Leaf pigment retrieval using the PROSAIL model:Influence of uncertainty in prior canopy-structure information

Ji Sun,Lunhe Wng,Shuo Shi,Zhenhi Li,Jin Yng,Wei Gong,Shoqing Wng,Torbern Tgesson

a Key Laboratory of Regional Ecology and Environmental Change,School of Geography and Information Engineering,China University of Geoscience,Wuhan 430079,Hubei,China

b Department of Physical Geography and Ecosystem Science,Lund University,Lund 117 SE-22100,Sweden

c State Key Laboratory of Information Engineering in Surveying,Mapping,and Remote Sensing,Wuhan University,Wuhan 430079,Hubei,China

d Key Laboratory of Quantitative Remote Sensing in Ministry of Agriculture and Rural Affairs,Beijing Research Center for Information Technology in Agriculture,Beijing 100097,China

e Department of Geosciences and Natural Resource Management,University of Copenhagen,Copenhagen 1172,Denmark

Keywords:Leaf pigment PROSAIL model Canopy structure Chlorophyll content Leaf area index Leaf angle distribution

ABSTRACT Leaf pigments are critical indicators of plant photosynthesis,stress,and physiological conditions.Inversion of radiative transfer models(RTMs)is a promising method for robustly retrieving leaf biochemical traits from canopy observations,and adding prior information has been effective in alleviating the‘‘ill-posed”problem,a major challenge in model inversion.Canopy structure parameters,such as leaf area index(LAI)and average leaf inclination angle(ALA),can serve as prior information for leaf pigment retrieval.Using canopy spectra simulated from the PROSAIL model,we estimated the effects of uncertainty in LAI and ALA used as prior information for lookup table-based inversions of leaf chlorophyll(Cab)and carotenoid (Car).The retrieval accuracies of the two pigments were increased by use of the priors of LAI(RMSE of Cab from 7.67 to 6.32 μg cm-2,Car from 2.41 to 2.28 μg cm-2) and ALA (RMSE of Cab from 7.67 to 5.72 μg cm-2,Car from 2.41 to 2.23 μg cm-2).However,this improvement deteriorated with an increase of additive and multiplicative uncertainties,and when 40% and 20% noise was added to LAI and ALA respectively,these priors ceased to increase retrieval accuracy.Validation using an experimental winter wheat dataset also showed that compared with Car,the estimation accuracy of Cab increased more or deteriorated less with uncertainty in prior canopy structure.This study demonstrates possible limitations of using prior information in RTM inversions for retrieval of leaf biochemistry,when large uncertainties are present.

1.Introduction

Foliar pigments,such as chlorophylls(Cab)and carotenoids(Car)are fundamental determinants of light capture and use[1].Leaf Cabpromotes the conversion of absorbed solar radiation into stored chemical energy,and an increase in Cabmay increase biomass production[2,3].Leaf Carhas a structural role in photosynthetic membranes and quenching of excited states of Cab[4].These pigments function in photosynthesis,protect against harmful effects,and provide useful information for studying plant physiology,productivity,and ecosystem-climate interactions [5,6].

Motivated by the ecological and practical implications of leaf pigments,substantial efforts have been exerted to estimate foliar pigments from canopy-level reflectance spectra acquired from various sensors [2,7,8].The increased spectral,spatial resolution,and revisit frequency of newly launched satellites have provided promising possibilities for discriminating the subtle absorption and extinction characteristics of leaf pigments.Although recently the first global distribution of leaf chlorophyll has been mapped[2],global leaf optical monitoring is limited by public field-based validation datasets [9] and the pigments’ low absorption features,particularly for leaf Car[10].Compared with studies of Cab,fewer have focused on direct estimation of Carat leaf and canopy scales[11].Generally,the retrieval methods based on canopy reflectance spectra can be grouped into two categories: empirical models and physical models [12].Empirical models are exemplified by the widely applied vegetation indices (VIs) [3,6,13].Given their simplicity,various VIs have been proposed and associated with multiple plant biochemical and biophysical characteristics [14,15].However,the performance of a VI is limited in terms of transferability and accuracy because of the limited spectral information carried by two to three bands and the weak physical foundation[16-18].Physical models,such as radiative transfer models(RTMs),have a rigorous physical foundation and incorporate light transmission through canopy or leaf components [19,20].Because its variables have explicit physical meanings,these models are expected to retrieve leaf and canopy traits with improved generalizability.The PRoperties Optique SPECTrales des feuilles (PROSPECT) model [21] is a leaf-level RTM that describes the relationship between leaf optical properties and foliar traits.The Scattering by Arbitrarily Inclined Leaves (SAIL) canopy model[22] connects canopy reflectance to canopy structure parameters,solar and viewing geometry,soil background reflectance,and leaf optical properties.Thus,the coupling of the two RTMs (PROSAIL)can be used to retrieve leaf biochemical traits from canopy reflectance observations and has proved to be one of the most successful canopy RTMs for crops,balancing model complexity and accuracy[23].

