern coast reported in previous studies (Chen, 2020;Fujinami et al., 2021).The large differences between daytime and nocturnal winds occur near the eastern coastal region of India under the effect of diurnal land-sea thermal contrast (Figure 1b).At night (03 LST), the core of monsoon LLJ shifts closer to the coast rather than the center of the Bay of Bengal (Figure 1c).These results suggest that the locations of monsoon LLJ varies on a diurnal basis, which will be further investigated in the following section.

Offshore Migration of the Monsoon Low-Level Jet
Figure 2 illustrates the diurnal variation of horizontal winds at 925 hPa, showing the monsoon LLJ migrates offshore by approximately 600 km on a diurnal scale.Specifically, the jet core is typically located near the eastern coast of India (82-85°E) At 03 LS, gradually moving offshore to 87°E and becoming slightly stronger between 09 and 12 LST.By 18 LST, the jet core reaches the center of Bay of Bengal (90°E), but it weakens.The strength further decreases with the nearly stationary jet core from 18 LST to 00 LST.At 00 LST, another jet core begins to form near the coast (81°E) and repeats its diurnal offshore migration later.
The diurnal perturbation winds, depicted by black vectors in Figure 2, are obtained are calculated by taking the differences between the wind speeds and directions at each specific time of the day and the average (mean) wind speeds and directions observed over the entire day.Notably, significant diurnal perturbation winds with magnitudes of approximately 3 m s −1 are observed near the eastern coast of India, as indicated by blue contours in Figure 2.These winds exhibit a clockwise rotation.At 18 LST, the perturbation winds are onshore, or easterly, and correspond to the sea breeze (Figure 2f).Conversely, at 06 LST, the winds are offshore, or westerly, and correspond to the land breeze (Figure 2b).This suggests that the perturbation winds are driven by the diurnal thermal contrast between land and sea (Figure 1b). Figure 1b shows that the temperature differences between daytime and nighttime over the land (e.g., India) are more significant than the ocean (e.g., Bay of Bengal).
While the maximum diurnal wind deviations primarily occur along the coast (blue contours in Figure 2), it is important to note that the clockwise rotation of diurnal perturbation winds also occur farther offshore, albeit with weakened intensity.The phase of diurnal wind deviations lags behind with increasing offshore distance, as seen in the westerly perturbation winds at 88°E at 00 LST when the coastal perturbation winds turn southerly (Figure 2h).The decaying magnitude and phase delay of diurnal wind deviations with increasing distance from the shore implies the offshore propagation and dispersion of inertia-gravity waves caused by the diurnal land-sea thermal contrast (their Figure 7 in Du & Rotunno, 2015).The winds are enhanced when the diurnal perturbation winds turn roughly parallel to the daily mean winds, and the times at which this occurs vary based on the distance from the shore, leading to the offshore migration of the jet.Since the daily mean core of the southwesterly jet is located near the 87°E (Figure 1a), the diurnal wind deviations in that region tend to veer toward a southwesterly direction just before the noon (Figures 2c and 2d).The enhanced wind associated with this veering contribute to the diurnal maximum of the LLJ occurring before the noon (Figure 1d).
The Longitude-Time Hovmöller diagram of winds at 925 hPa along 15°N (Figure 3a) provides clear evidence of the offshore migration of the jet.The core of the jet moves from 83°E to 90°E between 5 and 14 LST, with a migration speed of approximately 26.7 m s −1 .The migration track in the Hovmöller diagram is generally in agreement with the track of the southwesterly perturbation winds.
We further investigated the impact of monsoon synoptic scale systems on diurnal characteristics of the jet, focusing on specific monsoon seasons with varying occurrences of low-pressure systems near the Bay of Bengal.
Based on an hourly global track data set (Vishnu et al., 2020), we identified "active years" with occurrence hours greater than the 75th percentile and "inactive years" with occurrence hours less than the 25th percentile (Figure S1a in Supporting Information S1).Figures S1b and S1c in Supporting Information S1 revealed that both active and inactive years exhibited similar offshore propagation patterns.However, during active years, the jet had slightly higher intensities and faster propagation speeds, likely due to slightly stronger zonal background winds.
Finally, the presence of gravity wave driven by the diurnal land-sea thermal contrast is further confirmed through diurnal analysis of the vertical cross-section of divergence and perturbation temperature perpendicular to the coasts (Figure 4).In the ocean, constant phase lines of temperature and divergence exhibit positive slopes ranging from 0.003 to 0.006, moving eastward and downward.These slopes align with the calculated slope derived from the dispersion relationship for hydrostatic inertia-gravity waves, represented by the equation  √  2 − 2  = 0.005 .The observed negative divergence and positive temperature perturbations also exhibit an in-phase relationship in accordance with the polarization relationship of inertia-gravity waves (Figure 4).These results provide evidence for the existence of hydrostatic inertia-gravity waves.On the other hand, over the land, constant phase lines of temperature or divergence exhibit a westward tilt with height and are relatively stationary, suggesting mountain waves caused by the prevailing background westerlies.

