3.1. Spatial Variability of the Emissivities and Relation with the Lithology
 The spatial variability of the emissivities and their relation to the lithology are illustrated here by studying the 9.3 μm, 10.8 μm, and the 37 GHz emissivities for V and H polarizations. From the available emissivities in the data set of Seemann et al. , the 9.3 and 10.8 μm channels are selected due to their expected sensitivity to the presence of siliceous and carbonate rocks, as described in section 2.1 and illustrated in Figure 1. In the microwave, narrowband absorption features are not expected and are not visible in the available SSM/I-derived emissivity maps between 19 and 85 GHz (rather similar spatial structures are observed at all frequencies). The choice of the 37 GHz emissivities is motivated by a compromise between spatial resolution (degraded spatial resolution at lower frequency) and potential contamination by atmospheric water vapor and clouds (increased contamination at higher frequencies) [Prigent et al., 1997].
 Maps of the 2003 yearly averaged V and H emissivities at 37 GHz, along with the polarization difference (V-H), over northern Africa and the Arabian Peninsula, are presented in Figure 3. The main features are very stable over long time periods (several years of data have been examined). Low microwave emissivities observed over coastal regions are due to the presence of water in the coastal pixels. Low values can also be observed over the south of the Arabian Peninsula and in northeast Egypt, which have shown correlation with the distribution of outcrops with large proportion of carbonate rocks [Prigent et al., 2005b]. Higher V emissivities can be observed in regions with a larger presence of sand dunes. This is related to an emission of microwave radiation from deeper soil layers and an associated slight overestimation in the emissivities when deriving them with the infrared skin surface temperature [Prigent et al., 1999]. On the map of the emissivity polarization difference, smooth bare soils have a quasi-specular reflection, producing high polarization emissivity differences around the SSM/I 53° incidence angle. When the terrain gets rougher or vegetation appears (below ∼15°N), surface scattering causes the emissivity in horizontal polarization to increase and the polarization difference to decrease. As a consequence, mountainous regions (e.g., Tibesti, Ahaggar, and Hajar) appear with a low polarization difference on the map, whereas flat areas are characterized by high polarization differences. Maps of the 9.3 μm and 10.8 μm yearly averaged emissivities are also presented in Figure 3. At 9.3 μm low emissivity values are related to expected absorption features from silicate minerals and correspond well with the high emissivity values at 37 GHz V associated with the presence of sand dunes. The 10.8 μm emissivity has a limited amplitude of variation but present very clear spatial structures. There is a significant spatial agreement between the low emissivity values at 10.8 μm and the low emissivities at 37 GHz H.
Figure 3. Spatial distributions of yearly averaged emissivities (2003). From top to bottom: (1) 37 GHz H; (2) 37 GHz V; (3) 37 GHz difference (V-H); (4) 9.3 μm; (5) 10.8 μm.
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 Comparing these maps with the lithology map of Figure 2 allows a qualitative analysis of the emissivities in relation with the outcrops. In general, there is a good correspondence between areas with outcrops composed of siliceous rocks (sand dunes) and the low 9.3 μm and the high 37 GHz V emissivities, though it should be mentioned again that the sensitivity in the microwave emissivities is not related to a sensitivity to the lithology but to a microwave emission from deeper soil layers. The low 10.8 μm and 37 GHz H emissivities also appear in areas where carbonate minerals are present. However, the agreement with the carbonate outcrops does not seem as evident as with the silicates, especially in western Africa. If we zoom over some specific regions, the link between emissivities and lithology is certainly apparent. An example is given in Figure 4, where a cross section over the Arabian Peninsula (∼20° latitude) is plotted. The emissivities have been normalized (removing the mean value and dividing by standard deviation) to help the comparison. The changes in the emissivities reasonably follow the changes in the exposed lithology derived from the lithology map of Figure 2.
Figure 4. Example of latitudinal cross section over the Arabian Peninsula (20.25°N, 45°E–57°E) for September 2003. The normalized emissivities are plotted at 9.3 μm (green), 10.8 μm (red), 37 GHz V (blue), and 37 GHz H (black). The outcrop for each pixel is given by the different black symbols. The vertical dashed lines indicate the main changes in the lithology.