The main challenges in an RTM inversion include the‘‘ill-posed”problem,the small absorption coefficients of certain biochemical traits (such as Car,leaf anthocyanin,and leaf matter per area),and the domination by water absorption of the short-wave infrared region of canopy reflectance.The ill-posed problem results from different combinations of model parameters contributing to highly similar canopy reflectance spectra [24-26].Consequently,recognizing their respective contributions and consequently their quantities can be difficult.Considerable endeavors have been made to alleviate the impact of ill-posedness in model inversion,such as limiting the ranges of model parameters [12,27],avoiding unrealistic parameter combinations [18],and inverting one parameter at a time with its specific sensitive spectral range [25,28].The use of prior information,both temporal and spatial [18,26,29,30],is frequent among these attempts.Having this kind of prior information is likely to increase the retrieval accuracy of foliar pigments as it can exert additional constraints on inference and limit the solution space [7].

Although hyperspectral imaging technologies have developed rapidly,estimating foliar pigments from canopy observations remains a challenge.One reason is interference from canopy structural variation [28,31].To retrieve leaf Cabcontent,leaf area index(LAI)has been identified as a confounding factor that most VIs cannot distinguish from the influence of Cab[31,32].It has been found that using prior knowledge of Caband LAI distributions [3,28] or the relationship between Caband LAI[32]could improve estimates of Cab.Leaf angle distribution (LAD),which describes the orientation of leaves in a canopy,also influences the estimation of leaf biochemistry,though studies of this influence are comparatively rare[33,34].It was found that using adjusted ALA as prior information to consider heterogeneous canopy could result in higher accuracy of canopy Cab[35].That the sensitive spectral regions of foliar pigments overlap those of LAI and ALA in the range of 500-900 nm also suggests that prior information of these canopy structure parameters offers high potential for alleviating the ‘‘ill-posed”problem [36].New remote sensing methods and products of LAI have been developed[37,38].For LAD measurements,conventional methods involve using plant canopy imagers such as LAI-2000[39]and Plant Canopy Imager CI-110[40]and hemispherical photography [41].Other nondestructive-based methods used for this purpose include leveled digital photography [42] and terrestrial laser scanning [33,43].

However,the exact influence of prior canopy structure on retrieval of leaf pigments and whether this influence is consistent among the two pigments (Caband Car) remains unclear,especially when there is varying uncertainty in the prior information.The objective of the present study was to characterize the influence of prior canopy structural information,namely LAI and ALA,on estimation of contents of two foliar pigments (Caband Car) using PROSAIL inversions.The following questions were investigated:(i) whether the contributions of prior LAI and ALA information to improving the estimation of the two foliar pigments are identical;(ii) the influences of additive and multiplicative uncertainties in LAI and ALA,and whether the influences are consistent among the two pigments;and(iii)whether there are levels of uncertainty in prior canopy structural information at which LAI and ALA no longer help alleviate the ‘‘ill-posed” problem in inversions of the two foliar pigments.The results of this study were expected to help guide the precise inversion of leaf pigments,providing valuable information about vegetation photosynthesis and crop productivity.

2.Materials and methods

2.1.The PROSAIL model and the generation of a LUT

The PROSAIL model,which couples a canopy-level model of SAIL with a leaf-level RTM of PROSPECT,was adopted.The PROSPECT model was proposed on the basis of the plate model [44],and has been one of the most popular leaf-scale physical models in the remote sensing community [21].PROSPECT-D simulates the directional-hemispherical reflectance and transmittance spectra of vegetation leaves over the range of 400-2500 nm as a function of the leaf structure index (N),leaf chlorophyll content (Cab),leaf carotenoid content (Car),leaf anthocyanin content (Canth),equivalent water thickness(Cw),and dry matter per area(Cm)[11].

