A canopy height measurement system was installed on a center pivot ( Figure 1 ) in this study. The main components were integrated into a waterproof control cabinet, including an ultrasonic sensor (ToughSonic TSPC−15, Senix Corporation, Inc. USA), a multispectral reflectance sensor (SRS−NDVI, METER Group, Inc. USA), and a data logger (CR300, Campbell Scientific, Inc. USA). The ultrasonic sensors have a Field of View (FoV) of 14°and a measurement range of 0.25−9.1 m (accuracy is better than 0.5% of target distance). The ultrasonic transmission frequency is 75 kHz. The ultrasonic sensor used in this experiment had a rotating base ( Figure 1 ) to adjust observation direction. The multispectral reflectance sensor (measurement bands of red in the range 640−660 nm and near-infrared in the range 800−820 nm) consisted of up-looking and down-looking probes. The up-looking probe was pointed vertically to the sky without any shading object and had a field of view of 180° to receive radiation from the sky. The down-looking probe pointing ( Figure 1 ) was vertical to the canopy and had a FoV of 36° to receive radiation from the canopy. The multispectral reflectance sensor acquired observational data once per second and sent the average value to the laptop every 15 s during the measurement.

The Pearson correlation coefficient (r) between the relative error (percentage of the absolute error value over the true value) and the experimental parameters was calculated using the SPSS software (IBM Corp., Armonk, NY, USA) to explore the correlation between changes in the single environmental factor and measurements. Analysis of variance (ANOVA) was used in the same software to evaluate the effects of single-factor experimental parameters on the ultrasonic measurements. In addition, before performing ANOVA, the normality of the samples was verified using the Shapiro-Wilk normality test, and the variance homogeneity of the samples was verified using the Levene test.

In this study, a CH_m calibration model was established using the multiple regression method in Origin 8.5 software (OriginLab, Northampton, MA, USA), and the output value of the calibration model was the calibration value of canopy height (CH_c). The coefficient of determination R², and root mean square error (RMSE) were used for model evaluation by Equations (9, 10). The variance inflation factor (VIF) was chosen as the indicator of multicollinearity to avoid variables with severe multicollinearity from distorting the estimation of the regression model (Doi, 2019). It is calculated as follows in Equation 8:

where R i 2 is based on the variance of the ith independent variable around its mean that is explained by the other independent variables in the model. When the VIF > 10 (Miles, 2014), it indicates that the collinearity between the variables is too strong, so that the model cannot be reasonably constructed using these variables.

In the above formula: CH ¯ a = 1 n ( ∑ i = 1 n CH a i ) , CH_ci is the value of the i-th CH_c data, CH a i is the value of the i-th CH_a data, n is the number of samples.

It was necessary to verify the original measurement reliability of the ultrasonic sensor before conducting the crop canopy experiment. The results ( Supplementary Figure S1 ) show that the correlation between the measured values and the actual height of the bare-soil slab had R² values larger than 0.99 because a bare and flat soil surface has a much better smoothness than a crop canopy surface. And the average relative error of measurements was less than 0.51%. The above data indicates that the ultrasonic sensor had good measurement reliability.

Supplementary Figure S2 shows high repeatability of the ultrasonic sensor during the data collection period for measurement results. Data collection movements in the same and opposite directions showed no significant differences in the measurements. The R² values were higher than 0.97, the slopes were close to 1, and the intercept values for all measured fits were below 5 mm.

Figure 4 shows that maize had significantly better linear fitting results for all growth stages than that of wheat. This is because the maize plant leaves had not yet wilted and shed in large numbers during the silage harvesting stage. Moreover, CH_m (33.2−1462.1 mm for maize, 51.4−758.0 mm for wheat) and CH_a (155.5−2984.3 mm for maize, and 7.4−450.7 mm for wheat) showed consistency to some extent. However, the value obtained using the ultrasonic sensor was much lower than the actual value (measurement accuracy RMSE=374.5−976.3 mm) and was not suitable for direct use. Therefore, further experiments are required to determine the influencing factors, and the measurement results must be calibrated.

