Optimization of the Local Split-Window Algorithm for FY-4A Land Surface Temperature Retrieval

remote sensing

Article Optimization of the Local Split-Window Algorithm for FY-4A Land Surface Temperature Retrieval

Lijuan Wang 1,2,*, Ni Guo 2, Wei Wang 2 and Hongchao Zuo 1

1 College of Atmospheric Sciences, Lanzhou University, Lanzhou 730000, China 2 Institute of Arid Meteorology, China Meteorological Administration /Key Laboratory of Drought Climate Change and Disaster Reduction in Gansu Province/Key Laboratory of Drought Climate Change and Disaster Reduction, China Meteorological Administration, Lanzhou 730020, China * Correspondence: [email protected]; Tel.: +86-0931-2402480

Received: 16 July 2019; Accepted: 21 August 2019; Published: 27 August 2019

Abstract: FY-4A is a second generation of geostationary orbiting meteorological satellite, and the successful launch of FY-4A satellite provides a new opportunity to obtain diurnal variation of land surface temperature (LST). In this paper, different underlying surfaces-observed data were applied to evaluate the applicability of the local split-window algorithm for FY-4A, and the local split-window algorithm parameters were optimized by the artificial intelligent particle swarm optimization (PSO) algorithm to improve the accuracy of retrieved LST. Results show that the retrieved LST can efficiently reproduce the diurnal variation characteristics of LST. However, the estimated values deviate hugely from the observed values when the local split-window algorithms are directly used to process the FY-4A satellite data, and the root mean square errors (RMSEs) are approximately 6K. The accuracy of the retrieved LST cannot be effectively improved by merely modifying the emissivity-estimated model or optimizing the algorithm. Based on the measured emissivity, the RMSE of LST retrieved by the optimized local split-window algorithm is reduced to 3.45 K. The local split-window algorithm is a simple and easy retrieval approach that can quickly retrieve LST on a regional scale and promote the application of FY-4A satellite data in related fields.

Keywords: land surface temperature; split-window algorithm; FY-4A; particle swarm optimization algorithm

1. Introduction The land–atmosphere interactions at the regional or large scale have both been a focus and challenge in geoscientiﬁc research [1–3], and the acquisition of research data plays a crucial role in further investigating such interactions. In recent years, with the improvement of satellite detectors and the development of remote sensing technology, remote sensing and retrieval have become important techniques for collecting regional-scale research data [4–6]. As a key parameter of land–atmosphere interactions, the accurate estimation of land surface temperature (LST) is crucial in energy balance and climate change studies. With the launch of the TIROS-IIsatellite in the middle of last century, surface temperature retrieval using satellite thermal infrared data began to develop [7]. The initial retrieval work was limited to sea surface temperature [8–11]. With the improvement of the atmospheric radiation transfer model, and the atmospheric radiation transfer equation simpliﬁcation by the approximation and hypothesis, as well as the abundance of NOAA/Advanced Very High Resolution Radiometer (AVHRR), Moderate Resolution Imaging Spectroradiometer (MODIS), and other remote sensing data, the deviation of sea surface temperature retrieved by the split-window method was reduced to less than 1.0 K. After the successful retrieval of sea surface temperature, it became more attractive to use satellite thermal

Remote Sens. 2019, 11, 2016; doi:10.3390/rs11172016 www.mdpi.com/journal/remotesensing Remote Sens. 2019, 11, 2016 2 of 21 infrared data to retrieve land surface temperature [12,13], and research has also shown that there are obvious diurnal variations in land surface emissivity [14,15]. According to the number of channels selected, retrieval algorithms can be divided into single channel algorithm [16,17], split-window algorithm [18–20], temperature-independent spectral index (TISI) [21,22], and day–night algorithm [23,24]. The split-window algorithm was first proposed by McMillin [18] in 1975, based on two adjacent thermal infrared channels of NOAA. The linear combination of these two adjacent channels can be used to eliminate atmospheric effects and avoid the retrieval of atmospheric profiles. The original split-window algorithm was only used for sea surface temperature retrieval. By 1984, based on several approximation assumptions, the radiation transfer equation was simplified, and assumed emissivity was 1.0. Price [19] first introduced the split-window algorithm into the LST retrieval. With the development of satellite and remote sensing technology, the split-window algorithm has developed rapidly. After considering the effects of water vapor, vegetation, and surface emissivity, a series of LST retrieval models have been established [25–27], where the accuracy of retrieved LST was kept within 3 K. Although algorithms are different in form, they are all based on the combination of two adjacent thermal infrared channels of satellite. The coefficients of the algorithm are also based on the surface emissivity, atmospheric transmittance, and vegetation index. The existing research shows that [28] an error of surface emissivity of 0.01 can cause a deviation of surface temperature of about 1 K, which is far greater than the atmospheric influence on LST retrieval. Surface emissivity is one of the main error sources of surface temperature retrieval. The FY-4A satellite is a second-generation geostationary meteorological satellite launched by China in 2016. FY-4A is also the first geostationary meteorological satellite—with the largest number and variety of instruments—that shows improved capability and efficiency in earth observation, and employs high-precision and advanced image navigation and registration technologies [29]. Satellites can provide multi-spectral, high-frequency, high-precision, and quantitative observation data for weather services, disaster prevention and mitigation, land–atmosphere interaction research, ecological civilization construction, and climate change mitigation—as well as provide valuable resources for the research and application of satellite remote sensing in meteorology and related fields. In order to promote the role and application of FY-4A in scientific research and avoid waste of resources, it is necessary to solve the problem of obtaining accurate remote sensing products from the FY-4A satellite. In recent years, it has been found that physical based approaches and Kalman filter methodology are effective methods for LST and emissivity retrievals using geostationary satellites data. These methods can achieve accuracy for LST of about 1 K, correlation coefficients with in situ truth data better than 0.98 and the retrieval (both emissivity and LST) can follow the natural diurnal cycle [30–33]. Having said that, we prefer to use a local split window approach for its easier implementation and because we can optimize the algorithm based on in situ measurement of emissivity. In fact, the result shows that a non-optimized, straightforward implementation, of the split window gets estimated LST, which deviates, e.g., from the MODIS LST by more than 4K [34]. The thermal infrared channels of the multichannel scanning imagery radiometer (AGRI) design for the FY-4A satellite are similar to those for the MODIS detector. However, given the differences in the spectral response functions, detection angles, and spectral ranges of all channels, as well as the spatial resolution between AGRI and MODIS, the original ground information obtained from AGRI may differ from that detected by MODIS. Therefore, the applicability of the existing retrieval algorithms to the FY-4A satellite data must be verified, and the retrieval algorithms must be further optimized to improve the retrieval accuracy of FY-4A. The AGRI data from the FY-4A satellite and the ground observational data form the Dingxi, Kangle, and Qifeng stations were used in this study. First, these data were used to examine the applicability of local split-window algorithms for LST retrieval from the FY-4A satellite remote sensing data. Second, these data were used to optimize the algorithm parameters by artificial intelligence particle swarm algorithm to improve the accuracy of the LST retrieved from the FY-4A satellite data in Remote Sens. 2019, 11, 2016 3 of 21 Remote Sens. 2019, 11, x FOR PEER REVIEW 3 of 21 satellitNorthweste data China. in Northwest This study China. aims Thi tos promote study ai thems applicationto promote ofthe FY-4A application satellite of dataFY-4A and satellite to improve data athend accuracyto improve of regional-scalethe accuracy of LST reg retrieval.ional-scale LST retrieval.

