Estimating daily minimum and maximum air temperatures from MODIS land surface temperature data

Transcription

1 Centre for Geo-Information Thesis Report GIRS Estimating daily minimum and maximum air temperatures from MODIS land surface temperature data Marco B.J. Berghege March 24 I

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3 Centre for Geo-Information Thesis Report GIRS Estimating daily minimum and maximum air temperatures from MODIS land surface temperature data Marco B.J. Berghege L5, Soil-Water-Atmosphere, specialization meteorology Wageningen University Reg. NR; Supervisors: Drs. A.J.W. de Wit, Wageningen-UR, Centre for Geo Information. Dr. ir. J.G.P.W. Clevers, Wageningen-UR, Centre for Geo Information. March 24 III

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5 Acknowledgements This report is the result of a six months thesis/internship period at the Centre for Geo Information, Alterra Wageningen. This research completed my study Meteorology of the Wageningen University. As it has been a pleasant and instructive experience, I could not have wished for a better way to finish my study. I would like to thank Allard de Wit for all received assistance while working on this research; the IDL programming sessions improved my programming skills greatly. The opportunity to present my research at a MODIS workshop was helpful and instructive. I also would like to thank Jan Clevers for the evaluation and advice given on my concept reports. Further I would like to thank all other people who helped me with advice, facilities and received support. Marco Berghege March, 24 I

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7 Summary Crop growth Model systems are widely used to estimate agricultural production as a function of weather and soil conditions. For meteorological input, the distribution of agrometeorological data sources is rather scattered. Therefore an estimate of agrometeorological data by interpolation has to be made for a considerable amount of site locations (Hoogenboom, 2). De Wit et al (23) explored the possibilities of using AVHRR-derived air temperatures as a substitute for interpolated minimum and maximum air temperatures in a spatial crop monitoring and yield forecasting system. The approach led to temperature deviations on a daily basis, but it was found to be acceptable when the temperature time-series were plotted in cumulative form. Although the results were promising for most of the study area, the AVHRR-derived temperature sums were too large, particularly in the Southern parts of Spain. This study elaborates on the research done by de Wit et al (23) and focuses on the calibration of air temperatures for sites located on the Iberian Peninsula only. The MODIS- Terra LST product is more advanced and already corrected for cloud cover and atmosphere; therefore this product is used in this study instead of AVHRR data. Subject of the study is to explore the potential of estimating minimum and maximum air temperature by calibrating MODIS LST for sites located in a study area that covers the entire Iberian Peninsula. In order to account for the climatologic and geomorphologic differences, an environmental classification of Europe is included in the calibration procedure. The calibration of MODIS LST as applied in this study is based on the principle of linear regression. MODIS LST, actual air temperature and an environmental classification are the input parameters for the linear regression models. The difference between MODIS estimates and actual air temperatures is used for quantifying the performance of the calibration for both daily temperature estimates as well as for temperature sums. In a similar way, the performance of MODIS calibration compared to interpolation estimates is tested. Also the value of the environmental classification approach on the method is determined. III

8 Compared to Interpolation estimates, air temperature estimates based on MODIS LST proved to be less accurate for both minimum and maximum conditions and deviate on a daily basis, which is in accordance with the conclusions drawn by de Wit et al (23). Although this deviation on daily basis occur, long term averages approximate actual air temperature averages very well. However, the site (point data) approach of this study results in a larger number of missing data due to cloud cover especially compared to a grid cell (5x5 km) approach. The observed overestimation of temperature sums is therefore merely due to the substitutes of missing MODIS LST. Therefore, the calibration of MODIS LST potentially gives better estimated temperature sums compared to spatially interpolated values. Although the use of a linear regression method proved to generate in general satisfying results, it appeared that the including of an environmental classification did not result in better air temperature estimates. IV

9 Table of contents Acknowledgements.I Summary.III 1 Introduction Background Problem definition Study objectives and setup of the study Setup of the report.4 2 Data Terra-MODIS Introduction to the MODIS sensor onboard Terra Introduction to MODIS Land Surface Temperature product Data products used in this study Meteorological data Environmental classification The European Classification as used in this study.11 3 Data processing General overview of applied processing steps Processing of MODIS LST data Comparison of MODIS LST data and daily air temperature Statistical approaches Calibration of MODIS LST to air temperature estimates Air temperature interpolation from surrounding weather stations Error analysis Substitution of missing values for cumulative temperature sums.2 V

10 4 Results and analysis Relation between MODIS LST and daily air temperature Data availability Performance of air temperature estimation using MODIS LST and regression functions Comparison of MODIS estimates vs. interpolation estimates General Minimum MODIS estimates vs. minimum interpolation estimates Maximum MODIS estimates vs. maximum interpolation estimates Significance for environmental stratifications.3 5 Discussion.31 6 Conclusions and recommendations Conclusions Recommendations.34 References.35 Appendix Appendix A, General figures and tables Appendix B, Visualization of minimum air temperature estimates Appendix C, Visualization of maximum air temperature estimates VI

