Spatial and Temporal Distribution Characteristics of Water Requirements for Maize in Inner Mongolia from 1959 to 2018

: Crop water requirements are crucial for agricultural water management and redistribution. Based on meteorological and agricultural observation data, the e ﬀ ective precipitation ( P e ), water requirements ( ET c ), and irrigation water requirements ( I r ) in the maize growing areas of Inner Mongolia were calculated. Furthermore, climatic trends of these variables were analysed to reveal their temporal and spatial distributions. The research results are as follows: the average P e of maize in Inner Mongolia during the entire growth period was 125.9 mm, with an increasing trend from west to east. The P e in the middle growth period of maize was the highest and was small in the early and late growth stages. The P e climate exhibited a negative slope with a decreasing trend. The average ET c of maize during the entire growth period was 480.6 mm. The high-value areas are mainly distributed in the Wulatzhongqi and Linhe areas. The average I r of maize during the entire growth period was 402.9 mm, and the spatial distribution is similar to that of ET c . In each growth period, I r showed an increasing trend. Supplemental irrigation should be added appropriately during each growth period to ensure the normal growth of maize. This study can provide an e ﬀ ective basis for the optimisation of irrigation and regional water conservation in the maize cultivation area of Inner Mongolia.


Introduction
Climate change brings many significant challenges, and agriculture is considered to be one of the most vulnerable sectors to climate change [1][2][3][4]. In recent years, with the continuous intensification of the greenhouse effect, the problem of drought has become increasingly prominent, and agricultural water resources are facing serious challenges [5][6][7]. As water resources are mostly used in industrial aspplications, the remaining scope for agricultural water use is decreasing. Therefore, understanding spatial changes in crop water requirements in the context of climate change is conducive to crop irrigation system design and irrigation district planning. It can also provide a basis for studying the spatial distribution of crop water requirements and gaining an understanding of crop water consumption laws, agricultural water saving, and food security [8][9][10].
At present, many studies have been conducted on the spatiotemporal variation of the water requirements (ET c ) of different crops using the Penman-Monteith formula and the single crop coefficient method on a regional scale. The calculation of crop irrigation water requirements (I r ) by using the Inner Mongolia is located on the northern border of China (97-126 • E, 37-53 • N), with a land area of 1.183 million km 2 , accounting for 12.1% of the national territory. It has a temperate continental climate, with rare precipitation, short summers, hot and rainy periods, long winters and cold and windy springs [20,21]. The annual number of hours of sunshine is generally more than 2700, with a maximum of 3400 h. The annual average wind speed is more than 3 m s −1 , and the landforms are distributed in a band from east to west or from south to north, which is inlaid with plains, mountains, and high plains, thus affecting the redistribution of water and heat conditions on the surface, resulting in unique natural conditions and resources. There are many types of crops in this area, among which maize is the primary crop.

Meteorological Data
All meteorological data were obtained from the China Meteorological Administration (CMA). The data used in the study were derived from 31 meteorological stations and 9 agro-meteorological observation stations for the period of 1959-2018 ( Figure 1). The following variables were used: daily average temperature, maximum temperature, minimum temperature, average relative humidity, wind speed, precipitation, sunshine hours, elevation, and latitude and longitude. The agricultural meteorological observation index includes data on maize growth from 1991 to 2008. The distribution of agricultural meteorological observation in western Inner Mongolia is limited, and new agricultural meteorological observatories in the Hetao area were included. In this study, quality control of all weather stations was performed, weather stations with long-term meteorological data series were selected, and the missing values of meteorological data [22,23] were interpolated.

Division of Maize Growth Period
In this study, the growth period was divided into four stages: (i) early growth: sowing to seven-leaf stage, (ii): rapid growth: seven-leaf to tassel stage, (iii) middle growth: tassel to milk-mature stage, and (iv) late growth: milk-mature to mature [24]. Based on the data from nine agricultural meteorological observation stations and assuming that the variety of maize remained unchanged during the study period, the date and days of each growth period of maize were determined. For meteorological stations without observational data from the growth period, the adjacent agrometeorological observation station data in the same climate zone were used. Table 1 shows the duration of the maize growth period and adjacent meteorological stations for each agricultural meteorological station.

