The feedback between global vegetation greenness and surface air temperature and precipitation is assessed using remote sensing observations of monthly fraction of photosynthetically active radiation (FPAR) for 1982 to 2000 with a 2.5° grid resolution. Lead/lag correlations are used to infer vegetation–climate interactions. Furthermore, a statistical method is used to quantify the efficiency of vegetation feedback on climate in the observations. This feedback analysis provides a first quantitative assessment of global vegetation feedback on climate. In northern mid- and high latitudes, vegetation variability is found to be driven predominantly by temperature; in the meantime, vegetation also exerts a strong positive feedback on temperature with the feedback accounting for over 10%–25% of the total monthly temperature variance. The strongest positive feedback occurs in the boreal regions of southern Canada/northern United States, northern Europe, and southern Siberia, where the feedback efficiency exceeds 1°C (0.1 FPAR)−1. Over most of the Tropics and subtropics (outside the equatorial rain belt), vegetation is driven primarily by precipitation. However, little vegetation feedback is found on local precipitation when averaged year-round, with the feedback explained variance usually accounting for less than 5% of the total precipitation variance. Nevertheless, in a few isolated small regions such as Northeast Brazil, East Africa, East Asia, and northern Australia, there appears to be some positive vegetation feedback on local precipitation, with the feedback efficiency over 1 cm month−1 (0.1 FPAR)−1. Further studies suggest a significant seasonal variation of the vegetation feedback in some regions. A preliminary analysis also seems to suggest an enhanced intensity of the vegetation feedback, especially on precipitation, at longer time scales and over a larger grid box area. Limitations and implications of the assessment of vegetation feedback are also discussed. The assessed vegetation feedback is shown to be valuable for the evaluation of vegetation–climate feedback in coupled climate–vegetation models.
The terrestrial ecosystem is an important component of the earth system. It has long been known that the distribution of natural vegetation is governed above all by climate through precipitation, temperature, light, and CO2 (Budyko 1974; Prentice 2001; Nemani et al. 2003). Recent studies further indicate that vegetation can also feed back on climate, both directly on the energy budget through surface albedo and exchanges of heat, water, and momentum and indirectly on the biogeochemical process through its effect on the atmospheric CO2 (e.g., Pielke et al. 1998; Bonan 2002; Kaufmann et al. 2003). The improved understanding of global vegetation system has enabled us to build dynamic global vegetation models with sophisticated biophysical/biogeochemical processes (e.g., Dickinson and Shaikh 1998; Cramer et al. 2001; Bonan et al. 2003; Sitch et al. 2003). As a result, vegetation–climate interaction can be simulated in coupled vegetation–climate models (Foley et al. 1998; Levis et al. 2004; Gallimore et al. 2005; Notaro et al. 2005).
At monthly-to-interannual time scales, leaf phenology plays an important role in vegetation–climate interaction. The seasonal emergence and senescence of leaves on deciduous trees and grasses are affected by temperature and precipitation variability, and can in turn alter surface energy and hydrological budgets to impact the climate (Bonan 2002). In spite of this general understanding of vegetation–climate feedback, it has remained a great challenge to quantify global vegetation–climate feedback from observations. To our knowledge, there has been no observational assessment of vegetation–climate feedback at continental to global scales. With a few exceptions (Schwartz and Karl 1990; Schwartz 1992, 1996; Kaufmann et al. 2003; W. Wang et al. 2005, personal communication, hereafter W05), most previous work on global vegetation feedback has been carried out in numerical models using paired sensitivity experiments with and without changes of certain vegetation variables, such as the leaf area index (e.g., Bounoua et al. 2000; Buermann et al. 2001) and vegetation cover (e.g., Bonan et al. 1992; Kutzbach et al. 1996; Gallimore and Kutzbach 1996; Prentice et al. 2000).
The purpose of this paper is to provide the first observational assessment of vegetation feedback on climate variability of seasonal-to-interannual time scales and of continental-to-global spatial scales. This assessment provides an observational benchmark to be tested against by coupled global vegetation–climate models. Our strategy follows recent studies on ocean–atmosphere feedbacks because of some parallels between vegetation–atmosphere interaction and ocean–atmosphere interaction. The dynamic memory of the atmosphere is predominantly 1–2 weeks and atmospheric variability tends to be dominated by internal atmospheric variability, especially outside the Tropics. In comparison, the memories of both vegetation and the ocean are substantially longer. The persistence time of vegetation “greenness” is longer than 1–2 months (Fig. 1), as indicated by the persistence time of fraction of photosynthetically active radiation (FPAR),1 which is a remote sensing proxy of vegetation greenness. This time scale is about half that of the sea surface temperature (SST).
The vegetation feedback is assessed using a simple statistical method that was originally proposed by Frankignoul and Hasselmann (1977) and has been used recently in the evaluation of SST feedback on air–sea heat flux (Frankignoul et al. 1998; Frankignoul and Kestenare 2002) and the atmospheric response to extratropical SST (Czaja and Frankignoul 2002; Liu and Wu 2004). Specifically, we will assess the feedback between the observed interannual variation of surface air temperature/precipitation and FPAR in the period of 1982 to 2000. Over northern Asia and northern North America, our study suggests a significant positive vegetation feedback on temperature, most likely through the surface albedo feedback; this positive vegetation feedback is found to account for up to 10%–20% of the total variance of the monthly temperature variability. In the Tropics and subtropics, which include almost all Southern Hemisphere continents, vegetation is driven primarily by precipitation, while its feedback on monthly precipitation appears to be insignificant, usually accounting for less than 5% of the total variance, except for a few isolated regions. The vegetation feedback on precipitation also seems to be enhanced substantially at longer time scales and larger spatial scales. Our paper is arranged as follows. Section 2 describes the data. Section 3 introduces our statistical method to estimate the vegetation feedback. Section 4 illustrates our assessment by examining vegetation–atmosphere interaction in two regions: Northeast Brazil and southern Siberia. Global vegetation–climate interaction is discussed in terms of lead/lag correlations in section 5 and is further quantified in section 6. Further discussion on the sensitivity of the vegetation feedback on spatial and temporal scales is given in section 7, and a summary is given in section 8.
We use observed monthly mean surface air temperature and precipitation to represent the climate forcing on vegetation. The temperature data are from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis (Kalnay et al. 1996), while the precipitation data are from the Climate Prediction Center (CPC) Merged Analysis of Precipitation (CMAP) (Xie and Arkin 1997). Both datasets are used with a resolution of 2.5° × 2.5°. Mediated by cloudiness, solar radiation is another important climate forcing on vegetation processes in some regions (Nemani et al. 2003). The radiation forcing on vegetation and their feedback will not be studied here.
We use monthly FPAR as a proxy for vegetation greenness (value ranging from 0 to 1). FPAR represents the fraction of photosynthetically active radiation absorbed by the green plants and brown plants and is linked closely to the maximum photosynthetic capacity of vegetation. FPAR is proportional to the normalized difference vegetation index (NDVI) and leaf area index (LAI), all reflecting the intensity of vegetation activity. In general, greening vegetation during the growing season tends to increase FPAR, and vice versa. We use Pathfinder version 3 Advanced Very High Resolution Radiometer (AVHRR) FPAR data (Myneni et al. 1997) extended from 1982 to 2000 on a 0.5° × 0.5° grid. It should be pointed out that the FPAR data could still be contaminated by several factors. Huete (1988) and Kaufmann et al. (2000) determined that NDVI is sensitive to soil moisture characteristics over partially vegetated regions. In particular, boreal winter FPAR may be biased too low in the northern high latitudes owing to the high albedo of snow and limited available sunlight for vegetation use or detection by remote sensing (Los et al. 2000; Buermann et al. 2001; Tian et al. 2004). This bias may exaggerate the estimated vegetation feedback as discussed below. Although a detailed analysis of any FPAR data bias effect is beyond the scope of this paper, as a sensitivity test we have repeated some of our analyses using LAI observations and an improved version of FPAR (Los et al. 2000) from 1982 to 1998, which became available after our analysis. This new version of FPAR includes some corrections on sensor degradation, some cloud contamination over the Tropics, water vapor and aerosol effects, sun angle variations, and missing data for polar regions. However, no qualitative differences are found between the results using the different datasets. This suggests that our major conclusions are likely to be insensitive to the choice and type of vegetation data.
