Modeling vegetation interception under natural rainfall in yerba mate production systems

ABSTRACT Interception loss plays an important role in rainfall partitioning, retaining significant amounts of water that would be directed to the soil. In this work, the objective was to measure interception by vegetation and evaluate the Rutter and Gash models to estimate the interception in different yerba mate production systems. The study was conducted the period from July/2019 to March/2020 in the municipality of Guarapuava, southern Brazil. The total rainfall, stemflow, and the throughfall were monitored in each rainfall event. Rutter and Gash interception models were applied. The interception losses estimated by Rutter and Gash models were considered satisfactory but, in general, underestimated. In the yerba mate monoculture system, an average interception loss of 15.6% was recorded, in the yerba mate agroforest, 21.4%, and, in the native Mixed Ombrophilous Forest, 16.2%. Rutter's model presented estimates close to the measured rainfall interception estimate for the yerba mate monoculture system and Gash's model for the agroforestry system and the native Ombrophilous Mixed Forest.


INTRODUCTION
The rainfall interception by the canopy is an important component of hydrological cycles, and trees play an significant role in the water cycle, returning a large amount of water to the atmosphere through evapotranspiration (Linhoss & Siegert, 2020;Wei et al., 2022).
Interception studies in annual and perennial crops have often been expanded in recent years, while few studies have been conducted in different Ilex paraguariensis producing systems (Antoneli et al., 2021).However, Santos et al. (2022) found that interception loss in yerba mate in monoculture system represented an average of 13% of total rainfall.
Yerba mate (Ilex paraguariensis) is a shade-tolerant tree found in southern Brazil, Argentina, Paraguay, and Uruguay (Ávila Júnior et al., 2016;Vestena & Santos, 2022) and is cultivated in both consortium and monoculture systems.In addition, when properly managed in consortium with forest (agroforestry), it can contribute to the conservation of tree species, soil and water conservation, and the generation of ecosystem services (Vestena & Santos, 2022).Thus, measurement and modeling are essential for understanding water balances and formulating scientific management strategies in different ecosystems (Návar, 2017;Wang et al., 2022).And quantifying and modeling interception loss in Ilex paraguariensis under different production systems is important to improve our understanding of the effect of yerba mate planting on regional water balances and to formulate reasonable strategies for managing water resources in the southern region of Brazil.
In this study, we measured rainfall, throughfall, stemflow and interception loss during the period 07/2019 to 03/2020 in three production systems of Ilex paraguariensis in the municipality of Guarapuava, southern region of Brazil.We modeled interception loss using the Rutter and Gash model in monoculture and agroforestry of Ilex paraguariensis and in the Native Mixed Ombrophylous Forest (Native MOF).The objective of this study was: (1) to quantify the interception loss for different yerba mate production systems and (2) to evaluate the efficiency of Rutter and Gash models in determining interception loss in different yerba mate cultivation and production systems.

Study area
The experimental area is located in the municipality of Guarapuava, southern Brazil (Figure 1) on a private property (31 ha) with a monoculture yerba mate production system (6 ha), an agroforestry system (6 ha) and a native Mixed Ombrophilous Forest (19 ha).

Soil and vegetation
The Guarapuava region predominant soils are classified as Red-Yellow Latosols with low cation exchange capacity, deep, acidic, and with low base saturation (V < 50%).It presents low levels of natural fertility requiring the use of fertilizers for good productivity (Empresa Brasileira de Pesquisa Agropecuária, 2018; Santos et al., 2022).
The experimental plot is mostly occupied by yerba mate (Ilex paraguariensis).In the experimental area of the monoculture system, the yerba mate is planted at an average distance of 4 m x 4 m, with ages ranging from 25 to 28 years.The soil surrounding the yerba mate in the monoculture system is covered by grazed natural vegetation (grasses, herbaceous plants, and shrubs), such as barba-de-bode grass (Aristida pallens), rabo-de-burro (Andropogon sp.), vassourinha (Miconia candolleana and others), caninha grass (Andropogon icanus), and capim flexa (Tristachya chrysothrix) (Santos et al., 2022).
The yerba mate agroforestry system is characterized by the removal of the lower stratum to provide a greater incidence of sunlight, essential for the yerba mate development.The understory is formed by forage species and by extensively managed weeds, providing a layer of litter.The average spacing between the yerba mate plants in the agroforestry system is also 4 m x 4 m.In the experimental area (40m X 45m), 214 yerba mate trees (Ilex paraguariensis); five imbuia (Ocotea porosa); three canelas (Ocotea pulchella); fifteen araucárias (Araucaria angustifolia), two samambaia-açu (Dicksonia sellowiana), and one gabirobeira (Campomanesia xanthocarpa) were encountered.