Effective Precipitation
The method recommended by the Soil Conservation Bureau of the United States Department of Agriculture was used to calculate effective precipitation (FAO, 1992), using the following equations:

Division of Maize Growth Period
In this study, the growth period was divided into four stages: (i) early growth: sowing to seven-leaf stage, (ii): rapid growth: seven-leaf to tassel stage, (iii) middle growth: tassel to milk-mature stage, and (iv) late growth: milk-mature to mature [24]. Based on the data from nine agricultural meteorological observation stations and assuming that the variety of maize remained unchanged during the study period, the date and days of each growth period of maize were determined. For meteorological stations without observational data from the growth period, the adjacent agrometeorological observation station data in the same climate zone were used. Table 1 shows the duration of the maize growth period and adjacent meteorological stations for each agricultural meteorological station.

Effective Precipitation
The method recommended by the Soil Conservation Bureau of the United States Department of Agriculture was used to calculate effective precipitation (FAO, 1992), using the following equations: where P is the daily rainfall (mm day −1 ).

Calculation of Maize Water Requirements
The daily water requirement of maize during the growth period was calculated using the single crop coefficient method [24]. The water requirement in each growth period was obtained by summing the daily water requirements. The formula for this calculation is as follows: where ET c is the daily crop water requirements (mm day −1 ), ET 0 is the daily reference crop transpiration (mm day −1 ), and K C is the crop coefficient. According to the maize standard crop coefficient recommended by FAO-56, under the conditions of 45% minimum relative humidity, an average wind speed of 2 (m s −1 ), no water stress, and a high management level, the initial crop coefficient (K cini ), middle growth crop coefficient (K cmid ), and late growth crop coefficient (K cend ) attain values of 0.30, 1.20, and 0.35. Among them, the K cmid of each agrometeorological observation station was revised, as shown in the following equation: where K cmid(tab) is the crop coefficient value recommended in FAO-56, u 2 is the average daily wind speed (m s −1 ) at a height of 2 m during the middle crop growth period, RH min is the average value of the minimum relative humidity during the middle crop growth day (%), and h is the average height of mid-growing crops (m). The simplified form of the Penman-Monteith formula was used to calculate the reference crop water requirement (ET 0 ), thus: where ET 0 is the reference evapotranspiration (mm day −1 ), T is the air temperature at 2 m height ( • C), ∆ is the slope vapour pressure curve (KPa • C −1 ), R n is net radiation at the crop surface (MJ m −2 day −1 ), G is the soil heat flux density (MJ m −2 day −1 ), γ is the psychrometric constant (KPa • C −1 ), e s is the saturation vapour pressure (KPa), e d is the actual vapour pressure (KPa), and U 2 is the wind speed at 2 m height (m s −1 ).