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13 1 Introduction 1.1 Background Crop growth Model systems are widely used to estimate agricultural production as a function of weather and soil conditions. An example of a crop growth model is WOFOST (van Diepen et al. 1989). Meteorological inputs used by WOFOST are minimum temperature, maximum temperature, global radiation, wind speed, vapor pressure, evapotranspiration and rainfall. Air temperature is the main weather variable that regulates the rate of vegetative biochemical processes like CO 2 assimilation and photosynthesis (Hodges, 1991). Moreover, the cumulative temperature sum determines the reproductive development. In the WOFOST model, temperature exerts influence on many different aspects of plant growth and development. First of all, temperature influences the duration of the successive growth stages, and hence on the duration of the total growth cycle because the length of each growth stage is defined by the summation of the daily effective temperature. Daily effective temperature depends on the crop-specific base temperature, below which no phonological processes take place, and the maximum daily temperature, beyond which phonological activity does not increase anymore. Higher temperatures lead to faster ageing of the crop and shortening of successive growth stages (de Wit et al, 23). Air temperatures are usually measured on a daily basis at point locations. For meteorological input the distribution of agro-meteorological data sources is rather scattered. An estimate of agro-meteorological data by interpolation has to be made by using a considerable amount of site locations (Hoogenboom, 2). De Wit et al (23) explored the possibilities of using AVHRR-derived air temperatures as a substitute for interpolated minimum and maximum air temperatures in a spatial crop monitoring and yield forecasting system. In their study a two-year set of daily NOAA-AVHRR images over Western-Europe was used to derive estimates of daily surface temperature aggregated over 5x5 km grid cells whereby a land cover database was used to select only pixels that were classified as arable land. Monthly average surface temperatures were substitutes for days that did not yield data due to cloud cover. Although this approach led to temperature deviations on a daily basis, it was found to be acceptable when the temperature time-series were plotted in a cumulative form. Derived AVHRR-derived surface temperatures were usually higher than the maximum air temperature measured at a weather station. 1

14 An empirical model related to surface temperatures and maximum air temperature was used by de Wit et al (23) to account for this difference. The model was calibrated against measured maximum air temperature of five weather stations. The results were applied on the AVHRR data in order to convert it into a simulated maximum air temperature. 1.2 Problem definition Based on the results of the study mentioned above it was concluded that satellite derived temperatures can be used to obtain realistic spatial patterns of yearly temperature sums. Although the results were promising for most of the study area, the AVHRR-derived temperature sums were too large, particularly in the Southern parts of Spain. The overestimation of the temperature sums caused a shortening of the growing season and subsequently a lower accumulation of biomass at the end of the season. A dataset consisting of data of only five weather stations scattered over Western Europe was the basis of AVHRR calibration to land surface temperature (LST) as performed in the study of de Wit et al (23). Consequently, the procedure did not take into account the climatological and geomorphological variability over the study area. Therefore, the calibration of AVHRR proved less accurate for regions with extreme environmental conditions compared to the rest of the study area. 2

15 1.3 Study objectives and setup of the study This study elaborates on the research done by de Wit et al (23) and focuses on the Iberian Peninsula only. The MODIS-terra LST (Land Surface Temperature) product is used in this study instead of AVHRR data. The MODIS-terra LST product has a resolution of 1x1 km and is more advanced compared to AVHRR data as cloud cover algorithms correct for cloud cover and atmosphere. The objectives of this study are to explore the potential of estimating minimum and maximum air temperature by MODIS LST for sites located in a study area that covers the entire Iberian Peninsula. Air temperatures are normally measured at 1.5 meter height while MODIS provides in land surface temperatures. Linear regression based on differentiation in climatic and geomorphologic environmental circumstances enables a calibration of MODIS LST data to air temperature estimates. By the use of a number of reference sites makes that a comparison between estimated air temperatures and actual air temperature values can be made. This comparison quantifies the performance of daily estimated air temperatures as well as the performance of estimated temperature sums based on environmental dependent regression models. The main research questions for this study are: To what extent is the use of an environmental classification an improvement for the accuracy of estimated air temperatures based on MODIS LST for the Iberian Peninsula? Particularly compared to calibration based on regression that does not take into account climatological and geomorphological differences. What is the accuracy of MODIS and interpolated air temperature estimates compared to actual air temperatures? Does the accuracy of the estimated air temperatures differ per environmental zone and minimum or maximum temperature conditions? Does the MODIS LST calibration method performs better with respect to the overestimation of temperature sums as observed by the Wit et al (23)? Performs the MODIS LST calibration method better compared to interpolation methods? 3

16 1.4 Setup of the report In chapter 2, Data, an introduction on the environmental stratification of Europe and MODIS LST product content and properties is given. In chapter 3, Data processing, thoroughly discussed is the data processing performed on both MODIS LST data and weather station data. Also mentioned in this chapter is the applied approach towards the environmental classifications. Presented in chapter 4, Results, the performance of an environmental classification approach towards MODIS LST calibration is presented. Shown both in tables as in figures is the performance of estimated air temperatures compared to actual air temperatures and the performance of traditional interpolation methods. The discussion arising from the results can be found in chapter 5, Discussion. Major conclusions and recommendations conclude the report in chapter 6 and 7. 4

