Optimizing the Temporal Scale in the Assimilation of Remote Sensing

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Optimizing the Temporal Scale in the Assimilation of Remote Sensing and WOFOST Model for Dynamically Monitoring Heavy Metal Stress in Rice Feng Liu, Xiangnan Liu, Ling Wu, Zhao Xu, and Lu Gong

Abstract—Obtaining precise information regarding the levels of heavy metal stress in crops is vital for food security. The assimilation of remote sensing into the World Food Study (WOFOST) model provides a method for achieving the spatial–temporal evaluation of crop growth status, while the optimization of the temporal scale in assimilation framework has rarely been considered. In this study, the temporal scale was optimized based on a wavelet transform of the leaf area index (LAI) curves. The accurate simulation of LAI laid the foundation for high precision. As the dry weight of rice roots (WRT) was demonstrated to be the most stress-sensitive indicator, the measured WRT values were assimilated into the improved WOFOST model to realize the dynamic simulation of LAI. Finally, four optimal time points were determined based on the extreme areas in the d4 wavelet coefficient, providing a reference for the selection of remote sensing images. The verification in the two sample plots indicated that the assimilation with optimized temporal scale could significantly improve the efficiency on the basis of guaranteeing the accuracy, shortening the run time of model operation by more than 30%. Based on the optimized temporal scale, the RS-WOFOST assimilation framework was driven for each pixel in the study areas, achieving the spatial–temporal evaluation of heavy metal stress in rice. This study suggests that the wavelet transform to LAI is applicable for optimizing the temporal scale in assimilation, providing a reference for the improvement of assimilation results under the premise of balancing accuracy and efficiency. Index Terms—Assimilation, heavy metal stress, remote sensing, rice roots, temporal scale, wavelet transform.

I. I NTRODUCTION

F

OOD security is an important issue that affects agricultural production and people’s livelihoods. Heavy metal contamination of farmlands is one of the major environmental problems resulting from rapid industrialization and urbanization in China over the last several decades [1], [2]. According

Manuscript received July 03, 2015; revised September 19, 2015; accepted November 04, 2015. This work was supported by the National Natural Science Foundation of China under Grant 41371407 and the Fundamental Research Funds for the Central Universities under Grant 35732015025. (Corresponding author: Xiangnan Liu.) F. Liu, X. Liu, Z. Xu, and L. Gong are with the School of Information Engineering, China University of Geosciences, Beijing 100083, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). L. Wu is with the Institute of Remote Sensing and GIS, Peking University, Beijing 100871, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSTARS.2015.2499258

to the related statistics, the emission of heavy metals into the biosphere has risen sharply, and more than 12 million tons of grain is contaminated in China every year. Heavy metal elements can leak into the wider environment and easily enter the human diet through the food chain [3], [4]. Heavy metal contamination in farmlands is concealed, permanent, and irreversible. Most of the previous studies adopted empirical or semiempirical models that were established based on the relationships between sensitive spectral characteristics and the physiological parameters of crops (or heavy metal concentrations) [5]–[11]. The selected physiological parameters are primarily derived from the aerial organs of crops, whereas monitoring of heavy metal stress in roots has rarely been considered. Because heavy metals are taken up by roots from the soil, the greatest concentrations appear in plant roots. Although heavy metal ions can be transported from roots to the aboveground parts of plants, there are obvious interception effects on them. With the most direct contact to heavy metals and the strongest potential for enrichment, roots are more likely to respond to the heavy metal toxicity before other parts of plants [12]–[16]. As the dry weight of rice roots (WRT) is one of the most important root parameters under heavy metal stress, the assessment of WRT has considerable potential as a tool for monitoring stress levels in contaminated crops. However, with the existing remote sensing methods, the direct monitoring of stress levels in underground roots is difficult. Crop growth models provide an approach to establish the indirect relationship between remote sensing data and WRT values, making the combination more persuasive from the viewpoint of the stress mechanism and growth law of crops. Previous models were generally built based on the statistical analysis of data consisting of leaf-level spectral reflectance from the plants that were exposed to varying levels of heavy metal stress. Compared with the statistical analysis on spectral characteristics, the crop growth model World Food Study (WOFOST), which uses relevant environmental and crop parameters, has a stronger mechanism [17], [18]. The use of only remote sensing or spectral measurement focuses on the stress-induced variations at one or more discontinuous stages of crop growth, whereas the degrees of heavy metal stress are not the same at different growth stages, resulting in a dynamic trend [19]–[21]. Considering this problem, the WOFOST model enables temporally dynamic simulation and can describe the

