Staff Publications

Staff Publications

  • external user (warningwarning)
  • Log in as
  • language uk
  • About

    'Staff publications' is the digital repository of Wageningen University & Research

    'Staff publications' contains references to publications authored by Wageningen University staff from 1976 onward.

    Publications authored by the staff of the Research Institutes are available from 1995 onwards.

    Full text documents are added when available. The database is updated daily and currently holds about 240,000 items, of which 72,000 in open access.

    We have a manual that explains all the features 

    Records 1 - 20 / 30

    • help
    • print

      Print search results

    • export

      Export search results

    Check title to add to marked list
    Estimating aboveground net biomass change for tropical and subtropical forests: refinement of IPCC default rates using forest plot data
    Requena Suarez, Daniela ; Rozendaal, Danaë M.A. ; Sy, Veronique De; Phillips, Oliver L. ; Alvarez‐Dávila, Esteban ; Anderson‐teixeira, Kristina ; Araujo‐murakami, Alejandro ; Arroyo, Luzmila ; Baker, Timothy R. ; Bongers, Frans ; Brienen, Roel J.W. ; Carter, Sarah ; Cook‐Patton, Susan C. ; Feldpausch, Ted R. ; Griscom, Bronson W. ; Harris, Nancy ; Hérault, Bruno ; Honorio Coronado, Eurídice N. ; Leavitt, Sara M. ; Lewis, Simon L. ; Marimon, Beatriz S. ; Monteagudo Mendoza, Abel ; N'dja, Justin Kassi ; N'guessan, Anny Estelle ; Poorter, Lourens ; Qie, Lan ; Rutishauser, Ervan ; Sist, Plinio ; Sonké, Bonaventure ; Sullivan, Martin J.P. ; Vilanova, Emilio ; Wang, Maria M.H. ; Martius, Christopher ; Herold, Martin - \ 2019
    Global Change Biology 25 (2019)11. - ISSN 1354-1013 - p. 3609 - 3624.
    As countries advance in greenhouse gas (GHG) accounting for climate change mitigation, consistent estimates of aboveground net biomass change (∆AGB) are needed. Countries with limited forest monitoring capabilities in the tropics and subtropics rely on IPCC 2006 default ∆AGB rates, which are values per ecological zone, per continent. Similarly, research on forest biomass change at large scale also make use of these rates. IPCC 2006 default rates come from a handful of studies, provide no uncertainty indications, and do not distinguish between older secondary forests and old‐growth forests. As part of the 2019 Refinement to the 2006 IPCC Guidelines for National Greenhouse Gas Inventories, we incorporate ∆AGB data available from 2006 onwards, comprising 176 chronosequences in secondary forests and 536 permanent plots in old‐growth and managed/logged forests located in 42 countries in Africa, North and South America, and Asia. We generated ∆AGB rate estimates for younger secondary forests (≤20 years), older secondary forests (>20 years and up to 100 years) and old‐growth forests, and accounted for uncertainties in our estimates. In tropical rainforests, for which data availability was the highest, our ∆AGB rate estimates ranged from 3.4 (Asia) to 7.6 (Africa) Mg ha‐1 yr‐1 in younger secondary forests, from 2.3 (North and South Ameri09ca) to 3.5 (Africa) Mg ha‐1 yr‐1 in older secondary forests, and 0.7 (Asia) to 1.3 (Africa) Mg ha‐1 yr‐1 in old‐growth forests. We provide a rigorous and traceable refinement of the IPCC 2006 default rates in tropical and subtropical ecological zones, and identify which areas require more research on ∆AGB. In this respect, this study should be considered as an important step towards quantifying the role of tropical and subtropical forests as carbon sinks with higher accuracy; our new rates can be used for large‐scale GHG accounting by governmental bodies, non‐governmental organisations and in scientific research.
    Tree Biomass Equations from Terrestrial LiDAR: A Case Study in Guyana
    Lau, Alvaro ; Calders, Kim ; Bartholomeus, Harm ; Martius, Christopher ; Raumonen, Pasi ; Herold, Martin ; Vicari, Matheus ; Sukhdeo, Hansrajie ; Singh, Jeremy ; Goodman, Rosa - \ 2019
    Forests 10 (2019)6. - ISSN 1999-4907 - 18 p.