17 2 Data 2.1 Terra-MODIS On December 18 th 1999 the Terra AM-1 spacecraft was launched. MODIS (or Moderate Resolution Imaging Spectroradiometer) is a key instrument aboard the Terra (EOS AM) satellite. Terra's orbit around the Earth is timed such that it passes from north to south across the equator in the late morning and late evening. Terra MODIS is viewing the entire Earth's surface every 1 to 2 days, acquiring data in 36 spectral bands, or groups of wavelengths. One of the main objectives is to develop and launch MODIS is to improve our understanding of global dynamics and processes occurring on the land, in the oceans and in the lower atmosphere. MODIS is playing a vital role in the development of validated, global and interactive Earth system models able to predict global change accurately enough to assist policy makers in making sound decisions concerning the protection of our environment ( [1]) Introduction to the MODIS sensor onboard Terra The MODIS instrument provides high radiometric sensitivity (12 bit) in 36 spectral bands ranging in wavelength from.4 µm to 14.4 µm. Two bands are imaged at a nominal resolution of 25 m at nadir, with five bands at 5 m, and the remaining 29 bands at 1 km (Table 2.1). A ± 55-degree scanning pattern at the EOS orbit of 75 km achieves a 2,33-km swath and provides global coverage every one to two days. The MODIS instrument is designed with various subsystems and abilities providing a wide variety of available products. There are 44 standard MODIS data products that scientists are using and can be categorized as atmosphere, land, cryosphere and ocean products. For this study (Terra) product, MOD 11 Land Surface Temperature is used. 5

18 Table 2.1, Spectral bands of the MODIS Instrument band Bandwidth (nm) IFOV Primary use m L m À,L m L m L m L m A,L m A,L km O km O km O km O km O km O km O km O km O km A km A km A km Cirrus band Bandwidth (µm) IFOV Primary use km O,L km Fire, volcano km A,L km A,L km A km A km A km A km L km Ozone km A,L km A,L km A,L km A km A km A Note: A atmospheric studies; L Land studies; O Ocean studies (Wan, 1999) 6

19 2.1.2 Introduction to MODIS Land Surface Temperature product The Terra MOD11 product contains Level 2 and 3 LST and emissivity retrieved from Terra MODIS data at spatial resolutions of 1 km and 5 km over global land surfaces under clearsky conditions. Due to its orbit, terra overpasses the Iberian Peninsula twice a day, late in the morning and late in the evening, providing in respectively maximum and minimum LST. Atmospheric absorption of infrared radiation by water and other atmospheric gasses (particularly CO 2 ) make it difficult to predict the surface temperature accurately. Split window algorithms take advantage of the differential absorption in two close infrared bands to account for the effects of absorption by atmospheric gasses. A generalized split-window LST algorithm is therefore used to retrieve LST for MODIS pixels with known emissivities in bands 31 and 32. The thermal infrared bands have an IFOV (Instantaneous Field Of View) of approximately 1km at nadir. The MODIS instrument will view cold space and a full-aperture blackbody before and after viewing the Earth scene in order to achieve the calibration accuracy specification better than 1% absolute for thermal infrared bands (.75% for band 2;.5% for bands 31 and 32). MODIS is particularly useful for the LST product because of its global coverage, radiometric resolution and dynamic ranges for a variety of land cover types, and high calibration accuracy in multiple thermal infrared bands designed for retrievals of SST, LST and atmospheric properties. Specifically, band 26 will be used for cirrus detection, thermal infrared bands 2, 22, 23, 29, for correcting atmospheric effects and retrieving surface emissivity and temperature. Multiple bands in the mid-infrared range will provide, for the first time, a good opportunity to make accurate corrections of the solar radiation effects so that the solar radiation can be used as a TIR source for the purpose of retrieving surface emissivity in the mid-infrared range in the day/night MODIS LST method (Wan, 1999). 7

20 2.1.3 Data products used in this study For this study MODIS LST collection 3 data for the complete year 22 is used. The data is ordered via the Earth Observing System Data Gateway ( [2]) and is indicated as MODIS/TERRA SURFACE TEMPERATURE/EMISSIVITY DAILY L3 GLOBAL 1KM ISIN GRID V3. The MODIS LST is supplied in so-called data tiles (Figure 2.1). In order to gain a complete coverage of the Iberian Peninsula four data tiles were needed, these were: h18v4, h18v5, h17v4 and h17v5. The data contained day and night land surface temperatures for practically all days of the year. For 11 days, no data was available. In total 1416 granules were collected and processed. Figure 2.1, MODIS tiles covering the Iberian Peninsula ( [2]) 8

