Corn‐yield estimation through assimilation of remotely sensed data into the CSM‐CERES‐Maize model

One of the applications of crop simulation models is to estimate crop yield during the current growing season. Several studies have tried to integrate crop simulation models with remotely sensed data through data‐assimilation methods. This approach has the advantage of allowing reinitialization of model parameters with remotely sensed observations to improve model performance. In this study, the Cropping System Model‐CERES‐Maize was integrated with the Moderate Resolution Imaging Spectroradiometer (MODIS) leaf area index (LAI) products for estimating corn yield in the state of Indiana, USA. This procedure, inversion of crop simulation model, facilitates several different user input modes and outputs a series of agronomic and biophysical parameters, including crop yield. The estimated corn yield in 2000 compared reasonably well with the US Department of Agriculture National Agricultural Statistics Service statistics for most counties. Using the seasonal LAI in the optimization procedure produced the best results compared with only the green‐up LAIs or the highest LAI values. Planting, emergence and maturation dates, and N fertilizer application rates were also estimated at a regional level. Further studies will include investigating model uncertainties and using other MODIS products, such as the enhanced vegetation index.     

Yield estimation of winter wheat in the North China Plain using the remote-sensing–photosynthesis–yield estimation for crops (RS–P–YEC) model

The accurate prediction of crop yield is of great help for grain policy making. By assuming a horizontally homogeneous, vertically laminar structure and introducing a multilayer-two-big-leaf model, we develop a radiative-transfer equation for winter-wheat canopy and a model, named the remote-sensing–photosynthesis–yield estimation for crops (RS–P–YEC) model, for winter-wheat yield estimation. The yield is calculated by multiplying the net primary productivity (NPP) by the harvest index (HI). In this study, the yield of winter wheat in the North China Plain in 2006 is estimated using the RS–P–YEC model. The simulated yield is consistent with observations from 17 agro-meteorological stations, and the mean relative error is 4.6%. The results demonstrate that the RS–P–YEC model is a useful tool for winter-wheat yield estimation in the North China Plain with widely available remotely sensed imageries.     

A semi‐empirical backscattering model for estimation of leaf area index (LAI) of rice in southern China

Most paddy rice in southern China grows in warm, humid and rainy areas where it is hard to acquire optical remote sensing data. In this study, a semi‐empirical backscattering model was proposed to estimate leaf area index (LAI) of rice in the area using ENVISAT Advanced Synthetic Aperture Radar (ASAR) alternating polarization data. Ground measurements of LAI, water content and height of rice in the test site were collected and the model fitted at the same time as the acquisition of ASAR data. LAI estimated from the model was compared with ground measurements to evaluate the accuracy of the model. The results showed that the model provides a promising alternative to optical remote sensing data for predicting LAI of rice in southern China.     

A sleep model and an observer using the Lotka–Volsterra equation for real-time estimation of sleep

This paper describes a novel method that estimates sleep behaviors in a real-time manner. A Luenberger-type observer was employed, which requires a dynamic model of the sleep as a priori information about the sleep stages. A reasonable sleep model is essential in this approach. The classic Lotka–Voltera equation with interpretations associated with the sleep was built and an observer was developed. The observer using heartbeat rhythm and body movement as input signals estimated and compensated the sleep depths, which shows better results than the original inputs in the standpoint of the percentage of δ-waves in total brainwaves, used as a reference. The observer compensated for phase-shift errors and non-cyclic errors of the sleep cycle. The correlation between the reference and the compensated sleep cycle behavior was 0.79, whereas that between the reference and the measurement itself was 0.65. The application of the observer improved the accuracy of the sleep cycle measurement.     

Ultimate bound and optimal measurement for estimation of coupling constant in Tavis–Cummings model

We seek to study the problem of estimating the atoms-field coupling constant in Tavis–Cummings model for interaction between two atoms and an electromagnetic field by means of local estimation theory. We calculate the quantum Fisher information (QFI) for the most general pure probe state that undergoes evolution generated by the Hamiltonian of the Tavis–Cummings model; then, proper probe states which maximize the QFI are determined. Furthermore, we consider subspaces separately and show that QFI for atomic subspace (contains both qubits) and cavity field subspace can reach the maximum value of QFI in the whole space by choosing proper initial state. Finally, the optimal measurement that saturates the Cramer–Rao bound, i.e., the measurement with Fisher information equal to QFI, for considered states are determined in the whole space and the subspaces, separately.     

