Time Series Similarity Research Articles

Grouping of mood symptoms by time series dynamics

BackgroundUnderstanding how symptoms of mood disorders vary over time in relation to each other is potentially valuable for diagnosis and predicting episodes of illness. In this paper, we characterize the degree of similarity of time series of different mood disorder symptoms. MethodsWe collected 32,215 mood disorder symptom questionnaires, administered twice-daily over 18 months to (n = 19) subjects with rapidly cycling bipolar disorder and (n = 20) healthy control subjects, using visual analog scales to rate 11 sets of symptom severity ratings plus a control item. We used Dynamic Time Warping to calculate similarity ratings between all within-subject pairs of severity ratings followed by Exploratory Factor Analysis (EFA) to identify latent factors of symptom time series across all subjects. ResultsTwo latent factors were identified: one with depression and anxiety; and a second, with concentration, energy, irritability, fatigue, appetite, euphoria/elation and overall mood. Restlessness, racing thoughts, and the control item (daily hours of daylight) did not cluster with any of the others. LimitationsLimited sample size dictated that we pool bipolar and healthy patients and use an iterative EFA procedure. ConclusionThis analysis suggests that, in a pooled sample of individuals with bipolar disorder and in healthy controls, severity ratings of overall depression and overall anxiety vary jointly as one dynamic factor, while some but not all other DSM mood symptoms vary jointly along with overall mood rating as a second dynamic factor. Further investigation may determine if these findings can simplify subjective symptom reporting in mood-monitoring studies.

Assessment of the Similarity of the Situation in the EU Labour Markets and Their Changes in the Face of the COVID-19 Pandemic

The aim of the study is to assess the similarity of the situation in the EU labour markets and their evolution using selected indicators in the period before and during the COVID-19 pandemic. The benchmark are the countries that most closely meet the Sustainable Development Goals related to the labour market. We use quarterly data from Eurostat presenting the basic indicators of the labour market: unemployment, employment, and activity rates. We analyse all indicators for the total population, young people, and people aged 55+. We assess the similarity of the situation using the TOPSIS method and similarity of changes by means of the Dynamic Time Warping. We obtain homogeneous groups of countries due to similarity of time series using hierarchical clustering. We conduct the analysis in two periods: the years 2018 and 2019 (pre-pandemic period) and from the beginning of 2020 to the present (pandemic period). The composition of the clusters in the pre-pandemic and pandemic periods is different. The impact of the COVID-19 pandemic on the situation in the labour market can be noted. This is a result of different degree of development of labour markets, which had an impact on coping with the effects of the crisis caused by the pandemic.

Chatter detection in turning using machine learning and similarity measures of time series via dynamic time warping

Chatter detection from sensor signals has been an active field of research. While some success has been reported using several featurization tools and machine learning algorithms, existing methods have several drawbacks including the need for data pre-processing by an expert. In this paper, we present an alternative approach for chatter detection based on K-Nearest Neighbor (KNN) algorithm for classification and the Dynamic Time Warping (DTW) as a time series similarity measure. The used time series are the acceleration signals acquired from the tool holder in a series of turning experiments. Our results show that this approach achieves detection accuracies that can outperform existing methods, and it does not require data pre-processing. We compare our results to the traditional methods based on Wavelet Packet Transform (WPT) and the Ensemble Empirical Mode Decomposition (EEMD), as well as to the more recent Topological Data Analysis (TDA) based approach. We show that in two out of four cutting configurations our DTW-based approach is in the error range of the highest accuracy or attain the highest classification rate reaching in one case as high as 98% accuracy. Moreover, we combine the Approximate and Eliminate Search Algorithm (AESA) and parallel computing with the DTW-based approach to achieve chatter classification in less than 2 s thus making our approach applicable for online chatter detection.

