The characterization of turbulent heat and moisture transport during a gust-front event over the Indian peninsula

The ramifications of gust-front on atmospheric surface layer turbulence is a vexing issue, with nearly no information available over the Indian region where such events are not uncommon. Over the Indian peninsula, our recent field-experimental study has shown that a cold pool associated with the gust-front creates two distinct regimes in ASL turbulence, where temperature fluctuations display contrasting behavior. In this work, we use a multi-level observational dataset to evaluate the corresponding impacts on the moisture fluctuations and turbulent heat and moisture transport. We discover that the topology of the turbulent structures, which govern the temperature and moisture fluctuations, clearly exhibit a regime-wise distinction. In the first regime, the structures in temperature and moisture fluctuations are inclined in the vertical, while demonstrating a self-similarity in their time scales by being related through a power-law distribution. The inclination angle is inferred from the vertical shifts in the peak positions of the cross-correlation coefficients. However, in the second regime, the vertical inclination disappears for the temperature structures with hardly any change observed for the moisture. Moreover, the power-law exponents of the turbulent temperature time scales remain sensitive to the regimes, although no such effect is visible in the power-law character of the moisture time scales. Additionally, the dissimilarity in the heat and moisture transport is investigated through a novel polar-quadrant based approach that separates phases and amplitudes of the flux-transporting motions. During gust-front, temperature and moisture structures display sharp contrast between the active and quiescent regimes. The turbulent time scales of temperature and moisture vary in a power-law manner with different regime-wise exponents. The structural dissimilarity between the two scalars affects the heat and moisture transport between the two regimes. During gust-front, temperature and moisture structures display sharp contrast between the active and quiescent regimes. The turbulent time scales of temperature and moisture vary in a power-law manner with different regime-wise exponents. The structural dissimilarity between the two scalars affects the heat and moisture transport between the two regimes.


Introduction
The exchange of heat and moisture in the boundary layer has an astounding influence on convection in the tropics and especially during the cold pool events [1,2]. Initiation of isolated convection is favored when land surface is dry and depending on the moisture in lower atmosphere and in soil, wet conditions facilitate large organized convective clusters. The evaporative cooling of rain from such cloud clusters and the associated downdrafts initiate a cold pool, which introduces cold and moist air into the dry and sub-saturated boundary layer. As the moist air interfaces with the dry surrounding air, density differences between the two air masses create a gust-front, characterized by strong upward motions and heterogeneity in temperature and moisture. The development of cold pools indeed contributes to changes in the spatio-temporal patterns of the surface fluxes. Most of our understanding on the cold pools and the related impacts on the surface fluxes are from the mid-latitude systems [3,4]. These studies have revealed that the cold pools can significantly alter the turbulence properties of the atmospheric surface layer (ASL) by causing a significant reduction in temperature, which often lead to the formation of stable boundary layers. However, the modulations of surface fluxes due to the cold pools are still to be explored over the Indian subcontinent, where detailed measurements of ASL turbulence are somewhat lacking.
To close this gap, a detailed micrometeorological observation system was established over the rain shadow region of the Western Ghat as part of the Cloud Aerosol Interaction and Precipitation Enhancement Experiment (CAIPEEX), in an effort to understand the linkage between the cloud processes and surface-atmosphere exchanges. By using CAIPEEX datasets from a C-Band Doppler weather radar and 50-m micrometeorological tower, [5] studied the impact of a gust-front event on the ASL turbulence. They discovered that, similar to mid-latitude studies [6,7], the incidence of the gust front was followed by a convergence of cold air pool, which in turn affected the turbulent temperature structure in the ASL. Due to such event, two distinct regimes were visible, where in one regime the turbulent temperature fluctuations remained quite intense analogous to daytime convective periods, whereas in the second regime the fluctuations diminished significantly as in stable conditions. Additionally, [5] demonstrated that the time scales of the temperature fluctuations displayed a power-law behavior whose exponents changed between the two regimes. By drawing an analogy with self-organized criticality in complex systems [8][9][10], they interpreted this as, the deep-convective cells whose outflows generated the gust front, acted as an external stimuli which disturbed its surroundings beyond the tipping point and created a scale-free response. Accordingly, this response propagated to the surface layer of the convective boundary layer and generated turbulent structures having self-similar size distributions.
