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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 9, NO. 4, JULY 2012
An Enhanced Physical Method for Downscaling Thermal Infrared Radiance Desheng Liu and Xiaolin Zhu
Abstract—Thermal infrared (TIR) imagery plays a critical role in characterizing land surface processes and modeling energy balances. However, due to the low TIR radiance emitted from the Earth’s surface, TIR imagery acquired from satellite thermal sensors is often with limited spatial resolutions, which presents a serious obstacle to its applications in heterogeneous landscapes (e.g., the studies of urban heat island). In this letter, we developed a new method for downscaling TIR radiance by addressing the limitations of a previously developed physical downscaling method by Liu and Pu (2008). To validate our method, a 990-m TIR image was generated by upscaling a 90-m TIR image from the Advanced Spaceborne Thermal Emission and Reflection Radiometer and downscaled back to the 90-m resolution using the proposed method. The results show that the enhanced physical method not only greatly reduced the block effects and smooth effects found in the original physical method but also improved the downscaling accuracy over the original method. Index Terms—Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER), downscale, Moderate Resolution Imaging Spectroradiometer (MODIS), thermal infrared (TIR) radiance.
I. I NTRODUCTION
T
HERMAL infrared (TIR) remote sensing has a wide range of applications in various environmental and ecological studies [1]. One common application of TIR imagery is to retrieve land surface temperature (LST), which provides critical inputs for modeling land surface processes and energy balances [2]–[5]. Additionally, TIR imagery has been directly used in many other applications, such as detecting tropical forest regeneration [6], estimating green leaf area index [7], estimating regional scale evapotranspiration [8], and detecting lithology [9]. However, due to the low TIR radiance emitted from the Earth’s surface, satellite thermal sensors, particularly those with frequent temporal coverage (e.g., MODIS), often have limited spatial resolutions. This largely affects the utility of TIR imagery over heterogeneous landscapes [10], [11], where higher spatial resolution TIR data are needed for modeling the spatial heterogeneity. Numerous downscaling techniques have been developed to improve the spatial resolution of TIR data [12], including both the original TIR imagery (digital number or radiance) Manuscript received October 18, 2011; revised November 18, 2011; accepted November 22, 2011. D. Liu is with the Department of Geography and Department of Statistics, The Ohio State University, Columbus, OH 43210 USA (e-mail: liu.738@ osu.edu). X. Zhu is with the Department of Geography, The Ohio State University, Columbus, OH 43210 USA (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LGRS.2011.2178814
[13]–[18] and the retrieved LST products [19]–[23]. Compared with downscaling LST, downscaling TIR imagery is a more fundamental task because of the following: 1) TIR imagery has a variety of applications aside from retrieving LST [6]–[9], and 2) downscaling TIR imagery can be regarded as the first step for downscaling LST [17]. Methodologically, techniques for downscaling TIR data can be categorized into two groups: statistical and physical [24]. Statistical methods seek to find a scale-invariant statistical relationship between TIR data (TIR imagery or LST) and other nonthermal spectral bands (or spectral indices) using linear regression or artificial neural network approaches [13]–[16], [19]–[23]; physical methods (PMs) use thermal radiation principles and spectral mixture analysis (SMA) to establish a scale-invariant and physically meaningful functional relationship between TIR radiance and land cover fractions [17], [18]. This letter focuses on PMs for downscaling TIR radiance. Specifically, the purpose of this letter is to improve the physical downscaling method developed by Liu and Pu [18], where TIR radiances at coarse spatial resolution are modeled as a linear combination of multiple land cover components weighted