21 2.2 Meteorological data The weather station data is obtained from the European Climatological database. The dataset provided both minimum and maximum daily air temperatures for 15 stations on the Iberian Peninsula. Only data of stations with sufficient recordings have been used. For this purpose stations having more than 2 recordings a year were selected. A recording is assumed the occasion that both maximum and minimum surface temperature have been recorded on the same day. This resulted in a dataset containing 89 stations minimum and maximum air temperature observations. 2.3 Environmental classification An environmental classification as discussed and used in this study determines in geographical, climatological and geomorphological sense which areas and situations are comparable. Most existing environmental classifications are qualitative and can lead to ambiguous classes. They depend on the experience and judgement of the originators, and rely upon intuition of the observer in interpreting observed patterns based on personal experience. Although there were already several quantitative environmental classifications on national scale for various countries in Europe, there was a need for a quantitative classification on European scale which would enable representative studies over the continent (Metzger et al, 23). The Environmental Classification of Europe produced by Metzger et al (23) is based on a statistical clustering such that personal biases are minimized and classes can be seen in the context of Europe as a whole. At a European scale, climate and geomorphology are recognized as the key determinates of ecological patterns. These are conditional for the formation of soils, which in turn determine the local potential for vegetation. For the classification the following databases are used: climate geomorphology oceanity and northing The classification resulted in 84 environmental classes on a 1 km 2 resolution. Based on the defined 84 classes, 13 classified environmental zones were distinguished (Figure 2.2). 9

22 Figure 2.2, Aggregation structure of Environmental Clusters (Metzger et al, 23) 1

23 2.3.1 The European Classification as used in this study While the classification can provide up to 84 environmental classes it is believed that this number of classes would be too high for the Iberian Peninsula. Due to the limited amount of reference points (weather stations) a scarce distribution of stations over the classes would occur, obstructing statistical analysis due to a lack of data. Instead the classification of environmental zones is used. The Iberian Peninsula contains six different environmental zones (Figure 2.3). Joining of two adjacent zones in the Pyrenees region (Alpine South and Atlantic Central) was necessary as both were small and include only one weather station. However, it must be said that the low weather station density in the Pyrenees would not improve the data analysis potential. Figure 2.3, EnZ Classification on the Iberian Peninsula 11

24 According to the naming convention of the classification the following zones were distinguished (Table 2.2). Table 2.2, Environmental zones of the Iberian Peninsula. Per environmental zone, the number of weatherstations as well as the number of reference sites is given Environmental Zone Total number of Number of reference sites weather stations Alpine south / Atlantic central * 2 Lusitanian 3 24 Mediterranean mountains 1 7 Mediterranean North 3 27 Mediterranean South 2 28 * Not enough weather stations were located In the Alpine South / Atlantic Central EnZ to support a reference site. 12

25 3 Data processing 3.1 General overview of applied processing steps The data processing performed in this study involved various steps and phases that need some elaboration. In Figure 3.1a/b, the procedure is visualized. In general, the processing existed of data collection and ordering for both MODIS as weather station data (steps 1 t/m 5), statistical calculations performed on the data (steps 6 and 7) and error analysis for both MODIS and interpolated estimates (steps 8 t/m 1) European climatologic database MODIS Terra Land Surface Temperature Station selection Tiles selection, Tiles aggregation and Data cropping 1 2 MODIS TERRA data Iberian Peninsula, 22 Station data of 89 stations, 22 Station location Lat / Lon Location selection 3 EnZ Classification 4 MODIS TERRA Station data, 22 Data control 5 Data selection, MODIS and Weather station, based on EnZ classification Statistical calculations Regression parameters per EnZ 6 7 Calibration of MODIS LST data for reference sites Air temperature data of reference sites E std MOD 8 Estimated air temperatures Estimated cumulative air temperatures sums E root MOD 8 Figure 3.1a, Flowchart of data processing applied for this study and error analysis of MODIS estimates 13

26 In following text, the steps presented in the figure are further explained. 1. One of the two datasets used is the European climatological dataset. It contains meteorological data from weather stations scattered over Europe. From this dataset, all available data for the Iberian Peninsula and for the year 22 was extracted. 2. Several data tiles of MODIS LST data had to be ordered, aggregated and cropped for an efficient coverage of the Iberian Peninsula. 3. Based on the locations of the available weather stations (1) on the Iberian Peninsula, annual time series of LST were extracted from the MODIS LST data (2) for both minimum and maximum conditions. 4. Applying the environmental classification on the study area resulted in six different environmental zones. Effectively this results in five zones, as two zones are joined. 5. The data was filtered for missing data and abnormal values. New datasets for both minimum and maximum conditions were created containing both MODIS LST and air temperature data. For each environmental zone, a dataset was created. Each dataset contained only data of sites located in the concerning environmental zone. Station data of 89 stations, 22 9 Estimation of air temperature by spatial interpolation Air temperature data of reference sites E std int 1 MODIS estimated air temperatures MODIS estimated temperature sums E root int 1 Figure 3.1b, Flowchart of data processing applied for this study and error analysis of MODIS estimates 14

27 6. Regression coefficients were calculated for each environmental zone based on the available MODIS LST data and air temperature, both for minimum and maximum temperatures. Regression parameters for the entire Iberian Peninsula are determined as well. Nine sites were not included in the procedures mentioned above in order to act as reference site later in the study. 7. MODIS LST data was calibrated into air temperature estimates for each reference site. The regression coefficients used in this calibration were dependent on the environmental zone of the reference site and temperature condition (minimum or maximum temperatures). 8. The performance of the MODIS calibration per reference site is quantified by relating available estimated air temperatures and temperature sums to actual air temperatures and temperature sums of reference sites. 9. For each reference station, air temperatures were also estimated based on a spatial interpolation approach. These values were determined by using air temperatures of surrounding weather stations. In order to account for difference in distance and elevation, inverse distance weighting and height correction were applied. 1. Error analysis of interpolated estimates compared to actual air temperatures (idem 8). The results from steps 8 and 1 enabled a comparison of the performance of MODIS estimates vs. interpolated estimates. 15

