| Summary: | The Clumping Index (Ω) was introduced to quantify the spatial distribution pattern of vegetation elements. It is crucial to improve the estimation accuracy of vital vegetation parameters, such as Leaf Area Index (LAI) and Gross Primary Production (GPP). Meanwhile, the parameterization of Ω is challenging partly due to the varying observations of canopy gaps from different view angles. Many previous studies have shown the increase of Ω with view zenith angle through samples of gap size distribution from in situ measurements. In contrast, remote sensing retrieval algorithms only assign a constant value for each biome type to roughly correct the clumping effect as a compromise between the accuracy and efficiency. In this paper, analytical models are proposed that estimate the directional clumping index (Ω(θ)) of crop and forest at canopy level. The angular variation trend and magnitude of crop Ω(θ) was analyzed within row structure where vegetation elements are randomly spaced along rows. The forest model predicts Ω(θ) with tree density, distribution pattern, crown shape, trunk size, and leaf area and angle distribution function. The models take into account the main directional characteristics of clumping index using easy-to-measure parameters. Test cases showed that Ω(θ) magnitude variation for black spruce forest was 102.3% of the hemispherical average clumping index ( Ω ˜ ), whereas the Larch forest had 48.7% variation, and row crop variation reached 32.4%. This study provided tools to assess Ω(θ) of discontinuous canopies.
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