The changing trends in the main canopy parameters with the growth and development of canopies are shown in Figure 5 . V3−VT is part of the vegetative growth stage of maize. The canopy coverage increased during these stages as the leaves grew. The LAI increased from 0.103 to 3.979, and the NDVI increased from 0.062 to 0.863. In addition, the canopy height of the maize plants increased from 161 to 2421 mm as the plants grew. For wheat, the greening to heading stages are part of the vegetative growth stage, and there was a similar trend for the change in each parameter, as for maize. Wheat canopy height (from 83 to 628 mm), LAI (from 0.905 to 2.307), and NDVI (from 0.375 to 0.821) show the gradually increasing trend. The wheat heading to maturity stages belong to the reproductive growth stage, and the wheat height stops growing and leaves begin to fade during this time. There was no change in the wheat canopy height, whereas the LAI decreased to 0.291, and the NDVI decreased to 0.158.

The canopy structures during the maize VT and wheat heading stage were relatively complete and stable. Therefore, variables such as θ, D, H, t, and v were analyzed during these stages ( Table 4 ). The data at the significance level indicate that in the observation height range of 0.2−2.0 m, observation periods of 8:00−18:00, and moving speed of 0−2.0 m min⁻¹, changes in H, t, and v had no significant effect on measurements. However, T, θ, and D significantly affected measurements within the observation angle range of 0−60° and planting density range of 0.2 d−d. Hence, the growing period, the angle at which the sensor was placed, and the crop planting density were the key variables influencing ultrasonic measurement. In addition, the influences of atmospheric pressure, temperature, humidity, sound wave attenuation, and moving speed within a certain range in this experiment can be neglected in the field.

Figures 6A and B show that with an increase in the observation angle, the relative errors of measurement were reduced in an orderly manner, and the downward trend became more obvious. Figures 6A and C show that the relative error for maize from V3 to V9 continued to decrease from 0.877 to 0.274. VT had the smallest relative error among the growth stages with a range of 0.246−0.568. Figures 6B and D show that the relative error of wheat in the regreening to maturity stages first decreased and then increased with a variation range of 0.223−0.621. The relative error in the heading stage was the lowest within each period, ranging from 0.238 to 0.445. This is because the canopy coverage was highest during the VT of maize and heading stage of wheat during experiment. Similarly, the measurement accuracy showed the same trend for different canopy densities ( Figures 6C, D ). As the planting density increased from 0.2d to 1.0d, the relative error range of maize decreased from 0.667−0.950 to 0.561−0.862, and that of wheat decreased from 0.661−0.894 to 0.445−0.627.

From the above analysis, it can be determined that planting density and observation angle are the main factors affecting the ultrasonic measurements. Because the measurement error from observation angle can be reduced by fixing the observation direction, it is necessary to study the measurement changes caused by crop planting density. Figure 5 indicates that the NDVI correlates well with LAI, and this vegetation index is relatively mature and widely used in canopy measurement (Tucker, 1979). Hence, it is possible to use the NDVI to study the main factors affecting ultrasonic measurements.

The wheat leaves in the mature stage withered when the canopy height tended to be stable, and this situation did not comply with the trend that canopy height increased with increasing coverage ( Figure 4B ). In addition, crop height is stable during the late growth stages, and observing canopy height before these stages is more practical for production (Scotford and Miller, 2004; Aziz et al., 2004; Walter et al., 2019). Therefore, only the crop growth stage prior to leaf withering was studied when calibrating ultrasonic measurements to reduce the complexity of verification.

