A model for the estimation of fractional vegetation cover based on the relationship between vegetation and soil moisture

Based on surface temperature and the normalized difference vegetation index (NDVI), we calculated the temperature vegetation dryness index (TVDI). Using the relationship between TVDI and NDVI, we established a vegetation–soil moisture response model that captures the sensitivity of NDVI's response to changes in TVDI using a linear unmixing approach, and validated the model using Landsat Thematic Mapper (TM) images acquired in 1997, 2004 and 2006 and a Landsat Enhanced Thematic Mapper Plus (ETM+) image acquired in 2000. We determined the correlations between TVDI and field-measured soil moisture in 2006. TVDI was correlated significantly with soil moisture at depths of 0 to 10 cm and 10 to 20 cm, so TVDI can be used as an index that captures changes in soil moisture at these depths. By using fractional vegetation cover (FVC) data measured in the field to validate the estimated values, we estimated mean absolute errors of 0.043 and 0.137 for shrub and grassland vegetation coverage, respectively, demonstrating acceptable estimation accuracy. Based on these results, it is possible to estimate a region's FVC using the linear unmixing model. The results show bare land coverage values distributed similarly to TVDI values. In mountain areas, grassland coverage mostly ranged from 0.4 to 0.6. Shrub coverage mostly ranged from 0.4 to 0.6. Forest coverage was zero in most parts of the study area.     

Dynamic estimating of wetland vegetation cover based on linear spectral mixture and time phase transformation models

ABSTRACT

Globally, remote sensing is being used to monitor vegetation degradation in areas of concern. In recent years, drought and water shortages have caused significant degradation of the wetland vegetation in Zhalong Wetland of Heilongjiang province, China. This paper employed middle- and high-resolution Landsat images to construct a Linear Spectral Mixture Analysis of the wetland, with the end member extraction verified by feasibility analysis and with vegetation cover data extracted over nearly 30 years. By considering the problem of poor timing with middle- and high-resolution images, this paper proposes a phase-transform method that combines the time advantage of moderate-resolution spectroradiometer images with the spatial advantage of high-resolution Landsat imagery. Based on an intensity analysis model, the temporal and spatial characteristics of vegetation cover in the study area were analyzed using a time scale and the level of vegetation cover. The results show that (1) from 1985 to 2015, the vegetation cover showed an overall tendency to degrade, and (2) vegetation cover was extracted based on the phase transformation and linear spectral mixture models with an accuracy of 0.8628, which is higher than that of traditional remote sensing methods. Improving the prediction accuracy in vegetation transfer is of great theoretical value in relation to global climate change.     

Inversion of vegetation canopy reflectance models for estimating agronomic variables. I. Problem definition and initial results using the suits model

An important but relatively uninvestigated problem in remote sensing is the inversion of vegetative canopy reflectance models to obtain agrophysical parameters, given measured reflectances. The problem is here formally defined and its solution outlined. Numerical nonlinear optimization techniques are used to implement this inversion to obtain the leaf area index using Suits' canopy reflectance model. The results for a variety of cases indicate that this can be done successfully using infrared reflectances at different views or azimuth angles or a combination thereof. The other parameters of the model must be known, although reasonable measurement errors can be tolerated without seriously degrading the accuracy of the inversion. The application of the technique to ground based remote-sensing experiments is potentially useful, but is limited to the degree to which the canopy reflectance model can accurately predict observed reflectances.     

Estimating fractional cover of photosynthetic vegetation, non-photosynthetic vegetation and bare soil in the Australian tropical savanna region upscaling the EO-1 Hyperion and MODIS sensors

