Quantitative accuracy assessment of the revised sparse Gash model using distinct time-step climatic parameters

Rainfall is a major supply of water within forested catchments and is redistributed into throughfall (TF, mm), stemflow (SF, mm), and rainfall interception (I, mm) after reaching the canopy, thereby affecting the local water balance in a forested ecosystem (Mużyło et al. 2012; Ringgaard et al. 2014; Sun et al. 2014). I is defined as precipitation that does not reach the ground, but is rather stored and subsequently evaporated back into the atmosphere from the vegetation canopy, branches, and stems (Price & Carlyle-Moses 2003; Llorens et al. 2014; Attarod et al. 2015). I is, thus, an important component of the forest moisture cycle, with an important influence on the interactions among climate, hydrology, and biology. The amount of I is probably greater than that widely estimated (Bulcock & Jewitt 2012), and it has been recognized that I can account for a significant percentage of water from forest watersheds (Fan et al. 2014; Sadeghi et al. 2015), resulting in reduced soil moisture, transpiration, and surface and groundwater recharge (Wallace & McJannet 2006; Linhoss & Siegert 2016). Consequently, accurately identifying and describing the magnitude of I is crucial for improving the knowledge of biogeochemical cycling and related hydrological processes (Su et al. 2016).

Modeling I is an effective method for elucidating the mechanisms of underlying the interception process. The Gash-type models are the most commonly applied approaches (Muzylo et al. 2009). The original Gash analytical model (Gash 1979) was proposed to simplify the Rutter model (Rutter et al. 1971). It was subsequently reformulated into a sparse version due to its unsuitability for sparse forest stands (Gash et al. 1995). Furthermore, Gash model variants have been developed by reformulating parameterization to optimize the model structure for highly accurate simulations of I processes. For example, Valente et al. (1997) replaced mean evaporation from the saturated canopy (⁠⁠) in the formula of the sparse Gash model (Gash et al. 1995) with (⁠⁠, a constant describing the evaporation rate from saturated trunks as a proportion of that from the saturated canopy, is approximately 0.02). The modeling of SF and the calculation of I from trunks were also modified, and the results obtained for storms indicated that the relative error in the revised version was approximately 39% lower than that in the original version. The resulting model is referred to as the revised sparse Gash model (RSGM) in this paper. This version appears to be more rigorous in its conceptual and physical approaches than the classical and sparse Gash model. To date, however, there have been few applications of this model version in research relative to the sparse Gash model (Price & Carlyle-Moses 2003; Valente et al. 2020).

The stochastic nature of meteorological conditions makes the precise projection of the I incident a challenge (Chen et al. 2013). To simplify the computational steps as much as possible while maintaining simulation accuracy, Gash (1979) assumed that the average rates of evaporation (⁠ or ⁠) and rainfall (⁠⁠) during rainfall for saturated canopy conditions are equal for all storms. Subsequently, the hourly values of evaporation rate for saturated canopy conditions over the 4-week period and the entire study period (from 1975 to 1976) were averaged to drive the model separately to examine the assumption, and the validation results indicated that the assumption was justified. Most previous studies have directly accepted this setting (Zhang et al. 2018; Lopes et al. 2020), employing the Gash model to estimate I. However, this assumption has not received sufficient cases for further investigation. Furthermore, variable parameters have been also applied to run the Gash model on an event basis or to calculate the corresponding values of (⁠⁠) or for single rainfall events. For example, van Dijk & Bruijnzeel (2001a) established equations between or the canopy storage capacity (S, mm) and the leaf area index (LAI) to dynamically describe the interception characteristics of variable dense vegetation, making corrections to the simulated formula, which resulted in a substantial reduction in the calculated error (van Dijk & Bruijnzeel 2001b). Limousin et al. (2008) calculated I using the and of each rainfall event as inputs, with their outputs agreeing well with the measurements that were underestimated by 6.3%. The above potentially implies that the justification of this assumption in the Gash model has been questioned. Therefore, it is necessary to provide more examples for this assumption to confirm.

