Introduction

The real-time and macroscopic characteristics of remote sensing (RS) data complement the continuity and mechanisms of crop growth models; the data can promote the application of crop models at spatial scales, and help to both monitor crop growth and provide estimates of crop yield across large areas (Dorigo et al. 2007). There are three methods for coupling RS data and crop models. The driving method uses canopy physiological parameters obtained from RS data as input variables to force the crop model (Delecolle and Guerif 1988; Supit et al. 1994). The parameterization method minimizes the difference between a RS-derived variable and its simulated value, through re-initialization of the crop model (Huang et al. 2011; Wang et al. 2014). In recent years, radiative transfer models (RTMs) have been used to couple RS data and crop growth models. This assimilation method directly compares the spectral reflectance obtained from RS images with that simulated by the RTMs to optimize some simulating processes or adjust the initial parameter values (Guerif and Duke 2000; Fang et al. 2011; Li et al. 2011). Different types of RTMs have been used in several studies. The PROSAIL model (Baret et al. 1992) was usually used to simulate the canopy reflectance of crop. It can be joined with crop models well, to assimilate RS data. In general, the driving method is relatively simple, but it is easy to overlook the errors in the RS data. The parameterization method calibrates the growth model by comparing the RS data and simulated variables from models and it is easy to overlook the errors generated during the RS inversion process. The assimilation method directly compares the RS derived and RTM simulated reflectance data to initialize the crop model; this avoids errors from the RS inversion process and thus exhibits certain advantages, in theory.

Crop growth models face the problem that it is difficult to obtain accurate initial parameters at the spatial scale, when only field scale data are available (Doraiswamy et al. 2004). Assimilating RS information to initialize crop models is a relatively new approach, which can help to resolve this problem. The inversion of initial parameters, by coupling the RS data and crop models, is mainly done based on pixel by pixel. In this process, crop models need to be invoked many times, which involves a large amount of calculations and requires high performance computers (Nouvellon et al. 2001).

Simulation zone partitioning is used to separate and cluster a large area into smaller zones that have relatively consistent crop growth characteristics and environments. Then, the growth model can run on the basis of the partitioned units, which alleviates some of the large calculations required during the coupling of the RS data with the crop model. Miao et al. (2006) used a crop growth model to simulate maize grain yield at the spatial scale based on partitioned zones; these were divided according to their soil properties, and the precision achieved was above 90%. Basso et al. (2001) partitioned their simulation zones using soil properties, field measured data and the spatial distribution of the normalized difference vegetation index (NDVI); they simulated soybean yield using the CROPGRO model at the spatial scale based on these simulation zones and the weighted average root mean square (RMSE) error for all zones, between the simulated and measured yield, reached 101 kg ha−1. Thorp et al. (2008) developed the Apollo decision support system to partition their study area based on the soil and yield data, and ran the DSSAT model to simulate spatial maize yield, obtaining a standard deviation (SD) of 200 kg ha−1 between the average simulated and measured yield. Launay and Guerif (2005) ran the SUCROS model to simulate spatial sugarcane yield, based on simulation zones defined using soil zoning maps; they greatly optimized the simulation accuracy, with a relative root mean square error (RRMSE) value of 0.12 between the simulated and measured yield. These results show that simulation zone partitioning can effectively solve the spatialization utilization problem of crop growth models. The method provides an effective solution to improve the simulation efficiency during the assimilation of RS data with crop models at a spatial scale.

Different vegetation indices (VIs) used as assimilating parameters might achieve varied precisions in their predictions. The normalized difference vegetation index (NDVI) and ratio vegetation index (RVI) are commonly used, in terms of physiological parameters inversion, but the values of the NDVI are easily saturated when the canopy is dense (Liang 2004). Meanwhile, the RVI can slow down the speed of saturation under dense canopies and is still sensitive to changes in vegetation status after canopy closure (Pearson and Miller 1972). Ma et al. (2008) found that using the soil-adjusted vegetation index (SAVI) as a coupling index reduced the effect of soil background in the early stage of crop growth and highlighted the features of plants. Huete et al. (2002) found that the enhanced vegetation index (EVI) can remove atmospheric effects and improve the sensitivity of the index in high biomass vegetation. Therefore, different VIs such as NDVI, RVI, SAVI and EVI should be evaluated when chosen as the assimilating parameter or simulation zone partitioning criterion, respectively.

