Two-Dimensional Simulation of Barley Growth and Yield Using a Model Integrated with Remote-Controlled Aerial Imagery

: It is important to be able to predict the yield and monitor the growth conditions of crops in the ﬁeld to increase productivity. One way to assess ﬁeld-based geospatial crop productivity is by integrating a crop model with a remote-controlled aerial system (RAS). The objective of this study was to simulate spatiotemporal barley growth and yield based on the development of a crop-modeling system integrated with RAS-based remote sensing images. We performed ﬁeld experiments to obtain ground truth data and RAS images of crop growth conditions and yields at Chonnam National University (CNU), Gwangju, South Korea in 2018, and at Gyeongsang National University (GNU), Jinju, South Gyeongsang, South Korea in 2018 and 2019. In model calibration, there was no signiﬁcant di ﬀ erence ( p = 0.12) between the simulated barley yields and measured yields, based on a two-sample t -test at CNU in 2018. In model validation, there was no signiﬁcant di ﬀ erence between simulated yields and measured yields at p = 0.98 and 0.76, according to two-sample t -tests at GNU in 2018 and 2019, respectively. The remote sensing-integrated crop model accurately reproduced geospatial variations in barley yield and growth variables. The results demonstrate that the crop modeling approach is useful for monitoring at-ﬁeld barley conditions.


Introduction
Barley (Hordeum vulgare), a major cereal grain grown in temperate climates globally, is an important staple crop in the Korean peninsula and worldwide. It is used as animal fodder, a fermentable source material for beer, and a constituent of various health foods [1]. To increase productivity through integrated crop management practices, it is crucial to monitor growth conditions and to have an early estimation of barley yield. Crop modeling and remote sensing (RS) techniques are typical approaches to estimate crop yield and monitor growth [2]. Process-based crop models are useful for simulating seasonal patterns of crop growth and predicting yield, while empirical models can simulate certain environmental conditions for growth or crop yield [3]. Remote sensing is useful for surveying geospatial variability in crop growth conditions over the growing season [4]. Each technique for crop modeling and remote sensing has certain advantages, e.g., crop models are able to simulate growth sequentially, while RS can monitor geospatial variations in crop conditions dependably [5,6].
Process-based crop growth models include a set of equations that can define crop growth and development on a continuous scale up to harvest [3]. The parameters in a process-based mathematical model are highly dependent on the ecophysiological responses of the canopy growth that is specific to different cultivars [7]. Dependable simulation using a crop model requires a large number of inputs, including specific crop growth parameters and other variables related to soil and weather [8]. Biological system modelers use parameters to simplify the model and estimation of the crop growth specific variables, which generally makes things more difficult [9]. Crop models often require some specific parameters to model the correct growth response, which can limit the use of the model elsewhere. As a result, crop growth simulation models frequently fail to estimate the regional or geographical variations in crop yield with reasonable accuracy because they lack appropriate spatial and temporal information about canopy growth [10] and accurate input data [11].
Crop growth and yield can also be observed using the empirical relationship between biomass and remotely sensed information derived from a remote-controlled aerial vehicle (RAV) or a satellite [12,13]. Many studies have investigated the relationship between crop yield and vegetation indices for assessing crop growth conditions and phenology [14,15]. For practical reasons, these types of (semi-) empirical regression are only suitable for evaluating growth conditions in a specific region. Moreover, they ignore or cannot explain the interaction of radiation intercepted within the vegetation canopies [12]. In addition, most platforms, either RAVs or satellites, are unable to provide the required information continuously, either because of limited revisit periods to the fields of interest or adverse environmental conditions [6,11].
The integration of RS information into a crop model may reinforce the advantages of RS and crop modeling as well as compensate for the limitations of each approach, allowing for accurate geospatial crop productivity monitoring and yield forecasting at different scales in croplands [2,16]. Studies have proved the effectiveness of combining crop modeling and RS approaches [2,17,18]. One important advance is the gramineous crop model, GRAMI, which is able to use remote sensing data [19]. GRAMI [9,20] is a simulation model that uses simple crop parameters, weather variables, and RS information from any platform to simulate grain crop growth and yield. This model was expanded to simulate other crops such as cotton [21,22], soybean [23], and paddy rice [5,16,24,25] at different scales from fields to regions. The current version of the model has been renamed as the remote sensing-integrated crop model (RSCM) in order to incorporate the model updates mentioned above and for future applications for other crops [23].
We assumed that the RSCM would be applicable for the geospatial simulation of crops at a field scale because the RSCM system could use RAS-based RS images for the geospatial reproduction of crop growth conditions and productivity [16]. Moreover, there has been growing interest in utilizing RAS for various agricultural business activities, e.g., field-based crop monitoring and management [26][27][28]. Therefore, the objective of this study was to extend the RSCM for the geospatial simulation of barley growth and yield at a field scale based on parameterizing the model using ground-and RAS-based RS information.

