Hunan Province is located between 108°47′E-114°15′E and 24°38′N-30°08′N, and it contains 13 municipal administrative units (Figure 1). The terrain of Hunan Province is relatively complex: mountains surround the western, eastern and southern parts of this province, low hills are located in the central, while plains are found in the northern. Generally, the topographic terrain of Hunan is high in the west and south and low in the east and north, creating a horseshoe-like pattern.

The climate of Hunan is subtropical. The temperature is sufficient for rice growth, and the humidity is moderate. In addition, the river network is dense, and water resources are also abundant. Therefore, Hunan is very suitable for rice cultivation, especially for double-cropping rice. According to a report of the National Bureau of Statistics, over the past 10 years, the double-cropping rice yield accounted for more than one-fifth of the national yield.

In this study, the revised Advanced Space borne Thermal Emission and Reflection Radiometer Global Digital Elevation Model (ASTER GDEM) Version 2 was used to extract various terrain factors. The spatial resolution of the GDEM is 30 metres. The paddy field raster of Hunan Province was extracted based on the 100-m resolution land use data of 2010 (Liu et al., 2014). Moreover, to investigate the relationship between terrain factors and the environmental factors of rice growth, we obtained the spatial distribution of soils in Hunan Province based on the 1:1,000,000 soil map of China (NSSO, 1995), and we calculated the daily average temperature and sunlight from 2010-2012 based on the 0.25-degree daily meteorological grid data (Yuan et al., 2015). Given that Hunan is an irrigated area, our research did not take rainfall into consideration.

There are 102 county-level administrative units in Hunan Province. We collected rice yield data for each county based on the website of China Planting Information (http://202.127.42.157/moazzys/) and the China Rural Statistical Yearbook of Hunan (Department of Rural Survey, NBS, 2011-2013). However, data at the county level were difficult to access; finally, only the yield data from 2011 to 2013 for 33 counties were available. The spatial distributions of the selected counties are shown in Figure 2a. During this process, we obtained the yield of each county by calculating the average per unit area yield of three years. Information about rice phenology came from the agricultural meteorological sites (AMS) of the China Meteorological Administration National Meteorological Information Center. Considering that it represents the dominant style of rice production in Hunan, double-cropping rice was the only focus of this study. Figure 2b shows the spatial distribution of AMS.

The rice phenology recorded by the AMS included 10 stages: emerge, trefoil, transplant, green-up, tillering, jointing, booting, heading, milk-ripe and mature. Among these stages, transplanting, tillering, heading and mature are the four most important stages. Transplanting is the stage when rice is planted in the paddy fields; tillering is the most prosperous period of rice vegetative growth; heading is the stage when the rice transits from vegetative growth to reproductive growth; and mature is the stage of rice seeding and harvesting. Therefore, we focused on these four most important phenological stages of rice. Due to the different emergence dates of different areas in Hunan, in this study, the dates of transplanting, tillering, heading and mature stages are relative dates: we subtracted their corresponding emergence dates from these four actual dates. Moreover, to mitigate the adverse impact of differences in rice varieties, we used the record of indica hybrid rice data from 2010 to 2012 at each agricultural meteorological site. Meanwhile, to eliminate the impact of the use of different cropping systems on different rice varieties, we selected records from the same cropping system (i.e., all the early maturing varieties or medium maturing varieties in these three years) at each site and calculated their average value to reflect the phenological information for each site. Table 1 shows the phenological information of the double-cropping rice obtained at some sites.

2.3.1 Selection and extraction of terrain factors

To effectively describe the terrain features, we used the factors of altitude, slope, slope aspect, surface relief degree, surface roughness and slope position. Altitude and slope are the two basic terrain factors that form the basic skeleton of the surface. The slope aspect has a direct impact on the sunlight that the crop receives.

The degree of surface relief is the indicator that describes the regional relative elevation and influences the spatial distribution of surface nutrients. The formula of the surface relief degree is as follows:

$R{{F}_{i}}={{H}_{\max }}-{{H}_{\min }}$ (1)

where RF_i represents the relative difference in elevation within the window where the i-th raster is the centre. H_max and H_min are the maximum and minimum values of altitude, respectively, within this window. According to previous studies and the terrain features of our study region (Zhang et al., 2012), we selected 59*59 as the size of the calculated window to obtain the surface relief degree.

Surface roughness is an indicator that reflects the complexity and erosion of the surface (Jia et al., 2013; Tang et al., 2006). It represents the degree of surface fragmentation and is calculated using the following formula:

$M=1/\cos (\theta *\text{ }\!\!\pi\!\!\text{ }/180)$ (2)

where θ represents the slope.

