Symbolic regression-based allometric model development of a mangrove forest LAI using structural variables and digital hemispherical photography
Introduction
The leaf area index (LAI) is a response parameter for photosynthesis as it directly relates to the light interception and gas exchange through the stomata. It is a dimensionless biophysical variable, calculated as the ratio of leaf area to per unit ground surface area (Watson, 1947). Monitoring of the LAI provides an understanding of dynamic changes in productivity, energy balance, canopy water interception, and gas exchange (Bréda, 2003; Jonckheere et al., 2004). So, accurate estimation of the LAI is crucial for physiological, ecological, and climatological studies (Li et al., 2017). In allometric-based practices, the relationship is established between leaf area and associated plant parameters, which carry the green leaf biomass. Indirect optical methods are feasible for all kinds of vegetation covers, but their major limitation is that they cannot distinguish between the non-photosynthetically and photosynthetically active elements, and thus considered as plant area index (PAI) instead of LAI (Garrigues et al., 2008; Yin et al., 2017). Allometric equation development is a semi-direct approach (Gower et al., 1999), though they are specific to site, stand age, density, and climatic conditions (Duursma et al., 2003). LAI measurements vary significantly across time and space. Ariza-Carricondo et al. (2019) found that the LAI varies from 2 to 6, and 6 to 8 for moderate and high dense forests respectively. Behera et al. (2015) observed ground LAI using LAI-2200, and found that LAI values are highly correlated with annual litterfall (R2 > 0.8).
Indirect methods of LAI estimation, such as Digital Hemispherical Photography (DHP) (Leblanc et al., 2005) and LAI-2200 plant canopy analyzer (PCA) (Chen et al., 1997) are based on Beer-Lambert's law of light attenuation. A few studies have concluded that DHP-based LAI estimates are better than other indirect LAI estimation methods due to its ability to extract clumping index (Garrigues et al., 2008; Weiss et al., 2004). Van Gardingen et al. (1999) demonstrated that a correct clumping index reduces LAI underestimation by at least 15%. The clumping of foliage effects on gap fraction and hemispherical photography is a method to measure the gap fraction at multiple zenith angles, which finally estimates the LAI using the inverted Beer-Lambert law (Nilson, 1971).where is the canopy gap fraction; is the fraction of foliage on the plane, which is normal to the solar direction. determines the leaves' spatial distribution pattern. Leaves are normally clumped, and is considered the clumping index. The indirect methods assume that (i) light does not transmit through the foliage as it is black, (ii) the leaf sizes are smaller compared to the canopy and the field of view (FOV) of the sensor, and (iii) leaves are randomly distributed. DHP based estimates could progressively replace LAI-2200 and AccuPAR because of its accuracy, sensitivity, extraction of clumping effect, and cost-effectiveness (Fang et al., 2014; Garrigues et al., 2008; Klingberg et al., 2017).
The establishment of appropriate relationships between leaf area and other predictor variables such as diameter at breast height (DBH), canopy height (Ht), and tree density (TD) are essential in plant physiology research (Vyas et al., 2010). Shinozaki, Shaw, and Lichtin (1964) developed a relationship based on the ‘Pipe Model Theory’ (PMT), which interpreted the relationship between the amount of tissue in stem and corresponding leaves on the tree. For small trees, all xylem tissues may work as a functional conducting tissue, and therefore, according to PMT, tree basal area and leaf area are strongly related (Lehnebach et al., 2018). Though the non-conducting xylem tissues (heartwood) do not predict leaf area better than sapwood, and it is difficult to separate between them (Jones et al., 2015; Lehnebach et al., 2018). Hence, measurement of DBH at 1.3 m height is more relevant over sapwood area for LAI estimate (Shinozaki, Yoda, et al., 1964; Sirri et al., 2019; Wu et al., 2019). Sirri et al. (2019) demonstrated that height could be a part of leaf area prediction (Gower et al., 1999; West et al., 1999; Wu et al., 2019). Furthermore, Smith (1993) predicted the leaf area for a particular plot using DBH and relative stand density and established a relationship with effective light extinction. Wu et al. (2019) developed allometric equations to predict the leaf area using structural variables such as DBH and tree height wherein the leaf area was measured using a leaf scanner, though it is labour intensive and destructive method.
Khan et al. (2005) established less sensitive allometric equations using DBH and height for a mangrove site at Manko wetland in Japan, while stem diameter at 1/10th height of the tree provided a healthy relationship. Jonckheere et al. (2005) investigated the relationship between optical LAI and allometric LAI estimates; these two methods didn't show a significant difference which can replace the direct destructive method extracted LAI such as leaf pluck and scanning or wet test method. Eckrich et al. (2013) developed an allometric equation for LAI estimation using basal area and optical instrument (DHP, AccuPAR) based LAI which satisfied the direct allometric based estimates. Vyas et al. (2010) took canopy spread to estimate the LAI for Teak and Bamboo species and revealed that the canopy spread is better and more sensitive than DBH. Chaturvedi et al. (2017) developed allometric equations using wood density, DBH, and height to suggest the use of non-linear regressions. Studies on the allometric model development for leaf area assessment using plant structural parameters revealed that LAI estimates are understudied for the mangrove forests, and more so using symbolic regression (Table 1).