Prediction of rice crop yield using MODIS EVI−LAI data in the Mekong Delta,Vietnam

Predicting rice crop yield at the regional scale is important for production estimates that ensure food security for a country. This study aimed to develop an approach for rice crop yield prediction in the Vietnamese Mekong Delta using the Moderate Resolution Imaging Spectroradiometer (MODIS) enhanced vegetation index (EVI) and leaf area index (LAI). Data processing consisted of four main steps: (1) constructing time-series vegetation indices, (2) noise filtering of time-series data using the empirical mode decomposition (EMD), (3) establishment of crop yield models, and (4) model validation. The results indicated that the quadratic model using two variables (EVI and LAI) produced more accurate results than other models (i.e. linear, interaction, pure quadratic, and quadratic with a single variable). The highest correlation coefficients obtained at the ripening period for the spring–winter and autumn–summer crops were 0.70 and 0.74, respectively. The robustness of the established models was evaluated by comparisons between the predicted yields and crop yield statistics for 10 sampling districts in 2006 and 2007. The comparisons revealed satisfactory results for both years, especially for the spring–winter crop. In 2006, the root mean squared error (RMSE), mean absolute error (MAE), and mean bias error (MBE) for the spring–winter crop were 10.18%, 8.44% and 0.9%, respectively, while the values for the autumn–summer crop were 17.65%, 14.06%, and 3.52%, respectively. In 2007, the spring–winter crop also yielded better results (RMSE = 10.56%, MAE = 9.14%, MBE = 3.68%) compared with the autumn–summer crop (RMSE = 17%, MAE = 12.69%, MBE = 2.31%). This study demonstrates the merit of using MODIS data for regional rice crop yield prediction in the Mekong Delta before the harvest period. The methods used in this study could be transferable to other regions around the world.     

The L p -norm estimation of the parameters for the Jelinski–Moranda model in software reliability

The exponential model of Jelinski and Moranda [Software reliability research, in Statistical Computer Performance Evaluation, W. Freiberg, ed., Academic Press, New York, 1972, pp. 465–484] is one of the earliest models proposed for predicting software reliability. The estimation of its parameters has been approached in the literature by various techniques. The focus of this paper is on the L _p -norm (1≤p<∞) fitting approach. Special attention is paid to the nonlinear weighted least squares (LS) estimation. We show that it is possible for the best L _p -norm estimate to not exist. As the main result, a necessary and sufficient condition for the existence of the best L _p -norm estimate is obtained. This condition is theoretical in nature. We apply it to obtain two theorems on the existence of the LS estimate. One of them gives the necessary and sufficient conditions which guarantee the existence of the LS estimate. To illustrate the problems arising with the nonlinear normal equation approach for solving the LS problem, some illustrative examples are included.     

Estimating tree‐cover change in Australia: challenges of using the MODIS vegetation index product

Time series of the vegetation index product MOD13Q1 from the Moderate Resolution Imagery Spectroradiometer (MODIS) were assessed for estimating tree foliage projective cover (FPC) and cover change from 2000 to 2006. The MOD13Q1 product consists of the enhanced vegetation index (EVI) and the normalized difference vegetation index (NDVI). There were four challenges in using the MOD13Q1 product to derive tree FPC: assessing the impact of the sensor's varying view geometry on the vegetation index values; decoupling tree and grass cover contributions to the vegetation index signal; devising a method to relate the temporally composited vegetation index pixels to Lidar estimates of tree FPC for calibration; and estimating the accuracy of the FPC and FPC change measurements using independently derived Lidar, Landsat and MODIS cover estimates. The results show that, for complex canopies, the varying view geometry influenced the vegetation indices. The EVI was more sensitive to the view angle than the NDVI, indicating that it is sensitive to vegetation structure. An existing time series method successfully extracted the evergreen vegetation index signal while simultaneously minimizing the impact of varying view geometry. The vegetation indices were better suited to monitoring tree cover change than deriving accurate single‐date estimates of cover at regional to continental scales. The EVI was more suited to monitoring change in high‐biomass regions (cover >50%) where the NDVI begins to saturate.     

Modelling and analysis of inventory replenishment for perishable agricultural products with buyer–seller collaboration

In this article, we study the inventory replenishment model for perishable agricultural products in a simple two-level supply chain. Collaborative forecasting is introduced into the inventory replenishment decisions to avoid overstocking and understocking of agricultural products, and to maximise profits. We analyse the model with ordering cost, holding cost, shortage cost, deterioration cost and opportunity lost cost of perishable agricultural products. Extensive numerical analysis is carried out to study the performance of the inventory policy. The optimal replenishment policy that minimises the total cost can be obtained from the model. It has demonstrated that the supply chain cost decreases with supplier and retailer's collaborative forecasting.     