Meteorological data
Daily meteorological data were collected during the period from July/2019 to March/2020 by a weather station installed in an open area at the edge of the experimental area at a height of two meters above the ground surface.
The station monitored total rainfall (0.2 mm resolution), air temperature, relative humidity, solar radiation, wind speed and direction continuously at five-minute intervals.The weather station was installed 80 m away from the monoculture system and 100 m away from the yerba mate in consortium and Native MOF.

Throughfall and stemflow
The throughfall in the monoculture area was measured using 54 rain gauges distributed around three yerba mate trees, 18 rain gauges in each yerba mate tree (Figure 3a).In the agroforestry system and the Native MOF, six 2.00 m X 0.13 m gutters were used, four of these installed in the agroforest and two in the forest.
The stemflow was collected from eight randomly selected trees using either spiral or collar/funnel type collectors from flexible PVC hoses.The spiral-type collectors were used on trunks larger than 55 cm in diameter, and the collar-type collectors were used on trunks smaller than 55 cm in diameter (Figure 3b).The collars were adjusted to the trunk shape and sealed with silicone.The stemflow was diverted from the collars into a collection containers with a storage capacity of 5 to 20 L. The corresponding stemflow amount from each selected tree was calculated by dividing the stemflow volume by the crown area.Stemflow was monitored on three Ilex paraguariensis in the monoculture area; two Ilex paraguariensis, one Araucaria angustifolia, and one Campomanesia xanthocarpa in the agroforestry area; and finally, one Campomanesia xanthocarpa in the Native MOF.
Rainfall events in which the observed throughfall was greater than the total rainfall were excluded because they generated negative interception.

Modeling interception loss
The models of Rutter et al. (1971) and Gash (1979) were used to predict interception losses in different yerba mate production systems.The following section describes the interception models, their equations, and the methodology for calibrating the data.The potential evapotranspiration in the experimental area was estimated using the modified Penman method (Doorenbos & Pruitt, 1977), from temperature, relative humidity, incident solar radiation, and wind speed data monitored at the Simepar weather station.

(
) ( ) ( ) The modified Penman method results in daily averages of potential evapotranspiration.Here, p E is the potential evapotranspiration (mm/d -1 ); F is the correction factor for the region in question; W is the weighting factor related to temperature and altitude; n Rad is the net radiation expressed as equivalent evaporation (mm/d -1 ); ( ) f u is the wind-related function; a e is the water vapor pressure in saturated air (mbar); and d e is the water vapor pressure in the actual condition (mbar) (Sá et al., 2015).

Rutter model
Rutter's model is based on the estimation of throughfall, stemflow, and interception losses based on the amount of water in the canopy, including the timing of rainfall, evaporation, drainage, and changes in canopy storage, where evaporation from the wet canopy constitutes the interception loss (Rutter et al., 1971;Eliades et al., 2022).The main disadvantage of Rutter's model is that it requires hourly meteorological data that are often not available.
( ) (2) (5) Where R is the average rainfall rate, S is the maximum canopy storage capacity, t S is the maximum stem storage capacity, p is the free throughfall coefficient, t p is the stemflow coefficient, C is the actual canopy storage capacity, t C is trunk storage, P E is the potential evaporation, C E is the canopy evaporation, t E is stem evaporation, ∊ describes stem evaporation as a proportion of evaporation from the saturated canopy, S D is the rate at which water drips from the canopy when the canopy storage capacity has been reached, b is a drainage parameter, and I is interception (Linhoss & Siegert, 2020).Gash model Gash's model (1979) makes an analysis of rainfall from the capacity of vegetation to be saturated with considering the potencial evaporation during the rainfall event (Equations 8 and 9).The model was conceptually based on Rutter's model but replaced the numerical approach of that model with analysis by discrete storm events separated by intervals long enough for the canopy and stems to dry completely, making it simpler to apply, i.e., 1) the canopy wetting phase, (2) the canopy saturation phase, and (3) the canopy drying phase (Linhoss & Siegert, 2020). ) The p , t p , , and t S parameters of this model are equal to Rutter's model.Ē is the average evaporation rate during post-saturation rainfall, R ̄ is the average intensity of post-saturation rainfall, GJ P is the amount of rainfall in a given rainfall event, and ' G P is the amount of rainfall required to reach canopy saturation.In this model, n is the number of storms that saturate the canopy, m is the number of storms insufficient to saturate the canopy, q is the number of storms with stemflow.

