Decomposition of vegetation cover into woody and herbaceous components using AVHRR NDVI time series

A method is developed to separate Normalised Difference Vegetation Index (NDVI) time series data into contributions from woody (perennial) and herbaceous (annual) vegetation, and thereby to infer their separate leaf area indices and cover fractions. The method is formally consistent with fundamental linearity requirements for such a decomposition, and is capable of rejecting contaminated NDVI data. In this study, estimates of annual averaged woody cover and monthly averaged herbaceous cover over Australia are determined using Pathfinder AVHRR Land series (PAL) Global Area Coverage (GAC) Advanced Very High Resolution Radiometer (AVHRR) NDVI data from 1981 to 1994, together with ground-based measurements of leaf area index (LAI) and foliage projective cover (FPC).     

Estimating spatio-temporal patterns of agricultural productivity in fragmented landscapes using AVHRR NDVI time series

The characteristics of Normalized Difference Vegetation Index (NDVI) time series can be disaggregated into a set of quantitative metrics that may be used to derive information about vegetation phenology and land cover. In this paper, we examine the patterns observed in metrics calculated for a time series of 8 years over the southwest of Western Australia—an important crop and animal production area of Australia. Four analytical approaches were used; calculation of temporal mean and standard deviation layers for selected metrics showing significant spatial variability; classification based on temporal and spatial patterns of key NDVI metrics; metrics were analyzed for eight areas typical of climatic and production systems across the agricultural zone; and relationships between total production and productivity measured by dry sheep equivalents were developed with time integrated NDVI (TINDVI). Two metrics showed clear spatial patterns; the season duration based on the smooth curve produced seven zones based on increasing length of growing season; and TINDVI provided a set of classes characterized by differences in overall magnitude of response, and differences in response in particular years. Frequency histograms of TINDVI could be grouped on the basis of a simple shape classification: tall and narrow with high, medium or low mean indicating most land is responsive agricultural cover with uniform seasonal conditions; broad and short indicating that land is of mixed cover type or seasonal conditions are not spatially uniform. TINDVI showed a relationship to agricultural productivity that is dependent on the extent to which crop or total agricultural production was directly reduced by rainfall deficiency. TINDVI proved most sensitive to crop productivity for Statistical Local Areas (SLAs) having rainfall less than 600 mm, and in years when rainfall and crop production were highly correlated. It is concluded that metrics from standardized NDVI time series could be routinely and transparently used for retrospective assessment of seasonal conditions and changes in vegetation responses and cover.     

A curve fitting procedure to derive inter-annual phenologies from time series of noisy satellite NDVI data

Annual, inter-annual and long-term trends in time series derived from remote sensing can be used to distinguish between natural land cover variability and land cover change. However, the utility of using NDVI-derived phenology to detect change is often limited by poor quality data resulting from atmospheric and other effects. Here, we present a curve fitting methodology useful for time series of remotely sensed data that is minimally affected by atmospheric and sensor effects and requires neither spatial nor temporal averaging. A two-step technique is employed: first, a harmonic approach models the average annual phenology; second, a spline-based approach models inter-annual phenology. The principal attributes of the time series (e.g., amplitude, timing of onset of greenness, intrinsic smoothness or roughness) are captured while the effects of data drop-outs and gaps are minimized. A recursive, least squares approach captures the upper envelope of NDVI values by upweighting data values above an average annual curve. We test this methodology on several land cover types in the western U.S., and find that onset of greenness in an average year varied by less than 8 days within land cover types, indicating that the curve fit is consistent within similar systems. Between 1990 and 2002, temporal variability in onset of greenness was between 17 and 35 days depending on the land cover type, indicating that the inter-annual curve fit captures substantial inter-annual variability. Employing this curve fitting procedure enhances our ability to measure inter-annual phenology and could lead to better understanding of local and regional land cover trends.     