by their corresponding fractions and modified by atmospheric effects. One important assumption of the physical downscaling method is that the components within each coarse pixel are isothermal. While this method showed promise in resolving considerable spatial details in the downscaled TIR radiance image [18], the isothermal assumption had two undesirable outcomes: 1) Small objects were smoothed out in the downscaled image (referred to as smooth effects), and 2) pixels on the downscaled image showed obvious block boundary corresponding to the coarse-resolution pixels (referred to as block effects). In this letter, an enhanced PM (EPM) was developed to improve the downscaling accuracy and reduce the smooth effects and block effects due to isothermal assumption in the original PM. II. M ETHODOLOGY A. Review of the PM by Liu and Pu [18] The PM developed by Liu and Pu [18] is based on SMA of the TIR radiances of different land cover components. Specifically, under constant atmospheric conditions, the at-sensor TIR radiance Rs (i) of a given spectral channel in a coarse-resolution thermal image can be modeled by a linear mixing equation Rs (i) = τ
K
εk fk (i)B (Tk (i)) + RA
(1)
k=1
where τ is the transmissivity of the atmosphere, K is the total number of land cover components, εk is the emissivity
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of component k, fk (i) is the fraction of component k within coarse pixel i, Tk (i) is the surface temperature of component k within pixel i, B is the blackbody radiance given Tk (i), and RA is the atmospheric path radiance. With a slight change of notation, (1) can be rewritten as Rs (i) =
K
εk fk (i)B (Tk (i)) + RA
(2)
k=1
where εk = τ εk is the effective emissivity of component k. In (2), Rs (i) is the dependent variable, fk (i) and Tk (i) are the independent variables, and εk and RA are the unknown parameters. To solve (2), the at-sensor TIR radiance Rs (i) is directly obtained from the coarse-resolution TIR image. The land cover fraction fk (i) is derived by calculating the fraction of each land cover type within each coarse pixel using a high-resolution land cover classification map. To obtain the component temperature Tk (i), an isothermal assumption is made for each coarse pixel in the physical model. With this assumption, Tk (i) is simply taken from T (i), the LST retrieved from the coarse-resolution TIR image. Finally, parameters can be estimated by a least squares method using the data at all coarse pixels. To downscale the coarse-resolution TIR radiance, the paˆ A ) obtained from rameter estimates (denoted by ˆεk and R the coarse-resolution image are directly applied to the highresolution input variables. Suppose that each coarse pixel is decomposed into m fine pixels. For the jth fine pixel within the coarse pixel i (denoted by ij , j = 1, . . . , m), the TIR radiance can be initially estimated by ˆ s0 (ij ) = R
K
ˆA ˆεk fk (ij )B (Tk (ij )) + R
(3)
k=1
where the component fractions fk (ij ) can be obtained from a high-resolution land cover classification map; Tk (ij ) is obtained from the LST of the corresponding coarse pixel T (i) under the isothermal assumption. The initial estimate of the TIR radiance is then modified to reduce the bias caused by the isothermal assumption by adding an error term proportional to the initial estimate ⎛ ⎞ m 0 ˆ ˆ s (ij ) = R ˆ 0 (ij )+ Rs (ij ) ⎝ ˆ 0 (ij ) ⎠ (4) R Rs (i)− R s s m ˆ 0 (ij ) j=1 R s j=1
ˆ s (ij ) is the final estimate of the TIR radiance for fine where R pixel ij ; Rs (i) is the TIR radiance of the coarse pixel i. B. EPM The limitation of the original PM is the isothermal assumption, which can cause some smooth effects and block effects in the downscaled image. In this letter, the physical modeling method is further advanced in an attempt to reduce these effects. Fig. 1 presents a flowchart of this EPM. It requires two images of the same area acquired at about the same time. One is a high-resolution image with visible and near-infrared (VNIR) and short-wavelength infrared (SWIR) bands, such as the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER); the other is a coarse-resolution image
Fig. 1. Flowchart of the EPM for TIR downscaling.
