Simulation of Drainage Volume and Nitrogen Loss Load in Paddy Fields under Different Irrigation and Drainage Modes and Hydrological Years

Abstract

Controlled irrigation and drainage technology for rice is crucial water management that has been widely promoted in northeastern China. It is of great significance to clarify the response mechanism of the drainage volume and nitrogen loss load in the paddy field for realizing water saving, emission reduction, pollution control and high yield in rice-planting areas. In this study, we conducted field experiments and simulations on drainage volume and nitrogen loss load regulations of paddy fields in a cold black soil region under different hydrological years and irrigation and drainage modes. The key parameters for simulating drainage volume and nitrogen loss load in paddy fields using DRAINMOD-NII were determined by combining field experiments, data analysis, and numerical simulation. The results showed that the simulated drainage volume and nitrogen loss load showed a high coefficient of determination with the observed results, which were all above 0.83. The Nash–Sutcliffe efficiency coefficient ranged from 0.72 to 0.97 in model calibration and verification, indicating that the model effectively simulated drainage volume and nitrogen loss load in paddy fields under controlled irrigation and drainage in the cold black soil region. The paddy field drainage volume was not only influenced by rainfall frequency but also by the distribution of rainfall. Compared with traditional irrigation and drainage, the controlled irrigation and drainage significantly reduced the irrigation amount by 39.07% and increased rainwater utilization efficiency by 13.07%. It also reduced the drainage volume by 44.71% and NO₃⁻-N and NH₄⁺-N loss load by 59.38% and 44.96%. The controlled irrigation and drainage mode optimized natural rainfall resources and increased irrigation water productivity and rice yield by 97.85% and 16.88%, respectively. Controlled irrigation and drainage outperformed the traditional mode in different hydrological years, with more pronounced effects in dry years, which highlights its significant value in practical agricultural production.

1. Introduction

Water and nitrogen in paddy fields are key factors affecting rice growth, and the rational regulation of water and nitrogen can promote rice growth and improve water use efficiency [1,2]. When the soil moisture in the paddy field is sufficient, the water and nutrients are coordinated with each other to promote the release of nutrients to be absorbed and utilized by plants in time [3,4]. A field plot experiment is an important means to quantitatively study water and nitrogen transport in paddy fields, and the water transport model is an effective method to characterize the dynamic changes of water and nitrogen in paddy fields [5,6,7]. Most of the nitrogen fertilizer applied in paddy fields is partially absorbed by plants, and the ammonia volatilization accounted for about 14.0% [8]. Analysis of nitrogen loss load in paddy fields through field experiments showed that the average concentration of total nitrogen in paddy field drainage was about 6.60 mg·L⁻¹, with an average nitrogen loss of about 16.70 kg·hm⁻² [9]. Although the annual nitrogen loss load in agricultural ecosystems in China is constantly changing, the situation of nutrient loss load is not optimistic [10,11,12]. Controlled drainage improves rainwater utilization and reduces nitrogen loss in drainage by reducing paddy field drainage [13]. Lu and Xiao found that extending drainage time after rainfall effectively reduced nitrogen loss in paddy fields and increased fertilizer use efficiency [14,15].

At present, many mathematical equations directly explain the process of surface runoff and nitrogen migration in soil. The EPIC model proposed by Li et al. [16] accurately simulated soil nitrogen and phosphorus transport and crop uptake processes. The CREAMS model [17] can simulate and evaluate the effects of different tillage measures on farmland surface runoff migration and the quantitative description of non-point source pollution load. The CREAMS-PADDY coupling model proposed by Chung et al. [18] was used to simulate and predict the loss of nitrogen and phosphorus in paddy field surface water. Hao et al. [19] simulated the process of soil water and nitrogen transport and transformation in wheat fields by the HYDRUS-1D model. Li et al. [20] simulated the process of nitrogen migration and transformation in paddy fields by the HYDRUS-1D model under the premise of considering the influencing factors such as irrigation, rainfall, surface runoff and infiltration in paddy fields. The Agricultural Research Center of the United States Department of Agriculture proposed the SWAT model [21], which can use the spatial data provided by the geographic information system to simulate the migration and transformation of water quantity, water quality and solute in different hydrological processes [22]. Li et al. [23] used the DNDC model to quantitatively analyze the main sources of nitrogen pollutants in farmland. Moursi et al. [24] improved the drainage model and developed the DRAINMOD-DWR model to simulate the hydrology and crop yield of the water cycle system.

The DRAINMOD-NII model improved by Skaggs et al. [25,26,27] is a field-scale model based on process, which is used to simulate the dynamic migration process of nitrogen under different field management measures and different environmental and soil conditions. The model is based on a simple water balance principle and a complete nitrogen transport process. The number of parameter inputs is small and easy to obtain, and the model is easy to understand and operate. In recent years, many researchers have simulated farmland irrigation and drainage, nutrient and salt transport using the DRAINMOD-NII model, which provides a reference for optimizing agricultural management [28,29]. The research results of Salazar et al. [30] found that the model effectively simulated the actual drainage and nitrogen loss of farmland in southeastern Sweden by comparing the measured values of drainage and nitrogen loss with the simulation results of the model. Li et al. [31] simulated shallow groundwater utilization and salt accumulation using the model. Jia et al. [32] studied the impact of different drainage intensities on wetland hydrological processes using the mentioned model. Luo et al. [33,34] used the model to simulate the drainage in the upper reaches of the Yellow River and the hydrological processes of maize–soybean rotation in agricultural fields. The research conducted by Wang et al. [35] showed that they applied the model to simulate changes in groundwater level and drainage volume; Zhang et al. [36] used the calibrated model to simulate groundwater depth and salt content in soil profiles, and the simulation results were used for prediction of improvement in saline–alkali land. Abduljaleel, Y. et al. [37] simulated excess water in poorly drained irrigated areas through experiments to protect them from induced waterlogging and salinization problems.

