3.1. Case Analysis
The source of energy for turbulence is mainly mechanical movement work and buoyancy work. According to this energy theory, there are mainly three ways to generate turbulence. One is the turbulence caused by wind shear and topographic factors near the ground, and the energy is generated by tangential stress. The second is the turbulence that occurs in the region with thermal instability; its energy is produced by work done by buoyancy. The third is the turbulence caused by waves and wind shear that is large enough to flip the density of the upper and lower layers, and the gravity wave breaks because the amplitude is increasing. The waves generated at this density interface are called Kelvin–Helmholtz waves. Clear air turbulence is usually thought to be caused by the breaking up of the Kelvin–Helmholtz wave [
38]. What needs to be explained here is that the concept of the Ozmidov scale is relevant for stratified turbulence only. It has no meaning for convective-driven turbulence. Therefore, in the following, we do not discuss the results of the boundary layer.
Since the balloon does not rise at a constant speed, the vertical resolution of the data is uneven, and the original data are reinterpolated according to the average step size (5 m). When calculating the Richardson number here, the average value of five consecutive points is used to obtain the wind speed and the potential temperature at an interval of 25 m. The gradient Richardson number can be characterized by
where
corresponds to
(
) when the air is unsaturated (saturated).
is calculated over 50 m intervals. Because of the influence of small-scale fluctuations and noises, it is smoothed by five points, denoting a spatial moving average with a segment of 200 m. When
< 0, the atmosphere is statically unstable, generating thermal turbulence. When 0 <
< 0.25, the atmosphere is favorable for dynamic instability, and mechanical turbulence occurs. Firstly, the Thorpe method is applied to a finite number of radiosonde data to verify the feasibility of turbulence retrieval. We use wind shear, buoyancy frequency and the Richardson number to describe atmospheric instability.
Figure 3a–h respectively show the profiles of potential temperature, vertical wind shear (the square root of the denominator of the fraction in Equation (14), buoyancy frequency, gradient Richardson number, horizontal wind component, Thorpe length, energy dissipation rate and turbulent diffusivity calculated at 12 UT on 31 May 2018. In
Figure 3b, the maximum wind shear is between 18 and 20 km and is significantly higher than the surrounding area, which is caused by the tropical easterly jet stream. The buoyancy frequency in
Figure 3c is significantly larger in the stratosphere than that in the troposphere. There are some negative values of buoyancy frequency in the troposphere, corresponding to the static instability region in the atmosphere, while in the stratosphere, buoyancy frequency is mainly dominated by positive values.
Figure 3d shows that there are significant differences in the main mechanisms of turbulence between the stratosphere and the troposphere. Regions where
< 0 and 0 <
< 0.25 both exist in the troposphere, indicating that there is both thermal and mechanical turbulence in the troposphere. In the stratosphere, the Richardson number is significantly increased, showing that there is mainly mechanical turbulence in the stratosphere.
Figure 3e shows that the meridional and zonal components of the smoothed horizontal wind speed vary with height. It can be seen that the zonal wind is significantly larger than the meridional wind, and the values of u and v are significantly increased near the tropopause where the upper-level jet stream is formed.
Figure 3f shows the distribution of the Thorpe length after the real overturn is selected. The maximum value of
is around 10 km, corresponding to the area with the largest wind shear. The distribution of
is mainly concentrated between 10 and 20 km. The turbulence with static instability in the troposphere is widespread, corresponding to the relatively large Thorpe scale, while static instability in the stratosphere is rare, and the inversion scale of the
profile is small, with a correspondingly small Thorpe’s scale.
Figure 3g,h represent the distribution of the energy dissipation rate and the turbulent diffusion coefficient with height, respectively. It can be seen that the trends of the two have a good consistency. According to the formula of the turbulent diffusion coefficient calculated by the Thorpe method,
, it can be seen that their small differences in the changing trend are due to the buoyancy frequency. The region where the maximum value of
and
exist match the region of the maximum value of the Thorpe length. It should be noted here that the instantaneous profile of
is calculated according to whether the water vapor is saturated, and
and
are respectively selected to eliminate small-scale fluctuations and noise; a moving average in 200-m steps is applied to
to obtain
. When calculating
and
, we use the positive buoyancy frequency
calculated from the sorted potential temperature profile.
To make the results more universally applicable, the cumulative profile distribution from May 10 to 31 May 2018 is shown in
Figure 4. The wind shear decreases with height and then increases. The maximum value of wind shear is present near the tropopause, corresponding to the upper-level jet stream near the tropopause. The negative value of buoyancy frequency is more common in the upper troposphere, indicating that the static stability of the atmosphere decreases first and then increases with height. The above results show that static instability and dynamic instability coexist over the entire troposphere height range, while in the stratosphere, the atmosphere is dominated by dynamic instability. Thorpe’s length is obviously greater in the troposphere than that in the stratosphere.