Quantification study of temperature distribution based on time series similarity in lithium titanate oxide anode based pouch battery

Lithium titanate oxide (LTO) anode based lithium-ion battery has a large instantaneous output power and obvious uneven surface temperature distribution happens when discharging under ultrahigh discharge rates. To better know about the thermal characteristics, the thermal performance analysis of a 15 Ah LTO anode based pouch battery during the discharge is carried out under the discharge rates from 1C to 40C. In this work, the definition of different temperature zone is proposed, and four evaluation parameters are introduced to evaluate the temperature distribution from aspects of the temperature fluctuation, the aggregation degree, the time series similarity during the discharge process, and the distribution similarity under different discharge rates. Moreover, the strategy of the cooling device design is proposed. The results reveal the temperature distribution mode of the battery during the discharge. The similarity during each discharge rate is high. The battery has a fixed and aggregated high temperature zone at 10C and above, the medium temperature zone and low temperature zone moves outwards during the discharge, while the periphery of the battery is always in low temperature zone. Besides, the similarity between the adjacent discharge rates is high. In conclusion, this work reveals the temperature distribution mode of the battery and can instruct the specific cooling device design for the battery.

A Type-2 Fuzzy Time Series Model for Pattern Similarity Analysis: A Case Study on Air Quality Forecasting

Air quality forecasting is a crucial part of megacities control and planning. It is necessary to develop high-quality forecasting methods in real-world applications, especially the issues that affect public health. Like many real-world problems, air quality is affected by uncertainties of nonstationary characteristics that their statistical attributes frequently change over time. Type-2 fuzzy systems have the capability to handle high-order uncertainties such as sequential dependencies associated with time series. This study develops a type-2 fuzzy intelligent system for air quality forecasting. Additionally, a dynamic time warping algorithm has been applied to estimate the pattern's similarity in long time series. The proposed model has been evaluated on a real dataset that contains the one-decade information about outdoor pollutants from April 2011 to November 2020 in Tehran and Beijing. The experiments have confirmed that the proposed model has lower forecasting error than counterpart models in terms of the RMSE, MAE, and MPE for both Tehran and Beijing time-series datasets. Also, the results confirm the superiority of the proposed model with an average area under the ROC curve (AUC) of 95% with a 95% confidence interval. This is promising for the prediction of air quality and make strategic prevention decisions.

Wind power time series simulation model based on typical daily output processes and Markov algorithm

The simulation of wind power time series is a key process in renewable power allocation planning, operation mode calculation, and safety assessment. Traditional single-point modeling methods discretely generate wind power at each moment; however, they ignore the daily output characteristics and are unable to consider both modeling accuracy and efficiency. To resolve this problem, a wind power time series simulation model based on typical daily output processes and Markov algorithm is proposed. First, a typical daily output process classification method based on time series similarity and modified K-means clustering algorithm is presented. Second, considering the typical daily output processes as status variables, a wind power time series simulation model based on Markov algorithm is constructed. Finally, a case is analyzed based on the measured data of a wind farm in China. The proposed model is then compared with traditional methods to verify its effectiveness and applicability. The comparison results indicate that the statistical characteristics, probability distributions, and autocorrelation characteristics of the wind power time series generated by the proposed model are better than those of the traditional methods. Moreover, modeling efficiency considerably improves.

VERIFICATION OF SIMILARITY AND SIMILARITY OF DAILY SCHEDULES OF ELECTRIC LOADING OF INDUSTRIAL ENTERPRISES

The purpose of the study in this paper is based on a detailed analysis of various mathematical and statistical methods for determining the similarity and uniformity of daily schedules of electrical load to form an approach to solving several important tasks. Namely, method of forming a static sample of complex load measurement data for the same included composition of single electrical receivers, selection of the optimum declared schedule of electric loading at purchase of the electric power on "Energorinka", as well as solving other similar tasks, all this in general requires effective clustering of graphs.
 Due to the fact that daily schedules of electrical load are divided into working days, pre-weekend, pre-holiday and weekend in this paper it is proposed to express the data of electric load graphs in Cartesian or polar coordinates. This allowed us to record the difference between the daily schedule of electrical load on normal working days from the day before.
 The efficiency of application of these methods of search of identical and similar daily schedules of electric loading was analyzed by allocation of several basic types of similarity of time series, similar: in time, on the form, on structure.
 It is shown that the calculation of the Euclidean distance allows to determine the uniformity of daily load graphs. And phase analysis is their similarity. The most acceptable method is to determine the correlation coefficient, which reveals the similarity and similarity of daily schedules of electrical load.

Denoising EEG Signals for Real-World BCI Applications Using GANs.

