# Improving Jujube Fruit Tree Yield Estimation at the Field Scale by Assimilating a Single Landsat Remotely-Sensed LAI into the WOFOST Model

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}of 0.986 and RMSE of 0.624 t ha

^{−1}for total aboveground biomass (TAGP), R

^{2}of 0.95 and RMSE of 0.19 m

^{2}m

^{−2}for LAI, respectively. Normalized Difference Vegetation Index (NDVI) showed better performance for LAI estimation than a Soil-adjusted Vegetation Index (SAVI), with a better agreement (R

^{2}= 0.79) and prediction accuracy (RMSE = 0.17 m

^{2}m

^{−2}). The assimilation after forcing LAI improved the yield prediction accuracy compared with unassimilated simulation and remotely sensed NDVI regression method, showing a R

^{2}of 0.62 and RMSE of 0.74 t ha

^{−1}for 2016, and R

^{2}of 0.59 and RMSE of 0.87 t ha

^{−1}for 2017. This research would provide a strategy to employ remotely sensed state variables and a crop growth model to improve field-scale yield estimates for fruit tree crops.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Region

#### 2.2. Research Framework

- Model calibration and yield prediction without forcing LAI: The WOFOST model parameters were calibrated and validated using field experimental data (jujube, soil, and weather data). Default values calculated using the planting density of each orchard multiplied by the average TDWI per tree were input into the calibrated model to predict yields of 181 orchard samples.
- Yield prediction using remotely-sensed vegetation indices (VIs): The correlations between the vegetation index obtained from Landsat data during the main growing period and yield data were analyzed to determine the best modeling time. A single or composite vegetation index with highest correlation was chosen to establish the yield prediction model for 181 sample spots. The prediction accuracy was cross-validated using two years of yield data.
- Yield estimation after forcing LAI: A statistical regression model between LAI and the remotely-sensed vegetation index was firstly established for LAI estimation of 181 samples. Then, a single LAI (near to maximum LAI stages) derived from Landsat data was forced into the calibrated WOFOST model to re-calculate TDWIs, thereby re-driving the model for yield prediction. The yield of 181 samples was re-estimated.
- Accuracy evaluation: In addition to comparing the yield prediction accuracy of the above three methods, the TDWI values of 55 sampled orchards obtained from the assimilation method were also verified and evaluated.

#### 2.3. Description of the WOFOST Model

_{2}-assimilation, transpiration, respiration, and how these processes are influenced by environmental conditions [4]. However, the size of the area where WOFOST can be applied is limited because the crop model’s nonlinear response to the input causes the aggregation effect [66]. In practice, the limitation is resolved by splitting the model spatial domain into small spatial units where the model inputs can be assumed constant. WOFOST includes three operating modes: potential growth, limited growth, and reduced growth. In this study, a potential production pattern was adopted and water stress was not considered because local rainfall was less and jujube water requirements were largely dependent on precision irrigation. LAI is one of the most important state variables in the WOFOST model because it represents the ability of crops to absorb solar radiation, which drives CO

_{2}assimilation and is a key indicator of crop yield. Three depths in the canopy are selected according to the Gaussian integration method and at those levels the leaf area index, the amount of absorbed radiation, and the leaf CO

_{2}assimilation are calculated. The total instantaneous assimilation is easily obtained by multiplying the instantaneous assimilation with the total leaf area index [4].

^{−1})

- I
_{a}: Amount absorbed of specified radiation flux (J m^{−2}s^{−1}). - I
_{a,L}: Amount absorbed of total radiation flux at relative depth L (J m^{−2}s^{−1}). - I
_{0}: Photosynthetically active radiation flux at top of the canopy (J m^{−2}s^{−1}). - k: The extinction coefficient for the PAR flux.
- ρ: Reflection coefficient of the canopy.

_{2}assimilation rate can be obtained by introducing the absorbed amount of light into an assimilation-light response function of individual leaves, see Equation (3):

- A
_{L}: Gross assimilation rate at relative depth L (per unit leaf area) (kg ha^{−1}h^{−1}). - A
_{m}: Gross assimilation rate at light saturation (kg ha^{−1}h^{−1}). - ε: Initial light use efficiency (kg ha
^{−1}h^{−1})/(J m^{−1}s^{−1}).

