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Agricultural and Forest Meteorology 180 (2013) 44– 57

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Agricultural and Forest Meteorology

jou rn al hom epage : www.elsev ier .com/ locate /agr formet

Comparing hyperspectral index optimization algorithms to estimateaerial N uptake using multi-temporal winter wheat datasets fromcontrasting climatic and geographic zones in China and Germany

Fei Lia,b, Bodo Misteleb, Yuncai Hub, Xinping Chenc, Urs Schmidhalterb,∗

a College of Ecology & Environmental Science, Inner Mongolia Agricultural University, 010019 Hohhot, Chinab Chair of Plant Nutrition, Department of Plant Sciences, Technische Universität München, Emil-Ramann-Str. 2, D-85350 Freising-Weihenstephan, Germanyc College of Resources & Environmental Sciences, China Agricultural University, 100094 Beijing, China

a r t i c l e i n f o

Article history:Received 24 July 2012Received in revised form 20 April 2013Accepted 2 May 2013

Keywords:Area-based algorithmHyperspectral indexN uptakeNorth China PlainTwo-band combinations

a b s t r a c t

Timely and accurate quantification of aerial nitrogen (N) uptake in crops is important for the calculationof regional N balances and the study of the N budget in agro-ecosystems. Experiments in the presentstudy were conducted from 2007 to 2011 to remotely estimate the aerial N uptake of diverse winterwheat cultivars grown in contrasting climatic and geographic zones in China and Germany. Potentialsand limitations of hyperspectral indices obtained from (i) optimized algorithms and (ii) 15 representativeindices reported in the literature were tested for stability in estimating the aerial N uptake of winter wheatacross different growth stages, cultivars, sites and years. Growth stage, cultivar, N application rates, siteand year greatly influenced the relationship between hyperspectral indices and aerial N uptake. Theoptimized hyperspectral indices generally had more robust aerial N uptake prediction abilities thanthe published indices. Compared with the algorithms of all possible two-band combinations and red-edge position-based algorithms, area-based algorithms for a three-band optimized combination weremore stable in deriving the aerial N uptake of winter wheat. Optimized algorithms can potentially beimplemented in future aerial N uptake monitoring by hyperspectral sensing.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Chemical N fertilizers account for approximately 40% of theworld’s dietary protein (Smil, 2002) and play an increasingly impor-tant role in meeting rising demand for the agricultural productsthat are necessary to keep pace with population growth (Olfs et al.,2005). However, chemical N fertilizers produce 33% of the totalannual creation of reactive N and 63% of all anthropogenic sourcesof reactive N (Dobermann and Cassman, 2005). The rate of reactiveN production far exceeded the rate of population growth in the pastseveral decades, most likely creating an environmental risk due toa large increase in reactive N loading in the environment (Gallowayet al., 2008). Excessive N application in croplands primarily occursbecause farmers have difficulty understanding the crop N demandat different growth stages, sites and years due to the great effectsof weather conditions on crop growth (Lobell et al., 2004). Theaerial N uptake in crops, which serves as an important indica-tor of crop N diagnosis and fertilization, is closely related to cropyield (Dobermann and Cassman, 2002; Mistele and Schmidhalter,2008a). A clear knowledge of aerial N uptake is fundamental to

∗ Corresponding author. Tel.: +49 8161 713390; fax: +49 8161 714500.E-mail address: [email protected] (U. Schmidhalter).

efficient N fertilizer application to obtain high target yields, main-tain the soil N balance and minimize environmental risk (Cui et al.,2010; Ju and Christie, 2011). It is therefore necessary to effectivelyestimate the aerial N uptake on an on-farm regional scale, partic-ularly in the intensive and high-input agricultural regions of theNorth China Plain, which contributes more than 40% of the nationalgrain production (China Agricultural Yearbook, 2010). A timely andaccurate assessment of the aerial N uptake in winter wheat is essen-tial to calculate the regional N balance, to study the N budget andto reduce the release of reactive N into the environment in localagro-ecosystems (Eitel et al., 2011; Ju and Christie, 2011).

The most direct method to measure the aerial N uptake in cropsis with destructive plant samples in the field. This approach, cou-pled with wet chemical analysis in the lab, measures the aerial Nuptake in crops with great accuracy. However, it is difficult to obtainthis information over a larger spatial area. Thus, scaling up beyondthis localized sampling point is essential to evaluate the aerial Nuptake in crops with a regional N budget.

In recent decades, spectra reflectance-based techniques haveserved as expedient tools to rapidly and non-destructively esti-mate the aerial N status and related crop parameters on anon-farm scale. A promising application of this technique is thedevelopment of algorithms to quantify the agronomic variables ofinterest.

