林业碳汇项目基准线和监测方法学及应用分析——以贵州省贞丰县林业碳汇项目为例

气候变化给全球社会经济发展带来了重大影响,林业碳汇在适应和减缓气候变化、促进可持续发展三方面的重要作用日益被世界各国所认可。林业碳汇项目实施的难点在于准确掌握林业碳汇项目设计的规则、标准体系,重点在于基准线判别、碳汇计量、监测的方法学和工具。本文系统介绍了国际清洁发展机制造林再造林(CDM A/R)项目方法学和国内碳汇造林项目方法学、标准体系等最新成果,并以贵州省贞丰县林业碳汇项目为例,分析了基准线和监测方法学在林业碳汇项目开发设计中的实际应用。     

Estimating carbon supply curves from afforestation of agricultural land in the Northeastern U.S.

The Regional Greenhouse Gas Initiative for the northeastern states of the U.S. allows for terrestrial carbon (C) sequestration offsets generated by afforestation activities only. This paper estimates the maximum potential quantity and associated costs of increasing the storage of carbon by afforestation of existing agricultural land in the 11 states of the Northeast United States. The focus of the work was to describe location, the quantity, and at what cost it would be economically attractive to shift agricultural production to afforestation to increase carbon storage in the region. Widely available data sets were used to (1) identify spatially-explicit areas for lower costs carbon offsets and (2) estimate carbon supply curves related to afforestation of agricultural land over three time periods (10, 20, and 40 years). Carbon accumulation and total carbon offset project costs were estimated at a county scale and combined to identify expected costs per ton of carbon dioxide equivalents (CO₂e). Large variation in estimated costs per ton of CO₂e are driven by varying carbon accumulation potentials and opportunity costs of taking land out of agricultural production, as well as the duration of the project activity. Results show that the lowest cost carbon offset projects will be in certain counties of Maine, Vermont, and New York. Pasture land, with lower opportunity costs, generally presents the opportunity for lower cost carbon offset projects relative to cropland. This analysis estimates that afforestation of pasture land in the northeast will not become economically attractive until the price rises above 10 per metric tonne (MT) CO < sub > 2 < /sub > e and that up to 583 million MT could be economically sequestered if the price were to rise to10 per metric tonne (MT) CO₂e and that up to 583 million MT could be economically sequestered if the price were to rise to 50 per MT CO₂e, based on a 40-year project life. With regard to cropland in the northeast, afforestation does not become economically advantageous for land owners until the price rises above $40 per MT CO₂e. It is estimated that up to 487,000 MT could be sequestered from cropland if the price were to rise to $40 per MT CO₂e. It is estimated that up to 487,000 MT could be sequestered from cropland if the price were to rise to 50 per MT CO₂e, based on a 40-year project life.     

中国森林碳汇潜力与增汇成本评估——基于Meta分析方法

准确评估中国森林碳汇潜力与增汇成本的经济可行性,是科学制定碳中和林业行动方案的基础。然而针对中国森林碳汇潜力与增汇成本的不同结果差异明显,可靠性需要进一步验证。为此,基于相关文献,采用Meta分析方法,对中国森林碳汇潜力与增汇成本及其导致差异的原因展开评估。研究表明：（1）中国森林碳汇量呈现不断增长的态势,但不同研究对森林碳汇潜力测度结果存在较大差异。（2）中国森林增汇的平均成本为220.45元/t CO_2e（区间值为3.9~1457.02元/t CO_2e）,与工业减排成本相比,中国森林增汇更具有经济可行性,但波动幅度较大。（3）评估方法采用、碳库数量选择等因素是导致已有森林碳汇潜力文献估计结果差异的关键因素;森林增汇成本差异则主要受碳汇成本测度研究方法、成本收益数据来源等因素影响。（4）中国森林增汇对碳中和的贡献将会持续增加。基于研究结果,提出进一步深化森林碳汇潜力与成本测算相关研究等方面的政策建议。     

A virtual “field test” of forest management carbon offset protocols: the influence of accounting

Of the greenhouse gas (GHG) mitigation options available from U.S. forests and agricultural lands, forest management presents amongst the lowest cost and highest volume opportunities. A number of carbon (C) accounting schemes or protocols have recently emerged to track the mitigation achieved by individual forest management projects. Using 50-year C cycling data from the Calhoun Experimental Forest in South Carolina, USA, C storage is estimated for a hypothetical forest management C offset project operating under seven of these protocols. After 100 years of project implementation, net C sequestration among the seven protocols varies by nearly a full order of magnitude. This variation stems from differences in how individual C pools, baseline, leakage, certainty, and buffers are addressed under each protocol. This in turn translates to a wide variation in the C price required to match the net present value of the non-project, business-as-usual alternative. Collectively, these findings suggest that protocol-specific restrictions or requirements are likely to discount the amount of C that can be claimed in “real world” projects, potentially leading to higher project costs than estimated in previous aggregate national analyses.     

