Effects of fallow tillage on winter wheat yield and predictions under different precipitation types

Classification of precipitation types

In this study, we used the SPEI to determine the annual precipitation types. The SPEI is an index that is commonly used to describe the degree of drought (Stagge et al., 2016; Tirivarombo, Osupile & Eliasson, 2018; Faye, Grippa & Wood, 2019) by which the difference between precipitation and evapotranspiration in the fallow period (July–September) deviates from the average state. The calculations are as follows:

Step 1: Calculate the potential evapotranspiration (PET) according to the Thornth-Waite method adopted by Vicente-Serrano following:

(1) $$PE{T}_i=16.0{\left({\displaystyle \frac{10T_i}{H}}\right)}^A$$where: PET_i is the monthly potential evapotranspiration, T_i is the monthly average temperature, H is the annual heat index, and A is a constant.

Step 2: Calculate the difference between the monthly precipitation P_i and the evapotranspiration PET_i:

(2) $D_i=P_i-PE{T}_i$

Step 3: Normalize the D_i data sequence. The log-logistic probability distribution F(x) of the three parameters is used to normalize D_i, and the SPEI value corresponding to each D_i:

(3) $\mathrm{F}\left(x\right)={\left[1+\left({\displaystyle \frac{\propto }{x-\gamma }}\right)\beta \right]}^{-1}$where x is the value of the independent variable D_i, α is the scale parameter, β is the shape parameter, and γ is the origin parameter.

Step 4: Standardize the cumulative probability density, that is: p = 1 − F(x).

When the cumulative probability p ≤ 0.5, the SPEI value is calculated by:

(4) $\mathrm{S}\mathrm{P}\mathrm{E}\mathrm{I}=\mathrm{w}-{\displaystyle \frac{c_0+c_{1}w+c_2{w}^2}{1+d_{1}w+d_2{w}_2+d_3{w}_3}}$

(5) $\mathrm{w}=\sqrt{-2ln\left(p\right)}$where p is the cumulative probability, the constant term c₀ = 2.515517, c₁ = 0.802853, c₂ = 0.010328, d₁ = 1.432788, d₂ = 0.189269, d₃ = 0.001308.

In Eq. (5), when p > 0.5, p = 1 − p, and the SPEI sign is negative.

Step 5: Divide drought levels according to McKee, Doesken & Kleist (1993) standards.

Soil water storage

Before plot preparation, a 3 m-deep profile pit was excavated, and soil samples were taken from a 0 to 3 m depth in 0.2 m increments using the cutting ring method described by Dam et al. (2005) before the sowing, wintering, jointing, anthesis, and maturity stages. We used a soil drill to take soil from each of the 0.2–3 m soil layers, with every 0.2 m considered a soil layer. The soil profiles were cut and levelled, and the samples were taken from the bottom to the top according to their designated level. A drying method was used to determine soil moisture in which soil samples were placed in a 105 °C oven after weighing and let stand for 72 h. The dry soil weight was then measured and the storage capacity of soil water storage was calculated:

(6) $$GSW=(wetsoilmass-dryingsoilmass)/dryingsoilmass\times 100\mathrm{\%}$$

(7) $$Soilwaterstorage=GSW\times \rho b\times SD\times {10}^3$$where GSW is the soil water content (%), ρb is soil bulk density of given soil layer (g cm^–3), and SD refers to soil depth (m).

Grain yield and yield component

Fifty mature plants from each plot were randomly sampled from the inner rows to measure their yield components such as spike number, grains number per spike, and 1,000-grains weight. Grain yield was determined by harvesting all plants in the plot. After the plants were mechanically deshelled and the grains were air-dried, and the grain moisture meter (KETT PM-8188-A, Taiwan, Japan) was used to measure grain moisture content, and the actual yield was converted according to the national grain storage standard moisture content (12.5%).

Precipitation type and winter wheat yield

We used the SPEI as the classification standard of precipitation year types. Fallow period precipitation is critical for water use efficiency and high-yield/upland farming systems for dryland crops. During the study period, the average precipitation in the test site during the fallow period was 283.53 mm, accounting for 59.45% of the annual precipitation. The fallow period of winter wheat at the test site was from July to September. We calculated the SPEI values across a 3-month scale and selected the SPEI values corresponding to September of each test year (this was calculated based on the cumulative precipitation and potential evapotranspiration from July to September). We then determined the precipitation year type according to the SPEI value on the 3-month scale and categorized the 2009–2018 test points into normal and drought types. There were 5 normal years and 5 drought years (Table 3).