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fundamental processes of crop growth, such as photosynthesis, respiration, transpiration, and biomass partitioning, covering an entire growth cycle. The assimilation of remote sensing into the WOFOST model achieves the objective of spatial–temporal scale continuous simulation of rice growth parameters, solving the discontinuity of spatial scale simulation by crop model and temporal scale retrieval by remote sensing information [22]–[25]. However, there are massive parameters and variables incorporated in the WOFOST model, resulting in a high computational cost in the process of system operation. Meanwhile, the algorithm of assimilation is a process of iteration and optimization, and the computational efficiency affects and restricts the development of an assimilation model. The temporal scale in the assimilation framework determines the step length and time points of assimilation (time interval of remote sensing data acquisition), so different temporal scales require different numbers of remote sensing images. In most of the previous studies, the time points of assimilation were distributed evenly in the selected growing season, providing well-defined assimilation precision. Thus, larger amounts of remote sensing images were incorporated into the assimilation framework, which may inevitably lead to the large computation quantity and low assimilation efficiency. Meanwhile, the acquisition of remote sensing data may also encounter practical problems, including the influences of cloud and rain as well as the time resolution and swath width of remote sensing images. The lack of pertinence to the key periods of crop growth under stress may also lead to randomness and uncertainty in the assimilation. Research on the optimized temporal scale of assimilation model is often ignored, whereas the reasonable selection of time points in the observation data can significantly reduce the calculation amount, and meanwhile improves the assimilation efficiency at a defined accuracy. Furthermore, based on the reasonable temporal scale, there will be greater flexibility in the selection of remote sensing images, which are served as the observation data in the assimilation process. Hence, under the premise of balancing the accuracy and efficiency, the optimization of the temporal scale is vital to the improvement of the assimilation result. In this study, the temporal scale of the RS-WOFOST assimilation framework was optimized based on the wavelet transform (Daubechies 5 wavelets) to the original leaf area index (LAI) curves. To improve the accuracy of the LAI simulation under heavy metal stress, we embedded a specific stress factor fM into the original WOFOST model. Moreover, the time-series WRT values were assimilated into the WOFOST model, and the stress factor was optimized in the process of assimilation. The modified WOFOST model was driven with the optimum fM to realize the dynamic simulation LAI. Finally, the wavelet transform was conducted to the original LAI curve with db5 wavelet function, and the optimal time points were determined based on the extreme areas in the d4 wavelet coefficient. Based on the optimized temporal scale, appropriate remote sensing images could be selected for the RS-WOFOST assimilation framework with the intention of realizing the spatial– temporal continuous evaluation of heavy metal stress in rice tissues.

II. S TUDY A REA AND DATA A. Study Area The study area is located in the city of Zhuzhou, which lies in the primary commodity grain producing area of Hunan Province, China. The primary type of rice grown in this area is the hybrid rice Boyou9083, normally transplanted in early June and harvested in mid-September, lasting approximately 100 days. Rice phenological stages after transplant include the tillering stage, jointing–booting stage, heading–flowering stage, and ripening stage. The primary type of soil is red soil with sufficient organic matter content (2%–3%). This area belongs to a subtropical monsoon climate zone with sufficient sunlight and a mean annual temperature of approximately 16 ◦ C–18 ◦ C. However, Zhuzhou City is one of the old heavy industry bases and is an important railway hub in China. Several industries have existed in this area for decades, including metallurgy, electronics, chemical industry, and machinery. Consequently, the Xiangjiang River and its tributaries are contaminated by industrial pollutants from the nearby factories for a long time. Heavy metal contamination in rice fields has resulted from the direct use of sewage for irrigation [26]–[28]. Two study areas (labeled A and B) with a size of 1 km × 1 km were selected (Fig. 1), and each contained a large rice-growing area. According to the measured soil heavy metal concentrations in the sample plots (Table I), areas A and B were categorized as “safe level” and “stress level,” respectively. The study areas have similar climates, historical land uses, and the physicochemical characteristics of the soil are adequate to ensure the normal growth of rice based on local management experience. The planted rice in the areas was adequately fertilized and irrigated to avoid unintended stress caused by other environmental factors. B. Data Preparation The experiment was conducted in 2014. The remote sensing data used in this study is CCD data from the Environment and Disaster Reduction Small Satellites (HJ-1A/B) [29] due to its high time resolution (4 days) and high spatial resolution (30 m). The CCD camera has four bands of blue, green, red, and shortwave infrared spectral wavelengths (B1: 0.43−0.52 µm, B2: 0.52−0.60 µm, B3: 0.63−0.69 µm, B4: 0.76−0.90 µm). With the calibration coefficient of each band provided by China Centre for Resources Satellite Data and Application, radiometric calibration of CCD data was conducted, and then atmospheric correction based on FLAASH model [30] was also carried out. Considering the image quality and coverage area of CCD data in the growing season, seven appropriate CCD images (dating from June 13 to September 21) were selected for the inversion of LAI. The acquisition dates of the images covered the entire growing season of the study areas. In particular, according to the previous study, a modified calculation of NDVI was adopted to improve the accuracy of LAI inversion [31]. In this study, the WOFOST model was used to realize the dynamic simulation of LAI under heavy metal stress. The primary input parameters of this model were associated with both climate and crop characteristics. Climate parameters principally

