Modeling of Day-to-Day Temporal Progression of Clear-Sky Land Surface Temperature

Transcription

1 Duan et al.: MODELING OF DAY-TO-DAY TEMPORAL PROGRESSION OF CLEAR-SKY LST 1 Modeling of Day-to-Day Temporal Progression of Clear-Sky Land Surface Temperature Si-Bo Duan, Zhao-Liang Li, Hua Wu, Bo-Hui Tang, Xiaoguang Jiang, and Guoqing Zhou Abstract This letter presents a method to calculate the width ω over the half-period of the cosine term in a diurnal temperature cycle (DTC) model. ω deduced from the thermal diffusion equation (TDE) is compared with ω obtained from solar geometry. The results demonstrate that ω deduced from the TDE describes the shape of the DTC model more adequately around sunrise and the time of maximum temperature than ω obtained from solar geometry. Additionally, taking into account the physical continuity of land surface temperature (LST) variation, a day-to-day temporal progression (DDTP) model of LST is developed to model several days of DTCs. The results indicate that the DDTP model fits in situ (or SEVIRI) LST well with a root mean square error (RMSE) less than 1 K. Compared with the DTC model, the DDTP model slightly increases the quality of LST fits around sunrise. Assuming that only six LST measurements corresponding to the NOAA/AVHRR and MODIS overpass times for each day are available, several days of DTCs can be predicted by the DDTP model with an RMSE less than 1.5 K. Index Terms Day-to-day temporal progression, diurnal temperature cycle (DTC), land surface temperature (LST), modeling. L I. INTRODUCTION and surface temperature (LST) is a key parameter at the land-atmosphere interface [1]. Land surface diurnal temperature cycle (DTC) is an important element in a wide range of applications within climatology and meteorology []. For instance, information on DTC can be used to infer thermal inertia and soil moisture [3]. Due to the intrinsic scanning characteristics of the sensors onboard polar orbiting satellites (e.g. NOAA/AVHRR or MODIS), the differences of local solar time for pixels on the same day or the same pixel on different days in a revisit period may reach up to two hours [4]. Moreover, because LST changes with local solar time, it is not possible to directly compare LSTs of different pixels or of the same pixel at different days. DTC models have the potential to be used to interpolate LSTs to the same local solar time with a priori knowledge [5]. The performance of six DTC models was evaluated in terms of clear-sky in situ and satellite data [6]. All six models performed with similar accuracies at any time of the day except around sunrise and the time of maximum temperature. Nevertheless, none of the six DTC models were concerned with day-to-day temporal progression (DDTP) of LST, resulting in a physical discontinuity in the DTC models around sunrise. If no additional parameters are introduced, DTC models with the width over the half-period of the cosine term calculated from solar geometry cannot reproduce the slow and smooth increase of LST around sunrise well [6]. To improve the quality of LST fits around sunrise and the time of maximum temperature, a method is presented to calculate the width over the half-period of the cosine term in the DTC models. This width is deduced from the thermal diffusion equation (TDE). Taking into account the physical continuity of LST variation, a DDTP model of LST is developed to model several days of DTCs. The DDTP model can be used to further improve the quality of LST fits around sunrise. This letter is organized as follows: Section II introduces the DTC and DDTP models. Section III describes the data used in this study. Results and discussion are presented in Section IV. Conclusion is drawn in the last section. Manuscript received September 19, 01. This work was supported by the National Natural Science Foundation of China under Grants , and by the State Key Laboratory of Resources and Environment Information System under Grant 088RA800KA. S.-B. Duan is with the State Key Laboratory of Resources and Environment Information System (LREIS), Institute of Geographic Sciences and Natural Resources Research (IGSNRR), Chinese Academy of Sciences (CAS), Beijing , China, the University of Chinese Academy of Sciences (UCAS), Beijing , China, and the LSIIT, UdS, CNRS, Bld Sebastien Brant, BP10413, 6741 Illkirch, France ( duansibo@gmail.com). Z.-L. Li is with the LREIS, IGSNRR, CAS, Beijing , China, and the LSIIT, UdS, CNRS, Bld Sebastien Brant, BP10413, 6741 Illkirch, France (corresponding author; phone: ; fax: ; lizl@igsnrr.ac.cn). H. Wu and B.-H. Tang are with the LREIS, IGSNRR, CAS, Beijing , China ( wuhua@igsnrr.ac.cn; tangbh@igsnrr.ac.cn). X. Jiang is with the UCAS, Beijing , China ( xgjiang@aoe.ac.cn). G. Zhou is with the Guangxi Key Laboratory of Spatial Information and Geomatics, Guilin University of Technology, Guangxi , China ( glitezhou@glite.edu.cn). II. METHODOLOGY The DTC model proposed by [7] is used in this study. There are two reasons for the choice of this model. One reason is that this model is deduced from the TDE, which will be used in the following section. The other reason is that this model uses a hyperbolic function to more accurately describe the decay of LST at night. This model is referred to as the INA08 model in this work, and can be described as follows