Empirical calibration models were constructed using all data from the in-situ canopy experiments. These data were divided into training set and validation set by random sampling method (Shao et al., 2022; Shao et al., 2023; Zhang et al., 2023). Taking the four-year data as a whole when dividing these sets can enrich the year-differences of data set, and this method of data processing can improve the adaptability of the model to different years and make the model more robust. Stratified random sampling method (Zhu et al., 2020) was used in this study and all data from each growth stage was randomly divided into training and validation sets in a ratio of approximately 3 to 1. In all data, there were 403 groups of maize data in total (303 groups in the training set and 100 groups in validation set), and 286 groups of wheat data in total (216 groups in the training set and 70 groups in validation set). The statistical characteristics of the sample data are shown in Supplementary Table. S1 . The single-factor and double-factor calibration models were constructed based on above data and the method of multiple non-linear regression (Berthold and Hand, 2006), and the output was CH_c. In the single-factor model, only CH_m was considered as input. For the double-factor model, the input parameters were CH_m and NDVI. In this study, both NDVI and CHm (R² of 0.64−0.71 between them) increased with crop growth, but due to the growth difference between years and the saturation effect (the plant height was still increasing when the canopy coverage reached its limit) of NDVI, the variance inflation factor of maize and wheat (the VIF of 2.78−3.45) were within an acceptable range. Therefore, it is reasonable to build the model based on the above research. When establishing the calibration model, the equations ( Table 5 ) were first obtained based on the training set, and then the model were evaluated based on the validation set ( Figures 7A, B ). For both maize and wheat, the R² value of the double-factor model was consistently higher than that of the single-factor model. For example, the determination coefficient of the linear fitting equation in the model evaluation results increased from 0.986 to 0.989 for maize, and from 0.925 to 0.964 for wheat when using double-factor models. Meanwhile, there were decreases in the RMSE (100.1 mm to 89.1 mm) for maize and the RMSE (58.0 mm to 40.1 mm) for wheat.

Then, CH_m was calibrated based on all data from the in-situ canopy experiments (maize N=403, wheat N=286), and the results before and after using the double-factor model are shown in Figures 7C and D . The accuracy of ultrasonic measurements was significantly improved by using the double-factor calibration model in Table 5 . The measurement accuracy RMSE of maize decreased from 967.3 mm to 87.3 mm, and the RMSE of wheat decreased from 216.7 mm to 42.0 mm.

The actual value of canopy height and NDVI of maize (V6, V9, and VT) and wheat (jointing and pre-filling) are shown in Figure 8 . Maize canopy height increased from 735−1042 mm to 2134−2810 mm during the V6−VT period. The NDVI of maize increased from 0.42−0.66 in V6 stage to 0.76−0.92 in VT stage as leaves grew. The CH_a of wheat was lower than that of maize, and increased from 298−449 mm in the jointing stage to 533−716 mm in the early-filling stage. The CH_a and NDVI fluctuations observed during the early-filling stage were similar to those observed during the jointing stage.

The double-factor model ( Table 5 ) output for each year based on the experiment data ( Table 3 ) is shown in Figure 9 . The RMSE values for maize ( Figure 9 ) was diminished from a range of 894.1−1042.6 mm to 81.4−93.6 mm after calibration. Similarly, the RMSE for wheat ( Figure 10 ) decreased from 221.0−231.2 mm to 37.1−43.4 mm. There was no obvious difference in calibration effects between different years.

Figure 11 displays the residuals before and after calibration of canopy height measurements during growth stages of maize (V6, V9, and VT stages) and wheat (jointing and early-filling stage). The residual of CH_m was smaller in higher canopy coverage. Considering the jointing stage of wheat as an example ( Figure 11D ), the mean residuals of CH_m were 2019 (112 mm)<2020 (125 mm)<2021 (132 mm). Furthermore, maize (102−1491 mm) exhibits a greater CH_m residual than wheat (21−372 mm), owing to its lower planting density and higher overall canopy height. After the double-factor model calibration, the mean CH_a residuals of maize decreased from 307−1334 mm to 47−91 mm, the mean CH_a residuals of wheat decreased from 113−268 mm to 26−49 mm, and there was no obvious difference in the calibration results in different years.