Site Description
Field experiments were performed to evaluate the RSCM system for the simulation of barley growth and yield at two locations, namely, Gwangju and Jinju in South Korea, during the 2018 and 2019 growing seasons. The experiment in Gwangju was carried out to estimate model parameters and obtain a dataset to calibrate the modeling system at Chonnam National University (CNU) ( 6.5, organic carbon content (OCC) of 12.3 g C kg −1 , available phosphorus (P) of 131 mg P 2 O 5 kg −1 , cation exchange capacity (CEC) (Ca +2 , K + , and Mg 2+ ) of 14.4 cmol c kg −1 , and total nitrogen before fertilization (TN) of 1.0 g N kg −1 according to the National Institute of Agricultural Sciences (www.naas.go.kr/english/). At GNU, the topmost soil layer (0-20 cm) is categorized as sandy loam (sand 71.4%, silt 18.8%, clay 9.7%), with a pH (H 2 O) 5.9, OCC of 8.6 g C kg −1 , P of 185 mg P 2 O 5 kg −1 , CEC (Ca +2 , K + , and Mg 2+ ) of 6.3 cmol c kg −1 , and TN of 0.053 g N kg −1 . Detailed information on the cultivars can be found at the National Institute of Crop Science website (www.nics.go.kr/english/). The experimental blocks at both CNU and GNU were arranged in a randomized complete block design with three replications. The kernels were sown using a mechanical seed drilling device in a row spacing of 20 cm and a hill-to-hill spacing of 10 cm. Nitrogen (N) in CO(NH 2 ) 2 , phosphorus (P) in CaOBMgOP 2 O 2 NSO 2 -F, and potassium (K) in KCl fertilizers were applied at 80, 70, and 35 kg ha −1 , respectively. Among the three fertilizers, 40% of the N and full doses of P and K were spread on the soil surface as a basal application before seeding. The remaining 60% N was applied as a side dressing at the tillering and panicle initiation stages.

Field Experiment
The leaf area index (LAI) and above-ground dry mass (AGDM) were measured as growth variables in the principal stages of barley growth, i.e., initial-to-mid tillering, booting, heading, and early maturity. The LAI was measured using a plant canopy analyzer, LAI-2200C (LI-COR Inc., Lincoln, NE, USA), which can quantity the LAI of the canopy precisely and accurately, even in diffuse sunlight, using a light-diffusing cap and light scattering correction method. It measures the LAI using a fisheye lens based on gap fraction method [29].

