LPJmL4.0 is a process-based dynamic global vegetation model (DGVM) which simulates the surface energy balance, water fluxes, fire disturbance, carbon fluxes and stocks of the global land (Schaphoff et al., 2018a). Plant productivity is modelled on the basis of leaf-level photosynthesis responding to climatic and environmental conditions, atmospheric CO2 concentration, canopy conductance, autotrophic respiration, phenology, and management intensity. Fire disturbance is modelled using the simple fire module Glob-FIRM (Thonicke et al., 2001), which relates the length of the fire season to fractional annual area burnt. The model simulates 11 plant functional types (PFTs), 3 bioenergy functional types (BFTs) and 12 crop functional types (CFTs) to represent average plants of natural vegetation, bioenergy plantations and agriculture, respectively. Three PFTs represent the natural vegetation of the tropics and sub-tropics, namely the “tropical broadleaved evergreen tree” mainly representing tropical evergreen forest; the “tropical broadleaved deciduous tree” representing tropical dry forest and the woody component of savanna; and “tropical herbs” representing the herbaceous layer in grasslands, savanna and forests. The standard spatial model resolution is a 0.5∘ × 0.5∘ longitude–latitude grid. For each grid cell the fractional coverage of bioenergy and agricultural BFTs and CFTs follows a prescribed land-use data set, whereas in the remaining grid-cell area, natural PFTs grow in competition.

All changes made to LPJmL4.0 in order to simulate variable tree rooting strategies resulted in a new sub-version of LPJmL4.0 which we call LPJmL4.0-VR hereafter (where VR stands for variable roots). A detailed description of our modelling approach can be found in Appendix A.

For our purposes we extended the general maximum soil depth of 3 m in LPJmL4.0 to 20 m in LPJmL4.0-VR but restrict it to local soil depth information at the spatial model resolution of 0.5∘ × 0.5∘; see Sect. 2.3.2. We applied the same basic scheme for vertical soil layer partitioning from LPJmL4.0 (Schaphoff et al., 2018a) in order to keep model differences small (Appendix A, Sect. A1.1 and Table A1). We increased the number of rooting strategies for each of the two tropical tree PFTs (broadleaved evergreen and broadleaved deciduous), by splitting each PFT into 10 sub-PFTs. Each of those 10 sub-PFTs was assigned a different maximum vertical distribution of fine roots throughout the soil column following classical allometric rules applied in LPJmL4.0 (Appendix A, Sect. A1.3 and Fig. A1). Those distributions were chosen in order to allow the sub-PFTs to reach different maximum rooting depths in discrete steps between 0.5 and 18 m (Table A2). We here refer to the depth at which the cumulated fine-root biomass from the soil surface downwards amounts to 95 % (D95_max; Eq. A3). To account for additional carbon investments needed to grow deeper rooting systems, we introduced two new carbon pools, namely root sapwood and root heartwood (Appendix A, Sect. A1.4). Like stem sapwood in LPJmL4.0, root sapwood in LPJmL4.0-VR also needs to satisfy the assumptions of the pipe model (Shinozaki et al., 1964; Waring et al., 1982). This implementation creates a trade-off between below-ground and above-ground carbon investment. To allow for dynamic root growth, we implemented a logistic root growth function, which calculates a general maximum conceivable tree rooting depth depending on tree height (Appendix A, Sect. A1.5), in an approximation of the findings of Brum et al. (2019). Consequently, each sub-PFT shows a logistic growth of rooting depth which is dependent on the sub-PFT height and which saturates towards its specific D95_max (Fig. A2). Therefore, limitations of above-ground sub-PFT growth due to below-ground carbon investment of different tree rooting strategies (Sect. 2.2.4) are equal in the sapling phase of all sub-PFTs (starting from bare ground) but diverge with increasing sub-PFT height. In the case that temporal root depths exceed the grid-cell specific local soil depth (as prescribed by local soil depth information; see Sect. 2.3.2), all the respective fine-root biomass exceeding this soil depth is transferred to the last soil layer matching this soil depth (see also Fig. 1 and Supplementary Video 1 for a visualization of new below-ground carbon pools and root growth in LPJmL4.0-VR available at http://www.pik-potsdam.de/~borissa/LPJmL4_VR/Supplementary_Video_1.pptx, last access: 20 March 2020).