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Fig. 1. Location map for study areas in the city of Zhuzhou, Hunan Province, China. TABLE I I NFORMATION OF H EAVY M ETAL C ONCENTRATIONS IN THE S TUDY A REAS

Note: The unit of heavy metal contamination is mg/kg. The background values in soil are derived from Hunan Institute of Geophysical and Geochemical Exploration, China.

included solar radiation, air temperature (T), wind speed, vapor pressure, and precipitation. Some of the crucial data, such as the daily air temperature and sunshine duration, were collected from the China Meteorological Data Sharing Service System. Furthermore, the regionalization of climate parameters in the study areas was conducted with related MODIS data products [25]. The varieties of hybrid rice that were grown in the two study areas had the same hereditary properties. Thus, the crop parameters (such as leaf area, net photosynthetic rate, and dry matter distribution coefficient) and initial conditions in the model were adjusted to be constant throughout the measurements, and were constant in the literature review [32], [33]. According to local rice management experience, the sowing date, amount of irrigation, and the amount of fertilization were also collected as management information for the WOFOST model. Field measurements were conducted at four acquisition dates in 2014: 1) July 3 (the time is expressed as the day of the year, DOY; July 3 is thus called DOY 184); 2) July 30 (DOY

211); 3) August 29 (DOY 241); and 4) September 17 (DOY 260). The measurements were conducted to obtain the important agronomic and biological parameters of rice during the entire growing season, and there was one sample plot in each of the two study areas. The field measurements of soil and rice data were conducted in the sample plots, which primarily included the rice growth parameters and heavy metal concentrations. Rice LAI was measured by a botanical canopy analyzer (AccuPAR model LP-80), and the chlorophyll content was measured by a SPAD-502 portable chlorophyll meter (Minolta Corporation, NJ, USA). In particular, the soil and crop samples were preserved separately in sample bags and transported to the laboratory for analyses. These samples were dried at room temperature to achieve a constant weight. The roots of rice were weighed to be used for calculating WRT in the sample plots. The heavy metal concentrations in the samples were determined using flame atomic absorption spectrometry (AAS) following nitric-perchloric acid (2:1) digestion [34]. At every acquisition date, 30 sets of sample data were measured in each

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sample plot, with the average of the 30 sets being calculated as the representative of the corresponding sample plot.

TABLE II WRT OF R ICE IN S AMPLE P LOTS OF THE T WO S TUDY A REAS AT F OUR ACQUISITION DATES (DOY)

III. M ETHODS A. Improved WOFOST Model With Incorporated Stress Factor Previous studies have shown that the accumulation of heavy metals in rice tissues has a significant impact on photosynthesis and dry matter production, which, in turn, determines the relevant crop growth parameters [35]–[37]. LAI, since its definition in 1940s, has been widely used for monitoring crop growth as an important botany parameter. The accurate simulation of LAI under heavy metal stress provides a foundation for the optimization of the temporal scale with remote sensing observations. The WOFOST crop growth model allows for continuous simulation of LAI throughout the entire growing season. However, the simulation process of the WOFOST model is conducted under the potential production level (suitable water and nutrients). From the view of the growth mechanism, the model does not use any factor to monitor the impacts of heavy metals on crop growth. Focusing on this problem, a stress factor was incorporated into the WOFOST model, intending to simulate LAI values more accurately under heavy metal stress [38]. With the incorporated stress factor fM , the potential productivity level of rice was modified through carbohydrate assimilation efficiency (1) ES (D) = fM × Enon−S (D)

