Estimation of Daily Mean Air Temperature from Modis Lst in Alpine Areas

This study is aimed at demonstrating the feasibility of the MODIS Land Surface Temperature (LST) product as a source for calculating spatially distributed daily mean air temperature to be used as input for hydrological or environmental models. The test area is located in the Italian Alpine area. The proposed procedure solves, by empirical approaches, the problem of relating LST to the Air Temperature (Tair) and instantaneous Tair values to daily mean values, exploiting ground data weather station measurements as a reference. The relationship between LST and Tair is determined by correlation analysis and equation generalisation for spatial distribution. The extrapolation of daily mean values of Tair from instantaneous values is addressed again by correlation analyses taking into account the altitude variability and exploiting historical series. Validation was accomplished by accuracy assessment procedures both punctual and spatially distributed, the latter performed by comparison with the Inverse Distance Weighting (IDW) interpolation method. The proposed methodology produced satisfactory results as related to the objective: The daily mean air temperatures derived by LST showing an overall RMSE of 1.89°C, and slightly outperforms the interpolation method used as comparison. INTRODUCTION The air temperature near the Earth’s surface is a key variable to describe energy and water cycles of the Earth-atmosphere system and its measurement is necessary to run several snowmelt hydrological (HBV (1); SRM (2)) and environmental models. The measurement of this variable by meteorological stations, however, provides only punctual values, whereas most models require spatially distributed variables and parameters to evaluate physical processes with an adequate spatial scale. In most cases, an interpolation of point site data is carried out only by using a vertical temperature lapse rate because of the strong relationship between the air temperature and the elevation. But, when considering a regional scale, it’s necessary also to refer to spatial interpolation methods, allowing for land cover and topographic effect factors. Moreover, high-elevated areas are often not properly monitored by weather station networks. In several cases, weather stations are installed only after natural disasters (such as avalanches or landslides) leading to irregularly equipped regions: very dense station networks and un-gauged areas. In this context, remote sensing from satellites can offer a contribution since it regularly provides spatially distributed information also about isolated areas. However, radiometers cannot directly measure air temperature, but estimations of the land surface temperature (LST) can be obtained by means of specific algorithms from Thermal Infra-Red (TIR) channels satellite data (3). Coarse/medium spatial resolution sensors like the Advanced Very High Resolution Radiometer (AVHRR) and, more recently, the Moderate-resolution Imaging Spectroradiometer (MODIS) have already been extensively used and tested for the LST retrieval (4,5,6). In particular, MODIS furnishes a LST product at 1 km spatial resolution covering all the Earth’s surface twice a day. A strong correlation between LST and air temperature, already observed and analysed in previous works (7), represents the basis of our analysis. EARSeL eProceedings 6, 1/2007 39 However, there is a major constraint in the use of optical TIR remotely sensed observations which concerns the cloud coverage: Under cloud sky conditions it is impossible to retrieve any information. As compared to a weather station network that operates every day, information can therefore result incomplete, considering that most models require data on a daily basis for a long period. In previous research, similar analyses were carried out using a Temperature Vegetation indeX (TVX) technique (8,9). This methodology is based on the assumption that the surface temperature of a closed canopy is equal to the air temperature and so the air temperature can be derived by solving the regression equation SVI b a LST ⋅ + = for the saturated value of a Spectral Vegetation Index (SVI), usually the Normalized Difference Vegetation Index (NDVI). However, the aim of our study is to obtain an estimation of Tair in the Alpine area, where high altitudes make the NDVI unusable because of snow and bare ground. Moreover, by using the NDVI, only day-time satellite overpass can be considered, losing night-time observations. Other previous experiences about the derivation of air temperature from TIR channels analysed the problem at a continental scale in order to verify climate global change (10); in this work, we deal with a regional scale for which a higher accuracy and resolution are required. METHODS The selected sensor for the study is the Moderate Resolution Imaging Spectroradiometer (MODIS), onboard EOS NASA’s TERRA platform, that provides thermal infrared data in ten spectral bands (6.5-15 μm bandwidth) at a spatial resolution of 1 km. Its suitability for the purpose is based on the MODIS sensor’s spatial, temporal and spectral characteristics. The latter allow of the solution of the thermal infrared radiometric correction by means of the MODIS Generalized Split-Window LST Algorithm (11,12,13). This algorithm is based on average emissivity in bands 31 (10,780-11,280 μm) and 32 (11,770-12,270 μm) to retrieve LST from the MODIS sensor. Although satellites provide global coverage, this kind of measure requires two important operations in order to properly map daily mean air temperature as required by most models; therefore our study can be conceptually divided into two different steps. Since the satellite sensor gives information only about LST, the first step (hereafter STEP1) of