The study area is limited to the north part of Morocco covered by NOAA-AVHRR images (Figure 1) and covers all agricultural areas of 46 provinces of the country. It includes the main agro-ecological zones of Morocco except Saharan zone where agricultural activities concerns small plots in oases. The climate of the studied area is characterized by strong climatological gradients from south to north and from west to east. Mean annual air temperatures vary between 12°C and 14°C in winter and 22°C and 24°C in summer, over the period 1950-2000. Season’s total rainfall (September till April) varies between less than 150 mm in the southern desert and 1000 mm in the northern Morocco (Balaghi et al. 2012). The region of interest can be subdivided into three main regions, which are relatively homogeneous in term of rainfall (Knippertz et al. 2003): (1) the Atlantic region, including North and West of Morocco; (2) the Mediterranean region that includes the North eastern part of the country and, (3) the Atlas mountains. The climatic and topographic differences between these three regions strongly determine agriculture in each zone. As shown in Figure 1, the most important part of agricultural area of the country is concentrated in the first and the second regions.
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1.2. Data
– Remote sensing
In this study we used a time series of 349 free cloud NOAA-AVHRR images of land surface temperature. These images were acquired potentially every ten days between 1995 and 2012. The decadal distribution of these images is presented in Figure 2. As shown in this figure, the images are well distributed over all seasons. The spatial resolution was 1km² and each image covered the whole studied area. Geometric and atmospheric corrections were performed by The Flemish Institute for Technological Research in Belgium (VITO) for all images (Eerens et al. 2009).
The digital land cover map of 1Km spatial resolution described in Vancutsem et al. (2013) was used as a mask for extracting land surface temperature sub-images, covering only agricultural area studied zone. This area is manly dominated by cereal and rainfed crops. Finally; a digital terrain model of 90m spatial resolution was explored to discuss the obtained results.
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– Climatic data
Gridded daily maximum (Tmax) and average (Tavg) air temperatures were provided by the Direction of National Meteorology for the whole country. These data resulted from a spatial interpolation technique from CGMS-MAROC, (Crop Growth Monitoring System – Maroc, http://www.cgms-maroc.ma/), which is an institutionally distributed system which involves the Moroccan institutes like DNM, the National Institute for Agricultural Research (INRA) and the Department of Statistics (De Wit et al. 2014). The meteorological data is interpolated towards the centers of a regular climatic Grid (9.14kmX9.14km). The interpolation is executed in two steps: first the selection of suitable meteorological stations to determine representative meteorological conditions for a specific climatic grid cell. Second, a simple average is calculated for most of the meteorological parameters, with a correction for the altitude difference between the station and grid cell centre in case of temperatures (De Wit et al. 2014).
Finally, the surface temperature of agricultural areas for each province was extracted from the satellite imagery by superimposing administrative provincial boundaries and land cover mask.
1.3. Process data analysis
The approach adopted in this study is illustrated in Figure 3. Firstly, daily mean surface temperature (Ts) derived from NOAA-AVHRR images was compared with measured maximum (Tmax) and average (Tavg) air temperatures for nine meteorological stations well spatially distributed in the study area (see Figure 1). The objective of this part was to verify the accuracy of the relationship between remotely sensed surface temperature and in-situ measured air temperature before extending the study to the provincial scale.
Secondly, remotely sensed surface temperature was compared to gridded near surface air temperature derived from the national meteorological stations network for agricultural zones of 46 provinces of Morocco. The objective of this part was to derive near surface air temperature and maximum air temperature with much higher spatial resolution. To do so, the land cover mask and the official provincial boundaries were superimposed spatially to retain only agricultural areas. The time series of NOAA-AVHRR satellite images were then used to compute the average land surface temperature of all ‘agricultural’ pixels for each province. Finally, these surface temperatures were compared to the maximum and average interpolated air temperatures (see climatic data section). Linear relationships, as that described by the equation (1) below, with different slopes a and intersections b values were obtained between these two variables.
Tairi = a Tsi +b. equation (1)
Where Tairi refers to estimated maximum or average air temperature and Tsi corresponds to the remotely sensed surface temperature at the image acquisition date i.
At this stage, we note that we avoided extracting surface and air temperatures only for pixels located in a limited window surrounding each weather station because about 43% of available synoptic weather stations were located in airports or near urban zones. Since we are interesting only to agricultural areas, we assumed that such approach could bias the results.
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In addition to linear regression coefficients (slope, offset), two statistical indices have been calculated to analyze relationships for each province. These indices were the coefficient of determination (R²), the root mean square error (RMSE) and the mean absolute error (MAE). The formulas used to compute these indices are indicated below.
RMSE = [∑ni=1 (Tobsi – Tsimi) ²/n]0.5 equation (2)
MAE=1/n [∑ni=1 | Tobsi-Tsimi |] equation (3)
Tobsi refers to observed maximum or average air temperature and Tsimi corresponds to maximum or average predicted air temperature from remotely sensed surface temperature at the image acquisition date i while n is the number of available images.
According to Willmott and Matsuura (2005), the MAE is the most natural and unambiguous measure of average error magnitude. In addition, the MAE is preferred to evaluate regression quality because it’s less sensitive to outliers than the RMSE (Vogt et al. 1997).
To evaluate the accuracy of the regression models between surface temperatures and maximum air temperature, on the one hand, and average air temperature, on the other hand, the K-fold cross validation (K-fold CV) approach (Cassel 2007) was used. Cross-validation is a resampling method, which allows a different approach to model evaluation. This approach uses K replicate samples of observation data, builds model with (K-1)/K of data and tests with the remaining 1/k. K-fold CV is an effective and widely used method. In our case study, one third of each data set of surface temperature and maximum or average air temperature of each province was randomly chosen as the training sample and the remaining two thirds of the data set were used as the validation sample. This operation was repeated five times for each studied province to assure the stability of the relationships. Such process allowed replicating the number of values of each original data set to reach 580 values instead of 348 ones. Then, new statistical indices R² and RMSE values (noted bellow R²-K-fold and RMSE-K-fold) were recalculated for each new data set. Finally, the new R²-K-fold and RMSE-K-fold and the original R² and RMSE values were compared to verify the stability of the original relationships between surface temperature and maximum and average air temperatures for each province.