{ "document_id": 16694, "page": 11, "width_pt": 594, "height_pt": 756, "rotation": 0, "pipeline_version": "paddleocr-vl-1.6+paul-48", "engine": "paddleocr_vl", "source_run_id": 16805, "item_count": 76, "counts_by_type": { "footer": 2, "formula": 38, "header": 1, "link": 1, "text": 34 }, "build_ms": 11, "items": [ { "id": "p11.1", "order": 1, "type": "header", "bbox": { "l": 34.08, "t": 726.96, "r": 281.76, "b": 714.72 }, "text": "SCIENCE ADVANCES | RESEARCH ARTICLE", "attrs": { "block_label": "header" }, "level": 2 }, { "id": "p11.2", "order": 2, "type": "text", "bbox": { "l": 46.08, "t": 697.68, "r": 218.4, "b": 686.16 }, "text": "The functional form for the yield function is" }, { "id": "p11.3", "order": 3, "type": "formula", "bbox": { "l": 102.96, "t": 676.56, "r": 222.48, "b": 652.56 }, "text": "V_{a,t}^{i}(\\mathbf{m}_{a,t}^{i})=h*\\left[\\exp\\left(\\delta^{i}-\\frac{\\pi^{i}}{a}\\right)\\right]", "attrs": { "block_label": "display_formula", "latex": "V_{a,t}^{i}(\\mathbf{m}_{a,t}^{i})=h*\\left[\\exp\\left(\\delta^{i}-\\frac{\\pi^{i}}{a}\\right)\\right]", "notation": "latex", "alt": "V sub a, t to the power of i of mathbf m sub a, t to the power of i equals h* exp of delta to the power of i minus pi to the power of i over a", "mathml": "Va,ti(𝐦a,ti)=h*[exp(δi−πia)]" } }, { "id": "p11.4", "order": 4, "type": "text", "bbox": { "l": 278.64, "t": 670.56, "r": 290.16, "b": 659.52 }, "text": "(3)", "attrs": { "raw_type": "FORMULA_NUMBER", "block_label": "formula_number" } }, { "id": "p11.5", "order": 5, "type": "text", "bbox": { "l": 33.36, "t": 644.16, "r": 292.08, "b": 489.12 }, "text": "Per equation[p11.5.1], h is the stocking density, which can be adjusted depending on the intensity of management,[p11.5.2]. We restrict stocking elasticity,[p11.5.3], to be positive and less than 1. The[p11.5.4] affects the elasticity of management inputs in forestry to account for technology change. Initial stocking is denoted by[p11.5.5]. Increase in[p11.5.6] will increase h, e.g., $ dh/dZ > 0 $, but the increase diminishes as[p11.5.7] rises, e.g.,[p11.5.8]. The model chooses management intensity by optimally choosing[p11.5.9]. Increases in management intensity will increase yield and shift the entire yield function upward. Forests are assumed to grow according to[p11.5.10], where[p11.5.11] and[p11.5.12] are species-dependent growth parameters (fig. S3 shows a representative yield function assuming h = 1.32,[p11.5.13], and[p11.5.14]). $ C(Q_{t}^{tot}) $ is the cost function for harvesting and transporting logs to the center (mills or power plants) from each of timber type.", "children": [ { "id": "p11.5.1", "order": 6, "type": "formula", "bbox": { "l": 33.36, "t": 644.16, "r": 292.08, "b": 489.12 }, "text": "h = \\varphi^{i}(1 + m_{a,t}^{i})^{\\tau}", "attrs": { "latex": "h = \\varphi^{i}(1 + m_{a,t}^{i})^{\\tau}", "inline": true, "text_offset": 12, "text_span": 9, "bbox_estimated": true, "notation": "latex", "alt": "h equals varphi to the power of i of 1 plus m sub a, t to the power of i to the power of tau", "mathml": "h=φi(1+ma,ti)τ" } }, { "id": "p11.5.2", "order": 7, "type": "formula", "bbox": { "l": 33.36, "t": 644.16, "r": 292.08, "b": 489.12 }, "text": "m_{a=1,t}^{i}", "attrs": { "latex": "m_{a=1,t}^{i}", "inline": true, "text_offset": 113, "text_span": 9, "bbox_estimated": true, "notation": "latex", "alt": "m sub a equals 1, t to the power of i", "mathml": "ma=1,ti" } }, { "id": "p11.5.3", "order": 8, "type": "formula", "bbox": { "l": 33.36, "t": 644.16, "r": 292.08, "b": 489.12 }, "text": "τ", "attrs": { "latex": "\\tau", "inline": true, "text_offset": 156, "text_span": 9, "bbox_estimated": true, "alt": "tau", "mathml": "τ" } }, { "id": "p11.5.4", "order": 9, "type": "formula", "bbox": { "l": 33.36, "t": 644.16, "r": 292.08, "b": 489.12 }, "text": "τⁱ", "attrs": { "latex": "\\tau^{i}", "inline": true, "text_offset": 202, "text_span": 9, "bbox_estimated": true, "alt": "tau to the power of i", "mathml": "τi" } }, { "id": "p11.5.5", "order": 10, "type": "formula", "bbox": { "l": 33.36, "t": 644.16, "r": 292.08, "b": 489.12 }, "text": "\\varphi^{i}", "attrs": { "latex": "\\varphi^{i}", "inline": true, "text_offset": 332, "text_span": 9, "bbox_estimated": true, "notation": "latex", "alt": "varphi to the power of i", "mathml": "φi" } }, { "id": "p11.5.6", "order": 11, "type": "formula", "bbox": { "l": 33.36, "t": 644.16, "r": 292.08, "b": 489.12 }, "text": "m_{a=1,t}^{i}", "attrs": { "latex": "m_{a=1,t}^{i}", "inline": true, "text_offset": 354, "text_span": 9, "bbox_estimated": true, "notation": "latex", "alt": "m sub a equals 1, t to the power of i", "mathml": "ma=1,ti" } }, { "id": "p11.5.7", "order": 