Spatiotemporal Characteristics of the Evaporation Duct in the Kuroshio Extension

The evaporation duct over the sea affects the propagation of electromagnetic waves, impacts the performance of electromagnetic systems accordingly, such as the shipborne radars. In order to reveal the spatiotemporal variations of the evaporation duct in the Kuroshio Extension (KE) region, where is one of the most intense air-sea interaction regions, the study utilized a 30-year ERA5 reanalysis dataset (from 1993 to 2022) and conducted statistical analysis on the monthly, seasonal variations and spatial distribution characteristics of the evaporation duct based on the NPS evaporation duct diagnostic model. The results enrich the database of maritime evaporation duct characteristics and improve the resolution and accuracy compared to previous studies.


Introduction
Evaporation duct is a special atmospheric duct that frequently occurs in the marine atmospheric boundary.It is characterized by good stability, long duration, and extends over long distances horizontally, often reaching hundreds of kilometers.When both the radar antenna and the target locating within the atmospheric duct, the actual detection range of the radar can exceed the limits of normal detection, resulting in over-the-horizon radar detection.Furthermore, the errors in radar range, height, and velocity caused by the evaporation duct are much larger than those caused by normal refraction conditions [1] .
The formation of the evaporation duct is mainly due to the decrease in water vapor content in the air from saturation near the sea surface to low environmental levels at certain heights, resulting in a specific vertical distribution of atmospheric refractivity [2] .Since the evaporation duct occurs at relatively low altitudes over the sea, direct measurements within a few meters above the sea surface are not feasible.Additionally, disturbances from ocean waves, turbulence, and other factors render single-point instantaneous measurements of limited significance in characterizing the evaporation duct.Therefore, researchers are keen on developing evaporation duct diagnostic models based on empirical relationships derived from macroscopic observational data.These models indirectly calculate the distribution characteristics of evaporative duct parameters near the sea surface by using gradient meteorological data obtained from radiosondes and coastal towers [3] .For example, by using the meteorological data voluntarily collected by merchant ships between 1970 and 1984, the PJ (Paulus-Jeske) model is constructed to calculate the global evaporation duct database.However, due to the high time and monetary costs, this method has limitations in studying the characteristics of evaporation ducts in large sea areas over long periods of time, and the database has low spatial resolution of 10°×10° [ 4] .In the 21st century, with the popularity of high-resolution satellite data, methods utilizing satellite data to improve spatial resolution have been gradually adopted by many researchers.Jiao et al. [5] first inverted satellite data to obtain sea surface temperature, reference height temperature, wind field, and water vapor content field, and finally calculated the evaporation duct environment in large sea areas using the evaporation duct diagnostic model.Frederickson et al. [6] used NCEP reanalysis data in conjunction with the NPS evaporation duct model proposed by the US Naval Postgraduate School to establish a global evaporation duct database with higher spatial resolution.Subsequently, this method has been widely applied and has become an important means for researchers to diagnose and analyze the environmental characteristics of evaporation ducts in global seas [4,[7][8][9] .
Based on the comprehensive research findings of previous studies, it is known that evaporation ducts vary significantly with time and exhibit certain regional dependencies.As a key area of oceanatmosphere interaction, the KE region experiences unique evolution trends in evaporative duct parameters due to the ongoing small-scale processes in the ocean.So far, the environmental characteristics of evaporation ducts in the KE region could only be extracted from the characteristics of overall evaporation ducts in the global ocean or Pacific Ocean [4] , with relatively low resolution and accuracy.Therefore, we use the NPS results based on ERA5 data output in the third section to study the monthly and seasonal variations and corresponding spatial distribution characteristics of the average evaporative duct thickness and intensity in the KE region from 1993 to 2022.Further in the fourth section, we discuss the causes of the above-mentioned spatial-temporal distribution of evaporative ducts from two aspects: distribution of mesoscale eddies in the KE region and changes in Kuroshio current.The research findings of this article enrich the database of environmental characteristics of evaporative ducts, optimize its spatial resolution and parameter accuracy, and provide data support for optimizing the efficiency of detection and communication systems such as shipborne radars.

