Atmospherically resistant vegetation water indices using the 970-nm water absorption feature

Abstract. Atmospheric correction can introduce errors in surface spectral reflectance, and hence induces errors in plant water estimation from remote sensing water indices. We intend to develop water indices that are less impacted by atmospheric effects for plant water content estimation based on the 970-nm water absorption feature. A simulation study using the PROSAIL and 6S models showed that uncertainty in atmospheric water vapor (WV) content can induce large variation in existing 970-nm water indices, such as WI, NWI-1, and NWI-3. An attempt was made to incorporate atmospheric WV absorption at 940 nm to correct for the perturbation due to atmospheric WV variability, leading to the development of improved indices, named as ARWI, NARWI-1, and NARWI-3. The performance of these indices was evaluated using the simulated and field spectral reflectance data, as well as Hyperion and GF5 satellite data. Results showed that the new indices were resistant to uncertainty of WV and could be used to deliver improved estimation of canopy water content, with a smaller root-mean-square-error (ARWI: 7.4  mg/cm2, NARWI-1: 8.3  mg/cm2, and NARWI-3: 8.8  mg/cm2) compared to that obtained using the traditional water indices (WI: 8.9  mg/cm2, NWI-1: 9.4  mg/cm2, and NWI-3: 16.6  mg/cm2). The water indices developed in this study, although needing further assessment in wide application scenarios, have great potential for monitoring of vegetation water status using satellite hyperspectral data with reflectance measurement around 970 nm.


Introduction
1.0 to 2.5 μm) regions. The normalized difference water index (NDWI) using water absorption at 1240 or 1600 nm was developed as an indicator of vegetation water content using Landsat, SPOT, and MODIS data. [17][18][19][20] However, absorption by liquid water in vegetation and background soil is too strong in the SWIR region, hence signal returned from canopy is quite weak at these water absorption wavelengths. [21][22][23] Due to greater penetration of light into the vegetation canopy in the NIR spectral range, the water absorption band at 970 nm has been found to be better for retrieval of canopy water. 5 The reflectance water index (WI, R 900 ∕R 970 ) developed in Ref. 21 has been used to estimate plant water content for different vegetation types. 11,22 A normalized water index [NWI-1 ¼ ðR 970 − R 900 Þ∕ðR 970 þ R 900 Þ] has been proposed based on reflectance at 970 and 900 nm for wheat water status monitoring. 24 Through changing the reference band at 900 nm in NWI-1, other three normalized water indices have been proposed, e.g., NWI-2 using 850 nm, NWI-3 using 880 nm, and NWI-4 using 920 nm, for vegetation water estimation. 24,25 Among the above indices, NWI-3 was the most effective for canopy water status monitoring. 26 Indices based on the 970-nm absorption feature are supported by some silicon photodiode sensors limited to below 1100 nm. [27][28][29] Knowledge of atmospheric aerosol optical thickness (AOT) and water vapor content (WV) is needed in atmospheric correction for retrieving surface reflectance and deriving vegetation indices. However, retrievals of the two variables have considerable uncertainty. Using MODIS AOT and WV products as an example, uncertainty in MODIS AOT product was found to be AEð0.05 þ 0.15 Ã AOTÞ over land, 30,31 while uncertainty in MODIS WV product was found to be 10.4%. 32 Uncertainties in aerosol retrievals induces the largest error in surface reflectance retrieval in the visible bands, which impacts the calculation of visible-NIR-based vegetation indices, such as the normalized difference vegetation index (NDVI) and the soil-adjusted vegetation index. 33,34 To reducing this effect, the atmospherically resistant vegetation index (ARVI) 35 and the enhanced vegetation index 36 have been developed to account for impacts of aerosol on NDVI. 37 Similarly, uncertainty in WV will induce uncertainty in NIR reflectance and vegetation water indices, since absorption features of liquid water and WV overlap. 38,39 NDWI using SWIR water absorption band was developed to be less sensitive to atmospheric effect through radiative transfer (RT) simulation. 17 To our knowledge, uncertainty in 970-nm-based water indices due to atmospheric correction errors has not been evaluated. It is thus important to improve the performance of these water indices under atmospheric perturbation. The objectives of this study, therefore, were: (1) to assess the impact of atmospheric WV content on the 970-nm-based water indices; (2) to develop optimization method for improving these indices under atmospheric perturbation; and (3) to assess the sensitivity of these new indices and their performance of estimating vegetation water status. Since almost all the current water indices are more sensitive to CWC than to FMC and EWT, 2,13,14 only CWC is employed to evaluate the performance of different water indices for estimating vegetation water status. In this paper, canopy and atmospheric RT models are used to simulate canopy reflectance data for developing new atmospherically resistant vegetation water indices, by integrating WV absorption peak around 940 nm (Sec. 2). The results of parameterization of developed new water indices are introduced in Sec. 3.1, and the robustness of the parameterization is assessed and presented in Sec. 3.2. The effects of atmospheric WV on the water indices are assessed using simulated spectral reflectance data in Sec. 3.3. The water indices are then assessed for estimation of CWC using the simulated spectral data (Sec. 3.4) and the field spectral reflectance data (Sec. 3.5). In addition, the sensitivity of satellite-based water indices to WV effect is evaluated using Hyperion and GF5 hyperspectral data in Sec. 3.6. Discussion on the uncertainties and limitations of the atmospherically resistant water-sensitive indices are presented in Sec. 4.

