Multiple satellite-based data sets are used to evaluate the representation of climate–vegetation interactions in ESMs. The focus is on the key climatic drivers of vegetation growth, here assumed to be precipitation, net radiation, and air temperature, consistent with previous studies . Vegetation dynamics are diagnosed using LAI; in the following, when vegetation (state) is mentioned, the latter refers to LAI unless stated otherwise. All data sets have global coverage, are processed into 0.5∘ spatial resolution via bilinear interpolation, and are averaged to monthly values prior to the application of CSGC.

Multi-temporal-scale interactions between climate and vegetation are explored here using CSGC. To describe the method comprehensively, we first introduce the Granger causality in its classical formulation (parametric in the time domain; Sect. ), followed by the derivation of its spectral counterpart (non-parametric in the time–frequency domain; Sect.  and ).

Figure a, c, and e illustrate the Granger causality of air temperature, net radiation, and precipitation on LAI dynamics, based on observations, globally and latitudinally. Results are shown separately for monthly (Fig. a), seasonal (Fig. c), and inter-annual (Fig. e) timescales using a tri-variate colour map according to the fraction explained by each climatic driver (see Sect. ). Dotted pixels indicate that in at least 75 % of the ensemble members there is (a) agreement regarding the dominant climate impact and (b) statistical significance (at the 5 % level). At monthly scales, overall spatial patterns in the observation-based results (Fig. a) are in agreement with previous studies, showing the dominance of precipitation in arid and semi-arid regions, while radiation and temperature dominate in northern latitudes and rainforests, respectively . Strong radiation effects on vegetation can be observed over northern latitudes due to severe limitations in incoming radiation during winter months. However, in those latitudes, LAI retrievals are contaminated by snow cover signals. While focusing on the growing season could solve this issue, the CSGC requires continuous time series. Because in wintertime, due to limitations in solar radiation, plant growth is inhibited in northern latitudes, most variability captured at monthly scales will be dominated by the more dynamic spring and summer periods; therefore, our results suggest that radiation still dominates the behaviour of vegetation at these latitudes.

This dominant high-latitude radiation control was not reported by , who, based on a non-linear Granger causality framework, found that 61 % of the vegetated land surface is primarily driven by water availability at monthly timescales, while temperature and radiation are the primary factors in only 23 % and 15 % of the vegetated surface, respectively. These results also contrasted with earlier studies, which pointed to a less dominant role of water availability for global ecosystems . Here, our monthly-scale results also show a dominant role of precipitation, yet more moderate; 51 % of vegetated land is primarily controlled by precipitation, with radiation being the primary control factor in 40 % as well. When the analysis targets vegetation anomalies by detrending linearly and subtracting the average seasonal cycle for both LAI and climate (as was done in ), results show a similar dominance of precipitation, but air temperature gains importance over net radiation (being the dominant driver over 13 % and 36 %, respectively, as indicated in Fig.  in Appendix A). The higher importance of water availability in can be attributed to accounting directly for the effect of (root depth) soil moisture as a driver of vegetation, as opposed to the use of precipitation only in this study. Also, human practices, such as irrigation, can potentially bias our results. Nonetheless, irrigation is expected to increase the energy dependence of LAI dynamics, and as irrigation tends to be a seasonal phenomenon restricted to the growing period, this increase is found to be clearer at seasonal than monthly scales (as shown in Fig.  in Appendix B). A final difference with is their consideration of snow water equivalent as a water availability driver, which explains the divergence with our results in higher latitudes. Our results can also be reconciled with previous studies, such as , , and ; regional differences may relate to the specific focus of those studies on one temporal scale only, their calculation of covariances instead of inferring causality in a more formal manner, or the use of different variables to assess water availability drivers.

As mentioned before, a key feature of CSGC is that it also enables the assessment of interactions at longer temporal scales, such as seasonally (Fig. c) and inter-annually (Fig. e). As expected, radiation is found to dominate the seasonal phenology over 55 % of the global vegetated land. The strong radiation control over northern latitudes is attributed to the amplitude of the solar cycle, which ultimately inhibits vegetation growth during wintertime. In this analysis, net radiation instead of incoming radiation has been used, in order to be consistent with the investigation of vegetation–climate feedbacks in Sect. ; however, using incoming radiation as a driver instead leads to a similar 54 % dominance (see Fig.  in Appendix C). Compared to monthly scales, seasonal precipitation control is less widespread, as only 33 % of the vegetated land is primarily controlled by precipitation (compared to 51 % at monthly scales; Fig. a and c). This reduced importance of precipitation can be attributed to the observed temperature-driven hotspot in the Sahel region, but more importantly to increase in radiation control over the south of Eurasia and in tropical forests. Furthermore, the patterns in Amazonia tend to agree with the findings of , , and , showing a dominance of water availability in the southeastern side, while radiation is more limiting in the northwest.