28 3.2 Processing of MODIS LST data The MODIS LST data was received in tiles and with a integerized sinusoidal projection. In order to re-project, mosaic and crop the images, some operations were executed on the data. There are application tools available for editing MODIS data ( [3]). For the mosaicing of the data tiles the MODIS Mosaic tool was used. With this tool the data tiles were joined and were cropped efficiently such that there was a good fit over the Iberian Peninsula. For the re-projection to an Albers conical equal area projection, the MODIS reprojection tool was used. The MODIS LST data is given in 16 bit format, therefore the initial value had to be multiplied with a correction factor, which is for MODIS LST data.2. LST(p) = LST-DN(p) x (Equation 3.1) With LST(p) the land surface temperature in Celsius for pixel p and LST-DN(p) the MODIS digital number (DN value) in 16-bit format for the same pixel. In order to correlate weather station Air temperature data to MODIS LST point data was extracted from the MODIS data. The exact locations were chosen such that they coincided with the locations, based on longitude and latitude, of the 89 weather station selected from the European Climatological Database. Finally, missing values in the MODIS dataset were flagged. 3.3 Comparison of MODIS LST data and daily air temperature One of the first steps performed in the study was the comparison of point data of LST with point data of air temperature. The comparison is made for both minimum and maximum conditions. Comparison was limited to those days where both the weather station and MODIS dataset could provide values. Simple visualization by plots roughly gave an impression about the variability, range and reliability in the relation between air temperature and LST. Some plots showed very low values of LST compared to air temperature measurements of the same time and place. Missed cloud cover can result in low values of LST compared to air temperatures. Therefore, it is conceivable that the found low LST values originate from measured cloud top temperature instead of land surface temperature. Occasions with exceptional low LST compared to air temperature values were excluded from the datasets, as they would influence the accuracy of regression negatively. 16

29 The proved strong relation between satellite LST data and air temperature (de Wit, 23) enabled us to use air temperature data in the filtering of exceptionally low LST data. An analysis was performed where first all absolute errors between (minimum and maximum) LST and air temperature were calculated. Secondly, these values were sorted based on the absolute error. An absolute error threshold was set by the use of a percentile. For maximum temperatures this percentile was set at 99 %. Due to the larger variability between minimum LST and minimum air temperature a 95% percentile was used for minimum LST temperature conditions. 3.4 Statistical approaches The statistical variables which are used in this study are R-square coefficients and regression parameters. All parameters are calculated for each site separately, as well as for complete environmental zones. For each zone, except the Alpine south / Atlantic central, a number of sites (Table 2.2) are not included in the statistical analysis in order to be able to check the accuracy of the method at the end of the study (see paragraph 3.5). 3.5 Calibration of MODIS LST to air temperature estimates The estimation of both minimum and maximum air temperatures is based on a linear regression approach: T est = a + b*t LST (Equation 3.2) In this linear regression model T est represents the estimated air temperature and MODIS LST is represented by T LST. In the equation, a is the intercept and b is the slope of the regression line. They are dependent on the environmental zone and the location of the site. For each reference site the air temperature is estimated with this model. 17

30 3.6 Air temperature interpolation from surrounding weather stations The main objective of this study is to explore the potential of using MODIS data in estimating air temperatures with respect to conventional methods like spatial interpolation of data. The performance of both MODIS and interpolated estimates is quantified by relating these values to actual air temperatures. The comparison between the two methods is made based on the acquired performances. Air temperature estimates based on spatial interpolation methods are acquired by using air temperature data of surrounding weather stations. The air temperatures of the three closest sites to the reference station is interpolated to the location of the reference site. This is done by applying inverse distance weighting combined with an elevation correction algorithm. The weight factor of surrounding weather stations to the estimated air temperature is dependent on the distance to the reference site. We used a quadratic weight factor: W(d) = 1/d 2 (Equation 3.3) The distance is given by d, the weight factor is represented by W(d). Before the Air temperature of surrounding sites can be used a height correction must be applied as higher sites have commonly lower temperatures and visa versa. For this height correction a factor of -.6 degrees per 1 meter is applied (van der Voet et al 1994). In practice this means: hc(a) = [ H(r) - H(a) ] x.6 (Equation 3.4) In which hc(a) is the height correction factor for surrounding site a, H(r) is the height of reference site and H(a) the height of site a, both in meters. The interpolated air temperature value can next be calculated by: T int ( T + hc ( a ) air, a ) W + T a ( + hc ( b ) air, b ) W + T + hc b ( c ) air, c W a + W + W b c ( ) W c (Equation 3.5) With T air,x the air temperature of the surrounding station x and T int the interpolated air temperature for the reference station. 18