(1)

where D is the day number of the year, ES (D) is the actual assimilation efficiency of rice under heavy metal stress on Day D, and Enon−S (D) is the assimilation efficiency of the potential productivity level under normal growth conditions on Day D. According to prior knowledge and actual conditions, the stress factor fM is the quantitative description of the effect of heavy metal stress on crop growth, taking values from 0 to 1. When the value is closer to 0, the actual efficiency of carbohydrate assimilation declines at a certain rate, whereas when the value is closer to 1, the actual efficiency approaches the potential productivity level. As discussed above, the growth status of the roots reflects the degree of crop stress and the soil contamination conditions. Compared with the aerial organs of plants, roots are likely to have higher capacities for the absorption and enrichment of heavy metals. Hence, the selection of WRT as the assimilation target has great potential to improve the simulation accuracy of the WOFOST model under stress. The value of the stress factor was optimized by assimilating the measured WRT values into the WOFOST model. Through constant adjustment of the factor fM with the assimilation algorithm, the simulated values of WRT were adjusted until the differences between them and the measured values were minimized. Thus, the optimal value of fM was obtained, and the precision of the dynamic simulation of stressed LAI was improved by running the modified WOFOST model. Furthermore, to quantify the performance of the WRT-WOFOST assimilation model, two evaluation indicators between the measured and simulated LAI values were calculated: 1) the correlation coefficient (R2 ) and 2) absolute

Note: The unit of WRT is g/m2 .

percent error (APE). R2 was calculated to determine the accuracy of simulated LAI values, and APE indicated the estimation errors. The two indicators were computed by 2 N  (LAIS(ti) − LAIS )(LAIM (ti) − LAIM ) R2 = N i=1 N  2  2 (LAIS(ti) − LAIS ) (LAIM (ti) − LAIM ) i=1

i=1

 i=N  1  LAIS(ti) − LAIM (ti)    × 100% AP E = LAIM (ti)  N i=1

(2) (3)

where LAIS(ti) and LAIM (ti) represent the simulated LAI and measured LAI at one date point (time ti), respectively. LAIS and LAIM represent the average simulated value and average measured value of LAI, respectively. N is the number of data acquisition dates in the entire growing season (which is equal to 4 in this study). B. Assimilation of Measured WRT Into WOFOST Model Because the impact mechanisms of heavy metals on rice growth are uncertain, the direct acquisition of the stress factor fM is generally difficult. Thus, assimilating the time-series WRT values into the WOFOST model provides an attractive alternative for optimizing the value of the stress factor. The simulated values of WRT could be calculated using the modified WOFOST model, into which fM values were embedded. In contrast, the measured WRT values were considered to reflect the stress conditions more accurately, which were obtained from the field-measured data on the four acquisition dates (Table II). According to the measurements in sample plots, WRT values of contaminated rice are generally lower than those of uncontaminated rice. In this study, the particle swarm optimization (PSO) algorithm was used in the assimilation framework [39]. The values of fM in the WOFOST model were adjusted constantly until the simulated WRT values reached the best agreement with the measured values in the sample plots (Fig. 2). The property of the optimization algorithm and the dependence on a priori knowledge influence the application of an assimilated crop growth model [40]. The adjustment process of the PSO algorithm in this study is as follows: 25 random values of fM were first generated in the range of 0 to 1, and then the WOFOST model was driven to simulate 25 groups of time-series WRT values with the factors. By comparing the differences between every group of simulated WRT and the measured values, the local optimal value of fM was determined

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Fig. 2. Flowchart of WRT-WOFOST assimilation framework for the optimization of the temporal scale.

based on the criterion of minimizing the differences. Then, the 25 fM values were adjusted with different step sizes, and the corresponding 25 groups of simulated LAI values were generated. Again, the 25 new differences were calculated and compared with the last minimum difference, and the fM associated with the new minimum difference was determined as the new local optimal value. The adjustment process terminated when the iteration number reached the maximum value of 300, or the cost function value did not change when the iterations exceeded 50. The last local optimal fM was output as the global optimal value. The difference was quantified with the cost function, which described the process of time-series assimilation (4)   P 

2 1 WRT M (ti) − WRT S(ti) (4) Q= P i=1 where Q is the value of the cost function, P is the number of WRT data acquisition dates in the entire growing season, which is equal to 4 in this study. WRT M (ti) is the value of WRT measured in the sample plot at one date point (time ti), and WRT S (ti) is the value of WRT simulated by WOFOST model at the corresponding date point.

