Technical Appendix:
Forest timber and carbon estimation
We simulated the accumulation of forest timber and carbon in 2 distinct forest types in the White Mountain National Forest (WMNF) in New Hampshire, USA using an updated version of the model described in Gutrich and Howarth (2007). We selected the two most frequent forest types in the WMNF as our representative types: maple-beech-birch forest hereafter termed ‘hardwood’, containing Acer pensylvanicum, Acer saccharum, Fagus grandifolia, and Fraxinus Americana, and a spruce-fir forest, dominated by Abies balsamea and Picea rubens and containing trace amounts of Betula papyrifera. To model the growth of these forests, we used data from the United States Department of Agriculture (USDA) Forest Service Inventory and Analysis (FIA) database of stand information for the WMNF and New Hampshire as summarized by the United States Department of Energy’s Carbon On Line Estimator (COLE) 1605 (b) reports (Proctor et al. 2005) (Table S1). This data provides carbon tables based on forest type and stand age based on a sampling of FIA forest plots. Climate in the WMNF varies considerably upon elevation, but in general the area has warm summer temperatures upwards of the low 30s C and cold wintertime lows which can reach several degrees below 0° C, with annual snow accumulation between 150-180 cm(Adams et al. 2004; Stoleson et al. 2011). Temperatures are colder upon steeper slopes where spruce-fir forests dominate, generally above 750 meters (van Doorn et al. 2011). Snowfall is more frequent on these higher elevation slopes and snowpack lasts longer into the warm season(Bailey et al. 2003). Although we modeled 1000 years into the future, we did not consider the influence of climate change upon species composition of the forest plots or increased productivity of individual trees leading to variance among timber and carbon storage.
To simulate forest growth, we relied upon the method described in Gutrich and Howarth in their original manuscript describing their forest model (2007). This methodology relies on a series of mathematical equations relating forest stand properties to the accumulation of forest biomass. To summarize briefly, annual forest growth was based upon the curvilinear relationship between forest volume and stand age and total biomass was calculated in a series of annual time steps based on FIA stand data from our study sites. Timber volume is calculated over time as:
(1)
where α0is the maximum timber volume for the site, α1 is the volume growth rate, α2 is the youngest stand age when a stand can be harvested and contain valuable timber, and s is the stand age (Gutrich and Howarth 2007). Timber growth was partitioned into saw timber through the relationship:
(2)
wherein β0, β1, and β2 are coefficients, with fsaw representing the proportion of timber that is sawtimber (Gutrich and Howarth 2007). Harvested timber was valued using prices based on stumpage value estimates from the New Hampshire State Department of Revenue for the Northern region of the state for the time period of April 2013 to November 2013. We assumed timber stumpage price growth rates of 1.0% per year, based on region-wide estimates of the timber market (Sendak et al. 2003). We modeled annual stumpage prices as the function:
(3)
where Ppole and Psawrepresent the stumpage prices of poletimber and sawtimber, respectively(Gutrich and Howarth 2007). Therefore, total net present revenue from timber was calculated
(4)
where r(t) is the discount rate which decreases from a high of 0.045 in year 1 to a low of 0.037 in year 1000 as calculated by the DICE model.
In addition to timber yield, we also modeled forest carbon storage and sequestration. Forest carbon was disaggregatedinto a series of four pools: carbon in live biomass, carbon in dead and downed wood, carbon stored in forest soils, and carbon stored in long-lived timber products. Live biomass was simulated through the equation:
(5)
where γ0 represents the maximum storage of carbon in live biomass in tons per hectare and γ1 is a coefficient representing the annual growth of biomass in percent per year (Gutrich and Howarth 2007). The amount of dead and downed carbon is related to the quantity of living biomass in that:
(6)
such that δ1 and δ2 are formation coefficients for dead and downed wood, logging reside is D, while the decay rate of the dead carbon pool is represented by δ0. Tracking carbon in long-lived timber products required the calculation of carbon stored within products themselves, as well as the carbon lost through decay of logging residue, or slash, represented by D. We represented carbon stored in products by:
(7)
wherein i is the product category, φ0i represents the release of carbon from the decay of wood products, φ1i is the proportion of harvested carbon in timber that ends up in long-lived wood products, h represents the share of timber harvest that is allocated to each product category, and H is the rotation period (Birdsey 1996; Gutrich and Howarth 2007). We rely on parameters for this equation based on the work by Birdsey (1996) which are also used by the USDOE (U.S. Department of Energy 2004).
Once carbon has been placed into its respective pools, total carbon uptake is represented by:
(8)
and the net present value of carbon storage is generated through the equation:
(9)
where Vc(t) is the marginal benefit of carbon sequestration in dollars per ton. We derived the shadow price for carbon storage through the DICE model (Nordhaus 2008). Within DICE, the total impacts of carbon emissions on temperature and climate damages are calculated by measuring the change in social welfare through the increase in one unit of carbon emissions.