the analysis is the evaluation of relationships between the satellite-derived LST and the in situ measurements of Tair, taken as close as possible to the moment of the satellite overpass. The second step of the analysis (hereafter STEP2) concern the evaluation of daily mean values of air temperature from instantaneous values. In fact, unlike weather stations, Earth Observation data are acquired instantaneously twice a day, while hydrological and climate models often require a daily mean value (14). Nevertheless, polar orbit satellites overpass the same area every day at approximately the same time, so that data sets belonging to different dates are comparable. The study of both of these relationships – STEP1 and STEP2 enable input data to be obtained for different hydrological and environmental models. Naturally, the accuracy of this analysis affects that of the models, and so their sensitivity must be considered too. The selected study area (3,500 km) is located in the Italian Alps, Lombardia district (Figure 1), where Terra overpasses every day between 10 and 11 AM and between 9 and 10 PM. STEP1 consisted in a statistical procedure to retrieve a relationship between LST and Tair during the period between January and June 2003. The EO data set is composed of all passages of Terra satellite in this 182-day period: 364 MODIS LST products (MOD11_L2 swath, 182 day-time and 182 night-time). From this data set, the clear sky control resulted in 124 usable dates (70%); whereas only few pixels were sufficiently clear to be analysed in the remaining dates. In situ measurements of the air temperature, at 2-meter height, were collected at half-hour time steps in the January-June period from 1996 to 2003 by a network of 42 meteorological stations (Figure 1), managed by the Regional Environmental Protection Agency of Lombardia (ARPA Lombardia). EARSeL eProceedings 6, 1/2007 40 Figure 1: Study area. In evidence all the weather stations used in the analysis. Station sited at the highest altitudes (more than 2000 m) are shown as squares instead of triangles. Statistical analyses – STEP 1: Air temperature and land surface temperature relationship The STEP1 correlation analyses were applied at first separately to each of the 42 selected stations to assess the feasibility of such a statistical approach; then they were applied to the entire data set for identifying a typical equation representative of the area at hand, or of some sub-areas. The first correlations were obtained for each station, distinguishing between night-time and daytime satellite overpass, as a direct consequence of the different trend observed for each station during the two different moments. This analysis pointed out a strong linear correlation for all selected stations (determination coefficient R always higher than 0.75 and often higher than 0.9) and there were no evidences of different dynamic depending on different months. Obtained relationships were then compared with the Tair LST equation. In 69 of the 84 cases (42 day-time and 42 night-time) the regression line showed an angular coefficient lower than 1 and intersects the Tair LST line. This can be considered as a consequence of a physical characterisation of the area: For high temperatures LST is greater than Tair, while it is the opposite for low temperatures. Figure 2 shows this feature for one meteorological station (Alla Braccia). Figure 2: Night-time and day-time relationships estimated for Alla Braccia station. For low temperatures LST is lower than Tair, while for high temperatures LST is higher than Tair. Starting from these encouraging results, some procedures of generalization were tested in order to obtain, for a selected group of stations, a unique equation representative of the relationship between Tair and LST. On the basis of the statistical sample and considering the literature, we focused our attention on the land cover, on the altitude and on the proximity of available stations. These three criteria were used to introduce a sub-setting of the data set in different sub-areas, and their consistency and performances were tested during the analysis. EARSeL eProceedings 6, 1/2007 41 In particular, as regard to the land cover, the stations showed a similarity that did not allow of the evaluation of a different behaviour (31 of 42 stations belong to the Forest and seminatural area CORINE Land Cover macrocategory). The best generalization results were achieved by considering altitude as the main variable that affects this kind of relationship. In fact, on the assumption that stations at close altitude behave similarly, two relationships (one day-time and one night-time) for high altitude stations were found, using the 11 stations, among the 42 available (Figure 1), located at an altitude higher than 2,000 metres. In particular, from these selected 11 stations, we used six stations for the calibration of these two relationships over the 182-day period, while the other five were used to validate the relationships during the same period. Outcomes clearly demonstrated the actual possibility to obtain two general relationships (one daytime and one night-time) as the altitude is considered the sub-setting criterion. The most satisfactory results are obtained considering the night-time equation: In particular, the determination coefficients (R) are equal to 0.86 for night-time (see Figure 3) and to 0.80 for day-time, with validation Root Mean Square Error (RMSE) of 2.47 and 3.36°C, respectively. The resulting equations are: time day 4036 . 1 649 . 0 + ⋅ = LST Tair time night 7691 . 2 791 . 0 + ⋅ = LST Tair Figure 3: Relations estimated for high altitude stations during night-time. The calibration (left figure) shows a R of 0.86; from the validation (right figure) a regression line very close to the 1:1 line was obtained 2