Descriptive Statistics, Climatic Trends, Change Test, and Mapping
The coefficient of variation (Cv) is adopted to describe the temporal variability of the relevant elements, according to Cv ≤ 0.1, 0.1 < Cv < 1.0, and Cv ≥ 1.0. These were defined as weak, medium, or strong [25].
A linear equation was used to fit the meteorological variables and to define the trends of the meteorological elements [26]: where X represents the fitted values of the meteorological elements, b represents the slope of the change in climate, t represents the corresponding year, and a represents the intercept. Thus, b × 10 represents the slope of meteorological variables every 10 year. The Mann-Kendall [27] test is a non-parametric test used to identify trends in a dataset. Because it has the advantages of simplicity and resistance to interference by outliers, it is often used to detect trends in a sequence. The Mann-Kendall test was used to analyse the P e , ET c , and I r during the maize growing season. Positive and negative values of the standard normal system variable (Z) statistic indicate trends in the data. When the absolute value of Z is greater than or equal to 1.64, 2.32, and 2.56, it passes the significance test thresholds of 95%, 99%, and 99.9%, respectively. The statistical variables UF k and UB k were calculated and plotted to demonstrate the change and the year when the change began. In this approach, a neutral (0) sign, Sgn ( . . . ), was used, which is defined as follows.
where x j and x k are the time series values of n observations at the jth and kth moments, respectively. In addition, the Kendall sum statistic S is as follows: The monotonic trend can be judged according to the S value, variance, as follows: V ar (S) = n(n − 1)(2n + 5)/18 (8) when n > 10, another standard Z value is calculated, which is given as When the Mann-Kendall test is further used to test sequence mutations, the test statistic is different from the above Z by constructing a sequence, where k = 2, 3, 4, . . . , n. Among them, Considering 1 ≤ j ≤ i, statistical variables are defined: Water 2020, 12, 3080 6 of 18 where k = 1, 2, . . . , n. Thus, E(S k ) = K(K + 1)/4 (13) V ar (S k ) = K(K + 1)(2k + 5)/72 (14) where UF k is a standard normal distribution, given a significance level α, if |UF k | > U α/2 , which indicates that there is a significant trend change in the sequence. The time series X was arranged in reverse order and calculated according to the formula provided above.
By analysing the statistical sequence, the trend change of the sequence X can be further analyzed, and the time of the mutation can be clarified and the area of the mutation can be pointed out. If the UF k value is greater than 0, it indicates that the sequence is on an upward trend; if it is less than 0, it indicates a downward trend; when they exceed the critical straight line, it indicates a significant upward or downward trend. If the two curves of UF k and UB k intersect, and the intersection point is between the critical straight lines, then the moment corresponding to the intersection point is the moment when the abrupt change begins.
The kriging interpolation method has the advantages of providing unbiased estimates and fully reflecting the spatial structure of variables; therefore, it is widely used in geographic analysis and meteorology. This study uses the kriging method that comes with the ArcMap 10.1 toolbox for spatial interpolation and plotting of P e , ET c , and I r .

Irrigation Water Requirements
The difference between ET c and P e was used to determine whether irrigation was needed during the maize growing season. When P e exceeded ET c , irrigation was not required. Conversely, when Pe was less than ET c , irrigation was required. The difference between ET c and P e was calculated as follows: where n is the number of days in each growth period, I rm is the Irrigation water requirement in the m th growth stage (mm), and I ra is the total irrigation water requirement in the growth period (mm).

Degree of Coupling of Effective Precipitation and Water Requirement
The degree of coupling of crop water requirements and effective precipitation reflects the degree of utilisation of rainwater by the crop and is calculated using the following equation: where λ i is the degree of coupling of the i period of growth, P i is the effective precipitation in the i period of growth (mm), and ET ci is the water requirement of a crop in period i (mm).

Climate Classifications
The ratio of annual average precipitation to annual average potential evapotranspiration calculated by the Thornthwaite method can be used as a drought index. This method has been certified by the United Nations Convention and is used globally in studies undertaken to combat desertification [28]. In terms of its climate, Inner Mongolia can be divided into severe-arid, arid, semi-arid, arid and semi humid, and humid and semi-humid, according to the criteria established by the United Nations Environment Programme. The severe-arid region is mainly in the western region of Inner Mongolia, the arid region mainly includes the central and western regions of Inner Mongolia, the semi-arid region mainly includes the central and middle eastern regions of Inner Mongolia, the arid and semi-humid region is mainly in the hilly area of northeast Inner Mongolia, and the humid and semi-humid areas are mainly in the eastern part of Inner Mongolia. Because the severe-arid area is not suitable for maize cultivation, few meteorological stations are located in this region; thus, it was not included in this study.