In contrast to the extensive results available for water-saving irrigation or controlled drainage in paddy fields, information on drainage and nitrogen loss under controlled irrigation and drainage in the cold black soil region is scarce. In particular, the features of drainage and nitrogen loss in different hydrological years have not been reported. In this study, water depth in paddy fields was used as an indicator for irrigation and drainage regulation. By combining field plot experiments, theoretical analysis and numerical simulation, the study explores and simulates the drainage and nitrogen loss load during the whole growth period of rice under different irrigation and drainage modes, which is expected to provide a basis for water saving and emission reduction theory and technology development in the cold black soil region.

2. Materials and Methods

2.1. Experimental Site and Soil Properties

The experiments were conducted at the Station of National Agriculture Irrigation Experiment in Qingan County, which is in the southwestern part of Heilongjiang Province, northeastern China (127°30′04″ E, 46°52′41″ N). The effective accumulated perennial temperature (≥10 °C) is 2518 °C. The mean annual precipitation is 545.3 mm, and the variation range is 450~700 mm. The average annual surface evaporation is 664.5 mm, and the variation range is 462~873 mm. The soil in the experimental site is a sandy loam with heavy texture and good structural characteristics. The soil porosity was 53.4%, the organic matter mass ratio was 37.5 g·kg⁻¹, and the total nitrogen amount was 13.2 g·kg⁻¹.

2.2. Experimental Design and Field Management

2.2.1. Experimental Design

A field experiment was conducted to study the paddy field drainage volume and nitrogen loss load in the paddy. The rice variety selected in this experiment was Suijing 18, which has a growth period of about 120 days and is widely cultivated in the local area. It was a fragrant rice variety that was mainly distributed in the northeast of China. This Japonica rice in the cold region demonstrated strong adaptability and resistance to lodging and is famous for its high quality and great taste [38,39,40]. The water depth in the paddy field served as the indicator for regulating irrigation and drainage. The test plots (10 m × 10 m) were separated by a 30 cm wide ridge to prevent water and nitrogen permeation between adjacent plots. A 50 cm deep film was embedded in the soil ridge to eliminate the effects of water and nitrogen leakage.

The experiment comprised two irrigation treatments, namely, controlled irrigation and drainage (CID: Controlled irrigation and drainage is a new irrigation technology which determines irrigation time, irrigation times and irrigation quota according to soil moisture content in the root layer or water depth in paddy fields in each growth period after seedling transplanting) and traditional irrigation and drainage (TID: Compared with controlled irrigation and drainage, traditional irrigation and drainage refers to the irrigation of crops and drainage of paddy fields by traditional agricultural irrigation methods. Irrigation can be divided into border irrigation, furrow irrigation, inundation irrigation and flood irrigation according to different ways of wetting soil.). Each experiment treatment had three repeated test plots, and the observed results of different monitoring indicators were the average values of the repeated plots. Each plot had its own independent irrigation and drainage system. Irrigation was carried out when the water depth in the test plot dropped to the lower limit of the paddy field (CID: 1 cm at replanting stage, −10 cm at tillering stage, −20 cm from jointing and booting stage to milking ripening stage. TID: 1 cm from replanting stage to milking ripening stage), and irrigation continued until the water layer depth reached the upper limit (CID: 3 cm from replanting stage to milking ripening stage. TID: 5 cm from replanting stage to milking ripening stage.). After rainfall, if the water depth in the test plot exceeded the maximum allowable water depth for the paddy field (CID: 10 cm from replanting stag to tillering stage, 10 cm from jointing and booting stage to milk ripening stage. TID: 5 cm from replanting stage to milk ripening stage), the excess water would be drained to reach the maximum allowable water depth after rain. The paddy fields of both TID and CID received the same fertilization. The water depth designs in the paddy field at different growth stages are shown in

Table 1. Test design.

Mode	Growth Period	Water Depth of Paddy Field
CID	Replanting Tillering Jointing and booting Heading and flowering Milking ripening Yellow ripening	1~3~5 −10~3~5 −20~3~10 −20~3~10 −20~3~10 Dry naturally after drainage
TID	Replanting~Milking ripening Yellow ripening	1~5~5 Dry naturally after drainage

Notes: The regulation value of the water depth in the paddy field was based on the field surface. The water depth refers to the vertical distance from the paddy field water level to the field surface. For example, in −20~3~10, the left value represents the lower limit of paddy water depth, the middle value represents the upper limit of paddy water depth in the paddy field, and the right value represents the allowable maximum water depth after rainfall.

.

2.2.2. Field Management

The management of the experimental field is consistent with that of the local high-yield field. Seeds were sown in the greenhouse. The field test plots were flooded to a depth of 5 cm for approximately 1 week, and then the seedlings were transplanted to the paddy field at the 6-leaf stage with a transplanting size of 30 cm × 40 cm. The paddy field was fertilized three times: with base fertilizer (urea: 8.7 g·m⁻²; P₂O₅: 7.5 g·m⁻²; KCl: 6.0 g·m⁻²), tillering fertilizer (urea: 6.5 g·m⁻²) and ear fertilizer (urea: 6.5 g·m⁻²; KCl: 6.0 g·m⁻²), respectively. Please refer to

Table 2. Agronomic measures and time of rice cultivation.