Proximal and Remote Sensing
We obtained proximally sensed data on the ground at CNU, Gwangju in 2018 and both ground-based proximal sensing and UAS-based remote sensing data at GNU, Jinju in 2018 and 2019. A hand-held multispectral radiometer, MSR16R (CROPSCAN, Inc., Rochester, MN, USA), was used to measure the canopy reflectance of barley to determine growth conditions at the principal growth stages. The MSR16R can measure 16 wavebands in the range of 450-1750 nm. Further details on the system components, operation, and characteristics as well as the theory of operation can be found at the CROPSCAN website (http://www.cropscan.com/). The current study employed the three wavebands of 800, 660, and 560 nm with all the same band width of 10  We designed to evaluate seasonal changes in canopy reflectance and LAI, generally measuring every week at CNU and every two weeks at GNU during the barley growing season. A UAS, eBee (senseFly, Cheseaux-sur-Lausanne, Switzerland) was used to obtain aerial images for the experimental barley field at GNU. The UAS comprised a fixed-wing UAV (a size of 960 mm and a weight of 700 g) and a digital camera, Powershot S110 NIR (Cannon, Inc., Japan) with a 12.1 MP sensor and three wavebands of green (G), red (R), and near infra-red (NIR). The center wavelengths of the bands were 550 (G), 625 (R), and 850 nm (NIR). UAS-based aerial images were taken on DOY 87, 101, 115, 130, 144, and 158 in 2018 and DOY 53, 67, 81, 95, 102, 123, and 144 in 2019. These image data were processed radiometrically and mosaicked to form complete scenes of the experimental field using Pix4D mapper software (Pix4D S.A., Prilly, Switzerland). The processed images were then geometrically corrected using ERDAS IMAGINE software (Hexagon Geospatial, Madison, AL, USA), followed by georeferencing and registration using ArcGIS software (Esri, Inc., Redlands, CA, USA).
The VIs of interest for assessing the barley canopy growth based on the integrated modeling system were the normalized difference vegetation index (NDVI) [30], optimized soil adjusted vegetation index (OSAVI) [31], modified triangular vegetation index 1 (MTVI1) [32], and re-normalized difference vegetation index (RDVI) [33]. The four VIs were determined using the following formulas: where R 800 , R 660 , and R 560 represent reflectance at 800, 660, and 560 nm, respectively.

RSCM System for Barley
The RSCM is a process-based crop-modeling system, which can simulate crop growth and yield using simple inputs owing to the integration of RS information (Figure 1). The RSCM for barley simulated daily barley growth in four simple processes, i.e., determining daily growing degree days (GDD), absorption of incident solar radiation by the crop canopy, daily increase in above-ground dry mass, and daily change in LAI (increase or senescence), based on mathematical equations ( Table 1). The RSCM fitted a simulated LAI curve to the observed LAI curve using a Bayesian procedure as a part of the within-season calibration method. The LAI is a three-dimensional concept, while the reflectance by plants of solar radiation is two-dimensional since the plant canopies are the top surface of the plants. We assumed that a log-log regression model with a slope of ≈2/3 could define the relationship between reflectance and LAI [34]. Based on this, we formulated the correlations between the LAI and the four VIs (MTVI1, NDVI, RDVI, and OSAVI) using log-log linear regression models as follows.
where α VI , β VI , and t ( ∼ N 0, σ 2 VI represent intercept, slope, and error of the linear regression model, respectively. The progression of LAI for each pixel was described by the RSCM-barley system, using four parameters θ = (L 0 , a, b, and c). These parameters were designed to be generated from the prior distribution ψ ∼ N(µ, D), ranging between 0 and 1 using the following transformations.

Equations Description
∆D, daily change in growing degree days (GDD); T, daily mean temperature; T b , crop specific base temperature Q, absorption of incident solar radiation (R); β, fraction of R; k, crop-specific light extinction coefficient; LAI, leaf area index ∆M = E · Q ∆M, daily increase in above-ground dry mass; E, radiation use efficiency ∆L = ∆M · P 1 · S ∆L, daily LAI increase; P1, fraction of ∆M allocated to new leaves; S, specific leaf area P 1 = Max [1 − a · e b·D ,0] P 1 , dimensionless leaf-allocation function; a and b, parameters that control magnitude and shape of the function; D, cumulative GDD ∆G = P 2 · ∆M ∆G, daily increase in grain; P 2 , fraction of ∆M partitioned to grains P 2, dimensionless grain-partitioning parameter; P a and P b , parameters that control the magnitude and shape of the function; and f G d is the grain partitioning factor based on the cumulative GDD We obtained both the regression coefficients (α , β , σ 2 ), = 1, 2, 3, and 4 for each VI and the hyper-parameters (µ, D) from the data collected in this study for parameterization. These included both the VIs and the measured LAI values. The parameter µ was specified using the 'before-calibration' values (L 0 = 0.2, a = 3.25 × 10 −1 , b = 1.25 × 10 −3 , and c = 1.25 × 10 −3 ) as feasible minimum values before the calibration procedure. Parameter D is a diagonal matrix with all diagonal elements equivalent to 0.5. The following numerical procedure was implemented to achieve θ for each pixel: Step 1: µ was set as the initial estimate of ψ for each pixel.
Step 3: The simulated curve was generated for each pixel from the estimated ψ in Step 2.
Step 4: The µ, D was updated as the sample means and sample variances of the estimates in Step 2.
In this procedure, the parameter ψ was estimated by minimizing the above function, and the optimization was performed using the POWELL optimization routine [35] for one-point simulation cases and the Quasi-Newton minimizer [36] for two-dimensional simulation cases.