- A
_{C}: Total gross assimilation rate for the whole canopy (kg ha^{−1}h^{−1}). - A
_{C,t}: Total gross canopy assimilation rate per unit leaf area (kg ha^{−1}h^{−1}). - A
_{T,L,P}: Total instantaneous gross assimilation rate at relative depth L (kg ha^{−1}h^{−1}). - LAI: Total leaf area of the crop (ha ha
^{−1}).

#### 2.4. Study Data

#### 2.4.1. Field Experimental Data for WOFOST Calibration and Validation

_{2}assimilation parameters were obtained from a fitted light response curve based on a rectangular hyperbolic correction model [67]. The net photosynthetic rate was measured with a LI-COR 6400XT portable photosynthesis system (LI-COR, Lincoln, United States). For weather data, daily maximum and minimum temperatures, solar radiation, wind speed at 2 m high, actual vapor pressure, and precipitation were observed using an automatic weather station 500 m from the field experiment. For soil parameters, field capacity, saturated soil moisture content, soil moisture content at wilting point, bulk density, hydraulic conductivity, and water retention parameters were measured before emergence. The depth and weight of the root were sampled by digging a profile (Figure 2c) and measured in the lab.

#### 2.4.2. Field-Scale Observation Data for Different Orchards

#### 2.5. Calibration of WOFOST Model

#### 2.6. Input TDWIs for WOFOST Model without Forcing LAI and Yield Estimation

#### 2.7. Yield Estimation Using Remotely-Sensed Vegetation Index Regression Method

#### 2.8. Forcing Remotely Sensed LAI and Yield Estimation

#### 2.9. Accuracy Evaluation

^{2}) was used to evaluate the agreement between predicted or simulated values and measured values, see Equation (8). The root mean square error (RMSE) and a normalized root mean square error (NRMSE) were employed to quantify the prediction accuracy, see Equations (9) and (10). The relative bias error (RBE, %) and the % mean absolute error (MAE, %) were also used to evaluate prediction performance, which were shown in Equations (11) and (12), respectively:

## 3. Results

#### 3.1. Yield Estimation Using the Remote Sensing Regression Method

#### 3.2. Calibration of the WOFOST Model

^{2}of 0.986 (Figure 6a) and 0.95 (Figure 6b), respectively. The prediction errors (RMSE) were 0.624 t ha

^{−1}and 0.19 m

^{2}m

^{−2}, respectively. Yield and total biomass differences between simulated and observed were found to be 4.8% and 4%, respectively.

#### 3.3. Remotely-Sensed LAI

^{2}and RMSE were 0.89 and 0.12 (6.9%) m

^{2}m

^{−2}for NDVI, 0.79 and 0.17 (9.7%) m

^{2}m

^{−2}for SAVI, respectively, and the validated R

^{2}and RMSE were 0.79 and 0.16 (10%) m

^{2}m

^{−2}for NDVI, 0.51 and 0.25 (15%) m

^{2}m

^{−2}for SAVI, respectively. Previous studies had also confirmed that NDVI may perform better LAI prediction accuracy than SAVI when vegetation coverage was high [31]. The best regression equation for LAI and NDVI is shown in Equation (15):

#### 3.4. Forcing Remotely-Sensed LAI and Yield Estimation

#### 3.4.1. Re-Calibrated TDWI Evaluation after Forcing LAI

^{2}= 0.87 and R

^{2}= 0.89, respectively). The predicted RMSE (NRMSE) were 1.72 (11.4%) and 1.50 (11.1%) kg ha

^{−1}for 2016 and 2017, respectively. The percentage difference of more than half of the samples was between −10% and 10%, with 62% for 2016 and 55% for 2017 (Figure 9b). 93% and 98% of the samples had only a predicted deviation between −20% and 20% for 2016 and 2017, respectively.

#### 3.4.2. Aboveground Biomass Simulation after Forcing LAI

^{−1}and 2.1 to 1.81 m

^{2}m

^{−2}at forcing time, respectively. The input TDWI was designed as a default value (see Figure 4b) before assimilation, which was significantly higher than the actual measured value of 13.8 kg ha

^{−1}. Therefore, the actual yield and LAI were also overestimated. However, the forced TDWI value had a smaller deviation from the actual value. With these corrections in modelled growth parameters after assimilation, the actual yield per orchard was re-estimated.