As a measure of the brain's electrical activity, electroencephalography (EEG) is the primary signal of interest for brain-computer-interfaces (BCI). BCIs offer a communication pathway between a brain and an external device, translating thought into action with suitable processing. EEG data is the most common signal source for such technologies. However, artefacts induced in BCIs in the real-world context can severely degrade their performance relative to their in-laboratory performance. In most cases, the recorded signals are so heavily corrupted by noise that they are unusable and restrict BCI's broader applicability. To realise the use of portable BCIs capable of high-quality performance in a real-world setting, we use Generative Adversarial Networks (GANs) that can adopt both supervised and unsupervised learning approaches. Although our approach is supervised, the same model can be used for unsupervised tasks such as data augmentation/imputation in the low resource setting. Exploiting recent advancements in Generative Adversarial Networks (GAN), we construct a pipeline capable of denoising artefacts from EEG time series data. In the case of denoising data, it maps noisy EEG signals to clean EEG signals, given the nature of the respective artefact. We demonstrate the capability of our network on a toy dataset and a benchmark EEG dataset developed explicitly for deep learning denoising techniques. Our datasets consist of an artificially added mains noise (50/60 Hz) artefact dataset and an open-source EEG benchmark dataset with two artificially added artefacts. Artificially inducing myogenic and ocular artefacts for the benchmark dataset allows us to present qualitative and quantitative evidence of the GANs denoising capabilities and rank it among the current gold standard deep learning EEG denoising techniques. We show the power spectral density (PSD), signal-to-noise ratio (SNR), and other classical time series similarity measures for quantitative metrics and compare our model to those previously used in the literature. To our knowledge, this framework is the first example of a GAN capable of EEG artefact removal and generalisable to more than one artefact type. Our model has provided a competitive performance in advancing the state-of-the-art deep learning EEG denoising techniques. Furthermore, given the integration of AI into wearable technology, our method would allow for portable EEG devices with less noisy and more stable brain signals.

Mapping Dongting Lake Wetland Utilizing Time Series Similarity, Statistical Texture, and Superpixels With Sentinel-1 SAR Data

Wetland is of significant ecological value, which is very important and challenging for large-scale mapping. Sentinel-1 can continuously record wetland changes with its all-day, all-weather working capability. How to fully utilize multidimensional information, such as time and statistical texture of Synthetic Aperture Radar (SAR) image, to classify wetlands more accurately has become a research focus. Thus, this paper constructed Time Series Similarity parameters to describe the temporal change information of targets in wetland and introduced G <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sup> statistical texture parameters to describe texture characteristics of SAR images. Combining multi-features and superpixels, we proposed a classification method based on Random Forest (RF) to map Dongting Lake wetland. The overall classification accuracy was 97.57%, and the Kappa coefficient was 0.97. The classification accuracy of reed beach, grass marsh etc. was above 95%. The results showed the proposed SAR Time Series Similarity features could effectively utilize dynamical information among classes and was helpful to identify mudflat, grass marsh and reed beach with high dynamics in wetland. The introduced statistical texture features expressed the heterogeneity of targets, and enhanced the recognition and extraction ability of forest beach, mudflat and reed beach. Compared with Support Vector Machine (SVM), Decision Tree (DT) and RF classification methods, RF with superpixels optimized not only got high precision but also could effectively reduce the pepper-salt error in classification, because of the consideration of superpixels context information.

Extraction of Sugarcane Planting Area Based on Similarity of NDVI Time Series

Timely and accurate estimation of the sugarcane planting area is of vital importance to the country’s agricultural production and sugar development. In remote sensing crop mapping based on spectral similarity, there will be have a phenomenon of foreign matters with the same spectrum by obtaining an accurate crop reference curve for crop identification, limiting mapping accuracy. In this study, we improved the spectral reconstruction method based on singular value decomposition (SR-SVD). A decision tree model was established based on the similarity of the sugarcane Normalized Difference Vegetation Index (NDVI) time series curve and the fluctuation range of NDVI in different growth periods. Using the Sentinel-2 (Level-2A) image data set to extract sugarcane planting area in two regions of Chongzuo City, Guangxi, China, the overall accuracy was higher than 96%, respectively. The results show that through the spectral similarity and the determination of the threshold fluctuation range, not only high-precision mapping of sugarcane can be achieved, but the problem of “same spectrum with different objects” can also be solved. Therefore, this method can provide accurate information on the sugarcane planting areas and technical support for monitoring the structure of sugarcane planting in the region.