spectral singularity signal, and there may be no visible and steady symptoms in the original LAI curve. The wavelet transform technology can be used to detect singularity information and amplify subtle characteristics of LAI under heavy metal stress. First, it is suitable for the wavelet high-frequency component of original LAI curve to detect the stress information in crops growing in natural agro-ecosystems with relative low level of pollutants. Second, the wavelet transform has the ability for singularity signal localization in abnormal phenomenon of LAI curve of stress-induced crops. However, the selection of wavelet function depends on different signal processing problems. A related study showed that the Daubechies 5 wavelets was able to detect stress information in a satisfactory way by reducing the impacts of atmospheric scattering, absorption, background, and equipment noise on spectral signal of rice [46]. According to the research, the wavelet low-frequency component (a) and high-frequency component (d) were generated at each level of decomposition of an original LAI curve, intending to derive and enhance subtle characteristic information associated with heavy metal stress (5) f (λ) = aj (λ) +

j 

di (λ)

(5)

i=1

C. Singularity Analysis of LAI Based on Wavelet Transform The monitoring of heavy metal stress illustrates the need for a more accurate, dynamic simulation of LAI [41], [42]. The sample plots of the two study areas were used as experimental unites. With the incorporated optimal fM and input parameters, the WOFOST model was driven for the two sample plots. The dynamic simulations of LAI in the sample plots were obtained, covering the entire growing season with a time step of one day. Furthermore, the monitoring of LAI provides useful information for the estimation of rice growth status under heavy metal stress on a temporal scale. To effectively detect and amplify the subtle stress-induced variations of LAI, methods based on the wavelet transform were used in this study. With excellent time and frequency properties, the wavelet transform has been proven to be quite useful in spectral smoothing, noise removal and singularity signal detecting [43]–[45]. The characteristics of LAI variations under heavy metal stress were similar to the

where f (λ) is the original LAI signal, j is the wavelet decomposition level, and aj and di are the wavelet low-frequency component and high-frequency component, respectively. Low-frequency components (signals with relatively stable) can reflect the global characteristic of the signal curve, while high-frequency components can be used in the analysis of nonstationary signals and have particular advantages for detecting short-lived and singularity phenomena. In this study, the wavelet disassembled signal was performed by wavelet transform to original LAI curve with Daubechies 5 (db5) wavelet function. The result indicated that the four decomposition levels were able to detect stress information of rice under heavy metal pollution in a satisfactory way. In four decomposition levels, the wavelet components for LAI curve were denoted by a4 for low-frequency wavelet component, d1, d2, d3, and d4 for high-frequency wavelet component (Fig. 3). As shown in Fig. 3, large amplitude of d1, d2, and d3 presented noise

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TABLE III E FFICIENCY A SSESSMENTS FOR LAI S IMULATIONS IN THE T WO S AMPLE P LOTS

Fig. 3. Extraction of stress-induced subtle information based on db5 wavelet function.

signals and the large amplitude of d4 presented singularity signals. Particularly, the extreme points of the wavelet coefficient corresponded to the singularity points of original LAI curve. It was concluded that four decomposition levels were appropriate for both identifying the stress levels of rice under heavy metal pollution and removing noise.

IV. R ESULTS A. Performance of the WRT-WOFOST Assimilation Framework In the WRT-WOFOST assimilation framework, the values of WRT, as stated in Section III-B, were determined as the compared targets of the cost function. The measured values of WRT were considered to be the actual values of the sample plots. Then, the factor fM in the improved WOFOST model was constantly adjusted with the PSO algorithm, intending to minimize the differences between the simulated WRT and the measured values. Furthermore, in each sample plot, the WOFOST model was driven with the optimal fM , and the dynamic simulation of LAI was obtained. To quantify the performance of the improved WOFOST model in sample plots A and B, two evaluation indicators R2 and APE between the measured and simulated LAI values were calculated. The results of efficiency assessments for LAI simulations are presented in Table III, reflecting the performance of the improved WOFOST model in the two sample plots. As defined in Section III-A, R2 was calculated to determine the accuracy of simulated LAI values, and APE indicated the estimation errors. The simulation result corresponding to a higher value of R2 and a lower value of APE was considered to have a better performance. The efficiency assessments in Table III demonstrated that the WRT-WOFOST assimilation framework had a better performance for monitoring LAI variations, with R2 higher than 0.97 and APE lower than 9.5% in both sample plots. The potential productivity level corresponded to the suitable water and