It should be noted that we dropped the daytime data to avoid the interference of instrument noise and weak stratification, which are not suitable for Thorpe analysis [
39,
40]. Especially in the middle and upper troposphere in the daytime, the noise cannot be completely eliminated, which can cause a mixture of noise and turbulence, resulting in a thicker turbulent patch, so the retrieval result at night is closer to the real state of the atmosphere. Above 30 km,
and
become markedly concentrated and strengthened; this is the result of the abnormally increased Lt. We believe that because the tnr is relatively small above 30 km, small-scale turbulence is easily confused with increasing noise, resulting in a significantly larger Thorpe length. Therefore, in later discussions, our analysis of turbulence parameters is limited to 30 km.
To explore the statistical results and temporal evolution of turbulence parameters, we applied the Thorpe method to balloon sounding data in the Guam area in 2013–2018. A total of 2086 profiles were collected for these six years (for some days, the measurements are missing, and for other days, they are not adopted because the maximum height that the released balloon can detect is too low). It should be noted that the turbulence scale has anisotropy in the three-dimensional space. Here, we discuss the distribution rule of the turbulent vertical scale according to the calculation results of the sounding data.
3.2. Background Wind Field, Local Instability and Occurrence Rates of Turbulence
We calculated the wind component, wind shear and buoyancy frequency for a total of six years to reflect the atmospheric instability. The data are monthly averaged values, and the parameters at the vertical height are averaged at intervals of 200 m.
Figure 5 shows the monthly averaged zonal wind, meridional wind, shear and squared Brunt–Väisälä frequency from 2013 to 2018.
Figure 5a shows the zonal wind speeds, and
Figure 5b shows the meridional wind speeds. Zonal wind speeds range from −40 to 20 m/s, meridional wind speeds range from −10 to 10 m/s, and they all show significant annual oscillations (AO). From
Figure 5c, we can see that there is a large wind shear near the ground, and the wind shear decreases gradually as the height increases. There is a small wind shear between 11 and 15 km, indicating relatively weak stratification stability. The existence of jet streams near the tropopause and in the stratosphere allows the wind shear to return to a higher level.
Figure 5d shows the static stability of the atmosphere through the squared Brunt–Väisälä frequency. The stratospheric atmosphere has a strong stratification, while the middle and upper troposphere has a weak stratification, with a small buoyancy frequency between 11 and 15 km. Under the above atmospheric conditions, turbulence can be generated in various ways, including the fragmentation of gravity waves caused by wind shear, the wind shear near the jet stream, the work done by convection instability [
41], the larger wind shear near the ground and gravity waves excited by terrain [
42,
43,
44,
45]. Long-term wind field variation indirectly promotes turbulence by affecting gravity wave activity and shear instability.
Because turbulence is highly intermittent and random in space and time, it is more reasonable to express the frequency of turbulence in terms of the occurrence rates in a fixed area.
Figure 6a shows the monthly means for the Thorpe length
,
Figure 6b shows the monthly occurrence rates of
,
Figure 6c shows the monthly occurrence rates of
and
Figure 6d shows the monthly occurrence rates of
. The maximum value of
is distributed between 12 and 16 km below the cold point tropopause, which can reach over 100 m, and the value has pronounced seasonal variation. The maximum of
within this height range usually occurs from July to September. We call it the “strongest turbulent mixing band,” corresponding to the region where the monthly occurrence rates of
and the monthly occurrence rates of
are both higher. The occurrence rates of turbulence in this region can also reach more than 60%, indicating that turbulent mixing easily occurs in this region as a result of weak laminar stability, including mechanical turbulence and thermal turbulence. The monthly occurrence rates of turbulence below 10 km are probably around 20%, and the corresponding monthly means for the Thorpe length
are within 50 m. The turbulence in this region is caused by both convective instability (
) and dynamic instability (
), and the turbulence near the ground is mainly generated by the dynamic instability caused by topography and wind shear. In the stratosphere, however, the occurrence rate of turbulence is much lower, corresponding to a smaller turbulence scale and intensity, and turbulence in this region is mostly caused by dynamic instability. In the stratosphere, the variation law for the occurrence rates of
is highly consistent with the strongest turbulent mixing band; it can be reduced from 10% in July–September to less than 1% in the other months. According to
Figure 6, it can be observed that turbulent mixing in the weak stratification region has a high intensity and a larger Thorpe length, corresponding to larger turbulence intensity, while in the static stable region, the exchange of materials and energy between the upper and lower layers is weak, and the Thorpe length is smaller, corresponding to lower turbulence intensity.
