Analysis of spatial correlation of rainfall rate and of slant path rain attenuation in order to optimize site separation and baseline orientation in site diversity design is presented. For this study, 4 years of rainfall rate measurements were obtained from the Hydrological Radar Experiment dense rain gauge network and associated radar facility in South England. The slant path rain attenuation correlations are analyzed for a hypothetical Earth-space propagation path at 20 GHz. Results show that the correlation of slant path rain attenuations at two diversity sites reaches a minimum at a separation of about 20 km between the two sites and a baseline orientation of acute angle above 30°.
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 Earth-space propagation at EHF band of over 10 GHz is subjected to significant fading due to rain attenuation. Site diversity is being considered by satellite service providers [Wrede, 1999] as an efficient Fade Mitigation Technique (FMT) to overcome deep rain fades. The same satellite signal is received by two Earth stations with a separation distance and orientation with respect to each other selected to maximize the likelihood that the stations will encounter intense rainfall at different times. Thus in the event of deep rain fade, switching the transmission to the least attenuated path would considerably improve system performance. The performance of site diversity (SD) is quantified using the site diversity gain parameter which is defined as the difference between the equi-probable attenuations (in dB) exceeded in a single link system and a system employing site diversity.
 Owing to the localized spatial occurrence of intense rainfall, maximum diversity gain can be obtained by the proper configuration of the following two geometrical parameters in a site diversity setup:
 1. Site separation is the ground distance between the two sites. In order to benefit from site diversity, the site separation must be at least greater than the horizontal diameter of the intense rain cell.
 2. Site baseline orientation is the angle between the ground projection of the satellite path at one station and the horizontal line joining this station to the other. The diversity paths are less likely to intercept the same rain volume if their horizontal slant path projections are not collinear. Thus a nonzero baseline orientation perpendicular to the direction of the rain cell movement should improve site diversity gain [Ippolito, 1989].
 To design a site diversity Earth-space system that delivers high diversity gain at minimum cost, it is necessary to optimize the values of the above two parameters. Most studies in this regard have focused on the first parameter, namely the separation distance between the two sites. Goldhirsh  presented correlation results using 16 days of radar-observed rain events. Their analysis was limited to spatial points located on a line along the satellite azimuth, which is equivalent to a fixed baseline orientation of 0° between diversity stations, or a parallel site diversity setup. Goddard and Cherry  examined the dependence of diversity gain on site separation using radar scans recorded during one summer period. Enjamio et al.  have also reported correlation variations against short scale separation distances up to about 11 km.
 This paper examines the effect of both site separation and orientation on the correlation of observed rain attenuation using an extensive database of rain gauge and radar measurements. The data set used and the site diversity set up are explained in section 2. The computations of instantaneous rain rate and rain attenuation as well their distributions are discussed in section 3. Finally, correlation analysis and results are presented in section 4 followed by the conclusion.
2. Data Set
2.1. HYREX Dense Rain Gauge Network
 The Hydrological Radar Experiment (HYREX) [Moore et al., 2000] was set up in 1993 to examine the variation of spatial rainfall structure. As part of the campaign, a dense rain gauge network (DRN) was built in the Brue catchments in Lovington, Somerset, England. The network consists of 49 rain gauges, with separations ranging from approximately 600 m to 14.5 km. The location is a valley characterized by varying ground height above the mean sea level ranging from 40 m to 210 m.
 A 0.2 mm Casella tipping bucket rain gauge is used, which consists of a divided bucket placed at a pivoted center Water is collected on one side of the bucket and tips when the collected water level reaches 0.2 mm. As a tip occurs, the collected amount of water gets discharged and the other half of the bucket is positioned for filling. The data was recorded with a time resolution of 10 s and stored on a monthly basis for all the 49 gauges.
 Since entries were made in the record for a given 10-s interval only if one or more tips occurred in that interval, we simplified the rain rate averaging process by expanding the data record to 8640 entries per day, featuring one entry for each 10 s period, and a tip count of zero in each nonrainy interval.
 The rain gauge located at Bridge Farm (BFRM, 51.113°N, 2.5361°W) was chosen as the reference Earth station. A hypothetical slant path was selected to a geostationary satellite located at 13.2°E, giving elevation and azimuth angles from Bridge Farm of 30° and 160° respectively. The diversity stations were formed by choosing the rain gauges located from 0° to 90° baseline orientation as shown by the shaded region in Figure 1. The resulting 29 diversity stations provided site separations of up to 13 km.
 The data were validated using the information provided on dates of valid measurement. Invalid data was marked by setting the tip size and tip count to Matlab NaN for each of the 30 gauge locations, including the reference site at which approximately 8% (113 days) out of the total 1461 days had no valid data. The percentage of valid data is shown in Figure 2.