Several studies have focused on the accuracy of modeling I for individual rainfall events. For example, Fathizadeh et al. (2018) used the mean method (Klaassen et al. 1998) to separately estimate the corresponding parameters S and during the leafed and leafless periods, running the sparse Gash model to calculate the cumulative and single-event interceptions. They obtained a better model performance in the leafed period than in the leafless period. Linhoss & Siegert (2020) compared five canopy interception models (Rutter, Rutter sparse, Gash, sparse Gash, and Liu models) using the Parameter Estimation and Uncertainty Analysis program and the Penman–Monteith equation (Allen et al. 1998) between field measurements and predicted individual and cumulative interceptions. They found that the sparse Gash model estimated individual interception poorly and that the modeling accuracy in the leafed period was lower than that in the leafless period. Typically, it was considered that more detailed parameter values for the inputs in the model would result in better estimations. Then, whether the Gash model will be more accurate in estimating I for the single storm when the time step of the climate parameter is changed to be storm-based, additional cases are still required to answer this question. Accordingly, the present study, with several plots in the forest stands of Pinus tabuliformis (Pt), Platycladus orientalis (Po), and Acer truncatum (At) in Northern China, was performed to answer the following questions:

1. Is the setting in the Gash model that the climate parameters were equal for all storms correct? Which time-step climate parameters (storm-based, monthly, and fixed) are better for running the RSGM?

2. Does a change in the time step of the climate parameter improve the estimation accuracy of the RSGM of a single I event?

The research site (Figure 1) is located 8 km northeast of Mount Tai (Northern China) in Yaoxiang National Forest Park (E11°05′39″–117°09′26″, N36°17′58″–36°20′30″) at an elevation ranging from 400 to 956 m, with a mean elevation of approximately 710 m. The site is located in a warm temperate zone with a semi-humid and monsoon climate, corresponding to a Dwa Köppen climate-type (Zhu & Li 2015; Li & Ye 2019), with a mean annual temperature of 18.5 °C, and a mean yearly frost-free period of 198 days. The multi-year mean precipitation is 727.9 mm, 75% of which occurs from June to September. The soil type is brown soil, and the underlying rock is an ancient gneiss of high metamorphic grade, with an average thickness of 10–90 cm, mostly within 30–50 cm. The vegetation types belong to coniferous and deciduous broad-leaved forests in the warm temperate zone, and the main tree species include Pt Carr., Quercus acutissima Carr., Pinus densiflora Sieb., Robinia pseudoacacia, and Castanea mollissima (Sun et al. 2019).

The survey of the forest plots was conducted in March 2017 (Table 1). A total of eight plots (each with a projection area of 100 m², a length of 20 m, and a width of 5 m) were set up from September to October 2015 (Figure 1). Four plots were set up for Pt, two for Po, and two for At Bunge, as shown in Table 1. Every tree was the same species on each plot.

Three HOBO automatic weather stations (Onset, Bourne, USA) were installed in the surrounding open area of the plots in March 2016. The so-called open area was an unsheltered area within a radius of at least 5 m, with the automatic weather station at the center. Automatic weather stations were installed separately on a combined structure consisting of a metal pedestal (2 m) and a simple additional mast with height (MH, m). The value of MH was higher by 2 m than the highest tree height (TH, m) within a radius of 10 m from the automatic weather station, i.e., MH = TH + 2. The mast was held firmly in place by four metal chains that were connected to the ground. Data collectors (HOBO U30, Onset; CR1000, Campbell, Logan, USA) were mounted on the top of the metal base, and sensors for air temperature (S-THB, Onset), relative humidity (S-THB-M002, Onset), net radiation (CN1-R, Middleton Solar, Melbourne, Australia), atmospheric pressure (S-BPB-CM50, Onset), and wind speed (S-WSA-M003, Onset) were mounted on the top of the mast. A tipping bucket rain gauge (S-RGB-M002, Onset), with a diameter of 15.2 cm, was also mounted on the top of the mast. It was guaranteed that the total rainfall would not be sheltered and intercepted by the neighboring trees during the measurement process.

