Global cost estimates of forest climate mitigation with albedo: a new integrative policy approach

We use the GTM to simulate the optimal management of global forestland for climate change mitigation with albedo. GTM is a global model that combines the spatially detailed data on current forest stocks with an economic model that weighs optimal forest management alternatives (Sohngen et al 1999, 2001, Sohngen and Mendelsohn 2003). It is a dynamic intertemporal optimization model that manages forests by maximizing the net present value (NPV) of consumer and producer surplus in timber markets. The model contains 200 forest types (i) in 16 regions that interacts through the global timber market. By maximizing the NPV, the model optimizes the age of harvesting timber (a) and the intensity of regenerating and managing forests. It is an optimal control problem given the aggregate demand function, starting stock, costs, and growth functions of forest stocks (see section 1 of the supplementary material for details, available online: stacks.iop.org/ERL/13/125002/mmedia).

GTM relies on forward-looking behavior and solves all time periods at the same time; this means that when land owners make decisions today about forest management, they do so by considering the implications of their actions today on forests in the future with complete information. This assumption is consistent with those made in the DICE model, and it allows us to adopt the carbon prices from the DICE model for the policy analysis (Nordhaus 2014).

In GTM carbon storage is counted in three main pools: aboveground forest carbon, forest products and soil carbon.

Aboveground carbon ($TCar{b}_{t}^{i}$), accounts for the carbon in all tree components as well as carbon in the forest understory and sitting on the forest floor at each time t. It is a function of the stock of land (${X}_{a,t}^{i}$), the growth function (${V}_{a,t}^{i}$), and the management intensity (${m}_{t0}$) of age a and i forest type:

$$\begin{eqnarray}&&TCar{b}_{t}^{i}=\displaystyle \sum _{a}{\delta }^{i}{V}_{a,t}^{i}({m}_{t0}){X}_{a,t}^{i},\end{eqnarray} \tag{ 1 }$$

where δ is the conversion factor that converts forest biomass into carbon, it is forest and regional-specific.

Carbon in forest products ($Mk{t}_{t}^{i}$) is estimated by tracking forest products over time and it is calculated as follows:

$$\begin{eqnarray}&&Mk{t}_{t}^{i}=\displaystyle \sum _{a}{k}^{i}{V}_{a,t}^{i}{H}_{a,t}^{i},\end{eqnarray} \tag{ 2 }$$

where ${V}_{a,t}^{i}$ is the timber volume and ${H}_{a,t}^{i}$ is the harvested area in each age class a at any time t. ${k}^{i}$ is the factor to convert market biomass into carbon permanently stored in products. We here assume ${k}^{i}$ to be 0.30 (Winjum et al 1998).

Soil carbon ($SOL{C}_{t}^{i}$) is measured as the stock of carbon in forest soils of type i in time t. In this analysis, we capture the marginal change in carbon value associated with land use changes. When land use change occurs, we track net carbon gains or losses over time as follows:

$$\begin{eqnarray}&&SOL{C}_{t+1}^{i}=SOL{C}_{t}^{i}+SOL{C}_{t}^{i}({\mu }^{i})\left[\displaystyle \frac{\overline{{S}^{i}}-SOL{C}_{t}^{i}}{SOL{C}_{t}^{i}}\right].\end{eqnarray} \tag{ 3 }$$

The value of ${\bar{S}}^{i},$ the steady state level of carbon in forest soils, it is unique to each region and timber type i. The parameter ${\mu }^{i}$ is the growth rate for soil carbon. The same equation is used when land converts from forest to agriculture but with the reverse initial carbon and steady state numbers (Daigneault et al 2012, Favero et al 2017). Harvesting does not affect soil carbon if the land remains in forests but causes a decline in soil carbon if there is a change in land use (Houghton and Goodale 2004).

To include the albedo effect in the forestry model, we first collect and analyze albedo data for each political region and each dominant land cover type, then calculate the radiative forcing (in W m⁻²) caused by albedo change from land conversion, and finally convert the forcing to C emissions-equivalent (figure 1).