12, "type": "formula", "bbox": { "l": 33.36, "t": 644.16, "r": 292.08, "b": 489.12 }, "text": "m_{a=1,t}^{i}", "attrs": { "latex": "m_{a=1,t}^{i}", "inline": true, "text_offset": 432, "text_span": 9, "bbox_estimated": true, "notation": "latex", "alt": "m sub a equals 1, t to the power of i", "mathml": "ma=1,ti" } }, { "id": "p11.5.8", "order": 13, "type": "formula", "bbox": { "l": 33.36, "t": 644.16, "r": 292.08, "b": 489.12 }, "text": "d²h/dZ² < 0", "attrs": { "latex": "d^{2}h/dZ^{2} < 0", "inline": true, "text_offset": 454, "text_span": 9, "bbox_estimated": true, "alt": "d squared h over dZ squared is less than 0", "mathml": "d2h/dZ2<0" } }, { "id": "p11.5.9", "order": 14, "type": "formula", "bbox": { "l": 33.36, "t": 644.16, "r": 292.08, "b": 489.12 }, "text": "m_{a=1,t}^{i}", "attrs": { "latex": "m_{a=1,t}^{i}", "inline": true, "text_offset": 525, "text_span": 9, "bbox_estimated": true, "notation": "latex", "alt": "m sub a equals 1, t to the power of i", "mathml": "ma=1,ti" } }, { "id": "p11.5.10", "order": 15, "type": "formula", "bbox": { "l": 33.36, "t": 644.16, "r": 292.08, "b": 489.12 }, "text": "V_{a,t}^{i}(Z_{a=1,t}^{i})", "attrs": { "latex": "V_{a,t}^{i}(Z_{a=1,t}^{i})", "inline": true, "text_offset": 674, "text_span": 10, "bbox_estimated": true, "notation": "latex", "alt": "V sub a, t to the power of i of Z sub a equals 1, t to the power of i", "mathml": "Va,ti(Za=1,ti)" } }, { "id": "p11.5.11", "order": 16, "type": "text", "bbox": { "l": 33.36, "t": 644.16, "r": 292.08, "b": 489.12 }, "text": "δ", "attrs": { "inline": true, "text_offset": 691, "text_span": 10, "bbox_estimated": true } }, { "id": "p11.5.12", "order": 17, "type": "formula", "bbox": { "l": 33.36, "t": 644.16, "r": 292.08, "b": 489.12 }, "text": "\\text{Per equation } h = \\varphi^{i}(1 + m^{i}_{a,t})^{\\tau^{i}}, h \\text{ is the stocking density, which can be adjusted depending on the intensity of management, } m^{i}_{a=1,t}. \\text{We restrict stocking elasticity, } \\tau \\text{, to be positive and less than 1. The } \\tau^{i} \\text{ affects the elasticity of management inputs in forestry to account for technology change. Initial stocking is denoted by } \\varphi^{i}. \\text{Increase in } m^{i}_{a=1,t} \\text{ will increase } h \\text{, e.g., } dh/dZ > 0 \\text{, but the increase diminishes as } m^{i}_{a=1,t} \\text{ rises, e.g., } d^2h/dZ^2 < 0. \\text{The model chooses management intensity by optimally choosing } m^{i}_{a=1,t}. \\text{Increases in management intensity will increase yield and shift the entire yield function upward. Forests are assumed to grow according to } V^{i}_{a,t}(Z^{i}_{a=1,t}), \\text{ where } \\delta \\text{ and } \\pi \\text{ are species-dependent growth parameters (fig. S3 shows a representative yield function assuming } h = 1.32, \\delta = 5.2, \\text{ and } \\pi = 30). \\; C(Q^{\\text{tot}}_{t}) \\text{ is the cost function for harvesting and transporting logs to the center (mills or power plants) from each of timber type.}", "attrs": { "latex": "\\text{Per equation } h = \\varphi^{i}(1 + m^{i}_{a,t})^{\\tau^{i}}, h \\text{ is the stocking density, which can be adjusted depending on the intensity of management, } m^{i}_{a=1,t}. \\text{We restrict stocking elasticity, } \\tau \\text{, to be positive and less than 1. The } \\tau^{i} \\text{ affects the elasticity of management inputs in forestry to account for technology change. Initial stocking is denoted by } \\varphi^{i}. \\text{Increase in } m^{i}_{a=1,t} \\text{ will increase } h \\text{, e.g., } dh/dZ > 0 \\text{, but the increase diminishes as } m^{i}_{a=1,t} \\text{ rises, e.g., } d^2h/dZ^2 < 0. \\text{The model chooses management intensity by optimally choosing } m^{i}_{a=1,t}. \\text{Increases in management intensity will increase yield and shift the entire yield function upward. Forests are assumed to grow according to } V^{i}_{a,t}(Z^{i}_{a=1,t}), \\text{ where } \\delta \\text{ and } \\pi \\text{ are species-dependent growth parameters (fig. S3 shows a representative yield function assuming } h = 1.32, \\delta = 5.2, \\text{ and } \\pi = 30). \\; C(Q^{\\text{tot}}_{t}) \\text{ is the cost function for harvesting and transporting logs to the center (mills or power plants) from each of timber type.