2 Duan et al.: MODELING OF DAY-TO-DAY TEMPORAL PROGRESSION OF CLEAR-SKY LST T t T T cos t t, t t day 0 a m s Tnight t T0 T Ta cos ts tm T k, t ts k t t s (1) T Kb G 0, t K z0 cos t tm z D 4 Assuming that G(0,t) at the time t sr is equal to zero, i.e. G(0, t sr )=0, the width ω can be obtained from (6) by requiring an argument of π/ for the cosine, i.e. (6) with 1 T k tan t sin 1 s tm ts tm Ta where T day and T night are the LSTs of the daytime and night-time parts, respectively, t is the time, T 0 is the residual temperature around sunrise (t sr ), T a is the temperature amplitude, ω is the width over the half-period of the cosine term, t m is the time at which temperature reaches its maximum, t s is the starting time of free attenuation, δt is the temperature difference between T 0 and T(t ), and k is the attenuation constant. More detailed description of these parameters can be found in [6]. A. INA08_1 Model The width ω (in hours) in the INA08 model can be determined by the duration of daytime [8] () 4 t t (7) 3 m sr The INA08 model with ω calculated from (7) is referred to as the INA08_ model in this work. The free parameters in the INA08_ model are the same as those in the INA08_1 model (i.e. T 0, T a, δt, t m, and t s ). C. DDTP Model The INA08_ model is used in the DDTP model to model several days of DTCs. Taking into account the physical continuity of LST variation, the night-time part at day n and the daytime part at day n+1 in the DDTP model are taken to be continuous at the time of minimum temperature t min at day n+1. By equating the end (lowest) temperature at day n with the starting temperature (around sunrise) at day n+1, the value of T 0 at day n+1 can be obtained in terms of the values of the other parameters at day n or n+1 arccos tan tan (3) 15 where is the latitude and δ is the solar declination. The INA08 model with ω estimated from (3) is called the INA08_1 model in this study. There are five free parameters in the INA08_1 model (i.e. T 0, T a, δt, t m, and t s ). B. INA08_ Model Assuming the one-dimensional periodic heating of a uniform half-space of constant thermal properties, temperature obeys the TDE [9] K T z t c z, T z, t where K is the thermal conductivity, ρ is the density, c is the specific heat, and T(z,t) is the temperature at depth z below the surface and time t. A solution of cosine function for (4) is t z z T z, t a bcos t tm exp D D where D is the damping depth of the diurnal temperature wave, D=(ωK/πρc) 1/, and a and b are unknown coefficients. Under these conditions, the heat flux at the surface G(0,t), following the convention with positive sign in the downward direction, can be derived from (5) (4) n1 n n n n n n T0 T0 T Ta cos n ts tm T k k t t n n1 n1 n1 T cos n n 1 n a n 1 tmin t m min s where the superscript n or n+1 denotes day n or n+1. The total number of the free parameters in the DDTP model for n (n ) days is 5n (i.e. T a, t m, t s, and δt for each day, t min for each day except for the first day, and T 0 on the first day). To further reduce the number of the free parameters in the DDTP model, it is assumed that the values of t min for each day are equal within the range of several days. Therefore, the total number of free parameters in the DDTP model for n (n ) days is 4n+ (i.e. T a, t m, t s, and δt for each day, T 0 on the first day, and t min ). Except for the first day, the values of T 0 for the other days are calculated from (8). In addition, the values of ω for each day are calculated from (7). III. DATA Both of in situ measurements and geostationary satellite (5) (e.g. MSG or GOES) observations can provide DTC. To evaluate the performance of the DTC and DDTP models at different spatial scales, a group of in situ LSTs and three groups of SEVIRI LSTs were collected with different geographical coordinates and land covers. Because several days of DTCs are needed to test the performance of the DDTP model, only a group of in situ LSTs is available to us. The details of the collected data are presented in Table I. The (8)