We obtained the latest version of the global daily albedo products (MCD43A3, version 006) from 2010–2016 at 500 m resolution derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) (Schaaf et al 2002). To identify the land cover types, we summarized the dominant land cover types (figure 2) in each climatic region during 2010–2013, based on the Köppen–Geiger climate map and the annual MODIS IGBP land cover classes at 500 m resolution (Kottek et al 2006). For each dominant forest type over each region, we also generated the histograms of tree cover percentage from the MODIS Vegetation Continuous Field (VCF) data and identified the upper ¼ quantile. A forest pixel was assumed as mature forest if its tree cover is higher than 75% of all the forest pixels across a particular region.

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We here used the total shortwave white-sky albedo from MODIS during 2010–2016 to summarize the mean annual albedo for mature forests and cleared land (cropland or bare land) over each political region. We first calculated the 7-year average albedo value for each Julian day of the year for each land cover type. The mean annual albedo of each land cover type is then calculated as an average of daily albedo weighted by daily incoming shortwave radiation. We used the incoming solar radiation product, the surface Energy Balanced and Filled data at 1 × 1° from 01/2010 to 08/2016, from NASA CERES (the Clouds and the Earth's Radiant Energy System) science team, to calculate the 7-year average surface clear-sky shortwave solar radiation for each study region. (Table 2 in the supplementary material provides a detailed summary of albedo statistics for each political region.)

We estimated the resulting shortwave radiative forcing (${\rm{\Delta }}{r}_{net}$) at the surface caused by changes in albedo values from cleared land to mature forest:

$$\begin{eqnarray}&&{\rm{\Delta }}{r}_{net}=(1-{\alpha }_{cleared})K-(1-{\alpha }_{mature})K,\end{eqnarray} \tag{ 4 }$$

where ${\rm{\Delta }}{r}_{net}$ represents the absorbed surface radiative forcing; ${\alpha }_{cleared}$ and ${\alpha }_{mature}$ are the weighted mean albedo of the cropland (or bare land) and the mature dominant forest type respectively and they are both region and forest specific; K represents the average clear-sky shortwave solar radiation from 2010 to 2016.

The relationship between changes in radiative forcing induced by changes in albedo (${\rm{\Delta }}{r}_{net}$) and CO₂-equivalent emissions is well known in the literature (see for instance Betts 2000, Joos et al 2013, Caiazzo et al 2014, Mykelby et al 2017). First, ${\rm{\Delta }}{r}_{net}$ is converted into change in global atmospheric carbon concentration (${\rm{\Delta }}{C}_{atm}$) through the logarithmic relation:

$$\begin{eqnarray}&&{\rm{\Delta }}{C}_{atm}=({e}^{\left[\displaystyle \frac{{\rm{\Delta }}{r}_{net}}{5.35{A}_{E}}\right]}-1){C}_{atm},\end{eqnarray} \tag{ 5 }$$

where ${\rm{\Delta }}{C}_{atm}$ is the global atmospheric CO₂ concentration change (in parts per million, ppm) that would result from the radiative forcing ${\rm{\Delta }}{r}_{net},$ ${A}_{E}$ is the surface area of the Earth, and ${C}_{atm}$ is the current global mean atmospheric CO₂ concentration over the course of the 20th century. The value 5.35 represents a coefficient used to quantify the warming potential of atmospheric CO₂. The calculations are done for each region and forest type by determining the change in terrestrial carbon stock that is equivalent to a change in surface albedo resulting from a transition from cleared land to mature forestland. The equivalent increase in carbon stock are considered emissions because transition to forest lowers surface albedo and exerts positive radiative forcing, just like releases of carbon from timber harvest (Zhao and Jackson 2014).

