Atmospheric stability at the ground layer of wheat fields.

The 10-minute average of μ_x, μ_y, and μ_z and that of the horizontal wind speed, U, were calculated using Xu et al methods[33]. The atmospheric stability was obtained by examining the air temperature [34–35] and wind speed recorded by the 3D anemometers. In this study, the gradient Richardson number (Ri) was employed to determine the atmospheric stability at the ground layer [36]: (3) Where is the mean temperature of air (K), which was calculated using: = 273.16 + (T₂—T₁)/2. Here represents the difference in air temperature between two observation heights, z₁ and z₂ indicate the installation heights of two anemometers, and g is the acceleration due to gravity, 9.8 m/s². Ri > 0, Ri = 0, and Ri < 0 indicate that the atmospheric stratification is in a stable state, a neutral state, and an unstable state, respectively.

Wind speed profile and the apparent roughness length.

Since the lodging occurs on cloudy or rainy weather, it is necessary to study the effects of weather conditions on the daily variation of wind speed profile and apparent roughness length. The dataset obtained with the ultrasonic anemometers and the multi-channel anemometers were analyzed for two weather conditions—sunny and cloudy—for 24 hours. The variation in the wind speed profile and the apparent roughness with time and weather conditions was analyzed. (1) Wind speed data at six heights, as obtained by the multi-channel anemometers, were ranked according to that measured by the wind speed probe at 10 m. (2) The data were segmented based on a step size of 0.5 m/s, where the average wind speed at each section was calculated. (3) Wind speed profile was plotted by using 6 observation heights and corresponding wind speed, and the apparent roughness of the wheat field was calculated by extrapolating the wind profile curve to the coordinate axis (i.e. for an average wind speed of zero). (4) The curve of roughness versus wind speed was drawn by using the wind speed at a height of 10 m from the whole day and corresponding apparent roughness, and the best-fitting equation was determined by the least squares method.

Wind attack angle at the ground layer of wheat fields.

Since the wind direction is rarely parallel to the ground, the angle of attack, θ, describes the difference between the wind direction and the surface. When wind blows upward, the wind attack angle is positive, and vice versa [37]. The attack angle was determined as Xu et al[33]): (4)

To study the variation of wind attack angle with weather condition and observation time, the 3D wind speed data of sunny, cloudy and cloudy with light rain weather were used to calculate the wind angle of attack. The calculation steps of the wind attack angle as follows. (1) Wind speed data from the whole day with a maximum daily average wind speed greater than 8.0 m/s were segmented by 10 minutes. (2) Three-second moving averages of the wind attack angle in each 10-minute period were calculated. (3) The maximum and minimum wind angles of all samples were sorted, and the mean of the top 25% of the sequence was taken as the wind attack angle of the model.

Lodging CWS model for wheat population.

Basic principle of the model for calculating the lodging CWS of wheat population is that the lodging of wheat is caused by the load exerted vertically on the stalk of wheat population is greater than the maximum load that the stem base can bear. Field wheat population is taken as the observation object, the lodging CTF is firstly measured; then the ground equivalent lodging (EWS) is calculated according to the Bernoulli wind speed and wind pressure conversion principle and the wheat canopy parameters; and finally, it is converted into the standard wind speed at 10 m above the ground according to the near-surface layer wind speed profile characteristics of wheat field. The basic calculation procedure is as follows.

1. (1) Determine the lodging CTF of a wheat population, that is, the thrust force of the plant was pushed to a 45° from the ground (N/m^-1).
2. (2) Calculate the critical wind load of the wheat population W₀ (1000 N/m²):

(5)

Where P is the lodging CTF. L is the probe length (0.33 m). K_P is the resistance coefficient of the probe, which is 0.75–1.0 depending on the resistance of the probe, and 0.75 in this paper. h_c is the height of the wheat canopy. z₀ is the apparent roughness length of the wheat field.

1. (3) Calculate the corresponding lodging EWS (ν₀):

(6)

Substitute formula (5) into formula (6) and get formula (7): (7)

1. (4) Calculate the ground equivalent lodging EWS (ν₀^’) (m/s), that is, the wind speed at a specific height that can penetrate the canopy and cause lodging.