Spatial and Temporal Changes of P e in the Entire Growth Period of Maize
The spatial distribution of the average P e of each meteorological station during the entire growth period of Inner Mongolian maize is shown in Figure 2a. The variation range was 59.1-166.7 mm, and the average value was 125.9 mm. High-value areas of P e in Inner Mongolia, in which the average annual P e exceeds 160 mm, are mainly distributed in the areas of the Turi River, Xiaoergou, Suolun, and Zhalantun. The low value areas, in which the annual average P e is less than 82 mm, are mainly distributed in the areas of Urad Zhongqi and Linhe. The spatial distribution shows an increasing slope from west to east, with the lowest precipitation of 59.1 mm in Linhe and the largest value of 166.7 mm in the Turi River region. The temporal change of P e during the entire growth period of Inner Mongolian maize from 1959 to 2018 is shown in Figure 3a. There was moderate variation with a minimum P e of 77.8 mm (1966) and a maximum of 171.9 mm (1998). The spatial distribution of P e slope at each station during the entire growth period of maize is shown in Figure 4a, and the variation range was between

Spatial Variation of P e in Each Growth Stage of Maize
The average annual P e of Inner Mongolian maize during each growth period is shown in Figure 2b-e. At the beginning of the maize growing season, the average annual P e of maize was 20.7 mm, ranging from 6.6 to 38.1 mm, and P e increased from east to west. During the rapid growth stage of maize, the annual average P e ranged between 13.4 and 66.3 mm, and the average P e was 47.4 mm. In the middle stage of maize growth, the annual average P e of each site ranged between 26.5 and 56.5 mm, with an average annual P e of 38.9 mm, the spatial distribution was generally larger in the northeast region and was smaller in the other regions. In the late growth stage of maize, annual average P e ranged between 8.6 and 34.9 mm, average annual average P e was 18.8 mm, and a high value distribution was observed in the central and western regions. The average P e of each growth stage of maize exhibited the following ranking from smallest to largest: late stage, early stage, middle stage, and rapid stage of maize growth. P e was mainly concentrated in the rapid and middle growth periods, with a total of 86.3 mm, accounting for 68.61% of the average P e across the entire growth season.  The slope of the annual average P e in each growth stage of maize from 1959 to 2018 is shown in Figure 4b-e. At the beginning of the maize growth stage, the slope of P e ranged from −0.13 to 2.55 mm decade −1 , with an average value of 0.80 mm decade −1 . Except for Baotou and Dong Ujimqin Qi, which were negative, other slopes for P e were positive. The slope of P e during the rapid growth period of maize ranged between −2.85 to −1.38 mm decade −1 , with an average value of −0.50 mm decade −1 . The slope of P e in the middle growth period of maize ranged between −2.68 and 0.55 mm decade −1 , and the average was −1.21 mm decade −1 . Except for Zhalantun and Tongliao, which exhibited positive slopes, the remaining sites exhibited negative slopes. The slope of P e in the later growth period ranged between −1.15 and 1.47 mm decade −1 , with the average value of −0.33 mm decade −1 . However, Urad Zhongqi, Otog Qi, Dongsheng, Linhe, Dahl hamming'an United banner, and Abag Qi exhibited positive slopes. Generally, P e exhibited a positive slope in the early growth period of maize but exhibited a negative slope during the rapid and middle growth periods. The Mann-Kendall test showed that P e increased significantly (p < 0.05) in the early growth period and decreased significantly (p < 0.05) in the middle growth period.

Spatial Variation of ETc in Each Growth Stage of Maize
The average annual ETc of Inner Mongolian maize during each growth period is shown in Figure 5b-e. The initial ETc of maize ranged between 38.8 and 77.8 mm, with an average of 60.0 mm. The annual average ETc of the rapid maize growth period ranged between 78.8 and 230.5 mm, with an average of 167.1 mm. The spatial distribution of ETc during the early growth and rapid growth period was generally higher in the western and central regions and lower in the northeast region. In the middle growth stage, the annual average ETc ranged from 109.8 to 427.9 mm, with an average of 186.0 mm, and ETc in the late growth stage ranged from 28.7 to 116.7 mm, with an average of 67.5 mm. The ETc in the middle and late stages of fertility was generally larger in the western region and smaller in the central and eastern regions. The change in ETc during the various growth periods of maize initially exhibited a rapid increase, followed by a decrease, with the maximum in the middle growth period. The sum of the rapid growth and middle growth period was 351.8 mm, accounting for 73.48% of the total ETc.