To fully investigate the effects of 20 tropical sub-PFTs growing in competition, we adjusted the original PFT establishment routine of LPJmL4.0 (Appendix A, Sect. A1.6). The adjustments lead to a higher establishment rate for productive sub-PFTs relative to their spatial dominance and vice versa, without changing the overall establishment rate as originally set by Prentice et al. (1993). The adjusted establishment routine has the effect that non-viable sub-PFTs are outcompeted over time. Furthermore, we increased the universal and constant maximum background mortality rate of tree PFTs in LPJmL4.0-VR to 7 % in order to counter-balance increased survival rates and therefore biomass accumulation under enhanced water access (Appendix A, Sect. A1.7).

In order to investigate the impact of simulating variable rooting strategies and root growth, we employ three model versions of LPJmL in this study: (1) LPJmL4.0, (2) LPJmL4.0-VR and (3) LPJmL4.0-VR-base. LPJmL4.0-VR-base has the same settings as LPJmL4.0-VR except variable rooting strategies, i.e. using the two rooting strategy parameterizations of LPJmL4.0 (Appendix A, Sect. A1.3) for the respective 10 sub-PFTs of the tropical broadleaved evergreen PFT and the tropical broadleaved deciduous PFT. We regard LPJmL4.0-VR-base as the baseline model of this study because comparisons to LPJmL4.0-VR enable the investigation of differences caused by the presence or absence of variable tree rooting strategies.

Each simulation was initialized with 5000 simulation years of spin-up from bare ground without land use by periodically cycling the first 30 years of the respective climate data set (1901–1930 for WATCH+WFDEI, GSWP3, and CRU and 1948–1977 for GLDAS) and using a pre-industrial atmospheric CO2 level of 278 ppm. The first spin-up ensures that carbon pools and local distributions of PFTs and sub-PFTs are in equilibrium with the climate (Schaphoff et al., 2018a). In a second spin-up phase cycling the same 30 years of climate data, historical land use and changing levels of atmospheric CO2 concentration are introduced. The second spin-up starts in the year 1700 and ends with the first year available in each climate data set. Land use is updated annually as described in Schaphoff et al. (2018a). Before the year 1840 a constant pre-industrial atmospheric CO2 concentration of 278 ppm is prescribed. After this year atmospheric CO2 increases annually based on data of Tans and Keeling (2015) as described in Schaphoff et al. (2018a). After the second spin-up, transient simulations start with the first year available in each climate data set and end in 2010. Land use and atmospheric CO2 are consistently updated annually while continuing to follow the same data sets as used in the second spin-up.

At the beginning of the first spin-up, all sub-PFTs in LPJmL4.0-VR and LPJmL4.0-VR-base have the same chance to establish; i.e. tree rooting strategies are uniformly distributed. During the spin-up simulations, local environmental filtering and competition in connection with PFT-dominance-dependent establishment rates (Sect. 2.2 and Appendix A, Sect. A1.6) determine which tree rooting strategies are best suited and which are outcompeted. Therefore, the transient simulations already start with distinct distributions of tree rooting strategies.

In LPJmL4.0-VR the contribution of each tree rooting strategy to the overall net primary productivity (NPP) appears highly dependent on local environmental conditions.

