Land and Food Systems, Faculty of
Non UBC
DSpace
Remote Sensing 7 (3): 2238-2278 (2015)
Wu, Xiaocui
Ju, Weimin
Zhou, Yanlian
He, Mingzhu
Law, Beverly E.
Black, T. Andrew
Margolis, Hank A.
Cescatti, Alessandro
Gu, Lianhong
Montagnani, Leonardo
Noormets, Asko
Griffis, Timothy J.
Pilegaard, Kim
Varlagin, Andrej
Valentini, Riccardo
Blanken, Peter D.
Wang, Shaoqiang
Wang, Huimin
Han, Shijie
Yan, Junhua
Li, Yingnian
Zhou, Bingbing
Liu, Yibo
The reliable simulation of gross primary productivity (GPP) at various spatial and temporal scales is of significance to quantifying the net exchange of carbon between terrestrial ecosystems and the atmosphere. This study aimed to verify the ability of a nonlinear two-leaf model (TL-LUEn), a linear two-leaf model (TL-LUE), and a big-leaf light use efficiency model (MOD17) to simulate GPP at half-hourly, daily and 8-day scales using GPP derived from 58 eddy-covariance flux sites in Asia, Europe and North America as benchmarks. Model evaluation showed that the overall performance of TL-LUEn was slightly but not significantly better than TL-LUE at half-hourly and daily scale, while the overall performance of both TL-LUEn and TL-LUE were significantly better (p < 0.0001) than MOD17 at the two temporal scales. The improvement of TL-LUEn over TL-LUE was relatively small in comparison with the improvement of TL-LUE over MOD17. However, the differences between TL-LUEn and MOD17, and TL-LUE and MOD17 became less distinct at the 8-day scale. As for different vegetation types, TL-LUEn and TL-LUE performed better than MOD17 for all vegetation types except crops at the half-hourly scale. At the daily and 8-day scales, both TL-LUEn and TL-LUE outperformed MOD17 for forests. However, TL-LUEn had a mixed performance for the three non-forest types while TL-LUE outperformed MOD17 slightly for all these non-forest types at daily and 8-day scales. The better performance of TL-LUEn and TL-LUE for forests was mainly achieved by the correction of the underestimation/overestimation of GPP simulated by MOD17 under low/high solar radiation and sky clearness conditions. TL-LUEn is more applicable at individual sites at the half-hourly scale while TL-LUE could be regionally used at half-hourly, daily and 8-day scales. MOD17 is also an applicable option regionally at the 8-day scale.
Remote Sens. 2015, 7, 2238-2278; doi:10.3390/rs70302238 remote sensing ISSN 2072-4292 www.mdpi.com/journal/remotesensing Article Performance of Linear and Nonlinear Two-Leaf Light Use Efficiency Models at Different Temporal Scales Xiaocui Wu 1,2, Weimin Ju 1,2,*, Yanlian Zhou 3, Mingzhu He 4, Beverly E. Law 5, T. Andrew Black 6, Hank A. Margolis 7, Alessandro Cescatti 8, Lianhong Gu 9, Leonardo Montagnani 10,11, Asko Noormets 12, Timothy J. Griffis 13, Kim Pilegaard 14, Andrej Varlagin 15, Riccardo Valentini 16, Peter D. Blanken 17, Shaoqiang Wang 18, Huimin Wang 18, Shijie Han 19, Junhua Yan 20, Yingnian Li 21, Bingbing Zhou 3 and Yibo Liu 22 1 International Institute for Earth System Science, Nanjing University, Nanjing 210023, China; E-Mail: Xiaocui.Wu.1005@gmail.com 2 Jiangsu Center for Collaborative Innovation in Geographic Information Resource Development and Application, Nanjing 210023, China 3 School of Geographic and Oceanographic Science, Nanjing University, Nanjing 210023, China; E-Mails: Zhouyl@nju.edu.cn (Y.L.); zbb_nju@163.com (B.B.) 4 Numerical Terradynamic Simulation Group, the University of Montana, Missoula, MT 59812, USA; E-Mail: Mingzhu.he@ntsg.umt.edu 5 College of Forestry, Oregon State University, Corvallis, OR 97331, USA; E-Mail: bev.law@oregonstate.edu 6 Faculty of Land and Food Systems, University of British Columbia, Vancouver, BC V6T 1Z4, Canada; E-Mail: andrew.black@ubc.ca 7 Center ďÉtude de la Forêt, Laval University, Quebec City, QC G1V 0A6, Canada; E-Mail: Hank.Margolis@sbf.ulaval.ca 8 Institute for Environment and Sustainability, Joint Research Center, European Commission, 20127 Ispra, Italy; E-Mail: alessandro.cescatti@jrc.ec.europa.eu 9 Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA; E-Mail: lianhong-gu@ornl.gov 10 Forest Services, Autonomous Province of Bolzano, Via Brennero 6, 39100 Bolzano, Italy; E-Mail: leonar@inwind.it 11 Faculty of Science and Technology, Free University of Bolzano, Piazza Università 5, 39100 Bolzano, Italy 12 Department of Forestry and Environmental Resources, North Carolina State University, Raleigh, NC 27695, USA; E-Mail: asko_noormets@ncsu.edu 13 Department of Soil, Water, and Climate, University of Minnesota, St. Paul, MN 55108, USA; E-Mail: tgriffis@umn.edu OPEN ACCESSRemote Sens. 2015, 7 2239 14 Department of Chemical and Biochemical Engineering, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark; E-Mail: kipi@risoe.dtu.dk 15 A.N. Severtsov Institute of Ecology and Evolution, Russian Academy of Sciences, Lenisky pr.33, Moscow 119071, Russia; E-Mail: varlagin@sevin.ru 16 Department for Innovation in Biological, Aro-food and Forest Systems, University of Tuscia, 01100 Viterbo, Italy; E-Mail: rik@unitus.it 17 Department of Geography, University of Colorado, CO 80309, USA; E-Mail: Blanken@Colorado.EDU 18 Key Laboratory of Ecosystem Network Observation and Modeling, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Science, Beijing 100101, China; E-Mails: sqwang@igsnrr.ac.cn (S.Q.); wanghm@igsnrr.ac.cn (H.M.) 19 State Key Laboratory of Forest and Soil Ecology, Institute of Applied Ecology, Chinese Academy of Sciences, Shenyang 110016, China; E-Mail: hansj@iae.ac.cn 20 South China Botanical Garden, Chinese Academy of Sciences, Guangzhou 510650, China; E-Mail: jhyan@scib.ac.cn 21 Northwest Institute of Plateau Biology, Chinese Academy of Sciences, Xining 810008, China; E-Mail: ynli@nwipb.cas.cn 22 Jiangsu Key Laboratory of Agricultural Meteorology, College of Applied Meteorology, Nanjing University of Information Science and Technology, Nanjing 210044, China; E-Mail: Yiboliu2012@163.com * Author to whom correspondence should be addressed; E-Mail: juweimin@nju.edu.cn; Tel.: +86-25-8359-5670; Fax: +86-25-8359-2288. Academic Editors: Conghe Song, Dengsheng Lu and Prasad S. Thenkabail Received: 20 August 2014 / Accepted: 14 February 2015 / Published: 25 February 2015 Abstract: The reliable simulation of gross primary productivity (GPP) at various spatial and temporal scales is of significance to quantifying the net exchange of carbon between terrestrial ecosystems and the atmosphere. This study aimed to verify the ability of a nonlinear two-leaf model (TL-LUEn), a linear two-leaf model (TL-LUE), and a big-leaf light use efficiency model (MOD17) to simulate GPP at half-hourly, daily and 8-day scales using GPP derived from 58 eddy-covariance flux sites in Asia, Europe and North America as benchmarks. Model evaluation showed that the overall performance of TL-LUEn was slightly but not significantly better than TL-LUE at half-hourly and daily scale, while the overall performance of both TL-LUEn and TL-LUE were significantly better (p < 0.0001) than MOD17 at the two temporal scales. The improvement of TL-LUEn over TL-LUE was relatively small in comparison with the improvement of TL-LUE over MOD17. However, the differences between TL-LUEn and MOD17, and TL-LUE and MOD17 became less distinct at the 8-day scale. As for different vegetation types, TL-LUEn and TL-LUE performed better than MOD17 for all vegetation types except crops at the half-hourly scale. Remote Sens. 2015, 7 2240 At the daily and 8-day scales, both TL-LUEn and TL-LUE outperformed MOD17 for forests. However, TL-LUEn had a mixed performance for the three non-forest types while TL-LUE outperformed MOD17 slightly for all these non-forest types at daily and 8-day scales. The better performance of TL-LUEn and TL-LUE for forests was mainly achieved by the correction of the underestimation/overestimation of GPP simulated by MOD17 under low/high solar radiation and sky clearness conditions. TL-LUEn is more applicable at individual sites at the half-hourly scale while TL-LUE could be regionally used at half-hourly, daily and 8-day scales. MOD17 is also an applicable option regionally at the 8-day scale. Keywords: gross primary productivity (GPP); light use efficiency model; sunlit and shaded leaves; vegetation types; temporal scales 1. Introduction Efforts to mitigate climate change require the stabilization of atmospheric CO2 concentrations [1], which is significantly regulated by exchanges of carbon between terrestrial ecosystems and the atmosphere. Terrestrial gross primary productivity (GPP) is the largest component of the global carbon flux [2] and about 120 Pg C year−1 globally, considerably larger than the carbon annually emitted by human activities (about 9 Pg C year−1) [3]. Consequently, even a small change in GPP is likely to have a significant impact on atmospheric CO2 concentration. Thus, accurately simulating terrestrial GPP is of great significance to quantifying the global carbon cycle and predicting the future trajectories of the atmospheric CO2 concentration. Two approaches have been widely employed to investigate the spatial and temporal variability in GPP using remotely sensed data: (i) remote sensing driven process-based models, and (ii) light use efficiency (LUE) models [4]. The former is based on the mechanistic description of the photosynthetic biochemical processes and scales the Farquhar instantaneous leaf-level biochemical model [5] to the canopy level using big-leaf, two-leaf, and multilayer scaling approaches. A number of process-based models have been successfully applied to quantify spatial-temporal variations of GPP at regional and global scales