(8)

Where α is the ventilation coefficient. It is equal to the wind speed at the front of the population minus the wind speed at the back of the population for the same height, and it depends on the number of main stems per unit area in the wheat population. β is the gust factor. And k is the adjustment coefficient of the lodging CWS, generally 0.85.

1. (5) Calculate the lodging CWS ν₁₀ (m/s), this is, the standard wind speed at 10 m above ground (Instantaneous extreme wind speed):

(9)

Wind tunnel simulation verification of the lodging CWS model.

A wind tunnel simulation of wheat lodging resistance was carried out at the laboratory of the Henan Institute of Science and Technology in Xinxiang City, Henan from 2013 to 2015. Eleven wheat varieties (Triticum aestivum L.) with different lodging resistance were used as experimental materials: Yumai 18, Zhoumai 18, Aikang 58, Pingan 6, Zhengmai 9023, Bainong 418, Bainong 419, Zhonglian 2, Zhoumai 26, and Caizhi 9333. All of them were provided by the Wheat Center of Henan Institute of Science and Technology. The experimental material was divided into two periods in 2013–2014; the first planting was sown on October 10, 2013, and the second was sown on October 20, 2013. The experimental material was sown on October 10, 2014 for the 2014–2015 periods. The plants were grown in large plastic planting boxes of dimensions 0.60 m×0.40 m×0.25 m, following normal management practices.

The experiment section of the wind tunnel was 7.00 m×1.20 m×2.00 m, where a transducer was used to adjust the wind speed. The wind speed profile of the wind tunnel was similar to that of the ground layer in the field, and the wind speed increased with elevation following a logarithmic function. A horizontal clapboard was installed at 0.5 m above the bottom of the wind tunnel with a tilt board in front of it, which allowed wind to blow along the clapboard to the wheat population stalks 0.16 me above the ground. This was used to simulate the effect of strong wind on the lodging at an apparent roughness of 0.16 m.

Determination of the lodging CWS was carried out when wheat was at the mid-grain filling stage. Wheat materials used in the wind tunnel simulation experiments were first used to determine the lodging CTF by the rapid measuring instrument for crop lodging resistance, and the height of the wheat canopy was recorded at the same time. The wheat growing boxes were then moved into the wind tunnel, two at a time. They were placed side-by-side vertical to the direction of the wind. Two hot wire anemometer probes were installed horizontally in front of, and behind, the wheat population at 2/3 of the height of the canopy (another two anemometers were installed above the canopy). The wind speed was gradually increased until the plants tilted back at a 45° angle, whereafter the wind speed in front of and behind the population was recorded (Fig 3). The experiments were repeated three times, and their average was taken as the lodging EWS. This was then compared with the calculated wind speed based on the lodging CTF.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 3. Wind tunnel simulation of lodging resistance in wheat.

https://doi.org/10.1371/journal.pone.0224732.g003

Field experiment verification of the lodging CWS model.

Six wheat varieties were used in the field trial: Zhoumai 18, Aikang 58, Zhoumai 26, Bainong 418, Bainong 419, and Zhonglian 2. All of them were provided by the Wheat Center of Henan Institute of Science and Technology. The field experiments were performed at the wheat test field of Henan Science and Technology College, Xinxiang County, Henan Province from October 2013 to June 2014 and from October 2014 to June 2015. A randomized block design was implemented with three replicates. The plots were 4 m long with 10 lines, where the space between the lines was 0.23 m, which were managed according to general practice in the field.

The experiments began at the flowering stage until complete maturation, and data were measured every seven days. The lodging CTF was determined 10 times for each population. The critical wind load, the lodging EWS, and the lodging CWS were sequentially calculated.

Atmospheric stability on wheat fields.