with TIR bands and LST product, such as the MODIS. The major differences with the original PM are described as follows. First, in estimating the parameters in (2), instead of using all coarse pixels in the original method, the EPM only uses the m purest pixels (i.e., highest component fraction) in the coarse image for parameter estimation. This can partly reduce the effects of isothermal assumption on the parameter estimation because these purest pixels are closer to isothermal pixels than other pixels. The value of m is empirically determined based on two considerations: 1) it must satisfy the statistical requirement of a significantly large sample size, generally 30, and 2) it should be dependent on the homogeneity of the land surface. Second, in predicting fine-resolution TIR radiances using (3), the EPM estimates the component temperature Tk (ij ) by the LST of the fine pixel T (ij ) rather than by the LST of its corresponding coarse resolution T (i) as in the original PM. That is, the original estimate Tk (ij ) = T (i) is changed to Tk (ij ) = T (ij ). This could reduce the aforementioned block effects and smooth effects in the downscaled TIR image. However, the LST of each fine pixel T (ij ) is unknown and needs to be estimated. In this letter, the fine-resolution LST is estimated by a statistical method based on Normalized Difference Vegetation Index (NDVI) and Normalized Multi-band Drought Index (NMDI) given that LST is mainly affected by vegetation status and water content [19], [23]. Specifically, NDVI is used to describe the vegetation status and can be computed as NDVI =
RNIR − Rred RNIR + Rred
(5)
where RNIR and Rred are the reflectances of the near-infrared (NIR) band and the red band. NMDI is used to monitor the water content of soil and vegetation based on the absorption properties of vegetation water in the NIR band and the sensitive
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TABLE I PARAMETER E STIMATIONS BY THE O RIGINAL PM AND THE EPM∗
Fig. 2. False color display of the 15-m ASTER VNIR image in the study area.
characteristics of water absorption differences between soil and vegetation in the SWIR band [25]. It can be computed as NMDI =
RNIR − (R1640 nm − R2130 nm ) RNIR + (R1640 nm − R2130 nm )
(6)
where R1640 nm and R2130 nm are the reflectances of bands with 1640- and 2130-nm wavelengths, respectively. A linear model is used to establish the relationship between LST and the two spectral indices [19], [23] T (i) = a + b × N DV I(i) + c × N M DI(i)
(7)
where N DV I(i) and N M DI(i) are the NDVI and NMDI values of the coarse pixel i, respectively; a, b, and c are parameters that can be obtained by a least squares method from the coarse-resolution image. Then, this relationship is applied to estimate the LST at the fine pixel level Tˆ(ij ) = a ˆ + ˆb × N DV I(ij ) + cˆ × N M DI(ij )
(8)
where N DV I(ij ) and N M DI(ij ) are the NDVI and NMDI values of the fine pixel ij , respectively; a ˆ, ˆb, and cˆ are parameters estimated from the coarse-resolution image. III. A LGORITHM T ESTS To facilitate the comparison between the EPM and the original PM, the same data set used in [18] was used in this letter for algorithm tests. Specifically, ASTER level-1B data acquired on April 25, 2004, were obtained over Yokohama City, Japan. The level-1B data have been implemented for radiometric and geometric correction, and the thermal bands are with a noiseequivalent temperature difference of 0.3 K at 300 K. Fig. 2 shows a false color composite of the 15-m ASTER VNIR image over the study area, which is very heterogeneous and consists of various land use and land cover types from central business district to suburban to rural areas. The 90-m ASTER TIR
Fig. 3. (a) True 90-m ASTER TIR image, (b) simulated 990-m ASTER TIR image, and 90-m TIR image downscaled by (c) PM and (d) EPM.
radiance image at the band 13 served as the fine-resolution TIR radiance data. The coarse-resolution TIR radiance data were simulated by upscaling (i.e., simple average) the ASTER band 13 from the original 90-m resolution to the 990-m resolution. Moreover, the three-band ASTER VNIR data (15-m resolution) were first classified into seven land cover types, including water, soil, two urban classes, and three vegetation classes. The 15-m-resolution land cover classification map was then converted to land cover fraction maps at 90- and 990-m resolutions, respectively. Furthermore, the 1000-m LST products retrieved from MODIS data at the same date of the ASTER data were used as the coarse-resolution LST data required by EPM. Both PM and EPM were applied to downscale the simulated 990-m TIR radiance data back to the 90-m resolution. The estimated model parameters are summarized in Table I, where all coarse pixels were used in PM and the 80 purest coarse pixels were used in EPM. The estimated parameters in (8)
LIU AND ZHU: ENHANCED PHYSICAL METHOD FOR DOWNSCALING TIR RADIANCE
Fig. 4.
