Abstract

The Sahelian zone of West Africa is a semiarid area where strong amplitude of the seasonal and diurnal cycles of water vapor and temperature is observed. One year of continuous observation of vertical profiles of water vapor and temperature gathered from Niamey, Niger, with a profiling microwave radiometer is used to analyze the climatology of refractivity and microwave propagation regimes in the low troposphere. Seasonal and diurnal cycles of refractivity and ground-based radar anomalous propagation are emphasized. It is shown that the combined effect of water vapor and temperature vertical gradients is responsible for strong seasonal and diurnal cycles of the ducting propagation regime. Statistics of propagation regimes are given. The probability density functions of the refractivity gradient are found lognormally distributed. Three months of C-band radar data simultaneous with the profiling microwave radiometer observations have also been collected. Relations between the vertical refractivity gradient and the ground-based radar anomalous propagation echoes (APE) are illustrated and discussed. APE spatial distributions are found strongly related to the main features of the orography and topography inside the radar-observed area. Contingency tests show that the probability for APE to be linked to ducting is higher than 95%. In addition, this paper suggests that observing the refractivity vertical profiles from a microwave radiometer profiler located close to a meteorological radar provides information on whether anomalous propagation has to be considered as a potential cause of spurious signal in the measured reflectivity field.

1. Introduction

Microwave propagation depends on local meteorological conditions—but more precisely, for ground-based radar observations, on the vertical distribution of water vapor and temperature through the refractive index vertical profile above the surface. Microwave ray curvature follows the refractivity gradient, and under certain conditions nonstandard atmospheric refraction can result in anomalous propagation (AP) (e.g., Ulaby et al. 1982; Steiner and Smith 2002). AP can lead to ducting and detection of ground echoes beyond the geometrical horizon. These anomalous propagation ground echoes (APE) create a spurious signal in various contexts: meteorological radar observations and notably quantitative precipitation estimates, ground-to-ground or ground–air communications, Earth radiometric observations from space, etc.

To control the consequences of AP and APE on microwave applications, it is useful to better document the meteorological climatology of the atmospheric refractivity distribution at low atmospheric levels. If such climatology is sufficiently understood, then forecast and management of AP echoes in radar data are potentially conceivable.

Most studies about AP concern large areas above water surfaces for two reasons: 1) high occurrence of strong water vapor gradients, necessary to create strong refractivity gradients; and 2) flatness of the surface, which is compatible with the development of ducting over significant observable distances. Ducting is thus frequently observed with coastal radars (Brooks et al. 1999; Bech et al. 2000; Atkinson and Zhu 2006; Mesnard and Sauvageot 2010; Haack et al. 2010; Chang and Lin 2011). Recently, Ding et al. (2013) have observed ducting at the periphery of a tropical cyclone over the western North Pacific Ocean. Concerning continental areas, there are few AP studies. Using a 16-yr record of operational sounding data, Steiner and Smith (2002) presented a seasonal climatology of the various regimes of anomalous radar propagation and discussed the resulting contamination of quantitative precipitation estimates by radar across the continental United States. Global climatology of AP for ground-based weather radars has been documented using refractivity computations from European Centre for Medium-Range Weather Forecasts (ECMWF) temperature, moisture, and pressure analyses at 40-km horizontal resolution by Lopez (2009). Using the ECMWF climatology of refractivity derived by Lopez (2009) and two years of radiosonde observations in Dakar (Senegal), Douala (Cameroon), and Niamey (Niger), Kaissassou et al. (2014) have performed a seasonal climatology of AP over West Africa.

The Sahelian area of West Africa is of special interest in relation to this topic: because of the specificity of the local water vapor and temperature variations at low levels, the refractivity is expected to display strong diurnal and seasonal variations. The Sahel is a semiarid and flat strip of land that separates the southern part of the Sahara and equatorial Africa, approximately between the latitudes of 13° and 18°N for the western part of Africa. The seasonal atmospheric circulation in the low tropospheric levels of the Sahelian strip depends on the latitudinal location and activity of the intertropical convergence zone (ITCZ). The Sahel is thus characterized by an alternation of the Harmattan, a warm and dry wind coming from the Sahara Desert and blowing northeasterly, toward the ITCZ, and the West African monsoon (WAM), a moist flux coming from the Gulf of Guinea and blowing southwesterly, toward the ITCZ (Nicholson 2013).

The goal of the present paper is to document the seasonal and diurnal cycles of refractivity and associated anomalous propagation around Niamey, in the southwestern region of Niger, inside the west-central part of the Sahelian strip. Data are provided by a microwave radiometric profiler (MWRP) from the Atmospheric Radiation Measurement (ARM) program and by a C-band radar from the Massachusetts Institute of Technology (MIT). A detailed description of ARM can be found in Cadeddu et al. (2013) and online (at www.arm.gov). To our knowledge, such study has never been performed previously.

Section 2 describes the meteorological and instrumental context, the data used and data processing, and briefly recalls the anomalous propagation phenomenon. The seasonal and diurnal AP cycles are discussed in section 3. In section 4, a statistical analysis of the refractivity distribution through probability density functions is presented. Section 5 deals with the AP radar echoes’ spatial distribution. Conclusions are given in section 6.

2. Meteorological and instrumental context

a. Experimental site and meteorological context

The experimental site is located in Niamey, at Diori Hamani International Airport (13°29′N, 2°10′E, 205 m of altitude), southwest of Niger (Fig. 1). Radiometric data were collected by the ARM program in the framework of the African Monsoon Multidisciplinary Analysis (AMMA) campaign, continuously from 9 January up to 31 December 2006. The main objective of the AMMA campaign was the study of the dynamic and physical processes that control the WAM at different space and time scales (e.g., Redelsperger et al. 2006).

Fig. 1.

Topography of West Africa with the location of Niamey and the approximate position of the ITCZ in January and July.

Fig. 1.

Topography of West Africa with the location of Niamey and the approximate position of the ITCZ in January and July.