Finally, at inter-annual scales, despite co-dominance of multiple drivers in some regions, global ecosystems tend to be water limited with 43 % of the vegetated land surface being primarily dominated by precipitation (Fig. e), especially in the subtropics. Although patterns exhibit some heterogeneity, not only arid and semi-arid regions but also substantial parts of southern Eurasia show a (significant) dominant control by precipitation. This widespread inter-annual dependency on water availability of ecosystem dynamics may arise due to the large inter-annual variability of precipitation and has already been documented in relation to the impact of precipitation of global carbon budgets and terrestrial evaporation . Moreover, it agrees with the results of and , yet it does not necessarily contradict the findings by . reported a dominant role of temperature at the global scale, yet showed a dominance of water availability at regional scales that is compensated for when upscaling to global means. Inter-annually, the control of air temperature extends over the high northern latitudes and eastern China, dominating in 20 % of vegetated land, while radiation remains the most crucial driver for 37 % of the land surface, almost exclusively in the northern latitudes, likely affected by the strong seasonal patterns (Fig. e). Once the seasonality is removed, the inter-annual dominance of radiation control falls down to 20 % of the vegetated land surface (see Fig. c). Despite the heterogeneity, the overall control of climate on vegetation is higher at inter-annual scales than at shorter timescales, as can be observed in the latitudinal profiles, which show the total causality in absolute terms (Fig. ). This is partly a consequence of the time–frequency decomposition of CSGC, which generally results in higher values of explained variance at longer timescales due to the increased time frame over which a predictor variable is assessed, thus increasing the chance of incorporating memory effects. However, the significance test against the null hypothesis of exhibiting no causal effect ensures that regions exhibiting significant responses can be compared over different timescales.

Noteworthy is that anthropogenic effects, which are not directly addressed here, can also impact vegetation and climate at short temporal scales. For example, irrigation and deforestation can result in a decoupling between climate and vegetation . In the tropics, deforestation results in a warming effect due to reduced plant transpiration, which in turn may induce a decline in precipitation, creating a warmer and drier regime . Irrigation allows for growing crops in water-limited regions, consequently inducing energy constraints which are captured by the CSGC. Note that due to the limited data record, the effects of global warming trends and carbon dioxide fertilisation – and the consequent trends in vegetation greening and water use efficiency – are not directly addressed in this study.

Results of the observations are next used to benchmark CMIP5 ESM performance in representing the control of climate on vegetation (Fig. b, d, f). Dotted pixels indicate that at least three out of four models reach agreement regarding (a) dominant climate impact and (b) statistical significance (at the 5 % level). Comparison of Fig. a and b shows that the monthly impact of air temperature on ecosystems is strongly overestimated by ESMs, with 17 % and 26 % of vegetated land being primarily dominated by temperature for observations and ESMs, respectively. This coincides with a lower effect of net radiation in central Eurasia and, more importantly, elevated air temperature control in the Amazon and Congo rainforests. These contrasting results with observations might hint towards problems in ESMs with respect to representing the behaviour of the tropics but may also relate to the difficulties to retrieve LAI from satellites in dense forests . Nevertheless, ESMs agree on the general patterns that highlight the strong radiation effects in northern latitudes (albeit less extended) and the water availability as a main driver in arid and semi-arid regions at monthly timescales.

Seasonally, a larger control of precipitation and air temperature on vegetation phenology is also noticeable over the Equator for ESMs (see latitudinal profile in Fig. d). The dominant control of radiation on vegetation phenology over northern latitudes is similar for all models (inter-model agreement and significance represented by the black dotting), and, whereas the spatial extent agrees with the observational results, the magnitude is underestimated by the models (see Fig. c and d). Radiation is the primary driver of the seasonal LAI variation in 45 % of the vegetated land in models (compared to 55 % for the observations). The role of precipitation and air temperature as drivers of the phenological cycle gains in importance in ESMs, at the cost of radiation, with 40 % and 15 % of seasonal LAI variation being dominated by precipitation and air temperature variability, respectively, versus the 33 % and 12 % in observations, respectively. Despite the overall similarities in the patterns of dominant drivers, regional differences between observations and models are still observed. Models point towards a water-limited phenological cycle in the Sahel, while observations also hint at a dominant role of temperature (compare Fig. c and d). Furthermore, whereas observations clearly highlight a south-to-north water-to-energy-limited gradient in Amazonia, models tend to disagree and point towards temperature as a key driver over most of the Amazonian rainforest at seasonal scales. These differences might indicate difficulties to model climate–vegetation interactions across the basin where air temperature is found to be the only limiting control, yet they may again be influenced by the difficulties to retrieve LAI from satellites over dense canopies, as pointed out above.