}", "inline": true, "text_offset": 705, "text_span": 10, "bbox_estimated": true, "alt": "Per equation h equals varphi to the power of i of 1 plus m to the power of i sub a, t to the power of tau to the power of i, h is the stocking density, which can be adjusted depending on the intensity of management, m to the power of i sub a equals 1, t . We restrict stocking elasticity, tau, to be positive and less than 1. The tau to the power of i affects the elasticity of management inputs in forestry to account for technology change. Initial stocking is denoted by varphi to the power of i . Increase in m to the power of i sub a equals 1, t will increase h, e.g., dh over dZ is greater than 0, but the increase diminishes as m to the power of i sub a equals 1, t rises, e.g., d squared h over dZ squared is less than 0. The model chooses management intensity by optimally choosing m to the power of i sub a equals 1, t . Increases in management intensity will increase yield and shift the entire yield function upward. Forests are assumed to grow according to V to the power of i sub a, t of Z to the power of i sub a equals 1, t, where delta and pi are species minus dependent growth parameters of fig. S3 shows a representative yield function assuming h equals 1.32, delta equals 5.2, and pi equals 30 . ; C of Q to the power of tot sub t is the cost function for harvesting and transporting logs to the center of mills or power plants from each of timber type.", "notation": "latex", "mathml": "Per equation h=φi(1+ma,ti)τi,h is the stocking density, which can be adjusted depending on the intensity of management, ma=1,ti.We restrict stocking elasticity, τ, to be positive and less than 1. The τi affects the elasticity of management inputs in forestry to account for technology change. Initial stocking is denoted by φi.Increase in ma=1,ti will increase h, e.g., dh/dZ>0, but the increase diminishes as ma=1,ti rises, e.g., d2h/dZ2<0.The model chooses management intensity by optimally choosing ma=1,ti.Increases in management intensity will increase yield and shift the entire yield function upward. Forests are assumed to grow according to Va,ti(Za=1,ti), where δ and π are species-dependent growth parameters (fig. S3 shows a representative yield function assuming h=1.32,δ=5.2, and π=30).C(Qttot) is the cost function for harvesting and transporting logs to the center (mills or power plants) from each of timber type." } }, { "id": "p11.5.13", "order": 18, "type": "formula", "bbox": { "l": 33.36, "t": 644.16, "r": 292.08, "b": 489.12 }, "text": "δ = 5.2", "attrs": { "latex": "\\delta = 5.2", "inline": true, "text_offset": 821, "text_span": 10, "bbox_estimated": true, "alt": "delta equals 5.2", "mathml": "δ=5.2" } }, { "id": "p11.5.14", "order": 19, "type": "text", "bbox": { "l": 33.36, "t": 644.16, "r": 292.08, "b": 489.12 }, "text": "π = 30", "attrs": { "inline": true, "text_offset": 836, "text_span": 10, "bbox_estimated": true } } ] }, { "id": "p11.6", "order": 20, "type": "text", "bbox": { "l": 45.84, "t": 488.16, "r": 292.08, "b": 477.12 }, "text": "The stock of land in each forest type adjusts over time according to" }, { "id": "p11.7", "order": 21, "type": "formula", "bbox": { "l": 76.8, "t": 468.96, "r": 248.88, "b": 454.8 }, "text": "X_{a,t}^{i}=X_{a-1,t-1}^{i}-H_{a-1,t-1}^{i}+G_{a=0,t-1}^{i}+N_{a=0,t-1}^{i}", "attrs": { "block_label": "display_formula", "latex": "X_{a,t}^{i}=X_{a-1,t-1}^{i}-H_{a-1,t-1}^{i}+G_{a=0,t-1}^{i}+N_{a=0,t-1}^{i}", "notation": "latex", "alt": "X sub a, t to the power of i equals X sub a minus 1, t minus 1 to the power of i minus H sub a minus 1, t minus 1 to the power of i plus G sub a equals 0, t minus 1 to the power of i plus N sub a equals 0, t minus 1 to the power of i", "mathml": "Xa,ti=Xa−1,t−1i−Ha−1,t−1i+Ga=0,t−1i+Na=0,t−1i" } }, { "id": "p11.8", "order": 22, "type": "text", "bbox": { "l": 279.12, "t": 467.04, "r": 290.64, "b": 456.72 }, "text": "(4)", "attrs": { "raw_type": "FORMULA_NUMBER", "block_label": "formula_number" } }, { "id": "p11.9", "order": 23, "type": "text", "bbox": { "l": 33.12, "t": 446.16, "r": 293.04, "b": 367.92 }, "text": "The initial stocks of land[p11.9.1] are given, and all choice variables are constrained to be greater than or equal to zero, and the area of timber harvested[p11.9.2] does not exceed the total timber area.[p11.9.3] is the area of timber regenerated land planted, and[p11.9.4] is the new forest planted.[p11.9.5] is the cost function for planting land in temperate and previously inaccessible forests, while[p11.9.6] is the cost function for planting forests in subtropical plantation regions.", "children": [ { "id": "p11.9.1", "order": 24, "type": "formula", "bbox": { "l": 33.12, "t": 446.16, "r": 293.04, "b": 367.92 }, "text": "X_{t}^{i}", "attrs": { "latex": "X_{t}^{i}", "inline": true, "text_offset": 26, "text_span": 9, "bbox_estimated": true, "notation": "latex", "alt": "X sub t to the power of i", "mathml": "Xti" } }, { "id": "p11.9.2", "order": 25, "type": "text", "bbox": { "l": 33.12, "t": 446.16, "r": 293.04, "b": 367.92 }, "text": "H_{a,t}^{i}", "attrs": { "inline": true, "text_offset": 