    Large uncertainties in tree and forest carbon estimates weaken national efforts to accurately estimate aboveground biomass (AGB) for their national monitoring, measurement, reporting and verification system. Allometric equations to estimate biomass have improved, but remain limited. They rely on destructive sampling; large trees are under-represented in the data used to create them; and they cannot always be applied to different regions. These factors lead to uncertainties and systematic errors in biomass estimations. We developed allometric models to estimate tree AGB in Guyana. These models were based on tree attributes (diameter, height, crown diameter) obtained from terrestrial laser scanning (TLS) point clouds from 72 tropical trees and wood density. We validated our methods and models with data from 26 additional destructively harvested trees. We found that our best TLS-derived allometric models included crown diameter, provided more accurate AGB estimates ( R2 = 0.92–0.93) than traditional pantropical models ( R2 = 0.85–0.89), and were especially accurate for large trees (diameter > 70 cm). The assessed pantropical models underestimated AGB by 4 to 13%. Nevertheless, one pantropical model (Chave et al. 2005 without height) consistently performed best among the pantropical models tested ( R2 = 0.89) and predicted AGB accurately across all size classes—which but for this could not be known without destructive or TLS-derived validation data. Our methods also demonstrate that tree height is difficult to measure in situ, and the inclusion of height in allometric models consistently worsened AGB estimates. We determined that TLS-derived AGB estimates were unbiased. Our approach advances methods to be able to develop, test, and choose allometric models without the need to harvest trees.
    Global data and tools for local forest cover loss and REDD+ performance assessment: Accuracy, uncertainty, complementarity and impact
    Bos, Astrid B. ; Sy, Veronique De; Duchelle, Amy E. ; Herold, Martin ; Martius, Christopher ; Tsendbazar, Nandin-Erdene - \ 2019
    International Journal of applied Earth Observation and Geoinformation 80 (2019). - ISSN 0303-2434 - p. 295 - 311.
    Assessing the performance of efforts to reduce emissions from deforestation and forest degradation (REDD+) requires data on forest cover change. Innovations in remote sensing and forest monitoring provide ever-increasing levels of coverage, spatial and temporal detail, and accuracy. More global products and advanced open-source algorithms are becoming available. Still, these datasets and tools are not always consistent or complementary, and their suitability for local REDD+ performance assessments remains unclear. These assessments should, ideally, be free of any confounding factors, but performance estimates are affected by data uncertainties in unknown ways. Here, we analyse (1) differences in accuracy between datasets of forest cover change; (2) if and how combinations of datasets can increase accuracy; and we demonstrate (3) the effect of (not) doing accuracy assessments for REDD+ performance measurements. Our study covers five local REDD+ initiatives in four countries across the tropics. We compared accuracies of a readily available global forest cover change dataset and a locally modifiable open-source break detection algorithm. We applied human interpretation validation tools using Landsat Time Series data and high-resolution optical imagery. Next, we assessed whether and how combining different datasets can increase accuracies using several combination strategies. Finally, we demonstrated the consequences of using the input datasets for REDD+ performance assessments with and without considering their accuracies and uncertainties. Estimating the amount of deforestation using validation samples could substantially reduce uncertainty in REDD+ performance assessments. We found that the accuracies of the various data sources differ at site level, although on average neither one of the input products consistently excelled in accuracy. Using a combination of both products as stratification for area estimation and validated with a sample of high-resolution data seems promising. In these combined products, the expected trade-offs in accuracies across change classes (before, after, no change) and across accuracy types (user’s and producer’s accuracy) were negligible, so their use is advantageous over single-source datasets. More locally calibrated wall-to-wall products should be developed to make them more useful and applicable for REDD+ purposes. The direction and degree of REDD+ performance remained statistically uncertain, as CIs were overlapping in most cases for the deforestation estimates before and after the start of the REDD+ interventions. Given these uncertainties and inaccuracies and to increase the credibility of REDD+ it is advised to (1) be conservative in REDD+ accounting, and (2) not to rely on results from single currently available global data sources or tools without sample-based validation if results-based payments are intended to be made on this basis.
