Radio Science

Rain rate and attenuation statistics along paths in a tropical coastal area from radar data

Authors


Abstract

[1] A data set on rain rate distribution was collected by radar from a coastal site located at tropical latitude in West Africa where the rain field is strongly heterogeneous. It is used to compute rain rate (R) and microwave attenuation (A) statistics integrated along four paths located onshore, offshore, and perpendicularly to the coast, that is, north and south of the radar. These statistics are analyzed in order to see if coastal effects on rain fields induce significant differences between the conditions of microwave propagation along the four paths. R and A averaged along the paths are found to be mixed lognormal distributions with parameters μ and σ (mean and standard deviation, respectively) almost constant for the four paths, which shows that locally, the rain field is approximately ergodic. The probability of rain occurrence is found to be lower for the paths located offshore and north with respect to onshore and south. These differences are linked to the presence of positive gradients of rainfall occurrences between sea and land areas and between north and south areas. The magnitude of these differences is about 100%. The statistical variation coefficient, that is, CV = μ/σ, is found to be close to 2.24, a value observed in many other sites. For the attenuation, CV is found to be dependent on the exponential coefficient of the relation between the specific attenuation and the rain rate. For attenuation, the parameters of the probability density function are given for nine frequencies between 3 and 94 GHz.

1. Introduction

[2] The increasing needs of radiocommunication activities lead to considering the use of higher- and higher-frequency bands, whose propagation properties are dependent on the rainfall attenuation. That is why it is useful to document as completely as possible the microwave rain propagation characteristics of the various climatic areas of the Earth [e.g., Xie et al., 1995; Crane, 1996; Olonio and Riva, 1998; Castanet et al., 2001; Féral et al., 2003a, 2003b]. The prospect of using the strongly attenuated frequency bands for radiocommunication (ground to ground or ground to space) suggests that, for areas where a local heterogeneity of the rain field is suspected (e.g., mountainous areas with orographic effects, or coastal areas with land-sea effects), the climatology of the local precipitation distribution (notably distributions of rain rate and precipitation occurrence) be considered for planning the siting of the radiocommunication installation and link.

[3] Rainfall distribution for the offshore part of coastal areas is not well known because of the absence of rain data over sea. However, it is (now) recognized that there are some significant differences in the distribution of cloud, rain, and some of their over sea and over land by-products in coastal areas, notably the lightning activity, which is higher over land than over sea [e.g., Boccippio et al., 2000; Seity et al., 2001]; the hail size, which is smaller over sea than over land [Dessens et al., 2000; Vinet, 2001]; and the rainfall distribution. For the rainfall distribution, Nzeukou and Sauvageot [2002] (hereinafter referred to as NS), using radar data, have studied the areas of Bordeaux and Dakar, two sites located on the coast of southwestern France and western Africa, respectively. They found that the distribution of the rain rate R is locally approximately ergodic for the two sites (that is, the mean μ and variance σ2 of R are constant and independent from time and space) but that because of a space variation of the rain duration, the cumulative rainfall displays a strong positive gradient from sea to land and also from north to south. For the Dakar area, Kebe et al. [2005] have shown that the relation between rainfall and cloud area-time integrals is very stable in spite of the cumulative rainfall gradients.

[4] The present paper is an extension of NS to the microwave propagation aspects. From radar data, statistics of rain rate and microwave attenuation are computed along four linear paths forming a square surrounding the radar with one leg offshore, one leg onshore and two legs perpendicular to the coast, in order to bring out their respective merits for propagation. For conciseness sake, only the tropical case of Dakar, where the cumulative rainfall distribution is strongly heterogeneous, is presented in the present paper. Attenuation by radar-undetected cloud component is not discussed.

[5] It can be emphasized that while radar reflectivity analyses are not so accurate for single-path impairment estimation, they are particularly powerful for assessment of relative impairment levels, both real time and statistical. The present analysis is thus particularly relevant for improving the site-specific estimation of propagation impairment and may find useful application particularly in evaluation of site diversity performance, as the degree of spatial decorrelation of propagation impairments determines the benefit of diversity.

