improvements in the estimation of daily minimum air temperature in peninsular spain using modis land...

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Improvements in the estimation ofdaily minimum air temperature inpeninsular Spain using MODIS landsurface temperatureJuanjo Pena, Carmen Recondoab & Javier F. Callejaca Area of Cartographic, Geodesic and PhotogrammetricEngineering, University of Oviedo, 33600 Mieres, Asturias, Spainb Institute of Natural Resources and Spatial Planning (INDUROT),University of Oviedo, 33600 Mieres, Asturias, Spainc Department of Physics, Polytechnic School of Mieres, Universityof Oviedo, 33600 Mieres, Asturias, SpainPublished online: 17 Jul 2014.

To cite this article: Juanjo Pen, Carmen Recondo & Javier F. Calleja (2014) Improvementsin the estimation of daily minimum air temperature in peninsular Spain using MODIS landsurface temperature, International Journal of Remote Sensing, 35:13, 5148-5166, DOI:10.1080/01431161.2014.935831

To link to this article: http://dx.doi.org/10.1080/01431161.2014.935831

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Improvements in the estimation of daily minimum air temperature inpeninsular Spain using MODIS land surface temperature

Juanjo Pena*, Carmen Recondoa,b, and Javier F. Callejac

aArea of Cartographic, Geodesic and Photogrammetric Engineering, University of Oviedo, 33600Mieres, Asturias, Spain; bInstitute of Natural Resources and Spatial Planning (INDUROT),

University of Oviedo, 33600 Mieres, Asturias, Spain; cDepartment of Physics, Polytechnic School ofMieres, University of Oviedo, 33600 Mieres, Asturias, Spain

(Received 3 February 2014; accepted 27 April 2014)

Air temperature (Ta) is a key variable in many environmental risk models and plays avery important role in climate change research. In previous studies we developed modelsfor estimating the daily maximum (Tmax), mean (Tmean), and minimum air temperature(Tmin) in peninsular Spain over cloud-free land areas using Moderate ResolutionImaging Spectroradiometer (MODIS) data. Those models were obtained empiricallythrough linear regressions between daily Ta and daytime Terra-MODIS land surfacetemperature (LST), and then optimized by including spatio-temporal variables. The bestTmean and Tmax models were satisfactory (coefficient of determination (R

2) of 0.910.93;and residual standard error (RSE) of 1.882.25 K), but not the Tmin models (R

2 = 0.800.81 and RSE = 2.833.00 K). In this article Tmin models are improved using night-timeAqua LST instead of daytime Terra LST, and then refined including total precipitablewater (W) retrieved from daytime Terra-MODIS data and the spatio-temporal variablescurvature (c), longitude (), Julian day of the year (JD) and elevation (h). The best Tminmodels are based on the National Aeronautics and Space Administration (NASA)standard product MYD11 LST; and on the direct broadcast version of this product, theInternational MODIS/AIRS Processing Package (IMAPP) LST product. Models basedon Sobrinos LST1 algorithm were also tested, with worse results. The improved Tminmodels yield R2 = 0.910.92 and RSE = 1.75 K and model validations obtain similar R2

and RSE values, root mean square error of the differences (RMSD) of 1.871.88 K andbias = 0.11 K. The main advantage of the Tmin models based on the IMAPP LST productis that they can be generated in nearly real-time using the MODIS direct broadcastsystem at the University of Oviedo.

1. Introduction

Air temperature (Ta) is a descriptor of terrestrial environmental conditions (Prihodko andGoward 1997) and one of the most important climatic variables. It controls multiplebiological and physical processes between the hydrosphere, atmosphere, and biosphere. Tais widely used in climate change research and is a key factor in many environmental riskmodels. Many of these models need daily estimations of Ta at a regular spatial resolution.For example, in the Spanish fire risk project Fireglobe (Chuvieco et al. 2012), Ta was oneof the main meteorological variables involved in the risk index, and an operational methodwas developed in Recondo, Pen, et al. (2013), via remote sensing, to obtain this variabledaily over peninsular Spain at a spatial resolution of 1 km2. For the estimation of daily Ta,Recondo, Pen, et al. (2013) used data obtained from the Moderate Resolution Imaging

*Corresponding author. Email: [email protected]

International Journal of Remote Sensing, 2014Vol. 35, No. 13, 51485166, http://dx.doi.org/10.1080/01431161.2014.935831

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Spectroradiometer (MODIS). The MODIS instruments are currently on board the NationalAeronautics and Space Administration (NASA) Earth Observing System (EOS) Terra andAqua spacecraft, and data from both instruments are received in real time by the directbroadcast (DB) system installed since 2007 at the University of Oviedo. Terra crossesthe equator daily at about 10:30 am and 10:30 pm local solar time (10:30 UniversalTime Coordinated (UTC) and 22:30 UTC, respectively), while Aqua has a 1:30 am and1:30 pm equator crossing time (1:30 UTC and 13:30 UTC, respectively).

Meteorological stations generally provide accurate Ta observations for the sitesampled, but may not describe the spatial heterogeneity typically observed for thisvariable over larger land areas (Prihodko and Goward 1997). Spatial interpolation meth-ods, such as kriging or regression models, are widely used to estimate Ta between points(with an overall accuracy of around 2C; Mostovoy et al. 2006), but the meteorologicalstations are generally sparse and the number of stations is usually low, especially inmountain areas. Remote sensing improves the spatial coverage of the ground-meteorolo-gical stations and several methods have been developed to estimate Ta from remote-sensing data obtained with a wide range of sensors. The land surface temperature (LST),obtained from remotely sensed observations, is the variable typically used as proxy toestimate Ta. Still, the derivation of Ta from satellite data is not straightforward due to thedissimilarity of the genesis and temporal dynamics of both variables (Kloog et al. 2012).According to Zakek and Schroedter-Homscheidt (2009), the methods for estimating Tafrom LST can be divided into four groups: simple statistical approaches, usually based ona linear regression between Ta and LST (Vogt, Viau, and Paquet 1997; Recondo andPrez-Morandeira 2002; Mostovoy et al. 2006; Shen and Leptoukh 2011); advancedstatistical approaches (multiple linear regression or more complex models), which takeinto consideration at least two independent variables (Jang, Viau, and Anctil 2004;Cristbal, Ninyerola, and Pons 2008; Zhang et al. 2011; Benali et al. 2012; Kim andHan 2013; Recondo, Pen, et al. 2013); the temperature-vegetation index (TVX)approach, based on the assumption that the vegetation canopy temperature is close to Ta(Prihodko and Goward 1997; Zhu, L, and Jia 2013); and energy-balance approaches,which are developed from physically based processes (Sun et al. 2005). All these methodshave an inherent error of up to 23C with either a high temporal or a high spatialresolution (Zakek and Schroedter-Homscheidt 2009), and the error of estimates based onregression methods ranges from 1.0C to 2.6C (Zhang et al. 2011).