22.. M Materialsaterials and and Methods Methods

2.1. Materials Materials

2.1.1. Ground Ground Si Sitestes Introduction Introduction Dingxi station (35°34 (35◦34′0N,N, 1 10404°35◦35′E)0E) (or (or the the Dingxi Dingxi Drought Drought Meteorological and Ecological Environment TestTest Base) Base) is locatedis located at Dingxi at Dingxi City, Gansu City, Province. Gansu TheProvince. Dingxi Th statione Dingxi is a comprehensive station is a comprehensiveexperimental base experiment manageda byl base the China managed Meteorological by the China Administration. Meteorological The altitude Administration. of this station The is altitude1896.7 m, of annual this station mean temperatureis 1896.7 m, isannual 6.7 ◦C, mean annual temperature maximum monthlyis 6.7 °C, mean annual temperature maximum appears monthly in meanJuly, and temperature annual mean appears precipitation in July, and is 386annual mm. mean The observationalprecipitation is site 386 is mm. ﬂat andThe coveredobservational by wheat site isand fla potatot and covered plants, and by thewhea underlyingt and potato surface plants, is typical and the semi-arid underlying farmland. surface The is observed typical semi-arid variables farmland.can represent The basicobserved climate variables and land can surface represent characteristics basic climate in semi-aridand land regionssurface ofcha China.racteristics In-situ in semi-aridobservations regions have beenof China. widely In-situ used inobservations climate, hydrology, have been environment, widely used and in other clima scientiﬁcte, hydrology, research environment,in semi-arid areas and other of China scientific [35]. research in semi-arid areas of China [35]. Kangle (35(35°46◦460′N, 9999°49◦490′E)E) andand Qifeng Qifeng (39 (39°41◦410N,′N, 99 99°49◦490E)′E) stations stations were were established established on 4on June 4 June 2019 20at19 the at Kangle the Kangle Township Township and Qifeng and TibetanQifeng TownshipTibetan Township in Zhangye in City,Zhangye Gansu City, Province, Gansu respectively. Province, respectively.The Kangle Township The Kangle is located Township in the is middle located part in the of the middle Qilian part Mountains, of the Qilian with anMountains, altitude of with 3230 an m altitudeand has of a semi-humid3230 m and mountainhas a semi-humid grassland mountain climate, meangrassla annualnd climate, temperature mean annual of approximately temperature 3 ◦ ofC, aandpproximately mean annual 3 °C, precipitation and mean of annual 350 mm. precipitation The observation of 350 pointsmm. The and surroundingobservation points underlying and surroundingsurface in this underlying township surface are located in this in township grasslands are with located a high in grasslands vegetation with coverage. a highMeanwhile, vegetation coverage.the Qifeng Meanwhile, Tibetan Township the Qifeng is located Tibeta westn Township of the Hexi is located Corridor, west the northernof the Hexi foot Corridor, of the Qilian the northernMountain foot near of Jiuquan the Qilian City, Mounta and hasin near an elevation Jiuquan ofCity, 1900 and m. has Located an elevation in a semi-arid of 1900 climate m. Located of alpine in a semi-aridmountains, climate the Qifeng of alpine Tibetan mountains, Township the experiences Qifeng Tibetan long and Township cold winters, experiences short and long cool summers,and cold winters,a mean annualshort and temperature cool summers, of approximately a mean annual 3 ◦ temperatureC, and a mean of approximately annual precipitation 3 °C, and of 250a mea mm.n annualThe observation precipita pointstion ofand 250 surroundingmm. The observa areas intion this points township and aresurrounding typical desert areas underlying in this township surfaces awithre sparse vegetation. The underlying surface of each observation point is shown in Figure1.

(a) (b)

Figure 1. Cont. Remote Sens. 2019, 11, 2016 4 of 21 Remote Sens. 2019, 11, x FOR PEER REVIEW 4 of 21

FigureFigure 1 1.. OverviewOverview of of observation observation stations stations and and emis emissivitysivity observation observation instrument instrument 102F, 102F, where where ( (aa)) is is thethe Dingxi Dingxi station, ((b)) isis thethe emissivityemissivity observationobservation instrument instrument 102f, 102f, ( c()c is) is the the Kangle Kangle station, station, and and (d ()d is) isthe the Qifeng Qifeng station. station.

2.1.2.2.1.2. Ground Ground In-Situ In-Situ Data Data ToTo test the accuracy of the remote sensing retrieval model, observational data data collected collected at at the groundground sites, i.e., i.e., the Dingxi, Kangle, and and Qifeng stations, were were used in this study. The The LST LST data were from March to July 2018 2018 in in th thee Dingxi Dingxi station, station, and and the the Kangle Kangle an andd Qifeng Qifeng stations stations in in June June 2019. 2019. The LST was measured measured by an an SI-411 SI-411 infrared infrared temperature temperature sensor of Apogee Apogee company. company. It was was fixed ﬁxed at at 1.5 m of the observation tower for continuous observation, with a time interval of 30 min. TheThe emissivity datadata was was the the clear clear sky sky observation observation data data of theof the Dingxi Dingxi Station Station from from May May to June to June 2019. 2019.The wheat The wheat field, withfield, flatwith terrain flat terrain and uniform and uniform surface, surface, was chosen was chosen as the measuringas the measuring area. The area. surface The surfaceemissivity emissivity measurement measurement experiment experiment was carried was out carried under out sunny under and sunny windless and conditions,windless conditions, and it was andmeasured it was every measured 30 min every from 08:0030 minutes to 18:00 from Beijing 08:00 time. to The18:00 measuring Beijing time. instrument The measuring was a portable instrument Fourier wastransform a portable infrared Fourier spectrometer transform 102F, infrared produced spectr byometer D&P company 102F, produced of the United by D&P States. company The instrument of the Unitedwas mounted States. on The a tripod instrument 1 m above was the mounted ground. Theon workinga tripod temperature1 m above wasthe 15–35ground.◦C and The the working spectral -1 temperaturerange was 2–16 wasµ m.15–35°C A spectral and the resolution spectral of range 4 cm wasand 2–16 a calibrated µm. A spectral aperture resolution lens (field of of 4 viewcm-1 and angle a calibratedwas 4.8◦) wereaperture selected. lens (field The temperatureof view angle of was warm 4.8°) and were cold selected. blackbody The was temperature set to 40 ◦ofC warm and 10 and◦C, coldrespectively. blackbody Each was scan set wasto 40 set °C to and 8 times 10 °C, of spectralrespectively. superposition Each scan and was was set always to 8 times ensured of spectral that the superpositionDewar bottle wasand filledwas always with liquid ensured nitrogen. that the The Dewar measurements bottle was were filled carried with liquid out in nitrogen. the following The measurementsorder: Cold blackbody–warm were carried out blackbody–gold in the following plate-sample. order: Cold Finally, blackbody–warm the sample emissivity blackbody–gold curve was plate-sample.obtained by automatically Finally, the sample setting Planckemissivity function curve(setting was obtained 7–7.5µm by emissivity automatically to 1.0), setting as shown Planck in functionFigure2. (setting According 7–7.5µm to the emissivity spectral response to 1.0), as function shown ofin AGRIFigure (as 2. According shown in Figure to the3 spectral), the emissivity response functionvalues corresponding of AGRI (as shown to AGRI in channelsFigure 3), 12th the andemissi 13thvity are values calculated corresponding as follows: to AGRI channels 12th and 13th are calculated as follows: Pmax λ= [β(λ) e(λ)] ei = min · , (1) Pmax β(λ) λ=min ∑ [()∙()] ei = , (1) where ei is the emissivity of channel i; λ is the wavelength;∑ () min and max correspond to the minimum and maximum wavelength, corresponding to the spectral response function of channel i, respectively;

β(λ) is the percentage of spectral response corresponding to wavelength λ; and e(λ) is the measured where ei is the emissivity of channel i; λ is the wavelength; min and max correspond to the emissivity corresponding to wavelength λ. minimum and maximum wavelength, corresponding to the spectral response function of channel i, respectively; β(λ) is the percentage of spectral response corresponding to wavelength λ; and e(λ) is the measured emissivity corresponding to wavelength λ.

Remote Sens. 2019, 11, x FOR PEER REVIEW 5 of 21 Remote Sens. 2019, 11, 2016 5 of 21 Remote Sens. 2019, 11, x FOR PEER REVIEW 5 of 21

Figure 2. Measured emissivity spectral on 24 May 2019. Figure 2 2.. MeasuredMeasured emissivity sp spectralectral on 24 May 2019.

