The evaporation duct over the sea is usually assessed using bulk meteorological measurements. This paper investigates the utility of meteorological buoys as a source for these bulk measurements and compares evaporation duct assessments using two buoys in southern California waters separated by 128 km. A simple radio propagation experiment at 2.4 GHz between one of the buoys and the coast on an 18.2 km path is described. Observed propagation loss from this experiment is compared to modeled loss based on the meteorological measurements at each buoy. The purpose of this paper is to investigate radio propagation effects using established and accepted methods already described in the literature. Accordingly, no discussion of atmospheric surface layer meteorology affecting radio propagation is given.
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 The evaporation duct is usually assessed using measurements of sea surface temperature and, at a convenient reference height, bulk meteorological measurements of air temperature, moisture, and wind speed. One such method is described by Paulus . Using this method in conjunction with various propagation models to assess propagation loss on microwave over-the-horizon paths has generally given very good long-term statistical results. Median modeled loss is often within a few decibels of the median observed loss, as shown by Hitney and Vieth  and Paulus . Figure 1 is an accumulated frequency distribution of propagation loss from Hitney and Vieth  comparing modeled and measured path loss (equivalent to propagation loss for an omnidirectional antenna) at 9.6 GHz for a propagation link between Naxos and Mykonos, Greece, for eight weeks spread over four seasons. The modeled and observed median values match within approximately 2 dB. However, time series comparisons of modeled and observed losses have shown much more variation, presumably from the less-than-ideal meteorological measurements which were typically made at or near coastlines and may be influenced by land effects not representative of the propagation paths involved. Rogers and Paulus  have shown that the LKB method of Liu et al.  performs better than the Paulus method for unstable conditions (air temperature less than sea temperature). Both the Paulus and LKB methods will be considered here.
 In this paper, evaporation duct assessments are based on high-quality meteorological measurements made on oceanographic buoys. The 10-m-diameter buoys are operated by the Scripps Institution of Oceanography (SIO) for the Office of Naval Research (ONR) and are known as the SIO Marine Observatory. The buoys are located just west of Point La Jolla (SIO 1) and San Clemente Island (SIO 2) in California and separated by a distance of 128 km. Figure 2 is a picture of the Point La Jolla buoy (the San Clemente Island buoy is similar), and Figure 3 is a map showing the locations of both buoys. On each buoy the relative humidity and air temperature sensor is a Vaisala HMP45C, and the anemometer sensors (two on each buoy) are a R.M. Young 05106 marine anemometer and a Handar model 425A ultrasonic wind sensor. For the data used in this paper the two wind sensor readings were averaged. SIO constructed the water temperature sensor from a YSI 44016 thermistor. The wind speeds were measured at 9.3 m above sea level, and the air temperature and relative humidity were measured at 8.3 m above sea level. Data have been collected on both SIO buoys since May 1998. In section 2, comparisons of propagation assessments at the two buoy locations will be presented to assess horizontal variation. In section 3, comparisons between modeled loss and observed loss for a 2.4 GHz link between the Point La Jolla buoy and Point Loma in April 1999 will be presented.
2. Comparisons of Assessments at the Two Buoys
 The data from the two SIO buoys are available in real time and in archives over the Internet from the University of California, San Diego (http://tenby.ucsd.edu). The data are measured every minute, averaged for 1 hour, recorded hourly, and archived for public access. Although 5 min averages may be more common for assessing evaporation duct effects, only the 1 hour averages were readily available for this study. As a result, there may be some extra smoothing of the duct heights presented below. For this investigation, data from May 1998 through September 1999 were downloaded for both buoys. Twelve months of data are available for both buoys between May 1998 and September 1999 (SIO 1 was not deployed for the entire period). From these 12 months there were 5029 hourly observations for which both buoys had valid measurements of the four parameters needed to compute the Paulus duct height. These parameters are sea temperature, air temperature, relative humidity, and wind speed. However, since both buoys are fairly close to land, this set of 5029 observations was reduced based on wind direction to ensure that the air flowing past the buoys did not cross over land. For this purpose, wind directions at both buoys between 180° and 310° true were considered to be representative of sea conditions. Requiring the wind direction at both buoys to be within these limits reduces the number of observations considered here to 2618. Figure 4 shows the Paulus duct height for all 2618 hours for both buoys. These plots are monotonic but not continuous in time because of the observations that were eliminated. Table 1 lists the medians of various parameters and the resulting duct heights for the two buoys. The median air-sea temperatures and Paulus duct heights are the medians of all 2618 computed values.