The concentration ${\rm{\Delta }}{C}_{atm}$ is then converted into an equivalent carbon emission per unit of hectare subject to albedo change following the method described in Caiazzo et al (2014) and Myklby et al (2017). That is, ${\rm{\Delta }}{C}_{ter}$ corresponds to the C-equivalent emissions that will be released if one hectare of cleared land (cropland or bare land) would be converted in a hectare of mature forest.

$$\begin{eqnarray}&&{\rm{\Delta }}{C}_{ter}=\left(\displaystyle \frac{1}{A{F}_{TH=100}}\right){\rm{\Delta }}{C}_{atm}\left(\displaystyle \frac{{M}_{c}}{{M}_{air}}\right)\left(\displaystyle \frac{1}{{A}_{a}}\right){m}_{atm},\end{eqnarray} \tag{ 6 }$$

where ${M}_{c}$ and ${M}_{air}$ are the molecular weights of carbon and air respectively, $A{F}_{TH=100}$ is the airborne emission fraction of CO₂ for a time horizon of 100 years, A_a is the reference area subject to albedo expressed in hectare and ${m}_{atm}$ is the mass of Earth's atmosphere.

Since albedo varies with forest age, we need an expression that describes the albedo 'decay' due to forest growth and the corresponding effect. Yearly changes in albedo are based on the assumption that as forests grow from cleared land, albedo decreases and reaches a minimum when the forest reaches its maturity; we further assume that the resulting increase in the corresponding C-equivalent emissions follows an exponential function (Bright et al 2012, 2015, Cherubini et al 2012). Carbon-equivalent emissions change over forest age (a) is calculated by using the following function:

$$\begin{eqnarray}&&CAlbed{o}_{a}=\eta {\rm{\Delta }}{C}_{ter}\left[\exp \left(m-\displaystyle \frac{n}{a}\right)\right],\end{eqnarray} \tag{ 7 }$$

where parameters η, m and n are typical growth parameters and they include information about forest maturity. (Supplementary figure 5 shows the regional changes in albedo C-eq per hectare (tC-eq/ha) as a function of forest age.)

Finally, to determine total increase in C-eq albedo for a given timber type i, we sum over the hectares in each age class as follows:

$$\begin{eqnarray}&&TCAlbed{o}_{t}^{i}=\displaystyle \sum _{a}CAlbed{o}_{a,t}^{i}{X}_{a,t}^{i}.\end{eqnarray} \tag{ 8 }$$

Considering the uncertainties in the assumption on the age-dependency of albedo, we further tested the sensitivity of the results to the assumed forest maturity ages and corresponding decay functions for each region and forest type. In particular, in section 4.1 of the supplementary material, we tested two scenarios where forest reaches its maturity 50 years before and 50 years later than the base case.

The GTM captures mitigation potential of the forestry sector through a global carbon incentive that values forest climate change mitigation contribution in terms of net C-equivalent sequestration as follow:

$$\begin{eqnarray}&&\begin{array}{l}C{C}_{t}={P}_{t}^{c}\displaystyle \sum _{i}Mk{t}_{t}^{i}+(SOL{C}_{t+1}^{i}-SOL{C}_{t}^{i})\\ \,+\,{R}_{t}^{c}\displaystyle \sum _{i}(TCar{b}_{t}^{i}-TCAlbed{o}_{t}^{i}).\end{array}\end{eqnarray} \tag{ 9 }$$

The first part of equation (9) is the carbon transferred to long-lived wood products ($Mk{t}_{t}^{i}$) from each forest i valued at the carbon price ${P}_{t}^{c}.$ The change in soil carbon ($SOL{C}_{t}^{i}$) when land switches between forests and agriculture is also valued at the carbon price (Daigneault et al 2012, Favero et al 2017).