#### 3.4.3. Yield Estimation after Forcing LAI

#### 3.5. Comparison of Three Prediction Methods

_{2}assimilation rate increased with the increase of tree age, and this factor was not considered in this study, which led to the overestimation of the yield at low tree age and underestimation at high tree age.

^{2}of 0.62 and RMSE of 0.74 (10.9%) t ha

^{−1}for 2016, and a R

^{2}of 0.59 and RMSE of 0.87 (11.1%) t ha

^{−1}for 2017, followed by the remotely-sensed NDVI regression method (R

^{2}= 0.35, RMSE = 0.98 (14.8%) t ha

^{−1}for 2016 and R

^{2}= 0.43, RMSE = 1.02 (13.3%) t ha

^{−1}for 2017), and finally without assimilation (R

^{2}= 0.09, RMSE = 1.16 (17.6%) t ha

^{−1}for 2016 and R

^{2}= 0.13, RMSE = 1.67 (21.5%) t ha

^{−1}for 2017). The best MAE values were also achieved by assimilation method, showing an improvement of 31% and 28% versus the remote sensing regression method, and 38% and 47% versus the simulation without assimilation in 2016 and 2017, respectively.

## 4. Discussion

^{2}value ranging from 0.79–0.93 and RMSE from 7.9–9.1 kg tree

^{−1}for three orchards. However, phenology information should be considered when performing crop yield predictions, and a time series of VI shall be useful for crop yield forecasting [73]. In this research, the predicted yield based on the remotely-sensed NDVI was overestimated in 2016 and was underestimated in 2017 (Figure 12, red circle). The reason may be that the length of the 2016 growing season is about 12 days lower than in 2017. However, the effect of phenological length on yield is not considered when the cross-validation based on the remote sensing regression method is performed. In addition, although remote sensing satellites with medium and high spatial resolution have the potential to be used for field-scale yield prediction, it is a challenge to construct a time series of vegetation indices for consideration of phenological information due to low temporal resolution. In contrast, crop growth model can takes into account the growth process of the phenology. However, for the prediction method using the WOFOST model, the predicted yields of most samples are overestimated in 2017. The main reason may be that uncertainty in strongly varying tree age and planting densities may be introduced into the model structure, which may lead to a simulated yield bias for different orchards. For the assimilation method, the TDWI parameter is considered for responding to uncertainty in tree age and planting density for fruit tree crops in this research. An approach forcing the LAI near the peak vegetative stage into a calibrated WOFOST model was attempted to reduce the uncertainty and simulate the yield for a perennial jujube fruit tree crop at the field-scale, showing a well performance (MAE = 9.2% and 10.7% for 2016 and 2017, respectively). However, actual yields are slightly overestimated and underestimated at low yields and high yields in 2016 and 2017, respectively. Two reasons may cause this deviation. The first reason may be that the CO

_{2}assimilation rate increased with the increase of tree age, and the CO

_{2}assimilation parameters are set to fixed values in this research, which can lead to overestimation of yield at low tree age and underestimation at high tree age. The second reason may be the genetic varieties of phenological stages and crop characteristics, such as special leaf area (SLATB) and CO

_{2}assimilation parameters, thereby influencing potential yield. These parameters are expected to be further optimized by assimilation of remote sensing information.

_{2}assimilation, a single LAI does not accurately express the effect of effective radiation, temperature, nitrogen, and soil moisture content on jujube yield [31]. LAI, biomass, leaf nitrogen accumulation, evapotranspiration, and soil moisture obtained from remote sensing data can be expected to assimilate into calibrated WOFOST model to optimize state variables and improve simulated accuracy for jujube yield. In addition, the WOFOST model is carried out with a potential production simulation. The effects of other factors such as water stress have not been considered. Temporal evolution of LAI and final yields can change with irrigation management and soil properties in different regions. The state variable SM (soil moisture content) can be recommended to respond to water transport conditions in rain-fed or irrigated jujube gardens when the model is carried out in a moisture-limited production simulation [3]. Moreover, differences in plant diseases and pests, nitrogen stress, and jujube genetic parameters are not considered in the study. These several limiting factors can occur in the field, so that the external conditions are beyond the boundary conditions of the effective model range and influence the yield prediction accuracy while carrying out data assimilation [12]. How to respond to these factors in the model will also be a valuable research exploration. Furthermore, the same pruning structure, a small canopy permanent line tree shape, was performed in all sampled orchards to avoid the effect of pruning on the simulation results. For fruit tree crops, an extension of the analysis whether the proposed approach is suitable for jujube orchards with different tree shapes is also needed to be further validated.