using remotely sensed vegetation parameters, such as leaf area index (LAI) and land cover types, as inputs. However, the application of these process-based models is limited by the complexity and uncertainty of their parameterization [6]. In contrast, LUE models, such as CASA [7], MOD17 [8], EC-LUE [9], and VPM [10], were developed according to the LUE argument of Monteith [11,12] that productivity is linearly related to the amount of absorbed photosynthetically active radiation (APAR). A fundamental assumption underlying LUE models is that plant canopies behave like a big single-leaf and their LUE is independent of the directional nature of solar radiation and vegetation structure [13]. Many studies have indicated that both GPP and LUE vary with both quantity and quality of incoming solar radiation. Gu et al. [14] detected a 20% increase in Harvard Forest photosynthesis after the 1991 Pinatubo eruption owing to the increase of diffuse radiation caused by volcanic aerosols. Flux site data indicated that canopy LUE was enhanced under diffuse sunlight in comparison with that Remote Sens. 2015, 7 2241 under direct radiation [13,15,16]. Choudhury et al. [17] estimated an increase of 110% in crop LUE under diffuse radiation. Alton et al. [18] conducted a study for three forest sites (two broadleaf and one needleleaf) and found that the canopy LUE was enhanced by 6–33% under diffuse radiation. Alton [19] indicated that the enhancement of canopy LUE due to diffuse radiation varied with vegetation types, most significantly for tundra shrubs. Cai et al. [20] found that a single-leaf LUE model performed very well for a 56-year-old Douglas-fir stand when, instead of using total incident photosynthetically active radiation (PAR), they used the sum of incident diffuse PAR and a relatively small fixed fraction (22%) of incident direct PAR. Recently, Zhang et al. [21] reported that canopy LUE generally decreased with increasing sky clearness index, which is the ratio of solar radiation observed on the ground to radiation received at the top of the atmosphere, over 5 ChinaFLUX sites, including a temperate forest, a subtropical forest, a tropical rain forest, and two grassland sites. Therefore, the assumption that LUE is independent of the quality of radiation and GPP linearly increases with absorbed photosynthetic radiation would induce underestimation/overestimation of GPP in cloudy/clear skies [22,23]. Conceptually, a canopy is composed of clumps of sunlit and shaded leaves exposed to different levels of irradiance and showing variable LUE. Sunlit leaves receive both direct and diffuse radiation while shaded leaves mainly interact with diffuse beams. Under clear skies, solar irradiance is high and dominated by direct beams. Sunlit leaves are easily light saturated, and photosynthesis can even decrease with increasing radiation because of elevated temperature and enhanced photorespiration [13]. Consequently, the overall LUE of sunlit leaves is normally low [23]. In contrast, a large number of shaded leaves are only exposed to diffuse radiation, which is normally much lower than the radiation saturation point. Therefore, the photosynthesis of shaded leaves is typically light-limited. Under cloudy conditions, solar irradiance is dominated by diffuse sunlight, allowing shaded leaves to capture a large fraction of the solar irradiance. Even though the total incident radiation may be lower than that on clear days, the apparent improvement of the LUE for shaded leaves could lead to the enhanced LUE for the whole canopy [15,19]. More and more process models now calculate photosynthesis for sunlit and shade leaves separately [24–26]. However, this strategy has not been adopted by LUE models. To remedy this limitation, He et al. [23] recently developed a two-leaf LUE model on the basis of the MOD17 model. This new model considered differences in radiation absorption and in LUE of sunlit and shaded leaves. Validation at 6 ChinaFLUX sites demonstrated the improvement of the two-leaf LUE models over the MOD17 model in simulating GPP, especially at forest sites, with a R2 value increasing about 0.1 and a root mean square error (RMSE) value decreasing about 0.64 g C m−2 day−1 on average. In the two-leaf LUE model developed by He et al. [23], GPP of sunlit and shaded leaves increases linearly with APAR. However, many studies have shown a nonlinear increase of photosynthesis of sunlit leaves with increasing APAR because of light saturation of photosynthesis, especially at short temporal scales (minutes to hours) [15,27–31]. Recently, Wang et al. [6] developed a two-leaf temperature and vegetation type dependent rectangular hyperbolic model, which links quantum yield (α) and maximum photosynthetic rate (Pm) with the maximum carboxylation rate at 25 °C. The model is able to simulate GPP as accurately as a process-based model. Previously, linear LUE models have been mostly used to calculate GPP at daily, 8-day, and even longer temporal scales [7–10,32,33]. Recently, this type of models is used to calculate GPP at short temporal scales. For example, Carbon Tracker, a system to optimize terrestrial carbon flux, uses the Remote Sens. 2015, 7 2242 Carnegie-Ames Stanford Approach (CASA) biogeochemical model to calculate GPP every three hours as the prior carbon flux [34]. Such application of linear LUE models might induce biases in simulated GPP since observations have indicated the nonlinear response of canopy GPP to incoming PAR at short temporal scales [15,27–31]. Therefore, the assessment of applicability of different types of LUE models in simulating GPP at different temporal scales is of great significance to improving the simulation of GPP using remote sensing data. In this study, the ability of nonlinear two-leaf LUE, linear two-leaf LUE, and MOD17 to simulate GPP at half-hourly, daily, and 8-day temporal scales were verified using GPP derived from net ecosystem productivity (NEP) measured at globally distributed 58 sites as benchmarks. The main goals of this study are: (1) to compare the performance of the MOD17, linear and nonlinear two-leaf LUE models at three different temporal scales (half-hourly, daily and 8-day); (2) to analyze the possible causes for the different performances of three LUE models. For simplicity, the MOD17, linear two-leaf LUE, and nonlinear two-leaf LUE models will be referred to hereinafter as MOD17, TL-LUE, and TL-LUEn, respectively. 2. Data and Methods 2.1. Data In this study, we used meteorological data and ecosystem fluxes measured with the eddy covariance (EC) technique at 58 sites pertaining to the FLUXNET network and the processed MODIS leaf area index (LAI) product (MOD15A2) to simulate GPP at half-hourly, daily and 8-day temporal scales. The meteorological and flux data belongs to the LaThuile FLUXNET dataset and can be freely downloaded [35]. The sites were selected on the basis of the availability of key datasets, such as LAI, meteorology, and land surface C fluxes. GPP derived from tower measured NEP was used as benchmarks for model parameter optimization and model evaluation. All flux data were processed in the manner proposed within the Fluxnet project [36,37] as described by [38–41]. The 58 sites included 21 needle-leaf-forest (NF) sites, with 1 deciduous needle-leaf-forest (DNF) sites and 20 evergreen needle-leaf-forest (ENF) sites, 11 broadleaf-forest (BF) sites, with 2 evergreen broadleaf-forest (EBF) sites and 9 deciduous broadleaf-forest (DBF) sites, 4 mixed-forest (MF) sites, 7 crop (CROP) sites, 7 grassland (GRASS) sites, and 8 shrub (SHRUB) sites, located in Asia, Europe, and North America (Figure 1). The observations covered the period from January 2001 to December 2007 with at least two years of data for each site. In total, 143 site-years of data were used, of which 85 site-years of data were selected for parameter optimization (17 BF, 11 CROP, 10 GRASS, 6 MF, 29 NF, and 12 SHRUB site-years). The remaining 58 site-years of data were used for model evaluation, with one year of data for each site. Detailed information about each site is given in Table 1. Remote Sens. 2015, 7 2243 Figure 1. Distribution of all sites with data used for parameter optimization and validation in this study. The background is the MODIS global land cover product (MCD12C1) in 2003. Table 1. Name, location, vegetation type, and period of data used for each site. Site Name Country Lat. (°) Long. (°) Veg. Type Opti. Years Vali. Years Reference Austin Cary (ACA) USA 29.74 −82.22 NF 2003 2005 Gholz and Clark (2002) [42] ARM_SGP_Main (ASM) USA 36.61 −97.49 CROP 2003 2004 Fischer et al. (2007) [43] Audubon (AUD) USA 31.59 −110.51 GRASS 2003 2004 Wilson and Meyers (2007) [44] BC-DFir1949 (BD49) Canada 49.87 −125.33 NF 2003 2004 Humphreys et al. (2006) [45] Bartlett Experimental (BEP) USA 44.06 −71.29 BF 2005 2006 Jenkins et al. (2007) [46] BC-Harvest Dfir2000 (DF00) Canada 49.87 −125.29 NF 2003 2004 Humphreys et al. (2006) [45] BC-Harvest Dir1988 (DF88) Canada 49.53 −124.9 NF 2004 2005 Humphreys et al. (2006) [45] Bondville (BON) USA 40.01 −88.29 CROP 2004,2005 2006 Wilson and Meyers (2007) [44] Changbaishan (CBS) China 42.40 128.10 MF 2003 2004 Zhang et al. (2006a,b) [47,48] Dinghushan(DHS) China 23.17 112.53 BF 2003 2004 Zhang et al. (2000) [49] Donaldson (DON) USA 29.75 −82.16 NF 2003 2004 Gholz and Clark (2002) [42] El Saler (ES) Spain 39.35 −0.32 NF 2001,2002 2003 Reichstein et al. (2006) [50] Fort Peck (FPE) USA 48.31 −105.1 GRASS 2003 2004 Wilson and Meyers (2007) [44] Fyodorovskoye (FY) Russia 56.46 32.92 NF 2001 2003 Milyukova et al. (2002) [51] Goodwin Creek (GCR) USA 34.25 −89.87 GRASS 2004,2005 2006 Wilson and Meyers (2007) [44] Hainich (HA) Germany 51.08 10.45 BF 2001,2002 2003 Mund et al. (2010) [52] Harvard Forest (HAF) USA 42.54 −72.17 BF 2005 2006 Urbanski et al. (2007) [53] Haibei (HB) China 37.67 101.33 GRASS 2003 2004 He et al. (2013) [23] Hesse (HES) France 48.67 7.07 BF 2001,2002 2003 Granier et al. (2002) [54] Remote Sens. 2015, 7 2244 Table 1. Cont. Site Name Country Lat. (°) Long. (°) Veg. Type Opti. Years Vali. Years Reference Howland Forest (HOF) USA 45.2 −68.74 MF 2003 2004 Hollinger et al. (1999, 2004) [55,56] Hyytiala (HY) Finland 61.85 24.29 NF 2001 2002 Kramer et al. (2002) [57] Kendall (KED) USA 31.74 −109.94 GRASS 2006 2007 Scott (2010) [58] Kennedy (KEN) USA 28.61 −80.67 SHRUB 2004 2005 Powell et al. (2006) [59] Loobos (LOB) Netherlands 52.17 5.74 NF 2001,2002 2003 Dolman et al. (2002) [60] Mead Irrigated (MEI) USA 41.17 −96.48 CROP 2003,2004 2005 Verma et al. (2005) [61] Mead Rainfed (MER) USA 41.18 −96.44 CROP 2004 2005 Verma et al. (2005) [61] Metolius Intermediate (MIN) USA 44.45 −121.56 NF 2005 2007 Law et al. (2003) [62] and Thomas et al. (2009) [63] Mead Irrigated Rotation (MIR) USA 41.16 −96.47 CROP 2004 2005 Verma et al. (2005) [61] Mize (MIZ) USA 29.76 −82.24 SHRUB 2003 2004 Brocha et al. (2012) [64] Morgan Monroe State (MMS) USA 39.32 −86.41 BF 2003,2005 2006 Schmid et al. (2000) [65] Metolius New Young Pine (MNY) USA 44.32 −121.6 NF 2004 2005 Ruehr et al. (2012) [66] and Vickers et al. (2012) [67] Missouri Ozark (MOZ) USA 38.74 −92.2 BF 2005,2006 2007 Gu et al. (2006) [68] North Carolina Loblolly Pine (NCL) USA 35.8 −76.67 NF 2005 2006 Noormets et al. (2009) [69] Neustift (NEU) Austria 47.12 11.32 GRASS 2002 2003 Wohlfahrt et al. (2008) [70] Niwot Ridge (NR) USA 40.03 −105.55 NF 2003,2006 2007 Monson et al. (2002) [71] ON EpeatlandMerBleue (OEM) Canada 45.41 −75.52 SHRUB 2001 2004 Lafleur et al. (2003) [72] Puechabon (PUE) France 43.74 3.6 BF 2001,2002 2003 Allard et al. (2008) [73] QC-Black Spruce (QMB) Canada 49.69 −74.34 NF 2004 2005 Bergeron et al. (2007) [74] Qianyanzhou(QYZ) China 26.73 115.07 NF 2003 2004 Yu et al. (2006) [75] Renon (REN) Italy 46.59 11.43 NF 2002 2003 Montagnani et al. (2009) [76] Rosemount G19 (RG19) USA 44.72 −93.09 CROP 2004,2005 2006 Griffis et al. (2008) [77] Rosemount G21 (RG21) USA 44.71 −93.09 CROP 2004,2005 2006 Bavin et al. (2009) [78] Roccarespampani1 (ROC) Italy 42.39 11.92 BF 2002 2003 Keenan et al. (2009) [79] Sky Oaks New (SON) USA 33.38 −116.64 SHRUB 2004,2005 2006 Luo et al. (2007) [80] Soroe (SOR) Denmark 55.48 11.65 MF 2001,2002 2003 Pilegaard et al. (2001) [81] Santa Rita Mesquite (SRM) USA 31.82 −110.87 SHRUB 2004,2005 2006 Scott (2010) [58] San Rossore (SRO) Italy 43.73 10.29 NF 2001,2002 2003 Migliavacca et al. (2011) [82] Tharandt (THA) Germany 50.96 13.57 NF 2001,2002 2003 Grünwald and Bernhofer (2007) [83] Tomakomai (TMK) Japan 42.74 141.52 NF 2001,2002 2003 Hirano et al. (2003) [84] Tonzi Ranch (TRA) USA 38.43 −120.97 SHRUB 2004,2005,2006 2007 Baldocchi et al. (2004) [85] UCI 1850 (U50) Canada 55.88 −98.48 NF 2003 2004 Goulden et al. (2011) [86] UCI 1989 (U89) Canada 55.92 −98.96 SHRUB 2003 2004 Goulden et al. (2011) [86] UCI 1998 (U98) Canada 56.64 −99.95 SHRUB 2003 2004 Goulden et al. (2011) [86] UMBS (UMBS) USA 45.56 −84.71 BF 2003,2004 2006 Curtis et al. (2005) [87] Remote Sens. 2015, 7 2245 Table 1. Cont. Site Name Country Lat. (°) Long. (°) Veg. Type Opti. Years Vali. Years Reference Vaira Ranch (VRA) USA 38.41 −120.95 GRASS 2003,2004 2007 Baldocchi et al. (2004) [85] Vielsalm (VSA) Belgium 50.31 6.00 MF 2001,2002 2003 Aubinet et al. (2001) [88] Willow Creek (WCR) USA 45.81 −90.08 BF 2003 2005 Bolstad et al. (2004) [89] Wetzstein (WET) Germany 50.45 11.46 NF 2002 2003 Rebmann et al. (2009) [90] 2.2. Methods 2.2.1. Models Used TL-LUEn, TL-LUE, and MOD17 models were used in this study. The MOD17 algorithm is described in detail in Running et al. [8,91]. It relies on the assumption that GPP is linearly related to APAR [11,12,92]. The TL-LUE model stems from the MOD17 algorithm and discriminates the differences of upper and bottom canopy in receiving direct radiation and diffuse radiation and in their LUE. As a consequence, canopy GPP simulated by TL-LUE nonlinearly changes with incoming PAR. The TL-LUEn adopts the same methodology as the TL-LUE model to separate sunlit and shaded leaves and calculate their APAR. However, it takes the rectangular hyperbolic model to calculate GPP for sunlit and shaded leaves. The MOD17, TL-LUE, and TL-LUEn models are described in Equations (1–3), respectively, i.e.,    max minPAR aGPP fPAR f VPD g T     (1)     m m minmsu su su msh msh msh aGPP APAR LAI APAR LAI f VPD g T         (2)   minm msu m mshmsu msh am msu m mshAPAR APARGPP = LAI + LAI f VPD g TAPAR APAR                   (3)where εmax is the maximum LUE in MOD17; fPAR is the fraction of PAR absorbed by vegetation and calculated from LAI using the Beer’s Law (fPAR=1-e−k*LAI, where k is the light extinction coefficient and set as 0.5 as [23]); εmsu and εmsh are the maximum LUE of sunlit and shaded leaves in TL-LUE, respectively; εm is the quantum yield when incident PAR approaches zero and β is the maximum canopy photosynthetic flux density at light saturation in TL-LUEn [13]; f(VPD) and g(Tamin) denote the constrains imposed by atmospheric vapor pressure deficit (VPD) and minimum air temperature, respectively, and are used to downscale the maximum LUE values to real ones. APARmsu and APARmsh are the PAR absorbed by sunlit and shaded leaves per unit LAI; LAImsu and LAImsh are the leaf area index for sunlit and shaded leaves. In above equations, the two attenuation scalars, f(VPD) and g(Tamin), range from 0 (total inhibition) to 1 (no inhibition) and are calculated using the same formulas for MOD17, TL-LUE, and TL-LUEn. Parameters VPDmax, VPDmin, Tamin_min, and Tamin_max used to calculate f(VPD) and g(Tamin) depend on vegetation types [91] and are listed in Table 2. In Equations (2) and (3), APARmsu and APARmsh are calculated as: Remote Sens. 2015, 7 2246 ,cos( )(1 )cos( )dif dif umsu dirPAR PARAPAR PAR CLAI          (4),(1 ) dif dif umshPAR PARAPAR CLAI        (5)where α is the albedo varying with vegetation types (Table 2), PARdif and PARdir are the diffuse and direct components of incoming PAR, respectively, and they are empirically calculated (see Equation (6)); PARdif,u is the diffuse PAR under the canopy and calculated following [24]; (PARdif – PARdif,u)/LAI denotes the absorbed diffuse PAR per unit leaf area within the canopy; C indicates multiple scattering of total PAR within the canopy [24]; φ is the mean leaf-sun angle and set as 60º[24]; θ is the mean solar zenith angles of half an hour, a day, and 8 days. The average solar zenith angle in each half an hour is calculated according to latitude, Julian day, and local time [93]. The average solar zenith angle in a given day is calculated according to latitude and Julian day [24]. The 8-day average solar zenith angle is the mean of the daily average solar zenith angles during the 8 days period. Diffuse and direct PAR are empirically partitioned as [24]: 2 3 4(0.943 0.734 4.9 1.796 2.058 )     difPAR R R R R PAR (6)where PARdif is the estimated diffuse PAR; R is the sky clearness index (R=S/(S0cosθ)), S and S0 are the incoming solar radiation on the ground surface and solar constant (1367 Wm−2), respectively. In the conversion of incoming solar radiation into PAR, a constant of 0.5 is used [23] (PAR=0.5S). LAImsu and LAImsh in Equations (2) and (3) are calculated as [24]:  I 2 cos( ) 1 exp 0.5 cosmsuLAILA                (7)Imsh msuLA LAI LAI  (8)where Ω is the clumping index, which changes with land cover types, season and solar zenith angle. It was only assigned according to vegetation types here (Table 2) since spatially and temporally variant data are not available for this parameter. Table 2. Model parameters used for different vegetation types. Vegetation Type* DBF ENF EBF MF GRASS CROP savannas OS WS εmax (g C/MJ)** 1.044 1.008 1.259 1.116 0.604 0.604 0.888 0.774 0.768 Tamin_max (°C) 7.94 8.31 9.09 8.5 12.02 12.02 8.61 8.8 11.39 Tamin_min (°C) −8 −8 −8 −8 −8 −8 −8 −8 −8 VPDmax (kpa) 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4.1 VPDmin (kpa) 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.93 9.3 Albedo 0.18 0.15 0.18 0.17 0.23a 0.23b 0.16 0.16 0.23 Clumping index (Ωc) 0.8 0.6 0.8 0.7 0.9 0.9 0.8 0.8 0.8 *DBF: deciduous broadleaf forest; ENF: evergreen needleleaf forest; EBF: evergreen broadleaf forest; MF: mixed forest; GRASS: grassland; CROP: cropland; savannas: savannas; OS: open shrublands; WS: woody savannas; a Tang et al. [94]. b Grant et al. [95]. c Singarayer et al. [96]; ** Running et al. [91]. Remote Sens. 2015, 7 2247 2.2.2. Parameter Optimization The derived GPP in 85 calibration site-years was used to optimize parameters in MOD17, TL-LUEn, and TL-LUE models. The optimization was implemented using the Markov chain Monte Carlo (MCMC) method [97,98]. In the optimization, three models were driven using the same locally measured meteorological data and smoothed MODIS LAI. The MCMC simulation, as a stochastic simulation method, is based on Bayesian Theory, in which parameters are random variables instead of deterministic, but unknown constants in the classic thoughts. The fundamental formula of Bayesian Theory is:   ( | ) ( )|( | ) ( )p xxp x d       (9)where π(θ | x) is the posterior density of parameter  (a term distribution under the condition of given sample x); π(θ) is the prior distribution of parameter  (the knowledge possessed before measurement); and p(x | θ) is a