The SAIL model calculates scattering and absorption of four upward and downward fluxes at the canopy level by establishing and solving radiative transfer equations [22].It is a 1D bidirectional model that assumes that the canopy is a turbid medium in which leaves as absorbing and scattering particles are small and randomly distributed in space[22,45].Because of this assumption,the SAIL model is more suitable for agricultural canopies than for forests.During its development,a hotspot effect was included as a function of the ratio of leaf size to canopy height in SAILH [46].Thereafter,a numerically robust and efficient version,called 4SAIL,was developed by Verhoef et al.[47].The latter version was adopted in the present study,wherein three variables were used to describe canopy structure:the LAI,the ALA of an ellipsoidal leaf angle distribution function (typically used for approximation of leaf angle distribution) [48],and the hotspot parameter (hspot,ratio of mean leaf size to height of canopy).The coupled PROSAIL model provides top-of-canopy reflectance in the spectral range of 400-2500 nm at 1 nm resolution.

The input parameters of the PROSAIL model include leaf parameters (N,Cab,Car,Canth,Cw,and Cm),canopy structure parameters(LAI,ALA,and hspot),soil reflectance (psoil,assumed Lambertian in this study),and solar and viewing geometry (solar zenith angle θs,viewing zenith angle θv,and relative azimuth angle φsv).To generate a lookup table (LUT),as uniform distributions give poorer considerations for the most representative cases [49,50],we used Gaussian distributions for foliar pigments to obtain more frequent circumstances over the whole range of their variation.The input parameters of the PROSAIL model were assumed to be Gaussian distributed,with ranges of variations,means,and standard deviations set based on previous studies [10,18,51],as listed in Table 1.The solar zenith angle,viewing zenith angle,and azimuth angle were set to 45°,0°,and 0°,respectively,according to the setting of the experimental dataset in section 2.3.Thus,by running the PROSAIL model in the forward mode,a total of 100,000 cases were simulated and constituted the LUT.

Table 1 Ranges of the PROSAIL model variables used to conduct PROSAIL simulations.

2.2.Synthetic datasets

As the leaf surface is not flat,any leaf has an infinite number of inclination angles.For this reason,manual measurements of leaf orientation contain substantial errors as an individual’s perception of the ‘‘a(chǎn)verage” inclination angle is quite subjective [33,34,52].Thus,investigation of the influence of uncertainties in prior ALA information using field data presents a challenge,given that there is no ‘‘gold standard” to estimate the ALA’s uncertainty.Synthetically generated data are then a promising alternative,and can be an invaluable tool when real data are expensive,scarce,or as in this case unavailable[53].In the present study,synthetic data were not only useful but necessary,as they allowed a detailed analysis of the effect of measurement uncertainties and eliminate the influence of unknown extraneous factors.Also,running RTMs allows creating a large volume of data for different plant species and growing stages.All these advantages contribute to performing an extensive test on the inversion of leaf pigments using prior canopy structure parameters with uncertainties based on simulated data.

By incorporating multiple parameters with large variation and running the PROSAIL model in the forward mode,a large synthetic dataset could be generated.We generated canopy reflectance in the spectral range of 500 to 900 nm at 1 nm resolution,as this covered the spectral domain sensitive to Caband Carvariation according to the sensitivity analysis of the PROSAIL model[36].The close relationship between Caband Car(R2=0.86) found by Féret et al.[18] was considered in generating the synthetic dataset.As some model parameters exhibited minimal sensitivity in this spectral domain,they were fixed(Cw=0.01,hspot=0.10).The solar zenith angle,viewing zenith angle,and azimuth angle were set to 45°,0°,and 0°,respectively,to represent nadir observation.The input parameters of the PROSAIL model were assumed to follow a Gaussian distribution,similar to section 2.1 (Table 1).First,random combinations of leaf and canopy traits were generated in which all the parameters in Table 1 varied simultaneously.This sampling scheme considerably reduces the required simulations in comparison with a uniform random drawing,thereby introducing the widest possible variety of biochemical and structural heterogeneity [18].Then,running the PROSAIL model in the forward mode simulated 10,000 canopy reflectance spectra comprising a first synthetic dataset (synthetic dataset I).To link better with the experimental dataset in section 2.3,we also conducted simulations for winter wheat scenarios based on the experimental dataset(synthetic dataset II,Cab: minimum: 20 μg cm-2,maximum:95 μg cm-2,mean: 55 μg cm-2;Car: minimum: 4 μg cm-2,maximum:20 μg cm-2,mean:12 μg cm-2).To compensate for uncertainties in sensor data and potential model weaknesses,random white Gaussian noise with a standard value of 3% [25,54] was applied to the simulated leaf reflectance,transmittance,and canopy reflectance.