We will mainly examine monthly-to-interannual variability by examining the cross correlation/cross covariance between FPAR and climate variables during 1982–2000 at each grid point. For these calculations, all variables are first aggregated onto the 2.5° × 2.5° grid box of the atmospheric data. The anomalies are then calculated as the departure from their climatological annual cycles. The anomalies are finally linearly detrended before cross covariance is calculated.
The climatological seasonal cycle of FPAR can be seen in Fig. 2, which shows the global FPAR in boreal winter [December–February (DJF)] (Fig. 2a), summer [June–August (JJA)] (Fig. 2b), and annual mean (Fig. 2c). The discussion below on FPAR variability can be facilitated by the vegetation coverage map for (deciduous and broadleaf, or evergreen and needleleaf) trees and grasses/herbs/shrubs, derived from remote sensing observations (e.g., DeFries et al. 1999, 2000). Maximum FPAR values of over 0.8 are found over the equatorial regions of the Amazon, Congo, and Indonesia throughout the year with little differences in their seasonal cycle. The minimum seasonal cycle variability is caused by year-round precipitation and the dominant broadleaf evergreen rainforest there. Minimum FPAR values of less than 0.2 are found over the desert that extends from Central Asia to North Africa. In the Tropics/subtropics surrounding the equatorial tropical rainforest, such as the Sahel, southern Africa, northeastern Brazil, and Australia, FPAR exhibits a moderate seasonal cycle, reflecting to a large extent the fast response of the drought-stressed grassland/shrubland there. The largest seasonal cycle occurs in the northern mid- and high latitudes, stretching across southern Siberia into Europe and across southern Canada, where FPAR increases from a minimum of below 0.2 in winter to a maximum of over 0.8 in summer. These large seasonal changes are contributed by boreal trees as well as grasses and shrubs (the small FPAR in winter could also be biased by the snow cover as pointed out earlier). In the midlatitude temperate regions, such as Europe, eastern United States, and eastern China, FPAR exhibits moderate changes because of the dominant grasslands, croplands, and broadleaf deciduous trees. Overall, the FPAR seasonal cycle described here is in agreement with the general features of the seasonal evolution of global vegetation (Bonan 2002).
The monthly variability of FPAR anomalies (Fig. 3) also exhibits great spatial variation, somewhat similar to that of the seasonal cycle. Minimum variability is found over deserts (due to low total vegetation amount) and tropical evergreen rainforests (due to ample precipitation) with σ(FPAR) < 0.03. Moderate FPAR variability, σ(FPAR) > 0.05, is found over tropical and subtropical grasslands and shrublands, such as the Sahel, southern Africa, western United States, South America, and Australia. Maximum FPAR variability occurs in the northern mid- to high latitudes from Siberia to northern Europe and from the northern United States to Alaska, reflecting the variation of greenness of the boreal forests and grasslands.
With strong atmospheric internal variability, the causality of vegetation–climate interaction is better inferred from the lagged, rather than the simultaneous, vegetation–atmosphere covariance. A significant correlation with the atmospheric variable lead tends to imply an atmospheric forcing on vegetation, while a significant correlation with vegetation lead may be inferred as a vegetation forcing, or feedback, on the atmosphere. This has been pointed out in the study of ocean–atmosphere interaction (Frankignoul et al. 1998). However, the lead–lag regression/correlation themselves only illustrate some qualitative features of vegetation–climate interaction.
A further step is to quantify the strength of the vegetation feedback on climate. Here, we will use a simple method from Frankignoul et al. (1998), as described briefly below. The readers can gain much more insight into the nature of estimation method and vegetation–atmosphere interaction by referring to appendix A, which discusses in more detail vegetation–atmosphere interaction in an idealized model. In general, an atmospheric variable A(t+dta) is assumed to consist of two parts:
The λAV(t) represents the atmospheric response to a change in vegetation V(t) after time dta. The parameter λA represents the forcing efficiency, or feedback efficiency, of the vegetation on the atmosphere and will be referred to as the vegetation feedback parameter [analogous to the oceanic feedback parameter of Frankignoul et al. (1998)]. The term Na(t + dta) represents the climate noise generated internally by the atmosphere independent of vegetation. Multiplying Eq. (1) with V(t − τ) and ensemble averaging each term, denoted by angle brackets, we have a relation of lagged covariance as
The noise Na is unknown. However, the unknown effect of Na in (2) is eliminated when vegetation leads the atmospheric response by τ > dta > 0,
The atmospheric response is usually fast with dta less than one month. Therefore, dta can be neglected for our monthly data considered here. This simplifies the feedback parameter as
In theory, the estimator (4) is independent of lag (as long as τ > 0) because the changes with lag in the numerator and denominator cancel out (appendix A). In practice, the sampling error of the estimator tends to increase with the lag because the diminishing denominator due to decorrelation tends to amplify the sampling error in the numerator. This is particularly true when the vegetation memory is not too much longer than the atmospheric memory. Therefore, it is best to use the estimation only for the first few lags. The sampling error also varies with the memory of the vegetation, with a longer vegetation memory giving a smaller sampling error (appendix A).
In spite of the involvement of the lagged covariance, the estimator (4) differs significantly from the lagged regression coefficient, which has been used for the prediction of climate from preceding vegetation states (e.g., Kaufmann et al. 2003; Zhang et al. 2003; W05). The estimated feedback parameter (4) tends to be independent of lags because both denominator and numerator are lagged covariance. In contrast, a lagged regression/correlation coefficient usually decreases with the lag because its numerator is a lagged covariance but the denominator only consists of simultaneous covariance (i.e., variance). Physically, as discussed in appendix A, λA should be interpreted as the vegetation forcing efficiency for the atmosphere to reach a quasi-equilibrium response. Most importantly, λA reflects the “instantaneous” atmospheric response to a vegetation change (neglecting the atmospheric adjustment). This differs from the prediction of atmospheric variables using an earlier vegetation, which is related to the lagged regression. To see more clearly the relationship between the feedback parameter and the lagged regression, we consider a simple example in which the vegetation is used to predict the atmosphere with a lead time, τ. The regression equation for the prediction is A(t) = r(τ)V(t − τ) + ɛ, where r(τ) is the lagged regression coefficient and ɛ is the statistic residual. The regression coefficient r(τ) = 〈V(t − τ), A(t)〉/〈V(t), V(t)〉 is obtained by minimizing the residual noise ɛ using the least square fit. With (4), it is easy to show that
where c(τ) = 〈V(t − τ), V(t)〉/〈V(t), V(t)〉 is the lagged correlation coefficient. So, the regression coefficient is smaller than the feedback parameter estimator (4) by c(τ). Equivalently, the explained variance that can be predicted by vegetation is smaller than that due to vegetation feedback by a factor of c(τ)2
According to Eqs. (5) or (6), the predictability regression coefficient r(τ) can be interpreted as the “instantaneous” atmospheric response to vegetation λA with a decay following the decorrelation of the vegetation c(τ). The loss of predictability of the atmosphere with time lag is due completely to the memory (decorrelation) of the vegetation. It should also be noted that the feedback parameter cannot be obtained simply from the zero lag regression coefficient [Eq. (5) is invalid at τ = 0!].
