Method for improving grassland biomass inversion precision and adaptability based on SWIR

Abstract

The invention discloses a method for improving grassland biomass inversion precision and adaptability based on SWIR, and particularly relates to the technical field of vegetation remote sensing and application. A vegetation index is constructed by combining an ASIS global soil spectrum library by utilizing the characteristics that a vegetation spectrum has high absorption in red light and short wave infrared bands and high reflection in a near infrared band, and a soil spectrum curve monotonically rises, so that the influence of a soil background on grassland biomass remote sensing inversion is removed, and the grassland biomass remote sensing inversion accuracy is improved. And the grassland biomass inversion precision and the statistical model applicability under the low vegetation coverage are improved. By adopting the technical scheme of the invention, the problem that the existing grassland biomass remote sensing inversion method is easily influenced by the soil background is solved, and multi-scale measurement and estimation can be quickly and accurately carried out on the grassland biomass.

Description

Technical Field

[0001] The invention relates to the field of vegetation remote sensing and application technology, and in particular to a method for improving grassland biomass inversion accuracy and adaptability based on SWIR. Background Art

[0002] Grassland is one of the largest terrestrial ecosystem types in the world. It has important ecological, production and economic functions. It is not only an important herbivorous animal husbandry base, but also a huge green ecological barrier and terrestrial carbon pool, playing an important role in global carbon balance and national ecological security. Biomass is the most important canopy indicator of grassland ecosystems. Accurate monitoring of its spatiotemporal dynamics not only provides information for sustainable management of grasslands, but also helps to deeply understand the response mechanism of grassland ecosystems under the influence of global changes.

[0003] The mainstream method for remote sensing inversion of grassland biomass is to establish a statistical model or machine learning model based on the relationship between biomass and vegetation index. However, since grassland vegetation coverage is generally between 20% and 60%, the vegetation index designed based on the concept of soil line in the characteristic space of red light and near-infrared bands is easily affected by the soil background, such as NDVI, EVI, SAVI, etc. Although NDWI incorporates short-wave infrared band information to reduce the impact of soil background, it lacks comprehensive consideration of soil line characteristics, and improves the soil effect in grassland biomass inversion but not significantly. Summary of the invention

[0004] The present invention aims to provide a method based on SWIR to improve the accuracy and adaptability of grassland biomass inversion, which solves the problem that the existing grassland biomass remote sensing inversion method is easily affected by soil background.

[0005] In order to achieve the above object, the technical solution of the present invention is as follows: A method for improving the accuracy and adaptability of grassland biomass inversion based on SWIR, comprising the following steps:

[0006] S1. Obtain multi-source remote sensing images of the study area and preprocess them to obtain surface reflectance preprocessing data;

[0007] S2. Refer to the ESA authenticity verification framework, design ground measurement plots and standard sampling units, measure representative soil spectra and grassland biomass, and obtain soil spectral curves and field measurement data of grassland biomass at different scales in the study area;

[0008] S3. Construct vegetation index and parameters to remove soil background influence;

[0009] S4, using the surface reflectance to preprocess the data, extracting multiple spectral characteristic vegetation indices at the same time, and obtaining the biomass observation value of the sample plot;

[0010] S5. Perform statistical regression on the sample plot biomass observation values ​​obtained in step S4 and NDSI and other vegetation indices, select the model with the highest estimation accuracy as the grassland biomass inversion model, and perform accuracy evaluation to verify the accuracy and applicability of the grassland biomass inversion model.

[0011] Furthermore, the preprocessing method of step S1 includes radiation correction, geometric correction and atmospheric correction.

[0012] Furthermore, the specific method of step S1 is as follows:

[0013] S1.1. Perform radiation correction on multispectral images according to the absolute radiation calibration coefficient and convert the original radiation value into apparent radiation brightness;

[0014] S1.2. Geometric correction and geometric precision correction of remote sensing images from different sources by using ground control points;

[0015] S1.3. Use the atmospheric radiation transfer model 6S to calculate and obtain the atmospheric correction coefficient. Combine the apparent radiation brightness image and the atmospheric correction coefficient to obtain the surface reflectance preprocessing data.