The LST data obtained via remote sensing represent the instantaneous temperature of theland surface at the time of satellite overpass. Despite that, several authors have found a strongdirect relationship between LST and maximum, mean, and minimum air temperature (Tmax,Tmean, and Tmin, respectively), at a daily, monthly, or annual scale. Some of these results forTmin at a weekly and/or daily scale will be summarized now. Benali et al. (2012) estimatedweekly Ta over Portugal for a 10 year period using Terra-MODIS LSTand auxiliary data. Forweekly Tmin, they obtained as the best result a coefficient of determination (R

2) of 0.87 androot mean square error (RMSE) of 1.74C using both daytime and night-time LSTs. However,this result was only a bit better than that obtained using only a simple linear equation Tmin-LSTand only night-time LST: R2 = 0.86 and RMSE = 1.84C. Vancutsem et al. (2010) found thatnight-time Aqua-MODIS LST data provided a good estimation of Tmin over differentecosystems in four countries in Africa, with RMSE varying between 2.6C and 4.1C forthe daily scale, higher than for the 8 day estimations (2.12.8C). Jones et al. (2004) usedAqua-MODIS LST to estimate daily Tmin at night in northern Alabama, obtaining an averagecorrelation of 0.71 and a maximumRMSE of 0.74 K from 18 sampling sites and five nights inspring and autumn. Shen and Leptoukh (2011) estimated daily Tmax and Tmin from Terra-

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MODIS data over two Eurasia regions (northern China and the Former Union of SovietSocialist Republics, FUSSR), dividing the sample based on differing land cover. Theyobtained R2 = 0.900.94 and a standard deviation () of 3.54.2C for their daily Tmin-LSTmodels (from night-time data) and R2 = 0.92, = 3.9C, slope = 1, and bias = 0C in thevalidation of these models when combining all stations. They also concluded that the relation-ships between Tmin and night-time LST have little dependence on land-cover types, whereasTmax and daytime LST depend significantly on the land-cover types. Zhang et al. (2011) usedempirical models (based on linear regressions, but changing the coefficients depending on themonth) to estimate daily Ta over ChinawithMODIS LST (from the 6 kmLST products). Theydid not find significant differences between the LSTs of Terra and Aqua for estimating dailyTa. In the linear regression between Tmin versus night-time Aqua-LSTs for all the data, theyobtained R2 = 0.87 and = 3.64C; whereas in the validation of their empirical modelproposed for these data (model II), they obtained R2 = 0.88, RMSE = 3.46C, slope = 0.87,and annual bias equal to zero, with evident seasonal bias.

In Spain, National Oceanic and Atmospheric Administration (NOAA) Advanced VeryHigh Resolution Radiometer (AVHRR) LST data were used to estimate daily Tmax over aMediterranean region (Andalusia, southern Spain; Vogt, Viau, and Paquet 1997) and Tmaxand Tmean in Asturias (an Atlantic region in northern Spain; Recondo and Prez-Morandeira 2002), but neither of these studies estimated Tmin. Cristbal, Ninyerola, andPons (2008) presented a methodology for modelling Ta over Catalonia (a Mediterraneanregion in northeastern Spain) through a combination of remote-sensing and geographicalinformation system (GIS) data. As remote-sensing predictors, they used albedo, LST, andnormalized difference vegetation index (NDVI) obtained from Landsat-5 ThematicMapper (TM), Landsat-7 Enhanced Thematic Mapper Plus (ETM+), NOAA-AVHRR,and Terra-MODIS images. The geographical variables they included were altitude, lati-tude, continentality, and solar radiation. They concluded that the best models are obtainedwhen both types of variables are combined. From NOAA-AVHRR data, they obtainedR2 = 0.54 and RMSE = 2.12C for daily Tmin. From Terra-MODIS data, the results fordaily Tmin were R

2 = 0.54 and RMSE = 2.28C. They only used daytime LST data.Recondo, Pen, et al. (2013) developed models for estimating the daily Tmax, Tmean,

and Tmin in peninsular Spain over cloud-free land areas using MODIS and spatio-temporalvariables. The simplest models used only MODIS LST as proxy for estimating Ta, but thebest models also used other MODIS-based variables, such as the total precipitable water(W) and the NDVI, and the spatio-temporal variables of longitude, Julian day, andelevation. Models were obtained empirically through linear regressions using daytimeMODIS LST from the Terra satellite and the daily Ta obtained from 331 ground-levelmeteorological stations for the year 2010. Several products/algorithms for LST retrievalwere tested in Recondo, Pen, et al. (2013), obtaining the best results for the models basedon the NASA standard product MOD11 LST and on the DB version of this product: theIMAPP (International MODIS/AIRS Processing Package) LST product. Although themodels based on the MOD11 LST were slightly better than those based on the IMAPPproduct, the advantage of IMAPP products is that they can be generated in nearly realtime, for instance, using the MODIS DB system at the University of Oviedo. The bestRecondo models based on the MOD11/IMAPP LST products and also including spatio-temporal variables gave R2 = 0.910.93 and residual standard error (RSE) of 1.882.25K for Tmean and Tmax, and R

2 = 0.800.81 and RSE = 2.833.00 K for Tmin. Modelvalidations yielded R2 and RSE values similar to those obtained in the models, and a rootmean square error of the differences (RMSD) of 1.922.40 K for Tmean and Tmax andRMSD = 2.892.95 K for Tmin.

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In this article we intend to improve the Tmin models proposed by Recondo, Pen, et al.(2013), using night-time MODIS LST from the Aqua satellite instead of daytime LSTfrom Terra. The main hypothesis that we test in this work is that more accurate Tminmodels should be obtained by selecting the MODIS data from the overpass closer to thedaily Tmin recorded in the ground-level stations.