    Estimating architecture-based metabolic scaling exponents of tropical trees using terrestrial LiDAR and 3D modelling
    Lau, Alvaro ; Martius, Christopher ; Bartholomeus, Harm ; Shenkin, Alexander ; Jackson, Tobias ; Malhi, Yadvinder ; Herold, Martin ; Bentley, Lisa Patrick - \ 2019
    Forest Ecology and Management 439 (2019). - ISSN 0378-1127 - p. 132 - 145.
    The geometric structure of tree branches has been hypothesized to relate to the mechanical safety and efficiency of resource transport within a tree. As such, the topology of tree architecture links physical properties within a tree and influences the interaction of the tree with its environment. Prior work suggests the existence of general principles which govern tree architectural patterns across of species and bio-geographical regions. In particular, West, Brown and Enquist (WBE, 1997) and Savage et al. (2010) derive scaling exponents (branch radius scaling ratio α and branch length scaling ratio β) from symmetrical branch parameters and from these, an architecture-based metabolic scaling rate (θ) for the whole tree. With this key scaling exponent, the metabolism (e.g., number of leaves, respiration, etc.) of a whole tree, or potentially a group of trees, can be estimated allometrically. Until now, branch parameter values have been measured manually; either from standing live trees or from harvested trees. Such measurements are time consuming, labour intensive and susceptible to subjective errors. Remote sensing, and specifically terrestrial LiDAR (TLS), is a promising alternative, being objective, scalable, and able to collect large quantities of data without destructive sampling. In this paper, we calculated branch length, branch radius, and architecture-based metabolic rate scaling exponents by first using TLS to scan standing trees and then fitting quantitative structure models (TreeQSM) models to 3D point clouds from nine trees in a tropical forest in Guyana. To validate these TLS-derived scaling exponents, we compared them with exponents calculated from direct field measurements of all branches >10 cm at four scales: branch-level, cumulative branch order, tree-level and plot-level. We found a bias on the estimations of α and β exponents due to a bias on the reconstruction of the branching architecture. Although TreeQSM scaling exponents predicted similar θ as the manually measured exponents, this was due to the combination of α and β scaling exponents which were both biased. Also, the manually measured α and β scaling exponents diverged from the WBE's theoretical exponents suggesting that trees in tropical environments might not follow the predictions for the symmetrical branching geometry proposed by WBE. Our study provides an alternative method to estimate scaling exponents at both the branch- and tree-level in tropical forest trees without the need for destructive sampling. Although this approach is based on a limited sample of nine trees in Guyana, it can be implemented for large-scale plant scaling assessments. These new data might improve our current understanding of metabolic scaling without harvesting trees
    Introduction : REDD+ enters its second decade
    Angelsen, Arild ; Martius, Christopher ; Sy, V. de; Duchelle, Amy E. ; Larson, Anne M. ; Pham Thu Thuy, - \ 2018
    In: Transforming REDD+ / Angelsen, A., Martius, C., De Sy, V., Duchelle, A.E., Larson, A.M., Pham, T.T., Center for International Forestry Research (CIFOR) - ISBN 9786023870790 - p. 1 - 13.
    Information and policy change : Data on drivers can drive change – if used wisely
    Sy, V. de; Herold, M. ; Brockhaus, Maria ; Gregorio, Monica Di; Ochieng, R.M. - \ 2018
    In: Transforming REDD+ / Angelsen, A., Martius, C., De Sy, V., Duchelle, A.E., Larson, A.M., Pham, T.T., Center for International Forestry Research (CIFOR) - ISBN 9786023870790 - p. 55 - 66.
    Forests and carbon : The impacts of local REDD+ initiatives
    Simonet, Gabriela ; Bos, A.B. ; Duchelle, Amy E. ; Pradnja Resosudarmo, Ida Aju ; Subervie, Julie ; Wunder, Sven - \ 2018
    In: Transforming REDD+ / Angelsen, A., Martius, C., De Sy, V., Duchelle, A.E., Larson, A.M., Pham, T.T., Center for International Forestry Research (CIFOR) - ISBN 9786023870790 - p. 117 - 130.
    Climate-smart agriculture : Will higher yields lead to lower deforestation?
    Ngoma, Hambulo ; Angelsen, Arild ; Carter, S.L. ; Roman Cuesta, Rosa Maria - \ 2018
    In: Transforming REDD+ / Angelsen, A., Martius, C., De Sy, V., Duchelle, A.E., Larson, A.M., Pham, T.T., Center for International Forestry Research (CIFOR) - ISBN 9786023870790 - p. 175 - 187.