Quantitative estimation of fractional cover of photosynthetic vegetation (f_PV), non-photosynthetic vegetation (f_NPV) and bare soil (f_BS) is critical for natural resource management and for modeling carbon dynamics. Accurate estimation of fractional cover is especially important for monitoring and modeling savanna systems, subject to highly seasonal rainfall and drought, grazing by domestic and native animals, and frequent burning. This paper describes a method for resolving f_PV, f_NPV and f_BS across the ~ 2 million km² Australian tropical savanna zone with hyperspectral and multispectral imagery. A spectral library compiled from field campaigns in 2005 and 2006, together with three EO-1 Hyperion scenes acquired during the 2005 growing season were used to explore the spectral response space for f_PV, f_NPV and f_BS. A linear unmixing approach was developed using the Normalized Difference Vegetation Index (NDVI) and the Cellulose Absorption Index (CAI). Translation of this approach to MODerate resolution Imaging Spectroradiometer (MODIS) scale was assessed by comparing multiple linear regression models of NDVI and CAI with a range of indices based on the seven MODIS bands in the visible and shortwave infrared region (SWIR) using synthesized MODIS surface reflectance data on the same dates as the Hyperion acquisitions. The best resulting model, which used NDVI and the simple ratio of MODIS bands 7 and 6 (SWIR3/SWIR2), was used to generate a time series of fractional cover from 16 day MODIS nadir bidirectional reflectance distribution function-adjusted reflectance (NBAR) data from 2000-2006. The results obtained with MODIS NBAR were validated against grass curing measurement at ten sites with good agreement at six sites, but some underestimation of f_NPV proportions at four other sites due to substantial sub-pixel heterogeneity. The model was also compared with remote sensing measurements of fire scars and showed a good matching in the spatio-temporal patterns of grass senescence and posterior burning. The fractional cover profiles for major grassland cover types showed significant differences in relative proportions of f_PV, f_NPV and f_BS, as well as large intra-annual seasonal variation in response to monsoonal rainfall gradients and soil type. The methodology proposed here can be applied to other mixed tree-grass ecosystems across the world.     

Preliminary validation of two temporal parameter-based soil moisture retrieval models using a satellite product and in situ soil moisture measurements over the REMEDHUS network

This study aims to preliminarily validate two newly developed temporal parameter-based surface soil moisture (SSM) retrieval models, namely the mid-morning model and daytime model, using both microwave satellite soil moisture product and in situ SSM measurements over a well-organized soil moisture network named REd de MEDición de la HUmedad del Suelo (REMEDHUS) in Spain. Ground SSM measurements and geostationary satellite observations were primarily implemented to obtain the model coefficients for the two SSM retrieval models for each cloud-free day. These model coefficients were subsequently used to estimate SSM using the Meteosat Second Generation products over the study area. Preliminary verification using both a satellite product and in situ SSM measurements demonstrated that SSM variation can be well detected by both SSM retrieval models. Specifically, a generally similar accuracy (coefficient of determination R²: 0.419–0.379, root mean square error: 0.046–0.051 m³ m^?3, Bias: ?0.020 to ?0.025 m³ m^?3) was found for the mid-morning model and the daytime model with the microwave missions based climate change initiative SSM product, respectively. Moreover, except for the comparable R² (0.614–0.675), a better accuracy (Bias: 0.032–0.044 m³ m^?3, RMSE: 0.043–0.050 m³ m^?3) are achieved for the daytime model and the mid-morning model with network SSM measurements, respectively. These results indicate that the daytime model exhibited generally comparable or better accuracy than that of the mid-morning model over the study area. This study has strengthened the feasibility of using multi-temporal information derived from the geostationary satellites to estimate SSM in future research.     

Investigating the effects of soil moisture on thermal infrared land surface temperature and emissivity using satellite retrievals and laboratory measurements