Spatial Variation of ET c in Each Growth Stage of Maize
The average annual ET c of Inner Mongolian maize during each growth period is shown in Figure 5b-e. The initial ET c of maize ranged between 38.8 and 77.8 mm, with an average of 60.0 mm. The annual average ET c of the rapid maize growth period ranged between 78.8 and 230.5 mm, with an average of 167.1 mm. The spatial distribution of ET c during the early growth and rapid growth period was generally higher in the western and central regions and lower in the northeast region. In the middle growth stage, the annual average ET c ranged from 109.8 to 427.9 mm, with an average of 186.0 mm, and ET c in the late growth stage ranged from 28.7 to 116.7 mm, with an average of 67.5 mm. The ET c in the middle and late stages of fertility was generally larger in the western region and smaller in the central and eastern regions. The change in ET c during the various growth periods of maize initially exhibited a rapid increase, followed by a decrease, with the maximum in the middle growth period. The sum of the rapid growth and middle growth period was 351.8 mm, accounting for 73.48% of the total ET c . Water 2020, 12, x FOR PEER REVIEW 11 of 17 The change in the slope of annual average ETc in Inner Mongolian maize during each growth period is shown in Figure 6b-e. The initial slope ranged from −0.84 to 2.18 mm decade −1 , with an average of 0.35 mm decade −1 ; generally, the slope increased. The rapid growth period slope ranged from −5.33 to 4.53 mm decade −1 , the average was 0.54 mm decade −1 , and the slope at middle growth ranged between −4.13 to 8.87 mm decade −1 , with an average of 3.46 mm decade −1 . The slope of ETc in the later growth period ranged between −2.14-3.83 mm decade −1 , with an average of 0.82 mm decade −1 . The Mann-Kendall test demonstrated that the increase in ETc in the middle and end stages of growth was highly significant (p < 0.001).  The change in the slope of annual average ET c in Inner Mongolian maize during each growth period is shown in Figure 6b-e. The initial slope ranged from −0.84 to 2.18 mm decade −1 , with an average of 0.35 mm decade −1 ; generally, the slope increased. The rapid growth period slope ranged from −5.33 to 4.53 mm decade −1 , the average was 0.54 mm decade −1 , and the slope at middle growth ranged between −4.13 to 8.87 mm decade −1 , with an average of 3.46 mm decade −1 . The slope of ET c in the later growth period ranged between −2.14-3.83 mm decade −1 , with an average of 0.82 mm decade −1 .

Change of Irrigation Water Requirements During the Maize Growing Period
The Mann-Kendall test demonstrated that the increase in ET c in the middle and end stages of growth was highly significant (p < 0.001).

Spatial and Temporal Changes of I r in the Entire Growth Period of Maize
The spatial distribution of the average I r of each meteorological station during the entire growth period of Inner Mongolian maize is shown in Figure 7a. The variation range was between 188.7 and 627.9 mm, with an average of 402.9 mm. The Urad Zhongqi and Linhe areas exhibited the largest values, whereas the Ergun Youqi, Xiaoergou, and Turi Rivers exhibited the lowest I r values. The temporal change of I r during the entire growth period of Inner Mongolian maize from 1959 to 2018 is shown in Figure 3c. There was moderate variation, with a minimum I r of 316.7 mm (1959) and a maximum of 478.5 mm (1972). The spatial distribution of the I r slope at each station during the entire growth period of maize is shown in Figure 8a, and the variation ranged between −9.56 and 20.67 mm decade −1 , with an average of 6.32 mm decade −1 . Outside of Baoguotu, Linhe, Hohhot, Baotou, and Otog Qi, the slopes of the other stations were positive. I r increased significantly during the entire growth stage (p < 0.05). It can be seen from the curve UF that I r showed a downward trend from 1991 to 2001 and did not reach a significant level. After 2003, I r showed an increasing trend and reached a significant level in 2016, and the change date was 2001 (Figure 3f).