Finally, the statistical significance of λA can be assessed using the Monte Carlo bootstrap approach (Czaja and Frankignoul 2002). Here for the observational analysis, theλA are computed 1000 times, each using an atmospheric time series derived from a random permutation of the original observed time series A(t). The produced accumulative probability is then used to judge the significance of λA.
It is important to keep in mind the limitations of the analysis method here. First, our analysis is based on linear statistics, while vegetation dependence on climate can be nonlinear. For example, Zhou et al. (2003) suggested that the relationship between NDVI and climate is better shown (in both directions) as a quadratic equation, rather than a linear equation. Second, the analysis method is based on single variable statistics, assuming the atmosphere is mainly forced by the vegetation. In reality, the atmosphere may also respond to other variables, such as soil moisture (GLACE 2004). Third, the vegetation is assumed to interact with the atmosphere only locally. This is certainly not always true because atmospheric teleconnections can transmit significant climate impacts remotely. For example, vegetation may inject moisture into the atmospheric boundary layer (Freedman et al. 2001), and this moisture may precipitate downwind (e.g., Zhang et al. 2003). As another example, the atmosphere over land can also be affected by climate variability from the nearby ocean. Finally, our observational estimation below is severely limited by the quality of the data. The data is limited to only 19 years, from which it is difficult to obtain results with high statistical significance. Remote sensing data, including FPAR, may also have biases. In spite of these limitations, we believe it is important to assess observed vegetation–climate interactions using our statistical method because it represents a first step toward the assessment of global vegetation–climate interactions. Our assessment provides the first global-scale observational benchmark to be tested against by global vegetation–climate models. Two examples of preliminary model assessment will be presented in appendix B.
In the following, we will first examine climate–vegetation interactions in two regions as examples to illustrate our methodology. Then, we will investigate climate–vegetation interactions across the globe.
4. Two regional examples of climate–vegetation interaction
a. Northeast Brazil
In tropical steppe Northeast Brazil, the seasonal cycle of FPAR follows precipitation with a lag of about one month (Fig. 4a, right panel), reflecting the control of moisture stress on the dominant tropical grassland and shrubland. Similarly, the monthly variability of FPAR also lags rainfall by 1–2 months, as shown in the annual mean correlation between monthly precipitation and FPAR anomalies (top panel), which has a positive maximum with FPAR lagging by −1 to −2 months. Climate forcing on vegetation is seen more clearly in the seasonal march of the lagged correlation (lower left panel). The maximum precipitation driving, that is, the positive maximum correlation at negative lags, is dominant in the rainy season from February through May; the rainfall forcing can be traced back several months owing to the compounded memory of the vegetation and soil moisture (e.g., GLACE 2004). A secondary maximum in forcing from precipitation occurs in the dry season around October, reflecting perhaps the effect of drought stress on grasses and shrubs. The dry season rainfall, however, has a smaller contribution to the total vegetation growth since the correlation represents the relative contribution. Indeed, this secondary maximum correlation disappears in the lagged regression (not shown), which accounts for the effect of magnitude.
Vegetation feedback forcing on precipitation can be inferred from FPAR-lead correlations. The annual mean FPAR-lead correlation is positive and statistically significant at the 90% level at lags +1 to +3 months. [The degree of freedom is the number of years for the correlation of each month (Fig. 4, lower left panel), but for the number of months for the year-round correlation (top panel)]. This implies increased rainfall following vegetation greening: the emergence of leaves increases evapotranspiration, the local moisture supply, and, in turn, precipitation. The same sign of correlations at both vegetation lead and lag implies a positive vegetation–precipitation interactive feedback; an increase in rainfall drives more vegetation, which in turn induces more rainfall. The seasonal march of correlations (at positive lags) further shows that the positive vegetation feedback occurs mainly in the dry season from July through October. This positive correlation can be traced to the vegetation from several months earlier. This long lead reflects the persistence of the vegetation growth, rather than the delayed response of the rainfall to vegetation.2 The discussion above suggests that vegetation feedback occurs most efficiently after the vegetation has fully grown and it has the strongest relative impact on the rainfall of the dry season. This stronger relative impact on dry season rainfall is partly due to a smaller amount of precipitation in the dry season, rather than a larger amount of vegetation-induced precipitation. This is confirmed in the corresponding lagged regression map (not shown), which shows a positive regression with vegetation leading that is rather uniform from March to November, implying a comparable magnitude of vegetation feedback during that period. The different contributions of the vegetation feedback on the wet and dry seasons may also be related to the different states of the atmospheric circulation. In the dry season, the ITCZ migrates northward away from the equator, with the large-scale surface moisture flux diverging from Northeast Brazil. This makes the local recycling of moisture (due to land processes) relatively more important. In the rainy season, the ITCZ migrates toward the equator, with the background moisture flux converging toward Northeast Brazil. Now, the remote moisture supply, rather than the local moisture recycling, becomes more important for local rainfall.
In contrast to the vegetation–precipitation relationship, the seasonal cycles of vegetation and temperature vary out of phase (Fig. 4b, right panel). The correlation of vegetation variability with temperature is generally much weaker than with precipitation and, mostly, is not statistically significant (top and lower left panels). This suggests that the vegetation in Northeast Brazil interacts predominantly with precipitation rather than temperature, consistent with the general ecological features of the tropical steppe.
The efficiency of vegetation feedback on precipitation can be quantified using the τ = +1 month covariance in Eq. (4) as λP = 2.4 cm−1 month−1 (0.1FPAR)−1. [The unit cm−1 month−1 (0.1FPAR)−1 represents a change of precipitation in cm month−1 for a FPAR change of 0.1]. Averaged over the year, the precipitation variance induced by the feedback σ2(λPFPAR)is about 6% of the total monthly rainfall variance σ2(P). In the dry season, however, the contribution of the feedback-induced precipitation variability is more important (Fig. 4a), reaching up to 10%–15%.
The estimated λP is statistically significant at the 90% level according to the bootstrap method described in section 3. The robustness of the feedback parameter estimate can also be inferred from the statistical significance of the correlation coefficient at lag +1, which is higher than the 90% level (Fig. 4a, top panel). A sense of the robustness of the estimate can also be inferred from the estimations at successive lags. As discussed before (see also appendix A), in the context of a linear model, the ensemble mean estimate (4) should be independent of lags. Here, the λP estimated at lags +2 and +3 months are 2.5 and 5.2 cm month−1 (0.1FPAR)−1, respectively. These two estimates agree with the lag +1 estimate qualitatively. All three estimates consistently point to a positive feedback of about 3 cm month−1 (0.1FPAR)−1.
b. Eastern Siberia
In eastern Siberia, which is covered by boreal forests and grasslands, the seasonal cycle of FPAR follows temperature (Fig. 5a, right panel). The annual mean correlation of monthly variability (top panel) shows significant positive correlations at both negative and positive lags. This implies a positive FPAR–temperature interactive feedback: a higher temperature drives more vegetation (negative lags), which further warms the surface air (positive lags). The feedback efficiency, estimated using (4) at lag +1, is λT = 2.3°C (0.1FPAR)−1, statistically significant at the 90% level. This represents a significant feedback because the feedback-induced temperature variance σ2(λTFPAR)amounts to about 30% of the total variance σ2(T). The robustness of this positive feedback is also inferred from the correlation coefficient (top panel), which is statistically significant at the 90% level. Furthermore, the feedback estimates at the lags of +2 and +3 months are 1.9° and 1.5°C (0.1FPAR)−1, respectively, consistently suggesting a positive feedback around 2°C (0.1FPAR)−1.