2.3.Experimental dataset

A winter wheat field experiment was conducted at the National Precision Agriculture Experimental Base of Xiaotangshan town(40°10′31′′N-40°11′18′′N,116°26′10′′E-116°27′05′′E),Beijing,China in the growing season of 2012-2013.The experiment was designed as completely randomized with four winter wheat cultivars and four nitrogen (N) application rates.The wheat cultivars included Nongda 211,Zhongmai 175,Jing 9843,and Zhongyou 206 and the four N fertilizer application rates are shown in Table 2.There were 16 treatments and two replicates,totaling 32 plots.The size of each plot was 10 m×9 m,with a row spacing of 15 cm and density of 360 seeds per m2.Detailed information on experimental plot distribution is described in [32].

Table 2 N fertilizer application schedule (kg N ha-1) for the N rate treatments in the 2012-2013 wheat experiments.

Canopy reflectance spectra were acquired with an ASD Field-Spec Pro FR (Analytical Spectral Devices,field spectroradiometer,full-range,Inc.,Boulder,CO,USA,25° field of view) in the booting,anthesis,and milk development stages.During measurements,the instrument was fixed at nadir 1.0 m above the winter wheat canopy,under clear sky conditions between 10:00 and 14:00 Beijing time.For every plot,20 tillers were cut randomly and all leaves were collected.In subsequent chemical determination,95%ethanol was used to extract leaf pigments and Caband Carcontents were determined using a colorimetric spectrophotometer based on the standard methods of Arnon[55].The leaf area of samples was measured with a laser leaf area meter (CI-203;CID Inc.,Camas,WA,USA).Detail of measurements has been described previously [32].

2.4.Prior canopy structure information with uncertainties

The generated LAI and ALA datasets from the synthetic datasets and the LAI from the experimental dataset were used as accurate prior information to delineate canopy structure characteristics.In general,vegetation canopy structure estimates of LAI and ALA are produced on the basis of remote sensing observations and analytical algorithms [33,56-58].Thus,uncertainties associated with sensor measurement accuracy,data processing including radiometric calibration,atmospheric and geometric corrections,and model assumptions are passed on to the estimated LAI and ALA.For example,conventional estimation of LAI involves use of vegetation indices such as NDVI [59].As additive and multiplicative uncertainties of canopy reflectance come from instrumental noise,radiometric calibration results,and atmospheric correction [49],these errors propagate to LAI estimation.For ALA estimation,many remote sensing methods rely on laser scanning,where leaf surfaces are distinguished first and the normal directions are subsequently identified [34,60].It is thus difficult to quantify the uncertainties associated with the estimated LAI and ALA that can serve as prior information.In this study,we considered random Gaussian noise with no bias in two ways: additive noise (when noise isindependent of the exact value of LAI or ALA) and multiplicative noise (when noise is related to the exact value of LAI or ALA) of multiple levels:

where LAIsimand LAImearepresent LAI values simulated as accurate values and LAI values with uncertainties,respectively.ALAsimand ALAmearepresent ALA values simulated as accurate values and ALA values with uncertainties,respectively.（0，σ）represents a Gaussian distribution (mean value equal to 0 and variance,σ2).σmultiis the multiplicative uncertainties applied to LAI and ALA values.σaddiis the additive uncertainties applied to LAI and ALA values.The values for additive uncertainties of LAI and ALA were set 10 to 60%(in steps of 10%)of their respective mean values(3.5 for LAI and 60 for ALA).The values for multiplicative uncertainties used were also 10 to 60% in steps of 10%.To isolate the effect of uncertainty in prior canopy structure information,the contribution of LAI and ALA with uncertainty to foliar pigment inversion was assessed individually and compared with inversion without prior information.