likelihood function. To determine the posterior density π(θ|x), the prior density and the likelihood function should be given in advance. We specified the prior density function as a uniform distribution over the following ranges: max0 200 15000 , , 10mmsu msh      (10)The lower and upper limits of εm (unit: g C MJ−1) and  (unit: µg C m−2 s−1) were set according to the values compiled from 100 published datasets by Ruimy et al. [99]. The upper limits of εmsu, εmsh and εmax (unit: g C MJ−1) were assigned on the basis of previous findings [32,100]. In the optimization, these parameters were assumed uniformly distributed in the given limits with equal probability for all possible values. The likelihood function was specified according to the distribution of simulation errors, which were assumed following a multivariate Gaussian distribution with a zero mean. This assumption is commonly made in many studies [101–103]. With this assumption, the likelihood function can be written as:   2 2( ) /211|2i i inP Oi ip x e    (11)where Oi and Pi are the tower-derived GPP and simulated GPP, respectively; i are the standard error of tower-derived GPP. The sampling of parameters was implemented using the Metropolis-Hastings (M-H) algorithm. To find an effective proposal distribution, we first made a test run of the algorithm with 50,000 simulations. Based on the test run, a Gaussian distribution N(0, cov0(θ)) was constructed (cov0(θ) is a diagonal matrix with its diagonal elements equal to the estimated variances of parameters θ). Then, the following proposal distribution was adopted to execute the consecutive MCMC simulations formally for 30,000 times: 1 0(0,cov ( ))k k N    (12)where θk is the new parameters generated from its predecessor θk−1. Remote Sens. 2015, 7 2248 The running means and standard deviations of parameter samples need time to approach stable. For bettering the statistical analysis of parameters, we discarded the initial 10,000 samples in the burn-in period and only used the remaining 20,000 samples for further analysis of each parameter. The histograms of the samples for each parameter indicate these parameters were well constrained in most situations because the posterior density functions were near the normal distribution (see Figure A1 in Appendix). Uncertainties of estimated parameters were quantified with a 95% highest-probability density interval. Means of parameter θi were estimated as followings and used for model validation: ( )11( )  N ki ikEN (13)where N is the number of samples in the M-H algorithm. 2.2.3. Parameter Sensitivity Analysis Sensitivity of simulated GPP to parameters in three LUE models was analyzed using the factorial approach [104-106]. This method facilitates the statistically based representation of combinations of errors in several parameter sets. For a two-level complete factorial design, each of the model parameters is assigned upper and lower values based on specified perturbations of the magnitudes of the parameters, and the model is run using all combinations of parameter values. For n different parameters, this would require 2n simulation runs. Each parameter here was perturbed by an arbitrary magnitude ±10% [105]. The main effect of a parameter, which is also referred to the parameter sensitivity, is calculated as the average difference between a run in which the parameter is at its upper level (+10%) and a run in which the parameter at its lower level (−10%), but other parameters remain unchanged. For example, there are 4 simulation runs for TL-LUEn when considering the parameters εm and β. They are both εm and β at their lower levels (simulation #1), εm at its upper level and β at its lower level (simulation #2), εm at its lower level and β at its upper level (simulation #3), and both εm and β at their upper levels (simulation #4). The main effect of εm in TL-LUEn are the average of the difference between simulation #2 and simulation #1, and the difference between simulation #4 and simulation #3. A larger value of main effect indicates higher sensitivity of simulated GPP. 2.2.4. Model Performance Assessment The performance of TL-LUEn, TL-LUE, and MOD17 was assessed using root mean square error (RMSE) and determination coefficient (R2). The paired t test was then conducted to evaluate the significance regarding the differences in R2, RMSE between TL-LUEn and TL-LUE, TL-LUEn and MOD17, and TL-LUE and MOD17 when all vegetation types lumped together at three temporal scales for model evaluation, respectively [13]. Remote Sens. 2015, 7 2249 3. Results 3.1. Optimized Model Parameters Table 3 shows the averages of optimized εm, εmax, εmsu and εmsh for 6 different vegetation types at half-hourly, daily and 8-day temporal scales, respectively. εm was generally larger than εmsh, εmsu, and εmax. It increased sizably when the temporal scales increasing from half-hourly to 8-day, especially for CROP. CROP always had the highest εm in all the three temporal scales. At the half-hourly scale, three forest types, including BF, MF and NF, had lower εm values than CROP and SHRUB, but higher than GRASS. Through metadata analysis for more than 100 published datasets, Ruimy et al. [99] reported that CROP has the highest εm (about 5.17 g C MJ−1) at the half-hourly scale, followed by forests (about 4.37 g C MJ−1, mainly BF sites), and GRASS has the smallest one (about 2.71 g C MJ−1), similar to the identified changes of εm with vegetation types here. Optimized εmax was in between εmsh and εmsu for all vegetation types and at all temporal scales. εmsh is larger than εmsu and εmax due to the fact that shaded leaves are only exposed to diffuse radiation, which enters a canopy from all directions and distributes more evenly than direct radiation within the canopy [107,108]. The intensity of light absorbed by shaded leaves is normally lower than light saturation point. Thus, they have higher light use efficiency than sunlit leaves. The values of εmax, εmsu and εmsh showed smaller variations than εm across three temporal scales (Table 3). As expected, CROP had the highest εmax, εmsu, and εmsh values, which are 1.78, 1.21 and 5.23 g C MJ−1 at the half-hourly scale, 1.80, 0.95 and 4.67 g C MJ−1 at the daily temporal scale, and 1.80, 0.96 and 4.26 g C MJ−1 at the 8-day scale, respectively. MF had the second largest ones, followed by BF and NF. GRASS had the lowest εmax, εmsu and εmsh values among all 6 vegetation types. The εmax, εmsu and εmsh of GRASS were lower than half of the corresponding values of CROP at the three temporal scales, respectively. In general, the average optimized εmax was close to the default values used in the MOD17 algorithm (Table 2) for all vegetation types except CROP, which had much higher optimized εmax than the default (0.604 g C MJ−1). Many studies have indicated that the underestimation of CROP GPP by the MOD17 algorithm is mainly due to the low value of εmax used [109]. It has been reported that the mean LUE of croplands can approach 2.80 g C MJ−1 [110–112], slightly higher than the average value of about 2.0 g C MJ−1 optimized in this study. The parameter β in the TL-LUEn model showed complex changes with temporal scales and vegetation types. At the half-hourly scale, non-forest types had a relatively higher β value than forests, which is consistent with the findings reported by Ruimy et al. [99] and Wang et al. [6]. At the daily temporal scale, GRASS had the highest β (286.28 µg C m−2 s−1), followed by CROP, NF, MF, SHRUB and BF. At the 8-day temporal scale, the β values of BF, CROP, GRASS, MF, NF and SHRUB were 163.58, 214.64, 483.41, 267.39, 335.02, and 369.31 µg C m−2 s−1, respectively Remote Sens. 2015, 7 2250 Table 3. Average, standard deviation, variation of coefficient (CV), and uncertainties range of optimized εm, β, εmsu, εmsh and εmax for 6 different vegetation types at half-hourly, daily and 8-day temporal scales (εm, β in TL-LUEn, εmsu, εmsh in TL-LUE, and εmax in MOD17). The uncertainty was quantified with a 95% highest-probability density interval and averaged over each biome. εm (g C MJ−1) β (µg C m−2 s−1) εmsu (g C MJ−1) εmsh (g C MJ−1) εmax (g C MJ−1) Mean STD CV (%) Uncertainty Mean STD CV (%) Uncertainty Mean STD CV (%) Uncertainty Mean STD CV (%) Uncertainty Mean STD CV (%) Uncertainty Half-hourly BF 3.52 1.72 48.93 ±1.32 147.84 112.19 75.88 ±77.50 0.58 0.15 25.20 ±0.10 2.37 0.68 28.94 ±0.39 0.88 0.24 27.39 ±0.09 CROP 4.34 1.07 24.64 ±1.46 470.48 235.03 49.96 ±177.09 1.21 0.39 32.06 ±0.16 5.23 1.90 36.34 ±0.91 1.78 0.62 35.07 ±0.16 GRASS 2.14 1.35 63.22 ±1.13 273.55 333.25 121.83 ±143.44 0.48 0.23 48.42 ±0.16 1.69 1.06 62.74 ±0.70 0.64 0.37 58.17 ±0.14 MF 3.59 0.97 27.14 ±1.27 214.63 83.46 38.89 ±91.48 0.78 0.18 22.77 ±0.13 3.33 0.83 24.91 ±0.45 1.26 0.24 19.20 ±0.11 NF 2.79 2.19 78.67 ±0.92 308.14 272.11 88.31 ±161.84 0.66 0.22 33.20 ±0.16 2.35 0.79 33.57 ±0.56 0.88 0.29 33.24 ±0.11 SHRUB 2.41 3.48 144.64 ±0.94 540.16 481.89 89.21 ±242.72 0.53 0.17 32.29 ±0.20 1.70 0.63 37.08 ±0.95 0.65 0.24 36.44 ±0.21 Daily BF 4.39 3.10 70.56 ±1.05 99.88 93.92 94.04 ±16.16 0.47 0.16 34.76 ±0.02 2.06 0.63 30.47 ±0.06 0.95 0.29 30.23 ±0.02 CROP 12.02 5.05 42.06 ±2.85 189.06 79.53 42.06 ±23.26 0.95 0.30 31.47 ±0.02 4.67 1.55 33.27 ±0.12 1.80 0.58 32.19 ±0.03 GRASS 6.06 5.94 98.14 ±3.46 286.28 399.60 139.58 ±143.94 0.44 0.26 58.18 ±0.05 1.56 0.98 62.91 ±0.17 0.69 0.44 63.51 ±0.04 MF 3.41 0.73 21.48 ±0.32 147.65 53.43 36.19 ±14.80 0.61 0.14 22.19 ±0.02 2.97 0.65 21.98 ±0.06 1.40 0.26 18.76 ±0.02 NF 2.69 1.79 66.53 ±0.59 152.09 77.61 51.03 ±36.93 0.54 0.15 28.38 ±0.05 2.21 0.74 33.31 ±0.11 0.98 0.32 32.24 ±0.02 SHRUB 5.60 3.86 68.87 ±5.13 105.57 51.30 48.59 ±25.56 0.44 0.15 33.76 ±0.05 1.84 0.64 34.68 ±0.26 0.75 0.21 28.66 ±0.05 8-day BF 4.64 2.78 59.92 ±1.37 163.58 271.85 166.19 ±84.65 0.53 0.18 34.42 ±0.11 1.83 0.59 32.27 ±0.19 0.97 0.30 31.04 ±0.05 CROP 14.79 5.21 35.26 ±2.28 214.64 197.90 92.20 ±82.78 0.96 0.27 27.95 ±0.09 4.26 1.59 37.44 ±0.31 1.80 0.58 32.00 ±0.09 GRASS 3.19 3.93 123.31 ±1.20 483.41 489.70 101.30 ±192.63 0.48 0.29 59.81 ±0.14 1.33 0.79 58.88 ±0.28 0.70 0.45 64.58 ±0.10 MF 2.39 0.38 15.97 ±0.71 267.39 172.78 64.62 ±150.71 0.79 0.18 22.48 ±0.23 2.51 0.63 24.95 ±0.31 1.45 0.27 18.64 ±0.07 NF 2.31 1.66 71.68 ±0.79 335.02 341.62 101.97 ±206.24 0.68 0.25 36.09 ±0.17 1.81 0.63 34.79 ±0.28 1.01 0.34 33.65 ±0.07 SHRUB 2.08 1.61 77.58 ±1.19 369.31 399.01 108.04 ±242.47 0.47 0.14 30.39 ±0.14 1.62 0.77 47.12 ±0.33 0.74 0.22 29.68 ±0.13 Remote Sens. 2015, 7 2251 3.2. Model Performance in Calibration Site-Years At the half-hourly scale, TL-LUEn showed slightly better performance than TL-LUE when data in all 85 calibration site-years were lumped together (Figure 2). With the increase of temporal scales from half an hour to 8 days, the difference of TL-LUEn and TL-LUE became almost indistinguishable. The improvement of both TL-LUE and TL-LUEn over MOD17 was obvious at all three temporal scales. At the half-hourly scale, the average RMSE of MOD17 were larger than that of TL-LUEn by 8.1 mg C m−2 (30min)−1, and the corresponding average R2 was lower than that of TL-LUEn by 0.050 (Figure 2a,b). At the daily scale, MOD17 output an average RMSE higher by 0.3 g C m−2 day−1 and R2 lower by 0.051 than TL-LUEn (Figure 2c,d). As to the 8-day scale, the average RMSE of MOD17 was 1.0 g C m−2 8days−1 larger than that of TL-LUEn, and the corresponding average R2 was 0.025 lower than that of TL-LUEn (Figure 2e,f). Figure 2. The number of site-years within different root mean square error (RMSE) and R2 classes (left) and the averages of RMSE and R2 (right) of GPP simulated using the TL-LUEn, TL-LUE, and MOD17 models in 85 calibration site-years at half-hourly (a,b), daily (c,d), and 8-day (e,f) temporal scales, respectively. At three different temporal scales, the number of site-years in the same RMSE and R2 classes was similar for TL-LUEn and TL-LUE, confirming their similar ability to simulate GPP (see Figure 2). MOD17 performed poorer than TL-LUEn and TL-LUE in most site-years, indicated by larger RMSE and smaller R2. For example, at the half-hourly temporal scale, the number of site-years with small RMSE values (below 60 mg C m−2 (30min)−1), was 29 for MOD17, 40 for TL-LUEn, and 41 for TL-LUE, respectively. The R2 of GPP simulated by MOD17 was mostly in the range of 0.5–0.8 (in Remote Sens. 2015, 7 2252 58 site-years) while the R2 of GPP simulated by the TL-LUEn and TL-LUE mostly ranged from 0.7 to 0.9 (58 site-years for TL-LUEn and 59 site-years for TL-LUE). TL-LUEn performed better than TL-LUE for most vegetation types except CROP at the half-hourly and daily scale. However, it performed no better than TL-LUE for MF, NF and SHRUB at the 8-day scale (see Figure 3). Both TL-LUEn and TL-LUE outperformed MOD17 for most vegetation types at three temporal scales except for CROP at the half-hourly scale. The superiority of TL-LUEn and TL-LUE over MOD17 was most significant at forest sites. Figure 3. Average RMSE and R2 of GPP simulated using calibrated TL-LUEn, TL-LUE and MOD17 in the calibration site-years at half-hourly (the first and second columns), daily (the third and fourth columns), and 8-day (the last two columns) scales for individual vegetation types. Note: Broadleaf forest (BF); Mixed forest (MF); Needleleaf forest (NF); Crop (CROP); Grass (GRASS); Shrub (SHRUB). Solid black circles are the means and horizontal error bars denote standard deviations. 3.3. Model Performance in Evaluation Site–years 3.3.1. Model Performance at the Half-hourly Scale Model evaluation shows that TL-LUEn performed slightly better than TL-LUE in simulating half-hourly GPP when data in all 58 validation site-years was lumped together (Figure 4a,b). The RMSE and R2 of GPP simulated using TL-LUE against measurements averaged 64.3 mg C m−2 Remote Sens. 2015, 7 2253 (30min)−1 and 0.732, respectively, while the corresponding values of TL-LUEn were 63.9 mg C m−2 (30min)−1 and 0.735, respectively. However, the differences in RMSE value between TL-LUEn and TL-LUE were not significant (p = 0.45) as well as the differences in R2 between the two models (p = 0.27) (Table 4). The performance of MOD17 was the poorest, with average RMSE and R2 values equaled to 70.1 mg C m−2 (30min)−1 and 0.690, respectively. In addition, the differences in both the two statistics (RMSE, R2) between TL-LUEn and MOD17, and TL-LUE and MOD17 were significant, with p values smaller than 0.0001 (Table 4). Figure 4. The number of site-years within different RMSE and R2 classes (left) and the averages of RMSE and R2 (right) of gross primary productivity (GPP) simulated using the TL-LUEn, TL-LUE, and MOD17 models in 58 validation site-years at half-hourly (a,b), daily (c,d), and 8-day (e,f) temporal scales, respectively. In 58 evaluation site-years, the RMSE of GPP simulated using TL-LUEn, TL-LUE, and MOD17 was larger than 80 mg C m−2 (30min)−1 at 10, 11 and 17 sites, respectively. The R2 of GPP simulated using MOD17 mostly ranged from 0.5 to 0.8 (at 42 sites) while the R2 of GPP simulated using TL-LUEn and TL-LUE was in the range from 0.7 to 0.9 at 39 and 40 sites, respectively (Figure 4a,b). TL-LUEn performed better than TL-LUE at 31 sites. The poorer performance of TL-LUEn relative to TL-LUE occurred at CROP, GRASS, SHRUB and NF sites. MOD17 only performed better than TL-LUE and TL-LUEn at 9 sites (Table A1 in the Appendix). Remote Sens. 2015, 7 2254 Table 4. Statistics of the Paired t Tests on the differences between TL-LUEn and TL-LUE, TL-LUEn and MOD17, and TL-LUE and MOD17 in RMSE and R2 for model validation when all vegetation types lumped together at half-hourly, daily and 8-day scale. RMSE R2 TL-LUEn − TL-LUE TL-LUEn − MOD17 TL-LUE − MOD17 TL-LUEn − TL-LUE TL-LUEn − MOD17 TL-LUE − MOD17 Half-hourly t stat −0.75 −4.33 −5.09 t stat 1.12 6.10 7.13 p 0.45 0.00 0.00 p 0.27 0.00 0.00 Daily t stat 0.33 −4.88 −7.63 t stat 0.53 7.61 9.30 p 0.75 0.00 0.00 p 0.60 0.00 0.00 8-day t stat 2.24 −1.35 −5.96 t stat 0.98 4.70 0.98 p 0.03 0.18 0.00 p 0.33 0.00 0.33 Overall, TL-LUEn performed better than TL-LUE for BF, GRASS, MF and SHRUB, but poorer than TL-LUE for CROP and NF (see Figure 5). TL-LUEn and TL-LUE outperformed MOD17 for all vegetation types but CROP. The improvement of TL-LUE and TL-LUEn over MOD17 was most significant for forests (BF, MF and NF). Averaged over all forest sites, the RMSE of MOD17 was larger than those of TL-LUEn and TL-LUE by 10.1 mg C m−2 (30min)−1 and 8.8mg C m−2 (30min)−1, respectively. The corresponding average R2 of MOD17 was 0.063 and 0.060 lower than those of TL-LUEn and TL-LUE, respectively. 3.3.2. Model Performance at the Daily Scale TL-LUEn showed better performance than TL-LUE at the daily scale when 58 validation site-year data was lumped together (Figure 4c,d). The average RMSE of GPP simulated by TL-LUEn and TL-LUE was both 1.7 g C m−2 day−1. The average R2 of GPP simulated by TL-LUEn was slightly larger than that of TL-LUE. Results of the paired t test on the differences in average RMSE value between TL-LUEn and TL-LUE were not significant (p = 0.75), as well as the differences in average R2 value between the two models (p = 0.60) (Table 4). The average RMSE value of MOD17 was 1.9 g C m−2 day−1. The average R2 value of MOD17 was smaller than the corresponding values of TL-LUEn and TL-LUE by 0.046 and by 0.045, respectively. In addition, the differences in average RMSE value and R2 value between TL-LUEn and MOD17, and TL-LUE and MOD17 were significant, with p values were all smaller than 0.0001. In 58 validation site-years, MOD17 produced larger RMSE and lower R2 than TL-LUE and TL-LUEn at most sites. The RMSE of GPP simulated using MOD17, TL-LUE, and TL-LUEn was larger than 2.0 g C m−2 day−1 at 28, 15, and 15 sites, respectively. The values of R2 above 0.9 occurred at only 3 sites for MOD17, at 13 sites for TL-LUE, at 16 sites for TL-LUEn, respectively (Figure 4c,d). TL-LUEn showed better ability to simulate GPP than TL-LUE at 29 sites. MOD17 only outperformed TL-LUEn and TL-LUE at 12 and 8 sites, respectively, mainly CROP, SHRUB and GRASS sites (Table A2 in the Appendix). Remote Sens. 2015, 7 2255 As to MF, NF and SHRUB, TL-LUEn performed with a higher RMSE and R2 than TL-LUE. TL-LUEn only outperformed TL-LUE for BF, but performed poorer for CROP and GRASS (see Figure 5). Overall, TL-LUEn and TL-LUE outperformed MOD17 for forests and SHRUB. For three forest types, both TL-LUEn and TL-LUE outperformed MOD17. The average RMSE of both TL-LUEn and TL-LUE was 0.4 g C m−2 day−1 smaller than that of MOD17 while the average R2 of TL-LUEn and TL-LUE was 0.063 and 0.057 higher than that of MOD17, respectively. As to CROP and GRASS, both average RMSE and R2 of GPP simulated by TL-LUEn were higher than those of MOD17, while TL-LUE outperformed MOD17 with a smaller RMSE and a higher R2 (see Figure 5). Figure 5. Average RMSE and R2 of GPP simulated using calibrated TL-LUEn, TL-LUE and MOD17 in the validation site-years at half-hourly (the first and second columns), daily (the third and fourth columns), and 8-day (the last two columns) scales for individual vegetation types. Note: Broadleaf forest (BF); Mixed forest (MF); Needleleaf forest (NF); Crop (CROP); Grass (GRASS); Shrub (SHRUB). Solid black circles are the means and horizontal error bars denote standard deviations. 