This study investigates the effects of soil moisture (SM) on thermal infrared (TIR) land surface emissivity (LSE) using field- and satellite-measurements. Laboratory measurements were used to simulate the effects of rainfall and subsequent surface evaporation on the LSE for two different sand types. The results showed that the LSE returned to the dry equilibrium state within an hour after initial wetting, and during the drying process the SM changes were uncorrelated with changes in LSE. Satellite retrievals of LSE from the Atmospheric Infrared Sounder (AIRS) and Moderate Resolution Imaging Spectroradiometer (MODIS) were examined for an anomalous rainfall event over the Namib Desert in Namibia during April, 2006. The results showed that increases in Advanced Microwave Scanning Radiometer (AMSR-E) derived soil moisture and Tropical Rainfall Measuring Mission (TRMM) rainfall estimates corresponded closely with LSE increases of between 0.08-0.3 at 8.6 µm and up to 0.03 at 11 µm for MODIS v4 and AIRS products. This dependence was lost in the more recent MODIS v5 product which artificially removed the correlation due to a stronger coupling with the split-window algorithm, and is lost in any algorithms that force the LSE to a pre-determined constant as in split-window type algorithms like those planned for use with the NPOESS Visible Infrared Imager Radiometer Suite (VIIRS). Good agreement was found between MODIS land surface temperatures (LSTs) derived from the Temperature Emissivity Separation (TES) and day/night v4 algorithm (MOD11B1 v4), while the split-window dependent products (MOD11B1 v5 and MOD11A1) had cooler mean temperatures on the order of 1-2 K over the Namib Desert for the month of April 2006.     

Relationships between vegetation indices,fractional cover retrievals and the structure and composition of Brazilian Cerrado natural vegetation

This study explores the use of the relationship between the normalized difference vegetation index (NDVI) and the shortwave infrared ratio (SWIR32) vegetation indices (VI) to retrieve fractional cover over the structurally complex natural vegetation of the Cerrado of Brazil using a time series of imagery from the Moderate Resolution Imaging Spectroradiometer (MODIS). Data from the EO-1 Hyperion sensor with 30 m pixel resolution is used to sample geographic and seasonal variation in NDVI, SWIR32, and the hyperspectral cellulose absorption index (CAI), and to derive end-member values for photosynthetic vegetation (PV), non-photosynthetic vegetation (NPV), and bare soil (BS) from a suite of protected and/or natural vegetation sites across the Cerrado. The end-members derived from relatively pure 30 m pixels are then applied to a 500 m pixel resolution MODIS time series using linear spectral unmixing to retrieve PV, NPV, and BS fractional cover (F_PV, F_NPV, and F_BS). The two-way interaction response of MODIS-equivalent NDVI and SWIR32 was examined for regions of interest (ROI) collected within protected areas and nearby converted lands. The MODIS NDVI, SWIR32 and retrieved F_PV, F_NPV, and F_BS are then compared to detailed cover and structural composition data from field sites, and the influence of the structural and compositional variation on the VIs and cover fractions is explored. The hyperion ROI analysis indicated that the two-way NDVI–SWIR32 response behaved as an effective surrogate for the two-way NDVI–CAI response for the campo limpo/grazed pasture to cerrado sensu stricto woody gradient. The SWIR32 sensitivity to the NPV and BS variation increased as the dry season progressed, but Cerrado savannah exhibited limited dynamic range in the NDVI–CAI and NDVI–SWIR32 two-way responses compared to the entire landscape, which also comprises fallow croplands and forests. Validation analysis of MODIS retrievals with Quickbird-2 images produced an RMSE value of 0.13 for F_PV. However, the RMSE values of 0.16 and 0.18 for F_BS and F_NPV, respectively, were large relative to the seasonal and inter-annual variation. Analysis of site composition and structural data in relation to the MODIS-derived NDVI, SWIR32 and F_PV, F_NPV, and F_BS, indicated that the VI signal and derived cover fractions were influenced by a complex mix of structure and cover but included a strong year-to-year seasonal effect. Therefore, although the MODIS NDVI–SWIR32 response could be used to retrieve cover fractions across all Cerrado land covers including bare cropland, pastures and forests, sensitivity may be limited within the natural Cerrado due to sub-pixel heterogeneity and limited BS and NPV sensitivity.     