Our analyses of variance between precipitation types, tillage, yield, and yield components all passed the 0.05 significance test. The effects of different tillage treatments on yield and other components under different precipitation types are presented in Table 4. Fallow tillage achieved higher yields and yield components than NT under different precipitation types. Under the normal type, DP and SS produced significantly different yields, spike numbers, and grains number per spike, and the yield of winter wheat under DP was significantly higher than SS. SS had the highest yield (5,149.10 kg ha^–1), grains number per spike (32.44 grains per spike), and 1,000-grains weight (40.75 g) under drought precipitation conditions. DP’s yield and its components under drought years were significantly higher than those under normal years, and the yield obtained by SS showed no significant difference across the different precipitation types.

Tillage and winter wheat yield during the fallow period

When compared with NT, tillage during the fallow period significantly increased the test field yield (Fig. 3). DP significantly increased wheat yields under different precipitation types, especially drought years, and the highest yield was obtained under DP in 2015 (6,009 kg ha^–1). This was significantly higher than the yield of fields treated with SS. The yield of SS in 2010, 2011, and 2014 was higher than that of DP, which may be due to the precipitation during those fallow periods being slightly higher than that of other normal years, causing an increase in yield. This indicates that precipitation and tillage during the fallow period are closely related.

Selection of meteorological factors

In this study, we selected 14 meteorological indices, including precipitation in the fallow period, average temperature, daily maximum temperature, daily minimum temperature, accumulated temperature and sunshine duration, precipitation, average temperature, and accumulated temperature and sunshine duration during the two growth stages (sowing-jointing and jointing-anthesis). After analyzing the meteorological factors, a total of four common factors (Table 5) were extracted using a principle eigen value > 1. The cumulative explanatory power of variance was 85.51%, and factor 1 and factor 2 had the largest explanatory power (65.11%). After the maximum variance rotation of the meteorological factors, we selected the meteorological indices with the largest load values among the four factors (Table 6). The selected meteorological factors included fallow period precipitation, sowing-jointing stage precipitation, daily minimum temperature, average temperature, and average temperature during the sowing-jointing stage, sunshine hours during the jointing-anthesis stage, and six other items.

Correlation between soil water storage and yield

After analyzing the correlation between the water storage of each growth stage, yield, and its components, the relationship between soil water storage in each growth stage and its yield (including its components) under different precipitation types was clear (Table 7). The 0–3 m soil water storage of the jointing and anthesis stage was significantly correlated to the yield, spike number, and grains number per spike. Although the correlation between soil water storage and grains number per spike during the sowing stage was not significant, there was a certain correlation between soil water storage and grains number per spike during the other growth stages. Soil water storage during the sowing stage correlated with yield, and significantly correlated with spike number. Across different growth stages, the correlation between the 1,000-grains weight and soil water storage was not significant.

During the modelling process, we considered the soil water storage during the sowing and jointing-anthesis stages important variables affecting yield, spike number, and grains number per spike. In this study, soil water storage during the growth period was considered an important variable in modelling, and by combining modelling with uncontrollable meteorological factors, we could predict the yield and its components across different tillage methods.

Comparing prediction results of different target yields

In the scenario where the trend yield has not been eliminated, the maximum value of the training samples in the yield per unit area model was higher than that of the latter test set years, which resulted in higher prediction results. Theoretically, the meteorological and relative meteorological yield are only affected by meteorological conditions, but their values cannot be obtained directly by measurement--they depend on the selection of a detrend method. In our previous study, we compared a variety of methods for separating trend production. When building the model, we used 552 sets of data from 2009 to 2016 as training samples and, based on experience and parameter optimization, we set the RF algorithm parameter N tree to 200 and m to 5. We used 138 sets of data from 2017 to 2019 as validation samples to validate the model. Ultimately, the 3-year linear and sliding average method was selected to separate trend production. The three farming treatments were fitted with polynomials, the fitting effect was better, and the fitted curves of DP, SS, and NT had R² values of 0.88, 0.79, and 0.85, respectively (Fig. 4). The yield was detrended based on the 3a moving average method to obtain the meteorological and relative meteorological yield. To some extent, it eliminated the interannual impact of yields and highlighted the impact of meteorological factors on yield.