157, "text_span": 9, "bbox_estimated": true } }, { "id": "p11.9.3", "order": 26, "type": "formula", "bbox": { "l": 33.12, "t": 446.16, "r": 293.04, "b": 367.92 }, "text": "G_{t}^{i}", "attrs": { "latex": "G_{t}^{i}", "inline": true, "text_offset": 205, "text_span": 9, "bbox_estimated": true, "notation": "latex", "alt": "G sub t to the power of i", "mathml": "Gti" } }, { "id": "p11.9.4", "order": 27, "type": "formula", "bbox": { "l": 33.12, "t": 446.16, "r": 293.04, "b": 367.92 }, "text": "N_{t}^{i}", "attrs": { "latex": "N_{t}^{i}", "inline": true, "text_offset": 266, "text_span": 9, "bbox_estimated": true, "notation": "latex", "alt": "N sub t to the power of i", "mathml": "Nti" } }, { "id": "p11.9.5", "order": 28, "type": "formula", "bbox": { "l": 33.12, "t": 446.16, "r": 293.04, "b": 367.92 }, "text": "C_{G}^{i}(\\cdot)", "attrs": { "latex": "C_{G}^{i}(\\cdot)", "inline": true, "text_offset": 302, "text_span": 9, "bbox_estimated": true, "notation": "latex", "alt": "C sub G to the power of i of times", "mathml": "CGi(·)" } }, { "id": "p11.9.6", "order": 29, "type": "formula", "bbox": { "l": 33.12, "t": 446.16, "r": 293.04, "b": 367.92 }, "text": "C_{N}^{i}(\\cdot)", "attrs": { "latex": "C_{N}^{i}(\\cdot)", "inline": true, "text_offset": 406, "text_span": 9, "bbox_estimated": true, "notation": "latex", "alt": "C sub N to the power of i of times", "mathml": "CNi(·)" } } ] }, { "id": "p11.10", "order": 30, "type": "text", "bbox": { "l": 33.12, "t": 368.16, "r": 293.04, "b": 126.96 }, "text": "GTM takes into account the competition of forestland with crops and livestock using a rental supply function for land (2). In Eq. 1,[p11.10.1] is the rental cost function for the opportunity costs of holding timberland[p11.10.2]. For example, if timber prices rise relative to agricultural land prices, the model predicts that timber owners will rent suitable farmland for at least a rotation. Similarly, if timber prices fall relatively to agricultural land prices, suitable forest land will be converted back to farmland upon harvest. In addition, the model accounts for the aggregate global effects of moving land between forests and agriculture by shifting all of the land supply functions for individual forest types as a function of the aggregate global area of forestland. As more land globally moves from agriculture to forests, all rental functions shift inward, making it more costly to convert any land from agriculture to forestry. This captures the effect that having less land in agriculture would have on land prices. We have assumed that the elasticity of land supply is 0.25, such that a 0.25% reduction in the global area of agricultural land would cause all land rents to rise by 1%. Note also that the rental supply function is restricted to agricultural land that is naturally suitable for forests. It presumes that the least productive crop and pasture land will be converted first and that rental rates increase as more land is converted and sendogenous.", "children": [ { "id": "p11.10.1", "order": 31, "type": "formula", "bbox": { "l": 33.12, "t": 368.16, "r": 293.04, "b": 126.96 }, "text": "R_{t}^{i}(\\cdot)", "attrs": { "latex": "R_{t}^{i}(\\cdot)", "inline": true, "text_offset": 132, "text_span": 10, "bbox_estimated": true, "notation": "latex", "alt": "R sub t to the power of i of times", "mathml": "Rti(·)" } }, { "id": "p11.10.2", "order": 32, "type": "formula", "bbox": { "l": 33.12, "t": 368.16, "r": 293.04, "b": 126.96 }, "text": "X_{a,t}^{i}", "attrs": { "latex": "X_{a,t}^{i}", "inline": true, "text_offset": 218, "text_span": 10, "bbox_estimated": true, "notation": "latex", "alt": "X sub a, t to the power of i", "mathml": "Xa,ti" } } ] }, { "id": "p11.11", "order": 33, "type": "text", "bbox": { "l": 33.36, "t": 126.48, "r": 292.08, "b": 71.52 }, "text": "The model is also developed to account for the global forest carbon stocks and flows following a method first presented by Sohngen and Sedjo (50) and updated by Daigneault et al. (18). Carbon is tracked in four pools: aboveground carbon, soil carbon, forest product carbon, and slash." }, { "id": "p11.12", "order": 34, "type": "text", "bbox": { "l": 33.6, "t": 71.52, "r": 292.8, "b": 47.52 }, "text": "Aboveground carbon[p11.12.1] accounts for the carbon in all components of the living tree, including roots, as well as carbon in the forest understory and the forest floor, but does not include dead organic matter in slash, which is contained in a separate pool. For this analysis, we assume that carbon is proportional to total biomass, such that carbon in any forest of any age class is given as", "children": [ { "id": "p11.12.1", "order": 35, "type": "formula", "bbox": { "l": 