The stability of the atmosphere is related to the observation time and weather conditions. javascript:void(0);Cloudy days and rainfall are the main weather causing wheat lodging. In order to fully understand the variation of atmospheric stratification stability with time under different weather conditions, the variation of atmospheric stratification stability with time under sunny, cloudy and rainy weather conditions was studied. The pattern of variation in the Richardson number versus time and the three weather conditions—sunny, cloudy, and cloudy with rainy—is shown in Fig 4.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 4. Variation in the Richardson number and the atmospheric stability at the near-surface layer of wheat field.

https://doi.org/10.1371/journal.pone.0224732.g004

Under sunny and cloudy conditions, the atmosphere in the field was mainly stable from 00:00 to 6:30, but exhibited an unstable state from 06:30 to 18:00, and reverted to a stable state from 18:00 to 24:00. The atmosphere maintained an unstable state during strong or persistent winds and rainy days. At the ground layer, a neutral atmosphere only appeared for a short period, around 06:30 or 18:00, which is the transition state from a stable to an unstable state, or vice versa.

Wind speed profile and apparent roughness.

Under varying weather conditions and wind speeds, the patterns of variation in wind speed at various heights were comparable in the wheat field. Wind speed increased with elevation, where the change followed an exponential or logarithmic distribution. The smallest R² of the fitted equations was 0.764 and the maximum was 1.000, with an average of 0.969. The profile distribution of the wind speed at the ground layer of the wheat field was independent of atmospheric conditions.

The apparent roughness is related to the weather conditions and wind speed. The relationship between the apparent roughness and the wind speed at the near surface layer of the wheat field is shown in Fig 5.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 5. The relationship between the wind speed and the apparent roughness at the near surface layer of the wheat field.

https://doi.org/10.1371/journal.pone.0224732.g005

Under different weather conditions, the apparent roughness of the field linearly decreased with an increase in wind speed, and their relationships were best fit with an exponential function, with correlation coefficients, R², ranging from 0.916 to 0.926. In addition, the apparent roughness was also related to the weather conditions. For an 8–10 m/s wind speed, the apparent roughness ranged from 0.10 to 0.16 m in May 19^th and June 1^st (cloudy), but the apparent roughness ranged from 0.13 to 0.21 m in June 2nd (sunny). The apparent roughness during sunny days was significantly greater than that during cloudy days.

Variation in the wind attack angle.

The variation in the 10-minute average of the wind attack angle at the ground layer of the field for various times and weather conditions is shown in Fig 6.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 6. The variation in the 10-minute average of the wind attack angle at the ground layer of the field for various times and weather conditions.

https://doi.org/10.1371/journal.pone.0224732.g006

The wind attack angle showed a significant diurnal variation, exhibiting a saddle-shaped curve. In general, the negative attack angle gradually decreased during 0:00–6:30 followed by a positive attack angle from 06:30–18:00, whereafter the negative attack angle gradually increased again. The attack angle and its evolution were related to the observation time, weather, and height. During the evening, the attack angle was generally negative, and it was positive during the day. Compared with that measured during sunny weather, the positive attack angle decreased significantly during cloudy and rainy weather, and the negative attack angle increased significantly.

The variation of wind attack angle showed significant instantaneous characteristics, and its magnitude was closely related to the observation distance. The variation in the three-second average of the maximum wind attack angle under different weather conditions is shown in Table 2.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 2. Variation in the wind attack angle at the near-surface layer of the field under different weather conditions.

https://doi.org/10.1371/journal.pone.0224732.t002

The attack angle decreased with increasing altitude, and the amplitude of the variation at the ground layer was substantially larger than that at higher altitudes. There was a significant difference between the positive and negative attack angles between the two observational heights (P<0.01). Although the wind attack angles for the different weather conditions had obvious differences, it was not statistically significant (P>0.05). This preliminary analysis shows that the maximum and minimum wind attack angle tends to decrease gradually with an increase in the wind speed.

Wind tunnel simulation verification of the lodging CWS model.