The aforementioned results were illuminating to judge the structural characteristics of the turbulent temperature fluctuations in the ASL, as the gust-front traversed the tower location. However, in that particular study, they did not consider the effect of these structures on turbulent heat and moisture transport. Undoubtedly, such investigation is of fundamental interest, given the importance of heat and moisture fluxes in sustenance of convection associated with the gust-front. Moreover, it is timely as well, since to the best of our knowledge no prior information is available on these aspects over the Indian region. Therefore, one may ask, 1. Whether there is any structural similarity in the temperature and moisture fluctuations between the active and quiescent regimes? 2. How the structures in the scalar fluctuations interact with the vertical velocity to generate signatures in their fluxes? 3. Can such structural interaction explain any regime-wise dissimilarity between the heat and moisture fluxes?
In this article, we attempt to answer these questions through novel data analysis techniques employed on the same 50-m micrometeorological dataset from CAIPEEX, used in [5]. During our presentation, we arrange the paper in three different sections. In Sect. 2, we provide a brief description of the field-experimental dataset, in Sect. 3 we discuss the results, and lastly in Sect. 4 we summarize the key findings and lay out the scope for further research.

Dataset description
To investigate the characteristics of turbulent heat and moisture fluxes during the gust-front event, we used the same micrometeorological dataset from a 50-m instrumented tower as described in [5]. This dataset was collected during the Integrated Ground Observational Campaign (IGOC), as a part of the fourth phase (2018-2019) of CAIPEEX experiment. In this study, we specifically focus on the afternoon time of 22-September-2018 (14:00-16:10 PM, local time, GMT+05:30). During this period, by using a Doppler weather radar, [5] detected the passage of a gust-front (originated from the outflows of several deep convective clouds) over the tower location. The 50-m tower was erected over a non-irrigated and nearly-flat grassland in Solapur, India (17.6 • N, 75.9 • E, 510 m above mean sea level), equipped with time-synchronized eddycovariance (EC) systems at four levels with heights z = 4, 8, 20, and 40 m (z is the height above the ground). Each EC system comprised of a sonic anemometer (Windmaster-Pro, Gill instruments, UK) and an open-path CO 2 -H 2 O gas analyzer (LI-7542, Li-cor Inc., USA). The horizontal separation between the sonic anemometer and gas analyzer was approximately 20 cm towards the East and 7 cm towards the North. The close proximity between the two can be seen clearly in Fig. 1 where we show a close-up view of the sonic-anemometer and open-path gas analyzer system, positioned at z = 4 m on the instrumented tower. Due to such closeness, there was hardly any time-lag between the sonic anemometer and gas analyzer measurements.
The data from these four EC systems were synchronized in time through GPS clocks and sampled continuously at 10-Hz frequency, divided into 30-min intervals. No double-coordinate rotation was applied to the sonic-anemometer data which forces the mean vertical velocity to be zero [11]. This is because the non-zero values of the 30-min averaged vertical velocities could have occurred due to the presence of large-scale variability over the tower location [5]. Further details about the tower instrumentation and site description can be found in [5].

Results and discussion
We begin with delineating the statistical properties of the turbulence structures which impact heat and moisture fluxes during the passage of a gust-front on the afternoon time of 22-September-2018 (14:00-16:10 PM). As noted in [5], an increase in the horizontal wind speed was observed approximately beyond 15:00 PM, with a sudden drop of around 4K in the dry-bulb temperature. The wind-direction was from the South-West sector and stayed nearly constant between 14:00-16:10 PM.
As the gust-front traversed the tower location, two distinct turbulent regimes were created, reminiscent of convective and nocturnal periods [5]. In order to unveil the structural differences between these two regimes, the time scales of the turbulent motions are explored through persistence analysis. Subsequently, to assess the role of turbulence organization on the flux transport processes, a novel polar-quadrant based approach coupled with information theory is introduced. Furthermore, throughout the presentation, plausible physical interpretations are provided to explain the results.