Based on the information of how much NPP each sub-PFT contributes in each grid cell, we derived maps of mean rooting depth over the whole study region for the time span 2001–2010 for each climate input used in this study (Fig. 2). Figure 2 shows the mean of the actually achieved D95 of each sub-PFT (evergreen and deciduous combined) weighted by the respective relative NPP contribution of each sub-PFT to total forest NPP (which we call D95‾, hereafter). Therefore, the regional pattern of D95‾ reflects the effects of climate and soil depth. A general east-to-west gradient of D95‾ over the Amazon region follows climatic gradients of precipitation and the MCWD (Figs. B1–B2), while soil depth (Fig. A3) constrains D95‾ especially in the south-eastern Amazon. In general, areas with higher mean annual rainfall and a weaker dry season show lower D95‾ and vice versa (please also see Fig. B3 for a detailed exemplary comparison of sub-PFT NPP for two grid cells with contrasting climate conditions). This pattern holds true under all climate inputs, with some minor local differences, and is in line with an inversely modelled global gridded product of the maximum depth of root water uptake (MDRU in Fan et al., 2017). Nevertheless, we find considerable absolute differences between MDRU and D95‾ (Fig. B4), which can easily emerge from different model settings and assumptions, e.g. related to differences in spatial model resolution, simulated water percolation and underlying vegetation features.

Focussing on the climatological clusters (Sect. 2.5.1 and Fig. 3f) under CRU climate input, the western Amazon (EQ W), with mean annual precipitation (MAP) of 2708 mm and a mean MCWD of -163 mm, displays an overall mean D95‾ of 1.14 m and a maximum of 5.47 m, despite considerably deeper soils present. In this cluster Fan et al. (2017) find a mean and maximum MDRU of 1.26 and 17.95 m, respectively. In the northern, western and southern Amazon clusters (NSA, EQ E, SAMz) with lower MAP of 2299, 2190 and 2035 mm and considerably lower MCWDs of -488, -438 and -497 mm, respectively, mean D95‾ increases to 2.32, 3.20 and 2.68 m, respectively (mean MDRU of 1.85, 2.84 and 3.28 m). Here, maximum D95‾ values reach 11.97, 11.27 and 9.04 m, respectively (maximum MDRU of 14.28, 13.47 m and 16.57 m). In the monsoon-dominated region (SAMS), displaying the lowest MAP of 1449 mm and MCWD of -649 mm, mean D95‾ decreases to 1.37 m (mean MDRU 2.61 m). The maximum D95‾ of this region reaches 11.17 m located at the border with SAMz (maximum MDRU 49.37 m).

The regional simulation of D95‾ also allows us to generalize which tree rooting strategies occupy which climate space. Using the MCWD and MAP to define a climate space, we find a clear adjustment of D95‾ (Fig. B5). A core region with deep-rooted forests (mean D95‾>4 m) is found where the MCWD ranges between -1300 and -400 and where MAP is at least 1500 mm (see also maps of the MCWD and MAP in Figs. B1 and B2). This core region is surrounded by a small band of medium-rooting-depth forests (mean D95‾∼2–4 m). Rather shallow-rooted forests (mean D95‾<2 m) are found in increasingly drier climates where MAP is less than 1000 mm and in more seasonal climates where the MCWD is below -500 mm. Shallow-rooted forests are also simulated in very wet conditions where the MCWD is greater than -300 mm and MAP is 1200 mm or higher.

The climatological clusters within the Amazon region which undergo the strongest dry season (EQ E and SAMz) show the largest differences between simulations with variable (LPJmL4.0-VR) and constant (LPJmL4.0-VR-base and LPJmL4.0) tree rooting strategies. In those clusters LPJmL4.0-VR shows a significantly higher agreement with validation data (Fig. 3c, d and Table B3). Agreement is largest for EQ E where NME and r2 show values of 0.62 and 0.91, respectively, whereas constant rooting systems in the other two models lead to values of NME ≥1.92 and r2≤0.21 (Table B3). In NSA and EQ W model differences are less pronounced as annual precipitation deficits are lower and deep rooting systems play a lesser role. Still, variable rooting systems lead to noticeably higher agreement in NSA between January and April (Fig. 3a), where monthly precipitation is lower compared to the rest of the year. In the monsoon-dominated cluster SAMS outside the Amazon region (Fig. 3e), model differences are least pronounced, since shallow-rooting forests dominate this area in LPJmL4.0-VR (Fig. 2), which are very similar to the forests with constant tree rooting strategies in the other two model versions.

