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Where the Least Rainfall Occurs in the Sahara Desert, the TRMM Radar Reveals a Different Pattern of Rainfall Each Season [Journal of Climate](Journal of Climate Via Acquire Media NewsEdge) ABSTRACT Some previous studies were unable to detect seasonal organization to the rainfall in the Sahara Desert, while others reported seasonal patterns only in the less-arid periphery of the Sahara. In contrast, the precipitation radar on the Tropical Rainfall Measuring Mission (TRMM) satellite detects four rainy seasons in the part of the Sahara where the TRMM radar saw the least rainfall during a 15-yr period (1998-2012). According to the TRMM radar, approximately 20°-27°N, 22°-32°E is the portion of the Sahara that has the lowest average annual rain accumulation (1-5 mm yr-1). Winter (January and February) has light rain throughout this region but more rain to the north over the Mediterranean Sea. Spring (April and May) has heavier rain and has lightning observed by the TRMM Lightning Imaging Sensor (LIS). Summer rain and lightning (July and August) occur primarily south of 23°N. At a maximum over the Red Sea, autumn rain and lightning (October and November) can be heavy in the northeastern portion of the study area, but these storms are unreliable: that is, the TRMM radar detects such storms in only 6 of the 15 years. These four rainy seasons are each separated by a comparatively drier month in the monthly rainfall climatology. The few rain gauges in this arid region broadly agree with the TRMM radar on the seasonal organization of rainfall. This seasonality is reason to reevaluate the idea that Saharan rainfall is highly irregular and unpredictable. 1. Introduction During the past 50 years, it appears that no study has focused on the rainfall in the part of the Sahara Desert that receives the least rainfall, unlike the well-studied climates of neighboring regions. Earlier studies that did focus on this region (portions of Egypt within 208-278N) were unable to draw detailed conclusions because of insufficient data, which were limited to a decade or two at a few rain gauges (Lyons 1910; Soliman 1953). In these early studies and in passing references in broader, more recent studies, zero is reported as the average annual rainfall for all or part of this region within the Sahara (Lyons 1910, pp. 215 and 218; Soliman 1953; Wernstedt 1972; Nicholson 2011, p. 302; Haynes 2001, his Fig. 1). Obviously, if the average annual rainfall were really zero, then there would be no seasonal rainfall patterns. During the past 50 years, this region appears to have been examined only in pan-African studies such as Liebmann et al. (2012), Nicholson (2000), and Flohn (1964, his Fig. 10). Recently, the radar on the Tropical Rainfall Measuring Mission (TRMM) satellite has collected enough data to map the geographic extent of rainfall in various seasons over this very dry part of the Sahara, but previous TRMM radar studies of seasonality did not present such maps. These studies combined all observations from the driest region of the Sahara (Harada and Sumi 2003) or from the Sahara as a whole (Adeyewa and Nakamura 2003, their Fig. 2; Geerts and Dejene 2005, their Fig. 1a). Another TRMM study was conducted at 18318 resolution, but that study could not describe multiple rainy seasons at individual locations because it used an analysis procedure optimized for locating just one rainy season at each location (Liebmann et al. 2012, their Fig. 7). The present study attempts to provide this missing information about seasonal, geographic, and diurnal rainfall patterns in this very dry portion of the Sahara Desert. This study finds that some rainfall patterns here are connected to the rainfall patterns of surrounding regions, whose climates are well known. These surrounding regions include Africa's Mediterranean Sea coast to the north (Mehta and Yang 2008), the Red Sea (Krichak et al. 2012; Alpert et al. 2004) and Saudi Arabia to the east (Alyamani and Sen 1993; Subyani 2013), the Sahel to the south (Mohr 2004; Lélé and Lamb 2010), and north- western Africa to the west (Cuesta et al. 2010; Wu et al. 2013; Lafore et al. 2011; Davis et al. 2013; Nicholson 2008, 2009). 2. Data a. TRMM satellite The TRMM precipitation radar scans the earth in a 250-km-wide swath at 13.8 GHz (Kozu et al. 2001). The horizontal footprint of an individual line of sight is approximately 20 km2 (5-km diameter) with 250-m res- olution along the line of sight. The TRMM radar rain- estimation algorithm reports the instantaneous rainfall rate above the ground clutter (;1.5-2.5-km altitude) averaged over the footprint of the individual observa- tion (Iguchi et al. 2009). Several issues could affect the TRMM radar's ability to estimate accurately the surface rainfall rate in the Sahara. Some rain could evaporate as it falls through the unobserved bottom ;2 km of the atmosphere, causing the radar to overestimate the surface rainfall rate. Liu and Zipser (2013) considered factors, such as evapora- tion, that can cause the rain rate to vary between Earth's surface and the top of the radar ground clutter, but quantitative results about rainfall evaporation in arid regions will require further study. Two other potential issues over regions with light and rare rainfall like the Sahara Desert are the radar's limited sampling and its limited sensitivity to light rain. In terms of sensitivity, the TRMM satellite's orbit was boosted in August 2001, to conserve fuel, which greatly extended the mission but also slightly reduced the sensitivityoftheTRMMradarby1.2dB(Shimizuetal. 