Univariate modeling and forecasting of monthly energy demand time series using abductive and neural networks

Neural networks have been widely used for short-term, and to a lesser degree medium and long-term, demand forecasting. In the majority of cases for the latter two applications, multivariate modeling was adopted, where the demand time series is related to other weather, socio-economic and demographic time series. Disadvantages of this approach include the fact that influential exogenous factors are difficult to determine, and accurate data for them may not be readily available. This paper uses univariate modeling of the monthly demand time series based only on data for 6 years to forecast the demand for the seventh year. Both neural and abductive networks were used for modeling, and their performance was compared. A simple technique is described for removing the upward growth trend prior to modeling the demand time series to avoid problems associated with extrapolating beyond the data range used for training. Two modeling approaches were investigated and compared: iteratively using a single next-month forecaster, and employing 12 dedicated models to forecast the 12 individual months directly. Results indicate better performance by the first approach, with mean percentage error (MAPE) of the order of 3% for abductive networks. Performance is superior to naı¨ve forecasts based on persistence and seasonality, and is better than results quoted in the literature for several similar applications using multivariate abductive modeling, multiple regression, and univariate ARIMA analysis. Automatic selection of only the most relevant model inputs by the abductive learning algorithm provides better insight into the modeled process and allows constructing simpler neural network models with reduced data dimensionality and improved forecasting performance.     

Image data compression using autoregressive time series models

A two-dimensional image model is formulated using a seasonal autoregressive time series. With appropriate use of initial conditions, the method of least squares is used to obtain estimates of the model parameters. The model is then used to regenerate the original image. Results obtained indicate this method could be used to code textures for low bit rates or be used in an application of generating compressed background scenes. A differential pulse code modulation (DPCM) scheme is also demonstrated as a means of archival storage of images along with a new quantization technique for DPCM. This quantization technique is compared with standard quantization methods.     

Reducing error in neural network time series forecasting

Neural network time series forecasting error comprises autocorrelation error, due to an imperfect model, and random noise, inherent in the data. Both problems are addressed here, the first using a two stage training, growth-network neuron: the autocorrelation error (ACE) neuron. The second is considered as a post-processing noise filtering problem. These techniques are applied in forecasting the sunspot time series, with comparison of stochastic, BFGS and conjugate gradient solvers.     

Recursive prediction for long term time series forecasting using advanced models

There exists a wide range of paradigms, and a high number of different methodologies that are applied to the problem of time series prediction. Most of them are presented as a modified function approximation problem using input/output data, in which the input data are expanded using values of the series at previous steps. Thus, the model obtained normally predicts the value of the series at a time (t+h) using previous time steps (t-τ₁),(t-τ₂),…,(t-τ_n). Nevertheless, learning a model for long term time series prediction might be seen as a more complicated task, since it might use its own outputs as inputs for long term prediction (recursive prediction). This paper presents the utility of two different methodologies, the TaSe fuzzy TSK model and the least-squares SVMs, to solve the problem of long term time series prediction using recursive prediction. This work also introduces some techniques that upgrade the performance of those advanced one-step-ahead models (and in general of any one-step-ahead model), where they are used recursively for long term time series prediction.     

Vegetation dynamics from NDVI time series analysis using the wavelet transform

A multi-resolution analysis (MRA) based on the wavelet transform (WT) has been implemented to study NDVI time series. These series, which are non-stationary and present short-term, seasonal and long-term variations, can be decomposed using this MRA as a sum of series associated with different temporal scales. The main focus of the paper is to check the potential of this MRA to capture and describe both intra- and inter-annual changes in the data, i.e., to discuss the ability of the proposed procedure to monitor vegetation dynamics at regional scale. Our approach concentrates on what wavelet analysis can tell us about a NDVI time series. On the one hand, the intra-annual series, linked to the seasonality, has been used to estimate different key features related to the vegetation phenology, which depend on the vegetation cover type. On the other hand, the inter-annual series has been used to identify the trend, which is related to land-cover changes, and a Mann-Kendall test has been applied to confirm the significance of the observed trends. NDVI images from the MEDOKADS (Mediterranean Extended Daily One-km AVHRR Data Set) imagery series over Spain are processed according to a per-pixel strategy for this study. Results show that the wavelet analysis provides relevant information about vegetation dynamics at regional scale, such as the mean and minimum NDVI value, the amplitude of the phenological cycle, the timing of the maximum NDVI and the magnitude of the land-cover change. The latter, in combination with precipitation data, has been used to interpret the observed land-cover changes and identify those subtle changes associated to land degradation.     