FigureFigure 3. Spectral3. Spectral response response functions functions of of AGRI AGRI 12th 12th and and 13th 13th channels. channels. 2.1.3. Remote SensingFigure Data 3. Spectral response functions of AGRI 12th and 13th channels. 2.1.3. Remote Sensing Data The satellite remote sensing data used in this paper were provided by the National Satellite 2.1.3. RemoteThe satellite Sensing remote Data sensing data used in this paper were provided by the National Satellite Meteorological Center (http://www.nsmc.org.cn/NSMC/Home/Index.html). The remote sensing data Meteorological Center (http://www.nsmc.org.cn/NSMC/Home/Index.html). The remote sensing includedThe satellite level 1 products remote sensing and cloud data detection used in products this paper collected were provided by FY-4A by radiation the National from 12 Satellite March data included level 1 products and cloud detection products collected by FY-4A radiation from 12 Meteorological2018 to 22 July 2018Center with (http://www.nsmc.org.cn/ a 4 km resolution. The researchNSMC/Home/Index.html). of Quan et al. Quan et The al [36 remote] shows sensing that the March 2018 to 22 July 2018 with a 4 km resolution. The research of Quan et al. Quan et al [36] shows datareﬂectance included of 0.65 levelµm 1 andproducts 0.865 µandm bands cloud of detectio the satelliten products do not collected change substantially by FY-4A radiation with atmospheric from 12 that the reflectance of 0.65 µm and 0.865 µm bands of the satellite do not change substantially with Marchcorrection, 2018 and to 22 that July the 2018 split-window with a 4 km algorithm resolution. avoids The the research inﬂuence of Quan of the et atmosphere al. Quan et on al the[36] thermal shows atmospheric correction, and that the split-window algorithm avoids the influence of the atmosphere thatinfrared the reflectance channels. Inof this0.65 study,µm and the 0.865 FY-4A µm products bands of didthe notsatellite undergo do not atmospheric change substantially correction, with and on the thermal infrared channels. In this study, the FY-4A products did not undergo atmospheric atmosphericonly geographic correction, calibration and and that cloud the split-window detection were algorithm applied toavoids collect the the influence remote sensingof the atmosphere data. After correction, and only geographic calibration and cloud detection were applied to collect the remote onexcluding the thermal precipitation infrared andchannels. cloudy In dates, this study, the remaining the FY-4A (sunny) products days did were not 21 undergo for the Dingxi atmospheric station sensing data. After excluding precipitation and cloudy dates, the remaining (sunny) days were 21 correction,(the time is Marchand only 12 ,geographic March 13, March calibration 14, April and16 cl,oudApril detection 17, April were 19, May applied 2, May to collect 6, May the 12, Mayremote 13, for the Dingxi station (the time is March 12, March 13, March 14, April 16, April 17, April 19, May 2, sensingMay 14 ,data. May 15,After May excluding 22, May precipitation 31, June 12, Julyand 13cloudy, July dates, 16, July the 17 remaining, 2018 and May(sunny) 20, daysMay 24were, June 21 May 6, May 12, May 13, May 14, May 15, May 22, May 31, June 12, July 13, July 16, July 17, 2018 and for3, 2019), the Dingxi only 1station for Kangle (the time Station is March (June 12,12, March 2019), and13, March 4 for Qifeng 14, April Station 16, April (June 17 7,, JuneApril 12, 19, June May 16, 2, May 20, May 24, June 3, 2019), only 1 for Kangle Station (June 12, 2019), and 4 for Qifeng Station MayJune 6, 17, May 2019), 12 only, May 1 13, for May the Kangle 14, May station 15, May (12 22, June May 2019), 31, andJune 4 12 for, July the Qifeng13, July station 16, July (7 17 Jun,, 2018 12 June, and (June 7, June 12, June 16, June 17, 2019), only 1 for the Kangle station (12 June 2019), and 4 for the 16May June, 20, 17May June, 24, 2019). June The3, 2019), dates only in bold 1 for represent Kangle datesStation used (June for 12, algorithm 2019), and optimization 4 for Qifeng among Station the Qifeng station (7 Jun, 12 June, 16 June, 17 June, 2019). The dates in bold represent dates used for (June328 LST 7, June research 12, June samples 16, June and 3317, surface 2019), only emissivity 1 for the samples, Kangle and station the remainder (12 June 2019), are the and dates 4 for of testthe algorithm optimization among the 328 LST research samples and 33 surface emissivity samples, and Qifengsamples. station The bands’ (7 Jun, characteristics 12 June, 16 June, of AGRI 17 June, onboard 2019). FY-4A The aredates all shownin bold in represent Table1. dates used for algorithmthe remainder optimization are the among dates ofthe test 328 sa LSTmples. research The bands’ samples characteristics and 33 surface of emissivityAGRI onboard samples, FY-4A and are theall remainder shown in areTable the 1. dates of test samples. The bands’ characteristics of AGRI onboard FY-4A are all shown in Table 1.

Remote Sens. 2019, 11, 2016 6 of 21

Table 1. Performance of AGRI onboard FY-4A.

Spatial Channel Band (µm) Sensitivity Main Application Resolution (km) Signal to Noise Ratio(S/N) 90 0.45–0.49 1 ≥ Aerosol Visible Near (ρ = 100%) Infrared S/N 200 (ρ = 100%) 0.55–0.75 0.5–1 ≥ Fog, Cloud S/N 5 (ρ = 1%) @ 0.5 Km ≥ 0.75–0.90 1 Vegetation S/N 200 (ρ = 100%) 1.36–1.39 2 ≥ Cirrus Short- S/N 200 (ρ = 100%) ≥ Wave Infrared 1.58–1.64 2 Cloud, Snow 2.1–2.35 2–4 Cirrus, Aerosol Noise Equivalent Temperature 3.5–4.0(High) 2 Fire Mid-wave Infrared Diﬀerence(NE∆T) 0.7 K(300 K) ≤ 3.5–4.0(Low) 4 NE∆T 0.2 K(300 K) Land surface ≤ 5.8–6.7 4 NE∆T 0.3 K(260 K) Water Vapor (WV) Water Vapor ≤ 6.9–7.3 4 NE∆T 0.3 K(260 K) WV ≤ 8.0–9.0 4 NE∆T 0.2 K(300 K) WV, Cloud ≤ Long- Sea Surface 10.3–11.3 4 NE∆T 0.2 K(300 K) Wave Infrared ≤ Temperature Sea Surface 11.5–12.5 4 NE∆T 0.2 K(300 K) ≤ Temperature 13.2–13.8 4 NE∆T 0.5 K(300 K) Cloud, WV ≤

2.2. Methods

2.2.1. Local Split-Window Algorithms Given the accessibility of the parameters used in the algorithm and the practicability of their extension at the regional scale, two easy-to-implement algorithms, namely, the algorithm developed by Becker and Li (referred to hereinafter as the B&L algorithm) [21] and the algorithm developed by Kerr et al. (referred to hereinafter as the Kerr algorithm) [25], were applied in this work. A previous study [37] shows that the B&L and Kerr algorithms have good applicability in Northwest China. The RMSE between the retrieved LST and the observed value is kept at approximately 3 K on different underlying surfaces for MODIS data. Therefore, the LST retrieval in this study was performed by using the B&L and Kerr algorithms based on FY-4A data. The vegetation index was introduced into the split-window algorithm by Kerr et al. in 1992 [25] as follows: LST_K = fvTveg + (1 fv)T , (2) − soil Tveg = b1 + b2TB12 + b3TB13, (3)

Tsoil = b3 + b4TB12 + b6TB13, (4) fv = (NDVI NDVIs)/(NDVIv NDVIs), (5) − − where Tveg and Tsoil are vegetation and bare soil temperatures, respectively; LST_K is the LST estimated by the Kerr algorithm; the unit is K; TB12 and TB13 are the brightness temperatures of the 12th and 13th thermal infrared channels of AGRI, respectively; fv is the vegetation coverage; NDVIs and NDVIv are the normalized vegetation index (NDVI) values of the soil and vegetation conditions (NDVIs = 0.2 and NDVIv =0.5); and b1–b6 are coefficients used in the Kerr and optimized Kerr algorithms as shown in Table2.

Table 2. Calculation coeﬃcients for Kerr algorithm in this paper.