31 3.7 Error analysis For both interpolated estimates and MODIS estimates the root mean square error and the mean standard error are calculated. This is done for all reference sites and both minimum and maximum conditions and based on a comparison of estimates to actual air temperatures. Also a comparison between an EnZ-regression and non-enz-regression approach can be made based on these variables. The root mean squared error is defined as: dp n = 1 E root T ( n) T ( n ) 2 est ref dp 1 2 (Equation 3.6) In this equation, dp represents the number of data-pairs. A data-pair is formed when values of both estimated temperature and reference temperature for the same day are available. T est represents the estimated air temperature; this can be a MODIS estimate or an interpolated estimate. T ref represents the reference air temperature. In the mean standard error no square and consequently no root are included and can be written as: dp n = 1 E std T ( n) T ( n) est ref dp (Equation 3.7) Both methods quantify the error between estimated and reference temperatures. The E root approach especially emphasizes the error made in the daily air temperature estimation. Due to the root in this function, information regarding over- or underestimation of the air temperature is lost. In this study we are mostly interested in the behavior of cumulative sums of estimated air temperatures; it is therefore we choose to use an E std variable as well. The function does not include absolute differences and therefore air temperature deviations with respect to actual measurements are balanced out. Positive values of E std imply overestimation of air temperature while negative values imply underestimation. 19

32 3.8 Substitution of missing values for cumulative temperature sums Cumulative temperature sums are determined by taking the sum of all air temperature values of previous days in the ongoing year, including the air temperature of the day itself. Due to cloud cover MODIS LST data deals with a relatively large percentage of missing data. In order to have air temperature values for each day, missing values have to be a substituted value. When no data is available for a day, the monthly average is used. It has been proven that this method approaches the actual cumulative temperature sum well (de Wit, 23). When no monthly average can be calculated due to a lack of data, the average is taken by the average of the previous and following month. If this situation occurred for January or December the average of respectively February and November is taken instead. 2

33 4 Results and analysis 4.1 Relation between MODIS LST and daily air temperature As mentioned in paragraph 3.1, the comparison of MODIS LST and air temperature is performed in steps. In the explorative stage of the study the core MODIS LST data and air temperature were used. The first results gave a good impression of the correlation between the two. We found a strong relation between MODIS LST and air temperature, as expected. However, especially the MODIS data proved to have some abnormal low values, which weren t filtered out by previous steps. Based on absolute differences between LST and air temperature a 99% percentile for maximum temperatures and 95% for minimum temperatures increased the reliability of the data, resulting into more reliable results (Appendix A, Figures). The use of the percentile increased the values of R-square slightly for maximum temperatures, there was a larger increase of R-square for minimum temperatures (Table 4.1). It appeared that R-square is larger for maximum temperatures as it is for minimum temperatures. In general, the relationship between LST and air temperatures appeared to be more or less linear (Figure 4.1). Table 4.1, R-square of MODIS LST and air temperatures for minimum and maximum Temperatures for all defined environmental zones. Minimum temperatures Maximum temperatures Environmental zone R-square before use of percentile R-square after use of percentile R-square before use of percentile R-square after use of percentile (5/7) Alpine south / Atlantic central (9) Lusitanian (11) Mediterranean mountains (12) Mediterranean North (13) Mediterranean South

34 Figure 4.1, Visualized is the effect of extracting deviating data from the dataset by using a 99% percentile based the absolute difference between MODIS LST and air temperature. The figure above represents the dataset for environmental zone 9 before filtering, the figure below afterwards. 22

35 The regression parameters originating from the MODIS LST and air temperature dataset give an indication of the behavior of MODIS LST data with respect to air temperatures. The determined regression models for each zone and for both minimum and maximum temperatures conditions were used to estimate air temperatures in a later phase of the study. The found regression lines are skewed with respect to the 1:1 line. This line represents the favorable relation between LST and air temperature. In this situation, LST measurements are exactly the same as air temperature measurements for all temperatures. For both minimum and maximum conditions and all environmental zones, MODIS LST values are lower compared to air temperatures when relative low air temperature values occur. MODIS LST measurements are in general higher when relative high air temperatures occur (Figure 4.2). For each environmental zone the skewness of the regression line differs, especially the intercepts with the y-axis (Table 4.2). Where relatively large intercepts occur, the slope is also larger resulting in smaller differences between the models when LST increases. Table 4.2, regression parameters calculated from MODIS LST and air temperature. Environmental zone Minimum temperatures Maximum temperatures intercept slope intercept slope (5/7) Alpine south / Atlantic central 3,7,67 9,62,6 (9) Lusitanian 4,34,67 6,79,65 (11) Mediterranean mountains,86,77 4,12,74 (12) Mediterranean North 2,14,76 6,32,66 (13) Mediterranean South 1,95,82 7,46,65 Iberian Peninsula 2,51,78 6,76,66 23

36 Regression models for T min 6 Alpine south / Atlantic central Lusitanian M editerranean mountains 4 2 M editerranean North M editerranean South 1:1 c o rrelat io n Tair-Tlst T lst Regression models for T max 6 Alpine south / Atlantic central Lusitanian M editerranean mountains 4 2 M editerranean North M editerranean South 1:1 c o rrelat io n T air -T lst T lst Figure 4.2, Regression lines for the environmental zones. Minimum temperature conditions are visualized in the figure above, maximum temperature conditions below. On the x-axis MODIS LST, on the y-axis the deviation of air temperature with respect to MODIS LST. 24