General features
With an aim to characterize the vertical transport of heat and moisture, it is imperative to scrutinize the properties of the component signals (temperature, moisture, and vertical velocity) which constitute these fluxes. In Fig. 2, we show the 10-Hz time series of the sonic temperature ( T S ), water-vapor density ( H 2 O ), and vertical velocity (w) as measured by the EC systems at z = 4, 8, 20, and 40 m, between 14:00-16:10 PM (local solar time, GMT+05:30). Note that, this period relates to the time when the gust-front passed over the tower location [5]. [5] demonstrated that due to the cold-air outflow from the precipitating convective cells, a near-surface stable layer was established (early nightfall) that caused two clearly distinct regimes in the high-frequency sonic temperature measurements at all the four heights ( z = 4, 8, 20, and 40 m). In the first regime (14:10-15:00 PM), large temperature changes were observed analogous to daytime convective turbulence. Whereas in the second regime To further investigate the role of such different regime-wise behavior towards the transport of heat and moisture, it is important to segregate the turbulent fluctuations from the three signals. However, the computation of turbulent fluctuations is not a trivial task, especially for temperature and water-vapor densities, given the clear presence of a complicated trend in these signals. Therefore, to calculate the turbulent fluctuations the apparent trend in T S and H 2 O time series need to be removed. Previously, we computed the turbulent fluctuations in T S by removing a portion of the signal through applying a Fourier filter with a threshold frequency set at 0.01 Hz [5]. We noted that, for frequencies lesser than or equal to 0.01 Hz, the Fourier amplitudes of T S increased in a nearly linear fashion rather than attaining a saturation. From [11], we know that such an increase in the amplitudes of the Fourier spectrum is associated with low-frequency non-turbulent oscillations that need to be removed in order to compute the turbulent fluctuations.
In the present study, we extended this procedure to all the three signals ( T S , H 2 O , and w) to extract the turbulent fluctuations. The thick and dashed black lines in Fig. 2a-d show the respective low-frequency components of T S and H 2 O , overlaid on the original ones. Likewise, for w, the solid black lines in Fig. 2e-h convey the same information. It is interesting to observe that, among the three variables, w is the one least affected by such low-frequency variations. This is consistent with the expectation that the vertical velocities of large-scale motions are blocked by the ground [12,13]. Finally, the turbulent fluctuations were computed after removing the low-frequency oscillations from T S , H 2 O , and w signals.
Before we proceed further, it is important to note that for H 2 O , the fluctuations corresponding to the periods 14:00-15:00 PM and 15:10-16:10 PM were corrected by applying the density corrections following the procedure listed in [14]. The Eq. (5a) of [14] states that, where c is any scalar concentration ( H 2 O for our study), a is the density of dry air (1.225 kg m −3 ), is the ratio between the molecular mass of dry air and water vapor (1.61), and = H 2 O ∕ a . In our case, for periods 14:00-15:00 PM and 15:10-16:10 PM, ′ H 2 O and T ′ values in Eq. (1) were the ones computed after removing the low-frequency oscillations from the respective signals. Moreover, for the same two periods, H 2 O and T were the averaged values of the low-frequency oscillations in water-vapor density and temperature signals, respectively. Hereafter, we simply denote the turbulent fluctuations in temperature, water-vapor, and vertical velocities as T ′ , ′ , and w ′ , respectively.

Cross-correlation analysis
By separating the turbulent part from the low-frequency trend, we explore how strongly the fluctuations in the scalars and vertical velocity at different measurement heights are related to one another. To accomplish that, we employ cross-correlation analysis and estimate the relative strength of the fluctuations at higher heights with respect to the lowest measurement level. This information is crucial to quantify the vertical coherence among the turbulent structures and see whether there is any change in such property between the two regimes. In Fig. 3, the cross-correlation coefficients between the two signals among different heights (either for T ′ , ′ , or w ′ ) are presented individually for the two regimes. These coefficients have previously been used in several ASL studies to probe the vertical structure of turbulence [15][16][17] and can be evaluated mathematically as, where s x is the reference signal at z ref = 4 m, s y is the signal at higher heights ( z = 8, 20, 40 m) shifted through time, and is the time-lag. The values are either positive or negative, depending on whether s y leads or lags s x . Note that, Eq. 2 is designed when s y lags s x , but can also be used for a leading case by keeping s y fixed and moving s x ahead in time.
For the first regime, the cross-correlation coefficients of w ′ ( R w � xy ( ) ) decrease as the measurement heights increase (Fig. 3a). Apart from that, the peaks in R w � xy ( ) are clustered around the zero-lag, signifying a negligible shift with height. But, for T ′ and ′ , a prominent shift towards the positive values is observed in their cross-correlation peak positions as z gets larger (Fig. 3b, c). However, in the second regime, R w � xy ( ) and R � xy ( ) behave almost identically as in the first regime ( Fig. 3d and f). Conversely, for T ′ , R T � xy ( ) values decrease with no apparent shift in their peak positions, as the second regime is encountered (Fig. 3e).