2. Data

[6] Figure 1 shows the location of the coastal site considered in the present study, namely the area around Cape Verde (Dakar) in Senegal. A detailed description of the physical characteristics and climatology of this area is given by NS and Nzeukou et al. [2004]. That is why these points are only briefly restated in the present paper. The technical characteristics of the radar and the description of the data set are given in Tables 1 and 2, respectively.

Figure 1.

Location of the observation site.

Table 1. Technical Characteristics of the Dakar-Yoff Radar
Location of Radar14°34′N, 17°29′W
Wavelength, cm5.3
Peak power, kW250
Pulse repetition frequency, Hz250
Pulse duration, μs3
Beam width (3 dB), deg1.3
Table 2. Characteristics of the Radar Data Seta
Location of RadarDakar-Yoff
  • a

    PPI means plan position indicator, α is the elevation angle, and Z the radar reflectivity factor.

  • b

    α = 0.8°.

Period of observationJuly–Oct 1993–1999
Scanning modePPIb
Number of scans7407
Sampling interval, min10–20
Pixel size, km21 × 1
Number of steps for Z coding256

[7] The Dakar area is flat with a Sahelian type climate (that is, a transitional climate between desertic and equatorial areas) and a general circulation from the east. Most rainy events are tropical squall lines (a special kind of mesoscale convective system), going from land toward sea, observed only during the rainy season, between early July and late September, when the intertropical convergence zone is higher than 13°N. The conditional mean rain rate (i.e., when R > 0) is 5.1 mm h−1 [Nzeukou et al., 2004]. Figure 2 presents the gauge-based mean annual cumulative rainfall for West Senegal computed and interpolated over a period of 39 years (1951–1989). It shows that the mean annual cumulative rainfall displays a strong meridional gradient from 300 mm at the latitude of Saint Louis near the Mauritanian border to 1500 mm at Cap Skirring near the Guinea-Bissau border, which is 400 km away. Figure 3 from NS shows the mean annual cumulative rainfall for an area of 400 km of diameter around Cape Verde, including the offshore area, estimated from 7 years (1993–1999) of data collected with the radar of Dakar-Yoff (see below). It illustrates that, even after a 7 years averaging, the cumulative rainfall distribution displays a strong intrinsic variability, with respect to the gauge-interpolated 30 year average of Figure 2, and that the coastal isohyets have a southwest, northeast orientation. See notably the 500 mm isohyet separating low northwest (<500 mm) from high southeast (>500 mm) cumulative rainfall.

Figure 2.

Gauge-based mean annual cumulative rainfall for Senegal computed over a period of 39 years (1951–1989). Isohyetal lines are labeled in millimeters per year. The star shows the radar location. The dots are the synoptic observational stations handled by the national meteorological services [from L'hote and Mahé, 1996].

[8] The radar, located at the Dakar-Yoff airport (14°34′N, 17°29′W, altitude 30 m) is a Senegalese operational radar dedicated to meteorological observation. It is activated only during the rainy events. The data acquisition was performed with a scanning repetition period between 10 and 20 min in plan position indicator (PPI) mode (Table 2) using a “Sanaga” acquiring system [Sauvageot and Despaux, 1990]. Seven rainy seasons (1993–1999) were used. The reason for using 7 years of data is that, in the Dakar area, about 72% of the total annual precipitations fall in less than 8 hours (because of the high mean rain rate of the convective part of the Sahelian squall lines) with a strong variance (Figure 3). Accumulation over several years is necessary to reduce the variance of the data set. The scans judged to be anomalous propagations were removed after a careful examination by eye of the whole data set.

Figure 3.