Atmospheric circulation in the Sahelian area is discussed in several papers (Hastenrath 1985; Sultan and Janicot 2003; Slingo et al. 2008; Nicholson 2013; among others). Briefly, the WAM is associated with the northward progression of the intertropical front (ITF), which separates the monsoon flow (warm and moist), which comes southwesterly from the Gulf of Guinea, and the Harmattan (hot and dry), which comes northeasterly from the Sahara. The interface between the two air masses is located below 9 km of altitude (about 300 hPa in terms of pressure). The northward progression of the ITF and the ITCZ bring important precipitation. The ITF displacement starts slowly in mid-April and continues northward until mid-August. Then, the monsoon retreat takes place at the end of August until October. In addition, the diurnal variations of humidity in the Sahelian area are strongly affected by a nocturnal low-level jet (Lothon et al. 2008; Louf et al. 2015).

The MWRP is described in detail by Solheim et al. (1998) and Ware et al. (2003). Briefly, it measures the brightness temperature of the atmosphere at 12 frequencies: 5 in the K band (22–30 GHz), on the upper wing of the 22-GHz water vapor absorption line, and 7 others in the V band (51–59 GHz), on the lower wing of the 60-GHz oxygen absorption line. The radiometer is also equipped with in situ sensors for ground-level measurements of temperature, water vapor, and pressure. Radiances are inverted using statistical algorithms that permit retrieving up to 10 km above ground level (AGL), vertical profiles of water vapor content , pressure , and temperature (Liljegren et al. 2005; among others). According to the ARM documentation (www.arm.gov/instruments/mwrp), the vertical resolution of the MWRP is 100 m in the first 1 km and 250 m from 1 km up to 10 km AGL, leading to a vertical profile composed of 47 data values, including the data of temperature, water vapor, and pressure at ground level given by the in situ sensors. Measurements were performed approximately every 14 s, which gave about 6000 measurements each day. Uncertainties in and T measurements are 0.5–1 g m−3 and 1–2 K below 2 km AGL, respectively. These uncertainties reach 0.01–0.05 g m−3 and 3–4 K at 10 km AGL, respectively. Integrated water vapor uncertainty is 0.5–0.7 g cm−2 for the total column (10 km). In the presence of rain and liquid water on the radiometer, measurements are less accurate and/or are degraded (Ware et al. 2003). Consequently, the corresponding profiles were not taken into account (8% of the total data). Once these data were removed, a 5-min running average was applied, to the entire dataset, in order to smooth noisy data fluctuations.

Radar data are those of the MIT C band (wavelength of 5.37 cm; Doppler radar located at the Diori Hamani International Airport. The MIT C-band Doppler radar served as the transportable component of the MIT Weather Radar Laboratory from the early 1970s. The history of the scientific utilization and technical evolution of this radar, as well as its actual operating characteristics, can be found in Russell et al. (2010). Briefly, pulse width and half-power beamwidth are 1 μs and 1.4°, respectively. Data have been collected from 24 June 2006 to 27 September 2006 with scans based on a 10-min cycle. The scanning procedure in each 10-min cycle was composed of a long-range (250 km) azimuth scan at a single low-elevation angle of 0.7° with a pulse repetition frequency (PRF) of 250 Hz and a bin spacing of 125 m, followed by a volume scan at 15 elevation angles from 0.5° to 30°,1 with a PRF of 950 Hz, a bin spacing of 250 m, and a maximum range of 150 km (Rickenbach et al. 2009). During the 2006 field campaign in Niamey, the MIT C-band radar was carefully calibrated on tethered metal spheres as explained in detail by Russell et al. (2010). An additional check of the calibration was performed from detailed comparisons with the 2A25 dataset from the spaceborne Tropical Rainfall Measuring Mission (TRMM) precipitation radar by Rickenbach et al. (2009). In the present paper, to detect the maximum occurrences of AP echoes, only the long-range survey scan has been used because of the maximum range of 250 km.

Raw data were saved in Sigmet Interactive Radar Information System (IRIS) (polar coordinates) format. The dataset contained a large number of nonmeteorological AP echoes. Removal (i.e., discrimination) of nonmeteorological APE data was accomplished by employing the ground validation system (GVS) software available from the TRMM Satellite Validation Office (http://trmm-fc.gsfc.nasa.gov/trmm_gv/). The GVS software processes the Sigmet IRIS data and produces output universal format (.uf) files. The Reorder software, developed by NCAR, was used to interpolate the .uf files to a 1-km horizontal-and-vertical-spaced Cartesian coordinate grid. More information can be found online (https://www.eol.ucar.edu/software/reorder).

b. Refractivity index and vertical gradient

The index of refraction n of the atmosphere is documented in several papers (e.g., Bean and Dutton 1968; Fabry et al. 1997; Steiner and Smith 2002; Atkinson and Zhu 2006; Mesnard and Sauvageot 2010; Chang and Lin 2011; Bodine et al. 2011). Close to the ground, 1.000 250 < n < 1.004 00; that is why it is preferred to work with the refractivity (N), a scaled index, which can be approximated for microwave frequencies as

 
formula

where p is in hectopascals (hPa), T is in kelvins (K), and e is the partial pressure of water vapor (hPa).

Radar beam curvature depends on the vertical gradient of N—that is, (km−1), where z is the vertical coordinate (km) (e.g., Bean and Dutton 1968; Pratte et al. 1995). If , then radar beams are bended upward; this is subrefraction. If , three modes of microwave propagation can be distinguished: 1) normal refraction for , 2) superrefraction if , and 3) ducting (or trapping) for . Subrefraction, superrefraction, and ducting are APs. They mainly occur in the first 100 m above the ground, where the strongest water vapor gradients are usually observed. Ducting is the most severe case of AP. In this case, the lowest troposphere acts like a waveguide, so that ground echoes can be measured far from the horizon. Only radar rays launched with an angle inferior to 1° are trapped, which means that only the lowest elevation scans are affected; this point has been discussed and demonstrated by numerous authors of observations and numerical simulations (e.g., Bean and Dutton 1968; Brooks et al. 1999; Steiner and Smith 2002; Skolnik 2008; Haack et al. 2010; Mesnard and Sauvageot 2010; among others). For instance, Steiner and Smith (2002) states, “in order to propagate energy within the duct, the angle the radar ray makes with the duct should be small, usually less than one degree (e.g., only the lowest elevation scans of surface-based radar are affected),” and Skolnik (2008, 26–27) points out that, “To propagate energy within a duct, the angle made by the electromagnetic system’s energy with the duct must be small, usually less than 1°.” APE (i.e., ducting) disappeared for elevation larger than about 1°. Since the half-power beamwidth of the MIT C-band radar is 1.4°, only the lower elevation of the radar scans (i.e., 0.5° for the volumic scan and 0.7° for the long-range scan) is concerned by APE. What is called “elevation scan” is in fact the elevation of the beam axis. For example, for an azimuthal scan at 0.7° of elevation, due to the divergence of the radar beam (1.4°), the elevation of the rays making up the beam are distributed between 0.0° and 1.4°. The rays of the beam that have different elevations are refracted differently, and usually, in the presence of a duct, for a same radar scan, only a part of the beam is concerned by ducting. In addition, the distribution of the radiated power inside the half-power beam is approximately Gaussian, not uniform, and there is some power outside of the half-power beamwidth, notably inside the sidelobes of the antenna. Clearly, APs introduce strong distortions of the beam shape (width and power distribution are modified all along the ducted propagation).