## 5. Conclusions

_{2}assimilation parameters and specific leaf parameters is not considered. In addition, when the model is applied to orchards with different pruning trees, the CO

_{2}assimilation parameters may also need to be re-corrected. In future research work, the following two research contents can be highlighted:

- Remotely-sensed state variable SM can be recommended to be assimilated into the WOFOST model in response to the effects of irrigation and rainfall on the simulation results.
- The influence of tree age and shapes on CO
_{2}assimilation parameters and the use of remote sensing data to optimize these parameters are also worth exploring in order to improve simulation accuracy in high-yield and low-yield jujube gardens.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Study region and observations. Note: The LAI and TDWI sample set is a subset of yield observations.

**Figure 2.**(

**a**) A set of leaves scanned for LAI measurement. (

**b**) LAI measurement by using a canopy analyzer. (

**c**) Root depth and weight measurement.

**Figure 5.**Average correlation coefficient for two years between NDVI (

**a**)/SAVI (

**b**) and yields. Half-month 9 was the first half of May.

**Figure 9.**(

**a**) Re-calibrated TDWI for 2016 and 2017 versus measured value. (

**b**) Percent difference for the re-calibrated TDWI.

**Figure 10.**Simulated dry weight of leaves (WLV), dry weight of stems (WST), dry weight of total aboveground biomass (TAGP), and LAI before and after forcing.

**Figure 11.**(

**a**) Relative percentage difference for prediction yields for 2016. (

**b**) Relative percentage difference for prediction yields for 2017.

**Figure 12.**(

**a**) Predicted versus measured yields based on three methods for 2016. (

**b**) Predicted versus measured yields based on three methods for 2017.

**Figure 13.**Frequency distributions (%) of relative bias error (RBE; %) resulting from the comparison between observed and simulated yields. RBE % = 0% (red line) represented the perfect prediction. Bin size was equal to 5.

Index Based on NDVI | Year | Cross-validation (2016 versus 2017) | |
---|---|---|---|

R^{2} | NRMSE (%) | ||

14th half-month | 2016 | 0.25 | 16 |

2017 | 0.33 | 14.3 | |

Max | 2016 | 0.1 | 17.5 |

2017 | 0.24 | 15.3 | |

Average for 7th and 8th month | 2016 | / | 21.3 |

2017 | / | 18.2 | |

Average for 14th and 15th half-month | 2016 | 0.35 | 14.8 |

2017 | 0.43 | 13.3 |

^{2}is less than zero.

Parameter | Description | Value | Units | Source |
---|---|---|---|---|

*Emergence | ||||

TBASEM | Lower threshold temperature emergence | 10 | °C | e |

TEFFMX | Max effective temperature emergence | 30 | °C | e |

TSUMEM | Temperature sum from sowing to emergence | 230 | °C | m-c |

*Phenology | ||||

TSUM1 | Temperature sum from emergence to anthesis | 967 | °C d^{−1} | m-c |

TSUM2 | Temperature sum from anthesis to maturity | 960 | °C d^{−1} | m-c |

DTSMTB0 | Daily increase in temperature sum as function of at average = 0 °C | 0.00 | °C d^{−1} | e |

DTSMTB100 | Daily increase in temperature sum as function of at average = 10 °C | 0.00 | °C d^{−1} | e |

DTSMTB355 | Daily increase in temperature sum as function of at average = 35.5 °C | 25.5 | °C d^{−1} | e |

DTSMTB400 | Daily increase in temperature sum as function of at average = 40 °C | 25.5 | °C d^{−1} | e |