Because the distance between each plot of a single tree species was relatively close (<80 m), there was little variation in the climatic conditions, and only one meteorological station was required to be installed at each tree species to collect the necessary data. The weather stations collected data at 15-min intervals. Meteorological data from May–October 2017 as well as observations of rainfall, I, SF, and TF for the corresponding period were selected. Some meteorological data for At were lost due to a malfunction of the instrument. However, there was a negligible difference in the meteorological data between At and Po on comparing the daily monitoring data of the same period (May–October) in 2016 and 2017. Furthermore, the duration of most rainfall events in the two areas is similar, and the frequency of each rainfall event is remarkably consistent. Consequently, after careful consideration, meteorological data for At were replaced by those for Po, whereas the rainfall data for At remained unchanged.

This study used a simplified RSGM on the basis of studies by Valente et al. (1997) and Limousin et al. (2008), such that the I of each rainfall event was calculated as shown in Table 2. S was estimated using the regression method proposed by Leyton et al. (1967), which is based on the relationship between P_G and TF. Drainage partitioning coefficient (p_t, dimensionless) and trunk storage capacity (S_t, mm) were deduced based on the relationship between P_G and SF (Gash 1979). To further demonstrate the direct effect of meteorological parameters on model accuracy, S, S_t, c, and p_t were used as fixed values to run the model, regardless of versions, which is permissible for the operation of the model (Valente et al. 2020).

Assuming that hours with P_G > 0.4 mm represent saturated canopy conditions (Valente et al. 1997; Mużyło et al. 2012), the hourly values of were calculated by Equation (4), and subsequently three versions of the RSGM were run defined in this study. RSGM-E was defined as that the hourly values of for saturated canopy conditions were averaged over the storm period to obtain the estimate of to drive the RSGM, and these hourly P_G were extracted and averaged over the same period to obtain⁠, i.e., and were substituted for the corresponding and in Equations (6)–(7), respectively. Likewise, RSGM-M was defined as that running the RSGM using the monthly climatic parameters, and RSGM-G was defined as the RSGM run with the averaged and rainfall rates over the whole growing season under saturated canopy conditions. All three versions were based on independent rainstorms for calculating I. In the present study, independent rain events were defined such that each storm was separated by at least an 8-h rain-free period.

Because the number of rainfall events per plot is small, leave-one-out cross-validation was used in this study with reference to the research conducted by Fathizadeh et al. (2018). This approach is consistent in principle with the most common approach of generating parameters with half of the data and testing the model on the other half, assuming that the original data has N samples (here N for Pt is 25 and N for At and Po is 28), each sample individually as the validation set, and the remaining N − 1 samples as the training set. Several common quantitative methods were applied to determine model performance. All statistical indicators in this work were the mean of the validation set, and the presented estimations of I, SF, and TF were also the validation set.

The local sensitivity analysis technique was used in this study to assess parameter importance (Fathizadeh et al. 2018; Ma et al. 2020). The original values of S, S_t, p_t, c, ⁠, and were increased and decreased by 10% from −50 to 50%, and the results of running the model were compared with field-measured values. When RSGM-E was tested for sensitivity, the or of all single rainfall events was increased or decreased together. However, for RSGM-M, the monthly average values of or were treated as a whole (increased or decreased).

In total, 25, 28, and 28 events were monitored for Pt, Po, and At, with a total rainfall of 427.2 mm (P_{G, Pt}), 490.1 mm (P_{G, Po}), and 497.2 mm (P_{G, At}), respectively. The cumulative I increased in the same species with the planting densities increased, amounting to 59.7 mm in plot 1 (14.0% of P_{G, Pt}), 84.2 mm in plot 2 (20.7% of P_{G, Pt}), 96.8 mm in plot 3 (22.7% of P_{G, Pt}), and 115.9 mm in plot 4 (27.1% of P_{G, Pt}); 88.2 mm in plot 5 (18.0% of P_{G, Po}) and 100.8 mm in plot 6 (20.6% of P_{G, Po}); and 60.7 mm in plot 7 (12.2% of P_{G, At}) and 72.6 mm in plot 8 (14.6% of P_{G, At}).

