# Spatiotemporal Distribution of Atmospheric Ducts in Alaska and Its Relationship with the Arctic Vortex

Authors: Yanbo Mai; Zheng Sheng; Hanqing Shi; Qixiang Liao; Wei Zhang
Journal: International Journal of Antennas and Propagation
 (2020)

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## Abstract

In this paper, global position system high-resolution sounding data from 1998 to 2008 were used to statistically analyze the spatiotemporal distribution and determine the probability, thickness, and intensity of atmospheric ducts at 12 stations in Alaska. In addition, the singular value decomposition (SVD) was used to examine the relationship between the Arctic vortex and atmospheric ducts. The annual average probability of atmospheric ducts, primarily surface and elevation ducts, was approximately 30% in Alaska. The probability of elevation ducts was greater than that of surface ducts. The Arctic vortex area and intensity index of each subarea were significantly negatively correlated with the occurrence of atmospheric ducts. Thus, when the area of the Arctic vortex increased and the intensity index of each subarea strengthened, the probability of atmospheric ducts decreased and their characteristics weakened.


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## Body

## 1. Introduction

The propagation of electromagnetic waves in the atmosphere is affected not only by the absorption and scattering of molecules and aerosol particles but also by atmospheric refraction. Abnormal refractions such as negative, super, and trapping refraction can cause the abnormal propagation of electromagnetic waves. Particularly under trapping refraction conditions, electromagnetic waves are partially captured in a certain thickness of the atmosphere and reflect back and forth through the upper and lower atmospheric layers, similar to the propagation of waves in metal waveguides. This propagation phenomenon is called atmospheric duct propagation. The atmosphere that forms this propagation because of the uneven distribution of temperature and pressure in the vertical direction is called an atmospheric duct.Manjula et al. [1] used high-resolution vertical and temporal radiosonde measurements to study the diurnal variation in ducting over the Indian tropical region. Sirkova [2] reported on the occurrence and properties of tropospheric ducts along the Bulgarian shore of the Black Sea. Kaissassou et al. [3] used six years (2006–2011) of situ measurements of temperature, moisture, and pressure made by the Agency for the Safety of Air Navigation in Africa and Madagascar to determine the conditions for surface ducts over the Ngaoundere region. On the basis of global position system (GPS) radiosonde data near the sea surface, Cheng et al. [4] analyzed the characteristics of surface ducts over the South China Sea (SCS). Mufti and Siddle [5] analyzed the annual, seasonal, monthly, daily, and hourly trends of evaporation ducts occurring in the English Channel and found the annual mean duct height was 7.3 m, and for seasonal trends, there were higher values in autumn and lower ones in summer. On the basis of GPS radiosonde data collected four times daily during autumn open cruises from 2006 to 2012, Cheng et al. [6] analyzed the characteristics of lower atmospheric ducts over the SCS. Yang et al. [7] used reanalysis datasets from the National Centers for Environmental Prediction to statistically analyze the features of the evaporation ducts over the global ocean. Zhang et al. [8] used a 31-year high-resolution dataset from the climate reanalysis product of the National Centers for Environmental Prediction Climate Forecast System Reanalysis to determine the evaporation duct climatology for the Gulf of Aden. Hao et al. [9] analyzed the worldwide occurrence of atmospheric ducts using radiosonde data from 2005 to 2014 and found the probability of atmospheric ducts varied in different regions of the world. On the basis of the sounding data in Qingdao during 2005–2013, Shen et al. [10] analyzed the signatures of ducts, temperature inversions, and intense humidity gradients and found the effect of intense humidity gradients on the occurrence of ducts was more remarkable and direct than that of temperature inversions. Based on the theoretical derivation, Sheng and Huang [11, 12] used the simulated and measured radar echo data to retrieve the parameters of evaporation ducts and analyzed the inversion results and the antinoise ability of the inversion system. Liu et al. [13] compared the sensitivity of four prediction models of evaporation ducts to meteorological elements and provided the calculation results of the height of four models of evaporation ducts based on the meteorological observation of South China Sea, which provided certain theoretical basis and practical experience for future practical application.The cold air that affects China originates in the Arctic Ocean and its surrounding areas [14]. During winter nights, the intense radiant cooling forms a very cold, large-scale air mass, which is a very shallow, cold high pressure on the ground. Because of the difference in heat between sea and land, this shallow high pressure and the cold high pressure of Siberia and Canada constitute a large system [14]. This system can be replaced by low pressure at a certain height, and at this height, it becomes a cyclone vortex around the Arctic region called the Arctic vortex [14]. Schmidt et al. [15] analyzed the variation in available chlorine, Cly, in the Arctic vortex during EASOE. Knudsen et al. [16] calculated the diabatic cooling with PV-theta mapped ozone mixing ratios and large ozone depletion, particularly at the center of the vortex where most polar stratospheric cloud (PSC) was predicted and found increases in diabatic cooling of up to 80%. Konopka et al. [17] used simulations with the three-dimensional Chemical Lagrangian Model of the Stratosphere to analyze mixing and ozone loss in the 1999–2000 Arctic vortex. Hurwitz et al. [18] analyzed the Arctic vortex in March 2011 from a dynamical perspective and found tropospheric planetary wave driving was unusually weak, consistent with a strong, stable Arctic vortex in late winter and a relatively late vortex breakup. Wetzel et al. [19] studied the diurnal variations in reactive chlorine and nitrogen oxides observed by MIPAS-B inside the January 2010 Arctic vortex. Kim et al. [20] used observational analyses and model experiments to show that Arctic sea ice loss and cold winters in extrapolar regions are dynamically connected through the polar stratosphere. Hu and Guan [21] used reanalysis datasets and numerical simulations to study the relationship between the stratospheric Arctic vortex (SAV) and the Pacific decadal oscillation on decadal timescales. Hu et al. [22] used three reanalysis datasets to analyze the strengthening of the SAV response to warming in the central North Pacific (CNP) and found that the SAV intensity during 1998–2016 strengthened, in contrast to the weakening before that period. The warming of sea surface temperature over the CNP contributed approximately 25% to this strengthening. Zhang et al. [23] used a Eurasia-North America dipole mode in the total column ozone over the Northern Hemisphere to study the stratospheric ozone loss over the Eurasian continent induced by a polar vortex shift. Xie et al. [24] investigated the effect of ASO changes on North Pacific SST and the processes by which the stratospheric circulation anomalies caused by ASO changes propagate to the North Pacific, induce North Pacific Oscillation (NPO) anomalies, and then force North Pacific SST anomalies. Hu et al. [25] used a state-of-the-art general circulation model to study the impacts of the stratospheric ozone depletion from 1980 to 2000 and the expected partial ozone recovery from 2000 to 2020 on the propagation of planetary waves in December, January, and February. Zhang et al. [26] analyzed various datasets and model simulations to reveal that the vortex shift induces cooling over some parts of the Eurasian continent and North America which partly offsets the tropospheric climate warming there in the past three decades.However, the influence of the Arctic vortex on atmospheric ducts has not been studied. In this paper, high-resolution sounding data of the 11 years from 1998 to 2008 were used to statistically analyze the spatiotemporal distribution of atmospheric ducts at 12 stations in Alaska. The probability of occurrence and the intensity and thickness of atmospheric ducts were also determined. The mechanism for the influence of the Arctic vortex on the atmospheric ducts was examined using the SVD [27]. The results of this study will have reference value and are significant for future research on the influence of the Arctic vortex on atmospheric ducts.