The main objectives of this study were as follows: (1) to explore the simulation zone partitioning method, based on the soil nutrient indices and wheat canopy VIs, including NDVI, RVI, SAVI, EVI, and to identify the best VI to complete the cluster analysis together with soil data; (2) to develop a coupled model that integrates RS data and the WheatGrow model, based on particle swarm optimization (PSO) (Kennedy and Eberhart 1995) and the PROSAIL model; (3) to accurately predict the productivity and growth indices of winter wheat at the spatial scale, based on the defined partition zones.

Materials and methods

Field data collection

The data used in this study were obtained from two field experiments which were under artificial control and one survey of a wheat production area. Each experiment involved different cultivars, nitrogen (N) fertilization rates and planting densities.

Field experiment 1: this experiment was carried out in Qutang Town, Haian city, Jiangsu Province, China (120°20′E, 32°30′N) for a single season, from October 2009 to June 2010. The cultivar Yangmai 15 was sown on 27 October 2009, with a seeding rate of 67.5 kg ha−1 (D2). Urea N fertilizer was applied at 150 (N1), 210 (N2) and 270 (N3) kg ha−1; 40% of the N for each treatment was applied pre-sowing, another 40% was used for seedling dressing and the remaining 20% was used for jointing dressing. Two replications of each treatment were applied in a randomized block design. Each experimental plot comprised an area of 8100 m2 (90 × 90 m). For all treatments, basal doses of mono-calcium phosphate and potassium chloride were applied, at rates of 120 kg ha−1 (P2O5) and 190 kg ha−1 (K2O). Other field management strategies followed the local standard practices for wheat production.

Field experiment 2: this experiment was conducted at Changqingsha Farm, Changjiang Town, Rugao City, Jiangsu Province, China (120°35′E, 32°3′N) for a single season, from November 2009 to June 2010. The cultivar Yangmai 13 was sown on 7 November 2009 at two seeding rates: 60 kg ha−1 (D1) and 90 kg ha−1 (D3). Urea N fertilizer was applied at 150 (N1), 210 (N2) and 270 (N3) kg ha−1. The experimental block design and mono-calcium phosphate and potassium chloride applications were the same as described for field experiment 1. Other field management strategies followed the local standard practices for wheat production.

Wheat survey: Zhangjiagang city (120°20–120°50′E, 32°0–32°30′N) is the main production area for weak gluten wheat, located in the southeast of Jianghuai Plain, with a subtropical moist climate. 17 sampling sites scattered across the study area were measured using GPS in 2011, and field data were collected four times during the mid-jointing (27 March 2010), later-jointing (11 April 2010), heading (27 April 2010) and filling (13 May 2010) wheat growth stages. The survey was repeated on 27 March 2011, 11 April 2011, 27 April 2011 and 13 May 2011. Grain yield measurements were taken at the mature wheat stage.

Data acquisition

Acquisition of satellite imagery

Three Huanjing satellite charge coupled device (HJ-CCD) images of the study area (Zhangjiagang city) were acquired during the jointing, heading and filling stages of the winter wheat growth period, on 11 April 2011, 25 April 2011, and 13 May 2011, respectively. The HJ-CCD images were downloaded from the website of the China Center for Resources Satellite Data and Application (http://218.247.138.121/DSSPlatform/index.html). The revisit cycle of the HJ-1 satellite is 2 days and its spatial resolution is 30 m.