The influence of the different parameters of Eq. (1) on the refractivity vertical gradient has been discussed in the literature, notably by Bean and Dutton (1968). This vertical gradient is defined as

 
formula

Thus, depends on the pressure, temperature, and water vapor vertical gradients. The fourth term on the right of Eq. (2), proportional to , is negligible. The first term, proportional to and to , is almost constant in the shallow, low-level, horizontal layer related to AP. The refractivity vertical gradient in the AP layer is thus mainly dependent on the second and third terms on the right side of Eq. (2), that is, on the water vapor pressure and temperature vertical gradients, respectively. High negative values of (i.e., favorable to AP) are reached in the presence of strong negative values of and strong positive values of (temperature inversion), such as those observed above ground during a clear night.

Herein, the refractivity vertical gradient has been computed from the vertical profiles of humidity, temperature, and pressure measured by the MWRP. These last profiles give a vertical profile of refractivity [Eq. (1)] from ground to z = 10 km AGL from which the refractivity vertical gradient is obtained at time t. For the bin of index i, with (i increases with height): .

3. Seasonal and diurnal cycles of 

Recently, Louf et al. (2015) performed an extensive study of the water vapor seasonal and diurnal variations at Niamey, from the same dataset of MWRP that was used in the present study. Two seasonal periods have been considered: the dry season, from the end of October to the end of April, when the northeasterly Harmattan is flowing at a low tropospheric level, and the wet season, from end of April to end of October, which is associated with the southwesterly monsoon flux. In particular, Louf et al. (2015) showed that a water vapor diurnal cycle exists during the entire year, for the first 5–6 km AGL of the troposphere. Since the refractivity vertical gradient is partly controlled by the water vapor vertical gradient, seasonal and diurnal cycles of the refractivity vertical gradient are expected.

a. Seasonal cycle

The first part of Fig. 2 (i.e., Figs.2a–c) displays the evolution, during the entire year of 2006, of the tropospheric water vapor content (Fig. 2a), the temperature (Fig. 2b), and the integrated water vapor content (Fig. 2c). The vertical gradients of water vapor pressure, temperature, and refractivity, that is, , , and , are displayed in Figs. 2d–f, respectively. Clearly, in Fig. 2f, APs concern only the first kilometer of the troposphere and are dominated by the superrefraction regime. Ducting is often present, especially in March, April, and from August to the end of December. Subrefraction is mainly observed in January, February, and early to mid-March. It is rare the rest of the year. Normal refraction occurs otherwise. Not surprisingly, the refractivity vertical gradient presents a seasonal variation strongly correlated with the water vapor seasonal variations, that is, two well-defined seasons (the wet season between the end of April and the end of October, and the dry season the rest of the year). APs mainly occur close to the ground (below 300 m AGL) all over the year, except during the monsoon (mid-June–October), where superrefraction is encountered up to 600–700 m AGL. The seasonal variation is also correlated with the vertical gradients of water vapor pressure and temperature (Figs. 2d and 2e, respectively). During the dry season, because there is little water vapor in the troposphere, the water vapor vertical gradient is close to 0 and shows a low vertical variability. On the contrary, the temperature vertical gradient is important (30 K km−1 below 200 m AGL) and shows strong vertical variability. The opposite behavior is observed during the wet season, for , that is, important vertical extensions and low values of .

Fig. 2.

Temporal series in Niamey in 2006 of (a) , (b) T, (c) , and (d) , (e) , and (f) . On (b), the black solid line at about is the 0°C isotherm. The intervals of the values of , which correspond to the different modes of propagation, are represented with different colors: yellow for subrefraction , blue for normal refraction , green for superrefraction , and red for ducting . Vertical dashed lines represent month separation. The y axis is scaled 0–6 km AGL for (a) and (b), and is scaled 0–1 km AGL for (d)–(f).

Fig. 2.

Temporal series in Niamey in 2006 of (a) , (b) T, (c) , and (d) , (e) , and (f) . On (b), the black solid line at about is the 0°C isotherm. The intervals of the values of , which correspond to the different modes of propagation, are represented with different colors: yellow for subrefraction , blue for normal refraction , green for superrefraction , and red for ducting . Vertical dashed lines represent month separation. The y axis is scaled 0–6 km AGL for (a) and (b), and is scaled 0–1 km AGL for (d)–(f).

b. Diurnal cycle of the temperature and water vapor vertical gradients

Figure 3 displays the March and October averaged diurnal cycle of the temperature and water vapor pressure vertical gradients. Clearly, a diurnal cycle of and appears. The strongest variations are found close to the ground. The temperature vertical gradient is higher by night in March than in October . The opposite is observed for the water vapor vertical gradient, with in March (Fig. 3Mar.b) and in October. As shown in the previous section, the water vapor and temperature vertical gradients are the main contributors to the refractivity vertical gradient. Because of this well-defined diurnal cycle of and , we expect to see a well-defined diurnal cycle of .

Fig. 3.

(top) March and (bottom) October averaged diurnal cycle of the (first and third rows) temperature vertical gradient and (second and fourth rows) water vapor pressure vertical gradient in Niamey in 2006.

