Combining MWL and MSG SEVIRI Satellite Signals for Rainfall Detection and Estimation

: Accurate rainfall detection and estimation are essential for many research and operational applications. Traditional rainfall detection and estimation techniques have achieved considerable success but with limitations. Thus, in this study, the relationships between the gauge (point measurement) and the microwave links (MWL) rainfall (line measurement), and the MWL to the satellite observations (area-wide measurement) are investigated for (area-wide) rainfall detection and rain rate retrieval. More precisely, we investigate if the combination of MWL with Meteosat Second Generation (MSG) satellite signals could improve rainfall detection and rainfall rate estimates. The investigated procedure includes an initial evaluation of the MWL rainfall estimates using gauge measurements, followed by a joint analysis of the rainfall estimates with the satellite signals by means of a conceptual model in which clouds with high cloud top optical thickness and large particle sizes have high rainfall probabilities and intensities. The analysis produced empirical thresholds that were used to test the capability of the MSG satellite data to detect rainfall on the MWL. The results from Kenya, during the “long rains” of 2013, 2014, and 2018 show convincing performance and reveal the potential of MWL and MSG data for area-wide rainfall detection.


Introduction
Accurate rainfall detection and estimation are beneficial for many operational and research applications, including hydrological modelling, flash flood prediction, urban drainage planning, water resources management, and many more [1]. However, accurate rainfall estimation is a challenge because rainfall is intermittent and its intensities, in some cases, vary significantly in space and time [2,3]. The state-of-the-art in rainfall measurement consists of devices that can detect and quantify rainfall depending on their location [4].
Rain gauges measure rainfall accumulations as a function of time, and generally have a high degree of accuracy, especially at low to medium intensities [5]. However, rain gauges measure at a discrete point and therefore provide site-specific measurements with low spatial representativeness [6]. Interpolation techniques to obtain spatially continuous rainfall estimates from rain gauges are available, but they easily propagate errors from the point measurement and are unable to adequately capture the spatial variability of rainfall [7]. Also, installing and maintaining rain gauge networks can be practically challenging and expensive [8,9], resulting in sparse deployment and rapid decline in gauge stations, especially in developing and underdeveloped countries [10,11]. Gauge rainfall data were obtained from 14 aerodynamic 'tipping bucket' rain gauges (ARG 100 rain gauges, see www.emltd.net) and two rain gauges from Trans-African Hydrometeorological Observatory (TAHMO) [48]. In Kericho, five ARG rain gauges were aligned near a 15 GHz, 3.68 km MWL transect during the May-June 2013 evaluation period. In Naivasha, nine ARG rain gauges were aligned under a 15 GHz, 10 km MWL, with two TAHMO gauges installed close to the transmitting and receiving antennas during the May-June 2018 evaluation period. The location of the rain gauges is shown in Figure 1, per each study location. The ARG rain gauges were set to log data every minute, while the TAHMO stations recorded rainfall every 5 min. One tip of the ARG bucket equates to 0.198 to 0.202 mm rain. No rain gauge data was used during the 2014 evaluation period due to data unavailability.
Atmosphere 2020, 11, x FOR PEER REVIEW 4 of 32 Table 1. Characteristics of the MWL network used in each study location. Gauge rainfall data were obtained from 14 aerodynamic 'tipping bucket' rain gauges (ARG 100 rain gauges, see www.emltd.net) and two rain gauges from Trans-African Hydrometeorological Observatory (TAHMO) [48]. In Kericho, five ARG rain gauges were aligned near a 15 GHz, 3.68 km MWL transect during the May-June 2013 evaluation period. In Naivasha, nine ARG rain gauges were aligned under a 15 GHz, 10 km MWL, with two TAHMO gauges installed close to the transmitting and receiving antennas during the May-June 2018 evaluation period. The location of the rain gauges is shown in Figure 1, per each study location. The ARG rain gauges were set to log data every minute, while the TAHMO stations recorded rainfall every 5 min. One tip of the ARG bucket equates to 0.198 to 0.202 mm rain. No rain gauge data was used during the 2014 evaluation period due to data unavailability. The base map is SRTM DEM over the two study locations. Note: map coordinates are shown in decimal degrees, for some of the MWL in Naivasha no RSL data were available (red lines in (b)).

MWL Data
The MWL data was supplied by Safaricom, a Kenyan telecom service provider. Safaricom routinely collects and store the MWL data for monitoring purposes; access to the data is by contacting their office in Nairobi (https://www.safaricom.co.ke/). Received signal level (RSL) data, for the evaluation period, were acquired for a total of 19 MWL of variable lengths and frequencies. Figure 1 shows the MWL network in Kericho and Naivasha on a base map using a Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) [49]. All the MWL used were Aviat Eclipse. Table 1 gives further details on the MWL network in each study location and for each evaluation period.
The RSL data were characterized by minimum, maximum, and mean values at 15 min intervals and with a resolution of 0.1 dBm. The MWL used were vertically polarized and had constant transmitted signal levels (TSLs). Out of the 19 MWL, one link (8 GHz, 28.4 km), was not included in this study because, at such frequencies, the attenuation rainfall relationship for estimating path average rainfall is sensitive to variation in raindrop size distribution which can result in significant rainfall retrieval errors [50,51]

MWL Data
The MWL data was supplied by Safaricom, a Kenyan telecom service provider. Safaricom routinely collects and store the MWL data for monitoring purposes; access to the data is by contacting their office in Nairobi (https://www.safaricom.co.ke/). Received signal level (RSL) data, for the evaluation period, were acquired for a total of 19 MWL of variable lengths and frequencies. Figure 1 shows the MWL network in Kericho and Naivasha on a base map using a Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) [49]. All the MWL used were Aviat Eclipse. Table 1 gives further details on the MWL network in each study location and for each evaluation period.
The RSL data were characterized by minimum, maximum, and mean values at 15 min intervals and with a resolution of 0.1 dBm. The MWL used were vertically polarized and had constant transmitted signal levels (TSLs). Out of the 19 MWL, one link (8 GHz, 28.4 km), was not included in this study because, at such frequencies, the attenuation rainfall relationship for estimating path average rainfall is sensitive to variation in raindrop size distribution which can result in significant rainfall retrieval errors [50,51] Atmosphere 2020, 11, 884 5 of 32

MSG Satellite Data
MSG is a successor of Meteosat First Generation (Meteosat 1-7)-a series of operational geostationary meteorological satellites that continuously observe the earth-atmosphere system. Currently, 4 Meteosat satellites (Meteosat 8,9,10,and 11) are positioned overhead the equator and operate over Europe, Africa and the Indian Ocean [52]. We used data from the Meteosat at 0 • E (2013, 2014 evaluation periods) and 41.5 • E (2018 evaluation period), which corresponded to Meteosat 10 and 8 satellite respectively [53], at the time the data were acquired. The radiometric sensor onboard MSG, SEVIRI, observes the earth's full disk in 12 spectral channels: eight thermal infrared, three solar, and one high resolution visible (HRV) channels. SEVIRI's temporal resolution is 15 min. However, the spatial resolution is 3 km for the thermal infrared and solar channels and 1 km for the HRV channel (at nadir) [54]. The data are freely available at the European Organization for the Exploitation of Meteorological Satellites (EUMETSAT) website and were imported for processing using the GEONETCast Toolbox in ILWIS (Integrated Land and Water Information System, version 3.85) [55]. We selected solar and thermal infrared channels that are sensitive to cloud top properties: optical thickness, particle size, and phase during the day and nighttime. These correspond to visible (VIS 0.6 µm), near-infrared (NIR 1.6 µm), thermal infrared (IR 3.9 µm, IR 8.7 µm, IR 10.8 µm and IR 12.0 µm), and water vapour (WV 7.3 µm) channels.

Method
This section includes three broad parts. Part one (Sections 3.1 and 3.2) estimates rainfall from MWL and rain gauges in Figure 1a,b. Part two (Sections 3.3 and 3.4) describes the retrieval of MSG satellite signals (for different kinds of SEVIRI channels) from the neighbourhood of MWL and gauges in part one, and analyses the data with the ground rainfall estimates. The analysis considers a combination of SEVIRI visible, near-infrared, and brightness temperature differences to infer information about cloud top properties: cloud optical thickness, particle size and phase. Although the SEVIRI based cloud properties are representative of the cloud top and has indirect and nonlinear relationship with ground rainfall [18,37], the information retrieved is useful for quantifying rainfall due to the apparent statistical relationship between rainfall duration and amount [56]. The information content gained from the joint analyses of rainfall estimates with satellite signals (for inferring cloud top properties) was then used to test the potential of the satellite data to detect rainfall on the MWL. Finally, part three (Section 3.5) presents performance measures for evaluating the MWL rainfall estimates and rainfall detection on MWL.