Spatial Variation of I r in Each Growth Stage of Maize
The average annual I r of Inner Mongolian maize during each growth period is shown in Figure 7b-e. In the early stage of maize growth, I r ranged between 29.2 and 72.9 mm, with an average of 52.8 mm. I r in the rapid growth period of maize ranged between 53.6 and 208.4 mm, with an average of 138.5 mm. In the early and rapid growth periods, the annual average I r of maize tended to be larger in the central and western regions and smaller in the eastern region. The average annual I r in the middle growth period ranged between 84.64 and 304.6 mm, with an average of 153.5 mm. The average annual I r in the later growth period ranged between 21.2 and 101.9 mm, with an average of 58.1 mm. The average annual I r in the middle and later stages of maize growth was larger in the western region and smaller in the central and eastern regions. The I r was smallest in the early growth period, then initially increased and then decreased; thus, I r was largest in the middle growth period.  The average annual Ir of Inner Mongolian maize during each growth period is shown in Figure   Figure 7. Spatial variation characteristics of I r during the entire growth period (a), early growth period (b), rapid growth period (c), middle growth period (d), and end growth period (e) of maize from 1959 to 2018.
The average annual I r climatic trend rate of maize during each growth period is shown in Figure 8b-e. The slope of I r in the initial growth period ranged between −1.15 and 2.06 mm decade −1 , with an average of 0.21 mm decade −1 . A small trend was apparent, with negative values accounting for 61.92% of the total. The slope of I r during the rapid growth period ranged between −4.69 and 6.35 mm decade −1 , with an average of 1.12 mm decade −1 . The slope of I r in the middle growth stage ranged between −3.93 and 10.44 mm decade −1 , with an average of 3.93 mm decade −1 , and the slope of I r at the end of the growth period ranged between −1.97 and 3.78 mm decade −1 , with an average of 0.99 mm decade −1 . In the middle and late stages of growth, I r increased significantly (p < 0.05).
(d) Lmid (mm) (e) Llate (mm) Figure 7. Spatial variation characteristics of Ir during the entire growth period (a), early growth period (b), rapid growth period (c), middle growth period (d), and end growth period (e) of maize from 1959 to 2018.

Spatial Variation of Ir in Each Growth Stage of Maize
The average annual Ir of Inner Mongolian maize during each growth period is shown in Figure  7b-e. In the early stage of maize growth, Ir ranged between 29.2 and 72.9 mm, with an average of 52.8 mm. Ir in the rapid growth period of maize ranged between 53.6 and 208.4 mm, with an average of 138.5 mm. In the early and rapid growth periods, the annual average Ir of maize tended

Relationship
Between P e , ET c , and I r During Maize Growth As shown in Figure 2, Figure 5, and Figure 7, ET c decreased from west to east, and P e increased from west to east, which inevitably leads to the same change in I r as that observed for ET c . This is due to the complementary relationship between P e and I r . During the early, rapid, and middle growing season, the majority of P e was concentrated in the eastern and north-eastern regions. The differences in ET c and I r are consistent across growth periods: ET c and I r in the western region always maintained a higher range, whereas ET c and I r in the northeast region were smaller.
As shown in Figure 4, Figure 6, and Figure 8, for the western region, P e showed a slightly increasing trend, and ET c had a decreasing tendency. This indicates a potential to alleviate the relative lack of water in the western region. For the central and eastern regions, P e showed a decreasing trend and ET c showed an increasing trend, which lead to the obviously increasing slope of I r . In the early growing period, ET c only increased in some small areas, and P e increased in the western and north-eastern regions. Therefore, I r increased in the central region. In the rapid growth period, ET c showed an obvious increasing trend in the central and eastern regions, and P e showed a smaller increasing trend in the north-east region; therefore, I r also showed an increasing trend in the central and eastern regions. In the middle growth, ET c showed an increasing trend in the central region, and P e showed an increasing trend in the western region, causing I r to increase in the central and eastern regions, increasing significantly in Xilinhot, Abag Qi, and Linxi. At the end of the growing season, the increasing slope of ET c was not obvious, and the increasing slope of P e was not obvious in the northeast. Most the remaining areas exhibited a decreasing trend; thus, the slope of I r is consistent with ET c . Figure 9 shows the changes of P e , ET c , and I r at different growth stages across Inner Mongolia from 1959 to 2019. All variables initially increased and then decreased with crop development. The maximum values of ET c and I r appear in the middle growth period, but the maximum value of P e appeared in the rapid growth period. The slope of P e was only positive at the beginning of the growing season and was negative during other growth stages. The slopes of ET c and I r were positive for each growth period, reaching a maximum in the middle growth period. The ET c in the middle growth period increased significantly, whereas P e showed a decreasing trend; thus, the increase in I r during the middle growth period was greater.

