This study area is located in the Fukang state-owned forest region, where the north slope of Mt. Bogda, the main peak of the eastern Tianshan Mountains, is found. It is a typical complete continental mountainous landscape region of Inner Eurasia, which integrates glaciers, snowpack, forest, grassland, and alpine lakes (Zhou et al., 2009). The total annual sunshine duration is 2,600 h and the average annual temperature is below 1.9°C; the winter is long and cold with –12.4°C being the average temperature in the coldest month, while the summer is short and warm with 15.9°C being the average temperature of the hottest month (Wang et al., 2009; Wang et al., 2015). The weak wet and cold water vapor from the North Atlantic Ocean and the Arctic Ocean brought by the westerly circulation in the Northern Hemisphere is blocked and uplifted by the tall mountains of the Tianshan Mountains, forming topographic rain on the northern slope of the windward face (Hu et al., 2014), enabling the average annual precipitation in this region to reach 520.6 mm (Ma et al., 2010). The soil here consists mainly of taupe alpine forest gray-brown soil, with a thin layer of forest residue covering the ground surface, followed by humus layer and leaching layer, and gradually transitions to a sedimentary clay layer that contains white pseudomycelial calcium carbonate deposition nuclei. The vegetation consists mainly of pure spruce stands of P. schrenkiana in temperate mountain coniferous forest. However, one can find scattered trees such as Populus talassica, Sorbus tianschanica, and Betula tianschanica in the forest margins and gaps. In the sparse forest understory are the shrubs Cotoneaster melanocarpus, Berberis heteropoda, Rosa spinosissima, Spiraea hypericifolia, Sabina pseudosabina, and Lonicera hispida, and herbaceous plants such as Alchemilla tianshanica, Geranium divaricatum, and Aegopodium podagraria.

Both TF and TFR increased with I at all three elevations of 2,200 m, 1,800 m, and 1,450 m on the northern slope of Mt. Bogda ( Figure 1 ). For each, the relationship between TFR and I fitted using Eq. (7a) was significant: 2,200 m (R ² = 0.973, p< 0.001), 1,800 m (R ² = 0.966, p< 0.001), and 1,450 m (R ² = 0.983, p< 0.001) ( Figure 1 ). The estimated parameter a ₁ ( ± SE) was 2.24 ± 0.65, 3.50 ± 0.97, and 2.05 ± 0.49, while the parameter a ₂ ( ± SE) was 0.922 ± 0.085, 0.797 ± 0.082, and 0.942 ± 0.071 at the 2,200-m, 1,800-m, and 1,450-m elevation sites, respectively ( Figure 1 ).

Accordingly, when I was 5 mm, 10 mm, and 25 mm, TFR ( ± SE) was 9.9 ± 3.6%, 18.7 ± 4.3%, and 43.6 ± 3.8% at 2,200 m; 12.6 ± 4.4%, 22.0 ± 4.8%, and 45.6 ± 4.0% at 1,800 m; and 9.4 ± 2.8%, 18.0 ± 3.4%, and 42.6 ± 3.0% at 1,450 m, respectively ( Figure 1 ). Thus, for a given I, TFR was largest and smallest at 1,800 m and 1,450 m, respectively ( Figure 1 ).

Both SF and SFR increased significantly with I at all three elevation sites ( Figure 2 ). The relationship between SFR and I fitted via Eq. (8a) was found significant at 2,200 m (R ² = 0.892, p< 0.001), 1,800 m (R ² = 0.795, p< 0.001), and 1,450 m (R ² = 0.974, p< 0.001) ( Figure 2 ). The estimated parameter b ₁ ( ± SE) was 0.0164 ± 0.0022, 0.0188 ± 0.0036, and 0.0159 ± 0.0010, while the parameter b ₂ ( ± SE) was 5.25 ± 2.42 mm, 8.34 ± 3.13 mm, and 3.75 ± 1.22 mm at the three elevation sites of 2,200 m, 1,800 m, and 1,450 m, respectively ( Figure 2 ). Thus, stemflow first emerged at the 1,450-m elevation site, and then at the 2,200-m elevation site, and last at the 1,800-m elevation site ( Figure 2 ). However, according to the parameter b ₁, SFR accelerated the most at 1,800 m elevation, followed by the 2,200-m elevation, and least at the 1,450-m elevation ( Figure 2 ).