3 Duan et al.: MODELING OF DAY-TO-DAY TEMPORAL PROGRESSION OF CLEAR-SKY LST 3 selected 4-day period is just taken as an example of several days continuously in time. The in situ LSTs were measured in the HAPEX-Sahel field experiment that was undertaken in western Niger, in the West African Sahel region. To reduce the influence of wind on the in situ LSTs, each data point was averaged at 10-minute interval. The SEVIRI LSTs were derived from MSG-SEVIRI data using the algorithm proposed by [10] and [11]. The three groups of the SEVIRI LSTs respectively represent different land cover types according to the Global Land Cover 000 map. The selected date is based on the fact that more cloud-free days are available over the African and Iberian Peninsula area in August. The Levenberg-Marquardt minimization scheme is used to fit the DTC and DDTP models to the LST datasets. More detailed information on the initialization of the free parameters in the models can be found in [6]. SEVIRI) LSTs better than the INA08_1 model. However, the INA08_ model still cannot completely reproduce the slow and smooth increase of LST around sunrise. The fast increase of LST around sunrise for this model is still unphysical. TABLE I DESCRIPTION OF IN SITU AND SEVIRI LST DATA Site Date Longitude Latitude Land cover type A 4-7 Oct E N Mixed grassland and bare soil B -5 Aug W 40.87N Tree cover, needle leaved, evergreen * C -5 Aug W N Shrub cover, closed open, deciduous * D -5 Aug E 3.5N Bare areas * * According to the Global Land Cover 000 map produced by IES. IV. RESULTS AND DISCUSSION A. Evaluation of the INA08_1 and INA08_ Models The in situ LSTs on 7 October 199 at Site A and the SEVIRI LSTs on 5 August 008 at Sites B-D were taken as examples to evaluate the performance of the INA08_1 and INA08_ models. The LST differences (modeled LSTs minus in situ (or SEVIRI) LSTs) for the two models at the four sites are shown in Fig. 1(a)-(d). Because there are no significant differences between the INA08_1 and INA08_ models for the night-time part, only the LST differences from sunrise to around t s are displayed in Fig. 1(a)-(d). The INA08_ model shows a better performance around sunrise and tm than the INA08_1 model in terms of the LST differences and root mean square errors (RMSEs). The largest LST differences of the INA08_1 model around sunrise at Sites A-D are approximately -4.5 K, -3 K, -.4 K, and -4 K, respectively, while those of the INA08_ model are approximately -.5 K, -1.5 K, -1. K, and - K, respectively. In addition, the RMSEs of the INA08_1 model at Sites A-D are 0.99 K, 0.64 K, 0.68 K, and 0.9 K, respectively, while those of the INA08_ model are 0.6 K, 0.4 K, 0.4 K, and 0.43 K, respectively. The results can largely be explained by the fact that the width ω given by (7) is substantially smaller than that given by (3). The smaller width ω leads to the narrower shape of the cosine function in the INA08_ model. The real DTC do not follow a pure cosine function controlled by solar geometry, which is narrowed by atmospheric attenuation of solar irradiation at large zenith angle (i.e. large air mass) as pointed out by [1]. Therefore, the INA08_ model with smaller width ω fits the in situ (or Fig. 1. LST differences (modeled LSTs minus in situ (or SEVIRI) LSTs) for the INA08_1 and INA08_ models from sunrise to around ts on 7 October 199 at Site A and on 5 August 008 at Sites B-D. INA08_1 denotes the INA08 model with the width ω calculated from solar geometry. INA08_ represents the INA08 model with ω deduced from the thermal diffusion equation. B. Modeling of Day-to-Day Temporal Progression of LST Fig. (a)-(d) displays the DDTP model fitting the in situ LSTs on 4-7 October 199 at Site A and the SEVIRI LSTs on -5 August 008 at Sites B-D. The selected 4-day period is just taken as an example of several days continuously in time. The DDTP model shows a good performance to fit the in situ (or SEVIRI) LSTs with an RMSE less than 1 K. Fitting the DDTP model to several days of DTCs summarizes the thermal behavior of the land surface and yields representative and informative thermal surface parameters (TSP) [8]. These TSPs depend on all modeled LSTs and are not influenced by small gaps (see Fig. (a)) due to the technical problems or brief cloud cover as well as by outliers (see Fig. (b)) due to the undetected clouds. Therefore, these TSPs can be used to interpolate missing data [8] or to improve cloud screening algorithms [7]. However, the performance of the DDTP model depends on the quality of LST as well as on atmospheric and surface wind conditions.

