Based on the core collection of Web of Science (WoS) and China National Knowledge Infrastructure (CNKI), the research collected 277 articles related to the distribution of plant roots, including the vertical distribution data of plant roots at 281 research sites and 786 sections (Figure 1, references from Appendix). Among them, 20 (2.5%) sections are divided into two layers, 103 (13.1%) sections are divided into three layers, and 663 (84.4%) sections are divided into more than four layers. Among all sections, the maximum depth of 576 sections (73.3%) is less than 100 cm, and the maximum depth of 167 sections (21.2%) is between 100 and 200 cm. In addition to collecting and sorting out the root distribution data of each profile, this study also recorded other detailed information such as the geographic location (longitude, latitude, altitude), soil type, annual precipitation, annual average temperature, root measurement type (total, fine and thick), measurement methods, measurement items (root biomass, root length, root length density, etc.), sampling depth and others for each sample point. Because of the different measurement items of root distribution, this study will uniformly convert them into a proportional form to compare and analyze them.

The classification of vegetation types adopts the International Geosphere-Biosphere Program (IGBP) (Sweeney, 1997; Zeng, 2001; Friedl et al., 2010). This program divides all land cover types into 17 categories, including 12 types of natural vegetation (including wasteland) and five types of no vegetation cover. In this study, a land cover type map was drawn based on Moderate Resolution Imaging Spectroradiometer (MODIS) remote sensing data products (Figure 1). All root profiles collected were classified according to the IGBP classification scheme. Classification results are evergreen needleleaf forests (n = 43), evergreen broadleaf forests (n = 46), deciduous needleleaf forests (n = 1), deciduous broadleaf forests (n = 176), mixed forests (n = 2), closed shrublands (n = 33), open shrublands (n = 63), woody savannas (n = 1), savannas (n = 10), grasslands (n = 54), croplands (n = 315) and barren (n = 41). It should be noted that, although parameters of these vegetation types have been optimized in this study, the ET_a of deciduous needleleaf forests, mixed forests, and woody savannas were not analyzed statistically due to the small number of samples (n < 3).

In this study, three cumulative root distribution functions were selected for parameter optimization, i.e., finding the optimal parameters of the root distribution function within a given range based on the measured data. These three functions are all fitted from global root distribution data and consider several types of vegetation (Jackson et al., 1996; Schenk and Jackson, 2002a; Zeng, 2001). The cumulative distribution functions of the three root systems are shown in Eqs 1–3. Eq. 1 is a single factor function of the vertical distribution of root systems of major terrestrial communities in the world (Gale and Grigal, 1987). This equation has simple parameters and wide applications and is widely cited (Jackson et al., 1996). Zeng (2001) developed Eq. 2 using the single factor function (Jackson et al., 1996), considering the depth of the root and refined it to obtain a two-factor function. This equation and associated parameters were used in the open ECMWF model and the global reanalysis dataset. Eq. 3 is the LDR curve proposed by Schenk and Jackson (2002a), based on the relationship between root system depth and root system distribution. Y = 1 − β d (1) Y = 1 − 1 2 ∗ ( e − a ∗ D + e − b ∗ D ) (2) r ( d ) = R m a x 1 + ( d D 50 ) c   (3)

In the equation, Y is the cumulative root distribution ratio of the soil surface to the depth d (cm), the range is [0,1]; β is a single parameter with no physical significance; a and b are typical plant-related parameters, and the unit is m^{− 1}; D refers to the soil depth, in m; r(d) refers to the cumulative root number (or biomass, length) above the profile depth d, corresponding to the R m a x unit; R m a x refers to the total root number in the profile (or total biomass, total Length); D 50 refers to the depth when r(d) = 0.5 R m a x , in cm; c refers to a dimensionless parameter, which is only related to plant types.

Since Eq. 3 describes the cumulative distribution function of the root system, the unit of r(d) in the equation will with the change in R m a x . To unify the units of each function and make it easier to calculate the root distribution ratio of each layer of the plant, Eq. 3 is converted into a root cumulative distribution function, as shown in Eq. 4: Y = 1 1 + ( d D 50 ) c   (4)

In Eq. 4, Y is the cumulative proportion of the root system, and the range is [0,1]; D 50 is the root system depth when Y = 0.5, in cm; the other parameters are the same as in Eq. 3.

