http://tbrs.arizona.edu/project/MODIS/compositing.php

modis植被指数算法是基于像元进行运算的，并且采用16天的多次观测从而产生一个合成的植被指数。

16天观测周期合成原因：传感器轨道重叠并且一天可以多次观测，16天中，最多可以进行64次观测，但是由于云的存在以及传感器的空间覆盖范围限制，观测的次数从0到64，在赤道附近有较少的观测次数。当16天的数据被收集之后，modis植被指数算法用一个基于质量、云和观测几何滤波器的对进行数据滤波，只有高质量的、无云的滤波数据被用来进行合成，被云污染并且远离天底的像元被认为是低质量的数据，而无云的、很少大气气溶胶的天顶观测像元代表最高质量的像元。这样可用来进行合成的像元数量是很少的，一般的少于10，更多的时候是少于5，尤其是当考虑到平均全球云覆盖为50％－60％时

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合成方法的目的是选择最佳的观测数据，这种方法应该能保证植被指数值的时空一致性。modis植被指数合成算法有两种：

• CV-MVC: constrained-view angle - maximum value composite,
• MVC: maximum value composite.

应用那一种依靠观测像元的数量和质量，MVC最大值合成和NOAA AVHRR-NDVI是相似的，选取观测像元的最大NDVI值作为合成时期的植被指。MVC在用没有进行大气校正的NOAA AVHRR-NDVI数据时是一种有效的合成方法(Holben, 1986)。MVC方法对于未做大气校正的资料还是最好的方法，也是目前业务上使用的主要方法。 这个方法减少了云和多气溶胶的像元的选择，并且传感器观测角的影响并不像大气对像元的影响那么大（sensor view angle influences are not as strong in pixels uncorrected for atmosphere）、许多研究已经显示MVC方法去选择大的观测角和太阳高度角下的像元，而她们并不总是无云的。在前向散射方向上远离星下点和在晴空条件下观测的像元被优先选择，这是由于植被表面的强烈的各向异性的原因，这样MVC方法选择的像元其NDVi值一般都大于星下点的值

Holben, B.N., 1986, Characterization of maximum value composites from temporal AVHRR data, Int. J. Remote Sensing, 7:1417-1434.

在modis数据中，由于反射率值的大气校正先于合成和植被指数计算，大气效应算法校正以后，其表面各向异性效应更加突出。在这种情况下，MVC方法将会急剧的增加远离星下点像元的选择，尤其是open canopies，当倾斜观测时总是表现出更高的NDVI。而CV－MVC和BRDF合成技术可以限制用MVC进行选择时较强烈的角度变化，CV－MVC比较两个最高的NDVI并选择离天底最近的观测数据来表示16天合成，这有利于减少合成产品在时空上的不连续性，NDVI和EVI都是利用相同的观测像元进行计算，没有分离最大EVI的方法

MVC在近朗伯体表面的假定条件下效果很好，这时像元的变化主要是大气污染和光学路径的变化引起的，但是它的主要缺点是不适于各向异性表面，各种地表类型因叶冠结构、阴影和背景贡献等都能导致双向光谱特性，比值植被指数并不能消除依赖于双向反射率分布函数（BRDF）响应的表面各向异性。大气通过增加远离星下点的观测像元的光学路径抵消地面BRDF信号。前向散射产生较高的NDVI值，后向散射相反。因此选择的NDVI最大值与地表和大气的双向特性有关，当朗伯体为各向异性的表面所取代时，MVC选择结果变的不可预料。MVC倾向于选择最“晴空”的像元，但不一定必然选择最接近于星下点、大气污染最小的像元。尽管如果对资料进行了大气校正，NDVI倾向于增加，但最大的NDVI并不一定是大气订正最好的指标。

如果有好的观测数据可以得到，那么植被指数则利用这些数据进行计算。如果没有观测资料通过初始数据的筛选，那么MVC技术被用来作为CV－MVC方案的备选，最大的NDVI像元被选而不管数据的质量。Examples of the 16-day, 1 km composited NDVI and EVI products along with an EVI QA imageand 500m products

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BRDF方案是一种更加精细和限制的技术，所有的二向反射率观测数据被插到同一到等天底波段反射率值，The Walthall semi-empirical BRDF model被用于BRDF inversion scheme

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这种模型适合用最小平方程序去估算等天底观测的反射率值。经过初始筛选之后，至少需要5个高质量的数据用于模型反转。如果以内插值替换的反射率值在MVC选择NDVI规定的范围之内，则认为这个结果是合乎要求的

BRDF合成方案也有缺陷，它不仅需要5天清洁像元，而且还依赖于云掩模的精度，由于等天底值是从5个或者更多的像元来插值获取的，一个被云污染(residual cloud)的像元将会危害整个被计算的天底值，遗憾的是植被对云（雨）是最敏感的，这就限制了BRDF反转程序只能应用到干旱和云量较少的地区。因此，目前BRDF模型已经被取消关掉，直到对它的应用进行更完整的分析和评估完成

The MODIS VI algorithm operates on a per-pixel basis and relies on multiple observations over a 16-day period to generate a composited VI. Due to sensor orbit overlap and multiple observations in a single day, a maximum of 64 observations over a 16-day cycle may be collected, however, due to the presence of clouds and actual sensor spatial coverage, this number will range between 0 and 64 with fewer observations near equatorial latitudes. Once all 16 days of observations are collected, the MODIS VI algorithm applies a filter to the data based on quality, cloud, and viewing geometry (see figure). Only the higher quality, cloud-free, filtered data are retained for compositing. Cloud-contaminated pixels and extreme off-nadir sensor view angles are considered lower quality while cloud-free and nadir-view pixels with minimal residual atmospheric aerosols represent the best quality pixels. MODIS is a whiskbroom sensor that causes the pixel size to increase with scan angle by as much as a factor of four. Nadir-view pixels possess minimal distortions and match the extensive set of spaceborne (e.g. Landsat), airborne (e.g. AVIRIS), and ground-based field measurements routinely made at nadir-view throughout terrestrial surfaces. The number of acceptable pixels over a 16-day compositing period is thus, further reduced and is typically less than 10 and often less than 5, especially when one considers a mean global cloud cover of 50 - 60%.

