Interactive comment on “ Real time rainfall estimation using microwave signals of cellular communication networks : a case study of Faisalabad , Pakistan

Abstract. Water balance estimate requires high spatio-temporal water balance components and rainfall is one of them. Rainfall is stochastic variable, which varies with respect to space and time. There are different methods for rainfall estimation such as rain gauge, satellite data but the resolution of these methods are very low, which cause over and underestimation of rainfall. A real time rainfall estimation mechanism is tested using commercial cellular networks in Faisalabad, district of Pakistan. The microwave links are used to quantify rainfall intensities and estimate rainfall at high spatio-temporal resolution. The attenuation in electromagnetic signals due to varying rainfall intensities is measured by taking difference between the power transmitted and power received during rainy period and is the measure of the path-averaged rainfall intensity. This rainfall related distortion is converted into rainfall intensity. This technique is applied on a standard microwave communication network used by a cellular communication system, comprising 35 microwave links, and it allow for observation of near-surface rainfall at the temporal resolutions of 15 min. Signal data-set of year 2012–2014 and 2015–2017 is used for calibration and validation respectively with three rain gauge data-set. The accuracy of the method is demonstrated by comparing the daily cumulative rainfall depth of University of Agriculture Faisalabad rain gauge (UAF-RG), Ayub Agriculture Research rain gauge(AR-RG) and Water and Sanitation Authority rain gauge (WASA-RG) with link based rainfall depths estimated from L2, L28 and L34 respectively, reaching r2 up to 0.97. UAF-RG is considered reference to study the spatial variability of rainfall of all the selected links within the study area, observed 10 %–60 % average spatial error of all links with the reference UAF-RG. All the results show that microwave links are potentially useful compared to the low resolution methods of rainfall estimation and can be used for effective water resources management.


Introduction
The management of water resources requires high temporal and spatial information of rainfall.Rainfall is considered as an important input parameter for hydrological model that's why it needs to be managed and measured very carefully on high spatial and temporal basis.Any small error of a large water balance component that is rainfall can produce significant error in the small components such as runoff, leaching, capillary up flow from shallow groundwater.
Without exact measurement of rainfall, agricultural crops, surface and groundwater resources cannot be managed on sustainable basis (Yilmaz el al., 2005;Berndtsson and Niemczynowicz 1988).
Aerial rainfall for catchment and basin is normally interpolated from rain gauge, radar and satellite data but these sources provide very low resolution data and all these instruments has their own challenges.The spatial interpolation of point measurements in heterogeneous landscapes and mountains result in erroneous estimates.Dense networks are needed that are difficult to establish and maintain in under developing countries.Rainfall estimation by using satellite data cannot provide full coverage of rainfall due to low spatio-temporal resolution.
There are geostationary satellite observations are available having temporal resolution of 15 min but are often very indirect e.g.estimates through cloud physical properties (Roebeling and Holleman 2009).There is another new product of NASA called GPM mission having spatial Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2017-740Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 15 January 2018 c Author(s) 2018.CC BY 4.0 License.resolution 0.1 o and temporal resolution of 30 min but this is still very low resolution as compared to the rainfall estimated by microwaves links (Hou et al., 2014;Rios Gaona et al., 2016).
Similarly another data source which is mostly used is TRMM having spatial resolution 0.25 o and temporal resolution minimum 3 hours .The downscaling of satellite image is a technique that can estimate rainfall for a smaller range of distance, but this technique is indirect technique and produces biasness and uncertainty in results.The rainfall estimated from radar normally deteriorates for longer ranges from radar.
In Pakistan rain gauge networks are managed and operated by Pakistan Meteorological Department (PMD).There are total 97 rain gauge stations in Pakistan which include 28 in Punjab, 19 in KPK, 05 in Azad Kashmir, 09 in Northern Areas, 27 in Sindh-Balochistan and 09 observatories controlled by Geophysics Quetta which are insufficient to capture high spatiotemporal rainfall (PMD Website).The intensity of telecommunication tower is greater than the magnitude of rain gauges.Therefore the main focus of the study is to quantify the rainfall due to the signal attenuation and promote the use of microwave links for rainfall estimation in Pakistan.
The basic concept behind the rainfall estimation from signal attenuation is that the signal that travels between the two towers attenuates due to rainfall intensity and this attenuation depends upon the rainfall duration and rainfall intensity, as more intensity of rainfall will create more signal distortion.As the number of raindrops and intensity of rainfall increases, the attenuation of link also increases, which subsequently reduced the received power at the other end of the link.The power received at the other end of the link is considering a byproduct of the communication between the networks (Zinevich et al., 2008;Goldshtein et al., 2009;Zinevich et al., 2009;Overeem et al.,(2011Overeem et al.,( ,2013Overeem et al.,( ,2016)); Messer et al., 2006;Leijnse et al., 2007b;Zinevich et al., 2009;van het Schip et al. 2017, Rios Gaona et al., 2015).This new advancement of using link data for rainfall estimation is very helpful to estimate the rainfall at a very high resolution which will further use for flood prediction, drought management, crop productivity and risky climate warning.Similarly massive deployment of these microwave links provides a complementary network to measure rainfall, especially in countries where rain gauges are scarce or poorly maintained, and where ground-based weather radars are not (yet) deployed (Doumounia et al., 2014).
In section 2, the detail of cellular communication link and rain gauge data information is explained.In section 3, description about how to use signal data to measure path-averaged rainfall intensity, mapping technique for rainfall map and other methodology to study the spatial variability of rainfall and in section 4, final discussion and conclusion is elaborated.