Wheat Field Dataset
Field data were collected in a winter wheat experiment in 2002 at the National Precision Agriculture Experimental Base in Xiaotangshan, Changping District, Beijing, China (40°10.6′ N, 116°26.3′E). 40 The study site is located in a warm temperature zone and has a continental climate. The annual mean temperature is 13.8 deg and average annual precipitation is 507.7 mm. In the field experiment, three winter wheat varieties, Zhongyou 9507, Jing 9428, and Jingdong 8, were seeded in 48 plots with four levels of nitrogen fertilization (N1: 0, N2: 150, N3: 300, and N4: 450 kg∕ha) and four water application levels (W1: 0, W2: 225, W3: 450, and W4: 675 m 3 ∕ha). Each plot is 32.4 m × 30 m. The study area and winter wheat experiment design are shown in Fig. 1.
Canopy CWC and spectral reflectance data were collected at the tillering and stem elongation stages, resulting a total of 96 samples. In each sample, a 1-m 2 area of winter wheat was chosen for canopy spectral reflectance measurements as well biophysical and biochemical parameter. Canopy spectral reflectance was measured using a FieldSpec spectrometer (Analytical Spectral Devices, Boulder, Colorado, USA), at the time between 10:00 am and 2:00 pm local time. Leaves were sampled and taken for laboratory analysis to determine the CWC on the same day. The CWC is the weight of foliar water per unit area of ground and is the product of the EWT and the LAI. 10,41 All fresh leaf samples within the sampling area were weighed immediately to obtain fresh weight (FW) and then were oven-dried for 48 h at 60 deg to obtain the DW. Leaf area was manually measured. EWT was calculated as 7 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 1 1 6 ; 2 7 6 where AREA Leaf is the total area of the sampled fresh leaves, calculated as the ratio of DW to specific leaf weight. If EWT and LAI are measured, CWC is then calculated as 41 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 1 1 6 ; 2 1 6 CWC ¼ EWT × LAI: with 30-m spatial resolution and 60-km swath width. The spectral resolution is about 5 nm in visible-NIR range (0.4 to 1.0 μm) and 10 nm in SWIR range (1.0 to 2.5 μm). 42 The Hyperion and GF5 data were processed to derive surface reflectance using the Fast Line-of-sight Atmospheric Analysis of Spectral Hypercubes (FLAASH) module 43 in the ENVI software. The FLAASH module uses the MODTRAN RT code for atmospheric correction. AOT was retrieved from the Hyperion data using the FLAASH module. Sensitivity of water indices to atmospheric condition was assessed by changing WV in atmospheric correction.