2.2. HYREX Radar
 Rain measurements from the radar were used in order to extend the correlation analysis to site separations beyond 13 km. Rain data were obtained from the Plan Position Indicator (PPI) scans performed by the radar as part of the HYREX campaign [Moore et al., 2000]. This is a C band (5.3 cm wavelength or 5.66 GHz) radar located in Wardon Hill in South England, shown in Figure 3. The Wardon Hill radar is one of the 15 C band single site radars operated by the UK meteorological office. Radar reflectivity (Z, mm6 m−3) is converted to rain rate (R, mm/h) using the Marshall-Palmer Z-R relationship,
It should be noted that the rain rate estimation using (1) will have some error due to the assumption of a constant drop size distribution for all rainfall patterns. It is known that this is not always the case because the drop size distribution is a variant in that widespread stratiform rain contains small sized raindrops in larger numbers per volume whereas convective rainfall comprises large drops in small numbers. Also the raw radar data can be contaminated by ground clutter and spurious radar echoes arising from anomalous radar beam propagation as well as the presence of bright band. These errors are minimized by subjecting the raw data to quality control by using the rain gauge data, meteorological and the satellite imagery data in relation to the radar characteristics, as documented by Harrison et al. .
 Ground scans performed every 5 min at an elevation of 0.5° were chosen. Data are stored as rain rate (mm/h) mapped onto Cartesian grid of 84 × 84, each grid being a square pixel of side 5 km. This results in the spatial coverage of 210 km radius from the radar center (OSGrid = [360,100] km). The valid data availability at the reference grid location is shown in Figure 4. Ignoring the radar center, the reference site is chosen to be located at the OSGrid (380,120) km which translates into 50.9785°N and 2.2849°W. As before, the chosen slant path is a hypothetical link to a geostationary satellite at 13.2°E. The satellite azimuth and elevation at the reference site are 160° and 30° respectively.
 The site separation between the dual sites was selected up to 30 km. The baseline orientation of the diversity sites is chosen in a similar way as described for HYREX dense rain gauge network.
3. Rain Rate and Slant Path Rain Attenuation Distribution
3.1. Rain Rate
 The rain rate (Rt, mm/h) from rain gauge is calculated using the tip count (Nt) and the tip size (D, mm) at time instant t. The rain rate thus obtained is averaged over 30 samples to yield 5 min integrated rain measurements (Rt5).
Figure 5 shows the comparison of rain rate distribution at Bridge Farm with the prediction of the International Telecommunication Union Radiocommunication Sector (ITU-R) model [ITU-R, 2007a], which is based on 40 years of 1-min rainfall rate measurements around the world. The accumulated number of rainy days in each of the 12 months during the 4-year period for Bridge Farm and the radar reference location is shown in Table 1. To examine the overestimated predictions by ITU-R, rain rate distribution reported by Paulson et al.  which was obtained using 2 years of rain gauge measurements in Chilbolton, located within the same rain zone as Bridge Farm were used. The percentage error between the rain gauge data and ITU-R distribution are shown in Table 2, and it follows that the prediction errors are almost consistent for both Bridge Farm and Chilbolton. The distribution of the radar derived rain rate provides a good comparison with ITU-R predictions as shown in Figure 6. Table 3 shows the prediction error for the radar reference location and the Chilbolton data [Paulson et al., 2006]. The reason for the improved radar rain rate distribution could be because the radar provides spatially averaged rain measurement against the point rain rate recorded by the rain gauge.
Table 1. Accumulated Number of Monthly Rainy Days Over the 4-Year Period From January 1996 to December 1999 at Bridge Farm and Radar Reference Location
Radar Reference Location
Table 2. Statistical Rain Rate Comparison Between Rain Gauge Measurements and ITU-R [2007a]a
 The slant path rain attenuation at each rain gauge site is calculated using the Rt5. Assuming the rainfall to be vertically uniform, the attenuation is calculated up to the mean rain height hr using the 0° isotherm height ‘ho’ [ITU-R, 2001a] as:
The length ‘l’ of the slant path affected by rain is calculated using,
where hs is the ground height [ITU-R, 2001b] above the mean sea level for the rain gauge locations and θ is the elevation angle to the satellite.
 The instantaneous specific attenuation (γt, dB/km) is determined as:
where ‘a’ and ‘b’ are the link frequency dependent coefficients defined by ITU-R .
 In line with the procedure in the work of Enjamio et al. , the total slant path rain attenuation (At, dB) at each site over the 5 min averaged time series is determined for the following two scenarios:
 1. The first scenario is for n > = 1, n being the number of rain gauges along the path projection at the local horizontal of the rain gauge site,
such that ∑di = l × cos θ km, di being the separation between the consecutive gauges.
 2. The second scenario is for n = 0, where there is only the rain gauge at the ES location,
Thus At represents the attenuation time series. The rain fade time series for Bridge Farm is calculated using the instantaneous rain rate recorded by the gauges located at two sites, namely, Bridge Farm and Industrial Park (CAST). The Industrial Park rain gauge rain rate time series is used because it is located within the length of horizontal projection of the rain affected slant path at Bridge Farm as described in scenario 1 above. As an illustration, the rain rate and the associated rain fade time series on 2 September 1996 at Bridge Farm are shown in Figures 78–9.