Distribution of the annual rainfall accumulation averaged over 7 years (1993–1999) deduced from radar data. The radar is located at Dakar-Yoff, at the center of the range marker circles. The core of high values east of the radar for radial distances smaller than 50 km is partially due to ground echoes. The point values are smoothed. The four straight lines labeled North, East, South, and West are the paths along which the statistics are calculated.

[9] The radar was regularly calibrated in order to provide accurate values of the radar reflectivity factor Z of the target. The Z values were converted into rain rate R, using a relation of the usual form Z = aRb, where a and b are coefficients depending on the drop size distribution (DSD), if Z is assumed to be correctly measured [e.g., Joss and Waldvogel, 1990]. These coefficients were determined using the probability matching method (PMM) proposed by Calheiros and Zawadzki [1987]. PMM leads to the computation of corrected values (in the statistical sense) of a and b as a function of r, the radial distance from the radar, that is taking into account the differences in reflectivity between the precipitation observed aloft by the radar (whose beam rises above the ground with distance) and the rain at ground level. The parameters of the correction can be found in NS. To check the correctness of the PMM calibration process, the radar-determined cumulative rainfall ΣHi was compared with the measurements by a ground rain gauge network ΣGi. The observed difference E = ΣGiHi, inside the area of radius 100 km from the radar, was lower than 20% for the individual rainy events.

[10] Figure 4 displays the four paths considered for the computation of the statistics from the radar data. They are located between an inner circle inside which a permanent ground clutter is observed and an outer circle beyond which the radar beam is at an altitude sufficiently high to intersect the melting layer of precipitation. The four paths all have a length of 180 km. They are named North, South, West, and East. Using a 180 km range integration length enables to make clearer the differences we are looking for.

Figure 4.

Location and shape of the four areas used by Nzeukou and Sauvageot [2002] for the calculation of the area-averaged rainfall parameters. Western and eastern areas are hatched. Northern and southern areas are the half-annular areas located north and south of the latitude of the radar between the distance 60–180 km. The square shows the four paths used for the statistics.

[11] Last, Table 3 recalls some results from NS used in section 4. NS compute the mean and variance of R from the same data set as the one used in the present paper but for the four areas represented in Figure 4 named North, South, Land, and Sea. North and South are the annular areas located between the radial distances from radar 60 and 180 km and situated northern and southern of the Dakar latitude. Data for distances shorter than 60 km are not used because of the presence of ground echoes on the land side. Data for distances larger than 180 km are not considered because the radar beam is higher than the 0°C isotherm. Land and sea areas are hatched on Figure 4. The shape of the land area is tailored in order to cover the ground area which is observed by the radar. The sea area is determined by symmetry with respect to land for unbiased comparison. Table 3 gives the surfaces and some area-averaged rain parameters for the four areas. As seen in Figure 4, each of the four paths considered in the present paper is entirely included in one of the four areas.

Table 3. Area and Area Average of the Annual Rainfall Parameters Observed in the Individual Pixels of the Four Subtest Areas (West, East, North, and South) Defined in Figure 4a
 Dakar
WestEastNorthSouth
  • a

    The area-averaged parameters (in angle brackets) are rainfall accumulation H, rain duration T, time-averaged rain rate μR, and standard deviation σR. CV = σRR is the coefficient of variation of the rain rate. The annual averaging is over 7 years, 1993–1999 [from Nzeukou and Sauvageot, 2002].

Area, km222,60822,60845,21645,216
Area, deg2(1.5)2(1.5)2(2.1)2(2.1)2
H〉, mm298632344583
T〉, hours53.4105.056.797.5
〈μR〉, mm h–14.805.355.185.03
〈σR〉, mm h–111.6111.8811.4111.33
CV2.422.222.202.25

3. Theory

[12] The microwave attenuation rate by rain A is linked to the rain rate R by a relation of the form

equation image

where k and γ are coefficients depending on the frequency and temperature [e.g., Olsen et al., 1978]. A is usually expressed in dB km−1 for one way and R in mm h−1. In the present paper the attenuation by radar-undetected clouds and by atmospheric gas are not considered. If necessary, they have to be added to the attenuation by rain. Cloud attenuation component increases with frequency and is different for horizontal path or slant path. It can be significant for frequency higher than 10 GHz.