    Forest restoration : Getting serious about the ‘plus’ in REDD+
    Verchot, Louis V. ; Sy, V. de; Romijn, J.E. ; Herold, M. ; Coppus, R. - \ 2018
    In: Transforming REDD+ / Angelsen, A., Martius, C., De Sy, V., Duchelle, A.E., Larson, A.M., Pham, T.T., Center for International Forestry Research (CIFOR) - ISBN 9786023870790 - p. 189 - 202.
    Transforming REDD+ : Lessons and new directions
    Angelsen, A. ; Martius, C. ; Sy, V. De; Duchelle, A.E. ; Larson, A.M. ; Pham, T.T. - \ 2018
    Bogor : Center for International Forestry Research (CIFOR) - ISBN 9786023870790 - 278 p.
    Quantifying branch architecture of tropical trees using terrestrial LiDAR and 3D modelling
    Lau, Alvaro ; Bentley, Lisa Patrick ; Martius, Christopher ; Shenkin, Alexander ; Bartholomeus, Harm ; Raumonen, Pasi ; Malhi, Yadvinder ; Jackson, Tobias ; Herold, Martin - \ 2018
    Trees-Structure and Function 32 (2018)5. - ISSN 0931-1890 - p. 1219 - 1231.
    Tree architecture is the three-dimensional arrangement of above ground parts of a tree. Ecologists hypothesize that the topology of tree branches represents optimized adaptations to tree’s environment. Thus, an accurate description of tree architecture leads to a better understanding of how form is driven by function. Terrestrial laser scanning (TLS) has demonstrated its potential to characterize woody tree structure. However, most current TLS methods do not describe tree architecture. Here, we examined nine trees from a Guyanese tropical rainforest to evaluate the utility of TLS for measuring tree architecture. First, we scanned the trees and extracted individual tree point clouds. TreeQSM was used to reconstruct woody structure through 3D quantitative structure models (QSMs). From these QSMs, we calculated: (1) length and diameter of branches > 10 cm diameter, (2) branching order and (3) tree volume. To validate our method, we destructively harvested the trees and manually measured all branches over 10 cm (279). TreeQSM found and reconstructed 95% of the branches thicker than 30 cm. Comparing field and QSM data, QSM overestimated branch lengths thicker than 50 cm by 1% and underestimated diameter of branches between 20 and 60 cm by 8%. TreeQSM assigned the correct branching order in 99% of all cases and reconstructed 87% of branch lengths and 97% of tree volume. Although these results are based on nine trees, they validate a method that is an important step forward towards using tree architectural traits based on TLS and open up new possibilities to use QSMs for tree architecture.
    Independent data for transparent monitoring of greenhouse gas emissions from the land use sector – What do stakeholders think and need?
    Romijn, Erika ; Sy, Veronique De; Herold, Martin ; Böttcher, Hannes ; Roman-Cuesta, Rosa Maria ; Fritz, Steffen ; Schepaschenko, Dmitry ; Avitabile, Valerio ; Gaveau, David ; Verchot, Louis ; Martius, Christopher - \ 2018
    Environmental Science & Policy 85 (2018). - ISSN 1462-9011 - p. 101 - 112.
    The agriculture, forestry and other land use (AFOLU) sectors contribute substantially to the net global anthropogenic greenhouse gas (GHG) emissions. To reduce these emissions under the Paris Agreement, effective mitigation actions are needed that require engagement of multiple stakeholders. Emission reduction also requires that accurate, consistent and comparable datasets are available for transparent reference and progress monitoring. Availability of free and open datasets and portals (referred to as independent data) increases, offering opportunities for improving and reconciling estimates of GHG emissions and mitigation options. Through an online survey, we investigated stakeholders’ data needs for estimating forest area and change, forest biomass and emission factors, and AFOLU GHG emissions. The survey was completed by 359 respondents from governmental, intergovernmental and non-governmental organizations, research institutes and universities, and public and private companies. These can be grouped into data users and data providers. Our results show that current open and freely available datasets and portals are only able to fulfil stakeholder needs to a certain degree. Users require a) detailed documentation regarding the scope and usability of the data, b) comparability between alternative data sources, c) uncertainty estimates for evaluating mitigation options, d) more region-specific and detailed data with higher accuracy for sub-national application, e) regular updates and continuity for establishing consistent time series. These requirements are found to be key elements for increasing overall transparency of data sources, definitions, methodologies and assumptions, which is required under the Paris