The goal of compositing methodologies is to select the best observation, on a per pixel basis, from all the retained filtered data, to represent each pixel over the 16-day compositing period. The methodology should provide spatial and temporal consistency in VI values on an operational basis and be consistent with the goals of developing a long-term time series of VI values such that no biases detrimental to the time series record are introduced. The MODIS VI compositing algorithm consists of two components:

• CV-MVC: constrained-view angle - maximum value composite,
• MVC: maximum value composite.

The technique employed depends on the number and quality of observations. The maximum value composite (MVC) is similar to that used in the NOAA AVHRR-NDVI (Pathfinder) product, in which the pixel observation with the highest NDVI value is selected to represent the compositing period (16 days). The MVC method is an efficient method of compositing when applied to AVHRR-NDVI data that is not corrected for atmosphere (Holben, 1986). The method minimizes the selection of cloudy and heavy aerosol pixels and sensor view angle influences are not as strong in pixels uncorrected for atmosphere. Many studies, however, have shown the MVC method to select pixels with large view and solar zenith angles, which may not always be cloud-free. Pixels from off-nadir views in the forward scatter direction and under clear atmosphere conditions are preferentially selected due to the strong anisotropy of many vegetated surfaces. The MVC approach thus generally selects pixels with NDVI values greater than the nadir value.

In the MODIS case, surface anisotropy effects are more pronounced since reflectance values are atmospherically corrected prior to compositing and VI computation. The MVC method, in this case, will dramatically increase the selection of off-nadir pixels, particularly over open canopies, which exhibit higher NDVI values when viewed obliquely. The CV-MVC and BRDF compositing techniques are designed to constrain the strong angular variations encountered in the MVC selection method. The CV-MVC compares the two highest NDVI values and selects the observation closest to nadir view to represent the 16-day composite cycle. This helps to reduce spatial and temporal discontinuities in the composited product. Both the NDVI and EVI are computed using the same pixel observation, i.e., there is no separate maximum EVI methodology.

If only one good observation is available, then the VIs are computed from this observation. If no observations pass the initial data screening, then the MVC technique is used as the final backup to the CV-MVC schemes such that the highest NDVI pixel is selected, regardless of data quality, to complete a composite image. Examples of the 16-day, 1 km composited NDVI and EVI products along with an EVI QA image and 500m products

Experimental Compositing Approaches

The BRDF scheme is a more elaborate and constrained technique in which all bidirectional reflectance observations, of acceptable quality, are utilized to interpolate to their nadir-equivalent band reflectance values from which the VI is computed and produced. The Walthall semi-empirical BRDF model is utilized for the BRDF inversion scheme,

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The model is fitted to the observations by a least squares procedure on a per-pixel basis to estimate nadir view equivalent reflectance values. At least five good quality observations, after the initial screening process, are required for model inversion. The fitting results are considered to be satisfactory if the interpolated reflectance values are within a range specified by the MVC-selected NDVI.

The BRDF composite scheme has the disadvantage of not only requiring five clear pixels, but is also highly dependent on the accuracy of the cloud mask. Since the nadir equivalent value is interpolated from five or more pixels, one contaminated (residual cloud) pixel will compromise the final computed nadir value. Unfortunately, vegetation is most active when clouds (rainfall) are most prevalent and this limits the geographic extent of the BRDF inversion procedure to dry periods and areas with low cloud cover. As a result, the BRDF module is currently turned off until a more thorough analysis and evaluation of its utility can be completed.

Useful References

Cihlar, J., Ly, H., Li, Z., Chen, J., Pokrant, H., and Huang, F., 1997, Multitemporal, multichannel AVHRR data sets for land biosphere studies: artifacts and corrections, Remote Sens. Environ., 60:35-57.

Cihlar, J., Manak, D., and Voisin, N., 1994, AVHRR bidirectional reflectance effects and compositing, Remote Sens. Environ., 48:77-88.

Goward, S.N., Markham, B., Dye, D.G., Dulaney, W., and Yang, J., 1991, Normalized difference vegetation index measurements from the Advanced Very High Resolution Radiometer, Remote Sens. Environ., 35:257-277.

Holben, B.N., 1986, Characterization of maximum value composites from temporal AVHRR data, Int. J. Remote Sensing, 7:1417-1434.

Roderick, M., Smith, R., and Lodwick, G., 1996, Calibrating long-term AVHRR-derived NDVI imagery, Remote Sens. Environ., 58:1-12.

van Leeuwen, W.J.D., Huete, A.R., and Laing, T.W., 1999, MODIS vegetation index compositing approach: a prototype with AVHRR data, Remote Sens. Environ., 69:264-280.

Walthall, C.L., Norman, J.M., Welles, J.M., Campbell, G., and Blad, B.L., 1985, Simple equation to approximate the bidirectional reflectance from vegetative canopies and bare soil surfaces, Appl. Opt.,24: 383-387.