The underlying mechanisms are more evident from the seasonal march of correlations (lower left panel). A significant temperature forcing in spring and fall (negative lags) reflects the strong temperature driving of seasonal leaf emergence and senescence there. This temperature forcing in spring could be also related to the temperature–albedo feedback associated with the earlier snow melting.
The most significant vegetation feedback (positive lags) occurs as a positive feedback on the October temperature, with the positive correlation involving vegetation from several preceding months (see footnote 2). Prior to October, in August and September the temperature appears to be influenced by a weak (but statistically insignificant) negative vegetation forcing. These correlations, perhaps, suggests a weak negative feedback on the atmosphere in the early fall and a sudden change to a strongly positive feedback on the atmosphere in October. With a great uncertainty, we speculate that these temperature correlations may result from a competition of opposing effects. In the fall, an anomalously late leafout increases the evapotranspiration and, in turn, the latent heating relative to sensible heating, eventually producing anomalous cooling (Schwartz and Karl 1990). In the meantime, the late senescence of leaves reduces the surface albedo (relative to the leaves), leading to an anomalous surface warming (Bonan et al. 1992). Before October, the evapotranspiration cooling effect is slightly stronger than the albedo warming effect, resulting in a weak net cooling. The albedo-induced warming intensifies abruptly in October, when the snow cover suddenly increases from zero in September to about 40%, and therefore abruptly enhances the albedo contrast between the leaves and ground. This warming effect overwhelms the cooling effect associated with the evapotranspiration and, therefore, generates a dominant positive feedback in October abruptly. A seemingly similar strong positive vegetation-lead correlation also exists in February, followed abruptly by a weak (and insignificant) negative feedback in the growing season. It is, however, not obvious if the February feedback transition can be interpreted similarly to the October case because the snow season lasts through April/May. Perhaps, other mechanisms such as cloudiness and snow melting play an important role. This February positive feedback could also be exaggerated by the snow bias on FPAR data (Los et al. 2000; Tian et al. 2004) since all of the preceding FPAR data (from October to January) most likely reflect just snow.
The dominant temperature driving on vegetation variability in the boreal region is generally consistent with previous studies (Schultz and Halpert 1993; Eugster et al. 2000; Chen and Pan 2002; Zhang et al. 2003). The vegetation feedback on temperature seems to be consistent with Kaufmann et al. (2003) and W05, who have recently studied the seasonal vegetation feedback on boreal temperature using a sophisticated statistical prediction model (Granger 1969). As discussed before, their seasonal predictability study is not quantitatively comparable with our instantaneous feedback study. Nevertheless, qualitatively, their findings are consistent with ours in the overall tendency of strong positive feedback around winter and weak negative feedback around summer. We emphasize that, at this stage, the feedback mechanisms remain speculative, especially on those features of the seasonal change that do not have high statistical significance. There are potentially many other mechanisms in this boreal region, involving clouds, light, soil moisture, etc., in addition to temperature and precipitation (Eugster et al. 2000). The statistical significance of the correlations of monthly anomalies between temperature/precipitation and FPAR are especially low. More complete data, such as surface turbulent heat fluxes, radiation fluxes, cloudiness, light, soil moisture, and vegetation type, are needed in the future to clarify the mechanism of the vegetation feedback.
Finally, in contrast to the strong correlation with temperature, the correlation of FPAR with precipitation in Siberia (Fig. 5b) tends to be statistically insignificant, reflecting the dominant temperature-driving there in contrast to the precipitation-driven vegetation variability in the Tropics such as Northeast Brazil (Fig. 4).
In the following, the covariance analysis will be applied to each 2.5° × 2.5° grid box globally over the continents, with the focus on the major features of large-scale vegetation–climate interactions. A study of vegetation–climate interaction over the United States is presented in a subsequent paper (Notaro et al. 2006).
5. Vegetation–climate interactions
a. Climate forcing on vegetation
Global maps of lead/lag climate/FPAR correlation are useful for inferring qualitative features of large-scale vegetation–climate interaction. Over the northern mid- to high latitudes, the year-round temperature-lead correlation shows significant positive maxima over the United States, central eastern China, and from eastern Europe through southern Siberia along the region of the boreal forests (Fig. 6a). Furthermore, these positive correlations are most significant in spring and fall, as indicated in the seasonal mean of the monthly correlations (Figs. 7a–d). In comparison, the precipitation-lead correlation is small year-round (Fig. 6b) without a dominant sign with seasons (Figs. 7e–h). This reflects a dominant temperature forcing on forests and shrublands in boreal and temperate regions, especially in spring and fall when the leaf seasonality of the plants is affected the most, as discussed for Siberia (Fig. 5). Our analysis here is consistent with previous studies (e.g., Schultz and Halpert 1993; Eugster et al. 2000; Schaefer et al. 2002; Zhou et al. 2003; Chen and Pan 2002; Zhang et al. 2003; W05), which suggests that temperature is the major forcing for the vegetation variability observed in northern North America and Eurasia.
Over much of the Tropics and subtropics (except for the tropical rainforest where the correlation is small), vegetation variability is forced predominantly by precipitation. This can be seen over the Sahel and southern Africa, central and eastern Australia, Mexico/southwestern United States, India, and Southeast Asia, where the year-round precipitation-lead correlations are positive and highly significant (Fig. 6b). The major precipitation driving occurs in different calendar months in different regions, as seen in the seasonal mean of the monthly precipitation-lead correlations (Figs. 7e–h): boreal spring across North Africa and South/East Asia, boreal spring through summer in Mexico/south-central United States, austral summer in southern Africa, and austral spring and fall in Australia. Much of these regions is covered by grasslands and shrublands. Since temperature is sufficiently high year-round but moisture is limited, vegetation activity is most sensitive to drought stress. In addition, grasses and shrubs have a faster response time to precipitation forcing than trees and therefore contribute to the dominant precipitation-driving response there. In contrast to the precipitation-lead correlation, the temperature-lead correlation becomes weakly negative in these regions (Fig. 6a), reminiscent of the case of Northeast Brazil (Fig. 4b). The negative temperature-lead correlation in the Tropics and subtropics is also reflected in the seasonal mean of the monthly correlations (Figs. 7a–d), with the regions of maximum negative correlation largely corresponding to those of maximum precipitation driving (Figs. 7e–h). This weak negative temperature–vegetation correlation may be a byproduct of the strong positive precipitation forcing on vegetation (Fig. 6b). While forcing the vegetation, the increased precipitation also cools the surface air through increased cloudiness and evaporation, resulting in a generally negative temperature–precipitation correlation in these regions (Fig. 8).
In short, the climate-lead correlations above suggest that temperature is important for forcing vegetation variability in northern mid/high latitudes while precipitation is important in the Tropics/subtropics (Schultz and Halpert 1993). It is also interesting that the regions of strongest temperature/precipitation influence on vegetation (Fig. 6) coincide roughly with the regions of the maximum variability of anomalous FPAR (Fig. 3), suggesting a dominant role of temperature and precipitation forcing there.
b. Vegetation feedback on climate
Qualitative features of global vegetation feedback forcing on climate can be inferred from the vegetation-lead correlations. First of all, the vegetation-lead correlations (Figs. 9, 10) are overall weaker than the corresponding climate-lead correlations (Figs. 6, 7), implying a less significant impact of vegetation feedback on climate than that of the climate forcing on vegetation. This is expected because climate variability is generated predominantly by processes within the physical components, notably the atmosphere and ocean, with the vegetation primarily acting as a moderator. In contrast, vegetation variability is driven fundamentally by climate, through heat/cold stress, drought stress and light. The weak vegetation feedback is especially evident on precipitation correlation, with little spatial coherence and few regions of statistical significance (Fig. 9b). This suggests, overall, weak vegetation feedback on local rainfall—a point to be returned to later.