Explanation From a Linear Land-Sea Breeze Model
We established a linear land-sea breeze model in two dimensions under the Boussinesq and hydrostatic approximation (see Section 2.3).This land-sea breeze model differentiates itself from previous works (e.g., Du & Rotunno, 2015, 2018;Qian et al., 2009;Rotunno, 1983), by incorporating both the background wind and friction.
In the absence of a background wind (U = 0), the streamfunction in the model takes the form of inertia-gravity waves that extend along ray paths extending upward and outward from the coast, similar to the findings of Du and Rotunno (2015) and is not shown here.The model's ability to replicate the diurnal fluctuations in the wind components near the coast is demonstrated through the Longitude-Time Hovmöller diagrams of u and v at 925 hPa (Figure 3b).However, the diurnal wind fluctuations are restricted to the coastal regions (80-83°E) rather than spreading further offshore.Furthermore, Figure 3b shows the full wind speeds, calculated by combining the simulated diurnal perturbation winds with the mean daily winds of ERA5 at 925 hPa along 15°N.The simulation highlights that the near-coastal jet can advance offshore but at a slower speed of approximately 16.1 m s −1 .On the other hand, the simulated jet in the center of the Bay of Bengal remains relatively stationary.
Considering the existence of actual westerlies with vertical wind shear below 400 hPa at the coast (15°N, 80°E, not shown), which is not accounted for in the linear model, we chose to use the observed mean wind over the lower tropospheric layer (approximately 6 m s −1 within 1,000-400 hPa) as a representative constant background wind in the linear model (Figure 3c).By adopting this approach, we successfully reproduced the diurnal perturbation winds nearshore and offshore, showing a close agreement with the corresponding winds from ERA5 (Figure 3a).As a result, the simulated jet is able to migrate significantly offshore with a comparable speed (29.3 m s −1 ) and phase as ERA5 (26.7 m s −1 ).This result highlights the importance of the presence of zonal background winds, which enables the inertial-gravity waves to have a more extensive downstream effect.The zonal background wind modulates the pattern of inertial gravity waves through Doppler shifting.The magnitude of this Doppler shifting is directly correlated with the strength of the zonal background wind (U), with higher values of U resulting in greater tilting of the ray paths and a wider dispersion of wave energy (Du & Rotunno, 2018;Qian et al., 2009).
We conducted additional sensitivity experiments in the linear model, varying the zonal background winds (U = 4, 8, and 10 m s −1 ) are performed.These experiments clearly demonstrate the presence of extensive downstream effect in all sensitivity experiments when compared to the baseline scenario with U = 0, although their diurnal propagation speeds were found to be sensitive (Figure S2 in Supporting Information S1).If we were to employ the zonal wind at a single layer (10 m s −1 at 925 hPa) as the constant background wind in the linear model, a significant discrepancy in the simulated diurnal propagation speed compared to ERA5.This emphasizes the need for further investigation into the effect of vertical wind shear in future studies.
Therefore, the linear land-sea breeze model that incorporates inertia-gravity waves driven by the diurnal land-sea thermal contrast can effectively capture the observed diurnal offshore migration of the LLJ, particularly when a westerly background wind is included in the model.The background wind enables the LLJ to migrate extensively offshore with a similar speed and phase as observed.To further examine the influence of westerly background winds, we conducted a comparison of the diurnal offshore migration of the LLJ before and after the onset of the Indian monsoon (May vs. June).These periods were selected due to significant differences in the intensity of the background zonal flows.In May (Figure S3a in Supporting Information S1) characterized by relatively weak zonal background winds (∼0.4 m s −1 ), the migration of LLJ is primarily confined near the coast, exhibiting a lower speed of 13.7 m s −1 .In contrast, in June (Figure S3b in Supporting Information S1), as the zonal background winds strengthen (∼5.7 m s −1 ), the LLJ exhibits an extended eastward migration with a higher speed of 23.4 m s −1 .This comparison provides further confirmation of the effect of westerly background winds on the behavior of the LLJ.Unlike the significant deviation before and after the monsoon onset, the intra-seasonal variation of the monsoon LLJ's diurnal offshore propagation is relatively small (Figures S3b-S3d in Supporting Information S1).However, we observed a slight increase in propagation speed from June to August (23.4m s −1 , 24.4 m s −1 , and 25.4 m s −1 , respectively), attributed to a corresponding rise in background zonal flow (5.7 m s −1 , 6.9 m s −1 , and 7.5 m s −1 ).This consistency supports our findings on the impact of zonal flow on the diurnal offshore propagation of the LLJ.