Estimating Rainfall from Rain Gauges
For each ARG rain gauge, the rainfall in millimetres (mm) was estimated as the tipping count multiplied by the tip equivalent of rain in mm. The rainfall in mm per minute is then used to estimate rainfall intensities R mm h −1 at 15 min intervals. The rainfall data from the TAHMO stations were also used to estimate rainfall intensities at 15 min to ensure temporal consistency in the gauge data. During every 15 min, the average rainfall intensities that have occurred along the MWL transmission path were calculated as the mean of the gauge rainfall estimates.

Estimating Rainfall from MWL Data
The average attenuation along the MWL path can be used to estimate the average rainfall, R (mm h −1 ) using the formula [57]: where Z (dB km −1 ) is the rain-induced attenuation, a ((dB km −1 ) (mm h −1 ) −b ) and b (−) are empirical parameters that are known from the literature [57,58] and are dependent on MWL signal frequency and polarisation. Depending on the sampling strategy used for the MWL RSL data, different studies such as [27,59] have used different characteristics of the RSL data for rainfall estimation. Here, the RSL Atmosphere 2020, 11, 884 6 of 32 data received, consisted of two instantaneous signal levels (i.e., the minimum and maximum RSL) and a mean signal level over a 15 min interval. In this study, the mean RSL was used to retrieve R to ensure a homogeneous comparison of mean rainfall estimates from rain gauges and MWL. The steps used to retrieve R from the mean RSL are briefly described below.

Wet/Dry Classification of RSL Data
Attenuation of MWL signal can be from sources other than rainfall. For instance, variations in water vapour content and air temperature [60,61], strong solar irradiance and multipath propagation can all cause RSL attenuation even in clear sky conditions [30]. Therefore, to estimate R from RSL data, it is essential first to identify the rain periods (wet periods, i.e., when rain is present on the MWL path) in the RSL data and separate them from the no rain periods (dry periods, i.e., when rain is absent on the MWL path). Wet/dry classification in literature is based on two major concepts. One concept assumes rainfall is correlated in space, such that neighbouring links will experience mutual attenuation during the occurrence of rain. Hence, wet/dry classification is achieved for a particular link by comparing its attenuation measurement with several links within its vicinity [27]. The other concept analyses the statistical properties of the time series of link signals, see [62] and [63].
Rainfall varies considerably in space and time over the study area [64,65]. Therefore, a wet/dry classification based on mutual attenuation of nearby links might not be a practical approach in our study location. Thus, the approach adopted in this study is based on the latter concept. For every 10 mean RSL data (the equivalent of 150 min interval), a standard deviation was estimated as a measure of the local variability in the RSL. Since rain attenuates MWL signals, the standard deviation for a rainy interval will be high. Thus, a suitable threshold value was defined to separate the standard deviation values into wet/dry periods. As proposed by [62], such a value can be derived from the rainfall climatology of the area as inferred from, e.g., nearby rain gauges. Here, the threshold value was calibrated for each study location using the experimental links and rain gauge data ( Figure 1, the MWL with gauges underneath their transects). The threshold value was then applied to all the links in the respective locations, for wet/dry classification, assuming that the rainfall climatology is homogeneous for the small study location considered (Figure 1). When a 150 min interval had less than five mean RSL data, wet/dry classification and hence rainfall was not computed for that interval.

Estimating the Reference RSL
The reference RSL or the baseline level is an indication of the RSL levels during dry periods. According to, e.g., [27,51], accurate wet/dry classification is relevant for precise estimation of this parameter. Nevertheless, the baseline level fluctuates even in the dry period due to signal attenuations in clear sky conditions, e.g., [60,66]. For every 15 min labelled as a wet period, the corresponding baseline level was estimated as the median of the mean RSL from the previous 24 h, that was labelled as dry period.

Estimating R from Z
After classifying the mean RSL data into wet and dry periods, and subsequently estimating a baseline level, the effect of antenna wetting was taken into account by following the dynamic model described in [67]. Eventually, the path average attenuation, Z (dB km −1 ), was estimated for every 15 min wet period by subtracting the mean RSL from the baseline level, as shown in Equation (2). In some cases, negative values of path average attenuation were retrieved. This is the case when a 15 min period within a 150 min interval labelled as wet is however dry because rainfall was intermittent in the wet interval. In these cases, the attenuation was set to zero. where L is MWL length (km), while Pre f and P (dBm) are the reference and mean RSL (corrected from the effect of wet antenna), respectively. Finally, R (mm h −1 ) is estimated from Z via Equation (3) below The values of a and b were chosen from [58], and are shown in Table 2.

SEVIRI Data Retrieval and Processing
The MSG SEVIRI data were retrieved for the earth's full disk for the evaluation period. The zenith viewing angle of the Meteosat at 0 • E, over the study area, is approximately 41 • . As a result, depending on the location and the height of clouds, this viewing angle could cause displacement of cloud tops from their actual position due to the effect of parallax, which occurs because SEVIRI observes the Earth under an oblique angle [40]. According to [17], for very high clouds in Kenya, parallax displacement can amount to about 12 km in SEVIRI pixels. Therefore the data for the 2013 and 2014 evaluation period (retrieved from Meteosat at • E) were parallax corrected using a correction algorithm from EUMETSAT (see http://www.essl.org/cwg/?page_id=165). However, the zenith viewing angle of the Meteosat at 41.5 • E is about 5 • , and this small viewing angle does not require parallax correction.

