The global response of temperature to high-latitude vegetation greening in a two-dimensional energy balance model

ABSTRACT The relationship between vegetation greening and climate change remains unclear due to its complexity, especially in drylands. Against the background of global warming, arid and semi-arid areas, including mid-latitude deserts, are most sensitive to climate change. In recent decades, the mechanisms underlying the relationship between vegetation greening and climate change have been widely discussed in the literature. However, the influence of vegetation greening in high latitudes on regional climate has not been fully studied. In this paper, a two-dimensional energy balance model was used to study the influence of greening in high latitudes on mid-latitude deserts. The authors found that when greening occurs in high latitudes, the mid-latitude desert recedes at the south boundary, while the polar ice belt and low-latitude vegetation belt both expand. Simultaneously, greening in high latitudes can induce a negative temperature anomaly in northern latitudes and a positive temperature anomaly in southern latitudes. The mid-latitude desert expands at its north and south boundaries until the CO2 concentration reaches 600 ppm (saturated state). The greening in high latitudes could result in a lower global-mean temperature in the ‘saturated’ state, due to the stronger cooling in high latitudes. GRAPHICAL ABSTRACT


Introduction
Vegetation growth has been significantly affected by climate change, from the stomatal scale to the ecosystem scale, as reflected in increased vegetation greening worldwide. Such phenomena, in turn, affect the climate system through many biophysical processes. Understanding the interactions between vegetation and climate is important for predicting climatic conditions, especially in semi-arid and desert regions. Semi-arid regions are very sensitive to climate change and human activities, because of the low vegetation cover and relatively large human populations (Wang et al. 2012;Huang et al. 2019). Semi-arid regions have expanded during the past 60 years and have experienced the most enhanced warming, especially during the cold season (Huang, Guan, and Ji. 2012;Huang et al. 2016aHuang et al. , 2016b. Based on bias-corrected CMIP5 (phase 5 of the Coupled Model Intercomparison Project) projections, dryland areas will expand by 23% by the end of this century under the RCP8.5 (8.5 W m −2 Representative Concentration Pathways) scenario, such that they will account for 56% of the global land surface (Huang et al. 2016a). Such an expansion of drylands would affect the lives of many residents in arid and semi-arid regions and lead to serious social and economic problems. Therefore, understanding the expansion of drylands and the mechanisms behind the enhanced warming therein is important for developing strategies for climate adaptation.
Many mechanisms have been proposed to explain the enhanced warming in semi-arid areas, including land-atmosphere interactions (Huang et al. 2017b(Huang et al. , 2017a. Low soil moisture in semi-arid regions dictates that the surface available energy can only be released by sensible heating, which leads to more warming than in humid areas. Guan et al. (2015) applied the adjustment method proposed by Wallace et al. (2012) to divide the raw temperature into the dynamically induced temperature (DIT) and radiatively forced temperature (RFT). Their results suggest that the enhanced semi-arid warming is more attributable to RFT than DIT; circulation changes are also a contributing factor. He, Huang, and Ji. (2014) found the land-sea thermal contrast in winter decreases with greater global warming, in turn reducing the strength and frequency of blocking through its effects on planetary waves, and inducing additional warming in semi-arid regions. However, the above-mentioned mechanisms mainly involve local feedback or are influenced by oceans; the influence of high-latitude land warming on midlatitude semi-arid areas remains unclear.
As a special-case semi-arid region, Siberia has relatively low precipitation but with extensive forest coverage; it has also experienced significant warming due to climate change. Local climate changes have significantly affected forest composition and function in Siberia via changes in water-use efficiency, the length of the growing season and disturbance regimes (Piao et al. 2007). Both field observations and simulations conducted in Siberia have revealed a shift from deciduous conifer forest (Larix spp.) to evergreen conifer forest over a large area (Kharuk et al. 2005;Shuman, Shugart, and O'Halloran 2011;He et al. 2017). Conversion from larch to evergreen conifer could result in a decrease in albedo, especially when snow covers the tree canopy in winter. The albedo could decrease to 0.15 (from~0.3), which would potentially cause additional local warming and result in an albedo-temperature-vegetation positive feedback loop accelerating local warming and changes in forest composition. Comparing the areas of deciduous and evergreen conifer forests in Siberia, the deciduous conifer forest decreased by nearly 40%, while evergreen conifer forest increased by nearly 10%, during 2001-12. Although the changes in the area of deciduous and evergreen forests show large uncertainty, support was provided by an increasing trend in leaf area index (LAI) over high latitudes (Forzieri et al. 2017). In addition to the vegetation greening induced by the expansion of evergreen forest in Siberia, greening at the global scale was also observed in 25%-50% of vegetated areas, including semi-arid and high-latitude areas. Many mechanisms for this greening have been proposed in recent studies, including CO 2 fertilization, nitrogen deposition, climate change, and land-cover change (Zhu et al. 2016;Piao et al. 2015).
However, previous studies focused on the local effects of greening in high latitudes; the remote effects must also be investigated. Therefore, this paper focuses on the remote effects of greening in high latitudes on climate change in mid-latitude semi-arid areas. The twodimensional energy balance model (EBM) can well characterize the temperature distribution of the Earth's surface by considering the changes of radiation with latitude. Chao and Chen (1980) developed a twodimensional EBM suitable for studying the zonal distribution of surface temperature, which Li and Chao (2014) then used to study desertification. Using the twodimensional EBM represents a new way to investigate the remote effect of high-latitude greening.
The rest of the paper is organized as follows: section 2 describes the data and methods, including the twodimensional EBM; section 3 analyzes the greening in high latitudes; section 4 investigates the influence of greening in high latitudes on the mid-latitude desert; and section 5 provides the conclusion and discussion.