Over northern mid- and high latitudes, the year-round temperature/FPAR correlations are somewhat similar between the FPAR-lead (Fig. 9a) and climate-lead (Fig. 6a) patterns. Vegetation's impact on temperature occurs mainly in the positive centers across southern Canada, central/eastern Europe, south/eastern Siberia, and southwestern China. A positive FPAR anomaly tends to lower the albedo versus ground (even in the absence of snow) and results in more energy absorption. If snow is present, the change in albedo is even larger and may therefore enhance the warming. These positive centers of vegetation-lead correlation largely coincide with those of positive temperature-lead correlation, and therefore may represent the regions of significant positive vegetation–temperature interactive feedback. A comparison of the seasonal mean correlation (Figs. 7a–d versus Figs. 10a–d) further shows that the overlap of positive correlation centers tend to be stronger in boreal fall in these regions and, in addition, in boreal spring over the North America and southwestern China. This indicates a seasonal dependence of the positive feedback that may be associated with the seasonal leaf phenology as discussed for Siberia (Fig. 5a). This positive FPAR–temperature feedback is also consistent with Kaufmann et al. (2003) and W05, who showed a strong positive feedback between NDVI and temperature around winter. In comparison, there is little vegetation-lead correlation with precipitation in the northern mid- and high latitude, implying a dominant vegetation feedback only on temperature there.
In the Tropics and subtropics, the year-round vegetation-lead correlation with precipitation is generally weak, except for a few isolated dry grassland regions (Northeast Brazil, East Africa, northeastern Asia, and Alaska) where the FPAR-lead correlation is significant and positive (Fig. 9b). These isolated pockets may represent regions of positive vegetation–precipitation feedback because the precipitation-lead correlations also tend to be positive there (Fig. 6b), similar to the Northeast Brazil discussed in Fig. 4a. In some regions, the weak year-round precipitation feedback may result from a cancellation of opposite feedbacks in different seasons, as seen in the seasonal mean FPAR-lead correlations (Figs. 9e–h). For example, across North Africa in the Sahel region, the FPAR-lead correlations with precipitation are positive in spring and summer but become negative in fall and winter (Figs. 9e–h). The evolution of the feedback is seen more clearly in the seasonal march of the regional correlation (Fig. 11). The seasonal cycle of FPAR lags the monsoon precipitation by about a month (right panel), reflecting the rapid response of the grasses and shrubs there. The year-round correlation of monthly variability is dominated by a broad positive peak (significant at the 90% level) when precipitation leads by 1 to 4 months (top panel). This precipitation forcing, as seen in the seasonal march of the correlation (lower left panel), is contributed mainly by the rainy season of spring to fall. In the meantime, the vegetation-lead correlation is also positive from April to August, most significant in April and May during the onset of monsoon rainfall. This implies that increased vegetation may supply additional moisture to the atmosphere and in turn help the onset of the African monsoon, with the most significant contribution occurring in the dry season before the full monsoon rainfall. Averaged over the year, however, the positive correlation in spring and summer is partly canceled by the negative correlation from November to March, resulting in a weak positive year-round correlation that is no longer statistically significant (positive lags, top panel).
In short, the lagged correlation suggests a strong positive vegetation feedback on temperature over regions in the northern mid- and high latitudes. In contrast, the vegetation feedback on precipitation is generally insignificant except in some isolated semiarid pockets in the Tropics/subtropics.
6. Assessment of vegetation feedback on climate
Next, we quantify vegetation feedback using Eq. (4). On each grid box, the feedback parameter is estimated using the first three lags with the weights of 1, 0.5, and 0.25 for lag 1, 2, and 3, respectively (Figs. 12a, 13a). The statistically significance is judged at the 90% level for the year-round feedback (Figs. 12c, 13c) and the seasonal feedback (not shown). Consistent with the correlations in Fig. 8a, vegetation feedback on temperature is dominated by positive feedbacks in the northern temperate to subarctic regions (Fig. 12a). The strongest positive feedback occurs at high latitudes in southern Canada/northern United States [significant in March–May (MAM)], northern Europe (significant in DJF) and southern Siberia [significant in September–November (SON)] where the year-round feedback efficiency λTis statistically significant and exceeds 1°C (0.1FPAR)−1 (Fig. 12c). A comparable and significant positive feedback also occurs in southwestern China around the Tibetan Plateau (significant in MAM). In these regions, the feedback-induced variance σ2(λTFPAR) explains over 10%–25% of the total temperature variance σ2(T) (Fig. 12b). In the rest of the world, the FPAR feedback parameter does not pass the 90% confidence level with the magnitude much less than 1°C (0.1FPAR)−1 (Fig. 12a) and the feedback explained variance of less than 10% of the total variance (Fig. 12b).
Consistent with the correlation analysis (Fig. 9b), vegetation feedback on precipitation is not statistically significant at 90% level except in a few isolated regions in Northeast Brazil (significant year-round), East Africa (significant in DJF), northeast Asia (significant in JJA), and northern Australia (significant in JJA) (Figs. 13a,c). The feedback explained variance usually accounts for less than 10% of the total precipitation variance, also much weaker than the temperature feedback explained variance (Fig. 13b versus Fig. 12b). There are broad areas with weak negative vegetation feedback on precipitation over the boreal midlatitudes, such as southern Siberia and North America. These regions have been identified by W05 as areas of statistically significant vegetation causality of reduced precipitation using a predictive model for April to October. They interpret the negative feedback as soil moisture drying out after the initial evapotranspiration because of increased vegetation. In our feedback estimate, these regions are not significant. In the Tropics and subtropics, albeit not highly statistically significant, modest positive feedbacks on precipitation exist coherently over Northeast Brazil, East Africa, East Asia, the U.S. Great Plains, northern Australia, and part of Central Europe. These regions are dominated by grasslands and shrublands. Perhaps, the fast response of grasses and shrubs enable them to feed back on precipitation somewhat more efficiently at the monthly time scale discussed here.
The different vegetation feedbacks on temperature and precipitation are seen more clearly by comparing Table 1 and Table 2, which summarize the FPAR feedback explained variances in different latitude belts for temperature and precipitation, respectively. The most striking feature is a much larger explained variance for temperature than for precipitation. This can be seen in the magnitude of the explained variance (first rows). Except for northern high latitudes, the explained variance is about 11% for temperature (Table 1), but only 2% for precipitation (Table 2).
The other important difference is the sign of the dominant feedback. Worldwide, the feedback on temperature is dominantly positive, but the feedback on precipitation has no dominant sign. This can be seen by comparing the explained variances that are averaged over the areas of positive (second rows) and negative (third rows) feedback separately in Tables 1 and 2. For temperature, the magnitude of the explained variance for positive feedback is clearly larger than that for negative feedback (Table 1, rows 2 against 3). In comparison, for precipitation, the explained variances tend to be comparable for both signs (Table 2, row 2 against 3). Furthermore, the relative area of positive feedback on temperature is about 70% (bottom row, Table 1), about twice that of the negative feedback. In contrast, the positive feedback area on precipitation is about 50% (bottom row, Table 2), comparable with that of negative feedback.
In short, our assessment suggests a significant positive vegetation feedback on temperature with the maximum in northern mid- and high latitudes where the feedback-induced variability accounts for over 10%–25% of the total temperature variance. In contrast, the vegetation feedback on precipitation is largely insignificant, usually explaining less than 5% of the precipitation variance. In addition, there is no overall preferred sign of vegetation feedback on precipitation. It is, however, interesting to note that, if Fig. 13a was plotted with only statistically significant areas, it would be dominated by the positive sign. This implies that, in the regions where precipitation may be significant, it tends to be a positive feedback on local rainfall.