Coeﬃcients b1 b2 b3 b4 b5 b6 RMSE (K) Kerr 2.4 3.6 2.6 3.1 3.1 2.1 5.47 − − − Kerr_PSO 1 4.47 5.26 4.24 5.59 2.94 1.96 4.02 − − − 1 Kerr_PSO is the optimized Kerr algorithm. PSO, particle swarm optimization. Remote Sens. 2019, 11, 2016 7 of 21

The speciﬁc form of the B&L algorithm is as follows:

LST_SB = a + p(TB + TB )/2 + m(TB TB )/2, (6) 1 12 13 12 − 13 where LST_SB is the land surface temperature estimated by the B&L algorithm and the Sobrino emissivity model [38], the unit is K, and p and m are the calculation parameters related to emissivity:

p = a + a (1 e)/e + a de/e2, (7) 2 3 − 4 m = a + a (1 e)/e + a de/e2 (8) 5 6 − 7 e = (e12 + e13)/2, (9)

de = e12 e13, (10) − where e is the surface emissivity. An empirical method for calculating channel emissivity using the reﬂectance of visible and near infrared bands is obtained by Sobrino et al.(referred to as SB model) [38], based on the NOAA/AVHRR remote sensing data and the surface emissivity data provided by Salisbury. The calculation method of each channel emissivity is as follows: If NDVI < 0.2, e = 0.98 0.042ref2 (11) − de = 0.003 0.029ref2, (12) − − If 0.2 NDVI 0.5, ≤ ≤ e12 = 0.98 + 0.021fv, (13)

e13 = 0.974 + 0.015fv, (14)

If NDVI > 0.5, e12 = e13 = 0.989, (15)

e = 0.989, (16)

de = 0, (17) where e12 and e13 are the emissivity of the 12th and 13th thermal infrared channels of AGRI, respectively; ref2 and ref3 are the reflectance of the 2nd and 3rd channels of AGRI, respectively; fv is the vegetation coverage; e is the surface emissivity; de is channel emissivity difference; and a1–a7 are constants. The values of the B&L algorithm and the constants optimized by the particle swarm optimization (PSO) algorithm on the basis of different emissivity models are shown in Table3.

Table 3. Calculation coeﬃcients for the B&L algorithm in this paper.

Coeﬃcients a1 a2 a3 a4 a5 a6 a7 RMSE (K) B&L 1.274 1.0 0.15616 0.482 6.26 3.98 38.33 6.75 − B&L _SB_PSO 2 0.83 0.98 0.01 0.0 8.01 5.67 178.45 4.08 B&L _DX1_PSO 3 0.68 0.95 1.65 1.71 9.61 156.95 69.35 3.23 − B&L _DX2_PSO 4 0.65 0.98 0.79 0.07 12.2 118.34 246.19 3.22 − 2 B&L_SB_PSO is the optimized B&L algorithm based on the SB emissivity model. 3 B&L_DX1_PSO is the optimized B&L algorithm based on the DX1 emissivity model. 4 B&L_DX2_PSO is the optimized B&L algorithm based on the DX2 emissivity model.

2.2.2. Measured Emissivity Models The emissivity is an important parameter in LST retrieval by using the local split-window algorithm. To obtain a highly suitable model for emissivity retrieval in Northwest China, a correlation analysis between the measured emissivity at the Dingxi station (08:00–18:00) from May to June 2019 Remote Sens. 2019, 11, x FOR PEER REVIEW 8 of 21

_SB_PSO2 B&L 0.68 0.95 1.65 −1.71 9.61 156.95 69.35 3.23 _DX1_PSO3 B&L 0.65 0.98 0.79 −0.07 12.2 118.34 246.19 3.22 _DX2_PSO4 2 B&L_SB_PSO is the optimized B&L algorithm based on the SB emissivity model. 3B&L_DX1_PSO is the optimized B&L algorithm based on the DX1 emissivity model. 4B&L_DX2_PSO is the optimized B&L algorithm based on the DX2 emissivity model. Remote Sens. 2019, 11, 2016 8 of 21 2.2.2. Measured Emissivity Models and theThe AGRI emissivity remote is sensing an important data was parameter performed in toLST develop retrieval emissivity by using retrieval the local models split-window based on in-situalgorithm. data. To Given obtain that thea highly spring suitable wheat planted model in for the emissivity Dingxi station retrieval was at in the Northwest jointing and China, booting a stagescorrelation during analysis the observation between the period, measured the NDVI emissivity ranged at between the Dingxi 0.2 andstation 0.5, (08:00–18:00) and the new emissivityfrom May modelsto June were2019only and forthe 0.2 AGRI< NDVI remote< 0.5. sensing When NDVIdata was< 0.2, performed the SB model to develop was directly emissivity used, and retrieval when NDVImodels> based0.5, the on measured in-situ data. vegetation Given that emissivity the spring e = 0.993663, wheat planted de = 0, in was the directly Dingxi obtained.station was at the jointingTwo and emissivity booting retrieval stages during schemes the were observatio designedn period, based onthe the NDVI emissivity ranged model between of Sobrino 0.2 and et 0.5, al. Theand firstthe new scheme emissivity determines models emissivity were only by estimatingfor 0.2 < NDVI channel < 0.5. emissivity When NDVI as shown < 0.2, inthe Figure SB model4, which was illustratesdirectly used, the correlationand when NDVI between > 0.5, the the emissivity measured of vegetation the 12th and emissivity 13th channels e = 0.993663, of AGRI de = and 0, was the reflectancedirectly obtained. of its 2nd (red channel) and 3rd (near infrared channel) channels. Both e12 and e13 show a favorableTwo emissivity correlation retrieval with ref2schemes and ref3,were especiallydesigned ba insed terms on the of near emissivity infrared mo channeldel of Sobrino reflectance. et al. Therefore,The first scheme the new determines emissivity modelemissivity of the by 12th estimating and 13th channel channels emissivity of AGRI was as developedshown in Figure based on4, ref3.which In illustrates Figure4b,d, the the correlation emissivity between retrieved the by emissivi this modelty ofis the denoted 12th and by 13th DX1. channels of AGRI and

(a) (b)

FigureFigure 4.4. Correlation analysis between measured channelchannel emissivity and reﬂectance,reflectance, where ((aa)) isis thethe correlationcorrelation analysisanalysis betweenbetween e12 e12 and and ref2, ref2, (b ()b is) is the the correlation correlation analysis analysis between between e12 e12 and and ref3, ref3, (c) is(c the) is correlation analysis between e13 and ref2, and (d) is the correlation analysis between e13 and ref3.

the correlation analysis between e13 and ref2, and (d) is the correlation analysis between e13 and ref3.

Figure 4 also shows that despite the significant positive correlation between channel emissivity and reflectance, the scatters of e12, e13, and reflectance are relatively dispersed, thereby indicating potentially large deviations in the retrieved e12 and e13. Therefore, models that can directly retrieve Remoteaverage Sens. cha2019nnel, 11, 2016emissivity (referred to as e) and channel emissivity difference (referred to as9 of de) 21 were developed by using channel reflectance and its combined parameters, as shown in Figure 5. The correlations between e and channel reflectance, and between de and channel reflectance, are all reflectancestronger than and itsthose combined between parameters, channel whereas emissivity de shows and significantchannel reflectance. negative correlations Moreover, with e channel shows reflectancesignificant and positive its combined correlations parameters. with channel The correlation reflectance between and de its and combined NDVI, and parameters, that between whereas e and “ref3–ref2”,de are the most significant, with correlation coefficients reaching 0.86. The emissivity retrieved by this model is denoted by DX2.