0168-1923/$ – see front matter © 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.agrformet.2013.05.003


F. Li et al. / Agricultural and Forest Meteorology 180 (2013) 44– 57 45

Commonly used algorithms include the combination of twosensitive wavebands, such as ratio vegetation index (RVI)- or nor-malized difference vegetation index (NDVI)-like spectral indices(Hatfield et al., 2008). Several studies have reported a close relation-ship between the aerial N uptake of crops and RVI- and NDVI-likespectral indices. The RVI of R780/R740 was found to be the best ratioindex from which to derive the aerial N uptake of winter wheat andmaize (Mistele and Schmidhalter, 2008b, 2010), while the ratio ofR760 to R730 could accurately predict the aerial N uptake of win-ter wheat with both passive and active sensors (Erdle et al., 2011).When an algorithm combines all possible two-band combinationsrelating to the leaf N accumulation of winter wheat, a degree of dis-agreement existed in the selection of the sensitive bands (Hansenand Schjoerring, 2003; Yao et al., 2010). These findings indicatethat species and environmental conditions influence the selectionof bands sensitive to N.

An additional group of vegetation indices that are potentiallysensitive to plant N status at high aboveground biomass is basedon the red edge position. A study by Cho and Skidmore (2006)highlighted an algorithm to derive the red edge position. Usinga combination of optimized bands, the linear extrapolation tech-nique more strongly predicted the leaf N concentration of grasscompared to other algorithms that are used to derive the red edgeposition.

A third group area-based algorithm, the triangle vegetationIndex (TVI), was proposed to derive the LAI and canopy chlorophyllcontent by calculating the area under the concave curve of red lightabsorption (Broge and Leblanc, 2000). Subsequently, Haboudaneet al. (2004) modified the TVI to be less sensitive to chlorophylleffects and more responsive to variations in green LAI. Similarly,Oppelt and Mauser (2004) monitored wheat chlorophyll contentusing the area under the reflectance curve divided by the envelopebetween 600 and 735 nm during the vegetation period. However,few studies in the literature report area-based indices to estimateaerial N uptake.

Generally, the majority of these algorithms were not broadlytested; limited testing was performed on an on-farm scale usingmulti-temporal datasets.

Collectively, many algorithms and their corresponding opti-mized spectral indices have been developed to remotely estimatethe biochemical parameters of crops, and the selection of the sensi-tive bands was often inconsistent. Only a limited number of studieshave addressed the effect of cultivar, growth stage, N applicationrate, site and year on the algorithms to derive the spectral indicesand their sensitive band combinations in evaluating the aerial Nuptake of crops (Chen et al., 2010; Clevers and Gitelson, 2012).Therefore, the objective of the present study was to compare algo-rithms of optimized hyperspectral indices and test their stabilityin estimating the aerial N uptake of winter wheat across differentgrowth stages, cultivars, sites and years.

2. Materials and methods

2.1. Study sites

Two contrasting sites, located in Freising in southeasternGermany and Quzhou County in the North China Plain, wereselected during the winter wheat growing seasons of 2007 through2011. Freising is characterized by a typical oceanic climate withmild cloudy winters and cool summers. During the winter wheatgrowing season, the mean temperature is 7.7 ◦C, and the averageprecipitation from 1999 to 2008 is 654 mm; the wheat entirelyrelies on rainfall for its water resource. Quzhou County is locatedin the warm-temperate sub-humid-continental monsoon zone andcharacterized by cold winters and hot summers. The average

temperature in Quzhou County is 8.1 ◦C, and the mean rain-fall is 110 mm; the lowest values occurred during the winterwheat growing seasons from 2007 to 2011. Depending on theamount of precipitation during the growing season, the farm-ers in this area irrigate their winter wheat three to fourtimes during the season using flood irrigation with water fromwells.

2.2. Experimental design

Two winter wheat field experiments were conducted at theDürnast Research Station of the Technische Universität München(TUM) in Freising, Germany. In 2007/2008, Experiment 1 consistedof eight N rates (0, 60, 120, 180, 240, 300, 360 and 420 kg N ha−1)with four replicates. Four local winter wheat cultivars, i.e., Solitär,Pegasus, Ludwig and Cubus, were used. Experiment 2, in 2008/2009used similar treatments, designed with eight N rates and threereplications, three German winter wheat cultivars (Solitär, Ellvisand Tommi) and a Chinese cultivar (Nongda318). At the Quzhouexperimental station of China Agricultural University (CAU) in2009/2010, one German cultivar (Tommi) and two local cultivars(Heng4399 and Kenong9204) were used in Experiment 3 withseven N rates (0, 60, 120, 180, 240, 300, 360 kg N ha−1) based onthe residual soil mineral N previously assessed by a quick-testmethod (Schmidhalter, 2005). One Chinese wheat cultivar, Liangx-ing99, was used in Experiment 4; the five N treatments used in thisexperiment were the control (no N was applied), the optimum Nrate, 50% of the optimum, 150% of the optimum and conventionalN rate. The optimum was based on the aerial N requirement andthe soil N supply for the two growing periods (sowing to shooting,shooting to harvest) (Chen et al., 2006). The conventional N treat-ment represents the local farmer practice, in which 150 kg N ha−1

was applied before sowing and 150 kg N ha−1 was applied as top-dressed fertilizer at the shooting stage. Experiments 5 and 6, similarto Experiment 3 and 4, were performed in 2010/2011 at the Quzhouexperimental station of CAU. Experiment 7 was undertaken in eightfarmers’ fields near the Quzhou experimental station of the CAUin 2009/2010 and 2010/2011. The different farmers’ fields wereused as replications. Local cultivars were used, and the fields weremanaged by the farmers.