nutrients, which was not accurate to describe the real growth conditions of crops. Additionally, as shown in Fig. 4, the simulated LAI values with the improved WOFOST model achieved a better fit with the measured values in the two sample plots. The soil quality in sample plot A corresponded to a safe level, so the simulated LAI values were generally close to the potential productivity. As a contrast, sample plot B suffered moderate pollution, and the differences between the simulated values and the potential productivity were significant. Hence, the simulation results of the improved WOFOST model were stable and reliable. Additionally, the resulting fM value of sample plot A was clearly higher than that of sample plot B, reflecting different heavy metal soil concentrations in the two sample plots. B. Dynamic Monitoring of LAI Under Heavy Metal Stress The efficiency assessments indicated that the improved WOFOST model had a better performance to simulate rice LAI under heavy metal stress. As shown in Fig. 5(a), the variation trends of LAI in the two sample plots were roughly consistent throughout the entire growing season, increasing slowly at the tillering stage and increasing rapidly at the jointing– booting stage, subsequently reaching the maximum value at heading–flowering stage, and finally decreasing apparently at the ripening stage. Additionally, with different soil heavy metal concentrations, the simulation results in the two sample plots exhibited significant discrepancies. The stress factor value was higher in sample plot A than that in plot B, indicating that the planted rice in area B suffered more severe stress, similar to the actual contamination condition. The difference between LAI values of the two sample plots (LAIA − LAIB ) was computed, which quantitatively reflected the influences of heavy metal stress on rice LAI. The differences were relatively low at the tillering stage of the growing season, and then increased gradually until reaching the most significant discrepancy at heading–flowering stage, with a value of approximately 0.54. Finally, the differences generally remained unchanged as the growth period advanced into the ripening stage, indicating that the tolerance of rice tissues to heavy metal stress was stronger. In addition, the growth rate of LAI was calculated to make a further analysis on the mechanism of heavy metal stress [Fig. 5(b)]. The growth rate of LAI in sample plot B was generally lower than in sample plot A, and the most significant discrepancy appeared at the jointing–booting stage, with a value

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Fig. 4. LAI simulations with improved WOFOST model in sample plots A and B.

Fig. 5. Dynamic assessment for the variations of LAI under heavy metal stress.

of 0.04. In other words, the normal physiological process of rice LAI was inhibited by heavy metal toxicity, especially at the jointing–booting stage. Based on the analysis above, the heavy metal toxicity began to show an inhibiting effect on LAI at the jointing–booting stage. The effect then became significant and stable from the heading–flowering stage to the end of the growing season, indicating that the middle-late stage (from the jointing–booting stage to the ripening stage) was the optimal choice to monitor stress levels on LAI. C. Optimization of the Temporal Scale in Assimilation Heavy metal stress results in the variations of LAI on the temporal scale, consequently inducing the changes of shift and amplitude in the singularity points of the LAI curve. However, it is difficult to identify the singularity points in the original LAI curve, and the extraction of subtle characteristic information associated with heavy metal pollution is necessary for monitoring stress levels. A reliable method for detecting the singularity points is wavelet transform. As seen in Fig. 6, the singularity points of LAI curve across the entire growing season could be quantitatively calculated and analyzed. Additionally, the differences of positions and amplitudes of the extreme points in d4

curves of rice LAI with different stress conditions were displayed. Such differences can serve as a basis for distinguishing the stress levels of rice under heavy metal pollution. The rice tissues corresponding to a higher stress level were considered to have a stronger singularity in the original LAI curve, inducing more extreme points in the d4 curve and the amplitudes of the points were also larger. As discussed in Section IV-B, the optimal observation stage to monitor heavy metal stress on LAI was the middle-late stage. Hence, the selection of time points for the assimilation of remote sensing and the WOFOST model was conducted at this stage. Furthermore, intending to avoid the low coverage of rice associated with low values of LAI, the positions of the RS-WOFOST assimilation time points were determined based on the extreme points after DOY 200 (July 19) (Fig. 7). Apparently, there were four extreme areas in the d4 wavelet coefficients from the beginning of the middle-late stage to the end of the growing season. The extreme areas incorporated five extreme points in the d4 curve of the sample plot B, one more than that in sample plot A. As shown in Table IV, the positions of the first three extreme points in the two sample plots were consistent. The fourth extreme point in sample plot A located between the last two extreme points of sample plot B. The

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Fig. 6. Singularity points of the LAI curve and extreme points of wavelet coefficient (d4). TABLE V C OMPARISON OF THE ACCURACY AND E FFICIENCY B ETWEEN THE T WO A SSIMILATION T EMPORAL S CALES

Note: The efficiency of the schemes is represented with the run time of the assimilation model.

