Figure 4 represents an example of the relationships between surface temperature derived from NOAA-AVHRR images and air temperature discussed in this study. The figure compares remotely sensed surface temperature and maximal air temperature (scatterplot on the left) and average air temperature (scatterplot on the right) measured by the meteorological station of Oujda province. The lines are included in the scatterplots to illustrate divergence from a 1:1 relationship. The statistical indices R² and RMSE are also inserted on the figures. Table 1 summarizes the values of obtained statistical indices when comparing surface temperature and maximal and average air temperatures for the nine selected weather stations. For all stations, surface temperature is generally hotter than maximal air temperature, and thus average air temperature. Such difference is due to the fact that remotely sensed temperature takes into account for a radiative measurement taken at the surface of the earth where thermal energy is most concentrated while air temperature is measured at 1.5 m or 2 m above the ground (Jin and Dickinson 2010).
[Please, insert fig4 about here]
The values presented in table 1 proved the good relationships between remotely sensed surface temperature and air temperature. The coefficient of determination R² varied between 0.60 and 0.76 for the correlations between remotely sensed temperature Ts and maximum air temperature (Tmax), and between 0.67 and 0.80 when comparing Ts and average air temperature (Tavg). The root mean square error varied between 2.5°C and 4.6°C for Ts versus Tmax and between 2.2°C and 3.8°C for Ts versus Tavg. Such results are in good concordance with that obtained previously by Prince et al. (1998), Lakshmi and Susskind (2000) and Hengl et al. (2012).
The data in table 1 showed also that the correlations are better when comparing surface temperature with average air temperature. The average values of R² and RMSE for the nine selected stations were 0.75 and 3.1°C for Ts versus Tavg and 0.69 and 3.8°C for Ts versus Tmax, respectively.
[Please, insert table 1 about here]
III-2- Comparison between remotely sensed surface temperature and gridded near surface air temperature of agricultural areas
a- Results of the regression
Figure 5 compared the values of the coefficient of determination R² obtained when comparing average (Tavg) and maximum (Tmax) air temperatures and surface temperatures (Ts) derived from AVHRR-NOAA images for all studied provinces. As obtained in the first section, a quick look at the shape of the curves presented in Figure 5 showed that obtained correlations were slightly better for Tavg versus Ts than for Tmax versus Ts. Indeed, the coefficients of determination R² were greater than 0.70 in more than 80% of studied provinces when comparing average air temperature and surface temperature while its exceeded this value only for 59% of provinces when comparing maximum air temperature and surface temperature.
In general, Figure 5 showed high correlations between measured air temperatures and surface temperatures for all provinces except for the four provinces of Inzegane, Agadir, Essaouira and Safi characterized by R² values lower than 0.5. Excluding these four provinces, that will be separately analyzed below, the coefficients of determination R² range from 0.55 to 0.84, with an average value of 0.71 for Tmax versus Ts, and from 0.66 to 0.88, with an average value of 0.76 for Tavg versus Ts.
Concerning the four extreme provinces of Inzegane, Agadir, Essaouira and Safi, Table 2 summarized the values of their R², RSME and MAE errors. The coefficients of determination R² range from 0.17 to 0.49 for Tmax versus Ts, and from 0.29 to 0.63 for Tavg versus Ts. Their RMSE values vary between 2.7°C and 4.2°C for Tmax versus Ts and between 2.4°C and 3.5°C Tavg versus Ts. A deeper analysis showed that the main cities of theses provinces where the weather stations were installed are coastal cities (see map in Figure 1). The weather station of the Inezagane province, where the error was the largest, is a maritime station. The measures of air temperatures recorded by this station would distort the temperature of the agricultural area of the whole province. The same explanation would be valid for the weather station of Agadir province which is installed in Agadir airport, located at about 20km from the Atlantic Ocean. Concerning Essaouira, this city is also located on the Atlantic coast at about 170km from Agadir. It’s renowned for its windsurfing and kitesurfing because of the powerful wind trade that blow almost constantly throughout the year. Such conditions would be the origin of the poor relationship between air temperature and remotely sensed surface temperature. The city of Safi, located at about 120km from Essaouira, undergoes the same oceanic effects as that of the last city. Thus, the representatively of weather stations installed in the previous four cities would be insufficient to cover the whole areas of their respective provinces. These explanations are coherent with the fact that, in addition to the land cover, the distance to the coast may significantly influence the relationship between air and surface temperatures (Vogt et al. 1997).