Canopy spectral reflectance measurements

The canopy spectral reflectance at the field experiment sites was measured with a FieldSpec PRO FR2500 spectra-radiometer (Analytical Spectral Devices, Boulder, Colorado, USA) during the early-jointing, mid-jointing, heading and filling growth stages of the wheat, on 12 March 2010, 7 April 2010, 23 April 2010 and 12 May 2010, respectively. The spectral measurements were carried out between 10:00 and 14:00 on the specified dates, under clear sky and low wind speed conditions. The spectrometer was positioned to look vertically at a height of 1 m above the wheat canopy, with a 25º field of view. In each sample plot, 3 points were chosen to measure the canopy spectral reflectance, and each point had 3 scans, then each sample plot had 3 × 3 scans. Finally, the average value of 9 scans were used as the final canopy spectra data (Yao et al. 2014). A panel radiance measurement was taken before and after the vegetation measurements.

Determination of agronomy parameters

After each measurement of the canopy spectral reflectance in 2010, 10 plants at each of 3 points were selected in each sample plot, and their canopy heights and leaf inclinations were recorded under natural conditions. Then, the leaf areas of 20 of the plants were measured using an LI-3000C meter (Li-cor, Lincoln, Nebraska, USA). The fresh weights of three leaves from the tops of the plants were measured. Then, the leaves were oven-dried at 105 °C for 20 min, followed by 80 °C until a constant weight was reached. After the dried leaf samples were crushed, the total N content was measured by the Dumas combustion method, aided by Rapid N Cude (Elementar Analysen Systeme, Frankfurt, Hesse-Darmstadt, Germany). When mature, 3 × 1 m2 of plants from each sample plot were harvested and threshed, and the grains were dried and weighed for the calculation of grain yield. In 2011, these measurments were repeated on 27 March, 11 April, 27 April and 13 May.

Soil data acquisition

The soils properties of 1210 soil samples from Zhangjiagang city were analyzed to obtain data for the simulation zone partitioning (Fig. 1). The soil total N (TN), organic matter (OM) and available potassium (AK) contents were measured by the soil and fertilizer station of Jiangsu province.

Fig. 1
figure 1

Spatial distribution of soil sampling sites in Zhangjiagang City

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Data analysis and utilization

Satellite image preprocessing and wheat information extraction

This study used ENVI 5.1 (Exelis Visual Information Solutions, Boulder, CO, USA) software to complete the pre-processing of the RS data. Ground-based GPS control points were used for the geometric correction of the HJ-CCD images. The FLAASH module of ENVI was used for the atmospheric correction of the HJ-CCD images (ITT 2009). Supervised classification was carried out on the HJ-CCD images by combining them with the fixed field investigation (Yang et al. 2008). Then, the planting area data were extracted. Finally, the reflectance data of the wheat canopy in the study area were obtained using the FieldSpec PRO FR2500 spectra-radiometer.

VIs can enhance the sensitivity of agronomic parameters, including biophysical and biochemical parameters of vegetation. Four types of common VIs including NDVI (Rouse et al. 1974), RVI (Pearson and Miller 1972), SAVI (Huete 1988) and EVI (Justice et al. 1998) were used as the assimilation parameters between the coupling model and RS information, and the four VIs were respectively used as zone partitioning parameters together with soil data. The formulas for calculating VIs were as follows:

$$NDVI = (R_{Nir} - R_{Red} )/(R_{Nir} + R_{Red} )$$
(1)
$$RVI = R_{Nir} /R_{Red}$$
(2)
$$SAVI = 1.5 \times (R_{Nir} - R_{Red} )/(R_{Nir} + R_{Red} + 0.5)$$
(3)
$$EVI = 2.5 \times (R_{Nir} - R_{Red} )/(R_{Nir} + R_{Red} - 7.5 \times R_{Blue} + 1)$$
(4)

R Nir , R Red and R Blue refer to the reflectance of the near-infrared, red and blue bands, respectively, of the HJ-CCD images.