Fig. 3.

(top) March and (bottom) October averaged diurnal cycle of the (first and third rows) temperature vertical gradient and (second and fourth rows) water vapor pressure vertical gradient in Niamey in 2006.

c. Diurnal cycle of the refractivity vertical gradient

The time series and the monthly averaged diurnal cycle of the are represented in Fig. 4. These variations concern only the first 600–700 m AGL of the troposphere. The time series [Figs. 4a(1), b(1), c(1), d(1), e(1), f(1), g(1), h(1), i(1), j(1), k(1), and l(1)] show a regular cycle of for the entire year with an approximate 1-day period. During the dry season [Figs. 4a(1), b(1), c(1), d(1), k(1), and l(1)], the APs occur below 400 m AGL and consist mainly of superrefraction despite some frequent occurrences of ducting all along the year. Some conditions of subrefraction are also present but very rarely [Figs. 4a(1), b(1), d(1), and l(1)]. During the wet season, from May to October [Figs. 4e(1), f(1), g(1), h(1), i(1), j(1)], the cycle occupies the troposphere up to 600 m AGL. The temporal series exhibit less regularity for the altitude extent of the AP. Superrefraction is again the dominant mode of AP.

Fig. 4.

Temporal series of [a(1), b(1), c(1)] and [a(2), b(2), c(2)] monthly averaged diurnal cycle of for January–March 2006. SR and SS denote sunrise and sunset, respectively. The vertical dotted lines in a(1), b(1), and c(1) represent day separation at midnight. The y axis is scaled 0–1 km AGL. The intervals of the values of , which correspond to the different modes of propagation, are represented with different colors; see Fig. 2. Remaining panels as in a(1)–c(1): [d(1), d(2)] April, [e(1), e(2)] May, [f(1), f(2)] June, [g(1),g(2)] July, [h(1),h(2)] August, [i(1),i(2)] September, [j(1),j(2)] October, [k(1),k(2)] November, and [l(1),l(2)] December.

Fig. 4.

Temporal series of [a(1), b(1), c(1)] and [a(2), b(2), c(2)] monthly averaged diurnal cycle of for January–March 2006. SR and SS denote sunrise and sunset, respectively. The vertical dotted lines in a(1), b(1), and c(1) represent day separation at midnight. The y axis is scaled 0–1 km AGL. The intervals of the values of , which correspond to the different modes of propagation, are represented with different colors; see Fig. 2. Remaining panels as in a(1)–c(1): [d(1), d(2)] April, [e(1), e(2)] May, [f(1), f(2)] June, [g(1),g(2)] July, [h(1),h(2)] August, [i(1),i(2)] September, [j(1),j(2)] October, [k(1),k(2)] November, and [l(1),l(2)] December.

The monthly averaged diurnal cycle of (Figs. 4a(2), b(2), c(2), d(2), e(2), f(2), g(2), h(2), i(2), j(2), k(2), and l(2)] is quite simple. During the dry season [Figs. 4a(2), b(2), c(2), d(2), k(2), and l(2)], superrefraction is present by night, from about 2000–2200 to 0800 UTC. For January and February [Figs. 4a(2) and b(2)] it concerns only the vicinity of the ground AGL). For the other months [Figs. 4c(2), d(2), k(2), and l(2)], the superrefraction regime is encountered until 200 m AGL, by night, but for a shorter duration. Normal refraction occurs in daytime. At nighttime, the mode of microwave propagation can be superrefraction or normal refraction. Further, from January to August, it is striking to observe a progressive extension, both in time and vertically, of the superrefraction regime over the normal refraction [Figs. 4a(2)h(2)]. In August [Fig. 4h(2)], superrefraction is encountered until 400 m AGL and its presence decreases with height: this AP is present for the entire day for AGL and only by night from 2300 to 0600 UTC at AGL. Superrefraction decreases significantly from September to December [Figs. 4i(2)l(2)].

An interesting point is that ducting is the dominant AP by night (from 2000–2200 to 0600–0700 UTC) in October and November for AGL [Figs. 4j(2) and k(2)]; this is explained by the strong vertical gradients of water vapor pressure and temperature (Figs. 2d and 2e, which according to Eq. (2) contribute together to create strong negative refractivity gradients (Figs. 2f). These gradients are related to the transition periods between the wet and dry seasons. In Fig. 3, it can be seen that strong vertical gradients occur by night in October. The presence of ducting at the end of the wet season and a large part of the dry season has also been observed by Basha et al. (2013), who studied the AP conditions by means of GPS radiosondes over the tropical area of Gadanki (India). This region presents a meteorological annual cycle similar to that of Niamey, that is, an alternation of a dry season and a wet season.

4. Statistics of the propagation regimes

Figure 5 shows the probability of occurrence of the different regimes of propagation for the entire year, both day and night, for AGL and AGL. For each month, it represents the probability that a given mode of propagation occurs on average throughout the entire month, by night or by day. For instance, considering the normal refraction mode by night, in January, at AGL, the value means that, on average over January, microwaves propagate in the normal refraction mode 30% of the night duration. Night duration is from sunset to sunrise (next day). Day duration is from sunrise to sunset (same day). Nighttime, the probability has been computed with the data of the MWRP considering the total duration of a given AP event and then dividing by the total night duration over a month (i.e., number of days for a month multiplied by night duration), that is, . The same procedure holds for daytime and the other AP. Close to the ground AGL, nighttime, superrefraction is the dominant AP from January to October, with a probability of occurrence around 0.6 (Fig. 5a). Normal refraction and ducting are less probable . The rest of the year, ducting becomes dominant in October and November, and normal refraction is much less probable . Subrefraction never occurs significantly throughout the year. By day, superrefraction and normal refraction are the dominant modes of AP, the former being more probable than the later only during the monsoon, that is, July and August (Fig. 5c). Notably, subrefraction occurs only in January and February . Ducting is rare except from July to October .

Fig. 5.

Probability p of ducting, superrefraction, normal refraction, and subrefraction, for all of the year 2006: (a),(b) nighttime and (c),(d) daytime, and (a),(c) at ground (z < 100 m AGL) and (b),(d) for 100 < z (m) < 200 AGL. NR stands for normal refraction, SR for superrefraction, D for ducting, and SbR for subrefraction.

