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Dynamic Modelling of the Annual Cycle

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Boreal and Temperate Trees in a Changing Climate

Part of the book series: Biometeorology ((BIOMET))

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Abstract

A hypothetico-deductive framework for dynamic ecophysiological modelling of the annual cycle of boreal and temperate trees is described and discussed. In the framework used, the modelling is closely associated with experimental and observational empirical studies, so that inductive (‘empirical’) and deductive (‘theoretical’) phases alternate in the research. Computer simulations are deductive, and their results therefore contain nothing but implications of the assumptions of the model used in the simulations. Empirical data are used either for inductive formulation of the models or for testing the models after deducing their predictions by means of simulations. In dynamic modelling, the time courses of seasonal ecophysiological processes are simulated by first calculating the momentary rate of development on the basis of the input data of environmental factors, such as air temperature and night length. After that, the time course of the state of development is obtained by mathematical integration of the rate of development with respect to time. A unifying notation is described for the rate and state variables of different aspects of the annual cycle. Diverse model categories, based on major differences in the ecophysiological phenomena addressed, are described and compared. Finally, the realism, accuracy, and generality of the models are discussed. A novel concept of coverage is introduced for use in the assessment of the realism of the models. Biological levels of organisation, vertical reduction, and emergent properties are briefly discussed in relation to the realism of the models. The framework described and discussed in this chapter forms the basis for the subsequent chapters, in which different aspects of the annual cycle in boreal and temperate trees are addressed.

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Notes

  1. 1.

    The concept “development” is used here in a broad sense, including all biophysical, physiological, and morphological changes involved in the annual cycle of the boreal and temperate trees (Hänninen and Kramer 2007). In textbooks of plant physiology and plant developmental biology, the concept “development” is classically used in a more restricted sense, referring only to the irreversible anatomical and organological changes (ontogenesis) taking place in plants.

  2. 2.

    Levins originally used the concept of “precision” instead of “accuracy”, and that nomenclature has been used later by several other authors (e.g., Sharpe 1990; Hänninen 1995b). However, in the present volume the concept of “precision” is used only when referring to the exactness of the data with the concept of “precision of measurement”, so that in the comparisons of model output with empirical data, the concept of “accuracy” is used.

  3. 3.

    Following its standard usage, the concept of whole-tree ecophysiology is used in the present volume when different tree organs, such as buds or leaves, are discussed.

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Authors and Affiliations

  1. Department of Biosciences, University of Helsinki, Helsinki, Finland

    Heikki Hänninen

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  1. Heikki Hänninen
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List of Symbols

List of Symbols

t:

time

2.1.1 Time-Dependent Environmental Variables

E(t):

environmental factor(s)

T(t):

air temperature (°C)

Tmean(t):

daily mean air temperature (°C)

2.1.2 Time-Dependent Rate and State Variables

R(t):

rate of development

S(t):

state of development

Ri(t):

rate of development of ith attribute of the annual cycle

Si(t):

state of development of ith attribute of the annual cycle

Rdd(t):

accumulation rate of day degree units (dd day−1)

Sdd(t):

accumulated temperature sum (dd)

2.1.3 Model Parameters

Tthr :

air temperature threshold for accumulation of day degree units

Hcrit :

the high temperature requirement of growth onset (dd)

2.1.4 Other Symbols

dd:

day degree unit

f:

environmental response of the rate of development (function)

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Hänninen, H. (2016). Dynamic Modelling of the Annual Cycle. In: Boreal and Temperate Trees in a Changing Climate. Biometeorology. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-7549-6_2

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