Dataset
The LAI product derived from GIMMS (Global Inventory Modeling and Mapping Studies) LAI3g data (Zhu et al. 2013) was used to evaluate the LAI trend. The GIMMS LAI3g data are based on the AVHRR (Advanced Very High Resolution Radiation) and MODIS (Moderate Resolution Imaging Spectroradiometer) sensors onboard the NOAA satellite of NASA (Schaaf and Wang 2015). This dataset covers 1982-2014 and has a temporal resolution of 15 days and a spatial resolution of 1/12°.
The albedo data used in this paper are the global surface albedo product of MODIS (MCD43C3 Version 6 Albedo), which is generated daily in the Climate Simulation Grid using 16 days of Terra and Aqua MODIS data. The albedo dataset covers 2000-17 with a temporal resolution of 1 day and a spatial resolution of 1/20°. The data can be downloaded from NASA's Land Distributed Activity Archives Center.

Two-dimensional EBM
A two-dimensional EBM was used to investigate the remote effect of high-latitude greening. The temperature equation in the model can be written as where ρ a is the atmospheric density; c p is the specific heat at constant pressure; c v is the specific heat at constant volume. T is the atmospheric temperature; R is the specific gas constant; p is the atmospheric pressure; ε 1 , ε 2 , and ε 3 are the heat fluxes caused by the radiation, turbulence, and the condensation or evaporation, respectively. Let k j be the longwave radiation absorption coefficient for the wavelength λ j , and k 0 be the average absorption coefficient for solar radiation. A j (B j ) is the downward (upward) longwave radiation in the wavelength Δλ interval, E j is the blackbody radiation within the wavelength Δλ interval. Q means downward solar radiation. K h is the horizontal turbulent temperature coefficient; K is the vertical turbulent temperature coefficient; z is the altitude, and Ñ 2 h is the horizontal Laplacian, where both K h and K are constant.
Therefore, the heat flux due to radiation can be rewritten as: The temperature equation is averaged by latitude and rewritten as the equation in spherical coordinates. The following equation can be obtained: where κ h = ρ a c p K h , which is called horizontal turbulent thermal conductivity, κ z = ρ a c p K, which is called vertical turbulent thermal conductivity, and x = sinφ, in which φ is latitude and a is the radius of the Earth. If we regard the absorption spectrum as a whole part and divide the longwave absorption spectrum into two partsa strong absorption area and a weak absorption areaand lead the optical thickness into the equation, the analytical solution of the above equation can be obtained by using the Legendre series. This is the two-dimensional EBM used in this paper; more details can be found in Li and Chao (2014) and Li. (2010a, 2010b).