Statistical Analysis
The performance of the RSCM system was evaluated using a two sample-paired t-test, and two statistical indices of root mean squared error (RMSE) and the Nash-Sutcliffe model efficiency (NSE) [37] in R software (https://www.r-project.org/). The NSE determines the relative magnitude of the residual variance of simulated data compared to the observed data variance, evaluating how well the plot of observed versus simulated data fits the 1:1 line. NSE values can range between -∞ and 1, meaning that the model is dependable if the value is closer to 1. Simulated values are smaller or larger than the observed data when NSE values are close to zero.

Parameterization and Calibration of RSCM
We estimated the specific barley growth parameters of radiation use efficiency (RUE), specific leaf area (SLA), and light extinction coefficient (k) from the data set obtained at CNU in 2018 for effective calibration of the model. The RUE (ε) was determined from the slope of the linear regression model between the amounts of accumulated PAR absorbed by barley canopies and AGDM for four barley cultivars (Figure 2a). The estimated value of RUE was 3.1 g MJ −1 . The SLA was also determined using the linear relationship between LAI and leaf dry weight for five barley cultivars (Figure 2b). We included an additional cultivar in this specific case for the improved regression analysis. The slope from the linear regression model expressed the value (0.012 m 2 g −1 ) of SLA. The value of k was estimated based on the relationship between LAI and canopy light interception (Q 0 = 1 − e -k*LAI ) for four barley cultivars ( Figure 3). We determined k values presuming that barley canopies could intercept ≈90% of light at the maximum LAI. The estimated k values for the barley cultivars using the light interception equation (Q 0 ) varied from −0.58 to −0.65 (unitless). The parameter k was considered to have a mean value of −0.62.   Table 2), which were verified using a within-season calibration procedure (refer to Table  A1). The RMSE and NSE values for LAI ranged from 0.18 to 0.35 m 2 m −2 and from 0.78 to 0.91, while those for AGDM ranged from 53.4 to 91.4 g m −2 and from 0.78 to 0.88, respectively ( Table 2). Simulated grain yields agreed with the measured grain yields without a significant difference (p = 0.12) according to a two-sample t-test (α = 0.05) and with RMSE of 0.624 ton ha −1 ( Figure 5). It is assumed that the small arithmetic overestimation in the simulated yields of Heenchal, Hopum, and Saechal are attributable to somewhat small overestimations in the matching LAI values.   Table 2), which were verified using a within-season calibration procedure (refer to Table A1). The RMSE and NSE values for LAI ranged from 0.18 to 0.35 m 2 m −2 and from 0.78 to 0.91, while those for AGDM ranged from 53.4 to 91.4 g m −2 and from 0.78 to 0.88, respectively ( Table 2). Simulated grain yields agreed with the measured grain yields without a significant difference (p = 0.12) according to a two-sample t-test (α = 0.05) and with RMSE of 0.624 ton ha −1 ( Figure 5). It is assumed that the small arithmetic overestimation in the simulated yields of Heenchal, Hopum, and Saechal are attributable to somewhat small overestimations in the matching LAI values.    The number of data (n) with three replications = 11 for LAI in both Black and Heenchal, n = 10 for LAI in Hopum, n = 7 for LAI in Saechal, and n = 4 for AGDM for all the four cultivars.

Validation of RSCM and Two-Dimensional Simulation of Barley
The barley-modeling system was validated for its accuracy using a dataset separately obtained at GNU in the 2018 and 2019 barley seasons. The modeling system simulated LAI, AGDM, and yield in agreement with the corresponding measured values with statistically acceptable accuracies in both seasons (Figures 6 and 7, and Table 3) based on the model re-parameterization process (refer to  Table A1). Simulated LAI and AGDM values agreed with the measured values with an RMSE of 0.17 m 2 m −2 and an NSE of 0.82 for LAI and with an RMSE of 74.89 g m −2 and an NSE of 0.55 for AGDM in the 2018 season. There was no significant difference (p = 0.96) between simulated and measured yields according to a two-sample t-test (α = 0.05), with an RMSE of 0.701 ton ha −1 . During the 2019 barley season, the modeling system simulated LAI and AGDM with an NSE of 0.93 for LAI and 0.21 for AGDM for the autumn barley and with an NSE of 0.70 for LAI and 0.79 for AGDM for the spring barley ( Table 3). The simulated yield was not significantly different (p = 0.76 for the autumn barley and 0.37 for the spring barley) from the measured yield according to two-sample t-tests (α = 0.05), with RMSEs of 1.177 ton ha −1 in the autumn season and 1.178 ton ha −1 in the spring season.