## 2. Data and Methods

The high-resolution sounding data of the global telecommunication system from 1998 to 2008 were used in this study because these data were the latest high-resolution sounding data published for the Alaska region. The range of the data included Alaska and the surrounding sea in the United States. Twelve observation stations were used with a latitude range of 55°N–75°N and a longitude range of 130°W–175°W. The location of each station is shown in Figure1.Figure 1
Geographic location of 12 observation stations in the Alaska region.Atmospheric refraction in radio meteorology refers to the bending behavior of electromagnetic waves propagating in atmospheric media. The degree of refraction can be measured by the refractive indexn [28], which is defined as the ratio of the propagation velocity c (speed of light) of a radio wave in free space to the propagation velocity v in the medium as follows:(1)n=cv.The normal value of the atmospheric refractive index of the Earth’s surface is generally 1.000251.0004 [28]. Because of the small value, the value of n is not convenient for practical application in the study of radio wave propagation. Therefore, the refractivity of the atmosphere [28] is defined as N as follows:(2)N=77.6T×p+4810eT,where p is the atmospheric pressure (hPa), T is the atmospheric thermodynamic temperature (K), and e is the vapor pressure (hPa). The atmospheric refractivity N of a spherical surface generally varies between 250 N and 400 N units [28]. Because the atmospheric pressure and the rapid decrease in water vapor with height decrease slowly, the atmospheric refractive index or refraction generally decreases with increasing height [28]. When the distance of the electromagnetic waves propagation is close, the surface of the Earth can be approximated as a plane, but when the distance of the wave is far away, the influence of the curvature of the Earth must be considered. To treat the surface of the Earth as a plane and more easily evaluate the atmospheric refractivity gradient and its effect on the propagation of the electromagnetic waves, the atmospheric corrected refractivity [28] is defined as M as follows:(3)M=N+0.157z=77.6PT+3.73×105×eT2+0.157Z,where M is a dimensionless number. For the convenience of statistics, M was used as the unit. P, T, e, and Z are the atmospheric pressure (hPa), temperature (K), vapor pressure (hPa), and height from the ground (m), respectively. GPS high-resolution sounding data are records of meteorological parameters such as temperature and humidity at the height of a radiosonde balloon. The vertical resolution below 100 m is 10–80 m and that of 100–1000 m is 30–300 m [28]. The average thickness of surface and elevation ducts is between tens of meters and several hundred meters [28]. Therefore, sounding data can be used for the study of atmospheric ducts. However, multiple layers of atmospheric ducts are sometimes superimposed on one another, although this phenomenon is rare at high latitudes [28]. Therefore, only the first layer of an atmospheric duct was used for statistical analysis. First, the GPS data were preprocessed; the invalid data in the record were removed; the pressure, temperature, and dew point temperature data of each layer were extracted; and the corrected refractivity M of the layer was calculated by formula (3). Then, to determine the top height, thickness, and intensity of the ducts, the gradient of change in M was analyzed with height, according to the following specific methods and steps.When the atmospheric correction refractivityM satisfies dm/dz<0, then the atmospheric duct layer appears, and the height is called the bottom of the atmospheric duct. As the height increases, when dm/dz>0, the duct disappears, and this height is called the top of the duct layer [28]. The difference in height between the bottom of the duct layer and the top of the duct layer is called the thickness of the atmospheric duct and is represented by H. The difference between the atmospheric corrected refractivity M at the bottom and the top is called the intensity of the atmospheric duct layer, represented by ΔM. According to the change in M with height, atmospheric ducts are primarily divided into three categories: surface duct, elevation duct, and evaporation duct (Figure 2).Figure 2
Classification of atmospheric ducts: (a, b) surface duct; (c) elevation duct; (d) evaporation duct.
(a)
(b)
(c)