Data statistics and utilization

The data from field experiments 1 and 2 were used to validate the coupled model–RS model and assess its accuracy at the field scale. Image data from the study area and the sampling point survey data were used to validate the coupled model–RS model at the spatial scale. The soil data and image data were used for simulation zone partitioning. The RMSE and RE (relative error) were used to show the relative differences between the estimated and measured values (Jamieson et al. 1991).

Spatial data analysis

SPSS (SPSS Inc., Chicago, IL, USA) software was used to analyze the statistics and variance of the soil data. The least-significant difference (LSD) method was used to complete the pairwise differences between sub-zones. GS + 9.0 (Gamma Design Software, Plainwell, Michigan, USA) was used to conduct normality tests and half variant function analyses of the spatial data. To complete the kriging interpolation and produce the spatial distribution map of soil nutrient index, the geostatistical analysis module of ArcGIS 10.2 (ESRI Inc., Redlands, California, USA) was used; the spatial resolution of the spatial distribution map was resampled to 30 m. The Isodata module of ArcGIS 10.2 was used to conduct the clustering partition of the spatial data, and the parameter settings of the cluster analysis were as follows: classification number, 5–20; maximum iterations, 20; and transform threshold, 5. The partition results were evaluated through analyzing the variance and the coefficients of variation (CV).

$$CV = \frac{SD}{Mean} \times 100\%$$
(5)

SD is the standard deviation; Mean is the mean value; and CV is the coefficient of variation. The partition results were considered to have low variability if CV <10%, medium variability if it was 10–100%, and high variability if CV >100% (Cambardella et al. 1994). The decimal places of relevant parameters in normality tests and half variant function analyses referred to Chen et al. (2007), and other parameters keep two decimal places.

Models

WheatGrow model

The WheatGrow model was developed by describing the mechanistic relationships between the different components (soil, cultural practices and climate conditions) and the physiological and ecological processes of the wheat, based on the physiological development time (PDT) (Fig. 2). Its main function modules included the phase development and phenology (Yan et al. 2000), photosynthesis and dry matter production, dry matter distribution and organ formation (Cao et al. 2002), yield and quality formation (Pan et al. 2006, 2007) and the water and nutrients (N, P, and K) balance (Hu et al. 2004). The model system had a strong rationality and prediction.

Fig. 2
figure 2

Modular structure of the WheatGrow model

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The input parameters of the WheatGrow model included the weather, soil and wheat variety data. Weather data were downloaded from the website of the China meteorological data sharing service system (http://data.cma.cn/), and included the daily maximum and minimum temperatures (°C), the daily amount of sunshine hours (h) and the daily precipitation. Soil data were obtained from the soil database of the study area, and included the soil layer thickness (cm), physical clay content (cm), bulk density (g cm−3), field capacity (cm3 cm−3), wilting moisture (cm3 cm−3), saturated water content (cm3 cm−3), actual water content (cm3 cm−3), saturated hydraulic conductivity (mm d−1), OM (g kg−1), total N (g kg−1), nitrate N (mg kg−1), ammonium N (mg kg−1), effective phosphorus (mg kg−1) and AK (mg kg−1). The wheat variety data were estimated using the field survey data from the fertility period, including the physiological vernalization time, photo-period effect, the temperature sensitive factor, basic early maturing and the filling period factor, among others.

PROSAIL model

The PROSAIL model, considered the non-Lambertian characteristics of the soil, the specular reflection of the leaves, the hot spot effects of the vegetation canopy and the leaf angle distribution; it was previously found to describe the reflection characteristics of uniform canopies well (Nilson and Kuusk 1989). The PROSAIL model contained 14 input parameters: the LAI, chlorophyll (Cab) and dry matter (Cm) parameters were used to connect the WheatGrow model and PROSAIL model in this study. The remaining parameters for the PROSAIL model were determined from the experimental data and references. The equivalent water thickness (Cw), mean leaf inclination angle (θ l), hot spot size parameter (hot), soil reflectance and the solar diffusivity parameter (skyl) were relatively stable and defined from the mean value obtained for the study area. The solar zenith angle (θ s) was calculated according to the acquisition time of the images. The carotenoid content (Ccr) and brown pigment content (Cbp) were set as 20.0 and 0.0 (Thorp et al. 2012), the leaf structure parameter was 1.5 (Jacquemoud and Baret 1990), and the observed zenith (θ v) and relative azimuth (ψ v) angles were 0º. Specific settings are shown in Table 1.