[0016] Furthermore, the specific method of step S2 is as follows: using a ground object spectrometer to measure the spectral curve of a representative soil, using a harvesting method to measure the spectral curve of a 1m 2 The grassland biomass of the sampling unit was upscaled using the weighted average method to obtain field measurement data of grassland biomass at different scales.

[0017] Through the above settings, the true value of grassland ground biomass is obtained by referring to the ESA authenticity verification standard sampling unit. At the same time, vegetation and soil observation data suitable for modeling satellite images of different resolutions are collected to verify the effect of vegetation index removing soil background on grassland biomass inversion accuracy from different application scales.

[0018] Furthermore, the vegetation index formula after removing the soil background in step S3 is:

[0019]

[0020] Where α = (SWIR t -NIR t ) / (SWIR t -RED t ), SWIR t 、NIR t ,RED t It is the soil reflectance value of the soil type in the study area in the shortwave infrared, near infrared and red light bands. When the soil spectral measurement value is default, the ASIS Global Soil Spectral Library data is used.

[0021] Through the above settings, a vegetation index was constructed by utilizing the characteristics of vegetation spectrum (high absorption in red and shortwave infrared bands and high reflection in near-infrared band) and monotonically rising soil spectrum curve, combined with the ASIS global soil spectral library, to remove the influence of soil background on grassland biomass remote sensing inversion, and to improve the grassland biomass inversion accuracy and statistical model applicability under low vegetation coverage.

[0022] Furthermore, the spectral characteristic vegetation index in step S4 includes the normalized vegetation index NDVI, the enhanced vegetation index EVI, the soil adjusted vegetation index SAVI, and the normalized water index NDWI. The calculation formulas of different vegetation indices are:

[0023]

[0024]

[0025]

[0026]

[0027] Among them, BluE, Red, NIR, and SWIR1 are the DN values ​​of the blue light, red light, near infrared, and short-wave infrared bands, respectively.

[0028] Furthermore, the specific method of step S5 is as follows: the biomass observation value of the sample plot obtained in step S4 is used as the dependent variable, and the different vegetation indices NDSI, NDVI, EVI, SAVI and NDWI in the corresponding geographical location are used as driving variables to construct a statistical regression model. 2 , Bias were used to evaluate the model accuracy, and the model with the highest estimation accuracy was selected as the grassland biomass inversion model.

[0029] Furthermore, the calculation formula of the accuracy evaluation index is as follows:

[0030]

[0031]

[0032]

[0033]

[0034] Among them, MAE, RMSE, R 2 , Bias are mean absolute error, root mean square error, determination coefficient and bias, which are used to evaluate the accuracy and temporal and spatial applicability of the model; X model,i is the biomass of plot i calculated by the model, X obs,iis the measured biomass of plot i, and N is the number of plots used for precision evaluation.

[0035] Compared with the prior art, this solution has the following beneficial effects:

[0036] 1. This scheme can construct a robust grassland biomass inversion model for low vegetation coverage grassland, reduce the error caused by soil background influence, improve the accuracy of the model, and expand the applicability of the model in time and space.

[0037] 2. This scheme takes into account the full-band characteristics of soil and vegetation spectra, and uses the characteristics of high absorption of vegetation spectra in the red and short-wave infrared bands and high reflection in the near-infrared band, while the soil spectrum curve rises monotonically to construct a vegetation index that removes the soil background, providing ideas and methods for building a robust grassland biomass inversion model under low vegetation coverage. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a flow chart of a method for improving grassland biomass inversion accuracy and adaptability based on SWIR of the present invention;

[0039] Figure 2 It is a design drawing of a grassland ground measurement plot and a standard sampling unit in the present invention;

[0040] Figure 3 It is the grassland biomass inversion and evaluation map based on MODIS in the present invention;

[0041] Figure 4 It is a grassland biomass inversion and evaluation diagram based on OLI and MSI in the present invention. DETAILED DESCRIPTION

[0042] The present invention is further described in detail below through specific embodiments:

[0043] Example

[0044] like Figures 1 to 4 As shown in FIG. 1 , a method for improving the accuracy and adaptability of grassland biomass inversion based on SWIR includes the following steps:

[0045] S1. Obtain multi-source remote sensing images of the study area and perform preprocessing, including radiation correction, geometric correction and atmospheric correction, to obtain surface reflectance preprocessing data. This method is applicable to multispectral satellite data including red, near infrared and short-wave infrared bands, such as TERRA satellites, Landsat series satellites, Sentinal series satellites and GF series satellites.