Figure 10 shows the rain attenuation cumulative distribution compared with ITU-R [ITU-R, 2007b]. The ITU-R predicted attenuation distribution at Bridge Farm was determined by applying the procedure outlined under section 188.8.131.52 of ITU-R [2007b]. The parameters used were the exceedance time percentages obtained from the Bridge Farm data distribution, the link frequency of 20 GHz, elevation angle of 30°, 0° isotherm height of 1.9247 km, ground height above mean sea level of 0.102 km, latitude of 51.113°N and longitude of 2.5361°W and the required rain rate at 0.01% was chosen from the Bridge Farm rain rate statistics. The horizontal and the vertical path reduction factors determined by ITU-R are respectively 0.8516 and 1.1704, giving an effective slant path length affected by rain at Bridge Farm of 4.408 km. In Figure 10, the Bridge Farm attenuation distribution curve follows from the attenuation time series calculated using the instantaneous rain rate as described in section 3.2, whereas the Bridge Farm attenuation distribution predicted by ITU-R uses the observed rain rate at 0.01% (Figure 5) as the input to derive the entire distribution. The Bridge Farm attenuation distribution curve determined using the rain gauge data shows good agreement with the satellite beacon attenuation measurements from ITALSAT (13.2°E) recorded in South England [Venturas et al., 2000]. On the other hand the data provide a poorer concurrence with ITU-R predictions which could be due to the reason that the ITU-R uses the attenuation at 0.01% to extrapolate the CDF values for other time percentages shown in Figure 10.
 The specific rain attenuation for Earth station locations obtained using the radar is calculated as described above. The total slant path attenuation is calculated as:
where γt (dB / km) is the instantaneous specific attenuation obtained using the radar rain rate time series in (5).
4. Rain Rate and Rain Fade Correlation
 The correlation is determined by pairing the time series vector of the reference site with each of the diversity stations, taking care to ensure that the series consist exclusively of valid data. To ensure that the computed correlation values are not dominated by the long nonrainy intervals at both sites, the calculations were carried out only on intervals with rain on one or both sites.
Figures 11 and 12 respectively show the rain rate and rain fade correlation coefficients for the dual site scenario of the HYREX dense rain gauge network. The rain rate and rain fade correlation values are different because the rain rate correlation involves the rain measurements at the Earth stations whereas the attenuation correlation involves rain at the Earth stations located along the satellite azimuth as explained in section 3.2. It can be seen that the correlation continues to decrease with increasing separation. As a consequence, an increase in the diversity gain at larger separation values can be expected. This is evident from the results reported by Goddard and Cherry , where for example an increase in site separation from 1.2 km to 6 km provides an improvement in gain from 1.8 dB to 3.5 dB for a fixed rain fade of 7 dB at 30° elevation. Also, the sites with separation less than 10 km exhibit strong correlation of up to 0.62. This agrees with the physical phenomenon of spatial rain cell extent because when the separation between the sites is within the range of intense rain cell extent (i.e., 1∼10 km) [Matricciani and Bonati, 1997], the probability of simultaneous occurrence of deep rain fade is high at both sites.
 The plot of correlation variation for the radar data is shown in the Figure 13. It should be observed that the diversity sites oriented in the range 0° to 30° have higher correlation coefficient values as compared to those between 30° to 90°. In both of the above orientation categories, it can be observed that the correlation variation is negligible beyond 20 km. Figure 14 shows the correlation dependence on site separations at constant baseline orientation. It can be seen that sites along 70° provide least correlation. Also the plot of correlation versus baseline orientation at fixed separations is shown in Figure 15. Here the sites oriented above 30° show very small variation in correlation values, which agrees with the observations of Figures 13 and 14.
 The reduction in the likelihood of the diversity paths simultaneously intercepting the same rain cell due to the nonlinear alignment of the slant path projections results in the lower correlation coefficient values at the higher baseline orientations of acute angles above 30° as seen in Figures 13–15.
 The above correlation results shows that the likelihood of simultaneous rain events at two sites reduces as the site separation increases up to 20 km. No significant reduction in the likelihood of simultaneous rain events at dual sites of separation exceeding 20 km was observed. This is consistent with the theoretical claim that the optimum separation range lies between 10 and 30 km [Ippolito, 1989], owing to decreased rain fade correlation beyond 30 km. Furthermore, dual site diversity analysis performed in North America [Goldhirsh, 1982; Ippolito, 1989] found the diversity performance to be saturated at about 35 km and 20 km, respectively. We found that the likelihood of simultaneous rain events at two sites can be significantly further reduced by orienting the diversity site at an angle greater than 30° from the horizontal projection of the main site-to-satellite path. Therefore in the design of cost-effective Earth-space communication system utilizing site diversity in rain climates similar to UK's, the diversity gain could be maximized by choosing a site separation around 20 km and a baseline orientation of about 70°. Further studies are ongoing to model site diversity gain as a function of site separation, baseline orientation, signal frequency, and path elevation angle.
 The authors wish to thank the British Atmospheric Data Centre (BADC) for supplying the data from Natural Environment Research Council (NERC) HYREX data set (http://www.badc.rl.ac.uk/data/hyrex/).