1. Introduction
During the last 10 years, rainfall measurement from commercial microwave link (CML) network has gradually emerged as a useful complement to traditional rainfall measurement based on gauges, weather radar or satellites. Uijlenhoet et al. (2018) and Chwala and Kunstmann (2019) provide a good review of the state of the art and the research developed since the pioneering work of Messer et al. (2006) and Leijnse et al. (2007b). The CML technique is based on the analysis of attenuation induced by rain over the radio-frequency part of the mobile network, i.e., between pairs of telecommunication antennas. The main advantage of this technique is to exploit a network already in place and well maintained by mobile operators. In developing countries where the mobile network is already well developed (Noam 1999; ITU 2004) while hydrometeorological services have limited resources (Novella and Thiaw 2013; Dieulin et al. 2019) the prospect for operational use of the CML technique is very appealing (Hoedjes et al. 2014; Gosset et al. 2016). The telecommunication network density follows population density (i.e., the customers) and most of the antennas lay in urban areas. This means that urban hydrology and urban flood risk monitoring is a subject area that could benefit from the CML technique (Fencl et al. 2013, 2015, 2017; Stransky et al. 2018; Pastorek et al. 2019). Cities in developing countries and especially in Africa are suffering from an increase exposure to extreme weather events (Bradshaw et al. 2007; Ebi and Bowen 2016; Egbinola et al. 2017; Engel et al. 2017; CRED 2015; Kovacs et al. 2017). The amount of material damages and casualties due to flooding in West Africa has increased in the last decade under the conjunction of demographical pressure and population flow toward cities on one hand, and an increase of rainfall on the other hand. The mobile communication network could potentially contribute to a better monitoring of these hydrometeorological events. With current network monitoring systems (NMS) or dedicated software, CML rainfall is typically monitored at time steps of 5–15 min (Uijlenhoet et al. 2018; Chwala and Kunstmann 2019), which provides an interesting temporal resolution for urban hydrology. Data have been collected at even shorter time steps for some experiments (Schleiss and Berne 2010; Schleiss et al. 2013; Zinevich et al. 2009; Fencl et al. 2015; Chwala et al. 2016).
Most studies on CML estimation of rainfall have been based in European countries (Fenicia et al. 2012; Schleiss et al. 2013; Zohidov et al. 2016; D’Amico et al. 2016; Pastorek et al. 2019; de Vos et al. 2019; Polz et al. 2020; Graf et al. 2020; Roversi et al. 2020) and Israel (Messer et al. 2006; Zinevich et al. 2008, 2009; David et al. 2013). Most have focused on the quality of the estimate from this technique by comparison with rain gauges and/or weather radar. More recently, investigations on CML rainfall estimation have started outside Europe and Mediterranean countries (Hoedjes et al. 2014; Rios Gaona et al. 2017; Kim and Kwon 2018; Sohail Afzal et al. 2018). Doumounia et al. (2014) presented the first quantitative test of the technique in Africa, based on a single link.
A few studies discussed the interest of the CML rainfall for hydrological applications in Europe (Brauer et al. 2016; Smiatek et al. 2017) in particular for urban hydrology where the high spatial and temporal resolution of the rain maps is beneficial (Fencl et al. 2013, 2015, 2017; Stransky et al. 2018; Pastorek et al. 2019). These studies showed that the density of links in urban areas helps improving the simulation of the discharge dynamics compared to simulations based solely on rain gauges. They also pointed out some biases in CML rainfall estimate and their propagation in the simulated discharge. In African cities where the flood risk is very high and rainfall is due to intense convective systems, the CML technique seems particularly promising for urban hydrology. This study wishes to contribute to its development by analyzing the expected benefits.
The study by Doumounia et al. (2014) in Ouagadougou, Burkina Faso, was part of the Megha-Tropiques satellite ground validation (MTGV) program (Gosset et al. 2018; Guilloteau et al. 2018). During this experiment, a weather radar and a dense network of rain gauges were available. To take full advantage of the CML-based rain maps when they will be available, the Institut de Recherche pour le Développement (IRD) started the development of a fully distributed hydrological model compatible with this urban context. Bouvier et al. (2017, 2018) have adapted their modeling platform Atelier en Hydrologie Spatialisée (ATHYS; Bouvier and Desbordes 1990; Bouvier et al. 2010) with a first validated setup for the city of Ouagadougou. The primary purpose of the present work is to investigate how such a distributed hydrological model can benefit from CML-based rain estimation: what is the added value for hydrological prediction of the spatial information on rainfall provided by the CML network; how does it balance with the uncertainties brought in by CML estimation; what is the sensitivity of the predicted discharge to the CML network configuration. While CML and hydrological data are being gathered in various African testbeds (Cameroon; Niger), these questions are first investigated based on numerical simulations.
The proposed simulation framework is based on three components, (i) the distributed hydrological model ATHYS, currently set up for the city of Ouagadougou, (ii) high-resolution (1 km; 5 min) rain maps acquired with a weather radar in Ouagadougou during the MTGV campaign; these are the reference rain fields used for the reference hydrological simulations and to generate synthetic CML measurements, and (iii) the production of pseudoCML data simulated by positioning a virtual network inside the high-resolution rain fields. With this setup several aspects of CML-based rainfall measurement and uncertainty propagation into the model can be investigated.
There are many sources of uncertainty in rainfall estimation from a network of commercial microwave links (see Chwala and Kunstmann 2019 for a recent review). In this paper we primarily focus on two aspects that are directly linked to the network itself: (i) the uncertainty in rainfall estimation at each individual link due to the inaccuracy of the raw signal (digitizing step) and the length and frequency of the link, and (ii) the network spatial configuration and its capacity to represent rainfall characteristics over the basin.