The parameters that were used for the model calculations are presented in Table 3. Three model versions underestimated the accumulated I in all plots. However, the estimated results by RSGM-G were closer to the observed interception for all species, whereas the deviation of RSGM-E was the greatest (Figure 2). Overall, larger underestimations were obtained for RSGM-E, with 12.9–20.7% for Pt, 16.4–16.5% for Po, and 14.0–14.7% for At, whereas better fits were obtained for RSGM-G, in which cumulative I were underestimated by 9.9–16.1% for Pt, 13.6–15.9% for Po, and 15.7–20.2% for At. Moreover, differences were found between the estimated results of RSGM-M and RMGM-G, ranging from 0.13 to 0.34 mm.

All model versions showed poor variable accuracy in simulating the interceptions of individual rainfall events, irrespective of the tree species. More deviations occurred in certain small storms and large storms, which were correspondingly overestimated and underestimated (Figure 3).

As shown in Table 4, most I evaporated from the saturated canopy after the rainfall ceased. This component exceeded 50% of the total calculated volume of the I, regardless of the model version and tree species, ranging between 67.2 and 81.0%. The lowest losses were derived from n storms that saturated the canopy, ranging between 1.1 and 1.7%. The increase in evaporation from saturation until the rainfall ceased was the primary reason for the difference in calculation among the models. In the same plots, the maximum value was usually calculated by the RSGM-G model, followed by the RSGM-M and RSGM-E models.

Five statistical indexes for the different model versions are presented in Table 5. As shown, the APE, AE, RMSE, and MAE values for RSGM-G were lower than those for RSGM-M in all plots, followed by those for RSGM-E. The opposite trend is observed in other indexes.

The reduction in RMSE, MAE, APE, and AE values for RSGM-G compared with those for RSGM-E did not exceed 22.4% (for Pt), 15.7% (for Po), and 17.4% (for At) but was no more than 1.6% (for Pt), 1.7% (for Po), and 2.8% (for At) compared with those for RSGM-M. The mean NSE values for RSGM-G were 0.21 (for Pt), 0.15 (for Po), and 0.22 (for At) higher compared with those for RSGM-E, whereas the values varied slightly compared with those for RSGM-M in all tree species. In general, RSGM-G exhibited superior performance relative to RSGM-M and RSGM-E for all species.

Differing model performances according to the tree species depended on the type of statistical indexes and stem densities used. For example, when using APE, on the premise of a density of approximately 1,600 or 2,700 trees ha⁻¹, for all models, the most accurate predictions were obtained for Pt. However, all the models generated the best estimation of I for At when RMSE and MAE were used for a density of approximately 1,600 or 2,700 trees ha⁻¹.

Sensitivity analyses for six parameters (S, S_t, p_t, c, ⁠, and ⁠) were conducted to determine their influence on the predicted I and assess differences between the models (Figure 4). In general, showed a negative correlation with the cumulative interception throughout all tested parameters, whereas the other parameters showed an opposite trend (Liu et al. 2018; Lopes et al. 2020; Ma et al. 2020).

S was the main sensitive parameter that influenced interception prediction when the tested parameter changes were in the ±50% range, regardless of the model used and the tree species. The interception was less sensitive to parameters p_t and S_t, which presented changes smaller than ±2.0 and ±3.1%, respectively. Moreover, was the second most sensitive parameter when changed from 0 to 50%, leading to a change in cumulative I of approximately 8.4, 7.3, and 11.8% for Pt, Po, and At, respectively. In contrast, was the second most sensitive parameter in the range from −50 to 0%, resulting in variations of 16.8, 14.5, and 23.5% for Pt, Po, and At, respectively.

