VASIP: Visualizing Measurement and Process Errors in VASI Equations based on Monserud's Site Index Model

Abstract

We present VASIP (Variable Base-Age–Site-Index Predictions), software for visualizing error propagation in base-age–invariant, self-referencing site index models, based on Cieszewski's equation (Cieszewski, C.J. 2001. Three methods of deriving advanced dynamic site equations demonstrated on inland Douglas-fir site curves. Can. J. For. Res. 31:165–173). VASIP implements the parameters of such published models. The underlying mathematical structure of the VASI model is derived from a fractional base equation representing an improved parameterization of the Monserud-type log-logistic equation. The software displays prediction curves with error-propagation regions that combine (i) the process error approximation derived from the underlying model parameter standard errors, and (ii) the propagation of user-specified input of the measurement error in the reference height at any arbitrary age. The tool enforces model-domain limits encoded in species-specific parameter files (which can be edited for sensitivity tests). We provide the software with examples of parameters for the major commercial tree species in Alberta and Saskatchewan. These parameters and associated statistics are intended for exploratory use. For use with other models based on the same VASI equation, the users can provide their own parameters and fit statistics. We illustrate how the error propagation in the self-referencing equations depends on the distance of the prediction age from the measured height age, the errors in height measurements, and on the process errors reflected in the fitting data growth trajectory inconsistencies, captured by the parameter standard errors. VASIP provides tabular and graphical outputs suitable for management reporting and research and is designed to facilitate technology transfer of base-age–invariant modeling in scientific publishing, operational implementation, and public relations. Given the elusive nature of the self-referencing models, based on implicit equations having no inherent errors at the reference point, this software might be transformative in the understanding of the exceptional prediction power of VASI models that for short-term predictions, by definition, cannot be outperformed by any traditional explicit models.