Determination of complementary irrigation times for rainfed cultivation based on biomass optimization and soil erosion index in Yellow River Valley

Dryland agriculture under rainfed conditions is found mainly in Africa, the Middle East, Asia, and Latin America (Ahmadi et al. 2015; Lalehzari et al. 2016). Liu et al. (2021) reported that wheat production was affected by drought stress between flowering and seed filling. However, the use of deficit irrigation or rainfed irrigation can be considered as one of the sustainable solutions by applying one or more complementary irrigations (Stricevic et al. 2011; Nasiri et al. 2017). The rainfed cultivation of this crop is done after harvesting rice or alternating with other crops such as rapeseed, soybeans, or cereals. Assessment of supplemental irrigation and effective rainfall in rainfed cultivation should be considered for determining an optimal decision system. Hence, it is necessary to find the appropriate time and amount of water to achieve maximum water productivity (Wang et al. 2021). The basic principle of efficient water use for rainfed crops lies in optimizing each of the time and amount of the complementary irrigation.

Estimating the biomass, canopy cover, and water productivity was carried out using crop growth simulation in the past decades (Arvaneh et al. 2011; Zeleke et al. 2011; Kumar et al. 2015; Mousavizadeh et al. 2016; Sun et al. 2017; Lalehzari et al. 2020). The simulation model needs to be linked with an optimization algorithm to achieve an efficient solution by the predetermined feasible domain based on the objective function (Varade & Patel 2018; Varzi et al. 2019).

Different climatic conditions in China require the development and evaluation of different decision-making strategies appropriate for each region to improve production, reduce water consumption, and make optimal use of rainfall (Li et al. 2021, 2022; Yin et al. 2022; Liu et al. 2023). Due to the impact of climate variation on water consumption, production, and water use efficiency, the yield production models have been calibrated by three field datasets including the regions of Longnan (semi-humid), Tianshui (semi-arid), and Dingxi (dry) in Gansu area, China. The accuracy and stability of sustainable planning in agricultural water management is essential to its success in field experiments. This study attempts to deal with the gaps in previous studies by (1) developing an integrated framework to accurately estimate the crop growth simulation and (2) providing an optimal plan for irrigation of wheat in arid and semi-arid regions. Therefore, we focus on the modeling of the soil, water, and crop system with more details to improve the applicability of the developed models. The effects of soil moisture, precipitation, crop growth curve, variable irrigation intervals, and the time and depth of irrigation were incorporated to find complementary irrigation plans.

In this section, the process of simulating and optimizing continuous programming is developed to achieve sustainable planning and then determining the time and amount of complementary irrigations in wheat cultivation. The proposed framework is divided into three sections: (1) field and climate data collection and analysis, (2) development of the growth simulation model, and (3) find the optimal solution using grey wolf optimization (GWO) algorithm.

The constraints applied to the problem include a set of subroutines that prevent moisture and saturated soil stress. Furthermore, according to the growth stage of the plant, it divides the moisture stress in the entire growing season in water shortage conditions. These tensions are controlled at each time step, which is daily, and have been included in the feasible domain of the objective function.

The prey encircling and attacking are repeated until an optimum solution is obtained or it reaches the maximum number of iterations (Tikhamarine et al. 2020). As mentioned above, the grey wolves finish the hunt by attacking the prey when it stops moving. To mathematically model approaching the prey, we decrease the value of ⁠. Note that the fluctuation range of is also decreased by ⁠. In other words, is a random value in the interval [−a, a], where a is decreased from 2 to 0 throughout iterations. When random values of are in [−1, 1], the next position of a search agent can be in any position between its current position and the position of the prey. GWO has been widely used in different studies to search optimal solution in a predetermined feasible domain in recent years (Arora et al. 2019; Dehghani et al. 2019; Maroufpoor et al. 2019; Dhargupta et al. 2020; Tikhamarine et al. 2020).

The Yellow River Valley with an area of 752,500 km² and an average height of 4,000 m above sea level has a variety of climates from semi-humid to dry. The Yellow River originates from the Qinghai Tibetan Plateau at Bayan Har Mountain in Qinghai and passes through the provinces of Qinghai, Sichuan, Gansu, Ningxia, Inner Mongolia Autonomous Region, Shanxi, Shanxi, Henan, and Shandong to the Bohai Sea in Kanuli County, Shandong Province. Three climatic zones have been identified in this range, including the dry zone in the northwest, the semi-humid zone in the southeast, and the semi-arid zone in the middle parts (Li et al. 2020). Average annual rainfall and temperature are between 208 and 748 mm and between 4.4 and 14.2 °C, respectively. The area studied in this research is the southeastern part of Gansu Province, which is influenced by the Yellow River and has a dry to semi-humid climate. Longnan (33.40°N, 104.92°E), Tianshui (34.58°N, 105.72°E), and Dingxi (35.58°N, 104.62°E) were considered to evaluate the rainfed cultivation. The temperature and precipitation data of 326 national ground meteorological stations of China in the Yellow River Valley were collected from the China Meteorological Scientific Data Sharing Service Network (http://cdc.cma.gov.cn) between 2000 and 2022.