[0046] The specific method is as follows:

[0047] S1.1. Perform radiation correction on the multispectral image according to the absolute radiation calibration coefficient and convert the original radiation value into apparent radiation brightness.

[0048] S1.2. By using ground control points, geometric correction and geometric precision correction are performed on remote sensing images from different sources.

[0049] S1.3. Use the atmospheric radiation transfer model 6S to calculate and obtain the atmospheric correction coefficient. Combine the apparent radiation brightness image and the atmospheric correction coefficient to obtain the surface reflectance preprocessing data.

[0050] S2. Refer to the ESA authenticity verification framework, design ground measurement plots and standard sampling units, measure representative soil spectra and grassland biomass, obtain soil spectrum curves and field measurement data of grassland biomass at different scales in the study area; as shown in the attached Figure 2 The specific method is as follows: a ground spectrometer is used to measure the spectral curve of representative soil, and a harvesting method is used to measure 1m 2 The grassland biomass of the sampling unit was upscaled to 10m / 15m / 20m (GF5 and Sentinal series satellites), 30m (Landsat series satellites), 250m / 500m / 1000m (MODIS satellite), etc. using the weighted average method to obtain field measurement data of grassland biomass at different scales.

[0051] S3. Construct vegetation index and parameters to remove the influence of soil background. The principle is to use the characteristics of high absorption of vegetation spectrum in red and short-wave infrared bands and high reflection in near-infrared band in the mixed spectrum, while the soil spectrum curve rises monotonically. Construct parameter α so that the calculation result of soil reflectance in different bands in the vegetation index is 0, that is, to remove the influence of soil background.

[0052] The vegetation index formula for removing soil background in step S3 is:

[0053]

[0054] Where α = (SWIRt-NIR t ) / (SWIRt-RED t ), SWIR t 、NIR t ,RED t It is the soil reflectance value of the soil type in the study area in the short-wave infrared, near-infrared and red bands. The soil spectrum measurement value uses the ASIS global soil spectrum library data by default. When α = 1, NDSI = NDVI, which requires the assumption that the soil reflectance in the red and near-infrared bands is the same. Therefore, NDVI and other vegetation indices that do not consider removing the soil background are affected by the soil background when applied to low-coverage vegetation.

[0055] S4. Use the surface reflectance to preprocess the data and extract multiple spectral characteristic vegetation indices at the same time to obtain the biomass observation values ​​of the sample plot, including the normalized vegetation index NDVI, enhanced vegetation index EVI, soil adjusted vegetation index SAVI, and normalized moisture index NDWI; the calculation formulas of different vegetation indices are:

[0056]

[0057]

[0058]

[0059]

[0060] Among them, BluE, Red, NIR, and SWIR1 are the DN values ​​of the blue light, red light, near infrared, and short-wave infrared bands, respectively.

[0061] S5. Perform statistical regression on the sample plot biomass observation values ​​obtained in step S4 and NDSI and other vegetation indices, select the model with the highest estimation accuracy as the grassland biomass inversion model, and perform accuracy evaluation to verify the accuracy and applicability of the grassland biomass inversion model.

[0062] The specific method is as follows: the biomass observation value of the sample plot obtained in step S4 is used as the dependent variable, and different vegetation indices such as NDSI, NDVI, EVI, SAVI and NDWI in the corresponding geographical location are used as driving variables to build a statistical regression model. 2 , Bias were used to evaluate the model accuracy, and the model with the highest estimation accuracy was selected as the grassland biomass inversion model.

[0063] The calculation formula of the accuracy evaluation index is as follows:

[0064]

[0065]

[0066]

[0067]

[0068] Among them, MAE, RMSE, R 2 , Bias are mean absolute error, root mean square error, determination coefficient and bias, which are used to evaluate the accuracy and temporal and spatial applicability of the model; X model,i is the biomass of plot i calculated by the model, X obs,i is the measured biomass of plot i, and N is the number of plots used for precision evaluation.