ERA5 Reanalysis Dataset
The ERA5 reanalysis dataset is a global atmospheric climate dataset provided by ECMWF.It offers hourly data from 1940 to present with a spatial resolution of 0.25°×0.25°.In this study, we will extract hourly data from the KE region (141°E -165°E, 32°N-38°N) [10] .The parameters used include sea-level pressure (), sea surface temperature (  ), 2-meter dew point temperature (  ), 2-meter air temperature (), and 10-meter meridional () and zonal () wind components for calculating evaporation duct characteristics.

CMEMS Dataset
The satellite altimeter data SEALEVEL_GLO_PHY_L4_MY_008_047 from CMEMS (Copernicus Marine Environment Monitoring Service) is available at https://data.marine.copernicus.eu/product/SEALEVEL_GLO_PHY_L4_MY_008_047/download.This observational data provides daily measurements from January 1, 1993, to August 4, 2022, with a spatial resolution of 0.25°×0.25°.For this study, a subset of the data was used, with a spatial range covering the KE region.The parameters utilized include latitude and longitude grid data, sea level anomaly (), and geostrophic current velocities (, ).

NPS Evaporation Duct Diagnostic Model
Based on the similarity theory, the vertical profiles of temperature () and specific humidity () at a certain vertical height  in the near-surface layer can be represented by the following equations: where   and   are the sea surface temperature and specific humidity, respectively.Taking into account the effect of seawater salinity on specific humidity,   is set as 0.98  , where   is the saturation specific humidity calculated based on the sea surface temperature. * and  * are characteristic scales for potential temperature and specific humidity, respectively. is the von Karman constant. 0 is the roughness height for temperature.  is the temperature universal function.Γ  is the dry adiabatic lapse rate, approximately equal to 0.00976 K/m. is the similarity length.The COARE 3.0 algorithm is used to determine the surface-scale parameters and roughness calculations [11] .
Taking the atmospheric pressure at the sea surface height  0 as ( 0 ), the atmospheric pressure at a certain vertical height z in the near-surface layer can be represented as P(z) by combining the ideal gas law and fluid statics equation and integrating it [12] .
where  is the gas constant for dry air,  is the acceleration due to gravity, and   is the average virtual temperature between the measurement height  0 and the height .
Next, the water vapor pressure profile can be calculated using specific humidity () and atmospheric pressure (): where  is a constant value of 0.622.Finally, by substituting the obtained temperature, pressure, and water vapor pressure profiles into the refractive index correction formula, the corrected refractive index profile can be obtained, which allows for the determination of parameters such as the evaporative duct thickness and strength.

Evaporative Duct Parameters Calculation Flow
Sea surface temperature, air temperature, and sea-level pressure are directly obtained from the ERA5 dataset.The calculation of relative humidity (RH) (%) at a height of 2m is done using the Goff-Gratch formula and the Tetens empirical formula as follows: lg(  ) = 10.79574 ( =    (7)   where   represents the saturated water vapor pressure (hPa) at a height of 2m,  represents the water vapor pressure (hPa) at a height of 2m, and  0 = 273.16represents the triple point temperature of water.
Wind speed is calculated by data in ERA5:  = √ 2 +  2 (8) To sum up, the calculation flow of evaporative duct parameters is shown in the figure 1.

Temporal Change Trends
In order to better understand the overall evolution trend of the Kuroshio extension area, we averaged the thickness and intensity of evaporation ducts in the KE region on monthly and seasonal time scales from 1993 to 2022.The overall monthly and seasonal variation trends of the thickness and intensity of the evaporation pipeline are shown in the figures below.
From the overall seasonal average (Figure 2) and monthly average (Figure 3) of the duct parameters, it can be found that the monthly average evaporative duct thickness and intensity in the KE region exhibit similar evolutionary characteristics, with apparent seasonal and monthly variations.The duct parameters in the KE region are at a higher level during winter.From December to February of the following year, they show a relatively stable performance with a gradual downward trend.The duct thickness (intensity) fluctuates between 10.6-12.1m(28.4-35.5M).After winter, the duct parameters in the KE region begin to decrease, reaching lower values during spring and summer.The minimum values for duct thickness and intensity occur in summer, reaching 7.3m and 20.6M, respectively.The duct parameters recover to their highest level during autumn, with averages of 11.5m and 36.7M.In particular, the duct parameters in the KE region undergo a decreasing phase from January to June, reaching the minimum in June at 6.1m (15.9M).From June to July, the duct parameters gradually increase but remain at a low level of 6.1-6.6m(15.9-17.2M).In July and August, the duct thickness and intensity rapidly increase to higher levels.Thereafter, the rate of increase slows down but still shows positive growth, reaching the maximum values in November during autumn at 12.1m and 38.9M.