Vegetation greening in high latitudes
Because the LAI over high latitudes shows missing values in the non-growing season, we focused on the summer LAI to illustrate the vegetation greening phenomenon. Figure 1(a) shows the trend of summer LAI during the period 1982-2014, where shading corresponds to the 99% confidence level. Consistent with previous studies (Forzieri et al. 2017;Zhu et al. 2016), persistent and widespread greening over the Northern Hemisphere is evident from the summer LAI. According to the zonal mean trend of summer LAI, the greening is most significant in high latitudes.
Simulations based on ecosystem models demonstrated that the observed greening trend is mainly caused by CO 2 fertilization (~70%), nitrogen deposition (9%), climate change (8%), and land-cover change (4%) (Zhu et al. 2016). Therefore, vegetation greening may still occur due to increasing CO 2 concentrations, even though temperatures have exhibited a cooling trend during the recent warming hiatus. Due to the limited temporal coverage of the albedo dataset, the trend of albedo in summer during the period 2000-14 was investigated; most areas did not reach the 95% confidence level (Figure 1(b)). This suggests that the zonal-mean albedo trend in high latitudes is negative, which is consistent with the greening phenomenon. The decreasing albedo over high latitudes could induce increased warming by absorbing more solar radiation. However, in some regions, the changes in LAI and albedo are inconsistent, such as Europe. We focused on the remote effect of greening in the entire high-latitude belt, and not on detailed regional albedo changes.
4. Influence of high-latitude greening on the mid-latitude desert

Validation of the two-dimensional EBM
The albedo distribution is affected by many factors, and the zonal-mean albedo from the polar region to the equator first shows a decreasing trend, followed by an increasing trend, and then another decreasing trend; these trends are driven by polar ice, highlatitude vegetation, mid-latitude desert, and lowlatitude vegetation belts. Chao and Li. (2010a) presented a simplified theoretical model; they divided the albedo into four latitudinal belts and assumed that the boundaries between the four belts could be determined by an empirical 'critical temperature'. According to our observations and previous studies (Li and Chao 2014), we assumed that the critical temperature between polar ice and the high-latitude vegetation belt (T s ) is −10°C, versus 5°C between the highlatitude vegetation belt and mid-latitude desert (T d ), and 19°C between mid-latitude desert and low-latitude vegetation (T v ). In this way, the latitudinal distribution of the four belts is obtained; the belts are not fixed, because this two-dimensional EBM is a nonlinear model. The discontinuous latitudinal changes in albedo could induce nonlinear changes of temperature in local and remote areas. For example, when the temperature at 50°N changes from −9°C to −11°C, the surface changes from high-latitude vegetation to ice, corresponding to an increase of albedo from 0.1 to 0.75, which induces a decrease in local temperature. Local land-surface changes induced by temperature advection can influence the temperature in other latitudes, and even cause changes in land-surface type. The nonlinearity of the two-dimensional EBM can help us to determine the remote effects of high-latitude vegetation greening. The four latitudinal belts of the albedo are defined as Γ 1 , Γ 2 , Γ 3 , and Γ 4 ; xs, xd, and xv indicate the sines of boundaries between the four belts. When Γ 1 ¼ 0:75; Γ 2 ¼ Γ 4 ¼ 0:1; and Γ 3 ¼ 0:25, the calculated global-mean albedo is about~0.15, which is close to the actual situation and thus can be regarded as the current climate. Figure 2(a) compares the observations and simulations of zonalmean temperature. The results suggest that the zonal distribution of surface temperature can be well characterized, especially at mid-to-high latitudes; thus, the theoretical model has the ability to simulate the temperature distribution at different latitudes.