This article is organized as follows: Section 2 describes the study area; Section 3describes the proposed method and the data used, including also a review of the globalMODIS LST algorithms/products used in this study; Section 4 contains the data analysisand discusses the results of the proposed Tmin models and their validation; and finally,Section 5 presents the conclusions.

2. Study area

The study area comprises peninsular Spain, with a total area of 493,665 km2 (Figure 1). Theclimate of the Iberian Peninsula is highly heterogeneous due to its varied orography andlocation in the temperate zone of the northern hemisphere. There are two main climaticdomains: the oceanic-temperate and theMediterranean. The oceanic-temperate climate covers

Figure 1. Location of the study area, the peninsular territory of Spain, and distribution of the 331meteorological stations used in this study, and the institution that manages each station.

Note abbreviations in Spanish: Agencia Estatal de Meteorologa (AEMET); Servicio Meteorolgicode Catalua (SMC); Sistema de Informacin Agraria de Murcia (SIAM); Servicio Integral deAsesoramiento al Regante (SIAR).


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the north and northwest of the peninsula, and is characterized by mild temperatures, with anaverage annual temperature ranging between 9C and 15C. The annual precipitation isusually between 900 and 1000 mm. The Mediterranean climate, which extends through-out the rest of the Iberian Peninsula, is characterized by hot and dry summers, and mildwinters. The average annual temperature generally ranges between 15C and 19C, andthe annual precipitation is between 200 and 700 mm (Capel Molina 2000).

3. Method and data

In this work, linear regression models are developed to relate daily Tmin from ground-levelstations to LST obtained using three global MODIS LST products/algorithms, as we did inRecondo, Pen, et al. (2013): the product MYD11, the IMAPP LST product, andSobrinos LST1 algorithm. First, we propose a simple statistical method for estimatingdaily Tmin from night-time Aqua-MODIS LST data, based on simple linear regressionmodels, and then we investigate the possibility of improving these models by introducingmore variables, as done in Recondo, Pen, et al. (2013). Multiple linear regression modelsare developed in order to consider other factors with an impact on Ta, such as W obtainedfrom daytime Terra-MODIS data, the topography, the geographical location, and theseason or Julian day of the year.

3.1. Global MODIS LST algorithms/products: similarities and differences

The three global MODIS algorithms/products for estimating LST compared in this studyare: the algorithm by Wan (1999), the LST1 algorithm by Sobrino, El Kharraz, and Li(2003), and the IMAPP LST product. All of them use the MODIS Thermal Infrared (TIR)channels 31 and 32 (centred at 11.030 and 12.020 m, respectively; 1 km resolution), withlittle systematic error (Wan 2002).

Sobrino, El Kharraz, and Li (2003) proposed three MODIS LST algorithms for cloud-free land areas: a quadratic algorithm (LST1), a linear algorithm (LST2), and an algorithm(LST3) that follows the structure given by Becker and Li (1990). The three algorithms usethe same five variables (T31, T32, W, , and ), whose definitions are as follows: T31 andT32 are the brightness temperatures in MODIS channels 31 and 32; W is the total amountof atmospheric water vapour; = (31 + 32)/2 is the mean effective emissivity in channels31 and 32; and = (3132) is the spectral emissivity difference between both channels.The split-window coefficients of each algorithm are obtained by numerical simulations.W is obtained using Sobrinos MODIS W algorithm, based on the MODIS Near Infrared(NIR) water vapour channels. They also validated their LST models in wet conditions(W < 3.5 cm) using in situ data, obtaining the RMSD ranging between 0.6 and 1.2 K, withLST1 being the best algorithm.

Recondo, Pen, et al. (2013) also found that LST1 was the best of Sobrinos threealgorithms for estimating the daily Ta from daytime Terra-MODIS LST data. Therefore,LST1 was the only one of Sobrinos LST algorithms used in this article. Sobrino, ElKharraz, and Li (2003) do not propose different LST algorithms for night-time or daytime,and when estimating the night-time LST1 from night-time MODIS TIR data, we haveused W and NDVI estimated from daytime data. Therefore, it is assumed that, if theatmospheric conditions do not vary, then the differences between the daytime and night-time W values are low (differences

and 0.45 cm or typical errors in the range of 521%; see Recondo, Pen, et al. 2013 formore details). Regarding the calculation of and , we have used the formulas proposedby Recondo, Pen, et al. (2013), based on the NDVI only.

Wan (1999) proposed a MODIS LST algorithm (in clear-sky conditions) that general-ized the linear form of the WanDozier LST algorithm into a view-angle-dependent, split-window LST algorithm (Wan and Dozier 1996), which is similar to Becker and Lis localsplit-window method (Becker and Li 1990). The algorithm uses the variables T31, T32, ,and , whose definitions are the same as those given previously. The optimal coefficientsare obtained by simulation, but unlike Sobrinos algorithm, separating the atmospherictemperature profiles into groups according to the surface Ta (in night-time or daytimeconditions), W, and the viewing angle. The surface Ta and W are given by the MODISatmospheric profile product.

NASAs standard products MOD11 LST (for Terra) and MYD11 LST (for Aqua) weredeveloped following the LST algorithm by Wan (1999), and produced at 1 km resolution.Wan (2008) presented new refinements for Version 5 (V5) of the MODIS LST/Emissivityproducts, improving them significantly. Comparisons between V5 LSTs and in situ values(in the LST range from 10C to 58C and W range from 0.4 to 3.5 cm) indicate that theaccuracy of the MODIS LST product is better than 1 K in most cases.

As mentioned in Section 1, a DB version of the 1 km standard MODIS LST product isthe 1 km LST product generated by the software IMAPP (Huang et al. 2004). IMAPP is afreely distributed software package developed by the Space Science and EngineeringCenter (SSEC) at the University of WisconsinMadison (http://cimss.ssec.wisc.edu/imapp), also available as a Virtual Appliance (imapp_va). This software allows groundstations capable of receiving DB from Terra and Aqua to create a variety of products fromMODIS and other sensors. Technical details about how the IMAPP products needed inthis work have been obtained are given in Section 3.2. The IMAPP LST product isgenerated using an adaptation of Wan LST algorithm for its use in the MODIS RapidResponse (RR) System in order to provide real-time data. The RR LST has no dependenceon external products and it is suitable for DB and other processing systems (Pinheiro et al.2007). It contains no cloud mask. Initial validation with field data suggests that theabsolute uncertainty of the RR product is below 1 K. This 2007 version of the MODISRR LST product is currently included in IMAPP.