Microwave link data
In order to estimate the path-averaged rainfall intensities, signal data of 35 selected links in Faisalabad is obtained from international telecommunication Network Company Telenor, working in Pakistan.The maximum and minimum received power over 15 min temporal resolution having 38 GHz frequency is used.Figure 1

Rain gauge data
The employed rain gauges data are obtained from three different rain gauge stations namely UAF-RG, WASA-RG and AR-RG, operated by University of Agriculture Faisalabad, Ayub Agriculture research and Water and Sanitation Authority Faisalabad respectively.The data provided by all these rain gauge stations are daily cumulative rainfall values against each rainy day.For calibration and validation purpose, signal based rainfall having 15 min resolution data is converted into daily cumulative rainfall value for each day to compare it with UAF-RG, WASA-RG and AR-RG stations.Independent calibration and validation of three selected links i.e.L2, L28 and L34 against UAF-RG, AR-RG and WASA-RG respectively are performed and by considering UAF-RG as a reference point, calibration and validation of all the selected links against UAF-RG are performed to study the spatial variability of rainfall

Rainfall retrieval for signal based rainfall
Microwave links are the main source of communication between the telecommunication towers and these microwave links attenuate due to rainfall intensity (Upton et al., 2005).This distortion in the signal can be measured by using power law studied by Atlas and Ulbrich (1977) which is the relationship between rainfall and specific attenuation  =    (1) In Eq. (1) z is the specific attenuation, r is the intensity of rainfall (mmh -1 ), c is the coefficient and b is the exponent and the values of these coefficient and exponent depend upon polarization, frequency of the signal, temp of the surrounding, water phase and other important factor which include drop size distribution, canting angle distribution and shape of the rain drop (Jameson, 1991;Berne and Uijlenhoet, 2007;Leijnse et al., 2010a) and further explained by Overeem et al., (2016).During rainy period the entire length (km) of the signal between the two tower attenuate (dB) and thus the intensity of the rainfall is given by (2) In Eq. ( 2) F ref is the reference signal level, d stands for the entire length of the signal and F (L) is the received power (dBm).After approximation final form of power law is given below (Overeem et al., 2011(Overeem et al., , 2013(Overeem et al., , 2016) The value of coefficient c and exponent b as explained by Overeem et al., (2016).Berne and Uijlenhoet ( 2007) studied that how link length, frequency, precise drop size division effect the average rainfall intensity for links having frequency range between 12 to 38 GHz.They concluded that the value of coefficient c and exponent b will depend on the frequency of the link and not account much on the length of the signal.If the length of the signal increases, the frequency of the microwave link decreases.The reason behind is that if length increases, than the effect of rain drop on the frequency does not gives the best result, therefore links are usually selected within acceptable distances for making sure strong signal strength.
The concept of rainfall estimation is derived from the minimum and maximum received power having 15 min high resolution.This maximum and minimum received power is converted into corrected minimum and corrected maximum received power by comparing with reference signal power.In the first step, the pre-processing of link data is done using the code developed in R software (Overeem et al., 2016).In this step, the signal data of previous day and present day is converted into one file based on the selection of links having frequency of 12-42 GHz.If a unique link contains more than one record, that link is removed during the pre-processing, because one unique link can have only one record for a specific time interval.Also in this step, it is confirmed that whether frequency, link coordinates, and path length of a unique link remains same in whole day.This criteria is very important because these parameters should not change during a day, if this is the case, that link is also removed.
Based on above checks, one file is prepared which is free from errors.In the next step, the file prepared in the first step is used for further processing related with categorization of wet and dry signals using the code in R developed separately for this step (Overeem et al., 2016).In the next step, the link having both ends within 15 km from either side end selected link.Based on the threshold value of signal, the wet and dry signals are identified (Overeem et al., 2011(Overeem et al., , 2016)).In the third step rainfall intensities are estimation based on the corrected maximum and minimum received signal power of the file prepared in the above step using the power law relationship (Overeem et al., 2011(Overeem et al., ,2016)), Leijnseet al., 2007, van het Schip et al. 2017, Rios Gaona et al., 2015).
There are many type of errors that may come in the way to estimate the rainfall intensity and these errors may be because of the reflection and refraction of the beam, dew formation on the surface of the antennas, antenna icing, scintillation, multipath, reliable absorption by the atmosphere constituents (Upton et al., 2005).According to Upton et al. [2005] there is a very small fluctuation in the received signal power during dry season as compared to the fluctuation in the received power when there is no rain.There is another source of error in rainfall estimation because of the water films on the tower antenna .This type of signal attenuation is a major source of error which is modified by ( Kharadly and Ross 2001; Minda and Nakamura 2005; Leijnse et al., 2007aLeijnse et al., , 2007bLeijnse et al., , 2008)).When there is large distance between the link the change due to wet antenna is very small because the signal attenuation due to rainfall is very small (Leijnse et al., 2008).
The temporal sampling describes the number of sample per unit time and used this for collection of the samples.Leijnse et al. (2008) explained the three type of sampling strategies, which is averaged, intermittent and continuous.The intermittent and averaged strategies are mostly used for cellular communication link monitoring.In these two types of sampling strategies, signal power is observed over averaged 15 min resolution or sample may be selected in the middle of 15 min period.The intermittent sampling strategies has been used in the research for rainfall estimation, which is similar to the Messer et al. (2006) which is the maximum and minimum received power, F min and F max are collected over 15 min resolution.
There is another error that may occur and is responsible for the decrease the availability of data is due to the heavy rainfall.This type of error may be due to the storage issue arrives in the server of the telecommunication company.Overeem et al. (2016) suggested some fixed parameters on the basis of these errors and all these recommend parameters values are used in the paper.