33.6, "t": 71.52, "r": 292.8, "b": 47.52 }, "text": "C_{a,t}^{i}", "attrs": { "latex": "C_{a,t}^{i}", "inline": true, "text_offset": 18, "text_span": 10, "bbox_estimated": true, "notation": "latex", "alt": "C sub a, t to the power of i", "mathml": "Ca,ti" } } ] }, { "id": "p11.13", "order": 36, "type": "text", "bbox": { "l": 300.48, "t": 697.68, "r": 559.68, "b": 653.04 }, "text": "understory and the forest floor, but does not include dead organic matter in slash, which is contained in a separate pool. For this analysis, we assume that carbon is proportional to total biomass, such that carbon in any forest of any age class is given as" }, { "id": "p11.14", "order": 37, "type": "formula", "bbox": { "l": 391.44, "t": 644.16, "r": 466.32, "b": 630.24 }, "text": "C_{a,t}^{i}\\:=\\:\\sigma^{i}\\,V_{a,t}^{i}(m_{t0}^{i})", "attrs": { "block_label": "display_formula", "latex": "C_{a,t}^{i}\\:=\\:\\sigma^{i}\\,V_{a,t}^{i}(m_{t0}^{i})", "notation": "latex", "alt": "C sub a, t to the power of i : equals : sigma to the power of i, V sub a, t to the power of i of m sub t0 to the power of i", "mathml": "Ca,ti=σiVa,ti(mt0i)" } }, { "id": "p11.15", "order": 38, "type": "text", "bbox": { "l": 546, "t": 642, "r": 557.76, "b": 631.2 }, "text": "(5)", "attrs": { "raw_type": "FORMULA_NUMBER", "block_label": "formula_number" } }, { "id": "p11.16", "order": 39, "type": "text", "bbox": { "l": 299.04, "t": 622.32, "r": 560.16, "b": 586.8 }, "text": "where[p11.16.1] is a species-dependent coefficient that converts biomass to carbon. Given this, the total forest carbon pool[p11.16.2] for each timber type is calculated as", "children": [ { "id": "p11.16.1", "order": 40, "type": "text", "bbox": { "l": 299.04, "t": 622.32, "r": 560.16, "b": 586.8 }, "text": "σⁱ", "attrs": { "inline": true, "text_offset": 5, "text_span": 10, "bbox_estimated": true } }, { "id": "p11.16.2", "order": 41, "type": "text", "bbox": { "l": 299.04, "t": 622.32, "r": 560.16, "b": 586.8 }, "text": "TFCP_{t}^{i}", "attrs": { "inline": true, "text_offset": 124, "text_span": 10, "bbox_estimated": true } } ] }, { "id": "p11.17", "order": 42, "type": "formula", "bbox": { "l": 386.88, "t": 580.56, "r": 472.8, "b": 565.68 }, "text": "\\mathrm{TFCP}_{t}^{i}=\\sum_{a}C_{a,t}^{i}X_{a,t}^{i}", "attrs": { "block_label": "display_formula", "latex": "\\mathrm{TFCP}_{t}^{i}=\\sum_{a}C_{a,t}^{i}X_{a,t}^{i}", "notation": "latex", "alt": "TFCP sub t to the power of i equals the sum of sub a C sub a, t to the power of i X sub a, t to the power of i", "mathml": "TFCPti=∑aCa,tiXa,ti" } }, { "id": "p11.18", "order": 43, "type": "text", "bbox": { "l": 546, "t": 578.4, "r": 558, "b": 567.6 }, "text": "(6)", "attrs": { "raw_type": "FORMULA_NUMBER", "block_label": "formula_number" } }, { "id": "p11.19", "order": 44, "type": "text", "bbox": { "l": 300.72, "t": 557.76, "r": 559.2, "b": 534 }, "text": "Carbon in harvested forest products[p11.19.1] is estimated by tracking forest products over time as follows", "children": [ { "id": "p11.19.1", "order": 45, "type": "formula", "bbox": { "l": 300.72, "t": 557.76, "r": 559.2, "b": 534 }, "text": "HC_{t}^{i}", "attrs": { "latex": "HC_{t}^{i}", "inline": true, "text_offset": 35, "text_span": 10, "bbox_estimated": true, "notation": "latex", "alt": "HC sub t to the power of i", "mathml": "HCti" } } ] }, { "id": "p11.20", "order": 46, "type": "formula", "bbox": { "l": 363.36, "t": 526.32, "r": 496.8, "b": 510.96 }, "text": "\\begin{array}{rl}{\\mathrm{HC}_{t}^{i}=}&{{}\\left(1-\\tau_{t}\\right)\\kappa^{i}\\sum_{a}\\left(\\beta^{i}V_{a,t}^{i}H_{a,t}^{i}\\right)}\\end{array}", "attrs": { "block_label": "display_formula", "latex": "\\begin{array}{r l}{\\mathrm{H C}_{t}^{i}=}&{{}\\left(1-\\tau_{t}\\right)\\kappa^{i}\\sum_{a}\\left(\\beta^{i}V_{a,t}^{i}H_{a,t}^{i}\\right)}\\end{array}", "notation": "latex", "alt": "begin array rl HC sub t to the power of i equals & 1 minus tau sub t kappa to the power of i the sum of sub a of beta to the power of i V sub a, t to the power of i H sub a, t to the power of i end array", "mathml": "HCti=(1−τt)κi∑a(βiVa,tiHa,ti)" } }, { "id": "p11.21", "order": 47, "type": "text", "bbox": { "l": 545.76, "t": 523.68, "r": 557.76, "b": 512.64 }, "text": "(7)", "attrs": { "raw_type": "FORMULA_NUMBER", "block_label": "formula_number" } }, { "id": "p11.22", "order": 48, "type": "text", "bbox": { "l": 300, "t": 503.04, "r": 559.92, "b": 413.52 }, "text": "where[p11.22.1] is the proportion of harvested timber volume that is carbon stored permanently, and it is estimated to be 0.30 (51),[p11.22.2] is a parameter that converts forest products into carbon (regional and forest type based), while[p11.22.3] is the portion