Similar to observations, the climate impact on LAI increases with longer temporal scales in ESMs. However, more remarkable than in the observations is the strong water limitation across the globe at inter-annual scales, which is not restricted to arid and semi-arid regions (Fig. f). Water availability at inter-annual scales is dominant for vegetation over 62 % of land versus the 43 % found in observations (Fig. e) and is also strongly overestimated in absolute terms at most latitudes, especially in the tropics. Further analysis shows that the divergence in the considered period between observations and models (see Sect. ) does not substantially impact results; repeating the analysis for the overlapping time range for observations and models (1982–2005) yields very similar findings (Fig.  in Appendix D).

Analogous to the effect of climate on vegetation, vegetation can alter local (and remote) climate conditions via biophysical and biochemical feedbacks. These feedbacks arise from the effect of vegetation structure and physiological activity on the surface radiation budget, available energy partitioning into latent and sensible heat fluxes, aerodynamic conductance of the ecosystem, atmospheric chemical composition, and indirect processes affecting incoming radiation, atmospheric humidity, and temperature . The representation of these feedbacks in ESMs remains in need of improvement to accurately predict future climate . Here, we unravel these feedbacks of LAI on different climate variables based on observations (Fig. a, c, and e) and ESM data (Fig. b, d, and f) and at different temporal scales, from monthly (Fig. a and b) to seasonal (Fig. c and d) and inter-annual (Fig. e and f). Dotted pixels indicate that in at least 75 % of the ensemble members there is (a) agreement regarding the dominant feedback and (b) statistical significance (at the 5 % level). To aid comparison to the strength of climate impacts on vegetation – measured in relative or absolute percentage of caused variance (see Sect. ) – an identical tri-variate colour map to that in Fig.  is used.

Observed LAI feedbacks over the middle and high northern latitudes concentrate on surface net radiation at monthly timescales (Fig. a). As vegetation lowers the albedo in boreal regions, it allows for more energy storage and less reflection back into the atmosphere; this increases surface net radiation and may lead to a net warming effect e.g.. By repeating the analysis using only incoming (shortwave and longwave) radiation, instead of surface net radiation, the results indicate that the influence of LAI on cloud formation is limited, at least considering the local (in the sense of “spatially collocated”) scales revealed by the causal framework (see Fig.  in Appendix E). Monthly feedbacks of vegetation on precipitation and air temperature are spatially less widespread; however, significant feedbacks on precipitation are observed, especially in tropical forests. The patterns in Amazonia suggest a more dominant effect of vegetation on radiation in the north, while precipitation feedbacks dominate in the south (Fig. a). We note that the method does not differentiate whether higher or lower values of LAI cause more or less rainfall, only that a causal effect of LAI on rainfall exists. The south-to-north patterns in the Amazon agree with the larger dependency on precipitation recycling in the south . Tropical forests are known to regulate local (and global) precipitation as their large use of water increases atmospheric humidity and results in cloud formation . This also directly affects the incoming short- and long-wave radiation. Nevertheless, we restate that the method only focuses on the effects of LAI on its immediate climatic environment, not in neighbouring or remote locations.

At seasonal scales, an increase in feedbacks on temperature is observed in the Northern Hemisphere, and feedbacks on precipitation remain limited to the tropics, although practically no statistical significance is reached outside the tropics (Fig. c). Finally, at inter-annual scales, the observation-based results show a north-to-south gradient over the Sahel region, with the north exhibiting feedbacks on precipitation, while strong vegetation feedbacks on temperature are observed in the south (Fig. e). However, despite the highly significant interactions in the tropics, and except for the feedback on radiation in the Northern Hemisphere, the inter-annual feedbacks cannot be clearly disentangled using the CSGC, as shown by the incoherent spatial patterns in Fig. e. This may occur due to the long integration time and the somehow limited observational record. Individual ensemble members do achieve high significance, but little inter-product agreement is reached due to high spatial heterogeneity over ensemble members. Overall, and as expected, comparisons between Figs.  and reveal that the impact of climate on vegetation consistently exceeds the strength of the vegetation feedback on climate. This means that local climate variability leaves a larger imprint on LAI dynamics than vice versa. This can be partly attributed to the fact that only local interactions are considered here: while vegetation reacts to its most immediate environment, vegetation can lead to remote effects on climate that are not addressed in our analyses . Nevertheless, these results show the importance of LAI variability in explaining the variance in local climate at intra-annual scales – mainly through impacts on the net radiation induced by albedo changes – and the potential of the CSGC framework to disentangle the bidirectional interaction between vegetation and climate.