The Conceptual Model for Detecting Rainfall Using MSG SEVIRI Data
In this study, MWL rainfall estimates are linked to MSG SEVIRI data based on the assumption that clouds that rain over MWL can be detected (based on their cloud top properties) using the MSG SEVIRI data. A conceptual model was therefore defined that explored the relationship between spectral characteristics of different kinds of SEVIRI channels and cloud top properties (cloud top optical thickness, particle size and phase) for detecting rainfall. The model assumes that clouds with high optical thickness and large particle sizes (with the existence of ice or water hydrometeors at the top) have high rainfall probability, and intensity whereas clouds with low optical thickness and small particles sizes have low rainfall probability and intensity [37][38][39]68]. The physical basis underlying this assumption is that the conditions for the development of precipitation in clouds are (i) availability of sufficient moisture (ii) existence of an effective mechanism for converting small cloud droplets that are suspended in the air into large precipitating particles, and (iii) the existence of ice phase clouds at the cloud top to support rain generation by the Bergeron-Findeisen process [39,[69][70][71].
MSG SEVIRI based operational cloud property retrieval technique applicable to water and ice clouds is not available [37,39]. Nonetheless, many authors, including [37,69,[72][73][74] have shown that implicit information about the cloud top properties indicated above can be inferred from solar and thermal infrared satellite channels. For this reason, this study utilized the original reflectance and brightness temperature differences of SEVIRI channels to infer cloud top properties for detecting rainfall. Because the information about cloud properties differs between day and nighttime, the detection of raining clouds is done separately for day and nighttime. To be sure that only cloudy scenes are used in this analysis, EUMETSAT's operational cloud mask product [75] was used to identify cloudy pixels.
(i) Detecting raining clouds during daytime Reflection of solar radiation by clouds in the non-absorbing channels (i.e., in the visible channels between 0.4 µm and 0.8 µm) is strongly related to the cloud optical thickness, and that of the solar Atmosphere 2020, 11, 884 8 of 32 radiation in the slightly absorbing channels (1.6 µm and 3.9 µm) is related to the particle size [76][77][78]. The two kinds of channels combined can, therefore, provide information about cloud optical thickness and particle size. The optical thickness and particle size of clouds both represent a single parameter, cloud water path (CWP), and is directly related to rainfall probability of clouds. The CWP is an indicator of the amount of water vertically integrated into the cloud. It depends on the diameter of particle size and the thickness of clouds formed by these particles [72,73,79].
Consequently, CWP is often implicitly inferred from VIS 0.6 µm and NIR 1.6 µm channels from SEVIRI [39,80]. High VIS 0.6 µm reflectance indicates optically thick clouds and low NIR 1.6 µm reflectance corresponds to large cloud particle sizes. The implication is that large CWP is observed when high VIS 0.6 µm reflectance coincides with low NIR 1.6 µm reflectance. In [39], clouds with large CWP were found to coincide with high rainfall probabilities, when their SEVIRI reflectance was compared with weather radar data.
The difference in brightness temperature between IR 8.7 µm and 10.8 µm (∆T IR8.7-IR10.8 ) and that between IR 10.8 µm 12.0 µm (∆T IR10.8-IR12.0 ), can be used to infer information about cloud phase [39]. Based on the observations made by [81], water particle absorption is stronger between 11 µm and 12 µm than between 8 µm and 11 µm, whereas the reverse is true for ice particle. Thus, ∆T IR10.8-IR12.0 of water clouds are higher than ∆T IR8.7-IR10. 8 . On the contrary, ∆T IR8.7-IR10.8 of ice clouds is higher than coincident ∆T IR10.8-IR12.0 . [82] have rather suggested the simultaneous use of brightness temperature IR10.8 µm (T IR10.8 ) and the difference ∆T IR8.7-IR10.8 for identifying cloud phase. Their study found that ice crystals begin to form when T IR10.8 < 238 K and ∆T IR8.7-IR10.8 > 0.25 K. As earlier indicated, the existence of ice phase at the cloud top, supports rain generation and thus increases the likelihood of a cloud to produce rain. The ∆T IR10.8-IR12.0 has also been considered as a good indicator of cloud optical thickness, and is effective for discriminating optically thick cumulous clouds from optically thin cirrus clouds [74,83,84]. According to [85], optically thick cumulous clouds show small ∆T IR10.8-IR12.0 because of their black-body characteristics while optically thin cirrus clouds show larger difference because of the differential absorption between of ice crystals between the two channels. It is expected that optically thick cumulous-type clouds with small ∆T IR10.8-IR12.0 produce rain [83]. Although ∆T IR10.8-IR12.0 is effective in detecting and removing optically thin cirrus clouds, [86] found instances where optically thick cumulous-type clouds were incorrectly classified as optically thick cirrus clouds.
(ii) Detecting raining clouds during nighttime During the nighttime, the brightness temperature differences: ∆T IR3.9-IR10.8 , ∆T IR3.9-WV7.3 , ∆T IR8.7-IR10.8 , and ∆T IR10.8-IR12.0 were used to infer information about cloud optical thickness, particle size and phase [38,69,71,80] for rainfall detection. As explained by [38,80], the emissions in 3.9 µm are sensitive to particle size, such that large particles have high emissions than smaller particles. The dependence on particle size is less distinct in the IR10.8 µm than in IR3.9 µm. As a result, ∆T IR3.9-IR10.8 values are higher for large particle sizes compared to smaller particles. Using ∆T IR3.7-IR11 of TRMM satellite, [69] showed that optically thick raining clouds with large particles produced brightness temperature difference in the interval −1 to 4 K. Concerning the ∆T IR3.9-WV7.3 difference, [38] indicated that the characteristics should be similar to ∆T IR3.9-IR10.8 but with generally higher differences than ∆T IR3.9-IR10.8 . This is due to the diminishing effect of the water vapour absorption and emission in the mid-to-low tropospheric levels on the brightness temperature in WV7.3 µm channel [54] 3.3.2. The Spatial and Temporal Differences between SEVIRI and Ground Data The measurement characteristics of satellite and ground sensors are fundamentally different [87]. The satellite measures instantaneously over a wide area, while the ground sensors measure continuously in time from a single location (rain gauges), or aggregated measurements over time and space (MWL). The measurement differences, therefore, suggest a possible spatial and temporal mismatch between satellite and ground measurements that must be taken into account when analysing the two datasets. The description below presents the spatial and temporal difference between the SEVIRI and ground sensors (MWL or rain gauges) together with how they are treated in this study.
(i) Spatial mismatch The general assumption required for a comparison of ground rainfall and satellite data is that the measured rainfall is representative of the whole satellite pixel containing the ground sensors. In addition to the above-mentioned measurement mismatch, it has been shown that, for a heavy rain with hydrometeors falling out of a cloud in the height of 3 km, at a falling speed of 10 ms −1 and horizontal wind speed between 5 and 30 ms −1 , the hydrometeors can drift a horizontal distance anywhere between 1.5 and 90 km [88]. Thus, the rainfall recorded by a ground sensor might not correlate with the satellite signal from a collocated pixel but with the signal from other adjacent pixels. Furthermore, for tropical deep convective systems consisting of convective cores and anvil cloud areas having different cloud properties, dynamical regimes, and varying rainfall intensities, the retrieved cloud top properties might be biased towards the spatially dominant anvil cloud areas [89].
To minimise the effect of the above potential spatial mismatches between the satellite and ground data in our analysis, an approach is adopted that considers not only the pixel containing the ground sensor but also the surrounding three by three pixels. This implies that for a rain gauge, the surrounding three by three pixels of the pixel containing the gauge were considered and for the MWL, three by three pixels surrounding the centre of the MWL transect were considered. It is worth noting that, by including three by three pixels surrounding the centre of the link, all the pixels covering the MWL are also included in the analysis.
Two different spatial aggregation methods (i.e., summary statistics used to sample from the raw data in space) were used to retrieve a single satellite signal out of the three by three pixel environment that can be compared to the ground rainfall. For day time data, the method previously described by [37] was used because of its simplicity, and effectiveness in identifying the most effective satellite signal that can be analysed with the ground rainfall data. The method identifies the pixel with the most effective satellite signal as the pixel with the highest reflectance value in the VIS 0.6 µm (indicating high optical thickness, i.e., thick clouds) and lowest reflectance values in the NIR 1.6 µm (indicating large particle size). More precisely, for n ≥ 2 (where n is the number of cloudy pixels in the three by three pixels environment) the maximum and minimum reflectance values were expressed as: where x i is the reflectance value in the VIS 0.6 µm channel, and where y i is the reflectance value in the NIR 1.6 µm channel. In case the retrieved maximum VIS 0.6 µm and minimum NIR 1.6 µm values do not occur in the same pixel, the value combination that returns the highest difference between the two signals is used. The maximal difference was expressed as: The approach theoretically assumes that, by identifying the pixel with the maximum reflectance in VIS 0.6 µm, the pixel with the highest optical thickness is detected. For the NIR 1.6 µm reflectance, by identifying the pixel with the minimum reflectance, the pixel with the largest effective particle size is detected. Thus, the pixel with the highest optical thickness, large particle size, and the corresponding large CWP is detected. Once the cloudy pixel with large CWP is detected, the phase of clouds is then retrieved using ∆T IR8.7-IR10.8 and ∆T IR10.8-IR12.0 . By using this method, the satellite pixel with the most effective rainfall signal is identified and retrieved for analysis with the ground rainfall data.
However, for nighttime, the mean of brightness temperature differences retrieved from cloudy scenes was analysed with the ground rainfall. The mean brightness temperature differences for n ≥ 2 (where n is the number of cloudy pixels in the three by three pixels environment) was expressed as: where ∆T i is the brightness temperature difference for the various channel combinations considered.
(ii) Temporal mismatch The potential temporal mismatch between the satellite and ground data is mainly because SEVIRI instantaneous scenes over the study area are acquired in about 6 min (depending on the latitude) into each 15 min scan interval. Therefore, the measurement might be representative of the cloud top conditions that were available during the first few minutes of SEVIRI's 15 min scan interval. In contrast, the ground measurements were continuous in time. In particular, the gauges originally recorded data at least every minute, while the MWL recorded mean RSL every 15 min (Section 2.2). Moreover, during a 15 min interval, a raining cloud could have passed over the ground sensor during the first 6 min (when SEVIRI scenes were available) or the last 9 min. Thus, the satellite measurement might not necessarily coincide with the ground measurement in time. To minimise the effect of this temporal mismatch in our analysis, the dataset was aggregated in time. This implies that, for the satellite data, the mean satellite signal was computed and for the ground data, the rainfall sums were computed every 30 min.
Other measurement characteristics of the satellite that can potentially cause uncertainties in the analysis of the ground and satellite data are the effect of viewing and illumination geometries: solar zenith angle, viewing zenith, and relative azimuth angles [90]. These effects concern the data (for periods in 2013 and 2014) acquired from solar channels of the Meteosat at 0 • E. Since small study locations are considered ( Figure 1) in this study, the effects of viewing and illuminating geometries should be minimal. Additionally, we only used solar reflectance for daytime hours when sufficient solar illumination was available over the study area.