of wood used in the energy sector, and it is endogenously selected by the model; that is,[p11.22.4] accounts only for carbon stored in wood products, not woody biomass used for energy production. Carbon stored in woody biomass used for bioenergy production is calculated as follows", "children": [ { "id": "p11.22.1", "order": 49, "type": "formula", "bbox": { "l": 300, "t": 503.04, "r": 559.92, "b": 413.52 }, "text": "\\kappa^{i} is the proportion of harvested timber volume that is carbon stored permanently, and it is estimated to be 0.30 (51), \\beta^{i} is a parameter that converts forest products into carbon (regional and forest type based), while \\tau_t is the portion of wood used in the energy sector, and it is endogenously selected by the model; that is, HC^{i}_{t} accounts only for carbon stored in wood products, not woody biomass used for energy production. Carbon stored in woody biomass used for bioenergy production is calculated as follows", "attrs": { "latex": "\\kappa^{i} is the proportion of harvested timber volume that is carbon stored permanently, and it is estimated to be 0.30 (51), \\beta^{i} is a parameter that converts forest products into carbon (regional and forest type based), while \\tau_t is the portion of wood used in the energy sector, and it is endogenously selected by the model; that is, HC^{i}_{t} accounts only for carbon stored in wood products, not woody biomass used for energy production. Carbon stored in woody biomass used for bioenergy production is calculated as follows", "inline": true, "text_offset": 5, "text_span": 10, "bbox_estimated": true, "alt": "kappa to the power of i is the proportion of harvested timber volume that is carbon stored permanently, and it is estimated to be 0.30 times 51, beta to the power of i is a parameter that converts forest products into carbon of regional and forest type based, while tau sub t is the portion of wood used in the energy sector, and it is endogenously selected by the model; that is, HC to the power of i sub t accounts only for carbon stored in wood products, not woody biomass used for energy production. Carbon stored in woody biomass used for bioenergy production is calculated as follows", "notation": "latex", "mathml": "κiistheproportionofharvestedtimbervolumethatiscarbonstoredpermanently,anditisestimatedtobe0.30(51),βiisaparameterthatconvertsforestproductsintocarbon(regionalandforesttypebased),whileτtistheportionofwoodusedintheenergysector,anditisendogenouslyselectedbythemodel;thatis,HCtiaccountsonlyforcarbonstoredinwoodproducts,notwoodybiomassusedforenergyproduction.Carbonstoredinwoodybiomassusedforbioenergyproductioniscalculatedasfollows" } }, { "id": "p11.22.2", "order": 50, "type": "text", "bbox": { "l": 300, "t": 503.04, "r": 559.92, "b": 413.52 }, "text": "βⁱ", "attrs": { "inline": true, "text_offset": 132, "text_span": 10, "bbox_estimated": true } }, { "id": "p11.22.3", "order": 51, "type": "formula", "bbox": { "l": 300, "t": 503.04, "r": 559.92, "b": 413.52 }, "text": "\\tau_{t}", "attrs": { "latex": "\\tau_{t}", "inline": true, "text_offset": 239, "text_span": 10, "bbox_estimated": true, "notation": "latex", "alt": "tau sub t", "mathml": "τt" } }, { "id": "p11.22.4", "order": 52, "type": "formula", "bbox": { "l": 300, "t": 503.04, "r": 559.92, "b": 413.52 }, "text": "HC_{t}^{i}", "attrs": { "latex": "HC_{t}^{i}", "inline": true, "text_offset": 354, "text_span": 10, "bbox_estimated": true, "notation": "latex", "alt": "HC sub t to the power of i", "mathml": "HCti" } } ] }, { "id": "p11.23", "order": 53, "type": "formula", "bbox": { "l": 375.36, "t": 407.04, "r": 484.8, "b": 392.4 }, "text": "\\begin{array}{c} BIOC_{t}^{i}~=~\\tau_{t}\\sum_{a}\\beta^{i}\\left(V_{a,t}^{i}H_{a,t}^{i}\\right)\\end{array}", "attrs": { "block_label": "display_formula", "latex": "\\begin{array}{c} BIOC_{t}^{i}~=~\\tau_{t}\\sum_{a}\\beta^{i}\\left(V_{a,t}^{i}H_{a,t}^{i}\\right)\\end{array}", "notation": "latex", "alt": "begin array c BIOC sub t to the power of i equals tau sub t the sum of sub a beta to the power of i of V sub a, t to the power of i H sub a, t to the power of i end array", "mathml": "BIOCti = τt∑aβi(Va,tiHa,ti)" } }, { "id": "p11.24", "order": 54, "type": "text", "bbox": { "l": 546.24, "t": 404.88, "r": 557.76, "b": 393.84 }, "text": "(8)", "attrs": { "raw_type": "FORMULA_NUMBER", "block_label": "formula_number" } }, { "id": "p11.25", "order": 55, "type": "text", "bbox": { "l": 300.24, "t": 384, "r": 559.68, "b": 304.56 }, "text": "Soil carbon[p11.25.1] is measured as the stock of carbon in forest soils of type i in time t. The value of[p11.25.2], the steady-state level of carbon in forest soils, is unique to each region