**Quoted from**: *Petropoulos, George, Toby N. Carlson, and Martin J. Wooster. "An overview of the use of the SimSphere Soil Vegetation Atmosphere Transfer (SVAT) Model for the study of land-atmosphere interactions." Sensors** 9, no. 6 (2009): 4286-4308.* https://doi.org/10.3390/s90604286

This section provides a descriptive account of the SVAT model architecture, based on the most recent implementation by [14], termed “SimSphere”. The aim here is to provide a non-mathematical description, free of technical jargon, which allows the reader to understand the basic principles of the model architecture. Further systematic description of this architecture and the model initialisation procedure can be found in [21] as well as in the online e-learning site where the model is currently hosted (http://www.e-education.psu.edu/simsphere/). An extensive mathematical account of the basis of the model has been provided previously by [1,22], whilst the model's bare soil component is described by [22], its vegetation component by [16,23], and its representation of plant hydraulics by [24-26]. The most recent version of the SVAT model is freely available from the Department of Meteorology of Pennsylvania State University, USA (https://courseware.e-education.psu.edu/simsphere/ or http://www.agry.purdue.edu/climate/dev//simsphere.asp).

The SimSphere SVAT model is essentially a one-dimensional boundary layer model with a plant component (Figure 1). In the horizontal domain, the scale of the model implicitly represents a horizontal area of the Earth's surface of undefined size that can be considered to be composed of a mixture of bare soil and vegetation, in proportions (Fr) and (1-Fr) varying from 0 to 1.0, where Fr being the fractional vegetation cover per unit area. Thus, it is conceivable that the horizontal scale of the model is defined by the degree to which the model's initial conditions (i.e. input parameters) are representative of the horizontal area to be simulated. Simsphere applies to a point or, at least, a limited region as long as the atmospheric, surface slope and incident radiation are uniformly distributed over the domain. SimSphere has been developed to simulate the various physical processes that take place as a function of time in a column that extends from the root zone below the soil surface up to a level higher than the surface vegetation canopy. The model performs simulations over a 24-hour cycle, starting from a set of initial conditions given in the early morning (at 05:30 hours local time) and simulates the continuous evolving interaction between soil, plant and atmospheric layers. SimSphere requires a number of parameters for its initialization (53 in total), divided into seven groups: time and location, vegetation, surface, hydrological, meteorological, soil and atmospheric. From a set of initial parameters representative of the site conditions on which the model is implemented, a number of prognostic variables (32 in total) are calculated from the SVAT model including the surface energy fluxes (H, LE and ground heat flux) at the soil surface, and in, around and above the vegetation canopy, the flux of carbon dioxide between the atmosphere and the plants, the grid-cell scale integrated surface temperature (Ts) of the vegetation and soil mixture.

In the left figure are shown the different layers of the SimSphere SVAT model in the vertical domain, whereas the figure on the right provides a schematic representation of the surface energy balance components computation in SimSphere. Rn is the net radiation, LE, H and G are the latent, sensible and ground heat fluxes respectively. Figure adapted from the SimSphere user's manual (available at https://courseware.e-education.psu.edu/simsphere/workbook).

The different facets of the SVAT model's overall structure, namely the physical, the vertical and the horizontal, are illustrated in Figure 2. The overall model structure is expressed in terms of resistances as an Ohm's Law analogue (Figure 2b), with parameters referred to in Table 1. The different components of each of the model facets are described briefly below. The depths of the different model layers are variable with time. The top of the mixing layer is allowed to rise during the day in response to H fluxes from the surface, and is identified by the presence of a temperature inversion that caps the air in convective contact with the surface layer. The surface layer, or turbulent air layer, extends from the top of the bare soil transition layer (or from the top of the vegetation layer) to a height of 50 m. The transition layer, a somewhat mathematical ‘fiction’, applies only to the vertical transfer of heat and moisture over the bare soil component, and governs the flux of heat and momentum in a hypothetical layer from the roughness height for heat to the roughness height for momentum. In the case of vegetation, the transition layer is replaced by a vegetation layer. The substrate layer refers to the depth of the soil over which heat and water are conducted. In the model, soil water content is specified by the user for two layers, a surface layer and a root zone layer, by assigning a fractional volume of field capacity.

The figure on the left (a) depicts the different facets of the SVAT model architecture (figure adopted from SimSphere user's manual (available at https://courseware.e-education.psu.edu/simsphere/workbook). The figure on the right (b) is a synthesis of the figures provided by [23,24] and provides a representation of the vertical structure of the plant-canopy model in the form of an electrical analogy illustrating how the exchange of the LE and H fluxes between plant, atmosphere and surface is represented in the model. Definition of the individual model parameters described on Figure 2b is provided in Table 1.

### Table 1.

Variables and coefficients from the SVAT model of [1] which are shown in figure 2b that is illustrating an Ohm's electrical analogy of the model architecture.