2003). The sensitivity reduction caused the radar to detect light rainfall less frequently, to detect fewer storms, and to report a higher rain rate on average among the pixels where rain is detected. A rough esti- mate based on the Marshall-Palmer Z-R relationship (Doviak and Zrni^c1993, p. 226) would have the post- boost TRMM radar able to detect rain rates above approximately 0.7 mm h21 based on a sensitivity of 20.7 dBZ (Takahashi and Iguchi 2004). To maximize the amount of TRMM radar data, the present study uses the entire 15-yr record, including before and after the boost, essentially combining a shorter record of a more sensitive radar with a longer record of a some- what less sensitive radar. Since the goal of the present study is to detect seasonal variation, the absolute magnitude of the average annual accumulation is less important than the relative amount of rainfall in dif- ferent seasons. In terms of sampling, the TRMM radar observes, once a day, almost half of the area of the driest part of the Sahara: that is, almost half of the 208-278N, 228-328E study region. Because the TRMM satellite's orbit pre- cesses, the radar collects observations at all times of day over a period of 46 days (Nesbitt and Zipser 2003, p. 1459), making the TRMM satellite's 15-yr archive an approximately random sample over the entire diurnal cycle. Concerns about the radar's limited sampling and sensitivity are partially addressed by finding that the TRMM radar data and the long-term rain gauge record contain similar seasonal patterns in the driest part of the Sahara. The year-to-year reliability of many of the rain-season patterns further addresses the sampling issue (section 4a). The sample of rare events (e.g., desert rain) is larger because the TRMM satellite has been in orbit so long (since November 1997). While the TRMM radar's sensitivity may be limited, the radar's calibration appears to be stable (Anagnostou et al. 2001) and the radar's rainfall-rate measurements are similar to those measured by a dense rain gauge net- work (Amitai et al. 2012). The ability to detect the same seasonal pattern either with the full TRMM radar dataset or with only the footprints above the radar's sensitivity limit further addresses the sensitivity issue (section 4b). To simplify the data analysis in the present study, TRMM radar rainfall estimates are taken from the latest version (version 7) of various data products. These prod- ucts contain rainfall-rate estimates for either individual radar footprints (TRMM 2A25), monthly averaged 0.58-resolution grids (TRMM 3A25), or hourly averaged 0.58-resolution grids (TRMM 3G68) (JAXA 2011; ftp:// trmmopen.gsfc.nasa.gov/pub/README.3G68). Three variables must be read from the TRMM 3A25 monthly gridded product in order to obtain the average rainfall rate.Ineachgridbox,onemustmultiplytherainrate for raining footprints (surfRainMean2) by the number of raining footprints (surfRainPix2) and divide by the total number of observed footprints (ttlPix2). The TRMM Multisatellite Precipitation Analysis (TMPA) contains a monthly average precipitation rate on a 0.258 grid (Huffman et al. 2007) that is based on various satellites' passive microwave and infrared data and that is calibrated with rain gauges and with TRMM radar and passive microwave data. In the present study, the TRMM Lightning Imaging Sensor (LIS) data are taken from two data products. Lightning is so rare in the driest part of the Sahara (208- 278N, 228-328E) that it is practical to read all of the indi- vidual flashes from the LIS single-orbit science product in this region during the 15-yr period of 1998-2012. For larger regions, the present study uses the gridded monthly lightning climatology of Cecil et al. (2013). LIS takes a snapshot of 777.4-nm visible light every 2 ms on a 128 3 128 pixel field of view that covers approximately 580 km 3 580 km on the ground (Kummerow et al. 1998; Christian 2000, p. 10). LIS observes each location in the TRMM radar swath for approximately 90 s. b. Rain gauges The rain gauge record began before the satellite era and remains widely used today. Over the driest part of the Sahara, publically available archives contain rain gauge data covering approximately 50 years during the early to mid-1900s with an insubstantial number of ob- servations after the TRMM satellite launched in late 1997. A number of researchers have commented on the difficulty of obtaining rain gauge data collected during the satellite era over the arid parts of Africa (Nicholson et al. 2003, p. 616; Nicholson 2011,p.8;Elagib 2011, p. 507). The mismatch between the years of TRMM radar data and the years of rain gauge data appears not to be a problem because both radar and gauges detect similar seasonal patterns (section 4b). Compared with other gauge archives, the global ar- chive of Eischeid et al. (1991) provides the longest re- cord of observations at many gauge locations in or near the driest part of the Sahara (Table 1 and Fig. 1). From the monthly time series for each station (12 values for each year), the present study calculates a monthly cli- matology, 12 values in total, which are the long-term average rainfall accumulation for each month. Rain gauges can have data quality issues (Eischeid et al. 1991, pp. 3-9; Miller 1977, pp. 38-42; Menne et al. 2012, section 3; Elagib 2011, p. 507; Groisman and Legates 1995; Sevruk 1987), but error bars are not rou- tinely provided. For this reason, the initial stage of the present study examined several rain gauge datasets covering the driest part of the Sahara to get a sense of the variability present in the gauge record. The pub- lished climatologies examined were Soliman (1953, his Table 1), Wernstedt (1972), and the World Meteoro- logical Organization (WMO) climate normals for 1961- 90 (Obasi 1996). The gridded monthly gauge analyses examined were from the Climate Research Unit (CRU) version 3.21 covering 2001-10 (Harris et al. 2014)andfrom the Global Precipitation Climatology Centre (GPCC) version-7 full analysis covering 1901-2010 (Becker et al. 2013). The following four archives of gauge-station accu- mulations were examined. 1) The Egyptian Meteorological Department (EMD) or its predecessors published annual reports containing monthly gauge accumulations. These reports are available from the NOAA Central Library for 1900-70 (http://docs.lib.noaa.gov/rescue/data_rescue_ egypt.html). 