37 4.2 Data availability There is a clear difference in the total amount of available data-pairs, which actually amounts to the usefulness of MODIS LST data as weather station-data is mostly available. For the reference sites 1317 data-pairs are available for minimum temperature conditions. For maximum temperature conditions this is significantly less: 937 data-pairs. The division of data-pairs over the reference sites also differs for minimum and maximum temperature conditions. For minimum temperature conditions the number of available data-pairs roughly increase to the south, for maximum temperature conditions this behavior seems to be opposite which is rather remarkable. It is not surprising that the number of data-pairs available for the air temperature estimation based on MODIS LST is (much) smaller than for interpolated estimates. Data availability for weather-stations is after all not dependent on cloud cover as MODIS LST data does. The pattern of the increasing number of data-pairs to the south is obvious taking into account the climatologic differences on the Iberian Peninsula. The difference of data availability between MODIS LST and air temperature data is considerable. For MODIS LST data availability is approximately 3 to 6 percent, while for air temperatures this is significantly higher, 8 to 95 percent (Table 4.3). More information about data availability for all sites can be found in Appendix A, Tables. Table 4.3, Data availability for MODIS LST and weather station data Available min Available max Available min Available max MODIS data MODIS data WS data WS data (%) (%) (%) (%) (5/7) Alpine south / Atlantic central (9) Lusitanian (11) Mediterranean mountains (12) Mediterranean North (13) Mediterranean South

38 4.3 Performance of air temperature estimation using MODIS LST and regression functions The use of the zone-specific regression parameters on MODIS LST in general proved to generate reasonable results (Figure 4.3). The estimated air temperatures for the reference sites approach the actual daily air temperature to a certain extent as can be seen in the visualization of the data (Appendix B and C). Daily estimates are fluctuating around the actual air temperature. Due to the presence of cloud cover over the reference sites a substantial number of estimates can not be generated. The acquired MODIS estimated cumulative minimum and maximum temperature sums are of most interest for this research (Chapter 1). The MODIS based cumulative temperature sums are a good indication of the performance of air temperature estimates and its result on crop development in an ongoing season. Although performances of MODIS air temperature estimates differ for reference sites and environmental zones, cumulative minimum temperature sums are more accurate compared to those of maximum temperature sums. Only late in the season the method produces underestimated values for estimated minimum temperatures. Maximum cumulative temperature sums in general tend to overestimate, cumulative minimum temperature sums approach reference data better. In some cases slight underestimation occurs for minimum temperatures (Figure 4.3). For maximum temperatures however, overestimated values occur early in the season. Besides over-, or underestimation most reference sites (Appendix B and C) show cumulative temperature results which correlate well with those of the reference data. There is however an exception. For reference station 828 (Appendix C), the estimated cumulative maximum temperature sum follows an almost linear profile. Due to a large number of recordings with cloud cover on the reference site the amount of available MODIS LST and thus estimated air temperatures is very small, resulting in a strongly averaged temperature sum (see discussion). In the Appendix B and C, MODIS and interpolated estimates for daily air temperature and temperature sums are shown for all reference stations. Based on the graphs only, the interpolation method seems to produce better and more accurate results. However, for some reference sites the regression method seems to give better results for cumulative temperatures, especially for minimum temperatures. 26

39 Figure 4.3, Visualization of MODIS estimated air temperatures with respect to actual air temperature. The reference site is of station 884 in environmental zone 12. The Figure gives an impression of both daily and cumulative behavior of estimated air temperatures. Minimum air temperature condition in the figures above, maximum air temperature conditions in the figures below. 27

40 4.4 Comparison of MODIS estimates vs. interpolation estimates General It is difficult to present results based on a set of graphs as done in the previous paragraph. A quantitative approach to describe the results is of more value. Not only the accuracy of the MODIS LST calibration model can be described quantitatively, but also the accuracy of existing methods like spatial interpolation as is described in the chapter methodology. This enables us to relate the performance of the MODIS LST calibration method to an existing method and thus will give an indication of the accuracy of the method presented in this study. The results will be presented for minimum and maximum temperatures separately in the following paragraphs. Mostly the accuracy of the MODIS calibration method in relation to spatial interpolation accuracy will be dealt with Minimum MODIS estimates vs. minimum interpolation estimates The graphs already showed that for some reference sites the estimated air temperature by MODIS Calibration approached the reference data well. In Table 4.4 the accuracy of both MODIS estimates and interpolation estimates are shown. Table 4.4, Calculated errors of minimum MODIS estimates and interpolation estimates with respect to weather station data. Min. Temperature MODIS estimates Interpolation estimates Zone Site E root E std Data pairs E root E std Data pairs (9) 821 3,19, ,22 1, (9) ,86 1, ,93, (9) 842 2,38 -, ,25, (11) 875 2,94 -, ,96 -, (12) 884 2,94 -, , -, (12) ,71 1, ,88 -, (12) 828 2,62, , -1,3 192 (13) ,37-1, ,22-1,5 254 (13) ,55,39 2 2,54-1,