Section 2 provides an introduction to rainfall measurement from commercial microwave links (CMLs). Section 3 introduces the study area and the simulation setup, the high-resolution radar data used as input for the link simulations, the hydrological model ATHYS and the numerical experiments carried out. Section 4 presents the results from the numerical experiments, analyzing the impact of the precision in attenuation measurement and of the spatial configuration of the network inside the basins. For both topics, the impact is first analyzed on rainfall and then on the simulated discharge. Section 5 provides conclusions and perspectives.
2. Rainfall measurement from commercial microwave links: Principle and known limitations
Table 1 reports values of a, b for several frequencies typical of the range commonly used on operational mobile networks. The values of a and b were computed using the Mie scattering model (Mie 1908) and DSDs measured in West Africa (Moumouni et al. 2008).
Minimum detectable rainfall (mm h−1) as a function of frequency, signal precision, and link length. The second row reports the values of the prefactor (a) and exponent (b) of the attenuation–rainfall or k–R relationship (see text) for the indicated frequencies. The three last rows illustrate the equivalent in rain rate (mm h−1), of an increment in the measured attenuation (0.1 or 1 dB) for the indicated link length (1, 10 km) and frequency. The italic highlights frequency/length combinations that are not likely on operational networks (short link and low frequency; long link at high frequency).
3. Study area, data, and simulation setup
a. Study area
The area of Ouagadougou (12.3°N, 1.5°W) in Burkina Faso was selected as an illustrative test bed for the present sensitivity study for several reasons. Ouagadougou is representative of African cities exposed to increased flood risk as illustrated by several recent extreme events (Engel et al. 2017). In addition, all the information needed for the simulations is available for this city: (i) Ouagadougou hosted the first quantitative experimentation in Africa of rainfall measurement based on CMLs. This experiment, presented in Doumounia et al. (2014) was based on a single link, rain gauges and used data from the radar presented in section 3b. The operator provided metadata on the network lay out (Fig. 1), which has been included in some of our simulations; (ii) Doumounia et al. (2014) experiment was part of the larger Megha-Tropiques Ground Validation program (MTGV; http://meghatropiques.ipsl.polytechnique.fr/the-ouagadougou-super-site/; Gosset et al. 2018; Guilloteau et al. 2018) during which a weather radar was deployed for 2 years, providing high-resolution rain maps (see section 3b) representative of African squall lines (iii) a distributed hydrological model, well suited for flood prediction at the scale of a city and set up to use spatially distributed rainfall information was developed and calibrated for Ouagadougou (Bouvier et al. 2018) as presented in section 3c.
The study area in Ouagadougou. The gray shading is the urbanized (built) area, the blue lines represent the hydrographic network and the black lines the contours of the studied basins and sub-basins, and the blue stars are the outlets where the simulated discharge is analyzed for the various numerical experiments detailed in the text. The white lines are the positions of the 75 microwave-links (13 GHz) available for one of the operational mobile networks.
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0163.1
Figure 1 displays the domain used for simulations (1250 km2) and the layout of the CML network used for some of our simulations. For this urban network (one of several in Ouagadougou where more than one cellular phone company operates) all 75 links operate at 13 GHz, their lengths range from 0.3 to 26 km over the domain. In our experience this density and size distribution is quite typical of what is found in other African cities, but there is a variety among countries, operators and depending on when the network was installed. In Niamey in Niger or Douala in Cameroun where we work with another operator, the number of links available over the urban areas are 190 and 227, respectively; with frequencies ranging from 8.5 to 23 GHz and lengths from 0.16 to 6.59 km. Discussion with technical teams reveals that these networks are evolving with a tendency toward higher frequencies in the future.
The urban part of Ouagadougou is seen in the center (gray) of Fig. 1 and the basins that drainwater into the city are displayed. The two basins where rainfall estimation and discharge simulation are analyzed are highlighted. Their two outlets are, respectively, outlet 1060 (drainage area 448 km2) in the northern part of the city and outlet 1074 (drainage area 139 km2) more south. In each basin smaller sub-basins are also used for testing, with outlet Ri1 and Ri3 (drainage area resp. 84 and 193 km2) in the northern basin, and Sa1 (74 km2) in the South.
b. High-resolution rainfall maps from weather radar
The main data as input to the simulations are high-resolution rain maps from a weather radar located in Ouagadougou in 2012/13. The radar is an X-band polarimetric radar from which 5-min, 1-km2 rain maps were produced using an algorithm based on the polarimetric specific differential phase shift (R–Kdp) as in Matrosov (2010), Kacou (2014) and Koffi et al. (2014).
In Ouagadougou as in most West Africa the rainfall season is associated with organized convective systems characterized by a front of convective cells followed by a stratiform trail (Moumouni et al. 2008; Depraetere et al. 2009; Alcoba et al. 2016) and propagating mostly westward. Figure 2 displays the rain maps over Ouagadougou while a convective system recorded by the radar on 4 August 2012 is crossing the area. The front of heavy rainfall associated with the convection arrives first followed by more widespread and lower rain rates. Altogether three rainfall events that lead to heavy precipitations and were well sampled by the radar are used for the simulations. Figure 3 displays the hyetogram (rain rate versus time) of these events and the frequency distribution of rain intensities. The values are typical of African squall lines, with most of the rainfall accumulation due to the convective front which lasts about one hour, and only 20%–30% of the event accumulation due to the stratiform trail that lasts several hours. The heavy convective rainfall, with peak intensities well above 50 mm h−1 is the main driver for the floods and needs to be monitored. The spread in the value of the percentiles in Fig. 3 illustrates the spatial variability of rainfall over the domain, especially during the convective front. The ability of the CML network to capture this variability is crucial as discussed in section 4.