The effects of and showed increases with the temporal scale of calculation of the meteorological parameters within the same plots, whereas S, S_t, and p_t showed the opposite trend. For example, a 50% increase or decrease in S caused the cumulative interception predicted by RSGM-E to change within an average range from −40.7 to 39.5% for Pt, and from −39.3 to 37.6%, and from −39.3 to 37.5% for RSGM-M and RSGM-G, respectively. Conversely, increased to 50% for Pt, resulted in simulated interception increases of an average of 5.7% for RSGM-G, by 5.6% for RSGM-M, and by 3.7% for RSGM-E.

The value of was reported to be quite conservative among regions and species, ranging from 0.2 to 0.4 mm h⁻¹ (Miralles et al. 2010). However, in the present study, the values used to run RSGM-G in each plot were considerably smaller. The values involved in the model operations reported by Miralles et al. (2010) were derived from other reference values, related to experiments conducted in Britain, Amazonia, Netherlands, Bordeaux (France), Portugal, Mediterranean mountainous area, Puerto Rico, and Mississauga (Ontario, Canada). Therefore, differences in climatic conditions owing to interregional variability probably explain the small value in this study (approximately 0.06 mm h⁻¹). Moreover, monitored data measured in the scope of this research were reexamined and showed that most of the rainfall events occurred at night and were rarely accompanied by strong winds, which may have contributed to the relatively small ⁠. Furthermore, the values in this study were compared with those obtained in recent studies conducted in China (Shinohara et al. 2015; Liu et al. 2018; Ma et al. 2019, 2020), the observed values ranged between 0.01 and 0.10 mm h⁻¹, and the difference between them and this study is not large, indicating the potential correctness of the results in this study. Ghimire et al. (2017) used the Penman–Monteith equation and calculated an value of 0.07 and 0.08 mm h⁻¹ for modeling I in two differently aged secondary forests in Madagascar. Moreover, the higher S-values of Pt (3.845 mm, plot 4) have been explained in previous work (Li et al. 2020), and it can be explained by the large stem density in this study and the special plant physiology structure of Pt. S-values for the other plots were within the range previously reported (Llorens & Gallart 2000; Deguchi et al. 2006).

Muzylo et al. (2009) summarized studies published before March 2008 regarding I modeling. They found that the APE range of the sparse Gash model (Gash et al. 1995) was mostly less than 20%, whereas the ranges of APE in the present study also were in this interval for most sites regardless of the model versions, except for the use of all versions in plot 7 and RSGM-E in plot 1. This indicated that the cumulative annual interception could be accurately calculated by all three model versions (APE in the range of 9.9–24.3%). Furthermore, a negative NSE value was obtained by running RSGM-E in plot 1. This observation is different from those of studies by Hassan et al. (2017) and Fathizadeh et al. (2018) and similar to those by Krause et al. (2005) and Shi & Wang (2020). However, Equation (13) indicates that a range of NSE less than zero is entirely possible, as long as the top of the fraction is greater than the bottom, although it has been claimed to range from 0 to 1 (Sadeghi et al. 2015; Lopes et al. 2020).

The model framework of the three versions in this study is a combination of those proposed by Valente et al. (1997) and Limousin et al. (2008). Given that the former proposed model has relatively few applications in forest trees, the results of the present study were compared with those of the other studies using the latter model, and the APE values in this study were found to be higher than those reported in previous studies (Zhao et al. 2011; Liu et al. 2015, 2018). The differences among the tree species, stand density, and even the application mode could be responsible for this. Differences in tree species could cause variation in the canopy structure, concomitantly influencing the simulation of canopy interception. Fathizadeh et al. (2017) demonstrated strong relations of I and S with c, the LAI, and the wood area index. However, only S and c were used in the RSGM to characterize the canopy structure of the plant upper space, which is far from sufficient for tree species with a more complex canopy structure. The addition of forest structure parameters (branch inclination, stem length, bark characteristics, leaf shape, and forest age) to canopy interception models tends to more accurately reveal how changes in tree species affect model simulations and better indicate the differences in ecohydrological components under different canopy structures.