2.3. Canopy spectral measurements and spectral indicescalculation

Spectral reflectance data at the canopy level were collectedusing a passive bi-directional spectrometer (tec5, Oberursel,Germany). In 2008, the device was mounted on a tractor to collectthe reflectance information of the winter wheat canopy (see Erdleet al., 2011, for more details). In 2009, 2010 and 2011, the canopyspectral reflectance was measured using a Handy-Spec® field spec-trometer (Mistele and Schmidhalter, 2008a). The measuring head ofthis device includes two optics; the upper optic quantifies incominglight as a reference, and the lower optic records reflectance from thevegetation and the ground. The sensors have a bandwidth of 3.3 nmand can measure 256 bands, with a spectral detection range from300 to 1150 nm. Depending on the length of the plots, we measuredthe reflectance in the winter wheat by holding the sensor approxi-mately 0.8–1.0 m above the canopy and walking at the same speedin each plot. The sensing was performed before biomass samplingin all the wheat plots, and the sensor path was parallel to the sowingrows.

The present study developed, tested and compared three typesof algorithms and their corresponding indices, based on their rela-tionships with the aerial N uptake in the field measurements, toidentify the best performing algorithms and indices (Table 1).


46 F. Li et al. / Agricultural and Forest Meteorology 180 (2013) 44– 57

Table 1Algorithms corresponding to the hyperspectral indices used in this study.

Spectral index Formula Reference

Ratio and normalized-based algorithmsNormalized difference vegetation index (NDVI) (R780 − R670)/(R780 + R670) Rouse et al. (1974)Ratio vegetation index (RVI) R780/R670 Pearson and Miller (1972)NIR/NIR R780/R740 Mistele and Schmidhalter (2010)Optimized vegetation index 2 (VIopt2) R760/R730 Jasper et al. (2009)Zarco-Tejada & Miller (ZTM) R750/R710 Zarco-Tejada et al. (2001)Normalized difference red edge index (NDRE) (R790 − R720)/(R790 + R720) Fitzgerald et al. (2010)The MERIS terrestrial chlorophyll index (MTCI) (R750 − R710)/(R710 − R680) Dash and Curran (2004)Red-edge model index (R-M) (R750/R720) − 1 Gitelson et al. (2005)Green model (G-M) (R750/R550) − 1 Gitelson et al. (2005)Canopy chlorophyll content index (CCCI) (NDRE − NDREMIN)/(NDREMAX − NDREMIN) Fitzgerald et al. (2010)Normalized difference spectral index (NDSI) (R�1 − R�2)/(R�1 + R�2), R�1 > R�2 This studyRed-edge position-based algorithmsRed edge position (REP1) 700 + 40 × [(R670 + R780)/2 − R700]/(R740 − R700) Guyot et al. (1988)Red edge position (REP2) �0 + � Pu et al. (2003)

Red edge position (REP3) −(c1 − c2)/(m1 − m2)a Cho and Skidmore (2006)Area-based algorithmsTriangle vegetation index (TVI) 0.5 × [120 × (R750 − R550) − 200 × (R670 − R550)] Broge and Leblanc (2000)Modified triangular vegetation index 1 (MTVI1) 1.2 × [1.2 × (R800 − R550) − 2.5 × (R670 − R550)] Haboudane et al. (2004)Modified triangular vegetation index 2 (MTVI2) Haboudane et al. (2004)Optimized triangle vegetation index (OTVI) 0.5 × [(�2–550) × (R�1 − R�2) − (R�2 − R550) × (�1 − �2)]b This study

a m1/c1 and m2/c2 represent the slope and intercept of straight line through two point on the far red (680–720 nm) and two point on near infrared (720–750 nm) of thefirst derivative reflectance spectrum.

b �1 and �2 stand for the wavelength in 670–810 nm and R�1 and R�2 stand for the reflectance wavelength �1 and �2. We optimized the combinations of red reflectance(R670) and near-infrared reflectance (R750) in the range of 670–810 nm as an optimum triangle vegetation index (OTVI).

First, the commonly used algorithms are the two-band com-bination ratios, such as NDVI-like (NDVI, NDRE, MTCI, R-M, G-Mand CCCI) and RVI-like indices (RVI, NIR/NIR, VIopt2 and ZTM). Forthese algorithms, we tested all of the possible two-band combi-nations from 300 through 1150 nm to relate the combinations tothe aerial N uptake and identify the optimized band combinations.Using similar principles, we tested only the NDVI-like possible bandcombinations rather than the RVI-like indices.

