VASIP 2: Software Update for Visualizing Propagation of Measurement and Process Errors in VASI Based Site Models
Keywords:
Variable-age site index, VASI, Base-age invariance, BAI, Self-referencing models, Polymorphic height growth, Measurement error, Process error, Error propagation, Parameter sensitivityAbstract
This note follows Cieszewski and Wawrykowicz (2025) on VASIP 1.0 and presents VASIP 2, version 2.0.20, for variable-age site index (VASI) curves. The height model is unchanged, and the program retains sixteen historical Alberta and Saskatchewan parameter sets. New functions include: (1) animated graphs with live reference movement; (2) nested conditional bounds at one, two, and three standard errors (SEs); and (3) paired graphs of absolute and relative deviations and bound-sum bias, which measures bound asymmetry about the central curve. Site-index and height-crossing-age readouts update live with the reference point. Adjustable graphs, file imports and exports, named projects, and reporting tools further extend the workflow. Measurement-height variation and global-coefficient variation can be viewed separately or jointly at the selected sensitivity settings. In the program, Process is represented by global-coefficient variation, which changes growth efficiency (the relative height-growth rate). This propagates the coefficient uncertainty represented by the reported SEs, including any effects of lack of fit reflected in them, without simulating stochastic residual disturbances. The program includes a complete user guide; we trace its parameter sources to the 1991 Alberta note and the 1993–1995 Saskatchewan records. The bounds are deterministic sensitivity envelopes informed by marginal coefficient SEs, with no verified probability coverage.
References
Bailey, R. L., and J. L. Clutter, 1974. Base-age invariant polymorphic site curves. Forest Science 20(2):155–159. https://doi.org/10.1093/forestscience/20.2.155.
Bollandsås, O. M., T. H. Eid, and E. A. A. Hansen, 2023. Systematic and random errors of height measurements of individual trees using Vertex hypsometer. MINA fagrapport 87, Norwegian University of Life Sciences (NMBU), Faculty of Environmental Sciences and Natural Resource Management, Ås, Norway. https://static02.nmbu.no/mina/publikasjoner/mina_fagrapport/pdf/mif87.pdf.
Cieszewski, C. J., 1988. New Polymorphic Height Growth and Site Index Model for Lodgepole Pine in Alberta. M.F. Major paper. University of British Columbia, Vancouver, B.C.
Cieszewski, C. J., 1995. Base-age invariant polymorphic site index models for eleven timber species in Saskatchewan. Unpublished report manuscript to the Canada–Saskatchewan Partnership Agreement in Forestry. Northern Forestry Centre, Canadian Forest Service, Edmonton, AB.
Cieszewski, C. J., 2001. Three methods of deriving advanced dynamic site equations demonstrated on inland Douglas-fir site curves. Canadian Journal of Forest Research 31(1):165–173. https://doi.org/10.1139/x00-132.
Cieszewski, C. J., 2003. Developing a well-behaved dynamic site equation using a modified Hossfeld IV function Y3 = (axm)/(c + xm-1), a simplified mixed-model and scant subalpine fir data. Forest Science 49(4):539–554. https://doi.org/10.1093/forestscience/49.4.539.
Cieszewski, C. J., and R. L. Bailey, 2000. Generalized algebraic difference approach: Theory based derivation of dynamic site equations with polymorphism and variable asymptotes. Forest Science 46(1):116–126. https://doi.org/10.1093/forestscience/46.1.116.
Cieszewski, C. J., and I. E. Bella, 1989. Polymorphic height and site index curves for lodgepole pine in Alberta. Canadian Journal of Forest Research 19(9):1151–1160. https://doi.org/10.1139/x89-174.
Cieszewski, C. J., and I. E. Bella, 1991. Polymorphic height and site index curves for the major tree species in Alberta. Forest Management Note 51, Forestry Canada, Northwest Region, Northern Forestry Centre, Edmonton, AB. https://publications.gc.ca/site/eng/9.858350/publication.html.
Cieszewski, C. J., I. E. Bella, and A. A. Wawrykowicz, 1993. Site-index height growth curves for the commercial timber species in Saskatchewan. Unpublished draft note, Northern Forestry Centre, Forestry Canada, Edmonton, AB.
Cieszewski, C. J., and A. A. Wawrykowicz, 2025. VASIP: Visualizing measurement and process errors in VASI equations based on Monserud's site index model. Mathematical and Computational Forestry & Natural-Resource Sciences 17(2):41–57. https://mcfns.com/index.php/Journal/article/view/17.4.
Cieszewski, C. J., M. Zasada, and M. Strub, 2006. Analysis of different base models and methods of site model derivation for Scots pine. Forest Science 52(2):187–197. https://doi.org/10.1093/forestscience/52.2.187.
Hall, B. H., R. Schnake, and C. Cummins, 1992. TSP Version 4.2 Reference Manual. TSP International, Stanford, CA.
Jurjević, L., X. Liang, M. Gašparović, and I. Balenović, 2020. Is field-measured tree height as reliable as believed – Part II, A comparison study of tree height estimates from conventional field measurement and low-cost close-range remote sensing in a deciduous forest. ISPRS Journal of Photogrammetry and Remote Sensing 169:227–241. https://doi.org/10.1016/j.isprsjprs.2020.09.014.
Kangas, A. S., 1999. Methods for assessing uncertainty of growth and yield predictions. Canadian Journal of Forest Research 29(9):1357–1364. https://doi.org/10.1139/x99-100.
Monserud, R. A., 1984. Height growth and site index curves for inland Douglas-fir based on stem analysis data and forest habitat type. Forest Science 30(4):943–965. https://doi.org/10.1093/forestscience/30.4.943.
Wang, Y., M. Lehtomäki, X. Liang, J. Pyörälä, A. Kukko, A. Jaakkola, J. Liu, Z. Feng, R. Chen, and J. Hyyppä, 2019. Is field-measured tree height as reliable as believed – A comparison study of tree height estimates from field measurement, airborne laser scanning and terrestrial laser scanning in a boreal forest. ISPRS Journal of Photogrammetry and Remote Sensing 147:132–145. https://doi.org/10.1016/j.isprsjprs.2018.11.008.
White, K. J., 1978. A general computer program for econometric methods—SHAZAM. Econometrica 46(1):239–240.
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