The social welfare (W) in DICE is measured in decadal time periods and is the product of the instantaneous utility function for each time period, U, dependent upon per capita consumption, c, and total labor inputs by population, L, and the social rate of time preference, R(Nordhaus 2008):
(10)
A change in carbon emissions influences climate and causes damagesto social welfare. Thus, the shadow price of a unit of carbon emissions Vc is calculated by measuring the change in social welfare due to a one-unit increase in carbon emissionsE, divided through by the marginal utility of consumption (C):
(11)
Albedo Simulation and Calculations
To generate annual estimates of blue-sky shortwave albedo, we collected a combination of two Moderate Resolution Imaging Spectrometer (MODIS) albedo products, MCD43A (Schaaf et al. 2002) and MOD10A (Klein and Stroeve 2002), for an 11-year period (2002-2012) for our two New Hampshire forest types. We identified our three representative site locations by combining detailed forest stand maps from the National Forest Service for the White Mountain National Forest (United States Department of Agriculture 2013) with the MODIS global land cover product (Friedl et al. 2002) to ensure homogenous and contiguous forest type over each location (Figure 1). We used a total of 445 and 425 retrieval dates over 11 years from 2002-2012 for our spuce-fir (43°54'19.89"N, 71°47'33.77"W) and hardwood (44° 8'34.59"N, 71°25'19.51"W) study sites, averaging 7 and 6 high-quality pixels per retrieval respectively. To represent bare-ground albedo, we chose a large clear-cut harvest area 5 miles west of Berlin, NH (44°29'0.60"N, 71°13'52.23"W) that was previously occupied by a mix of both deciduous broadleaved and coniferous needle-leaved elements. The area was harvested in the fall of 2009 and we utilized albedo data from 2010-2012. We utilized a total of 124 retrieval dates for this site, averaging 8 high-quality pixels per retrieval.
The MODIS MCD43A albedo product combines 16 days worth of information from both the Terra and Aqua satellites along with a bidirectional reflectance model to generate 8-day surface reflectances at 500 meter gridded resolution (Schaaf et al. 2002; Wanner et al. 1997). Data is flagged based on the angular sampling and sufficiency of input data which provides users with an ability to select reliable data (Schaaf et al. 2002; Wang et al. 2012). MCD43A data has been validated on a variety of land surfaces (Jin 2002; Salomon et al. 2006) as well as in snowy conditions (Stroeve et al. 2005; Wang et al. 2012) and in forests (Wang et al. 2014). When data was flagged as being of poor quality, those pixels were eliminated from the analysis. For cloudy periods when the MCD43A data was not of sufficient quality, particularly in winter months, we supplemented with MOD10A data correspondingly. The MOD10A product (Klein and Stroeve 2002) is a daily snow albedo product, which incorporates the MOD35 MODIS cloud mask (Frey et al. 2008) and a radiative transfer model to correct issues relating to surface scattering (Hall and Riggs 2007). Although considered technically at provisional status, validation work has considered the MOD10A product to be highly accurate depending on the land cover type (Hall and Riggs 2007). We did not consider the influence of climate change on variations on snow cover, and thus assumed the baselines provided by the collected MODIS data would continue through the modeling period.
We calculated the net shortwave radiation flux from simulated forest stands upon the atmosphere following the methodology utilized by Bright et al. (2012)and containing several fundamental physical equations to calculate incipient energy transfer from the sun to the land surface (CHEN and OHRING 1984; Lacis and Hansen 1974). Here, shortwave radiation flux, RFfs, of a forest stand onto the atmosphere is assumed to be directly related to the incoming top-of-the-atmosphere solar radiation, RTOA, the surface albedo, αa, and a measure of the opacity and transmittance of the atmosphere, fa:
(12)
The calculation of RTOAis based upon the latitude L, the sunset hour angle ω, the solar constant Rsc, and the declination angle δ at Julian day di (Bright et al. 2012; Kalogirou 2009):
(13)
In order to calculate the total amount of radiation being reflected off the surface of the Earth and escaping at the top of the atmosphere, we calculate the two-way atmospheric transmittance parameter faas a function of both the clearness of the atmosphere, KT, at month j, and atmospheric transmittance, Ta, as used by Bright et al.(2012):
(14)
For the value of Ta, we use a global average of 0.854 (Bright et al. 2012; Lenton,T.M. and Vaughan,N.E. 2009). The clearness index KT,j was collected for the region by using monthly data from NASA’s Surface meteorology and Solar Energy (SSE) project (NASA 2009) which provides satellite-based indices of cloudiness and atmospheric clearness.
As albedo for bare ground slowly and systematically decreases throughout the course of forest growth and canopy closure, we represented albedo change in time with an exponential decay function operating between the cleared area annual average, αcleared, and the saturated mature forest annual average, αmature. We calculated these average albedos through a stepwise linear regression of each year's albedo retrievals, weighed by seasonal top-of-the-atmosphere radiation, and then averaged across all retrieval years. This albedo decay function is similar to that used in Cherubini et al.(2012):
(15)
Whereupon b is calculated:
(16)
Our forest model is based on a series of annual time steps, thus we calculated average annual radiative flux, RTOA,ann, for each forest type by averaging daily top-of-the-atmosphere solar radiance (Bright et al. 2012):
(17)
A shadow price for the shortwave radiative flux associated with albedo was based on the same method used to calculate carbon shadow prices within DICE. However, in this case we examined the change in social welfare (W) based on marginal changes in shortwave radiation from a singleunit of radiative forcing (RF). Thus, we could calculate a shadow price of albedo (Va) using the equation:
(18)
Where C is consumption units per util, and therefore could calculate the net present value from albedo benefits by:
(19)
where RFfs is shortwave radiation flux from albedo and r is the discount rate. The total net present value of a forest stand was calculated by combining the benefits provided by timber, carbon, and albedo:
(20)
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