Fig. 7. The selection of time points for RS-WOFOST assimilation based on d4 wavelet coefficient. TABLE IV T HE P OSITION AND A MPLITUDE OF E XTREME P OINTS IN D 4 C URVES OF THE T WO S AMPLE P LOTS

under stress. Next, the time points for RS-WOFOST assimilation were selected based on the extreme areas. The first three time points were determined as DOY 203, DOY 217, and DOY 228. The time intervals between them were approximately 15 days, generally reflecting the phenology and growth law of crops in the area [47], [48]. Thus, the fourth time point was scheduled as DOY 243 (15 days later than the third time point), just locating in the fourth extreme area. Considering the practical issues in the acquisition of remote sensing images, the acquisition dates were not confined to the four time points. Instead, the acquisition dates should be close to the time points as far as possible, meanwhile taking the dates of available remote sensing images into account. D. Spatial–Temporal Continuous Evaluation of Stress Levels

amplitudes of the extreme points in the two d4 curves showed significant discrepancies, indicating that the four extreme areas were reliable for reflecting the overall variation of rice LAI

Compared with the traditional ground-based detection, the remote sensing technology provides a new alternative to achieve rapid, nondestructive and real-time monitoring of the stress-induced inhibitions on crop growth. As stated in Section I, the values of WRT could clearly reflect the heavy metal stress level in rice tissues. Hence, the spatial–temporal

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Fig. 8. Spatial–temporal continuous simulation of WRT in the study areas.

variation of stress levels was represented with the continuous simulation of WRT in the study areas [31]. The two sample plots were first used as experimental areas, scheduling the RSWOFOST assimilation model with different temporal scales. Scale 1 incorporated all seven CCD images into the assimilation model, while scale 2 incorporated four images that were close to the optimal time points in Section IV-C. WRT values in the two sample plots were simulated with the RS-WOFOST assimilation framework, and the measured values were obtained from the field measurements. In each sample plot, the accuracy and efficiency of WRT simulation between different temporal scales could be compared. As shown in Table V, the simulated WRT in scale 1 achieved a better fit with the measured values in each sample plot, but the simulation accuracy was slightly higher than in scale 2. However, the efficiency in scale 2 was significantly improved in the process of assimilation, shortening the run time of model operation by more than 30%. The comparison between the two scales indicated that the optimized temporal scale could apparently improve the assimilation efficiency on the basis of guaranteeing the accuracy. Hence, the four CCD images based on the optimal time points were incorporated into the RS-WOFOST assimilation model. Moreover, considering the issues of spatial heterogeneity, regionalization of parameters in the assimilation framework was required. With the regional input parameters, the RSWOFOST assimilation framework was driven for each pixel in the study areas, realizing the spatial–temporal continuous simulation of WRT. In particular, the four data acquisition dates (Section II-B) were chosen as representatives of the crucial growing stages (Fig. 8). After the transplanting date, the WRT values were relatively low at the tillering stage (DOY 184), and there was little difference between the two study areas. As the rice growth entered the jointing–booting stage (DOY 211), rice tissues gave priority to vegetative growth and a large amount of water and nutrients were needed in the process. Toxic heavy metal elements were also absorbed into the root cells at the same time. Hence, WRT apparently increased, and the values of the safe level began to exceed those of the stress level, highlighting the stress effect on the growth of rice roots. Next, the growth rate gradually slowed down until WRT reached the

maximum value at the heading–flowering stage (DOY 241), also resulting in the most significant difference between the two study areas. Finally, after entering the ripening stage (DOY 260), the rice growth gave priority to the increase in the storage organs, leading to the aging process of rice roots and a decrease in WRT. In the latter part of the growing season, the stress level remained relatively stable as the tolerance of roots to heavy metal elements was stronger [49], [50]. V. C ONCLUSION AND D ISCUSSION The monitoring of heavy metal contamination in farmlands has become one of the most critical environmental issues in recent years. Remote sensing technology is becoming a potentially promising method to obtain precise information regarding soil and crop contamination. The assimilation of remote sensing into the WOFOST model has been demonstrated to be effective in the spatial–temporal evaluation of crop growth status. However, the optimization of temporal scale in the RSWOFOST assimilation framework has rarely been considered previously. In this study, the optimal assimilation time points were determined based on the wavelet transform to the original LAI curves. As a key aspect in the process, the accurate simulation of the LAI curve laid the foundation for the precision guarantee. Compared with the aboveground parts of crops, the root was considered to have the highest potential for the absorption and enrichment of heavy metals. Hence, WRT was selected as an appropriate indicator of heavy metal stress, and the measured WRT values were assimilated into the improved WOFOST model to realize the dynamic simulation of LAI. Finally, based on the optimized temporal scale, the RSWOFOST assimilation framework was driven for each pixel in the study areas. The continuous simulation of WRT allowed for the dynamic and quantitative assessment of heavy metal stress in rice tissues. In this study, the optimized temporal scale of RS-WOFOST assimilation framework was determined based on the wavelet transform to the original LAI curves. The extreme points of d4 wavelet coefficient corresponded to the singularity points of original LAI curve. The positions and amplitudes of the