Conclusions
The present study provides a first examination of the diurnal migration of a southwesterly monsoon LLJ in the Bay of Bengal.The LLJ, which occurs during the summer months of June through August, and reaches its peak strength at 925 hPa, is found to exhibit a pronounced diurnal variation in both strength and location.Typically, the jet intensifies from midnight to morning, and weakens from noon to midnight, and shifts in location along the zonal direction.Figure 5 summarizes this process and associated mechanism.
The diurnal migration of LLJ starts near the eastern coast of India after midnight (Figure 5a), and gradually moves eastward toward the center of the Bay of Bengal until the afternoon (Figures 5b and 5c), with an offshore speed of approximately 26.7 m s −1 .This migration is caused by the varying phases of the clockwise rotation of diurnal perturbation winds in relation to offshore distance.Along the coast, significant onshore sea-breeze (offshore land-breeze) is observed in the late afternoon (early morning), while coast-parallel perturbation winds occur at noon or midnight.These veering perturbation winds extend offshore to the entire bay, though with weaker magnitude and a delayed phase.The delayed diurnal winds offshore are attributed to diurnal inertia-gravity waves caused by the land-sea thermal contrast at low latitudes.The presence of these waves is confirmed through analysis of dispersion and polarization relationships, with phase lines tilting eastward with height over the ocean, and the in-phase warm-temperature and convergence meeting the polarization relationship (Figure 5).
The study found that a linear land-sea breeze model that incorporates inertia-gravity waves driven by the diurnal land-sea thermal contrast can effectively capture the observed diurnal offshore migration of the LLJ, particularly when a westerly background wind is included in the model.The background wind enables the LLJ to migrate extensively offshore with a similar speed and phase as observed.
The significance of this study lies in its pioneering application of the theory of diurnal inertia-gravity waves to the diurnal migration of a jet, as previous studies have only applied this theory to the diurnal offshore propagation of rainfall (Fang & Du, 2022;Kilpatrick et al., 2017;Li & Carbone, 2015).Future research can explore the downstream impact of the offshore-moving LLJ on diurnal rainfall, as well as investigate the exist-ence of similar migration phenomena in other coastal LLJs.It is important to note that there still exist some still discrepancy in the phase speed between the LLJ and precipitation, even when both are derived from ERA5.The mechanisms governing the diurnal propagation of rainfall are more complex than the migration of the LLJ alone.Factors such as cold pool dynamics (Jain et al., 2018) and convectively generated gravity waves (Love et al., 2011) can also influence the diurnal propagation of rainfall, in addition to gravity waves resulting from the land-sea thermal contrast.Given biases in ERA5 resulting from numerical resolution and convective parameterizations, it is imperative to utilize high-resolution simulations in order to gain a comprehensive understanding of the offshore propagation of rainfall and LLJ and their interactions.High-resolution model simulations, incorporating the analysis of vertical shear components, would be the most effective approach to address the complexities of the studied phenomena.Given the significant impact of topography on offshore propagation rainfall (Zhou et al., 2023), it would be intriguing to investigate the influence of topography in offshore LLJs through sensitivity experiments.The findings in the present study deepen our understanding of the complex dynamics of the southwesterly monsoon LLJ and provide a basis for future research on the regional monsoon system.