Discussion
Parameterization in crop simulation modeling is used to reduce the complexity of the model and explore the best fit for the experiment [7,20]. In this study, specific barley growth parameters (RUE, SLA, and k) were estimated from the CNU data set at Gwangju for the successful calibration of the model. The RUE can be determined from the slope of the linear regression of the gross amount of AGDM that is produced by absorbing PAR [38]. Earlier studies report that different cultivation management and stress conditions can affect the RUE value of barley [39][40][41]. The estimated RUE value in this study was somewhat higher than those reported earlier. A crop model simulates the crop responses based on ideal growth and management practices. In the current study, we estimated the barley RUE value from the optimum cultivation field. According to Charles-Edward et al. [42], the amount of PAR intercepted in crop canopy can depend on leaf canopy distribution. Additionally, leaf angle distribution can significantly affect light interception [43]. The k value (-0.62) estimated in the current study was a bit larger than the k value (-0.69) from the earlier reports [44,45]. The SLA, which is defined as the total leaf area divided by the total leaf weight, was adopted as a concept in the analysis of whole plant growth [46]. The SLA, which is sensitive to leaf thickness and leaf area, is likely to affect net photosynthesis, leaf structure, crop growth rate, and yield [47].
A well-calibrated crop model can reproduce field conditions of crop productivities with a dependable accuracy [7]. Our calibration study demonstrated this feature in crop modeling. The RSCM system is designed to simulate crop growth with simple inputs owing to the integration of remote sensing information. There were earlier efforts to develop the integrated crop-modeling system for rice and soybean [2,6,23]. The current study showed that the RSCM system, utilizing the within-season calibration procedure, could reproduce barley growth (i.e., LAI and AGDM) and grain yield with statistically acceptable accuracy. Although there were some abnormalities for the simulated AGDM in validation for both the 2018 and 2019 barley seasons, the simulated LAI and yield showed statistically significant agreement with the corresponding measured values in the RSCM for barley. There have been a few of earlier study results comparable to the current report, in terms of evaluating and monitoring barley growth conditions based on RAS images [48][49][50]. One of these studies applied an empirical modeling approach to estimate barley biomass [48]. The other studies investigated experimental methodologies for yield and fertilization analysis [49] and monitoring growth of biennial cereal crops including barley [50]. We assume that a process-based mathematical crop model has an advantage of understating crop growth and development processes in comparison with an empirical crop modeling technique [16]. A substantial benefit of the current mathematical modeling system is that it can simulate the development of major agronomic crops based on the integration of RS information from various platforms, i.e., either earth observing optical satellites [24,25] or RAS [16].
The current study also showed the practical possibility of monitoring barley growth and yield using a RAS. Nevertheless, the modeling system requires better quantitative RS images for more advanced applications. The desired improvements include radiometrically well-calibrated image data accompanied by a reasonably detailed sensor. It is clear that improved RAS images will be more useful for monitoring crop conditions and productivity [16]. It would also add value to test the extendibility of the system.

Conclusions
In this study, we estimated barley growth parameters (i.e., 3.10 g MJ −1 for RUE, 0.65 for k, and 0.012 m 2 g −1 for SLA) to use in an RSCM for barley and demonstrated the capability of the modeling system of reproducing barley growth and yield. We assumed that the modeling system was well adaptable for barley growth monitoring and field management projects owing to the integration with RS information from various platforms (e.g., satellite aboard sensors and human or remotely controlled UAS). The barley RSCM system should use well-quantified RS images for more precise monitoring of barley productivity and other cultivation management options.

Conflicts of Interest:
The authors declare no conflict of interest.