Fig. 5.

Probability p of ducting, superrefraction, normal refraction, and subrefraction, for all of the year 2006: (a),(b) nighttime and (c),(d) daytime, and (a),(c) at ground (z < 100 m AGL) and (b),(d) for 100 < z (m) < 200 AGL. NR stands for normal refraction, SR for superrefraction, D for ducting, and SbR for subrefraction.

For AGL, the normal refraction and the superrefraction are the main AP. By night, the latter is more probable than the former from June to December (Fig. 5b). Ducting is quite rare except from August to November with a maximum probability of occurrence of about 0.4 in October. By day, the normal refraction is the dominant propagation regime all along the year . Superrefraction takes significant values of p only from June to November (Fig. 5d).

The statistical distribution of the four propagation regimes can also be computed using the probability density functions (pdfs) of the refractivity vertical gradient. The pdf theory is well known and will not be recalled herein (see Forbes et al. 2010). Four representative months are shown in Fig. 6, for AGL.

Fig. 6.

Pdfs of the refractivity gradient below 200 m AGL for (a),(b) March; (c),(d) June; (e),(f) August; and (g),(h) October. (a),(c),(e),(g) Nighttime pdfs and (b),(d),(f),(h) daytime pdfs. The continuous curve is the shifted lognormal fitting. The y axis is scaled by a factor × 1000. NR, SR, D, and SbR as in Fig. 5. For each figure, r denotes the correlation coefficient between the data and the corresponding lognormal fit.

Fig. 6.

Pdfs of the refractivity gradient below 200 m AGL for (a),(b) March; (c),(d) June; (e),(f) August; and (g),(h) October. (a),(c),(e),(g) Nighttime pdfs and (b),(d),(f),(h) daytime pdfs. The continuous curve is the shifted lognormal fitting. The y axis is scaled by a factor × 1000. NR, SR, D, and SbR as in Fig. 5. For each figure, r denotes the correlation coefficient between the data and the corresponding lognormal fit.

Pdfs of the refractivity gradient are found well fitted by the lognormal distribution. The lognormal function is commonly used for characterizing the distribution of atmospheric quantities, for example, rain cell size (Mesnard and Sauvageot 2003), rain rate (Sauvageot 1994), precipitable water (Foster et al. 2006), and water vapor (Jeannin et al. 2008; Iassamen et al. 2009). It is observed that the vertical refractivity gradient can be at minimum around −550 km−1, while it can reach a maximum around 150 km−1. To support these negative values, the refractivity vertical gradient distribution is shifted by an offset , so that the parameter of interest is . Thus, the general expression of the lognormal function is, with (Forbes et al. 2010):

 
formula

where the mean μ and variance of y are defined through the expected value and the standard deviation of x ( and , respectively):

 
formula

Figure 6 represents the pdfs of below 200 m AGL for March, June, August, and October, nighttime and daytime. Notable differences are seen between night (Figs. 6a, 6c, 6e, and 6g) and day (Figs. 6b, 6d, 6f, and 6h). By night, the pdfs confirm that the superrefraction regime is the dominant AP, especially in March, June, and August (Figs. 6a, 6c, 6e). By day, the normal refraction regime dominates in March (Fig. 6b), but the propagation regime progressively shifts toward a superrefraction regime until August (Figs. 6d and 6f). In October, the pdfs are more extended and indicate that, by night, the dominant propagation regime is ducting (Fig. 6g). By day, in October, microwaves propagate through the normal refraction regime (Fig. 6h). Subrefraction AP is observed frequently in January and February and also appears occasionally by day in March and October, but it is rare the rest of the year. In addition, the pdfs seem to be monomodal and quite well fitted by the lognormal distributions (continuous curve in Fig. 6), except nighttime in August and both daytime and nighttime in October. Also, the peaks of the lognormal fits are slightly shifted from the peaks of the actual pdfs, except for October, when shifting is more severe. This discrepancy and the departure from monomodality are likely due to some extreme but yet frequent AP events that occur in August and October. Refractivity can reach values as low as −550 km−1 during these two months, provoking the pdfs to spread wider with multiple modes. Correlation coefficients r between the data and the lognormal fits are greater than 0.96 except for October (0.92 nighttime and 0.94 daytime).

The mean value and the standard deviation are displayed in Figs. 7 and 8 , respectively. For the mean value (Fig. 7), the same behavior holds for the entire year, both day and night: is negative and takes its lowest values at ground, increases rapidly up to around 200 m AGL and, still more slowly, above until 800 m AGL, where it reaches a constant value (between . Note also that the values of for March are generally higher both day and night throughout the profile than those of the other months. Above 200 m AGL, presents close values for June, August, and October. The standard deviation (Fig. 8) decreases from ground level up to 200 m AGL and then slowly moves toward zero. This indicates that the pdfs are wider at the ground and shrink rapidly with height. It also shows that the pdfs are a bit more largely spread nighttime than daytime (Figs. 8a and 8b). Note as well that overall, both day and night, the values of in March are a bit smaller than those of the other months, with these last ones keeping values close to above 200 m AGL.

Fig. 7.

Variation of the mean value () of the refractivity vertical gradient pdf with respect to height in March, June, August, and October, for (a) nighttime and (b) daytime.

Fig. 7.

Variation of the mean value () of the refractivity vertical gradient pdf with respect to height in March, June, August, and October, for (a) nighttime and (b) daytime.

Fig. 8.

Variation of the standard deviation of the refractivity vertical gradient pdf with respect to height in March, June, August, and October, for (a) nighttime and (b) daytime.

Fig. 8.

Variation of the standard deviation of the refractivity vertical gradient pdf with respect to height in March, June, August, and October, for (a) nighttime and (b) daytime.

To sum up, by day, normal refraction is dominant most of the time during the dry season and superrefraction and ducting are significant during the wet season. By night, superrefraction is dominant most of the time with a wide probability of occurrence of ducting during the dry season and at the end of the wet season.