41 E root values for MODIS estimates do not vary much for the reference sites and environmental zones but are larger compared to E root values of the Interpolation estimates. E std behavior per environmental zone of MODIS estimates with respect to interpolation estimates is for most sites smaller. MODIS estimates are, according to E std, more accurate than interpolated estimates. For most reference sites, MODIS estimates are overestimating, for Interpolation estimates underestimation is more likely to occur. Remarkable is the succession of meanstandard-error values for interpolated estimates which are steadily decreasing from north to South. For MODIS estimates, the data availability is increasing towards the south. For interpolated estimates, the data availability does not show to have a clear pattern with environmental zone or latitude Maximum MODIS estimates vs. maximum interpolation estimates Also for maximum temperatures the root-mean-square-error of MODIS estimates are larger compared to those of interpolated estimates (Table 4.5). The majority of individual meanstandard-errors of MODIS estimates is smaller compared to interpolated values. The number of useful data-pairs is in general larger for northern environmental zones as it is for southern zones like the Mediterranean South. Table 4.5, calculated errors of maximum air temperature estimates for MODIS calibration and spatial interpolation methods. Max. Temperature MODIS estimates Interpolation estimates Zone Site E root E std Data pairs E root E std Data pairs (9) 821 2,39 -, ,29 -, (9) ,66-2, ,26 -, (9) 842 2,39 -, ,4-1, (11) 875 2,52 -, ,29-1, 329 (12) 884 3,6-1, ,79 -, (12) ,86, ,35-1, (12) 828 2,31, ,69 -, (13) ,11-2, ,3-1, (13) ,95 -, ,41-1,

42 4.5 Significance for environmental stratifications The relative similarity between regression parameters of environmental zones on one hand and the Iberian Peninsula as a whole on the other hand is already mentioned in paragraph 4.1. As the air temperature estimates depend on these regression parameters, the difference in air temperature estimates will in general not differ much (Table 4.6). In general the differences in performance of both methods are very small. E root values of air temperature estimates based on EnZ-regression are somewhat larger. For E std no clear difference can be found. This is especially true compared to the difference between the performance of MODIS air temperature estimates and interpolated air temperature estimates as can be seen in paragraph 4.4, Comparison of MODIS estimates vs. interpolation estimates. Table 4.6, Performance of air temperature estimation based on EnZ-specific regression compared to air temperature estimation based on non-enz-specific regression. Minimum air temperature conditions Maximum air temperature conditions EnZ-specific Non-EnZ-specific EnZ-specific Non-EnZ-specific Zone Site regression regression regression regression E root E std E root E std E root E std E root E std (9) 821 3,19,41 3,26 -,24 2,39 -,7 2,39 -,4 (9) ,86 1,4 2,7,39 3,66-2,49 3,63-2,46 (9) 842 2,38 -,14 2,69-1,14 2,39 -,55 2,38 -,52 (11) 875 2,94 -,76 2,98,9 2,52 -,47 2,5,9 (12) 884 2,94 -,25 2,94,22 3,6-1,31 2,91 -,92 (12) ,71 1,41 2,97 1,86 2,86,3 2,93,71 (12) 828 2,62,35 2,72,83 2,31,51 2,43,91 (13) ,37-1,1 2,44-1,15 3,11-2,2 3,42-2,62 (13) ,55,39 2,55,18 1,95 -,56 2,1 -,98 3

43 5 Discussion The use of a linear regression method proved to be accurate, particularly when applied in cumulative temperature sums. However, the significance of applying an environmental classification in the calibration procedure is only minor. Air temperature is largely dependent on incoming shortwave radiation (Monteith, 199) and vegetation cover hampers air temperatures (Pal Arya, 1988). A more physical approach of calibration might be more suited to relate regression models to environmental properties. In such approach not only MODIS LST and air temperature are input parameters for a regression model, but incoming solar radiation NDVI data (Lillesand et al, 2) and the amount of cloud cover could be used as well. Based on the results the question remains to what extent the here applied regression method proves to give better estimates for minimum and maximum air temperatures on the Iberian Peninsula compared to traditional methods like spatial interpolation of data. The difference in E root for MODIS estimates and interpolated estimates proves that the method is not able to estimate daily minimum or maximum air temperatures better than a traditional interpolation method does. The results for E std are however promising. For most sites and temperature conditions, E std values are smaller for MODIS estimates than they are for the interpolation estimates. Based on these results one might expect more accurate temperature sums as well. However, this observation leads to a contradiction especially for maximum estimates. While the error analysis indicates more accurate cumulative air temperature sums for MODIS estimates, the plots regularly demonstrate the opposite; more accurate interpolated estimated temperature sums instead of MODIS estimated temperature sums. Besides, according to the error analysis, MODIS estimates for maximum air temperature conditions tend to underestimate the cumulative maximum air temperatures while the graphs once again prove otherwise. So which observation to believe? The calculation of cumulative temperature sums for a whole year is only possible if 365 recordings are available, however, this is an ideal situation. In reality missing data is abound; the substitute for these missing values is a monthly average. The absence of MODIS data for a day indicates mostly the presence of cloud cover. Due to this cloud cover air temperature decreases as incoming shortwave radiation is blocked. It can be expected that available MODIS LST data therefore ignores relative low temperatures. The substitute air temperature 31