2) Menne et al. (2012) describe daily rain accumulations in the archive of the Global His- torical Climatology Network (GHCN). 3) The Florida State University Meteorology Department archive of monthly accumulations covers 1901-84 (FSU 2014). 4) Since 1948, the National Climatic Data Center has published each month the Monthly Climatic Data for the World, which contains monthly gauge accumulations (http://www.ncdc.noaa.gov/IPS/mcdw/mcdw.html). Table 2 shows that the published climatologies and the climatologies calculated from various gauge time series archives differ at some locations by more than a factor of 2. Some of this variation is likely due to dif- ferent year ranges in various archives. At some gauge stations, however, the archives disagree about the storms during the same years. A particularly severe example is the gauge at Kufra, Libya, which is the only gauge in the western half of the 208-278N, 228-328E study region. In- formation is not readily available in published sources or online about the type of rain gauge, the data collection procedure at this station, the name of the organization collecting the rainfall data, or how these things have changed over the decades. During 1933-83, there were always at least two gauge-station time series archives re- porting monthly or daily accumulations for Kufra. The archives agreed about the amount of rain in the 10 rainy months before 1951 and for the 6 rainy months after 1969, but for 1953-63 the archives disagreed about 10 rainy months and agreed on only 3 rainy months. Because of the variation among archives, the primary results of the present study will be couched in general terms (e.g., 1-5 or 5-10 mm yr21) and will be supported by multiple gauge locations when possible. 3. Locating the portion of the Sahara with the least rainfall As described below, all but one of the rainfall datasets consulted agree fairly well with the TRMM radar about where in the Sahara the least rain falls. The agreement is fairly good in that these datasets have considerable overlap in the region that they each identify as having an average annual accumulation of 1-5 mm. In 1998-2012, the TRMM radar estimates that the area that receives 1- 5mmyr21 is mostly contained by the rectangular box that the present study refers to as the study region: 208-278N, 228-328E. The curvy boundary of the radar-detected #5mmyr21 area is shown with red in Figs. 1 and 2a,g, whereas the rectangular box is shown in gray in Fig. 1. The TRMM radar location for the #5mmyr21 area agrees well with TMPA, the GPCC gridded gauge anal- ysis, and the gauge station archives of both Eischeid et al. (1991) and the GHCN (Figs. 2b,c,g). In terms of which part of the Sahara receives the least rainfall, the one outlier dataset is the CRU gridded gauge analysis (cyan in Fig. 2d). The CRU analysis shows #5mmyr21 across most of the Sahara but excludes much of the 208-278N, 228-328E study region, where the other rainfall datasets estimate #5mmyr21. The location of the #5mmyr21 TRMM radar area appears to be unaffected by land surface type and to be mostly unaffected by orography. The land surface types in this region include sand seas of shifting dunes, sand sheets of fixed dunes, gravel fields, boulder fields, and exposed rock sheets shown in Fig. 1. In the 208-278N, 228-328E study region, the TRMM radar detects only one place where rainfall appears to vary with orography. The sharpest geographic feature in this relatively flat region (Fig. 2e) is a cluster of three 1900-m-high mountains that rise about 1000 m above the surrounding desert at the intersection of Egypt, Libya, and Sudan (Fig. 1). The tallest of these mountains is called Uweinat Mountain (21.98N, 25.08E). In the vi- cinity of these three mountains, the TRMM radar shows a slightly elevated average annual rainfall of 5-10 mm yr21 instead of the 1-5 mm yr21 found over the desert about 100 km to the west, north, and east of these mountains. The TRMM radar detects no rainfall enhancement over the 1000-m-high Gilf Kebir Plateau (23.58N, 25.88E), which rises about 300 m above the surrounding desert. Siliotti (2009, p. 37) also describes a rainfall enhancement over Uweinat Mountain but not over Gilf Kebir. 4. Identifying rainy seasons An initial examination the monthly rainfall clima- tology of rain gauges and TRMM radar suggested that, in the part of the Sahara that receives the least rainfall, there are short rainy seasons (1-2 months long) that are geographic extensions of the longer rainy seasons (3-7 months long) that are well documented in the less-arid regions to the north and south. In fact, the initial analysis for the present study suggested that the climatology of the driest part of the Sahara might be described, to a first approximation, as four 2-month- long rainy seasons that are separated from each other by one comparatively dry month. Sections 4a and 4b present this analysis. Looking at previous studies, it becomes clear that thresholds must be carefully chosen in order to detect multiple rainy seasons in the part of the Sahara that receives the least rainfall. For example, 2 mm month21 is too high of a threshold to detect more than just a sum- mer rain season here. Nicholson and Chervin (1983, p. 8b) make this point for rain gauges along 268E. At 1 mm month 2 1, four seasons can be detected, but only along the Nile River, where the average annual rainfall is somewhat higher than the average over the 208-278N, 228-328E study region. Flohn (1964, his Fig. 10) makes this point for rain gauges along 328E. Consistent with previous studies, the present study finds that a threshold under 1 mm month21 is best for distinguishing more-rainy months from less-rainy months in the monthly climatology of the driest part of the Sa- hara. A 0.25 mm month21 threshold detects four seasons in TRMM radar data, while a threshold as low