Verification methodology
For calibration and validation purpose path-averaged rainfall intensities estimated from the signal data having 15 min resolution are converted in to daily (24hrs) cumulative rainfall value against each day to compare it with daily (24hrs) cumulative rainfall values of UAF-RG, AR-RG and WASA-RG.Independent calibration and validation of L2, L24 and L34 are performed against UAF-RG, AR-RG and WASA-RG respectively.

Percentage error analysis
By considering UAR-RG as reference point to study the spatial variability of rainfall in the study area, calibration and validation is performed for all 35 no of selected links between UAF-RG and signal based rainfall depths.After estimated signal based rainfall, percentage error for all the all selected links is calculated according to the Eq. ( 4) and Eq. ( 5), where d is cumulative signal based rainfall, f is cumulative UAF-RG rainfall depth, PD is percentage error of each day and L no is link number.
Percentage error analysis for each selected link against each day (PD) = (1 − ( d f )) * 100 (4) Average percentage spatial error for all selected days for each link = L no (5)

Maximum, minimum received, corrected maximum and minimum received power
The signal attenuation due to rainfall is the main factor to find the rainfall intensities which is the difference between the received signal level and some reference signal level which is representation of the dry period when there is no rain.The attenuation in the signal is estimated by using the procedure explained in the section 3 and compared that attenuation with the reference signal power to find corrected maximum power received and corrected minimum power received (Overeem et al., 2015(Overeem et al., , 2016)).Overeem et al., (2016)

Calibration and validation of signal based rainfall for the all selected links with UAF-
RG to study the spatial variability of rainfall.