Results of regional ET are in line with results of site-specific ET. On the local level, the variable tree rooting strategies of LPJmL4.0-VR lead to a major improvement in reproducing measured FLUXNET NEE and ET (Appendix B, Sect. B1.1 and Fig. B6–B7), increasing the confidence of regional modelling results.

The simulated relative dominance of tropical tree PFTs across the study area differs substantially between model versions (Fig. 4). In simulations with LPJmL4.0, more than half of the grid cells show the evergreen and deciduous PFTs to be equally dominant (Fig. 4g–h). Only in areas outside moist tropical climate regions does the model tend towards dominance of the deciduous PFT, whereas in the Amazon region, for example, the evergreen and deciduous PFTs co-exist in almost equal abundance. These patterns strongly differ from satellite-derived geographical PFT distributions (Fig. 4a–b) and therefore yield in respective comparisons the highest NME values among all models (Table B4). In contrast LPJmL4.0-VR and LPJmL4.0-VR-base show clear dominance patterns of both tropical tree PFTs across the study area (Fig. 4c–f). Nevertheless, differences between LPJmL4.0-VR and LPJmL4.0-VR-base are quite substantial. In LPJmL4.0-VR-base the tropical evergreen PFT dominates the north-western Amazon region only, negligibly extending further than the borders of climatological clusters NSA and EQ W combined. Beyond these borders the tropical deciduous PFT dominates (Fig. 4e–f). In contrast, in LPJmL4.0-VR (Fig. 4e–f) the evergreen tree PFT dominates the entire Amazon region including EQ E and SAMz, and the deciduous PFT is pushed towards drier and more seasonal climates (including parts of SAMS). Therefore, LPJmL4.0-VR yields the lowest NME values in comparison to satellite-derived PFT distributions (Table B4).

The geographical patterns of simulated D95‾ are very similar under four different climate input data sets (Fig. 2). This gives confidence in the general robustness of our results and modelling approach as differences in climate data do not lead to substantially different model behaviour. This is further supported by similar regional rates of ET simulated under the different climate data inputs (Fig. 3).

Simulated D95‾ (Fig. 2) clearly follows climate gradients and soil depth found in the study region (Figs. A3, B2, B3). Here, MAP and the MCWD can serve as explanatory variables of simulated D95‾ (Fig. B5). These findings are in line with the general ecological expectation and former studies that seasonal water depletion of upper soil layers, as a combination of annual precipitation and dry-season length and strength, is positively correlated with the rooting depth of tropical evergreen trees (Baker et al., 2009; Ichii et al., 2007; Kleidon and Heimann, 1998, 1999). We also find lower thresholds for MAP and the MCWD where D95‾ strongly decreases again (Fig. B5), which can be explained by different mechanisms leading to a regime shift from the evergreen to the deciduous tree PFT as discussed below (see Sect. 4.2).

To evaluate our model results against empirical data, we checked the data availability on maximum rooting depth across South America in the TRY database (Kattge et al., 2020; data downloaded September 2019). As is also shown in Fan et al. (2017), we found the number of sites within the TRY database where maximum rooting depth has been measured in South America to be very low. Moreover, the number of data entries per site appeared very small, where 33 TRY sites falling within our study area showed a mean of nine and a median of six data entries, while 15 sites showed five or fewer data entries. Therefore, we decided not to include site-specific comparisons of rooting depth as it is not clear how representative these measurements are for the local forest communities. More research is necessary to increase the number of observation sites and improve the empirical basis of field-based rooting depth to allow for site-specific model evaluation. Nevertheless, as shown in Fan et al. (2017) measured, site-specific maximum rooting depth across the Amazon region follows the known climatic gradient as expected (Figs. B1, B2). The same holds true for the inversely modelled MDRU of Fan et al. (2017; shown in Fig. B4), which gives confidence in our results.