Evolution of rain intensity maps over the area on the 4 Aug 2012 event as seen by the radar and the simulated links. The three images show the radar rain maps crossing the study domain at three moments in time (a) 0210, (b) 0230, and (c) 0250 UTC; the color shading over the 1 km × 1 km pixels show the rainfall intensity as indicated by the legend. The 19 straight lines superimposed on each image represent the simulated microwave links and their color indicates the mean rainfall over the link, as calculated by the link simulator [see text and Eq. (5)].
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0163.1
Time evolution of radar rainfall over the studied area (from Fig. 1) for the three indicated rainfall events. For each 5-min time step the distribution of the rainfall rates among the 1060 radar pixels is illustrated by the percentiles.
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0163.1
c. Simulation setup
The objective of the simulations is to analyze the capacity of the CML network to reproduce the characteristics of the rain field that are needed to simulate the discharge. The benchmark is the hydrological model forced by the high-resolution radar rain maps; they provide the reference simulation.
CML-like data, mimicking various network configurations are generated from the radar maps. The quality of these synthetic-CML rainfall estimates is first compared with the original rainfall maps. Then these rainfall estimates are used as forcing to the hydrological model, and the simulated discharges is compared to the reference (i.e., the model forced by the high-resolution rain map).
1) CML simulation from radar data
The CML simulation is based on calculating the interception between the links and the radar maps. The lines in Fig. 2 display simulated links with their colors representing the mean rainfall over the link path.
From the principle above a variety of CML network configurations can be tested by varying the frequency, length, position and orientation of the links. Several sources of uncertainty can be included in the simulations.
2) Hydrological model
A distributed hydrological model is needed to analyze the impact of rainfall spatial variability and to assess the ability of the CML network to reproduce rainfall characteristics that are important for the hydrological response. This work concentrates only on sensitivity analysis, by comparing the simulated response for various rainfall forcing. The purpose is not to evaluate the model output against real discharge data as these were not available when the radar was operating. However, the model was set up and compared with real data in some areas of Ouagadougou, using rain gauge data, as described in Bouvier et al. (2018). The model is based on the open source platform ATHYS (www.athys-soft.org; Bouvier and Desbordes 1990; Bouvier et al. 2010). The model has been used for flood modeling in many areas, especially for small catchments. Recently Bouvier et al. (2018) proposed a version of the model suited for the analysis of urban floods in African cities. The motivation was to propose a distributed gridded model operating over the whole city, with small computation time allowing real-time forecasting. ATHYS distributed event-based parsimonious model, with Soil Conservation Service Lag-and-Route (SCS-LR) formula for runoff production and propagation is well suited for these constraints. As detailed in Bouvier et al. (2018) the model was set up over a 1000-km2 domain which includes the city of Ouagadougou as represented in Fig. 1. The hydrographic network was defined using the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) elevation model. This defines the “natural” network in the rural area while the flux is forced by the street layout provided by the OpenStreetMap (/www.openstreetmap.org) database for the built areas. The runoff is calculated based on the SCS formulation on elementary grid cells of resolution 10 m, and then propagated through the connected grid cells downstream using a “lag and route” formula. The velocity of propagation over a given grid cell is parameterized by the slope at this grid point and by the drainage area upstream that grid. This is a simplified version compared to Bouvier et al. (2018) who also considered hydraulic propagation (kinematic wave) in some parts of the network. Another simplification is that the SCS parameters are uniform for the whole area (the interception parameter S is equal to 100 mm, in the range used by Bouvier et al. 2018) as the purpose here is to analyze the relative impact of various rain products, rather than the discharge simulation itself.
In this study rainfall is provided each 5 min, either on the radar grid (1-km resolution) for the reference simulation, or at the position of the links (center of each link) when testing the various network configurations. Inside ATHYS, the rainfall is interpolated at each gridpoint-based on the Thiessen polygons method (Thiessen 1911).
3) Reference simulation
The reference simulations are based on the model above with the high-resolution rainfall maps (1-km resolution; 5-min time step) as forcing. A reference simulation is provided for each 3 rainfall events displayed in Fig. 3. The discharge is calculated in 1078 intermediary points within the simulated area. In the next sections the discharge sensitivity to the rain forcing is analyzed specifically at the outlets of the two main basins in Fig. 1 (1060 and 1074) and their sub-basins (Ri1, Ri3, and Sa1). Part of the northern basin (outlet 1060) lays in rural areas which are poorly observed by the telecommunication network (Fig. 1), while the southern basin (outlet 1074) is located mostly in the urban area, thus better covered by the mobile network.
4. Analysis of CML rainfall uncertainty and propagation in discharge simulation
The simulation framework is used in this section to analyze uncertainties in rainfall estimation based on CMLs and its impact on the hydrological simulations. The reference simulation is based on the full resolution (1 km) rain maps. Synthetic CML rainfall estimates are produced using the link simulations introduced in section 3c for several network configuration.
First the impact of the precision of the attenuation data provided by the operator is tested in section 4a. For this experiment the links are positioned and oriented as in Fig. 1 and the impact of the rounding error on attenuation (0.1 or 1 dB) is analyzed considering several frequencies and link lengths. The impact is first analyzed on the retrieved rainfall distribution and then on the simulated discharge over the 2 main outlets 1060 and 1074.