Slope position is an indicator that measures the location of a target point in the vertical profile of a given terrain. Additionally, the slope position can influence the spatial pattern of soil nutrients. We obtained the slope position based on the Topographic Position Index (TPI). The principle of the TPI is to calculate the difference between the altitude of a target point and that of its neighbour and then classify the slope position based on this difference. The formula of the TPI is as follows:

$TPI=Z-{{Z}^{*}}$ (3)

where Z represents the altitude of the target point, while Z^* represents the altitude of the neighbouring area. It can be observed that TPI is scale-dependent. Therefore, based on previous research, we chose 11*11 as the size of the calculated window and obtained the TPI of Hunan. Based on the TPI and slope of the target point, we obtained the slope position of Hunan. The classification criterion of slope position based on the TPI and slope is shown in Table 2 (Weiss, 2001; Gong, 2015).

Figure 3 shows the 6 terrain factors of Hunan Province. Previous studies have demonstrated that the extraction of terrain factors is scale-dependent (Tang, 2014). It has been well acknowledged that the altitude and slope establish the framework of the surface and its landforms (Zhou and Liu, 2006). Meanwhile, the slope is relatively sensitive to changes in resolution (Tang et al., 2003; Yang et al., 2013). Thus, we selected 8 typical sample areas in Hunan Province, including all geomorphic types (plains, tablelands, hills and mountains), and we resampled the DEM with a 30 m resolution to 50 m, 70 m, 90 m and 110 m; then, we calculated the altitude and slope in those 8 sample areas. We performed this analysis to investigate whether the effect of scale can influence the extraction of terrain factors.

2.3.2 Research on the relationship between terrain factors and distribution of paddy fields

The spatial distribution of paddy fields is the basis of rice production; thus, we investigated the impact of terrain factors on the paddy fields at both county level and provincial level.

At the province scale, we used the terrain distribution index (TDI) to compare differences in the distribution of paddy fields at different terrain levels. The formula of the TDI is as follows (Sun et al., 2004):

$P={\left( \frac{{{S}_{paddy e}}}{{{S}_{paddy}}} \right)}/{\left( \frac{{{S}_{e}}}{S} \right)}\;$ (4)

where P represents the TDI, which is a standardized and dimensionless index; e represents a type of terrain factor, such as slope or the surface relief degree. S_{paddy e} represents the area of the paddy fields at a level of terrain factor e. S_paddy is the total area of paddy fields. S_e represents the total area of a terrain factor at a given level. S is the total area of the region. A P value of larger than 1 indicates that the distribution of paddy fields at a class of terrain factor e has an advantageous position. A larger P value means that more paddy fields are distributed at this terrain level. Based on previous studies (Liang et al., 2010) and the characteristics of rice production in Hunan, we classified the altitude of Hunan into 13 levels; altitudes of higher than 1200 m and lower than 100 m are divided into two levels, respectively, and the altitudes ranging from 100 m to 1200 m are divided into a level every 100 metres. Similarly, we also divided the slope into 13 levels: one level comprises slopes of larger than 36 degrees, and slopes of less than 36 degrees are divided into a new level every 3 degrees. Because no studies have classified the surface relief degree and surface roughness, we applied quantile to classify the surface relief degree and surface roughness, which were also divided into 13 levels. In contrast to the four abovementioned terrain factors, we classified slope aspects into five levels (flat, ubac, semi-ubac, adret and semi-adret), and we classified slope positions into six levels (valley, uphill, flat, mid-hill, downhill and ridge). We argue that this classification can clearly describe the redistribution of radiation and soil nutrients, such as nitrogen.

At the county level, to compare the number of paddy fields in different counties, we used the ratio of paddy field areas in a county to the entire county area (R_PF) as an indicator to evaluate the amount of paddy fields. We obtained the average values of terrain factors from 102 counties in Hunan Province and calculated the correlation coefficients between the R_PF values and different terrain factors. Then, we selected terrain factors with correlation coefficients of greater than 0.5 to perform spatial statistics. Notably, because the slope aspects and slope position cannot be quantified, only altitude, slope, surface relief degree and surface roughness were used in this analysis at the county level.

We used the classical Moran’s I and Getis-Ord Gi* (Getis et al., 1992; Jin and Lu, 2009) to investigate the global spatial patterns of terrain factors and R_PF, and we also obtained hotspot maps. First, we calculated the Moran’s I of terrain factors and R_PF to measure the spatial autocorrelation; then, we calculated the Getis-Ord Gi* to map the hot and cold spots at different locations in Hunan.