To put these above results into perspective, it is prudent to recognize that the shifts in peak positions of the cross-correlation coefficients are associated with inclination angles of turbulent structures, apparently caused due to the presence of vertical wind shear [15]. In an appendix, we provide a calculation that computes the inclination angle from the vertical shifts in the peak positions of the cross-correlation coefficients. For this particular gust-front case, [5] have shown that a substantial amount of wind shear was present during the period between 14:00-16:10 PM (see their Fig. 5). This wind shear can be computed as, where U is the mean horizontal wind speed computed from the sonics and z 2 and z 1 are the highest and lowest measurement heights, respectively (40 m and 4 m). By substituting the observations, the wind shear estimated from Eq. (3) remains close to 0.07 s −1 .
Despite a considerable amount of wind shear being present, the near zero-shifts in R w � xy ( ) ( Fig. 3a and d) indicate that the turbulent structures, which govern w ′ , display almost no vertical inclination in both of the two regimes. Contrarily, the effects of wind-shear on the vertical orientation of turbulent structures related to T ′ and ′ are different between the two regimes. For the first regime, a significant inclination exists in both the structures which affect the turbulent fluctuations in temperature and water-vapor (Fig. 3b-c). Whereas in the second regime, the inclination almost disappears for temperature, while it is intact for the water-vapor (Fig. 3e-f). This is a remarkable result with serious implications towards the heat and moisture transport, as will be revealed in subsequent sections.

Heat and moisture fluxes
From the aforementioned discussion, we infer that the fluctuations in temperature and water-vapor are generated due to similar turbulent structures in the first regime. However, as the second regime is approached, a structural disparity prevails between the two scalars, although such difference happens to be nearly absent in w ′ . Therefore, a complex interaction between turbulent structures with contrasting vertical orientations influence the characteristics of the heat and water-vapor fluxes ( w ′ T ′ and w ′ ′ ) at all the four measurement heights. To gain more insight into what type of flux signatures are generated due to such interaction, in Fig. 4 the instantaneous time series of w ′ T ′ and w ′ ′ are shown at z = 4, 8, 20, and 40 m. During the first regime, across all the four heights, one can see occasional occurrences of large bursts (intense activities lasting for a small time) in both the heat and water-vapor fluxes (Fig. 4). These kinds of bursts in the scalar fluxes, found for the first regime, are regarded as a prevalent feature of convective turbulence [18][19][20][21][22]. Nevertheless, in the second regime, the bursts become exceedingly rare for w ′ T ′ (Fig. 4a-d), while still being present in w ′ ′ with reduced intensities (Fig. 4e-h). To examine further about the scales of turbulent motions which cause such intermittent behavior in the heat and moisture fluxes, we present results from persistence analysis [22][23][24] in Sect. 3.2.

Persistence analysis
Persistence is a concept widely applied in non-equilibrium statistical mechanics and defined as the probability that the local value of a fluctuating field does not change its sign for a certain amount of time [25,26]. In other words, the persistence timescale t p is the time up to which a signal stays positive or negative, before switching its sign (see [23,24] for a brief review). For wall-bounded turbulence, several studies have shown that the distributions of the persistence time scales can be interpreted as equivalent to the size distributions In (e)-(h) the information is presented for the water-vapor fluxes ( w ′ ′ ). The gray-shaded regions carry the same meaning as in Fig. 2 of the turbulent structures in such flows [27][28][29][30]. In convective ASL flows, [22,23] have illustrated that the persistence analysis is an effective tool to provide a structural description behind the intermittent fluctuations in velocity and temperature, and in the associated heat and momentum fluxes. Additional details about the computation of persistence probability density functions (PDFs) are laid out in [23]. [5] showed through persistence analysis that the passage of the gust-front created a scale-free response, which generated self-similar structures affecting the turbulent temperature fluctuations at all the four measurement heights [5]. To comprehend the role of these structures towards the transport of heat and moisture, we present persistence PDFs of T ′ , ′ , w ′ , w ′ T ′ , and w ′ ′ in Fig. 5. The persistence time scales are denoted by t p and to document any discrepancies, the top and bottom panels in Fig. 5 display the persistence PDFs ( P(t p ) separately for each of the two regimes. Note that a log-log representation is used in these plots, so any power-law emerges as a straight line.