The ultrasonic sensor is a device with good stability and repeatability in distance measurement, but it has relatively low precision in measuring maize or wheat canopy height. The experiment results show that the observation height (0.2-2.0 m), observation period (8:00-18:00) and relative moving velocity (0-2.0 m min^-1) have no significant effect on measurement results (P≥0.05). It can be seen that the effect of distance change on canopy height is negligible in real conditions, although this will cause a change in the observed area, and the sound attenuation increases with the increase of propagation distance. At the same time, although ambient temperature changes can significantly affect ultrasonic propagation (Scotford and Miller, 2004), the built-in temperature compensation module (-40−70 °C) guarantees that temperature changes (16-38 °C) during the experiment will not interfere with the ultrasonic sensor measurements. Barmeier et al. (2016) found that relative moving velocity affects ultrasound measurements, which is contrary to the conclusions of this study. This is due to the fact that the center pivot system cannot move at a high speed (at a low speed of 0-2.0 m min^-1) and the flat pavement in the experiment can effectively avoid the vibrations and oscillations of the ultrasonic system. Of course, it is possible to try to include stabilization devices in subsequent studies based on this conclusion. In addition, the results showed that the growth period (V3-R of maize, green—pre-filling stage of wheat), observation angle (0-60°), and planting density (0.2-1.0 times of the standard planting density) had significant effects on ultrasound measurement (P<0.05). Combined with Figures 4 and 5, the above results can be attributed to the change in canopy coverage within the sensor's field of view. Studies have shown that only a plane with sufficient area at a suitable angle can effectively reflect the ultrasonic signal (McKerrow and Harper, 2002; Andújar et al., 2012). In this experiment, maize plants were widely spaced, wheat leaves were narrow, and their leaves grow obliquely. As a result, at low leaf densities, the effective signal of the sound wave was reflected by the lower canopy leaves or soil, resulting in measurements lower than the actual canopy height. This rationale explains why Sui and Baggard (2018) and Chang et al. (2017) obtained relatively accurate measurements for soybean (the RMSE of 58 mm), cotton (the RMSE of 31 mm), and blueberry (the RMSE of 23 mm). The leaves of these crops are more horizontally oriented and denser than those of maize and wheat. This orientation and density effectively reflect acoustic signals, as noted by Yuan et al. (2018).

Some scholars (Aziz et al., 2004; Farooque, 2013; Chang et al., 2017) have measured the performance of ultrasonic sensors in the laboratory or with the crops in a single growth period, and some influencing factors in their research have been measured and analyzed. However, few studies have identified the main factors influencing ultrasound measurements in the field environment through continuous and systematic multi-year maize and wheat experiments, as in the present study. At present, most of the crop field research on ultrasonic sensors is mainly focused on the direct application without calibration in field. For example, Sui and Baggard (2018) integrated a variety of sensors (including ultrasonic sensors and infrared temperature sensors) into a center pivot system to measure the soybean canopy, but their experiment did not consider using spectral reflectance data to further assist the ultrasonic sensor in obtaining more accurate measurements. Of course, the reason why they did not conduct such a study may also be related to the fact that the experimental crop was soybean, but this is more indicative of the importance of the research on maize and wheat in this study. Therefore, based on their meaningful and valuable research foundation, this study attempts to combine NDVI and ultrasonic data to accurately measure the canopy height of maize and wheat. Similarly, Pittman et al. (2015) built a tractor-based platform with an ultrasonic sensor, the NDVI sensor, and the laser sensor, but their model of alfalfa canopy height was constructed using only ultrasonic and laser data. In addition, many scholars have obtained more accurate ultrasonic measurements by continuously and repeatedly measuring the same experimental plot (Scotford and Miller, 2004) or taking the 95.5-100th percentile (Jimenez-Berni et al., 2018; Madec et al., 2017; Sun and Li, 2016), but these operations will affect the measurement efficiency or the integrity of the original data. In summary, the content of this study can serve as a further supplement and improvement in their research. In this study, we attempted to introduce the canopy coverage into the calibration model. It is possible for the methods of fitting with empirical formulas (Section 3.4) to compensate for the errors caused by ultrasound. The calibration model achieved satisfactory results in the measurement of canopy height in maize and wheat, and the calibration results for different years and growth periods had satisfactory accuracy (Section 3.5), which shows the reliability and applicability of this model.