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 Histograms of the emissivities for different outcrops in comparison with the histograms of the global emissivities are presented in Figure 5 to highlight the sensitivity of the different emissivities to the silicate and carbonate outcrops. The histograms confirm the observed low emissivity values for carbonates (37 GHz H and 10.8 μm) and silicates (9.3 μm) and show that the lithology types can be well identified. The width of the distributions indicates significant variability within a type, and the overlap with the other histograms confirms that misclassifications can certainly happen. This is anticipated: no perfect matching from a single observation at these large scales can be expected due to the large spatial resolutions, the emissivity errors, the difficulty to interpret the geological maps, or the sensitivity of the observations to other surface parameters. Using multi-observations (i.e., combining microwave and infrared emissivities) could be used to reduce the sensitivity to some of these errors. This will be discussed further in section 3.3.
Figure 5. Normalized histograms of the (a) 37 GHz H, (b) 37 GHz V, (c) 9.3 μm, and (d) 10.8 μm emissivities for different outcrops. The histograms for carbonate rocks (red), loose siliceous rocks (green), and indurated siliceous rocks (blue) are displayed over Northern Africa and the Arabian Peninsula. The histograms of the emissivities are also plotted for the whole globe (black). The numbers correspond to the mean emissivity and its standard deviation (in brackets).
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3.2. Characterization of the Relation Between Lithology and Emissivities
 The relation between emissivities and lithology is statistically characterized here. Table 1 shows the mean and standard deviation of the emissivities for the different outcrop types. At 9.3 μm the lowest mean corresponds to the loose siliceous rocks, the next four lower means also have a siliceous component. At 10.8 μm the carbonate rocks have a smaller emissivity than the siliceous sediments, but the differences in the means are much smaller than at 9.3 μm. At 37 GHz V the carbonate rocks have a lower emissivity than the siliceous sediments, and the same is true at 37 GHz H. The regions with evaporites in Tunisia and Algeria have very low emissivities at 37 GHz H, but the signals can also originate from the presence of standing water during a large part of the year in these shatts and sabkhas.
Table 1. Mean and Standard Deviation (in Brackets) of Infrared and Microwave Emissivities by Outcrop Typea,b
|Group||9.3 μm||10.8 μm||37 GHz V||37 GHz H||Pixels|
 The statistics presented in Table 1 are also used for an analysis of variance (ANOVA). This analysis tries to estimate what part of the observed variability can be assigned to the existence of different outcrops (variance between outcrop type), and what part can be assigned to all other factors contributing to the observed variability (within outcrop type). For each of the four emissivities considered the analysis is carried out by calculating (1) the sum of squares of the deviations of the emissivities around the overall mean (measure of the total variability in the data set), (2) the sum of squares of the deviations of the emissivities for each outcrop type around their respective outcrop means (measure of the variability within different outcrops), and (3) the sum of squares of the deviations of the outcrop mean emissivities from the overall mean (measure of the variability between different outcrops). The sum of squares are then expressed as a variance normalized by their respective degrees of freedom. The variances are given in Table 2. The results show that a large part of the variability in the emissivities (more than 50% for 9.3 μm and ∼40% for the other frequencies) can be explained by the lithology. The other parts of the variance are to be attributed to other surface parameters affecting the observations (e.g., roughness), to errors in the geological interpretation mapping, or to uncertainties in the satellite products.