Second, we tested red edge position-based algorithms. As a tran-sition from red light to near infrared, the red edge provides usefulinformation on crop growth and N status. Several techniques wererecently developed to derive the red edge position; we tested thelinear interpolation technique (Guyot et al., 1988), an invertedGaussian fitting technique (Pu et al., 2003) and a linear extrapo-lation technique (Cho and Skidmore, 2006).

Third, the area-based indices were tested. Broge and Leblanc(2000) proposed a triangle vegetation index (TVI). In this study,we optimized the combinations of red reflectance (R670) and near-infrared reflectance (R750) as an optimum triangle vegetation index(OTVI).

2.4. Field measurements

The above-ground biomass was destructively sampled by ran-domly cutting five 1-m consecutive rows in each plot or farmer’sfield within the scanned areas immediately after the reflectancemeasurements. All of the plant samples were oven-dried at 70 ◦Cto a constant weight, weighed and ground for subsequent chem-ical analysis. A subsample was taken from the ground samplesfor Kjeldahl-N determination. The aerial N uptake was deter-mined by multiplying the aerial N concentration by the drybiomass.

2.5. Data analysis

The data from Experiments 2, 3, 4, 5 and 6 were used to developthe relationships between the spectral indices and the aerial Nuptake, and the data from Experiments 1 and 7 from the farmers’fields were used to validate relationships.

In recent decades, many algorithms for deriving N-sensitivespectral indices were developed to remotely estimate a crop’sN status. However, there was variation in the selected sensitiveband combinations used in the spectral indices related to cropN status, particularly when the same algorithm was used underdifferent conditions. To determine how certain factors influencethe selection and combination of sensitive bands in estimatingthe aerial N uptake of winter wheat and to test the perfor-mance of the algorithms and their corresponding spectral indices,we arranged the data into the following 12 data sets: shootingstage, booting stage, flowering stage, German cultivars, Chinesecultivars, N application rates less than 150 kg ha−1, N applica-tion rates greater than 150 kg ha−1, Quzhou and Dürnast sitelocation, 2010 and 2011 year status, and all of the data com-binations. The algorithms of the optimized band combinationsfor the spectral indices and the regression analyses were con-ducted with the MATLAB 7.0 software (The MathWorks, Inc., Natick,MA).

The model’s performance was estimated with a comparisonof the differences in prediction abilities using the coefficient ofdetermination (R2), the root mean square error (RMSE) and thecoefficient of variation (CV, %). A greater R2 and lower RMSE andCV indicated greater model precision and accuracy to predict theaerial N uptake.

3. Results and discussion

3.1. Evaluating ratio and normalized-based algorithms toestimate aerial N uptake

To identify the statistical significance of each normalized dif-ference spectral index (NDSI) band combination, the 300–1150 nmwavelength region was used to calculate and test all possible NDSIsfor linear relationships with aerial N uptake in 12 datasets. Fig. 1shows the contour maps of R2 between NDSIs and the aerial Nuptake. The most significant area in all dataset formations was pri-marily concentrated in the red edge (740–760 nm) paired with theshoulder of the NIR reflection (765–810 nm). The greatest R2 for dif-ferent relationships ranged from 0.51 to 0.85 (Table 2). Similarly,



Fig. 1. Contour diagrams showing the coefficient of determination (R2) for the relationships between the aerial N uptake and the narrow band NDSI calculated from allpossible two-band combinations in the range of 300–1150 nm with 12 data formations. The letters a, b, c, d, e, f, g, h, I, j, k and l represent different data set formations: (a)shooting stage, (b) booting stage, (c) flowering stage, (d) German cultivar, (e) Chinese cultivar, (f) N application rate <150 kg ha−1, (g) N application rate >150 kg ha−1, (h)Quzhou site located in China, (i) Dürnast site located in Germany, 2009, (j) 2010, (k) 2011, and (l) all of the data combinations.

the findings of Inoue et al. (2012) confirmed that the combina-tion of NIR over the red edge wavelengths was the most sensitiveto canopy N content of rice. The results suggest that normaliza-tion of the red edge wavelength using the NIR region improves

the assessment of canopy N in crops. This situation may existbecause these wavelengths have greater suitability to estimatethe chlorophyll content (Wu et al., 2008), which is closely relatedto the N content (Lamb et al., 2002). In contrast to optimized



Table 2Coefficients of determination (R2) of the linear relationships between aerial N uptake in 12 datasets and published ratio and normalized-based algorithms compared withnormalized spectral indices (NDSI) using optimized band combinations.