As for Ta retrieval from LST data in peninsular Spain using daytime Terra-MODIS data,Recondo, Pen, et al. (2013) found that the product MOD11 LST (V5) was the best of thetested products, followed by the IMAPP product. In order to include the variable W incombination with these LST products in this work, the daytime standard product MOD05(Total Precipitable Water) and the IMAPP WVNIR (Near-Infrared Water Vapour) producthave been combined with the standard MODIS LST product and the IMAPP LST product,respectively, as done in Recondo, Pen, et al. (2013). All products have a spatial resolutionof 1 km. MOD05 and IMAPP WVNIR are generated following different algorithms, thoseof Gao and Kaufman (2003) and Albert et al. (2005), respectively. An exhaustive review ofthe literature comparing the three global MODIS NIR algorithms for W estimation (incloud-free land areas) used in this study is given in Recondo, Pends, et al. (2013).

3.2. Data

Several types of data were used in this work: meteorological data from ground-levelstations, MODIS data, and other spatio-temporal data for 28 days during the year 2010.


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http://cimss.ssec.wisc.edu/imapphttp://cimss.ssec.wisc.edu/imapp

The meteorological stations are the same as those used in Recondo, Pen, et al. (2013)and also all the dates except one. The 29 dates in that article were chosen by selecting themost cloud-free daytime Terra-MODIS images representing all seasons more or lessequally. For the night-time Aqua-MODIS data used in this work, there were problemswith one date and 28 days were finally used: five in winter, eight in spring, nine insummer, and six in autumn. Daily Tmin data measured in 331 ground-level stationsdistributed across peninsular Spain were obtained from the online archive of 10 Spanishinstitutions. The spatial distribution of the stations is shown in Figure 1. These data werealready collected and used for estimating daily Tmin from daytime Terra-MODIS data inRecondo, Pen, et al. (2013). However, as expected, the time histogram of these Tmin forthe 28 dates used in 2010 shows that Tmin is attained in peninsular Spain mainly between4:00 and 7:00 UTC and, consequently, the night-time Aqua-MODIS data should be themost adequate for estimating the daily Tmin.

MODIS data were obtained from two sources: the DB system at the University ofOviedo and NASA.

Regarding data from the DB system at the University of Oviedo, a total of 42 night-time Aqua-MODIS granules from the 28 dates were used. These data were capturedbetween 1:18 and 3:34 UTC, with the mean hour being 2:13 0:45 UTC. In most cases,two images were necessary each night to complete peninsular Spain, because each imageonly took one part of it (East or West). These data were analysed with the IMAPPsoftware, in order to generate several MODIS products (all of them at 1 km2 spatialresolution) at different levels of processing (see Figure 2).

The night-time product MYD021KM (Guenther et al. 1998) was obtained usingthe package MODISL1DB (version 1.7) included in the IMAPP Virtual Appliance (ver-sion 1.1). This Level 1B product contains calibrated and geolocated (World GeodeticSystem (WGS) 84) radiances in W m2 m1 sr1 for 16 thermal emissive channels, butonly channels 31 and 32 were used in this work. The geolocation product (MYD03) wasobtained using the same software package.

Level 0

Level 1

Level 2/3

Level 2/3

LST1 SobrinoW SobrinoNDVI

Land:Atmosphere:

MOD/MYD021KM (Level 1B)

MOD/MYD01 (Level 1A)

IMAPP Virtual Appliance

MODISL1DB

Raw data (DB system)

IMAPP LSTIMAPP CMIMAPP WVNIR

Science ProcessingAlgorithms

Com

puted usingcom

mercial softw

are

MOD/MYD03 (Geolocation)

Figure 2. Processing flow chart of the MODIS data received by the DB system at the University ofOviedo.

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The IMAPP Virtual Appliance also includes several software packages to create land,atmosphere, and ocean Level 2 products from the Level 1B products. The packageMODLST-SPA (Science Processing Algorithm), version 4.14, was applied to the night-time products MYD02 in order to obtain the IMAPP LST product. The IMAPP MODIScloud mask (IMAPP CM) was obtained from the MODIS Atmosphere Level 2 software(version 2.1). IMAPP CM is the DB version of NASAs standard product MOD35(Ackerman et al. 1998). The MODIS Atmosphere Level 2 software is also used for thegeneration of the IMAPP WVNIR product. But this product, as any 1 km MODISW product, is not available for the night-time, because it is obtained from theMODIS NIR bands. Thus, the daytime IMAPP WVNIR product, from the earliestTerra-MODIS data, was used in combination with the night-time Aqua-MODIS products.The IMAPP WVNIR product for the 28 dates selected in this study was already generatedand used in Recondo, Pen, et al. (2013). It was obtained from Terra-MODIS databetween 10:43 and 11:35 UTC (with the mean time point being 11:08 00:16).

Since Sobrinos data cannot be obtained via download or through freely distributedsoftware, Sobrinos LST was calculated using night-time MYD021KM. To obtain theW data, however, daytime MOD021KM was used, because Sobrinos algorithm for Wretrieval is based on the NIR channels. MOD021KM data were also employed to calculatethe NDVI for the 28 dates selected. All the daytime Terra-MODIS products (at around11:08 UTC) were already generated and used in Recondo, Pen, et al. (2013) and usedagain in this work. The night-time Aqua-MODIS products (at around 2:13 UTC) weregenerated in this work.

As for NASAs data, two standard products were obtained for the 28 dates selected:night-time Aqua-MODIS LST/Emissivity product (MYD11_L2), from which only LSTdata (MYD11 LST) were used in this work, and daytime Terra-MODIS Total PrecipitableWater product (MOD05). As it occurs with the IMAPP WVNIR product, the productMOD05 from daytime Terra-MODIS data was used together with the night-time Aqua-MODIS products. The products MYD11_L2 and MOD05 (Collection 5) were obtainedvia download from the Level 1 and Atmosphere Archive and Distribution System(LAADS, http://ladsweb.nascom.nasa.gov) at the NASA Goddard Space Flight Center,because they cannot be obtained in real time. The products MOD05 were already used inRecondo, Pen, et al. (2013) and the products MYD11 LST were obtained in this work.The spatial resolution of all MODIS products used is 1 km2.