Table 2. ANOVA Table for Infrared and Microwave Emissivitiesa
|9.3 μm||Between outcrop type||64.12 (50.4)||1544.4|
| ||Within outcrop type||63.18 (49.6)||(p < 0.01)|
|10.8 μm||Between outcrop type||0.1857 (38.1)||933.2|
| ||Within outcrop type||0.302 (61.9)||(p < 0.01)|
|37 GHz V||Between outcrop type||4.057 (37.7)||918.2|
| ||Within outcrop type||6.720 (62.3)||(p < 0.01)|
|37 GHz H||Between outcrop type||7.83 (42.3)||1146.6|
| ||Within outcrop type||10.70 (57.7)||(p < 0.01)|
 The partitioning of variance is also used to carry out an F test. Under the hypothesis that the lithology is not exerting any control over the emissivities (the null hypothesis), the ratio of the “between” and “within” variances (F ratio) follows an F distribution. Table 2 shows the F ratios for the four emissivities. The ratios are much larger than 1, and the p values obtained assuming that the null hypothesis is true are well below 0.01, allowing to reject the null hypothesis at the 1% significance level. These results suggest that the lithology exerts a notable control on the emissivities. This is consistent with a similar analysis at smaller scales by Zhou et al. .
3.3. Potential Mapping of Large-Scale Lithology From the Emissivities
 The potential of the emissivities for a large-scale mapping of major lithology features is studied by deriving a lithology classification of the area using the satellite observations. Different supervised and unsupervised classification approaches exist [e.g., Lu and Weng, 2007]. The technique adopted here is an unsupervised clustering technique called K means [e.g., Celeux et al., 1989]. It partitions n observations into k clusters in which each observation belongs to the cluster with the nearest mean. It is an efficient and fast method when faced with a large classification matrix (as in our case), but the nature of the derived classes can be difficult to interpret, and a postclassification phase is often needed to regroup the initial classes. Supervised classifications (targeting to the same final classes obtained from the unsupervised classification) were also tested (results not presented), with similar results. This suggests that for this specific study the nature of the data is a more limiting factor than the ability of the classification technique.
 Previous to the classification, the 9.3 μm, 10.8 μm, and the 37 GHz V and H emissivities are first normalized (zero mean, unity standard deviation, as in Figure 4) and then organized in an emissivity matrix (4 emissivities × n geographical pixels). The K means algorithm is then applied over the emissivity matrix. Different numbers of clusters were tested, with satisfactory results obtained with 20 clusters. The geographical patterns of the derived classes can be observed in Figure 6. Some of the classes can be easily related to specific outcrops (e.g., class 9 with loose siliceous rocks and class 4 with carbonate rocks), but for other classes the interpretation is more difficult. For instance, the classification suggests that we cannot clearly separate the igneous rocks from the metamorphic rocks of the Precambrian shield, and they will be regrouped under a common class. To aid the interpretation of the derived outcrop map, all classes are then regrouped into five new classes in a postclassification phase, where the new classes are established by grouping together the original classes having similar characteristics (as described in the lithology map). The new classes identify the presence of (R1) siliceous rocks, (R2) carbonate rocks, (R3) metamorphic and igneous rocks, (R4) mixture, and (R5) vegetation. The map of the new classes are plotted in Figure 6.
Figure 6. Classes derived from the K means nonsupervised classification applied to the annual mean emissivities. (a) The first 10 classes and (b) the remaining 10 classes. (c) The grouping of the original 20 classes into five new classes: (1) siliceous rocks (R1 = C1, C2, C9); (2) carbonate rocks (R2 = C4, C11, C17, C20); (3) metamorphic and igneous rocks (R3 = C6, C12); (4) mixture (R4 = C7, C8, C13, C14); (5) vegetation (R5 = C3, C5, C10, C15, C16, C18, C19). See the text for more details.
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 An evaluation of the classification is presented in Table 3. The table lists the number of pixels of a given outcrop type interpreted by the K means classification as siliceous rocks (R1), carbonate rocks (R2), and metamorphic and igneous rocks (R3). In general, there is a good correspondence between the K means new classes and the outcrops identified in the lithology map. For the carbonate rocks of L1, the largest Pixel Number (PN) is in class R2. L2 is a mixture of carbonate, siliceous, and evaporite rocks (in decreasing order of presence within the mixture), and the PN in R2 > PN in R1 > PN in R3, in accordance with the expected presence of carbonate, siliceous, and metamorphic rocks in the mixture. The loose siliceous rocks of L3 have a very large PN within R1. The indurated siliceous rocks of L4 seem more difficult to classify (PN in R1 > PN in R3 > PN in R2 but not with large differences as for L3). L5, L6, and L7 are mixtures having a large percentage of siliceous rocks, and the largest PN corresponds to R1. The Precambrian shield, granite, and basalt of L8, L9, and L10 have the largest PN in their expected class, that is, R3.
