Research on the Mutual Effect of the Parameters on Inversion of Canopy Reflectance Model
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Some bio-physical parameters(e.g.leaf area index,LAI) are often inverted using remote sensing data for its large cover scope,high temporal and spatial resolution.The common way of mapping LAI is through the inversion of physically based canopy-reflectance(CR) models using the optimization methods.The information of remote sensing data is usually not enough for the LAI inversion;furthermore,the inversion problem is ill-posed because of many unknown parameters and the relatively insufficient information in remote sensing data.It is necessary to make suitable inversion strategy(such as which parameter(s) should be inverted) for high accuracy of parameters estimation.We should learn the factors which affect the inversion result in order to design the suitable inversion strategy.Different from the research of parameter sensitivity for suitable inversion strategy,we made progress in the inversion process.For the information of the inversion process,some key points are needed to investigate,such as the factors affecting the parameters estimation,the mutual effect of different parameters in inversion process and so on.In the paper,we investigated the factors which affect the parameter estimation from the inversion process aiming at directing the parameter inversion.One of the accuracy indices for the inversion result is the root mean square error(RMSE).For the inversion result,the smaller RMSE is,the higher inversion accuracy is.We investigated the formulae of the RMSE based on the physically based canopy-reflectance model.Through mathematical formulae and physical mechanism,we can know that the factors affecting the RMSE consist of canopy reflectance data quality,the sensitivity of parameters and the correlation of the parameter sensitivity.That is to say,as to the sensitivity of parameters,not only the parameter sensitivity but the correlation of the parameter sensitivity the factors affect the parameters inversion accuracy.In other words,the relative sensitivity of the parameter has effect on the parameter inversion.We should make two kinds of progress for high accuracy parameter inversion.One is about the quality of canopy reflectance data.Remote sensing data are often contaminated with noise from various sources,such as radiation calibration,atmosphere correction,geometric registration and some random noises.The other is the sensitivities of the parameters and the correlation of the parameter sensitivity.We can make the suitable inversion strategy based on both the quality of the canopy reflectance data and the parameters sensitivities.The CR model is the SAIL model and the inversion method is the modified least square method in this paper.We validated the factors which affect the LAI inversion accuracy through LAI inversion based on simulated CR data sets.Keywords:
Inverse transform sampling
Root mean square
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Improving the inversion of ocean color data is an ever continuing effort to increase the accuracy of derived inherent optical properties.In this paper we present a stochastic inversion algorithm to derive inherent optical properties from ocean color, ship and space borne data.The inversion algorithm is based on the cross-entropy method where sets of inherent optical properties are generated and converged to the optimal set using iterative process.The algorithm is validated against four data sets: simulated, noisy simulated in-situ measured and satellite match-up data sets.Statistical analysis of validation results is based on model-II regression using five goodness-of-fit indicators; only R 2 and root mean square of error (RMSE) are mentioned hereafter.Accurate values of total absorption coefficient are derived with R 2 > 0.91 and RMSE, of log transformed data, less than 0.55.Reliable values of the total backscattering coefficient are also obtained with R 2 > 0.7 (after removing outliers) and RMSE < 0.37.The developed algorithm has the ability to derive reliable results from noisy data with R 2 above 0.96 for the total absorption and above 0.84 for the backscattering coefficients.The algorithm is self contained and easy to implement and modify to derive the variability of chlorophyll-a absorption that may correspond to different phytoplankton species.It gives consistently accurate results and is therefore worth considering for ocean color global products.
Ocean color
Data set
Goodness of fit
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We describe a methodology to quantify and separate the errors of inherent optical properties (IOPs) derived from ocean-color model inversion. Their total error is decomposed into three different sources, namely, model approximations and inversion, sensor noise, and atmospheric correction. Prior information on plausible ranges of observation, sensor noise, and inversion goodness-of-fit are employed to derive the posterior probability distribution of the IOPs. The relative contribution of each error component to the total error budget of the IOPs, all being of stochastic nature, is then quantified. The method is validated with the International Ocean Colour Coordinating Group (IOCCG) data set and the NASA bio-Optical Marine Algorithm Data set (NOMAD). The derived errors are close to the known values with correlation coefficients of 60-90% and 67-90% for IOCCG and NOMAD data sets, respectively. Model-induced errors inherent to the derived IOPs are between 10% and 57% of the total error, whereas atmospheric-induced errors are in general above 43% and up to 90% for both data sets. The proposed method is applied to synthesized and in situ measured populations of IOPs. The mean relative errors of the derived values are between 2% and 20%. A specific error table to the Medium Resolution Imaging Spectrometer (MERIS) sensor is constructed. It serves as a benchmark to evaluate the performance of the atmospheric correction method and to compute atmospheric-induced errors. Our method has a better performance and is more appropriate to estimate actual errors of ocean-color derived products than the previously suggested methods. Moreover, it is generic and can be applied to quantify the error of any derived biogeophysical parameter regardless of the used derivation.
Atmospheric correction
Data set
Imaging spectrometer
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Kernel (algebra)
Albedo (alchemy)
Matrix (chemical analysis)
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In most recently developed linear kernel-driven BRDF (bidirectional reflectance) models, there are usually 3 unknowns for each band. Usually a least square (LS) approach is employed for inversion. Assuming the observations are well sampled over the viewing hemisphere (viewing zenith angle /spl theta//sub /spl upsi//, azimuthal difference /spl phi/ with the solar zenith angle /spl theta//sub i/) for a single /spl theta//sub i/, as in most cases of space-borne multiangular observations such as POLDER and MISR, the LS solution can be obtained for the three unknowns. It was once hoped that if the kernel-driven model has sound physical meaning, the three parameters estimated from such good 2-D sampling can be used over the whole 3-D (/spl theta//sub i/, /spl theta//sub /spl upsi//, /spl phi/) bidirection space (3DBS for short). However, inversion of 395 BRDF datasets acquired by POLDER of CNES (France) shows that when we apply the inversion results over the whole 3-D space, for example, at a far different /spl theta//sub i/, the estimation errors in parameters will propagate differently and thus yield different pattern of prediction errors, independent of the soundness of the BRDF model physics. Our analysis concludes that general knowledge of BRDF shapes of the land surface has to be applied to constrain the inversion of single (or narrow-range) /spl theta//sub i/ multiangular observations.