[13] The two quantities discussed in the present paper are the rain rate averaged over each of the four paths of length L or RL, that is, for each of them,

equation image

and the cumulative attenuation AΣL = equation imageAi over the same paths, that is, with Ai given by (1):

equation image

where ΔL is the range bin width along the paths and L = n ΔL.

3.1. RL Distribution

[14] In the general case, at a given moment, the random sample R1, R2, …, Rn along the path L contains some zero values. If m is the number of nonzero values, there are nm zeroes.

[15] Then the distribution of R along the path L has a mixed distribution [see Aitchison and Brown, 1966; Crow and Shimizu, 1988; Kedem et al., 1990], with a density g(r) given by

equation image

where f(r) is the point density of R conditional on R > 0 in the climatic area where the path L is located. The kth moment of this distribution is

equation image

Notably, the mean and variance are

equation image
equation image

[16] Many authors have shown that the point conditional rain rate R can be represented by a lognormal density [e.g., Kedem and Chiu, 1987; Atlas et al., 1990; Sauvageot, 1994], namely,

equation image

where μy and σy2 are the mean and variance of Y = ln R for R > 0.

[17] Using (8) in (6) and (7) gives

equation image
equation image

[18] Because of the spatial dependence of rain structure, RL may be approximated by a mixed lognormal distribution with parameters given by (9) and (10). This mixed lognormal distribution is noted Δ(δ, μy, σy2) by Aitchison and Brown [1966] with δ = 1 − p. The maximum likelihood estimation of p is given by equation image = m/n.

[19] For p = 1, that is, m = n, the relations (9) and (10) gives the mean and variance of the conditional R, namely,

equation image
equation image

[20] Inverting (11) and (12) gives reciprocally

equation image
equation image

where CVR = σRR is the variation coefficient.

[21] Combining (9) and (11) gives

equation image

[22] The lognormality of f(R) and the values of the various parameters μR, σR2, μy and σy2 observed in the area of Dakar by radar and from a disdrometer, are given by NS and Nzeukou et al. [2004].

3.2. AL Distribution

[23] Knowing the shape of RL distribution, the distribution of the attenuation by rain over the path L can be inferred. Before considering the cumulative attenuation over L or AΣL, the discussion first bears on the distribution of AL, the (noncumulative) attenuation in the range bins of the path L.

[24] First, when two variables are linked by a power function, if one is lognormally distributed, the other is also lognormally distributed [e.g., Aitchison and Brown, 1966]. The coefficient of attenuation by rain in a range bin where R > 0, which is linked to R by (1), thus has a pdf lognormally distributed Λ(μlnA, σlnA2) with, between the parameters of the distribution of R and A, the relations

equation image
equation image

[25] The distribution of AL is lognormal Λequation image and described by relations of the same form that (9) and (10). Replacing, in (9) and (10), μy and σy2 by μln A and σln A2 given by (16) and (17), leads to relations giving the mean and variance of AL as functions of μy and σy2:

equation image
equation image

3.3. AΣL Distribution

[26] The cumulative distribution of attenuation over L or AΣL is the sum of n independent random variables having the same distribution Λequation image. It is thus a lognormal distribution with

equation image

and variance

equation image

3.4. Curve Fitting

[27] To fit a lognormal curve to an observed distribution one only has to arithmetically compute the mean and variance from the raw data on the logarithmic variable and to put them in (8). However, section 4 shows that the data display a truncation on the left side, that is for the small RL and AL values. The bias introduced by such a truncation on the estimate of the lognormal distribution parameters can be corrected using a method of maximum likelihood proposed by Cohen [1959, 1991] and discussed by Aitchison and Brown [1966], Crow and Shimizu [1988], and more recently by Hong et al. [1997]. This truncation correction was used for the computation of all the fitting to lognormal functions presented in section 4.