Section 4b concentrates on the spatial configuration of the network and its ability to sample rainfall variability within the basin. As above the analysis is first focused on the uncertainty on rainfall estimation over the basins and then on the simulated discharge. Several sub-basins of various size and shape are used.
a. Impact of PIA rounding error
As discussed in section 2 (Table 1) the accuracy of rainfall estimation from Eq. (4) depends on the precision of the PIA measurement itself, on the frequency (through the parameters a and b) and on the link length L. The most recent network monitoring systems (NMS) provide Tx and Rx with 0.1 dB or better, but more basic NMS provide only 1 dB precision (Leijnse et al. 2007b; Fencl et al. 2015; Kim and Kwon 2018). The relative effect of PIA precision is stronger for the lowest rain rate and sets the lower limit of rainfall detection. According to Table 1 for instance the theoretical limit of detection for a link of 1 km operating at 12 GHz and with a coarse accuracy of 1 dB is 22 mm h−1; rainfall below this threshold cannot be measured with such a link. For the highest end of the rainfall spectra (and specially for intense convective rainfall as in Africa) the relative error due to PIA is low (Leijnse et al. 2008a).
To analyze the impact of PIA precision on rainfall and subsequently discharge simulation, synthetic CML networks with precision 1 or 0.1 dB, and a range of frequency and length are simulated.
1) Numerical experiment
For this experiment the links’ center position and their orientation are those provided by the operator metadata in Ouagadougou for the 75 links shown in Fig. 1 but the links’ length, operating frequency, and the PIA precision can be changed. Three link lengths: 1, 5, and 10 km; five frequencies: 6, 12, 18, 24, and 30 GHz; and two rounding errors on the PIA: 0.1 and 1 dB, are considered. For each experiment the network is homogenous (same length, frequency and precision for all links).
The values of a and b used to simulate the PIA and the estimated rainfall at each link are those from Table 1. The only source of uncertainty in the simulation is the rounding error of the PIA.
2) Analysis of the errors in rainfall estimation
Figure 4 illustrates the error in the frequency distribution of the rainfall rates due to the rounding error, for links of size 1 km and the indicated frequencies. The calculation is done considering all three rainfall events. The curves in Fig. 4 show the mean rainfall accumulation per link and per event, as a function of the rain intensity class. The blue line is for a link with perfect precision [where the retrieved rainfall is exactly the mean link rainfall as in Eq. (5)], the other curves show the degradation as function of precision (0.1 or 1 dB) for the various frequencies. Figure 4 is consistent with the numbers displayed in Table 1. A 1-km-long link operating at 6 GHz would miss a substantial amount of rainfall, because an intensity above 26 mm h−1 is needed to create a 0.1-dB shift in attenuation, and 150 mm h−1 to create a 1-dB shift. Fortunately, short links (common in urban areas) usually operate at higher frequency, and a 10-km-long 6-GHz link would have better detection (cf. Table 1). As expected from Table 1, the distribution of rain intensity is better reproduced for higher frequencies and for all frequencies the errors are relatively lower for higher rain rates. This last point is important when considering the impact of the highest rain rates on floods. For 1-dB precision the overall bias on the mean event rainfall is small (about 10%) from frequency 24 GHz and above. For a precision of 0.1 dB all the frequencies from 12 GHz and above provide a good reproduction of the rain rates, with biases below 5%. The rendering would be better for longer links (and worse for shorter links) following Eq. (4).
Cumulated rainfall distribution per rain-rate classes as a function of link frequency and attenuation precision—here for links of length 1 km. The y axis is the mean amount of rainfall per link and event (see text), and the x axis is the intensity classes. The dark blue line is for a link with perfect precision; for the others, the color indicates the frequency (GHz), the plain lines are for precision 1 dB, and the dash line for precision 0.1 dB.
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0163.1
It is worth stressing again that our simulations do not account for the wet antenna effect. Antenna wetting would typically increase the measured PIA by about 1 dB (this is indicative; the range of values reported in the literature and by engineers is wide), with a risk of overestimating rainfall and creating false alarms. The existence of this positive bias can in practice counterbalance (compensating errors) some of the negative bias due to missing low rain rates with a coarse precision. Other effects such as the nonlinearity of the attenuation–rainfall relationship (as discussed in section 2) tend to add a positive bias for long links (above 5 km) and frequency below 15 GHz if they are not accounted for in the retrieval. The strength of this effect depends on the variability of rainfall at small scale. According to our tests (based on the present radar data, not shown) the resulting impact of nonlinearity is negligible compared to 1-dB rounding error.
3) Propagation of the errors into the simulated discharge
Figure 5 displays the discharge simulated by the model at the outlets 1060 and 1074 (Fig. 1), for the 4 August 2012 event. The black line is the reference simulation based on the high-resolution radar map. The dark blue line is the simulation based on the CML (1-km length and position as in Fig. 1) with perfect precision (no error on the rainfall retrieval over the link), and the other colors display the tests with precision 0.1 dB (left) or 1 dB (right), and frequencies 6, 12, 18, 24, and 30 GHz as in Fig. 4. The difference between the reference (black) and the links with no error (dark blue) reflects solely the impact of rainfall sampling. This will be discussed further in the next section. The difference between the various colors and the dark blue line is related to the signal precision and its impact on rainfall estimation over the basin. Figure 5 confirms what was seen in Fig. 4, rain rates below a given threshold are undetected if the precision is coarse, especially for the lower frequencies. With a precision of 0.1 dB—except for the unlikely case of 1-km/6-GHz link—the discharge is well reproduced; a coarse precision of 1 dB has a negative impact on the simulated discharge, especially for frequencies below 24 GHz.