In Fig. 5a-e, one could spot roughly a similar power-law behavior ( P(t p ) ∝ t p ) in all the five variables, with hardly any difference among different heights. Physically, it indicates that in the first regime the statistical characteristics of both the scalars, vertical velocities, and the associated fluxes are all governed by the same self-similar structures at all the heights, although their vertical orientations depend differently on the wind-shear (Fig. 3a-c). On the other hand, in the second regime, a significant disparity is observed in P(t p ) between the temperature and moisture. In Fig. 5f-g, the exponent of the power-law in P T � (t p ) is equal to −2.5 (shown in thick green lines), whereas for P � (t p ) the exponent remains close to the first regime ( −2.1 , shown in dash-dotted gray lines). This outcome reinforces our statement about Fig. 3e-f, i.e., the topology of the structures which govern the variations in moisture do not alter their attributes despite the observation that the temperature structures exhibit a behavioral change between the two regimes. Interestingly, for w ′ , w ′ T ′ , and w ′ ′ the exponents in P(t p ) are comparable to T ′ (Fig. 5h-j), suggesting that the transport of heat and moisture are primarily accomplished through those turbulent structures which have identical effects on temperature and vertical velocity fluctuations.

Amplitude PDFs
Notwithstanding the fact that persistence analysis is a convenient method to describe the sizes of the intermittent patterns which affect the turbulent signals, it remains insensitive to the fluctuation amplitudes [22]. It is thus instructive to see the amplitude signatures associated with the structures whose geometrical features have been explored till now (Figs. 3  and 5). To disseminate such information, in Fig. 6 we show the PDFs of temperature, moisture, vertical velocity, and scalar fluxes for the two regimes. In order to better highlight the height variations in the statistical properties of turbulent fluctuations, no normalization has been performed while computing the PDFs. It is immediately noticeable that the w ′ PDFs collapse for all the four heights, with nearly no change in the shapes between the two regimes ( Fig. 6c and h). For T ′ and ′ PDFs, a little variation with height can be detected in the first regime ( Fig. 6a-b). However, in the second regime, the height dependence disappears for temperature and moisture. In addition to that, only a narrow range of amplitudes dominate the PDFs of temperature, while the range being slightly larger for moisture ( Fig. 6f-g). A similar impact of the two regimes could also be observed on the scalar flux PDFs. The heat and moisture fluxes remain substantially skewed to the positive values in Fig. 6d-e (first regime), but become largely attenuated in the second regime as depicted in Fig. 6i-j.
By combining results from the persistence analysis and amplitude PDFs, we infer that in the first regime heat and moisture are both transported by topologically similar turbulent structures which mostly give rise to the positive values in the fluxes. Conversely, for the other regime, the turbulent fluctuations associated with temperature and moisture remain structurally quite different, although their signatures on the flux amplitudes appear to be similar. To elucidate more on the connection between the organized turbulent motions and scalar flux transport, one may ask: Fig. 6 The PDFs of a T ′ , b ′ , c w ′ , d w ′ T ′ , and e w ′ ′ are shown. A description of different markers depicting the four different heights is provided in the legend of (a). The bottom panels (f-j) represent the same information as in the top panels (a-e) but for the period 15:10-16:10 PM 1. What type of turbulent motions cause burst-like activities in the fluxes corresponding to the first regime? 2. What is the role of turbulence organization towards the heat and moisture transport efficiencies associated with the two regimes?
To answer those, in Sect. 3.3 we introduce a polar-quadrant based approach through which the characteristics of the scalar fluxes are evaluated in terms of organized structures in the flow.

Polar-quadrant analysis
Generally, quadrant analysis is regarded as a standard technique to quantify the contributions of organized motions in the turbulent fluxes [31]. In this approach, usually the flux fractions and time fractions from each quadrant are reported to assess the relative importance of the various turbulent motions, associated with different flow structures [32][33][34].
The normal practice while performing quadrant analysis is to choose a Cartesian co-ordinate system where the x and y axes denote the fluctuations in the two variables. However, in this representation, a fundamental question remain unanswered, i.e., what governs the strength of the coupling between the two turbulent signals owing to which the fluxes exist?
