1. Introduction
Waterlogging is a natural disaster that affects agricultural production [
1,
2,
3,
4]. Globally, approximately 10% of the agricultural area is affected by waterlogging, resulting in an approximately 20% reduction in crop yield [
1,
5]. In China, the area of waterlogged arable land is 3.11 × 10
5 km
2, accounting for 25% of the total area of cultivated land [
6]. Due to its wide range, severity, and great economic consequences, waterlogging has negative impacts on agricultural production and economic development [
7]. In addition, due to climate change and rapid urbanization, the intensity and frequency of precipitation have increased [
8] and resulted in frequent waterlogging disasters, which are serious threats to agriculture [
9,
10]. The control of waterlogged arable land has drawn great attention from governments, researchers, and food producers. The drainage engineering of farmland and the sponge city strategy are the main components of waterlogging control work measures [
11,
12]. The study of farmland drainage engineering and design parameters is crucial for controlling waterlogging in agricultural regions.
The drainage modulus, which is the runoff per unit area per unit time, is an important indicator in the drainage system design of farmlands and in drainage engineering, and it is very important for controlling waterlogged arable land [
12,
13]. Many researchers worldwide have performed substantive research on calculating the drainage modulus [
13,
14,
15,
16]. For example, El-Sadek, Feyen and Berlamont [
14] incorporated Hooghoudt’s steady-state equation into the WAVE model to calculate drainage flux. Arnold, Williams and Maidment [
15] developed the continuous-time water and sediment-routing model to calculate drainage flux. You, Wang, Tao and Liu [
16] calculated the drainage coefficient based on the calculation results of the theoretical runoff using the empirical formula and the average draining method in the Wanyan River Surface Waterlogged Area (Suibin County) of the Sanjiang Plain. In China, the empirical formula, average draining method, water balance method, Nash’s instantaneous unit curve method, infiltration-runoff math-theoretical model, and hydraulic model have been used to calculate the drainage modulus [
13,
15,
17,
18]. Due to its reliable computational results and because the required data are available and reliable, the average exclusion method has been used to calculate the drainage modulus in China’s plain lake areas. The primary input data include the design rainstorm, evaporation from an evaporation pan, and land-use type areas.
The Huaibei Plain is an important grain production area in China, on which dry land crops are widely cultivated [
19]. This area is located in the Huaihe River Basin, which is characterized by low-lying terrain and a diverse network of rivers. Due to climate warming and human activities, the intensity and frequency of precipitation have increased [
8]. Affected by the drainage project and the water level of the river, precipitation during heavy rainfall cannot be discharged in a timely manner, resulting in serious waterlogging [
20,
21]. In addition, imperfect field drainage systems and inadequate management have resulted in an increase in waterlogging disasters and crop losses [
22]. The drainage modulus is an important indicator in the drainage system design of farmlands and the drainage pump station, and it is very important to agricultural production in this area.
Recent research has focused on the changing trends of extreme rainfall [
8], hydrological process modeling [
23,
24], and waterlogging control on cultivated land [
19,
21]. Applying the results of these studies to the practice of irrigation and drainage engineering is challenging. The drainage modulus is one of the important parameters in the design of drainage canal sections and drainage pump stations. However, less attention has been given to the changing trends of the drainage modulus. Investigating changes in the drainage modulus can help guide regional water resource management and the adjustment of cropping structures. The main purposes of this paper are to (1) explore changes in the spatial and temporal distributions of the drainage modulus and to (2) analyze the key environmental elements affecting the drainage modulus.
3. Results
3.1. Temporal Variation in Annual Maximum 1-Day and 3-Day Precipitation Amounts
The change trends of Rx1day and Rx3day in the Huaibei Plain are shown in
Table 3 and
Figure 2. The MK test showed increasing trends in Rx1day and Rx3day, with rates of increase of 0.2 mm·10 a
−1 and 0.8 mm·10 a
−1, respectively. The minimum value of Rx1day was 67.11 mm, which occurred in 1994, and the maximum value was 159.44 mm, which occurred in 1972. For Rx3day, the minimum value was 92.64 mm, which occurred in 1993, and the maximum value was 227.86 mm, which occurred in 2005.
For Rx1day, 25% of the sites showed decreasing trends, and the rate of decrease ranged from 0.74 mm·10 a−1 to 4.62 mm·10 a−1. Seventy-five percent of the sites showed increasing trends, and the rate of increase ranged from 0.71 mm·10 a−1 to 3.43 mm·10 a−1. For Rx3day, 37.5% of the sites showed decreasing trends, and the rate of decrease ranged from 0.27 mm·10 a−1 to 6.50 mm·10 a−1. A total of 62.5% of the sites showed increasing trends, and the rate of increase ranged from 0.38 mm·10 a−1 to 4.65 mm·10 a−1.
Figure 3 displays the spatial distributions of the MK test results for Rx1day and Rx3day. For Rx1day, four sites exhibited decreasing trends, which were localized in the northeast and southwest parts. Twelve sites, which were spread throughout the plain, exhibited increasing trends. For Rx3day, six sites exhibited decreasing trends, which were localized in the northeast, southeast, and southwest parts. Ten sites, which were spread throughout the plain, exhibited increasing trends.