中国四大林区固碳效率:测算、驱动因素及收敛性

论文将林业碳汇纳入到林业经济核算体系之中,构建含有正外部性产出的DEAMalmquist效率分析模型,在系统测算林业固碳量的基础上,对1988—2013年中国四大林区的林业固碳效率变动及驱动因素进行了分析,并进一步对其效率收敛性进行了检验。研究结果表明:1)全国四大林区间的固碳量及固碳价值差异较大,固碳总价值从高到低依次为西南(1 870.69×108元)、东北(1 335.41×108元)、南方(842.73×108元)、北方林区(407.35×108元)。2)1988—2013年不含碳汇产出的林业生产Malmquist指数较低,为0.958;而把碳汇纳入林业产出进行考量,全国林业Malmquist指数整体有所提升,主要源于技术效率推动,年均增长速度为0.6%;其中南方、东北林区固碳效率处于提升状态,而西南林区和北方林区呈下降趋势。3)西南和南方林区固碳效率随时间变动呈现倒"U"型态势;四大林区中南方林区效率均值最高,为1.036,其次是东北林区,为1.020。4)我国四大林区地区间固碳Malmquist指数没有出现σ收敛,相反,还存在绝对β发散现象,即四大林区地区内的林业固碳效率绝对值和增长率差异并没有随着时间而缩减。     

Monitoring of Carbon Abatement in Forestry Projects — Case Study of Western Ghat Project

The forestry sector is being increasingly considered for abatement of greenhouse gases. A number of projects are likely to be implemented, particularly in tropical countries. It is essential to measure, record, and verify the carbon sequestered or emission avoided due to implementation of the forestry mitigation options. In this paper a set required parameters to be monitored for estimating carbon flows, monitoring methods, and institutional arrangements are presented along with a case study of the Western Ghat Forestry and Environment project. Monitoring carbon flows in forestry sector projects is different due to a long gestation period and location- or site-specific variations in various parameters, particularly rates of C sequestration and emission. Parameters to be monitored include C sequestration in vegetation and soil, rates of wood extraction, wood use related emission, litter, production, decomposition from litter, and soil. Methods include field vegetation monitoring, soil study, houschold and industry surveys, and laboratory investigation. Investigations, analysis, and report writing should be carried out using local educational institutions, NGOs, and consultaney firms. Verification could be taken care of by external agencies. Case studies of the Western Ghat Forestry and Environment project showed that less than 10% of the project budget may be adequate for intensive monitoring of carbon flows. The parameters to be monitored and methods required for any forestry mitigation project is nearly identical to that of any typical forest conservation or reforestation project.     

Forestry Mitigation Options for Mexico: Finding Synergies between National Sustainable Development Priorities and Global Concerns

We examine carbon (C) reference and mitigation scenarios for the Mexicanforest sector between the year 2000 and 2030. Estimates are presentedseparately for the period 2008–2012.Future C emissions and capture are estimated using a simulation modelthat: a) allocates the country land use/land cover classes among differentfuture uses and categories using demand-based scenarios for forestryproducts; b) estimates the total C densities associated to each land usecategory, and c) determines the net carbon implications of the process ofland use/cover change according to the different scenarios.The options analyzed include both afforestation/reforestation, such ascommercial, bionenergy and restoration plantations, and agroforestrysystems, and forest conservation, through the sustainable management ofnative forests and forest protection.The total mitigation potential, estimated as the difference between the totallong-term carbon stock in the reference and the mitigation scenario reaches300 × 10⁶ Mg C in the year 2012 and increases to 1,382 × 10⁶ Mg C in 2030. The average net sequestration in the 30 year period is 46 × 10⁶ Mg C yr^-1, or 12.5 × 10⁶ Mg C yr^-1 within the period 2008 to 2012. The costs of selected mitigation options range from 0.7–3.5 Mg C^-1 to 35 Mg C^-1. Some options are cost effective.     