(a) (b)

(f) (e)

Figure 5. Correlation analysis between average channel emissivity and channel reﬂectance and its combined parameters, where (a) is the correlation analysis between e and ref2, (b) is the correlation analysis between e and ref3, (c) is the correlation analysis between de and ref2, (d) is the correlation analysis between de and ref3, (e) is the correlation analysis between e and “ref3–ref2”, and (f) is the correlation analysis between de and normalized vegetation index (NDVI). Remote Sens. 2019, 11, 2016 10 of 21

2.2.3. PSO Algorithm From the above local split-window algorithms, seven constant parameters in the B&L algorithm and six constant parameters in the Kerr algorithm need to be redefined based on specific regions and for FY-4A. In this paper, the artificial PSO was used to determine these parameters. PSO was implemented given its wide use in different fields [39,40]. The global optimal solutions of nonlinear algebraic equations can be obtained by constantly updating the combination of parameters, which minimizes the difference between observed and estimated values. The time needed for computation is less than that using the traditional iteration method. The PSO was first proposed by Kennedy and Eberhart [41] based on a study of the foraging behavior of birds. The PSO is a simple and effective spatial search method. This algorithm aims to find the minimum of the objective function in parameter space by updating the position and velocity of a group of random particle swarms. Supposing that n-dimensional problem is optimized to select m particles, the position and velocity functions of i particles can be respectively shown as follows: poi = poi1, poi2, ...... , poin , (18)

vi = (vi1, vi2, ...... , vin), (19) The updated position and velocity of i particle are respectively computed as follows: Y+1 ω Y Y Y Y Y v = vin + c1r1 Lin pin + c2r2 Gn poin (20) in − − poY+1 = poY vY , (21) in in − in where po and v refer to position and velocity functions, respectively; Y denotes iterations; ω represents inertia weight; c1 and c2 correspond to acceleration constants; r1 and r2 are random numbers between 0 and 1; and Li and Gn refer to the local and global optimal locations searched by i particles, respectively. In this paper, the root mean square error (RMSE) was used as the objective function, and the solution corresponding to minimum RMSE during the iteration was taken as the optimal parameter. The PSO algorithm depends on parameters of the algorithm itself. These parameters include the number of particle swarms and variation range of position and velocity of particles. Based on a large number of simulation experiments [42], the number of particle swarms is 200. Variation range of inertia weight is 0.2–0.5. Acceleration constant is 2.0. Variation range of particle position is 1.0–1.0, and that of particle − velocity is 0.01–0.01. All parameters to be optimized were changed into an interval [ 1.0, 1.0] unit − − by mapping: Rx = [2Ro (Rmax + R )]/(Rmax R ), (22) − min − min where Rx refers to the value after parameter mapping; Ro denotes the actual parameter value; and Rmax and Rmin represent the actual maximum and minimum parameter values, respectively. In this paper, the maximum and minimum values of parameters were set to 100 times of the parameter ± values used in the B&L algorithm.

2.2.4. Accuracy Evaluation of Estimation Results In this paper, three statistics were used to evaluate estimation results: (1) Root mean square error (RMSE)

 N 1/2  1 X 2 MSE = (E O )  , (23) N i − i  i=1 Remote Sens. 2019, 11, x FOR PEER REVIEW 11 of 21

R = [2R − (R +R)]/(R −R), (22)

where Rx refers to the value after parameter mapping; Ro denotes the actual parameter value; and Rmax and Rmin represent the actual maximum and minimum parameter values, respectively. In this paper, the maximum and minimum values of parameters were set to ±100 times of the parameter values used in the B&L algorithm.

Remote Sens. 2019, 11, 2016 11 of 21 2.2.4. Accuracy Evaluation of Estimation Results In this paper, three statistics were used to evaluate estimation results: (2) Mean absolute percent error (MAPE) (1) Root mean square error (RMSE)  N  / 1 X  MSE= [ ∑(𝐸 −𝑂) ] , (23) MAPE =  Ei Oi  100%, (24) N O  | − | × (2) Mean absolute percent error (MAPE) i=1 (3) Correlation coefficient (R) MAPE= ∑| E −O| × 100%, N|| (24) PN (3) Correlation coefficient (R) i=1 Ei E Oi O R = q − − , (25) 2 2 PN ∑( P)N() R=i=1 Ei E i=1 Oi O, − · − (25) ∑() ∙∑() where Ei refers to the estimate sequence; E—represents the mean value of the estimate sequence; Oi where Ei refers to the estimate sequence; E represents the mean value of the estimate sequence; Oi denotes the measured sequence; O—corresponds to the mean value of the measured sequence; and N denotesdenotes the the number measured of samplessequence; participating O corresponds in the to calculation. the mean value of the measured sequence; and N denotes the number of samples participating in the calculation. 3. Results 3. Results To verify the applicability of the Kerr and B&L algorithms in Northwest China, the variables optimizedTo verify by PSO the are applicability marked by “PSO”,of the Kerr whereas and theB&L variables algorithms in the in original Northwest Kerr andChina, B&L the algorithms variables areoptimized left unmarked. by PSO are marked by “PSO”, whereas the variables in the original Kerr and B&L algorithms are left unmarked. 3.1. Diurnal Variation of Emissivity 3.1. FigureDiurnal6 showsVariation the of diurnal Emissivity variation of the measured emissivity for two typical sunny days from 08:00Figure to 18:00. 6 Inshows Figure the6a, diurnal the e12 variation and e13, whichof the measured correspond emissivity to the 12th for and two 13th typica channelsl sunny of days the AGRI,from 08:00 are between to 18:00. 0.97 In Figure to 0.99 6a, and the 0.97 e12 to and 1.005, e13, respectively. which correspond Their diurnal to the 12th amplitudes and 13th are channels 0.02 and of 0.03the andAGRI, their are range between of variation 0.97 to 0.99 is small. and 0.97 However, to 1.005, the respectively. diurnal variations Their arediurnal obvious amplitudes and reach are their 0.02 maximumand 0.03 and values their at range noon. of Figure variation6b shows is small. the diurnalHowever, variation the diurnal of the variations mean and are di ff obviouserence of and channel reach emissivity.their maximum The diurnal values at variation noon. Figure of channel 6b shows emissivity the diurnal difference variation is also of obvious,the mean butand it difference reaches its of minimumchannel emissivity. value at noon. The Whendiurnal compared variation with of channel the parameters emissivity of channel difference emissivity is also onobvious, 24 May but and it 3reaches June, the its average minimum emissivity value at of noon. the two When channels compared increases with and the theparameters difference of of channel emissivity emissivity decreases on along with the growth of vegetation.

(a) (b)

Figure 6. The diurnal variations of measured emissivity, where (a) is the band emissivity corresponding to the 12th and 13th channels of FY-4A (referred to as e12 and e13), and (b) is the variations of mean and diﬀerences of emissivity (referred to as e and de) of the 12th and 13th channels of FY-4A.

3.2. LST Retrieved by Local Split-Window Algorithms On the basis of FY-4A satellite data, the LSTs retrieved by diﬀerent split-window algorithms and the measured values of various underlying surfaces in Northwest China are compared in Figure7. Given Remote Sens. 2019, 11, x FOR PEER REVIEW 12 of 21

Figure 6. The diurnal variations of measured emissivity, where (a) is the band emissivity Remote Sens. 2019corresponding, 11, 2016 to the 12th and 13th channels of FY-4A (referred to as e12 and e13), and (b) is the 12 of 21 variations of mean and differences of emissivity (referred to as e and de) of the 12th and 13th channels of FY-4A. the large amount of precipitation in the summer of 2018 and 2019 in Gansu Province, the measured 3.2. LST Retrieved by Local Split-Window Algorithms LSTs at all stations are all near 330 K. As shown in Figure7a, samples 1–123 were collected from the Dingxi station,On the samplesbasis of FY-4A 124–140 satellite were data, collectedthe LSTs retrieved from the by different Kangle split-window station, and algorithms samples 141–169 and the measured values of various underlying surfaces in Northwest China are compared in were collectedFigure from7. Given the the Qifeng large station.amount of The precipitation time series in diagramsthe summer shown of 2018 in and this 2019 work in Gansu are the same as Figure7a.Province, Compared the measured with the LSTs measured at all stations value, are the all LSTnear 330 retrieved K. As shown by both in Figure the B&L7a, samples and Kerr 1–123 algorithms can reproducewere collected the diurnal from the variation Dingxi station, characteristics samples 124–140 of LST.were collected The correlation from the Kangle coeﬃ station,cients and between the LST estimatedsamples by 141– the16 split-window9 were collected algorithms from the Qifeng and station. the measured The time valueseries diagrams all reached shown 0.84. in this However, the work are the same as Figure 7a. Compared with the measured value, the LST retrieved by both the estimatedB&L LST and of theKerr two algorithms algorithms can reproduce is higher the thandiurnal the variation measured characteristics value. In of theLST. low The temperaturecorrelation region, the deviationcoefficients between between these the two LST algorithmsestimated by the is small,split-window and the algorithms estimated and the LST measured is close value to the all measured value. However,reached 0.84. with However, an increasing the estimated LST, LST the of deviation the two algorithms becomes is higher greater than (especially the measured at value. noon), and the maximumIn deviation the low temperature can reach region, approximately the deviation 10 K.between The LST these estimated two algorith byms the is Kerrsmall, algorithm and the is closer estimated LST is close to the measured value. However, with an increasing LST, the deviation to the measuredbecomes valuegreater than(especially that at estimated noon), and bythe the maximum B&Lalgorithm. deviation can The reach RMSEs approximately of the 10 Kerr K. and B&L algorithmsThe are LST 5.55 estimated K and by 6.28 the K,Kerr respectively. algorithm is closer From to the the analysismeasured ofvalue di ﬀthanerent that underlying estimated by surfaces,the both split-windowB&L algorithmsalgorithm. The overestimate RMSEs of the theKerr LST and ofB&L the algorithms vegetation are underlying5.55 K and 6.28 surface K, respectively. and underestimate the LST ofFrom the desert the analysis underlying of different surface. underlying surfaces, both split-window algorithms overestimate the

Remote Sens. 2019, 11, x FOR PEER REVIEW (a) 13 of 21

Figure 7. TheFigure comparison 7. The comparison of LST retrievedof LST retrieved by di byﬀerent different split-window split-window algorithms algorithms and and measured measured values, values, (a) is the time series, (b) is the LST retrieved by B&L algorithm, (c) is the LST retrieved by (a) is the time series, (b) is the LST retrieved by B&L algorithm, (c) is the LST retrieved by Kerr algorithm. Kerr algorithm.