Relating spatial patterns of fractional land cover to savanna vegetation morphology using multi-scale remote sensing in the Central Kalahari

Understanding, monitoring, and managing savanna ecosystems requires characterizing both functional and structural properties of vegetation. From a functional perspective, in savannas, quantitative estimation of fractional cover of photosynthetic vegetation (f_PV), non-photosynthetic vegetation (f_NPV), and bare soil (f_BS) is important as it relates to carbon dynamics and ecosystem function. On the other hand, vegetation morphology classes describe the structural properties of the ecosystem. Due to high functional diversity and structural heterogeneity in savannas, accurately characterizing both these properties using remote sensing is methodologically challenging. While mapping both fractional cover and vegetation morphology classes are important research themes within savanna remote sensing, very few studies have considered systematic investigation of their spatial association across different spatial resolutions. Focusing on the semi-arid savanna ecosystem in the Central Kalahari, this study utilized f_PV, f_NPV, and f_BS derived in situ and estimated from spectral unmixing of high- (GeoEye-1), medium- (Landsat TM), and coarse- (MODIS) spatial resolution imagery to investigate: (i) the impact of reducing spatial resolution on both magnitude and accuracy of fractional cover; and (ii) how fractional-cover magnitude and accuracy are spatially associated with savanna vegetation morphology classes. Endmembers for Landsat TM and GeoEye-1 were derived from the image based on purity measures; for MODIS (MCD43A4), the challenge of finding spectral endmembers was addressed following an empirical multi-scale hierarchical approach. GeoEye-1-derived fractional estimates showed comparatively closest agreement with in situ measurements and were used to evaluate Landsat TM and MODIS. Overall results indicate that increasing pixel size caused consistent increases in variance of and error in fractional-cover estimates. Even at coarse spatial resolution, f_PV was estimated with higher accuracy compared with f_NPV and f_BS. Assessment considering vegetation morphology of samples revealed both morphology- and cover-specific differences in accuracy. At larger pixel sizes, in areas with dominant woody vegetation, f_PV was overestimated at the cost of mainly underestimating f_BS; in contrast, in areas with dominant herbaceous vegetation, f_NPV was overestimated with a corresponding underestimation of both f_PV and f_BS. These results underscore that structural and functional heterogeneity in semi-arid savanna both impact retrieval of fractional cover, suggesting that comprehensive remote sensing of savannas needs to take both structure and cover into account.     

Inversion of vegetation canopy reflectance models for estimating agronomic variables. IV. Total inversion of the SAIL model

The estimability of all the canopy parameters for a vegetation canopy using only canopy reflectance (CR) data and the SAIL model is investigated, using techniques described earlier (Goel and Thompson, 1984a). It is shown that in principle such an estimation is possible, i.e., the SAIL model is mathematically totally invertible. An analysis of the sensitivity of the calculated values to changes in the CR data is presented. This analysis suggests that, given the expected accuracy of CR measurements and the accuracy of the SAIL model in representing CR in the infrared region, the agronomic parameters, leaf area index, and leaf angle distribution, can be estimated fairly accurately using ancillary data on spectral parameters.     

Reducing the effects of vegetation cover on airborne radiometric data using Landsat TM data

The gamma-ray spectrometry responses from bedrock in Canadian Shield areas are substantially masked by overburden and vegetation. Proper interpretation of airborne gamma-ray spectrometry data is dependent on accounting for the interference provided by surface cover. In this paper, a method is tested to correct airborne gamma-ray spectrometry, acquired over the Canadian Shield of northeastern Alberta, for vegetation screening by estimating the proportions of bedrock and vegetation cover from Landsat TM data. TM pixel values, due to the patchy network of bedrock and vegetation, result from a spectral mixture of these ground cover classes. Linear unmixing was implemented to deconvolve TM bands in abundance images to estimate proportions of bedrock and vegetation for each pixel. The outcrop abundance image, representing spatial variation in area percentage of bedrock, is used in linear regression analysis to calibrate co-registered K, eTh, and eU gamma-ray spectrometry channels to 40 per cent bedrock endmember images.     