Analysing MWL Rainfall and SEVIRI Data
The ground rainfall and satellite data were analysed separately for both day and night using rainfall data from the experimental setup in Figure 1, and SEVIRI satellite signals retrieved (for different channels) from the neighbourhood of the setup. The rainfall data were aggregated in time, and satellite data was aggregated in both space and time to reduce the effect of measurement discrepancies between the satellite and ground sensors (see above for details). The collocated ground rainfall and satellite data allowed us to separate raining from non-raining satellite signals. The raining satellite signals were further classified based on different rainfall categories to investigate the satellite signals for varying rainfall intensity ranges. The rainfall classes were determined by analysing the frequency distribution of the gauge rainfall intensities (not shown in this study) and using the following criteria if possible: (1) each rainfall class should have sufficient amount of data to enable the computation of some descriptive statistics; (2) the rainfall classes should be equal for both study locations to ensure homogenous rainfall analysis across the two areas.
A scatter plot of rainfall intensities as a function of the retrieved satellite signals for different combination of SEVIRI channels (that provide information about cloud top properties) was used to investigate rainfall occurrences in each rainfall class and the corresponding values in the satellite signal. The satellite signals for each rainfall class was statistically analysed using descriptive statistics.
Based on the statistical information, the potential of combining the information content from the different kinds of SEVIRI channels to detect rainfall occurrences on individual MWL was further tested. Rainfall occurrences are inferred from joint analysis of satellite and rainfall data [74,91] by evaluating, at each timestamp, a four-dimensional matrix of VIS 0.6, NIR 1.6, ∆T IR8.7-IR10.8 , ∆T IR10.8-IR12.0 (during day time), and ∆T IR3.9-IR10.8 , ∆T IR3.9-WV7.3 , ∆T IR8.7-IR10.8 , ∆T IR10.8-IR12.0 (during nighttime) to make a rain or no-rain decision. The rain detection test was conducted using independent MWL and satellite dataset. All cloudy pixels that were considered for analysis based on the conceptual model (Section 3.3.1) were used in evaluating the capability of the test to detect rain occurrence on individual MWL.

Evaluating MWL Rainfall Intensities
The MWL rainfall estimates (R MWL ) were evaluated against the rain gauge estimates (R RG ) using the relative bias (RB), coefficient of variation (CV), coefficient of determination (r 2 ), and root mean square error (RMSE) (see Table 3). Table 3. Performance measures for evaluating R MWL . Full name of each measure is indicated in the text. j and n represent all timestamps for the evaluation period.

Performance Measure
Formula Range Var is the variance, Cov is the covariance of the R MWL , and the R RG and S is the standard deviation.
RB indicates whether the R MWL systematically over or underestimates the R RG [92], and ranges from −1 to +∞, with 0 being an unbiased case. The CV indicates how the R MWL varies around the mean of the R RG [5], and ranges from 0 to ∞. The r 2 shows the strength of the linear relationship between the R MWL and the R RG . It ranges from 0 to 1, where 1 indicates a perfect linear correlation between the R MWL and the R RG [93]. Finally, the RMSE shows how close the R MWL is to R RG and ranges from 0 to positive ∞, where 0 is a hypothetical case, and larger RMSE indicates decreasing accuracies of R MWL [93,94]. All the performance measures were computed across the evaluation period.

Evaluating the Performance of SEVIRI Based Rain Detection on MWL
The performance of the rain detection test was evaluated by computing the values of a, b, c and d as described in [93,95]. The formulation of these elements differs for day and nighttime because of the different SEVIRI channels and information content used for each time of the day (i.e., day or nighttime). For daytime, a d , b d , c d , and b d were computed as: Vis ≥ Vis thres AND Nir ≤ Nir thres AND c d = R sat Vis ≥ Vis thres AND Nir ≤ Nir thres AND d d = noR sat Vis < Vis thres AND Nir > Nir thres AND Atmosphere 2020, 11, 884 12 of 32 where: a d , b d , c d , and d d are the hits, misses, false alarms and correct negatives events respectively; R sat and noR sat are raining and non-raining conditions in the satellite data; Vis, Nir, are VIS 0.6 µm and NIR 1.6 µm as well as their respective thresholds Vis thres and Nir thres ; ∆T β1 , ∆T β2 are ∆T IR10.8-IR12.0 and ∆T IR8.7-IR10. 8 and their brightness temperature ranges [x 1 , x 2 ] and [y 1 , y 2 ], respectively. During the nighttime, the corresponding values of a n , b n , c n , and b n were computed as: where: a n , b n , c n , and d n are the hits, misses, false alarms and correct negatives events respectively during the nighttime; ∆T γ1 and ∆T γ2 are ∆T IR3.9-IR10.8 , ∆T IR3.9-WV7. 3 and their brightness temperature With the computation of these values, a set of standard verification scores: the probability of detection (POD), false alarm ratio, (FAR), probability of false detection (POFD), accuracy (ACC), critical success index (CSI), and Heidke skill score (HSS) were computed. POD is used here to evaluate the fraction of the R MWL that was correctly detected by the test POD = a (a+b) . FAR answered the question, 'what fraction of the number of R MWL detected by the test was incorrect?' FAR = a (a+c) . POFD indicates the fraction of no rain (R MWL < 1 mm h −1 ) on the MWL that was incorrectly identified as rain (R MWL > 1 mm h −1 ) by the test POFD = c c+d . The overall fraction of rain and non-rain that was correctly detected by the test was evaluated by the ACC ACC = a+d a+b+c+d . CSI is used to show how well the rain detected by the test corresponds to R MWL on individual MWL CSI = a a+b+c . The HSS evaluates the accuracy of the rain detection test by taking into account the detection that was due to random chance.
It is calculated as: where a random = (a+b) × (a+c)+ (d+b) × (d+c) N and N is the sum of a, b, c and d.

Results
The first part of this section presents the results of evaluating the MWL rainfall against gauges measurements. The second part shows the results of analyzing the rainfall estimates in part 1 with the SEVIRI satellite signals for rainfall detection. The final part summarizes the performance of the satellite data when used to detect rainfall on MWL.

R MWL versus R RG
The rainfall estimates evaluated in this section were from the experimental setup in Figure 1 (i.e., the MWL with gauges under their transects). The period for which the rainfall intensities were evaluated was during the long rains of 2013 and 2018 for the Kericho and Naivasha setup respectively. The frequency of both links is 15 GHz, and their lengths are approximately 3.7 and 10 km for the Kericho and Naivasha MWL respectively. The MWL rain estimates were evaluated using 16 rain gauges; 5 for the Kericho link and 11 for the Naivasha link. Here, the gauge rainfall intensities were considered as the reference rainfall measurement.
The transformation of MWL RSL to R MWL is compared with R RG for both Kericho and Naivasha in Figures 2 and 3, respectively. The comparison was made at 15 min interval using 48 h of gauge and MWL measurements.
Atmosphere 2020, 11, x FOR PEER REVIEW 13 of 32 The transformation of MWL RSL to RMWL is compared with RRG for both Kericho and Naivasha in Figures 2 and 3, respectively. The comparison was made at 15 min interval using 48 h of gauge and MWL measurements.   The transformation of MWL RSL to RMWL is compared with RRG for both Kericho and Naivasha in Figures 2 and 3, respectively. The comparison was made at 15 min interval using 48 h of gauge and MWL measurements.  The Naivasha link (Figure 3a) had frequent intermittent periods of no data compared to the Kericho link (Figure 2a). The data gaps were considered during the MWL rainfall estimation The Naivasha link (Figure 3a) had frequent intermittent periods of no data compared to the Kericho link (Figure 2a). The data gaps were considered during the MWL rainfall estimation procedure (see Section 3.2). The estimated threshold for wet/dry classification using a rolling standard deviation method was 0.8 dB for Kericho and 0.7 dB for Naivasha (Figures 2b and 3b). Comparatively, rain detection in the Kericho link was better than in the Naivasha link.
The R MWL and R RG are also compared in a scatter plot at 15 min, half-hourly and hourly evaluation timestamps for both study locations (Figure 4). The half-hourly and hourly values were computed by summing the 15 min rainfall intensities. The values of the performance measures are also summarised in Table 4 for each evaluation timestamp and study location. For the scatter plot comparison and computation of the performance measures, R MWL and R RG pairs that are less than 1 mm h −1 , were set to 0 mm h −1 (i.e., considered as dry). However, data with the 0 mm h −1 were included in all analysis to evaluate the MWL's detection and estimation capabilities for both wet and dry periods. All performance measures were computed across each evaluation period.
Atmosphere 2020, 11, x FOR PEER REVIEW 14 of 32 procedure (see Section 3.2). The estimated threshold for wet/dry classification using a rolling standard deviation method was 0.8 dB for Kericho and 0.7 dB for Naivasha (Figures 2b and 3b). Comparatively, rain detection in the Kericho link was better than in the Naivasha link.
The RMWL and RRG are also compared in a scatter plot at 15 min, half-hourly and hourly evaluation timestamps for both study locations (Figure 4). The half-hourly and hourly values were computed by summing the 15 min rainfall intensities. The values of the performance measures are also summarised in Table 4 for each evaluation timestamp and study location. For the scatter plot comparison and computation of the performance measures, RMWL and RRG pairs that are less than 1 mm h −1 , were set to 0 mm h −1 (i.e., considered as dry). However, data with the 0 mm h −1 were included in all analysis to evaluate the MWL's detection and estimation capabilities for both wet and dry periods. All performance measures were computed across each evaluation period.  Regarding the accuracy of the RMWL, both links exhibited different skill, when their RMWL were compared to the RRG. As can be seen from Table 4, the link in Kericho overestimated the observed rainfall. The overestimation, however, decreased at increasing aggregation timestamp. The RB decreased from 0.50 at the 15 min timestamp to 0.32 for both half-hourly and hourly timestamps. Likewise, the CV decreased from 9.87 at 15 min to 5.09 at the hourly timestamp. The strength of the relationship between RMWL and RRG (see also Figure 4a-c) increased for increasing timestamps, with r 2 values reaching approximately 0.6 at the hourly timestamp. The RMSE, however, increased from 1.22 mm h −1 at 15 min to 2.77 mm h −1 at the hourly timestamps.
In contrast, the link in Naivasha (Table 4) marginally underestimated the observed rainfall. The value of RB increased minimally from −0.05 at 15 min to −0.18 at half-hourly and hourly timestamps.  Regarding the accuracy of the R MWL , both links exhibited different skill, when their R MWL were compared to the R RG . As can be seen from Table 4, the link in Kericho overestimated the observed rainfall. The overestimation, however, decreased at increasing aggregation timestamp. The RB decreased from 0.50 at the 15 min timestamp to 0.32 for both half-hourly and hourly timestamps. Likewise, the CV decreased from 9.87 at 15 min to 5.09 at the hourly timestamp. The strength of the relationship between R MWL and R RG (see also Figure 4a-c) increased for increasing timestamps, with r 2 values reaching approximately 0.6 at the hourly timestamp. The RMSE, however, increased from 1.22 mm h −1 at 15 min to 2.77 mm h −1 at the hourly timestamps.
In contrast, the link in Naivasha (Table 4) marginally underestimated the observed rainfall. The value of RB increased minimally from −0.05 at 15 min to −0.18 at half-hourly and hourly timestamps. The CV decreased from 5.78 to 4.07 for 15 min to hourly evaluation timestamps. The strength of the relationship between R MWL and R RG (Figure 4d-f) also increased for increasing timestamp with r 2 above 0.5 for all timestamps. Even though the RMSE increased with aggregation time, the values ( Table 4) were comparatively lower than those of the Kericho link.