Table 1 Parameter settings used in the PROSAIL model
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Optimization algorithm and optimization parameters

Initial parameters in WheatGrow model, including sowing date, sowing rate and N rate, P rate, K rate, seeding depth, irrigation parameters and straw mulching parameters, are difficult to be accurately obtained at the spatial scale. To make better use of the WheatGrow model to invert the initial parameters, a sensitivity analysis was conducted in previous work (Huang et al. 2011; Wang et al. 2014). Ultimately the cultivation and management parameters (sowing date, sowing rate and N rate), which varied significantly at the regional scale, were selected as the model input parameters to be optimized. The rest of the management parameters were defined as empirical values, obtained by local investigation.

The particle swarm optimization (PSO) algorithm, proposed by Kennedy and Eberhart (1995), was used during the assimilation process (Li et al. 2015; Wu et al. 2012). The PSO algorithm assumed that m particles (Particle) were grouped into a swarm and fought at a certain speed in D dimensional search space. Each particle adjusted its flight direction and speed according to its own experience and that of others around them, forming the positive feedback mechanism of group optimizing. Then, every particle gradually moved to more suitable position based on the fitness to environment of the individual, and eventually find optimal location (Yi and Ge 2005; Elbeltagi et al. 2005). Once iteration happened, the particles moved, and the iteration would not stop until cost function value was minimized. Three optimized parameters were used in this study and the largest iteration time was set as 400 times.

Assimilation and simulation process

The WheatGrow model was used to simulate the leaf N accumulation (LNA) (g m−2), the leaf dry matter (g m−2) and the LAI. Cab (µg cm−2) was calculated as the LNA multiplied by 23.7059 and divided by the LAI (Thorp et al. 2012). Leaf dry matter was divided by the LAI to calculate the Cm (g cm−2). The Cab and Cm were used as input parameters for the PROSAIL model, together with the LAI. Finally, the coupled WheatGrow and PROSAIL model was developed to simulate the wheat canopy reflectance. A cost function was established, using the VIs simulated by the coupled model and the actual VIs extracted from the RS images. When the cost function value reached the minimum, the best fit between the model simulations and the satellite observations was obtained. At this moment, the initialized parameters (sowing date, sowing rate and N rate) were defined as the optimum parameters. Then, these optimized parameters were input into the WheatGrow model for a re-simulation. The simulation units of the spatial scale model were based on the simulation zone partitioning results (Fig. 3).

Fig. 3
figure 3

Flow chart of the study methods employed

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The cost function was constructed between the simulated and actual VIs based on the least squares method:

$$J = \sum\limits_{k = 1}^{n} {(VI_{Obs} (k) - VI_{Sim} (k))^{2} }$$
(6)

n is the number of RS images obtained; and J is the cost function value; VI Sim (k) are the simulated VIs at time k; VI Obs (k) are the observed VIs at time k.