The remote effects of high-latitude vegetation greening
To determine the influence of greening over high latitudes on the mid-latitude desert, we designed a sensitivity experiment in which the albedo of the high-latitude vegetation belt slowly changes around the value of 0.1 under the current climatic condition; we then determine the boundaries of the four latitudinal belts. Figure 2(b) shows the variations of xs, xd, and xv for the high-latitude vegetation albedo Γ 2 . When the albedo of the high-latitude vegetation belt (Γ 2 ) is less than that of the current climate (0.1), as Γ 2 decreases (indicating greening), the boundary of polar ice (xs) gradually expands southward, while the north boundary of mid-latitude desert (xd) is almost unchanged and the south boundary of midlatitude desert (xv) moves northward; overall, the mid-latitude desert belt decreases and the lowlatitude vegetation belt increases. When the albedo of the high-latitude vegetation belt (Γ 2 ) is higher than that of the current climate, as Γ 2 increases, xd and xv both move southward, with the latter moving faster, that is the mid-latitude desert increases and low-latitude vegetation decreases. Figure 2(c,d) show the variation of globalintegrated temperature and albedo with Γ 2 . When Γ 2 is smaller than the current climate, the globalintegrated albedo first decreases and then increases with the decrease of Γ 2 , before reaching a minimum at Γ 2 = 0.09. When Γ 2 decreases from 0.1 to 0.09, the areas of polar ice and low-latitude vegetation become larger, the global-integrated albedo decreases, and the global-mean temperature increases. During this process, the expansion of the low-latitude vegetation belt contributes more than that of polar ice to the decrease of the global-integrated albedo. When Γ 2 further decreases from 0.09 to 0.08, the expansion of the polar ice belt accelerates, which induces an increase in the global-integrated albedo and a decrease in the global-mean temperature. On the other hand, when Γ 2 > 0.1, as Γ 2 increases, the highlatitude vegetation belt and mid-latitude desert both expand, and the low-latitude vegetation belt shrinks. Because the shrinkage of the low-latitude vegetation belt is faster than the expansion of the high-latitude vegetation belt, the area of global vegetation will decrease and gradually be converted into a desert. Then, the global-integrated albedo increases due to the expansion of the mid-latitude desert. In summary, when the high-latitude vegetation becomes greener than it is under the current climate (Γ 2 < 0.1), the mid-latitude desert shrinks and its south boundary moves northward, in contrast to the expansion of semi-arid areas driven by enhanced warming. However, the greening in the high-latitude vegetation belt is also conducive to increasing polar ice. By contrast, if the LAI of high-latitude vegetation is reduced, it encourages a decrease of global vegetation area and an increase of mid-latitude desert, which will greatly damage the ecological environment around the desert.
To investigate the response of temperature at different latitudes, Figure 3 shows the latitudinal distribution of surface temperature anomalies relative to current climatic conditions. When Γ 2 is smaller than the current climate, a negative temperature anomaly occurs in high latitudes (north of~45°N) and a positive temperature anomaly occurs in low latitudes. The global-mean temperature would thus increase due to the greater contribution of the positive anomaly over low latitudes. As Γ 2 decreases, the area of the negative temperature anomaly gradually expands southward, which leads to a decrease in global-mean temperature. When Γ 2 is greater than the current climate, the positive temperature anomaly only occurs north of 50°N; the area of the negative anomaly expands with the increase of Γ 2 , which indicates that desertification of high-latitude vegetation will induce a global cooling trend.