    Agreement. Raising awareness and improving data availability through centralized platforms are important for increasing engagement of data users. In countries with low capacities, independent data can support countries’
    mitigation planning and implementation, and related GHG reporting. However, there is a strong need for further guidance and capacity development (i.e.‘
    readiness support’) on how to make proper use of independent datasets. Continued investments will be needed to sustain programmes and keep improving datasets to serve the objectives of the many stakeholders involved in climate change mitigation and should focus on increased accessibility and transparency of data to encourage stakeholder involvement.
    Estimation of above-ground biomass of large tropical trees with terrestrial LiDAR
    Gonzalez De Tanago, Jose ; Lau, Alvaro ; Bartholomeus, Harm ; Herold, Martin ; Avitabile, Valerio ; Raumonen, Pasi ; Martius, Christopher ; Goodman, Rosa C. ; Disney, Mathias ; Manuri, Solichin ; Burt, Andrew ; Calders, Kim - \ 2018
    Methods in Ecology and Evolution 9 (2018)2. - ISSN 2041-210X - p. 223 - 234.
    1. Tropical forest biomass is a crucial component of global carbon emission estimations. However, calibration and validation of such estimates require accurate and effective methods to estimate in situ above-ground biomass (AGB). Present methods rely on allometric models that are highly uncertain for large tropical trees. Terrestrial laser scanning (TLS) tree modelling has demonstrated to be more accurate than these models to infer forest AGB. Nevertheless, applying TLS methods on tropical large trees is still challenging. We propose a method to estimate AGB of large tropical trees by three-dimensional (3D) tree modelling of TLS point clouds. 2. Twenty-nine plots were scanned with a TLS in three study sites (Peru, Indonesia and Guyana). We identified the largest tree per plot (mean diameter at breast height of 73.5 cm), extracted its point cloud and calculated its volume by 3D modelling its structure using quantitative structure models (QSM) and converted to AGB using species-specific wood density. We also estimated AGB using pantropical and local allometric models. To assess the accuracy of our and allometric methods, we harvest the trees and took destructive measurements. 3. AGB estimates by the TLS–QSM method showed the best agreement in comparison to destructive harvest measurements (28.37% coefficient of variation of root mean square error [CV-RMSE] and concordance correlation coefficient [CCC] of 0.95), outperforming the pantropical allometric models tested (35.6%–54.95% CV-RMSE and CCC of 0.89–0.73). TLS–QSM showed also the lowest bias (overall underestimation of 3.7%) and stability across tree size range, contrasting with the allometric models that showed a systematic bias (overall underestimation ranging 15.2%–35.7%) increasing linearly with tree size. The TLS–QSM method also provided accurate tree wood volume estimates (CV RMSE of 23.7%) with no systematic bias regardless the tree structural characteristics. 4. Our TLS–QSM method accounts for individual tree biophysical structure more effectively than allometric models, providing more accurate and less biased AGB estimates for large tropical trees, independently of their morphology. This non-destructive method can be further used for testing and calibrating new allometric models, reducing the current under-representation of large trees in and enhancing present and past estimates of forest biomass and carbon emissions from tropical forests.
    Above-ground biomass assessment of tropical trees with Terrestrial LiDAR and 3D architecture models
    Lau Sarmiento, A.I. ; Gonzalez de Tanago Meñaca, J. ; Bartholomeus, H.M. ; Herold, M. ; Avitabile, V. ; Raumonen, Pasi ; Martius, Christopher ; Goodman, R.C. ; Disney, Mathias ; Manuri, Solichin ; Burt, Andrew ; Calders, Kim - \ 2017
    In: SilviLaser 2017 Program. - Blacksburg : Virginia Tech - p. 123 - 124.
    Unravelling uncertainty - Combining forest cover change products and biomass datasets in the context of REDD+
    Bos, A.B. ; Avitabile, V. ; Sy, V. de; Duchelle, Amy E. ; Herold, M. ; Martius, Christopher - \ 2017
    In: Book of abstracts. - - p. 119 - 119.