Hotspot prediction of e-commerce network users based on improved K-nearest neighbour algorithm

Aiming at the problems of low accuracy and poor prediction effect in traditional e-commerce network users' hot spot prediction, this paper proposes an e-commerce network users' hot spot prediction method based on improved K-nearest neighbour algorithm. According to the users' hotspot prediction impact indicator, the K-nearest neighbour algorithm is improved in pattern matching process. The key point method is used to remove the noise interference of the original time series. The dynamic time warping algorithm is used to measure the similarity of time series of users' hotspot. The distance weight and trend coefficient are introduced according to the difference of users' hotspot time series to deduce the future users' hotspot and realise hotspot prediction of e-commerce network users. Experimental results show that the method in this paper greatly reduces the deviation of prediction results, which fully shows that the method has better prediction effect.

A 30 m Resolution Distribution Map of Maize for China Based on Landsat and Sentinel Images

As the second largest producer of maize, China contributes 23% of global maize production and plays an important role in guaranteeing maize markets stability. In spite of its importance, there is no 30 m spatial resolution distribution map of maize for all of China. This study used a time-weighted dynamic time warping method to identify planting areas of maize by comparing the similarity of time series of a satellite-based vegetation index at each pixel with a standard time series derived from known maize fields and mapped maize distribution from 2016 to 2020 over 22 provinces accounting for more than 99% of the maize planting area in China. Based on 18800 field-surveyed pixels at 30-meter spatial resolution, the distribution map yields 76.15% and 81.59% of producer’s and user’s accuracies averaged over the entire investigated provinces, respectively. Municipality- and county-level census data also show a good performance in reproducing the spatial distribution of maize. This study provides an approach to mapping maize over large areas based on a small volume of field survey data.

TSPol-ASLIC: Adaptive Superpixel Generation With Local Iterative Clustering for Time-Series Quad- and Dual-Polarization SAR Data

The superpixel generation is a key step for object-based classification and change detection. For the time-series polarimetric synthetic aperture radar (PolSAR) superpixel generation, the traditional polarimetric similarity measure based on the joint covariance matrix has limitations in discriminating different time-series similarity sequences with different fluctuations. Besides, in the traditional time-series PolSAR superpixel generation methods, it is difficult to determine the tradeoff factor between polarimetric and spatial similarity. In this article, an adaptive time-series PolSAR superpixel generation method based on the simple local iterative clustering (SLIC) is proposed, named time-series polarimetric SAR (TSPol)-adaptive simple local iterative clustering (ASLIC). There are three main improvements. First, a novel time-series polarimetric similarity measure based on the root mean square (rms) is proposed. Multitemporal polarimetric statistical information is combined to describe the polarimetric proximity between pixels, referring to the rms of the multitemporal proximities. Second, an edge detection method based on the stacked 2-D Gaussian-shaped (s2-D GS) window is proposed to initialize the central seeds for superpixel generation. Third, an improved SLIC clustering similarity combined with the time-series polarimetric, time-series power, and spatial similarities is proposed. Meanwhile, a homogeneity factor is applied to adaptively balance the relative weights of various similarities. We use eight Radarsat-2 quad-polarization synthetic aperture radar (SAR) images and 14 Sentinel-1 dual-polarization SAR images to evaluate the effectiveness. The results show our similarity measure and superpixel generation results are superior to those of the traditional methods. For example, as for the Radarsat-2 data, the improvement of the boundary recall by the proposed similarity measure and homogeneity factor is about 4% and 10%, respectively.

Large-Area Land-Cover Changes Monitoring With Time-Series Remote Sensing Images Using Transferable Deep Models

