Predictive models for stemflow and throughfall estimation in four fruit tree species under hot and sub-humid climatic region

Inclusion of stemflow and throughfall processes in rainfall-runoff modelling requires reliable models for their estimation. In the present paper, stemflow and throughfall generation processes were investigated in relation to rainfall, and morphological properties of four major fruit species grown in hot and sub-humid climatic region. Two types of models, rainfall-based and morphology-based, were developed and validated using observed data. Morphology-based models included relative roughness of branch (RR), leaf area index (LAI), canopy length (CL), tree height (TH) and diameter at breast height (DBH) as input variables. Rainfall-based stemflow prediction models, namely, Weibull, Logistic, Allometric and Exponential (R1⁄4 0.74 to 0.82) and throughfall prediction models, namely, Weibull, Allometric, Linear and Linear (R1⁄4 0.94 to 0.99) provided the best goodness-of-fit statistics for mango, litchi, guava and jackfruit, respectively. The parameters RR and LAI affected stemflow irrespective of rainfall depth. However, different sets of variables, namely, CL-LAI, CL-LAI-TH, CL-LAI-TH and DBH-CL-LAI affected throughfall in rainfall ranges <5, 5–10, 10–20 and >20 mm, respectively. The higher range of interception loss (6.5% for guava to 21.3% for jackfruit) indicated that interception loss from fruit trees needs to be considered in the water balance modelling of watersheds having larger areas under orchards. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/). doi: 10.2166/nh.2019.052 s://iwaponline.com/hr/article-pdf/51/1/47/649590/nh0510047.pdf S. S. Mali (corresponding author) P. K. Sarkar S. K. Naik A. K. Singh ICAR Research Complex for Eastern Region, Research Centre, Plandu, Ranchi 834010, Jharkhand, India E-mail: santosh.icar@gmail.com B. P. Bhatt ICAR Research Complex for Eastern Region, Patna 814014, Bihar, India


INTRODUCTION
Tree canopies modify rainfall trajectory by partitioning it into stemflow and throughfall, affecting the vertical and horizontal spatial distribution of rainwater (Zheng et al. ). The proportion of rain that falls from foliage as 'leafdrip' or passes directly through small gaps in the canopy is termed 'throughfall'. Stemflow is the portion of rainfall which is drained from the branches and leaves of a tree and runs down towards the bole or stem of the tree (Ahmed et al. ). Rainfall is intercepted and retained temporarily on leaf surfaces, branches and stems. Some of this intercepted rainfall subsequently evaporates and is lost to the atmosphere. This evaporated portion of rainfall is termed 'interception-loss' (IL). These interception losses are an important component of the hydrological budget.
The relationship between rainfall (R), stemflow (SF), throughfall (TF) and interception loss is represented as (Krusche et al. ): The generation of stemflow has been studied in recent decades for diverse forest types in various climatic regions Studying throughfall and stemflow dynamics in diverse climatic conditions is a measurement challenge and many times measurements are not possible due to adverse biophysical conditions. Also, the stemflow and throughfall fluxes are typical responses of the complex interaction between climate, rainfall and plant morphology. In such situations, physically based analytical or semi-analytical models can be developed to predict these parameters (Zeng et al. ).
Keeping in view that quantifying and analysing the species-wise variation of stemflow and throughfall production from tree crops could help in accurate estimation of hydrological water budget components, this study aims to characterize the canopy-specific morphological parameters of fruit trees and evaluate their influence on throughfall and stemflow generation at variable rainfall depths. The main objective of the study was to develop prediction models using two distinct modelling approaches, namely, rainfall-based models and tree morphology-based models, for estimation of stemflow and throughfall from fruit tree species. The modelling exercise provides insight into the stemflow and throughfall generation processes, and the most influential factors affecting the stemflow and throughfall from these tree species.

Study area
The study was conducted in Ranchi district, located in the central part of the East Indian plateau (Figure 1)   between minimum and maximum thickness. Higher roughness ratio indicated smoother branch surface.