4 Duan et al.: MODELING OF DAY-TO-DAY TEMPORAL PROGRESSION OF CLEAR-SKY LST 4 A successful application of the DDTP model requires two or more nearly cloud-free DTC. Such conditions can be met over arid and semi-arid areas. those data have relatively large fluctuations, which may be caused by the wind, leading to relatively poor data quality compared with the SEVIRI LSTs. One useful application of the DDTP model is to implement data interpolation in terms of limited satellite measurements. We assume that only six in situ (or SEVIRI) LSTs corresponding to the NOAA/AVHRR and MODIS overpass times (01:30, 07:30, 10:30, 13:30 19:30, and :30) for each day are available. Several days of DTCs are predicted by the DDTP model by means of only six in situ (or SEVIRI) LSTs for each day on 4-7 October 199 at Site A and on -5 August 008 at Sites B-D. The results are shown in Fig. 4(a)-(d). The predicted LSTs are in good agreement with the in situ (or SEVIRI) LSTs with an RMSE less with 1.5 K. Compared Fig. 4(a)-(d) with Fig. (a)-(d), the RMSEs using only six LSTs for each day are approximately two times larger than the RMSEs using all LST measurements. Relatively larger LST differences can be observed between approximately 15 h and 18 h for each day due to the lack of LST measurements over this period. If one more LST measurement can be obtained over this period, the predicted LST accuracies can be improved. In addition, if six LST measurements more evenly distributed (e.g. 01:00, 05:00, 09:00, 13:00, 17:00, and 1:00), the predicted LST accuracies can also be improved. Fig.. The DDTP model fitting in situ (or SEVIRI) LSTs on 4-7 October 199 at Site A and on -5 August 008 at Sites B-D. Fig. 3(a)-(d) shows the LST differences (modeled LSTs minus in situ (SEVIRI) LSTs) for the INA08_ and DDTP models on 7 October 199 at Site A and on 5 August 008 at Sites B-D. Because of negligible differences between the INA08_ and DDTP models after 11h, only the LST differences from sunrise to around 11h are displayed in Fig. 3(a)-(d). The DDTP model shows a slightly better performance around sunrise than the INA08_ model at the four sites in terms of the LST differences and RMSEs. The largest LST differences of the INA08_ model around sunrise at Sites A-D are approximately -.5 K, -1.5 K, -1 K, and - K, respectively, while those of the DDTP model are approximately -1 K, -0.5 K, -0.5 K, and -1 K, respectively. Furthermore, the RMSEs of the INA08_ model at Sites A-D are 0.96 K, 0.53 K, 0.51 K, and 0.57 K, respectively, while those of the DDTP model are 0.53 K, 0.37 K, 0.45 K, and 0.35 K, respectively. These results mainly come from the fact that the DDTP model takes into account the continuity of LSTs at the time tmin. Compared Fig. 3(a) with Fig. 3(b)-(d), the differences between the INA08_ and DDTP models for the in situ LSTs are larger than those for the SEVIRI LSTs. By carefully analyzing the in situ LST data, we found that Fig. 3. LST differences (modeled LSTs minus in situ (or SEVIRI) LSTs) for the INA08_ and DDTP models from sunrise to around 11h on 7 October 199 at Site A and on 5 August 008 at Sites B-D. INA08_ represents the INA08 model with ω deduced from the thermal diffusion equation. DDTP represents the model of day-to-day temporal progression of LST.