Root Mean Square Error (RMSE) ranged from 0 to 1 was chosen as a quantitative index (Kennedy and Neville, 1986), which is given by: R M S E = ∑ ( P i − O i ) 2 n (5)

In Eq. 5, O i and P i represent the proportion of observed and predicted roots in layer i, and n is the number of root layers. The optimization ranges of the parameters of the single factor function (Eq. 1) are fixed at [0.9,1] (Jackson et al., 1996). The range of the four parameters (a, b, D 50 , c) in the two-factor function (Eq. 2) and LDR curve (Eq. 4) is defined between the maximum and minimum values, that is, the ranges of a, b, D 50 , and c are 4.372 to 10.74, 0.978 to 2.614, 5 to 28, and -2.621 to -1.176, respectively (Zeng, 2001; Schenk and Jackson, 2002a).

In this study, each vegetation type will be fitted according to three root distribution models, and the three mean RMSE will be calculated according to the three fitting results. The root distribution model with the smallest mean RMSE was selected for each vegetation type.

A one-dimensional SPAC model was constructed in this study, including a soil infiltration module, a soil water movement module, a topsoil evaporation module, and a root water absorption module. The model’s basic assumption is that the water in the cell mainly moves vertically, and the water movement in the horizontal direction is ignored. The SPAC model concept diagram was shown in Figure 2.

The root distribution of twelve vegetation types in China was parameterized based on three types of global-scale root cumulative distribution functions and root distribution data from 786 plant roots. The results are shown in Figure 3. The results show that there are four types of optimal functions as single factor functions, namely evergreen needleleaf forests (β = 0.967); deciduous needleleaf forests (β = 0.983); woody savannas (β = 0.912); savannas (β = 0.908). Among them, savannas have the smallest β, and deciduous needleleaf forests have the largest β. It is also evident from the results that there are five types of optimal functions as two-factor functions, namely evergreen broadleaf forests (a = 8.28, b = 2.45), deciduous broadleaf forests (a = 5.51, b = 1.66), mixed forests (a = 9.71, b = 2.61), crops (a = 7.78, b = 2.18) and barren (a = 5.89, b = 1.51). From the results, three types of optimal functions as LDR function, namely closed shrublands ( D 50 = 20.21, c = -1.83), open shrublands ( D 50 = 17.74, c = -1.85), and grasslands ( D 50 = 13.47, c = -1.79). Among them, D 50 of grasslands is the smallest, and D 50 of closed shrublands is the largest. Based on the parameter optimization results, the average value of each vegetation type is taken as the vegetation type parameter (Supplementary Table S1).

A statistical analysis of the data collected on the root distribution depth revealed that 94.5% of the plant root profile maximum depth is within 200 cm (Jackson et al., 1996; Schenk and Jackson, 2002a; Schenk and Jackson, 2002b). However, most of the collected articles did not specify the maximum root depth of the root profile (Schenk and Jackson, 2002a). Therefore, this study uses the maximum sampling depth of 200 cm as the maximum root depth to analyze the vertical distribution characteristics of the root system.

The processed data were compared to the root distribution curve obtained by optimizing the parameters of the root distribution ratio of 12 types of plantation in each layer (Figure 4). In general, the root distribution simulation curve (line) basically conforms to the changing trend of the measured data (point). The simulation curves are all single-peak curves. As the depth of the soil layer increases, the proportion of roots first increases and then decreases, and the peak value is often found at a depth of 10–20 cm. Although the proportion of roots of some vegetation in the measured data tends to decrease with increasing soil depth, a large number of research results show that the distribution of plant roots mainly increases with increasing soil depth, and the root distribution first increases and then decreases.

The distribution ratio of shallow roots (0–30 cm) can reflect the depth of the root distribution to a certain extent; that is, the higher the ratio of shallow roots, the shallower the root distribution (Jackson et al., 1996). According to the simulation curve of the vertical distribution of roots of 12 vegetation types, the average distribution of the shallow roots is about 70.6%. In general, the root systems of the grassland (3 species) are relatively shallow, with an average shallow root system distribution rate of 89.6%. Trees (5 species) have a deep root distribution, with an average shallow root distribution ratio of 62.0%. The depth of shrubs and crops root distribution is between those of grasslands and trees. Among all vegetation types, savannas have the shallowest root system distribution, and the distribution ratio of the shallow root systems is 94.5%. The deciduous needleleaf forests have the deepest distribution of roots, and the distribution of shallow roots is 40.2%.