Finally, the distinction in the model application mode can be considered as the fundamental cause of differences in APE between the present study and previous works. In this study, the RSGM was run on an event basis, to estimate the cumulative I even when fixed climatic parameters were used, rather than directly calculating total I (Liu et al. 2015). The application mode used in the latter approach may allow annual total I to be determined more accurately. However, it is not possible to elaborate on the variations in the canopy water flux for a single interception event. This mode may be successful in simplifying modeling and exploring gross interception, because I is most often estimated over a season or a year, instead of a single rainfall event (Fan et al. 2014). Model applications with simplified parameters would thus be useful (Mużyło et al. 2012), but their validity in terms of physical and practical aspects remains to be discussed. Besides, comparing the use of different models to determine the best combination of model type, application environment (region, species, dormant or growing season, and rainfall patterns), and usage mode will facilitate the development of Gash-type models.

In general, the operational performance of RSGM-G for calculating cumulative I was clearly superior to that of RSGM-E, and slightly better than that of RSGM-M. This implies that using constant climatic parameter values in the RSGM to simulate the cumulative canopy interception on the basis of single events during the growing season in the studied region and considering the studied tree species could lead to better performance. A part of these results contradicts those reported by Jackson (2000), who applied the sparse Gash model to single trees using long-term (3 years) and monthly separately to estimate the gross interception and found that the error of the former exceeded that of the latter. This could result from a difference in the length of the simulated period. Furthermore, in this study, the total interception during the study period was estimated on an event basis, regardless of the model version used, rather than on a month-to-month basis as reported by Jackson (2000). Moreover, previous research focused only on the effects of time-step variability in the rainfall rate and neglected the consideration of the evaporation rate. The combined efforts of those parameters may lead to more complex effects and, subsequently, reduce the error, as noted in the present study.

Changes in seasons and weather patterns may also result in changing climatic and canopy parameters, and subsequent errors would be counteracted in model calculations. Thus, the modeled errors of annual interception using fixed parameters are considered to be minimal, as explained by Wallace & McJannet (2008), Ghimire et al. (2012), and Fan et al. (2014). However, in the present study, canopy parameters in the RSGM (S and c) were fixed regardless of the model version used, because the study period of the present research is the growing season rather than the entire year. Therefore, the satisfactory performance of RSGM-G in calculating the cumulative interceptions was considered to arise from the mutual compensation between the overestimation of smaller rainfall events and the underestimation of larger rainfall events (Figure 3). Simultaneously, an unknown mutual compensation between climatic parameters might occur during the modeling process, and this effect is not from the climate and canopy parameters as previously reported, because the canopy parameters were fixed in this study. This may lead to less calculated errors when using constant parameters to simulate cumulative interception on the basis of a single event. Nonetheless, using short-term parameters may slightly weaken this mutual compensation effect, resulting in a higher error for RSGM-E than for RSGM-M and RSGM-G. Consequently, using fixed climatic parameters in the model calculation, the accuracies of individual intercepted events were also improved (Table 5 and Figure 3), although this improvement was still inadequate to meet the expected requirements. Furthermore, this modeling approach will improve the user-friendliness of the model, because it is less complex, less computationally difficult, and cost-effective. Additionally, it requires tests to be conducted in more areas and includes more tree species, as this study only demonstrated the effectiveness for Pt, Po, and At, while Zhang et al. (2018) suggested using storm-based parameters (both canopy and climatic) to run the model in shrub forests.