A neural network ensemble method with jittered training data for time series forecasting

Improving forecasting especially time series forecasting accuracy is an important yet often difficult task facing decision makers in many areas. Combining multiple models can be an effective way to improve forecasting performance. Recently, considerable research has been taken in neural network ensembles. Most of the work, however, is devoted to the classification type of problems. As time series problems are often more difficult to model due to issues such as autocorrelation and single realization at any particular time point, more research is needed in this area.In this paper, we propose a jittered ensemble method for time series forecasting and test its effectiveness with both simulated and real time series. The central idea of the jittered ensemble is adding noises to the input data and thus augments the original training data set to form models based on different but related training samples. Our results show that the proposed method is able to consistently outperform the single modeling approach with a variety of time series processes. We also find that relatively small ensemble sizes of 5 and 10 are quite effective in forecasting performance improvement.     

Short-term time series forecasting based on the identification of skeleton algebraic sequences

A new short-term time series forecasting method based on the identification of skeleton algebraic sequences is proposed in this paper. The concept of the rank of the Hankel matrix is exploited to detect a base fragment of the time series. Particle swarm optimization and evolutionary algorithms are then used to remove the noise and identify the skeleton algebraic sequence. Numerical experiments with an artificially generated and a real-world time series are used to illustrate the functionality of the proposed method.     

Combining medium and coarse spatial resolution satellite data to improve the estimation of sub-pixel NDVI time series

The potential of multitemporal coarse spatial resolution remotely sensed images for vegetation monitoring is reduced in fragmented landscapes, where most of the pixels are composed of a mixture of different surfaces. Several approaches have been proposed for the estimation of reflectance or NDVI values of the different land-cover classes included in a low resolution mixed pixel. In this paper, we propose a novel approach for the estimation of sub-pixel NDVI values from multitemporal coarse resolution satellite data. Sub-pixel NDVIs for the different land-cover classes are calculated by solving a weighted linear system of equations for each pixel of a coarse resolution image, exploiting information about within-pixel fractional cover derived from a high resolution land-use map. The weights assigned to the different pixels of the image for the estimation of sub-pixel NDVIs of a target pixel i are calculated taking into account both the spatial distance between each pixel and the target and their spectral dissimilarity estimated on medium-resolution remote-sensing images acquired in different periods of the year. The algorithm was applied to daily and 16-day composite MODIS NDVI images, using Landsat-5 TM images for calculation of weights and accuracy evaluation.Results showed that application of the algorithm provided good estimates of sub-pixel NDVIs even for poorly represented land-cover classes (i.e., with a low total cover in the test area). No significant accuracy differences were found between results obtained on daily and composite MODIS images. The main advantage of the proposed technique with respect to others is that the inclusion of the spectral term in weight calculation allows an accurate estimate of sub-pixel NDVI time series even for land-cover classes characterized by large and rapid spatial variations in their spectral properties.     

作物产量预测的粒度分析法

针对作物产量预测,提出基于商空间粒度计算的分析法。在商空间粒度计算理论思想下,分析作物产量序列中粒度的选取,用属性划分方法对论域X进行颗粒化,对属性f取不同的粒度进行颗粒化。通过属性的粒度变化对论域进行划分,得到新的商空间并应用其解决问题,可以降低问题复杂度。通过商空间理论中的分层与合成技术选取大小合适的粒度,能全面获取产量序列中的信息,也更加符合人类智能特点。冬小麦产量预测实验结果也证明这种粒度分析和选取方法是有效的。     