and timber type. The parameter[p11.25.3] is the growth rate for soil carbon. In this analysis, we capture the marginal change in carbon value associated with management or land use changes. When land use change occurs, we track net carbon gains or losses over time as follows", "children": [ { "id": "p11.25.1", "order": 56, "type": "formula", "bbox": { "l": 300.24, "t": 384, "r": 559.68, "b": 304.56 }, "text": "\\text{Soil carbon } SOLC_{t}^{i} \\text{ is measured as the stock of carbon in forest soils of type } i \\text{ in time } t. \\text{ The value of } \\overline{K}, \\text{ the steady-state level of carbon in forest soils, is unique to each region and timber type. The parameter } \\mu^{i} \\text{ is the growth rate for soil carbon. In this analysis, we capture the marginal change in carbon value associated with management or land use changes. When land use change occurs, we track net carbon gains or losses over time as follows}", "attrs": { "latex": "\\text{Soil carbon } SOLC_{t}^{i} \\text{ is measured as the stock of carbon in forest soils of type } i \\text{ in time } t. \\text{ The value of } \\overline{K}, \\text{ the steady-state level of carbon in forest soils, is unique to each region and timber type. The parameter } \\mu^{i} \\text{ is the growth rate for soil carbon. In this analysis, we capture the marginal change in carbon value associated with management or land use changes. When land use change occurs, we track net carbon gains or losses over time as follows}", "inline": true, "text_offset": 11, "text_span": 10, "bbox_estimated": true, "notation": "latex", "alt": "Soil carbon SOLC sub t to the power of i is measured as the stock of carbon in forest soils of type i in time t. The value of K bar, the steady minus state level of carbon in forest soils, is unique to each region and timber type. The parameter mu to the power of i is the growth rate for soil carbon. In this analysis, we capture the marginal change in carbon value associated with management or land use changes. When land use change occurs, we track net carbon gains or losses over time as follows", "mathml": "Soil carbon SOLCti is measured as the stock of carbon in forest soils of type i in time t. The value of K―, the steady-state level of carbon in forest soils, is unique to each region and timber type. The parameter μi is the growth rate for soil carbon. In this analysis, we capture the marginal change in carbon value associated with management or land use changes. When land use change occurs, we track net carbon gains or losses over time as follows" } }, { "id": "p11.25.2", "order": 57, "type": "formula", "bbox": { "l": 300.24, "t": 384, "r": 559.68, "b": 304.56 }, "text": "K̄", "attrs": { "latex": "\\overline{K}", "inline": true, "text_offset": 106, "text_span": 10, "bbox_estimated": true, "alt": "K bar", "mathml": "K―" } }, { "id": "p11.25.3", "order": 58, "type": "formula", "bbox": { "l": 300.24, "t": 384, "r": 559.68, "b": 304.56 }, "text": "μⁱ", "attrs": { "latex": "\\mu^{i}", "inline": true, "text_offset": 223, "text_span": 10, "bbox_estimated": true, "alt": "mu to the power of i", "mathml": "μi" } } ] }, { "id": "p11.26", "order": 59, "type": "formula", "bbox": { "l": 335.76, "t": 296.64, "r": 522.24, "b": 267.12 }, "text": "\\mathrm{SOLC}_{t+1}^{i}=\\mathrm{SOLC}_{t}^{i}+\\mathrm{SOLC}_{t}^{i}(\\upmu^{i})\\left[\\frac{(\\overline{K}-\\mathrm{SOLC}_{t}^{i})}{\\mathrm{SOLC}_{t}^{i}}\\right]", "attrs": { "block_label": "display_formula", "latex": "\\mathrm{S O L C}_{t+1}^{i}=\\mathrm{S O L C}_{t}^{i}+\\mathrm{S O L C}_{t}^{i}(\\upmu^{i})\\left[\\frac{(\\overline{K}-\\mathrm{S O L C}_{t}^{i})}{\\mathrm{S O L C}_{t}^{i}}\\right]", "notation": "latex", "alt": "SOLC sub t plus 1 to the power of i equals SOLC sub t to the power of i plus SOLC sub t to the power of i of upmu to the power of i frac of K bar minus SOLC sub t to the power of i SOLC sub t to the power of i", "mathml": "SOLCt+1i=SOLCti+SOLCti(μi)[(K―−SOLCti)SOLCti]" } }, { "id": "p11.27", "order": 60, "type": "text", "bbox": { "l": 546.24, "t": 287.76, "r": 557.52, "b": 276.48 }, "text": "(9)", "attrs": { "raw_type": "FORMULA_NUMBER", "block_label": "formula_number" } }, { "id": "p11.28", "order": 61, "type": "text", "bbox": { "l": 300.72, "t": 258.72, "r": 559.2, "b": 236.16 }, "text": "Last, we measure slash carbon AS[p11.28.1] as the carbon leftover on site after a timber harvest", "children": [ { "id": "p11.28.1", "order": 62, "type": "text", "bbox": { "l": 300.72, "t": 258.72, "r": 559.2, "b": 236.16 }, "text": "_{t}^{i}", "attrs": { "inline": true, "text_offset": 32, "text_span": 10, "bbox_estimated": true } } ] }, { "id": "p11.29", "order": 