2.5.LUT-based inversion

LUTs provide a convenient approach to RTM inversion,compared with numerical iterative optimization and artificial neural networks.The advantages of the LUT approach include the ability to avoid converging to local minima,its simplicity,and its high computational efficiency during inversion once the LUT is established [3,14,15].LUT-based inversions aim to find the optimal set of input variables (Cab,Car,Canth,Cm,LAI,and ALA) by comparing measured and modeled canopy reflectance and determining combinations with minimal differences.Cost functions during inversion of an RTM can be categorized into three families:M-estimates,minimum contrast,and information measures [61].The estimation of leaf or canopy parameters from reflectance spectra is hindered by the diverse magnitude and distribution of errors residing in spectral measurements,and various cost functions provide various minimization criteria.Belonging to the M-estimate category,the mean square error(MSE)cost function is the one that has been most widely applied [40,62,63].The MSE assumes the maximum likelihood criterion,making it efficient for errors following a Gaussian distribution[64].Accordingly,we adopted the MSE cost function in LUT-based inversion of the PROSAIL model.The mean of 1000 parameter sets yielding the lowest MSE between measured and LUT spectra was taken as a solution to the inverse problem,following the recommendations of [65,66].

As the ill-posedness in RTM inversion results from different biochemical and biophysical characteristics contributing to similar reflectance spectra,prior canopy information is often used to alleviate this problem.For pigment retrievals with prior canopy properties,impossible combinations could be avoided and the solutions be further narrowed down.The mean of the 400 sets of parameters with the most similar LAI and ALA as the prior information among the 1000 sets yielding the lowest MSE was taken as the solution to the inverse problem.Inversions of the PROSAIL model were conducted using a specific subset of spectral range (500 to 900 nm,1 nm resolution) instead of the entire spectral domain of 400 to 2500 nm,as this approach has proven beneficial for alleviating the ill-posed problem and improve performance in model inversions [9,25].Moreover,researchers may not be able to measure the whole spectral range.We accordingly adopted the spectral range of 500-900 nm for estimating leaf pigments in the PROSAIL model inversion.The purpose of including part of the near-infrared range was to stabilize the inversion.

2.6.Statistical analysis

The retrievals of foliar pigments were compared against reference values from simulations or chemical analysis results using coefficient of determination (R2),absolute RMSE,and normalized RMSE (nRMSE).These were used to compare the performances across inversions with canopy structure prior information with varying levels of uncertainty.Lower RMSE and nRMSE indicate less residual variance and more successful retrievals.Let yjandbe the observed and estimated leaf pigment respectively,be the mean of yj,ymax,yminbe the maximum and minimum of observed leaf pigment,respectively,and n be the number of observations.

3.Results

3.1.Leaf pigment inversion with prior LAI information

Uncertainty in canopy structure information was estimated in terms of additive and multiplicative noise.The use of accurate prior LAI improved the estimation of the two foliar pigments Caband Car(Tables 3 and 4;Figs.1 and 2).With an increase of additive or multiplicative noise in LAI,the inversion accuracy of leaf pigments decreased gradually (Fig.3).When the level of additive noise reached 50%,inclusion of LAI prior information no longer improved the retrieval of Cabcompared with no prior information.This threshold was 40% for Car.In contrast,using prior structural information ceased to make a positive contribution to inverting Cabat multiplicative noise as large as 60%(Table 3;Fig.3),whereas nearly 50%multiplicative noise became detrimental for Carestimation(Table 4;Fig.3).The retrieval accuracy of Cabwas higher than that of Carin terms of all three statistics(Tables 3 and 4).The detrimental influence of additive noise in LAI was greater than that of multiplicative noise,and the difference between the two was more significant in the case of Carestimation than in that of Cab(Fig.3).Overall,the nRMSE of retrieval of the two leaf pigments increased nearly linearly with additive/multiplicative noise in prior LAI information.As the trends of influence of LAI under different levels ofuncertainties were similar using synthetic datasets I and II,the inversion results of Caband Carusing synthetic dataset II are provided in the Appendix Tables S1 and S2.The evaluation of Caband Caragainst the experimental dataset was less accurate than that against the synthetic datasets (Tables 5 and 6;Figs.1,2,4 and 5).The thresholds of prior LAI with uncertainties making a positive contribution (additive noise: 30%,multiplicative noise:20%) on Cabinversion were smaller than those in the case of synthetic datasets (additive noise: 50%,multiplicative noise: 60%)(Tables 5 and 6).The overall trend was that with an increase of additive noise and multiplicative noise in prior LAI,the inversion accuracy of Cabdecreased(Fig.3).In particular,Table 5 shows that even with the most accurate LAI available,the improvement of Cabinversion was limited.