Year	Raise Seedlings	Steeping Field	Transplanting	Base Fertilizer	Tillering Fertilizer	Ear Fertilizer	Harvest
2020	4.5	5.8	5.15	5.12	5.26	7.5	9.25
2021	4.1	5.1	5.18	5.12	5.28	7.18	9.28

for specific agronomic measures implemented and the corresponding time in the paddy field.

2.3. Measurement Items and Methods

2.3.1. Meteorological Indicators

The meteorological data were automatically collected from a small automatic meteorological observation station (Watchdog 2000, Spectrum, Aurora, IL, USA) and nearby weather stations. The data included rainfall, evaporation, air temperature, relative humidity, wind speed, atmospheric pressure, total radiation, and net radiation. The temperature input format of the model took in the daily maximum and minimum temperatures. The rainfall data used in the model were measured by the meteorological monitoring equipment in the experimental site. The time step for rainfall was set to 1 h.

The daily evapotranspiration of DRAINMOD refers to the standard reference crop under high uniformity and sufficient water supply, rather than the actual crop. The potential evapotranspiration of the reference crop was calculated using the Thorthwaite formula in DRAINMOD and calibrated using monthly check coefficients. The input parameters of the model were revised to improve the accuracy of the simulation results. The potential evapotranspiration of reference crops was calculated using the Penman Monteith formula (Formula (1)), which is as follows [41]:

$$E{T}_0=\frac{0.408\times \Delta \times (R_n-G)+\gamma \times \frac{900}{273+T}\times u_2\times (e_a-e_d)}{\Delta +\gamma \times (1+0.34\times u_2)}$$

(1)

where ET₀ is the reference crop evapotranspiration, mm·d⁻¹; ∆ is the slope of the saturated water vapor pressure curve, kPa/°C; R_n is the net radiation at the reference crop canopy surface, MJ·m⁻²·d⁻¹; G is the soil heat flux, MJ·m⁻²·d⁻¹; γ is the psychrometric constant, kPa/°C; T is the daily average temperature at 2 m, °C; u₂ is the Wind speed at 2 m, m·s⁻¹; e_a is the saturated vapor pressure, kPa; and e_d is the actual vapor pressure, kPa.

According to the rice crop coefficient in

Table 3. K_c of rice.

Month	May	June	July	August	September
Kc	0.38	0.78	1.34	1.06	0.45

, the potential evapotranspiration of reference crops was modified, and the actual evapotranspiration of crops was calculated according to Formula (2).

$$ET=K_c\times E{T}_0$$

(2)

where ET is the actual crop evapotranspiration, mm·d⁻¹; K_c is the crop coefficient; and ET₀ is the reference crop evapotranspiration, mm·d⁻¹.

2.3.2. Soil Physicochemical Parameters

A total of 72 soil samples from different depths (0~20, 20~40, 40~60, 60~80 cm) were taken with a ring knife at three points in the six test plots. The saturated water content and bulk density were measured using the ring knife method. The soil water characteristic curve was observed using a pressure membrane meter (NSSP-15, SEC, Goleta, CA, USA). The saturated water conductivity was measured using a soil water conductivity meter (KSAT, METER, MUC, Germany). The soil particle gradation was measured using sieving analysis and the siphon gravity bottle. The content of organic matter was determined by the volumetric method. The total nitrogen was analyzed by the alkaline potassium persulfate digestion method [42] (MEPC, 2002). The soil physical properties and hydraulic parameters of different soil layers in the test area are shown in

Table 4. Soil physical properties and hydraulic parameters of different soil depths.

Soil Depth /cm	Distribution of Soil Particle Size/%			Bulk Density /g·cm−3	Field Capacity /cm3·cm−3	Wilting Coefficient /cm3·cm−3	Saturated Moisture Content /cm3·cm−3	Lateral Saturation Conductivity /cm·d−1
	2.0~0.05 /mm	0.05~0.002 /mm	<0.002 /mm
0~20	20.0	67.2	12.8	1.47	0.29	0.093	0.49	1.40
20~40	9.1	76.9	14.0	1.48	0.28	0.068	0.43	1.12
40~60	11.3	74.9	13.8	1.53	0.26	0.058	0.44	0.95
60~80	17.8	71.7	10.5	1.29	0.23	0.051	0.41	0.75

.

2.3.3. Irrigation and Drainage

(1)

Water Depth

A paddy water level observation well is set up in each experimental plot to measure the water depth of the paddy field. The observation well is composed of a PVC pipe with a diameter of 4 cm and a length of 200 cm, and small holes are staggered at the end of the PVC pipe, for 50 cm, and then wrapped with geotextile and buried in the field. The outer wall of the PVC pipe is in close contact with the soil, and the pipe mouth is about 30 cm from the ground. The water level is observed regularly at 8:00 am every day. The soil surface in the field plot serves as the reference point, and the water level is positive above the ground line and negative below the ground line. The vertical distance from surface to water level in each field plot was measured, accurate to 1 mm. According to the irrigation test specification, the observation well is located in the middle of the field test plot and 1 m away from the ridge.