as 0.04 mm month21 does so for rain gauges in this region. What these thresholds have in common is that they are approximately 20% of the rainiest months in the TRMM or gauge climatology, respectively. This result suggests that seasonality can be detected with a relative thresh- old that is adjusted to the climatology at a particular location: that is, a percentage of the average accumu- lation in the climatologically rainiest month or in the annual total. a. Using the TRMM precipitation radar and lightning sensor To illustrate the seasonal organization of rainfall, Fig. 3 shows plots of average monthly rainfall accumu- lation as function of month and latitude. Contours are drawn as low as 0.1 and 0.25 mm month21 based on 15 years of TRMM radar data. While it is true that an individual, 20-km2 TRMM radar footprint with a rain rate this low would have limited accuracy because of the radar's limited sensitivity, a 15-yr average this low would be more accurate at least in terms of having a smaller random error (Montgomery and Runger 2003, p. 225). In the driest part of the Sahara Desert, each 15-yr rain average for a single month is calculated from more than 20 000 radar footprints in each 0.58 grid box. Approxi- mately 99.9% of these radar footprints have a zero rain rate. Approximately 67% of the TRMM estimated rain accumulation comes from footprints with rain rates above 1 mm h21 (Table 3), which is above the radar's previously mentioned sensitivity limit of around 0.7 mmh21. In the month-latitude plot of the 15-yr TRMM radar dataset, distinct winter, spring, summer, and autumn sea- sons can be identified in the part of the Sahara that receives the least rain (208-278N, 228-328E; Fig. 3b, green box). In January and February, there is winter rain with limited accumulation (generally only 0.25-1.0 mm month21). During winter, almost no lightning is detected by the TRMM LIS in the study region. In April and May, spring rain produces greater accumulation throughout the study region with lightning throughout the entire region too (black plus symbols in Fig. 3b). In April and May, heavy rain rates (;10 mm h21) contribute almost as much to the total accumulation as do light rain rates (;1mmh21), as shown by the black line in Fig. 4f.In contrast, in January and February, heavy rain contrib- utes very little to the total accumulation (black line in Fig. 4e). In July and August, Fig. 3b shows that the summer rainy season is limited almost exclusively to the southern half of the study region (208-238N). In October and November, the autumn rainy season occurs pri- marily in the northern half of the study region (248- 278N). Subsequent mention of winter, spring, summer, or autumn will refer to the above-mentioned 2-month- long periods, unless otherwise noted. Considering the longitude bands to the east or west of the driest part of the Sahara (Figs. 3a,c), the Mediterranean climate north of 308N is essentially the same in all three longitude bands, as is the tropical climate south of 188N. In the hour-latitude plot of the 15-yr TRMM radar dataset (Fig. 5), a diurnal pattern can be seen in spring and summer, with no clear diurnal pattern detectable in winter and fall within the driest latitudes (208-278N). Figure 5 plots rainfall as a function of local time on the x axis and latitude on the y axis over the 228-328E longitude band. These time-versus-latitude images are generated instead of line plots of rainfall as a function of time of day because the time versus latitude images show how, in spring and summer, the diurnal pattern in the 208-278N study region connects with the diurnal pattern of the less-arid regions to the north and south. This figure is constructed in such a way that it can de- tect if an hour of the day has more rainfall than average, no matter how little rain falls at a particular latitude. First, the mean rainfall per hour rm is calculated as the total rainfall at that latitude divided by 24 h. Then, an hour's fractional deviation fi (unitless) from mean rm can be calculated using the rainfall during that hour ri: fi 5 (ri 2 rm)/rm. For example, an hour that contributes double the average hourly amount would have fi equal to 1 (red in Fig. 5) and an hour with close to zero rainfall would have fi near 21 (deep blue in Fig. 5). Because rain is so rarely observed in the driest latitudes (208-278N), a smoothing filter is applied repeatedly (three times) to fi to make the diurnal pattern easier to see. This smooth- ing filter is a 3 3 3 element average, so applying it three times will change the original fi resolution of 0.58 latitude and 1 h approximately to a resolution of 2.58 latitude and 5h. The diurnal pattern in spring and summer is a late- afternoon and evening peak in both rainfall and light- ning at approximately 1400-2200 local time (LT) (Figs. 5b,c). Looking at the whole Sahara with the TRMM radar, Geerts and Dejene (2005, their Table 5) found similar timing: summertime low-altitude rainstorms peak at 1200-1500 LT and summertime deep rainstorms peak at 1800-2400 LT. Using the TRMM Microwave Imager, Mohr (2004, her Fig. 8a) reports a rainfall maximum for Africa's Sahel region at 1800-2200 LT (158-208N; Atlantic to 328E). Rain in the driest part of the Sahara can be called reliable to the extent that such a description can be ap- plied to a place where it rains so rarely. At a point lo- cation that experiences, on average, less than one rainy day per year (Table 2), it is not possible to have reliable rain in the ordinary sense of multiple storms in the same 2- or 3-month period every year (Warner 2004, p. 371). In another sense, a season could be called reliable if, in most years, the TRMM radar detects rainfall during that season somewhere in the 208-278N, 228-328Estudy region. To help estimate the reliability of the four previously discussed rainy seasons, Fig. 6 displays a month-latitude plot for each individual year in the 15-yr TRMM radar archive for the same