# Climate Change and Terrestrial Ecosystem Modeling by Gordon Bonan

Climate models have evolved into Earth system models with representation of the physics, chemistry, and biology of terrestrial ecosystems.
*Climate Change and Terrestrial Ecosystem Modeling* describes the modeling of terrestrial ecosystems in Earth system models.
This companion book to Gordon Bonan's
*Ecological Climatology*
builds on the concepts introduced there,
and provides the mathematical foundation upon which to develop and understand ecosystem models and their relevance for Earth system models.
*Ecological Climatology* describes why the biosphere matters for understanding climate and climate change.
*Climate Change and Terrestrial Ecosystem Modeling* decscibes how to model the biosphere.

Chapters describe the theory underlying process parameterizations and present the equations to numerically implement parameterizations in a model. Review questions, supplemental code, and modeling projects are provided, to aid with understanding how the equations are used. The book is an invaluable guide to climate change and terrestrial ecosystem modeling for graduate students and researchers in climate change, climatology, ecology, hydrology, biogeochemistry, meteorology, environmental science, biometeorology, and environmental biophysics.

The book is written as an introductory textbook for graduate students and advanced undergraduates. To aid professors in lectures and to help students understand concepts, the book contains 216 illustrations, 1200 equations, 212 review questions, 50 modeling projects, and 24 supplemental online MATLAB programs. The comprehensive bibliography references over 900 scientific studies.

Cambridge University Press | 2019 | 437 pages

### Reviews

Forthcoming

### Synopsis

**Chapter 1. Terrestrial Biosphere Models**

Earth system models simulate climate as the outcome of interrelated physical, chemical, and biological processes. With these models, it is recognized that the biosphere not only responds to climate change, but also influences the direction and magnitude of change. Earth system models contain component atmosphere, land, ocean, and sea ice models. The land component model simulates the world’s terrestrial ecosystems and their physical, chemical, and biological functioning at climatically relevant spatial and temporal scales. These models are part of a continuum of terrestrial ecosystem models from models with emphasis on biogeochemical pools and fluxes; dynamic vegetation models with focus on individual plants or size cohorts; canopy models with focus on coupling leaf physiological processes with canopy physics; and global models of the land surface for climate simulation. This latter class of models incorporates many features found in other classes of ecosystem models, but additionally includes physical meteorological processes necessary for climate simulation. This book describes these models and refers to them as terrestrial biosphere models.

**Chapter 2. Quantitative Description of Ecosystems**

Terrestrial biosphere models characterize ecosystems by features that control biogeochemical cycles and energy, mass, and momentum fluxes with the atmosphere. These include: leaf area index and its vertical profile in the canopy; the orientation of leaves, or leaf angle distribution; the vertical profile of leaf mass and leaf nitrogen in the canopy; the profile of roots in the soil; the size structure of plants; and the distribution of carbon within an ecosystem. This chapter defines these descriptors of ecosystems.

**Chapter 3. Fundamentals of Energy and Mass Transfer**

Energy and materials cycle throughout the Earth system. Heat in the atmosphere is exchanged by radiation, conduction, and convection. These fluxes determine the balance of energy gained, lost, or stored in a system and relate to temperature. A system that gains energy increases in temperature; a system that loses energy decreases in temperature. Convection similarly transfers materials in the movement of air. This transfer of materials is measured by the amount (mass or moles) and is commonly seen in gas diffusion (Fick’s law). This chapter introduces the fundamental scientific concepts of energy and mass transfer needed to understand biosphere-atmosphere coupling.