Coefficients of determination (R2) Wavelengthcombinationfor NDSI

NDVI RVI NIR/NIR VIopt2 ZTM NDRE MTCI R-M G-M CCCI NDSI �1 �2

Shooting stage 0.19 0.14 0.54 0.51 0.36 0.42 0.52 0.36 0.24 0.58 0.58 962 950Booting stage 0.38 0.42 0.53 0.69 0.57 0.63 0.57 0.57 0.06 0.67 0.72 770 756Flowering 0.12 0.23 0.30 0.18 0.09 0.19 0.04 0.09 0.01 0.21 0.55 788 760German cultivar 0.25 0.25 0.69 0.54 0.33 0.52 0.33 0.33 0.04 0.61 0.80 782 754Chinese cultivar 0.23 0.24 0.41 0.38 0.27 0.38 0.25 0.27 0.14 0.46 0.68 788 764Applied N <150 kg ha−1 0.31 0.31 0.55 0.50 0.38 0.49 0.34 0.38 0.16 0.53 0.67 782 756Applied N >150 kg ha−1 0.17 0.20 0.49 0.39 0.21 0.37 0.17 0.21 0.01 0.48 0.73 790 760Quzhou, NCP 0.48 0.53 0.65 0.62 0.59 0.61 0.60 0.59 0.57 0.60 0.67 794 742Dürnast, TUM, 2009 0.07 0.12 0.66 0.44 0.19 0.38 0.23 0.19 0.00 0.56 0.85 810 7562010 0.54 0.76 0.72 0.71 0.73 0.68 0.70 0.73 0.74 0.66 0.77 766 7582011 0.34 0.17 0.46 0.38 0.29 0.40 0.35 0.29 0.26 0.41 0.51 786 764

All data 0.24 0.29 0.54 0.46 0.31 0.44 0.27 0.31 0.07 0.51 0.73 788 760

NDSIs, published NDVI- and RVI-like indices had a weaker cor-relation with aerial N uptake of winter wheat. The R2 for thebest performing published indices varied between 0.30 and 0.76(Table 2). The NIR/NIR and CCCI indices were relatively strongerthan the other published indices for the aerial N uptake estima-tion.

The prediction accuracies greatly differed depending on thedataset formation, and the best-performing band combinationsvaried with different growth stages, cultivars, N application rates,sites and years (Table 2). This study confirms the inconsistency inthe performance of these indices in deriving agronomic variablesand differences in sensitive waveband selection, as often found inthe literature. For example, Hansen and Schjoerring (2003) exam-ined all possible two-waveband combinations from 400 to 900 nmand revealed that 734 nm and 750 nm were the best combina-tion of NDSI (R2 = 0.68) to estimate the leaf N density of winterwheat. However, Yao et al. (2010) showed that the combination of720 nm and 860 nm formed the best-performing NDSI (R2 = 0.90) inderiving the leaf N accumulation of winter wheat. These inconsis-tencies suggest that plant and non-plant factors, such as species,site and year, greatly affect the performance of hyperspectralindices for agronomic parameters estimation. This finding mayexplain why the effectiveness of the selected published hyperspec-tral indices was inconsistent with estimation of the aerial N uptakeof winter wheat across the different datasets formations in thisstudy.

3.2. Evaluating red-edge position-based algorithms for theestimation of aerial N uptake

The results of the sensitivity analysis of the red-edge position-based algorithm REP3 derived by the linear extrapolation methodshow that the far-red wavelengths varied greatly from 686–696to 702–720 nm, whereas the near-infrared wavelengths wererelatively stable from 744 to 748 nm (Fig. 2). The sensitive bandcombinations yielded high correlation coefficients with aerial Nuptake across all 12 spectral datasets. The REP3 extracted fromcanopy spectral data of nearly all of the dataset formations exhibitclearly similar contour patterns for both the German and Chinesecultivars, N application rates at either <150 kg ha−1 or >150 kg ha−1,at the anthesis and primarily at the Dürnast site for all the datacombinations.

To compare the performance of the linear four-point inter-polation, inverted Gaussian fitting and linear extrapolation, weestablished linear relationships between the aerial N uptake vs.REP1, REP2. The optimized REP3 for 12 datasets and their R2

are listed in Table 3. The relationships between REP3 and theaerial N uptake were better than the relationships betweenREP1 and REP2 and the aerial N uptake for nine out oftwelve datasets. In agreement with Cho and Skidmore (2006)a linear extrapolation approach greatly improved the predict-ing performance of the red edge position compared to otherapproaches.

Table 3Coefficients of determination (R2) of the linear relationships between the aerial N uptake and the extracted red edge position using a linear four-point interpolation technique(REP1), an inverted Gaussian fitting technique (REP2) and a linear extrapolation technique (REP3) and the optimized band combinations of 12 datasets.