(d)The evaporation ducts mainly appear in the near layer of the ocean atmosphere, where the potential temperature decreases slightly with the vertical height, while the specific humidity decreases rapidly with the vertical height [28]. In the band of microwave, the contribution of the vertical gradient of humidity to the vertical gradient of the atmospheric refractive index is greater than that of the vertical gradient of temperature, so the atmospheric corrected refractive index decreases rapidly with the increase of the vertical height in the near-Earth layer, which forms an evaporation duct. Surface ducts and elevation ducts are mainly found in the atmospheric inversion layer, in which the potential temperature increases rapidly with the increase of the vertical height, while the specific humidity decreases rapidly with the increase of the vertical height [28], so the atmospheric corrected refractive index decreases with the decrease of the vertical height in the inversion layer, which is easy to form the atmospheric ducts. When the bottom height of the inversion layer is high, the lower boundary of ducts is ungrounded to form an elevation duct, while the bottom height of the inversion layer is low, the lower boundary of the duct will be grounded to form a surface duct [28].The Chinese Climate Center provides monthly Arctic vortex indices for the Northern Hemisphere and its subzones. The Arctic vortex indices of 1–13 are the following: polar vortex area indices in Asia, the Pacific region, North America, Atlantic Europe, and the Northern Hemisphere; polar vortex intensity indices in Asia, the Pacific region, North America, the North Atlantic-European region, and the Northern Hemisphere; and the polar vortex center meridional position index, the polar vortex center latitudinal position index, and the polar vortex center strength index in the Northern Hemisphere [29]. The SVD is a diagnostic technique applied to study the correlation characteristics of two meteorological fields [27]. The SVD is primarily used to decompose the spatiotemporal fields of a coupled field, thereby extracting useful information about time and space, according to the following specific steps.In the case of two variable fields, one field can be called the left field, consisting ofp spatial points and the sample size of n, which is recorded as matrix X. The other field is called the right field, consisting of q spatial points and the sample size also of n, which is recorded as matrix Y. The elements in X and Y are standardized. The covariance matrix between the two fields is sp×q, and therefore, the SVD for any asymmetric matrix S of p×q order can be obtained as follows:(4)S=L⋀m000RT.The component form of equation (4) is as follows:(5)S=∑k=1mλklkrkT,m≤minp,q.For the left singular vector, the number of vectorslk is m, which are orthogonal to one another. For the right singular vector, the number of vectors rk is m, which are also orthogonal to one another. The purpose of SVD is to identify a linear combination of two variable fields, that is, construct two matrices from the left and right fields as follows:(6)U=LTX,V=RTY.To uniquely decompose equation (4), let L and R meet the conditions of normalized vectors, namely:(7)LLT=I,RRT=I.Simultaneously, a maximization of covariance occurs between the matricesU and V, namely:(8)COVU,V=LTSR=MAX.The time coefficient matrixUt, Vt of the left and right fields is calculated by formula (8), and the left heterogeneous correlation coefficient is defined as follows:(9)rkX,V=ExitvktExi2t1/2Evk2t1/2=λklkEvk2t1/2.The right heterogeneous correlation coefficient is defined as follows:(10)rkY,U=EyituktEyi2t1/2Euk2t1/2=λkrkEuk2t1/2.The distribution structure of the relationship between the two variables is represented in the distributions of the correlation coefficients for equations (9) and (10). The significant correlation region is the key region of the interaction between two variables. rX,V and rkY,U are usually referred to as heterogeneous correlation coefficients.In this paper, the SVD decomposition method was used to treat the monthly average Arctic vortex indices 1–13 of the 11-year period from 1998 to 2008 as the left element field and the monthly average probability, intensity, and thickness of the 12 stations in this text as the right element field. Their left and right heterogeneous correlation coefficients were analyzed separately to obtain the relationship between them.