7. Scale dependence of the feedback
a. Nonlocal process and the dependence on spatial scales
It is somewhat unexpected that vegetation–precipitation interaction shows little significant positive feedback even in the Tropics. Many modeling studies have suggested that an increase in vegetation leads to enhanced evapotranspiration, local moisture supply, and eventually more rainfall (e.g., Shukla and Mintz 1982; Dickinson and Henderson-Sellers 1988; Gallimore and Kutzbach 1996; Zhang et al. 1996; Claussen et al. 1999). We speculate that there might be physical reasons why our assessed feedback on precipitation is weak. One possibility is that vegetation feedback on precipitation is more nonlocal than on temperature. Physically, the direct local hydrological impact of vegetation on the atmosphere is a supply of moisture into the boundary layer. This extra moisture, however, may be transported by the wind to precipitate downstream. A recent analysis of spring NDVI and subsequent summer precipitation in China seems to show some evidence of a downstream vegetation impact (Zhang et al. 2003). Indeed, horizontal moisture advection usually overwhelms local moisture recycling at small scales. On a 500-km scale, recycling over land only accounts for 9% of local precipitation; even on a 1000-km scale, less than 20% of rainfall comes from local evaporation (Trenberth 1999). Therefore, the role of local moisture recycling on precipitation tends to increase with spatial scales. This suggests a possible sensitivity of the feedback to spatial resolution. A larger area may more fully capture the precipitation feedback. To test this hypothesis, we repeated our feedback analysis using data that is first aggregated onto 5° × 5° grid boxes. The latitudinal distribution of the feedback explained variance is shown in brackets in Tables 1 and 2. Compared with the analysis from the 2.5° × 2.5° grid, the magnitude of the feedback is increased for precipitation by over 20%–50% (row 1 of Table 2), but remains almost unchanged for temperature (row 1 of Table 1). In the meantime, there is no systematic change of positive feedback relative to negative feedback on precipitation. Indeed, feedbacks of both signs are enhanced by about the same factor such that the relative magnitude (rows 2, 3) and area (row 4) remain almost unchanged (Table 2). Therefore, a larger area may enhance the magnitude of the feedback on precipitation, but not its preferred sign.
The physical argument above, if correct, also implies a more positive feedback of vegetation on the column-averaged precipitable water than on precipitation. This seems to be confirmed by analyzing the feedback between FPAR and total precipitable water using the NCEP–NCAR reanalysis (Kalnay et al. 1996). This feedback does appear to be largely positive, especially over the Tropics (Fig. 14). The latitudinal distribution of FPAR feedback explained variance is now dominated by positive feedback (Table 3). The explained variance of the positive feedback on precipitable water (row 2 of Table 3) more than doubles that on precipitation (row 2 of Table 2) in the low and midlatitudes (from 1%–3% to 3%–6%) and is about twice that for negative feedback (row 3 of Table 3). The relative area of positive feedback is also increased from around 50% to over 70% (row 4 of Table 3). Therefore, vegetation feedback may indeed add moisture to the atmosphere locally, but the increased moisture may not precipitate locally.
b. Dependence on time scales
Vegetation–climate feedback may also vary with time scale because of the different physical and ecological processes dominant at different time scales. At monthly-to-seasonal time scales, vegetation variability involves mainly leaf phenology. At annual-to-decadal time scales, vegetation succession and dynamics, including vegetation fractional coverage, become more important. In addition, grasses and shrubs may be more active at shorter time scales, such as monthly to seasonal, because of their fast response time, while the forest may be more effective in affecting climate at longer time scales. To examine the dependence of the feedback on time scales, we repeated the feedback analysis on seasonally binned FPAR, temperature, and precipitation. The feedback estimated using Eq. (4) is now caused by processes longer than a season. Similarly, we also repeated the feedback analysis to the annually binned data to assess the feedback for variability longer than a year. The overall magnitude of the feedback efficiency is found to increase significantly at longer time scale, especially on precipitation. For the feedback on temperature, the global mean of the magnitude of the feedback efficiency increases from 0.9°C (0.1FPAR)−1 for the monthly data to 1.4°C (0.1FPAR)−1 for the seasonal data to 2.2°C (0.1FPAR)−1 for the annual data. For the feedback on precipitation, the global mean of the magnitude of the feedback efficiency increases from 1.8 cm month−1 (0.1FPAR)−1 for the monthly data to 2.8 cm month−1 (0.1FPAR)−1 for the seasonal data to 3.9 cm month−1 (0.1FPAR)−1 for the annual data. This implies, probably, a stronger vegetation feedback efficiency on a longer time scale. However, we point out that this result is very preliminary because of the very short data length here.
The feedback explained variances also increase for temperature (Table 4 compared with Table 1) and precipitation (Table 5 compared with Table 2). A comparison of the monthly (Table 2) and seasonal (Table 5) analysis of the precipitation feedback, however, shows a much larger increase in the explained variance than in the feedback efficiency: the seasonal analysis has an explained variance of 20%, 10 times larger than the monthly analysis, while the overall magnitude of the feedback efficiency only increases by 2.8/1.9 ∼1.5 times. The dramatic increase of the explained variance of the feedback on precipitation for the seasonal data is due mostly to the much larger reduction of the total variance of the precipitation than the FPAR feedback effect after the seasonal average because the former has a much shorter persistence time. Therefore, in spite of the weak vegetation feedback on precipitation on monthly variability (Fig. 13b), the potential vegetation feedback on precipitation could be much stronger toward longer time scales.
As in the case of increased spatial resolution, one notices that the feedback and its explained variance increase for both positive and negative feedback almost equally such that the relative intensity of positive and negative feedback remain largely unchanged. For example, the relative areas of positive and negative feedbacks remain around 70% and 50% for temperature and precipitation, respectively, similar to the monthly analysis (the last rows of Tables 1 and 2). Similar conclusions seem to hold for another derivation of the annual FPAR data, the vegetation fractional coverage. We repeated the feedback analysis using the annual fractional coverage derived from NDVI (Zeng et al. 2003). The results are largely consistent with the estimated feedback using the annual mean FPAR.
The analyses of the feedback dependency on spatial and temporal scales should be treated as largely speculative because of the low statistical significance for seasonal and, especially, annual, data analysis. This is especially true for the feedback on precipitation, which itself has intrinsically large internal variability, as discussed before.
We presented a first observational assessment of vegetation–climate feedback over the globe, with the focus on the interaction of vegetation and climate variability of interannual time scales. In the northern mid- and high latitudes, which is covered mostly by boreal forests, vegetation variability is forced predominantly by temperature; in the meantime, vegetation variability also exerts a strong positive feedback on temperature, notably in southern Canada/northern United States, northern Europe, and southern Siberia, where the feedback efficiency exceeds 1°C (0.1FPAR)−1 and the feedback-induced variability explains over 10%–25% of the temperature variance. In the Tropics and subtropics, which are dominated by grass/shrubland, vegetation is driven primarily by precipitation. However, there is little vegetation feedback on local precipitation. In a few isolated regions located in Northeast Brazil, eastern Africa, East Asia, and northern Australia, there appears to be modest vegetation feedback exceeding 1 cm month−1 (0.1FPAR)−1 and explaining over 5% of the precipitation variance. In contrast to the dominant positive vegetation feedback on temperature at northern high latitudes, there is no evidence of a preferred positive feedback on precipitation in the Tropics/subtropics. Finally, the tropical region of rainforest has the smallest variability and does not interact significantly with climate.
With a larger spatial scale and a longer time scale, our study suggests an increased vegetation feedback, especially on precipitation, although the relative dominance of positive and negative feedbacks remain largely unchanged. This scale dependence should be treated with caution here. On the other hand, this scale dependence, in general, is not unexpected, because different scales may involve different physical and ecological processes.