(2)

Irrigation and Drainage

The irrigation amounts were calculated using the water meter. Drainage occurred according to the test requirements when the water depth of the paddy field exceeded the allowed depth after rainfall. The water depths before and after drainage were recorded to calculate drainage volume.

(3)

Nitrogen in Water Samples

The water samples were manually collected in 500 mL plastic bottles every 10 min at the outlet of the plot when drainage occurred, and they were stored in a container and transported to the laboratory for analysis. Each water sample had three replicates. The concentrations of ammonia nitrogen (NH₄⁺-N) and nitrate nitrogen (NO₃⁻-N) in the water samples were determined using the indophenol blue method and the disulfonic acid–phenol method, respectively (MEPC 2002). A UV spectrophotometer (Cary 50 Spectrophotometer, Varian, Palo Alto, CA, USA) was used for measurement [42]. The nitrogen concentrations were calculated based on the three replicates.

2.3.4. Yield

The theoretical yield of rice was calculated according to Formula (3) [43].

T_y = P × G × S × W × 0.85

(3)

Notes: T_y means the theoretical yield, kg·hm⁻²; P means effective panicle number, 10,000·hm⁻²; G means the number of grains per panicle; S means the average setting rate, %; and W means thousand grain weight, g.

2.4. Drainage Design Parameter of Model

DRAINMOD was initially developed as a field hydrological model for dry farmland in humid coastal alluvial plains. The parameter needed to be adjusted when the model was applied to paddy fields. The effective diameter of the drainage pipe was replaced with the hydraulic radius of the drainage ditch, and the irrigation data were included in the corresponding rainfall data. The design parameters for the drainage system in the model include both surface drainage and underground drainage. Surface drainage parameters consist of maximum and minimum surface water depths. Underground drainage parameters included drainage spacing, drainage depth, relative impervious depth, drainage coefficient, and initial groundwater level. The relative impervious depth and drainage coefficient were calculated according to the actual situation of the paddy field combined with the model calibration. Maximum surface water storage depth (Sm) and Krikham water depth (SI) were determined based on the surface roughness and actual drainage conditions of the paddy field and relevant literature [27]. The drainage depth and drainage spacing were measured in the test area (

Table 5. Main input parameters of drainage design parameters.

Relative Impervious Depth /cm	Maximum Surface Water Storage Depth (Sm) /cm	Drainage Coefficient /cm·d−1	Drainage Depth /cm	Drainage Spacing /cm	Krikham Water Depth (SI) /cm
280	10.0	3.0	50	1000	0.8

). The maximum nitration and denitrification rate and optimum temperature were derived from model calibration, and the NH₄⁺-N and NO₃⁻-N concentration in the rain were measured in the test area (

Table 6. Main input parameters of nitrogen parameters.

Maximum Nitration Rate /µg·ng−1·d−1	Optimum Nitration Temperature /°C	Maximum Denitrification Rate /µg·ng−1·d−1	Optimum Denitrification Temperature /°C	Nitrogen Dissolution Rate /d−1	NO3−-N Concentration in Rain /mg·L−1	NH4+-N Concentration in Rain /mg·L−1
25	25	3.5	20	1.5	1.0	0.75

).

2.5. Model Evaluation Parameters

The model’s applicability was assessed by comparing simulated values with observed values using various indicators. Statistical parameters and a combination of numerical and graphical methods were utilized to evaluate the model’s suitability in simulating paddy field drainage and nitrogen loss load [44]. The absolute root mean square error (RMSE_a), relative error (ε), Nash–Sutcliffe efficiency coefficient (NSE), and coefficient of determination (R²) were used to assess the approximation between the simulated and observed values of the drainage and nitrogen loss load [45]. The calculation formulas are as follows:

$${RMSE}_a=\sqrt{\frac{1}{n}{\sum }_{i=1}^n{\left(P_i-Q_i\right)}^2}$$

(4)

$$\overline{Q}=\frac{1}{n}{\sum }_{i=1}^n{Q}_i$$

(5)

$$\epsilon =\left({\sum }_{i=1}^n{Q}_i-{\sum }_{i=1}^n{P}_i\right)/{\sum }_{i=1}^n{P}_i\times 100\%$$

(6)

$$NSE=1-{\sum }_{i=1}^n{\left(P_i-Q_i\right)}^2/{\sum }_{i=1}^n{\left(P_i-\overline{P}\right)}^2$$

(7)

$$R^2={\left[{\sum }_{i=1}^n\left(P_i-\overline{P}\right)\left(Q_i-\overline{Q}\right)\right]}^2/\left[{\sum }_{i=1}^n{\left(P_i-\overline{P}\right)}^2{\sum }_{i=1}^n{\left(Q_i-\overline{Q}\right)}^2\right]$$

(8)

where n is the number of samples, P represents the ith simulated value, Q represents the ith observed value, $\overline{P}$ represents the average of the simulated value sequence, and $\overline{Q}$ represents the average of the observed value sequence. RMSE_a represents the degree of closeness between the simulated and observed values. R² indicates the regression effect of the model. RMSE_a and ε reflect the difference between the simulated and observed values. NSE reflects the simulation efficiency of the model.

2.6. Data Statistical Analysis Methods

The test data were processed using Microsoft Excel 2016 (Microsoft, Redmond, WA, USA). SPSS 17.0 software (IBM SPSS Statistics, Chicago, IL, USA) was used to perform standard deviation and other statistical analyses. Microsoft Excel 2010 and Origin 9.1 (OriginLab, Ampton, Kissimmee, FL, USA) were employed for data visualization and chart production.