Table 3 Accuracy of Cab inversion using the PROSAIL model using synthetic dataset I,with prior LAI or ALA information under six levels of random additive or multiplicative noise.

Table 4 Accuracy of Car inversion by the PROSAIL model using synthetic dataset I,with prior LAI (Prior_LAI) or ALA information (Prior_ALA) under six levels of random additive and multiplicative noise.

Carretrieval was not improved by addition of prior LAI information (Table 6).The inversion accuracy was not directly related to the levels of additive and multiplicative noise added to prior LAI information.The inversion of Cabwas superior to that of Carwith varied uncertainties of prior LAI information,in accordance with the synthetic datasets.

Fig.1.Estimation of leaf Cab by PROSAIL model inversion using synthetic dataset I(a)with no prior information,(b-c)with accurate LAI or ALA information,(d-f)with prior LAI information under three levels of additive noise,(g-i)with prior LAI information under three levels of multiplicative noise,(j-l)with prior ALA information under three levels of additive noise,and (m-o) with prior ALA information under three levels of multiplicative noise.

Fig.2.Estimation of leaf Car by PROSAIL model inversion using synthetic dataset I(a)with no prior information,(b-c)with accurate LAI or ALA information,(d-f)with prior LAI information under three levels of additive noise,(g-i)with prior LAI information under three levels of multiplicative noise,(j-l)with prior ALA information under three levels of additive noise,and (m-o) with prior ALA information under three levels of multiplicative noise.

Fig.3.The influence on leaf pigment retrieval of six levels of uncertainty (additive noise and multiplicative noise) in prior LAI or ALA information (horizontal dash line:nRMSE of leaf pigment retrieval with no prior information) using synthetic dataset I.

3.2.Leaf pigment inversion with prior ALA information

As with the trend of LAI,the inclusion of prior ALA improved the retrieval of the two leaf pigments,but the effect became detrimental at levels of 20 and 30% additive noise for Caband Car,respectively (Tables 3 and 4;Figs.1 and 2).Multiplicative noise as large as 20%in ALA exerted a negative effect on the inversion of Cabcompared with no prior information (Fig.2).In comparison with Car,the estimation accuracy of Cabwas increased more(or deteriorated less) with varied uncertainties of prior ALA information (Fig.3).The accuracies of retrieval of leaf pigments with additive and multiplicative noise at the same level in ALA showed no significant difference,in contrast to using prior LAI information (Fig.3).Overall,the nRMSE of retrieval of the two leaf pigments increased in a trend similar to a logarithmic function with increase of additive or multiplicative noise in prior LAI information.As the trends of influence of ALA under multiple levels of uncertainties were similar using synthetic datasets I and II,the inversion results of Caband Carusing synthetic dataset II are presented in Tables S1 and S2.

Table 5 Accuracy of Cab inversion by the PROSAIL model using experimental dataset,with prior LAI information under four levels of random additive noise and three levels of multiplicative noise.

Table 6 Accuracy of Car inversion by the PROSAIL model using an experimental dataset,with prior LAI information (Prior_LAI) under three levels of random additive and multiplicative noise.

3.3.Comparison of prior LAI and ALA information on leaf pigment inversion

Fig.4.Estimation of leaf Cab by PROSAIL model inversion against measured Cab in the experimental dataset.(a)with no prior information,(b)with accurate LAI information,(c-f) with prior LAI information under four levels of additive noise,(g-i) with prior LAI information under three levels of multiplicative noise.