Effect of raw signal precision for different frequencies on the simulated discharge for the 4 Aug 2020 event (top row in Fig. 3). (top) Outlet 1060 and (bottom) outlet 1074. Precision (left) 0.1 dB and (right) 1 dB. As in Fig. 4 the length is 1 km for all links, and their frequency is indicated by the color. The dark blue line is for links with perfect precision, and the black line is for the reference simulation based on the high-resolution radar map.
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0163.1
The results are generalized in Fig. 6 for all three events and several numerical experiments: five frequencies, two precision levels, and three link lengths (1, 5, and 10 km). The time series of the discharge simulated at outlets 1060 and 1074 for each network configuration is compared with the discharge simulated with the high-resolution radar maps. The average over the three events of the following statistics is displayed as a function of frequency/length/precision: the mean bias on the discharge, the relative error on the peak discharge and Kling–Gupta efficiency (KGE; Gupta et al. 2009).
Effect of signal precision, link length, and frequency on the simulated discharge. The simulated discharge when the model is forced by microwave links (with positions as in Fig. 1) is compared with the reference simulation based on the radar maps. Three criteria are presented: the mean bias on the event’s discharge, the error on the maximum discharge, and the KGE. For each of the criteria, the average value for the three events is plotted. (left) Outlet 1060 and (right) outlet 1074. The results are shown as a function frequency (x axis), link length (blue for 1 km, green for 5, and red for 10 km), and signal precision (hollow circles for 0.1 dB and plain dots for 1 dB). The results for the links with perfect precision are shown by the horizontal lines.
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0163.1
Because of the high value of the coefficient a [Eq. (4); Table 1] the frequency 30 GHz is mostly immune to a lack of precision up to 1 dB, even for the shortest link length considered here, 1 km. For this frequency all three scores are good. For frequencies in the range 12–24 GHz, which is very common in current mobile networks in urban areas, a precision better than 1 dB is needed to reproduce rainfall and discharge satisfactorily. For short links (1 km) with coarse precision (1 dB) in this range, the loss of small to medium rain rates means an underestimation of the discharge and its dynamic (also seen in Fig. 5), impacting all 3 scores. For lower frequencies (6 GHz) a lot of rainfall is undetected leading to a strong underestimation of the discharge, its peak and its dynamic, unless the precision is 0.1 dB or better, and the length above 5 km.
The horizontal lines in Fig. 5 show the scores for the links with perfect precision, considering the retrieved rainfall is exactly the weighted average over the radar pixels [Eq. (5)]. In that case the difference with the reference simulation is due to the difference in spatial sampling. We note that this difference is higher for outlet 1060 than for outlet 1074; this is explained by the position of the links inside the basin as seen in Fig. 1. The network is more homogeneous and denser for the southeastern basin (outlet 1074), though not perfect, while rainfall in the eastern part of the northern basin (outlet 1060) is poorly sampled. For the latter, the mean and peak discharge are underestimated. The results are also impacted by the length of the links as expected given the spatial variability of the rain field within squall lines (Figs. 2 and 3). The next section analyses further the question of the network spatial layout and its capacity to capture rainfall characteristics within the basin.
b. Impact of network spatial layout
The network overall geometry, which includes the length, the position and the orientation of the links, determines its ability to capture and quantify rainfall variability inside the basin. As discussed with Figs. 2 and 3, the convective systems that bring rainfall in West Africa exhibit high space–time variability.
This section investigates the impact of the network geometry on rainfall QPE (quantitative precipitation estimate) over the basin, then on the simulated discharge. This is based on several numerical experiments, either with varying length, density, and random positions and orientations of the links inside the basins or using the actual network of 75 links (Fig. 1).
1) Numerical experiment
The effect of the network geometry is investigated for three sub-basins of size 74–193 km2 with outlets marked Ri1, Ri3, and Sa1 in Fig. 1. The number of links per basin (i.e., a link which center is inside the basin) N varies from 1 to 100. For each value of N, 10 experiments with random positions and orientations of the links are generated. For each of these link positions and orientations, three lengths (1, 5, and 10 km) are considered as in section 4. Altogether 410 synthetic network configurations are simulated for each three sub-basins. For each, the three rainfall events are sampled with the link simulator (section 3c). In these experiments only the network geometry is investigated, no error is considered in the estimation of the mean rainfall intensity over each link, which is simply calculated as in Eq. (5).
2) Rainfall estimation and variability within the basin
Figure 7 illustrates the spatial variability of rainfall as captured by the link network. The rainfall time series is from the 4 August 2012 event (Fig. 2 and 3). The 75 links positions of Fig. 1 are used, but a heterogenous network of length 1 km (top) or 10 km (bottom) is simulated. At every 5-min time step there is a subsequent spread among the links. The spread is slightly reduced for the 10-km-long links because of a spatial smoothing effect.
Illustration of the spread within the rainfall time series among all 75 links (center position and orientation as in Fig. 1) for links of length (top) 1 km or (bottom) 10 km for the 4 Aug 2012 event. The average rainfall over all links by 5-min time steps is the thick black line.