Rainfall
The study was conducted during the monsoon season (June to September) of 2016, covering 49 rainfall events. The daily rainfall data were obtained from the field meteorological observatory located within 100 m of the experimental plots. A standard tipping bucket type of rain gauge was used to record the daily rainfall. A rainfall event occurring 1 hour after the previous event was considered as a separate rainfall event for data collection and analysis (Ahmed et al. ). At the end of each rainfall event, rainfall depth and stemflow volume were recorded.

Stemflow measurement
To measure stemflow volumes, five plants were randomly selected from the blocks of four fruit species. These sample sizes were based on the equation of Freese () using 95% confidence limits from preliminary sampling.
Trees were fitted with stemflow collars and pipe connections were made to collect the stemflow into calibrated black 20-litre plastic cans. Stemflow collars were constructed at the base of the stem using high quality cement mortar. The collar was 50 mm wide and 40 mm deep, with inert silicon sealant applied at the stem-mortar interface. Stemflow volume (L) was divided by crown area (m 2 ) to convert the volume units of stemflow into depth units (mm). Per cent stemflow (%SF) and per cent throughfall (%TF) were determined as: Throughfall measurement vs stemflow (mm) and rainfall (mm) vs throughfall (mm).
Six types of models, namely, Linear, Allometric, Logistic, Exponential, Mitscherlich and Weibull were tested to predict the stemflow and throughfall for each of the fruit tree species using rainfall as the explanatory variable.
Since coefficient of determination (R 2 ) value alone is not a sufficient criterion to judge the best fitting model, the Akaike information criterion (AIC) (Akaike ) was used to select the best fitting model for each tree species. The AIC is a measure of the relative quality of statistical models for a given set of data (Burnham & David ). It tends to penalize over-fitting models, and is a widely used    tertiary branches (angle 56-90 ), whereas in the case of jackfruit, the tertiary branches showed negative inclination (7 to À53 ), i.e., after branching point, the branch inclined towards the ground instead of inclining upward.

Rainfall
During the study period, 49 and 33 rainfall events were available for the stemflow and throughfall analysis, respectively. Rainfall received during these events was 661.3 and 477.0 mm with an average depth of 13.5 and 14.4 mm, respectively. The smallest and largest events recorded rainfall of 1 and 53 mm, respectively ( Figure 4).
Fewer datasets in the case of throughfall indicates that rainfall during some events was just enough to wet the tree canopy but did not generate any throughfall. Lowest stemflow percentage (0.45%) was recorded in jackfruit, with the highest in guava (2.32%) ( Table 3).     Concave orientation of leaves led to higher stemflow, as evident from the concave shape of guava leaves ( Table 2).
The concave shape of leaves directed a considerable part of the precipitation to their petiole and subsequently to the stems, leading to increased stemflow. Plant branches with lower inclination angle generated less stemflow as compared to the species having higher inclination angle (e.g., guava showed that, while estimating the throughfall from cacaobased agroforestry, the tree height was much more influential than the leaf area. Although the mango plant is taller than the litchi plant, its leaves are more inclined to horizontal, promoting dripping of water from the tips of the leaf. This type of leaf arrangement increased throughfall (83.8%) from the mango trees. Highest throughfall in the case of guava was related more to its leaf and branch configuration. The leaf orientation of guava is such that the leaves droop to the outside. The drooping of leaves to the outward side contributes more to throughfall (Ahmed et al. ). Also, low density canopy of guava plant (Table 2) allowed rain to fall directly through the canopy without coming into contact with leaf, leading to increased throughfall. The presence of higher numbers of primary branches, as in the case of mango and jackfruit, led to enhanced canopy storage, ultimately reducing the throughfall. Herwitz () also reported that in the case of tropical rain forests, the higher number of primary branches of long crowns enhanced the water storage, especially in heavy rains. The longer canopy of jackfruit and mango also implies that a droplet travelling through its canopy has the lower kinetic energy and lower distance to fall from the canopy to the ground, and can cause less erosion. The difference between throughfall recorded for mango and litchi was statistically non-significant (P ! 0.05).
The amount of throughfall varied significantly (P 0.05) among the species. Throughfall observed for mango and litchi was 9.3 and 11.7% less than that observed for guava, respectively.