When I was 42 mm, SFR was 0.60 ± 0.13%, 0.63 ± 0.22%, and 0.61 ± 0.06% at the three elevation sites of 2,200 m, 1,800 m, and 1,450 m, respectively ( Figure 2 ). Thus, they are all ca. 0.60%, and so I is in the range of 0–42 mm, and SFR was determined by the threshold I of the parameter b ₂. That is, the larger threshold I, the smaller SFR was when I was the same ( Figure 2 ).

As ICR decreased, the IC increased but its acceleration decreased gradually with I at the three elevations ( Figure 3 ). Thus, there was an asymptote for IC when I was large enough and its acceleration was close to 0. There was a significant relationship between ICR and I as fitted by Eq. (9a) at each elevation site: 2,200 m (R ² = 0.975, p< 0.001), 1,800 m (R ² = 0.976, p< 0.001), and 1,450 m (R ² = 0.962, p< 0.001) ( Figure 3 ). The estimated parameter d ₁ ( ± SE) was 0.066 ± 0.005, 0.066 ± 0.005, and 0.060 ± 0.006, whereas the parameter d ₂ ( ± SE) was 1,647 ± 100, 1,604 ± 96, and 1,768 ± 136 at the three elevation sites of 2,200 m, 1,800 m, and 1,450 m ( Figure 3 ). Hence, d ₂/100 represents the saturation value of IC, which was 16.47 ± 1.00 mm, 16.04 ± 0.96 mm, and 17.68 ± 1.36 mm at the 2,200-m, 1,800-m, and 1,450-m elevation sites, respectively ( Figure 3 ).

Accordingly, when I was 5 mm, 10 mm, and 25 mm, ICR ( ± SE) was 93.1 ± 4.9%, 80.0 ± 3.5%, and 53.4 ± 4.0% at 2,200 m; 90.1 ± 4.6%, 77.4 ± 3.3%, and 51.8 ± 3.8% at 1,800 m; and 91.6 ± 5.7%, 79.7 ± 4.2%, and 54.9 ± 4.8% at 1,450 m, respectively ( Figure 3 ). Thus, ICR was smallest at the 1,800-m elevation site, and when I was low, ICR was largest at the 2,300-m elevation site, and when I was heavy, ICR was largest at the 1,450-m elevation site ( Figure 3 ).

TFR decreased significantly with DBH (r = –0.870, p< 0.001) and HWR (r = –0.862, p< 0.001), yet increased insignificantly with PD (r = 0.244, p = 0.445), but decreased insignificantly with LAI (r = –0.391, p = 0.209, Figure 4Aa–d ). By contrast, ICR increased significantly with both DBH (r = 0.874, p< 0.001) and HWR (r = 0.844, p< 0.001), and decreased insignificantly with PD (r = –0.245, p = 0.444) and increased insignificantly with LAI (r = 0.377, p = 0.227, Figure 4Ca–d). The trends of SFR were the same as those of ICR with respect to DBH, HWR, PD, and LAI, but the correlations were considerably weaker. Finally, ICR increased insignificantly with DBH (r = 0.026, p = 0.936), HWR (r = 0.487, p = 0.108), and LAI (r = 0.359, p = 0.251), but decreased insignificantly with PD (r = –0.011, p = 0.973, Figure 4Ba–d ).

With increasing CD, ICR increased sharply at first and then gradually tapered off ( Figure 5A ). After the double-reciprocal transformation, there was a significant linear relationship (R ² = 0.497, F = 9.86, p = 0.011), whose slope and intercept ( ± SE) were 0.0258 ± 0.0082 and 0.0182 ± 0.0003, respectively ( Figure 5B ). Thus, the maximum predicted ICR was 55.01 ± 0.86% ( Figure 5A ). When CD was 1.36 ± 0.49 Mg C hm⁻², ICR was the half of its maximum value; when CD was 20 Mg C hm⁻², ICR was 51.51 ± 1.24% or 93.6 ± 2.3% of the maximum ICR attainable ( Figure 5A ).