[28] To appraise the quality of the lognormal function fitting to the observed distribution, the Fisher coefficients γ1 and γ2, which are the shape parameters of the distribution, were calculated. If μk is the kth-order moment of the distribution, γ1 = μ323/2 describes the skewness and γ2 = (μ422) − 3 describes the flatness (or kurtosis) [e.g., Aitchison and Brown, 1966].

3.5. Cumulative Distribution Function

[29] From the probability distribution function of RL, or P(RL), and the annual probability F of the event {R > 0} on a path, the cumulative distribution function F(τ) that a particular value of RL be exceeded on the corresponding path can be computed, namely,

equation image

[30] By the same token, using the pdf of AΣL, or P(AΣL), a relation similar to (22) enables to calculate the cumulative distribution function F(a) where a is a threshold of the cumulative attenuation. Cumulative distribution functions F(τ) and F(a) can also be interpreted as giving the percentage of time during which either rain rate or attenuation exceeds the threshold value τ or a.

4. Rain Rate Distribution

[31] Figure 5 displays the observed probability distribution of RL and the lognormal curves fitted to the histogram for the four paths of the Dakar areas. For the calculation of the fitted curves, the left truncation of the histogram was corrected as specified in section 3. The results of the fitting are given in Table 4.

Figure 5.

Probability distribution of the rain rate averaged over each path RL. The curves are the lognormal distributions fitted to the data.

Table 4. Parameters of the Path-Averaged Rain Rate RL Distribution and Probability of Occurrence of Rain in at Least One Range Bin Over the Four Trajectories for 1 Year fa
 γ1γ2μRLσRLCVRLpf, %
  • a

    Here γ1 and γ2 are Fisher's coefficient; μRL and σRL are mean and standard deviation of RL, respectively; CV is the coefficient of variation (σ/μ); and p = μRLR with μR taken from Table 3.

North0.41–0.382.646.342.400.510.65
South0.09–0.812.435.342.200.481.11
West (sea)0.37–0.722.897.712.670.600.61
East (land)0.41–0.783.017.132.370.561.20
Mean0.32–0.672.746.632.410.540.89

[32] Fisher's coefficients are small which shows that a fitting to a lognormal distribution is justified. What can be seen in Table 4 is that the rain rate parameters are almost the same for the four paths. μequation image is the smallest for South with a −13% difference with respect to East which is the highest. equation image values are notably not in the same order of increasing values as μR or H of Table 3 (for H, Sea, North, South, Land; for μR, Sea, South, North, Land; and for equation image, South, North, Sea, Land). It is obvious that the climatological gradients of the cumulative rainfall height from North to South and from Sea to Land, which are very high, have almost no influence on the rain rate statistics, which is in agreement with the results of NS concerning the ergodicity of the rain field.

[33] The path-averaged values of equation image and equation image, given in Table 4, are smaller than the conditional point values μR and σR (i.e., without averaging over a path) recalled in Table 3, from NS, due to the decreasing effect of the path averaging. The ratio p = equation imageR from (15) is given in Table 4. Its mean value is 0.54.

[34] Sauvageot [1994] observed that the value of σy2, the variance of ln R, is almost constant in nature and around 1.8 (a pure number). A mean value of σy2 is given by Nzeukou et al. [2004, Table 7]; it is 1.84, similar to the ones found for West Africa by Sauvageot [1994]. Using this value (1.84) in the second bracket of the right term of (10), p (∼0.54) can be seen to be small with respect to exp (σy2) (∼6.29) in such a way that the result is not strongly modified if p is replaced by 1 in the second bracket of the right term of (10), that is,

equation image

[35] Thus we can write from (10) and (12) that

equation image

[36] The values of equation image calculated for the four paths are given in Table 4. The mean is 2.41, that is very close to 2.24 found for CVR in many place in the world [Sauvageot, 1994; Nzeukou et al., 2004; NS].