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extreme points in the d4 curves of the two sample plots displayed apparent differences, clearly reflecting the stressinduced variations of rice LAI. There were four primary extreme areas in d4 curves at the middle-late stage, incorporating the optimal assimilation time points. The interval of approximately 15 days also reflected the phenology and growth law of rice in the study areas. However, the optimized temporal scale was determined based on the analysis of LAI, which was primarily applicable to the assimilation of LAI into the WOFOST model. In the practical application, the acquisition dates of remote sensing images should be as close to the four time points as far as possible but not confined to the time points. Additionally, further study is still needed to gain a better understanding of the role of each growth stage in stress monitoring. Previously, the wavelet transform was primarily used in spectral smoothing, noise removal and singularity signal detecting. The spectral reflectance displayed a stronger singularity than the LAI curve, so wavelet transform was able to detect stress information in a satisfactory way by identifying the singularity points in the original spectrum. In this study, the LAI curve served as the target of the db5 wavelet function, and the wavelet transform also displayed the ability for detecting the abnormal phenomenon of the stress-induced LAI variation. We determined the optimal time points based on the positions of the extreme points in d4 curves. Nevertheless, further work will place greater emphasis on the analysis of positions and amplitudes of the extreme points. To detect the subtle characteristic information related to heavy metal pollution and discriminate different stress levels of rice tissues, the stress mechanism and phenology in the study areas should also be taken into account. The optimized temporal scale of the RS-WOFOST assimilation framework was consistent with the determination of the best observation stages, making the selection of remotely sensed observations more efficient and targeted. However, the temporal scale in this study was determined based on the rice growth cycle (approximately 100 days) in the study areas. When the constructed method is applied to other types of crops (or climate zones), the growth cycle may be different, so the temporal scale should be further modified according to the practical situations. In summary, wavelet transform technology can be widely used to detect singularity information and amplify subtle characteristics of crop stress under various environmental conditions.

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Feng Liu received the B.S. degree in geographic information system from China University of Geosciences, Beijing, China, in 2013, where he is currently pursuing the M.S. degree in surveying and mapping engineering. His research interests include environmental remote sensing and the assimilation of crop model and remote sensing information.

Xiangnan Liu received the B.S. degree in geography from Hunan Normal University, Changsha, China, in 1987, and the M.S. and Ph.D. degrees in remote sensing and geographic information system from the Northeast Normal University, Changchun, China, in 1990 and 1996, respectively. In 1990, he joined the Faculty of Northeast Normal University, Changchun, China. Since 2006, he has been a Professor with the School of Information Engineering, China University of Geosciences, Beijing, China. He is the author of four books and more than 100 articles. His research interests include modeling, quantitative analysis of natural resources, ecological, and environmental systems by remote sensing, GIS, and geostatistics.

Ling Wu recevied the B.S. degree in geographic information system, and the M.S. and Ph.D. degrees in cartography and geographic information engineering from China University of Geosciences, Beijing, China in 2007, 2010 and 2013, respectively. He is currently a PostDoc with the Institute of Remote Sensing and GIS, Peking University, Beijing, China. His research interests include inversion of agricultural vegetation parameters and assimilation of crop growth model and remote sensing information.

Zhao Xu received the B.S. degree in geographic information system from China University of Geosciences, Beijing, China, in 2011, where she is currently pursuing the Ph.D. degree in surveying and mapping. Her research interests include environmental remote sensing and quantitative analysis of crop parameters.

Lu Gong received the B.S. degree in computer science and technology from Changchun University of Science and Technology, Changchun, China, in 2012. He is currently pursuing the M.S. degree in cartography and geographic information engineering at China University of Geosciences, Beijing, China. His research interests include environmental remote sensing and agriculture environmental monitoring.