In addition to LST, W, and NDVI, eight other spatio-temporal variables were alsotested (as done in Recondo, Pen, et al. 2013): Julian day of the year (JD) and UTC hour(hour) of the night-time Aqua-MODIS granules, and latitude (), longitude (), elevation(h), slope (s), curvature (c), and distance to the coast (dcoast) of the 331 ground-levelmeteorological stations. The geodetic coordinates (, ) of the stations were provided bythe Spanish institutions that manage the stations. The elevation was obtained from adigital elevation model (DEM) of peninsular Spain of 1 km2 spatial resolution, providedby the National Geographic Institute (IGN). Slopes and curvatures were computed fromthe DEM. Finally, the distance to the coast of the stations was calculated using thecoastline of the 1:200,000 National Cartographic Base provided by IGN.

3.2.1. Data preparation

Night-time Aqua-MODIS products (MYD021KM) were projected on to the WGS84-UTM30N (Universal Transverse Mercator, zone 30 North) coordinate system andradiances of channels 31 and 32 converted into T31 and T32. Cloudy areas of


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http://ladsweb.nascom.nasa.gov

MYD021KM and IMAPP LST were masked using the IMAPP CM products. Onlyconfident clear areas, with a confidence level greater than 0.99, were considered forfurther analysis. IMAPP CM is not used for masking MYD11 LSTs, because they havetheir own cloud mask, obtained from NASAs standard product MOD35 (Ackerman et al.1998). Then, thermal data from MYD021KM, IMAPP LST, and MYD11 LST wereextracted for the location of the meteorological stations. The next step was to includethe extracted values in a database, in order to combine these night-time Aqua-MODISdata with other data obtained in Recondo, Pen, et al. (2013): satellite-retrieved data fromthe daytime Terra-MODIS overpass (W obtained with the different products/algorithmsand NDVI), meteorological data (Tmin), and spatio-temporal data. All these data werecombined to create a single data record for each of the 28 dates selected and eachmeteorological station with data availability. The combining criteria between meteorolo-gical and satellite-retrieved data for a date are based on a one-to-one relationship, relatingdaily Tmin from a station with daily satellite-retrieved data (night-time LST and daytime Wand NDVI). Data from the overlapping area between two granules of the same day wereaveraged in order to obtain a single satellite-based record for each date. Finally, LST1sfrom Sobrinos algorithm were calculated using T31 and T32 (extracted from the night-timeproducts MYD021KM), and W-Sobrino, , and obtained from the daytime productsMOD021KM used in Recondo, Pen, et al. (2013).

4. Analysis and results

Statistical computing and graphics generation throughout this article were performed inthe free software environment R (http://www.r-project.org/, Crawley 2007). Simple andmultiple linear regressions were employed as statistical methods for daily Tmin estimation,using only LST as the predictor variable in the simplest models, and including othervariables besides LST in the multiple linear regression models. In all cases, we have usedrobust regressions, less sensitive to the presence of potential outliers than classic linearregressions. Robust regression models were performed with the R package MASS(Modern Applied Statistics with S; Venables and Ripley 2002). Several statistical para-meters were calculated to evaluate the performance of the different models, such as thecoefficient of determination (R2) and the residual standard error (RSE):

RSE ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP

y y 2

s; (1)

where y is the value of y predicted by the model and v refers to the degrees of freedom,calculated as the total number of observations, n, minus the number of parameters,k (v = n 2 in a simple linear regression). The accuracy of the Tmin predictions by agiven model was measured during the process of validation using two additional para-meters: the root mean square error of the differences (RMSD) and the bias for the mean ofthe residuals:

RMSD ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP

yobserved yestimated 2n 2

s; (2)

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http://www.r-project.org/

Bias P

yobserved yestimated n

: (3)

Statistical analysis was carried out in two steps: first, models were developed using acalibration data set, and then models were evaluated using an independent data set, whichis referred to as the validation data set. These calibration and validation data sets are thesame as those obtained in Recondo, Pen, et al. (2013) by randomly dividing the samplein half (50% of the data for calibration and the remaining 50% for validation). However,fewer observations in each data set are available for this work, given that some of thedaytime cloud-free samples used in Recondo, Pen, et al. (2013) are affected by cloudcover during night-time, and thus, they have been removed in this analysis. Section 4.1presents the models for estimating daily Tmin, which have been developed using thecalibration data set; and Section 4.2 covers the validation of these models, which hasbeen performed with the validation data set.

For the complete data set, the data distribution per season is as follows: 13.8% inwinter, 37.9% in spring, 31.1% in summer, and 17.2% in autumn. The value ranges ofthe data in our study are: Tmin = [263, 300 K] = [10C, 27C], LST = [263, 300 K] =[10C, 27C], W = [0.1, 5 cm], NDVI = [0.03, 0.70], c = [0.03, 0.02 cm1], h =[1, 1735 m], s = [0.01, 10.8], dcoast = [0, 370 km], = [9, 3], = [36, 43.5],JD = [29, 360], and hour = [1:18, 3:34 UTC]. Therefore, our results and conclusions arerestricted to these values ranges.

4.1. Models for estimating daily TminWe first developed simple linear regression models between daily Tmin and night-timeLST obtained with the different products/algorithms. The structure of the models is

Tmin c1 c2 LST ; (4)

with Tmin and LST in K. The results for IMAPP LST, MYD11 LST, and LST1 are shownin Table 1, where n, R2, RSE, and the constants c1 and c2 (error) for each model are alsoindicated. For comparison purposes, we also include in Table 1 the models obtained inRecondo, Pen, et al. (2013) using daytime LST.

As shown in Table 1, the Tmin models based only on night-time LST obtained fromAqua-MODIS give an R2 between 0.88 and 0.91 and an RSE between 1.81 and 1.83 K.Similar results were obtained for the three products/algorithms, with maximum difference

Table 1. Models for estimating daily Tmin from night-time LST obtained with the differentproducts/algorithms (labelled Night-time), in comparison with those obtained in Recondo, Pen,et al. (2013) using daytime LST (labelled Daytime). The structure of the models is Tmin = c1 + c2(LST), with Tmin and LST in K.

