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International Journal of Remote Sensing Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tres20
Improving the estimation of noise from NOAA AVHRR NDVI for Africa using geostatistics a
b
A. Chappell , J. W. Seaquist & L. Eklundh
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Telford Institute of Environmental Systems, Division of Geography, School of Environment and Life Sciences , University of Salford , Manchester, M5 4WT, England, UK b
Department of Physical Geography , Lund University , Sölvegatan 13, Lund, S-223 62, Sweden Published online: 25 Nov 2010.
To cite this article: A. Chappell , J. W. Seaquist & L. Eklundh (2001) Improving the estimation of noise from NOAA AVHRR NDVI for Africa using geostatistics, International Journal of Remote Sensing, 22:6, 1067-1080 To link to this article: http://dx.doi.org/10.1080/01431160120633
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int. j. remote sensing, 2001, vol. 22, no. 6, 1067± 1080
Improving the estimation of noise from NOAA AVHRR NDVI for Africa using geostatistics A. CHAPPELL² Telford Institute of Environmental Systems, Division of Geography, School of Environment and Life Sciences, University of Salford, Manchester M5 4WT , England, UK
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J. W. SEAQUIST and L. EKLUNDH Department of Physical Geography, Lund University, SoÈlvegatan 13, S-223 62, Lund, Sweden (Received 5 February 1998; in ® nal form 5 May 2000) Abstract. The accuracy of NOAA AVHRR NDVI data can be poor because of interference from several sources, including cloud cover. A parameter of the variogram model can be used to estimate the contribution of noise from the total variation in an image. However, remotely sensed information over large areas incorporates non-stationary (regional ) trend and directional eVects, resulting in violation of the assumptions for noise estimation. These assumptions were investigated at ® ve sites across Africa for a range of ecological environments over several seasons. An unsupervised spectral classi® cation of multi-temporal NDVI data partially resolved the problem of non-stationarity. Quadratic polynomials removed the remaining regional trend and directional eVects. Isotropic variograms were used to estimate the noise contributing variation to the image. Standardized estimates of noise ranged from a minimum of 18.5% in west Zambia to 68.2% in northern Congo. Cloud cover and atmospheric particulates (e.g. dust) explained some of the regional and seasonal variations in noise levels. Image artifacts were also thought to contribute noise to image variation. The magnitude of the noise levels and its temporal variation appears to seriously constrain the use of AVHRR NDVI data.
1.
Introduction One of the primary sources of data for famine early warning systems (Ottichilo 1993 ) is the Advanced Very High Resolution Radiometer (AVHRR) on the National Oceanic and Atmospheric Administration (NOAA) series of polar orbiting satellites. The red and near-infrared (NIR) bands from the AVHRR sensor are often used to compute the Normalized DiVerence Vegetation Index (NDVI). This index is related empirically to green leaf biomass (Tucker et al. 1985), and is an established method for monitoring regional to global scale photosynthetic activity from space (Prince 1991 ). The NDVI data from NOAA AVHRR are used for famine early warning programmes, land cover classi® cations and global change modelling. Such ² e-mail:
[email protected] Internationa l Journal of Remote Sensing ISSN 0143-116 1 print/ISSN 1366-590 1 online Ñ 2001 Taylor & Francis Ltd http://www.tandf.co.uk/journals
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investigations commonly use maximum value composite (MVC) images (Holben 1986 ) of the NDVI data. The MVC procedure was designed to reduce the eVect of cloud, atmosphere and variable illumination on the NDVI. However, signi® cant residual eVects remain. Optically thick clouds might decrease NDVI values by up to 0.7 (Los et al. 1994 ) as they re¯ ect nearly equally in the red and NIR wave bands (Moody and Strahler 1994 ). Cloud shadow suppresses NDVI values signi® cantly because of its in¯ uence on the NIR band (Simpson and Stitt 1998). Atmospheric constituents leading to Rayleigh and Mie scattering may either increase or decrease the NDVI respectively. Absorption by oxygen, ozone, water vapour and other trace gasses also suppress NDVI values (Holben 1986). Moroever, surfaces re¯ ect radiation diVerently in diVerent directions (anisotropy) because of the structure of the surface and the optical properties of the scattering media. This contributes another source of uncertainty in the NDVI values. The AVHRR records re¯ ected radiation from a wide range of satellite scan angles (Õ 56ß to 56ß ) and solar zenith angles (20ß to 90ß ) (Los et al. 1994 ). The bi-directional re¯ ectance factor (BRDF) describes re¯ ected radiation from the surface as a function of solar zenith angle, satellite scan angle and the angle between the Sun and the satellite sensor. The NDVI data are dependent on the BRDF. The MVC algorithm is implemented without regard to surface anisotropy and a large NDVI value might result from directional eVects rather than atmospheric ones (Meyer et al. 1995 ). Another