The ET_a, T_a and E_a of China in 2015 were calculated based on the calculation of the SPAC model (Figure 5). The ET_a showed a gradually decreasing trend from southeast to northwest (Figure 5A), ranging from 18 to 1,172 mm/y, with an average value of 342.2 mm/y ± 244.2 mm/y, and a median value of 273.2 mm/y. The T_a range is between 0 and 700 mm/y, with an average value of 123.9 ± 98.1 mm/y, and the median value is 104.7 mm/y. The E_a in China exhibits prominent regional distribution characteristics, showing lower value in the Qinghai-Tibet Plateau and desert areas while highest in the semi-humid regions. The E_a range is 1–968 mm/y, with an average value of 218.3 ± 183.0 mm/y, and the median value is 161.2 mm/y, with a decreasing trend from southeast to northwest.

In 2015, the average ET_a order of nine different vegetation types in China’s land area was evergreen broadleaf forests (773 mm/y) > savannas (618 mm/y) > evergreen needleleaf forests (612 mm/y) > deciduous broadleaf forests (451 mm/y) > croplands (387 mm/y) > closed shrublands (287 mm/y)> grasslands (228 mm/y) > open shrublands (180 mm/y) > barren (151 mm/y) (Supplementary Table S2). The average ET_a of evergreen broadleaf forests is the highest, and the barren is the lowest. The ET_a of the three tropical and subtropical vegetation types, viz., evergreen broadleaf forests, savannas and evergreen needleleaf forests, are much higher than the ET_a of other vegetation types. The average ET_a of closed shrubs is much higher than that of open shrubs. It is also evident from Supplementary Table S2 that the average T_a (299 mm/y) and E_a (474 mm/y) of evergreen broadleaf forests are the highest. The average T_a (53 mm/y) of open shrublands and the average E_a of barren (85 mm/y) are the lowest. The average ET_a of open shrublands is higher than that of the barren, but the average T_a is lower than that of the barren. The average E_a of nine vegetation types is generally higher than the average T_a, a relatively large proportion. The average T_a accounted for about 24–51% of ET_a, and the average E_a accounted for 49–76% of ET_a. It should be noted that the ET_a of deciduous coniferous forests, mixed forests and woody savannas are not analyzed due to limited root systems data.

Among the three root distribution functions, the parameter β in the single factor function and D 50 in LDR function may reflect the depth of root distribution to a certain extent (Jackson et al., 1996; Schenk and Jackson, 2002a). Although the parameters a, b, and c do not directly reflect the depth of root distribution, they may also indirectly reflect the relationship to the root distribution by calculations. Therefore, this paper selects the four factors of mean annual temperature (MAT), mean annual precipitation (MAP), latitude, and altitude to analyze the correlation between plant root distribution parameters and explore the relationship between environmental factors and root distribution parameters.

The results showed that the parameter β has a significantly negative correlation with MAP and MAT, and a significantly positive correlation with latitude (Supplementary Table S3), which the correlation with the MAT is the largest (r = -0.845, p < 0.01). With increasing precipitation and temperature, the distribution of plant roots becomes shallower. As latitude increases, the temperature and precipitation decrease, and the distribution of plant roots become deeper. The parameter D 50 is negatively correlated with the average annual precipitation and has no significant correlation with the other three factors. It shows that the root distribution becomes shallower as precipitation increases. All root distribution parameters correlate significantly with MAP (p < 0.01), indicating that the influence of precipitation on root distribution is more significant than that of temperature and latitude. This trend may be because plants need to develop deeper roots to absorb water and nutrients in areas with low rainfall and relatively low soil moisture. On the contrary, in areas with high rainfall, the water content of the shallow soils is sufficient for plant growth and utilization, and the shallow root system can meet its growth needs (Fan et al., 2017). Some studies have shown that root distribution strongly correlates with soil moisture. Insufficient surface soil moisture capacity will cause roots to grow deeper to find water sources (Yu et al., 2007; Yu et al., 2015; Fan et al., 2017). The depth of water infiltration and the demand for evaporation are the main factors affecting the vertical distribution of root systems. Deep root systems are less likely to occur in humid areas (Dawson and Pate, 1996; Pregitzer et al., 2000; Powers and Peréz-Aviles, 2013; Fan et al., 2017). Previous studies have shown that in regions rich in water resources, the root distribution does not need to grow deeper but will still grow laterally, resulting in a larger proportion of shallow roots (Fan et al., 2017). However, the size of plant roots will increase with the increase in the aerial part of the plant, so that the tree roots are larger than shrub roots, and shrub roots are larger than grassroots (Schenk and Jackson, 2002b).