Spatial Distribution Pattern Evolution
Compared to the variation of the average evaporative duct parameters in the Kuroshio extension region, the spatial distribution characteristics of these parameters with the evolution of months or seasons are more notable.Therefore, the average distribution of the evaporative duct thickness for each grid point in the KE region from 1993 to 2022, for each month, as well as for the spring to winter seasons, is plotted as follows.Looking at the spatial distribution of the evaporative duct thickness across seasons (Figure 4) and its monthly variations (Figure 5), it shows distinct seasonal and monthly changes.The evaporative duct intensity exhibits similar evolutionary characteristics to the duct thickness.
(1) In winter, the low-value centers with duct thickness below 10m are concentrated in the northwest region.The average duct thickness in the KE region ranges from 7.2m to 13.1m, indicating a generally higher level.From December to February, the duct parameters gradually decrease but still maintain a relatively high level.
(2) In spring, the duct thickness in the KE region ranges from 7.1m to 11.0m, with a spatial distribution characterized by high values in the southwest region and low values in other areas.The high-value area with duct thickness between 10-11m is concentrated in the seas east Japan.
(3) In summer, the high-value region of the duct thickness is concentrated near the Kuroshio axis, while other regions show relatively lower levels.The average duct thickness during this season is below 9m, reaching the lowest level throughout the year.In June, the duct parameters reach their lowest values, with some areas having duct thickness approaching 5m.
(4) In autumn, the high-value region of the duct thickness expands eastward, eventually bringing the duct parameters in the Kuroshio axis and its southern area back to a high level.However, the sea areas east of Fukushima and Mito in Japan still maintain relatively lower levels.

Discussions
To explore the reasons for the aforementioned changes in evaporative duct parameters in the KE region, we have plotted the anomalies of sea surface height and the average distribution of ocean currents over the past thirty years in the following figures.Previous studies have indicated that the formation of evaporative ducts is primarily influenced by the sharp decrease in humidity from the sea surface to the atmosphere and atmospheric stability [2] .From the Figure 6, it can be observed that warm eddies dominate in the KE region during autumn, when the duct parameters quickly recover.Conversely, during spring, when the duct parameters reach lower levels, cold eddies dominate in the KE region.In summer, when the overall duct parameters are at their lowest, the area of maximum values corresponds to a concentrated distribution of warm eddies.Ma et al. [13] indicated that under the dominance of momentum mixing mechanisms, the upward latent and sensible heat fluxes caused by warm eddies weakened the atmospheric stability, thereby enhancing turbulent mixing and ultimately leading to positive anomalies in humidity and temperature.Franklin et al. [14] revealed in their recent study that these changes can lead to an increase in duct parameters.It is worth noting that the seasonal variation of the current of the Kuroshio makes the air-sea interaction weaker in spring and summer and stronger in autumn and winter.Whether this causes the relative seasonal variation of evaporative duct parameters in the KE region is still a problem worth studying.