In all three model versions used in this study, the same land use is applied (Sect. 2.4), which shapes the geographical extent and maximum dominance of natural vegetation in our results. This is why FPC maps of all model versions show the shape of the Amazon region as a distinct pattern (Fig. 4), even though it is less visible for LPJmL4.0-VR-base and one has to consider both tropical tree PFTs at the same time (Fig. 4e–f). Within the Amazon region, LPJmL4.0 simulates similar dominance of the evergreen and deciduous PFT (Fig. 4g–h) which contradicts evaluation data (Fig. 4a–b) and indicates similar performance of the two PFTs or missing mechanisms rewarding better performance over time. We here find that introducing a performance-dependent tree establishment rate (Sect. 2.2 and Appendix A, Sect. A1.6) clearly resolves this issue. This feature produces clear dominance patterns of both PFTs in LPJmL4.0-VR and LPJmL4.0-VR-base. Apparently, by rewarding better performance, variable tree rooting strategies (LPJmL4.0-VR) become necessary to reproduce the dominance of the evergreen PFT throughout the Amazon region (Fig. 4e–f). To remain superior in drier and more seasonal environments in the south to south-eastern Amazon region, the evergreen PFT needs to access deep water by adjusting its rooting depth (Fig. 2). Clearly, this adjustment of rooting depth is only possible within a certain climatic envelope. Below certain thresholds of MAP (around 1000 mm) and the MCWD (around -500 mm), mean D95‾ decreases again (Fig. B5), which coincides with a transition from the evergreen to the deciduous PFT. Those thresholds are similar to thresholds between evergreen forests and savanna found by, for example, Malhi et al. (2009) at annual precipitation of 1500 mm and at an MCWD of -300 mm. The substantially lower MCWD value found in our study can be explained by the differences in calculating the CWD. While Malhi et al. (2009) assume a constant rate of ET per month of 100 mm, we use the monthly variable PET (Sect. 2.5.3). Since PET is often significantly higher than 100 mm, our monthly CWD and therefore MCWD values are lower.

Similarly to Malhi et al. (2009), Staver et al. (2011) find that the climatic thresholds for evergreen forest are not very distinct and savanna can simultaneously be found in a climatic range around the mean threshold. The authors ascribe this forest–savanna bi-stability to climate–fire–vegetation feedbacks. Many recent studies investigating potential forest–savanna bi-stability and tipping points of forests in and around the Amazon region rely solely on such climatic ranges of tropical biomes (Hirota et al., 2011; Wuyts et al., 2017; Zemp et al., 2017; Staal et al., 2018; Ciemer et al., 2019). The results of LPJmL4.0-VR show that knowledge on local tree root adaptations is another important explanatory variable of vegetation cover, reducing the uncertainty and width of anticipated climatic ranges where vegetation cover could be bi-stable. These findings are supported by a recent study that finds rooting depth more crucial than fire dynamics for explaining PFT dominance in South America (Langan et al., 2017).

Whether the transition between the evergreen and deciduous tree PFT for the thresholds of MAP and the MCWD we find with LPJmL4.0-VR is mainly caused by (a) environmental filtering (including vegetation–fire feedbacks) of deep tree rooting strategies, (b) their competitive exclusion by shallow-rooted deciduous sub-PFTs together with the tropical herbaceous PFT (Fig. B8) or (c) most probably a combination of both is yet to be determined. Given that we used the most simplistic fire module of LPJmL (Glob-FIRM; Thonicke et al., 2001) and current land-use input to allow model evaluation against remotely sensed data in this study, investigating the natural mechanisms of tropical PFT shifts should be the focus of further studies.