Table 1. Median Values for Several Quantities at Each Buoy
Air temperature, °C
Sea temperature, °C
Air-sea temperature, °C
Relative humidity, %
Wind speed, m/s
Paulus duct height, m
 The median condition at both buoys was unstable, with the air temperature being colder than the sea temperature by medians of 2.7° and 2.1°C. Less than 1% of the cases were stable. The most noticeable difference between the two buoys is the median wind speed, which is nearly twice as high at SIO 2 as at SIO 1. However, the resulting median duct height was only about 15% larger at SIO 2 than at SIO 1. To illustrate how the two computed duct heights compare on an hour-by-hour basis, Figure 5 shows a superposition of the duct heights at each buoy versus hour number for the first 300 hours only. The duct heights for SIO 1 and SIO 2 are shown by the solid and dotted curves, respectively. Most remarkable is how well the two duct heights agree and follow each other, even though the SIO 2 value is normally a little larger than the SIO 1 value. For the 300 hour sample the median duct height at SIO 2 is 18% larger than the median at SIO 1, compared to 15% larger for the 2618 sample. The correlation coefficients for the large and small data sets are 0.33 and 0.56, respectively. For both the large and small data sets the median difference in the duct height between the two buoys is about 1.1 m (the difference of the medians and the median difference are the same in this case). To assess how significant these changes in duct height are, we must consider the radio frequency and geometry of the application in question.
Figure 6 shows propagation loss in decibels versus duct height for frequencies of 1, 3, 5, and 10 GHz for a hypothetical propagation path. Both terminal heights are 10 m, and the path length is 50 km, which is approximately twice the horizon range for these terminal heights. The 50 km path length is a purely arbitrary range of an electromagnetic system such as a radar that has nothing to do with the 128 km range separation of the buoys. The propagation loss was computed using a normal mode waveguide model known as MLAYER, which is described by Hitney et al. . Vertical polarization was assumed, and the evaporation duct profiles were computed using the Paulus method assuming neutral stability (air and sea temperatures being equal). Past experience in modeling has shown that nearly identical results would be obtained using reasonable stable or unstable conditions or the LKB method instead of the Paulus method. The approximate slopes of the curves in Figure 6 are 0.95, 2.4, 3.5, and 6.9 dB per meter of duct height for 1, 3, 5 and 10 GHz, respectively (for 10 GHz the slope was computed only below 10 m duct height, since the curve levels off above this value). Multiplying these slopes by the 1.1 m median difference of duct heights implies that median errors in propagation assessments of 1.0, 2.6, 3.9, and 6.9 dB would be expected for 1, 3, 5, and 10 GHz, respectively. For many applications an uncertainty of 3 dB in propagation loss may be tolerated, so for frequencies of 3 GHz and below, it can be argued that horizontal homogeneity over ranges in excess of 100 km is reasonable, at least in the southern California offshore area. Other regions of the world may, of course, be different.
3. Assessment of a 2.4 GHz Propagation Link
 A radio propagation link was implemented between the Point La Jolla buoy and a land station on Point Loma to verify the utility of the buoy meteorological measurements in assessing propagation effects. This link was implemented using relatively low cost, license-free, spread-spectrum digital transceivers. Since they are license free, there was no need to obtain a frequency allocation or frequency assignment, which together have taken as long as 2 years to obtain for other propagation experiments. There are several companies that make spread-spectrum transceivers for the purpose of establishing wireless data, voice, and video communications, and some of these have diagnostic features that measure received field strength. For this experiment, Utilicom Long Ranger 2020 (model ISM2.4-1T24) transceivers were chosen. They operate in the 2.4 GHz industrial, scientific, and medical (ISM) band and have convenient software-configurable RF link diagnostics that will sample and report received signal level in dBm. These transceivers consist of a small modem box for indoor mounting and an exterior up/down converter to minimize cable loss at 2.4 GHz. The intermediate frequency between the modem and converter is 900 MHz. A 9 dBi gain omnidirection antenna was selected for mounting on one of the outboard towers on the buoy, and a 24 dBi gain wire-mesh parabolic reflector antenna was selected for the land station. Total cost of all the equipment was $5000. The maximum transmitted power is +18 dBm, and the receiver sensitivity is −110 dBm, which allows a theoretical maximum propagation loss of 161 dB to be measured (18 + 9 + 24 + 110 = 161). The exact center frequency selected for operation was 2.4317 GHz, and vertical polarization was used.