3.3. Distribution of Turbulent Overturn Size, Energy Dissipation Rate and Diffusion Coefficient
The turbulent overturn size can be represented as the vertical thickness of an independent turbulent patch, and the thickness is calculated as , where a and b denote the lowermost and uppermost bin of the patch, and is the average sampling step. The turbulent energy dissipation rate and turbulent diffusion coefficient determine the ability of the flow to maintain turbulence or develop into turbulence. and need to be calculated precisely, as they can control the transport of matter and energy in the atmosphere.
3.3.1. Distribution Characteristics of the Statistical Histogram
Figure 7a–b shows the frequency distribution of the turbulence overturn size from 2013 to 2018 in the troposphere and stratosphere, respectively. Generally speaking, the amount of turbulence decreases with the increase in the overturn size, and the scale of turbulence is dominated by a small scale. However, limited by the resolution of the sensor, the minimum overturn size detected here is 10 m. Through the experimental results of [
25], we know that the turbulence detected by low-resolution detection (5–9 m) in the troposphere is only 7% of the high-resolution detection (10–20 cm), while in the stratosphere, the value is reduced to 4%. That is to say, the smaller-scale turbulence is undetectable, so the exploration of turbulence characteristics in this paper is based on the turbulence of a large vertical scale. In the troposphere, the most abundant turbulence scale is between 100 and 200 m, accounting for 34.2% of the total turbulence, while in the stratosphere, the most abundant turbulence scale is below 100 m, accounting for 73.0% of the total turbulence. The overturn size that exceeds 100 m accounts for 75.5% in the troposphere, and even 39.7% of the turbulence scales can exceed 500 m. As for the stratosphere, the overturn size that exceeds 500 m only accounts for 3.0% of the total turbulence.
The number of turbulence layers in the troposphere (stratosphere) accounts for 82% (18%) of the total. The amount of turbulence detected in the troposphere is far more than that in the stratosphere. In the stratosphere, the stratification is stable, the buoyancy work is relatively difficult, and the convective exchange of the upper and lower layers is weak. Therefore, the Thorpe displacement of a single particle is small, and the thickness of the independent overturn region calculated by the Thorpe method is relatively thin, which leads to the relatively small thickness of the turbulent patch. Strong wind shear in the stable stratified atmosphere will cause the atmospheric density to invert up and down, causing the amplitude of the gravity wave to increase and then break, resulting in clear-air turbulence (CAT), which is also the main form of turbulence in the stratosphere.
Figure 8a,b shows the frequency distribution of
in the troposphere and stratosphere.
Figure 8c,d show the same distribution but for
. The magnitude of
is between 10
-6 and 10
0 m
2 s
−3, which is mainly distributed between 10
−4 and 10
−2 m
2 s
−3 in the troposphere, accounting for 71.48% of the total and between 10
−5 and 10
−3 m
2 s
−3 in the stratosphere, accounting for 76.67% of the total. The magnitude of
is between 10
−2 and 10
2 m
2 s
−1, which is mainly distributed between 10
−1 and 10
1 m
2 s
−1 in the troposphere, accounting for 78.64% of the total and between 10
−2 and 10
0 m
2 s
−1 in the stratosphere, accounting for 90.82% of the total. Regardless of whether it is in the stratosphere or troposphere,
has a normal distribution; the mean value in the troposphere is 0.0068, as computed by
, and the standard deviation is 1.0060, as computed by
. In the stratosphere, the mean value is 0.0016, and the standard deviation is 0.8171.
has an apparent normal distribution only in the troposphere. Regardless of whether we examine
or
, the main frequency distribution area in the troposphere is an order of magnitude higher than that in the stratosphere. If the turbulence is divided into strong turbulence according to the value of the energy dissipation rate (
> 10
−4 m
2 s
−3) and weak turbulence (
< 10
−4 m
2 s
−3) [
46], strong turbulence accounts for 77.48% in the troposphere and 65.98% in the stratosphere. The proportion of strong turbulence over the entire detection height is 74.27%.
3.3.2. Distribution Characteristics of Time Series
In order to explore the characteristics of the temporal and spatial distribution of the turbulence thickness, turbulent energy dissipation rate and diffusion coefficient, the height is stratified at intervals of 200 m, and the monthly average is taken. According to the previous statistical distribution results, turbulence patches with thicknesses of more than 1000 m are discarded, and the ranges of and are set at 10−6–100 m2 s−3 and 10−2–102 m2 s−1, respectively.