Tree crown allocation of rainfall is a crucial yet an understudied component of the forest water balance (Allen et al., 2020). The complex crown structure determines the allocation pattern of water and its relative quantities, which can change depending on the age and species of trees, and the biome, and other factors (Gonzalez-Ollauri et al., 2020). For example, the maximum interception and held rainfall of broad-leaf, scale-leaf, and needle-leaf types is about 2.0 mm, 3.7 mm, and 4.3 mm, respectively, differences that translate into a significantly higher rainfall interception effect from the crowns of coniferous than broad-leaf trees; hence, the crown throughfall ability in coniferous trees is weaker than that in broad-leaved trees (Klamerus-Iwan et al., 2020). During the observation period of the present study, TFR ranged from 44.3% to 50.0%, while ICR ranged from 49.6% to 55.4% for a pure coniferous forest. Also, due to the large interception and attachment effect, the SFR did not exceed 0.5% ( Figure 4 ).

The rainfall interception effect of a forest stand is mainly affected by crown interception, retention, and absorption capacity; this is manifested as the interception of rainfall by leaves and branches, retention in branches/buds/leaf axils, and water absorption by relative dry branch/leaf surfaces. In general, at the individual tree level, the greater the surface area, the coarser and drier the surface of the above-ground protrusions (branches and leaves) per unit area of crown foliage and the stronger the crown capture, retention, and absorption capacity tend to be. Accordingly, in this study, although insignificant, ICR increased but TFR decreased with LAI ( Figure 4 ), which is the amount of leaf surface area per unit land surface. Both ICR and TFR were more significantly correlated with DBH, a measure of tree size and age ( Figure 4 ). In the process of forest stand development, with the thickening of the trunk DBH, the competition between adjacent individuals intensified, influencing to a greater extent the growth in crown width than height of trees. Therefore, HWR increased gradually, and there was a positive correlation between HWR and DBH (N = 12, r = 0.742, p = 0.006). Consequently, HWR was significantly positively correlated with ICR but significantly negatively correlated with TFR ( Figure 4 ).

In addition, we did not find a significant positive correlation between LAI and either SFR or HWR ( Figure 4Bb ), a result that does not support the commonly held notion that horizontal crown expansion increases the rainfall harvesting capacity of crowns (André et al., 2008; Hofhansl et al., 2012). However, in the Cerrado savanna of Brazil, South America, regardless of individual density, the interaction between HWR and DBH in three groups of trees differing in bark smoothness compensated for the adverse effects of bark roughness on stemflow (Tonello et al., 2021). It is generally considered that HWR is conducive to the formation and amplification of stemflow and that it could also reflect the branching angle of trees; however, measuring branching angles is very difficult to do in the field (Sadeghi et al., 2020). Along with the development of a forest stand, irrespective of whether or not the branching angle of its trees changed due to the competition between adjacent individuals, the relative growth rate of tree height must surpass that of crown width. Therefore, HWR gradually magnified, PD declined, and LAI also rose, which inevitably resulted in the higher SFR and ICR but lower FTR in the studied stands ( Figure 4 ).

Throughfall could form through the gaps between pine needles of a tree without being intercepted by the crown. However, there is an evident temporal lag effect in the formation of stemflow, because it only occurs after rainfall has been intercepted by pine needles and branches above a certain crown threshold. Therefore, in addition to biological factors, outside rainfall is the most important abiotic environmental factor affecting the forest crown allocation of rainfall (Zimmermann et al., 2015). As the amount of outside rainfall increased, the proportion of rainfall allocated among throughfall, stemflow, and interception routes varied. The basic rule discerned for P. schrenkiana stands was as TFR and SFR increase, the ICR decreases. However, there is a certain maximum for IC ( Figures 1 – 3 ).