## 3. Results and Discussion

### 3.1. Annual Average Probability Distribution of Atmospheric Ducts

Figure3 and Table 1 show the annual average probability distribution of the atmospheric ducts at each station. The annual average probability of the elevation ducts, approximately 20% at most stations, was higher than that of the surface ducts at approximately 10%. The total probability of atmospheric ducts exceeded 35% at stations 25339, 25501, and 25713, and although the probability at the other stations was lower, the total probability at most stations was greater than 25%. Overall, the annual probability of atmospheric ducts at most stations in Alaska was approximately 30%, and the stations with the highest frequencies were primarily located in the southern and northern areas of the study region.Figure 3
Annual average probability distribution (%) of surface, elevation, and total ducts at 12 stations in Alaska.Table 1
Annual average probability of surface and elevation ducts.
Number
Station
Surface duct (%)
Elevation duct (%)
Total (%)
1
25339
12.51
26.57
39.07
2
25501
12.05
23.58
35.56
3
25503
6.96
20.54
27.49
4
25624
6.64
27.94
34.57
5
25713
17.26
26.15
43.41
6
26409
11.29
21.87
33.16
7
26411
11.76
16.56
28.32
8
26510
8.02
17.09
25.12
9
26615
12.60
21.93
34.53
10
26616
7.14
20.00
27.15
11
26617
5.50
17.83
23.33
12
27502
8.38
24.08
32.46


### 3.2. Annual Average Intensity Distribution of Atmospheric Ducts

Figure4 shows the annual average intensity distribution of the atmospheric surface and elevation ducts at each station. The annual average intensity of surface ducts was different at each station. The annual average intensity at stations 25339, 26411, 26510, and 26616 was higher than that at other stations and exceeded 2.5 M. The lowest annual average intensity was at station 27502 and was less than 2 M. The annual average intensity of elevation ducts was approximately 2 M, with some stations showing relatively high values. For example, station 25713 had the highest strength of approximately 3 M. Overall, the differences in annual average intensity among all stations in Alaska were less for elevation ducts than for surface ducts.Figure 4
Annual average intensity (M) distribution of atmospheric (a) surface ducts and (b) elevation ducts at 12 stations in Alaska.
(a)
(b)


### 3.3. Annual Average Thickness Distribution of Atmospheric Ducts

Figure5 shows the annual average thickness distribution of the atmospheric surface and elevation ducts at each station. The annual average thickness of the surface ducts differed substantially among stations but for most stations was between 30 and 40 m. Among the stations, the thickness at stations 25339, 26411, 26510, and 26616 was relatively high, exceeding 40 m. The annual average thickness of the elevation ducts was approximately 30 m but was relatively high at some individual stations. For example, the thickness at station 21573 was approximately 45 m. Overall, the differences in the thickness among all stations in the Alaska region were less for elevation ducts than for surface ducts.Figure 5
Annual average thickness (m) distribution of atmospheric (a) surface ducts and (b) elevation ducts at 12 stations in Alaska.
(a)
(b)


### 3.4. Seasonal Distributions of Average Probability of Atmospheric Ducts

Figures6 (surface ducts) and 7 (elevation ducts) show the seasonal average probability distributions of atmospheric ducts at each station. The probability of atmospheric duct occurrence among the four seasons was different. The probability of surface ducts was higher in the summer, with that of most stations greater than 3%, whereas the probability was lower in winter, with the probability between 1% and 2%. The probability of elevation ducts was similar to that of the surface ducts. The highest frequencies of elevation ducts occurred in summer, with the probability at most stations greater than 10%. The lowest frequencies of elevation ducts occurred in winter, with the probability less than 5%.Figure 6
Seasonal (spring, summer, autumn, and winter) average probability (%) distributions of surface ducts at 12 stations in Alaska.Figure 7
Seasonal (spring, summer, autumn, and winter) average probability (%) distributions of elevation ducts at 12 stations in Alaska.