Dense time-series remote sensing images have transformed the traditional bitemporal land-cover change detection to continuous monitoring. Previous work mostly employs linear fitting, prediction, or decomposition methods, and the detection accuracy is not high. The latest progress of deep learning (DL) shows its advantages in time-series change monitoring. However, DL models are computationally expensive and require lots of labeled samples, resulting in often employed prediction-threshold-based unsupervised change detection method. However, the determination of a reasonable threshold has always been a big problem. Therefore, we proposed the similarity-measurement-based deep transfer learning for time-series adaptive change detection (SDTL-TSACD) model. First, a standard dynamic time warping (SDTW) distance was proposed and used to cluster large-scale time series into multiple subcategories with high time-series similarity. Second, a time convolutional network (TCN) was used for nonlinear time-series fitting and prediction, and an early stop strategy was used to prevent overfitting. Then, the trained TCN model would be transferred and performed pixel-by-pixel time-series prediction within the same category, and the SDTW was also used to evaluate the prediction accuracy. Finally, the Otsu adaptive threshold was used to detect change points, and the spatial neighbor relationship was used to eliminate the pseudo-change points. Change detection results using 132 benchmark datasets showed that the SDTL-TSACD performed well in both accuracy and efficiency. In addition, the MOD13Q1-EVI images from 2001 to 2020 were used to study the land-cover change of the Loess Plateau, and the SDTL-TSACD also showed a good ability to solve practical problems.

A Flexible Top-Down Data-Driven Stochastic Model for Synthetic Load Profiles Generation

The study of the behavior of smart distribution systems under increasingly dynamic operating conditions requires realistic and time-varying load profiles to run comprehensive and accurate simulations of power flow analysis, system state estimation and optimal control strategies. However, due to the limited availability of experimental data, synthetic load profiles with flexible duration and time resolution are often needed to this purpose. In this paper, a top-down stochastic model is proposed to generate an arbitrary amount of synthetic load profiles associated with different kinds of users exhibiting a common average daily pattern. The groups of users are identified through a preliminary Ward’s hierarchical clustering. For each cluster and each season of the year, a time-inhomogeneous Markov chain is built, and its parameters are estimated by using the available data. The states of the chain correspond to equiprobable intervals, which are then mapped to a time-varying power consumption range, depending on the statistical distribution of the load profiles at different times of the day. Such distributions are regarded as Gaussian Mixture Models (GMM). Compared with other top-down approaches reported in the scientific literature, the joint use of GMM models and time-inhomogeneous Markov chains is rather novel. Furthermore, it is flexible enough to be used in different contexts and with different temporal resolution, while keeping the number of states and the computational burden reasonable. The good agreement between synthetic and original load profiles in terms of both time series similarity and consistency of the respective probability density functions was validated by using three different data sets with different characteristics. In most cases, the median values of synthetic profiles’ mean and standard deviation differ from those of the original reference distributions by no more than ±10% both within a typical day of each season and within the population of a given cluster, although with some significant outliers.

Evaluating time series similarity using concept-based models

Time series similarity evaluation is a crucial processing task performed either as a stand-alone action or as a part of extensive data analysis schemes. Among essential procedures that rely on measuring time series similarity, we find time series clustering and classification. While the similarity of regular (not temporal) data frames is studied extensively, there are not many methods that account for the time flow. In particular, there is a need for methods that are easy to interpret by a human being. In this paper, we present a concept-based approach for time series similarity evaluation. Firstly, a global model describing a given dataset of time series (made of two or more time series) is built. Then, for each time series in the dataset, we create the corresponding local model. Comparing time series is performed with the aid of their local models instead of raw time series values. In the paper, the described processing scheme is implemented using fuzzy sets representing concepts. The proposed approach has been applied to the task of time series classification, yielding highly satisfactory results.

TT-graph: A new model for building social network graphs from texts with time series

Social network analysis is a fundamental problem inherent in various applications, which can be handled mainly based on a graph model given in advance. However, it is generally ignored in most existing studies that the social networks may only contain users and no users' connections are explicitly available. Then the connections between users play a considerable role in building the graph, and it is necessary to calculate users' similarities. Traditional methods of user similarity calculation are extensively based on the topics of text content because they can effectively reflect users' interests. Nevertheless, these methods mostly ignore the importance of time series in the texts, where the texts with time series can reveal the activity trends of users in social networks. In this work, we explore a new problem of building a social network graph over text with time series. Our basic idea is that social media users are more similar if they have similar text semantics in similar time sequences. To obtain the semantics of text with time series, we extract topic words of each user from the corresponding text with our proposed Time-Biterm Topic Model (T-BTM), which improves the BTM model by taking the time-topic distribution into account. On this basis, we further propose a novel time series-based graph model with text, called Text with Time series for Graph (TT-Graph) model, which explicitly considers the user similarity and time series similarity. With the TT-Graph model, we propose novel methods for topic detection, community detection, and link prediction in social network analysis. Extensive experiments demonstrate that topic detection, community detection and link prediction can be effectively conducted on the TT-Graph model, and the credibility of our model can be proved.