longitude band that is shown in Fig. 3b. For an individual year, a season is judged as having significant rainfall if enough rain is observed to produce a 0.25 mm month 2 1 contour over at least part of the study region (208-278N). Winter, spring, and summer meet this criterion in most years, while autumn does so in 6 of the 15 years. The reliability of rain in winter, spring, and summer should reduce concern about the TRMM radar having insufficient sampling or sensitivity to detect seasonal patterns in this arid region. The seasonal maps in Fig. 7 graphically convey the idea that the rain that reaches the driest part of the Sa- hara, in most seasons, is the tail of a geographic probability distribution that is maximum in a neighbor- ing, less-arid region. Figures 7a-d map where at least 10% or 50% of the average annual rainfall occurs during a particular season using blue-violet or yellow-orange- red, respectively. Figures 7e-h map where a particular season experiences at least 10% or 50% of the LIS- observed annual number of lightning flashes using the same colors. Based on TRMM radar data, the winter rain (January and February in Fig. 7a) appears to be the tail of the distribution of rain that occurs primarily to the north over the eastern Mediterranean Sea. Mehta and Yang (2008) found heavy winter rain in the eastern Mediter- ranean in January and February. Summer rain storms occasionally reach as far north as 238N(Figs. 7c,g). These summer storms appears to be the northernmost extreme of the tropical rain systems that are maximum in summer between 58 and 158N over Africa (Nicholson 2009, p. 1163). Autumn rain contributes most of the annual total rainfall on the side of the study region closest to the Red Sea and over the Red Sea itself (Figs. 7d,h). Heavy rain in spring can be brought by a synoptic situation that is rare in other seasons. A midlatitude trough becomes elongated toward the south and becomes oriented southwest-northeast through in- teractions with westward-moving tropical disturbances to the south (Nicholson 2000, p. 142; Nicholson 1981, p. 2192). Spring in the driest part of the Sahara has no analog in the immediately adjacent, less-arid regions but does have an analog 1000 km to the east in Saudi Arabia (outside the area displayed in Fig. 7). Using rain gauges not available in the gauge archives used in the present study, Alyamani and Sen (1993, their Table 2) published a monthly rain gauge climatology that shows that Saudi Arabia has a somewhat early spring (March-April) at 208-278N. Incidentally, all four rainy seasons are present in this Saudi rain gauge climatology including autumn (November), winter north of 218N (January), and sum- mer south of 218N (July and August). So far, the maps discussed display gridded averages (from TRMM 3A25), but additional details about sea- sonality can be gleaned by looking at maps that plot individual TRMM radar footprints (from the TRMM 2A25 swath product). Looking at individual footprints also allows one to remove footprints that appear odd, although in the present study removing these footprints turned out to have an insignificant effect on rain accu- mulation (see also Kelley et al. 2010, section 2c). In the present study, there appears to be no danger in using the TRMM 3A25 grids that do not undergo this check. For the present study, TRMM 2A25 footprints were re- moved for which the vertical profile of radar reflectivity was unusually flat (,5-dBZ variation). Also, footprints were removed that had large ''holes'' in their vertical profile: that is, radar reflectivity was undetectable in $10 of the 250-m range gates above the ground clutter and below the storm top. These two kinds of footprints ac- count for 12.5% of rainy footprints in the study region but only 5.9% of the rainfall accumulation. Plotted in black in Figs. 7i-l are TRMM radar foot- prints with at least a moderate rain rate ($1mmh21). Plotted in red are $1mmh21 footprints that have evidence of electrification (i.e., of thunderstorms). Electrified footprints are only 1.6% of all rainy TRMM radar footprints and contribute 16% of the rain accu- mulation. Evidence of electrification is that a footprint is within 20 km of a LIS lightning flash and the radar footprint itself suggests the presence of ice-phase pre- cipitation. Specifically, the 2A25 algorithm classifies the footprint as convective and 30-dBZ radar reflectivity reaches 5-km altitude or higher, which is near or slightly above the 08C isotherm in this region during the three- quarters of the year when lightning is most common (from spring through autumn). The integrated global radiosonde archive of Durre et al. (2006) calculates the 08C isotherm for each radiosonde profile. This archive includes only one station within the 208-278N, 228-328E study region (Kufra, Libya), at which 1008 soundings were observed between 1973 and 1991. The middle 50% of this distribution of radiosonde-observed 08C heights is 2.7-3.8 km in winter (January and February), 3.8- 4.3 km in spring (April and May), 4.4-5.0 km in summer (July and August), and 3.7-4.2 km in autumn (October and November). The individual TRMM radar footprints plotted in Figs. 7k,l reveal details about summer and autumn. In summer, the TRMM radar only detects electrified storms below 228N, while nonelectrified storms can reach farther north to 258N (lines A and B in Fig. 7k). In autumn, electrified storms are confined to the northeast corner of the study region, while nonelectrified storms generally reach all but the southwest corner of the study region (lines C and D in Fig. 7l). The northeast corner of the study region is close to the Red Sea, where intense storms are known to form in the autumn (Krichak et al. 2012; Alpert et al. 2004). b. Comparing rain gauges with the TRMM radar To identify which months are rainier than others at an individual rain gauge, the present study uses a threshold that is adjusted to the rainiest month at that