The conclusions above remain tentative. First, the available FPAR data may have biases. For example, the strong vegetation feedback in northern high latitudes could be exaggerated by the snow bias on the FPAR data (Los et al. 2000; Tian et al. 2004). Second, the statistical significance remains poor, even for monthly data analysis, because of the short observational record. Third, particular caution should be exercised in interpreting vegetation–precipitation feedback because of the intrinsically higher level of noise of the precipitation data and of the seemingly more complex processes involved in vegetation–precipitation interaction. Finally, as discussed in section 3, the analysis method itself has limitations, which may have excluded nonlinear processes and nonlocal responses.
As a pilot study here, we have focused on the quantification of the vegetation feedback. Many interpretations of the vegetation feedback, however, have remained speculative, and many of the identified features of vegetation–climate interaction have remained unexplained. Much effort is needed in the future to understand the complex nature of climate–vegetation feedback with more complete datasets and more focused analyses.
In spite of these shortcomings, our assessment provides a useful first guess of global vegetation feedback that can serve as a benchmark to be tested against by coupled climate–vegetation models. As a demonstration, we present in appendix B a preliminary analysis of vegetation feedback in two fully coupled climate–dynamic vegetation GCMs, the Fast Ocean Atmosphere Model–Lund Potsdam Jena (FOAM-LPJ) (Gallimore et al. 2005; Notaro et al. 2005) and NCAR community climate systems model (CCSM2) coupled with a dynamic global vegetation model that incorporates part of LPJ vegetation dynamics [hereafter referred to CCSM2 (coupled to LPJ)] (Levis et al. 2004). Compared with observations, FOAM-LPJ shows a reasonable agreement in vegetation–temperature feedback but a strong bias toward positive vegetation–precipitation feedback, while CCSM2 shows good agreement with observations in vegetation–precipitation feedback, but a lack of positive vegetation–temperature feedback in the northern high latitudes. The significant model–observation and model–model differences indicate a strong need for model improvement. In the meantime, the partial success of the models suggests that such models may be useful in improving our understanding of vegetation–climate interaction.
We thank Drs. S. Hotchkiss, J. Williams, S. Levis, and R. Gallimore for helpful discussions, and Dr. X. Zeng for providing the vegetation fractional coverage data. We are also grateful to two anonymous reviewers, whose insightful comments and constructive criticism have improved the paper substantially. This work is supported by NSF, DOE, and NOAA.
Vegetation–Atmosphere Feedback in an Idealized Coupled Model
To shed light on the essence of the feedback estimate, we study a pedagogic coupled vegetation–atmosphere model as an example. The model is a linear coupled model forced by stochastic internal atmospheric variability [symbolically similar to the coupled atmosphere–ocean model of Bretherton and Battisti (2000)]
Here A and V represent the atmospheric and vegetation variables, respectively; M is the ratio of the memories of the vegetation and atmosphere. Model parameters a, b, c, and d are ∼1, such that the atmospheric memory in nondimensional time is t ∼ 1 (corresponding to about four days here) while the vegetation memory is t ∼ M. More specifically, a > 0 and d > 0 represent the internal damping (without coupling) of the atmosphere and vegetation, respectively. The atmosphere forces the vegetation through cA while the vegetation forces the atmosphere through bV as the feedback. Thus, bc > 0 represents a positive vegetation–atmosphere interactive feedback, and bc > 0 a negative interactive feedback. The stochastic atmospheric internal variability is represented by a white noise random variable N of the variance σ2, such that
δ(u) being the delta function and angle brackets the ensemble mean. When ad − bc > 0, the coupled system is stable and therefore is analogous to a linear stochastic climate model with the SST replaced by vegetation (Frankignoul and Hasselmann 1977; Bretherton and Battisti 2000).
The analysis can be simplified by taking advantage of the long memory of the vegetation relative to the atmosphere (M ≫ 1). Averaged over a time interval longer than the atmospheric memory (∼1), but shorter than the vegetation memory (∼M), the vegetation equation (A1b) should remain approximately unchanged. The atmosphere, however, will be in quasi-equilibrium such that Eq. (A1a) can be approximated as 0 = −aA + bV + N, or
Now b/a = λa is the vegetation feedback parameter, which can be interpreted physically as the forcing efficiency of the vegetation on the atmosphere such that the atmosphere reaches a statistic equilibrium response 〈A(t)〉 = (b/a)〈V(t)〉. Substitution of Eq. (A3) into Eq. (A1b) leads to an approximate coupled equation for vegetation as
Here B = (ad − bc)/Ma > 0 is the effective damping rate on vegetation in the coupled system. The forced vegetation variability in the coupled system is therefore
With the aid of (A2), we can derive the lagged covariance as
where the discontinuity at τ = 0 in (A7) is due to the neglect of the atmospheric adjustment in (A3). The vegetation autocovariance (A6) shows that the effective damping rate on vegetation in the coupled system is now B (corresponding to a persistence time 1/B). Compared with the internal vegetation damping rate d/M in (A1b), we have B − d/M = −bc/Ma. Thus, a positive vegetation–atmosphere feedback (bc > 0) reduces the damping on (increases the persistence time of) vegetation. Multiply Eq. (A3) by V(t − τ) and ensemble average, we have
Note that the cross-covariance (A9) (and the corresponding regression/correlation coefficients) decay toward both sides with the memory of the vegetation in the coupled system. With (A6), (A7), and (A9), it is straightforward to show that the covariance ratio is
This shows explicitly, in our idealized model, that the covariance ratio is an unbiased estimator of the vegetation feedback parameter b/a only when the vegetation leads the atmosphere (τ > 0). When the vegetation lags the atmosphere (τ < 0), the covariance ratio is larger (smaller) than the true feedback parameter, depending on the sign of c because vegetation variability is now forced by previous atmospheric noise such that 〈V(t − τ), N(t)〉 > 0 (<0) as shown in (A7).
The estimator (A10a) gives the most accurate estimate at the first few lags even though, in theory, it should remain as a constant at any lag τ > 0. The ratio of the covariance is independent of lag because the covariance in both the numerator and denominator decrease with the lag as e−B|τ| as in Eqs. (A6) and (A7). The sampling error of (A10a), however, tends to increase with lag, because the diminishing autocovariance in the denominator amplifies the sampling error in the numerator. [In the similar spirit, although various estimators can be derived for the feedback parameter b/a, the estimator (A10a) appears to be the optimal one because of the relatively smaller sampling error.]
Figure A1a shows an example of the covariance ratio (A10) for a vegetation memory of 40 days (M = 10). The result is calculated numerically from the fully coupled system (A1) using monthly data from a 10-member ensemble (each of 20 yr length). The ensemble mean estimate (circle) reproduces the feedback b/a at positive lags very well (up to five as plotted here). Furthermore, the sampling error, as measured by the standard deviation of the ensemble (dash lines in Fig. A1a), is small for the first few lags, but increases at larger lags. Figure A1b further shows a case with a vegetation memory of only 12 days (M = 3). With the shorter vegetation memory, the sampling error increases because of a larger damping rate B and in turn a smaller denominator with lags in the covariance ratio in (A10a) and (A10b). Nevertheless, at the first two lags, the ensemble mean estimate remains accurate and the sampling error remains small. Therefore, qualitatively, a smaller B (or longer persistence time of vegetation variability in the coupled system) seems to give a smaller sampling error and in turn a more accurate estimation. The memory of the vegetation (M), although not present in the estimator (A10), is therefore important in determining sampling error of the estimator (A10) with a longer vegetation memory favoring a more accurate estimation.