Outside rainfall is recognized as the driving force for changes to IC, such that IC increases at first and then tends to stabilize (Macinnis-Ng et al., 2014; Wan et al., 2016; Li et al., 2020). The process of ICR’s change in response to I could be divided into three stages (Dang et al., 2005): rapid increase (I< 5 mm, ICR ≥ 36.1%), gradual increase (5 ≤ I< 25 mm, 20.4% ≤ ICR< 36.1%), and stable (I ≥ 25 mm, ICR< 20.4%). Analogously, for the three levels of outside rainfall of 0–5, 5–25, and 25–40 mm, the corresponding relative change in IC was 0.90, 0.42, and 0.13 mm/mm ( Figure 3A ). Notably, stemflow did not occur when little rain fell (i.e., 0–5 mm) ( Figure 2A ), and thus almost all the rainfall intercepted by the tree crown was converted into IC, keeping ICR above 93.1 ± 4.9% ( Figure 3A ). Finally, IC did not increase though ICR gradually decreased with I. As a result, IC at the 2,300-m, 1,800-m, and 1,450-m elevation sites remained at 16.47 ± 1.00 mm, 16.04 ± 0.96 mm, and 17.68 ± 1.36 mm, respectively ( Figure 3 ). There was a linear relationship between IC and I (Zhang et al., 2015a), which could be related to the fact that the observed I was not large enough to reach a stable stage.

All biotic and abiotic factors that could variously affect IC should influence the generation and amplification of SF, but there are also differences in this respect. For example, a small branching angle is conducive to the generation of SF but not conducive to IC, while bark thickness and roughness are conducive to IC but not conducive to SF (Hu et al., 2018). This may be related to forest crown allocation of rainfall, which may be divided into two steps: first, rainfall interception occurred, and then once the interception capacity was exceeded, a portion of it was collected onto the trunk to form SF, while another portion dropped directly from the crown to form TF (Gonzalez-Ollauri et al., 2020). Therefore, in the process of influx to the trunk, the dryness and hygroscopicity of the crown and bark as well as the roughness of the bark and the branching angle could have jointly affected stemflow, eventually leading to the existence threshold of SF (Macinnis-Ng et al., 2014). For example, in this study, at the 2,200-m, 1,800-m, and 1,450-m elevations, when SF emerged, outside rainfall was 5.25 ± 2.42 mm, 8.34 ± 3.13 mm, and 3.75 ± 1.22 mm, respectively ( Figure 2 ).

In this study, across the 2,200-m, 1,800-m, and 1,450-m elevation sites, their forest crown allocation of rainfall clearly differed, mainly for the threshold value of I when SF emerged and the saturation of IC. These disparities should be explainable in terms of local stand factors at the three elevations. For the same amount of I, ICR was highest at 1,800 m, followed by 2,300 m, and the lowest was at 1,450 m ( Figure 1 ), a ranking related to different average values of DBH, HWR, and LAI among three sites ( Table 1 ) as implied by the positive correlation of ICR with DBH, HWR, and LAI ( Figure 4 ).

At all three elevation sites, the threshold value of I when stemflow emerged showed a trend opposite to the acceleration of SF with I ( Figure 2 ). That is, the rank ordering among sites for their threshold of outside rainfall when stemflow emerged was 1,450 m > 2,200 m > 1,800 m, but vice versa (1,800 m > 2,200 m > 1,450 m) for the acceleration of SF ( Figure 2 ), which may be related to the stand differences in DBH, HWR, and LAI across elevation ( Table 1 ). There was no significant negative correlation between SFR and LAI ( Figure 4 ), likely because just two stages of forest crown allocation of rainfall were involved: (1) when the interception and capture ability was within the water-holding ability, and (2) when the interception and capture ability exceeded that holding ability. Due to the greater DBH, growth in tree height, and enhanced bark water absorption, the first stage above, the more important one, could offset the adverse effects of the latter stage on stemflow, leaving SFR only very weakly positively correlated with DBH and HWR ( Figure 4 ).

