Leaf

The leaf module contains all functions related to estimating vegetation cover. These functions only work on an instantaneous basis.

vegetation_cover(ndvi, nd_min=0.125, nd_max=0.8, vc_pow=0.7)

Computes vegetation cover based on NDVI.

\[\begin{split}c_{veg} = \begin{cases} \begin{array}{cc} 0 & I_{NDVI}\leq I_{NDVI,min}\\ 1-\left(\frac{I_{NDVI,max}-I_{NDVI}}{I_{NDVI,max}-I_{NDVI,min}}\right)^ {a} & I_{NDVI,min}<I_{NDVI}<I_{NDVI,max}\\ 1 & I_{NDVI}\geq I_{NDVI,max} \end{array}\end{cases}\end{split}\]

Parameters

• ndvi (float) – Normalized Difference Vegetation Index, \(I_{NDVI}\) [-]

• nd_min (float) – NDVI value where vegetation cover is 0, \(I_{NDVI,min}\) [-]

• nd_max (float) – NDVI value where vegetation cover is 1, \(I_{NDVI,max}\) [-]

• vc_pow (float) – Exponential power used in vegetation cover function, \(a\) [-]

Returns

vc – vegetation cover, \(c_{veg}\) [-]

Return type

float

Examples

>>> from ETLook import leaf
>>> leaf.vegetation_cover(0.1, nd_min=0.2)
0
>>> leaf.vegetation_cover(0.5)
0.4331446663885373
>>> leaf.vegetation_cover(0.85)
1

leaf_area_index(vc, vc_min=0.0, vc_max=0.9677324224821418, lai_pow=-0.45)

Computes leaf area index based on vegetation cover. It is based on the Kustas formulation of LAI vs NDVI.

\[\begin{split}I_{lai} = \begin{cases} \begin{array}{cc} 0 & c_{veg}\leq c_{veg,min}\\ \frac{\ln\left(-\left(c_{veg}-1\right)\right)}{b} & c_{veg,min}<c_{veg}\leq c_{veg,max}\\ \frac{\ln\left(-\left(c_{veg,max}-1\right)\right)}{b} & c_{veg}>c_{veg,max} \end{array}\end{cases}\end{split}\]

Parameters

• vc (float) – vegetation cover, \(c_{veg}\) [-]

• vc_min (float) – vegetation cover where LAI is 0, \(c_{veg,min}\) [-]

• vc_max (float) – vegetation cover at maximum LAI, \(c_{veg,max}\) [-]

• lai_pow (float) – exponential factor used in LAI function, \(b\) [-]

Returns

lai – leaf area index, \(I_{lai}\) [-]

Return type

float

Examples

>>> from ETLook import leaf
>>> leaf.leaf_area_index(0.0)
0
>>> leaf.leaf_area_index(0.5)
1.5403270679109895
>>> leaf.leaf_area_index(1.0)
7.6304274331264414

effective_leaf_area_index(lai)

Computes effective leaf area index, this describes the leaf area which actively participates in transpiration. It is based on the actual leaf area index and an extinction function. So with a higher leaf area index the effective leaf area index is a smaller percentage of the total leaf area index.

\[I_{lai,eff}=\frac{I_{lai}}{0.3 \cdot I_{lai}+1.2}\]

Parameters

lai (float) – Leaf area index, \(I_{lai}\) [-]

Returns

lai_eff – effective leaf area index, \(I_{lai,eff}\) [-]

Return type

float

Examples

>>> from ETLook import leaf
>>> leaf.effective_leaf_area_index(3.0)
1.4285714285714288
>>> leaf.effective_leaf_area_index(5.0)
1.8518518518518516