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The monsoon low-level jet migrates eastward from the eastern offshore of India at midnight to the center of the Bay of Bengal by afternoon • The offshore diurnal migration is driven by inertia-gravity waves resulting from the diurnal thermal contrast between land and sea • The westerly upstream wind from the Indian subcontinent extends the offshore migration, rather than confining it to the coast Supporting Information:Supporting Information may be found in the online version of this article.

Figure 1 .
Figure 1.Horizontal and vertical structure of monsoon LLJ and its diurnal variation.(a) Horizontal distribution of daily mean wind speed (color shaded, m s −1 ) and wind vectors at 925 hPa.The green contours indicate the terrain greater than 200 m with a 200 m interval.(b) The differences in temperature below 925 hPa (K) and winds at 925 hPa (black vectors) between daytime (16 local standard time (LST)) and nighttime (04 LST), superimposed with the geopotential height at 925 hPa (blue contours, gpm).(c) Vertical cross-section of daily mean wind speed (shaded, m s −1 ) and horizontal wind vectors along the black dashed line in (a).The green contours (greater than 12 m s −1 in a 0.5 m s −1 interval) represent the wind speeds at 03 LST.The terrain is indicated by black shading.(d) Diurnal evolution of vertical wind profiles (m s −1 ) averaged over the white box in (a).

Figure 2 .
Figure 2. Diurnal offshore migration of monsoon LLJ and associated with diurnal wind perturbations.Diurnal evolution of wind speed (color shaded, m s −1 ) and wind vectors (white) at 925 hPa, and diurnal wind deviation speed (blue contours greater than 2 m s −1 with intervals of 0.5 m s −1 ) and wind deviation vectors (black) at 925 hPa.The thick white dashed arrows depict the diurnal offshore migration of the LLJ over the Bay of Bengal.

Figure 3 .
Figure 3. Comparisons in diurnal offshore migration of monsoon LLJ between ERA5 and analytical model.Longitudetime Hovmöller diagrams showing wind speed (color shaded, m s −1 ) and perturbation horizontal wind vectors at 925 hPa along 15°N derived from (a) ERA5 analysis, (b) an analytical model without background wind, and (c) an analytical model with background wind.White dots indicate the diurnal wind peaks and white arrows are linearly regression of those peaks, indicating the offshore migration speed of the LLJ.

Figure 4 .
Figure 4. Diurnal evolution of inertia-gravity waves driven by diurnal land-sea thermal contrast.Vertical cross-section of divergence (color shaded, 10 −6 s −1 ) and perturbation temperature (contours with interval of 0.1 K, dashed contours indicate negative values) with diurnal variation.Black solid and dashed lines represent tilted phase rays of inertia-gravity waves.

Figure 5 .
Figure 5. Conceptual model of the offshore migration of the monsoon LLJ driven by inertia-gravity waves resulting from the diurnal thermal contrast between land and sea.(a) At midnight, the southwesterly LLJ is located close to the coast because of diurnal southwesterly perturbations occurring offshore.(b) By morning, the LLJ migrates eastward and strengthens as southwesterly perturbations propagate eastward due to inertia gravity waves.(c) In the afternoon, the LLJ move further offshore but with a weakened intensity.