Summary and Conclusion
This study utilizes the latest ERA5 reanalysis data and the NPS diagnostic model to calculate the characteristic parameters of evaporation duct.Compared to the previous research, improvements have been made in terms of resolution and accuracy.Statistical analysis was conducted specifically for the KE region to investigate the temporal and spatial characteristics of evaporation duct environments.The research findings are as follows: (1) In terms of temporal trends, the thickness and intensity of evaporative ducts in the KE region exhibit clear monthly and seasonal variations.The duct parameters show a trend of weakening followed by strengthening throughout the year, reaching the minimum value in June and subsequently increasing to reach the maximum value in November.
(2) Regarding the spatial distribution pattern, starting from December and continuing until June of the following year, the thickness of evaporative ducts gradually decreases, and the spatial distribution shifts from a pattern of lower values in the northwest to a distribution of higher values near the Kuroshio axis.After June, the thickness of evaporative ducts gradually increases, spreading from the southwest to the east and finally reaching the northeast, recovering to the pattern of higher values in the northwest and lower values in other areas.
(3) In terms of causative analysis, preliminary analysis suggests that the seasonal variation of the Kuroshio and the seasonal variation of mesoscale eddies along the Kuroshio ultimately lead to the observed seasonal changes in duct parameters.
The statistical analysis of the environmental change of the evaporation duct in the KE region can provide research support for the communication and ranging of shipborne radar, provide a reference for the application of evaporation duct in China, and provide favorable conditions for the establishment of a more accurate database.However, it is difficult to obtain the measured data at sea, so it is difficult to implement the correction process of the research results.It is still necessary to modify the parameters of the diagnostic model for evaporation duct through the measured data in the KE region to improve the accuracy of the conclusion.Secondly, it should be noted that this paper only put forward two factors that may cause the characteristic distribution of the evaporation duct through qualitative analysis.Whether there are other influencing factors and the quantitative analysis of their respective proportions will be the next research focus.

Figure 1 .
Figure 1.Schematic diagram of evaporative duct parameter calculation flow.

Figure 2 .
Figure 2. Seasonal variations in the average evaporative duct parameters in the KE region.

Figure 3 .
Figure 3. Monthly variations in the average evaporative duct parameters in the KE region.

Figure 4 .
Figure 4. Seasonal variations in the spatial pattern evolution of evaporative duct thickness (above) and intensity (below).

Figure 5 .
Figure 5. Monthly variations in the spatial pattern evolution of evaporative duct thickness (above) and intensity (below).Looking at the spatial distribution of the evaporative duct thickness across seasons (Figure4) and its monthly variations (Figure5), it shows distinct seasonal and monthly changes.The evaporative duct intensity exhibits similar evolutionary characteristics to the duct thickness.(1)In winter, the low-value centers with duct thickness below 10m are concentrated in the northwest region.The average duct thickness in the KE region ranges from 7.2m to 13.1m, indicating a generally higher level.From December to February, the duct parameters gradually decrease but still maintain a relatively high level.(2)In spring, the duct thickness in the KE region ranges from 7.1m to 11.0m, with a spatial distribution characterized by high values in the southwest region and low values in other areas.The high-value area with duct thickness between 10-11m is concentrated in the seas east Japan.(3)In summer, the high-value region of the duct thickness is concentrated near the Kuroshio axis, while other regions show relatively lower levels.The average duct thickness during this season is below 9m, reaching the lowest level throughout the year.In June, the duct parameters reach their lowest values, with some areas having duct thickness approaching 5m.(4)In autumn, the high-value region of the duct thickness expands eastward, eventually bringing the duct parameters in the Kuroshio axis and its southern area back to a high level.However, the sea areas east of Fukushima and Mito in Japan still maintain relatively lower levels.

Figure 6 .
Figure 6.Seasonal variations in the spatial pattern evolution of Sea surface height above sea level (color) and Ocean Current (arrow).Previous studies have indicated that the formation of evaporative ducts is primarily influenced by the sharp decrease in humidity from the sea surface to the atmosphere and atmospheric stability[2] .From the Figure6, it can be observed that warm eddies dominate in the KE region during autumn, when the duct parameters quickly recover.Conversely, during spring, when the duct parameters reach lower levels, cold eddies dominate in the KE region.In summer, when the overall duct parameters are at their lowest, the area of maximum values corresponds to a concentrated distribution of warm eddies.Ma et al.[13] indicated that under the dominance of momentum mixing mechanisms, the upward latent and sensible heat fluxes caused by warm eddies weakened the atmospheric stability, thereby enhancing turbulent mixing and ultimately leading to positive anomalies in humidity and temperature.Franklin et al.[14] revealed in their recent study that these changes can lead to an increase in duct parameters.It is worth noting that the seasonal variation of the current of the Kuroshio makes the air-sea interaction weaker in spring and summer and stronger in autumn and winter.Whether this causes the relative seasonal variation of evaporative duct parameters in the KE region is still a problem worth studying.