Simulation of Spectral Reflectance Data
In order to analyze the effect of the atmospheric correction on vegetation water indices, atmospheric correction was conducted using a vegetation RT model and an atmospheric RT model, to generate an error-free canopy reflectance dataset-which assumes that the atmospheric correction is accurate-and an inaccurately retrieved reflectance dataset. Simulation of spectra reflectance data using RT models helps to obtain enough samples with a wide range of conditions that actual field experiments cannot achieve.
First, the PROSAIL model, as a combination of the PROSPECT leaf model 44 and the SAIL canopy reflectance model, 45 was used to simulate the error-free canopy reflectance for a range of leaf and canopy parameter values. The PROSAIL model is optimized for a spatially continuous canopy, applicable for a closed winter wheat canopy. CWC can be calculated from EWT and LAI using Eq. (2). Both EWT and LAI are input parameters to the PROSAIL model. EWT ranged from 4 to 24 mg∕cm 2 and LAI ranged from 1 to 6 in PROSAIL model simulation. A range of leaf dry matter (C m ) and leaf structure parameter (N) were considered in simulation experiment. The influence of leaf chlorophyll content on reflectance in the 970-nm range is negligible. 41 Thus, leaf chlorophyll parameter can be fixed to a nominal value. The average leaf inclination angle (ALA) was set to 35 deg for winter wheat. A typical spectra of bright soil was used for Xiaotangshan site. The Sun-sensor geometry parameters are corresponding to the location and time of the above winter wheat field experiment. A list of the parameters used in the PROSAIL model simulation is presented in Table 1.
The 6S model 46 was then used to simulate atmospheric effect on retrieving of reflectance and vegetation water indices. Using the forward mode of the 6S model with true values for atmospheric parameters, canopy reflectance data simulated by the PROSAIL model were converted into top-of-atmosphere spectral data. For a sunny day, a true value of AOT at 550 nm (AOT 550 ) was set to 0.2 and a true value of WV was set to 2.0 g∕cm 2 . An altitude of 40 m of Xiaotangshan site was used. Other atmospheric parameters in the 6S model were set to their default values in this simulation.
Third, inaccurate reflectance data were simulated from the top-of-atmosphere data simulated above using the 6S model in its reverse mode. As can be seen from Fig. 2(a), the reflectance changes due to AOT are relatively spectrally smooth and flat compared to those due to the selective absorption by atmospheric WV. 47 In addition, the effect of aerosols on the shortwave infrared bands is much smaller than that in the visible bands. 17,46 Thus, atmospheric correction at around 970 nm is more sensitive to errors in WV than to errors in AOT, and the impact of AOT is negligible to reflectance retrieval, 30,32 which are also shown in Fig. 2. However, when a 20% relative error was added to WV at 2.0 g∕cm 2 (i.e., 0.4 g∕cm 2 ), large errors in the simulated reflectance can be introduced, especially at the NIR WV absorption band [ Fig. 2(b)]. We intended to reduce atmospheric WV effect on spectral water indices based on 970-nm absorption. Referring to the accuracy level of MODIS WV production, 32 errors in the WV were set to AE0.1, AE0.2, AE0.3, and AE0.4 g∕cm 2 for the simulation experiment in the atmospheric correction step.

Vegetation Water Indices
Different water indices may be impacted differently by the errors in WV for atmospheric correction. In this study, three 970-nm-based water indices, WI, NWI-1, and NWI-3, were selected for testing their sensitivity to atmospheric WV effect. These indices use reflectance at 970 nm and reflectance at a reference wavelength nearby: 900 nm for WI and NWI-1, 880 nm for NWI-3. Compared to 970 nm, absorption by liquid water in vegetation canopy in these reference wavelengths is weaker. 21,24,25 WI is calculated as the ratio of the reflectance at the 900-nm reference wavelength to that at the water absorption peak of 970 nm: 21 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 1 1 6 ; 2 6 1 where R 900 and R 970 are the surface reflectance at 900 and at 970 nm, respectively. NWI-1 is formulated as 24 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 4 ; 1 1 6 ; 2 0 6 and NWI-3 is formulated as 25 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 5 ; 1 1 6 ; 1 6 3 In addition, NDWI using reflectance at 1240 nm (NDWI 1240 ) and NDWI at 1640 nm (NDWI 1640 ) were also selected for comparison with 970-nm-based water indices, since the two NDWIs have been considered to be less sensitive to atmospheric effect. 17-19 NDWI 1240 and NDWI 1640 are calculated as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 6 ; 1 1 6 ; 8 3 NDWI 1240 ¼ ðR 860 − R 1240 Þ∕ðR 860 þ R 1240 Þ; and E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 7 ; 1 1 6 ; 7 2 3