**Chapter 4. Mathematical Formulation of Biological Flux Rates**

Fick’s law describes many rate processes in environmental physics, including diffusive fluxes, conduction, and water flow. Many biological fluxes are biochemical rather than biophysical and require formulations other than Fick’s law. For example, the rate of photosynthesis increases with higher irradiance and higher CO_{2} concentration. The rate of carbon loss during respiration increases with higher temperature. Rates of plant productivity and soil organic matter decomposition vary with temperature, soil moisture, and other factors. Common formulations for these processes are: the Michaelis-Menten equation for a biochemical reaction; the Arrhenius equation to describe the temperature dependence of a biochemical reaction; minimum, multiplicative, and co-limiting rate multipliers; and first-order, linear differential equations to describe mass transfers within an ecosystem. In addition, mathematical principles of optimization provide a formal method to frame many ecological processes.

**Chapter 5. Soil Temperature**

The diurnal cycle of soil temperature and seasonal variation over the course of a year are important determinants of land surface climate. This chapter reviews the physics of soil heat transfer. Heat flows from high to low temperature through conduction. Thermal conductivity and heat capacity are key soil properties that determine heat transfer. These vary with the mineral composition of soil and also with soil moisture. In seasonally frozen soils, it is necessary to account for the different thermal properties of water and ice. Additionally, the change in phase of water consumes or releases heat during melting and freezing, respectively.

**Chapter 6. Turbulent Fluxes and Scalar Profiles in the Surface Layer**

Monin-Obukhov similarity theory provides mathematical expressions for the momentum, sensible heat, and evaporation fluxes between the land surface and the atmosphere, the corresponding vertical profiles of wind speed, temperature, and water vapor, and the aerodynamic conductances that regulate surface fluxes. Above rough plant canopies, however, these fluxes and profiles deviate from Monin-Obukhov similarity theory due to the presence of the roughness sublayer. This chapter develops the meteorological theory and mathematical expressions to model turbulent fluxes and scalar profiles in the surface layer of the atmosphere.

**Chapter 7. Surface Energy Fluxes**

Surface temperature is the temperature that balances net radiation, sensible heat flux, latent heat flux, soil heat flux, and storage of heat in biomass. This chapter develops the theory and mathematical expressions to model the surface energy balance and surface temperature. The surface energy balance is a non-linear equation that must be solved for surface temperature using numerical methods. A more complex solution couples the surface energy balance with a model of soil temperature and a bucket model of soil hydrology. The Penman-Monteith equation is a linearization of the surface energy balance.

**Chapter 8. Soil Moisture**

Water flows from high to low potential as described by Darcy’s law. The Richards equation combines Darcy’s law with principles of water conservation to calculate water movement in soil. Particular variants of the Richards equation are the mixed form, head-based, and moisture-based equations. Water movement is determined by hydraulic conductivity and matric potential, both of which vary with soil moisture and additionally depend on soil texture. This chapter reviews soil moisture and the Richards equation. Numerical solutions are given for the various forms of the equation.

**Chapter 9. Hydrologic Scaling and Spatial Heterogeneity**

The hydrologic cycle on land includes infiltration, runoff, and evapotranspiration. This chapter reviews the principles of infiltration and runoff and discusses parameterizations to scale runoff over large regions with heterogeneous soils. These parameterizations rely on statistical distributions to characterize soil moisture variability. A similar statistical approach accounts for non-linearity in soil moisture effects on evapotranspiration using either continuous or discrete statistical distributions. Snow cover is particularly patchy, and models divide land into snow-covered and snow-free areas when calculating surface fluxes. Many models additionally account for heterogeneity in vegetation and soils by dividing a model grid cell into several tiles.

**Chapter 10. Leaf Temperature and Energy Fluxes**

Extension of the bulk surface energy balance described in Chapter 7 to include vegetation involves formulation of leaf fluxes. Energy from the net radiation absorbed by a leaf is stored in biomass or is dissipated as sensible and latent heat, and the balance of these fluxes, as influenced by prevailing meteorological conditions, leaf biophysics, and leaf physiology, determines leaf temperature. This chapter develops the biophysical foundation and mathematical equations to describe leaf temperature and the leaf energy budget. A critical determinant of leaf fluxes and temperature is leaf boundary layer conductance, which depends on wind speed and leaf size.