Interception loss
The interception loss in the selected fruit species varied from 6.5% (guava) to 21.3% (jackfruit Y, Dependent growth variable; X, independent growth variable; a, b and c are parameter estimates and ε is the additive error term.

Rainfall-based models for throughfall estimation
Similar to stemflow, six models were also fitted for throughfall to derive the relationship between throughfall and rainfall for the four tree species. The functional form and the parameter estimates for the best fitting models are presented in Table 5. The adjusted R 2 value (observed vs predicted) was more than 0.94 for all the best fitting functions to throughfall data of all tree species. The nonlinear models, namely, Weibull (R 2 ¼ 0.99) and Allometric  Table 6. All the regressions were highly significant (P < 0.001) and performed well with adjusted R 2 varying from 0.856 to 0.944 and RMSE in the range of 0.141 to 0.492 (Table 6). The number of variables in the best performing models varied from 2 (RR and LAI), in the case of low rainfall depths (<5 mm) to 4 (RR, LAI, TH, CA), in the 10-20 mm rainfall class. Park & Cameron () also observed that the relative importance of different  The Anderson-Darling tests confirmed that, for all the morphology-based throughfall estimation models, the residuals were normally distributed. The plots (Figure 7(e)-7(h)) ensured that the residuals are not continuously over/ underestimating stemflow.

Morphology-based throughfall prediction
The model variables, coefficients of variables and intercepts of the best performing throughfall prediction models are presented in Table 7 In the assessment of throughfall, the role of LAI was statistically significant and this parameter appeared in the best performing models for all the rainfall classes. This is mainly because leaf area significantly influences the canopy water storage capacity, consequently increasing the   normality showed that the residuals were normally distributed and the developed models are acceptable for estimating throughfall with a reasonable degree of accuracy.
From this study it can be inferred that, among the four species studied, jackfruit is the best species to plant, if the aim of the plantation is to reduce soil erosion from the degraded uplands of the East Indian plateau region. Jackfruit, having a comparatively longer canopy and higher LAI, intercepted more rainfall (21.2%). Although mango had a higher LAI, litchi plant also showed comparatively a lower throughfall and higher interception loss (18.7%), mainly because of its dense canopy. The higher the ability of the plant to reduce throughfall, the greater is the potential to reduce throughfall kinetic energy, consequently reducing the potential for rill initiation (Keim & Skaugset ).
However, these protective functions of fruit tree species must be balanced against interception losses (Wallace

CONCLUSIONS
The partitioning of rainfall into stemflow, throughfall and the resulting interception loss by the major fruit crops of the East Indian plateau was analysed, considering the rainfall and canopy traits. Stemflow, throughfall and interception loss were strongly influenced by canopy architecture and tree morphological characteristics. Among the studied fruit species, jackfruit has the highest per cent of interception loss relative to gross rainfall and the guava plant has the least per cent of interception loss. Among rainfall-based models, Weibull, Logistic, Allometric and Exponential model were found as the best fit models for stemflow estimation for mango, litchi, guava and jackfruit, respectively, whereas Weibull, Allometric, Linear and Linear were the best fit models for throughfall estimation from mango, litchi, guava and jackfruit, respectively. The morphology-based models can only be used over the range of tree morphological parameters considered in this study, because these models do not consider other sources of variation. The models clearly identified the specific set of morphological parameters that are affecting the stemflow and throughfall generation process at different rainfall depths. We found that these static models are capable of describing rainfall partitioning from the fruit tree species.
Although the developed models did not explain the stemflow and throughfall generation processes at canopy level, the models clearly identified the extent to which rainfall partitioning is controlled by the morphological parameters.
Rainfall-and tree morphology-based models developed in this study will be useful to hydrologists in modelling runoff and soil erosion processes. Although the study presents quantitative results of stemflow and throughfall from four important fruit species of the East India plateau region, future studies should also focus on assessment of spatial variations in the soil hydraulic and physical properties as triggered by stemflow and throughfall patterns.