Inversion of vegetation canopy reflectance models for estimating agronomic variables. III. Estimation using only canopy reflectance data as illustrated by the suits model

The technique for estimating agronomic and spectral parameters for a vegetation canopy from the canopy reflectance (CR) data, described earlier (Goel et al., 1984), has been improved. These improvements are twofold: first, one can now, in principle, estimate various parameters using only CR data, in the infrared band, for a set of solar/view angles; second, the method is now computationally much more efficient. These improvements are illustrated via Suits' model. An analysis of the sensitivity of the calculated agronomic and spectral parameters to changes in the CR is also carried out. This analysis suggests that, in general, for expected levels of errors in the measurement of CRs and the accuracy with which the Suits model is likely to represent CR, one is unlikely to be able to estimate agronomic parameters like leaf area index (LAI) and average leaf angle (ALA) using only measured CR data. Such a determination will likely require ancillary data on the reflectance and transmittance of vegetation elements and on the soil reflectance.     

Validation of a practical normalized soil moisture model with in situ measurements in humid and semi-arid regions

Soil moisture is an important parameter that influences the exchange of water and energy fluxes between the land surface and the atmosphere. Through the simulation by a Soil–Vegetation–Atmosphere Transfer model, Carlson proposed the universal spatial information-based method to determine soil moisture that is insensitive to the initial atmospheric and surface conditions, net radiation, and atmospheric correction. In this study, a practical normalized soil moisture model is established to describe the relationship among the normalized soil moisture (M), the normalized land surface temperature (T*), and the fractional vegetation cover. The dry and wet points are determined using the surface energy balance principle, which has a robust physical basis. This method is applied to retrieve soil moisture for the Soil Moisture-Atmosphere Coupling Experiment campaign in the Walnut Creek watershed, which has a humid climate, and at the Linzestation, which has a semi-arid climate. The validation data are obtained on days of year (DOYs) 182 and 189 in 2002 in the humid region and on DOYs 148 and 180 in 2008 for the semi-arid region; these data collection days are coincident with the overpass of the Landsat Thematic Mapper/Enhanced Thematic Mapper Plus. When the estimates are compared with the in situ measurements of soil water content, the root mean square error is approximately 0.10 m³ m^?3 with a bias of 0.05 m³ m^?3 for the humid region and 0.08 m³ m^?3 with a bias of 0.03 m³ m^?3 for the semi-arid region. These results demonstrate that the practical normalized soil moisture model is applicable in both humid and semi-arid regions.     

Estimation and model predictive control of non-linear batch processes using linear parameter varying models

In this paper, feedback control is implemented for batch processes using linear models which describe the batch dynamics locally along its optimal trajectory. A Linear Parameter Varying (LPV) model obtained by interpolation between these multiple models is used to emulate the behaviour of the non-linear batch. The interpolation functions and state estimates are computed using a recursive Bayesian technique. The control technique is based on model predictive control (MPC) which is used for regulation and targeting the product specifications at the end of the batch.     

Spatial-temporal dynamics of land surface temperature in relation to fractional vegetation cover and land use/cover in the Tabriz urban area, Iran

Rapid changes of land use and land cover (LULC) in urban areas have become a major environmental concern due to environmental impacts, such as the reduction of green spaces and development of urban heat islands (UHI). Monitoring and management plans are required to solve this problem effectively. The Tabriz metropolitan area in Iran, selected as a case study for this research, is an example of a fast growing city. Multi-temporal images acquired by Landsat 4, 5 TM and Landsat 7 ETM+ sensors on 30 June 1989, 18 August 1998, and 2 August 2001 respectively, were corrected for radiometric and geometric errors, and processed to extract LULC classes and land surface temperature (LST). The relationship between temporal dynamics of LST and LULC was then examined. The temperature vegetation index (TVX) space was constructed in order to study the temporal variability of thermal data and vegetation cover. Temporal trajectory of pixels in the TVX space showed that most changes due to urbanization were observable as the pixels migrated from the low temperature-dense vegetation condition to the high temperature-sparse vegetation condition in the TVX space. The uncertainty analysis revealed that the trajectory analysis in the TVX space involved a class-dependant noise component. This emphasized the need for multiple LULC control points in the TVX space. In addition, this research suggests that the use of multi-temporal satellite data together with the examination of changes in the TVX space is effective and useful in urban LULC change monitoring and analysis of urban surface temperature conditions as long as the uncertainty is addressed.     