5. Spatial distribution of AP radar echoes (APE)

APE have been determined as being “radar objects” with reflectivity but zero Doppler velocity. Another type of physical echo corresponds to this definition: the short-distance returns directly detected (along straight lines of sight) by the radar, from the ground target, notably from hills, buildings, pylons, etc. Such echoes are permanent. Because of the earth’s curvature, ground-based meteorological radars detect only permanent ground echoes located at short distances. In the present case, a range distance of 50 km is enough to encompass all the permanent ground echoes (see Fig. 9b, inside the 50-km range marker). In the present paper, these short-distance permanent echoes are not removed in the figures because they are useful as graphic and reflectivity-level reference. Short-distance permanent echoes are not considered as APE. Beyond the permanent ground echo area, the objects with radar reflectivity and zero Doppler velocity are considered as APE. Echoes due to precipitation are those with radar reflectivity and nonzero Doppler velocity. To discriminate and separate precipitation echoes and APE, the GVS and Reorder software programs, as specified in section 2a, are used. For the calculation of precipitation and APE spatial distributions, a radar reflectivity factor threshold of 15 dBZ is applied to the radar data. This 15-dBZ cutoff enables a strong signal-to-noise ratio on the radar measurements with the MIT C-band radar (e.g., Russell et al. 2010). This value is equivalent to a rain rate of 0.2 mm h−1 using the relation , with Z in mm6 m−3 and R in mm h−1, observed for continental Africa by Sauvageot and Lacaux (1995).

Fig. 9.

PPI of reflectivity fields for (a) a squall line (precipitation echoes) at 0420 UTC 11 Aug 2006 and (b) APE at 2100 UTC 14 Aug 2006. (left) Figures represent the radar reflectivity factor fields. (right) Corresponding panels show the result of the criterion to separate precipitation echoes from APE. Distances on the ordinates and abscissa axes are in kilometers. Range markers are 50 km from each other.

Fig. 9.

PPI of reflectivity fields for (a) a squall line (precipitation echoes) at 0420 UTC 11 Aug 2006 and (b) APE at 2100 UTC 14 Aug 2006. (left) Figures represent the radar reflectivity factor fields. (right) Corresponding panels show the result of the criterion to separate precipitation echoes from APE. Distances on the ordinates and abscissa axes are in kilometers. Range markers are 50 km from each other.

To illustrate the difference between APE and precipitation echoes and to demonstrate the efficiency of the criteria used to separate these two kinds of echoes, Fig. 9a(1) displays a plan position indicator (PPI) of the measured reflectivity of a tropical squall line observed at 0420 UTC 11 August 2006 at around Niamey by the MIT C-band radar (radial range of 250 km, beam elevation of 0.7°). This is a powerful mesoscale convective system (MCS) typical of the rain-bearing events observed during the wet season over the Sahelian strip (e.g., Houze 1993). Such MCSs move westward with a velocity of about 60 km h−1 over distances usually greater than 1000 km. In front of the MCS, there is a line of strong convective storm cells (cumulonimbus) with and a width of about 30 km releasing heavy rain with a rate frequently higher than 100 mm h–1. East of the convective line, there is a transition line with , and east of the transition line, there is a wide stratiform area with weak stratiform rain usually smaller than 10 mm h–1. In the case of Fig. 9a(1), the north–south length of the MCS is around 500 km with an east–west width of about 300 km in the northeast quadrant of the PPI. In the azimuth direction of about 240°, there is a small circular sector of weak reflectivity . This is due to blocking of the radar beam by a building located close to the radar. This building creates a specular reflection that redirects the radar beam along an azimuth of about 90°. What is seen along the azimuth of 240° on the PPI is thus what is observed along the azimuth of 90°. The annular area beyond 150 km is dotted by little points with a concentration increasing with radial distance. These points are noise peaks related to the amplifier of the radar receiver. In the presence of convective rainy systems, there is no anomalous reflectivity gradient in the low atmospheric levels (e.g., Steiner and Smith 2002). The radar echoes remaining after applying the APE selection criterion (i.e., elimination of pixels with nonzero Doppler velocity) are displayed in Fig. 9a(2) (labeled ”APE only”). It can be seen that almost all of the precipitation echoes are eliminated. There is only some signal inside individual and isolated pixels mainly located over the area occupied by the MCS in Fig. 9a(1). They are due to precipitation pixels with zero radial velocity. In Fig. 9a(2), these pixels occupy only 2.01% of the precipitation area, which is negligible. The noisy pixels are eliminated by the GVS software.

Figures 9b(1) and 9b(2) display two PPIs of AP echoes observed with the MIT C-band radar in the same conditions as Figs. 9a(1) and 9a(2) (i.e., 0.7° of elevation, 250 km of radial distance) at 2100 UTC 14 August 2006. Figure 9b(1) shows the reflectivity fields observed by the radar, that is, total. Reflectivities are weak, and the texture of the echoes, the absence of motion when analyzing a sequence of several consecutive PPI (i.e., an animation), suggests that they are AP echoes. Figure 9b(2) displays the same PPI as Fig. 9b(1) but after applying the APE selection (i.e., rain eliminating) criterion. It can be seen that most of the echoes are preserved and that the noisy pixels are also eliminated. The echoes observed around the radar location, inside the ring marker of a distance of 50 km, in Fig. 9b(1), are the permanent ground echoes detected by the main lobe and possibly the sidelobes of the radar beam. These permanent echoes are not observed in Fig. 9a(2) because they are partly suppressed by the APE selection process. In fact, when strong precipitation echoes (with nonzero Doppler velocity) are mixed in the same pixels with short-distance permanent echoes (with zero Doppler velocity), the pixels are classified in the nonzero Doppler velocity class by the software and thus eliminated by the APE selection process. They are maintained in Fig. 9b(2).