Approach to Compensating Atmospheric Water Vapor Effects
To reduce the effect of atmospheric WV on 970-nm-based water indices, the self-correction approach of ARVI 35 was adopted in this study by introducing WV absorption band at 940 nm. ARVI uses a combination of NDVI and the blue band reflectance to correct the atmospheric effects, and the resistance of ARVI to atmospheric aerosol effect is accomplished using the difference in sensitivity of the blue and red channels to aerosols. Even though the absorptions of atmospheric WV and plant liquid water may overlap, their absorption peaks in 800 to 1000 nm range are different by about 30 nm [ Fig. 2(a)]. When there is error in WV used for atmospheric correction, the changes in the retrieved surface reflectance at the 940-nm wavelength will be larger than that in nearby wavelengths. Therefore, it is possible to separate the contributions from canopy water absorption and reference wavelength for water index calculation by incorporating reflectance at 940 nm. First, to design new spectral water indices resistant to atmospheric WV effect, we adjusted the reflectance at 970 nm and the reference wavelength using the reflectance at 940 nm (referred to as R 0 λ ). The WV absorption peak at 940 nm is impacted more by WV, which can be exploited to correct reflectance in other bands less affected by errors in atmospheric conditions. We assume that R 0 λ obtained this way is resistant to atmospheric effects: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 8 ; 1 1 6 ; 4 6 5 where λ is a given wavelength in the range 800 to 1000 nm, and k λ is the correction coefficient that makes R 0 λ resistant to WV effect; R λ is the surface reflectance retrieved through atmospheric correction, which may bring errors caused by inaccurate knowledge of atmospheric WV. As a special case of R λ , R λ;true is the result using the accurate WV thus represents the true surface reflectance. In contrast to R λ;true , the values of R 0 λ includes errors caused by the atmospheric WV effect.
Second, it is a key step to derive the correction coefficient k λ in Eq. (8). We transformed Eq. (8) into Eq. (9) E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 9 ; 1 1 6 ; 3 3 6 Equation (9) means that change of reflectance from its true value due to inaccurate WV correction at any wavelength λ is proportional to that at 940 nm: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 1 0 ; 1 1 6 ; 2 8 0 If the above assumption is valid, k λ can be obtained through regression analysis, using simulated retrieved reflectance dataset with variable values of WV input shown in Table 2.
Following the above steps, we developed a new simple ratio index based on WI through integration of the band at 940 nm, named as an atmospherically resistant water index (ARWI), which is the ratio of R 0 900 to R 0 970 . This ARWI index can be calculated using the surface reflectances retrieved using atmospheric correction at 900, 940, and 970 nm, expressed as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 1 1 ; 1 1 6 ; 1 7 6 A new normalized, atmospherically resistant water index based on NWI-1 (NARWI-1) using the band at 940 nm also is designated as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 1 2 ; 1 1 6 ; 1 0 6 Another new normalized, atmospherically resistant water index based on NWI-3 (NARWI-3) using the reference wavelength of 880 nm is calculated as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 1 3 ; 1 1 6 ; 5 1 8 3 Results and Analysis