The results of the wind tunnel simulation of lodging resistance during 2013–2015 are shown in Table 3.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 3. Wind tunnel simulation experiments for lodging resistance during 2013–2014.

https://doi.org/10.1371/journal.pone.0224732.t003

Wind tunnel test results in different years showed that Aikang58 had the strongest resistance to stem lodging, and the lodging CWS was 22.64 m/s; followed by Zhoumai 26, Bainong 419 and Bainong 418, with the lodging CWS of 19.70–20.85 m/s; Yumai 18, Caizhi 9998 and Zhengmai 9023 had the weakest lodging resistance, and the lodging CWS was 16.62–16.81 m/s. This results were consistent with the field performance of these varieties. The lodging CTF was positively correlated with the actual wind speed measured in the wind tunnel (MCWS), the ground wind speed of lodging calculated by the model (SCWS-1), the ground wind speed of lodging determined by the model and the ventilation coefficient (SCWS-2) and the wind speed at 10 m above ground (with correlation coefficients of 0.641^**, 0.972^**, 0.866^**, and 0.855^**, respectively). Moreover, the ‘lodging MCWS’ also showed a positive correlation with the ‘lodging SCWS-1’ and ‘lodging SCWS-2’, and the wind speed at 10 m above ground (with correlation coefficients of 0.721^**, 0.898^**, and 0.903^**, respectively). Due to the penetration and loss of the wind to the wheat population, the ‘lodging SCWS-1’ was significantly smaller than the ‘lodging MCWS’, but they were consistent following calibration with the ventilation coefficient.

Field experimental verification of the lodging CWS model.

The lodging CTF was measured from 10 days after flowering during 2013–2014, and the determination time was on May 9, 16, 23, and 30, respectively. The test of lodging CTF for 2014–2015 started at wheat flowering on April 22, April 29, May 6, May 13, May 20, and May 27. To facilitate a comparative analysis, we selected four dates during the filling stage, the results of which are shown in Table 4.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 4. The experiment of lodging resistance in the field from 2013 to 2015.

https://doi.org/10.1371/journal.pone.0224732.t004

The results of field trials showed that Aikang58 had the strongest resistance to stem lodging from the flowering stage to full maturity in the two experimental years, and the average lodging CWS was 20.84 m/s; followed by Bainong 419 and Bainong 418, with the lodging CWS of 18.21 m/s and 18.56 m/s respectively. Zhoumai 18 and Zhoumai 26 with the lodging CWS of 16.71 m/s and 17.50 m/s respectively. The lodging CTF and CWS values were consistent between the years and among the different wheat varieties. Both were high at the early filling stage, and gradually decreased until maturity, followed by a slight increase thereafter. The field experiment results were basically consistent with the wind tunnel experiment results.

Basic characteristics of the wind field at the ground layer.

The stability of the atmosphere is related to the observation time, the weather conditions and the wind speed. During the daytime, the atmosphere was mainly unstable, while it was predominately stable during the evening (Fig 4A–4C). During rainy days or persistent strong winds, Ri was relatively small, suggesting an unstable or neutral state of the atmosphere (Fig 4C). These results are consistent with those from a previous study of tropical rain forests in Xishuangbanna [38].

Wind speed profile.

The wind speed profiles below 10 m were similar among the various times and wind speed conditions. The wind speed increased with height, where the change followed an exponential or logarithmic distribution with an R² of 0.97. The distribution of wind speed profiles at the ground layer of the field was not affected by atmospheric conditions; thus, the influence of the atmosphere can be ignored when calculating wind speeds at heights below 10 m at the ground layer of the field [36].

Apparent roughness of wheat fields.