Evaluation of the VI–T s method for estimating the land surface moisture index and air temperature using ASTER and MODIS data in the North China Plain

Two conditions are required when a remotely sensed vegetation index–land surface temperature (VI–T _s) diagram is used to estimate the land surface moisture index (LSMI) and air temperature (T _a). First, a suitable sampling window size is required to define an ideal VI–T _s diagram. Second, T _a must be homogeneous across the sampling window. In this study, the Shannon diversity index (SDI) and the semivariogram method were used to evaluate the VI–T _s diagram for estimating LSMI and T _a from Advanced Spaceborne Thermal Emission Reflection Radiometer (ASTER) and MODerate-resolution Imaging Spectroradiometer (MODIS) datasets. The results show that T _a is homogeneous across a sampling window with a width of several tens of kilometres (46.0–83.6 km) based on the semivariogram method and spatial autocorrelation analysis of the T _a from 83 meteorological stations in the North China Plain (NCP) in 2003. When the SDIs of VI and T _s are respectively larger than 77% and 63% of their maximums within predetermined sampling windows, LSMI estimations by ASTER and T _a estimations by ASTER and MODIS are reliable.     

The Depletion–Power–Integration–Latency (DPIL) model of spaced and massed repetition

Although several models have been suggested in the literature to describe the relationship between learning and forgetting, this relationship is still not fully understood. This paper proposes the Depletion–Power–Integration–Latency (DPIL) model, which assumes that performing a task repetitively depletes the available encoding resources for that task. The DPIL model fitted five empirical datasets well, reflecting different procedural/episodic learning settings, experimental paradigms (massed/spaced repetition, study time), tests (accuracy, latency), and retention intervals. The model was also fitted to empirical data collected from a quality inspection station at an industrial firm. The DPIL model has the advantage of predicting the length of the final break (interruption) that optimizes performance. This finding is important as it has many industrial engineering applications. The numerical results in this paper show that performance improves as the length of each break preceding the final break increases. This is consistent with empirical findings that moderately short breaks are optimal for performance.     

Temporally smoothed and gap‐filled MODIS land products for carbon modelling: application of the fPAR product

TIMESAT software is used to produce a temporally and spatially Gap‐Filled and Smoothed (GFS) version of the MODIS (Moderate Resolution Imaging Spectro‐radiometer) fPAR (fraction of absorbed photosynthetically active radiation) product (MOD15). We apply this new ?PAR product within two commonly used carbon and vegetation productivity models, CASA (Carnegie‐Ames‐Stanford Approach) and the MODIS GPP (Gross Primary Production) algorithm (MOD17). The GFS product removes noise present within the original MOD15 fPAR dataset, yet is comparable to the linearly interpolated UMT (University of Montana) fPAR used in the MOD17 algorithm. However, the GSF data provides a realistic fPAR time‐series in relation to magnitude and seasonality associated with radiation in regions where persistent cloud cover is an issue. It is available for North America and the northern part of South America covering the Amazon basin for the MODIS acquisition period (2000–2005).     

Precision approximations for Fermi–Dirac functions of the integer index

The Fermi–Dirac functions of the integer index are widely used in electron transport problems in dense substances. Polynomial approximations are constructed for their quick calculation. A simple algorithm yielding the coefficients of such approximations based on the interpolation with a special linear-trigonometric grid is developed. It is demonstrated that this grid gives almost optimal results. For the functions of indices 1, 2, and 3, the coefficients of such interpolations ensuring the relative error of 2 × 10^?16 under 9 free parameters are obtained.     

Usability of noise-free daily satellite-observed green–red vegetation index values for monitoring ecosystem changes in Borneo

We examined the usability of daily green–red vegetation index (GRVI) observations from the Terra and Aqua Moderate Resolution Imaging Spectroradiometer satellite on cloud-free days for monitoring ecosystem changes in Bornean tropical forests at a 500 m spatial resolution over 11 years (2003–2013). The number of observational days of cloud-free GRVI data in the southwest monsoon period (May–October; 1–5 days/month) was greater than that in the northeast monsoon period (November–April; 0–2 days/month). Spatial variation in the observation frequency was noticed, with Terra (morning) and Aqua (afternoon) data showing different geographic distribution patterns of cloud-free data. The observation frequency in the western Kalimantan mountains (Sarawak and Sabah) was 1–2 days/month greater than that in the eastern mountains (Kalimantan). The quality of cloud-free GRVI data was validated by using sky images taken at the same time as the satellite observations and canopy surface images in a tropical rainforest. In oil palm and acacia plantations and peatlands, which were mainly distributed in coastal regions of Sarawak and West and Central Kalimantan, the cloud-free daily GRVI value fell below zero owing to deforestation and forest degradation caused by forest fire and increased with replanting and vegetation recovery. These results indicate that daily cloud-free GRVI data from multiple satellites collected at different times of the day are required for accurate monitoring of intra- and interannual phenological variation and forest degradation attributed to changes in climatic conditions and deforestation caused by human activities in tropical ecosystems.     