Assessment of land surface temperature in relation to landscape metrics and fractional vegetation cover in an urban/peri-urban region using Landsat data

Land surface temperature (LST) is essentially considered to be one of the most important indicators used for assessment of the urban thermal environment. It is quite evident that land-use/land-cover (LULC) and landscape patterns have ecological implications at varying spatial scales, which in turn influence the distribution of habitat and material/energy fluxes in the landscape. This article attempts to quantitatively analyse the complex interrelationships between urban LST and LULC landscape patterns with the purpose of elucidating their relation to landscape processes. The study employed an integrated approach involving remote-sensing, geographic information system (GIS), and landscape ecology techniques on bi-temporal Landsat Thematic Mapper images of Southwestern Sydney metropolitan region and the surrounding fringe, taken at approximately the same time of the year in July 1993 and July 2006. First, the LULC categories and LST were extracted from the bi-temporal images. The LST distribution and changes and LST of the LULC categories were then quantitatively analysed using landscape metrics and LST zones. The results show that large differences in temperature existed in even a single LULC category, except for variations between different LULC categories. In each LST zone, the regressive function of LST with fractional vegetation cover (FVC) indicated a significant relationship between LST and FVC. Landscape metrics of LULC categories in each zone in relation to the other zones showed changing patterns between 1993 and 2006. This study also illustrates that a method integrating retrieval of LST and FVC from remote-sensing images combined with landscape metrics provides a novel and feasible way to describe the spatial distribution and temporal variation in urban thermal patterns and associated LULC conditions in a quantitative manner.     

Inversion of a radiative transfer model for estimating vegetation LAI and chlorophyll in a heterogeneous grassland

Radiative transfer models have seldom been applied for studying heterogeneous grassland canopies. Here, the potential of radiative transfer modeling to predict LAI and leaf and canopy chlorophyll contents in a heterogeneous Mediterranean grassland is investigated. The widely used PROSAIL model was inverted with canopy spectral reflectance measurements by means of a look-up table (LUT). Canopy spectral measurements were acquired in the field using a GER 3700 spectroradiometer, along with simultaneous in situ measurements of LAI and leaf chlorophyll content. We tested the impact of using multiple solutions, stratification (according to species richness), and spectral subsetting on parameter retrieval. To assess the performance of the model inversion, the normalized RMSE and R² between independent in situ measurements and estimated parameters were used. Of the three investigated plant characteristics, canopy chlorophyll content was estimated with the highest accuracy (R² = 0.70, NRMSE = 0.18). Leaf chlorophyll content, on the other hand, could not be estimated with acceptable accuracy, while LAI was estimated with intermediate accuracy (R² = 0.59, NRMSE = 0.18). When only sample plots with up to two species were considered (n = 107), the estimation accuracy for all investigated variables (LAI, canopy chlorophyll content and leaf chlorophyll content) increased (NRMSE = 0.14, 0.16, 0.19, respectively). This shows the limits of the PROSAIL radiative transfer model in the case of very heterogeneous conditions. We also found that a carefully selected spectral subset contains sufficient information for a successful model inversion. Our results confirm the potential of model inversion for estimating vegetation biophysical parameters at the canopy scale in (moderately) heterogeneous grasslands using hyperspectral measurements.     

Experimental data for separation of vegetation and soil and estimation of soil moisture using passive microwaves

Abstract

Microwave radiometer measurements of soil moisture content were made over bare and vegetated fields with dual polarized microwave radiometers at 1·55GHz (L-band) and 19·1 GHz (K.-band). Two typical Indian crops Bazra and Gawar have been studied. The bare field measurements were used to investigate the effect of soil texture on sensitivity of a radiometer to soil moisture and for soil moisture sampling depth. It is found that expression of soil moisture as available moisture content in the soil can minimize the texture effect. The estimated soil moisture sampling depth for L-band is 2-5 cm, while for K-band it is less than 2 cm. The vegetation cover affects the sensitivity of the radiometer to soil moisture. This effect is more pronounced the denser the vegetation and higher the frequency of observation. The measured polarization factor over a vegetated field at L-band was found to be appreciably reduced compared to that over a bare field. The difference between normalized brightness temperature from L-band and K-band is sensitive to vegetation type. The soil moisture under vegetation cover at L-band can be predicted well using Jackson's parametric model.     