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0163.1
Figure 8 summarizes the ability of different network configurations to quantify the time evolution of the mean area rainfall, and the spatial variability inside a basin. This example is for the 4 August 2012 event and the sub-basin Ri3 (Fig. 1). Four configurations are considered: 1-km-long (left) or 10-km-long (right) links; 1 (green) or 10 (red) links. For each configuration 10 realizations were done, with random positioning of the links (center position and orientation). The black line is for the high-resolution radar map. The extension of the vertical green/red lines in Fig. 8 illustrates the uncertainty due to the random positioning of the links to sample a highly variable rain field, consistent with Fig. 7. The uncertainty on the areal mean rain intensity (top plots) is very high when only one link is available per basin (green), and much reduced for 10 links (red). For the same number and position of links, the estimation of the areal mean is more robust with the 10 km than with the 1-km links, as the former provide a “natural averaging” of the rain field. Rainfall variability inside the basin is important for the hydrological response. The bottom plots of Fig. 8 display the time evolution of the standard deviation (std) of rainfall within the sub-basin. The std is calculated at each five minutes time steps, among 10 links (red) or among the radar pixels (black). As for the mean areal rainfall, random sampling of a variable field creates an uncertainty in the estimation, as illustrated by the red spread. Over 10 realizations, the estimate of the std is unbiased for the 1-km-long links and underestimated for the 10-km-long links. Figure 8 is only illustrative, the quantitative impact of the link density and size within a given basin and rainfall event varies according to the rain field structure and the basin hydrological response.
Rainfall variability between realizations and among simulated links, illustrated for 4 Aug 2012 event over the sub-basin Ri3. (top) The time evolution of the sub-basin average rain rate for links of size (a) 1 km or (b) 10 km, in green for a network of one link and in red for a network of 10 links. The links are assumed to have perfect precision. The vertical lines illustrate the spread (from minimum to maximum) among 10 realizations of network simulations. The black line shows the sub-basin mean rainfall calculated from the reference radar rain field. (bottom) The time evolution of the standard deviation of rain rate inside the basin as captured by 10 links (red) of length (c) 1 km or (d) 10 km and by the radar (black). The vertical red lines illustrate the spread in the standard deviation (from minimum to maximum) among the 10 realizations.
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0163.1
3) Simulated discharge
Figure 9 illustrates the uncertainty in the simulated discharge due to the imperfect sampling of rainfall variability inside the basin. The simulated discharge is analyzed at Ri3; the tested network configurations are the same as for Figs. 8a and 8c: 10 realizations (various colors) of a network with 10 links of length 1 km. The spread within the 10 realizations is larger for the simulated discharge (Fig. 9) than for the mean rainfall (Fig. 8a). For several random positions of the links the peak discharge is overestimated by a factor close to 2; while for one of the simulations (set 1), the peak is underestimated by a factor of 3 and not in phase. The enhanced sensitivity of the discharge simulation to the position of the links is explained by the impact of rainfall variability within the basin on the hydrological response. The reproduction of discharge sensitivity to the rainfall pattern is model-dependent. The sensitivity is enhanced by the nonlinearity of the model equations (SCS formula) and well perceived with a high-resolution distributed model like ATHYS.
Simulated discharge over the Ri3 sub-basin outlet for the 4 Aug 2012 rainfall event, here for a simulated network of 10 links of length 1 km. The outputs for 10 realizations are displayed with different colors together with the reference simulation (black) using the radar map.
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0163.1
Figure 10 synthetizes the results for all the experiments with the randomly positioned network (3 link lengths × 10 realizations × 3 events × 3 sub-basins; Figs. 10a,b) and with the actual network of 75 links (Fig. 10c); for the latter, tests were made keeping all links, or only links up to 5-km length, or only links longer than 5 km. To summarizes the total length of links inside the basin for each configuration a link linear density (km km−2) equal to the sum of the link lengths divided by the sub-basin area, is introduced. The KGE of the simulated discharge compared to the reference simulation is plotted against the link density. The numerical experiments with different link lengths are plotted in color (1 km, blue; 5 km green; 10 km, red). Figures 10a and 10b, based on the randomly distributed network, show that the quality of the hydrological simulations increases sharply with the density of information provided by the links. From about 0.5 km km−2 (i.e., for instance, ten 5-km links in a basin of 100 km2) all simulations have a positive KGE. The increase in the simulation quality is sharper and the KGE for a given density higher for short links, as the rain field structure is better sampled with several small links than a single long one. For instance, the mean KGE is above 0.5 for a density equivalent to ten 1-km link (100 km2)−1 (density, 0.1), but five 5-km or two 10-km length 100 km2 (density 0.25) are needed for the same scores. Figure 10c provides a similar analysis for the real network configuration of 75 links seen in Fig. 1, with their lengths ranging from 0.3 to 26 km. As for the top figures the rainfall at each link is the weighted average [Eq. (5)], no estimation error is considered. To compare the relative impacts of the shortest and longest links, the results are also presented, when only the 18 links longer than 5 km, or on the contrary the 57 links shorter than 5 km, are kept. For link linear density below 0.5 (km km−2) the spread for a given basin and network configuration (same shape and color) illustrates the variability of the rainfall structure among the three rain events. For a given linear density (in km km−2), event and basin there is no significant difference between the tests where we kept only the smallest (below 5 km) or on the contrary the longest (above 5 km) links. It is noteworthy that because of the Thiessen interpolation method, a link which is partially or entirely outside a sub-basin may or not contribute to the rain estimation for this basin and a given configuration, depending on the other links available. The differences between events and the impact of the configuration are marked for outlet Ri3 which is mostly rural and poorly sampled by the real network.