中国森林碳汇的空间溢出效应与影响因素——基于大陆31个省（市、区）森林资源清查数据的空间计量分析

科学估算各地区森林碳汇量并探讨其空间关联性特征是制定差异化碳汇发展政策的重要基础。根据1988—2013年中国大陆31个省（市、区）的6次森林资源清查数据,论文利用森林蓄积量扩展法测算了各地区的森林碳汇量,进而检测和比较了省域间碳汇总量空间关联性的方向和强弱,最后运用空间计量模型分析了碳汇的溢出效应与影响因素。结果表明：1）我国的森林碳汇量整体呈上升态势,各地区间碳汇量差异明显,其中西藏、黑龙江等地区碳汇量丰富,而上海、北京等地则碳汇增长率较快;2）研究期内的Moran’s I指数整体表现为倒“S”型的波动变化特征,全国森林碳汇在省域空间分布上的差异性并不是随机的,而是具备一定关联性;3）我国森林碳汇存在显著的近邻空间溢出效应,森林资源采伐、森林受灾程度和降水量等因素对森林碳汇水平的影响显著。因此,研究认为：我国在发挥森林生态功能时,应当考虑省份间的地理区位因素,合理制定兼具差异化和协调性的森林碳汇发展政策。     

厦门市森林生态系统固碳服务评估

生态系统固碳服务是生态系统服务评估的重要指标之一,也是区域碳循环研究的重要组成部分,可以为减缓气候变化的区域碳管理提供决策依据.以厦门市森林生态系统为研究对象,选取VPM（Vegetation Photosynthesis Model）和ReRSM（Remote Sensing Model for Ecosystem Respiration）评估其2015年的固碳服务,并阐明其固碳服务的时空变异.结果表明:2015年厦门市森林生态系统固碳量（以C计）为31.36×104 t/a,平均固碳量为644.86 g/（m2·a）,其时间动态总体呈单峰曲线分布,但受台风影响该曲线波动较大.厦门市森林生态系统固碳量空间格局总体表现为西北边缘地区较高、其他地区相对较低,与DEM的空间分布较为相似,且绝大部分区域为碳汇区.厦门市分区统计显示,同安区森林生态系统面积和固碳量均最大,分别占厦门市总量的52.58%和57.10%,其与翔安区、集美区的固碳量之和占厦门市总量的88.27%,是厦门市森林生态系统固碳的主体;湖里区固碳量最少,平均固碳量仅为14.25 g/（m2·a）,几乎为碳中性.研究显示,厦门市森林生态系统具有较好的固碳能力.      

Transaction costs for carbon sequestration projects in the tropical forest sector

There is general consensus that carbon (C) sequestration projects in forests are a relatively low cost option for mitigating climate change, but most studies on the subject have assumed that transaction costs are negligible. The objectives of the study were to examine transaction costs for forest C sequestration projects and to determine the significance of the costs based on economic analyses. Here we examine four case studies of active C sequestration projects being implemented in tropical countries and developed for the C market. The results from the case studies were then used with a dynamic forest and land use economic model to investigate how transaction costs affect the efficiency and cost of forest C projects globally. In the case studies transaction costs ranged from 0.38 to 27 million US dollars ($0.09 to $7.71/t CO₂) or 0.3 to 270 % of anticipated income depending principally on the price of C and project size. The three largest cost categories were insurance (under the voluntary market; 41–89 % of total costs), monitoring (3–42 %) and regulatory approval (8–50 %). The global analysis indicated that most existing estimates of marginal costs of C sequestration are underestimated by up to 30 % because transaction costs were not included.     