693
Scatterplots of the true values and estimated values of (a) PM and (b) EPM. Lines are 1:1 lines. Units for both axis are w/(m2 · sr · μm). TABLE II S UMMARY S TATISTICS OF THE T RUE I MAGE AND D OWNSCALED I MAGES [U NIT: w/(m2 · sr · μm)]
were a ˆ = 280.49, ˆb = −6.67, and cˆ = 21.38, respectively. The downscaling results were evaluated by visual assessment and quantitative assessment with the true 90-m TIR radiance data. Fig. 3 shows the 90-m TIR radiance images downscaled by PM and EPM as well as the original 90-m ASTER TIR radiance image and the simulated 990-m TIR radiance image. Compared with the downscaling results by PM [see Fig. 3(c)], the TIR radiance image downscaled by EPM [see Fig. 3(d)] is visually more similar to the true TIR radiance image as demonstrated by improved spatial continuity across coarse pixel boundaries (less block effects) and more spatial details in heterogeneous regions (less smooth effects). Fig. 4 shows the scatterplots between the predicted TIR radiance values by the two methods and the actual 90-m TIR radiance values. The data points in the scatterplot of the EPM prediction fall closer to the 1:1 line than that of the PM prediction, and the R2 value of the EPM prediction is 0.828, which is larger than the R2 value 0.771 of the PM prediction. Root-mean-square errors (rmses) were also calculated to provide the quantitative assessment of the prediction accuracy. The rmse of the EPM prediction is 0.252, which is smaller than 0.283 of the PM prediction. In addition, summary statistics of the true image and downscaled images are reported in Table II. From the Table II, all the statistics of the EPM prediction are closer to those of the true image, while the image downscaled by PM is with a smaller range and standard deviation, indicating that the PM prediction lost some colder (darker) objects and some hot spots (brighter objects). The aforementioned results indicate that EPM not only greatly reduced the block effects and smooth effects in the original PM but also improved the prediction accuracy of the downscaled TIR radiance data over PM. IV. C ONCLUSION AND D ISCUSSION This letter developed an EPM for downscaling TIR radiance. Compared with the original PM, the proposed method can overcome the limitations of isothermal pixel assumption by
making better use of the land surface information from highresolution VNIR and SWIR images. The results show that the TIR radiance prediction by the EPM was more accurate than the original PM. More importantly, the block effects and smooth effects in the PM were significantly reduced in the proposed method. The improved performance of the new method can be ascribed to two aspects. First, the purist coarse pixels were selected to estimate the parameters in the physical model, which can reduce the negative effects of isothermal assumption to some extent, particularly when there are large homogeneous patches for each land cover type. Second, a statistical model was developed to estimate the fine-resolution LST which can better approximate the fine-resolution component temperature than the coarse-resolution LST used in the original PM. It should be noted that the estimated LST does not have to be very accurate. As long as the relative difference of the estimated fineresolution LST reflects the spatial variability of thermal properties among different fine pixels, it can help reveal more spatial details in the downscaled TIR radiance image and thus reduce the aforementioned effects from the isothermal assumption. In addition, if the initial prediction of TIR radiance is more accurate, the final prediction would show less block effects because the bias is redistributed according to the variability of the initial prediction. It should be noted that the proposed method is not specific for downscaling ASTER TIR imagery but can be applied to downscale other TIR imagery, including MODIS, AVHRR, and Landsat TM/ETM+. The simulation of 990-m ASTER TIR imagery based on 90-m ASTER TIR imagery is mainly for validation purposes. This simulation approach to algorithm test has the advantage of avoiding the bias introduced by the different filter functions of TIR bands between two real TIR images (e.g., MODIS versus ASTER) and the impacts of their registration errors. There are some limitations while using this new method in practice. First, the improvement of parameter estimation in