Figure 9 shows the time series of atmospheric column characteristics from 2013 to 2018;
Figure 9a–c show the monthly means of the turbulence thickness, turbulent energy dissipation rate and turbulent diffusion coefficient, respectively. There is a region with large turbulence scales that range between 11 and 16 km, in which the maximum turbulence thickness also appears in July–September every year, showing the same annual oscillations (AO) as the Thorpe length since they are directly physically related. Turbulence scales in this region range from 300 to 1000 m. Below 10 km, the turbulence thickness is within 200 m, and the thickness also varies alternately with time. In the stratosphere, the turbulence thickness is relatively small, with the average scale not exceeding 10 m after a 200 m vertically spaced average. The energy dissipation rate and turbulent diffusivity have the same distribution characteristics as the overturn size in the troposphere. From July to September, compared with other months, there are larger values of
and
in the upper troposphere, while the smaller values of
and
remain in the lower troposphere.
It can be seen from Equations (5) and (6) that the values of and are affected by the value of , and the extreme value distribution area of is also the extreme value distribution area of and . Although is related to , it is also related to the buoyancy frequency according to the Thorpe method. Specifically, the variables in Equation (5) include and . is significantly increased, while is significantly decreased in the stratosphere, and the term has a more obvious impact than the term. Therefore, in the stratosphere, can still be larger, though the value of is relatively small. This also shows that under the condition of stable stratification, even if turbulent overturn does not easily occur or if the turbulence scale is small, a relatively large energy dissipation rate can still exist. In other words, small-scale turbulence in a stratified stable atmosphere can also generate fast energy dissipation. The subterms in Equation (6) include and ; the magnitude of is much larger than that of , and is a quadratic term, while is in the first degree, so the value of is more susceptible to the term. The values of and have almost consistent variation trends in the troposphere, but for the stratosphere, although there is an interval with a relatively large value of , it corresponds to a relatively small value of , which indicates that it is in the unstable region of the atmosphere. The larger turbulent scale corresponds to stronger dissipation and diffusion, while in the stable region of the atmosphere, where the turbulence scale is usually small, the turbulent diffusion is weak, while the energy dissipation is strong.
3.3.3. Profile Distribution Characteristics of Multiyear Monthly Averages
The results in the previous discussion clearly demonstrate the annual oscillation characteristics of turbulence parameters, and the period from July to September is when the turbulence scale and turbulence intensity are significantly enhanced. Therefore, we divided the six-year data into four groups: January–March, April–June, July–September and October–December; the data in each group were averaged according to a height interval of 2 km to obtain the distribution characteristics of the turbulence parameters with height in different seasons. The result is shown in
Figure 10.
Figure 10a–d shows the vertical distribution of
,
, turbulence thickness and Thorpe length, respectively (blue: January–March; red: April–June; magenta: July–September; cyan: October–December). The averaging was done across the whole data set.
It can be seen from the results that the distribution characteristics of the turbulence scale, turbulence intensity, turbulent energy dissipation rate and turbulent diffusion coefficient have significant seasonal differences with height. The turbulent energy dissipation rate and turbulent diffusion coefficient change little with heights below 7 km; the values of are distributed between 0.0010 and 0.0032 m2 s−3, and the values of are distributed between 0.5 and 1.9 m2 s−1. They both reach the maximum value at around 15–16 km, and their values from July to September are significantly higher than those in the other months. The maximum values of and can reach 0.0116 m2 s−3 and 9.7 m2 s−1, respectively, from July to September. From 15 to 23 km, and decrease significantly and reach their minimum value at 23 km, which is 3 × 10−5 m2 s−3 and 0.0163 m2 s−1, respectively. Above 23 km, they both increase with altitude.
The turbulence scale and Thorpe length are consistent with the variation trend of and below 20 km. Below 7 km, the average turbulence thickness is within 100 m, and the average Thorpe length is between 8 and 20 m. Between 7 and 20 km, the turbulence scale and Thorpe length increase rapidly with height and reach the maximum value at around 15 km, which is 600 and 77 m, respectively, and then they decrease rapidly with height. Above 20 km, the mean values of turbulence thickness and length are close to 0, indicating only sporadic small turbulence above this height.
It can be seen that significantly enhanced turbulence parameters are concentrated between 14 and 16 km for all balloon flights. The obvious enhancement of turbulent mixing near the tropopause is a long-term stable feature over Guam.