Forests in climate policy: technical,institutional and economic issues in measurement and monitoring

Despite the economic and environmental significance of the world’s forests, we have limited data about them. Estimates of deforestation in tropical countries and rates of reforestation or afforestation in boreal and temperate countries are inconsistent. Accordingly, estimates of emissions released in deforestation vary widely and range from 7% to 17% of all sources of greenhouse gas (GHG) emissions. The lack of good data severely hampers efforts to shape climate policy because it is difficult to model the role of forests both in the physical global carbon (C) cycle and in cost-effective regimes to abate GHG. Data limits strain the capacity of even the best models to estimate marginal cost functions for forest carbon (C) sequestration. It is technically possible to obtain better information, but for institutional and economic reasons these technologies have not yet been fully deployed. The emergence of carbon (C) trading or tax policy in which forest carbon (C) storage becomes valued would strengthen incentives to supply better data, as would nonmarket regulation if it elicited a shadow value of forest carbon (C) in substituting for reductions in greenhouse gas emissions. “Geo-wiki” may provide a short-term solution to at least part of the data problem. The ultimate solution is the development of a comprehensive forest monitoring system involving remote sensing and on-the-ground truthing. This paper briefly discusses the role of forests in climate policy and then describes data gaps, the capability of technology to fill them, the limits of institutions and budgets in realizing this capability, and possible near-term solutions.     

Factoring out natural and indirect human effects on terrestrial carbon sources and sinks

The capacity to partition natural, indirect, and direct human-induced effects on terrestrial carbon (C) sources and sinks is necessary to be able to predict future terrestrial C dynamics and thus their influence on atmospheric CO₂ growth. However, it will take a number of years before we can better attribute quantitative estimates of the contribution of various C processes to the net C balance. In a policy context, factoring out natural and indirect human-induced effects on C sources and sinks from the direct human-induced influences, is seen as a requirement of a C accounting approach that establishes a clear and unambiguous connection between human activities and the assignment of C credits and debits. We present options for factoring out various groups of influences including climate variability, CO₂ and N fertilization, and legacies from forest management. These are: (i) selecting longer accounting or measurement periods to reduce the effects of inter-annual variability; (ii) correction of national inventories for inter-annual variability; (iii) use of activity-based accounting and C response curves; (iv) use of baseline scenarios or benchmarks at the national level; (v) stratification of the landscape into units with distinct average C stocks. Other, more sophisticated modeling approaches (e.g., demographic models in combination with forest inventories; process-based models) are possible options for future C accounting systems but their complexity and data requirements make their present adoption more difficult in an inclusive international C accounting system.     

Making carbon sequestration a paying proposition

Atmospheric carbon dioxide (CO₂) has increased from a preindustrial concentration of about 280 ppm to about 367 ppm at present. The increase has closely followed the increase in CO₂ emissions from the use of fossil fuels. Global warming caused by increasing amounts of greenhouse gases in the atmosphere is the major environmental challenge for the 21st century. Reducing worldwide emissions of CO₂ requires multiple mitigation pathways, including reductions in energy consumption, more efficient use of available energy, the application of renewable energy sources, and sequestration. Sequestration is a major tool for managing carbon emissions. In a majority of cases CO₂ is viewed as waste to be disposed; however, with advanced technology, carbon sequestration can become a value-added proposition. There are a number of potential opportunities that render sequestration economically viable. In this study, we review these most economically promising opportunities and pathways of carbon sequestration, including reforestation, best agricultural production, housing and furniture, enhanced oil recovery, coalbed methane (CBM), and CO₂ hydrates. Many of these terrestrial and geological sequestration opportunities are expected to provide a direct economic benefit over that obtained by merely reducing the atmospheric CO₂ loading. Sequestration opportunities in 11 states of the Southeast and South Central United States are discussed. Among the most promising methods for the region include reforestation and CBM. The annual forest carbon sink in this region is estimated to be 76 Tg C/year, which would amount to an expenditure of $11.1–13.9 billion/year. Best management practices could enhance carbon sequestration by 53.9 Tg C/year, accounting for 9.3% of current total annual regional greenhouse gas emission in the next 20 years. Annual carbon storage in housing, furniture, and other wood products in 1998 was estimated to be 13.9 Tg C in the region. Other sequestration options, including the direct injection of CO₂ in deep saline aquifers, mineralization, and biomineralization, are not expected to lead to direct economic gain. More detailed studies are needed for assessing the ultimate changes to the environment and the associated indirect cost savings for carbon sequestration.     