The saturated hydraulic conductivity (K_Sat), the moisture content in the field capacity (θ_FC), and the moisture at the permanent wilting point (θ_PWP) determine the water availability in the root zone, which are introduced to the model. The soil characteristics of each of the selected farms are summarized in the four studied farms in Table 2.

Three irrigation strategies were considered for each field to calibrate the wheat yield simulation model. In full irrigation strategy, irrigation time and depth were measured and summarized in Table 3. To evaluate the effect of deficit irrigation and to find the best points for complementary irrigation, two deficit irrigation events (25% full irrigation) were defined for each sample and its production was recorded. The results of these tests are presented in Table 4. The irrigation depth presented for each scenario (It) were considered equal to I1 = 0.25 × I(D1) and I2 = 0.5 × I(D2) which D1 and D2 are the irrigation numbers indicated in the table. Therefore, 9, 16, and 14 different scenarios were obtained for simulation by the plant growth model for Longnan, Dingxi, and Tianshui, respectively.

Table 5 shows a summary of the error statistics results for the calibration of input parameters. According to the error statistics in the table, the accuracy of the simulation model is confirmed to estimate yield production.

In this structure, two complementary irrigations in Dingxi farm in the amount of 57 and 65 mm are recommended on 154 and 168 days from sowing, respectively. The proposed plan will increase the biomass by about 230 kg/ha, from 2,960 kg/ha in rainfed conditions to 3,190 kg/ha. According to the growth pattern program, this period is the stage of reproductive growth and seed filling, which is the most important and sensitive stage of the water supply of the crop to increase yield.

In the Longnan area, complementary irrigation does not play a significant role in improving the yield throughout the growing season. The growing biomass curve produced by the plant only declines in the last 2 weeks due to a lack of rainfall, which can be compensated by one or two irrigations with a depth of less than 40 mm (Figure 5). The difference between yield production values with and without complementary irrigation is about 150 kg of biomass or 60 kg/ha of the final product. Complementary irrigation in the Tianshui Plain requires more accurate time management and irrigation planning than in other areas. Because the distribution of rainfall over time, the amount of rainfall, and the length of the growing season, provide a wide range of cultivation components. The interval between two complementary irrigations is 63 days from 30 February to 1 May which raises 240 kg/ha of biomass (Figure 5).

The runoff in the water balance equation in the experimental field located at the arid region (Dingxi) less than 20 mm/day of rainfall is calculated by 6.7% (Table 6). Rainfed cultivation has reduced wheat yields in Dingxi to less than one-third of the expected economic yield in previous studies (Li et al. 2019). As shown in the table, complementary irrigations can be improved the yield production by more than 100 kg/ha.

Wheat as a priority in the cultivation pattern of different regions of Gansu needs to be considered in irrigation management, especially in rainfed cultivation conditions. Therefore, this study was conducted to simulate the wheat growth model and find the optimal amount and time of complementary irrigations using GWO in four different climatic regions of Gansu. The growth pattern of wheat in different climatic conditions has been evaluated using real-time simulation with daily time steps. The calibration process was carried out based on the collection and analysis of farm information from experimental farms (Dingxi (arid), Tianshui (semi-arid), and Longnan (semi-humid)). The total water demand for wheat cultivation are estimated at 8,350, 6,520, and 5,260 m³/ha for Dingxi, Tianshui, and Longnan, respectively. Moreover, the total transpiration was obtained in Dingxi, Tianshui, and Longnan farms equal to 790, 717, and 407 mm, respectively. A summary of production and evaluation parameters showed that the best area for wheat cultivation in different climatic conditions of Gansu is Tianshui Plain with water productivity of 0.48 kg/m³ and a yield of more than 4,800 kg/ha in a full irrigation plan. Distribution of rainfall and temperature in a long growth period could be completed by the vegetative and reproductive growth of the wheat and could be considered as an economic policy by applying rainfed management and complementary irrigation. Furthermore, rainfed cultivation for the Longnan area and rainfed cultivation with complementary irrigation at the end of the growing season under climate conditions close to Tianshui could be recommended.

This work was supported by the Self-initiated Project of Gansu Agricultural University, grant number GSAU-ZL-2015046.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.