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the physical model may be limited if sufficient pure pixels cannot be found in the study area. Second, as this method focuses on the TIR radiance, the low signal-to-noise ratio generally associated with thermal imagery might impact the accuracy of downscaled results. Third, similar to other existing methods, it requires a high-spatial-resolution image with VNIR and SWIR bands to provide land surface information. Therefore, the temporal resolution of downscaled TIR radiance is determined by the high-spatial-resolution image with VNIR and SWIR bands. However, high-spatial-resolution satellites are often with long revisit cycles, for example, Landsat with 16 days. Therefore, it is difficult to downscale TIR radiance with higher temporal resolution, which impedes the investigation of frequent surface energy dynamics at a fine spatial resolution. Recently, a fusion model was proposed to produce reflectance data with both high spatial and temporal resolutions [26]. In future study, we will consider using this fusion model to provide high spatial and temporal resolution VNIR and SWIR images in the PM for downscaling TIR radiance with higher temporal resolution. Finally, only simulated data were used to test the proposed method. For a more comprehensive validation, testing the proposed method with additional data can be carried out in the future. R EFERENCES [1] G. R. Diak, J. R. Mecikalski, M. C. Anderson, J. M. Norman, W. P. Kustas, R. D. Torn, and R. L. Dewolf, “Estimating land-surface energy budgets from space: Review and current efforts at the University of WisconsinMadison and USDA-ARS,” Bull. Amer. Meteorol. Soc., vol. 85, no. 1, pp. 65–78, Jan. 2004. [2] Z. Wan and J. Dozier, “A generalized split-window algorithm for retrieving land-surface temperature from space,” IEEE Trans. Geosci. Remote Sens., vol. 34, no. 4, pp. 892–905, Jul. 1996. [3] A. R. Gillespie, S. Rokugawa, T. Matsunaga, J. S. Cothern, S. Hook, and A. B. Kahle, “A temperature and emissivity separation algorithm for Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) images,” IEEE Trans. Geosci. Remote Sens., vol. 36, no. 4, pp. 1113–1126, Jul. 1998. [4] Z. Qin, G. D. Olmo, and A. Karnieli, “Derivation of split window algorithm and its sensitivity analysis for retrieving land surface temperature from NOAA-Advanced Very High Resolution Radiometer data,” J. Geophys. Res., vol. 106, no. D19, pp. 22 655–22 670, 2001. [5] R. Pu, P. Gong, R. Michishita, and T. Sasagawa, “Assessment of multiresolution and multi-sensor data for urban surface temperature retrieval,” Remote Sens. Environ., vol. 104, no. 2, pp. 211–225, Sep. 2006. [6] D. S. Boyd, G. M. Foody, P. J. Curran, R. M. Lucas, and M. Honzak, “An assessment of radiance in Landsat TM middle and thermal infrared wavebands for the detection of tropical forest regeneration,” Int. J. Remote Sens., vol. 17, no. 2, pp. 249–261, Jan. 1996. [7] H. D. Williamson, “Evaluation of middle and thermal infrared radiance in indices used to estimate GLAI,” Int. J. Remote Sens., vol. 9, no. 2, pp. 275–283, Feb. 1988. [8] J. C. Price, “Estimation of regional scale evapotranspiration through analysis of satellite thermal-infrared data,” IEEE Trans. Geosci. Remote Sens., vol. GRS-20, no. 3, pp. 286–292, Jul. 1982. [9] Y. Ninomiya, B. Fu, and T. J. Cudahy, “Detecting lithology with Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) multispectral thermal infrared ‘radiance-at-sensor’ data,” Remote Sens. Environ., vol. 99, no. 1/2, pp. 127–139, Nov. 2005.