possible artifact caused by MVC is that surface biomass might be overestimated during periods of rapid plant growth or senescence. This problem is exacerbated as the compositing period increases (Meyer et al. 1995 ). Other sources of error that might be introduced arti® cially by the MVC method include the mis-registration of pixels (Holben 1986). Finally, variation in soil colour (Huete 1989) in areas of partial vegetation cover introduce error to NDVI values. Several studies have suggested that these factors might limit the accuracy of the NOAA AVHRR NDVI data for monitoring biomass and reduce its capabilities for famine prediction (e.g. Eklundh 1995). However, few studies have quanti® ed the magnitude or spatial variation of unwanted interference eVects across Africa. Various methods exist for calculating noise in satellite data (Gao 1993, Aleksanina 1994 ). Curran and Dungan (1989) used geostatistics to estimate the amount of noise in AVIRIS (Airborne Visible/Infra Red Imaging Spectrometer) data. The technique was applied successfully to NOAA AVHRR data (Eklundh 1995 ), and was considered recently to be the best method available for noise estimation using remote sensing (Atkinson 1997 ). The aim of this paper is to assess the importance of noise to the MVC NDVI images of NOAA AVHRR data. The primary objective is to address the extent to which the assumptions of geostatistics are violated when estimating noise in MVC NDVI images of NOAA AVHRR data. The secondary objective is to examine the relative contribution of noise to the NDVI data over Africa to assess the accuracy of the NDVI data for future applications, e.g. biomass monitoring. An attempt will also be made to identify the main factors responsible for interference with the NDVI signal in order to suggest improvements for the NDVI data across Africa. 2.
Geostatistical estimation of image noise In essence, spatial data are deterministic; they are a function of their position in space, but their variation is so irregular that the best way of treating them is as if they were random variables. The spatial variation of continuous random variables
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can be described and estimates of their values at un-sampled locations provided by a suite of statistical techniques known as geostatistics. These techniques are based on Regionalized Variable Theory (Matheron 1971), which treats spatial properties as random functions in a stochastic manner rather than deterministically. The spatial model underpinning the theory is that the variation in an attribute Z may be de® ned by a stochastic component and a constant. Following Oliver et al. (1989) this may be written as: Z (x)= mR + e(x)
(1)
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where x denotes the spatial coordinates, mR is the mean in a region R and the quantity e(x) is the spatially dependent random variable. This last component has a mean of zero, E[e(x)]= 0
(2)
and a variance de® ned by var[e(x)Õ
e(x+ h)]= E [{e(x)Õ
2
e(x+ h)} ]= 2c(h)
(3)
where h is a vector, the lag, that separates the two places x and x+ h in both distance and direction. Thus, the variance of e(x) depends on the separation h and not on the actual position of x. This assumes that the variable is second-order stationary and that the mean, variance, covariance and variogram exist. Matheron (1971) realized that second-order stationarity was too strong for many spatial variables and reduced the assumptions to stationarity of the mean and variance of the diVerences. This is the intrinsic hypothesis. Equation (3) is then equivalent to: var[z(x)Õ
z(x+ h)]= E[{z(x)Õ
2
z(x+ h)} ]= 2c (h)
(4)
The semi-variance, c (h), is half the expected squared diVerence between two values separated by h. The function that relates c to h is the semi-variogram or, more commonly, the variogram. The intrinsic hypothesis assumes weak local stationarity, i.e. within the region R. There are situations where this does not hold. In large regions the mean values of variables change predictably or deterministically from place to place. This is evidence of regional trend and the assumptions of stationarity no longer hold (Chappell 1995 ). Del® ner (1976) suggested that trend could be removed by ® tting a polynomial to the geographic coordinates. The variogram can then be estimated from the residuals, which are random variables (Olea 1975, 1977), of the trend. The usual formula for computing the variogram is ( h)
1 M (5) {z(x i )Õ z(x i + h)}2 2M (h) i= 1 where M is the number of pairs of observations (pixels) separated by the lag h. Thus, by increasing h an ordered set of values (semi-variances) is produced and this set constitutes the sample variogram (Webster and Oliver 1990). The initial slope of the variogram indicates the intensity of change in a property with distance and the rate of decrease in spatial dependence. Where the full extent of variation for a region has been encompassed, the variogram reaches a maximum, called the `sill variance’, where it becomes ¯ at (® gure 1). The lag distance at which the sill is reached is the `range’, or limit of spatial dependence. The variogram often has a positive intercept on the ordinate called the `nugget variance’. The nugget c ( hÃ)=
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Figure 1.