Model n R2 RSE (K) c1 (K) c2

LST IMAPP Night-time 2086 0.89 1.83 10 2 0.964 0.007LST IMAPP Daytime 3014 0.67 3.73 128 2 0.514 0.007LST MYD11 Night-time 2218 0.91 1.81 9 2 0.966 0.006LST MOD11 Daytime 2788 0.68 3.69 123 2 0.527 0.007LST1 Sobrino Night-time 2086 0.88 1.83 18 2 0.932 0.007LST1 Sobrino Daytime 3014 0.70 3.61 134 2 0.488 0.006


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in R2 and RSE between models of only 0.03 and 0.02 K, respectively. The best results areobtained using MYD11 LST, followed closely by IMAPP LST and finally SobrinosLST1. The modelled Tmin results obtained in this study are significantly better than thoseobtained in Recondo, Pen, et al. (2013) using daytime LST. The improvement rangesfrom 26% to 34% in terms of R2 and from 49% to 51% in terms of RSE (Table 1). Adirect relationship was found between daily Tmin and LST, with slope values close to 1 inthe models with night-time LST, compared to a slope of about 0.5 in the models withdaytime LST.

The simplest models (Table 1) were improved by including other variables. Thefollowing variables were tested in addition to the night-time LST: W, NDVI, hour, JD,, , h, s, c, and dcoast. In the models with IMAPP LST and MYD11 LST, we includedW obtained from IMAPP WVNIR and MOD05, respectively. W was not added in themodel using Sobrinos LST1, because this variable is already included in the LST1formulation. Only the variables with lower p-values from the t-test were selected to beincluded in the models. The variables finally used are LST, W (only in models withIMAPP LST or MYD11 LST), c, , JD, and h. The p-values associated with these sixvariables are smaller than 0.0009. When using IMAPP LST and MYD11 LST, Tmin wasmodelled as

Tmin c1 c2 LST c3W c4c c5 c6 JD c7h (5)

and with LST1 as

Tmin c1 c2 LST c4c c5 c6 JD c7h: (6)

The parameters of these models are given in Table 2. The units of Tmin, LST, W, c, , and hare K, K, cm, cm1, , and m, respectively, and JD has values between 1 and 365. Thecurvature is considered positive when the surface is concave (bottoms of the valleys andbasins) and negative when it is convex (ridges and top of the mountains). Table 2summarizes the results of the models with night-time LST and other variables, in termsof n, R2, and RSE, compared to those obtained in Recondo, Pen, et al. (2013) using

Table 2. Models for estimating daily Tmin from night-time LST obtained from IMAPP LST, MYD11LST, and LST1 (models with LST and other variables). The structure of the models is Tmin = c1 + c2(LST) + c3 W + c4 c + c5 + c6 (JD) + c7 h; c3 = 0 for LST1. See Section 4.1 for the units. Values inbrackets correspond to models obtained in Recondo, Pen, et al. (2013) using daytime LST.

Parameter LST IMAPP LST MYD11 LST1 by Sobrino

n 2080 (2996) 2218 (2788) 2086 (3014)R2 0.91 (0.80) 0.92 (0.81) 0.90 (0.75)RSE (K) 1.75 (3.00) 1.75 (2.83) 1.79 (3.30)c1 20 3 26 3 13 2c2 0.92 0.01 0.90 0.01 0.948 0.007c3 0.6 0.1 0.67 0.08c4 110 8 114 8 118 9c5 0.04 0.02 0.08 0.01 0.05 0.02c6 0.0027 0.0005 0.0032 0.0004 0.0038 0.0005c7 0.0008 0.0001 0.0004 0.0001 0.0010 0.0001

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daytime LST and other variables. A noticeable improvement is observed in the modelledTmin based on night-time LST with respect to the daytime models of Recondo, Pen, et al.(2013), as shown in Table 2: the improvement ranges from 14% to 20% in terms of R2 andfrom 38% to 46% in terms of RSE.

As shown in Table 2, the Tmin models based on night-time LST and other variablesgive R2 between 0.90 and 0.92 and RSE between 1.75 K and 1.79 K. The results aresimilar for the three products/algorithms used in this work. The inclusion of othervariables in addition to night-time LST slightly improves the modelled Tmin, given thatthe R2 only increases 0.010.02, and the RSE only decreases 0.040.08 K, with respect tothe simplest models. These results contrast with those obtained in Recondo, Pen, et al.(2013), where a more significant improvement was obtained when other variables wereincluded in addition to daytime LST (R2 increased 0.050.13 and RSE decreased 0.310.86 K for the different Tmin models). Note also that the spatio-temporal variablesincluded in this work are slightly different from those included in Recondo, Pen, et al.(2013). NDVI was one of the most explanatory variables in the daytime models, but it isnot significant in this case; conversely c, which is very significant in this work, was notespecially relevant in the daytime models.

Compared with previous similar works that derived daily Tmin from MODIS LSToutside Spain (see Section 1), our models based only on LST give similar or even higherR2 values, and lower errors. Our simplest modelled Tmin from MYD11 LST (see Table 1)gave similar R2 and lower errors than the modelled Tmin of Shen and Leptoukh (2011),also based on night-time data. Comparing our modelled Tmin from MYD11 LST with theresults of Zhang et al. (2011) for the linear regression between Tmin and night-time Aqua-LSTs, our model gives higher R2 and lower error. We cannot compare the models ofseveral authors with ours because they usually provide the statistical results of thevalidation, but not the parameters or the statistical results of the models. Hence, wepresent a wider comparison in Section 4.2, which deals with the validation of the models.

Regarding the spatio-temporal variables, in addition to LST and W, which we haveselected as the most explanatory for estimating Tmin (c, , JD, and h), our findings coincidewith previous similar studies. Jones et al. (2004), who also used MODIS LST to estimateTmin at night, pointed out that differences in terrain height allow cold surface air to settleunder the influence of gravity into the lowest levels in valleys and basins, where it is colderrelative to the surrounding warm slopes and ridges; this is related to the inclusion of thevariables c and h in our Tmin models. In the models developed by Cristbal, Ninyerola, andPons (2008), h was also one of the most important geographical variables. Zhang et al.(2011) found evident seasonal bias in their Tmin models using night-time MODIS LST,which is reduced in our modelled Tmin by the inclusion of the temporal variable JD. NDVI isone of the most explanatory variables in the daytime Ta models of Recondo, Pen, et al.(2013), but it is not significant in the night-time Tmin models proposed in this work.Therefore, we also conclude, like Shen and Leptoukh (2011), that the relationships betweenTmin and night-time LST have little dependence on land-cover types, whereas Tmax anddaytime LST depend significantly on land-cover types.