[37] The results on equation image and equation image given in Table 4 can be retrieved using in the relations (9) and (10), the μy and σy radar observed over the four areas of Figure 4 by NS, and the values of p given in Table 4. As expected, the calculated values are found close to the observations.

[38] Of course, the gradient of the cumulative annual rain height of Figure 2 is linked to the differences in the rainfall duration since the mean rain rate is homogeneous over the area. Table 4 gives the annual probability f, in percent, to observe a precipitation over a path. North and West have a probability about half those of South and East, that is in the ratio of the cumulative annual rain of Figure 2. These values corroborate the climatic observations on rain. For example the mean conditional point rain rate μR in West Senegal is around 5.1 mm h−1 [Nzeukou et al., 2004; NS]. The cumulative annual rainfall along East is around 600 mm. The percentage time of rain is thus around 1.3%, which is close to the 1.2% of Table 4.

[39] Figure 6 displays the nonconditional cumulative probability distribution of RL, that is, F(τ) = F P(RL > τ), the probability (or percentage of time) that RL be larger than the value in abscissa, knowing that it is raining at least in one range bin of the path. The curve order is related with the values of the cumulative rain height and time of Table 3, that is, the highest percentage of time for East (or Land), the lowest for North, and the two others (South and West) enclosed between the two previous ones.

Figure 6.

Percentage of time during which the nonconditional rain rate averaged over path L, or RL, exceeds the abscissa for the four paths.

5. Distribution of Attenuation by Rain

[40] For the attenuation distribution, 9 microwave frequencies between 3 and 93.4 GHz, including the meteorological radar bands, were considered. These frequencies and the coefficients of (1) for each of them are given in Table 5. As specified above, the attenuation by radar-undetected clouds is not considered in the present paper. As frequency increases, notably for the millimetric domain, cloud attenuation can be very significant and not negligible with respect to attenuation by rain (notably for slant path). We emphasize that statistics included in the present section are presented in a goal of comparison of the rain term contribution to attenuation for various paths and frequencies and not for total attenuation statistics usable for applications.

Table 5. Coefficients k and γ of (1) for the Nine Frequencies Considered in the Present Paper [from Xie et al., 1995]
f, GHzkγ
30.00031.00
5.260.00221.17
9.3750.0111.17
12.50.0231.16
16.040.0421.13
24.190.101.1
34.880.221.04
500.420.96
93.750.840.79

[41] Figure 7 displays the pdf of the cumulative attenuation by rain along the four paths AΣL for the particular frequency of 16 GHz (chosen as an example). A lognormal curve has been fitted to the observed distribution. The parameters of the fitting are given in Tables 6 and 7. Fisher's coefficients are found to be very low, showing that the lognormal distribution is convenient for the P(AΣ,L) representation. As anticipated in section 3, the attenuation averaged over the paths has a lognormal fitting like P(RL).

Figure 7.

Probability distribution of the cumulative attenuation by rain AΣ,L at 16 GHz for the four paths. The curves are the lognormal distribution fitted to the data.

Table 6. Fisher's Coefficients of the Lognormal Fitting to the AΣL Probability Distribution for the Four Paths
 γ1γ2
North1.35–1.00
South1.35–1.02
West1.30–1.18
East1.30–1.16
Table 7. Mean μ, Standard Deviation σ, and Variation Coefficient CV of the Cumulative Attenuation by Rain AΣ,L Over the Four Paths for Nine Frequenciesa
 f = 3f = 5f = 9f = 2f = 16f = 24f = 5f = 50f = 94
  • a

    Values are given in GHz.