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[Please, insert table 2 about here]
In what follow, the four problematic provinces of Inezagane, Agadir, Safi and Essaouira discussed above have been excluded from the analysis.
Figure 6 presents the values of the errors RMSE (Figure 6a) and MAE (Figure 6b) between measured average and maximum air temperatures (Tavg and Tmax) and surface temperatures derived from NOAA-AVHRR images obtained for the 42 retained studied provinces. The values of these errors were rearranged in the order of increasing altitude above sea level of studied provinces. As observed in the case of coefficient of determinations R², the errors values are lower for Tavg versus Ts than for Tmax versus Ts. That means that, in this case study, surface temperature derived from NOAA-AVHRR images is more correlated to average than maximum air temperature. For Tmax versus Ts, the RMSE values vary between 2.5°C and 4.6°C with an average value of 3.6°C. The MAE values fluctuate between 2°C and 3.5°C with an average value of 2.8°C. Concerning Tavg versus Ts, the RMSE values vary between 2.3°C and 3.8°C with an average value of 3.0°C. The MAE values vary between 1.8°C and 2.9°C with an average value of 2.3°C. These results are in a good concordance with those obtained by Vogt et al. (1997) and by Recondo and Pérez-Morandeira (2002) in Andalusia and in the region of Asturia in Spain, by Shen and Leptoukh (2011) in central and eastern Eurasia and by Hengl et al. (2012) in Croatia.
Figure 6 showed also that the values of the errors increased progressively with the altitude. This increase can be explained by incertitude of both interpolated air temperature and remotely sensed surface temperature. On the one hand, the density of weather stations is the lowest in mountainous zones of studied area, and thus, interpolated values of air temperature will be less accurate compared to that of plain area. This problem has been widely discussed in the literature (e.g. (Ishida and Kawashima 1993; Söderström and Magnusson 1995). On the other hand, remotely sensed signal is more easily stopped by the reliefs in the high latitude regions because the angle ground-satellite is lower and the shaded area became larger. This phenomenon very known in remote sensing field makes the value of a pixel in mountain area not as reliable as in a plain area (Dedieu 1989; Proy et al. 1989). Despite these problems, the order of magnitude of the errors obtained was in good agreement with that encountered the literature (e.g. (Ishida and Kawashima 1993; Recondo and Pérez-Morandeira 2002; Shen and Leptoukh 2011; Vogt et al. 1997).
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b- Analysis of the relationships between air temperature and surface temperature as a function of altitude
One of the main strengths of this study was that it was conducted on a large scale (scale of the country). This allowed to cover a large area (about 328311km²) and to include all the agroecological zones of the Morocco. The maximal altitude of studied provinces varied from 200 to 4100m above sea. The analysis of resulted relationships between air and surface temperatures showed the existence of a direct relation between the slopes and offsets (parameters a and b in equation 1), in one hand, and the altitude of studied provinces, in other hand. Figure 7 shows the variation of the parameters a and b as a function of the median altitude of each province. Presented plots showed the existence of almost linear relations between the slopes and the offsets of obtained regression equations between air and remotely surface temperature. The correlation was positive for the slopes versus median altitudes, with a value of R² superior to 0.60, while it was negative for the offset versus median altitudes, with R² superior to 0.70.
For the linear correlations between maximal air and surface temperature, the values of the slope a varied between 0.295 and 0.708 with an average value of 0.493 and the offset b varied between -2.911°C and 11.957°C with an average value of 6.104°C. Concerning average air temperature versus surface temperature, the values of the slope a varied between 0.317 and 0.669 with an average value of 0.456 and the offset b varied between -8.982°C and 1.076°C with an average value of 1.081°C. Mildrexler et al. (2011), who studied the relation between remotely sensed surface temperature and maximum air temperature as a function of land cover, reported for croplands the value of 0.5398 and 9.8453°C for parameters a and b, respectively.