Joint Analysis of Rainfall and SEVIRI Satellite Data
In this section, the results of analysing rainfall estimates with SEVIRI satellite data are presented in two parts. First, collocated ground rainfall (from MWL and rain gauge) and satellite data from the experimental setup in Figure 1a,b were jointly analysed for detecting rainfall. The gauge rainfall intensities presented in this analysis were from the rain gauges close to the centre of each MWL. Note, however, that the inclusion of the gauge rainfall data gave a perspective of the rainfall satellite analysis from a reference measurement point of view. To further investigate the satellite signals for different rainfall intensity ranges, the rainfall values were grouped into different rain classes ( Table 5). The analysis was done separately for the two study areas and for during day and nighttime. Next, inferences deduced from the rainfall satellite analysis are summarised based on observations from the two study areas and separately for during day and nighttime. (i) MSG satellite rainfall Figure 5 is a scatter plot of rainfall intensities as a function of the MSG satellite signals during the daytime in May-June 2013 (in total 313 MSG SEVIRI scenes). A clear observation from the figure is the difference in the scatter of data points between the raining satellite signals (0-5 mm h −1 and above 5 mm h −1 rainfall classes) and non-raining satellite signals (0 mm h −1 rainfall class). This feature was evident in both reflectance and brightness temperature difference combination, as well as from both the R RG and R MWL scatter plots.
Atmosphere 2020, 11, x FOR PEER REVIEW 16 of 32 plot that, some coincident values ∆TIR10.8-IR12.0 are larger than those of ∆TIR8.7-IR10.8. Likewise, coincident values of ∆TIR8.7-IR10.8, in some cases, are larger than those of ∆TIR10.8-IR12.0. This was evident for both the rainfall between 0-5 mm h −1 and those above 5 mm h −1 as well from both the RRG and RMWL plots. The scatter plot of rainfall intensities as a function of the MSG satellite signal during nighttime in May-June 2013 (altogether 218 MSG SEVIRI scenes) is also shown in Figure 6. From the plot, it is clear that the 0 mm h −1 rainfall scatter over the whole range of the satellite signal for all the brightness differences analysed. The raining satellite signals, however, scatter differently for the RRG and RMWL, and in different ranges for all the brightness temperature differences considered.
For instance, the values of ∆TIR3.9-WV7.3 were larger than those of ∆TIR3.9-IR10.8 (Figure 6a,c). Moreover, the RRG plot (Figure 6a) scatter below 10 K for the ∆TIR3.9-WV7.3 whereas the differences that are shown in the RMWL plot (Figure 6c), in particular, those between 0-5 mm h −1 , scatter over a wide range of the satellite signals. On the other hand, the RMWL scatter above 0 K for the ∆TIR3.9-IR10.8 whereas the differences shown in the RRG plot scatter over a wide range (between −5 and 3 K) of the satellite signal.
For the brightness temperature differences in Figure 6 b,d, the ∆TIR10.8-IR12.0 scatter above 0 K with a large concentration of the scatter between 0 and 1 K whereas the ∆TIR8.7-IR10.8 scatter over a comparatively large range of values (between −1.5 and 1 K) of the satellite signal. In addition, some coincident values of ∆TIR10.8-IR12.0 are larger than those of ∆TIR8.7-IR10.8 whereas coincident values of ∆TIR8.7-IR10.8, for some cases, are also larger than those of ∆TIR10.8-IR12.0. This can be observed for both the rainfall between 0-5 mm h −1 and those above 5 mm h −1 and is evident from the RRG and RMWL plots. Also, these observations were comparable to those found during the daytime analysis. As can be seen for the SEVIRI reflectance combination in Figure 5a,c the 0 mm h −1 rainfall scatter throughout the whole range of the satellite signals, with a high concentration of the scatter in the lower-left corner of the plot, where low VIS 0.6 µm reflectance are connected to low NIR 1.6 µm reflectance. On the other hand, the combination of high VIS 0.6 µm versus low NIR 1.6 µm reflectance is generally evident for the occurrence of rainfall. The 0-5 mm h −1 R MWL scatter over a wide range of the satellite signal but with a slight tendency to scatter in the lower right corner of the plot. In some cases, the value combination of the VIS 0.6 µm and NIR 1.6 µm reflectance in this rainfall class were comparable. The rainfall above 5 mm h −1 was generally restricted to the lower right corner of the plot where high VIS 0.6 µm reflectance is connected with low NIR 1.6 µm reflectance.
For the satellite brightness temperature difference (Figure 5b,d) indicative of cloud phase, water (∆T IR10.8-IR12.0 ) and ice (∆T IR8.7-IR10.8 ), the 0 mm h −1 rainfall also scatter throughout the whole range of the satellite signal, although the values of ∆T IR10.8-IR12.0 were generally higher than those of (∆T IR8.7-IR10.8 ). In contrast, the raining satellite signals tend to scatter in a different range of values for ∆T IR10.8-IR12.0 and ∆T IR8.7-IR10. 8 . Most of the raining satellite signals in the ∆T IR10.8-IR12.0 scatter above 0 K, with a large concentration of the scatter falling within a narrow range (approximately 0 to 1 K) whereas those of ∆T IR8.7-IR10.8 , scatter over a large range of values (between −2 and 1.5 K). It can also be seen from the plot that, some coincident values ∆T IR10.8-IR12.0 are larger than those of ∆T IR8.7-IR10.8 . Likewise, coincident values of ∆T IR8.7-IR10.8 , in some cases, are larger than those of ∆T IR10.8-IR12.0 . This was evident for both the rainfall between 0-5 mm h −1 and those above 5 mm h −1 as well from both the R RG and R MWL plots.
The scatter plot of rainfall intensities as a function of the MSG satellite signal during nighttime in May-June 2013 (altogether 218 MSG SEVIRI scenes) is also shown in Figure 6. From the plot, it is clear that the 0 mm h −1 rainfall scatter over the whole range of the satellite signal for all the brightness differences analysed. The raining satellite signals, however, scatter differently for the R RG and R MWL , and in different ranges for all the brightness temperature differences considered. A scatter plot of rainfall intensity as a function of the MSG satellite signal, analogous to the daytime analysis in Kericho ( Figure 5) is presented for Naivasha (Figure 7). Altogether 713 MSG SEVIRI scenes were analysed during the period of May-June 2018. As was also observed in the Kericho analysis ( Figure 5), most of the raining satellite signals did not scatter over the whole range of value combinations of satellite reflectance (Figure 7a,c) and brightness temperature difference (Figure 7b,d) and was evident from both the RRG and RMWL plots.  RRG (a,b) and RMWL (c,d) as a function of VIS 0.6 µm versus NIR 1 .6 µm (a,c), and ∆TIR10.8-IR12.0 versus ∆TIR8.7- IR10.8 (b,d) for Naivasha. For instance, the values of ∆T IR3.9-WV7.3 were larger than those of ∆T IR3.9-IR10.8 (Figure 6a,c). Moreover, the R RG plot (Figure 6a) scatter below 10 K for the ∆T IR3.9-WV7.3 whereas the differences that are shown in the R MWL plot (Figure 6c), in particular, those between 0-5 mm h −1 , scatter over a wide range of the satellite signals. On the other hand, the R MWL scatter above 0 K for the ∆T IR3.9-IR10. 8 whereas the differences shown in the R RG plot scatter over a wide range (between −5 and 3 K) of the satellite signal.
For the brightness temperature differences in Figure 6 b,d, the ∆T IR10.8-IR12.0 scatter above 0 K with a large concentration of the scatter between 0 and 1 K whereas the ∆T IR8.7-IR10.8 scatter over a comparatively large range of values (between −1.5 and 1 K) of the satellite signal. In addition, some coincident values of ∆T IR10.8-IR12.0 are larger than those of ∆T IR8.7-IR10. 8 whereas coincident values of ∆T IR8.7-IR10.8 , for some cases, are also larger than those of ∆T IR10.8-IR12.0 . This can be observed for both the rainfall between 0-5 mm h −1 and those above 5 mm h −1 and is evident from the R RG and R MWL plots. Also, these observations were comparable to those found during the daytime analysis.
A scatter plot of rainfall intensity as a function of the MSG satellite signal, analogous to the daytime analysis in Kericho ( Figure 5) is presented for Naivasha (Figure 7). Altogether 713 MSG SEVIRI scenes were analysed during the period of May-June 2018. As was also observed in the Kericho analysis ( Figure 5), most of the raining satellite signals did not scatter over the whole range of value combinations of satellite reflectance (Figure 7a,c) and brightness temperature difference (Figure 7b,d) and was evident from both the R RG and R MWL plots.
For the satellite reflectance combination, the 0 mm h −1 rainfall scatters over the whole range of the satellite signal; and like in the Kericho day time analysis (Figure 5a,c), a large concentration of this scatter was located in the lower-left corner of the plot where VIS 0.6 µm and NIR 1.6 µm reflectance were very low. However, in contrast to the daytime analysis in Kericho, the R RG between 0-5 mm h −1 , tend to scatter over the whole range of the satellite signals (Figure 7a). Also, for some of the rainfall intensities in this R RG class, the value combination of the VIS 0.6 µm and NIR 1.6 µm were comparable. From this plot, it can also be seen that majority of the rainfall above 5 mm h −1 scatter in the lower right corner where high VIS 0.6 µm reflectance were connected to low NIR 1.6 µm reflectance. Although some of the R RG above 5 mm h −1 do not scatter in the lower right corner, for all these instances the VIS 0.6 µm reflectance were higher than those of the NIR 1.6 µm. Figure 6. Nighttime RRG (a,b) and RMWL (c,d) as a function of ∆TIR3.9-IR10.8 versus ∆TIR3.9-WV7.3, (a,c) and ∆TIR10.8-IR12.0 versus ∆TIR8.7- IR10.8 (b,d) for Kericho.
A scatter plot of rainfall intensity as a function of the MSG satellite signal, analogous to the daytime analysis in Kericho ( Figure 5) is presented for Naivasha (Figure 7). Altogether 713 MSG SEVIRI scenes were analysed during the period of May-June 2018. As was also observed in the Kericho analysis ( Figure 5), most of the raining satellite signals did not scatter over the whole range of value combinations of satellite reflectance (Figure 7a,c) and brightness temperature difference (Figure 7b,d) and was evident from both the RRG and RMWL plots.  As can be seen from the rainfall intensities for the ∆T IR10.8-IR12.0 and ∆T IR8.7-IR10.8 plot (Figure 7b,d), the 0 mm h −1 scatter over the whole range of the satellite signal, with generally larger values of ∆T IR10.8-IR12.0 than those of ∆T IR8.7-IR10.8 . However, the raining satellite signals scatter over varying ranges of the two brightness temperature differences. For ∆T IR10.8-IR12.0 , this range is above 0 K, with the majority of the signals falling between 0 and 1 K. For the ∆T IR8.7-IR10.8 , the range is comparatively wider; in particular, the R RG falls between −2 and 2 K. It can also be observed from the plot that, some coincident values of ∆T IR10.8-IR12.0 are larger than those of ∆T IR8.7-IR10.8 and likewise, values of ∆T IR8.7-IR10.8 , in some cases are larger than those of ∆T IR10.8-IR12.0 . This feature was evident for both the rainfall between 0-5 mm h −1 and those above 5 mm h −1 and can as well be seen from the R RG and R MWL plots. Moreover, these observations were also similar to those found in the previous analysis of daytime rainfall intensities and MSG satellite signals in Kericho ( Figure 5). Figure 8 shows rainfall intensities as a function of MSG signals during nighttime in May-June 2018 (altogether 733 MSG SEVIRI scenes) for Naivasha. A clear observation from the figure is that the 0 mm h −1 rainfall is scattered over the whole range of values for all the brightness temperature differences presented. Rainfall, however, scatters in a different range of values for the various brightness temperature differences shown.
From the rainfall intensity scatter plot for ∆ TIR10.8-IR12.0 and ∆T IR8.7-IR10.8 (Figure 8b,d), it can also be observed that most of the rainfall scatter above 0 K for the ∆T IR10.8-IR12.0 , and between -2 and 2 K for the ∆T IR8.7-IR10. 8 . It is also clear from this plot that, the rainfall between 0-5 mm h −1 scatter differently from those above 5 mm h −1 . In particular, the R RG between 0-5 mm h −1 scatters over a wide range of value combinations of ∆T IR10.8-IR12.0 and ∆T IR8.7-IR10. 8 . By contrast, the rainfall intensities above 5 mm h −1 are grouped in a narrow range of value combinations of the brightness temperature differences (Figure 8b). This feature can also be observed in the R MWL (Figure 8d), although here, the rainfall above 5 mm h −1 showed a slight tendency to scatter over a wide range of values. particular, the RRG falls between −2 and 2 K. It can also be observed from the plot that, some coincident values of ∆TIR10.8-IR12.0 are larger than those of ∆TIR8.7-IR10.8 and likewise, values of ∆TIR8.7-IR10.8, in some cases are larger than those of ∆TIR10.8-IR12.0. This feature was evident for both the rainfall between 0-5 mm h −1 and those above 5 mm h −1 and can as well be seen from the RRG and RMWL plots. Moreover, these observations were also similar to those found in the previous analysis of daytime rainfall intensities and MSG satellite signals in Kericho ( Figure 5). Figure 8 shows rainfall intensities as a function of MSG signals during nighttime in May-June 2018 (altogether 733 MSG SEVIRI scenes) for Naivasha. A clear observation from the figure is that the 0 mm h −1 rainfall is scattered over the whole range of values for all the brightness temperature differences presented. Rainfall, however, scatters in a different range of values for the various brightness temperature differences shown.  (ii) Inferences from analyzing rainfall estimates with MSG satellite data Overall, it can be stated based on the observations in Figures 5 and 7 that, most of the rain cases (i.e., 0-5 mm h −1 and above 5 mm h −1 ) defined by R RG and R MWL during day time were covered by optically thick clouds that were characterized by high VIS 0.6 µm and low NIR 1.6 µm reflectance, and with different ranges of ∆ TIR10.8-IR12.0 and ∆T IR8.7-IR10.8 . The high VIS 0.6 µm and low NIR 1.6 µm reflectance is an indication of the cloud's large CWP and high rainfall probabilities and intensities [39]. Notice that the ∆ TIR10.8-IR12.0 (between 0 and 1 K) and ∆T IR8.7-IR10.8 (between −2 and 2 K) ranges found in this study were also indicative of medium (i.e., low optical thickness with large particle sizes and high optical thickness with small particle sizes) to large (i.e., high optical thickness with large particle sizes) CWP with high rainfall probabilities and intensities according to radiative transfer calculation by [38]. Further, the value ranges of ∆ TIR10.8-IR12.0 and ∆T IR8.7-IR10.8 are characteristic of optically thick cumulous-type clouds with ice at the top, based on cloud classification presented by [74,96]. In contrast, most of the no rain cases (i.e., 0 mm h −1 ) correspond to non-precipitating thin and thick cirrus clouds and N-type clouds (edges of optically thick clouds, optically thinner cumulous clouds, or low-level cumulous cloud overlaid by thin cirrus clouds) [74,85].
The results are consistent with the conceptual model introduced in Section 3.3.1 that clouds with high optical thickness and large particle sizes, indicative of large CWP (with the existence of ice or water hydrometeors at the top) have a high probability of producing rainfall.