Coefficients of determination (R2) Wavelength combination for REP3

REP1 REP2 REP3 �1 �2

Shooting stage 0.58 0.55 0.58 720 744Booting stage 0.52 0.26 0.64 714 744Flowering 0.26 0.29 0.50 686 744German cultivar 0.68 0.71 0.66 716 744Chinese cultivar 0.39 0.46 0.61 718 748Applied N <150 kg ha−1 0.52 0.56 0.60 716 746Applied N >150 kg ha−1 0.48 0.56 0.60 716 746Quzhou, NCP 0.64 0.63 0.58 702 746Dürnast, TUM, 2009 0.65 0.66 0.69 716 7462010 0.69 0.67 0.69 696 7442011 0.48 0.48 0.43 706 748

All data 0.51 0.49 0.61 716 744



Fig. 2. Contour diagrams indicating the sensitivity of red edge positions calculated using the linear extrapolation method (REP3) using fixed bands from 680 to 750 nm. Themaps show the coefficients of determination (R2) between the red edge position and the aerial N uptake with 12 data formations. The letters a, b, c, d, e, f, g, h, I, j, k and lrepresent different data set formations: (a) shooting stage, (b) booting stage, (c) flowering stage, (d) German cultivar, (e) Chinese cultivar, (f) N application rate <150 kg ha−1,(g) N application rate >150 kg ha−1, (h) Quzhou site located in China, (i) Dürnast site located in Germany, 2009, (j) 2010, (k) 2011, and (l) all data combinations.

3.3. Evaluating area-based algorithms for the estimation of aerialN uptake

The published indices, TVI (Triangle vegetation index), MTVI1(Modified triangular vegetation index 1) and MTVI2 (Modified

triangular vegetation index 2), showed poor relationships to esti-mate the aerial N uptake (Table 4). This situation may existbecause the indices were originally proposed to derive the canopychlorophyll content and the leaf area index (Broge and Leblanc,2000; Haboudane et al., 2004).



Fig. 3. Contour diagrams showing the coefficient of determination (R2) for the relationships between the aerial N uptake and the narrow band OTVI calculated from allpossible two-band combinations in the range of 670–810 nm with 12 data set formations. The letters a, b, c, d, e, f, g, h, I, j, k and l represent different data formations: (a)shooting stage, (b) booting stage, (c) flowering stage, (d) German cultivar, (e) Chinese cultivar, (f) N application rate <150 kg ha−1, (g) N application rate >150 kg ha−1, (h)Quzhou site located in China, (i) Dürnast site located in Germany, 2009, (j) 2010, (k) 2011, and (l) all data combinations.



Fig. 4. The average coefficients of determination (R2) corresponding to the rela-tionship between the aerial N uptake of winter wheat, the published indices andthe optimized NDSI- and OTVI-based spectral indices on contour diagrams.

In the current study, we optimized the TVI index by combin-ing the green peak 550 nm with all possible two-band groups fromthe red concave 670 nm to the infrared shoulder 810 nm to forman optimized triangle vegetation index (OTVI) (Table 4). Matrixplots of coefficients of determination (R2) between the aerial Nuptake and the narrow-band OTVI are illustrated in Fig. 3. All ofthe maps showed nearly identical contour patterns varying from760 to 780 nm for �1 and 748 to 758 for �2, indicating that the

Fig. 5. The average coefficients of determination (R2) corresponding to the relation-ship between the aerial N uptake of winter wheat, the best-performing publishedindices and the optimized spectral indices based on contour diagrams of 12 datasets.

optimized band combinations are more stable compared to ratio-or red-edge position-based algorithms. Across all of the datasets,the index OTVI had greater correlation to the aerial N uptake thanpublished spectral indices (Table 4). The results further confirmthat optimum bands play a significant role in agronomic parameterestimation.

Table 4Coefficients of determination (R2) of the linear relationships between the aerial N uptake and the TVI, MTVI1, MTVI2 and the best performing OTVI with the optimized bandcombinations of 12 datasets.

Coefficients of determination (R2) Wavelength combinationfor OTVI

TVI MTVI1 MTVI2 OTVI �1 �2

Shooting stage 0.00 0.00 0.03 0.55 774 756Booting stage 0.15 0.16 0.16 0.75 780 754Flowering 0.30 0.37 0.38 0.69 778 754German cultivar 0.00 0.01 0.13 0.85 780 754Chinese cultivar 0.00 0.01 0.09 0.62 776 756Applied N <150 kg ha−1 0.00 0.01 0.10 0.69 776 754Applied N >150 kg ha−1 0.00 0.02 0.11 0.79 782 754Quzhou, NCP 0.08 0.13 0.24 0.61 772 756Dürnast, TUM, 2009 0.12 0.05 0.01 0.87 780 7542010 0.04 0.08 0.20 0.75 768 7582011 0.13 0.20 0.28 0.43 780 748

All data 0.01 0.03 0.13 0.78 780 754

Table 5Root mean square errors (RMSE) and coefficients of variation (CV = RMSE/mean aerial N uptake) of the relationships between the aerial N uptake and the optimized spectralindices based on algorithms of the red edge position, ratio and area.