### 3.5. Seasonal Distributions of Intensity of Atmospheric Ducts

Figures8 (surface ducts) and 9 (elevation ducts) show the seasonal average intensity distributions of atmospheric ducts at each station. Substantial seasonal differences were observed for the average intensity of the atmospheric ducts. The highest average intensity of surface ducts was in summer, and for most of the stations, the intensity was approximately 3 M. The weakest average intensity of surface ducts was in winter, with values only between 1 and 1.5 M. The average intensity of the elevation ducts was similar to that of the surface ducts. The average intensity was the highest in summer, ranging around 3 M, and the lowest in winter, ranging from 1 to 1.5 M.Figure 8
Seasonal average intensity (M) distributions of surface ducts at 12 stations in Alaska: (a) spring; (b) summer; (c) autumn; (d) winter.
(a)
(b)
(c)
(d)Figure 9
Seasonal average intensity (M) distributions of elevation ducts at 12 stations in Alaska: (a) spring; (b) summer; (c) autumn; (d) winter.
(a)
(b)
(c)
(d)


### 3.6. Seasonal Distributions of Thickness of Atmospheric Ducts

Figures10 (surface ducts) and 11 (elevation ducts) show the seasonal average thickness distributions of atmospheric ducts at each station. The average thickness of surface ducts was the greatest in summer, with most stations at approximately 40 m; the thickness was slightly lower in spring and autumn than in summer. The thickness was the least in winter, with the average of most stations less than 30 m. The thickness of elevation ducts was similar to that of surface ducts and was the greatest in summer, with the thickness of most stations approximately 40 m. The thickness was the least in winter, with that of most stations less than 30 m.Figure 10
Seasonal average thickness (m) distributions of surface ducts at 12 stations in Alaska: (a) spring; (b) summer; (c) autumn; (d) winter.
(a)
(b)
(c)
(d)Figure 11
Seasonal average thickness (m) distributions of elevation ducts at 12 stations in Alaska: (a) spring; (b) summer; (c) autumn; (d) winter.
(a)
(b)
(c)
(d)


### 3.7. The Connection between Atmospheric Ducts and the Arctic Vortex

The monthly average Arctic vortex indices 1–13 of the 11 years from 1998 to 2008 were used as the left element field, and the monthly average probability, intensity, and thickness at the 12 stations in this text were used as the right element field for the SVD decomposition. The variance contribution of the first mode exceeded 95% and passed the 95% significance test. The contribution was less than 5% of the second and third modes to the variance, much smaller than the first mode. Thus, the first mode could reflect the relationship between the Arctic vortex and the atmospheric ducts. The heterogeneous correlation coefficients between the Arctic vortex and the atmospheric ducts are presented in the following figures.Figures12 (surface ducts) and 13 (elevation ducts) show the results of the correlations between the Arctic vortex indices and the atmospheric ducts for the SVD decomposition method. As shown in Figures 12(a), 12(c), and 12(e) and 13(a), 13(c), and 13(e), Arctic vortex indices 1–10 were negatively correlated with the probability, intensity, and thickness of the atmospheric ducts. All correlation coefficients exceeded 0.6 and passed the significant t-distribution test of 0.1. Polar vortex index 11 was also negatively correlated with these parameters, but the correlation was not significant according to the t-distribution test of 0.1. Polar vortex indices 12 and 13 were significantly positively correlated with the parameters, passing the significant t-distribution test of 0.1. As shown in Figures 12(b), 12(d), and 12(f), and 13(b), 13(d), and 13(f), the probability, intensity , and thickness showed a large response to the Arctic vortex index of each zone, and all right heterogeneous correlation coefficients passed the significant t-distribution test of 0.1. Therefore, when the polar vortex area index and the intensity index of each zone strengthened, the probability, intensity, and thickness of the atmospheric ducts weakened. This relation can be explained because the Arctic vortex disrupts the conditions necessary for the formation of atmospheric ducts. Atmospheric ducts form when the positional temperature in an inversion layer increases rapidly with the increase in vertical height and the humidity decreases rapidly with the increase in vertical height. Therefore, the stronger the inversion temperature is, the easier the formation of atmospheric ducts is. The Arctic vortex is the low-pressure center of the Arctic region, and when it moves southward, it transports large amounts of cold air and water vapor. The cold air and water vapor reduce the temperature and humidity gradients in the inversion layer and thereby inhibit the occurrence of the atmospheric ducts.Figure 12
(a) Left heterogeneous correlation coefficients of the Arctic vortex indices (1–13) and the probability of surface ducts. (b) Right heterogeneous correlation coefficients of the Arctic vortex indices and the probability of surface ducts. (c) Left heterogeneous correlation coefficients and (d) right heterogeneous correlation coefficients of the Arctic vortex indices and the intensity of surface ducts. (e) Left heterogeneous correlation coefficients and (f) right heterogeneous correlation coefficients of the Arctic vortex indices and the thickness of surface ducts.
(a)
(b)
(c)
(d)
(e)
(f)Figure 13
(a) Left heterogeneous correlation coefficients of the Arctic vortex indices (1–13) and the probability of elevation ducts. (b) Right heterogeneous correlation coefficients of the Arctic vortex indices and the probability of elevation ducts. (c) Left heterogeneous correlation coefficients and (d) right heterogeneous correlation coefficients of the Arctic vortex indices and the intensity of elevation ducts. (e) Left heterogeneous correlation coefficients and (f) right heterogeneous correlation coefficients of the Arctic vortex indices and the thickness of elevation ducts.
(a)
(b)
(c)
(d)
(e)
(f)