The inclusion of other variables in addition to night-time LST only improves slightly, interms of global accuracy (R2 or RSE), the simplest Tmin models. However, we should pointout that the inclusion of other variables in the simplest models might improve the localestimation of Tmin, because these variables take into account local factors, such as topo-graphy and geographical location, which influence the different variability of LST and Tmin(and W) along the year. Although further analysis is required to demonstrate this assertion,the influence of c, h, , and JD on T for peninsular Spain is shown in Figures 3(a)(d).


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(c)

()10 9 8 7 6 5 4 3 2 1 0 1 2 3 4

Number ofobservations

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Figure 3. Effect of some spatio-temporal variables in the difference Tmin MYD11 LST obtained inthe stations: the two spatial variables related to the topography, c (a) and h (b); the other spatialvariable, (c); and the temporal variable, JD (d). Finally, two maps (spring (e)(i), and summer (e)(ii))to illustrate graphically the influence of ; and the variation of Tmin and LST through the year (f).

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T is the difference between Tmin observed in the stations and LST (T = Tmin LST; thevalue of MYD11 LST has been used in the figure). T decreases with increasingc (indicated by the minus sign of the constant c4 of the models; see Table 2), the generaltrend being that Tmin > LSTwhen c is negative (top of mountains) and Tmin < LSTwhen c ispositive (valleys). On the other hand, T increases slightly when h increases (c7 is positive,although very small), the general trend being that Tmin < LST until h 1000 m, andTmin > LST, for h > 1200 m, although we have few stations above 1200 m to assert that Tminis always higher than LST at these altitudes. The behaviour of Tmin and LST with thecurvature and the altitude is explained in Jones et al. (2004). With respect to longitude, Tdecreases with increasing (c5 is negative) and its behaviour marks the great differencebetween the west ( = 79 W, Galicia, at the north of Portugal) with Tmin > LST and therest of Spain, where Tmin < LST. This different behaviour of Tmin in both areas of Spain isalso illustrated in Figure 3(e). The difference between the northwest and the rest ofpeninsular Spain coincides with a well-known climatic difference (see Section 2). T alsodecreases with increasing JD (c6 is negative, although very small) with Tmin LST in springand Tmin < LST in autumn. In general, LST is more stable than Tmin and, therefore, the localvariations observed in Tmin can only be explained by using other variables in addition toLST. However, these local differences between Tmin and LST seem to be compensated in thesimplest models, which explains the slight improvement in R2 and RSE.

Daily temperature dependence on JD is usually taken to be a sine function (Figure 3(f)).In this case, several parameters are needed in the model, such as the amplitude, JD formaximum Ta and LST, etc. Data from winter in this work are scarce due to the presence ofclouds, making it difficult to estimate reliable values of the parameters in the case of a sinefunction modelization. On the other hand, T depends linearly on JD during most of the

(e)(i)Spring: 21 May (JD 141)

Tmin MYD11 LST (K)

(e)(ii)Summer: 30 August (JD 242)

(f)

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Figure 3. (Continued).


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year and for most of the data in this work (spring, summer, and autumn, with 86.2% of thedata, see Figure 3(d)). So we decided to use a linear dependence on JD for the whole year.In any case, the value of c6 in Equations (5) and (6) is very small, especially at thebeginning of the year.

4.2. Validation of the models for estimating daily TminThe validation parameters of the Tmin based only on night-time LST (Table 1) are shownin Table 3, where the results for the daytime models of Recondo, Pen, et al. (2013) werealso included for comparison purposes. The accuracy of the models was evaluated bymeans of several validation parameters: R2 = 0.880.91, RSE = 1.751.80 K,slope = 1.0081.011, RMSD = 2.002.15 K, and bias = 0.130.17 K (Table 3). The R2

and RSE values obtained in the validation are similar to those from the generation of themodels, the slope is close to 1, the RMSD is slightly greater than RSE, and the values forthe bias are low. These values demonstrate the validity of the models. In terms ofaccuracy, the results are similar for the three products/algorithms used in this work,with MYD11 LST being the best product, followed by IMAPP LST and SobrinosLST1, in this order.

The accuracy of the models including night-time LST and other variables was alsoevaluated, obtaining the following results: R2 = 0.900.92, RSE = 1.671.73 K,slope = 1.0081.014, RMSD = 1.871.99 K, and bias = 0.11 K (Table 3). These resultsare slightly better than those obtained for the models based only on night-time LST andare similar to those obtained in the generation of the models. The best results are obtainedusing MYD11 LST, followed by IMAPP LST and finally by Sobrinos LST1. The modelfrom MYD11 LST is slightly better than the model from IMAPP LST, but the mainadvantage of the latter, for our purposes, is that it can be generated in nearly real timefrom the data obtained by our MODIS antenna. The results for both models are alsoshown graphically in Figure 4.

Table 3. Validation of the models for estimating daily Tmin from night-time LST (labelled Night-time) in comparison with the validation of those obtained in Recondo, Pen, et al. (2013) usingdaytime LST (labelled Daytime). The structure of the fits is Tmin, o = a + b Tmin, e whereTmin, o = observed Tmin and Tmin, e = estimated Tmin.