[0069] Specific case 1:

[0070] This paper introduces the large-scale grassland biomass inversion, accuracy evaluation and applicability verification based on the MODIS shortwave infrared band. This implementation case uses sample plots of specific regions and grassland types in the central and eastern Inner Mongolia to model and predict grassland biomass in the entire central and eastern Inner Mongolia, and evaluates the spatial applicability of the grassland biomass model.

[0071] Step S1: Taking the natural grassland in the central and eastern part of Inner Mongolia as the specific implementation object, obtain the EOS-HDF format LIB data of the TERRA-MODIS satellite after calibration and positioning in the implementation area; use remote sensing software such as ENVI or ERDAS, use the MCTK tool for radiation calibration, and use FLAASH atmospheric correction to generate surface reflectance data; use the information provided by the parameter file to perform geometric correction and radiation correction on the image to ensure that each point in the image has accurate geographic coding, reflectivity and radiation rate; use ground control points to perform geometric precision correction on the MODIS image of the study area so that the matching error of images in different phases is less than 1 pixel; use Fourier transform, homomorphic filtering and other algorithms to remove clouds and obtain a series of clear images of the grassland growing season in the study area.

[0072] Step S2: According to the attached Figure 2 The plot design and ground sampling framework were designed. A 3km×3km grassland area with a relative mean was selected to set up the plot. The longitude and latitude of the plot center were recorded. A representative area was selected within the plot to measure the soil spectrum. The harvest method was used to measure 45 1m 2 Grassland biomass within the sampling unit. For each 1 km × 1 km sub-plot, the average biomass of the nine sub-plots was calculated using the weighted average method based on the proportion of vegetation distribution area represented by the five sampling units. The average grassland biomass of the nine sub-plots was further calculated to obtain the plot-scale grassland biomass measurement value.

[0073]

[0074] Among them, AGB obs is the observed value of the biomass of the sample plot, i is the number of the 9 sub-sample plots, j is the number of the representative sample plot in each sub-sample plot, and p j is the area ratio represented by plot j, which is obtained by visual inspection when setting up the plot.

[0075] Step S3: Construct a vegetation index that removes the influence of soil background. The main soil types in the grasslands of central and eastern Inner Mongolia are dark chestnut soil and chestnut soil. The soil spectral curves of 30 plots of each soil type are averaged to obtain short-wave infrared (SWIR t , 1628-1652nm), near infrared (NIR t, 841-876nm) and red light band (RED t , 620-670nm) reflectance value, chestnut soil SWIR t 、NIR t ,RED t The SWIRt, NIRt, and REDt of dark chestnut soil are 42.15, 34.01, and 29.98, respectively. The SWIRt, NIRt, and REDt of dark chestnut soil are 41.32, 33.16, and 29.18, respectively. t -NIR t ) / (SWIR t -RED t ) can be calculated:

[0076] α 栗钙土 =α 暗栗钙土 =0.67

[0077] Therefore, in the grasslands of central and eastern Inner Mongolia, the vegetation index formula after removing the soil background is:

[0078]

[0079] Step S4: Use the surface reflectance to preprocess the data and extract multiple spectral characteristic vegetation indices, including NDSI, NDVI, EVI, SAVI, etc., to obtain the biomass observation value of the sample plot. The calculation formula of different vegetation indices is:

[0080]

[0081]

[0082]

[0083]

[0084] Among them, BluE, Red, NIR, and SWIR1 are the DN values ​​of the blue light, red light, near infrared, and short-wave infrared bands, respectively.

[0085] Step S5: Taking the biomass observation value of the sample plot obtained in step S2 as the dependent variable and taking different vegetation indices NDSI, NDVI, EVI, SAVI and NDWI in the corresponding geographical location as the driving variables, a statistical regression model is constructed:

[0086] AGB=754.12×NDSI-15.074R 2 =0.7307

[0087] AGB=611.3×NDVI-77.396R 2 =0.6658

[0088] AGB=948.73×EVI-77.16R 2 =0.6884

[0089] AGB=1031.1×SAVI-107.16R 2 =0.6901

[0090] The MAE, RMSE, and R of different vegetation index statistical models are calculated according to the following formulas when using different regions, different times, and different numbers of observation data for modeling. 2 、Bias:

[0091]

[0092]

[0093]

[0094]

[0095] The results show that the model constructed by NDSI performs best. 2 The model performance is relatively stable when the number of observed data is ≥40, and the model has strong universality. Figure 3 .