Parameters a and b have the same correlation, which is significantly positively correlated with MAP and MAT (p < 0.01) and significantly negatively correlated with latitude (p < 0.01). However, it is opposite to the correlation of parameters β. In the two-factor function, the larger a and b, the more shallow the root distribution. The parameter c in the LDR function reflects the plant type, which is significantly positively correlated with MAP (p < 0.01) and significantly negatively correlated with latitude (p < 0.05), indicating that the plant type has some correlation with MAP and latitude. For example, in the lower latitudes of southeast China, which is in a humid or semi-humid area, the vegetation mainly consists of tall trees (Su et al., 2015; Xiang et al., 2015). However, in the arid and semi-arid areas of high latitudes regions of northwest China, the vegetation is mainly shrubs, grasslands, and other low vegetation (Jia et al., 2012; Chen et al., 2017; Du et al., 2017).

Although the root distribution functions and parameters of different vegetation types were obtained in this study, there are also some differences in the root systems of the same plant under different growing environments. Multiple regression analyses on the root system distribution parameters and environmental factors were conducted, to quantify the relationship between each other (Supplementary Table S4). The results show that the adjustment R ² of parameter β is the best ( R a d j 2 = 0.631). Except for parameter c, the regression results for the remaining four parameters are Sig (P) < 0.001, indicating that the four fitted multiple linear regression equations are statistically significant when the significance level is 0.01. However, the equation does not consider some factors such as soil properties, vegetation characteristics and climate characteristics (Schenk and Jackson, 2002a; Laio et al., 2006). The results are uncertain but statistically significant. Therefore, it has a certain guiding significance.

The simulation results show that as the soil depth increases, the root ratio first increases, peaks around 10–20 cm, and gradually decreases (Figure 4). However, the measured root distribution has two trends. The first is that as the soil depth increases, the proportion of roots gradually decreases; the second is the same as the simulation results. It may be because, under the field measurement conditions, the amount of root coefficients is mainly based on range statistics (such as 0–10 cm, 0–20 cm). It is impossible to measure the proportion of the root system within 1cm, and it is impossible to accurately obtain the change in the surface layer (0–20 cm). Therefore, the measured data tends to decrease gradually. In addition, the distribution of plant roots will also be affected by the local climate, so that the plant roots will exhibit different distribution trends in different climate zones. Studies have shown that water infiltration depth and evaporation demand are the main factors affecting the vertical distribution of roots (Schenk and Jackson, 2002b), and root distribution have a strong correlation with soil moisture (Yu et al., 2015; Wang B. et al., 2016; Wang Y. et al., 2016). Soil moisture is a relevant independent variable in some root distribution models (Jarvis, 1989; Wu et al., 2020). Therefore, many field measurements of the root system show that the root system decreases as depth increases (Guo et al., 2016; Feng et al., 2017; Chen et al., 2018). Studies have also shown that the vertical distribution of roots first increases and then decreases (Hao et al., 2013; Jian et al., 2015; Li et al., 2015).

The vertical root distribution is usually assumed following a single-peak curve in the root distribution model. This trend can also be verified in the model where plants absorb water from the soil profile (Ojha and Rai, 1996; Wu et al., 1999; Li et al., 2010). In addition, Schenk and Jackson (2002a) pointed out that the average D 50 of global vegetation is mainly between 5 and 28 cm, indicating that the peak value of root systems of most vegetation in the world ranged is between 5–28 cm. It also proves that the simulated curve in this article may better reflect the actual trend of the root distribution than the measured data.

Of all vegetation types, crops are most affected by human activities (Schenk and Jackson, 2002a). However, this study did not consider the impact of human management practices on crops. The root distribution curve still has a good fit result (RMSE = 0.079) (Figure 4).

This study focuses on the ET_a of different vegetation types and does not consider and use water bodies and wetlands with high ET_a capacity. Therefore, the results may differ slightly from those of other studies. But the overall spatial distribution trend is consistent with other studies and has certain credibility. For example, it is evident from Figure 5 that the trend of ET_a results in 2015 is similar to previous studies, showing a decreasing trend from southeast to northwest (Li et al., 2017; Bai and Liu, 2018; Ma N. et al., 2019). The trend estimated from the GLEAM dataset (Bai and Liu, 2018) is most similar to our study.