Regardless of the mechanisms that eventually lead to a PFT shift, we can state that neither costs for deep-root investment nor a heterogeneous pattern of soil depth across the study region disproves that locally adapted tree rooting depth is key for explaining the current geographical distribution of tropical evergreen forests in South America. Given the large differences between LPJmL4.0-VR and LPJmL4.0-VR-base (Fig. 4), it is clear that in roughly half of the Amazon region the carbon balance of the evergreen PFT is superior to the deciduous PFT only when investing substantial amounts of carbon in deeper roots, i.e. below-ground biomass (Fig. B9). On the one hand this investment has a direct negative effect on productivity, because during growth the allocation of assimilated carbon shifts towards respiring below-ground biomass while investments in productive AGB (Fig. B10) need to be reduced. On the other hand, drier and more seasonal environments show less cloud cover during the dry season (Nemani et al., 2003), enhancing photosynthesis at this time of the year which increases productivity as long as water access is assured (Costa et al., 2010; Wu et al., 2016). The trade-off between AGB and BGB investment most probably leads to a more homogenous AGB pattern across the Amazon region with similar values over a wide climatic range (compare EQ E and SAMz in Fig. B10c–e).

LPJmL4.0-VR simulates rates of local ET and NEE which reasonably match respective measurements at different FLUXNET sites throughout the Amazon region (Figs. B6–B7), even though we run the model with regionally gridded instead of locally measured climate data. While potentially lacking information on local short-term weather events, gridded climate input still seems to be sufficient to capture broad seasonal signals for our comparisons on a monthly basis. This also increases the confidence in our results on a regional scale.

Across large parts of the Amazon region, variable tree rooting strategies decrease the intra-annual variability in ET and maintain high rates of NEE and ET during the dry season in accordance with the intra-annual trends suggested by evaluation data (Figs. 3, B6, B7). More than that, simulated rates of ET and productivity can peak during the dry season, e.g. in EQ E, which has been explained by increased solar radiation during this time of the year (Nemani et al., 2003; da Rocha et al., 2004). Especially in EQ E and SAMz, at least parts of the forest area must have access to sufficient water in the model and in reality (Costa et al., 2010; Wu et al., 2016). Given that LPJmL4.0-VR and LPJmL4.0-VR-base are essentially identical models with the same soil depth input and subsequent hydrology over the whole soil column, their differences in simulated ET and NEE must emerge from their only difference, which is the number of simulated tree rooting strategies. Therefore, local root adaptations in LPJm4.0-VR can be regarded as a buffer against seasonal precipitation deficits by usage of deep water (exemplarily shown in large detail for the FLUXNET Site STM_K67 in Fig. B11).

We can here quantify this water access for the first time on the basis of carbon investment and return and limited by spatial heterogeneous soil depth. Without limits to rooting depth in the form of local soil depth (e.g. by applying a universal soil depth of 20 m) and below-ground carbon investment, seasonally dry climatological clusters would potentially shift towards deeper-rooted sub-PFT dominance, consequently leading to an overestimation of ET rates. Therefore, we argue that both factors are of great importance in explaining regional rates of ET. This also means that forests in the same climatological cluster contribute very differently to the overall ET and therefore to moisture recycling across South America. We can here mechanistically explain this coherence as we show for the first time on the regional scale how PFTs with variable tree rooting strategies adjust to local environmental conditions and in return lead to simulated rates of ET very close to validation data (Figs. 3, B6). The heterogeneous picture of D95‾ we find (Fig. 2) might provide a direct guideline for where to put emphasis on forest conservation to maintain continental-scale moisture recycling, as D95‾ directly scales with rates of ET.

Being able to mechanistically reproduce and explain the broad-scale stabilization of water fluxes into the atmosphere has wide implications for DGVM frameworks and simulation of ET as moisture input to the atmosphere in Earth system models (ESMs). Our approach can help to better quantify the role of forests for local- to continental-scale moisture recycling and to project the fate of forests under future climate and land-use change. The approach presented here is easily applicable for a wide range of DGVMs and ESMs which simulate fine-root distribution in a similar way to in the LPJmL model family (based on Jackson et al., 1996). A first and easy-to-implement step for other models could be to prescribe the relative fine-root distribution in a spatially explicit way in accordance with D95‾ values presented in this study.