**Chapter 11. Leaf Photosynthesis**

Photosynthetic CO_{2} assimilation provides the carbon input to ecosystems from the atmosphere and also regulates leaf temperature and transpiration through stomatal conductance. Current representations of these processes in terrestrial biosphere models link the dependencies of leaf biophysics with the biochemistry of photosynthesis. This chapter develops the physiological foundation and mathematical equations to describe photosynthesis for C_{3} and C_{4} plants. While the equations that describe C_{3} photosynthesis are fairly well understood, key parameters such as *V _{cmax}* and

*J*are less well known. Moreover, terrestrial biosphere models can differ greatly in how they implement the photosynthesis equations. C

_{max}_{4}photosynthesis is less well understood for global models.

**Chapter 12. Stomatal Conductance**

Of particular importance for leaf energy fluxes is that leaf temperature, transpiration, and photosynthesis are linked through stomatal conductance. Current representations of these processes in terrestrial biosphere models recognize that the biophysics of stomatal conductance is understood in relation to the biochemistry of photosynthesis. Stomata act to balance the need for photosynthetic CO_{2} uptake while limiting water loss during transpiration. Consequently, an accurate depiction of photosynthesis is required to determine the stomatal conductance needed for transpiration and leaf temperature. This chapter develops the physiological theory and mathematical equations to describe stomatal conductance, photosynthesis, transpiration, and their interdependencies. Four main types of models are: empirical multiplicative models; semi-empirical models that relate stomatal conductance and photosynthesis; water-use efficiency optimization models; and plant hydraulic models. This chapter reviews the first three types of models. Plant hydraulic models are discussed in Chapter 13.

**Chapter 13. Plant Hydraulics**

Additional understanding of stomatal behavior comes from transport of water through the soil-plant-atmosphere continuum based on the principle that plants reduce stomatal conductance as needed to regulate transpiration and prevent hydraulic failure. As xylem water potential decreases, the supply of water to foliage declines and leaves may become desiccated in the absence of stomatal control. Stomata close as needed to prevent desiccation within the constraints imposed by soil water availability and plant hydraulic architecture. This chapter develops the physiological theory and mathematical equations to model plant water relations.

**Chapter 14. Radiative Transfer**

Absorption and reflection of solar radiation by plant canopies are related to the amount of leaves, stems, and other phytoelements, their optical properties, and their orientation. This chapter develops the biophysical theory and mathematical equations to describe radiative transfer for plant canopies, incorporating these concepts as well as accounting for the spectral composition of light and distinguishing between direct beam and diffuse radiation. Key derivations are *K _{b}* and

*K*, which describe the extinction of direct beam and diffuse radiation, respectively, in relation to leaf angle, solar zenith angle, and leaf area index. Equations for radiative transfer describe horizontally homogeneous, plane-parallel canopies in which variation in radiation is in the vertical direction. The distinction between sunlit and shaded leaves is also important. Similar equations pertain to longwave fluxes.

_{d}**Chapter 15. Plant Canopies**

Terrestrial biosphere models scale physiological and biophysical processes such as photosynthesis, stomatal conductance, and energy fluxes from individual leaves to the entire plant canopy. Critical to this is an understanding of leaf gas exchange, plant hydraulics, and radiative transfer presented in Chapters 10-14, and a theory and numerical parameterization to scale over all leaves in the canopy. This chapter focuses on the latter requirement and considers how to scale leaf fluxes to the canopy. Three general approaches to do so treat the canopy as: analogous to a big leaf with a single flux exchange surface without vertical structure; a dual source with separate fluxes for vegetation and soil; and in a multilayer framework in which the canopy is vertically structured and fluxes are explicitly resolved at multiple levels in the canopy.