Results

Spatial heterogeneity analysis based on soil nutrients and VIs in the study area

The statistical analysis of the soil data and wheat canopy VIs in the study area showed that the variation coefficients of the soil nutrient indices (including OM, total N and AK) were between 24.68 and 42.89%, that is, there was medium heterogeneity of these variables. The coefficients of variation of the wheat canopy VIs (including the NDVI, RVI, SAVI, EVI at jointing, heading and filling stages) were between 8.70 and 12.97%, 13.03 and 22.34%, 11.63 and 15.63%, 12.24 and 16.28% respectively, that is, they were of low–medium heterogeneity (Table 2). The normality tests of the soil nutrient indices and wheat VI showed that the NDVI, RVI, SAVI and EVI distributions in the three growth stages were close to normal (Table 2; Fig. 4). The three soil nutrient indices were not normally distributed; however, after being lnx transformed, a normal distribution was obtained, with variation coefficients of 7.63–59.66% (Table 2).Spatial autocorrelation analysis of the soil nutrient indices was conducted with the semi-variance function. The fitting effect of the semi-variance from the Gaussian model was the best, with OM, total N and AK, R2 values of 0.981, 0.976 and 0.994, respectively, and C0/(C0 + C) values (C0: Nugget value, C0 + C: Sill value) of 34.7, 33.2 and 27.2%, respectively (Fig. 5). This indicated a medium spatial autocorrelation (Cambardella et al. 1994). A spatial interpolation of the three soil nutrient indices was then produced using Ordinary Kriging in ArcGIS, and then the spatial distributions of soil nutrient indices were obtained (Fig. 6).

Table 2 Descriptive statistics of the soil nutrient indices and the wheat VIs (NDVI, RVI, SAVI, EVI) values for the whole study area
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Fig. 4
figure 4

Frequency histograms of the soil nutrient indices and wheat VIs (NDVI, RVI, SAVI, EVI) values

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Fig. 5
figure 5

Semi-variance of the soil nutrient indices: a organic matter; b total nitrogen; and c available potassium. C 0 nugget value, C 0  + C sill value, A 0 range

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Fig. 6
figure 6

Spatial distributions of the soil nutrient indices (a organic matter; b total nitrogen; c available potassium) and the wheat VIs (NDVI, RVI, SAVI, EVI) values in the study area (Color figure online)

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Simulation zone partitioning based on soil nutrients and RS data

Cluster analysis of the spatial distributions of the NDVI, RVI, SAVI and EVI (at the jointing, heading and filling stages) and the three soil nutrient indices, using the Isodata algorithm in ArcGIS 10.2, obtained eight, eight, nine, sixteen sub-zones, respectively (Fig. 7). The statistical analysis of the soil nutrient indices and wheat canopy VIs in each sub-zone showed that the variation coefficients of LN (OM), LN (TN) and LN (AK) and VIs were all lower than the coefficients of each parameter for the whole area, especially when the SAVI was used as zone partitioning parameter together with soil data (Table 3).

Fig. 7
figure 7

The simulation sub-zones, partitioned based on a cluster analysis (a cluster analysis based on soil data and NDVI data; b cluster analysis based on soil data and RVI data; c cluster analysis based on soil data and SAVI data; d cluster analysis based on soil data and EVI data) (Color figure online)

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Table 3 Descriptive statistics of the soil nutrient indices and the wheat canopy soil-adjusted vegetation index (SAVI) values in each sub-zone
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Analyses of the data from the 473 soil sampling sites located across the sub-zones and the corresponding wheat canopy VIs, indicated that significant differences in the soil nutrient indices and wheat canopy VIs existed between each sub-zone, and the SAVI performed best among these VIs (Table 4). In addition, multiple comparison results of the six indices in each sub-zone showed that significant differences existed in the indices between the sub-zones (p < 0.05) (Table 5). These results indicate that the simulation zone partitioning performed well when the soil nutrient indices and wheat canopy SAVI were used as partitioning zone parameters.

Table 4 Analysis of variance among the soil nutrient indices and wheat canopy soil-adjusted vegetation index (SAVI): the main effects of the sub-zones
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Table 5 Least-significant difference analysis among the soil nutrient indices and wheat canopy soil-adjusted vegetation index (SAVI): differences among the sub-zones
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Model validation and case study with ground-based RS data