gauge. To be considered rainy, a month must have an average accu- mulation that is at least 20% of the average accumula- tion of that gauge's rainiest month. If any of the previously discussed 2-month-long seasons have at least one rainy month, then that season is considered to be rainy. Once rainy seasons are identified in this way, the gauges' seasonal patterns can be compared with those found in TRMM radar data. Based on the just-described threshold, rainy months are shown in boldface in Table 4. Several variants on the 20%-of-the-rainiest-month rule (e.g., 10% of the raini- est month or 10% of the annual accumulation) would produce similar results. The fact that about half of the months in the gauge climatology qualify as dry even when using such a low threshold (the above-mentioned 20% threshold) is, in itself, evidence that seasons are well defined in this part of the Sahara Desert. In com- parison, the eastern United States has less-well-defined seasons because, in general, all months have more than 50% of the accumulation of the rainiest month in the eastern U.S. monthly climatology (Arguez et al. 2012). Previous studies that looked at the Saharan monthly rainfall climatology noted that the fractional variation among months suggests the existence of particularly well-defined seasons (Walsh and Lawler 1981). Armed with Tables 4 and 5, one can describe how the well-marked seasons surrounding the study region ap- pear to extend into the study region itself. Taking the seasons one at a time, one can start with summer. The gauges to the south of the study region (from Abu Hamed to Khartoum in Table 4) have only a summer rainy season, and this season is at maximum in July and August. This pattern matches the summer tropical monsoon that others have described to the south of the studyregion(Mohr2004;LéléandLamb2010,theirFig.3; Liebmann et al. 2012, their Fig. 8). This summer rainy season extends up to only the southernmost gauge within the 208-278N, 228-328E study region (Wadi Halfa). One could say that some of the northernmost gauges in Table 4 (Benghazi and Helwan) have only one rainy season-a long winter-because these gauges' monthly climatologies decrease monotonically from a December or January peak going earlier or later toward the July- August minimum. This pattern matches the Mediterra- nean rainy winter climate described by Mehta and Yang (2008). This long-winter rain season is color coded as a single season in Fig. 8 for the northernmost gauges even though it is approximately 6 months long. The winter rain season is shorter (2-3 months long), farther south, at three gauges in the study region: Dakhla, Kharga, and Kufra. Autumn rainstorms are known to be strong over the Red Sea (Krichak et al. 2012; Alpert et al. 2004) and gauges between the study region and the Red Sea show that this season extends at least that far (Qena, Quseir, Luxor, and Aswan). In fact, two of the four gauges in the study region itself see what might be called the western tail of the Red Sea autumn rainy season (Dakhla and Wadi Halfa). The four gauges in the study region show a spring (April-May) rainy season, although spring rainfall is weaker than winter rainfall in three of these gauges (January-February). The weakness of the spring season in the long-term gauge record can be contrasted with spring rainfall seen by the TRMM radar in 1998-2012 (Figs. 7b, 3b), which has the greatest accumulation among all four seasons see by the TRMM radar. Agreeing more with the TRMM radar archive than with the gauge record, Nicholson (2000, p. 142) and Soliman (1953, p. 390) find that spring and autumn tend to have the heaviest rain of the year, on average, in the central Sahara Desert. To compare gauges and TRMM radar more directly, monthly climatology rows were added to Table 4 based on TRMM radar data averaged over 228-328E longitude and over the four latitude ranges labeled A-D in Fig. 3b. Many of the raining TRMM radar footprints have low rain rates: near to or somewhat below the radar's pub- lished sensitivity limit. To address concerns about the sensitivity of the TRMM radar, the monthly climatology is recalculated excluding such light rain. Specifically, the two rows of Table 4 that are labeled as TRMM $1mmh21 repeat the calculation of the TRMM radar monthly climatology using only the 20-km2 radar footprints with rain rates of $1mmh21.The$1mmh21 TRMM rows in Table 4 have a similar seasonal pattern as do the full-dataset TRMM rows above them. In Table 4, the number of lightning flashes each month observed by TRMM LIS provides one more confirmation of the sea- sonal pattern described so far. One difference between the rain gauge and TRMM radar seasonal patterns is that the summer and autumn rainy seasons appear to be 1 month shorter in gauge data than in TRMM radar data. Table 4 shows that the summer rainy season, which occurs only in the southern portion of the study region, is 2 months long in the gauge record (July and August) while it appears to be 3 months long in the TRMM radar monthly climatology (July through September). The autumn season that occurs primarily in the northern half of the study region is 1 month long in the gauge record (a wet October followed by a dry November), while it is 2 months long in the TRMM radar monthly climatology (a wet October and November followed by a dry December). It is beyond the scope of this study to determine whether these dif- ferences are related to instrument characteristics or to actual differences in the climate in the early to mid- 1900s (rain gauges) versus 1998-2012 (TRMM radar). A statistical test can estimate how unlikely it would be that the observed differences between typically wet and dry months would have occurred randomly. Sen (2008, p. 39) and Husak et al. (2007) recommend that, in arid locations, rain frequency be analyzed separately from rainfall accumulation, which is done here with the binomial proportion (BP) test and the paired-sample sign test (ST), respectively. Von Storch and Zwiers (1999) describes these two tests, and a number of climate studies use one or the other of them [binomial test: Neelin et al. (2013,theirFig. 