[10] W. Kustas and J. Norman, “Evaluating the effects of subpixel heterogeneity on pixel average fluxes,” Remote Sens. Environ., vol. 74, no. 3, pp. 327–342, Dec. 2000. [11] J. A. Voogt and T. R. Oke, “Thermal remote sensing of urban climates,” Remote Sens. Environ., vol. 86, no. 3, pp. 370–384, Aug. 2003. [12] W. Zhan, Y. Chen, J. Zhou, J. Li, and W. Liu, “Sharpening thermal imageries: A generalized theoretical framework from an assimilation perspective,” IEEE Trans. Geosci. Remote Sens., vol. 49, no. 2, pp. 773–789, Feb. 2011. [13] D. Fasbender, D. Tuia, P. Bogaert, and M. Kanevski, “Support-based implementation of Bayesian data fusion for spatial enhancement: Applications to ASTER thermal images,” IEEE Geosci. Remote Sens. Lett., vol. 5, no. 4, pp. 598–602, Oct. 2008. [14] M. D. Carmen Valdes and M. Inamura, “Improvement of remotely sensed low spatial resolution images by back-propagated neural networks using data fusion techniques,” Int. J. Remote Sens., vol. 22, no. 4, pp. 629–642, Mar. 2001. [15] G. P. Lemeshewsky and R. A. Schowengerdt, “Landsat 7 thermal-IR image sharpening using an artificial neural network and sensor model,” in Proc. Visual Inf. Process. X, 2001, pp. 181–192. [16] M. S. Moral, “A window-based technique for combining Landsat thematic mapper thermal data with higher-resolution multispectral data over agricultural lands,” Photogramm. Eng. Remote Sens., vol. 56, no. 3, pp. 334–337, Mar. 1990. [17] W. T. Gustavson, R. Handcock, A. R. Gillespie, and H. Tonooka, “An image sharpening method to recover stream temperatures from ASTER images,” in Proc. Remote Sens. Environ. Monitoring, GIS Appl. Geology, 2003, pp. 72–83. [18] D. S. Liu and R. L. Pu, “Downscaling thermal infrared radiance for subpixel land surface temperature retrieval,” Sensors, vol. 8, no. 4, pp. 2695–2706, Apr. 2008. [19] N. Agam, W. P. Kustas, M. C. Anderson, F. Q. Li, and C. M. U. Neale, “A vegetation index based technique for spatial sharpening of thermal imagery,” Remote Sens. Environ., vol. 107, no. 4, pp. 545–558, Apr. 2007. [20] W. Kustas, J. Norman, M. Anderson, and A. French, “Estimating subpixel surface temperatures and energy fluxes from the vegetation indexradiometric temperature relationship,” Remote Sens. Environ., vol. 85, no. 4, pp. 429–440, Jun. 2003. [21] C. C. Wang, G. J. Yang, Z. L. Ma, and Z. R. Xing, “Fusion of VNIR and thermal infrared remote sensing data based on GA-SOFM neural network,” Geo-Spatial Inf. Sci., vol. 12, no. 4, pp. 271–280, Dec. 2009. [22] G. J. Yang, R. L. Pu, W. J. Huang, J. H. Wang, and C. J. Zhao, “A novel method to estimate subpixel temperature by fusing solar-reflective and thermal-infrared remote-sensing data with an artificial neural network,” IEEE Trans. Geosci. Remote Sens., vol. 48, no. 4, pp. 2170–2178, Apr. 2009. [23] G. J. Yang, R. L. Pu, C. Zhao, W. Huang, and J. Wang, “Estimation of subpixel land surface temperature using an endmember index based technique: A case examination on ASTER and MODIS temperature products over a heterogeneous area,” Remote Sens. Environ., vol. 115, no. 5, pp. 1202–1219, May 2011. [24] Y. Liu, T. Hiyama, and Y. Yamaguchi, “Scaling of land surface temperature using satellite data: A case examination on ASTER and MODIS products over a heterogeneous terrain area,” Remote Sens. Environ., vol. 105, no. 2, pp. 115–128, Nov. 2006. [25] L. Wang and J. J. Qu, “NMDI: A normalized multi-band drought index for monitoring soil and vegetation moisture with satellite remote sensing,” Geophys. Res. Lett., vol. 34, p. L20 405, Oct. 2007. DOI:10.1029/2007GL031021. [26] X. Zhu, J. Chen, F. Gao, and J. G. Masek, “An enhanced spatial and temporal adaptive reflectance fusion model for complex heterogeneous regions,” Remote Sens. Environ., vol. 114, no. 11, pp. 2610–2613, Nov. 2010.