Determination of Correction Coefficients
Using simulated data, the relationship between reflectance changes at 970 and 940 nm due to atmospheric WV perturbation is shown in Fig. 3. In the simulation, WV was changed in a range 0.4 g∕cm 2 above and below the true WV at 2.0 g∕cm 2 . It can be observed that the reflectance changes at 970 nm from the true values were strongly correlated with that at 940 nm (R 2 ¼ 0.998). The correction coefficient in Eqs. (8)-(10) for 970 nm (k 970 ) was 0.394. Using the same approach, the correction coefficients k λ in Eqs. (8)-(10) for any wavelength between 860 nm and 1000 nm can also be determined, and the results are shown in Fig. 4. The correction coefficient at different wavelengths varies between 0 and 2.8. As shown by the coefficient of determination, the linear relationships are strong between reflectance changes at 940 nm and at most of wavelengths below 860 nm. The coefficient was 0.534 for 900 nm (k 900 ), whereas 0 for 880 nm (k 880 ), which means that reflectance at 880 nm is hardly affected by variation in WV. The results for the three wavelengths are reported in Table 3, and the values of k 970 , k 900 , and k 880 can be used to derive the improved water indices given in Eqs. (11)-(13). Fig. 3 The relationship between reflectance changes induced by the WV effect at 940 nm and that at 970 nm, illustrated by the WV content error.

Influence of water vapor errors
The influence of WV in the parameterization of the new water indices was tested, and the results were shown in Fig. 6. The strong linear relationship indicates that the correction efficient is stable for different levels of WV error (ranging from −0.8 to 0.8 g∕cm 2 ).

Influence of aerosol errors
The influence of aerosol in the parameterization of the new water indices was also tested, and the results were shown in Fig. 7. Aerosol will influence the assumed relationship in Eqs. (9) and (10) but is acceptable if the AOT 550 error is retained below 0.1.

Water Vapor Effect Assessment on Calculation of Water Indices Using Simulated Spectra
The root mean square error (RMSE) is regularly employed in accuracy evaluation. Relative root mean squared error (RRMSE) can be considered as a normalized RMSE metrics. Because different water indices own different value ranges, RRMSE is a better matrix to increase the comparability of the sensitivity of calculation of different water indices to the WV effect. The values of water indices with atmospheric WV errors were compared to those corresponding error-free values, and R 2 and RRMSE were calculated in Table 4.   Table 4 shows that there is little difference between NDWI 1240 with atmospheric correction errors and the error-free NDWI 1240 , and a similar situation occurred with NDWI 1640 . That implies that NDWIs using SWIR water absorption band are hardly affected by WV input error in atmospheric correction. However, all of three existing 970-nm water indices (WI, NWI-1, and NWI-3) are more sensitive to WV errors in atmospheric correction process than NDWIs. Table 4 also shows that all three improved water indices including ARWI, NARWI-1, and NARWI-3 can minimize their WV effect as NDWIs. The linear regression between the values between ARWI, NARWI-1, and NARWI-3 with atmospheric correction errors and their errorfree values shows a high correlation (R 2 more than 0.99), with the better RRMSE (less than 3%) than the RRMSE results (more than 10%) of WI, NWI-1, and NWI-3.
NWI-3 is most affected by the WV effect. The R 2 of regression between NWI-3 values with atmospheric correction error and error-free NWI-3 values is only 0.856 with the largest RRMSE of 41.0%. Compared with NWI-3, the RRMSE calculated between NARWI-3 with atmospheric correction errors and its error-free values was improved to 2.8%. The scatter plot between NWI-3 with atmospheric correction errors and its error-free values appears more discrete than its improved index NARWI-3, as shown in Fig. 8. It means that the improvement of NARWI-3 from NWI-3 against atmospheric WV effect is rather obvious.