**Chapter 16. Scalar Canopy Profiles**

Vertical profiles of temperature, water vapor, CO_{2}, and other scalars within plant canopies reflect a balance between turbulent transport and the distribution of scalar sources and sinks. Scalar sources and sinks depend on leaf biophysical and physiological processes, as well as at the soil surface. Vertical transport depends on turbulence within the canopy. This chapter develops the theory and mathematical equations to calculate scalar profiles in plant canopies. A common approach calculates scalar concentrations from one-dimensional conservation equations with a first-order turbulence closure in an Eulerian framework. Analytical solutions are possible with some assumptions. A more general numerical method requires an iterative solution because of the coupling between fluxes and concentrations. An implicit solution is possible for temperature and water vapor using the leaf energy budget as an additional constraint. An alternative approach represents fluid transport with a Lagrangian framework, either directly through use of a dispersion matrix to characterize turbulent motion or through use of localized near-field theory.

**Chapter 17. Biogeochemical Models**

Carbon gain from gross primary production is the single largest term in the terrestrial carbon budget, but the carbon balance is controlled not just by photosynthesis. Allocation of carbon to the growth of leaves, wood, and roots, loss of carbon during autotrophic respiration, and carbon turnover (comprising litterfall, background mortality, and disturbances) are critical determinants of carbon storage. Litter decomposition and resulting soil organic matter formation provide a long-term carbon store. Associated with the flows of carbon through an ecosystem is the parallel flow of nitrogen and other nutrients. This chapter develops the ecological foundation and mathematics to describe ecosystem carbon dynamics using biogeochemical models. The CASA-CNP model is used to illustrate the basic details of biogeochemical models.

**Chapter 18. Soil Biogeochemistry**

Soils store vast quantities of carbon, more than in the atmosphere or in plant biomass. Decomposition loss of soil carbon is a large term in the global carbon budget and mineralizes nitrogen and other elements needed for plant growth. This chapter develops the biogeochemical foundation and mathematical theory to describe litter decomposition, soil organic matter formation, and nutrient mineralization. The DAYCENT model is used to illustrate the basic details of soil biogeochemical models. Advanced modeling concepts include vertically-resolved soil carbon, microbial models, and competition among multiple nutrient consumers.

**Chapter 19. Vegetation Demography**

Terrestrial ecosystems undergo temporal dynamics in plant populations, community composition, and ecosystem structure. These changes in ecosystems are driven by demographic processes of recruitment, establishment, growth, and mortality and require models distinctly different from biogeochemical models. This chapter provides an overview of this class of models with three specific examples. Individual-based forest gap models track the birth, growth, and death of individual trees in an area of land. Dynamic global vegetation models simulate changes in the area occupied by discrete patches of plant functional types. Ecosystem demography models define patches based on age since disturbance and simulate the dynamics of cohorts of similar plant functional types rather than tracking every individual. Common to each model is the representation of vegetation demography, with age- and size-dependent growth and mortality and in which growth is constrained by allometric relationships of stem diameter with height, sapwood area, leaf area, and biomass. Rather than biogeochemical cycles as in Chapter 17, vegetation demography provides the dynamical core for the next generation of terrestrial biosphere models.

**Chapter 20. Canopy Chemistry**

Terrestrial ecosystems exchange many chemical gases and particles with the atmosphere. These emissions alter atmospheric composition and affect climate through radiative forcing. Some flux exchanges (CH_{4}, N_{2}O) alter the concentration of long-lived greenhouse gases. Others alter short-lived gases that affect atmospheric chemistry and air quality. Chemistry-climate interactions from these short-lived climate forcers (NO_{x}, biogenic volatile organic compounds, ozone, secondary organic aerosols) are significant and comparable in magnitude to other climate forcings. Stable isotopes are useful to diagnose biogeochemical and hydrologic cycles. A research frontier is to link the biogeophysical and carbon cycle influences of terrestrial ecosystems with a full depiction of biogeochemical feedbacks mediated through atmospheric chemistry.

Gordon Bonan is a scientist in the Climate and Global Dynamics Laboratory (CGD) at the National Center for Atmospheric Research (NCAR). He is head of the Terrestrial Sciences Section.