Rainfall Detection with MSG SEVIRI Data
The different combination of MSG channels that were jointly analysed with rainfall data in the previous section was used to test rain detection on individual MWL. In this section, the results of detecting rain on MWL using MSG SEVIRI satellite signals are presented.
In Table A1, the calculated descriptive statistics of SEVIRI satellite signals for each of the R MWL class are shown per each study location for both day and nighttime. A summary of the data used for calculating these statistical values are shown in Table 5, and the data were analysed in Figures 5-8 in the previous section. What is clear from Table A1 is the low and high standard deviation values of the reflectance and brightness temperature differences, respectively. When the standard deviation is interpreted together with the mean, mode, and median values, it becomes evident that the satellite reflectance tends to spread close to their mean. In contrast, the brightness temperature differences spread over a large range of values. Moreover, there were large differences in the statistical values between raining and non-raining satellite signals. However, the differences in statistical values between 0-5 mm h −1 and above 5 mm h −1 rainfall classes were rather low.
Based on the descriptive statistics in Table A1, reflectance threshold and brightness temperature difference range ( Table 6) were derived that were used to compute the elements a, b, c, and d in Equations (8)-(15) for rainfall detection. Since the satellite signals of 0-5 mm h −1 and above 5 mm h −1 rainfall classes were not statistically different, separate threshold and brightness temperature difference range for the two-classes was not necessary. Thus, a single threshold and brightness temperature difference range were defined separately for day and nighttime, and the two study locations. The reflectance thresholds: Vis thres and Nir thres ( Table 6) were derived from the median and mean statistical values respectively, whereas the brightness temperature difference range was derived from a combination of minimum, maximum, mean and mode values, depending on the channel difference. The results in Table 6 show that the reflectance thresholds were comparable (during daytime). In contrast, the brightness temperature difference ranges (during day and nighttime) varied across the two study locations. Table 6. Reflectance threshold and brightness temperature range used for rain detection.