1), Naud et al. (2012, their Fig. 10), and Higgins et al. (2004) and sign test: D'Odorico et al. (2001, p. 4238) and Oyama and Nobre (2004, p. 3206)]. The binomial proportion test is used to test the frequency of rain events. For the rain gauges in the study region, most months have zero accumulation, so the binomial pro- portion test is used to evaluate the evidence that typically rainy months really do have nonzero accumulation more often than typically dry months. For the TRMM radar, most months have nonzero accumulation, so the binomial proportion test is used to evaluate the evidence that more satellite overflights detect rain in typically rainy months than in typically dry months. To count as rainy, an over- flight must contain at least one radar footprint with a $ 1mmh2 1 rain rate. As an example of the binomial proportion test, con- sider the test in the top-left corner of Table 6, which pools observations from three gauges in the northern half of the study region. One sample contains ntotal 5 161 monthly accumulations from typically dry summer months (July or August). The second sample is equal in size and contains monthly accumulations from typically wet winter months (January and February). In the wet sample, nwet 5 17 monthly accumulations were nonzero, while none of monthly accumulations in the dry sample were nonzero (ndry 5 0). In this example, the binomial proportion test estimates that there is less than a 5% chance (i.e., a p value , 0.05) of two samples with such markedly different rain/no-rain frequencies coming from the same population. The p value is the probability of ndry nonzero accumulations in ntotal trials when the binomial proportion p is set to nwet/ntotal (Montgomery and Runger 2003, section 9.5). After rejecting this ''null hypothesis'' based on this p value, a natural alternative would be to think of January and February as experi- encing more frequent rain than July and August. Throughout the present study, the Interactive Data Language (IDL) is used to calculate the exact binomial probability (see online at http://www.exelisvis.com/ docs/BINOMIAL.html), with one exception. The ex- ception is the binomial proportion tests on TRMM radar data, where the large sample size (ntotal . 500) necessitates that IDL calculate p values using the normal approximation to the binomial distribution. The normal approximation is sufficiently accurate because, for all radar-based binomial proportion tests in Tables 6-8, the product of the binomial proportion (nwet/ntotal)and the sample size (ntotal)is$40. A value that was just $5 would suggest that the normal approximation was suf- ficiently accurate according to Montgomery and Runger (2003, p. 310) and Sheskin (2011, p. 314). The paired-sample sign test is used to test rain accu- mulation in this study because the data appears less well suited for other paired-sample tests: a t test would require that both samples be normally distributed (Sheskin, 2011, p. 763) and a signed-rank test would require that both samples be symmetric about their median (Sheskin, 2011, p. 809). To employ the paired-sample sign test, one first pairs off the data, with one value in each pair coming from a typically dry month and the other value in the pair coming from a typically wet month. Next, one subtracts the wet month's accumulation from the dry month's ac- cumulation, and one keeps only the pairs in which this difference is nonzero (Gibbons and Chakraborti 2011, section 5.4.3; Sheskin 2011, p. 825). After removing zero differences, the sign test in the top-left corner of Table 6 has nnonzero 5 17 pairs remaining and among these 17 pairs, the wet-month accumulation (January and Febru- ary) was never less than the accumulation for the dry months (July and August), so n2 5 0. The paired-sample sign test reports a probability of under 5% that 0 out of 17 paired differences would be negative if both samples came from a single population. IDL calculates the exact p value as the probability of n2 or fewer events in nnonzero years under the null-hypothesis binomial proportion of 0.5 (Montgomery and Runger 2003, section 15.2). At the 0.05 significance level, the just-described sta- tistical tests support the following three conclusions using either the TRMM radar or rain gauges in the 208- 278N, 228-328E study region within the Sahara Desert. First, Table 6 presents statistical evidence that winter, spring, and autumn are each wetter than summer in the northern portion of the study region (248-278N). Sec- ond, Table 7 presents statistical evidence that there is a dry month terminating winter and spring but not necessarily autumn. Also affecting Table 7, the TRMM radar observes in January and February heavy monthly accumulations on average, but with a strong positive skew to these months' distributions. For this reason, the sign test between wet winter and dry March only achieves a 0.05 significance level for the TRMM radar if January and February are averaged together first before comparing them to the relatively dry March. Last, Table 8 presents statistical evidence that the wet summer is preceded and followed by a dry month, at least in the one part of the study region that has a rainy summer: the southern portion of the study region (208-238N). c. Qualitative descriptions of rainfall patterns It is difficult to find a brief yet complete description of Sahara rainfall because the long-term record has well- marked seasons, yet it rains sporadically, if at all, in a single year at a single location. Some of the Saharan rain gauges examined in the present study experience rainfall less of- ten than once a year on average (Table 2). In this specific sense, rainfall is irregular: a point location in the 208-278N, 228-328E study region cannot be expected