Figure 10a displays a PPI of the spatial distribution of the averaged APE radar reflectivity factor. All AP echoes observed at the time sampling of 10 min over the available radar dataset from 1 to 30 September 2006 have been considered. The average (i.e., arithmetic mean) has been calculated in mm6 m–3 but is expressed in dBZ in Fig. 10a. Radar reflectivity of the pixels is used for Fig. 10a because it is the quantity measured by the radar. However, its interpretation is not simple since it depends on numerous physical factors intervening simultaneously, namely, the shape and slope of the pixel surface with respect to the radar beam incidence, the nature of the ground material (including roughness, humidity, vegetation, conductivity, and permittivity; the presence of structure, such as pylon, etc.). A single month is used for Fig. 10a because summing all the available APE data over the entire 3-month period leads to a blurred APE spatial distribution (see below). September is chosen without a particular reason since other periods give similar APE spatial distributions. Figure 10b shows a map of the ground altitude inside the PPI area of Fig. 10a, and Fig. 10c displays the local height variations of the ground over the area covered by Fig. 10a. Local height variations have been obtained by subtracting from the altitude of each pixel that of the radar site and then averaging over the surrounding pixels, included in a square of 10 × 10 pixels. Such variations sketch the topography and orography of this area at a scale comparable to the pixel size—that of the ground features that are able to generate APE. Topography and orography have been obtained from the ground numerical model the Shuttle Radar Topography Mission (SRTM30) of NOAA.2

Fig. 10.

(a) Distribution of the mean radar reflectivity factor of APE averaged over September, (b) ground altitude in the area corresponding to (a), and (c) variation of the ground altitude with respect to the altitude of the radar in the area corresponding to (a). Range markers are 50 km from each other (maximal radial distance is 250 km). In (a) and (b), the figures locate particular ground structures: 1: hills, 2: Niger River, 3: Dallol Bosso, 4: Dallol Mauri, and 5: northern extremity of Atakora chain.

Fig. 10.

(a) Distribution of the mean radar reflectivity factor of APE averaged over September, (b) ground altitude in the area corresponding to (a), and (c) variation of the ground altitude with respect to the altitude of the radar in the area corresponding to (a). Range markers are 50 km from each other (maximal radial distance is 250 km). In (a) and (b), the figures locate particular ground structures: 1: hills, 2: Niger River, 3: Dallol Bosso, 4: Dallol Mauri, and 5: northern extremity of Atakora chain.

Figure 10 is presented to illustrate how the spatial distribution of the averaged APE (Fig. 10a) is related to some topographical and orographical features of the observed area (Fig. 10c). Overall, Fig. 10a displays strong relations with Fig. 10c. As an example of such relations, some features of Fig. 10b can be easily found in Fig. 10a. One can identify particularly 1) the hills north of Niamey; 2) the Niger River bed; 3) the ancient riverbed of the Dallol Bosso (nowadays dry) along the north–south direction at about 80 km east of the radar in Figs. 10a and 10b; 4) the Dallol Mauri along the 200-km range marker, east of the radar between the azimuths of 55° and 115°; and 5) the northern extremity of the Atakora Mountains.

It can be noted that ground features with a direction perpendicular to that of the radar beam at the location of the observation are better detected than those having a direction close to that of the radar beam. This is because most of the ground surfaces are not Lambertian (i.e., isotropic) reflectors. The strongest radar returns from ground surfaces are observed around a direction close to the perpendicular of the reflector surface (e.g., Skolnik 2008). For example, the Niger River bed (number 2 in Figs. 10a and 10b) crossing Fig. 10b along a diameter oriented from northwest to southeast is weakly apparent in Fig. 10a, whereas the segments of the Dallol Bosso and Dallol Mauri (numbers 3 and 4 in Figs. 10a and 10b), which are perpendicular to the radial east of the radar, appear much better in Fig. 10a. A similar behavior was observed by Mesnard and Sauvageot (2010) from a coastal site southwest of France.

In some parts of the PPI (Fig. 10a), some areas of indefinite shape are also devoid of echoes, while echoes are present at shorter and farther distances; see, for example, the locations of the Dallol Bosso and Dallol Mauri riverbeds. The reason is that the ground inside these areas is not seen by the ducted radar beam because it is located in the shadow (i.e., behind) of higher orographic structures. This “shadow effect” thus concerns the ground structure of small areas forming a local topographical depression (see Fig. 10c). The shadow effect contributes to the mapping of the ground-level variations. However, this mapping by the AP echoes is not clearly visible everywhere. In the southwest quadrant, between azimuths of approximately 185° and 240°, some radar beam directions are devoid of echoes (such around 240°, already mentioned in the comment of Fig. 9a) or display radially weakened echoes; this is due to beam blocking (a kind of shadow effect) by some obstacles located close to the radar (the radar was set at the ground).

If the averaged APE spatial distribution of Fig. 10a is calculated over the total 3-month period of available radar data, then the APE spatial distribution is blurred. Blurring increases with distance. The blurring is linked to several processes. First, the ducting increases the radar-target distance with respect to a straight-line detection, notably in the case of ducting associated with several reflexions inside the duct (e.g., Fig. 1 in Lopez 2009). The bias in distance due to ducting can be different for different ducting events. The result is a blurring effect that increases when different ducting events are averaged. Another possible cause of APE spatial distribution blurring is the range folding, that is, the second trip echoes coming from ground targets located beyond the maximum unambiguous distance of the radar (i.e., the interpulse distance) in the case of long-distance ducting. This cause of blurring is suspected to manifest in the east and southeast sectors of Fig. 10a. Indeed, we have observed from the SRTM30 that the topography shows high structures (the Aïr Mountains) far from 250 km (not shown) of the radar. However, it is not easy to demonstrate this effect because the range folding strongly modifies the shape of the folded structures (range folding preserves the radial dimensions but strongly diminishes the lateral ones). Last, conditions for AP and ducting are not usually isotropically distributed around the radar, as shown clearly on the PPIs in Fig. 9b. The result is to increase the heterogeneity inside the PPI of averaged APE spatial distribution, such as in Fig. 10a.

It can also be noted, in Fig. 10a, that small-size isolated echoes have frequently a lateral size larger than the radial one, resulting in a small bow shape with the radar as vertex (e.g., in the hills area labeled 1 in Fig. 10a). The bow size enlarges with distance from the radar. This is an artifact due to the finite width of the radar beam.

The conclusions of the preceding discussion is that the APE spatial distribution and the ground features (i.e., Figs. 10a and 10b) are strongly linked but cannot be simply correlated in the mathematical sense.