Model n R2 RSE (K) a (K) b RMSD (K) Bias (K)

Models with LSTLST IMAPP Night-time 2101 0.90 1.76 3 2 1.011 0.007 2.00 0.13LST IMAPP Daytime 2969 0.68 3.82 6 4 1.02 0.01 3.85 0.01LST MYD11 Night-time 2230 0.91 1.75 2 2 1.008 0.006 2.03 0.16LST MOD11 Daytime 2764 0.69 3.81 5 4 1.02 0.01 3.78 0.04LST1 Sobrino Night-time 2101 0.88 1.80 3 2 1.010 0.007 2.15 0.17LST1 Sobrino Daytime 2969 0.71 3.59 3 3 1.01 0.01 3.63 0.00

Models with LST and other variablesLST IMAPP Night-time 2099 0.91 1.67 3 2 1.010 0.007 1.88 0.11LST IMAPP Daytime 2958 0.81 2.90 1 3 1.002 0.009 2.95 0.11LST MYD11 Night-time 2230 0.92 1.68 2 2 1.008 0.006 1.87 0.11LST MOD11 Daytime 2764 0.82 2.80 1 3 1.004 0.009 2.89 0.07LST1 Sobrino Night-time 2101 0.90 1.73 4 2 1.014 0.007 1.99 0.11LST1 Sobrino Daytime 2969 0.75 3.43 0 3 1.00 0.01 3.40 0.05

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The results obtained in the validation of our models were compared with thoseobtained in previous similar studies that derived Tmin from LST (see Section 1). Ourmodels give similar or higher R2 and errors are usually lower. Shen and Leptoukh (2011)obtained similar R2, but a higher error. The slope and bias are also similar. As compared toZhang et al. (2011) the validations of our simplest Tmin model from MYD11 LST gave ahigher R2, slope closer to 1, and also a lower error. Compared to the validations ofVancutsem et al. (2010), our model from MYD11 LST has a lower error, at both daily and8 day scale. The validation of our simplest Tmin model from MYD11 LST gave a higherR2, but a worse error than that obtained by Jones et al. (2004); however, they only used 18sampling sites and data from five nights. Compared to previous similar works at thenational scale in the Iberian Peninsula, the validation of our simplest model for estimatingdaily Tmin from MYD11 LST gave a higher R

2 than that obtained by Benali et al. (2012)in Portugal for the estimation of weekly Tmin (they obtained as best result R

2 = 0.87 andRMSE = 1.74C). Daily models are expected to have a greater error than weekly modelsaccording to Vancutsem et al. (2010), but our daily Tmin gave a similar error to Benalismodel for estimating weekly Tmin, which is a very satisfactory result. Finally, at theregional scale in Spain, Cristbal, Ninyerola, and Pons (2008) obtained R2 values lowerthan those obtained in the validation of our Tmin model from MYD11 LST, and a highererror.

5. Conclusions

In this work, we present an improved version of existing models for the determination ofTmin, which significantly enhances the accuracy of Tmin estimations. The proposed modelsestimate daily Tmin in peninsular Spain over cloud-free land areas using MODIS data andspatio-temporal variables, allowing the generation of daily maps of Tmin with 1 km

2

spatial resolution. The original Tmin models were improved by replacing daytime Terra-MODIS LST by night-time Aqua-MODIS LST. The Tmin models were obtained empiri-cally through linear regressions using night-time Aqua-MODIS LST and the daily Tminobtained from 331 ground-level meteorological stations for the year 2010. The simplestmodels only used MODIS LST as proxy for estimating Tmin.

260

y = 1.010 3R2 = 0.92R2 = 0.91

n = 2230n = 2099RSE = 1.68 KRSE = 1.67 K

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RMSD = 1.88 K

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Figure 4. Daily Tmin from the stations versus Tmin estimated from the two best Tmin models usingnight-time LST and other variables (W, c, , JD, and h).


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These simple models were improved including other MODIS-based variables andspatio-temporal variables. The best Tmin models are those based on MYD11 LST,followed by IMAPP LST, with W retrieved from daytime Terra-MODIS data and thespatio-temporal variables c, , JD, and h. Models based on Sobrinos LST1 algorithmwere also tested, with worse results.

Compared with previous similar studies that derived daily or weekly Tmin fromMODIS LST outside Spain, at the national scale in the Iberian Peninsula, and at theregional scale in Spain, our simplest Tmin model from MYD11 LST gives similar or higherR2 values and lower errors, which is a very satisfactory result.

From the results, we conclude that the night-time Aqua-MODIS LST, which is theMODIS LST closer to the daily Tmin recorded in the ground-level stations, is moreadequate than daytime Terra-MODIS LST for estimating the daily Tmin in peninsularSpain.

AcknowledgementsWe wish to thank NASA for providing the products MYD11 used in this work and the SpaceScience and Engineering Center (University of WisconsinMadison) and NASA for the IMAPPsoftware, all free of charge.

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Crawley, M. J. 2007. The R Book. Chichester: John Wiley & Sons. ISBN-13 978-0-470-51024-7.Cristbal, J., M. Ninyerola, and X. Pons. 2008. Modeling Air Temperature through a Combination

of Remote Sensing and GIS Data. Journal of Geophysical Research 113: D13106.doi:10.1029/2007JD009318.

Gao, B.-C., and Y. J. Kaufman. 2003. Water Vapor Retrievals Using Moderate Resolution ImagingSpectroradiometer (MODIS) Near-Infrared Channels. Journal of Geophysical Research 108:43894398. doi:10.1029/2002JD003023.

Guenther, B., G. D. Godden, X. Xiong, E. J. Knight, S.-Y. Qiu, H. Montgomery, M. M. Hopkins, M.G. Khayat, and Z. Hao. 1998. Prelaunch Algorithm and Data Format for the Level 1Calibration Products for the EOS-AM1 Moderate Resolution Imaging Spectroradiometer(MODIS). IEEE Transactions on Geoscience and Remote Sensing 36: 11421151.doi:10.1109/36.701021.

Huang, H.-L., L. E. Gumley, K. Strabala, J. Li, E. Weisz, T. Rink, K. C. Baggett, J. E. Davies, W. L.Smith, and J. C. Dodge. 2004. International MODIS and AIRS Processing Package (IMAPP):A Direct Broadcast Software Package for the NASA Earth Observing System. Bulletin of theAmerican Meteorological Society 85: 159161. doi:10.1175/BAMS-85-2-159.

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Abstract1. Introduction2. Study area3. Method and data3.1. Global MODIS LST algorithms/products: similarities and differences3.2. Data3.2.1. Data preparation

4. Analysis and results4.1. Models for estimating daily Tmin4.2. Validation of the models for estimating daily Tmin

5. ConclusionsAcknowledgementsReferences

improvements in the estimation of daily minimum air temperature in peninsular spain using modis land...

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