[0096] Specific case 2:

[0097] Using Landsat-OLI and Sentinal-MSI data as information sources, this paper introduces the inversion of grassland biomass at a small scale and its accuracy evaluation. This implementation case uses the July sample plot of Hulunbuir grassland in Inner Mongolia to model and predict the grassland biomass from June to August, and evaluates the temporal scalability of the grassland biomass model.

[0098] Step S1: Taking the Hulunbuir grassland in Inner Mongolia as a typical area for specific implementation, the Sentinal2 satellite MSI data and Landsat8 satellite OLI data of the typical area are selected. First, the original image is radiometrically calibrated with the help of the radiometric calibration parameters of the MSI / OLI sensor, and the original DN value is converted into the pixel radiometric brightness value; then the OLI image after radiometric calibration is atmospherically corrected with the FLAASH model, and the MSI data is atmospherically corrected with the help of Sen2cor, a plug-in specially released by ESA for producing L2A-level data, so as to convert the radiometric brightness value into the actual reflectivity of the surface; then the image after atmospheric correction is geometrically precisely corrected, and the same-name ground object points are selected, and the correction is performed using a quadratic polynomial, the correction error is controlled within 0.1 pixel, and the nearest neighbor pixel method is used for resampling.

[0099] Step S2: Set up a 90m×90m ground measurement plot and standard sampling unit. See the attached Figure 2 The spectral curve of soil in a typical area was measured using a ground spectrometer, and the harvesting method was used to measure 45 1m 2 The grassland biomass within the sampling unit was calculated by arithmetic averaging. 2 The grassland biomass of the sampling unit was upscaled to 20m (Sentinal-MSI) and 30m (Landsat-OLI) to obtain field measurement data of grassland biomass at different scales.

[0100] Step S3: construct a vegetation index that removes the soil background effect. Select 15 sample plots in a typical area to measure the soil spectrum curve and calculate the average value. OLI , 1600-1620nm), near infrared (NIR OLI , 837-847nm) and red light band (RED OLI , 660-670nm) reflectivity values, calculate α based on OLI data OLI Value and NDSI OLI , using short-wave infrared (SWIR MSI , 1570-1650nm), near infrared (NIR MSI , 850-880nm) and red light band (RED MSI , 640-670nm) reflectance values, calculate α based on MSI data MSI Value and NDSI MSI .

[0101] α MSI =α OLI =0.73

[0102] Therefore, whether based on OLI or MSI data, in the typical grassland area of ​​Hulunbuir, Inner Mongolia, the vegetation index formula after removing the soil background is:

[0103]

[0104] Step S4: Use the surface reflectance to preprocess the data and extract multiple spectral characteristic vegetation indices, including NDSI, NDVI, EVI, SAVII, etc. The calculation formulas for different vegetation indices are:

[0105]

[0106]

[0107]

[0108]

[0109] Among them, BluE, Red, NIR, and SWIR1 are the DN values ​​of the blue light, red light, near infrared, and short-wave infrared bands, respectively.

[0110] Step S5: Taking the biomass observation value of the sample plot obtained in step S2 as the dependent variable and the different vegetation indices NDSI, NDVI, EVI, SAVI and NDWI in the corresponding geographical location as the driving variables, a statistical regression model was constructed, and the MAE, RMSE, R 2 , Bias to evaluate the model accuracy, and select the model with the highest estimation accuracy as the grassland biomass inversion model. The following indicators are used to evaluate the accuracy of different models:

[0111]

[0112]

[0113]

[0114] The results show that no matter whether MSI or OLI data is used, the model based on NDSI is more robust than NDVI, EVI, SAVI and NDWI.

[0115] Through specific examples 1 and 2, we can know that: 1. This method can use the data set of a specific time period (a certain year or a specific month) to model and predict the grassland biomass in other years or months, and use the measured data to calculate MAE, RMSE, R 2 , Bias, etc., to evaluate the scalability of grassland biomass model in time and space. 2. This scheme can also use the data set of a certain grassland type or a specific area to model, predict the grassland biomass of other types or areas, and use the measured data to calculate MAE, RMSE, R 2 , Bias, etc., to evaluate the spatial applicability of grassland biomass models.