3.3. Kerr Algorithm3.3. Kerr Algorithm Optimization Optimization The LSTThe retrieved LST retrieved by the by Kerr the Kerr algorithm algorithm deviatesdeviates from from the the measured measured value, value,especially especially in the in the high temperaturehigh temperature region. region. In order In order to improve to improve the the accuracyaccuracy of ofthe the estimated estimated LST in LST Northwest in Northwest China, China, the Kerr algorithm was directly optimized by PSO, while any other surface parameters, such as the Kerr algorithm was directly optimized by PSO, while any other surface parameters, such as emissivity, were not included in the algorithm. Figure 8 compares the LST estimated by the optimized Kerr algorithm with the measured value. Comparing this figure with Figure 7c reveals that the PSO optimization cannot improve the accuracy of the LST estimated by the Kerr algorithm as a whole, and that the RMSE between the estimated LST and measured value is 5.84 K. Given the different underlying surfaces, as shown in Figure 8a, when the vegetation of the Dingxi Station (i.e., before 13 May; samples 1–57 in the figure) and the Kangle Station (samples 124–140) is relatively low, the accuracy of the LST estimated by the Kerr algorithm is obviously improved after PSO optimization. In Figure 8a, the blue line is closer to the black line (which denotes the time series of measured LST) than the red line (which denotes the time series of LST estimated by the Kerr algorithm before PSO optimization). In this case, with a higher LST, the improvements in the accuracy of the estimated LST becomes highly obvious. The vegetation of the Dingxi station is improved, along with the growth of wheat (that is, after 13 May; samples 58–123 in Figure 8a), but such improvement significantly weakens the effect of PSO optimization. At the same time, the coefficients obtained by PSO on the vegetation underlying surface in the Dingxi station are not applicable to desert underlying surfaces as in the Qifeng station, where the deviation of the LST estimated by the optimized algorithm is larger than that of the LST estimated by the original Kerr algorithm. In sum, the Kerr algorithm has a simple calculation, and the LST estimated by the optimized Kerr algorithm on a sparse vegetation underlying surface is closer to the measured value than that before optimization.

Remote Sens. 2019, 11, 2016 13 of 21 emissivity, were not included in the algorithm. Figure8 compares the LST estimated by the optimized Kerr algorithm with the measured value. Comparing this figure with Figure7c reveals that the PSO optimization cannot improve the accuracy of the LST estimated by the Kerr algorithm as a whole, and that the RMSE between the estimated LST and measured value is 5.84 K. Given the different underlying surfaces, as shown in Figure8a, when the vegetation of the Dingxi Station (i.e., before 13 May; samples 1–57 in the figure) and the Kangle Station (samples 124–140) is relatively low, the accuracy of the LST estimated by the Kerr algorithm is obviously improved after PSO optimization. In Figure8a, the blue line is closer to the black line (which denotes the time series of measured LST) than the red line (which denotes the time series of LST estimated by the Kerr algorithm before PSO optimization). In this case, with a higher LST, the improvements in the accuracy of the estimated LST becomes highly obvious. The vegetation of the Dingxi station is improved, along with the growth of wheat (that is, after 13 May; samples 58–123 in Figure8a), but such improvement significantly weakens the e ffect of PSO optimization. At the same time, the coefficients obtained by PSO on the vegetation underlying surface in the Dingxi station are not applicable to desert underlying surfaces as in the Qifeng station, where the deviation of the LST estimated by the optimized algorithm is larger than that of the LST estimated by the original Kerr algorithm. In sum, the Kerr algorithm has a simple calculation, and the LST estimated by the optimized Kerr algorithm on a sparse vegetation underlying surface is closer to the measuredRemote Sens. 2019 value, 11, thanx FOR thatPEER beforeREVIEW optimization. 14 of 21

(a)

(b)

FigureFigure 8. The 8. The comparison comparison of of LSTLST retrieved by by the the opti optimizedmized Kerr Kerr algorithm algorithm and measured and measured values; (a values;) (a) isis the the time time series,series , ((bb)) is the scatters. scatters.

3.4. B&L Algorithm Optimization The accuracy of the LST estimated by the B&L algorithm is not only affected by the algorithm coefficients, but also by emissivity. Therefore, the influence of emissivity on the LST estimated by the B&L algorithm is discussed. Figure 9 compares the observed value with the LST estimated by the B&L algorithm combined with different emissivity models. The variations in the LST estimated by the B&L algorithm combined with different emissivity models are in line with the measured values, and the correlation coefficients are all above 0.8. These numerical values all show that the LST estimation results deviate from the measured values. Comparing the LST estimated by different emissivity models reveals that the deviations among the LSTs estimated by the three emissivity models are small, and that the two new models developed by measured emissivity do not significantly reduce the retrieval error. The RMSE is only reduced by 0.2 K when using the new emissivity models for LST retrieval.

Remote Sens. 2019, 11, 2016 14 of 21

3.4. B&L Algorithm Optimization The accuracy of the LST estimated by the B&L algorithm is not only affected by the algorithm coefficients, but also by emissivity. Therefore, the influence of emissivity on the LST estimated by the B&L algorithm is discussed. Figure9 compares the observed value with the LST estimated by the B&L algorithm combined with different emissivity models. The variations in the LST estimated by the B&L algorithm combined with different emissivity models are in line with the measured values, and the correlation coefficients are all above 0.8. These numerical values all show that the LST estimation results deviate from the measured values. Comparing the LST estimated by different emissivity models reveals that the deviations among the LSTs estimated by the three emissivity models are small, and that the two new models developed by measured emissivity do not significantly reduce the retrieval error. The RMSE is only reduced by 0.2 K when using the new emissivity models for LST retrieval. Remote Sens. 2019, 11, x FOR PEER REVIEW 15 of 21

(a)

FigureFigure 9. Comparison 9. Comparison of LSTof LST retrieved retrieved by by di differentﬀerent emissivity emissivity modelsmodels and measured values; values; (a ()a is) is the timethe series, time (b series,) is the (b LST) is the results LST basedresults on based the DX1on the emissivity DX1 emissivity model, model, and ( cand) is ( thec) is LST the resultsLST results based on the DX2based emissivity on the DX2 model. emissivity model.

GivenGiven that that the measuredthe measured emissivity emissivity cannot cannot signiﬁcantly significantly improve improve thethe accuracyaccuracy of of LST LST retrieval, retrieval, one one should consider whether the coefficients of the B&L algorithm are not optimal for the emissivity should consider whether the coeﬃcients of the B&L algorithm are not optimal for the emissivity models. models. In this case, the PSO algorithm is applied to optimize the B&L algorithm. Given that both In this case, the PSO algorithm is applied to optimize the B&L algorithm. Given that both emissivity emissivity and LST are included in the B&L algorithm, the emissivity estimated by each model is assumed to be the “true emissivity” when the PSO is used to optimize the B&L algorithm. The coefficients in the B&L algorithm are then redefined based on this assumption. Figure 10b compares the observed value with the LST estimated by the B&L algorithm optimized based on the SB emissivity model. By comparing this figure with Figure 7b, one can see that the estimated LST is closer to the measured value in the high temperature region, but the estimated LST is lower than the measured value in the low temperature region. Therefore, the LST estimated by the B&L algorithm optimized based on the SB emissivity model is not ideal, and the RMSE increases by 0.6 K after optimization, thereby suggesting that the original coefficients of the B&L algorithm are appropriate for the SB emissivity model and that local optimization cannot improve the retrieval accuracy of this algorithm.