The roughness of field crops is generally considered to be related to characteristics of the crop canopy and atmospheric stability. Because it is difficult to accurately determine the displacement height of the zero plane under the condition of the field, in this study, we used the apparent roughness to represent the height where the wind speed was zero at the ground layer, which is the “displacement of the zero plane + the roughness of the field crops”. Our results indicate that for strong winds, the apparent roughness decreases with an increase in the wind speed, and the relationship was exponential with an R² varying from 0.916 to 0.926 (Fig 5). In the field, and at a crop canopy height of 0.7–0.8 m, the minimum standard wind speed that can disturb the crop canopy is about 2.0–2.5 m/s. The apparent roughness ranged from 0.10 to 0.24 m for wind speeds of 8.0–12.0 m/s. The apparent roughness values of wheat fields measured in this paper are significantly lower than those reported in the literature[36]. The main reason for this is related to the wind speed conditions when the roughness measurements were made. The apparent roughness in this paper is measured with strong wind but the values in the literature with weak wind. The results are consistent with the observation results of Liu [39] and Mao[40]. The apparent roughness of wheat field is not only related to the stability of the crop canopy structure and the atmospheric layer, but it is also related to the observed wind speed. This phenomenon is mainly related to the flexibility of the crop stems. The apparent roughness decreases with an increase in the wind speed, and eventually stabilizes at a minimum value. Thus, the magnitude of wind speed must be taken into account when measuring and calculating the apparent roughness of field crops. The apparent roughness was positively correlated with wind speed, where the lodging CWS increased by 2% with every 0.01 m decrease in the apparent roughness. The apparent roughness was generally 0.10–0.24 m during strong winds, and was 0.16 m in this study.

Wind attack angle.

The attack angle is related to the observation time, the weather conditions and the height of the observation (see Fig 6A–6C and Table 3). Generally, the attack angle at night was negative, and it was positive during the day. Compared with sunny weather, the negative attack angle increased significantly on cloudy and rainy days, and the positive angle of attack decreased significantly (Fig 6A–6C). The phenomenon of wheat lodging occurring at night may be related to the attack angle. The wind attack angle exhibited an instantaneous variation and it decreased rapidly with an increase in the interval of observation. However, the range of the attack angle was much larger than that reported in the general literature, which may be related to the flexible structure of the crop canopy.

Due to the downward spread of wind at the ground layer of a field, wind can penetrate the canopy and cause lodging. Thus, the actual wind speed experienced by a wheat stem is larger than just the horizontal wind speed, that is, the wind speed impinging on the wheat stem = wind speed/cos θ. As lodging occurs instantaneously, and the wind angle of attack is related to the observation time and height, the attack angle is the maximum moving average of the attack angle over three seconds within 10-minute records of wind speed at 1.0 m above ground. To be conservative, the average of the top 25% of the “maximum moving average of the attack angle in three seconds” was used for the model. The lodging CWS decreased by 0.45% with every degree of increase in the negative attack angle.

Height of the ground-equivalent lodging CWS.

The height of the ground-equivalent lodging wind speed is H = 1+(h_c -z₀). The lodging CWS decreased by 2.2% with every 0.10 m decrease in the height. The value of this parameter is similar to that found in studies that used models of wheat lodging [1]. However, the canopy height of wheat in China is generally between 0.70 and 0.85 m, and some differences in the canopy heights exist among the different varieties.

Ventilation coefficient of wheat canopies.

The ventilation coefficient of a wheat canopy depends on the number of main stems per unit area of the considered wheat population. The number of main stems (i.e. the panicle number) in the high-yield wheat population of China is generally 615–675 panicles/m². According to our preliminary analysis, the ventilation coefficient at 2/3 of canopy height is 0.10–0.30 (for a canopy width of 1.0 m). The horizontal distribution of wind speed in the wheat canopy follows an exponential law, and the wind speed in the canopy decreases rapidly with the increase of the distance between the canopy and the edge of the population. The result is consistent with that of Wong et al [41]. The coefficient was smaller in the early growth stage of wheat than in the mature stage. The coefficient was set to 0.10–0.15 in our model because of the difficulty of accurate determination under the field conditions.

wheat population lodging CTF determination method.

The accurate determination of the lodging CTF of wheat population is the basis for calculating the lodging CWS based on the Bernoulli equation. The lodging CTF measuring instrument used in this paper is a new instrument based on the electronic measuring device of crop lodging resistance[24]). The instrument still uses a dynamometer as the lodging CTF measuring component, and a ball guideway as the dynamometer horizontal moving component. However, the rotary positioning disc is used to replace ball joints to change the bearing of the dynamometer, and the combination of the circular scale rod and steel fork is used to replace the field fixation of the multi-functional tripod for the measuring device. Compared with the original device, the new instrument has the following four improvements. (1) The conversion of the horizontal and vertical positions of the dynamometer is faster and more accurate. (2) The measurement range of the lodging CTF is wider (0.10 m to 1.0 m above ground). (3) The canopy height and gravity center height can be measured directly by using the circular scale rod. (4) With three tooth steel fork as the fixed part of the measuring device, the field fixation of the instrument is faster and more convenient.