Table 3. Number of Pixels From Some of the Original Lithology Types Classified Within the K means Regrouped Classesa
|L1 Carbonate Rocks||130||588||46|
|L2 Carbonate Siliceous and Evaporite Rocks||310||637||245|
|L3 Loose Siliceous Rocks||2592||206||123|
|L4 Indurated Siliceous Rocks||312||210||229|
|L5 Siliceous Argillaceous and Evaporite Rocks||99||52||91|
|L6 Siliceous Argillaceous and Carbonate Rocks||732||96||117|
|L7 Siliceous and Argillaceous Rocks||172||42||26|
|L8 Precambrian Shield||121||183||911|
 An attempt to derive classification scores follows. For the siliceous rocks, the score is computed as the percentage of pixels in lithology types L3, L4, and L6 classified as R1; for carbonate rocks, the percentage of pixels in L1 and L2 identified as R2; and for metamorphic and igneous rocks, the percentage of pixels in L8, L9, and L10 classified as R3. The respective classification scores are given at the bottom of Table 3. The figures indicate that approximately one of two pixels is well classified. Taking into account the limitations in the satellite observations and in the lithology mapping, this result is encouraging. The spatial resolution of the satellite data, their processing errors, and the sensitivity of the observations to other surface parameters hamper a more accurate mapping. At these large scales, no official lithology map exists and the methodology we adopted to derive one is not perfect. Uncertainties come from the ambiguities in the age of the geological formations, the precise composition of the sedimentary rocks, the geological structure in the lithostratigraphic columns, the fact that the lithostratigraphic information has been geographically extrapolated, and the necessary spatial integration of the lithology information into a pixel of a given area. Moreover, the geological structures are not perfectly mapped at these large scales. As an example, two sections of the USGS geological map (used to derive the lithology map in section 2.3) are plotted in Figure 7 together with the corresponding sections from a different map (the “Bureau de Recherches Géologiques et Minières” (BRGM) SIG Afrique geological map). The regions correspond to Northwest and Northeast Africa. Relatively large differences in the mapped geological structures can be found in some regions. For instance, less geological details can be observed in the BRGM map over Northeast Africa between Egypt and Libya (large light yellow region), compared with the USGS map. These features are also well captured by our satellite-derived map (Figure 6) but are absent on the BRGM map that is devoted to mineral exploration and much more focused on ore-rich shields. These structures are actually related to the carbonate outcrops that are already visible on the raw emissivity map at 37 GHz H (emissivity values of ∼0.7 at the top panel in Figure 3). In the Precambrian shields over Northwest Africa, it is now the USGS map (large dark brown areas) that shows much less details, compared with the BRGM map. These differences possibly reflect the main objectives of the two geological maps. The satellite systematic observations with global coverage provide a consistent and objective analysis of the large areas, regardless of specific local studies or particular interest for a given region.
Figure 7. Example of large-scale available geological maps. (a and c) Regions from the USGS map; (b and d) the same regions from the BRGM map. Each map uses a different color map to represent the different geological periods (legends not given). Northwest Africa is presented in Figures 7a and 7c and Northeast Africa in Figures 7b and 7d. See the text for more details.
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 Taking into account the uncertainties, both in the satellite observations and in the lithology, this exercise shows that a combined exploitation of the infrared and microwave emissivities can help characterize arid regions, as a complement to more traditional methods and observations at other wavelengths. Note that the low spatial resolution of the present microwave observations from space limits their potential to large-scale applications. The combined exploitation is particularly useful at large scales, where the downgraded spatial resolution (compared with only using the infrared emissivities) is not a drawback. In particular, we argue that in order to better specify emissivities in GCMs and NWP schemes the satellite-derived data is a direct and efficient way to specify the surface lithology and to complement the derivation of relevant surface properties from existing geological maps. In addition, this technique can also be very valuable for the mapping of inaccessible regions, e.g., for planetology exploration.