Remote Sens. 2019, 11, x FOR PEER REVIEW 16 of 21

RemoteFigure Sens. 2019 10c, 11 compares, 2016 the observed value with the LST estimated by the B&L algorithm that15 of is 21 optimized based on the DX1 emissivity model. By comparing this figure with Figure 9b, one can see that the estimated LST is much closer to the measured value on the whole. The accuracy of LST retrievaland LST areis effectively included inimproved the B&L algorithm,by the local the opti emissivitymization estimated of this algorithm, by each model the RMSE is assumed decreases to be fromthe “true 6.08 emissivity”K to 4.84 K, when and the the PSO error is used decreases to optimize by about the B&L 1.2 algorithm.K via the Thelocal coe optimizationfficients in the of B&Lthe aalgorithmlgorithm. areHowever, then redefined Figure based10a shows on this that assumption. the LST estimated by the B&L algorithm that is optimizedFigure based 10b compares on the DX1 the emissivity observed value model with agrees the LSTwith estimated the measured by the values B&L algorithm at the Dingxi optimized (i.e., samplesbased on 1–123) the SB and emissivity Kangle stations model. (i.e., By comparingsamples 124–140). this figure However, with Figure this LST7b, is one significantly can see that lower the thanestimated the measured LST is closer value to at the the measured Qifeng station value (i.e., in the the high last temperature 29 samples), region, and a huge but the deviation estimated can LST be observedis lower thanbetween the measuredthe estimated value LST in theand lowmeasured temperature value. region.Therefore, Therefore, for the measured the LST estimated emissivity, by thethe coefficients B&L algorithm of the optimized B&L algorithm based on are the no SB longer emissivity applicable. model The is not accuracy ideal, andof LST the retrieval RMSE increases can be effectivelyby 0.6 K after improved optimization, via local thereby optimization suggesting of that the the algorithm, original coebutffi cientsthe DX1 of themodel B&L algorithmhas poor universality.are appropriate From for the the correlation SB emissivity analysis model of and cha thatnnel localemissivity optimization and reflecta cannotnce improve as shown the in retrieval Figure 5accuracy, both e12 of and this e13 algorithm. are well correlated with the reflectance of the near-infrared channel. Therefore, the developedFigure 10 cemissivity compares retrieval the observed model value is suitable with the for LST the estimatedvegetationby underlying the B&L algorithmsurface, such that as is theoptimized Dingxi basedand Kangle on the stations, DX1 emissivity and can model. estimate By comparingLSTs that are this close figure to with the Figuremeasured9b, onevalues. can However,see that the the estimated LST retrieval LST iserrors much become closer tolarger the measured when this value model on is the extended whole. Theto other accuracy underlying of LST surfaces,retrieval such is effectively as the Qifeng improved station by thewhere local the optimization estimated LST of this is lower algorithm, than the the measured RMSE decreases value. from 6.08Figure K to 4.84 10d K, compares and the errorthe measured decreases value by about with 1.2 the K LST via estimated the local optimization by the B&L algorithm of the algorithm. that is optimizedHowever, Figurebased on10 athe shows DX2 thatemissivity the LST model. estimated By comparing by the B&L this algorithm figure with that Figure is optimized 9c, one based can see on thatthe DX1the scatters emissivity between model the agrees estimated with the LST measured and the values measured at the value Dingxi are (i.e., uniformly samples and 1–123) closely and distributedKangle stations on both (i.e., sides samples of the 124–140). 1:1 line, the However, correlation this coefficient LST is significantly increases lowerfrom 0.84 than to the 0.91, measured and the RMSEvalue atdecreases the Qifeng from station 6.1 K (i.e., to 3.45 the last K. The 29 samples), accuracy and of the a huge LST deviation retrieval canis therefore be observed effective between by the the localestimated optimization LST and of measured the B&L value.algorithm. Therefore, An analysis for the of measured Figure 10a emissivity, reveals that the coetheffi emissivitycients of the model B&L developedalgorithm arebased no longeron the applicable.differences Thein band accuracy reflectance of LST is retrieval highly canuniversal be effectively in Northwest improved China. via localThe estimatedoptimization LST of of the various algorithm, underlying but the surfac DX1 modeles are all has close poor to universality. the measured From values. the correlation analysis of channelIn sum, emissivity for the B&L and algorithm, reflectance to as obtain shown highly in Figure accurate5, both LST e12 retrieval and e13 areresults well based correlated on FY-4A with satellitethe reflectance data, an of improved the near-infrared emissivity channel. retrieval Therefore, model that the is developed suitable for emissivity FY-4A must retrieval be developed. model is Comparingsuitable for thethe vegetationLSTs retrieved underlying by the surface, two new such emissivity as the Dingxi models and Kangle reveals stations, that for and the can measured estimate emissivity,LSTs that are the close coefficients to the measured of the B&L values. algorithm However, are the the LST main retrieval limiting errors factors become for largerimproving when LST this estimationmodel is extended accuracy to otherbased underlying on FY-4A surfaces,data. Ther suchefore, as the to Qifeng improve station thewhere accuracy the estimatedof FY-4A LST LST is lower than the measured value.

(a)

Figure 10. Cont. Remote Sens. 2019, 11, 2016 16 of 21 Remote Sens. 2019, 11, x FOR PEER REVIEW 17 of 21

(b) (c)

(d)

FigureFigure 10.10. TheThe comparisoncomparison ofof LSTLST retrievedretrieved byby thethe optimizedoptimized split-windowsplit-window algorithmalgorithm andand measuredmeasured values;values; ( a(a)) is is the the time time series, series, (b) ( isb) the is LSTthe LST results results based based on the on SB the emissivity SB emissivity model, model, (c) is the (c) LST is the results LST basedresults on based the DX1 on the emissivity DX1 emissivity model, and model, (d) is and the LST(d) is results the LST based results on thebase DX2d on emissivity the DX2 model.emissivity model. Figure 10d compares the measured value with the LST estimated by the B&L algorithm that is optimized4. Discussion based on the DX2 emissivity model. By comparing this figure with Figure9c, one can see that the scatters between the estimated LST and the measured value are uniformly and closely The results show that the Kerr algorithm only involves the calculation of vegetation coverage, distributed on both sides of the 1:1 line, the correlation coefficient increases from 0.84 to 0.91, and while the calculation of vegetation coverage involves the determination of NDVIv and NDVIs. The the RMSE decreases from 6.1 K to 3.45 K. The accuracy of the LST retrieval is therefore effective by differences in the LSTs estimated by the Kerr algorithm resulting from the changes in NDVIv and the local optimization of the B&L algorithm. An analysis of Figure 10a reveals that the emissivity NDVIs are shown in Figure 11. Based on FY-4A data, a smaller NDVI corresponds to a higher model developed based on the differences in band reflectance is highly universal in Northwest China. correlation and a smaller RMSE between the LST estimated by the Kerr algorithm and the measured The estimated LST of various underlying surfaces are all close to the measured values. value. By contrast, a larger NDVIv value corresponds to a smaller correlation coefficient and a In sum, for the B&L algorithm, to obtain highly accurate LST retrieval results based on FY-4A larger RMSE between the LST estimated by the Kerr algorithm and the measured value in satellite data, an improved emissivity retrieval model that is suitable for FY-4A must be developed. Northwest China. With increasing NDVIs, the color change becomes more obvious and the contour Comparing the LSTs retrieved by the two new emissivity models reveals that for the measured distribution becomes denser, especially at NDVIs values of above 0.2. In other words, with emissivity, the coefficients of the B&L algorithm are the main limiting factors for improving LST increasing NDVIs, the gradient of the correlation coefficient and the RMSE between the LST estimated by the Kerr algorithm and the measured value obviously increases. Given that the results of the B&L algorithm are similar to those of the Kerr algorithm, these results will not be discussed

Remote Sens. 2019, 11, 2016 17 of 21 estimation accuracy based on FY-4A data. Therefore, to improve the accuracy of FY-4A LST retrieval, algorithm coeﬃcients suitable for FY-4As satellites must be obtained via an algorithm optimization based on measured emissivity.