The second term of equation (9) is the annual rent scheme ${R}_{t}^{c}$ whereby the total carbon stocks in forests ($TCar{b}_{t}^{i}$) net of C-eq albedo ($TCAlbed{o}_{t}^{i}$) are rented during the time period that the carbon is stored following Sohngen and Mendelsohn (2003) and Thompson et al (2009). The rental value for carbon is:

$$\begin{eqnarray}&&{R}_{t}^{c}={P}_{t}^{c}-{P}_{t+1}^{c}/{(1+r)}^{t},\end{eqnarray} \tag{ 10 }$$

where r is the interest rate. This equation accounts for potential price increases in carbon that occur as carbon accumulates in the atmosphere.

To estimate the forest mitigation supply functions (with and without albedo), we run multiple simulations using GTM under five exgoneous carbon price paths (${P}_{t}^{c}$) from DICE-2013R (Nordahus 2014), following the approach outlined in Sohngen and Mendelsohn (2003). Carbon price paths start in 2010⁴ at prices ranging from 14 to 57 USD/tC, and reaching 264 to 540 USD/tC in 2100. The starting price, the price path, and the final price depend on assumptions in the DICE-2013R model about the damage function or policy implementation. Section 2 of the supplementary material describes in detail the assumptions behind each carbon price path from DICE-2013R.

We first simulate a No Policy (Reference) scenario where no climate mitigation policy exists and forest owners only receive revenue from timber market. Under this scenario $({P}_{t}^{c}=0),$ therefore there are no carbon payments for forest mitigation $(C{C}_{t}=0).$

Then, we simulate a Traditional Policy forest mitigation policy where forest owners are compensated by annual rents ${R}_{t}^{c}$ for providing annual carbon storage services and, at harvest, they are paid the carbon price ${P}_{t}^{c}$ for carbon stored permanently in wood products and they receive revenue from timber market. Under this policy scenario albedo is not considered $(TCAlbed{o}_{t}^{i}=0).$

Under the Integrative Policy scenario, forest carbon sequestration net of albedo converted in C-equivalent is rewarded following the rent scheme and at harvest, landowners are paid the carbon price for carbon stored permanently in wood products and receive revenue from timber market.

We first focus on three regions and one of their dominant forest types (Brazilian Tropical Evergreen forest, Northern Europe Temperate Evergreen forest, and Canadian Boreal Softwood forest) to illustrate the effect of the alternative policy regimes on NPV of an heactare of forestland and the optimal rotation age.

Table 1 column a shows the changes in radiative forcing of mature forestland with respect to cleared land in the three regions and forest types. In column b radiative forcing is converted in tC-eq per heactare (tC-eq/ha) following equations (4)–(7) presented above. Column c shows the estimated aboveground forest sequestration of each mature forest and in column d we measure the net mitigation of each mature forest in terms of C-eq/ha.

Table 1.  Regional estimates of (a) changes in radiative forcing albedo from cropland to mature forestland; (b) albedo carbon equivalent values; (c) aboveground forest C sequestration and (d) net carbon sequestration for regional mature forests.

	(a) W m−2 difference forest-bareland ${\rm{\Delta }}{r}_{net}$	(b) Albedo change in C-eq (tC/ha) $CAlbed{o}_{a=mature}$	(c) Aboveground forest sequestration (tC/ha) $Car{b}_{a=mature}$	(d = c − b) Net C-eq sequestration mature forest (tC/ha)
Brazil tropical evergreen	10	59	150	91
Northern EU temperate evergreen	28	161	192	31
Canada boreal softwood	22	129	76	(53)

Results presented in supplementary table 3 show that under the No Policy scenario, the optimal rotation year is 26 years for Brazil, 46 for Northern Europe and 57 for Canada, the merchantable biomass yield is 18 m³/ha, 75 m³/ha and 29 m³/ha and the corresponding NPV of the stand is 633 $/ha, 684 $/ha and 171 $/ha respectively.