The evaluation of prior LAI and ALA information with varying levels of uncertainty in estimating leaf pigments through the PROSAIL model is illustrated in Fig.6.The general trends of nRMSE for Caband Car(Fig.6a and b) were similar,and the positive contribution of ALA information was greater than that of LAI in the presence of little noise (below 10%).However,with the increase of additive or multiplicative noise,the retrieval of leaf pigments with prior ALA deteriorated more rapidly than with prior LAI until certain thresholds of prior canopy structure information no longer improved inversion performance.This result indicated that the influence of prior ALA information is more sensitive to data uncertainties than that of LAI in facilitating estimation of leaf pigments.

Fig.6.The influence of level of uncertainty in LAI and ALA prior information on leaf pigment retrieval.As comparison,the accuracy of standard PROSAIL model inversion without prior information is indicated by the gray horizontal line.

4.Discussion

4.1.Use of prior information in RTM inversion

With respect to inversion of an RTM,the use of prior information has been considered an effective strategy to alleviate the ill-posed problem and improve inversion [67].The finding of the present study that accurate LAI and ALA information improved the inversion of leaf Caband Carcontent using the PROSAIL model is in accordance with some previous studies [3,28,32].Although the utility of prior information has been shown,the results presented in this study suggest that estimates using prior information can deteriorate with the increase of uncertainty in the prior information,to a level even worse than having no prior information at all.This is likely due to that additive and multiplicative noises in prior information cause large deviations of simulated from measured canopy reflectance,leading to poor inversion of leaf pigments.As to the two synthetic datasets,though the ranges of leaf pigment distributions were smaller in dataset II(winter wheat scenarios) than I (the general scenario),the estimation accuracies of leaf pigments in them were similar (Tables 3 and 4,Tables S1 and S2).The influences of prior LAI (also ALA) between two synthetic datasets were also similar,with almost identical levels of additive and multiplicative uncertainties when these priors ceased to improve estimates of leaf pigments (lower thresholds of ALA than LAI and lower thresholds for Carthan Cab).

Fig.5.Estimation of leaf Car by PROSAIL model inversion against measured Car in the experimental dataset(a)with no prior information,(b)with accurate LAI information,(c-f) with prior LAI information under four levels of additive noise,(g-i) with prior LAI information under three levels of multiplicative noise.

When the experimental wheat dataset was used,the inversion of Carwith‘‘a(chǎn)ccurate”prior LAI was even less accurate than having no prior information at all,though in the synthetic datasets the thresholds of additive and multiplicative noise in LAI resulting in less accurate estimates than no prior information were 40% and 50%,respectively.The case with Cabwas similar,with the thresholds of additive and multiplicative in LAI being 50% and 60% using the synthetic datasets and 30% and 20% using the experimental dataset.The differences between synthetic and experimental datasets can be attributed to several factors.One is that although a strong correlation between Caband Car(R2=0.86) was assumed in the generation of LUT and synthetic datasets,the correlation between the two parameters in the wheat dataset was weaker(R2=0.65).The close relationship between Caband Carin the LUT may have constrained the variability of retrieved Carand led to the inferior estimation results with prior LAI.However,it was claimed[18]that this high correlation between Caband Caris general by compiling large experimental datasets.Besides,the inversion of Carwas more difficult than Cabwith smaller absorption coefficients in the visible spectral domain,and the PROSPECT-D model was reported [68,69] to be less accurate in retrieving Carthan previous versions.The uncertainty of the PROSAIL model in row-structured open crop canopies may also have an influence[70].

4.2.Consideration of using prior ALA and LAI information

Though accurate ALA provided better inversions of both leaf pigments than LAI,with the increase of uncertainties in the canopy structure information,LAI was found more useful for improving the retrieval of leaf pigments.As multiple long-term global LAI products are now available [37,38],use of LAI is expected to facilitate RTM inversion.However,spatial and temporal discontinuity among diverse biome types,periods,and products must be considered [33,71,72].Related to LAI,ALA is another parameter for describing canopy structure.Its influence has not received much attention possibly because it is harder to obtain from remote sensing technologies.Aside from manual measurements of leaf orientation using a clinometer,ALA information can be obtained together with LAI by LAI-2000 or hemispherical photography[41,73].Other indirect methods include leveled digital photography[42,74]and terrestrial laser scanning,which has been increasingly used in leaf angle estimation with new algorithms proposed[43,60,75],such as plane fitting[76,77],grid triangulation[34],and estimation of surface normal [56].However,the accuracy of this method is constrained by leaf segmentation[78]and its validation is hampered by a lack of accurate ground reference data [33].The uncertainties in canopy structure properties such as LAI and ALA can come from sensor measurement accuracy [49,51] and data processing procedures[49].Retrieval of LAI via imaging spectrometry becomes poor when its value is lower than 1 owing to the effect of soil reflectance or higher than 4 owing to the saturation effect [7].Thus,the quality of the adopted prior information(canopy structure in the case of the current study) should be considered in estimating leaf biochemical traits by RTM inversion.

