Abstract

This article reviews the scientific debate of big-leaf vs multi-layer canopy modeling for land surface models. Comparisons with flux tower measurements show supremacy of good multi-layer models (5-10 layer suffice).

  • big leaf: one-layer canopy

Important vertically resolved quantities:

  • canopy air temperature
  • specific humidity
  • wind speed
  • water leaf potential (for dry soils)

1. Introduction

George Box’s often quoted statement that “all models are wrong but some are useful” was part of a discussion regarding the process of building scientific models (Box, 1979). He argued for parsimonious models because “simplicity illuminates, and complication obscures” and because “indiscriminate model elaboration is in any case not a practical option because this road is endless”.

  • dual source canopy: one leaf layer, separate fluxes for leaves and soil
  • wind speed decreases with canopy depth
  • relatively dense forests: daytime air temperature varies, mod-canopy maximum a few degrees warmer than in understort
  • vertical profiles in leaf water potential can create water-stressed leaves in upper canopy with reduced stomatal conductance and photosynthesis
  • heterogeneity in leaf temperature
  • CLM5: one canopy layer but > 20 soil layers (despite poorly known necessary vertical thermal and hydraulic parameters)
  • Raupach (1991):
    • canopy-atmosphere models (CAM, multi-layer): locally useful
    • simplified canopy-atmosphere models (SCAM): globally useful
  • profound differences in microclimate between overstory and understory: important for ecological impact studies
  • today:
    • better numerical solutions, CAM might also globally be useful
    • better surface flux modeling

2. Background

  • multi-layer models compute generally: radiative transfer, stomatal conductance, leaf energy fluxes,turbulent diffusion; coupled to temperature and water vapor concentration, CO$_2$ concentration at each layer
  • big leaf: Penman-Monteith equation for evaporation, atmosphere governed by
    • $R^{‘}_n$: net energy availabe to canopy after accounting for soil and biomass heat storage
    • $\delta^{‘}$: saturation deficient at some height above canopy
    • $g_a$: buld aerodynamic conductance for scalar transport (assumed equal for heat and water vapor, only for convenience)
    • $g_c$: bulk stomatal conductance (canopy conductance)
  • relationships between multi-layer and single-layer parameters not uniquely determined
  • physical meaning of Penman-Monteith equation gets lost if accumulated over several layers, in particular $g_c$ is impossible to be precisely specified
  • leaf nitrogen gradient in canopy less steep than light gradient
  • both types of models can be separated into sunlit and shaded leaves
  • also leaf inclination angle and leave age cohorts added later to multi-layer models
  • green leaf area index and brown stem area index:
    • leaf surface: transpiration and photosynthesis
    • leave and stem surface (plant area index): radiative transfer, canopy evaporation, sensible heat flux, momentum absorption
  • plant canopy models must parameterize turbulent fluxes between vegetation and atmosphere
    • MOST: Monin-Obukhov Similarity Theory
    • RSL: roughness sublayer, region within and just above canopies where observed flux-gradient relationships depart from MOST
  • Lagrangian approach to turbulent eddies
  • localized near-field theory

CLM5 also requires a complex iterative calculation of surface fluxes and canopy temperature (Lawrence et al., 2019). Up to 40 iterations are allowed in CLM5, but convergence is not guaranteed, in which case arbitrary adjustments to fluxes are implemented to achieve energy conservation.

  • vertical distribution of leaf area most important
  • in data-rich world of today it can be measured (opposing to soils)
  • also leaf angular inclination, vertical nitrogen profile

3. The multilayer canopy model

Model revised from Bonan et al (2018) to allow for a generalized continuum of 1 to N layers and is identified as CLM-ml v1.

  • mesic habitat: moderate or well-balanced supply for moisture
  • xeric habitat: dry

4. Comparison of one-layer and multilayer canopies

In general, the multilayer model’s fluxes come much closer to the observations.

Reasons

  • sunlit leaves dominate upper canopy, most shaded leaves in lower canopy
  • $V_{\text{cmax}}$ declines with canopy depth down to 1/2
  • daytime air temperature peaks in mid-canopy and decreases by 1 degree or more in lower canopy
  • nighttime minimum temperature in upper canopy
  • daytime specific humidity less in upper canopy
  • wind speed decreases with canopy depth
  • much of solar radiation absorbed in upper canopy
  • leaf transpiration peaks in upper canopy: lower mid-day leaf water potential in upper canopy
  • leaves in upper canopy 2 degrees warmer than in lower canopy

Important variabales

  • within-canopy air temperature, specific humidity, wind speed profiles
  • sensible heat flux most sensitive to temperatire profile, sunlit and shaded proportion sensible to wind speed (not the total)
  • latent heatflux sensible to temperature and humidity
  • GPP differences between multi-layer and big leaf driven by their light profiles, low response to well-mixed assumption, temperature, humidity and wind profiles

Number of layers

  • better results with increasing number of layers
  • little immprovements beyond 10 layers
    • valid for simply-structured canopies (not tropical ones)
    • might be model dependent
  • proportion of absorbed solar radiation between sunlit and shaded leaves independent of number of layers

5. Discussion

The results presented in this study show that resolving vertical profiles of air temperature, specific humidity, and wind speed in forest canopies reduces surface flux biases compared with a single canopy layer.

6. Conclusions

The modeling analyses presented herein show that the dismissal of multilayer canopy models as too complex is no longer valid. Multilayer canopy models are not a complication that obscures; they are instead a simplification that illuminates the processes controlling surface flux calculations compared with land surface models such as CLM5. Multilayer canopy models are a necessary model elaboration, not the indiscriminate model elaboration that Box (1979) believed was endless and argued against.

Indeed, a comparison of technical descriptions reveals the multilayer canopy (Bonan et al., 2018) to be the simpler, not more complex, implementation of surface fluxes compared to CLM5 (Lawrence et al., 2019).

CLM5 has an ecosystem demography component (FATES; Fisher et al., 2015; Koven et al., 2020), but in coupling FATES to CLM5 the vertically-structured canopy, utilized for photosynthesis and light competition in FATES, is reduced to a canopy leaf area index and a canopy conductance for CLM5’s big-leaf surface flux formulation (Lawrence et al., 2019). A more consistent coupling between the models would utilize the vertical structure of FATES in a multilayer model of surface fluxes.

Personal conclusion

In general, multilayer canopy models are much better than big leaf models. However, for our purpose of computing GPP, we can omitt many of the overwhelmingly complicated processes and concentrate on the light profile.