Calibration and validation
The UAF-RG is used as a reference point to study the spatial variability of rainfall in the selected study area.The cumulative rainfall depths of UAF-RG are compared with all the selected 35 links based rainfall depth to study the spatially variability within area of 225 km 2 .Overeem et al. (2011Overeem et al. ( , 2013Overeem et al. ( , and 2016)), Van het Schip et al (2017), Rios Gaona et al., (2015) used a gauge-adjusted radar data set to calibrate and validate the microwave link rainfall retrieval algorithm but in this study due to limited data availability of radar, daily cumulative rainfall values of UAF-RG are compared with the daily cumulative rainfall depth measured by link based approach for all the selected links.For calibration purpose, total 32 numbers of days are selected for years 2012-2014.The distance of all the selected links from the reference UAF-RG and distance between the transmitter and receiver of all the links are measured.The links 02 was very close to reference UAF-RG nearly 0 km distance and all the other remaining points are in the area of 225 km 2 around the UAF-RG.
The comparisons are carried out on the basis of scatter density plots and three metrics: mean rainfall, coefficient of variation (CV), and coefficient of determination (r 2 ).34, 3.39, 4.13, 6.21, 5.67 and 10.39 respectively from Reference UAF-RG, level of significance deceases.For validation data-set, the coefficient of determination for L7, L15, L18, L23, L22 and L29, are 0.96, 0.79, 0.82, 0.78, 0.71 and 0.67 respectively.All the above results proved that rainfall is stochastic and erratic pattern variable, as the distance increases from reference UAF-RG due to spatial variation, rainfall depth increases or decreases.Similarly for all selected 35 links, as the distance increases

Spatial percentage error analysis
As it is discussed that there are mostly two sources available for rainfall estimation in Pakistan, which is rain gauge and satellite data.There are limited number of rain gauge networks operating in Indus basin irrigation system (IBIS), which is the largest irrigation system in the world, similarly rainfall estimated by satellite is also of low spatio-temporal resolution, so it is declared as data limited basin (Cheema 2012).Even the instruments which are installed on the existing meteorological stations in Pakistan are outdated and of low spatio-temporal resolution, so these low resolution data is used to estimated rainfall in basins and catchments, which is not the true presentation of the reality because rainfall is stochastic variable and its varies within radius of 1-2 km.Because of the factors discussed above, it is needs of the time that system should be established that provide high spatio-temporal resolution data, which is used for water resources management.Keeping in view of all these factors, rainfall is estimated by using signal based approach and by considering UAF-RG as reference point, percentage spatial error analysis is performed in the study area.

Rainfall mapping
The rainfall maps are prepared in GIS by using IDW technique for rainfall event of 10  This novel approach of measuring rainfall using the cellular communication network is the Information and Communication Technology (ICT) revolution, which will definitely enhance the role of ICT in agriculture and surface and groundwater resources on sustainable basis.
explains the location of 35 selected microwave links and location of rain gauges.It is clear from the Fig.1 that L2, L28 and L34 are close to UAR-RG, AR-RG and WASA-RG respectively.All the selected links are vertically polarized and in the radius of 225 km 2 area.The data format required to process the code is acquired from Overeem et al. (2016).Total 32 and 33 days from years 2012-2014 and 2015-2017 are selected for calibration and validation of link based approach with standard rain gauges dataset respectively.The path length, i.e. distance between the sender and receiver, for all the selected links is between 0.50-2.5 km.Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2017-740Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 15 January 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 1 .
Figure 1.Map of study area with location of selected microwave links (red, zinc, green and purple towers), and triangles: yellow color (University of Agriculture), orange color (Ayub Research) and blue color (Water and Sanitation Authority) rain gauge.
, van het Schip et al. (2017), Rios Gaona et al., (2015) presented graphs showing the minimum and corrected minimum received power compared with gauge-adjusted radar having 15 min resolution but due to no data availability of radar with same 15 min temporal resolution, it is not possible to make such comparison in this study so only attenuation due to rainfall intensity is shown in fig.2.The Fig. 2 shows the maximum and minimum power received and corrected minimum and maximum power received compared with reference signal level.The top (right, middle and left) plots present attenuation due to rainfall of three different links and bottom (right, middle and right) plots present corrected maximum and minimum received power which is compared with reference signal level.It is clear from Fig 02 that all the links show the different attenuation due to rainfall intensity but the time of distortion remains the same in all the links, which is located index number 66 to 70 time interval.Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2017-740Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 15 January 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 2 .
Figure 2. Top (right, middle and right) plots present maximun recevied power (black line) and minimun recevied power (blue line) for three different links for 12 May 2014.Bottom (right, middle and left) plots present maximun corrected recived power (black line) and minimun correted recevied power (blue line) and reference signal level (red line) for three different links for same day dated 12 May 2014.There are total 96 time intervals having 15 min resolution in each plot against each day (24 hours).