63, "type": "formula", "bbox": { "l": 358.32, "t": 225.84, "r": 499.68, "b": 211.2 }, "text": "\\begin{array}{rl}{\\mathrm{AS}_{t}^{i}=}&{{}\\sum_{a}(\\upomega_{a}^{i}V_{a,t}^{i}H_{a,t}^{i}-\\upkappa^{i}V_{a,t}^{i}H_{a,t}^{i})}\\end{array}", "attrs": { "block_label": "display_formula", "latex": "\\begin{array}{r l}{\\mathrm{A S}_{t}^{i}=}&{{}\\sum_{a}(\\upomega_{a}^{i}V_{a,t}^{i}H_{a,t}^{i}-\\upkappa^{i}V_{a,t}^{i}H_{a,t}^{i})}\\end{array}", "notation": "latex", "alt": "begin array rl AS sub t to the power of i equals & the sum of sub a of upomega sub a to the power of i V sub a, t to the power of i H sub a, t to the power of i minus upkappa to the power of i V sub a, t to the power of i H sub a, t to the power of i end array", "mathml": "ASti=∑a(ωaiVa,tiHa,ti−κiVa,tiHa,ti)" } }, { "id": "p11.30", "order": 64, "type": "text", "bbox": { "l": 541.44, "t": 223.92, "r": 557.76, "b": 213.12 }, "text": "(10)", "attrs": { "raw_type": "FORMULA_NUMBER", "block_label": "formula_number" } }, { "id": "p11.31", "order": 65, "type": "text", "bbox": { "l": 300.24, "t": 203.52, "r": 558.72, "b": 180.48 }, "text": "Over [p11.31.1]me, the stock of slash SP ti builds up through annual additions and decomposes as follows", "children": [ { "id": "p11.31.1", "order": 66, "type": "text", "bbox": { "l": 300.24, "t": 203.52, "r": 558.72, "b": 180.48 }, "text": "_{t}^{i}", "attrs": { "inline": true, "text_offset": 5, "text_span": 10, "bbox_estimated": true } } ] }, { "id": "p11.32", "order": 67, "type": "formula", "bbox": { "l": 378.72, "t": 171.6, "r": 481.2, "b": 157.44 }, "text": "\\mathrm{SP}_{t+1}^{i}=\\mathrm{AS}_{t}^{i}+\\left(1-\\vartheta^{i}\\mathrm{SP}_{t}^{i}\\right)", "attrs": { "block_label": "display_formula", "latex": "\\mathrm{SP}_{t+1}^{i}=\\mathrm{AS}_{t}^{i}+\\left(1-\\vartheta^{i}\\mathrm{SP}_{t}^{i}\\right)", "notation": "latex", "alt": "SP sub t plus 1 to the power of i equals AS sub t to the power of i plus 1 minus vartheta to the power of i SP sub t to the power of i", "mathml": "SPt+1i=ASti+(1−ϑiSPti)" } }, { "id": "p11.33", "order": 68, "type": "text", "bbox": { "l": 541.44, "t": 169.44, "r": 557.52, "b": 158.64 }, "text": "(11)", "attrs": { "raw_type": "FORMULA_NUMBER", "block_label": "formula_number" } }, { "id": "p11.34", "order": 69, "type": "text", "bbox": { "l": 300, "t": 147.6, "r": 559.2, "b": 125.76 }, "text": "Decomposition rates[p11.34.1] differ, depending on whether the forest lies in the tropics, temperate, or boreal zone.", "children": [ { "id": "p11.34.1", "order": 70, "type": "formula", "bbox": { "l": 300, "t": 147.6, "r": 559.2, "b": 125.76 }, "text": "\\vartheta^{i}", "attrs": { "latex": "\\vartheta^{i}", "inline": true, "text_offset": 19, "text_span": 10, "bbox_estimated": true, "notation": "latex", "alt": "vartheta to the power of i", "mathml": "ϑi" } } ] }, { "id": "p11.35", "order": 71, "type": "text", "bbox": { "l": 300, "t": 125.28, "r": 560.16, "b": 47.28 }, "text": "Last, in Eq. 1, the term[p11.35.1] represents the carbon payments/penalties for forest owners according to the policy implemented. For this study, GTM has been enhanced to capture public policy efforts that either penalize bioenergy demand or value climate mitigation benefits of forests sequestration. GTM assumes that the incentives in the timber product, woody biomass, and carbon sequestration system can be implemented efficiently. That is, GTM portrays an ideal", "children": [ { "id": "p11.35.1", "order": 72, "type": "formula", "bbox": { "l": 300, "t": 125.28, "r": 560.16, "b": 47.28 }, "text": "CC_{t,RCP,policy}", "attrs": { "latex": "CC_{t,RCP,policy}", "inline": true, "text_offset": 24, "text_span": 10, "bbox_estimated": true, "notation": "latex", "alt": "CC sub t, RCP, policy", "mathml": "CCt,RCP,policy" } } ] }, { "id": "p11.36", "order": 73, "type": "text", "bbox": { "l": 572.16, "t": 502.32, "r": 582.96, "b": 255.6 }, "text": "Downloaded from http://advances.sciencemag.org/ on June 25, 2020", "attrs": { "block_label": "aside_text" }, "children": [ { "id": "p11.36.1", "order": 74, "type": "link", "bbox": { "l": 574, "t": 436.152, "r": 584, "b": 318.984 }, "text": "http://advances.sciencemag.org/", "attrs": { "uri": "http://advances.sciencemag.org/", "action_type": "/URI" } } ] }, { "id": "p11.37", "order": 75, "type": "footer", "bbox": { "l": 34.08, "t": 38.64, "r": 215.04, "b": 29.28 }, "text": "Favero et al., Sci. Adv. 2020; 6: eaay6792 25 March 2020", "attrs": { "block_label": "footer" } }, { "id": "p11.38", "order": 76, "type": "footer", "bbox": { "l": 530.64, "t": 38.16, "r": 559.2, "b": 29.04 }, "text": "11 of 13", "attrs": { "block_label": "number" } } ], "excluded_furniture": { "first": [], "last": [] } }