Study Location
Time Vis thres Nir thres ∆T IR8.7-IR10. 8 Table 7 summarises the verification scores of the satellite-based rain detection on MWL for Kericho and Naivasha, during the day and nighttime. The scores are based on MWL and satellite data from the two study locations, that are independent of those used in the previous analysis in Section 4.1.2. The numbers in Table 7 (first column) are used to represent the MWL name and were derived from the link identification supplied by the telecommunication provider. The scores were computed across the evaluation period, and for MWL, from which more than five R MWL were retrieved during day or nighttime.
The results, as shown in Table 7, were effective in identifying periods of no rain. As can be seen from the percentage of correct negatives, more than 95% of no rain on individual MWL was correctly identified by the test on the satellite signals as non-raining. However, the rain detection skill varied between the day and nighttime, as can be seen from the hit percentage.
In Kericho, the day time detection performed better than nighttime detection. For most of the MWL, between 58.1% and 78.6% of the R MWL were successfully detected, and between 21.4% and 42.9% were incorrectly identified as non-raining. For the nighttime, between 25% and 50% of success was achieved, and between 50% and 75% of the R MWL , was incorrectly detected as non-raining. The percentage of false alarms, FAR and POFD were generally higher in the daytime than the nighttime. Nonetheless, the good performance of the daytime detection over the nighttime was supported by the POD, CSI and HSS scores. Similarly, the daytime detection results in Naivasha were comparatively better than those of nighttime. For daytime, it succeeded in detecting between 57.1% and 62.5% of the R MWL , and between 35% to 42.9% were erroneously detected as non-raining. However, for the nighttime, between 30% and 91.7% of success was achieved, with 8.3% to 70% of the R MWL , erroneously identified as non-raining. The percentage of false alarms, FAR and POFD for the daytime were lower than the nighttime. The scores of POD, CSI, and HSS further support the good performance of the day time over the nighttime. For the daytime: POD range between 0.57 and 0.65; CSI range between 0.44 and 0.62; and HSS range between 0.61 and 0.76. For the nighttime, values ranging between 0.3 and 0.92; 0.14 and 0.58 and 0.23 and 0.73 were computed for POD, CSI, and HSS respectively. Regarding the overall accuracy for the day and nighttime, the previous comment for the Kericho case is also valid.

Accuracy of the MWL Rainfall Estimates
Two MWL of the same frequency (15 GHz) but different lengths: 3.7 and 10 km, and from different study locations: Kericho and Naivasha were used to estimate R MWL . The results were then compared, at different evaluation timestamps, with R RG derived from rain gauges. Overall, the results demonstrate the potential and capacity of MWL networks to provide rainfall data in areas where ground monitoring systems are lacking or insufficient. The overall accuracy of the R MWL derived from the two MWL can be described as good. Despite the high values of CV observed, the low RB and RMSE values show that reliable rainfall information can be derived from MWL networks. The hourly r 2 values were about 0.60, for both MWL and more specifically for the Naivasha link, and the values for all evaluation timestamps were above 0.5, which can be described as convincing considering these values were achieved at fine resolution.
The discrepancies found between R MWL and R RG are expected when comparing rainfall data from two sensors with differences in their nature of measurement. The R MWL were retrieved from the mean RSL data that were derived every 15 min from instantaneous RSL measurements. On the other hand, the R RG was computed from rain gauges that recorded rainfall accumulations every minute. Also, the differences between R MWL and R RG could be explained in part by uncertainties in the R MWL rainfall estimation approach [97][98][99]. Additionally, the discrepancies could be due to the spatial variability of rainfall [100].