Performance of Water Indices for Vegetation Water Content Estimation Using Simulated Spectra
Based on simulated datasets without atmospheric correction errors, regression models were built to assess relationships between CWC and water indices. The results in Fig. 9 show all of these eight water indices had high correlations with CWC (R 2 more than 0.94), when the atmospheric correction is error-free. Based on simulated dataset with atmospheric correction errors, scatter plots of the CWC and the selected eight water spectral indices were built (Fig. 10). The three existing water indices with atmospheric correction errors have lower correlations with the CWC (WI: R 2 ¼ 0.937, NWI-1: R 2 ¼ 0.929, NWI-3: R 2 ¼ 0.807) than those result of their improved water indices (ARWI: R 2 ¼ 0.958, NARWI-1: R 2 ¼ 0.946, NARWI-3: R 2 ¼ 0.942). In addition, all of the three improved water indices with atmospheric correction errors have similarly good correlations with the CWC (Fig. 10), compared with their result without atmospheric correction errors (Fig. 9). Like the three improved 970-nm-based water indices, the two NDWIs also keep high correlations with CWC, whether there is atmospheric correction error or not.
Using models presented in Fig. 9, CWC was estimated from the simulated datasets with and without atmospheric correction errors (Table 5). When there are no atmospheric WV errors in simulated dataset, both the existing and developed 970-nm-based water indices produced similar results of CWC estimation with R 2 from 0.942 to 0.958 and RMSE from 7.3 to 8.6 mg∕cm 2 . The two NDWIs also obtained good R 2 in CWC estimation, and only NDWI 1640 produced a large CWC RMSE more than 10 mg∕cm 2 .
As shown in Table 5, the three developed atmospherically resistant water indices improve estimation of the CWC, compared with their three original water indices against to the WV effect. Compared with their results based on simulated dataset without atmospheric correction   Table 5 Accuracy assessment for the estimation of CWC by vegetation water indices based on simulated datasets with and without WV content errors. The used water index-CWC regression relations from error-free data simulated using PROSAIL model (as shown in Fig. 9) were shown (y denotes CWC and x denotes water index). errors, WI, NWI-1, and NWI-3 have much poorer performance of CWC estimation based on simulated dataset with atmospheric correction errors. However, all of three new water indices (ARWI, NARWI-1, and NARWI-3) obtain better estimation of the CWC than their original water indices, for both the simulated dataset with and without atmospheric correction errors. When there are atmospheric correction errors, RMSE of CWC estimation by ARWI is 7.4 mg∕cm 2 less than WI (RMSE ¼ 8.9 mg∕cm 2 ), and the CWC estimation result of NARWI-1 (RMSE ¼ 8.3 mg∕cm 2 ) is better than NWI-1 (RMSE ¼ 9.4 mg∕cm 2 ). NARWI-3 has the most improvements of CWC estimation (RMSE: 8.8 mg∕cm 2 ) compared with NWI-3 (RMSE: 16.6 mg∕cm 2 ). The trend between WVerror and the RMSE of CWC estimated using NWI-3 versus NARWI-3 is shown in Fig. 11. The RMSE in the CWC estimated using NWI-3 increases greatly with the increasing error in the atmospheric WV and the maximum RMSE value reach about 25 mg∕cm 2 , while the RMSE values in the CWC estimated by NARWI-3 remain <10 mg∕cm 2 . Compared to the estimation of the CWC made using NWI-3, the CWC values estimated by NARWI-3 were more resistant to the WV input errors in atmospheric correction. It can be implied that the greater the error of WV in atmospheric correction, the greater the influence on the CWC estimation by existing 970-nm-based water index; while the result of CWC estimation using new 970-nm-based water index could be resistant to the WV effect.

Validation of Vegetation Water Content Estimation Using Field Dataset
The previously recalibrated formulae for estimating the CWC derived from the error-free simulated dataset (Fig. 9) were validated with the field data obtained in the Beijing study area. Field reflectance data are regarded as having no atmospheric correction errors. Figure 12 shows the results of CWC accuracy assessment from the observations of winter wheat. All six 970-nm-based water indices can get good CWC estimation with RMSE less than 8 mg∕cm 2 and R 2 higher than 0.8. The results of simulated dataset without WV errors (Table 5) and field dataset (Fig. 12) show that both the existing and developed 970-nm-based water indices produced good estimation of the CWC when these error-free reflectance data were used. Figure 12 also shows that all of six 970-nm-based water indices got a little better estimation of CWC based on the field measured reflectance data than the two NDWIs. The NDWI 1640 −CWC formula produced the CWC estimation with a maximum RMSE, and NDWI 1240 followed with a second largest RMSE. The validation results of CWC estimation using the two NDWIs also yielded lower R 2 than that using either existing or developed 970-nm-based water indices.