North
equation image0.141.899.4719.0731.1866.63119.08175.27214.52
equation image0.346.5932.9464.7998.83197.39309.75388.74345.48
equation image2.413.483.483.403.172.962.602.221.61
 
South
equation image0.162.2211.0822.2235.9075.85132.59189.92221.73
equation image0.429.0445.1888.24131.74257.73388.54461.76373.11
equation image2.674.084.083.973.673.402.932.431.68
 
West
equation image0.131.738.6717.4828.6261.26109.83162.27200.61
equation image0.295.4427.2053.6282.24165.17261.77330.03301.99
equation image2.203.143.143.072.872.702.382.031.51
 
East
equation image0.162.2311.1722.4436.4677.46136.86198.61237.29
equation image0.387.7538.7576.04115.14228.35353.30433.60374.68
equation image2.373.473.473.393.162.952.582.181.58

[42] The parameters of the P(AΣL) distribution are given in Table 7 for the nine frequencies. Table 7 shows that, for each frequency, the parameters equation image and equation image for the four paths are weakly scattered, notably equation image, as a consequence of the ergodicity of the rain field. Table 7 shows that attenuation strongly increases with frequency; the mean value of AΣL, that is equation image, is smaller than 0.2 dB at 3 GHz but larger than 30 dB at 16 GHz, precluding a correct observation of the Dakar rain field with a radar at that frequency. Only 3 and 5 GHz are convenient for such a tropical rain field observation. In Table 7, the variation coefficient for AΣ,L is given. equation image increases with frequency from 3 to 5 GHz, is stable from 5 to 9 GHz, then decreases for frequencies higher than 9 GHz. This evolution mirrors the variation of the exponent coefficient of (1), that is γ, higher values of γ being linked to a higher variability of A for a same distribution of R.

[43] Figure 8 shows the distribution of the relative cumulative attenuation AΣL/AΣL, 0.01, that is, the distribution of percentage of time the relative attenuation is larger than the abscissa for the frequency 16 GHz (as an example) for the four paths. These curves have been obtained by integrating P(AΣL) of Figure 7 with the corresponding F value. Because of the shorter rainfall duration, attenuation is smaller for North and West than for South and East.

Figure 8.

Percentage of time during which the relative cumulative attenuation exceeds the abscissa for the frequency 16 GHz for the four paths.

6. Summary and Conclusions

[44] A data set on rainfall distribution has been gathered by radar over a coastal region at the western end of Sahelian West Africa. The rainfall field, throughout the observed region, is strongly heterogeneous with strong gradients of cumulative rainfall, both along the north-south and east-west direction (that is, between land and sea). Rainfall statistics along four paths of 180 km surrounding the radar, namely North, South, West (over sea), and East (over land) have been considered. Rain rate has a mixed lognormal distribution over the four paths with almost the same mean and variance, which shows that the rain field over the observed area is approximately ergodic. The space gradients of cumulative rainfall are thus mainly due to differences in rainfall duration. The cumulative rainfall attenuations along the four paths have been calculated for nine frequencies between 3 and 94 GHz. They are found to be lognormally distributed again, with weakly scattered parameters for the four paths. On the other hand, the percent of time cumulative attenuation exceeds a given value is found higher for South and East, where the rainfall duration are longest, than for North and West. It can thus be concluded that northwestern locations are more favorable than southeastern ones for a microwave ground-space communication site, but only owing to shorter rainfall durations. The mean cumulative rainfall attenuation for the 180 km long path is found around 10 dB at frequencies lower than 9 GHz and higher than about 30 dB for frequencies higher than 16 GHz. These values show that, for meteorological and hydrological radar observations over distances of about 200 km, frequencies higher than 5 GHz are not favorable because of a high occurrence of backscattered signal extinction for stratiform rain. The present conclusions related to the microwave propagation conditions are partial since only the rain component of attenuation is considered. Of course attenuation by radar-undetected cloud component, not discussed in the present paper, can add a significant contribution for slant path.

Ancillary