The saturated values of IC at the 2,200-m, 1,800-m and 1,450-m elevation sites were 16.47 ± 1.00 mm, 16.04 ± 0.96 mm, and 17.68 ± 1.36 mm, respectively ( Figure 3 ), this order matching the DBH, HWR, and LAI ( Table 1 ). ICR was positively correlated with DBH, HWR, and LAI ( Figure 4 ). Yet, when I was small, ICR at 2,200 m surpassed that at 1,450 m ( Figure 3 ), which may be related to the fact that stemflow emerged later in the former (at 5.25 ± 2.42 mm) than latter (at 3.75 ± 1.22 mm). Rainfall captured by the crown did not exceed the interception capacity that fell to form throughfall or that was collected to form stemflow.

Although mountains cover less than 1/5 of the earth’s land surface, they feed 50% of the world’s population and provide 80% of terrestrial fresh water resources, and even in some arid and semi-arid areas provide 90% of fresh water resources (Wang et al., 2001a; Wang et al., 2011). Especially in Xinjiang of China, water shortage has become a bottleneck problem now restricting local economic and social development (Sun et al., 2021). As an important water conservation forest in Xinjiang, Tianshan Mountain forest has various pressing problems, such as its single tree species dominance, stand structure, and difficult renewal; thus, soil erosion and water resource shortages are accompanied by a vicious cycle of ecological environment degradation that worsens over time. Thus, how to achieve greater runoff production and improved water and soil conservation functions through reasonable ecological protection and restoration has become a major problem that needs to be solved now (Aru et al., 2019). However, from a data analysis of 504 typical watersheds and more than 600 observation points worldwide, combined with the simulation results of ecological and economic models, it was concluded that enlargement of the carbon sink by afforestation can substantially reduce the production of runoff, being reduced by as much as 52% (Wang et al., 2011). In the forest and grassland zone at middle elevation in the Tianshan Mountains, the runoff yield varies greatly among different types of vegetation cover, as follows in descending order: bare land (32.74 m³·hm⁻²), grassland (17.15 m³·hm⁻²), natural forest (9.78–17.70 m³·hm⁻²), and artificial forest (10.26–11.18 m³·hm⁻²). With an increase in age of forest stands and their crown density, the runoff yield decreases gradually, amounting to only 54.1%–29.9% of bare land. Yet, the runoff yield of artificial forest was only equivalent to the lower limit of natural forest (Sun et al., 2021).

In this study, with the increase of CD, at first ICR increased sharply and then its acceleration declined and eventually did not increase any more ( Figure 5 ). This result indicates that water conservation capacity and biomass carbon fixation exhibit a synergistic increasing trend when the forest stand is young. However, when the stand age exceeded a certain threshold, ICR did not increase with the accumulation of CD ( Figure 5 ). Thus, at least from the perspective of rainfall allocation by the crown, when the stand age of P. schrenkiana reaches a certain stage, its carbon sequestration did not influence the complementary relationship between water conservation (IC) and runoff production (TF) in the forest. The accumulation of biomass carbon in forest ecosystems is mainly embodied in the expanding tree timber volume (coarse roots, trunks, and branches) whereas functional organs such as fine roots and leaves do not always increase, having asymptotic values, rendering their biomass rather small relative to the total individual tree biomass (Thomas, 1996). Fine roots absorb water and nutrients, whereas leaves assimilate CO₂ through photosynthesis and discharge H₂O through transpiration. When forest stand was at a mature stage and resources are fully utilized, the quantity and biomass of those functional organs appeared quasi-static because a dynamic equilibrium between their growth and death is maintained. Thus, despite the trees’ accumulation of biomass carbon, the runoff yield as well as water consumption of the stand remained relatively stable. However, artificial afforestation to expand the area of woodland will lessen the area of other vegetation types, such as grassland and shrubland. While this land use change would reduce runoff yield, it would increase water consumption in the upstream runoff-producing mountains and concomitantly reduce the amount of water available to reach the downstream oasis of this inner arid zone of Eurasia.