## 3.1. Annual Average Probability Distribution of Atmospheric Ducts

Figure3 and Table 1 show the annual average probability distribution of the atmospheric ducts at each station. The annual average probability of the elevation ducts, approximately 20% at most stations, was higher than that of the surface ducts at approximately 10%. The total probability of atmospheric ducts exceeded 35% at stations 25339, 25501, and 25713, and although the probability at the other stations was lower, the total probability at most stations was greater than 25%. Overall, the annual probability of atmospheric ducts at most stations in Alaska was approximately 30%, and the stations with the highest frequencies were primarily located in the southern and northern areas of the study region.Figure 3
Annual average probability distribution (%) of surface, elevation, and total ducts at 12 stations in Alaska.Table 1
Annual average probability of surface and elevation ducts.
Number
Station
Surface duct (%)
Elevation duct (%)
Total (%)
1
25339
12.51
26.57
39.07
2
25501
12.05
23.58
35.56
3
25503
6.96
20.54
27.49
4
25624
6.64
27.94
34.57
5
25713
17.26
26.15
43.41
6
26409
11.29
21.87
33.16
7
26411
11.76
16.56
28.32
8
26510
8.02
17.09
25.12
9
26615
12.60
21.93
34.53
10
26616
7.14
20.00
27.15
11
26617
5.50
17.83
23.33
12
27502
8.38
24.08
32.46


## 3.2. Annual Average Intensity Distribution of Atmospheric Ducts

Figure4 shows the annual average intensity distribution of the atmospheric surface and elevation ducts at each station. The annual average intensity of surface ducts was different at each station. The annual average intensity at stations 25339, 26411, 26510, and 26616 was higher than that at other stations and exceeded 2.5 M. The lowest annual average intensity was at station 27502 and was less than 2 M. The annual average intensity of elevation ducts was approximately 2 M, with some stations showing relatively high values. For example, station 25713 had the highest strength of approximately 3 M. Overall, the differences in annual average intensity among all stations in Alaska were less for elevation ducts than for surface ducts.Figure 4
Annual average intensity (M) distribution of atmospheric (a) surface ducts and (b) elevation ducts at 12 stations in Alaska.
(a)
(b)


## 3.3. Annual Average Thickness Distribution of Atmospheric Ducts

Figure5 shows the annual average thickness distribution of the atmospheric surface and elevation ducts at each station. The annual average thickness of the surface ducts differed substantially among stations but for most stations was between 30 and 40 m. Among the stations, the thickness at stations 25339, 26411, 26510, and 26616 was relatively high, exceeding 40 m. The annual average thickness of the elevation ducts was approximately 30 m but was relatively high at some individual stations. For example, the thickness at station 21573 was approximately 45 m. Overall, the differences in the thickness among all stations in the Alaska region were less for elevation ducts than for surface ducts.Figure 5
Annual average thickness (m) distribution of atmospheric (a) surface ducts and (b) elevation ducts at 12 stations in Alaska.
(a)
(b)


## 3.4. Seasonal Distributions of Average Probability of Atmospheric Ducts

Figures6 (surface ducts) and 7 (elevation ducts) show the seasonal average probability distributions of atmospheric ducts at each station. The probability of atmospheric duct occurrence among the four seasons was different. The probability of surface ducts was higher in the summer, with that of most stations greater than 3%, whereas the probability was lower in winter, with the probability between 1% and 2%. The probability of elevation ducts was similar to that of the surface ducts. The highest frequencies of elevation ducts occurred in summer, with the probability at most stations greater than 10%. The lowest frequencies of elevation ducts occurred in winter, with the probability less than 5%.Figure 6
Seasonal (spring, summer, autumn, and winter) average probability (%) distributions of surface ducts at 12 stations in Alaska.Figure 7
Seasonal (spring, summer, autumn, and winter) average probability (%) distributions of elevation ducts at 12 stations in Alaska.