More than 56.67% of the sample forecast results were higher than the true value, and there were many phenomena where the yield forecast value under DP and NT was higher than the true value (Fig. 5). Following the tillage during the fallow period, the DP and SS yield prediction models’ R² both passed the significance test, and the RMSE reached 94.15 kg ha^–1 and 114.5 kg ha^–1, respectively. The samples were mostly concentrated at 4,500–5,000 kg ha^–1. The NT R² between the predicted yield value and the measured value was 0.86. According to the significance test threshold of p ≤ 0.05, the RMSE was 154.4 kg ha^–1, which was slightly higher than the yield prediction result following the fallow period. NT’s yield prediction was not as high as the yield prediction result under the tillage treatment during the fallow period.

The meteorological production forecast was similar to the unit yield forecast. DP and SS’s meteorological production forecast R² was above 0.9, and the RMSE were 97.43 kg ha^–1and 119 kg ha^–1, respectively. The intersection of the SS fitting line and the 1:1 line was closer to the scale 0. In terms of relative meteorological yield, there was a small error of determination coefficient between tillage and NT during the fallow period, indicating that the RF was highly fitted in terms of relative meteorological yield. It also showed its ability to influence the inter annual production technology level of the yield. The fitting line was closest to the 1:1 line, which shows that under the influence of different meteorological conditions, the relative meteorological yield had a better fitting effect than the unit yield model.

Comparing forecast results of yield and yield components

We used the RF model to predict the yield under different tillage methods, and the error between the predicted value and the true value was small, ranging from 0 to 23.46% (Table 8). Under different precipitation types, the average relative error was 5.66%, which was slightly higher than the true value. The average relative error of tillage treatment during the fallow period was less than that of NT. This shows that the RF algorithm can better predict yield under tillage in the fallow period. During the test period, the average yield of DP was higher than the predicted yield by 15.83 kg ha^–1, with an average relative error of 4.51%. The average yield of SS was lower than the predicted yield by 16.29 kg ha^–1 with an error of 5.98%. The error between the predicted value and the true value of the average yield under NT was 6.49%. Generally, the error value was small and the prediction result was better in field production. The predicted value of 60% of the yield samples in the normal years was higher than the true value. The DP, SS, and NT values were 133.14 kg ha^–1, 80.8 kg ha^–1, and 122.19 kg ha^–1 higher, respectively. About 53.33% of the predicted yields in drought years were higher than the measured values, and the average predicted performance of tillage during the fallow period was better than that of NT.

Additionally, RF was used to predict the number of spikes and grains number per spike under different tillage methods. The spike number prediction model R² passed the significance test: R² was 0.92 and the RMSE was 18.92 10⁴·ha^–1 (Fig. 6). The grain number samples were in the range of 400–500 10⁴·ha^–1, which was close to the 1:1 line. Additionally, the average prediction error was 4.8%, indicating that the prediction results had a high degree of credibility. The sample distribution of grain number per spike was more scattered, with an R² and RMSE of 0.89 and 0.83, respectively, and the predicted value of most samples concentrated in the range of 22–30. The average prediction error was 7.53%.

By comparing the prediction errors of spike number and grains number per spike under different tillage methods, we found that the prediction accuracy of tillage during the fallow period was higher than that of NT (Fig. 7). Under different precipitation types, the average prediction error of spike number was 4.8%. This prediction result was better than that of grains number per spike (with an average prediction error of 7.53%), and the grains number per spike had better prediction results under normal year types. The predicted farming performance across different years’ fallow periods was better than that of NT, and the true value was closer to the predicted value. The spike number prediction in drought years was better than that of normal years, and the grains number per spike was better in normal years. The results show that the prediction method obtained lower error when predicting spike number and grains number per spike of winter wheat under tillage during the fallow period, and the prediction results were closer to the true value.

After fitting the measured value and predicted value, RF showed good prediction ability for winter wheat yield, spike number, and grains number per spike after fallow period tillage under different precipitation types in the studied dryland region. We considered it suitable for the prediction of winter wheat yield and its component factors in the dryland wheat region. The yield prediction results were the most accurate, followed by spike number and grains number per spike, whereas the 1,000-grains weight was not suitable for the model.