 Although each modem is individually calibrated at the factory for received signal strength (RSS), the manufacturer recommended that an additional calibration be performed that included modem operating temperature, since RSS was known to be sensitive to the modem temperature. Without this calibration the manufacturer believed the RSS to be accurate to about 5 dBm, but with the temperature correction the accuracy should be approximately 1 dBm. Only the modem for the land station needed calibration, since RSS was only measured at this end of the path. The transceivers were set up on a 747 m line-of-sight path for this calibration. A Ryan TempMentor temperature sensor was affixed to the modem case, and the modem was placed in a refrigerator and on a bench with and without forced air cooling and allowed to run at various temperatures from 7° to 37°C over several days while the link operated. Figure 7 shows the results of these calibrations and the correction factor required to bring the RSS back to a value consistent with free-space propagation at a range of 747 m, corresponding to a propagation loss of 98 dB. The curve through the data in Figure 7 is a quadratic regression fit to the data given by
where C is the correction factor in decibels and T is the modem temperature in degrees Celsius. During all subsequent operation of the modem the case temperature was monitored over a range of 20° to 27°C, and the correction factor computed from equation (1) was added to the measured propagation loss. Sensitivity of RSS to up/down converter temperature was also investigated but found to be minimal. During this calibration it was also determined that the modem would stay in synchronization down to the specified −110 dBm sensitivity of the receiver by placing a variable attenuator between the antenna and the up/down converter. The variable attenuator was only used for calibration and maximum sensitivity tests and was not in the receiver system during the propagation loss measurements described below.
 The transceiver antenna was placed at 7 m above sea level on one of the buoy's towers with the up/down converter and all connections to the antenna in a well-sealed waterproof utility box. The modem was below deck and powered by the buoy's 24 V battery system. The land station antenna was initially installed about 6 m above mean sea level (msl) at a range of 21 km from the buoy. Operation began on 9 April 1999, but with the exception of some surface-based duct conditions [see Hitney et al., 1985] the modems would not stay in synchronization at this location. The land site was moved to an 18.2 km path with the antenna at 21.5 m above msl on 16 April. At this location the system stayed in synchronization most of the time. Surface-based ducts continued to dominate the propagation conditions until 21 April, but after this date, evaporation duct conditions prevailed. Unfortunately, the system on the buoy failed on 26 April, so only about 6 days of useful data were collected. Figure 8 shows the propagation loss that is expected versus duct height for this land station location.
Figure 9 shows a time series plot of hourly averaged air-sea temperature difference, air temperature, relative humidity, wind speed, and the resulting Paulus duct height at the Point La Jolla buoy (SIO 1, solid circles) and the San Clemente Island buoy (SIO 2, open circles). The conditions were all unstable, with the air being colder than the sea. Maximum wind speeds were about 8 and 14 m/s for SIO 1 and 2, respectively, and the Paulus duct heights ranged from about 5 to 15 m. The figure clearly shows that duct height follows the wind speed trend. LKB duct heights (not shown) were also computed and are about 20% less than the Paulus duct heights. Figure 10 shows the modeled and observed propagation loss versus time based on the conditions at SIO 1. Modeled results are shown for both the Paulus and LKB methods. Each method was used to compute the stability-dependent vertical refractivity profile, and then MLAYER was used to compute the loss. The observed data are the peak values observed during each hour. The average observed values were typically lower than the diffraction limit for reasons that are not clear. Figure 11 is similar to Figure 10, except that hourly meteorological data from the San Clemente Island buoy were used. The observed propagation loss data are not exactly the same in Figures 10 and 11 since only the hours that match valid meteorological observations at each buoy are used, and the two buoys frequently did not report concurrent observations. Table 2 lists the median modeled and observed loss and the median absolute error of all the hourly observations for the four combinations shown in Figures 10 and 11. The modeled losses from both methods and from both buoys are in reasonable agreement with each other and with the observations, but the LKB method is slightly better than the Paulus method (especially for SIO 1), which is consistent with the findings of Rogers and Paulus . The models based on SIO 2 are nearly as good as the models based on SIO 1, which again implies that horizontal homogeneity of conditions seems reasonable at this frequency over the range separation of 128 km.
Table 2. Median Modeled and Observed Loss and Median Absolute Error for the Four Combinations of Figures 10 and 11
Modeled Loss, dB
Observed Loss, dB
SIO 1, Paulus
SIO 1, LKB
SIO 2, Paulus
SIO 2, LKB
 High-quality meteorological measurements on oceanographic buoys appear very suitable for assessing evaporation duct conditions. Based on the results of this study for the San Diego area, horizontal homogeneity of evaporation duct conditions can reasonably be expected over paths in excess of 100 km for frequencies below 3 GHz, provided there are no influences of airflow coming from or over land. The LKB evaporation duct method appears to be slightly better than the Paulus method for the unstable conditions encountered.
 The author thanks Lloyd Regier of the University of California, San Diego (UCSD), Scripps Institution of Oceanography and George Trekas of UCSD Marine Physics Laboratory for their help in installing the radio link on the buoy. This project was funded by the Laboratory Independent Research Program of the Space and Naval Warfare Systems Center, San Diego.