*Initial parameters | ||||

TDWI | Redefine initial total emergence dry weight | / | kg ha^{−1} | m |

LAIEM | Leaf area index at emergence | 0.0007 | ha ha^{−1} | d |

RGRLAI | Maximum relative increase in LAI | 0.05 | ha ha^{−1} d^{−1} | d |

*Green area | ||||

SLATB000 | Specific leaf area while DVS = 0 | 0.00165 | ha kg^{−1} | m-c |

SLATB55 | Specific leaf area while DVS = 0.55 | 0.0013 | ha kg^{−1} | m-c |

SLATB100 | Specific leaf area while DVS = 1 | 0.0013 | ha kg^{−1} | m-c |

SLATB200 | Specific leaf area while DVS = 2 | 0.0014 | ha kg^{−1} | m-c |

SPAN | Life span of leaves growing at 35 °C | 60 | [d] | e |

TBASE | Lower threshold temp. for ageing of leaves | 10 | °C | e |

*CO_{2} assimilation | ||||

KDIFTB00 | Extinction coefficient for diffuse visible light at DVS = 0 | 0.8 | \ | m-c |

KDIFTB200 | Extinction coefficient for diffuse visible light at DVS = 2 | 0.8 | \ | m-c |

EFFTB19.5 | Light-use efficiency single leaf at average temp. = Celsius | 0.495 | kg ha^{−1} hr^{−1}J^{−1} m^{2} s | m-c |

EFFTB355 | Light-use efficiency single leaf at average temp. = Celsius | 0.495 | kg ha^{−1} hr^{−1}J^{−1} m^{2} s | m-c |

AMAXTB00 | Maximum leaf CO2 assimilation. Rate at DVS = 0 | 39.0 | kg ha^{−1} hr^{−1} | m-c |

AMAXTB170 | Maximum leaf CO2 assimilation. Rate at DVS = 1.7 | 39.0 | kg ha^{−1} hr^{−1} | m-c |

AMAXTB200 | Maximum leaf CO2 assimilation. Rate at DVS = 2 | 20.0 | kg ha^{−1} hr^{−1} | m-c |

TMPFTB10 | Reduction factor of AMAX of at 10 ℃ | 0 | \ | d |

TMPFTB195 | Reduction factor of AMAX of at 19.5 ℃ | 1 | \ | d |

TMPFTB355 | Reduction factor of AMAX of at 35.5 ℃ | 1 | \ | d |

*Conversion of assimilates into biomass | ||||

CVL | Efficiency of conversion into leaves | 0.732 | kg kg^{−1} | m-c |

CVO | Efficiency of conversion into storage organs | 0.780 | kg kg^{−1} | m-c |

CVR | Efficiency of conversion into roots | 0.690 | kg kg^{−1} | m-c |

CVS | Efficiency of conversion into stems | 0.751 | kg kg^{−1} | m-c |

*maintenance respiration | ||||

Q10 | Relative increase in respiration rate per 10 °C temperature increase | 2 | kg CH_{2}O kg^{−1} d^{−1} | d |

RML | Relative maintenance respiration rate of leaves | 0.03 | kg CH_{2}O kg^{−1} d^{−1} | d |

RMO | Relative maintenance respiration rate of storage organs | 0.01 | kg CH_{2}O kg^{−1} d^{−1} | d-c |

RMR | Relative maintenance respiration rate of roots | 0.01 | kg CH_{2}O kg^{−1} d^{−1} | d |

RMS | Relative maintenance respiration rate of stems | 0.015 | kg CH_{2}O kg^{−1} d^{−1} | d-c |

*Partitioning parameters | ||||

FRTB00 | Fraction of above-ground dry matter to roots at DVS = 0 | 0.3 | kg kg^{−1} | m-c |

FRTB154 | Fraction of above-ground dry matter to roots at DVS = 1.54 | 0.0 | kg kg^{−1} | m-c |

FLTB00 | Fraction of above-ground dry matter to leaves at DVS = 0 | 0.67 | kg kg^{−1} | m-c |

FLTB012 | Fraction of above-ground dry matter to leaves at DVS = 0.12 | 0.31 | kg kg^{−1} | m-c |

FLTB022 | Fraction of above-ground dry matter to leaves at DVS = 0.22 | 0.41 | kg kg^{−1} | m-c |