Afforestation opportunities when stand productivity is driven by a high risk of natural disturbance: a review of the open lichen woodland in the eastern boreal forest of Canada

Afforestation has the potential to offset the increased emission of atmospheric carbon dioxide and has therefore been proposed as a strategy to mitigate climate change. Here we review the opportunities for carbon (C) offsets through open lichen woodland afforestation in the boreal forest of eastern Canada as a case study, while considering the reversal risks (low productivity, fires, insect outbreaks, changes in land use and the effects of future climate on growth potential as well as on the disturbances regime). Our results suggest that : (1) relatively low growth rate may act as a limiting factor in afforestation projects in which the time available to increase C is driven by natural disturbances; (2) with ongoing climate change, a global increase in natural disturbance rates, mainly fire and spruce budworm outbreaks, may offset any increases in net primary production at the landscape level; (3) the reduction of the albedo versus increase in biomass may negatively affect the net climate forcing; (4) the impermanence of C stock linked to the reversal risks makes this scenario not necessarily cost attractive. More research, notably on the link between fire risk and site productivity, is needed before afforestation can be incorporated into forest management planning to assist climate change mitigation efforts. Therefore, we suggest that conceivable mitigation strategies in the boreal forest will likely have to be directed activities that can reduce emissions and can increase C sinks while minimizing the reversal impacts. Implementation of policies to reduce Greenhouse Gases (GHG) in the boreal forest should consider the biophysical interactions, the different spatial and temporal scales of their benefits, the costs (investment and benefits) and how all these factors are influenced by the site history.     

Mitigation,adaptation, and climate change: results from recent research on US timber markets

This paper reviews recent studies that have addressed how US timber markets may adapt to climate change, and how US forests could be used to mitigate potential climate change. The studies are discussed in light of the ecological and economic assumptions used to estimate adaptation. Estimates of both economic impacts and carbon sequestration costs depend heavily on the assumptions and methods used, although some general conclusions can be drawn. Studies of economic impacts suggest that average market effects in the United States may range from +$1.3 to +7.4 billion per year by the middle of the next century. Estimates of the cost of sequestering carbon have generally increased over the last 10 years, with a current range of <1–73 million metric t per year of additional sequestration from afforestation projects costing $5–66 per metric t. Estimates of the potential for alternative methods for carbon sequestration, such as product markets and recycling, are as large as afforestation estimates, with up to 50 million metric tons per year of additional storage considered possible. Cost estimates have not been developed for these alternative methods, however.     

1975—2005年中亚土地利用/覆被变化对森林生态系统碳储量的影响

土地利用/覆被变化(LUCC)对碳循环的影响研究已覆盖全球绝大多数地区,但中亚LUCC对森林生态系统碳库的影响仍属未知。论文以人工林面积、森林产品收获产量及林地转移面积为基础数据,应用Bookkeeping模型,分析了1975—2005年期间三种LUCC方式对中亚森林碳库的影响。近30 a LUCC对其碳库的影响总体表现为碳汇,固碳量为3.07 Tg。植树造林表现出强烈的碳汇功能,总固碳量为12.97 Tg。森林采伐是最主要的碳释放来源,共释放碳5.80 Tg。林地转移呈现较强的碳释放特征,共排放为4.10 Tg。结果表明1975—2005年该区域LUCC对森林碳库具有明显的增汇效应。研究结果将有利于减少LUCC对全球碳收支影响的不确定性。     

不同气候带退耕还林对区域气温的影响差异分析

退耕还林改变陆表覆盖状况,导致碳收支和地表能量平衡变化,从而影响区域气温。论文通过定量估算耕地转为林地导致生态系统吸收大气CO₂和地表能量平衡的变化,分析21世纪初10 a中国不同气候区开展退耕还林对区域气候调节的影响差异。结果表明：1）仅考虑碳调节,各气候区退耕还林皆表现为241.6~470.2 Mg CO₂-eq hm^-2的碳蓄积过程,具有2.2~16.5 Mg CO₂-eq hm^-2的碳汇作用即致冷效应,特别是亚热带湿润区。2）仅考虑地表能量平衡,中温带干旱与半干旱区退耕还林引起的净辐射增加程度大于潜热通量的增加程度,因此地表对大气供热表现为增温效应;而亚热带湿润区退耕还林引起净辐射减少及潜热通量增加,青藏高原、中温带湿润区净辐射增加程度小于潜热通量的增加程度,因此地表对大气供热皆表现为致冷效应。3）同时考虑碳调节和地表能量收支,中国亚热带湿润区退耕还林的致冷效应是仅考虑碳调节致冷效应的1.25~1.45倍,而中温带干旱区退耕还林的致冷效应则为仅考虑碳调节效应的近一半。     