Figure 7 showed that the slope values increased with the median altitudes and one can distinguish between two distinct groups of provinces: the first group is characterized by median altitudes inferior to 1600m while the median altitudes of the second group fluctuated between 2000 and 3000m. This could be related to the crop land difference between plain areas and mountainous zones of studied area. Indeed, plain areas of Morocco are dominated by annul crop (cereals, leguminous and vegetable crops) while fruit trees (rosaceae, carob and olive) are principally located in mountainous regions. Such explanation is in a good agreement with the previous results obtained by Mildrexler et al. (2011) and Shen and Leptoukh (2011) that confirmed that the slope of the linear regression between maximal air and remotely sensed surface temperatures is closely associated with the land cover type. The authors found that the value of slope is relatively low in barren land, while the value is higher in forest or croplands.
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III-3- Stability tests of the relationships between air and remotely sensed surface temperatures
Figure 8 compared the statistical indices R²-K-fold and RMSE-K-fold values and the original values of R² and RMSE between surface temperature and maximum air temperature (Figure 8a, b), in the one hand, and between surface temperature and average air temperature (Figure 8c, d), on the other hand, for the 42 retained provinces. These figures showed good linear correlations between statistical indices obtained when using the original data set and that obtained after sampling this data set using K-fold method. The values of R² were 0.68 and 0.93 when comparing the coefficient of determination values of surface temperature versus maximum air temperature and surface temperature versus average air temperature, respectively. Concerning the RMSE, The values of R² were 0.78 and 0.91 for surface temperature versus maximum air temperature and for surface temperature versus average air temperature, respectively. These results proved the high stability of the relationships discussed in previous sections, and consequently, it is possible to retrieve maximum and average air temperatures from surface temperature retrieved from NOAA-AHRR images.
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III-4- Spatial analysis of the relationships between surface and air temperatures
First of all, we present the results obtained from comparison between surface temperature derived from NOAA-AVHRR images and interpolated air temperatures for three provinces representing three different agro-climatic zones of Morocco. Such presentation could give the reader an idea about the relationships obtained for all studied provinces. Figure 9 shows six scatter plots between remotely sensed surface temperature and maximum and average air temperatures of agricultural areas of the three selected provinces. The province of Tangier is located in the extreme north west of Morocco (see map in Figure 1) and is characterized by homogenous annual rainfall distribution and a relatively flat topography. The province of Errachidia is located in the south eastern of the country. It is characterized by a desertic climate and flat topography. The province of Ifrane is located in the middle Atlas Mountains at about 2000 m above de the sea.
The six scatter plots presented in Figure 9 showed high correlations between the two studied variables with R² varying between 0.70 and 0.84 and RMSE between 2.3°C and 4.2°C for the three selected provinces. As cited before, statistical indices obtained for maximum and average air temperatures showed also that the correlations were slightly better for average rather than for maximum air temperature.
Another aspect that appeared interesting to discuss in this study was the variability in the quality of correlations between provinces. In this example, the correlation was strong for the province of Tangier, moderate for the province or Errachidia and was worst for the province of Ifrane. However, the highest error was obtained for the province of Ifrane located in a mountainous area and the lowest error was obtained. For Tangier and Errahidia provinces, this result could be related mainly to the distribution of weather stations which is likely not representative at provincial level to capture provincial climate variability due to topography or other. These two provinces were each covered by one weather station even if the area of Errachidia province is about 38955 km² while the area of Tangier province is only 914km². Concerning Ifrane province, the topography could be the main factor affecting the relationship between air and surface temperatures.
To present the variability of obtained relationship for all provinces, Figure 10 showed the spatial distribution of RMSE values between surface temperature and maximum and average air temperature.