FLTB032 | Fraction of above-ground dry matter to leaves at DVS = 0.32 | 0.55 | kg kg^{−1} | m-c |

FLTB051 | Fraction of above-ground dry matter to leaves at DVS = 0.51 | 0.4 | kg kg^{−1} | m-c |

FLTB097 | Fraction of above-ground dry matter to leaves at DVS = 0.97 | 0.15 | kg kg^{−1} | m-c |

FLTB100 | Fraction of above-ground dry matter to leaves at DVS = 1.00 | 0.1 | kg kg^{−1} | m-c |

FSTB00 | Fraction of above-ground dry matter to stems at DVS = 0 | 0.33 | kg kg^{−1} | m-c |

FSTB012 | Fraction of above-ground dry matter to stems at DVS = 0.12 | 0.69 | kg kg^{−1} | m-c |

FSTB022 | Fraction of above-ground dry matter to stems at DVS = 0.22 | 0.59 | kg kg^{−1} | m-c |

FSTB032 | Fraction of above-ground dry matter to stems at DVS = 0.32 | 0.45 | kg kg^{−1} | m-c |

FSTB051 | Fraction of above-ground dry matter to stems at DVS = 0.51 | 0.6 | kg kg^{−1} | m-c |

FSTB097 | Fraction of above-ground dry matter to stems at DVS = 0.97 | 0.85 | kg kg^{−1} | m-c |

FSTB100 | Fraction of above-ground dry matter to stems at DVS = 1.00 | 0.43 | kg kg^{−1} | m-c |

FSTB145 | Fraction of above-ground dry matter to stems at DVS = 1.45 | 0.2 | kg kg^{−1} | m-c |

FOTB100 | Fraction of above-ground dry matter to storage organs at DVS = 1.00 | 0.47 | kg kg^{−1} | m-c |

FOTB145 | Fraction of above-ground dry matter to storage organs at DVS = 1.45 | 0.8 | kg kg^{−1} | m-c |

FOTB164 | Fraction of above-ground dry matter to storage organs at DVS = 1.64 | 1.0 | kg kg^{−1} | m-c |

FOTB200 | Fraction of above-ground dry matter to storage organs at DVS = 2.00 | 1 | kg kg^{−1} | m-c |

*Death rates | ||||

RDRSTB00 | Relative death rate of stems at DVS = 0 | 0 | \ | e |

RDRSTB200 | Relative death rate of stems at DVS = 2.0 | 0 | \ | e |

Prediction Method | Year | R^{2} | RMSE (%) t ha ^{−1} | MAE (%) |
---|---|---|---|---|

Without assimilation | 2016 | 0.09 | 1.16 (17.6) | 14.9 |

2017 | 0.13 | 1.67 (21.5) | 20.3 | |

Remotely sensed average NDVI prediction (cross-validation) | 2016 | 0.35 | 0.98 (14.8) | 13.3 |

2017 | 0.43 | 1.02 (13.3) | 14.9 | |

Forcing LAI (assimilation) | 2016 | 0.62 | 0.74 (10.9) | 9.2 |

2017 | 0.59 | 0.87 (11.1) | 10.7 |

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## Share and Cite

**MDPI and ACS Style**

Bai, T.; Zhang, N.; Mercatoris, B.; Chen, Y.
Improving Jujube Fruit Tree Yield Estimation at the Field Scale by Assimilating a Single Landsat Remotely-Sensed LAI into the WOFOST Model. *Remote Sens.* **2019**, *11*, 1119.
https://doi.org/10.3390/rs11091119

**AMA Style**

Bai T, Zhang N, Mercatoris B, Chen Y.
Improving Jujube Fruit Tree Yield Estimation at the Field Scale by Assimilating a Single Landsat Remotely-Sensed LAI into the WOFOST Model. *Remote Sensing*. 2019; 11(9):1119.
https://doi.org/10.3390/rs11091119

**Chicago/Turabian Style**

Bai, Tiecheng, Nannan Zhang, Benoit Mercatoris, and Youqi Chen.
2019. "Improving Jujube Fruit Tree Yield Estimation at the Field Scale by Assimilating a Single Landsat Remotely-Sensed LAI into the WOFOST Model" *Remote Sensing* 11, no. 9: 1119.
https://doi.org/10.3390/rs11091119