4. Discussion The results show that the Kerr algorithm only involves the calculation of vegetation coverage, while the calculation of vegetation coverage involves the determination of NDVIv and NDVIs. The differences in the LSTs estimated by the Kerr algorithm resulting from the changes in NDVIv and NDVIs are shown in Figure 11. Based on FY-4A data, a smaller NDVI corresponds to a higher correlation and a smaller RMSE between the LST estimated by the Kerr algorithm and the measured value. By contrast, a larger NDVIv value corresponds to a smaller correlation coefficient and a larger RMSE between the LST estimated by the Kerr algorithm and the measured value in Northwest China. With increasing NDVIs, the color change becomes more obvious and the contour distribution becomes denser, especially at NDVIs values of above 0.2. In other words, with increasing NDVIs, the gradient of the correlation coefficient and the RMSE between the LST estimated by the Kerr algorithm and the measured value obviously increases. Given that the results of the B&L algorithm are similar to those of the Kerr algorithm,Remote these Sens. 2019 results, 11, x FOR will PEER not REVIEW be discussed in detail. In sum, for retrieving LSTs in Northern18 of China 21 using FY-4A satellite data, the NDVIs and NDVIv should not exceed 0.12 and 0.5, respectively. In this way, thein deviationsdetail. In sum, in thefor retrieving RMSE resulting LSTs in fromNorthe thern changesChina using in theFY-4 NDVIsA satellite and data NDVIv, the NDVIs values and can be controlled within 0.1 K when the LST is estimated by the Kerr algorithm.

(a)

(b)

FigureFigure 11. Distribution 11. Distribution of the of correlationthe correlation coe coefficienﬃcientt and and RMSE RMSE between the the estimated estimated LST LST and and the the measured values. The colors represent the correlation coefficients, and the isoline and numbers measured values. The colors represent the correlation coeﬃcients, and the isoline and numbers represent the RMSE values; (a) is the estimated LST by the Kerr algorithm and (b) is the LST represent the RMSE values; (a) is the estimated LST by the Kerr algorithm and (b) is the LST estimated estimated by the B&L algorithm. by the B&L algorithm. Given that the water vapor content products of FY-4A can be downloaded online from January 2019, the local split-window algorithm, which is related to water vapor, was not considered in this work. According to Quan, although the reflectance of 0.65 µm and 0.865 µm bands remains unchanged before and after atmospheric correction, the value of NDVI changes. However, the NDVI index is always used as a threshold parameter for classifying the underlying surface. Therefore, any change in NDVI will lead to different NDVI thresholds but will not greatly influence the accuracy of the LST estimated by the local split-window algorithm. As can be observed from the LST estimated by the local split-window algorithm with optimized PSO, the original algorithm coefficients are identified as the optimal values for the local split-window algorithms after a long period of testing and improvement. Moreover, the accuracy of LST retrieval cannot be improved by algorithm optimization without changing any other parameter estimation model. To improve the LST retrieval accuracy, each parameter of the algorithm must be carefully estimated, and the coefficients of this algorithm must be redefined by using the artificial intelligence algorithm.

5. Conclusions Remote Sens. 2019, 11, 2016 18 of 21

Given that the water vapor content products of FY-4A can be downloaded online from January 2019, the local split-window algorithm, which is related to water vapor, was not considered in this work. According to Quan, although the reflectance of 0.65 µm and 0.865 µm bands remains unchanged before and after atmospheric correction, the value of NDVI changes. However, the NDVI index is always used as a threshold parameter for classifying the underlying surface. Therefore, any change in NDVI will lead to different NDVI thresholds but will not greatly influence the accuracy of the LST estimated by the local split-window algorithm. As can be observed from the LST estimated by the local split-window algorithm with optimized PSO, the original algorithm coefficients are identified as the optimal values for the local split-window algorithms after a long period of testing and improvement. Moreover, the accuracy of LST retrieval cannot be improved by algorithm optimization without changing any other parameter estimation model. To improve the LST retrieval accuracy, each parameter of the algorithm must be carefully estimated, and the coefficients of this algorithm must be redefined by using the artificial intelligence algorithm.

5. Conclusions LST plays an important role in achieving energy balance. Therefore, accurately estimating the LST components is critical in studying land–atmosphere interaction and climate change. Remote sensing is the most convenient and effective means for obtaining regional-scale LST. Previous studies have shown that high-accuracy LST can be obtained by using the local split-window algorithm. Although a large number of local split-window algorithms have been developed to estimate LST for polar orbiting satellites, especially MODIS sensors, only few studies have attempted to develop algorithms for geostationary satellites. In 2016, China launched the FY-4A geostationary meteorological satellite, which can obtain high-resolution observational data. However, given the difference between FY-4A and polar orbiting satellites, the local split-window algorithm cannot be directly used for FY-4A. The data measured by FY-4A need to be revised and examined. The accuracy of the local split-window algorithm is verified based on the LST measured on different underlying surfaces in Northwest China. Meanwhile, on the basis of different emissivity models, the parameters of the B&L algorithm are optimized by using the artificial intelligence PSO algorithm. The major conclusions of this work are as follows: (1) Based on FY-4A satellite data, the LST estimated by the Kerr and B&L algorithms can be used to reproduce diurnal variation characteristics. The estimated and measured values show a good correlation, but huge deviations can be observed in the estimated values. The correlation coefficients between the estimated LST and the measured value are all higher than 0.8, and the RMSEs of the Kerr and B&L algorithms are 5.55 K and 6.28 K, respectively. When the LST is high at noon, the deviation between the estimated and measured values increases. The estimated LST on the vegetation underlying surface is higher than the measured value, whereas the estimated LST on the desert underlying surface is lower than the measured value with a maximum deviation that can reach up to 10 K. (2) The accuracy of the LST estimated by the optimized Kerr algorithm cannot be improved but can be influenced by the NDVIs and NDVIv values. For FY-4A satellite data, the NDVIs should not exceed 0.12 and NDVIv should not exceed 0.5 in Northwest China. (3) The measured emissivity has obvious diurnal variation characteristics, but a small daily amplitude. The accuracy of the LST estimates retrieved by the B&L algorithm with measured emissivity also do not significantly improve. (4) On the basis of different emissivity models, the B&L algorithm was optimized by the PSO algorithm, and the results show that the emissivity model and coefficients of the algorithm are two factors that limit LST retrieval accuracy. Only the optimal combination of these two factors can effectively improve the retrieval accuracy. According to the measured emissivity model, PSO can effectively reduce the deviation and improve the estimation accuracy, and the minimum RMSE of the LST estimated by the optimized B&L algorithm is 3.45 K. Remote Sens. 2019, 11, 2016 19 of 21

This study is based on the idea that the FY-4A sensor is similar to the MODIS sensor in partial channel observations. Therefore, the B&L algorithm can be extended to FY-4A, and only a few empirical parameters need to be revised. As a new generation of geostationary satellite, FY-4A has its own characteristics in channel design, sensor response function, and satellite positioning. An important research task is to develop high-accuracy retrieval algorithms for the FY-4A satellite. Results of the present study show that, on the one hand, the existing split-window algorithms can be used for FY-4A. Combined with the advantages of the FY-4A satellite, such as the high-temporal-resolution observation data, the split-window algorithm can be applied to study diurnal variations of various variables, and the results could provide references for studies on diurnal variation characteristics of land surface variables or other parameters on regional and even larger scale. On the other hand, algorithm coeﬃcients in the existing split-window algorithm and emissivity model cannot simply be used for FY-4A.

Author Contributions: Funding acquisition, N.G.; Validation, W.W.; Methodology and Writing—original draft, L.W.; Writing—review and editing, H.Z. Funding: Funding for this work was provided by the China Special Fund for Meteorological Research in the Public Interest (Major projects) (GYHY201506001-5), the arid region study funding (IAM201716), and the ground application system project for FY-4 satellite. Acknowledgments: We would like to thank the National Satellite Meteorological Center for providing remote sensing data and technical support for data processing. Conﬂicts of Interest: The authors declare no conﬂicts of interest.

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