3. Results

3.1. Model Calibration

The calibration process of model parameters is to adjust the parameter values, compare the model simulation values with the measured data in the same period, and adjust the parameters to make the simulation results infinitely close to the measured values to the greatest extent. The soil parameters, drainage volume, nitrogen loss, crop parameters and irrigation systems were obtained from a field test. The soil water characteristic curve was determined by a pressure membrane meter in the laboratory after sampling, the hydraulic conductivity was determined using a soil water conductivity meter in the field, and the other soil input parameters were deduced by a theoretical method according to the soil water characteristic curve. The horizontal saturated hydraulic conductivity has an obvious influence on the simulation results. In this paper, PEST was used to focus on the adjustment of horizontal saturated hydraulic conductivity. PEST (Parameter Estimation) is comprehensive software for parameter estimation and uncertainty analysis independent of the model. The control file (pest.pst), description file (dhp.ins) and template file (dhp.tpl) were established in the installation directory of PEST while running DRAINMOD-NII, and the check command of the relevant file was run in the DOS interface to determine whether the established file was normal. PEST uses a nonlinear evaluation method, which can not only converge quickly and effectively towards the objective function but also estimate the parameters with as few model runs as possible. After 51 iterations of the DRAINMOD-NII model, the parameters were optimized (Figure 1 and

Table 7. Drainage and evaporation capacity of soil.

Groundwater depth/cm	15	25	35	75	120	150	200	500
Drainage/cm	0.07	0.22	0.40	1.80	4.25	6.85	11.50	55.10
Submersible rising flux/cm	0.30	0.28	0.25	0.19	0.18	0.15	0.10	0.05

,

Table 8. Green–Ampt infiltration parameters of the model.

Water table/cm	0	10	40	60	80	100	200
A/cm·h−1	0.85	0.15	0.72	1.20	1.65	1.90	3.60
B/cm·h−1	0.90	0.90	0.90	0.90	0.90	0.90	0.90

and

Table 9. Saturated water conductivity.

Soil depth/cm	0~20	20~40	40~60
Vertical saturated hydraulic conductivity/cm·h−1	1.74	0.92	0.78
Horizontal saturated hydraulic conductivity/cm·h−1	1.25	1.02	0.45

).

3.1.1. Paddy Field Drainage

The rainfall during the whole crop growth period was 547.9 mm in 2020. The irrigation times were two, due to the low rainfall in the early growth period. The paddy field drainage occurred in the later period of rice growth because rainfall was increased and concentrated at this time. The drainage times were four, and the overall trend of the observed and simulated field drainage values was consistent, and the time of drainage peak simulation was basically consistent with the actual time of drainage under CID mode during different growth stages in the paddy field. However, the simulated drainage values are higher than the observed values for the four drainage instances in the paddy field; the observed value of the total drainage volume was 54.0 mm, and the simulated value was 68.0 mm. The maximum drainage occurred at the heading and flowering stage, with the observed value of 28.0 mm and the simulated value of 32.0 mm (Figure 2). This may be because the simulation process considers irrigation as equivalent rainfall and does not fully account for the actual drainage of the test field. It could also be related to the accuracy of manual measurement of paddy field drainage, as the human factors of the drainage process are not considered in the model.

The scatter plot in the graph represents the simulated drainage values corresponding to the observed values. The simulation results of the model overestimate the measured values, but the dispersion falls near the equality line (Y = X), indicating a reasonable alignment between the simulated and observed drainage volumes (Figure 3). The measured values of paddy field drainage are basically consistent with the simulated values, which are 54.0 mm and 68.0 mm, respectively. The R² and NSE are 0.88 and 0.94, and the RMSE_a and ε are 2.08 and 0.14, suggesting that the errors are within an acceptable range (

Table 10. Evaluation value of paddy field drainage volume in 2020 (model calibration).

Evaluation Parameter	RMSEa	ε	NSE	R2
Drainage volume	2.08	0.14	0.94	0.88

). These indicate that the model performs well and effectively simulates the paddy field drainage volume under CID in the cold black soil region.

3.1.2. Nitrogen Loss Load

DRAINMOD-NII introduced the nitrogen cycle module, and the water balance result was used as the input value of nitrogen migration. The multi-phase one-dimensional convection–dispersion equation is used to model the nitrogen migration, and the first-order finite difference method is used to approximate the equation; then, the migration process of nitrogen in the soil unit is simulated. The simulated values of the NO₃⁻-N load in drainage were consistently higher than the observed ones, with the simulated and observed values being 0.75 kg·hm⁻² and 0.60 kg·hm⁻², respectively. The simulated results of the NH₄⁺-N loss load were higher than the observed values, except for the heading and flowering stage, when the cumulative simulated value was lower than the observed value, with a simulated value and measured value of 4.10 kg·hm⁻² and 3.60 kg·hm⁻², respectively (Figure 4). The paddy field drainage volume was larger and the drainage time was longer due to the heavy rainfall at the heading and flowering stage. It was possible that the nitrogen concentration varied greatly in different periods due to digestion and denitrification during the drainage process. In order to improve the accuracy of the monitoring value, it is recommended to take more samples to calculate the average value. In addition, the inaccuracy may also be caused by the interference of human factors, leading to the increase in the error of the test index.