The influence of high-latitude greening on the evolution of mid-latitude desert with increasing CO 2
The CO 2 produced by human activities is an important factor in global warming. Since the industrial revolution, the concentration of CO 2 in the atmosphere has steadily increased (currently standing at 400 ppm), and the global-mean temperature will continue to rise in the future under anthropogenic forcing. However, how the temperature will change as CO 2 increases remains unclear. Will high-latitude greening affect the response of mid-latitudes under anthropogenic forcing caused by the rising CO 2 ? In the simple two-dimensional EBM, the absorption coefficients can be parameterized to change with CO 2 concentration, to further investigate the response of global temperature to increasing CO 2 concentrations. This model may provide insight, especially into the changes of the four latitudinal belts. Figure 4(a-d) shows the variations of globalmean surface temperature, xs, xd, and xv, with the concentration of CO 2 when Γ 2 = 0.1. As the concentration of CO 2 rises, global-mean temperature shows a transient decrease, corresponding to the expansion of polar ice and mid-latitude desert when the concentration of CO 2 is lower. The global-mean temperature continues to increase as CO 2 increases until the concentration of CO 2 reaches 600 ppm, i.e. a 'saturated' state. During this process, the south boundary of polar ice (xs) continues to move northward and the north boundary of the low-latitude vegetation belt (xv) continues to move southward. However, the north boundary of the mid-latitude desert (xd) moves northward until the concentration of CO 2 reaches 600 ppm. This suggests that under increasing CO 2 , the mid-latitude desert will expand both northward and southward. When the concentration of CO 2 reaches 600 ppm, the mid-latitude desert only expands southward.
When the albedo of the high-latitude vegetation belt is reduced by 20% (Γ 2 = 0.08, Figure 4(a-d) and the concentration of CO 2 is greater than at present (400 ppm), the global-mean temperature rises as CO 2 increases, and reaches a 'saturated' state when the CO 2 concentration reaches 600 ppm. However, the global-mean temperature in the 'saturated' state when Γ 2 = 0.08 is always lower than that when Γ 2 = 0.1, which is likely due to the stronger cooling in high latitudes induced by high-latitude greening (Figure 3).

Conclusion and discussion
Changes in the mid-latitude desert belt greatly affect the ecological environment of the surrounding areas, and the desert ecosystem is vulnerable to climate change; various factors and mechanisms are involved. This paper investigated the remote effects of greening in the highlatitude vegetation belt using a two-dimensional EBM. We found that when greening occurs in the high- latitude vegetation belt, the mid-latitude desert recedes at the south boundary, while the polar ice belt and lowlatitude vegetation belt both expand. In addition, highlatitude greening also induces a cooling trend in high latitudes and a warming trend in low latitudes. Therefore, high-latitude greening is helpful in offsetting the shrinkage of polar ice and the expansion of semi-arid regions driven by global warming.
When the concentration of CO 2 increases, the simulation results suggest that the mid-latitude desert will expand its southern and northern boundaries. However, the response of global-mean temperature and the north boundary of the mid-latitude desert both reach 'a saturated' state when the CO 2 concentration reaches 600 ppm; i.e. the global-mean temperature remains constant although CO 2 continues to increase. In contrast to the greening phenomenon in high latitudes, the abovementioned feature always exists. The only change induced by high-latitude greening is that the global-mean temperature in the 'saturated' state is lower than that without high-latitude greening.
The expansion of the semi-arid area results from many mechanisms, including positive and negative feedback. The simple EBM can distinguish the influences of different mechanisms according to its simple and concise nature. The results suggest that high-latitude vegetation greening may induce shrinkage of desert areas when only temperature advection and albedo-temperature feedback are considered. However, regarding the remote effects of high-latitude vegetation greening, the model did not consider circulation changes. In addition, greening over high latitudes could also lead to lower surface temperatures via intensified evaporation, which is weaker than the warming induced by decreasing albedo demonstrated in a recent study (Forzieri et al. 2017). Therefore, the influence of high-latitude vegetation greening on global temperatures requires further investigation via a fully coupled Earth system simulation model, such as the Community Earth System Model.

Disclosure statement
No potential conflict of interest was reported by the authors.