2.3.3 Research on the relationship between terrain factors and rice growth

Investigating the relationship between terrain factors and rice growth can be divided into two steps. First, we explored the association between the terrain factors and environmental factors of rice growth. Based on the daily average temperature and duration of sunlight, we calculated the accumulated temperature (A_T) and accumulated sunlight (A_S) during the rice growth period (from April to the end of October) of each grid and then mapped the spatial distribution of the A_T and A_S values of Hunan Province. Moreover, we mapped the soil spatial distribution of Hunan Province based on the 1:1,000,000 soil dataset of China. Finally, we could analyse the impact of terrain factors on the environmental factors of rice growth by comparing the spatial distribution of the meteorological factors, soil, paddy fields and altitude of Hunan.

In the second step, we used the phenology of rice as a direct indicator to reflect the rice growth process and investigated the impact of terrain factors on the length of the rice growth period. We performed a correlation analysis on the terrain information and phenological information of double-cropping rice at the site scale and then selected the significantly correlated terrain factors to perform a stepwise regression with the corresponding phenological information.

2.3.4 Research on the relationship between terrain factors and rice yield

Similar to the methods used in section 2.3.2, to analyse the relationship between terrain factors and paddy fields at the county level, we first applied the correlation analysis between the per unit rice yield and the mean values of terrain factors of each county and then calculated the Moran’s I and Getis-Ord Gi* values of both the terrain factors and yield. Finally, we obtained the spatial patterns of the yield and terrain factors. Notably, when we established the relationship between terrain factors and yield, data from only 33 counties were included.

Table 3 shows the average slope and average altitude extracted from the DEMs with different resolutions. The observed effect of scale on terrain factors differs between different regions: with decreasing resolution, the average slope and average altitude decrease significantly in plains and tablelands; in steep mountainous areas, this decrease is more obvious. This result is consistent with many previous studies (Niu, 2010; Gong, 2015). However, in hilly areas, such as Changning County and Yongxing County, the average slope increases with decreasing resolution. As the resolution becomes coarser, the slope value become lower. In addition, this made the steepest areas flat so that the average slope in those sub-steep areas increased. Chen et al. (2006) also observed a similar phenomenon where, with the decreasing resolution of DEM, areas with slopes ranging from 8 to 15 degrees also increased. Admittedly, different scales of DEM showed some impact on the slope and altitude, but it is also evident from Table 3 that the changes in both altitude and slope are not as obvious in the plains and tablelands, where paddy fields are more widespread. Thus, the GDEM with a resolution of 30 m used in this study is sufficiently accurate to ensure the reliability of the extraction of terrain factors.

3.2.1 Spatial pattern of paddy field distribution at the provincial level

Figure 4 shows the terrain distribution index (TDI) values of paddy fields in Hunan Province at different levels. Figure 4a reveals that the distribution index (DI) of paddy fields is greater than 1 in areas with altitudes of less than 200 m and that the DI is close to 1 in areas with altitudes ranging from 200 m to 300 m. As the altitude increases, the DI decreases; in those areas above 900 m, the DI is close to zero. This change in DI reflects that most of the paddy fields are distributed below 300 m; at altitudes of greater than 900 m, there are few paddy fields in Hunan. When the altitude ranges from 300 m to 900 m, paddy fields are sparsely distributed. This spatial distribution of paddy fields is consistent with the distribution of farming activities in Hunan. Figure 4b shows the DI values of paddy fields with different slopes. It is clear that the DI is greater than 1 in areas where the slope is less than 9 degrees. As the slope increases, the DI tends to zero. No paddy fields appear to be distributed in areas with slopes of greater than 24 degrees. Figure 4c shows that the DI of a paddy field is greater than 1 if the surface relief degree is less than 140 m. Similar to the altitude and slope, with increasing surface relief, the DI decreases; if the surface relief degree is more than 400 m, the DI tends to zero. However, the DI seems to be sensitive to surface roughness: if the surface roughness is greater than 1.02, the areas of paddy fields decrease sharply, and if the surface roughness is greater than 1.1, the DI tends to zero. Surface roughness reflects complexity and erosion. The greater the surface roughness value, the more complex and eroded the surface is. Terrain factors have been viewed as the driving force of soil nutrients (Zhang et al., 2010; Zhan, 2009). Too much roughness could lead to soil erosion in these areas, thus causing decreases in the soil nutrients in these paddy fields. Therefore, roughness is a considerable terrain factor that may limit the distribution of paddy fields. Figure 4e shows the DI values associated with different slope aspects. It can be observed that the paddy fields in flat areas are more widespread. Additionally, it is worth noting that the DI values of the other four types of slope aspects, such as adret slope, are all near 1.0; additionally, the DI values of flat areas tend to be 1.5, which indicates that the distribution of paddy fields is not sensitive to changes in slope aspects. Previous studies have also pointed out that the impact of slope aspects is not significant for the spatial distribution of soil nutrients (Zhang et al., 2008), which adequately explains the low dependence of paddy fields on slope aspects. Figure 4f shows the relationship between the distribution of paddy fields and different slope positions. It can be observed that most paddy fields are distributed in mid-hill and flat regions due to their abundant water and heat resources, which can benefit rice production.