To resolve this issue, [22] proposed a novel method where they designated each point in the quadrant plane with two parameters, the phase angles and amplitudes (for a graphical demonstration see their Fig. 5). They used a polar co-ordinate system to define the phase angles ( ) and amplitudes (r) as, where x ′ is the other turbulent variable (for this study T ′ or ′ ) apart from w ′ which constitutes the flux. The phase angles vary between − to and their ranges are related to the four different quadrants (see Table 1 from [22]). In the polar co-ordinate system, the instantaneous fluxes associated with each point are expressed as, with the detailed derivation being provided in [22]. Besides that, the PDFs of the phase angles P( w � x � ) are related to the time-fractions (T f ) X spent in each quadrant X as, where I X (ŵ̂x) is an identity function which is unity when w ′ x ′ lies within quadrant X or zero elsewhere. Based on these formulations, it is possible to ascertain the properties of the turbulent motions occurring in each quadrant by investigating the phase angle PDFs and the corresponding flux amplitudes. In Fig. 7 such information is displayed for the present case in hand. The gray-and yellow-shaded regions in Fig. 7 illustrate the motions occurring (4) w � x � = arctan (w � ∕x � ), in the down-gradient and counter-gradient quadrants, respectively. The flux values plotted in Fig. 7c, d, g, and h are computed from Eq. 6 and averaged between the same phase angle bins used to estimate P( w � T � ) and P( w � � ) (see Fig. 7a, b, e, and f). The error-bars shown in Fig. 7c, d, g, and h, convey the amount of spread (one standard deviation) that exists with respect to the averaged flux values in each phase angle bins. It is worthwhile to note that the spreads in the flux values remain insignificantly small. By inspecting the phase angle PDFs, one can see that in the first regime P( w � T � ) and P( w � � ) behave in a nearly similar fashion (Fig. 7a and e). Two peaks are observed in the PDFs, corresponding to the ejection ( 0 ≤ w � x � ≤ ∕2 ) and sweep ( − ≤ w � x � ≤ − ∕2 ) motions, whose heights increase with z. Moreover, the peak heights of P( w � T � ) related to the sweeps are somewhat larger in number than the ones related to the ejections. At the same time, from the flux amplitude plots, we notice that the fluxes associated with the ejection motions exceed the ones associated with the sweeps (Fig. 7c and g). Therefore, the ejections occur a little less frequently than sweeps but are accompanied with large intensities, causing burst-like activities in the fluxes as observed in the first regime (Fig. 4). Intriguingly, in both phase angle PDFs and flux amplitudes, variations with z appear to be more prominent for the sweep motions rather than for the ejections.
Even though the reason behind such phenomenon is elusive at present, the phase angle PDFs and flux amplitudes become almost independent of z in the second regime. The phase angle PDFs of w ′ T ′ attain two peaks at ± ∕2 , suggesting near-zero transport of heat in that regime (Fig. 7b). This is confirmed with Fig. 7d, where the heat flux amplitudes are significantly diminished as compared to Fig. 7c (first regime). On the other hand, the peak positions of P( w � � ) remain slightly shifted from ± ∕2 (Fig. 7f), thus yielding higher moisture flux values than heat (Fig. 7h).

Information entropy
Overall, the results in Fig. 7 provide a detailed description about the relative roles of ejection and sweep motions in the scalar flux transport, commensurate with the gust-front event. Fig. 7 The phase angle PDFs of T ′ -w ′ and ′ -w ′ quadrants ( P( w � T � ) and P( w � � ) ) are shown in panels (a), Nevertheless, it remains unclear whether the discrepancies observed in heat and moisture fluxes between the two regimes are in any way linked to different organizational structure of turbulence. In order to evaluate that, one can compare the information entropy of the phase angles for both heat and moisture, corresponding to the two regimes. [22] theoretically showed that if in Eq. 6 the amplitudes r are considered to be independent of and the PDFs P( ) resemble a uniform distribution (i.e., the phase angles are randomly oriented with no order whatsoever), then the time-averaged flux becomes zero under such constraints. As a consequence, the departure of the phase angle PDFs from a uniform distribution could be used to quantify the role of turbulence organization on the flux transport, given the assumption that the information about r remains largely irrelevant [22]. Therefore, it is appropriate to investigate whether the