The retrieval accuracy of leaf Cabwas higher than that of Carfor any set of prior information.With accurate prior canopy structure information,the improvement of Cabinversion was greater than that of Car,and the thresholds of additive and multiplicative noises at which prior information was no longer useful were higher.It is well known that the specific absorption coefficient of Caris much smaller than that of Cab,as can be seen from sensitivity analysis of the PROSPECT model [79].Previous studies also found that the dominant influence of Cabin the optical domain of leaf reflectance of healthy plants makes inversion of Cardifficult [11,80].The efficacy of prior canopy structure information for accurate Carestimation,according to our results,remains limited.

4.3.Limitation and future prospect

This study demonstrates the necessity to consider uncertainties in prior canopy structure information used to enhance the performance of foliar pigment retrieval using PROSAIL model inversion.Although both synthetic and experimental datasets were used,ALA was incorporated only in the synthetic datasets.This is because the leaf area meter used to measure LAI could not measure ALA together with LAI.Accordingly,the findings on the effect of prior ALA information based on the simulated dataset await further validation in future studies.

Further study could consider investigation using other RTM models than 4SAIL,such as GeoSail[81]and multiple-layer canopy RTM [82],as clumping effects were not included in 4SAIL and improvement is needed for row-structured open crop canopies[70].There are multiple ways to incorporate prior information in RTM inversion,for example,Combal et al.[26] proposed adaptations to consider prior information in LUT,quasi-Newton algorithm,and neural network-based inversion,and their efficacy can be tested in subsequent studies.The specific thresholds at which prior canopy structure information no longer plays a positive role may vary in specific circumstances,such as geographical locations,plant species,canopy structure and background reflectance.We also hope to further validate the conclusions presented here with more experimental datasets.To acquire canopy structure prior information as accurate as possible,combining the observation of a hyperspectral spectrometer and a lidar system,or directly using a hyperspectral lidar,could be considered [83,84].Efforts should also be made toward determining how uncertainties are delivered along the remote sensing chain(e.g.,use of sensors,digitizing,georeferencing,and successive corrections).

5.Conclusions

This study investigated the effect of prior canopy structural parameters of LAI and ALA on the modeling of leaf-level Caband Carcontent via RTM inversion.Variation in this influence under two kinds of uncertainty,random additive and multiplicative noise,were also characterized.Although accurate prior LAI or ALA information improved leaf pigment retrieval,this improvement showed a rapid deterioration with the increase of uncertainty in prior canopy structure information,until it ceased.LAI was also more robust to uncertainties than ALA with respect to facilitating leaf pigment retrieval.Estimation of Cabimproved more or deteriorated less than Carwith prior canopy structure properties.The results of this study may guide the precise inversion of crop leaf pigments and provide important insights on vegetation photosynthesis and crop yields.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

CRediT authorship contribution statement

Jia Sun:Conceptualization,Methodology,Software,Visualization,Writing -original draft,Writing -review &editing.Lunche Wang:Resources,Writing-review&editing.Shuo Shi:Conceptualization.Zhenhai Li:Resources,Data curation.Jian Yang:Investigation.Wei Gong:Resources,Supervision.Shaoqiang Wang:Resources,Writing-review&editing.Torbern Tagesson:Writing-review &editing.

Acknowledgments

This study was supported by the National Natural Science Foundation of China (41975044),the Open Research Fund of the State Laboratory of Information Engineering in Surveying,Mapping,and Remote Sensing,Wuhan University (20R02),and the Fundamental Research Funds for the Central Universities,China University of Geosciences (Wuhan) (111-G1323520290).Torbern Tagesson was funded by SNSA(Dnr 96/16)and the EU-Aid funded CASSECS Project.

Appendix A.Supplementary data

Supplementary data for this article can be found online at https://doi.org/10.1016/j.cj.2022.04.003.