Under the policy that values only carbon sequestration and ignores albedo (Traditional Policy), forest owners have the incentive to hold timber longer than in the No Policy scenario and forestland increases its value in all regions. That is, lengthening rotations increases carbon storage by increasing the size of trees per hectare. The optimal rotation age increases to 29–31 years (Brazil), 48–51 years (Northern EU) and 59–62 years (Canada) with an increase in the NPV of the stand of 984–3,979 $/ha, 199–820 $/ha and 33–135 $/ha depending on the carbon price.

Finally, when albedo is included in the valuation of forest-based actions (Integrative Policy), the optimal rotation is shorter and NPV is reduced with respect to the Traditional Policy scenario. With albedo, the optimal rotation falls under the Integrative Policy scenario compared to the Traditional Policy scenario because the albedo penalty increases as the forest ages, reducing the value of maintaining forest cover for additional years.

In the case of Canadian Boreal forest, the NPV of the albedo effect is bigger than the NPV of carbon sequestration, suggesting that mitigation with this forest type would not provide economic, or atmospheric, benefits. Similar results have been found in Lutz et al (2016) for some locations in New Hampshire. In the case of the other two species, the albedo effect detracts from carbon value, but for those species there are overall carbon benefits associated with increasing forest cover. In addition to showing the optimal rotation age, these results also illustrate that policies aimed at slowing deforestation in Brazil would still be effective because net sequestration is positive, albeit less effective than suggested by studies that do not include albedo.

A climate policy (like a carbon price) that values forest carbon sequestration (Traditional Policy) creates the incentive to reduce deforestation, convert land to forest (afforest), to grow forest more quickly (increase management intensity), and to extend the rotation of forests (possibly indefinitely). These actions not only increase the amount of carbon sequester in forest but also affect land albedo through both land cover change (avoided deforestation and afforestation) and land management change (changes in management intensity and forest rotation). In order to measure the global implications of changes in albedo on the climate mitigation potential of forests, we simulate the Traditional Policy under the carbon price paths and then measure ex-post the resulting carbon-equivalent changes in surface albedo.

Figure 3(a) shows the changes of global forest carbon stock in three different pools under the Traditional Policy scenario relative to the No Policy scenario. The conversion of more land to forest, the increase in management intensity and the more extended forest rotation produce an increase in the stock of carbon sequestered above and below ground (soil) with respect to the No Policy scenario. Timber supply also increases in the long-run adding extra market carbon.

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By 2100 under an assumed carbon price of 540 USD, global forest will increase the stock of carbon by 298 GtC-eq relative to the No Policy scenario, sequestering approximately 3.3 GtC-eq/yr for 2010–2100. However, all the forest-activities driven by the Traditional Policy indirectly change surface albedo, resulting in a warming effect, with respect to the No Policy scenario. Once the albedo is converted in carbon equivalent and included in the calculation (Traditional Policy Net), the net climate mitigation potential of forests under a carbon price of 540 USD is reduced by 46%, falling to 153 GtC-eq (about 1.7 GtC-eq/yr). This suggests that a traditional policy that values only the carbon sequestration benefits of forest without considering albedo underestimates the costs of a forest mitigation by about 50%, and thus is an inefficient policy.

In order to avoid the implementation of counterproductive climate change mitigation (like the Traditional Policy), we propose a novel approach where both carbon sequestration and albedo are incorporated into pricing (Integrative Policy). Does the proposed Integrative Policy fully address the albedo issue in an effective way? Figure 3(b) answers this question. Under the Integrative Policy scenario, global average carbon benefits of forest actions are greater than the corresponding negative climate impacts of changes in surface albedo, therefore there is still the incentive to reduce deforestation, increase forestland and extend forest rotations relative to the No Policy scenario. However, to minimize the effects of albedo, the policy re-allocates forests mitigation activities in regions where changes in surface albedo are smaller, reduces forest rotation and decreases global land conversion to forest relative to the Traditional policy. These changes produce lower forest carbon storage as well as lower changes in C-eq albedo relative to the Traditional Policy scenario. However, under the same carbon price path, when albedo is included in the policy, the Integrative Policy provides greater net mitigation than the Traditional Policy (net).