Figure 11 shows the average profile distribution of the atmospheric background field. Wind shear, horizontal wind field and buoyancy frequency are averaged at an altitude interval of 1 km. This turbulent layer may be mainly caused by static instability as
at this level reaches the minimum value. Another possible cause is the intense shear instability in trop-stratospheric jet streams. There is more intense turbulence activity in the height range from July to September compared with the annual average level. This is because there is a stronger horizontal wind field near the tropopause from July to September, where meridional and zonal winds increase significantly, which can lead to significantly increased wind shear. At the same time, between 15 and 19 km, the rapid increase in
with height will lead to an increase in the amplitude of the gravity wave [
47], and the strong wind shear within the corresponding height will lead to the breakup of the gravity wave and produce turbulence.
3.4. Overview and Discussion
The results show that p(
> 0) exceeds 60% in the altitude range of 12–16 km, and it decreases to a level below 10% above 20 km. In Zhang’s research [
27], p(
> 0) varies from as high as 90% in the altitude range of 9–11 km to around 10% above 25 km. He et al. [
8] also show that the area with the strongest turbulent activity is around 10 km. Zhou [
48] proposed the concept of the “Strongest Mixed Layer,” that is, the area of the maximum value of
. The result shows that the height of the strongest mixing layer gradually decreases from the equator to the poles, which is a direct consequence of the fact that the height of the tropopause increases from the poles to the equator. Considering the different areas studied, this is also the reason that the extreme regions of Thorpe length are not the same in different studies. The overturn size, turbulent kinetic energy dissipation rate and turbulent diffusion coefficient also show obvious annual oscillations (AO), consistent with
. It is worth noting that low-value areas with buoyant frequencies near the tropopause also correspond to areas where the Richardson number is weak, indicating that turbulence is more likely to occur near the upper troposphere than the lower troposphere. As can be seen from the results, the turbulent maximum mixing zone corresponds to the minimum value of static stability, the maximum value of wind speed and the minimum value of vertical shear. Considering that the gravity wave activity will reduce the local static stability [
49], the small average wind shear is sufficient to induce Kelvin–Helmholtz instability. This phenomenon is also consistent with the result of [
50], which shows that the low-frequency gravity wave easily induces Kelvin–Helmholtz instability. In other words, the gravity wave activity can reduce the static stability, so small vertical shear is also prone to dynamic instability [
51]. The vertical scale of turbulence is considerably larger than that in other regions; this is referred to as the “strongest turbulent mixing band” in this article. Its existence is very important for the material exchange and interaction between the troposphere and stratosphere [
52].
At a given time, if the turbulence scale in the upper troposphere is relatively large, then the turbulence scale in the lower troposphere is relatively small and vice versa. The same occurs with
ε,
K and even wind speed. Because the tropical western Pacific is the main area where Madden–Julian Oscillation (MJO) occurs, it has an approximate barometric vertical structure, showing that the zonal wind field tilts westward with height. The antiphase of the upper and lower troposphere appears. We speculate that this may be a possible reason that the turbulent activity at the corresponding height presents a similar antiphase; however, this needs to be further demonstrated. Because of the seasonal evolution of the Earth’s orbital parameters, the direct solar point moves from north to south with the seasons, and the influence of the sun on the region also changes throughout the year. Considering that the direct solar point is passing through the tropical western Pacific from north to south at this time, a significant increase in turbulence activity may occur from July to September. Kohma et al. [
26] mentioned that seasonal variation in radar-based ε shows a broad maximum in August–October and low values in November–January in the lower stratosphere, which is similar to our results. The statistical characteristics of gravity waves at Gadank, which has the same latitude as Guam, are discussed in detail in [
53,
54,
55], which have a certain reference significance for the turbulence distribution characteristics in this paper. Clear seasonal variation in the wave activity was noted in their study, and during the monsoon season, they found that the significant enhancement of gravity wave activity was related to the westward phase of the zonal wind. In the results in this paper, the turbulence enhancement area in the strongest mixing zone also corresponds to the westward propagation of the zonal wind, indicating a correlation between turbulence and the gravity wave activity behind it.
All our results show that regardless of the variation in time and space, there is always a strong turbulent mixing band with significant AO caused by both shear instability and static instability near the tropopause, and it is localized in the portion of the wave characterized by reduced static stability where the turbulence activity is markedly enhanced. These results can be used for reference to understand the turbulence characteristics over the tropical Western Pacific Ocean [
56,
57,
58,
59], and the continuous high-resolution radiosonde data can also be helpful for model calibration and the verification of turbulence parameters. The link between the gravity wave and turbulence is worthy of further study, and the roles that they play in the complex air–sea system of the tropical western Pacific need further research.