Bounded (a), unbounded ( b) and pure nugget (c) variogram functions.
variance arises partly from measurement error, purely random variation, but mainly from the spatially dependent variation that occurs over distances much smaller than the image pixel. Where features of the variogram vary with direction this suggests that the variation is anisotropic. Anisotropy arises from diVerent degrees of variation in diVerent directions that might repeat in the processes controlling the variation. Our approach for estimating noise follows the work of Curran and Dungan (1989) and assumes that the nugget variance corresponds to the spatially unresolved variation in the image. Intuitively this is reasonable because the nugget variance is composed almost entirely of random sensor noise and intra-pixel variability (Curran and Dungan 1989 ). The square root of the nugget variance was used by Curran and Dungan (1989) to estimate the standard deviation of the random noise and intrapixel variation. They calculated the signal-to-noise ratio (SNR) by dividing the mean value (z) of an AVIRIS image by the square root of the nugget variance (c0 ): 0.5
SNR= z/(c0 )
(6)
The total variance of the image can be used to standardize noise by dividing the square root of the nugget variance by the standard deviation of the image and expressing it as a percentage (Eklundh 1995). The standardized noise statistic can be used to directly compare the estimates from diVerent images. The main assumptions of the geostatistical approach to estimating noise are as follows. (1) The pixel values calculated over a large area must be stationary over some local neighbourhood. Remotely sensed NDVI data covering large areas are likely to contain spatial trends in green leaf biomass mainly because of variations in climatic gradients, causing non-stationarit y and directional eVects in the NDVI data. Discontinuities in NDVI corresponding to ecotones or cloud shadow might extend over large distances and contribute to non-stationarit y in the data. (2) The nugget variance should be independent of directional variation, which assumes that variograms calculated for diVerent directions should be similar (isotropic). Single-date NDVI images are inherently anisotropic due to
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variable Sun± sensor± target geometry. Some of this anisotropy is removed by the MVC process as pixels from various dates are re-assembled into one image. These considerations suggest that the ® rst two main assumptions of the method for estimating noise are not satis® ed using MVC images of NOAA AVHRR NDVI. (3) The sensor must have a ® xed spatial resolution: intra-pixel variation and nugget variance depend on spatial resolution. The condition of ® xed spatial resolution is generally not met for sensors with wide scan angles such as the NOAA AVHRR. This eVect is partially compensated by the MVC criterion by excluding pixels from scan angles larger than 42ß . Furthermore, the point spread function of the AVHRR sensor means that the contribution of the spatially autocorrelate d NDVI variance to the semi-variance at small lags is negligible in relation to the spatially uncorrelated variance. The implication is that the semi-variance is nearly equal to the noise variance at small lags (Curran and Dungan 1989 ). (4) The pixel values are not randomly arranged and have spatial dependence. Random information in an image caused, for example, by seasonal changes in rainfall and manifested in vegetation patterns for diVerent images acquired at diVerent times of the year might aVect the nugget variance (Curran and Dungan 1989). Normalizing the estimate of noise by the standard deviation of the image can partially compensate for this eVect (Eklundh 1995). Moreover, the NDVI is a nonlinear index that saturates at larger values of the NDVI, so providing a potential source of similarity between pixel values where none might exist. (5) The nugget variance does not depend on the structure of the spatial dependence. This assumption is rarely satis® ed because of the uncertainty that the measured underlying variation has a variogram with a nonlinear form near the origin (Atkinson 1997). However, Curran and Dungan (1989) suggest that violation of this assumption is minimized by the similarity of pixels at small lags due to the point spread function.