Summary of the effect of rainfall sampling by the link network considering all numerical experiments: (a),(b) experiments with the randomly generated network, 3 link lengths (blue dots, 1 km; green circles, 5 km; red crosses, 10 km) × 10 realizations × 3 events × 3 sub-basins. In (a) KGE for the simulated discharge compared to the reference (radar based) is shown as a point for each experiment. The x axis expresses the density of information as the cumulated length of all links inside the sub-basin (km) per sub-basin area (km2); in (b) mean KGE per link density (average by bins of 0.2 km km−2 width) is shown. The fit in (b) is only there for readability. (c) KGE of the simulated discharge in the indicated outlets compared to the reference, for the simulations based on the actual network configuration (Fig. 1), keeping the whole network (circles), keeping only links of length 5 km and below (triangles), and keeping only links longer than 5 km.
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0163.1
Figure 10 is illustrative. More case studies would be needed to account for the complexity of the problem and all the parameters to be considered like the orientation of the links compared to the anisotropy of the rain field, the spatial decorrelation of the rain field, the size and shape of the basin etc. Figure 10 and the other figures in this section tend to show that a dense (in km km−2) network of short links, if they are evenly spread inside the basin (not clustered), is more suited for hydrology than the same linear density of longer links, because it samples better rainfall variability inside the basin. As noted in section 3c the rain information is spatialized in ATHYS by considering each rainfall estimate as a punctual value at the center of the link and using Thiessen interpolation. Other interpolation methods (Zinevich et al. 2008, 2009) could be used to exploit the spatial information provided by the links and account for their length and orientation. This a field of research on its own. Capturing the spatial variability of rainfall is, however, only one aspect of the problem.
c. Discharge spatial distribution
Figures 11 and 12 illustrate the spatial variability of rainfall and of the simulated discharge quality. Figure 11 show the rainfall accumulation for the 4 August 2012 event as seen by the high-resolution radar map. A strong gradient is seen from North to South, and in several locations inside the city the rainfall accumulation is high, with the maximum value over the domain at 70 mm and a minimum at 7 mm. This is consistent with the strong variability observed at 5-min time steps in Figs. 2 and 3. As discussed previously, the CML network captures only partially this intense rainfall variability. Figure 12 analyses the ability of the model, forced by the CML network to represent the spatial variability of the discharge. The experiment is with the original network as seen in Fig. 1, with all links operating at 13 GHz. The top left map is for precision 1 dB and the top-right precision 0.1 dB. The values of the KGE of the simulated discharge compared to the reference (simulation with high-resolution radar map) are mapped in different points within the basin. The simulation for a 0.1-dB precision is improved, but the simulation with 1 dB is already satisfactory, with the KGE for most points within the basin above 0.4. To put the performance of the CML-based simulations in perspective compared to other types of rainfall measurement, the bottom figures display the results for two extra experiments: for Fig. 12c the sampling of a satellite rainfall product was emulated by averaging the high-resolution radar rain maps over the whole domain (about 1000 km2)—no error on the satellite estimation is considered which is a strong idealization; for Fig. 12d the rainfall series used to force the hydrological model comes from the central pixel (white star) emulating what a single rain gauge situated in the city center would see. In most of the basin the simulations based on the CML sampling represent much better the discharge and its variability than the simulations based on a single source of information (spatial average or single gauge). This good results in the urban part of the basin are consistent with previous findings. Fencl et al. (2013, 2015) also found that the density of the network at urban scale is beneficial to reproduce the hydrological dynamics. They also notice that the links, especially when short, may introduce bias in the rainfall and recommend using both gauge and link information (Fencl et al. 2017; Smiatek et al. 2017). Similar conclusions were drawn by Pastorek et al. (2019) and Stransky et al. (2018). Only at the very east end of the basin, where only two long links are available, the simulation based on the central pixel or the average perform slightly better than the CML. The benefit of the CML sampling for distributed hydrological modeling, even when a coarse precision is considered in the raw signal, is clearly striking in Fig. 12. The results are very similar for the two other rainfall events presented in the supplementary material (A). Table 2 summarizes the results of these experiments for the three events, and supplementary material B shows examples of the simulated hydrographs. The statistical scores for the discharge at two main basins outlets (1060 and 1074) are reported in Table 2. The error on the mean and on the maximum discharge are much lower for the links, even with coarse precision, than for the single pixel or spatial mean forcing. The benefit of the CML ability to capture rainfall is also marked on the KGE, confirming the importance of the spatial information on rainfall to reproduce the discharge dynamics. For both sub-basins the linear link density (defined in section 4b) is above 0.4 km km−2 and KGE above 0.7, even with coarse precision. The results are even better for outlet 1074, with KGE above 0.9 whatever the precision, because the network covers this basin more homogenously.
Rainfall accumulation map over the area for the 4 Aug 2012 event, as measured by the radar.
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0163.1
Spatial distribution of KGE for the simulations with various rain forcing compared to the reference simulation based on the high-resolution radar rain map, for the 4 Aug 2012 event: (a) rain forcing based on the network seen in Fig. 1 with 13-GHz frequency and 1-dB precision; (b) as in (a), but with precision 0.1 dB; (c) rain forcing based on the area average rainfall from the radar and (d) rain forcing from the central pixel (shown by a white star).