3.2. Temporal Variability of Drainage Modulus
The change trends of the drainage modulus on the Huaibei Plain are shown in
Table 4 and
Figure 4. Overall, the MK test showed increasing trends in
q1 and
q3, and the rates of increase were 0.345 mm·day
−1·10 a
−1 and 0.346 mm·day
−1·10 a
−1, respectively. The minimum value of
q1 was 11.837 mm·day
−1, which occurred in 1994, and the maximum value was 41.731 mm·day
−1, which occurred in 1972. For
q3, the minimum value was 11.837 mm·day
−1, which occurred in 1994, and the maximum value was 37.843 mm·day
−1, which occurred in 2005.
The trends in q1 and q3 varied among different sites with different microclimatic characteristics. Among the sites, 23.5% (q1) and 29.4% (q3) showed decreasing trends, and 76.5% (q1) and 70.6% (q3) showed increasing trends. For q1, the rate of increase ranged from −14.774 mm·day−1·10 a−1 to 10.368 mm·day−1·10 a−1. For q3, the rate of increase ranged from −12.182 mm·day−1·10 a−1 to 9.331 mm·day−1·10 a−1.
Figure 5 displays the spatial distributions of the MK test results on
q1 and
q3. For
q1, four sites exhibited decreasing trends, which were localized in the northeast and southwest parts. Twelve sites, which were spread throughout the plain, exhibited increasing trends. For
q3, five sites exhibited decreasing trends, which were localized in the northeast, southeast, and southwest parts. Eleven sites, which were spread throughout the plain, exhibited increasing trends.
3.3. Periodic Variation in the Drainage Modulus
The Morlet wavelet can reveal the periodicity of the high and low indices of the drainage modulus and was used to analyze the phase change and the periodic intensity at different time scales [
30,
34]. The wavelet variances, wavelet coefficients, and significant time sections of the drainage modulus were obtained using a Morlet wavelet function and are shown in
Figure 6 and
Figure 7. The wavelet variances of the high and low indices for
q1 and
q3 had significant 2.4-year and 2.5-year periodicities, respectively, on the basis of a chi-square test at a confidence level of 95%. In addition, there were also main periods of 8.4 years and 12.5 years for
q1 and 7.9 years, 19.7 years, and 32.5 years for
q3, which did not pass the 95% confidence level.
According to the wavelet red-noise test at a confidence level of 95%, the most significant periodic fluctuation of
q1 had a 2.4-year period and occurred during 1961~1975 and 1997~2010, and the most significant periodic fluctuation for
q3 was a 2.5-year period and occurred during 1961~1966, 1972~1974, and 1997~2010 (
Figure 7). For
q1, significant periodic fluctuations of 8.4 years and 12.5 years occurred during 1973~2007 and 1972~1992, respectively. For
q3, significant periodic fluctuations of 7.9 years, 19.7 years, and 32.5 years occurred during 1984~2011, 1983~2017, and 1976~2017, respectively (
Figure 7).
3.4. Environmental Factors That Affect Drainage Modulus Variability
Environmental factors, such as the areas of paddy land, dryland, water bodies, building lots, and precipitation, represent important input data for calculating the drainage modulus, and changes in these elements have important impacts on the drainage modulus. To analyze the effects of environmental factors, sensitivity analysis and contribution rate analysis were performed.
The results of the sensitivity analysis showed that the average
q1 and
q3 over the whole plain were most sensitive to Rx1day and Rx3day, followed by
Sdl,
Sbl,
Spf, and
Swb; the sensitivity coefficients were 1.81, 0.68, 0.30, 0.01, and 0.0 for
q1 and 1.71, 0.74, 0.23, 0.02, and 0.0 for
q3, respectively (
Table 5). These results showed that precipitation, dryland area, and building lots had important effects on the drainage modulus.
The results of the contribution rate analysis suggested that over the whole plain, increases in Rx1day, Rx3day, and
Sbl positively contributed to an increase in the drainage modulus. In addition, decreases in
Spf and
Sdl negatively contributed to an increase in the drainage modulus. Because the total positive contribution was greater than the total negative contribution, the drainage modulus generally increased from 1960 to 2017 (
Table 6). Because the absolute value of the contribution of
Sbl was greater than those of other factors,
Sbl was the main factor that influenced the variability in the drainage modulus. On the Huaibei Plain, there has been an increasing trend in the proportion of construction lands and a decreasing trend in that of paddy fields and dry fields, while the proportion of water bodies has remained unchanged (
Figure 8). These results suggested that rapid urbanization increased the risk of agricultural waterlogging.
5. Conclusions
In this study, the drainage modulus was estimated using the average draining method at 16 meteorological stations located in different areas of the Huaibei Plain. The MK method and Sen’s slope estimator were used to study the spatiotemporal distribution of the drainage modulus. In addition, a wavelet transform was applied to investigate the periodic trends in the drainage modulus, and the contribution rate method was used to identify the causes of drainage modulus changes. The following conclusions were drawn from this study.
The mean maximum 1-day and 3-day precipitation amounts had significant increasing trends. The rates of increase of Rx1day and Rx3day were 0.2 mm·10 a−1 and 0.8 mm·10 a−1, respectively. The mean drainage modulus had significant increasing trends. The rates of increase of q1 and q3 were 0.345 mm·day−1·10 a−1 and 0.346 mm·day−1·10 a−1, respectively. The significant wavelet power spectra of q1 and q3 were very similar, and the significant wavelet power spectra of q1 and q3 had significant 2.4-year and 2.5-year periodicities, respectively. The sensitivity analysis showed that the average q1 and q3 values were most sensitive to Rx1day and Rx3day, followed by areas of dryland, building lots, fields, and water bodies. However, the contribution rate analysis suggested that building lots were the main factor influencing the variability in the drainage modulus. Rapid urbanization increased the risk of agricultural waterlogging.