Moreover, it is necessary to analyze the propagation and reflection mechanism of ultrasonic signals under complex canopy conditions to improve the adaptability of the model to different regions and crops. Therefore, it is important to use more advanced image or laser point cloud techniques to understand the distribution of the leaves, and to optimize the measurement results in combination with more accurate mathematical models. In addition, due to the rapid technological innovation, there are other methods of measuring canopy height in addition to ultrasonic technology, such as LiDAR or UAS imagery technology. Therefore, in the following section, a comparative analysis of various measurement methods is presented to further clarify the characteristics of the calibrated ultrasonic measurement method.

In addition to ultrasonic measurements, the technologies widely used in canopy height measurement include LiDAR (Jimenez-Berni et al., 2018; Walter et al., 2019) and UAS imagery (Friedli et al., 2016; Madec et al., 2017). Among them, LiDAR is based on the principle of time of fly (Sun et al., 2017). The canopy height was obtained by converting the raw data from LiDAR into a three-dimensional (3D) point cloud. This technique has achieved good measurement accuracy in various researches, and for example, the measurement accuracy of rye (Busemeyer et al., 2013), barley (Tilly et al., 2015), rice (Tilly et al., 2014), cotton (Sun and Paterson, 2017), and pea (Underwood et al., 2017) is 24 mm, 30−60 mm, 50 mm, 35−65 mm, and 46 mm respectively. UAS Imagery uses a UAS platform with a high−resolution camera. This technique retrieves a digital surface model (3D point cloud) of the canopy from multiple photographs using the triangulation principle (Yuan et al., 2018) and estimates plant height based on this principle. This method is also widely used in the measurement of barley (Bendig et al., 2014), sorghum (Malambo et al., 2018), shrub (Díaz-Varela et al., 2015; Fraser et al., 2016) and forest (Dandois and Ellis, 2013; Puliti et al., 2015) canopy height, and the measurement accuracy of UAS imagery on above canopy types is 100, 120−240, 80−200, and 400−1400 mm respectively.

After conducting a comparison, researchers (Yuan et al., 2018; Yuan, 2019) found that the ultrasonic measurements had the lowest accuracy, the LiDAR measurements had the highest accuracy (Madec et al., 2017), and the UAS imagery measurements had the moderate accuracy. This is because LiDAR has the high resolution (3−5 mm) and the strong penetration (Madec et al., 2017). LiDAR can directly generate a fine canopy 3D point cloud (Friedli et al., 2016) from the raw measurements obtained via top-down scanning (Walter et al., 2019). The UAS imagery indirectly generates 3D point clouds using a large number of overlapping canopy images at different angles. UAS requires a high flight altitude to increase the measurement range and prevent propeller airflow from disturbing the canopy. Due to the limited penetration ability of UAS imagery when photographing canopy (Yuan et al., 2018), this technique cannot accurately identify canopy features such as wheat ears or corn male ears. Some scholars (Grenzdörffer, 2014; Bareth et al., 2016; Van der Voort, 2016) have got the similar conclusion that UAS lacks effective canopy top reconstruction capacity. As a result, the accuracy of UAS imagery was lower than that of lidar data. Compared to the above two methods, ultrasonic sensors are affected by the large deviation in the direction of reflection of leaves when using ultrasonic measurements (Yuan et al., 2018) although they have the resolution of 0.172 mm. The top of the canopy of maize or wheat cannot form a continuous plane. Therefore, the error in the ultrasonic measurement value is relatively large.