The scatter plots illustrate the relationship between the simulated and observed values of paddy field drainage. In the model calibration period, the scatter falls around the equality line (Y = X), indicating that the simulated values tend to be higher than the observed values (Figure 5). The ε and NSE for NO₃⁻-N and NH₄⁺-N loss load cumulative values were 0.23, 0.88 and 0.80, 0.92, respectively. The RMSE_a and R² were 0.22, 1.09 and 0.83, 0.85, respectively. These values suggest that the model performs well, with errors falling within an acceptable range. The results indicate that the simulated values of NO₃⁻-N and NH₄⁺-N loss load in paddy field drainage are consistent with the observed ones under the CID in 2020, indicating that the model performed well in simulating nitrogen loss load (

Table 11. Evaluation value of nitrogen loss load in 2020 (model calibration).

Evaluation Parameter	RMSEa	ε	NSE	R2
NO3−-N loss load	0.22	0.23	0.88	0.83
NH4+-N loss load	1.09	0.80	0.92	0.85

).

3.2. Model Verification

In this paper, the climate data, crop data, paddy field drainage and nitrogen loss load data in 2021 were used to verify whether the soil parameters, drainage parameters and nitrogen transport module parameters of the model were reasonable. The verification effect of the model was evaluated by the graphical display method and statistical parameter index. In the graphical display method, the observed values of paddy field drainage and nitrogen loss load data were compared with the simulated values, and the simulation effect was judged intuitively from the graphical trend and the degree of coincidence. It shows that the model parameter value can represent the actual situation in this area, and the model parameter calibration is reasonable, if the simulated value is close to the measured value in the same period, and the error is within the acceptable range.

3.2.1. Paddy Field Drainage

The rainfall during the whole growth period of rice was 455.4 mm in 2021. The irrigation times were 4, which mainly occurred at the jointing and booting stage with less rainfall. The paddy field drainage occurred at the tillering stage because the water requirement in the paddy fields was less and rainfall was more. The results indicate a close consistency between the simulated and observed values, exhibiting similar peak values and occurrence times. The drainage times were 5, and the simulated value was 70.0 mm, while the observed value was 59.0 mm, resulting in a difference of 11.0 mm (Figure 6).

The scatter points were uniformly distributed around the equality line (Y = X), indicating a good fit between the simulated and observed values (Figure 7). The ε was 0.19, the R² was 0.90, the NSE was 0.19, and the RMSE_a was 2.72 (

Table 12. Evaluation value of paddy field drainage volume in 2021 (model verification).

Evaluation Parameter	RMSEa	ε	NSE	R2
Drainage volume	2.72	0.19	0.72	0.90

). Thus, results indicate a satisfactory calibration of the model with the simulated paddy field drainage processes being reasonably well modeled. Additionally, these results suggest that the model effectively represents the dynamics of paddy field drainage in the cold black soil region with accuracy.

3.2.2. Nitrogen Loss Load

In the model verification period, the simulated NO₃⁻-N loss load exceeded the observed values at all growth stages except for the milking ripening stage. Specifically, the cumulative simulated value for NO₃⁻-N loss load was 0.68 kg·hm⁻², slightly lower than the measured value of 0.70 kg·hm⁻². On the other hand, the simulated NH₄⁺-N loss load was consistently higher than the observed values throughout the whole growth period. The total cumulative simulated value for NH₄⁺-N loss load in drainage was 3.60 kg·hm⁻², surpassing the observed result of 3.50 kg·hm⁻² (Figure 8).

During the model verification period, the simulated values exhibit good agreement with the observed ones, as evident from the evenly dispersed data points around the equality line (Y = X) (Figure 9). These results indicate that the model effectively simulates nitrogen loss load under CID in the cold black soil region. The ε for NO₃⁻-N and NH₄⁺-N loss load were 0.08 and 0.12, respectively. The NSE were 0.97 and 0.93, the R² were 0.88 and 0.90, and the RMSE_a were 0.04 and 0.29, respectively (

Table 13. Evaluation value of nitrogen loss load in paddy field in 2021 (model verification).

Evaluation Parameter	RMSEa	ε	NSE	R2
NO3−-N loss load	0.04	0.08	0.97	0.88
NH4+-N loss load	0.29	0.12	0.93	0.90

). Overall, the simulated values align well with the observed values, indicating a satisfactory model performance in simulating nitrogen loss in paddy fields. However, the nitrogen loss load exhibited deviations at certain time periods for the following reasons. The accuracy of experimental observation needs to be improved. The drainage volume in the experimental area was observed manually, and the observation error of drainage volume was caused by the reason that led to the error of nitrogen loss. The accuracy of ammonium nitrogen simulation depends on the dispersion coefficient, nitrification reaction parameters and the appropriate decomposition temperature of organic matter, while the accuracy of nitrate nitrogen simulation depends on denitrification parameters and nitrification parameters [46]. Experimental means should be strengthened to ensure the accuracy of field measurements. Most of the parameters in the model calculation are determined by experiments, but some parameters are obtained indirectly by other means. The selection of parameters will affect the simulation results, so the experimental means should be expanded in the subsequent work to obtain as many measured parameters as possible. These aspects introduce uncertainties in the model simulation, and it is recommended to improve the accuracy of model simulation by improving the above aspects.