## 3.5. Seasonal Distributions of Intensity of Atmospheric Ducts

Figures8 (surface ducts) and 9 (elevation ducts) show the seasonal average intensity distributions of atmospheric ducts at each station. Substantial seasonal differences were observed for the average intensity of the atmospheric ducts. The highest average intensity of surface ducts was in summer, and for most of the stations, the intensity was approximately 3 M. The weakest average intensity of surface ducts was in winter, with values only between 1 and 1.5 M. The average intensity of the elevation ducts was similar to that of the surface ducts. The average intensity was the highest in summer, ranging around 3 M, and the lowest in winter, ranging from 1 to 1.5 M.Figure 8
Seasonal average intensity (M) distributions of surface ducts at 12 stations in Alaska: (a) spring; (b) summer; (c) autumn; (d) winter.
(a)
(b)
(c)
(d)Figure 9
Seasonal average intensity (M) distributions of elevation ducts at 12 stations in Alaska: (a) spring; (b) summer; (c) autumn; (d) winter.
(a)
(b)
(c)
(d)


## 3.6. Seasonal Distributions of Thickness of Atmospheric Ducts

Figures10 (surface ducts) and 11 (elevation ducts) show the seasonal average thickness distributions of atmospheric ducts at each station. The average thickness of surface ducts was the greatest in summer, with most stations at approximately 40 m; the thickness was slightly lower in spring and autumn than in summer. The thickness was the least in winter, with the average of most stations less than 30 m. The thickness of elevation ducts was similar to that of surface ducts and was the greatest in summer, with the thickness of most stations approximately 40 m. The thickness was the least in winter, with that of most stations less than 30 m.Figure 10
Seasonal average thickness (m) distributions of surface ducts at 12 stations in Alaska: (a) spring; (b) summer; (c) autumn; (d) winter.
(a)
(b)
(c)
(d)Figure 11
Seasonal average thickness (m) distributions of elevation ducts at 12 stations in Alaska: (a) spring; (b) summer; (c) autumn; (d) winter.
(a)
(b)
(c)
(d)


## 3.7. The Connection between Atmospheric Ducts and the Arctic Vortex

The monthly average Arctic vortex indices 1–13 of the 11 years from 1998 to 2008 were used as the left element field, and the monthly average probability, intensity, and thickness at the 12 stations in this text were used as the right element field for the SVD decomposition. The variance contribution of the first mode exceeded 95% and passed the 95% significance test. The contribution was less than 5% of the second and third modes to the variance, much smaller than the first mode. Thus, the first mode could reflect the relationship between the Arctic vortex and the atmospheric ducts. The heterogeneous correlation coefficients between the Arctic vortex and the atmospheric ducts are presented in the following figures.Figures12 (surface ducts) and 13 (elevation ducts) show the results of the correlations between the Arctic vortex indices and the atmospheric ducts for the SVD decomposition method. As shown in Figures 12(a), 12(c), and 12(e) and 13(a), 13(c), and 13(e), Arctic vortex indices 1–10 were negatively correlated with the probability, intensity, and thickness of the atmospheric ducts. All correlation coefficients exceeded 0.6 and passed the significant t-distribution test of 0.1. Polar vortex index 11 was also negatively correlated with these parameters, but the correlation was not significant according to the t-distribution test of 0.1. Polar vortex indices 12 and 13 were significantly positively correlated with the parameters, passing the significant t-distribution test of 0.1. As shown in Figures 12(b), 12(d), and 12(f), and 13(b), 13(d), and 13(f), the probability, intensity , and thickness showed a large response to the Arctic vortex index of each zone, and all right heterogeneous correlation coefficients passed the significant t-distribution test of 0.1. Therefore, when the polar vortex area index and the intensity index of each zone strengthened, the probability, intensity, and thickness of the atmospheric ducts weakened. This relation can be explained because the Arctic vortex disrupts the conditions necessary for the formation of atmospheric ducts. Atmospheric ducts form when the positional temperature in an inversion layer increases rapidly with the increase in vertical height and the humidity decreases rapidly with the increase in vertical height. Therefore, the stronger the inversion temperature is, the easier the formation of atmospheric ducts is. The Arctic vortex is the low-pressure center of the Arctic region, and when it moves southward, it transports large amounts of cold air and water vapor. The cold air and water vapor reduce the temperature and humidity gradients in the inversion layer and thereby inhibit the occurrence of the atmospheric ducts.Figure 12
(a) Left heterogeneous correlation coefficients of the Arctic vortex indices (1–13) and the probability of surface ducts. (b) Right heterogeneous correlation coefficients of the Arctic vortex indices and the probability of surface ducts. (c) Left heterogeneous correlation coefficients and (d) right heterogeneous correlation coefficients of the Arctic vortex indices and the intensity of surface ducts. (e) Left heterogeneous correlation coefficients and (f) right heterogeneous correlation coefficients of the Arctic vortex indices and the thickness of surface ducts.
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(f)Figure 13
(a) Left heterogeneous correlation coefficients of the Arctic vortex indices (1–13) and the probability of elevation ducts. (b) Right heterogeneous correlation coefficients of the Arctic vortex indices and the probability of elevation ducts. (c) Left heterogeneous correlation coefficients and (d) right heterogeneous correlation coefficients of the Arctic vortex indices and the intensity of elevation ducts. (e) Left heterogeneous correlation coefficients and (f) right heterogeneous correlation coefficients of the Arctic vortex indices and the thickness of elevation ducts.
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## 4. Conclusions