Figure 3 .
Figure 3. Calibration and validation of signal based rainfall with standard rain gauges operated in Faisalabad.Left (top and bottom) plots present calibration and validation of L2 with UAR-RG, middle (top and bottom) plots present calibration and validation of L28 with AR-RG and right( top and bottom) plots present calibration and validation of L34 with WASA-RG.
Figure 04 explains scatter density plots between the daily commutative signal based and daily cumulative rainfall of UAF-RG station rainfall depth (mm/day).The statistical analysis between observed UAF-RG and signal based rainfall is analyzed.The values of CV, r 2 , and the average commutative rainfall measured using UAF-RG, as indicated by R UAF and average commutative rainfall depth using signal approach, indicated by R LINK, are included in the plots.The coefficient of variation CV and coefficient of determination for link which is close to the UAF-RG show significant results, but as the distance of links increases from the reference UAF-RG, level of significance decreases.It is clear from the fig.3 that for L7, L15, L18, L22, L23 and L29, as the distance increases 0.34 km, 3.39 km, 4.13km, 6.21 km, 5.67 km and 10.39 km respectively from Reference UAF-RG, level of significance i.e. coefficient of determination deceases.For calibration data-set, the coefficient of determination for L7, L15, L18, L23, L22 and L29, are 0.97, 0.82, 0.79, 0.91, 0.79 and 0.67 respectively, Similarly data-set having frequency 38 GHz is used in this study for the validation purpose.The same links are used for the validation purpose as used from calibration purpose but data-set used are of different time period.For validation purpose data-set of years 2015-2017 are used and total 33 rainy included non rainy days are selected.Figure 05 explains validation scatter density plots between the daily cumulative signal based and daily cumulative rainfall of UAF-RG station.The statistical analysis between observed UAF-RG and signal based rainfall is analyzed.It is clear from the fig.4 that for L7, L15, L18, L23, L22 and L29, as the distance increases 0.

Figure 4 .
Figure 4. Scatter density plots of calibration data-set of daily (24hr) cumulative rainfall depths of signal data of 33 no of days against daily cumulative rainfall depths of UAF rain gauge.

Figure 5 .
Figure 5. Scatter density plots of validation data-set of daily (24hr) cumulative rainfall depths of signal data of 33 no of days against daily cumulative rainfall depths of UAF rain gauge.

Figure 06
Figure 06 left (top and bottom) plots present percentage spatial variation of different links against no of rainy days from reference point UAR-RG.For calibration and validation dataset, the percentage spatial error for links no L2, L5, L7, L21, L25, and L28 varies between 20%-80% for different no of rainy days.It is clear from Fig. 06 left (top and bottom) plots that the percentage Error associated with spatial variation of rainfall from reference point (UAF-RG) i.e.the L2, L5 and L7 are close to reference UAF-RG, so there is small spatial error exist between these links, but the L21, L25 and L28 are far away from the UAF-RG reference point, so there is more spatial error exist.It is clear as the distance increase from the reference point point (UAF-RG) percentage error varies due to spatial variation of rainfall.Similarly fig.6right (top and bottom) plots presents overall average percentage spatial error of all the selected links against the distance from reference UAF-RG.It is clear from the fig.6right (top and bottom) plots that as the distance from the reference UAF-RG increases, for calibration and validation data-set, overall percentage average spatial error of all the selected links from reference UAF-RG varies between 10%-50% and 10%-60% respectively, which is logical and makes sense.

Figure 6 .
Figure 6.Left (top and bottom) plots present calibration and validation of percentage spatial error analysis of different links against no of rainy days.Right (top and bottom) plots present calibration and validation of percentage average spatial error of all links from reference UAF-RG.

Figure 7 .
Figure 7. Signal based daily cumulative rainfall depths for all links on 10 March 2014 (left panel).Signal based cumulative rainfall depths for all links on 23 July 2016 (right plot).(Black tower represent different links location) ; RiosGaona et al., (2015)suggested two type of interpolation techniques i.e. ordinary kriging (OK) and inverse distance weighted (IDW).Both these interpolation methods are well suited for dealing with spatially disturbed data locations.The ordinary kriging requires variogram model, so it is not possible to reboust such variogram in this study because of limited data-set.IDW technique is used to interpolate the rainfall maps of study area.The path-averaged rainfall estimated from link approach is considered at the center of the sender and receiver, so that point data can be used in IDW interpolation.Rainfall maps are prepared in GIS by using IDW interpolation technique to study spatial variation in rainfall estimates between signal and rain gauge rainfall depths.Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2017-740Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 15 January 2018 c Author(s) 2018.CC BY 4.0 License.
March 2014 and 23 July 2016.Figure 07 explains how rainfall varies within area of 225 Km 2 .
is 19mm and 40mm respectively and similarly rainfall recorded by WASA-RG on 10 March 2014 and 23 July May 2016 is 30mm and 26.3mm respectively.So one point based value is not a