[0116] The above are only embodiments of the present invention, and the common knowledge such as the known specific structures and / or characteristics in the scheme are not described in detail here. It should be pointed out that for those skilled in the art, several deformations and improvements can be made without departing from the structure of the present invention, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. A method for improving grassland biomass inversion accuracy and adaptability based on SWIR, characterized by: The steps include: S1. Obtain multi-source remote sensing images of the study area and preprocess them to obtain surface reflectance preprocessing data; S2. Refer to the ESA authenticity verification framework, design ground measurement plots and standard sampling units, measure representative soil spectra and grassland biomass, and obtain soil spectral curves and field measurement data of grassland biomass at different scales in the study area; S3. Construct vegetation index and parameters to remove soil background influence; S4, using the surface reflectance to preprocess the data, extracting multiple spectral characteristic vegetation indices at the same time, and obtaining the biomass observation value of the sample plot; S5. Perform statistical regression on the sample plot biomass observation values ​​obtained in step S4 and NDSI and other vegetation indices, select the model with the highest estimation accuracy as the grassland biomass inversion model, and perform accuracy evaluation to verify the accuracy and applicability of the grassland biomass inversion model.

2. The method for improving grassland biomass inversion accuracy and adaptability based on SWIR according to claim 1, characterized in that: The preprocessing method of step S1 includes radiation correction, geometric correction and atmospheric correction.

3. The method for improving grassland biomass inversion accuracy and adaptability based on SWIR according to claim 2 is characterized in that: The specific method of step S1 is as follows: S1.

1. Perform radiation correction on multispectral images according to the absolute radiation calibration coefficient and convert the original radiation value into apparent radiation brightness; S1.

2. Geometric correction and geometric precision correction of remote sensing images from different sources by using ground control points; S1.

3. Use the atmospheric radiation transfer model 6S to calculate and obtain the atmospheric correction coefficient. Combine the apparent radiation brightness image and the atmospheric correction coefficient to obtain the surface reflectance preprocessing data.

4. The method for improving grassland biomass inversion accuracy and adaptability based on SWIR according to claim 1, characterized in that: The specific method of step S2 is as follows: use a ground spectrometer to measure the spectral curve of representative soil, and use the harvesting method to measure 1m 2 The grassland biomass of the sampling unit was upscaled using the weighted average method to obtain field measurement data of grassland biomass at different scales.

5. A method for improving grassland biomass inversion accuracy and adaptability based on SWIR according to claim 1, characterized in that: The vegetation index formula for removing soil background in step S3 is: Where α=(SWIR t -NIR t ) / (SWIR t -RED t ), SWIR t 、NIR t ,RED t It is the soil reflectance value of the soil type in the study area in the shortwave infrared, near infrared and red light bands. When the soil spectral measurement value is default, the ASIS Global Soil Spectral Library data is used.

6. A method for improving grassland biomass inversion accuracy and adaptability based on SWIR according to claim 1, characterized in that: The spectral characteristic vegetation index in step S4 includes the normalized vegetation index NDVI, the enhanced vegetation index EVI, the soil adjusted vegetation index SAVI, and the normalized water index NDWI. The calculation formulas of different vegetation indices are: Among them, BluE, Red, NIR, and SWIR1 are the DN values ​​of the blue light, red light, near infrared, and short-wave infrared bands, respectively.

7. A method for improving grassland biomass inversion accuracy and adaptability based on SWIR according to claim 1, characterized in that: The specific method of step S5: The biomass observation value of the sample plot obtained in step S4 is used as the dependent variable, and the different vegetation indices NDSI, NDVI, EVI, SAVI and NDWI in the corresponding geographical location are used as driving variables to build a statistical regression model. 2 , Bias were used to evaluate the model accuracy, and the model with the highest estimation accuracy was selected as the grassland biomass inversion model.

8. The method for improving grassland biomass inversion accuracy and adaptability based on SWIR according to claim 7, characterized in that: The calculation formula of the accuracy evaluation index is as follows: Among them, MAE, RMSE, R 2 , Bias are mean absolute error, root mean square error, determination coefficient and bias, which are used to evaluate the accuracy and temporal and spatial applicability of the model; X model,i is the biomass of plot i calculated by the model, X obs,i is the measured biomass of plot i, and N is the number of plots used for precision evaluation.

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