Our results suggest that for all the carbon prices tested a policy that ignores the albedo consequences of forest-based activities underestimates marginal costs (figure 4(a)). For carbon prices below 150 USD, the forestry sector delivers 2–104 Gt of carbon in forested ecosystems, but when albedo effects are included, net mitigation potential is less than 29 GtC-eq. For carbon prices of 150–400 USD/tC, the mitigation potential is 57%–84% lower than what is estimated without albedo. Finally, for carbon prices higher than 400 USD/tC the mitigation potential is 50%–55% lower when the albedo is included in the estimates.

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Second, by comparing the net mitigation of the Traditional Policy with the net mitigation of the Integrative Policy, results suggest that the Integrative Policy is cheaper, or more efficient, than a policy that does not include albedo in the pricing formula. For instance, to attain net mitigation of around 100 GtC-eq will cost 20%–26% more if the pricing formula ignores albedo. That is, the Integrative Policy is always more effective than the Traditional Policy.

Furthermore, at the global level, the Integrative Policy requires less land to be converted to forestland for the same level of net mitigation, and thus is less intrusive than the Traditional Policy. For instance, to achieve a net mitigation of 100 GtC-eq, it will require about 750 million hectares (Mha) more if the pricing formula ignores albedo (figure 4(b)).

Forest mitigation costs were found to vary significantly across regions under the Traditional Policy and Integrative Policy scenarios (figure 5). In temperate and boreal regions, North America and Russia have significantly higher marginal costs of net mitigation, and albedo increases the costs (figures 5(a) and (b)). Estimates for Europe are about the same with or without consideration of albedo (figure 5(c)). While costs are higher when albedo is included in the carbon pricing regime, the Integrative Policy still encourages mitigation in Canada and Russia. For instance, in Russia the Integrative Policy affects forest management by encouraging the conversion of older forests to young forests. Under the Integrative Policy, the amount of forestland in Russia is almost unchanged relative to the Traditional Policy, but forests are converted from old natural forest to young managed forests. This important interaction between albedo, carbon sequestration and forest age arises because the albedo penalty increases as forests age, thus reducing the value of climate mitigation in mature forests. This result can have important policy implications since the Integrative policy might not guarantee the preservation of natural forests. In section 4.2 of the supplementary material we tested how our results will be affected under a scenario where the world natural unmanaged forests are fixed to current values. Our results suggest that under this constrained scenario, the Integrative policy delivers almost the same amount of climate mitigation as the Traditional Policy (net). However, the Integrative Policy is still a preferable policy because it is less intrusive than the Traditional Policy in terms of hectares used for forest mitigation (supplementary figure 9).

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In tropical regions, the effects of albedo on marginal costs in South East Asia and Central and South America are relatively modest (figures 5(d)–(e)), however, albedo has important implications for marginal costs in Africa (figure 5(f)). Because native soil surfaces are fairly light in Africa, conversion of land to forests, or reduced deforestation, both have strong effects on albedo, making most actions in Africa counterproductive for net mitigation. Africa differs because cleared land has a very high albedo with respect to the same land cover types in other tropical regions (Fuller and Ottke 2002). Therefore, the variation of albedo with respect to mature forestland in this region is particularly high. Moreover, the incoming solar radiation of Africa is slightly higher than other tropical regions.

In order to measure to what extent Africa is skewing the global mitigation supply functions of forest, in section 4.3 of the supplementary material we simulate the same scenarios excluding forest-based mitigation actions in Africa. Our results indicate that even if Africa is excluded the Traditional Policy still underestimates the forest mitigation potential because forest-based actions are implemented in other regions in which changes in albedo are significant with respect to the carbon sequestration benefits (supplementary figure 10). Moreover, the Integrative policy is still more efficient than the Traditional Policy (net) even if not as substantial as in the scenario with Africa and less intrusive than the Traditional Policy in terms of hectares used for forest mitigation actions (supplementary figure 11).