Sensitivity of Water Index on Atmospheric Correction Errors Using Satellite Data
The impact of atmospheric WV on the selected existing and new water indices was assessed using different satellite hyperspectral data, including the Hyperion and GF5. For calculation Fig. 11 The RMSE of CWC estimated by NWI-3 and NARWI-3 plotted against the error in the value of the atmospheric WV content in atmospheric correction.
of the water indices from Hyperion imagery, the wavelength of the channel correspondent to WV absorption peak is 943 nm, and that of vegetation water absorption is 973 nm. The reference channel at 895 nm is chosen for WI, ARWI, NWI-1, and NARWI-1, and 885 nm for NWI-3 and NARWI-3. Figure 4 shows the correction coefficient k λ at different wavelengths. k λ for a specific satellite hyperspectral sensor (e.g., Hyperion) could be determined through spectral sampling using the spectral response function, for example 0.187 at 973 nm band, 0.145 for 895 nm band, and 0 for 883 nm band. Using these correction coefficients, the three new atmospherically resistant water indices for Hyperion data are given in Table 6. For GF5 data, the WV absorption peak is at the 942-nm channel, and vegetation water absorption peak is at the 973-nm channel.
The reference channels at 899-and 886-nm channels were selected for the water indices. The coefficients for the GF5 are determined as 0.208 for k 972 , 0.313 for k 899 . The results are also given in Table 6. Reflectance was retrieved from the Hyperion and the GF5 hyperspectral data using the FLAASH atmospheric correction module, with the WV parameters set to a range of 0.5 to 2.5 g∕cm 2 . All the selected 970-nm-based water indices were calculated from the Hyperion and GF5 reflectance data retrieved with WV varying within the given ranges following a normal distribution. Figure 13 shows the calculation results of standard deviation (SD) of the water indices induced by inaccurate atmospheric WV inputs in the FLAASH atmospheric correction module for three land cover types (shown in Fig. 14) of crop (green), grass (blue), and sparse forest (yellow) in the Hyperion and GF5 images. As shown in Fig. 13, the existing 970-nm-based water indices (WI, NWI-1, and NWI-3) are more affected by atmospheric WV effect than the   respective improved indices (ARWI, NARWI-1, and NARWI-3), as indicated by the much smaller SD of the improved indices derived for both Hyperion and GF5 satellite data. Using the developed CWC estimation equations built from error-free simulated data presented in Fig. 9, the SD of CWC derived using different indices from the two Hyperion images and the two GF5 images are calculated (Fig. 14). The results showed that different water indices have different CWC SD. For Hyperion data, most of CWC SD values range between 30 and 50 mg∕cm 2 for WI and NWI-1 and are more than 60 mg∕cm 2 using NWI-3. When using ARWI, NARWI-1, and NARWI-3, most of CWC SD values are between 0 and 20 mg∕cm 2 . Similar results can be observed for GF5 (Fig. 14).
The results of both Hyperion and GF5 showed that our three improved 970-nm-based water indices could bring lower uncertainty in CWC estimation against WV effect in atmospheric correction.  feature overlap spectrally. 39,48,49 By exploiting the differences in these absorption peaks, this study provided an effective approach of compensating atmospheric WV effect on 970-nmbased vegetation water indices. The approach leads to the development of a few indices that can provide robust estimation of vegetation CWC from satellite hyperspectral remote sensing data. This is important, since great uncertainty in surface reflectance retrievals can be induced through atmospheric correction due to inaccurate knowledge of atmospheric WV. 32 New 970nm-based atmospherically resistant water indices are applied to Hyperion and GF5 hyperspectral images, and the results in Figs. 13 and 14 demonstrate the effectiveness of our approach in minimizing the uncertainties. This approach could also be applied to narrow-band multispectral cameras with suitable spectral configuration around the 970-nm water absorption feature. Future study will test the applicability of the developed water indices for FMC or EWT estimation.