3.3.3. Model Performance at the 8-day Scale When data in all 58 validation site-years was lumped together, TL-LUEn performed similarly with TL-LUE at the 8-day scale (Figure 4e,f). The differences between the two models were significant (p < 0.05) in average RMSE value but was not significant (p = 0.33) in average R2 value (Table 4). TL-LUEn outperformed MOD17 with significant differences (p < 0.05) in their average R2 value but not Remote Sens. 2015, 7 2256 significant differences in their RMSE value (p = 0.18), while TL-LUE outperformed MOD17 with significant differences (p < 0.0001) in their average RMSE value but not significant differences in their average R2 value (p = 0.33) (Figure 4e,f, Table 4). However, the improvement of both TL-LUE and TL-LUEn over MOD17 was smaller in comparison with the improvement at half-hourly and daily temporal scales. MOD17 produced an average RMSE value of 13.0 g C m−2 (8days)−1 and an average R2 value of 0.755. The average RMSE and R2 of TL-LUE were 12.0 g C m−2 (8days)−1 and 0.775, respectively. The RMSE of GPP simulated by TL-LUEn, TL-LUE and MOD17 were smaller than 12 g C m−2 (8days)−1 at 35, 34 and 27 sites. The three models had similar numbers of sites in each R2 class. TL-LUEn performed poorer than TL-LUE at 32 sites, while MOD17 outperformed TL-LUEn and TL-LUE at 20 and 13 sites, respectively, which were mainly non-forest and NF sites (Table A3 in the Appendix). TL-LUEn only performed better than TL-LUE for BF. As to non-forest types (CROP, GRASS and SHRUB), TL-LUEn performed similarly with MOD17. The average RMSE and R2 of the former were larger than those of the latter by 1.0 g C m−2 (8days)−1 and 0.012, respectively. TL-LUE outperformed MOD17 in all the three non-forest types. As to forests, both TL-LUEn and TL-LUE showed a better performance than MOD17 with an average RMSE smaller than that of MOD17 by 1.5 g C m−2 (8days)−1 and 1.6 g C m−2 (8days)−1 and corresponding average R2 larger than that of MOD17 by 0.030 and 0.022, respectively. 4. Discussion 4.1. The Ability of the Three LUE Models to Simulate GPP At the half-hourly temporal scale, TL-LUEn and TL-LUE performed better than MOD17 for three types of forests (MF, BF, and NF), GRASS and SHRUB and their differences between these vegetation types are significant. With the increase of temporal scales, the improvement of TL-LUEn and TL-LUE over MOD17 gradually became less distinct. The changes in the ability of TL-LUEn, TL-LUE, and MOD17 to simulate GPP with vegetation types and temporal scales are, at least in part, related to the different structure of various vegetation types and the different response of canopy GPP to incident PAR described by three models. It was found that scaling up in time tended to linearize the relationship between CO2 flux and PAR [99]. Observations also showed that changes in canopy GPP with incident PAR are nonlinear at the half-hourly scale and become approximately linear at the daily and 8-day scales [29]. GPP simulated by MOD17 always linearly increase with incident PAR while the increase of GPP with incident PAR is nonlinear in both TL-LUEn and TL-LUE. The non-linearity of TL-LUEn and TL-LUE can be modified through changing parameters εm, β, εmsu, and εmsh. For example, if εmsu equals εmsh in the TL-LUE model, the response of simulated canopy GPP to incident PAR would be close to linear. This is the reason why the improvement of TL-LUEn and TL-LUE over MOD17 is much smaller at the 8-day scale than at the half-hourly temporal scale. The better performance of TL-LUEn and TL-LUE models over MOD17 changed with vegetation types, most significantly for forests, then for SHRUB, GRASS. Leuning et al. [113] pointed out that the canopy CO2 exchange rates of crops is a quasi-linear function of absorbed PAR. In contrast, forests Remote Sens. 2015, 7 2257 and sparse vegetation often show a markedly nonlinear response of canopy CO2 exchange rates to absorbed PAR [99,113,114]. TL-LUEn and TL-LUE are able to capture both the nonlinear and linear responses of GPP to incident PAR while MOD17 is only able to describe the linear change of canopy GPP with incident PAR. Therefore, TL-LUEn and TL-LUE outperform MOD17 for forests, shrub and grass sites. The higher performance is the most significant for forests at the half-hourly scale. The linear response of GPP to PAR in MOD17 led to the underestimation/overestimation of GPP under conditions of low/high incident PAR, which has been confirmed by Propastin et al. [22] and He et al. [23]. TL-LUEn and TL-LUE were, at least partially, able to correct this weakness. Figures 6–8 show the RMSE of simulated GPP as a function of incident PAR at three different temporal scales. Under medium PAR conditions, TL-LUEn, TL-LUE, and MOD17 performed similarly. The improvement of TL-LUEn and TL-LUE over MOD17 mainly occurred under low or high incident PAR conditions. Figure 6. The RMSE of modeled GPP against tower-derived GPP within different photosynthetically active radiation (PAR) classes for six different vegetation types: (a) BF, (b) CROP, (c) GRASS, (d) MF, (e) NF and (f) SHRUB, at the half-hourly scale. Remote Sens. 2015, 7 2258 Figure 7. The RMSE of modeled GPP against tower-derived GPP within different PAR classes for 6 different vegetation types: (a) BF, (b) CROP, (c) GRASS, (d) MF, (e) NF and (f) SHRUB, at the daily scale. The ratio of diffuse to direct PAR changed with clearness index. Under conditions of low clearness index, canopy LUE is high [23] owing to more diffuse PAR being absorbed by shaded leaves with high LUE. MOD17 did not differentiate the different effects of diffuse and direct PAR on GPP and tended to underestimate/overestimate GPP under low/high clearness index conditions (Figure 9). In TL-LUEn and TL-LUE, incident PAR is first decomposed into diffuse and direct components according to clearness index. Under conditions of low clearness index, increased diffuse PAR will be mainly absorbed by shaded leaves, which have high LUE. Thus, GPP simulated by TL-LUEn and TL-LUE is higher than that simulated by MOD17 (Figure 9). In contrast, when clearness index is high, increased direct PAR will be mostly absorbed by sunlit leaves, which have low LUE. Consequently, GPP simulated by TL-LUEn and TL-LUE is lower than that simulated by MOD17. Therefore, the systematic biases of GPP simulated by MOD17 model under low and high clearness index can be alleviated by TL-LUE and TL-LUEn. Remote Sens. 2015, 7 2259 Figure 8. The RMSE of modeled GPP against tower-derived GPP within different PAR classes for 6 different vegetation types: (a) BF, (b) CROP, (c) GRASS, (d) MF, (e) NF and (f) SHRUB, at the 8-day scale. 4.2. The Applicability of Different Models The different performances of three LUE models at different temporal scales and for different vegetation types suggest that it should be selective when using them. Prior to regional simulations of GPP using these models, we must be careful with the applicability of the optimized parameters. In this study, optimized parameters changed significantly among different vegetation types. The across-site variability of these parameters is also sizeable even for a specific vegetation type (Table 3). The sensitivity of simulated GPP to εm and β in TL-LUEn, to εmsu and εmsh in TL-LUE, and to εmax in MOD17 was assessed using the factorial approach described in section 2.2.3. The calculated main effect of εmax, εm, β, εmsu and εmsh are 20%, 11.50%, 8.50%, 8.09% and 11.91% at the half-hourly scale, and 20%, 10.72%, 9.28%, 6.84% and 13.16% at the daily scale, and 20%, 11.26%, 8.74%, 7.52% and 12.48% at the 8-day scale, respectively (Table 5). The sensitivity of simulated GPP to εmax in MOD17 is higher than the sensitivity of simulated GPP to individual parameters in TL-LUEn and TL-LUE. The Remote Sens. 2015, 7 2260 sensitivity of simulated GPP to the simultaneous uncertainties of εm and β in TL-LUEn and to the simultaneous uncertainties of εmsu and εmsh in TL-LUE is the same as the sensitivity of simulated GPP to εmax in MOD17. In addition, parameters in TL-LUE and MOD17 showed similar variations within each vegetation type, indicated by the similar CV in Table 3. However, as the two parameters in TL-LUEn vary not only with biomes but also with temperature [6], optimized εm and β exhibited larger variations and uncertainties than εmax, εmsu, and εmsh for all vegetation types (Table 3). Above analyses on the performance of three models at different temporal scales and their sensitivity to parameter uncertainties indicate that TL-LUEn is more applicable in individual site at the half-hourly scale. TL-LUE can be used regionally at the half-hourly, daily, and 8-day scales. MOD17 is also a good option for simulating regional GPP at the 8-day temporal scale and it is able to simulate GPP with accuracy close to TL-LUE. Figure 9.The average differences of modeled daily GPPs with observations for different ranges of clearness index Q. ΔGPP means the difference between the simulated and tower-derived daily GPP for certain biome. (a–f) denoteΔGPP for 6 different vegetation types (BF, CROP, GRASS, MF, NF and SHRUB), respectively. Remote Sens. 2015, 7 2261 Table 5. Design of the 22 complete factorial sensitivity analyses for parameters of TL-LUEn, TL-LUE with all the vegetation types lumped together at half-hourly, daily, and 8-day scales. Simulations TL-LUEn TL-LUE MOD17 εm β ΔGPPrel(%) εmsu εmsh ΔGPPrel(%) εmax ΔGPPrel(%) Half-hourly 1 - - −10.00 - - −10.00 - −10.00 2 + - 0.78 + - −1.91 3 - + −2.23 - + 1.91 4 + + 10.00 + + 10.00 + 10.00 Main effect(%) 11.50 8.50 8.09 11.91 20.00 Daily 1 - - −10.00 - - −10.00 - −10.00 2 + - 0.72 + - −3.16 3 - + −0.73 - + 3.16 4 + + 10.00 + + 10.00 + 10.00 Main effect (%) 10.72 9.28 6.84 13.16 20.00 8-day 1 - - −10.00 - - −10.00 - −10.00 2 + - 0.60 + - −2.48 3 - + −1.92 - + 2.48 4 + + 10.00 + + 10.00 + 10.00 Main effect (%) 11.26 8.74 7.52 12.48 20.00 Note: Columns three-four and six-seven show contrast coefficients for εm, β in TL-LUEn, and εmsu, εmsh in TL-LUE, respectively. A plus symbol indicates that the parameter was set at 110% of the estimate while a minus symbol indicates 90% of the estimate. ΔGPPrel is the relative differences between the simulated GPP calculated by introducing a perturbation to a certain parameter and the simulated GPP calculated using optimized parameters. 