For applicability validation of assimilation strategies, a set of given initial parameters are usually used to drive a model and simulate growth parameters. Then, the established assimilation algorithm is tested, in its use of the indices as outside assimilation data and whether it can accurately invert the given initial parameters (Zhao et al. 2005). In this study, the cultivation management parameters from experiments 1 and 2 were input into the WheatGrow model and the corresponding LAI and LNA values were simulated on the dates that the RS data were obtained. Then, the LAI and LNA values were input into the PROSAIL model to calculate the VIs, which served as the observed RS data. Therefore, the values of the three input parameters to be optimized (sowing date, sowing rate and N rate) were inverted using the observed RS data as outside assimilation data. These values were compared to the measured values (Fig. 8); the RMSEs of sowing date, sowing rate and N rate were 5.22 d, 10.63 and 24.64 kg ha−1, respectively, which indicates that the simulation algorithm of the coupled model performed well. The estimated values of sowing date, sowing rate and N rate were then used to drive the WheatGrow model and the growth parameters (LAI, LNA) and grain yield were simulated for comparison with the corresponding measured values. The RMSE and RE values between the simulated and measured indices were 1.00 g m−2 and −0.09 (LAI), and 1.15 g m−2 and −0.02 (LNA), respectively (Fig. 9). The RMSE and RE values of grain yield were 373.24 kg ha−1 and −0.05, respectively (Fig. 10). These results also indicate that the coupled model had a good prediction ability at the field scale.

Fig. 8
figure 8

Validation of the assimilation model (N1, N2 and N3 denote that nitrogen fertilizer was applied at 150, 210 and 270 kg ha−1, respectively. D1, D2 and D3 denote seeding rates of 60, 67.5 and 90 kg ha−1, respectively)

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Fig. 9
figure 9

Comparisons of the measured and estimated leaf area index (a LAI ) and leaf nitrogen accumulation (b LNA) values; estimations made by the WheatGrow model assimilating the remote sensing data at the field scale

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Fig. 10
figure 10

Grain yield predictions from the WheatGrow model, after assimilation based on the field data. (N1, N2 and N3 denote that nitrogen fertilizer was applied at 150, 210 and 270 kg ha−1, respectively. D1, D2 and D3 denote that seeding rate was applied at 60, 67.5 and 90 kg ha−1, respectively)

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Spatial simulations, based on the sub-zone partitions

Based on the results of the simulation zone partitioning, the wheat canopy NDVIs, RVIs, SAVIs and EVIs were used as coupling parameters to estimate the cultivation management parameters (sowing date, sowing rate and N rate) in each sub-zone, respectively. This was then used to drive the WheatGrow model and re-simulate the growth parameters and grain yield in wheat at the spatial scale. The simulated and field measured values were compared, then the RMSE and RE values of LAI, LNA and grain yield were calculated (Fig. 11; Table 6). These results indicate that the coupled model based on the sub-zone partitions had the best prediction ability at the spatial scale, when SAVI was used as the assimilating parameter. Figure 12 shows the spatial distributions of LAI and LNA at the late jointing stage, and the grain yield of winter wheat at the maturity stage, in the study area.

Fig. 11
figure 11

Comparisons of the measured and estimated leaf area index (a LAI), leaf nitrogen accumulation (b LNA) and yield (c) values, based on the WheatGrow model assimilating RS data at the spatial scale

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Table 6 RMSE and RE values between the simulated and measured agronomic parameters when NDVI, RVI, SAVI, EVI are used as the assimilating parameters
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Fig. 12
figure 12

Simulated spatial distributions of leaf area index (a LAI), leaf nitrogen accumulation (b LNA) and grain yield (c) values of wheat in the study area when SAVI was used as partitioning zone and assimilating parameters (Color figure online)

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Discussion

The definition of simulation partitioning zone relies on spatial information sources that are predictable over time and are related to crop yield. Most previous studies used one or multi-line variations in soil nutrient indicators as a partitioning criterion (Thorp et al. 2008; Launay and Guerif 2005; Kravchenko and Bullock 2000; Johnson et al. 2003; Moral et al. 2010). This method did not take the temporal variability of these variables into account (Li et al. 2007). RS information can well indicate the spatial and temporal variations of crop growth status (Basso et al. 2001). Boydell and McBratney (2002) found that there was high correlation between RS information and yield data collected in the same year. Since the variations in soil nutrient indicators, together with RS information, can be effectively used to partition simulation zones, the soil nutrient indices and wheat canopy VIs during critical growth stages were used to make the partitions in this study. The results showed that the variations of the data in the sub-zones were all smaller than those of each index across the whole area. There were significant differences of each index between partitions, indicating that the soil data combined with the canopy VIs can be used to obtain appropriate simulated partitions. These results agree with those of Li et al. (2007).