The machine learning techniques increase model's prediction accuracy. The conventional machine learning approaches are popular but known as black boxes for their complicated internal mechanism. Symbolic Regression (SR) is based on a semi-supervised algorithm that searches for a set of mathematical expressions to determine the most direct relationship with minimal error (Koza, 1994) ready been applied in physics, neurology, and psychological studies, it is least explored in vegetation biophysical parameters analysis.
Though mangroves are carbon-rich ecosystems with high carbon sequestration potential, yet they are understudied due to the challenges in field observation. BhitarKanika Wildlife Sanctuary (BWS) is a highly productive, dense tropical mangrove forest along the eastern Indian coast and is a designated Ramsar site. Researchers have studied biomass estimates, species-level classification, forest cover change, and canopy height estimate in BWS (Reddy, Pattanaik, & Murthy, 2018; Upadhyay & Mishra, 2010; Kumar et al., 2013; Thakur et al., 2019; Ghosh et al., 2020), but none have estimated LAI before. There have been studies on LAI estimate using satellite and field measurements (Kale et al., 2005; Srinet et al., 2019), empirical models (Sinha et al., 2020; Joshi & Garkoti, 2020) from tropical forests, and using only field measurements from grasslands (Misra & Misra, 1981). To the best of our knowledge, mangroves across the world in general, and Indian mangroves in particular, are understudied with respect to field-based structural variables and DHP measurements for LAI estimates using symbolic regression to derive synergy.
This study aims to develop allometric equations for LAI estimate of mangrove forests using non-destructive, indirect, optical measurements using DHP images as a response variable, structural variables as predictor variables, and SR modelling. We selected three preliminary predictor variables of LAI such as DBH, TD, and Ht; those were measured in the field using established protocol and further regressed with DHP based LAI in singlet, duplet, and triplet combinations to establish the best allometric model. The model was developed and tested using 122 ESUs. We emphasised on development of a better equation using a genetic programming-based SR approach that has the capability to build the model by the mathematical combination of targeted predictors besides the coefficient optimization. To the best of our knowledge, it is the first allometric model developed to estimate LAI for a mangrove ecosystem in India.
Section snippets
Study area
Bhitarkanika Wildlife Sanctuary (BWS) lies in the estuarine region of Brahmani-Baitarani rivers along the Bay of Bengal on India's eastern coast, which is the second-largest mangrove ecosystem in India with a core area of 165 km2 (FSI, 2017). (Fig. 1, Fig. S1a). BWS receives an average rainfall of about 1642 mm, and mean relative humidity ranges from 70 to 85% throughout the year. In summer (April–May) the maximum temperature reaches up to 41 °C and in winter (January) minimum temperature dips
LAI, DBH, TD, and Ht estimates
The DHP-based LAI values range from 1.50 to 5.22 (mean = 3.414; standard deviation (SD) = 0.692; standard error (SE) = 0.062) and follows the normal distribution (Fig. 4a). The majority of average DBH (Fig. 4b) lies between 10 cm and 20 cm (mean = 15.257; SD = 5.164; SE = 0.467). The TD varied between 0.04 and 0.34 (mean = 0.136; SD = 0.054; SE = 0.004), with most of the ESUs demonstrated a range of 0.05–0.2 (Fig. 4c). The Ht distribution varied between 3.2 m and 15.8 m (mean = 9.787;
Discussion
This study collected ground data over 122 ESUs to establish an allometric model to estimate LAI for mangrove forests from commonly measured vegetation structural variables. It was found that there exists a strong relationship between leaf area and plant structural variables such as DBH, TD, and Ht as per the PMT. Here, owing to a similar growth stage, an average DBH value was considered per ESU. It may also be understood that sum of all DBH could be the representative value per ESUs as DHP
Conclusions
Mangroves play a crucial role in regulating many coastal ecosystem services; consequently, accurate information on key biophysical variables such as LAI is essential to understand the functioning of such services. It is also a well-known fact that field sample collection from the mangrove ecosystem is quite challenging due to inaccessibility; therefore, the dataset on mangrove biophysical and structural variables are minimal. At a maiden attempt this study showed that using the forest inventory
Authors' contributions
Conceptualization, S·P.; M.D.B. and J.D.; methodology, S·P.; formal analysis, S·P.; writing—original draft preparation, S·P.; writing—review and editing, M.D.B. and J.D.; visualization, S·P.; supervision, M.D.B and J.D. All authors have read and agreed to the published version of the manuscript.
Declaration of competing interest
The authors declare no conflict of interest.
Acknowledgements
The Authors acknowledge the authorities of IIT Kharagpur for faciliting the study. SP thanks the Ministry of Education, Government of India for grant of a PhD Research Fellowship. The support of Odisha State Forest department during Field inventory is thankfully acknowledged. We thank the two anonymous Reviewers, who have given very valuable feedback to its earlier version that has improved the manuscript to a great extent.
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