Policies,Measures and the Monitoring Needs of Forest Sector Carbon Mitigation

Forest sector mitigation options can be grouped into three categories: (1) management for carbon (C) conservation, (2) management for C storage, and (3) management for C substitution. The paper provides background information on the technical potential for C conservation and sequestration worldwide and the average costs of achieving it. It reviews policy measures that have been successfully applied at regional and project levels toward the reduction of atmospheric greenhouse gases. It also describes both national programs and jointly implemented international activities. The monitoring methods, and the items to monitor, differ across these categories. Remote sensing is a good approach for the monitoring of C conservation, but not for C substitution, which requires estimation of the fossil fuels that would be displaced and the continued monitoring of electricity generation sources. C storage, on the other hand, includes C in products which may be traded internationally. Their monitoring will require that bi- or multi-lateral protocols be set up for this purpose.     

Development of an agroforestry carbon sequestration project in Khammam district,India

This paper addresses methodological issues in estimating carbon (C) sequestration potential, baseline determination, additionality and leakage in Khammam district, Andhra Pradesh, southern part of India. Technical potential for afforestation on cultivable wastelands, fallow, and marginal croplands was considered for Eucalyptus clonal plantations. Field studies for aboveground and belowground biomass, woody litter, and soil organic carbon for baseline and project scenarios were conducted to estimate the carbon sequestration potential. The baseline carbon stock was estimated to be 45.3 t C/ha, predominately in soils. The additional carbon sequestration potential under the project scenario for 30 years is estimated to be 12.8 t C/ha/year inclusive of harvest regimes and carbon emissions due to biomass burning and fertilizer application. Considering carbon storage in harvested wood, an additional 45% carbon benefit can be accounted. The project scenario has a higher benefit/cost ratio compared to the baseline scenario. The initial investment cost requirement, however, is high and lack of access to investment is a significant barrier for adoption of agroforestry in the district.

Accounting of forest carbon sinks and sources under a future climate protocol—factoring out past disturbance and management effects on age–class structure

Today, forests in the northern hemisphere are a sink for carbon dioxide (CO₂) from the atmosphere, partly due to changes in forest management practice and intensity. Parties of the Kyoto Protocol had the option to elect to account for direct human-induced carbon (C) sources and sinks from land management activities since 1990. The effect of age–class structure of a forest landscape resulting from past practices and disturbances before the reference year 1990 should be excluded, but methods for “factoring out” the effects of this age–class legacy on carbon emissions and removals are lacking. The legacy effect can be strong and can even overwhelm effects of post-1990 management. It therefore needs to be “factored out”, i.e., removed from the direct human-induced post-1990 effects. In this study we examine how the contributions to forest biomass carbon stock changes of (1) past (pre-1990) disturbances and harvest and (2) recent (post-1990) changes in forest management can be differentiated in present and future observable carbon dynamics in managed forest ecosystems. We also calculate the consequences of different accounting rules for the magnitude and direction of accountable C stock changes in European countries in the period 2013–2017.Different accounting approaches are compared in terms of applicability and their ability to provide incentives for management changes to increase carbon sinks and reduce carbon sources. We demonstrate implications of the various ways of accounting for a sample of European countries with different initial age–class structures. The current forest age–class distribution in countries determines whether and how many credits can be created by the various accounting approaches. We suggest an approach that includes a dynamic, forward-looking baseline as reference and list options to define such a baseline. Accounting of recent management change against such a baseline factors out the contribution of the legacy effect to accounting results and only rewards the effect of recent changes in forest management practices in support of climate change mitigation. We demonstrate that relatively simple, state-of-the-art forest models can factor out effects of past practices and past disturbances on present and future carbon stock changes. Factoring out of past practice effects is thus technically feasible but the numerical results are highly dependent on the choice of baseline which will be subject to negotiation. It is possible, however, to select a dynamic baseline that represents “business-as-usual”, and to isolate and account for only the changes in management. Changes in accounting rules will always be advantageous for some countries and disadvantageous for others, but using a dynamic “business-as-usual” baseline effectively removes the legacy of pre-1990 age–class effects, and thus overcomes one of the acknowledged shortcomings of the current accounting approach.