The Analysis of R MWL with MSG SEVIRI Data
R MWL from the two links presented above were jointly analysed with satellite signals from MSG SEVIRI solar and thermal infrared channels. Both data were temporarily aggregated, and the satellite data were spatially aggregated to reduce the effect of potential temporal and spatial mismatch between the rainfall and satellite data in our analysis. The premise for analyzing the MWL rainfall with the SEVIIRI data is that raining clouds that attenuate individual MWL can be detected based on their cloud top properties, using the satellite data. Therefore, a conceptual model was defined for detecting rainfall based on the assumption that clouds with high cloud top optical thickness and large particle sizes (with the existence of ice or water hydrometeors) have high rainfall probabilities and intensities. During day time, the model infers cloud top optical thickness and particle sizes from SEVIRI solar channels: VIS 0.6 µm and NIR 1.6 µm, respectively, whereas the brightness temperature difference between IR 8.7 µm and 10.8 µm (∆T IR8.7-IR10.8 ) and that between IR 10.8 µm 12.0 µm (∆T IR10.8-IR12.0 ), supplied additional information on cloud phase namely: ice and water, respectively. During the nighttime, the brightness temperature differences: ∆T IR3.9-IR10.8 , ∆T IR3.9-WV7.3 , ∆T IR8.7-IR10.8 , and ∆T IR10.8-IR12.0 were used to infer similar information about the cloud top properties.
When R MWL was considered as a function of cloud optical thickness (VIS 0.6 µm reflectance) and particle sizes (NIR 1.6 µm reflectance) during daytime, the raining satellite signals had high values of VIS 0.6 µm and low values of NIR 1.6 µm reflectance. On the other hand, R MWL as a function of ∆T IR8.7-IR10.8 and ∆T IR10.8-IR12.0 , showed that the raining satellite signals grouped in a different range of values of the two brightness temperature differences. ∆T IR8.7-IR10.8 , indicative of ice clouds, covered a large range of values while ∆T IR10.8-IR12.0 , indicative of water clouds, a narrow range. The nighttime analysis of R MWL as a function of ∆T IR3.9-WV7.3 and ∆T IR3.9-IR10.8 also showed that the raining satellite signals spread over a wide range of value combination of ∆T IR3.9-WV7.3 and ∆T IR3.9-IR10.8 . The differences of ∆T IR3.9-WV7.3 were, however, mostly higher than those of ∆T IR3.9-IR10. 8 . For the analysis R MWL as a function of ∆T IR8.7-IR10.8 , and ∆T IR10.8-IR12.0 , the range of brightness temperature differences in the raining satellite signals were comparable to those found in the daytime analysis.
The above results corroborate the proposed conceptual model that clouds with high optical thickness and large particle sizes (with ice or water particles at the top) have high rainfall probability and show the possibility for an area-wide rainfall detection based on the combination of the different MSG satellite signals for both day and night.
A test for detecting rainfall on individual MWL using the different kinds of MSG SEVIRI channels analysed in this study was also presented. The results indicate an appreciable capability of the satellite data to detect rainfall intensities on individual MWL. The verification scores showed that the test performed better during daytime and comparable across the two study locations. This could be due to the higher and reliable information content on CWP and rainfall, that is available in the VIS 0.6 µm and NIR 1.6 µm reflectance pair, compared to channel differences used during nighttime [80]. As was also shown in the results, a strong relationship can be found between VIS 0.6 µm and NIR 1.6 µm reflectance (Figure 5a,c and Figure 7a,c) and R MWL during the daytime. Moreover, descriptive statistical values from the analysis of R MWL and satellite data indicate that the daytime satellite reflectance was statistically different between the rain and non-raining satellite signals. This might explain the high rain detection with good CSI and HSS scores based on the daytime test. The statistical values derived from the nighttime data were rather often comparable between rain and non-raining satellite signals and could explain its high false detection with comparatively weak CSI and HSS scores.
The good performance of the test suggests that the MWL and MSG data have the potential for area-wide rainfall studies. A possible implication is that the MWL and MSG data could be potential input to optical satellite-based models for rainfall detection and estimation. In this context, data fusion [101,102] and statistical machine learning offer techniques to explore relationships (linear and non-linear) between multiple large input variables. Further, current developments in parallel computing with machine learning have increased the training and predicting speeds of these learning algorithms and can make the automatization and improvement of the method in real-time feasible [103,104]. Also, for MWL based rainfall studies in areas lacking in-situ data, the results suggest that the satellite-based rain information may be a useful tool for wet/dry classification of the MWL signal. Therefore, future research involving analysis with large datasets would also focus on investigating the MWL and satellite data for such an application.
Uncertainties that were found in the analysis of R MWL with MSG satellite data could be due to measurement differences between the satellite and MWL. The satellite signal is acquired instantaneously over an area, while the R MWL is acquired from MWL every 15 min, and is representative along the link transmission path. It is therefore not surprising that the satellite signal might not correspond with the rainfall intensities. Furthermore, the spatiotemporal aggregation employed to retrieve the most effective satellite signal from the satellite data is perhaps not enough to compensate for measurement differences inherent of the two sensors. Additionally, horizontal wind drift within or outside raining clouds will have a strong influence on falling hydrometeors of light rainfall. It could explain in part, the high uncertainty that was observed for the 0-5 mm h −1 rainfall intensity class. In case of deep convective cores with anvil cloud areas, the retrieval of the satellite signal of high rainfall intensities clouds might be biased towards anvil cloud areas, which have characteristics of light rainfall intensities. This could explain why some rainfall intensities above 5 mm h −1 (e.g., Figure 5c) did not correspond with the satellite signals. Moreover, in the case of multilayered clouds [105], with cloud properties differing between layers, the satellite signals may not correlate with the ground rainfall [106].
To this end, the ability to distinguish different raining cloud types, e.g., convective/stratiform and track their footprints surrounding the individual MWL will provide valuable information relevant for retrieving and linking the MSG satellite signals to the MWL rainfall. The identification of different cloud types and tracking their location around the MWL should reduce the spatial aggregation problems (Section 3.3.2) and the resulting uncertainties between MWL rainfall and the MSG satellite signals. In this context, the promising results demonstrated by [68,80,107,108] for raining cloud classification and [109,110] for tracking raining clouds accentuate the potential of a more accurate MWL and satellite-based raining cloud detection. Thus, future studies which consider these concepts will be undertaken.

Conclusions
This study investigated the combination of MWL rainfall estimates with MSG SEVIRI satellite data for rainfall detection using observations from two areas in Kenya: Kericho and Naivasha. The approach involves: (i) an evaluation of the MWL rainfall estimates using an experimental setup consisting of two MWL (of varying lengths) and several rain gauge measurements as ground truth; (ii) next, the MWL rainfall estimates were analysed as a function of the MSG SEVIRI satellite signals. The satellite signals were used to infer information on cloud top properties by means of a conceptual model that, clouds with high cloud top optical thickness and large particle size (with ice or water hydrometeors) are linked to high rainfall probabilities and intensities; (iii) finally, the information content gained from analyzing the MWL rainfall with MSG SEVIRI satellites signals, was then used for detecting rainfall on individual MWL.
The results show that the MWL can estimate rainfall intensities with reliable accuracies when compared with rain gauges. However, limitations, such as inherent measurement differences between the MWL and the gauge, remain a challenge and affect rainfall retrieval accuracies.
Analysing the MWL rainfall estimates as a function of the MSG satellite signals, revealed characteristics of the raining satellite signals that corroborates with the conceptual model for detecting raining clouds. During the daytime, high VIS 0.6 µm and low NIR 1.6 µm reflectance (indicative of high optical thickness and large particle sizes and thus large CWP) were often consistent with MWL rainfall between 0-5 mm h −1 and above 5 mm h −1 . These raining satellite signals also differed from the non-raining satellite signals (satellite signals indicative of 0 mm h −1 ) and were comparable across the two study locations. For nighttime, MWL rainfall between 0 and 5 mm h −1 and above 5 mm h −1 was characterized by ∆T IR3.9-IR10.8 and ∆T IR3.9-WV7.3 brightness temperature ranges, indicative of medium to large CWP. Nonetheless, the ranges varied between the two study areas and were not different between rain and non-raining satellite signals. Additionally, day and night temperature ranges of ∆T IR8.7-IR10.8 and ∆ TIR10.8-IR12.0 for the MWL rainfall between 0 and 5 mm h −1 and above 5 mm h −1 suggests that most of the rain cases were from optically thick cumulous-type clouds.
The analysis also produced descriptive statistics: minimum, maximum, mean, mode, median and standard deviation of the satellite signal, from which threshold and brightness temperature difference range were derived for testing the potential of the combining information from the different satellite signals to detect rainfall on MWL. Overall, the verification scores indicate a considerable capability of the satellite data to detect rainfall on MWL, particularly during the daytime.
The findings of this study should be interpreted while considering the potential limitations of the study. The assumed relationship between MWL rainfall and MSG SEVIRI satellite signals (for inferring cloud optical and microphysical properties) was confirmed using a limited dataset and of local origin. Thus, the descriptive statistics of the rain and non-raining satellite and the corresponding parameters (i.e., the thresholds and brightness temperature difference ranges) should be considered restricted to the study locations. Nonetheless, the approach is applicable to other areas to retrieve representative thresholds using sufficient dataset. Moreover, to allow for the operational and large-scale application of MWL and MSG data for rainfall studies based on the findings of this study, further research involving large datasets are necessary to support the observed relation between MWL rainfall and MSG based cloud top properties. In this regard, the dataset should be enlarged in both space and time. A larger time series of MWL and MSG data pairs that is retrieved from a spatially dense MWL network should compute more representative descriptive statistics and parameter estimates while improving the retrieval technique [111]. Also, data fusion and machine learning techniques offer possibilities for exploring relationships between large numbers of input variables from different sensors. These learning algorithms provide efficient alternatives and may be suitable to overcome limitations of parametric approaches (as demonstrated in this study), while potentially automating the retrieval approach [103,112].
Altogether, it can be stated based on the findings of this study that, the combination the MWL rainfall and MSG SEVIRI data have the potential for area-wide rainfall detection at a high temporal resolution. This is especially significant for areas lacking in-situ monitoring systems but having good MWL coverage established (and maintained) over the last decade, and being still further developed. Using both in-situ and MW-link data will potentially enhance the density of the observation network to monitor rainfall on the ground, and with high temporal resolution remote sensing derived information, as acquired by geostationary satellites, better temporal and spatial extrapolation will be possible.

Conflicts of Interest:
The authors declare no conflict of interest.
Appendix A Table A1. Descriptive statistics of SEVIRI satellite signals for each rainfall intensity class and study location.