3. Methods 3.1. NOAA/NASA Path® nder L and data set Twelve monthly MVC images of NDVI were extracted from the NOAA/NASA Path® nder AVHRR Land (PAL) data set over Africa to establish a multi-temporal database for 1992. The PAL data were generated in a consistent way and include post-¯ ight sensor calibration, correction for sensor drift and atmospheric corrections for Rayleigh scattering and ozone absorption. The eVects of aerosol and water vapour concentrations were not taken into account as these vary widely over time and space (James and Kalluri 1994, Smith et al. 1997). Pixels with scan angles larger than 42ß were excluded by the MVC procedure to minimize radiometric and geometric distortion. Known errors in the PAL data relevant to this investigation include: (1) underestimation of the atmospheric corrections for Rayleigh scattering and ozone absorption; (2) visible and NIR channels not normalized for variation in solar zenith angle; and (3 ) incorrect calculation of the solar zenith angle. Subsequent investigations have revealed that diVerences in NDVI computed from uncorrected and corrected data are of the order of 0.02 NDVI units (Smith et al. 1997 ).
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3.2. Image classi® cation and site selection An unsupervised spectral classi® cation using a migrating means algorithm (Richards 1995), which minimized and maximized variation within and between classes respectively, was conducted with the PAL data. It was performed to aid the selection of relatively homogenous sites so that the variation in NDVI was minimized. Five test sites were selected from the classi® cation (® gure 2) to provide a range of ecological environments and seasonal variation in NDVI (table 1). All sites were 20 pixels by 20 pixels (160 kmÖ 160 km) to make extraction straightforward, and to provide su cient data (400 pixels) to compute reliable variograms. Any class that was not large enough or that might introduce edge eVects into the site was excluded. The location of the centre of each site is shown in table 1 and these remained
Figure 2.
Multi-temporal classi® cation of NOAA AVHRR NDVI for Africa showing the locations used to estimate noise.
Table 1.
Location of the centre of each study site (160 kmÖ 160 km), its ecotone and the variance explained by the polynomial ® tted to the NDVI data. Location
Site 1 2 3 4 5
Country N. Sudan Sudan/Chad N. Congo N.E. Angola W. Zambia
Ecotone Desert Semi-desert Rainforest Sub-rainforest Savannah
Latitude 19.5ß 11.3ß 1.8ß 7.5ß 16.0ß
N N N S S
Longitude 24.5ß 21.0ß 21.6ß 20.1ß 24.1ß
E E E E E
Polynomial variance (%) 82.14 52.78 23.91 39.92 53.76
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constant for the four time periods selected (January, April, July and October). This provided 20 NDVI MVC windows. 3.3. Variogram analysis Experimental variograms of NDVI were computed from the data at each site. Most variograms suggested that there was regional trend in the data and evidence of non-stationarit y (§4.1). The trend was removed from the data by ® tting secondorder (quadratic) polynomials to the coordinates for each region (table 1). The polynomial was ® tted using nonlinear regression that used an iterative numerical search procedure based on the Marquardt algorithm to achieve a least-squares solution. The experimental variograms were again computed from the residuals of the ® tted polynomial, and models were ® tted to them using a weighted least-squares technique. The best model had the smallest sum of squares between the experimental variogram and the ® tted model. Power, spherical and exponential models were ® tted as follows. a
Power: c= c0 + b(h) Spherical:
c (h)= c0 + c1
G
3h 3 1/2(h/ a ) 2a
= c0 + c1
H
(7) for 0