3.2.2 Effect of scale on the extraction of terrain factors

Table 4 shows the correlation coefficients between different terrain factors and the ratio of paddy fields to county areas (R_PF). We observed clear negative correlations between the R_PF values and all four terrain factors.

It can be observed from Table 5 that the values of the Moran’s I of R_PF and the four terrain factors are all greater than 0 and their standard Z scores are greater than 2.58, which is the threshold value of the corresponding standard Z score (99% Confidence Interval). This reflects that both R_PF and the chosen four terrain factors of Hunan Province exhibit significant spatial autocorrelation, which means that the distribution patterns of all these factors represent spatial clusters.

We mapped the spatial hotspots of the R_PF and four terrain factors at the county level (Figure 5). We found that the spatial distributions of the hotspots of all those terrain factors are almost the same and that they are consistent with the spatial distribution of cold spots of R_PF. In other words, there seemed to be a negative spatial relationship between the distribution of R_PF and terrain factors. There were evident hotspots of paddy fields in northern and central Hunan, which means that there were high R_PF values in these counties and their adjacent counties; cold spots were commonly located in west, southwest and southeast Hunan. The terrain condition exhibits the opposite spatial pattern: hotspots were aggregated in west, southwest and southeast Hunan, while cold spots were located in the northern and central parts. Additionally, although the hotspots of altitude are not as obvious in western Hunan, such as Sangzhi, Yongshun and Baojing counties, there are obvious hotspots of slope and relief in this area. This implies that the complexity of terrain conditions in west Hunan cannot be entirely ascribed to its high altitude. Similarly, although some counties in south Hunan, such as Dong’an County, have high altitudes, some paddy fields are located in these areas because the slope and degree of relief are not as high. Thus, even though the spatial distribution between paddy fields and terrain factors in Hunan Province showed a negative correlative tendency, there are still some abnormal areas in the mountainous areas of west and south Hunan.

3.3.1 Effect of terrain factors on environmental factors of rice growth

Based on the daily meteorological grid data and soil data, we mapped the spatial distribution of the environmental factors of rice growth. From Figure 6a, we found that the accumulated sunlight during the growing period (AS_g) of rice decreased from the Dongting Lake plain to its surrounding areas, which was similar to the spatial distribution of altitude in Hunan. Comparison of Figure 6b with Figure 6e revealed that the spatial pattern of accumulated temperature during the growing period (AT_g) is almost the same as its spatial distribution in the northern plain and southern hills. This demonstrates that the terrain condition can determine the spatial distribution of heat. Based on the information obtained from the spatial distribution of soil (Figure 6c) and paddy fields (Figure 6d) in Hunan Province, we found that fluvo-aquic soils and paddy soils are mainly distributed in the Dongting Lake plain in northern Hunan. In the central and southern parts, i.e., tableland areas, the soil types comprised red earth and paddy soil. Brown earth, yellow-brown earth, limestone soil and minor purplish soils are distributed in the hills of southern Hunan. In the mountainous areas of west Hunan, there are yellow earth, brown earth and limestone soil, but few paddy soils. Hence, terrain factors can influence the rice growth process through the spatial distribution of meteorological factors and soil types.

3.3.2 Effect of terrain factors on rice phenology

According to the phenological information of double-cropping rice at the site level, we calculated the correlation coefficients between phenology and the four terrain factors. The results of early rice are shown in Table 6. It was observed that the transplanting stage and altitude are negatively correlated, which means that the higher the altitude is, the shorter the transplanting stage. Moreover, there is also a negative correlation between the tillering stage and slope as well as surface roughness. In other words, the steeper the surface is, the shorter the tillering stage.