4.3. Uncertainties and Remaining Issues Both TL-LUEn and TL-LUE separate a canopy into sunlit and shaded leaves, and TL-LUEn further describe nonlinear response of their respective photosynthesis to APAR. These two models demonstrated powerful ability to simulate GPP. However, there are still some uncertainties remained. As indicated by Gebremichael and Barros [105], uncertainties in meteorological and LAI data, parameters, and model structure all might induce errors of simulated GPP. The change of linear response of GPP to VPD and PAR to nonlinear one and the inclusion of a soil moisture scalar might improve GPP simulation. Similar to MOD17, TL-LUEn and TL-LUE only use VPD and minimum air temperature as environmental constraints on GPP. VPD represents the effect of atmospheric dryness on vegetation photosynthesis as a result of stomatal conductance. Soil moisture also plays an important role in regulating GPP via effects on leaf cell turgor pressure directly affecting photosynthesis or by stomatal conductance [10,115,116]. Because VPD and soil water availability did not co-vary, it would be most appropriate to have soil water availability as a constraint on photosynthesis in addition to VPD [117]. In MOD17, soil drought stress was approximated through the increase in the sensitivity of GPP to VPD [118]. Photosynthesis is considered to be totally shut off during periods of very high VPD, but in fact soil moisture and other environmental conditions might be still favorable to maintain photosynthetic activity at a certain level even if atmosphere is very dry [105]. Thus, the lack of soil Remote Sens. 2015, 7 2262 water availability as a photosynthetic constraint in all three LUE models surely increases uncertainties in simulated GPP, especially for crops and grasses with shorter roots and high dependence on shallow soil moisture. In this study, parameters in three LUE models are assumed invariant seasonally, which could induce some uncertainties in optimized parameters and calculated GPP. Many studies have shown that these parameters vary with both temperature and vegetation types [14,119,120]. Wang et al. [6] recently reported that with the consideration of seasonal changes of two parameters associated with temperature, the two-leaf nonlinear hyperbolic model (i.e., TL-LUEn) could simulate GPP as well as a process-based model. Chen et al. [121] indicated that the exclusion of seasonality of parameters in one-leaf and two-leaf LUE models is one of major drivers responsible for the failure of these models to capture the seasonality of GPP well. Thus, the proper representation of seasonal variations of these parameters needs further investigation. Simulated GPP is also affected by the quality of meteorological and LAI inputs. In the calibration and validation periods, the models were driven by tower-measured meteorological data and processed MODIS LAI. The errors caused by inaccuracies of meteorological inputs are likely relative small [41]. However, the MODIS LAI contained considerable uncertainties, especially for crops [122], mainly caused by uncertainties in land cover and surface reflectance inputs and in the LAI inversion algorithm, and by the prevalence of persistent cloud cover [105]. The four variables in both TL-LUEn and TL-LUE (APARmsh, APARmsu, LAImsh and LAImsu), are all linked to LAI [23]. Our analysis showed that GPP simulated by TL-LUEn and TL-LUE is slightly more sensitive to LAI than that simulated by MOD17 (not shown here), which could be one of possible explainers for the poorer performance of TL-LUEn and TL-LUE relative to MOD17 at crop sites. Of course, this speculation is still worth of deep study. The LUE of crops changes with species. At the BON, MIR, MER, RG19, and RG21 crop sites, the corn or soybeans were cultivated every other year. At the ASM site, the dominant species was wheat in 2003–2004 and 2006, while it was changed to corn in 2005. Corn is a C4 plant while soybeans and wheat are C3 plants. The LUE of corn is much higher than that of soybeans and wheat. The application of optimized parameters of C3/C4 plants for C4/C3 plants in the validation years might result in large uncertainties in simulated GPP. This is a possible cause for the poorer performance of models for crops in the validation period than in the calibration period. In addition, the uneven numbers of flux sites for different vegetation types could also result in uncertainties in the identified overall robustness of individual models. 5. Conclusions In this study, the ability of three different types of LUE models (MOD17, TL-LUE and TL-LUEn) to simulate GPP at various temporal scales for different vegetation types was assessed using measurements at 58 flux sites in Asia, Europe and North America. The main conclusions that were drawn as follows: (1) Optimized model parameters vary distinctly not only among different vegetation types, but also among different sites for the same vegetation type, especially for TL-LUEn. The parameters in Remote Sens. 2015, 7 2263 TL-LUEn change sizably with temporal scales while the parameters in TL-LUE and MOD17 are almost invariant with temporal scales. (2) The overall performance of TL-LUEn was slightly but not significantly better than TL-LUE at half-hourly and daily scale, while the overall performance of both TL-LUEn and TL-LUE were significantly better (p < 0.0001) than MOD17 at the two temporal scales. The improvement of TL-LUEn over TL-LUE was relatively small in comparison with the improvement of TL-LUE over MOD17. However, the differences between TL-LUEn and MOD17, and TL-LUE and MOD17 became less distinct at 8-day scale. (3) At the half-hourly temporal scale, TL-LUEn and TL-LUE outperformed MOD17 for all vegetation types but CROP. The outperformance of TL-LUEn and TL-LUE over MOD17 was more distinct for forests than for GRASS and SHRUB vegetation types. With the increase of temporal scales, the improvement of both TL-LUEn and TL-LUE over MOD17 decreased. At the daily temporal scale, both TL-LUEn and TL-LUE performed better than MOD17 for forests and SHRUB. TL-LUE also outperformed MOD17 slightly for other non-forest types (CROP and GRASS). TL-LUEn only performed better than TL-LUE for BF. At the 8-day temporal scale, TL-LUEn only outperformed MOD17 for forests while TL-LUE performed better than MOD17 for all vegetation types. TL-LUEn only slightly outperformed TL-LUE for BF. (4) The improvement of TL-LUEn and TL-LUE over the MOD17 for forests was mainly achieved by the correction of the underestimation of GPP under low incident PAR and the overestimation of GPP under high incident PAR occurring in the MOD17. (5) TL-LUEn is more applicable at individual sites at the half-hourly scale. TL-LUE could be regionally used at half-hourly, daily and 8-day scales, owing to its excellent performance and small parameter variations at different temporal scales and for most vegetation types. MOD17 is also an applicable option at 8-day scale. Acknowledgements This work was supported by Chinese Academy of Sciences for Strategic Priority Research Program (No. XDA05050602-1), National Basic Research Program of China (2010CB950702), National Natural Science Foundation of China (41371070), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). This work used eddy covariance data acquired by the FLUXNET community and in particular by the following networks: AmeriFlux (U.S. Department of Energy, Biological and Environmental Research, Terrestrial Carbon Program (DE-FG02-04ER63917 and DE-FG02-04ER63911)), AfriFlux, AsiaFlux, CarboAfrica, CarboEuropeIP, CarboItaly, CarboMont, ChinaFlux, Fluxnet-Canada (supported by CFCAS, NSERC, BIOCAP, Environment Canada, and NRCan), GreenGrass, KoFlux, LBA, NECC, OzFlux, TCOS-Siberia, USCCC. We honestly thank all PIs of flux sites for providing the data for us. We appreciate the financial support to the eddy covariance data harmonization provided by CarboEuropeIP, FAO-GTOS-TCO, iLEAPS, Max Planck Institute for Biogeochemistry, National Science Foundation, University of Tuscia, Université Laval and Environment Canada and US Department of Energy and the database development and technical support from Bekeley Water Remote Sens. 2015, 7 2264 Center, Lawrence Berkeley National Laboratory, Microsoft Research eScience, Oak Ridge National Laboratory, University of California - Berkeley, University of Virginia. Author Contributions Weimin Ju, Xiaocui Wu, Yanlian Zhou and Mingzhu He designed the research. Xiaocui Wu, Mingzhu He, and Yanlian Zhou processed data preparation, and ran the models. Xiaocui Wu and Weimin Ju mainly analyzed data and prepared the manuscript and figures. Beverly E. Law, T. Andrew Black, Hank A. 