In general, ESMs seem to correctly capture the spatial extent of LAI effects on net radiation throughout most of the Northern Hemisphere, but they underestimate feedbacks of vegetation on air temperature, which originates from either an actual underestimation of the air temperature feedback by ESMs or an overestimation of the feedback on net radiation in these regions, as reported by and confirmed by the latitudinal profiles (Fig. b, d, f), which mask the vegetation feedback on air temperature. Despite the overestimation, models do agree with each other on the influence of LAI on net radiation at polar latitudes (see dotted pixels), and the overall mean ensemble patterns for monthly and seasonal timescales also agree with observational results. Interestingly, while observations show significant impacts of LAI on precipitation in the (sub)tropics, these effects are not entirely reproduced by ESMs, which tend to show a larger influence of LAI on temperature in those regions. This may suggest a lower dependency of tropical forests on rainfall recycling and/or an overall wet bias in the ESMs ; the latter is however not supported by the results in Fig.  that indicate an overall overestimation of water limitations in models. Nonetheless, these local feedbacks on temperature and precipitation are overall weak – in both observations and models – as indicated by the absolute magnitudes shown in the latitudinal profiles (Fig. ).

Finally, to better visualise the multi-temporal-scale vegetation–climate interactions in observations and models, results are presented averaged per biome type. Figure  shows the biome-averaged absolute observed and modelled climate control on LAI dynamics, while Fig.  presents the vegetation feedbacks on climate. Forest ecosystems are generally found to be energy-driven, in agreement with previous studies . ESMs tend to agree with the observations on the magnitude of the response of ecosystems to radiation at all temporal scales, with the exception of the oversensitivity of evergreen broadleaf forests (EBF) at monthly scales and for most models. In regards to the influence of air temperature, strong differences with observations can be noticed at seasonal timescales for forest biomes; this is most remarkable for broadleaf forests, both evergreen and deciduous (EBF and DBF), which show a model overestimation of the control of temperature on LAI dynamics, even for the minimum modelled temperature control. Interestingly, models also overestimate the sensitivity of broadleaf forests (EBF and DBF) to precipitation, especially at inter-annual timescales. Observation results show limited water stress in tropical and mid-latitude forests, arguably due to the deep rooting system and mild climate. However, this apparent model overdependency of broadleaf forests on climate may also emerge from the under-sensitivity of the observational results due to the saturation of the greenness signal received by satellites in dense canopies. Models unambiguously overestimate the importance of water availability for LAI in most biome types at inter-annual timescales and to a more limited extent at monthly and seasonal scales – this appears in contrast with the results of . As expected, savannas are found to be mainly driven by precipitation across all timescales in both observations and models, although models strongly disagree among each other, as reflected by the large error bars in Fig. .

On the other hand, short-term feedbacks of LAI on climate seem to be better represented in ESMs, as small differences can be seen when compared to the observational results in Fig. . Note that this statement only holds true if looking at biome-averaged patterns due to compensatory effects, as comparison of observations and models in Fig.  does indicate clear regional differences. Deciduous needleleaf forests (DNF) and evergreen needleleaf forests (ENF) exhibit the strongest feedback on net radiation (and temperature) at all temporal scales; once again this appears related to albedo changes and not impacts on cloud formation (see Fig. ). Nonetheless, the effect of needleleaf forests on the radiation budget tends to be overestimated by most CMIP5 models, especially at monthly and seasonal timescales, which aligns with the findings of . ESMs also overestimate the influence of ecosystem phenology on net radiation in mixed forests (MF), open shrublands (OS), and woody savannas (WS); yet, large inter-model disagreements exist on the seasonal influence of LAI on net radiation for almost all biomes, as illustrated by the large error bars in Fig. . The strength of the effect of LAI on precipitation is overall lower than its impact on net radiation and air temperature, partly due to the non-consideration of downwind influences, which have been shown to be crucial, in this analysis . However, similar to the results of , a strong influence of LAI on precipitation can be observed in savannah regimes.