Variable |
Name of variable |
Units |

ea |
Air vapour pressure in the atmosphere |
mbar |

eaf |
Leaf-air boundary vapour pressure |
mbar |

eL(TL) |
The saturation vapour pressure at the temperature of the leaf |
mbar |

Fw |
Flow of water from soil to leaf |
Wm-2 |

Hf |
Foliage sensible heat flux |
Wm-2 |

Hg |
Soil sensible heat flux |
Wm-2 |

LeEf |
Foliage latent heat flux |
Wm-2 |

LeEg |
Soil latent heat flux |
Wm-2 |

ra |
Air resistance in surface layer |
sm-1 |

raf |
Resistance of heat and water vapour flux for interleaf air spaces |
sm-1 |

rag |
Air resistance between the ground and the interleaf air spaces |
sm-1 |

rb |
Air resistance in transition surface layer |
sm-1 |

rg |
Soil resistance from the substrate |
sm-1 |

rL |
Leaf resistance |
sm-1 |

θv |
Soil water content of the root zone |
cm3cm-3 |

θvo |
Surface soil water content |
cm3cm-3 |

ψg |
Soil water potential |
bar |

ψL |
Mesophyllic leaf water potential |
bar |

Ta |
Air temperature of the surface layer |
Kelvin |

Taf |
Temperature of the interfoliage air spaces |
Kelvin |

Tg |
Temperature of the ground surface |
Kelvin |

TL |
Temperature of the leaf surface |
Kelvin |

Zroot |
Root resistance |
bar(Wm-2)-1 |

Zstem |
Stem resistance |
bar(Wm-2)-1 |

Zg |
Soil root surface resistance |
bar(Wm-2)-1 |

σf |
Shielding factor |
unitless |

As depicted in Figure 2a, the model planetary boundary layer (PBL) (i.e. the layer of atmosphere whose behavior is directly influenced by its contact with the planetary surface) consists of a vegetated surface fraction (Fr) and a bare soil fraction. Each of these two regimes is treated separately, but the fluxes are blended at the base of the surface layer, nominally set at 50 m height. The PBL receives most of its heat and virtually all of its water vapour from the surface through the vertical transfer of heat, momentum, water vapour and carbon dioxide. This is accomplished primarily by turbulent eddies that are driven by surface heating, and by mechanical turbulence produced by wind between the surface and the atmosphere. The underlying constraint in the model is that the energy fluxes at the Earth's surface and within the plant canopy must balance appropriately. Initial forcing of the model begins with the calculation of solar radiation, determined from a one-dimensional solar radiation model. Details of the solar and long wave radiative transfer models are provided by [27]. Briefly, the total down-welling irradiance absorbed in the substrate layer is calculated from the solar geometry, atmospheric transmission coefficients and the surface albedo for the particular date, time and latitude/longitude location being simulated. Calculation of the radiation fluxes by default assumes cloud-free conditions, though an adjustment for a set percentage cloud cover can be made in the initialisation, if required.

As regards the vegetation parameterisation of the SimSphere SVAT model (Figure 2b), when the vegetation component is activated the model accounts for a layer of vegetation between the atmospheric surface layer and the ground. Vegetation density is expressed in terms of Leaf Area Index (LAI) (that being the one sided green leaf area per unit ground area) and Fr. When combining the separate bare soil and vegetation representations to account for conditions of partial vegetative cover, at the level of the canopy, the bare soil and vegetation regimes operate separately, but are allowed to interact through exchanges of momentum, heat and water vapour with the common surface and mixing layers above the canopy and the common substrate below (Figure 2b).

The shortwave incoming radiation and downward long-wave radiation are calculated in an identical way for the bare soil and vegetation regimes, and the radiation partitioning is computed as a function of the foliage density. In a similar way, the LE and H fluxes and the upward flux of long-wave radiation above the plant canopy and the substrate heat flux (G) are taken in the SVAT model as averages of the bare soil and vegetation components, weighted according to the vegetation fraction. Temperature and specific humidity at the top of the surface layer (Ta; qa), and the temperature and water content in the soil, are identical for both bare soil and vegetation fractions. Computation of canopy Ts is conducted from the weighted average of the bare soil and vegetation components of upward long-wave radiation fluxes.

A fundamental part of the vegetation parameterisation constitutes the modelling of plant stomatal resistance. This is because essentially this parameter in the model expresses the resistance of vegetation to transpire and also because it plays a key role in the regulation of energy partitioning between LE and H fluxes. The SVAT model used in the present study allows the choice between two stomatal resistance parameterisations either the [28] or the [25] formulation. The first parameterisation has the advantage that it is able to capture the gross aspects of stomatal behaviour as affected by soil water and sunlight, but its dominant disadvantage is that it ignores plant hydraulics, which accounts for significant shifts in transpiration rate over the diurnal period. In [25], stomatal resistance is expressed as a product of a dimensionless function that describes the effect of incident solar flux, leaf water potential and vapor pressure deficit on the stomatal resistance. Stomatal resistance in this type of parameterization is also a function of leaf-atmosphere vapor pressure difference. The latter is expressed as the difference between the mesophyl and epidermal leaf water potentials and the stomatal effect is modeled as being proportional to the vapor pressure difference. In this last type of stomatal resistance parameterisation, the product of these functions is scaled to the units of resistance, by multiplying by a factor termed the minimum stomatal resistance, which is set as a constant for each simulation. An important aspect of the [25] stomatal resistance formulation is the imposition of a threshold epidermal water potential, below which stomatal resistance increases rapidly with decreasing leaf water potential. When the threshold leaf water potential is reached, the transpiration tends to remain nearly constant until the leaf water potential again crosses the threshold toward higher values. [25] have termed this “flattening” of the transpiration curve the “transpiration plateau”.

In terms of scaling the simulated parameters from leaf to canopy, the calculations by the SVAT model are made initially for a single ‘big leaf’, in a similar way to other SVAT model approaches (e.g. the “DAISY” model of [29]). Simulated fluxes are expressed in units of Watts per m2 of leaf area, in order that they can be related to the surface energy balance. Conversion from flux per unit leaf area to flux per unit surface area is made by scaling the fluxes by the leaf area index divided by a “shelter factor” as defined in [30]. The shelter factor accounts for the fact that not all leaves transpire at the sunlit amount due to the fact that available solar radiation decreases with height beneath the top of the canopy. A detailed description of the scaling factor concept employed in the model can be found in [16,24].