A layer-wise Reissner–Mindlin-type model for the vibration analysis and suppression of piezoactuated plates

A layer-wise model of three-layer piezoelectric sandwich plates is presented. Each layer is modeled according to a first-order shear deformation theory. Both a variational formulation and a locking-free finite-element formulation of the sandwich-plate problem are developed. The latter is based on a new bilinear quadrangular four-node finite element with 13 degrees of freedom per node and is validated by comparing the numerical and the analytical solution of a special problem. The proposed model is applied to the analysis of the vibration suppression problem of a thick cantilever steel plate equipped with a piezoelectric actuator, and turns out to be especially useful when a thick piezoelectric actuator is used.     

Human–robot collision model with effective mass and manipulability for design of a spatial manipulator

As the use of service robots becomes more popular, many solutions to ensure human safety during human–robot collision have been proposed. In this paper, we address one of the most fundamental solutions to design an inherently safe robot manipulator. A collision model is developed to evaluate the collision safety of any spatial manipulator. Most collision studies have focused on collision analysis and safety evaluation, but not on the use of evaluation results to design a safer robot arm. Therefore, we propose a collision model that relates design parameters to collision safety by adopting effective mass and manipulability. The model was then simplified with several assumptions. Furthermore, experimental results from biomechanical literature were employed to describe a human–robot collision. The major advantage of this collision model is that it can be used to systemically determine the design parameters of a robot arm.     

An empirical study on the utility of BRDF model parameters and topographic parameters for mapping vegetation in a semi‐arid region with MISR imagery

In this study we show that multiangle remote sensing is useful for increasing the accuracy of vegetation community type mapping in desert regions. Using images from the National Aeronautics and Space Administration (NASA) Multiangle Imaging Spectroradiometer (MISR), we compared roles played by Bidirectional Reflectance Distribution Function (BRDF) model parameters with those played by topographic parameters in improving vegetation community type classifications for the Jornada Experimental Range and the Sevilleta National Wildlife Refuge in New Mexico, USA. The BRDF models used were the Rahman–Pinty–Verstraete (RPV) model and the RossThin‐LiSparseReciprocal (RTnLS) model. MISR nadir multispectral reflectance was considered as baseline because nadir observation is the most basic remote sensing observation. The BRDF model parameters and the topographic parameters were considered as additional data. The BRDF model parameters were obtained by inversion of the RPV model and the RTnLS model against the MISR multiangle reflectance data. The results of 32 classification experiments show that the BRDF model parameters are useful for vegetation mapping; they can be used to raise classification accuracies by providing information that is not available in the spectral‐nadir domain, or from ancillary topographic parameters. This study suggests that the Moderate Resolution Imaging Spectroradiometer (MODIS) and MISR BRDF model parameter data products have great potential to be used as additional information for vegetation mapping.     

Long-time behavior of the solutions of Murray–Thomas model for interacting chemicals

This paper is concerned with the Murray–Thomas model for interacting chemicals or species, under Robin boundary data. It is shown that the solutions are bounded and asymptotically converging toward an absorbing set of the phase-space. The stability of the positive constant steady states is discussed via a symmetrization procedure.     

Cournot–Nash and Bertrand–Nash equilibria for a heterogeneous duopoly of differentiated products

Under Cournot–Nash and Bertrand–Nash equilibria, analytical expressions are found for outputs, prices, and profits in the case when all duopoly parameters of differentiated products are different. It is shown that the signs of differences between such outputs, prices, and profits depend on the complementarity or substitutability of products. The concepts of exogenous, endogenous, and asymmetric differentiated products are introduced.     

Jacobian–Free Newton–Krylov Methods for the Accurate Time Integration of Stiff Wave Systems

Stiff wave systems are systems which exhibit a slow dynamical time scale while possessing fast wave phenomena. The physical effects of this fast wave may be important to the system, but resolving the fast time scale may not be required. When simulating such phenomena one would like to use time steps on the order of the dynamical scale for time integration. Historically, Semi-Implicit (SI) methods have been developed to step over the stiff wave time scale in a stable fashion. However, SI methods require some linearization and time splitting, and both of these can produce additional time integration errors. In this paper, the concept of using SI methods as preconditioners to Jacobian–Free Newton–Krylov (JFNK) methods is developed. This algorithmic approach results in an implicitly balanced method (no linearization or time splitting). In this paper, we provide an overview of SI methods in a variety of applications, and a brief background on JFNK methods. We will present details of our new algorithmic approach. Finally, we provide an overview of results coming from problems in geophysical fluid dynamics (GFD) and magnetohydrodynamics (MHD).