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ID RMSE (mg C m −2 (30min)−1) R2 TL-LUEn TL-LUE MOD17 TL-LUEn TL-LUE MOD17 BF BEP 63.381 66.958 76.423 0.819 0.783 0.689 DHS 60.435 63.478 71.283 0.724 0.703 0.633 HA 59.667 64.036 71.053 0.910 0.888 0.807 HAF 71.021 72.580 85.082 0.862 0.853 0.801 HES 76.049 85.382 99.336 0.807 0.774 0.671 MMS 73.369 75.175 82.751 0.770 0.759 0.709 MOZ 68.622 68.328 73.618 0.770 0.758 0.711 PUE 49.406 49.861 54.236 0.806 0.801 0.770 ROC 79.484 80.577 84.508 0.636 0.640 0.635 UMBS 49.415 66.195 79.444 0.900 0.895 0.851 WCR 56.459 59.721 75.943 0.899 0.887 0.822 Average RMSE 64.301 68.390 77.607 Average R2 0.809 0.795 0.736 CROP ASM 48.448 50.368 46.187 0.599 0.578 0.642 BON 112.395 108.419 102.831 0.639 0.650 0.635 MEI 142.000 139.843 134.365 0.678 0.687 0.711 MER 161.440 158.377 158.585 0.688 0.700 0.728 MIR 178.555 175.665 174.733 0.724 0.736 0.771 RG19 70.821 69.495 72.853 0.737 0.744 0.709 RG21 99.387 85.314 83.437 0.582 0.600 0.579 Average RMSE 116.149 112.497 110.427 Average R2 0.664 0.671 0.682 GRASS AUD 21.885 21.481 22.053 0.200 0.212 0.276 FPE 34.699 34.544 35.134 0.541 0.531 0.496 GCR 55.747 56.305 58.141 0.831 0.823 0.815 HB 11.792 14.484 17.945 0.906 0.853 0.795 KED 33.405 33.165 32.512 0.498 0.502 0.518 NEU 80.230 81.569 93.599 0.821 0.821 0.767 VRA 85.744 84.997 82.802 0.310 0.315 0.352 Average RMSE 46.215 46.649 48.884 Average R2 0.587 0.580 0.574 MF CBS 65.447 67.410 78.617 0.819 0.813 0.750 HOF 55.397 58.873 70.669 0.881 0.862 0.776 SOR 62.126 60.641 78.508 0.915 0.909 0.832 VSA 56.961 55.160 62.589 0.861 0.862 0.819 Average RMSE 59.983 60.521 72.596 Average R2 0.813 0.805 0.750 NF ACA 77.015 76.300 75.549 0.413 0.413 0.402 BD49 74.576 78.571 106.579 0.847 0.834 0.720 DH00 56.199 63.847 63.684 0.605 0.602 0.561 DH88 50.135 52.940 76.208 0.881 0.877 0.782 DON 87.427 87.770 84.239 0.682 0.680 0.685 ES 64.787 57.208 60.443 0.770 0.769 0.726 FY 65.602 61.214 67.128 0.844 0.855 0.770 HY 31.505 30.950 38.836 0.951 0.947 0.885 LOB 75.394 73.753 80.112 0.782 0.781 0.739 Remote Sens. 2015, 7 2275 Table A1. Cont. ID RMSE (mg C m −2 (30min)−1) R2 TL-LUEn TL-LUE MOD17 TL-LUEn TL-LUE MOD17 NF MIN 62.065 59.961 64.929 0.826 0.828 0.788 MNY 42.416 45.296 44.548 0.738 0.721 0.663 NCL 93.203 91.163 116.335 0.838 0.842 0.793 NR 38.822 36.581 43.257 0.792 0.805 0.739 QMB 26.751 25.044 29.041 0.633 0.673 0.597 QYZ 78.560 78.520 80.415 0.756 0.758 0.747 REN 77.531 79.238 79.692 0.663 0.657 0.617 SRO 81.280 78.843 77.470 0.725 0.719 0.682 THA 67.968 68.762 76.497 0.850 0.848 0.765 TMK 59.161 64.370 105.229 0.935 0.919 0.799 U50 34.898 30.674 36.441 0.633 0.710 0.606 WET 70.679 72.746 75.443 0.862 0.862 0.803 Average RMSE 62.665 62.560 70.575 Average R2 0.763 0.767 0.708 SHRUB KEN 59.876 58.965 62.697 0.811 0.811 0.789 MIZ 73.406 73.674 73.614 0.840 0.844 0.831 OEM 16.690 19.447 23.973 0.818 0.785 0.713 SON 28.248 29.451 25.293 0.381 0.400 0.391 SRM 30.431 29.824 30.056 0.450 0.457 0.462 TRA 55.896 52.920 51.908 0.639 0.663 0.680 U89 23.456 21.613 27.365 0.779 0.781 0.679 U98 20.229 23.686 27.612 0.746 0.648 0.543 Average RMSE 38.529 38.698 40.315 Average R2 0.683 0.674 0.636 Table A2. Assessment of daily GPP simulated using TL-LUEn, TL-LUE and MOD17 for the 58 evaluation site-years. ID RMSE (g C m −2 day −1) R2 TL-LUEn TL-LUE MOD17 TL-LUEn TL-LUE MOD17 BF BEP 1.291 1.401 1.818 0.914 0.883 0.794 DHS 1.328 1.418 1.695 0.379 0.362 0.321 HA 1.590 1.646 2.165 0.929 0.909 0.829 HAF 1.495 1.650 2.155 0.940 0.923 0.851 HES 1.522 1.905 2.503 0.914 0.880 0.781 MMS 1.810 1.792 1.895 0.849 0.854 0.829 MOZ 1.824 1.782 2.055 0.780 0.770 0.706 PUE 1.477 1.624 1.888 0.549 0.524 0.450 ROC 2.006 2.045 2.063 0.689 0.670 0.682 UMBS 1.318 2.147 2.330 0.924 0.944 0.917 WCR 1.343 1.402 1.848 0.949 0.941 0.891 Average RMSE 1.546 1.710 2.038 Average R2 0.801 0.787 0.732 CROP ASM 1.095 1.061 1.165 0.608 0.630 0.595 BON 3.166 2.821 2.793 0.727 0.737 0.696 MEI 3.054 2.911 3.076 0.852 0.867 0.845 MER 4.742 4.396 4.350 0.855 0.879 0.863 Remote Sens. 2015, 7 2276 Table A2. Cont. ID RMSE (g C m −2 day −1) R2 TL-LUEn TL-LUE MOD17 TL-LUEn TL-LUE MOD17 CROP MIR 5.375 5.075 4.996 0.835 0.876 0.875 RG19 2.223 2.202 2.345 0.741 0.740 0.710 RG21 2.476 2.480 2.570 0.691 0.691 0.664 Average RMSE 3.162 2.992 3.042 Average R2 0.758 0.774 0.750 GRASS AUD 0.609 0.611 0.618 0.412 0.435 0.427 FPE 1.147 1.093 1.091 0.493 0.507 0.511 GCR 2.312 1.493 1.608 0.803 0.806 0.790 HB 0.328 0.349 0.357 0.912 0.917 0.913 KED 0.949 0.948 0.958 0.574 0.578 0.560 NEU 2.785 2.755 2.860 0.740 0.746 0.733 VRA 2.907 2.938 2.991 0.025 0.020 0.013 Average RMSE 1.577 1.455 1.498 Average R2 0.566 0.573 0.564 MF CBS 1.550 1.603 1.868 0.899 0.893 0.842 HOF 1.039 1.123 1.661 0.932 0.922 0.840 SOR 1.386 1.361 2.024 0.951 0.948 0.887 VSA 1.606 1.542 1.966 0.853 0.862 0.811 Average RMSE 1.395 1.407 1.880 Average R2 0.909 0.906 0.845 NF ACA 1.417 1.406 1.473 0.338 0.337 0.319 BD49 1.567 1.714 2.756 0.922 0.908 0.755 DH00 1.495 1.483 1.619 0.805 0.809 0.746 DH88 1.357 1.518 2.270 0.908 0.912 0.780 DON 2.057 2.032 2.073 0.287 0.279 0.318 ES 1.358 1.416 1.712 0.440 0.432 0.397 FY 1.747 1.703 2.062 0.877 0.874 0.795 HY 0.851 0.849 1.111 0.955 0.955 0.915 LOB 1.849 1.824 2.175 0.876 0.878 0.839 MIN 2.284 2.294 2.407 0.726 0.726 0.716 MNY 1.191 1.096 1.155 0.800 0.796 0.742 NCL 1.826 1.917 2.612 0.862 0.858 0.801 NR 1.030 1.053 1.194 0.796 0.799 0.751 QMB 0.618 0.638 0.727 0.789 0.779 0.726 QYZ 1.217 1.260 1.530 0.903 0.909 0.863 REN 1.906 1.871 2.016 0.779 0.778 0.751 SRO 2.68 2.213 2.425 0.424 0.437 0.416 THA 1.878 1.864 2.305 0.847 0.847 0.752 TMK 1.368 1.422 2.266 0.965 0.962 0.884 U50 0.771 0.817 0.965 0.819 0.808 0.738 WET 2.288 2.276 2.645 0.818 0.818 0.773 Average RMSE 1.560 1.556 1.881 Average R2 0.759 0.757 0.704 SHRUB KEN 1.070 1.073 1.398 0.641 0.641 0.559 MIZ 2.377 2.345 2.536 0.401 0.410 0.451 OEM 0.590 0.459 0.520 0.866 0.899 0.847 SON 0.896 0.746 0.696 0.383 0.340 0.348 SRM 0.730 0.730 0.748 0.661 0.657 0.628 Remote Sens. 2015, 7 2277 Table A2. Cont. ID RMSE (g C m −2 day −1) R2 TL-LUEn TL-LUE MOD17 TL-LUEn TL-LUE MOD17 SHRUB TRA 1.252 1.211 1.325 0.730 0.716 0.658 U89 0.466 0.559 0.727 0.909 0.889 0.810 U98 0.578 0.662 0.777 0.804 0.755 0.665 Average RMSE 0.995 0.973 1.091 Average R2 0.674 0.663 0.621 Table A3. Assessment of 8-day GPP simulated using TL-LUEn, TL-LUE and MOD17 for the 58 evaluation site-years. Vegetation Type ID RMSE(g C m −2 (8days) −1) R2 TL-LUEn TL-LUE MOD17 TL-LUEn TL-LUE MOD17 BF BEP 8.797 9.867 11.087 0.940 0.908 0.875 DHS 8.040 8.081 9.379 0.489 0.483 0.454 HA 11.839 12.680 15.534 0.948 0.919 0.893 HAF 10.318 11.533 13.496 0.952 0.939 0.905 HES 11.323 13.312 17.844 0.940 0.913 0.858 MMS 12.139 13.032 12.506 0.878 0.862 0.873 MOZ 10.735 12.913 13.328 0.859 0.799 0.788 PUE 10.386 11.343 13.264 0.564 0.518 0.443 ROC 14.711 14.755 14.760 0.731 0.727 0.738 UMBS 14.479 16.448 16.701 0.966 0.956 0.960 WCR 9.311 10.438 9.748 0.961 0.952 0.956 Average RMSE 11.098 12.218 13.422 Average R2 0.839 0.816 0.795 CROP ASM 9.940 7.639 8.004 0.646 0.668 0.658 BON 22.047 21.025 20.760 0.760 0.753 0.722 MEI 21.868 22.272 23.100 0.883 0.878 0.868 MER 36.640 34.434 33.774 0.889 0.888 0.883 MIR 41.373 39.191 38.325 0.870 0.886 0.897 RG19 14.858 15.987 16.825 0.797 0.776 0.738 RG21 18.381 18.880 19.199 0.718 0.708 0.694 Average RMSE 23.587 22.775 22.855 Average R2 0.795 0.794 0.780 GRASS AUD 4.462 4.377 4.424 0.505 0.531 0.520 FPE 8.178 7.494 7.389 0.565 0.601 0.614 GCR 12.983 10.570 11.432 0.841 0.84 0.832 HB 1.467 1.825 1.632 0.977 0.963 0.973 KED 7.285 6.912 6.773 0.620 0.670 0.656 NEU 20.615 20.126 20.91 0.776 0.779 0.769 VRA 22.565 22.917 23.431 0.032 0.020 0.010 Average RMSE 11.079 10.603 10.856 Average R2 0.617 0.629 0.625 MF CBS 9.285 10.630 11.117 0.944 0.936 0.918 HOF 6.798 6.388 7.703 0.96 0.955 0.935 SOR 11.469 9.027 12.070 0.959 0.960 0.938 VSA 10.844 9.517 12.613 0.929 0.933 0.906 Average RMSE 9.599 8.891 10.876 Average R2 0.948 0.946 0.924 Remote Sens. 2015, 7 2278 Table A3. Cont. Vegetation Type ID RMSE(g C m −2 (8days) −1) R2 TL-LUEn TL-LUE MOD17 TL-LUEn TL-LUE MOD17 NF ACA 9.207 9.107 9.201 0.349 0.382 0.380 BD49 10.080 10.342 13.791 0.943 0.952 0.904 DH00 10.258 10.962 10.835 0.846 0.850 0.841 DH88 9.043 10.307 14.822 0.943 0.949 0.880 DON 14.970 14.370 14.779 0.217 0.213 0.215 ES 11.749 10.039 12.075 0.490 0.467 0.437 FY 13.414 13.072 14.767 0.889 0.888 0.829 HY 5.923 5.976 6.865 0.971 0.964 0.951 LOB 15.885 13.218 14.689 0.943 0.940 0.926 MIN 17.790 17.128 17.869 0.832 0.830 0.829 MNY 7.965 7.875 8.036 0.870 0.857 0.808 NCL 10.917 13.249 17.512 0.872 0.857 0.808 NR 6.918 7.253 7.520 0.853 0.851 0.852 QMB 8.092 7.034 7.159 0.589 0.586 0.577 QYZ 8.782 8.131 9.146 0.951 0.953 0.939 REN 14.123 13.660 13.975 0.862 0.863 0.862 SRO 20.316 15.779 18.341 0.466 0.478 0.433 THA 14.245 13.288 14.906 0.899 0.896 0.872 TMK 9.117 9.443 10.819 0.968 0.972 0.963 U50 5.158 4.878 5.818 0.895 0.887 0.854 WET 20.463 18.842 21.864 0.878 0.882 0.862 Average RMSE 11.639 11.141 12.609 Average R2 0.787 0.787 0.763 SHRUB KEN 5.735 6.356 8.740 0.701 0.660 0.535 MIZ 18.357 16.033 19.194 0.454 0.475 0.435 OEM 8.708 3.493 3.302 0.933 0.938 0.912 SON 13.356 5.074 4.735 0.403 0.407 0.455 SRM 5.992 5.427 5.358 0.737 0.734 0.721 TRA 14.741 8.007 8.603 0.758 0.797 0.758 U89 4.485 4.168 4.582 0.868 0.909 0.895 U98 5.674 4.391 4.793 0.867 0.813 0.782 Average RMSE 9.631 6.619 7.413 Average R2 0.715 0.717 0.687 © 2015 by the authors; licensee MDPI, Basel, Switzerland. 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Faculty
Gross primary productivity (GPP)
Light use efficiency model
Sunlit and shaded leaves
Vegetation types
Temporal scales
Performance of Linear and Nonlinear Two-Leaf Light Use Efficiency Models at Different Temporal Scales
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