5 Duan et al.: MODELING OF DAY-TO-DAY TEMPORAL PROGRESSION OF CLEAR-SKY LST 5 ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their constructive and insightful comments which helped to significantly improve this manuscript. Mr. Si-Bo Duan is financially supported by the China Scholarship Council for his stay in LSIIT, France. Fig. 4. Several days of DTCs predicted by the DDTP model in terms of only six in situ (or SEVIRI) LSTs for each day on 4-7 October 199 at Site A and on -5 August 008 at Sites B-D. LST differences (modeled LSTs minus in situ (or SEVIRI) LSTs) are also shown. Filled squares represent the LST measurements correspond to the NOAA/AVHRR and MODIS overpass times (01:30, 07:30, 10:30, 13:30, 19:30, and :30). V. CONCLUSION In this letter, we have presented a method to calculate the width ω over the half-period of the cosine term in the INA08 model. ω was deduced from the TDE and compared with ω calculated from solar geometry. The INA08_ model shows a better performance around sunrise and tm than the INA08_1 model. However, for the INA08_ model it is still difficult to describe the slow and smooth increase of LST around sunrise. The INA08_ model was used in the DDTP model to model several days of DTCs. The DDTP model shows a good performance in fitting the in situ (or SEVIRI) LSTs with an RMSE less than 1 K. Compared with the INA08_ model, the DDTP model slightly improves the quality of LST fits around sunrise. Furthermore, the performance of data interpolation of the DDTP model was investigated assuming only six LST measurements corresponding to the NOAA/AVHRR and MODIS overpass times for each day are available. The results demonstrate that several days of DTCs can be predicted by the DDTP model with an RMSE less than 1.5 K. REFERENCES [1] Z. Wan and Z.-L. Li, A physics-based algorithm for retrieving land-surface emissivity and temperature from EOS/MODIS data, IEEE Trans. Geosci. Remote Sensing, vol. 35, no. 4, pp , Jul [] A. Ignatov and G. Gutman, Monthly mean diurnal cycles in surface temperatures over land for global climate studies, J. Clim., vol. 1, no. 7, pp , Jul [3] J. C. Price, Thermal inertia mapping: a new view of the Earth, J. Geophys. Res., vol. 8, no. 18, pp , Jun [4] A. C. R. Gleason, S. D. Prince, S. J. Goetz, and J. Small, Effects of orbital drift on land surface temperature mesured by AVHRR thermal sensors, Remote Sens. Environ., vol. 79, pp , Feb. 00. [5] M. Jin and R. E. Dickinson, Interpolation of surface radiative temperature measured from polar orbiting satellites to a diurnal cycle 1. Without clouds, J. Geophys. Res., vol. 104, no. D, pp , Jan [6] S.-B. Duan, Z.-L. Li, N. Wang, H. Wu, and B.-H. Tang, Evaluation of six land-surface diurnal temperature cycle models using clear-sky in situ and satellite data, Remote Sens. Environ., vol. 14, pp. 15-5, Sep. 01. [7] A. K. Inamdar, A. French, S. Hook, G. Vaughan, and W. Luckett, Land surface temperature retrieval at high spatial and temporal resolutions over the southwestern United States, J. Geophys. Res., vol. 113, no. D7, pp. D07107, doi:10.109/007jd009048, 008. [8] F.-M. Göttsche and F.-S. Olesen, Modelling of diurnal cycles of brightness temperature extracted from METEOSAT data, Remote Sens. Environ., vol. 76, no. 3, pp , Jun [9] Y. Xue and A. P. Cracknell, Advanced thermal inertia modelling, Int. J. Remote Sens., vol. 16, no. 3, pp , Feb [10] G.-M. Jiang, Z.-L. Li, and F. Nerry, Land surface emissivity retrieval from combined mid-infrared and thermal infrared data of MSG-SEVIRI, Remote Sens. Environ., vol. 105, no. 4, pp , Dec [11] G.-M. Jiang and Z.-L. Li, Split-window algorithm for land surface temperature estimation from MSG1-SEVIRI data, Int. J. Remote Sens., vol. 9, no. 0, pp , Oct [1] F.-M. Göttsche and F.-S. Olesen, Modelling the effect of optical thickness on diurnal cycles of land surface temperature, Remote Sens. Environ., vol. 113, no. 11, pp , Nov. 009.