In this study, it was verified that the calibration model reached the RMSE (ultrasonic measurement error) of 87.3 mm for maize and 42.0 mm for wheat. Other studies have also taken measurements of the same crop canopy. The measurement accuracy of LiDAR for maize is 50−170 mm (Li et al., 2015; Hu et al., 2023: Anthony et al., 2014) and 17−50 mm for wheat is (Virlet et al., 2016; Jimenez-Berni et al., 2018; Yuan et al., 2018). The measurement accuracy of UAS imagery for maize is 90−190 mm (Varela et al., 2017; Malambo et al., 2018) and 30−90 mm for wheat (Holman et al., 2016; Madec et al., 2017; Yuan et al., 2018). The calibrated ultrasonic measurement accuracy was already at the same level as the measurement accuracy of the above technique after comparing the above results. Considering that lidar is expensive (Fricke and Wachendorf, 2013), and UAS has limited payload and flight time (Deery et al., 2014). In addition, the processing of large amounts of point cloud data is cumbersome (Singh et al., 2016), and special software is required for accurate information evaluation (Gebbers et al., 2011; Llorens et al., 2011). In contrast, ultrasonic sensors are a relatively low−cost (Sui et al., 2012) and user−friendly (Madec et al., 2017). The ultrasonic output is easy to handle and its relatively low cost allows users to use multiple sensors in parallel (Andújar et al., 2012). The installation on the platform of ground−based agricultural machinery, allows the sensing equipment to remain on site, and enables quick and rapid canopy measurements. These systems facilitate the timely implementation of key management decisions. Hence, the established calibration models in this study have effective application values.

A four-year field experiment of the ultrasonic sensor was conducted based on of the field data in this study. The constructed ultrasonic calibration model was verified as suitable for canopy height measurements (maize/wheat) in different years and the constructed system can acquire CHm and canopy NDVI data stably and efficiently based on a center pivot. Although the use of spectral sensors inevitably increases the cost, the price of this type of sensor combination is still lower than that of LiDAR. Additional observational indicators such as spectral data indicate that more comprehensive and real-time crop growth information can be obtained. These indicators can help ultrasonic measurement systems to play a more important role in the field of non−destructive prediction of important crop growth parameters such as leaf area index and aboveground biomass (Scotford and Miller, 2004; Fricke and Wachendorf, 2013; Pittman et al., 2015). Compared with the UAS, the ultrasonic measurement system built by the ground-based platform does not have an advantage in the data throughput of canopy information acquisition (Yuan et al., 2018). However, this disadvantage can be compensated by the ease with ultrasonic data. The relatively slow measurement speed allows for sufficient data processing time for platforms such as center pivot irrigation machines. These data processing time make it possible for the system to make flexible and timely management decisions. In follow-up research, researchers can try to efficiently combine the measurement system with the agricultural machinery platform toward the field management goal of “canopy measurement−data processing−decision implementation”.

Future research should focus on improving canopy height measurements throughout the growth cycle of most field crops. Cost comparison tests can be carried out under field conditions. These tests help to determine the types of sensors that are suitable for long-term monitoring. In addition, it is important to conduct the research on the optimal configuration of multi-type sensor combinations. These tests can help to improve the observation efficiency of multi-sensor systems.

It is undeniable that LiDAR and UAS Imagery possess numerous irreplaceable measurement advantages. The use of fine imaging or 3D cloud mapping technology facilitates further analysis of the reflection propagation principle of ultrasonic signals in complex crop canopy structures. Therefore, combining ultrasonic systems with various remote sensing technologies (e.g., LiDAR, UAS, and satellites) to complement the advantages of multi-source data is another important research direction (Schirrmann et al., 2017).