    To measure the effectiveness of efforts to reduce emissions from deforestation and forest degradation (REDD+), one requires data on
    both forest cover (change) and biomass stocks. Regional to global datasets with increasing levels of coverage, spatial and temporal detail, and
    accuracy stem from innovations in remote sensing and forest monitoring. Still, these datasets do not necessarily align with each other, and it
    remains unclear how their uncertainties influence carbon emission estimates.
    Our study area covers six REDD+ subnational initiatives in five countries across the tropics. We compared approaches to quantifying impacts on
    carbon emissions. We performed an accuracy assessment on the activity data using several tree cover change datasets such as locally
    calibrated products based on dense time series data and a global dataset on annual tree cover change. For the error estimation, we used
    validation tools for human interpretation based on Landsat Time Series data and high resolution optical imagery. Next, we calculated carbon
    emission estimates based on pantropical biomass maps and field inventory data. We differentiated emissions from before and after the start of
    the REDD+ initiatives and also considered control areas to estimate REDD+ impact.
    We found that forest change products based on locally calibrated algorithms had a higher accuracy than the global product assessed. Biomass
    datasets built on both remote sensing and local field inventory data led to better carbon emission estimates. REDD+ impact was limited but
    varied considerably between initiatives. Still, the choice of datasets and assessment methods had an influence on the measured local and
    regional REDD+ performance. This study contributes to carbon measurement, reporting and verification by providing insight into what extent both
    activity data and biomass data influence the uncertainty of carbon emission estimates.
    Connecting Earth observation to high-throughput biodiversity data
    Bush, Alex ; Sollmann, Rahel ; Wilting, Andreas ; Bohmann, Kristine ; Cole, Beth ; Balzter, Heiko ; Martius, Christopher ; Zlinszky, András ; Calvignac-Spencer, Sébastien ; Cobbold, Christina A. ; Dawson, Terence P. ; Emerson, Brent C. ; Ferrier, Simon ; Gilbert, M.T.P. ; Herold, Martin - \ 2017
    Nature Ecology & Evolution 1 (2017)7. - ISSN 2397-334X - 9 p.
    Understandably, given the fast pace of biodiversity loss, there is much interest in using Earth observation technology to track
    biodiversity, ecosystem functions and ecosystem services. However, because most biodiversity is invisible to Earth observation,
    indicators based on Earth observation could be misleading and reduce the effectiveness of nature conservation and even
    unintentionally decrease conservation effort. We describe an approach that combines automated recording devices, highthroughput
    DNA sequencing and modern ecological modelling to extract much more of the information available in Earth
    observation data. This approach is achievable now, offering efficient and near-real-time monitoring of management impacts
    on biodiversity and its functions and services.
    Application of terrestrial LiDAR and modelling of tree branching structure for plant-scaling models in tropical forest trees
    Lau Sarmiento, A.I. ; Bartholomeus, H.M. ; Herold, M. ; Martius, Christopher ; Malhi, Yadvinder ; Bentley, Lisa Patrick ; Shenkin, Alexander ; Raumonen, P. - \ 2017
    Terrestrial LiDAR and 3D Reconstruction Models for Estimation of Large Tree Biomass in the Tropics
    Lau Sarmiento, A.I. ; Gonzalez de Tanago Meñaca, J. ; Bartholomeus, H.M. ; Herold, M. ; Raumonen, P. ; Avitabile, V. ; Martius, Christopher ; Goodman, R.M. ; Manuri, Solichin - \ 2016
    - 1 p.
    Application of Terrestrial LiDAR and Modelling of Tree Branching Structure for Plant-scaling Models in Tropical Forest Trees
    Lau Sarmiento, A.I. ; Bartholomeus, H.M. ; Herold, M. ; Martius, Christopher ; Malhi, Yadvinder ; Bentley, Lisa Patrick ; Shenkin, Alexander ; Raumonen, P. - \ 2016
    Quantification of Tropical Forest Biomass with Terrestrial LiDAR and 3D Tree Quantitative Structure Modelling
    Gonzalez deTanago Meñaca, J. ; Lau Sarmiento, A.I. ; Bartholomeus, H.M. ; Herold, M. ; Raumonen, P. ; Avitabile, V. ; Martius, Christopher ; Joseph, Shijo - \ 2016
    Check title to add to marked list
    << previous | next >>

    Show 20 50 100 records per page

    Please log in to use this service. Login as Wageningen University & Research user or guest user in upper right hand corner of this page.