We modelled the relationship between the transplanting stage and latitude and the relationship between the tillering stage and slope and roughness using stepwise regression to investigate whether terrain factors can influence the change in early rice phenology. We obtained the following regression equation between the transplanting stage and altitude:

${{y}_{transplant}}=-0.023*{{x}_{altitude}}+36.835$ (1)

The R-square value of this equation is 0.57; in other words, altitude can account for almost 60% of the change in the transplanting stage of early rice. This equation also demonstrates that as the altitude decreases, the transplanting stage may be prolonged. However, the R-square of the equation of the tillering stage and slope or roughness was 0.39, which means that although the slope and roughness are correlated with the tillering of early rice, it is not substantial enough to explain this change.

Table 7 displays the correlation between terrain factors and late rice phenology. It can be observed that only altitude is related to phenology, and it has a negative correlation with the heading stage and mature stage. Similarly, the length between heading and tillering as well as the length between mature and heading are also negatively correlated with altitude. This means that with increasing altitude, the heading stage and mature stage will shift to earlier dates, and both the length between heading and tillering and the length between mature and heading may decrease.

Based on the results of correlation analysis, we used two phenological stages and two stage gaps of early rice as dependent variables, and we used altitude as an independent variable to establish the regression equations. We found that it is hard for altitude to account for the change in the heading stage of late rice and the length between heading and tillering because the R-squares of these two regression equations were 0.398 and 0.342, respectively. However, the altitude can sufficiently explain the change in the mature stage and the length between the heading stage and mature stage using the following equations:

${{y}_{mature}}=-0.07*{{x}_{altitude}}+129.81$ (2)

${{y}_{heading-mature}}=-0.028*{{x}_{altitude}}+41.65$ (3)

The R-square values of these two equations are 0.59 and 0.55, respectively, which reflects that the altitude had an impact on the change from mature to late rice as well as the length of the gap between the mature and heading stages.

To sum up, the slope, surface roughness and altitude are all related to the phenology of rice; of these variables, altitude shows the closest relationship with the phenology. For early rice, the altitude affects the transplanting stage: with increasing altitude, the transplanting date will occur earlier. For the late rice, the altitude can influence the mature stage and the length of the gap between the mature date and the heading date: with increasing altitude, the mature date will occur earlier and the length between the heading and mature dates will shorten.

Based on the rice yield of 33 counties from 2010 to 2012 in Hunan Province, we calculated the correlations between terrain factors and the final yield. Table 8 shows that there is a significant negative correlation between yield and the altitude, relief degree and surface roughness, while the correlation between the yield and slope is not significant. In these three factors, the correlation coefficient is only strong between altitude and yield (-0.584 95% CI). In summary, compared with the relationship between terrain conditions and the distribution of paddy fields or rice growth, although there was a relationship between terrain factors and rice yield, it was relatively weaker.

Table 9 and Figure 7 reveal the characteristics of the spatial pattern of rice yield and terrain factors. It was observed that the Moran’s I of both altitude and yield was greater than zero, and their standard Z scores were above the threshold. This means that the rice yields of 33 counties and altitude exhibit spatial clustering. Figure 7 further shows the map of the spatial hotspots of the yield and altitude. Generally, the distribution of hotspots of yield matched the cold spots of altitude. However, this match is not as consistent. In the areas around Dongting Lake, such as Nanxian, Xiangyin and Yiyang counties, although the altitude is low, these areas also contain the cold spots of yield. Moreover, while Taoyuan County is located in an area of altitude hotspots, i.e., the transition zone between the hills of central Hunan and the mountains of west Hunan, it is also an area of yield hotspots. This phenomenon demonstrates that even though terrain factors can impact the spatial patterns of rice yield, the influences of other factors appear to be more important.

Terrain factors exhibit obvious impacts on the spatial distribution of paddy fields in Hunan Province at both the province scale and the county scale. At the provincial level, we found that most paddy fields were distributed in the northern plains and central hills, where the altitude is below 300 m, the slope is less than 9 degrees and the relief is less than 140 m. Additionally, most paddy fields are located in flat areas. Meanwhile, we found that the distribution of paddy fields is not sensitive to the slope position and roughness. Although some studies have shown that the vegetation in Hunan Province is influenced by the slope aspect (Wang et al., 2004), our results demonstrated that rice production is not related to the slope aspect because the spatial anisotropy of soil nutrients resulting from slope aspects can be reduced by agricultural management measures (Zhang et al., 2015). At the county level, R_PF is negatively correlated with the altitude, slope, relief degree and surface roughness. Moreover, both the R_PF and these terrain factors exhibit spatial autocorrelation. The spatial pattern of R_PF also shows a negative relationship with the spatial patterns of these terrain factors.