3.3. Simulation of Drainage Volume and Nitrogen Loss Load in Different Hydrological Years

3.3.1. Selection of Representative Hydrological Year

According to the rainfall data of 61 years from 1961 to 2021, the sum of the rainfall from May to September during the main growth period of rice in each year was calculated and the frequency was calculated. Based on the optimum line method of the Pilson-Ⅲ type, the rainfall of different years during the growth period was obtained, and the rainfall frequency of p ≤ 37.5%, 37.5% < p ≤ 62.5% and p > 62.5% were divided into the wet year group, normal year group and dry year group, respectively. According to the years corresponding to the rainfall frequency of 25%, 50% and 75%, the typical representative years of wet, normal and dry year are determined, and the typical representative years and rainfall of different rainfall frequencies are obtained (

Table 14. Rainfall of different typical years in the test area.

Rainfall Frequency /%	Rainfall /mm	Hydrological Year	Representative Year
1	742.4	Wet year	2012
5	700.4	Wet year	1985
10	633.3	Wet year	1988
25	551.3	Wet year	1998
50	483.5	Normal year	1966
75	416.4	Dry year	2006

Notes: % is the average probability of one occurrence per hundred years.

). The model was subsequently employed to simulate the drainage volume and nitrogen loss load in paddy fields in different representative hydrological years, and the variations in drainage volume and nitrogen loss load in different hydrological years were analyzed.

3.3.2. Simulation of Drainage and Nitrogen Loss Load in Different Hydrological Years

A comparison of simulation results from different hydrological years simulating paddy field drainage volume is depicted in Figure 10. Rainfall had a significant impact on paddy irrigation and drainage. Paddy field drainage varies significantly across different hydrological years. The greater the rainfall during the rice growth period, the smaller the irrigation quota and the greater the drainage volume. The paddy field drainage of CID mode in the normal representative year decreased by 74.7%, and the drainage times decreased by 50.0% compared with the wet years. Furthermore, no drainage occurred in the representative year of 75% hydrology. Because the paddy field makes full use of natural rainfall, the drainage volume and drainage times were reduced, so as to achieve the effect of controlling irrigation and emission reduction and saving manpower. During the rice growing period, the paddy field drainage is 57.4%, 82.9%, and 296.0% higher than that in the 5%, 25%, and 50% hydrological years, respectively, but 7.7% lower than that in the 10% hydrological year. This discrepancy is attributed to the more concentrated drainage-producing rainfall in the 10% hydrological year, resulting in higher drainage compared with the 1% hydrological year. Furthermore, no drainage occurred in the representative year of 75% hydrology, indicating that paddy field drainage is influenced not only by the total annual rainfall amount but also by the distribution pattern of rainfall throughout the year.

4. Discussion

4.1. The Simulation of Drainage Volume and Nitrogen Loss Load in the Paddy Field

It was highlighted that the model was calibrated and validated using two years of data from field experiments. The simulated paddy field drainage showed a high level of agreement with the observed results, as evidenced by the R² above 0.88, the ε within 0.19, the RMSE_a within 2.72, and the NSE above 0.72. These results demonstrated that the model was capable of accurately simulating the paddy field drainage under controlled irrigation and drainage in the cold black soil region. Some scholars applied the DRAINMOD-NII to the other irrigation areas and believed that it simulated the dynamic changes of paddy field drainage well, and these research results are basically consistent with those described in this study [47,48].

Simulation analysis of paddy drainage in different hydrological years revealed that the paddy field drainage volume was not only determined by annual precipitation, but was also significantly affected by precipitation distribution during the crop growth period. Specifically, the drainage volume tended to increase when the rainfall was more concentrated during the growth period. In addition, the risk of nitrogen loss in rice fields was higher under extreme climate conditions with 1%, 5% and 10% rainfall frequencies.

The model effectively simulated the nitrogen loss load of the paddy field. The simulated cumulative loss load of NO₃⁻-N and NH₄⁺-N closely matched the observed values, as indicated by the R² above 0.83, the ε within 0.80, the RMSE_a within 1.09, and the NSE above 0.88. These findings substantiated the ability of the model to successfully simulate the nitrogen loss load under CID mode in the cold black soil region. Some scholars use the DRAINMOD-NII to explore the nitrogen changes during drainage [49]. Gao et al. [46] simulated the nitrogen loss load of paddy fields using DRAINMOD-NII and found that the model predicted the nitrogen loss characteristics of paddy fields effectively in typical irrigation areas in southern China, and the relative error ranged from 2.8% to 16.0%. Hashemi et al. [50] found that the DRAINMOD-NII simulated the NO₃⁻-N loss load well in paddy fields, and the relative error ranged from 1.0% to 35.0%. Morris [51] found that the simulated drainage and NH₄⁺-N loss load in the whole growth period of rice were in good agreement with the measured values, with relative errors of 4.6% and 2.8%, respectively. However, in terms of the different growing stages of paddy rice, there was a large deviation between simulated and observed values. Preliminary analysis indicated that the parameters used in the model were not calibrated well due to limited observed data. On the whole, DRAINMOD-NII can efficiently describe and predict drainage and nitrogen loss processes in paddy fields, which can play an important role in improving the efficiency of water and nitrogen use in the paddy field as well as in reducing agricultural pollution. Those findings are consistent with the results of this study conducted in the cold black soil region.

4.2. Optimizing Water Management of Paddy Fields

The CID mode is crucial for optimizing resource management in paddy fields. The results showed that the CID mode reduced paddy field drainage compared to the TID mode, with decreases of 60.93% and 24.48% in 2020 and 2021, respectively. The loss load of NO₃⁻-N and NH₄⁺-N in the CID paddy field decreased by 59.38% and 44.96%, respectively, compared with TID. Additionally, the yield of the CID mode surpassed that of the TID mode in different years, with increases of 14.15% and 19.62% in 2020 and 2021, respectively (

Table 15. Evaluation and comparison of different irrigation and drainage modes.