Wind tunnel verification of the lodging CWS model.

Our results show that lodging CWS is significantly and positively correlated with the CTF; the correlation coefficient was 0.86 and 0.91 in 2014 and 2015, respectively, suggesting that it is feasible to calculate the lodging CWS by measuring the CTF. As wind can penetrate the wheat population, the actual wind pressure on the wheat stems is less than the wind pressure that can be generated by the field wind speed. Therefore, it is necessary to calibrate the Bernoulli equation with a ventilation coefficient when calculating the wind speed of lodging resistance for wheat.

Field experimental verification of the lodging CWS model.

There was a significant correlation between the lodging instantaneous CWS measured by wind tunnel and field test in the same period (middle stage of wheat grouting) of 5 same wheat varieties (Zhoumai 18, Zhoumai 26, Aikong58, Bainong 418 and Bainong 419), with a correlation coefficient of 0.963^***. The results of the field trials were consistent with those of the wind tunnel simulation.The results of the field lodging tests were significantly higher than those of the lab tests, which were mainly due to the difference in the environments for the wheat growth and test conditions. However, the lodging CWS obtained by the existing model was much larger than the value of general wheat varieties investigated. There were two main reasons for this phenomenon. The first was the friction resistance caused by existing population lodging thrust probe. To understand the influence of the probe’s friction resistance on the simulation results, we designed a new type of low-friction resistance probe. Compared with the new low-friction resistance probe, the measurement result of the existing population thrust probe was more than 25% higher. Second, the "radial width of wheat population" used in the determination of the lodging CTF exceeds the width of wheat population that can be penetrated by canopy wind speed. Due to the limitation of field environmental conditions, the population lodging thrust can only be measured by pushing forward pressure towards the population, so the lodging CTF must be corrected when calculating the lodging CWS. Where, the lodging CTF deviation caused by the friction resistance of the probe was corrected by the friction resistance coefficient K_P of the probe, K_P = 1- ((CTF_{Existing probe} -CTF_{Low resistance probe})/CTF_{Low resistance probe}), K_P takes 0.75–1.0 depending on the resistance of the probe used. The lodging CTF deviation caused by the radial width of wheat population was corrected by the adjustment coefficient k of the population thrust, and k is generally 0.85. Aikang 58 exhibited the highest lodging resistance, followed by Bainong 418, Bainong 419, and Zhoumai 18 (Tables 3–4). The same was also seen in the field observations, indicating that the model is reliable for calculating the lodging CWS.

Field investigation and verification of the lodging CWS model.

To explore the influence of wind speed and rainfall on wheat lodging, we conducted two surveys. For the first time, we used literature information to investigate the meteorological factors of 52 time’s large-scale wheat lodging in 2007–2015[42]. Large-scale wheat lodging in China can be classified into three types: strong winds, persistent rainfall, and strong winds with heavy rainfall, which account for 8%, 19% and 73% of all lodging events, respectively. Without rain, a wind speed above 16.75 m/s can lead to large-scale wheat lodging. The second time, on May 23, 2017, a large-scale wheat lodging occurred in the Huanghuai wheat area of China. We conducted field surveys on the lodging of wheat in 11 counties (cities) in Zhengzhou, Xinxiang and Jiaozuo, and conducted statistical analysis on meteorological factors. The results also showed that under the condition of no rainfall, a wind speed below 17.5–17.9 m /s would not cause large areas of wheat lodging. Two survey results are similar, revealing that the critical wind speed of general wheat lodging in China is about 17.0–18.0 m/s. Of course, the lodging wind speed is also related to the considered wheat variety and its growth stage.