phase angle PDFs of heat and moisture fluxes deviate from a uniform distribution in the two regimes. For this purpose, in Fig. 8a-d we show the cumulative distribution functions (CDFs) of w ′ T ′ and w ′ ′ ( F( w � x � ) ), since in such plots the uniform distribution appears as a straight line (solid black lines). In the first regime, both F( w � T � ) and F( w � � ) closely follow the uniform distribution at all the four heights ( Fig. 8a and c). Conversely, the CDFs of the same phase angles deviate more from the solid black lines in the second regime ( Fig. 8b and d). Following [22], to measure the deviation we compute the Shannon entropy of the phase angles as, where N b is the number of bins in which the w ′ x ′ values are divided (60 in our case), and P i ( w � x � ) is the probability of occurrence of a particular binned value w ′ x ′ . For a uniform (8) Fig. 8 The CDFs of T ′ -w ′ and ′ -w ′ phase angles ( F( w � T � ) and F( w � � ) ) are shown in panels (a)-(d), corresponding to the two regimes (14:00-15:00 PM and 15:10-16:10 PM). The shaded regions convey the same information as in Fig. 7. The solid black lines indicate the CDFs of a uniform distribution. In (e), the vertical profiles of the normalized Shannon entropy of the phase angles ( H N ( w � T � ) and H N ( w � � ) ) are displayed for the two regimes. The thick and dashed red (blue) lines denote the H N values from the first (second) regime, as described in the legend of (e). distribution, H N ( w � x � ) in Eq. 8 is equal to 1, given P i ( w � x � ) = 1∕N b for all the bin indexes. Hence, the departure from unity in H N ( w � x � ) illustrates that the orientation of the phase angles differs from a random configuration. To estimate how sensitive H N ( w � x � ) is on the number of bins chosen, we varied the number of bins from 30 to 120 in an increment of unity and computed the corresponding values of H N ( w � x � ) . All those values were compared with the H N ( w � x � ) value computed for 60 number of bins and the amount of spread that was found to exist remained extremely small (see the error-bars in Fig. 8e).
In Fig. 8e, the vertical profiles of H N ( w � x � ) are presented for the same two periods. The error-bars in Fig. 8e show the spread in H N ( w � x � ) values if the bin numbers were varied from 30 to 120. The spread is almost negligible, thus providing confidence in the computed values. One can observe that, H N ( w � T � ) and H N ( w � � ) are close to unity for all the z values (red lines in Fig. 8e), consistent with Fig. 8a and c. Contrarily, for the other regime, H N ( w � � ) values do not change much from 1, while H N ( w � T � ) shows a pronounced deviation (blue lines in Fig. 8e).
At a first glance, Shannon entropies of the phase angles dictate that in the first regime the flux transporting motions from the four quadrants exhibit quasi-random patterns. According to the model of [22], this configuration transports very little flux when the amplitudes play no role. However, from Fig. 7 it is evident that in the first regime a substantial amount of heat and moisture is carried by the ejection and sweep motions. To explain this conundrum, the amplitude information must be invoked. By doing so, it becomes clear that in the first regime a strong coupling exists between the amplitudes and phases of T ′ ( ′ ) and w ′ , which strengthens the heat (moisture) transport. On the other hand, in the second regime, the role of such coupling is different for heat and moisture. For instance, in this regime, H N ( w � T � ) values display a strong deviation from unity accompanied with almost no transport of heat. A far-from-random organization of the phase angles would have increased the flux, but the phases and amplitudes of T ′ and w ′ remain coupled in a way so that small heat flux values are observed in the second regime (Figs. 4 and 7). But, for moisture, the flux values are larger than w ′ T ′ , while H N ( w � � ) is close to unity. This indicates that the nature of coupling between the phases and amplitudes of ′ and w ′ is nearly-similar to the first regime, causing enhancement in the moisture fluxes.
By condensing all the details rendered so far, we deduce that the regime-wise distinction between heat and moisture originates due to two main reasons. First, the topology of the turbulent structures which affect T ′ and ′ disagrees between the two regimes. Second, the phase and amplitude coupling of the flux-transporting motions, associated with the presence of such structures, also display opposing behavior as the regime transition occurs. We present our conclusions in the next section.