Dynamics of the relationship between NDVI and SWIR32 vegetation indices in southern Africa: implications for retrieval of fractional cover from MODIS data

Fractional cover of photosynthetic vegetation (F_PV), non-photosynthetic vegetation (F_NPV), and bare soil (F_BS) has been retrieved for Australian tropical savannah based on linear unmixing of the two-dimensional response envelope of the normalized difference vegetation index (NDVI) and short wave infrared ratio (SWIR)32 vegetation indices (VI) derived from Moderate Resolution Imaging Spectroradiometer (MODIS) reflectance data. The approach assumes that cover fractions are made up of a simple mixture of green leaves, senescent leaves, and bare soil. In this study, we examine retrieval of fractional cover using this approach for a study area in southern Africa with a more complex vegetation structure. Region-specific end-members were defined using Hyperion images from different locations and times of the season. These end-members were applied to a 10-year time series of MODIS-derived NDVI and SWIR32 (from 2002 to 2011) to unmix F_PV, F_NPV, and F_BS. Results of validation with classified high-resolution imagery indicated major bias in estimation of F_NPV and F_BS, with regression coefficients for predicted versus observed data substantially less than 1.0 and relatively large intercept values. Examination with Hyperion images of the inverse relationship between the MODIS-equivalent SWIR32 index and the Hyperion-derived cellulose absorption index (CAI) to which it nominally approximates revealed: (1) non-compliant positive regression coefficients for certain vegetation types; and (2) shifts in slope and intercept of compliant regression curves related to day of year and geographical location. The results suggest that the NDVI–SWIR32 response cannot be used to approximate the NDVI–CAI response in complex savannah systems like southern Africa that cannot be described as simple mixtures of green leaves, dry herbaceous material high in cellulose, and bare soil. Methods that use a complete set of multispectral channels at higher spatial resolution may be needed for accurate retrieval of fractional cover in Africa.     

A fast routine for fitting Cox models with time varying effects of the covariates

The S-plus and R statistical packages have implemented a counting process setup to estimate Cox models with time varying effects of the covariates. The data set has to be re-arranged in a repeated measurement setting: the time is divided into small time intervals where a single event occurs and for each time interval, the covariate values and outcome in the interval for each subject still under observation are stacked to a large data set. This is the known (Tstart,Tstop] algorithm implemented in Therneau's Survival library (S-plus), which has been ported into an R package by Thomas Lumley. However, the expansion of a data set leads to a larger set, which can be hard to handle even with fast modern computers. We propose the use of a fast and efficient algorithm, written in R, which works on the original data without the use of an expansion. The computations are done on the original data set, with significant less memory resources used. This improves the computational time by orders of magnitude. The algorithm can also fit reduced rank Cox models with time varying effects. We illustrate the method on a large data set of 2433 breast cancer patients, a smaller study of 358 ovarian cancer patients, and compare the computational times on simulated data of up to 10,000 cases with SAS proc phreg and survival package in R. For larger data sets our algorithm was several times faster, and was able to handle larger data sets then SAS and R.     

Development of discharge-stage curves affected by hysteresis using time varying models,model trees and neural networks

Flow data forms the base on which much of the edifice of water management is raised. However, flow measurements are expensive and difficult to conduct. Therefore, the more accessible stage measurements are employed in combination with stage–discharge relationships. Setting up such relationships is often infeasible using traditional regression techniques. Two case studies are examined that show hystereses using various approaches, namely (1) single rating curves, (2) rating curves with dynamic correction, (3) artificial neural networks (ANN) and (4) M5′ model trees. All methods outperform the traditional rating curve. The presented approach that uses a dynamically corrected rating curve delivers accurate results and allows for physical interpretation. The ANNs mimic the calibration data precisely, but suffer from overfitting when a small amount of data is applied for training. The rarely used M5′ model tree's architecture is easier to interpret than that of neural networks and delivers more accurate results.