Characteristics of Water Requirements of Maize in Different Climatic Regions
To better study and compare the growth periods of Pe, ETc, and Ir in different climate regions and the rules governing the coupling of Pe and ETc, Inner Mongolia was divided into several climatic regions, and representative climate stations in each climatic region were selected for comparison. These stations include Linhe in the arid area, Chifeng in the semi-arid area, Zhalantun in the semi-arid and humid area, and Turi River in the humid and semi-humid area.
Changes in Pe at each weather station are ranked as follows in ascending order: Linhe, Chifeng, Zhalantun, and Turi River ( Table 2). Both Ir and ETc during the maize growth period changed as a function of the degree of drought-the higher the degree of drought, the higher the Ir and ETc, and the change trend was opposite to that of Pe. As the climate zone changed from arid to moist and semi-moist, the degree of coupling of ETc and Pe also increased. The degree of coupling of ETc and Pe throughout the growth period was 0.09, 0.29, 0.45, and 0.62. The degree of coupling of ETc and Pe in different growth stages was less than 1, and water deficits were therefore apparent. The degree of coupling of ETc and Pe in the arid area was less than 0.1, except for the end of the growing season, when it was 0.14. Pe in different growth periods of each weather station was less than ETc. In arid and semi-arid regions, the degree of coupling of ETc and Pe in different growth periods did not exhibit large changes; both were small.

Characteristics of Water Requirements of Maize in Different Climatic Regions
To better study and compare the growth periods of P e , ET c , and I r in different climate regions and the rules governing the coupling of P e and ET c , Inner Mongolia was divided into several climatic regions, and representative climate stations in each climatic region were selected for comparison. These stations include Linhe in the arid area, Chifeng in the semi-arid area, Zhalantun in the semi-arid and humid area, and Turi River in the humid and semi-humid area.
Changes in P e at each weather station are ranked as follows in ascending order: Linhe, Chifeng, Zhalantun, and Turi River ( Table 2). Both I r and ET c during the maize growth period changed as a function of the degree of drought-the higher the degree of drought, the higher the I r and ET c , and the change trend was opposite to that of P e . As the climate zone changed from arid to moist and semi-moist, the degree of coupling of ET c and P e also increased. The degree of coupling of ET c and P e throughout the growth period was 0.09, 0.29, 0.45, and 0.62.
The degree of coupling of ET c and P e in different growth stages was less than 1, and water deficits were therefore apparent. The degree of coupling of ET c and P e in the arid area was less than 0.1, except for the end of the growing season, when it was 0.14. P e in different growth periods of each weather station was less than ET c . In arid and semi-arid regions, the degree of coupling of ET c and P e in different growth periods did not exhibit large changes; both were small.
The degree of coupling of ET c and P e changed from large to small and then to large values from the early growth to the end of the growth stages, with the smallest values in the middle growth stage, indicating severe water deficits. The largest degree of coupling of ET c and P e was apparent in the early growth stage; indicating a small water deficit.