A review and comparison of strategies for multi-step ahead time series forecasting based on the NN5 forecasting competition

Multi-step ahead forecasting is still an open challenge in time series forecasting. Several approaches that deal with this complex problem have been proposed in the literature but an extensive comparison on a large number of tasks is still missing. This paper aims to fill this gap by reviewing existing strategies for multi-step ahead forecasting and comparing them in theoretical and practical terms. To attain such an objective, we performed a large scale comparison of these different strategies using a large experimental benchmark (namely the 111 series from the NN5 forecasting competition). In addition, we considered the effects of deseasonalization, input variable selection, and forecast combination on these strategies and on multi-step ahead forecasting at large. The following three findings appear to be consistently supported by the experimental results: Multiple-Output strategies are the best performing approaches, deseasonalization leads to uniformly improved forecast accuracy, and input selection is more effective when performed in conjunction with deseasonalization.     

A method to convert AVHRR Normalized Difference Vegetation Index time series to a standard viewing and illumination geometry

The bi-directional reflectance distribution function (BRDF) alters the seasonal and inter-annual variations exhibited in Advanced Very High Resolution Radiometer (AVHRR) Normalized Difference Vegetation Index (NDVI) data and this hampers the detection and, consequently, the interpretation of temporal variations in land-surface vegetation. The magnitude and sign of bi-directional effects in commonly used AVHRR data sets depend on land-surface properties, atmospheric composition and the type of atmospheric correction that is applied to the data. We develop an approach to estimate BRDF effects in AVHRR NDVI time series using the Moderate Resolution Imaging Spectrometer (MODIS) BRDF kernels and subsequently adjust NDVI time series to a standard illumination and viewing geometry. The approach is tested on NDVI time series that are simulated for representative AVHRR viewing and illumination geometry. These time series are simulated with a canopy radiative transfer model coupled to an atmospheric radiative transfer model for four different land cover types—tropical forest, boreal forest, temperate forest and grassland - and five different atmospheric conditions - turbid and clear top-of-atmosphere, turbid and clear top-of-atmosphere with a correction for ozone absorption and Rayleigh scattering applied (Pathfinder AVHRR Land data) and ground-observations (fully corrected for atmospheric effects). The simulations indicate that the timing of key phenological stages, such as start and end of growing season and time of maximum greenness, is affected by BRDF effects. Moreover, BRDF effects vary with latitude and season and increase over the time of operation of subsequent NOAA satellites because of orbital drift. Application of the MODIS kernels on simulated NVDI data results in a 50% to 85% reduction of BRDF effects. When applied to the global 18-year global Normalized Difference Vegetation Index (NDVI) Pathfinder data we find BRDF effects similar in magnitude to those in the simulations. Our analysis of the global data shows that BRDF effects are especially large in high latitudes; here we find that in at least 20% of the data BRDF errors are too large for accurate detection of seasonal and interannual variability. These large BRDF errors tend to compensate, however, when averaged over latitude.     

A distance-based fuzzy time series model for exchange rates forecasting

Fuzzy time series model has been successfully employed in predicting stock prices and foreign exchange rates. In this paper, we propose a new fuzzy time series model termed as distance-based fuzzy time series (DBFTS) to predict the exchange rate. Unlike the existing fuzzy time series models which require exact match of the fuzzy logic relationships (FLRs), the distance-based fuzzy time series model uses the distance between two FLRs in selecting prediction rules. To predict the exchange rate, a two factors distance-based fuzzy time series model is constructed. The first factor of the model is the exchange rate itself and the second factor comprises many candidate variables affecting the fluctuation of exchange rates. Using the exchange rate data released by the Central Bank of Taiwan, we conducted several experiments on exchange rate forecasting. The experiment results showed that the distance-based fuzzy time series outperformed the random walk model and the artificial neural network model in terms of mean square error.     