To illustrate, in a different way, the nature of the relations between the ducting conditions and the APE spatial distribution, Fig. 11 displays the temporal series of (Fig. 11a), the algebraic value of for AGL (Fig. 11b), and the surface occupied (in percentage; Fig. 11c) by the APE on the radar PPI (i.e., the spatial extent of APE) for September 2006. The total surface of the radar scan is 196 350 km2. Permanent ground echoes were not considered for Fig. 11c. Figure 12 shows an enlargement of Fig. 11 for the daytime on 26 September. Figure 12 enables visualizing the raw sampling of APE and , that is, 10 min and 14 s, respectively. Figures 11 and 12 show that there is a qualitative relation between the ducting event detected by the microwave radiometer (Figs. 11a and 11b and Figs. 12a and 12b) and the APE on the radar PPI (Figs. 11c and 12c). However, the values of shown in Fig. 11b are weakly related to those of the relative APE surfaces shown in Fig. 11c. The largest APE surfaces are not associated with the smallest values of . The linear correlation coefficient between and the relative APE area is very weak (around 0.2). The reasons for that are likely all the causes of blurring mentioned above, notably the shadow effect, the nonisotropy of ducting conditions around the radar, and the complex nature of the microwave scattering processes at the ground. It seems thus that there is only a relation of contingency between and the APE surface. That is why a Fisher’s test of contingency (e.g., Wasserman 2004) was performed to test the hypothesis that the nonzero APE surface is independent of the condition (null hypothesis or H0). For the Fisher’s test calculation, the raw data were interpolated in order to produce pairs of corresponding values of APE and at the time interval of 10 min. We found that the p value—that is, the probability to obtain a smaller value of the test if the null hypothesis were true—is 3.4 × 10−109 and that the odds ratio is 4.0579 with a 95% confidence interval (3.5665, 4.6207). Thus, the test leads to concluding a very strong improbability of the null hypothesis.

Fig. 11.

Temporal series for September 2006 of (a) , (b) for AGL (y axis scaled to show only ducting), and (c) the surface occupied by the APE (percentage) on the radar PPI. There are no radar data available after 27 Sep 2006. In (a), y axis is scaled 0–1 km AGL. The dotted vertical lines represent day separation at midnight. Colors as in Fig. 2.

Fig. 11.

Temporal series for September 2006 of (a) , (b) for AGL (y axis scaled to show only ducting), and (c) the surface occupied by the APE (percentage) on the radar PPI. There are no radar data available after 27 Sep 2006. In (a), y axis is scaled 0–1 km AGL. The dotted vertical lines represent day separation at midnight. Colors as in Fig. 2.

Fig. 12.

As in Fig. 11, but for the daytime on 26 Sep 2006. In (a), y axis is scaled 0–1 km AGL. The dotted vertical lines represent hour separation. The sampling interval is 10 min for APE and 14 s for with a standard deviation of 18.2 km–1.

Fig. 12.

As in Fig. 11, but for the daytime on 26 Sep 2006. In (a), y axis is scaled 0–1 km AGL. The dotted vertical lines represent hour separation. The sampling interval is 10 min for APE and 14 s for with a standard deviation of 18.2 km–1.

6. Conclusions

This study aimed to document the occurrence and space and time distributions of the anomalous propagation (AP) of microwaves in a continental area, by using both a radiometric profiler and a C-band radar. A 1-yr record of radiometric profiling and a 3-month record of radar measurements have been analyzed in order to assess the likelihood of anomalous propagations over the Sahelian area of Niamey.

The annual cycle of the refractivity vertical gradient and its relation to the vertical gradients of water vapor and temperature are discussed. The temporal series of the diurnal cycles and the monthly averaged diurnal cycles of refractivity and propagation regimes for the entire year of 2006 are shown. It has been found that the anomalous propagations occur the entire year and are notably common in the driest conditions, especially during nighttime. The AP concerns only the low troposphere, that is, below 600 m AGL during the wet season and below 200 m AGL during the dry season. Superrefraction is the dominant mode of AP by night. It progressively extends, both in time and vertically, from January to August, and then decreases the rest of the year. Ducting is the dominant nocturnal AP regime in October and November. Subrefraction is present only at the beginning of the year, during the dry season, when the water vapor vertical gradient shows low variability while the temperature vertical gradient shows strong variability with positive values during nighttime and negative ones during daytime. Statistics of propagation regimes are presented under the form of probability density functions of the refractivity vertical gradient. It is found that pdfs fit well a monomodal distribution (almost a lognormal function), which is more largely spread during nighttime than during daytime. The superrefraction regime is the most probable mode of microwave propagation.

Relations between the vertical refractivity gradient and the ground-based radar APE are illustrated and discussed. APE spatial distributions are found strongly related to the main features of the orography and topography, up to the farthest distance (250 km) inside the radar-observed area. However, it is found that the relations between , the APE spatial distribution, and the main features of the ground surface are not simple, and that they cannot be easily quantified. Observations suggest that these relations are blurred by the ducting processes (e.g., the anisotropy of the duct along the azimuthal direction) and by various factors affecting the radar reflectivity of the ground. On the other hand, contingency tests show that the probability for APE to be linked to ducting (i.e., is higher than 95%.

This paper suggest that observing the refractivity vertical profiles from a microwave radiometer profiler located close to a meteorological radar enables knowing whether anomalous propagations have to be considered as a potential cause of spurious signal in the measured reflectivity field.

Acknowledgments

Based on a French initiative, AMMA was built by an international scientific group and is currently funded by a large number of agencies, especially from France, the United Kingdom, the United States of America, and Africa. We want to give special thanks to the cooperation of the U.S. Department of Energy as part of the Atmospheric Radiation Measurement program for operating the microwave radiometric profiler in Niamey and for providing freely the data. We also want to thank E. Williams, B. Russell, T. Rickenbach, and the Massachusetts Institute of Technology for providing freely data from the C-band radar that was installed in Niamey during AMMA.

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Footnotes

1

Values, available online (at http://database.amma-international.org/), are 0.5°, 1.3°, 2°, 2.8°, 3.9°, 5°, 6.3°, 7.5°, 9°, 11.1°, 13.5°, 16.5°, 20°, 24.1°, and 30°.