Rice is a short-day crop that prefers a warm and humid environment. Because transplanting is the main method of cultivation in rice production in Hunan, rice growth does not lack water; thus, temperature and sunlight are the two direct environmental factors affecting rice production. It can be observed that terrain conditions can directly influence the spatial distributions of temperature and sunlight: the spatial distributions of A_T and A_S are similar to the spatial pattern of altitude in Hunan Province. Although the flat Dongting Plain in northern Hunan is very suitable for rice cultivation, the temperature conditions are better in the central and eastern parts of Hunan, such as Changsha, Xiangtan, Zhuzhou and Hengyang. Previous studies have pointed out that the rice yields per unit in Xiangtan and Zhuzhou were higher than those in Changde and Yueyang of northern Hunan (Qing et al., 2007). Meanwhile, some other environmental factors were also nonnegligible for rice production. For example, Huaihua, a city located in the hilly area of western Hunan, has the basic conditions for double-cropping rice growth, but there are few double-cropping rice areas distributed in this region, where the average altitude ranges from 400 m to 800 m and the A_T during the growth period is over 5000 degrees Celsius. This is because the basic soils in this area are purplish soil and yellow-brown earth. Compared to the red earth and paddy soil that are more beneficial to rice growth (Xi, 1994), the parent material of purplish soil is relatively loose, which indicates that terraced fields should be built to plant rice here. In summary, terrain factors can determine the spatial patterns of some environmental factors and thus indirectly influence rice growth.

Compared with the environmental factors of rice growth, such as meteorological conditions and soil types, the phenology of rice can directly reflect the process of rice growth. Our results show that the altitude, slope and surface roughness are related to the phenology of double-cropping rice. Among these factors, altitude may influence the transplanting stage of early rice, mature stage of late rice and the interval between the heading and mature stages. For early rice in high-altitude areas, if the transplant date is late, it is difficult to harvest rice and to transplant late rice due to the limited heat. Thus, the higher the altitude is, the earlier the transplanting stage. Furthermore, altitude also impacts the mature stage of late rice. Because of the low temperature, the harvesting stage in hilly and mountainous areas are often earlier than that in plains. This can avoid a short interval between the heading stage and mature stage and insufficient grain-filling (Liu et al., 2012), which also suggests that the per unit area rice yield is relatively lower in high-altitude areas.

Compared with the impact of terrain factors on paddy field distribution and rice phenology, the impact of terrain factors on the final yield is not as significant. Only altitude has a negative correlation with the rice yield. Similar to the spatial distribution of paddy fields, the spatial pattern of rice yield also shows a clustering feature and has a negative correlation with the spatial pattern of altitude. However, when we compared the spatial distribution of yield to the spatial pattern of altitude, we found some abnormal areas: the areas where the yield per unit area is the highest are often distributed in areas where paddy fields are the next-densest and the altitude is moderate (such as Ningxiang County, Xiangxiang County and Taoyuan County). This phenomenon can be ascribed to the better conditions of temperature and sunlight and agricultural management compared to the plains in northern Hunan (e.g., Dongting Lake Plain). Based on the spatial patterns of paddy fields and environmental factors of rice, we argued that the problem with rice production in Hunan Province is the spatial mismatch in the distribution of paddy fields and the per unit area rice yield: although paddy fields are distributed very densely in the northern plains of Hunan around Dongting Lake, the per unit area rice yield in this area is lower than that in eastern and central Hunan due to the spatial distribution of heat. This impedes efficient and scale rice production in Hunan Province. Hence, in the northern plains of Hunan, it is necessary to select spring-cold-tolerant early rice varieties as well as autumn-cold-tolerant late rice varieties and to implement more management measures to increase the per unit area yield, which can benefit the optimal configuration of rice production.

There are some limitations in our research. First, the yield data at the county level are still insufficient. When analysing the relationship between rice yield and terrain factors, we only collected yield data from 33 counties; in future research, we hope to collect data from the statistical yearbook of each county to expand data. Moreover, we did not take some non-environmental factors into consideration, such as the amounts of fertilizer and pesticide, the use of agricultural machinery and so on, which can influence the rice growth and final yield because these data are difficult to obtain at the county level. In the next step, we would like to cooperate with the agriculture departments of local governments to collect specific agricultural management data.