Uncertainty in Parameterization of the New Water Indices
Stability of the correction coefficients in Eqs. (8)-(10) is very important for the application of the three new water indices in Eqs. (11)- (13). It may be affected by several factors including canopy reflectance, atmospheric correction, and sensor spectral configuration. Both canopy and leaf parameters determine canopy reflectance. 50,51 Therefore, the PROSAIL coupled leaf-canopy reflectance model was used to assess the water indices with a range of canopy conditions described in Table 1. Our results show that variations of canopy and leaf parameters in Table 1 produced the parameterization result of the proposed 970-nm-based water indices with high R 2 (see Fig. 4). We did not consider the cases where target pixel is mixed with apparent water.
Impacts of atmospheric conditions, characterized by WV, AOT, aerosol type, imaging suncanopy-sensor geometry, have also been considered using the 6S model simulations. Our results in Sec. 3.2 show that the error differences in WV used for atmospheric correction does not bring apparent variation in the correction coefficients in the proposed new water indices, whereas larger errors in AOT do. At AOT of 0.2, the normal error level of MODIS aerosol products (refer to Refs. 30 and 31) is AEð0.05 þ 0.15 Ã AOTÞ and will only have very little effect on the parameterization results (see Fig. 7). Retrieval of aerosol from hyperspectral data such as Hyperion will be more accuracte than that from multispectral sensor such as MODIS. 52 Thus, incoporating AOT retrievals from hyperspectral data helps to ensure a more stable parameterization of the new water indices.
Parameterization of the proposed water indices is sensor-specific, dependent on spectral configurations, such as band position and spectral response function, thus, the specific k λ values should be adapted from Fig. 4 for specific sensors, such as the Hyperion and the GF5 AHSI.

Limitations of New Atmospherically Resistant Water Indices in Improving Estimation of Vegetation Water Content
The ability for monitoring vegetation water status varies with different vegetation water indices. WI and NWIs are found to provide estimation of CWC with a higher accuracy than FMC and EWT. 2,13,14 NDWI is found to be inferior for CWC estimation than the 970-nm-based water indices, 13,53 which is consistent with our studies (see Fig. 12). The sensitivity of vegetation water indices to variations in vegetation water status is influenced by other canopy factors such as LAI, leaf angle distribution function, and mixed pixels. 41,50,51 As shown in Fig. 15, the proposed water indices in this study are strongly correlated with their original water indices calculated using error-free reflectance data. Therefore, the new atmospherically resistant water indices would provide similar performance compared to their original 970-nm-based water indices calculated from error-free reflectance data in monitoring vegetation water status. Our results have showed that ARWI, NARWI-1, and NARWI-3 provide CWC estimation with an accuracy comparable with that provided by WI, NWI-1, and NWI-3 using field reflectance dataset (see Table 5 and Fig. 12).

Conclusion
This study presented a simple method for reducing the impact of atmospheric correction errors on 970-nm-based vegetation water indices, e.g., WI, NWI-1, and NWI-3, by exploiting the differences in WV and liquid water absorption in this spectral region. We proposed atmospherically resistant version of the water indices, ARWI, NARWI-1, and NARWI-3. The proposed indices have been tested using simulated experimental data, winter wheat field data, as well as Hyperion and GF5 satellite hyperspectral data. The proposed indices are proven to be more resistant to atmospheric WV effect and can provide more accurate estimation of CWC than WI, NWI-1, and NWI-3, respectively. NWI-3 was the most affected by WV effect, and NARWI-3 provided the largest improvement in estimating CWC. Through adaptation, the proposed approach to developing the new 970-nm-based water indices could be applied in multispectral data with NIR water absorption peak. Further experiments are needed to assess the new indices using more satellite hyperspectral or narrow-band multispectral data covering different vegetation types. Fig. 15 Scatter plots of (a) WI vs. ARWI, (b) NWI-1 vs. NARWI-1, and (c) NWI-3 vs. NARWI-3 using field reflectance data obtained in Xiaotangshan, Beijing. The field reflectance data are considered having no atmospheric correction errors.