Conclusion
In this study, we address the impact of a gust-front on the turbulent heat and moisture fluxes by using multi-level high-frequency measurements from a 50-m micrometeorological tower. A cold-pool event associated with the gust-front separates two turbulence regimes, where in one the temperature fluctuations are intense (first regime) and in the other those remain subdued (second regime). In order to evaluate the structural features of turbulent motions which determine the heat and moisture transport characteristics in these two regimes, we employ advanced statistical techniques, such as cross-correlation, persistence, and polar-quadrant analyses. The results obtained from these methods are directed towards providing answers to the research questions posed in the introduction and can be summarized as: 1. The vertical orientations of the turbulent structures corresponding to the temperature and moisture fluctuations differ significantly between the two regimes. In the first regime, the structures remain vertically inclined in a similar fashion for both temperature and moisture. However, in the second regime, such inclination disappears for temperature while being retained for moisture. 2. In addition to the vertical inclination, the time scales of the turbulent structures show a conspicuous regime-wise distinction between the temperature and moisture. The temperature time scales in both the regimes follow a power-law albeit with different exponents. On the other hand, the moisture time scales too display a power-law behavior, but their exponents remain regime-invariant and equal to the temperature structures from the first regime. 3. The observed difference in such topology has a profound influence on the organized motions (ejections and sweeps) that govern the dissimilarity between the scalar fluxes in the two regimes. By employing a polar-quadrant based approach, it is discovered that in the first regime, the efficient transport of heat and moisture is tied to the fact that the phases and amplitudes of the flux-transporting motions remain strongly coupled. Nevertheless, in the second regime, the phase and amplitude coupling between the temperature and vertical velocity gets altered in such a way that it induces a substantial decrease in the heat flux. Conversely, for moisture and vertical velocity, the nature of coupling is nearly identical to the first regime, causing an enhancement in the fluxes.
To conclude, the physical insights gained from this study are useful in developing new parametrizations of turbulent heat and moisture fluxes, which would aid better simulations of the gust-front dynamics. The issue of momentum transport is not addressed in this work, given an inherent difficulty of defining the streamwmise and cross-stream axes under the presence of non-stationary flow features as the gust-front traverses the tower location. In our future endeavors, we wish to push the envelope by tackling the problem of momentum transport, leading towards further advancements in surface drag formulations related to the gust-front.
Be that as it may, we subsequently locate the peak positions of R � xy (Δx) for each x and y values (see the black squares in Fig. 9a). These peak positions are plotted against Δz , which are simply the differences in heights between the reference level (4 m) and the other three observation levels (8, 20, and 40 m). This information is presented as a scatter-plot in Fig. 9b, accompanied with a best-fit straight line ( R 2 > 0.98 ) to the data. The inclination angle ( ) is computed as, where m is the slope of the best-fit straight line. From Eq. (9), is evaluated to be ≈ 37 • , which is extremely close to the value of 35 • found by [15] in a convective ASL flow. This indicates that the turbulent structures, which govern the moisture fluctuations, share nearly similar characteristics with the structures found in a convectively driven ASL flow. Furthermore, the vertical shear in U (Fig. 9c) confirms the fact that the inclination angles of the turbulent structures are indeed related to the presence of vertical wind shear. Acknowledgements CAIPEEX is conducted by the Indian Institute of Tropical Meteorology, which is an autonomous institute and fully funded by the Ministry of Earth Sciences, Government of India. Authors are indebted to several colleagues who contributed to the success of the CAIPEEX project. The authors extend their heartfelt gratitude to Dr. Anand K Karipot who helped immensely with the data-collection, instrument set-ups, quality checks, and critical scientific suggestions. The authors also acknowledge the local support and hospitality provided by N. B. Navale Sinhgad College of Engineering (NBNSCOE), Kegaon-Solapur, during the experiment. The authors are grateful to three anonymous reviewers for their comments and suggestions. The author Subharthi Chowdhuri thanks Dr. Tirtha Banerjee for many insightful discussions on persistence and polar-quadrant analyses.
Author Contributions Subharthi Chowdhuri and Thara V Prabha conceptualized the study. The data collection was performed by Subharthi Chowdhuri and Kiran Todekar. All the analyses were carried out by Subharthi Chowdhuri. The first draft was written by Subharthi Chowdhuri and the others commented on previous versions of the manuscript. All authors read and approved the final manuscript.
Data availibility On reasonable request, the EC dataset analyzed during the current study can be made available to the interested researchers by contacting Thara V Prabha (thara@tropmet.res.in). The computer codes needed to reproduce the figures are available by contacting Subharthi Chowdhuri at subharthi.cat@tropmet. res.in. (9) = arctan (m), Fig. 9 For the period between 15:10-16:10 PM, we show, a the cross-correlation coefficients ( R xy ) between the 4-m ( x = 4 m) and other three observation levels ( y = 8, 20, and 40 m) against the spatial-lags ( Δx ) for the water-vapor density fluctuations ( ′ ), b the scatter plot between Δz and Δx with a best-fit straight-line, whose slope determines the inclination angle, and c the vertical variation of the horizontal mean windspeed ( U ). The description of different colored lines is provided in the legend of (a)