We end the section with a brief discussion of the covariance ratio at negative lags as in (A10b). These covariance ratios, in principle, should reflect the atmospheric forcing on vegetation. The true atmospheric forcing efficiency on vegetation in our simple system is d/c because this parameter allows the vegetation equation (A1b) to reach the quasi-equilibrium response, cA(t) − dV(t) = 0, in response to a persistent atmospheric forcing cA.A1 This atmospheric forcing efficiency d/c can be easily shown to be smaller than the estimation (A10b). The overestimation of (A10b) relative to d/c can also be seen in Figs. A1a,b (dash–dot) at negative lags. Rather, the forcing efficiency d/c is correctly estimated at τ = 0 in Figs. A1a,b. This can be confirmed in our approximate solution (A10a), (A10b) if we take the covariance ratio at τ = 0as the average of the limits from both sides [i.e., the average of (A10a) and (A10b) at the limit of τ → 0].A2
Vegetation Feedback in Climate–Vegetation Models
As a preliminary model–observation comparison, we applied the statistical assessment (4) to the vegetation feedback in two fully coupled atmosphere–ocean–dynamic vegetation model simulations: a 400-yr simulation of FOAM-LPJ (Gallimore et al. 2005; Notaro et al. 2005) (Figs. B1, B2) and a 100-yr simulation of CCSM2 (coupled to LPJ) (Levis et al. 2004) Figs. B3, B4). Overall, FOAM-LPJ shows a reasonable agreement with the observations in vegetation–temperature feedback but a strong bias toward positive feedback for vegetation–precipitation; in contrast, CCSM2 shows a good agreement with the observation in vegetation–precipitation feedback, but a lack of positive vegetation–temperature feedback in the boreal areas. It is worth note that, owing to the longer time series of the model simulations than the observation, most major features discussed below are statistically significant over 90%.
We first discuss vegetation–temperature feedback using monthly data. Compared with the observation (Fig. 12), in the northern mid- to high latitudes, FOAMLPJ (Fig. B1) reproduces the maximum positive feedback and shows good agreement with the observations in both feedback efficiency and explained variance. In the Tropics and subtropics, FOAM-LPJ tends to have a negative feedback, but the extent of negative feedback is somewhat stronger than in the observation. Since LPJ only models natural vegetation, this difference from the observation may be partly caused by the lack of crops in the LPJ model. In comparison, CCSM2 (Fig. B2) does not capture the dominant maximum positive feedback in Siberia, partly because of the lack of tree coverage there, which in turn is caused partly by a dry bias of the model climatology. Like FOAM-LPJ, CCSM2 also tends to produce a stronger negative feedback on temperature from northern midlatitude all the way to the Southern Hemisphere. This stronger negative feedback in the model seems to be consistent with some other modeling works (e.g., Bounoua et al. 2000). The model–observation difference could be due to the model bias of a negative vegetation feedback on temperature owing to, for example, to an evapotranspiration-induced negative feedback stronger than the albedo-induced positive feedback relative to the observations. One should also be cautious about the observational analysis. The observations are rather short for robust conclusions. There are also observational features that are not well understood. For example, the observations seem also to indicate a positive vegetation feedback on temperature in the warm seasons (e.g., over the northwestern United States) (Fig. 10c). In the warm season, there is no snow and the associated positive albedo feedback. Therefore, the temperature may be lowered by a dominant evapotranspiration effect (Bounoua et al. 2000; Bonan 2002). Thus, the model–observation discrepancies require further studies.
The vegetation–precipitation feedback in FOAM-LPJ (Fig. B2) shows an overwhelming bias toward positive feedback compared with the observations (Fig. 13). Also in contrast to the observations, this model positive feedback is statistically significant at the 90% level almost everywhere, because of the much longer data in FOAM-LPJ. This strong positive vegetation–precipitation feedback may be partly related to a wet bias of the model climatology, especially in the Tropics (R. Gallimore 2004, personal communication). CCSM2 (Fig. B4), however, seems to produce a vegetation–precipitation feedback that appears to agree well with the observations (except for the northern high latitudes), although there are few regions of high statistical significance. Relative to the observations, the overall feedback intensity is stronger in FOAM-LPJ, but weaker in CCSM2 (see Table B1). Similar to the discussion above on temperature feedback, at this stage, the model–observation discrepancy should be treated as tentative and requires further studies.
Feedback analysis is also performed on the seasonally and annually binned data, as in the observations. Overall, the patterns of the feedback of seasonal and annual data analyses (not shown) remain largely similar to the monthly analyses, as in the observations. Furthermore, the magnitude of the feedback and the explained variance tend to increase from monthly to seasonal analysis (Table B1), also as in the observations. However, the magnitude of the increased feedback from monthly to seasonal is smaller than those observed; the model feedbacks also appear to weaken from seasonal to annual analysis, opposite to the observations.
The analysis on the model simulations could also help us understand the observational analysis. Since the model FPAR has no bias due to, say, snow, the model provides a consistency check of the vegetation feedback (to the extent that the model is correct). The strong positive vegetation–temperature feedback at high northern latitudes in FOAM-LPJ suggests that this strong feature in the observations is probably not distorted by the potential bias of the FPAR data there. The similarity of the patchy patterns of vegetation–precipitation feedback in CCSM2 and the observations also suggests the possibility of the patchy nature of the vegetation feedback on precipitation. Furthermore, the model simulations also show dependence of the feedback on time scales. Since the model output, especially of FOAM-LPJ, is rather long, the time-scale dependence of the feedback is likely to be statistically significant in the model. This suggests that the scale dependence may also be relevant in the observation. Finally, sensitivity experiments can be performed in the models, together with the statistical assessment, to assess the vegetation feedback explicitly. This is impossible with the observations. This suggests that a combined model–data approach, with both statistical assessment and explicit model simulations, will be the most fruitful method to understand vegetation–climate feedback.
It is beyond the scope of this study to identify the cause of the model biases. It suffices to point out here that the model deficiency on vegetation–climate feedback is caused by the model shortcomings, not only in the vegetation model but also in other model components such as the atmosphere and soil, or the different spatial resolution of the models.
* CCR Contribution Number 874
Corresponding author address: Z. Liu, Center for Climatic Research, 1225 West Dayton Street, Madison, WI 53706. Email: email@example.com
The vegetation memory estimated here needs to be treated as tentative. First, the vegetation memory here is in a compounded sense, because part of the memory of FPAR could be contributed indirectly by processes other than vegetation, such as soil moisture. Second, the decorrelation time of vegetation may be shorter than the true vegetation memory in a coupled system such as the observation. This is because vegetation is forced significantly by the atmosphere. Therefore, the vegetation variance obtained in a coupled system could be contributed significantly by the rapid atmospheric variability, which leads to a biased decorrelation time that is shorter than the true vegetation memory.
The quasi-equilibrium response of the atmosphere to vegetation in (A3) is approximately true in the coupled system, because vegetation is usually slower than the atmosphere. To the contrary, the quasi-equilibrium vegetation response to the atmosphere dV = cA is unlikely to be realized in the coupled system, because the atmosphere is usually faster than the vegetation.
At positive lags, the estimator (A9a) is the most robust and tends to be insensitive to the details of the model, because (A9a) is valid as long as 〈V(t − τ), N(t)〉 = 0. If the coupled variability is forced predominantly not by the atmospheric internal noise N, but by, say, an external forcing, or coupled variability, or internal variability of the slow component, the estimator in (A9a), (A9b) tend to give the correct feedback parameter b/a across all the lags, including negative and zero lags. Qualitatively, this can be understood from (A8), or more generally Eq. (2) (in section 3). If the dominant variability in the vegetation and atmosphere is not forced by N, the vegetation covariance with the atmospheric noise 〈V(t − τ), N(t)〉 is negligible relative to the autocovariance 〈V(t − τ), V(t)〉 and the atmosphere–vegetation covariance 〈V(t − τ), A(t)〉 at all the lags.