RMSE (kg N ha−1) CV (%)

REP3 NDSI OTVI REP3 NDSI OTVI

Shooting stage 19 19 20 32.8 32.7 34.7Booting stage 33 29 28 25.4 22.4 21.4Flowering 48 45 40 30.0 28.6 25.1German cultivar 50 38 33 37.0 28.5 24.6Chinese cultivar 29 26 29 29.5 26.5 29.0Applied N <150 kg ha−1 30 27 26 33.0 30.0 28.8Applied N >150 kg ha−1 50 41 36 35.8 29.0 25.6Quzhou, NCP 30 27 30 31.8 28.3 30.9Dürnast, TUM, 2009 47 33 30 32.8 23.2 21.22010 27 23 24 30.4 26.1 27.02011 31 29 31 28.9 26.6 28.6

All data 43 36 33 37.4 31.2 28.5



Fig. 6. Relationships between the aerial N uptake of winter wheat and the unified spectral index OTVI. The letters a, b, c, d, e, f, g, h, I, j, k and l represent different datasetformations: (a) shooting stage, (b) booting stage, (c) flowering stage, (d) German cultivar, (e) Chinese cultivar, (f) N application rate <150 kg ha−1, (g) N application rate>150 kg ha−1, (h) Quzhou site located in China, (i) Dürnast site located in Germany, 2009, (j) 2010, (k) 2011, and (l) all data combinations.

3.4. Comparing the performance of different algorithms forestimating aerial N uptake

To assess the robustness of published and the newly proposedindices to estimate aerial N uptake, we averaged the R2 obtained

for the 12 datasets and compared their accuracy (Fig. 4). The resultsshow that the performances of the optimized spectral indices NDSIand OTVI were better than the performances of the selected pub-lished indices. The optimized NDSI and OTVI were the strongestindices to detect the aerial N uptake in nine dataset formations



Fig. 7. Relationships between the aerial N uptake of winter wheat and the unified spectral index NDSI. The letters a, b, c, d, e, f, g, h, I, j, k and l represent different dataformation: (a) shooting stage, (b) booting stage, (c) flowering stage, (d) German cultivar, (e) Chinese cultivar, (f) N application rate <150 kg ha−1, (g) N application rate>150 kg ha−1, (h) Quzhou site located in China, (i) Dürnast site located in Germany, 2009, (j) 2010, (k) 2011, and (l) all data combinations.

(Fig. 5), suggesting that ratio- and area-based optimized indicestechniques were more effective in estimation of the aerial N uptake.Similarly, Ullah et al. (2013) used ratio-based optimized algorithmsto extract the best performing hyperspectral indices for estimat-ing leaf water content. By optimizing the band combinations of

the spectral indices, Gitelson et al. (2003, 2005, 2008) successfullypredicted the chlorophyll content in crops and turbid water, andPeng and Gitelson (2011) could estimate the gross primary pro-ductivity in maize. The use of a hyperspectral index with fixedwavelength combinations to derive N-related parameters may be



Fig. 8. Relationship between the estimated and observed aerial N uptake in farmer field data, using the established unified OTVI model at (a) shooting stage, (b) bootingstage, (c) flowering stage and (d) all data combinations.

less efficient. However, the important point is not the selection ofthe spectral indices but the selection of algorithms and optimizedwavelength combinations to derive the agronomic parameters ofinterest.

Notably, all pigment-related bands in the present study wereabsent from the optimized wavelength combination. The sensi-tive wavelengths, particularly for the algorithms based on theratio and area, primarily focus on the region at the beginning ofthe infrared shoulder and the near-infrared plateau (Tables 2–4).This situation may be due to the sensitivity of the beginning ofthe infrared shoulder and the near-infrared plateau to the canopystructure, which can affect the patterns of scattering and absorp-tion of spectra. Furthermore, the aerial N uptake not only includesthe influence of the plant N concentration but also the abovegroundbiomass, which is associated with canopy structure. The results fur-ther confirm the interesting paradox reviewed by Ollinger (2011),stating that the physiological indicators of vegetation are oftenmore strongly related to the reflectance at wavelengths that arenot used in photosynthesis compared with those wavelengths thatare.

The results of the RMSE and CV of the aerial N uptake in Table 5confirm that the NDSI and OTVI linear prediction of the aerial Nuptake was better than the REP3 linear prediction. However, thelinear relationships strongly depend on the developmental stages,study area and experimental conditions of the reflectance acqui-sition. Nonetheless, similar distribution patterns in the contourmaps can be observed for the different datasets. The sensitive

wavebands �1 and �2 for the best performing NDSI ranged between780 and 800 nm and 750 and 760 nm, respectively. Compared withthe NDSI, the relatively stable sensitive wavebands for the mostsignificant OTVI varied from 770 to 780 nm for �1 and narrowlyranged from 754 to 756 nm for �2 (Figs. 1 and 3). Based on thisfinding, we weighted the R2 for the relationships between aerialN uptake and optimized NDSI and OTVI from different datasetsof growth stages, cultivars, applied N rates, sites and years, andselected 788 nm (�1) and 756 nm (�2) as the optimized bandcombinations for a unified NDSI. Similarly, the wavelengths of776 nm (�1) and 754 nm (�2) were used as the optimized bandcombinations for a unified OTVI. The relationships between theunified OTVI, NDSI and the aerial N uptake of winter wheatare presented in Figs. 6 and 7. Except for the datasets with theshooting stage and 2011, the R2 was greater than 0.6. Consid-ering heterogeneous fields and contrasting climatic conditions,this result is acceptable to estimate aerial N uptake on a regionalscale.