To understand the coincidence between the calculated lodging CWS of this model and the actual value of wheat varieties, the lodging CTF and lodging CWS of 68 winter wheat varieties in China's Huanghuai wheat area or regional test materials (hereinafter referred to as varieties) measured in the field from 2011 to 2016 were statistically analyzed (Fig 7).

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 7. The lodging resistance distribution of common winter wheat varieties in China's Huanghuai wheat area.

A. The lodging CTF distribution of winter wheat population; B. The lodging CWS (instantaneous extreme wind speed) of winter wheat population.

https://doi.org/10.1371/journal.pone.0224732.g007

The maximum of the lodging CTF of 68 varieties (K_p was 0.75, the same below) was 26.21 N, the minimum 8.3 N, and the average 15.21 N±4.008N (Fig 7A). Among them, there were 5 varieties with CTF below 10N, accounting for 7.4%; 27 varieties with 10N to 15N, accounting for 41.1%; 24 varieties with 15N to 20N, accounting for 38.3%; 9 varieties with more than 20N, accounting for 13.2%. At present, the canopy height of wheat varieties is about 0.75 m. Under the condition that the canopy height is 0.75m and other parameters are the same, the lodging CWS of the 68 varieties was calculated by using this model. The results showed that the minimum of the lodging CWS was 15.62 m/s, the maximum was 27.62m/s, and the average was 20.87 m/s±2.732 m/s (Fig 7B). Among them, there were 33 varieties with the lodging CWS below 21.0m/s, accounting for 48.5%; 21 varieties with 21.0 to 23.0m/s, accounting for 30.9%; and 13 varieties with 23.0m/s or above, accounting for 19%. The calculation results are basically consistent with the lodging CWS of the current wheat varieties.There is a significant correlation between the lodging CTF and the lodging instantaneous CWS in 68 wheat varieties, with a correlation coefficient of 0.997^***. This result further indicates that the model and parameter setting are appropriate.

In this paper, wind speed and its related factors were studied, where the ventilation coefficient and the wind attack angle were introduced in our model, so that the model could more fully reflect the relationship between wheat lodging and meteorological factors. The lodging resistance of wheat depends on many factors such as plant height, height of gravity, plant stem strength, plant morphology, stem chemical composition, planting density, developmental period, etc [3,12–19]. These factors often have complex mutual constraints, such as plant height, plant stem strength, plant morphology, if these simple correlation factors are directly used to evaluate the lodging resistance of wheat, it is often difficult to accurately and truly evaluate the lodging resistance of wheat. On the contrary, if the black box theory is used, many factors, which are related to the lodging resistance of wheat but their real effects and their correlation with each other are difficult to be simply analyzed, can be included in a black box. The lodging evaluation process can be greatly simplified by studying from the perspective of the whole, namely "the lodging CTF of wheat population".

Compared with the stalk strength measurement method, this method for measuring the lodging resistance are similar, and the essence is the comparison of the bending strength of the stalk [9]. Compared with the lodging index method [8], there are four main characteristics: (1) The lodging CTF of wheat population in the field is used as an evaluation index, which can eliminate bias when calculating wheat lodging resistance by considering only the stalk strength, the stalk breaking strength, the plant height, planting density, etc. and the complex interactions that may exist between these evaluation indicators. (2) The measurement process has no obvious damage to the normal growth of wheat population evaluated, and is a non-destructive evaluation method for lodging resistance. (3) The method can not only determine the stem lodging resistance of wheat, but also its resistance to root lodging. (4) The model uses the lodging CWS as an indicator, and the result is related to the wind that causes the natural lodging of wheat lodging, which helps people to intuitively understand and compare the lodging resistance of different varieties.

Due to a limitation of available measured wind attack angles and ventilation coefficients, accurately determining their values will undoubtedly improve the accuracy of future results. Furthermore, many investigations have showed that lodging arising from strong winds coupled with rainfall is the main type, and how to calculate the lodging wind speed under the condition of rainfall is an important problem that needs to be studied urgently. Although the mechanism and cause of wheat stem lodging are different from root lodging, the analysis and research methods of wheat stem lodging are also applicable to root lodging.