In this paper, the high-resolution sounding data of the global telecommunication system were used to calculate the spatiotemporal distribution of atmospheric ducts in the Alaska region. The occurrence of atmospheric ducts is related to the Arctic polar vortex for the first time, and the effect of the polar vortex on the formation of atmospheric ducts is explained.The probability of elevation ducts was greater than that of surface ducts at 12 stations in Alaska. The average probability of atmospheric ducts was approximately 30% per year. The average annual probability was relatively high at stations 25339, 25501, and 25713, exceeding 35%. Seasonal differences were observed, with the highest probability for the occurrence of atmospheric ducts in summer and the lowest probability in winter. The annual average intensity of the surface ducts at each station was different, with values at stations 25339, 26411, 26510, and 26616 relatively high, exceeding 2.5 M. For the elevation ducts, stations 25539, 25624, 25713, and 27502 had higher annual average intensity than that at other stations, exceeding 2 M. The intensity at the other stations was approximately 2 M. The seasonal variation in the average intensity of the two types of atmospheric ducts was significant. The average intensity was highest at each station in summer, whereas the average intensity in winter was relatively small. The annual average thickness of the surface ducts of most stations was between 30 and 40 m. Among the stations, the thickness was relatively high at stations 25339, 26411, 26510, and 26616, exceeding 40 m. For the average annual thickness of elevation ducts, the thickness at stations 25539, 25624, 25713, and 27502 was higher than that at other stations, exceeding 30 m. The average annual thickness at the other stations was approximately 30 m. The average thickness of surface and elevation ducts was the greatest in summer, exceeding 30 m for both. The thickness was least in winter, generally less than 30 m. The different distances from the ocean lead to the obvious differences in the characteristic of the atmospheric ducts between these stations. For the stations closed to the ocean, the water vapor is relatively sufficient, and the phenomenon of atmospheric ducts is more likely to occur. The Arctic vortex area and intensity indices were significantly negatively correlated with the probability and characteristics of the atmospheric ducts in the Alaska region. Thus, when the intensity and area of the polar vortex increased, the probability and characteristics of the atmospheric ducts decreased substantially. Atmospheric ducts occur because of the rapid increase in the potential temperature in an inversion layer and the rapid decrease in the humidity with the increase in vertical height. The sharper the gradient is, the easier the formation of atmospheric ducts is. With a strong gradient, the characteristics of the atmospheric ducts are also more pronounced (strong). The Arctic vortex is the low-pressure center of the Arctic, and when it moves southward, large amounts of cold air and water vapor are transported. The cold air and water vapor reduce the temperature and humidity gradients in an inversion layer and thus inhibit the formation of atmospheric ducts. As a result, the probability of occurrence of atmospheric ducts is reduced, and the intensity and height are weakened of those that form.Although the spatiotemporal distribution characteristics of atmospheric ducts were analyzed for some stations in Alaska because not many stations (10) were included, and some of the high-resolution sounding data were incomplete and lost, and these results do not represent the phenomenon in the whole of Alaska. The overall distribution within the Alaska area remains to be further verified. In addition, for the first time, the Arctic vortex was associated with the atmospheric ducts of the Alaska region, with the vortex area and intensity indices negatively correlated with the probability of atmospheric ducts. The results of this study will have certain significance as a reference for the future study of the relationship between the Arctic vortex and atmospheric ducts.



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*Source: 9673289-2020-01-07.xml*