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The map presented in Figure 10. showed the spatial variation of RMSE error between interpolated average air temperature and surface temperature derived from NOAA-AVHRR images. In this figure, the location of weather stations was indicated. To give an idea about the topography of studied area, the altitude was also presented. The figure showed that the lowest values of RMSE were obtained for the provinces located in the flat zones along the Atlantic and Mediterranean Coasts and these values increased with the altitude (red zone in the map). When analyzing the distribution of weather stations, it appeared that their density is more representative in flat areas than in mountainous zones. However, it is known that accuracy of spatially interpolated air temperatures is strongly correlated to the density of weather stations and topography (Marquı́nez et al. 2003). This is confirmed through the observation of varying accuracies of interpolated values of maximum and average air temperatures between flat and mountainous zones. For this case study, the difference isn’t so important since the most important cropped areas we are interested in are located in flat zone of the country (see Figure 1).
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IV. Conclusions, recommendations and perspectives
The main goal of this paper is to propose a simple method to derive average and maximum air temperatures from surface temperature measured by NOAA-AVHRR sensor for all agricultural areas of Morocco. Firstly, remotely surface temperature was compared with measured maximum and average air temperature of nine meteorological stations between 1995 and 2012. This first step showed the existence of good linear correlations between remotely sensed surface temperature and measured stations air temperatures. The coefficient of determination R² varied between 0.60 and 0.76 for Ts versus Tmax, and between 0.67 and 0.80 for Ts versus Tavg. The root mean square error (RMSE) varied between 2.5°C and 4.6°C for Ts versus Tmax and between 2.2°C and 3.8°C for Ts versus Tavg. The accuracy of obtained results is in good concordance with that obtained by previous studies (Prince et al. 1998); (Lakshmi and Susskind 2000); (Hengl et al. 2012).
Secondly, the two variables, maximum and average air temperatures Tmax and Tavg, and surface temperature Ts were compared for agricultural areas of 46 provinces of Morocco. As proved by many studies in the literature in other countries over the world, good linear relationships where obtained between average and maximum air temperatures and surface temperature retrieved from NOAA-AVHRR data for each province. The slopes and the offsets of obtained regression models were highly correlated with median altitude of studied provinces. The K-fold cross validation method was used and confirmed the stability of obtained regression models.
For 42 provinces, the average value of the coefficients of determination R² was 0.71 for Tmax versus Ts and 0.76 for Tavg versus Ts. The average values of the RMSE and the MAE were 3.6°C and for Tmax versus Ts and 3.0°C and 2.3°C for Tavg versus Ts, respectively. Such results were in a good concordance with those discussed in the literature (ex. (Recondo and Pérez-Morandeira 2002; Shen and Leptoukh 2011; Vogt et al. 1997).
However, the accuracy of these relationships depended mainly on the topography and the density of weather stations and their representativeness for the overall landscape. For a given point of a province, air temperature is often obtained by interpolating the temperature values measured by the nearest weather stations. When the density of weather stations is weak, interpolated value can be incorrect. That is also true when the topography changes from flat area to mountainous zones. That was observed in this case study where the lowest errors between air and surface temperatures were obtained in plain zones.
The worst relationships between air and remotely sensed temperatures were obtained for the four provinces of Inezagane, Agadir, Safi and Essaouria located in the Atlantic Ocean coast of Morocco. The values of the R² ranged between 0.17 and 0.49 with an average value of 0.39. The value of the MAE ranged from 2.7°C and 4.2°C, with an average value of 3.4°C. The location of weather stations of these provinces could be the main problem affecting the quality of interpolated air temperature. Indeed, the climate of theses provinces is known by powerful winds and thus, one whether station could not be enough to represent the variability of air temperature over the whole province. For this reason, it is considered important to improve the density of weather stations in these provinces in particular to improve the quality of air temperature interpolation. Such recommendation is also valid for mountainous zone even if the topography can also affect the quality of remotely sensed surface temperature.
This study is a preliminary attempt to retrieve air temperature from remotely sensed surface temperature over agricultural areas of Morocco. Obtained results were encouraging despite the multiple sources of errors related to different spatial data sources exploration. For further work, we intend to analyze the seasonality effects on obtained relationships between surface and air temperatures.