While applying the SPAC model to regional simulation, this study also tried to partition the ET_a of China’s land area and obtained the spatial distribution of T_a and E_a. Among them, the spatial distribution trend of average T_a is similar to that of MAT, and the spatial distribution trend of average E_a is identical to that of MAP. The main reason is that temperature is the main factor controlling plant transpiration in this model, and precipitation is the main factor influencing soil evaporation. Gonzalez Miralles et al. (2011) obtained the spatial distribution of worldwide evaporation for the first time and found that the evaporation is the highest near the equator. The higher the latitude, the lower the evaporation. The general trend in China is that evaporation from the southeast is higher than from the northwest, which is consistent with this study.

This study shows that the average T_a in different vegetation regions in China’s terrestrial land accounts for about 36%, and the average E_a accounts for about 64%. Gu et al. (2018) estimated the worldwide ET of different biomes based on the optimized remote sensing method, and the T/ET range is between 0.29 and 0.72. Due to differences in the proportion of ET of different scales and ecosystems (Hu et al., 2009; Kool et al., 2014; Talsma et al., 2018), there are significant errors in the evaporation of soil estimated from each model (Talsma et al., 2018). Therefore, the results obtained in this research are consistent with Gu et al. (2018).

There are some differences in ET_a under different vegetation cover (Zhang et al., 2001; Peters et al., 2011; Yang et al., 2012; Zheng et al., 2016; Du et al., 2019). The maximum ET_a of the evergreen broad-leaved forest is 773 mm/y, and the minimum of barren is 151 mm/y. Perhaps this is because the evergreen broadleaf forests are mainly located in tropical and subtropical humid areas with sufficient water and energy, so the ET_a is the highest. The barren is primarily located in arid regions with high temperature, low precipitation, low soil water content, less vegetation, and weak transpiration and evaporation capacity. Therefore, ET_a of the barren is the lowest. Liu et al. (2010) estimated the ET_a under different land-use types in the Skeleton Creek urban area. The results showed that the ET from the forest was the highest, around 850mm, except for open water and wetlands. Li et al. (2017) studied the changes in ET under different vegetation, showing that the impact of deforestation on ET is much more significant than other types of land cover. It also reflects that the ET capacity of forests is much greater than that of other vegetation. Zhang et al. (2001) studied the relationship between vegetation change and average annual ET at the regional scale. They found that the ET in forested catchments is higher than in grassed catchments.

The ET_a under different vegetation types varies due to variation in climate types, geographic distribution and plant characteristics, and the main influencing factors will also change to some extent. Many studies have analyzed the influencing factors of ET_a in different regions and different vegetation types. The main influencing factors are precipitation, temperature, radiation, vegetation types, soil moisture, leaf area index, etc. (Liu et al., 2019; Lu et al., 2011; Ma Z. et al., 2019; Peel et al., 2010; Sun et al., 2020; Zhang et al., 2001). Studies have shown that precipitation is the main factor affecting the actual spatial distribution of ET in the arid and semi-arid regions of northwest and northeast China. In the humid and semi-humid areas of southeast China, shortwave radiation, precipitation, temperature, and soil moisture are the main controlling factors (Sun et al., 2020). Therefore, according to the ET_a estimation results of different vegetation types, this paper examines the main factors influencing the ET_a under different vegetation types through correlation analysis. The results are shown in Figure 6. It is evident from the results that the four influencing factors were significantly correlated with the actual annual ET of nine vegetation types. The precipitation and the ET_a of all vegetation were significantly positively correlated (p < 0.01) and impacted all vegetation types considerably. The results show that among the four factors, precipitation has the most significant impact on the ET_a, and it is the main factor affecting the ET of the nine vegetation types (Zhang et al., 2001). Except for evergreen needleleaf forests, evergreen broadleaf forests and open shrubs, latitude has a significant negative correlation with other vegetation types, which may be related to the correlation between latitude and types of climate. Except for precipitation, the temperature significantly negatively correlates with most vegetation types (p < 0.01). However, the correlation coefficients between temperature and other vegetation are generally low (|r|<0.2) except for closed shrublands (|r| = 0.663).

In addition to these influencing factors, plant physiological characteristics and soil texture also affect the ET capacity of plants (Schenk and Jackson, 2002a; Xue et al., 2020). Some studies have shown that the available water content of plants and the morphology of the plant growth somehow affect ET (Zhang et al., 2001; Kotani and Sugita, 2005; Balogun et al., 2009). The soil texture (such as sand, silt or clay) where vegetation grows affects water infiltration, which in turn affects the plant root depth (Fan et al., 2017), and also has some impact on ET_a (Schenk and Jackson, 2002a).