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0163.1
Statistics on the simulated discharge for different rainfall sampling experiments compared to the reference simulation (based on the high-resolution rain map). The following statistics are reported for the two main outlets (1060 and 1074, see text): the absolute error on the event mean discharge (%); the absolute error on the event maximum discharge (%); the KGE. For each statistic, the mean over the three events is reported. The scores are reported for the following rainfall forcing as described in section 5c: spatial mean of radar rainfall, rainfall at central pixel, rainfall from the 75 links at 13-GHz network (Fig. 1) with perfect precision, precision 0.1 dB, or precision 1 dB.
5. Conclusions
This work investigates the potential benefits of CMLs rainfall estimation for urban hydrology in West Africa. One expected benefit of CMLs for hydrological application is the density of the network, especially in urban, thus populated, areas; on the other hand, as for any indirect measurement, rainfall estimation from CMLs is subject to uncertainties. A pending question for the development of CML-based hydrological applications is: what is the final balance between the benefits and drawbacks of CMLs rain measurements, and how basin dependent and network dependent are they.
A simulation setup based on high-resolution radar rain maps and a distributed hydrological model was used for a case study over the city of Ouagadougou. The radar is a research radar that operated in Burkina Faso as part of a satellite validation program in 2012/13. The distributed model (ATHYS) was developed and calibrated for Ouagadougou area in the framework of an urban flood prediction project. Here the radar rain maps were used as a reference rainfall, as forcing to the hydrological model and for generating synthetic CML measurements which can in turn be used as model input. This setup was used to analyze the ability of the microwave link network to (i) quantify rainfall over the urban basins, (ii) to capture rainfall space and time variability. In this work we primarily focused on two characteristics of the CMLs network that influence rainfall estimates: (i) the accuracy of the raw information (digitizing step) provided by the operator and (ii) the network configuration that includes the position and orientation, length and operating frequency of the links.
For the majority of numerical experiments, the discharge simulated with the synthetic links data as entry is close to the reference based on the high-resolution radar map. The performance is reduced when the raw data from the operator is provided with a coarse precision (1 dB), especially if the frequency is low (below 10 GHz) and for short links, because the lower rain rates are undetected. The trend in mobile communication networks is for the operating frequencies to increase in order to match the operational needs (need for increase bandwidth in particular), this will help the detection of rainfall from CMLs. Higher operating frequencies are also expected in the perspective of the next generation networks (5G). As the networks modernize the built in monitoring software are also improved and accessing to the data with a good sampling rate (15 min or less) and fine precision (0.1 dB) becomes common (personal communications from Orange and Nokia engineers). The number of links inside the basin is important. To quantify this effect, numerical experiments with an increasing number of links randomly distributed within the sub-basins were performed. The performance in terms of discharge dynamics (KGE criteria), mean bias and error on the maximum discharge increases quickly with the network density—expressed in total length of link (km per km2 of basin)—and especially with the number of short (1 km) links. For the present simulations satisfactory results (KGE close to or above 0.5) are obtained from a density of 0.1 km km−2 for 1-km-long links (i.e., 10 links inside a 100-km2 basin) and 0.3 km km−2 (3 links of size 10 km for 100 km2). When the positions of a real network are used, with a total of 75 links of various lengths for the Ouagadougou area (1000 km2) the simulations with the CML sampling are very close to the reference (KGE above 0.5) for most of the basin. The CML sampling, even when a coarse precision is considered, outperforms the simulation based on idealized satellite pixel or a single gauge situated in the city center.
These good results are partly explained by the nature of rainfall systems in the study region. Rainfall in West Africa (and in most of the tropics) is provided by deep convection, where most of the rain accumulation is associated with intense rain rates. These intense rain rates create a strong microwave attenuation which is well detected by the CML network, whatever the length and frequency. The present work and previous studies show indeed that the relative error on rainfall estimation from CML decreases with rainfall intensity (Leijnse et al. 2008a,b). The spatial organization and dynamics of the convective cells influence the space–time structure of the rain fields. The relevant observational scales to capture these structures are kilometric and subhourly, which is compatible with the current CML networks in populated areas.
This positive outcome encourages us to continue promoting CMLs as a source of information on rainfall quantities and space–time distribution in urban basins, especially in tropical regions where weather radar is not yet routinely available.
The presented simulation setup could be used for further sensitivity studies and for accounting for other sources of uncertainties that were not explicitly considered here (wet antenna; error in the baseline determination; uncertainty in the attenuation–rain rate relationship etc.). Here only the errors brought in by the difference in the rain forcing were considered, by comparing the output to a reference simulation based on a high-resolution radar map and a given setup of the hydrological model. The radar data are used as a realistic proxy of rain fields for simulations purposes. In reality radar estimation of rainfall is subject to many uncertainties, described at length in the literature (Berne and Krajewski 2013; Cecinati et al. 2017). The hydrological brings in its own uncertainties in the discharge prediction system (Beven and Binley 1992; Ajami et al. 2007). They come from the simplistic representation of hydrological processes, the equifinality problem in the optimization of parameters and other factors such as the interpolation of the rain information inside the model. These were beyond the scope of this paper but are being investigated.
Acknowledgments
Maxime Turko’s Ph.D. was funded by the French Space Agency CNES and Meteo-France CNRM. The radar experiment in Ouagadougou was financed by the French Space Agency CNES as part of the Megha-Tropiques Ground Validation (MTGV) program. We thank Frédéric Cazenave who installed the radar and supervised its operation. We are very thankful to the technical teams from telecommunication operators who have provided us with meta-data and data from their networks in several African countries, in particular at Telecel and Orange.
Data availability statement
The data used for this study are openly available. Please send an email to the corresponding author for access. ATHYS code is freely available here: http://www.athys-soft.org.
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