Mode	Year	Water Saving		Emission Reduction			High Yield
		Irrigation Amount /mm	Rainwater Utilization Rate /%	Drainage /mm	NH4+-N Loss Load /kg·hm−2	NO3−-N Loss Load /kg·hm−2	Yield /kg·hm−2
CID	2020	74.5	89.12	54.0	3.6	0.6	12,117.15
	2021	140.6	90.50	59.0	3.5	0.7	10,843.51
TID	2020	150.2	75.64	138.2	8.5	2.1	10,615.35
	2021	194.6	83.65	82.5	4.4	1.1	9065.12

). The rainfall utilization efficiency of a paddy field is determined by the ratio of the difference between rainfall and paddy field drainage to the total rainfall. Meanwhile, the irrigation water productivity is measured by the ratio of yield to irrigation, and the crop water productivity is evaluated using the ratio of yield to water consumption. In the CID paddy field, the rainfall utilization efficiency is 89.12% and 90.50% in 2020 and 2021, respectively. It is noteworthy that the CID mode exhibits a higher rainfall utilization efficiency compared to the TID mode, indicating an enhanced capability of the paddy field to store rainwater (Figure 11). Furthermore, the CID mode demonstrates higher crop water productivity compared to the TID mode, with increases of 17.04% and 22.57% in 2020 and 2021, respectively. The irrigation water productivity of the CID mode reached 162.65 and 77.12 kg·hm⁻²·mm⁻¹ in 2020 and 2021, respectively, with the TID mode of 70.67 and 46.58 kg·hm⁻²·mm⁻¹. The irrigation water productivity showed significant improvements, with increases of 130.13% and 65.56% in 2020 and 2021, respectively, compared to the TID mode. This indicated that the CID mode effectively reduced paddy field drainage and improved the irrigation water productivity of rice. Xie et al. [52] simulated the drainage volume and nitrogen loss load under different irrigation and drainage modes and found that the CID mode utilized nutrients and water efficiently and gave full play to the wetland function of paddy fields compared with the TID mode. The CID mode regulated the water status of the paddy field to achieve a high yield of rice, and the yield was increased by 10% compared with the TID mode; the difference was not significant [53]. The results are basically consistent with those of this experiment.

The CID mode proves to be an effective method of utilizing natural rainfall resources, and it not only improves rice yield and rainwater utilization efficiency but also reduces the drainage volume and nitrogen loss load. As a result, it achieves the goals of water saving, emission reduction, and high yield of the paddy field. During the main period of rice growth and development in the experimental area, from July to August, the CID mode effectively captured and utilized rainfall resources. Water saving was achieved by reducing paddy field drainage and improving rainfall utilization efficiency. Moreover, the CID mode optimally utilized the water storage function of the paddy field during flood seasons, reducing downstream flood control pressure [47]. Simultaneously, the CID mode minimized the loss of nitrogen in the paddy field and reduced the risk of non-point source pollution [48]. China’s rice planting area exceeds 30 million ha, which is widely distributed in the cold black soil region, where the growth period is synchronized with the rainy period. The CID mode improved the effective utilization efficiency of rainwater and reduced the irrigation quota, while the lower irrigation limit improved the water storage capacity of the paddy field and achieved the goal of water saving. Compared with TID, the irrigation amount of the paddy field in the CID mode decreased by 11.89~29.88% [48]. Therefore, the CID mode can effectively reduce runoff, which is of practical significance for reducing downstream drainage and flood control pressure.

However, there are challenges and considerations when implementing the CID mode, which should be adapted to suit local soil types, climate, and water availability. Tailoring practices to specific environmental conditions ensures the effectiveness of water resource optimization strategies. In conclusion, controlled irrigation and drainage play a pivotal role in optimizing water resources in paddy fields, contributing to sustainable and efficient rice cultivation. By implementing efficient and sustainable practices, it is possible to conserve water, improve nutrient utilization, and ultimately enhance the overall productivity and sustainability of rice cultivation.

5. Conclusions

These results demonstrate that the model effectively simulated drainage volume and nitrogen loss load in paddy fields under controlled irrigation and drainage in the cold black soil region; the coefficient of determination between the simulated paddy field drainage volume and nitrogen loss load results and the observed values were all above 0.83, and the Nash–Sutcliffe efficiency coefficient ranged from 0.72 to 0.97 in model calibration and verification. The CID mode effectively reduced both irrigation amount and frequency, enhanced the utilization of natural rainfall resources, significantly reduced the irrigation amount by 39.07% and increased rainwater utilization efficiency by 13.07% compared with the TID mode. The CID paddy field decreased the drainage volume by 44.71% and NO₃⁻-N and NH₄⁺-N loss load by 59.38% and 44.96%, respectively, compared with TID mode. The CID mode can optimize natural rainfall resources and increase irrigation water productivity by 97.85%. At the same time, the yield of rice increased by 16.88% compared with the TID mode, thereby achieving the goal of water saving, emission reduction, and high-yield goals in paddy fields. The results of this study can serve as a valuable reference for rice production under similar environmental conditions in other regions. Field studies were conducted for only two years on a sandy loam with a heavy texture and good structural properties. It is necessary to test and promote research in subsequent years and on the other types of soil, different field scales, different hydrological years and geographical divisions to improve the model.