Dynamic Time Wrapper Based Local Predictor for Wind Speed Prediction

The quality of training sample is an important factor for wind speed prediction using data‐driven approaches, such as deep learning. This paper proposes a novel local predictor based on dynamic time wrapper (DTW) as training sample adaptation for wind speed prediction. After analyzing the similarity of wind speed time series using dynamic time wrapper, a local predictor is applied to improve the quality of training sample. An evaluation index is firstly proposed for estimating the quality of selected training sample. To verify the effectiveness of the proposed method, a random forest model with local predictor based on dynamic time warping (RF‐DTWLP) is applied to predict the wind speed. The simulation results demonstrate the prediction of wind speed by local predictor based on DTW has higher prediction accuracy. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Estimation of the Conifer-Broadleaf Ratio in Mixed Forests Based on Time-Series Data

Most natural forests are mixed forests, a mixed broadleaf-conifer forest is essentially a heterogeneously mixed pixel in remote sensing images. Satellite missions rely on modeling to acquire regional or global vegetation parameter products. However, these retrieval models often assume homogeneous conditions at the pixel level, resulting in a decrease in the inversion accuracy, which is an issue for heterogeneous forests. Therefore, information on the canopy composition of a mixed forest is the basis for accurately retrieving vegetation parameters using remote sensing. Medium and high spatial resolution multispectral time-series data are important sources for canopy conifer-broadleaf ratio estimation because these data have a high frequency and wide coverage. This paper highlights a successful method for estimating the conifer-broadleaf ratio in a mixed forest with diverse tree species and complex canopy structures. Experiments were conducted in the Purple Mountain, Nanjing, Jiangsu Province of China, where we collected leaf area index (LAI) time-series and forest sample plot inventory data. Based on the Invertible Forest Reflectance Model (INFORM), we simulated the normalized difference vegetation index (NDVI) time-series of different conifer-broadleaf ratios. A time-series similarity analysis was performed to determine the typical separable conifer-broadleaf ratios. Fifteen Gaofen-1 (GF-1) satellite images of 2015 were acquired. The conifer-broadleaf ratio estimation was based on the GF-1 NDVI time-series and semi-supervised k-means cluster method, which yielded a high overall accuracy of 83.75%. This study demonstrates the feasibility of accurately estimating separable conifer-broadleaf ratios using field measurement data and GF-1 time series in mixed broadleaf-conifer forests.

Mapping and forecasting of rice cropping systems in central China using multiple data sources and phenology-based time-series similarity measurement

Precise mapping and forecasting of rice cropping systems are essential for guaranteeing regional and even global food security. The central areas of China are the dominant Chinese rice-producing areas. However, due to limited land and a scarcity of skilled rural labourers in China, it has been difficult to meet the growing demand for rice production in recent years. Furthermore, the complex topography and climate in central China make it difficult to map paddy rice accurately. This paper maps the spatial pattern of rice in central China by using multiple data sources and a phenology-based time-series similarity approach, explores the driving forces for rice patterns through grey relational analysis (GRA), and presents a simulated future rice cropping system map by adding socio-economic factors to a cellular automata-Markov (CA-Markov) model. This study concluded that for 2015, the overall classification accuracy of rice was 88.12%, with a Kappa coefficient of 0.90. The planting acreage accuracies for single- and double-season rice in 2015 were 89.51% and 77.00%, respectively, and the corresponding R2 value for both were 0.80. From 2005 to 2015, the planting acreage of single-season rice significantly increased, while the planting acreage of double-season rice generally decreased. The planting acreage of total rice exhibited an overall increasing trend during 10 years. The cumulative temperature, slope and distance to water bodies were key influencing factors for the spatial distribution of rice. Compared with that for 2015, the simulated total planting area of rice for 2030 was slightly higher, and the spatial pattern of double-season rice exhibited an obvious southward trend. These findings show that the proposed rice mapping and forecasting method is effective. This method allows us to predict future rice patterns precisely under the influence of human activities in complex cropping conditions and various rice cropping systems.