to experience multiple storms in the same season, year after year. ''Irregular'' or ''unpredictable'' may not be the best one-word descriptions for the rainfall in the part of the Sahara where the least rainfall occurs. It is true that, with rain falling only once every year or two at some gauge stations, a single decade of data at a single gauge will not adequately sample the underlying probability distribu- tion of rain. Such a limited sample will not realize the structure present in the monthly rainfall climatology. Sections 4a and 4b show, however, that there is a seasonal pattern to the monthly rainfall climatology when it is calculated either with several decades of data at a single gauge station or with 15 years of TRMM radar data cov- eringa783108 latitude-longitude area. Within the 208- 278N, 228-328E study region, some months, locations, and times of day do experience greater rain accumulation on average than other months, locations, and times of day. Some studies suggest there is predictability in arid North Africa in terms of forecasting single-year, sea- sonal departures from the rainfall climatology or in terms of forecasting individual rain events (Nicholson 2011, p. 188; Nicholson 1996, p. 31). In West Africa, seasonal rainfall prediction (Nicholson 2008, 2009; Harada and Sumi 2003; Wu et al. 2013) may be assisted by forecasting seasonal forcing (Sultan et al. 2010; Zhu et al. 2014; Beraki et al. 2014; Endris et al. 2013). In- dividual rain events over the Sahara might be predict- able because they involve a particular set of interactions between tropical and extratropical waves, jets, and air masses (Lafore et al. 2011,p.9;Knippertz 2003; Davis et al. 2013) that are routinely predicted in global weather-forecast models (Waliser et al. 2012). These results advise against describing the Sahara's rainfall with a single adjective without elaborating in what sense that adjective applies. Some early and recent studies, however, do not elaborate [irregular: Meigs (1952), FAO (1977), Laity (2008,p.7),andHerrmann and Mohr (2011) and unpredictable: Alyamani and Sen (1993, p. 114), UN (2006,p.9),andSubyani (2013, p. 804)]. Over the driest part of the Sahara, rainfall prediction is, at present, difficult on the much longer time scales of climate-forecast models. According to a recent In- tergovernmental Panel on Climate Change report, such models give divergent predictions about whether Saharan rainfall will increase or decrease in future decades (Stockeret al.2013,pp. 1118,1266-1268,1281,and 1356- 1357; James and Washington 2013, their Fig. 6). The present study describes the observed rainfall patterns in one part of the Sahara, which may contribute to the cli- mate reference data that might someday prove useful for evaluating climate-forecast models. Seeing how well models can reproduce the climate of the past century is one way to evaluate their ability for forecast the next (Giannini et al. 2008). 5. Conclusions During 1998-2012, the radar on the TRMM satellite detected seasonal organization to the rainfall over the portion of the Sahara Desert that receives the least rain. The four rain gauges in this area have a similar, although not identical, seasonal organization in their long-term record, covering approximately 50 years in the early to mid-1900s. These two kinds of instruments have different limitations and complementary strengths. Detecting such similar pat- terns with both radar and rain gauge increases confidence that the seasonal patterns are real. The four gauges in the driest part of the Sahara have very limited spatial coverage (four points) but excellent (i.e., nearly continuous) time coverage. The TRMM radar has much better spatial cov- erage (nearly continuous within the swath) but has limited sensitivity to light rain and has temporal coverage limited to rarely more than one snapshot per day. The TRMM radar estimates that the part of the Sahara that receives the least rainfall experiences 1-5 mm yr21 of rain on average and is mostly confined to 208-278N, 228-328E. In winter (January and February), the TRMM satellite observes that this part of the Sahara receives light rain with almost no lightning. These winter systems appear to be the geographic tail of the proba- bility distribution of much heavier rain 500 km to the north over the Mediterranean Sea. The Mediterranean receives a smaller portion of its rain in spring (April and May), but most of the driest part of the Sahara receives the majority of its annual rainfall during spring as late- afternoon or evening systems (some electrified). In summer (July and August), Africa's tropical monsoon dominates the annual rainfall cycle to the south. Yet, in the summer, late-afternoon or evening storms (some electrified) were seen by the TRMM satellite to occur farther to the north and within the driest part of the Sahara up to about 238N. To the east, the Red Sea has much of its rainfall and most of its lightning in autumn (October and November). These autumn rain systems can reach west to approximately 288E, which is within the driest part of the Sahara. Rainfall in the part of the Sahara with the least rain is regular in that it occurs in four seasons with well-defined geographic patterns with some indication of diurnal patterns in spring and summer. 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Hudson, 2014: Seamless precipitation prediction skill in the tropics and extratropics from a global model. Mon. Wea. Rev., 142, 1556- 1569, doi:10.1175/MWR-D-13-00222.1. OWEN A. KELLEY Precipitation Processing System, NASA Goddard Space Flight Center, Greenbelt, Maryland, and Center for Earth Observing and Space Research, George Mason University, Fairfax, Virginia (Manuscript received 21 February 2014, in final form 5 June 2014) Corresponding author address: Owen A. Kelley, NASA Goddard Space Flight Center, Code 610.2, Greenbelt, MD 20771. E-mail: [email protected] (c) 2014 American Meteorological Society |