Discussion
In terms of ET 0 , Wang et al. (2015) [29] found that reference crop evapotranspiration (ET 0 ) was between 570 and 1674 mm from 1961 to 2010, and the highest value areas were distributed in western Inner Mongolia. Additionally, Tong et al. (2018) [30] noted that the average annual ET 0 in western Inner Mongolia was the largest, with values between 1300 and 1600 mm, and the ET 0 in Inner Mongolia from 1961 to 2010 in this study was between 567.4 and 1282 mm. Meteorological stations in the western region, and the western region per se were not within the scope of this study; thus, the highest ET 0 in Inner Mongolia in the present study was less than 1674 mm, the value reported in the former study. However, the minimum value was extremely close to that reported by Wang et al. (2015) [29].
Anon. (1993) [31] calculated the ET c of 21 stations in the maize cultivation area of Inner Mongolia from 1961 to 1980 using the Penman formula and a single crop coefficient. The average value of ET c in that study was 531.5 mm. The average water shortage was 280 mm. In the present study, the average value of water requirement ET c from 1961 to 1980 was 481.6 mm; however the water shortage was 356.8 mm. Because K c was divided and corrected in each growth period in the present study, and the former study applied a fixed value of K c (0.8) when calculating ET c , the average value of ET c in the present study was 9.3% lower than that reported by Anon. (1993) [31]. In calculating the effective precipitation, the empirical coefficient method was used in the former study, but the method recommended by the USDA Soil Conservation Service was used in the present study. These two reasons ultimately led to the crop water shortage in this study being 76.8 mm higher than that of the former study.
The multi-year average I r values in this study were 402.9 mm. The area with a large I r was mainly located in the Urad Zhongqi and Linhe areas. For the Hetao Irrigation District, in which Linhe is located, the groundwater depth was relatively shallow, and this study did not consider the decrease in the irrigation amount caused by groundwater supplementation, nor did it consider the increase in the irrigation amount due to the serious harm of salinity in this area. Because of climate change, the temperature in Inner Mongolia increased at a rate of 0.45 • C decade −1 , and precipitation also decreased to varying degrees [32]. The Inner Mongolian maize sowing period has advanced by 1.0 d decade −1 on average, and the maturity period has been delayed by 3.3 d decade −1 , on average, and the whole growth period of maize has been extended by 4.5 d decade −1 . Moreover, due to the increase in accumulated temperature, the range of maize planting in Inner Mongolia has been expanded, and maize varieties have also been converted to late varieties [33]. Therefore, calculations using crop production data from 1991 to 2008 may overestimate the value of ET c in the first 30 years of 1959-2018. In this study, the effective precipitation P e in the maize cultivation area of Inner Mongolia decreased at a rate of −0.05 mm decade −1 , whereas the ET c increased at a rate of 5.16 mm decade −1 . With the increase in temperature, the risk of drought will increase further [34].

Conclusions
This study used the single crop coefficient method and the spatial analysis function of ArcMap to calculate and plot the P e , ET c , and I r in each growth period of maize in Inner Mongolia, and their respective climate gradients, to show the water supply requirement relationships of maize in Inner Mongolia.
During the growth period of maize in Inner Mongolia, P e showed a downward trend, but ET c showed an overall upward trend, indicating that the I r of maize in Inner Mongolia will continue to increase in the future. North-eastern Inner Mongolia is rich in rainwater resources; as the temperature rises, the northeast will be more suitable for maize growth. Therefore, the scope of maize planting in the northeast can be appropriately expanded. For the western regions with greater demand for I r , in addition to adopting water-saving measures such as deficit irrigation, mulching, and pipeline water delivery, appropriate adjustments should be made to the crop planting structure in western Inner Mongolia, such as reducing the range of maize sowing and increasing the number of crops that require less water and have higher economic benefits. The peak period of ET c in maize is mainly in the rapid and middle growing period. In these periods, P e shows a downward trend, whereas ET c and I r increase notably. Therefore, we should focus on supplementing irrigation in the rapid and middle growing periods for maize.