3.5. Evaluation and validation of unified indices based onoptimized algorithms

The algorithms presented in Figs. 6 and 7 were validated usingthe data from the farmers’ fields in southeastern Germany in 2008and the North China Plain in 2010 and 2011. Measured reflectancein the validation dataset was used to calculate the unified NDSI andOTVI and predict aerial N uptake values, and the predicted aerial N



Fig. 9. Relationship between the estimated and observed aerial N uptake in farmer field data, using the established unified NDSI model at (a) shooting stage, (b) bootingstage, (c) flowering stage and (d) all data combinations.

uptake values were compared with aerial N uptake measured usingthe wet chemical analysis method in the lab. Figs. 8 and 9 indicatethe accuracy of the aerial N uptake prediction by the establishedalgorithms. Across the cultivars, sites and years, the OTVI deliveredthe most precise assessment of aerial N uptake, with an RMSE of29 kg N ha−1, a CV of 25.2% and an R2 of 0.70 in the shooting growthstage. Because the validated data were from the shooting stage, fur-ther validation using data from other growth stages will be requiredto substantiate this finding.

The successful remote estimation of aerial N uptake of win-ter wheat in the farmers’ fields is very important in agriculturalproductive systems at the shooting stage, which is the crit-ical period of fertilization. Optimized spectral indices can beused for timely temporal and spatial detection of crop aerialN uptake to guide local farmers in the accurate applicationof N fertilizer and ensure an optimized balance of N fertil-izer, soil N and crop N uptake. Techniques to determine theamount of N fertilizer needed for application are very useful,particularly in the intensive winter wheat/summer maize rota-tion systems of the North China Plain. Cost effective nitrogendiagnosis tools are lacking. Another important possible outcomeof the present study is the suggestion that proximal sensingallows for the detection of N over-fertilization. As shown, theoptimized unified hyperspectral indices successfully derived theaerial N uptake of winter wheat at an applied N rate greaterthan the optimized N rate of 150 kg ha−1 compared to publishedhyperspectral indices (Tables 2–4; Figs. 6 and 7). With this goal

in mind, a very powerful and efficient approach using proxi-mal sensor-based information will now be available to conductregional surveys of local agricultural nitrogen fertilization prac-tices. The third application of this study is facilitation of efficientselection of optimum wavelengths to remotely derive other plantor ecological variables using existing airborne and space-bornesensors. Particularly for the existing and forthcoming launchedhyper- or super-spectral satellite sensors, such as CHRIS, MODIS,MERIS, Sentinel-2 and VEN�S, the optimized band combinationsof satellite data may be used to estimate regional crop yield, grossprimary productivity (GPP), leaf area index (LAI), chlorophyll a,chlorophyll b and carotenoid levels (Stagakis et al., 2010; Pengand Gitelson, 2011; Herrmann et al., 2011; Guindin-Garcia et al.,2012; Bolton and Friedl, 2013). However, a great challenge of satel-lite data-based remote sensing is separation of plant or ecologicalparameters of interest from confounding factors, such as canopystructure, soil background and atmospheric effects. The study willneed to be further validated and tested in other ecosystems withreal satellite data.

4. Summary and conclusions

To explore the limitations and potentials of hyperspectralindices and their related algorithms for deriving the aerial Nuptake of winter wheat, 12 dataset formations were testedacross growth stages, cultivars, N application rates, sites andyears. Hyperspectral indices using algorithms to optimize bands



significantly increased the prediction power in deriving the aerialN uptake of winter wheat compared with hyperspectral indicesusing fixed-band combinations. The combination of optimizedwavelengths varied across growth stages, cultivars, N applicationrates, sites and years. The selection of sensitive bands to deter-mine ratio-based and particular area-based algorithms had greaterrelative stability than the selection of red-edge-position algo-rithms.

The unified hyperspectral index OTVI (550, 754, 776), opti-mized using an area-based algorithm, showed robustness duringthe assessment of winter wheat aerial N uptake across sites, culti-vars, development stages, nitrogen rates and years.

These findings may be useful for precise application of N fertil-izer by farmers and, especially, local agricultural regulators seekingto identify N over-fertilization using a proximal hyperspectral sen-sor. These data will also be important for the study of the N budgeton an on-farm regional scale.

Acknowledgements

This research was financially supported by the German Fed-eral Ministry of Education and Research (BMBF) (Project No. FKZ0330800A), and the International Bureau of the German Fed-eral Ministry of Education and Research (Project No: CHN11/052).Helpful comments of an anonymous reviewer are gratefullyacknowledged.

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