Calibration and validation
Model calibration is a phase that ensures improved results based on realistic, physically-based parameter values and can be used to identify flaws in the way systems that are perceived and modeled (Linhoss & Siegert, 2020).For modeling the interception process, the parameters required by the Rutter et al. (1975) and Gash (1979) models were estimated by applying existing equations (Ribeiro Filho et al., 2019).In each area (Table 1), the storage capacity (S) and the free throughfall coefficient (p) were applied according to the method of Leyton et al. (1967) and Rutter et al. (1971), respectively.The stemflow parameters and the proportion of rain that runs off the branches and trunks were deduced using a regression calculation methodology between stemflow versus rainfall.The parameter b was obtained from the methodology proposed by Schellekens et al. (1999), and the parameter Ds from the value given by Lloyd & Marques (1988).
The calibration and validation of Rutter and Gash models were determined by means of linear regression.In order to calculate the model estimate error, the Nash & Sutcliffe (1970) coefficient was also used for the data set measured in the field and estimated by the models.This coefficient can range from -1 to 1, and the performance of a model is considered adequate and good if the NSE value exceeds 0.75, and it is considered acceptable if the NSE value is in the range between 0.36-0.75(Ribeiro Filho et al., 2019).
The Percent Bias (Pbias) calculation was also used to identify the overall over or underestimation settings of the sample.The ideal value of Pbias is 0 (zero).Positive values indicate an underestimation, and negative values indicate an overestimation.The ranges of values used for satisfactory or unsatisfactory judgment of the models are NSE ≥0.5 and Pbias ≤±25% (Moriasi et al., 2007).

RESULTS AND DISCUSSION
In the years 2019 and 2020, the total annual rainfall was below the average of the historical series (1,892.2mm), 1,401.6 (-25.9%) and 1,338.3mm (-29.3%),respectively.The monthly rainfall during the study period was lower than the monthly average of the historical serie.The lower average rainfall volume in the period was due to the formation of "veranicos" because of longer than usual dry spells (Sistema de Tecnologia e Monitoramento Ambiental do Paraná, 2020).
Interception loss in the different yerba mate production systems ranged from 15.2 to 21.4% of total rainfall (Table 2).The interception patterns recorded are associated with variations in canopy cover and rainfall characteristics.Thus, our results are within the interception pattern in tropical forests, where the vegetation characteristic is dense, but the interception loss depends on the intensity and amount of rainfall.Gash's model produced better interception estimates in a study by Jackson (2000) in a Kenya Forest, which resulted in an underestimate of only 0.4%.Our results show a result closer to that obtained in a Coniferous Forest in China (Cui & Jia, 2014), which showed an underestimate of 3.4 and 5.1%.
The results obtained by both models were considered satisfactory when evaluated by the NSE and Pbias coefficients (NSE≥0.5 and Pbias≤±25%) (Table 3).
The results showed that the Rutter and Gash models underestimated the interception loss in the three yerba mate production systems.In analyzing the performance of the models, in general, an underestimation of interception loss values of 19% by the Rutter model and 21% by the Gash model was observed, differences considered acceptable.Návar (2017) investigated the interception estimated by the models in a temperate forest in Mexico and also concluded that the models can be used to satisfactorily estimate interception in that environment.
Rutter's model resulted in higher underestimates, except in the yerba mate monoculture.The model showed underestimates on the order of 6.3 and 9.3% for the agroforestry system of yerba mate and native MOF, respectively (Table 4).

Figure 1 .
Figure 1.Location map of the study site in the District of Guará, Paraná, in the municipality of Guarapuava, in the south of Brazil.The abbreviation MO represents yerba mate in monoculture system; AGF yerba mate in agroforestry system, and N-FOM represents Mixed Native Ombrophylous Forest.

Figure 3 .
Figure 3. Materials used to measure throughfall and stemflow in this study.(a) Monoculture system; (b) Agroforestry system; and (c) Native Mixed Ombrophilous Forest.

Figure 5 .
Figure 5.Comparison of observed and calculated losses by Rutter and Gash model.(a) Yerba mate monoculture; (b) Yerba mate agroforestry; and (c) Native mixed ombrophilous forest.

Figure 6 .
Figure 6.BoxPlot of interception (mm) occurring in the production systems.Note: a) is the monitored interception, b) is the Rutter estimates, and c) is the Gash estimates.

Table 1 .
Parameter values of Rutter and Gash models.

Table 2 .
Summary of data measured in the different yerba mate production systems.

Table 4 .
Comparison among the Rutter and Gash total interception estimations to difference vegetation formations.

Table 3 .
NSE and Pbias values in the performance analysis of Rutter and Gash models.NSE -Nash-Sutcliffe efficiency; Pbias -percent bias.