428
W. Beyschlag et al.
questions of a comparative nature. For example, for the same canopy
structure, how are photosynthesis and water loss influenced by changes in
light conditions outside the canopy, air temperature, ambient-C0 2 partial
pressures, or humidity? Or, how do changes in structural attributes (e.g.,
leaf orientation, foliage density distribution) influence canopy gas exchange
or competition for light under given weather conditions? Such comparisons
usually tend to reduce the effect of parameter errors since these inaccuracies
are common to both canopy data sets being compared.
The confidence in these model outputs can be increased by performing
sensitivity analyses of model outputs as a function of input parameter estimates. Although the possibilities for such sensitivity analyses over various
ranges and interactions of parameter values, are seemingly infinite, procedures are available to limit such endeavors to appropriate bounds (e.g.,
see Forrester 1961; Innis 1978; Thornley and Johnson 1990). In addition,
sensitivity analyses can help identify where parameters need to be more
accurately defined.
Independent empirical measurements also provide a check of model performance. Whole-plant gas exchange measurements for individual plants
provide one assessment in the case of the three-dimensionaf models (Ryel et
al. 1993). For continuous canopies, eddy correlation techniques also provide
a powerful approach to measuring whole-canopy fluxes if certain conditions
are met (Verma 1990). Even though these flux measurements do not provide
information on the contribution of different species or plant parts to canopy
gas exchange, they do provide a means of assessing aspects of model
performance.
Acknowledgments. We gratefully acknowledge funding of this work by the Deutsche
Forschungsgemeinschaft (SFB 251, University of Wiirzburg) and the US National Science
Foundation (BSR 87-05492).
References
Barnes PW, Jordan PW, Gold WG, Flint SD, Caldwell MM (1988) Competition, morphology and canopy structure in wheat (Triticum aestivum L.) and wild oat (Avena
fatua L.) exposed to enhanced ultraviolet-B radiation. Funct Ecol2: 319-330
Barnes PW, Beyschlag W, Ryel RJ, Flint SD, Caldwell MM (1990) Plant competition for
light analyzed with a multi species canopy model. III. Influence of canopy structure in
mixtures and monocultures of wheat and wild oat. Oecologia 82: 560-566
Beyschlag W, Barnes PW, Ryel RJ, Caldwell MM, Flint SD (1990) Plant competition for
light analyzed with a multispecies canopy model. II. Influence of photosynthetic characteristics on mixtures of wheat and wild oat. Oecologia 82: 374-380
Beyschlag W, Ryel RJ, Ullmann I (1992) Experimental and modelling studies of competition for light in roadside grasses. Bot Acta 105: 285-291
Brutsaert W (1975) On a derivable formula for long-wave adiation from clear skies.
Water Resour Res 11: 742-744
Burt JE, Luther FM (1979) Effect of receiver orientation on erythema dose. Photochem
Photobiol 29: 85-91
W. Beyschlag et al.
questions of a comparative nature. For example, for the same canopy
structure, how are photosynthesis and water loss influenced by changes in
light conditions outside the canopy, air temperature, ambient-C0 2 partial
pressures, or humidity? Or, how do changes in structural attributes (e.g.,
leaf orientation, foliage density distribution) influence canopy gas exchange
or competition for light under given weather conditions? Such comparisons
usually tend to reduce the effect of parameter errors since these inaccuracies
are common to both canopy data sets being compared.
The confidence in these model outputs can be increased by performing
sensitivity analyses of model outputs as a function of input parameter estimates. Although the possibilities for such sensitivity analyses over various
ranges and interactions of parameter values, are seemingly infinite, procedures are available to limit such endeavors to appropriate bounds (e.g.,
see Forrester 1961; Innis 1978; Thornley and Johnson 1990). In addition,
sensitivity analyses can help identify where parameters need to be more
accurately defined.
Independent empirical measurements also provide a check of model performance. Whole-plant gas exchange measurements for individual plants
provide one assessment in the case of the three-dimensionaf models (Ryel et
al. 1993). For continuous canopies, eddy correlation techniques also provide
a powerful approach to measuring whole-canopy fluxes if certain conditions
are met (Verma 1990). Even though these flux measurements do not provide
information on the contribution of different species or plant parts to canopy
gas exchange, they do provide a means of assessing aspects of model
performance.
Acknowledgments. We gratefully acknowledge funding of this work by the Deutsche
Forschungsgemeinschaft (SFB 251, University of Wiirzburg) and the US National Science
Foundation (BSR 87-05492).
References
Barnes PW, Jordan PW, Gold WG, Flint SD, Caldwell MM (1988) Competition, morphology and canopy structure in wheat (Triticum aestivum L.) and wild oat (Avena
fatua L.) exposed to enhanced ultraviolet-B radiation. Funct Ecol2: 319-330
Barnes PW, Beyschlag W, Ryel RJ, Flint SD, Caldwell MM (1990) Plant competition for
light analyzed with a multi species canopy model. III. Influence of canopy structure in
mixtures and monocultures of wheat and wild oat. Oecologia 82: 560-566
Beyschlag W, Barnes PW, Ryel RJ, Caldwell MM, Flint SD (1990) Plant competition for
light analyzed with a multispecies canopy model. II. Influence of photosynthetic characteristics on mixtures of wheat and wild oat. Oecologia 82: 374-380
Beyschlag W, Ryel RJ, Ullmann I (1992) Experimental and modelling studies of competition for light in roadside grasses. Bot Acta 105: 285-291
Brutsaert W (1975) On a derivable formula for long-wave adiation from clear skies.
Water Resour Res 11: 742-744
Burt JE, Luther FM (1979) Effect of receiver orientation on erythema dose. Photochem
Photobiol 29: 85-91