Construction of a new BRB based model for time series forecasting

It is important to predict the future behavior of complex systems. Currently there are no effective methods to solve time series forecasting problem by using the quantitative and qualitative information. Therefore, based on belief rule base (BRB), this paper focuses on developing a new model that can deal with the problem. Although it is difficult to obtain accurately and completely quantitative information, some qualitative information can be collected and represented by a BRB. As such, a new BRB based forecasting model is proposed when the quantitative and qualitative information exist simultaneously. The performance of the proposed model depends on the structure and belief degrees of BRB simultaneously. Moreover, the structure is determined by the delay step. In order to obtain the appropriate delay step using the available information, a model selection criterion is defined according to Akaike's information criterion (AIC). Based on the proposed model selection criterion and the optimal algorithm for training the belief degrees, an algorithm for constructing the BRB based forecasting model is developed. Experimental results show that the constructed BRB based forecasting model can not only predict the time series accurately, but also has the appropriate structure.     

Multiple neural networks for a long term time series forecast

The artificial neural network (ANN) methodology has been used in various time series prediction applications. However, the accuracy of a neural network model may be seriously compromised when it is used recursively for making long-term multi-step predictions. This study presents a method using multiple ANNs to make a long term time series prediction. A multiple neural network (MNN) model is a group of neural networks that work together to solve a problem. In the proposed MNN approach, each component neural network makes forecasts at a different length of time ahead. The MNN method was applied to the problem of forecasting an hourly customer demand for gas at a compression station in Saskatchewan, Canada. The results showed that a MNN model performed better than a single ANN model for long term prediction.

Fuzzy forecasting based on fuzzy time series

This article presents an improved method of fuzzy time series to forecast university enrollments. The historical enrollment data of the University of Alabama were first adopted by Song and Chissom (Song, Q. and Chissom, B. S. (1993). Forecasting enrollment with fuzzy time series-part I, Fuzzy Sets and Systems, 54, 1–9; Song, Q. and Chissom, B. S. (1994). Forecasting enrollment with fuzzy time series-part II, Fuzzy Sets and Systems, 54, 267–277) to illustrate the forecasting process of the fuzzy time series. Later, Chen proposed a simpler method. In this article, we show that our method is as simple as Chen's method but more accurate. In forecasting the enrollment of the University of Alabama, the root mean square percentage error (RMSPE) of our method is 3.1113% while the RMSPE of Chen's method is 4.0516%, which shows that our method is doing much better.     

Distribution forecasting of high frequency time series

The availability of high frequency data sets in finance has allowed the use of very data intensive techniques using large data sets in forecasting. An algorithm requiring fast k-NN type search has been implemented using AURA, a binary neural network based upon Correlation Matrix Memories. This work has also constructed probability distribution forecasts, the volume of data allowing this to be done in a nonparametric manner. In assistance to standard statistical error measures the implementation of simulations has allowed actual measures of profit to be calculated.     

A new class of hybrid models for time series forecasting

Applying quantitative models for forecasting and assisting investment decision making has become more indispensable in business practices than ever before. Improving forecasting especially time series forecasting accuracy is an important yet often difficult task facing forecasters. Both theoretical and empirical findings have indicated that integration of different models can be an effective way of improving upon their predictive performance, especially when the models in the ensemble are quite different. In the literature, several hybrid techniques have been proposed by combining different time series models together, in order to overcome the deficiencies of single models and yield hybrid models that are more accurate. In this paper, in contrast of the traditional hybrid models, a new methodology is proposed in order to construct a new class of hybrid models using a time series model as basis model and a classifier. As classifiers cannot be lonely applied as forecasting model for continuous problems, in the first stage of the proposed model, a forecasting model is used as basis model. Then, the estimated values of the basis model are modified in the second stage, based on the distinguished trend of the residuals of the basis model and the optimum step length, which are respectively calculated by a classifier model and a mathematical programming model. Empirical results with three well-known real data sets indicate that the proposed model can be an effective way in order to construct a more accurate hybrid model than its basis time series model. Therefore, it can be used as an appropriate alternative model for forecasting tasks, especially when higher forecasting accuracy is needed.