Some studies used NDVI combined with soil data as zone partitioning parameters (Basso et al. 2001; Li et al. 2007). However, NDVI is easily saturated after plant canopy closure (Liang 2004), which may reduce the differences of crop growth status in spatial scale and partition accuracy. In this study, the partition results were compared when soil nutrient indices combined respectively with NDVI, RVI, SAVI and EVI were used as partitioning criterion. The results showed that the performance of the simulation zone partitioning method was highly dependent on different data sources. The best zone partitioning result was achieved when SAVI was selected to partition simulation zones. The reason may be that SAVI can well reduce the effect of soil background and enhance vegetation characteristics, which confirms the results of Moulin and Guerif (1999). However, in the application of a crop model at the spatial scale, spatial variation is found not only in the soil and crop growth parameters, but also in the climate. Thus, further research should focus on climatic factors as a data source for even more comprehensive zoning. The next step would be to test the accuracy of the partition results with some landscape ecology index (Li et al. 2005), like the focusing or fragmentation degree, and to try some new methods, like fuzzy c-means clustering (Fridgen et al. 2004).

Crop growth models coupled with RS information are one of the most effective means of improving the accuracy of crop growth estimates. Computing pixel by pixel is the main method used for crop models when simulated at the spatial scale. However, large-scale RS images and large numbers of pixels result in huge computation requirements. These limit its wide use at the spatial scale (Nouvellon et al. 2001). Simulation zone partitioning is an alternative method; it can avoid the repeated simulations of those regions with similar attributes, by defining simulation zones according to variations of crop management, nutrient use efficiency and environmental effects caused by different soil types, nutrient contents and weather factors (Khosla et al. 2002). In this paper, a coupled model was run based on sub-zones defined by combining soil nutrient indices and VIs; this avoided repeated simulations of regions with similar attributes and improved the simulation efficiency. In addition, the coupled model based on the sub-zone partitions had the best prediction ability when SAVI was used as the assimilating parameter, which was consistent with the results of Zhang et al. (2016). The case study indicated that the simulation zone partitions led to good prediction accuracy at the spatial scale. Therefore, this was an effective solution for the application of the crop model at the spatial scale.

Conclusion

This paper proposed a wheat growth prediction method by coupling the WheatGrow model with the PROSAIL model, based on simulation zone partitions. The simulation zone partitioning technology was established by fusing soil nutrient indices and the corresponding spatial characteristics of wheat growth, as indicated by RS data. A coupled model that integrated RS data and the WheatGrow model, using NDVI, RVI, SAVI and EVI as the coupling parameters respectively, based on the PSO algorithm and PROSAIL model, was developed to realize the accurate prediction of wheat growth parameters and grain yield at the spatial scale. Each index was significantly different between the defined sub-zones, indicating appropriate partitioning was achieved. The minimum RMSE of LAI, LNA and yield between the measured values and estimated values, which were simulated based on the partition zone results, respectively reached 0.92, 1.12 g m−2 and 409.70 kg ha−1 when SAVI was used as a partitioning zone and assimilating parameter. This means that the temporal and spatial distribution of winter wheat growth and productivity indices were simulated well. Further research is needed to test the accuracy of the partition results with some landscape ecology indices, and to try some new cluster methods. The research should focus on climatic factors as a data source for more comprehensive zoning. These results provide important technical support for winter wheat growth monitoring and prediction using crop models and RS information, at the spatial scale.