Zenith
Kernel (algebra)
Position (finance)
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Ceilometer
Backscatter (email)
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The inverse ocean color problem, i.e., the retrieval of marine reflectance from top-of-atmosphere (TOA) reflectance, is examined in a Bayesian context. The solution is expressed as a probability distribution that measures the likelihood of encountering specific values of the marine reflectance given the observed TOA reflectance. This conditional distribution, the posterior distribution, allows the construction of reliable multi-dimensional confidence domains of the retrieved marine reflectance. The expectation and covariance of the posterior distribution are computed, which gives for each pixel an estimate of the marine reflectance and a measure of its uncertainty. Situations for which forward model and observation are incompatible are also identified. Prior distributions of the forward model parameters that are suitable for use at the global scale, as well as a noise model, are determined. Partition-based models are defined and implemented for SeaWiFS, to approximate numerically the expectation and covariance. The ill-posed nature of the inverse problem is illustrated, indicating that a large set of ocean and atmospheric states, or pre-images, may correspond to very close values of the satellite signal. Theoretical performance is good globally, i.e., on average over all the geometric and geophysical situations considered, with negligible biases and standard deviation decreasing from 0.004 at 412 nm to 0.001 at 670 nm. Errors are smaller for geometries that avoid Sun glint and minimize air mass and aerosol influence, and for small aerosol optical thickness and maritime aerosols. The estimated uncertainty is consistent with the inversion error. The theoretical concepts and inverse models are applied to actual SeaWiFS imagery, and comparisons are made with estimates from the SeaDAS standard atmospheric correction algorithm and in situ measurements. The Bayesian and SeaDAS marine reflectance fields exhibit resemblance in patterns of variability, but the Bayesian imagery is less noisy and characterized by different spatial de-correlation scales, with more realistic values in the presence of absorbing aerosols. Experimental errors obtained from match-up data are similar to the theoretical errors determined from simulated data. Regionalization of the inverse models is a natural development to improve retrieval accuracy, for example by including explicit knowledge of the space and time variability of atmospheric variables.
Ocean color
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The University of Nebraska has recently developed a neural network inversion algorithm for the estimation of surface snow properties, viz., surface roughness, wetness, and average grain size. The algorithm uses concurrent measurements of the near-infrared reflectance and millimeter-wave backscatter of the snow surface. The performance of the inversion algorithm was found to be satisfactory under noise-free conditions. However, under operational conditions, noise is invariably present in the data, and the addition of noise causes errors in estimation. The performance of the inversion algorithm was investigated under noise-added conditions. A parameter that was varied was the signal-to-noise ratio. Inversions of free-water content and the grain size were relatively robust, while the surface roughness estimation was very sensitive to added noise. The results of the authors' study can be useful in setting bounds for system performance for accurate snow surface parameter inversion.
Inverse transform sampling
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The model presented here is an improvement over the semiempirical model of Roujean et al. [1992] for estimating the bidirectional reflectance from vegetation. Roujean's model has been considered for global applications because of its simplicity and the underlying physics. However, the model does not adequately describe the hotspot near the Sun's illumination direction. In this paper, a hotspot kernel based on a canopy gap size distribution theory developed by Chen and Leblanc [1997] is used to modify Roujean's model. The modified model requires two additional coefficients for controlling the hotspot magnitude and width, respectively. It is found that the hotspot magnitude coefficient is only weakly dependent on cover type and can be treated as a constant at a given geographical location. The hotspot width parameter is determined by the ratio of the characteristic foliage clump size and canopy height. The ratio varies in a small range across different cover types because the foliage clump size and canopy height are usually correlated. For example, the ratio of leaf size to crop height is similar to the ratio of crown size to tree height. Because of the small variabilities of these parameters, the modified model can be a substantial improvement over the original model by just using best estimates for the parameters. With this hotspot adjustment the simple form of the semiempirical model is preserved for remote sensing applications without additional input requirements. The performance of the modified model is shown using data from the advanced very high resolution radiometers (AVHRR). The results show that the patterns of reflectance distribution with the view angle are similar among all cover types investigated, suggesting that one simple model may be sufficient for global applications. The modified model based on simplified physics with four adjustable coefficients may be adequate for this purpose. The model can be further improved to consider the noncircular hotspot shape. Formulae for this purpose are suggested.
Hotspot (geology)
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This paper presents a method for generating groups of electrostatic images for the estimation of soil parameters in the case of multilayered horizontal soil. The method can be utilized for the interpretation of resistivity sounding measurements of stratified soil. The maximum errors of the calculated resistivity values can also be estimated and are used to validate the soil model. Errors and variations in apparent resistivity values used in the interpretation process can originate from slow convergence in calculations or variations during field measurements, such as local fluctuations in soil resistivity at points of measurements and instruments precision. An estimation of the effect of these variations on the calculated soil model parameters can be used to provide a confidence level in the results. This paper demonstrates the necessity of evaluating the sensitivity of the soil parameters and proposes methods of estimating a confidence level in the soil model. Confidence levels are also used to delimit boundaries during geophysical inversion with respect to the information available in the field measurements. Simulation results are presented for three-layer soil.
Vertical electrical sounding
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