A previous study demonstrated that the model operates better in storms in which I is strongly dependent on S (canopy structure conditions), whereas meteorological parameters dominate the modeling accuracy when the storms could rapidly saturate the canopy (Sadeghi et al. 2015). A study indicated that for the dormant season with lower S-values than the growing season, storms that saturated the canopy occurred more frequently and climatic parameters had a greater influence on interception (Ma et al. 2019). In the present study, better model results were obtained using fixed climatic parameters, when the canopy parameters were constant, which is closely similar to the changes in canopy structural conditions during the dormant period. This implies that such use of the model may also lead to a positive result during the dormant period for Pt, Po, and At. However, given the possible differences in rainfall patterns between the dormant and growing seasons in the study area, this is still a speculation that requires further experimentation for verification.

Even though fixed climatic parameters were used in this study, the RSGM performed poorly in estimating individual interception events. The detailed reasons for this have been discussed by Linhoss & Siegert (2020), such as measurement errors and conceptual errors in the model. This result indicates that the modeling canopy interception or even the entire ecohydrological cycle process remains a great challenge, especially for extreme precipitation events (few but intense rainfall events) that are expected to become more frequent in the context of climate change. Hence, increasing the simulation accuracy of the RSGM for a single rainfall event is still a pressing problem.

The sensitivity analysis showed that the cumulative canopy interception is most sensitive to S parameter, whereas climatic parameters (i.e., and ⁠) have lower influence on the estimated interception than S, but generally have greater influence than S_t and p_t, and, at times, have greater influence than c. Similar sensitivity results were reported by Ma et al. (2019) and Liu et al. (2018) but not by Fan et al. (2014) and Su et al. (2016). This difference can be attributed to the rainfall patterns. Sadeghi et al. (2015) proposed that I was controlled mainly by climatic parameters during large storms but S played a more significant role during small storms. The amount of rainfall recorded in the present study (427.2–497.2 mm) was similar to that reported by Ma et al. (2019) and Liu et al. (2018). It was significantly less than that (1,492.1 mm during 1 year and 1,574.0 mm during the growing season) reported by Fan et al. (2014) and Su et al. (2016), respectively. Hence, if extreme events with less small rainfall become more frequent with climate change, particularly in semi-arid regions with scarce rainfall resources, it is necessary to investigate the possibility of enhancing the accuracy of the RSGM in terms of estimating S and reasonably parameterizing the canopy structure. Recent developments in measurement technology have been allowing direct quantification of S (Van Stan et al. 2013). Conversely, if the frequency of intense rainfall tends to increase with climate change (Limousin et al. 2008), methods for correctly and conveniently estimating and climatic parameters for forests will assist RSGM modeling. Pereira et al. (2016) indicated that the wet-bulb approach was a good alternative for estimating the maximum evaporation rates within very sparse forests with a narrow canopy depth. However, the Penman–Monteith approach seemed preferable when the canopy was not fully ventilated. Given its ability to minimize unnecessary simulation errors due to different methods, the Penman–Monteith approach was uniformly used for forests with different plant densities in the present study. Furthermore, the choice of storm separation time could affect the calculated values of (Wallace & McJannet 2006), thereby influencing the modeled results. To ensure that the canopy remains dry as much as possible as assumed by the model, an interval of 8 h was maintained between all rainfall events during the study period, which is slightly larger than those maintained in previous studies, which were 3 h (Ghimire et al. 2017), 4 h (Wallace & McJannet 2008), and 6 h (Ma et al. 2019). Wallace & McJannet (2006) reported that uncertainty in the choice of the interval time only impacts the estimated interception by less than 10%.

Although the experimental plots were not far from each other, the presented of Pt was different from that of the other two species, which can be explained by a malfunction of the data collector, and resulted in several rainfall events that were not monitored by the automatic weather station at Pt. Thus, these were directly deleted during the modeling process. Besides, the growing season of a single year was considered in the present study, and to the best of our knowledge, very few studies had reported that the interannual variation in rainfall patterns is small for the study region, whereas the opposite is probably true. The study area has a temperate monsoon climate, and rainfall is mainly influenced by the southeastern monsoon and simultaneous rain and hot climate (Cheng et al. 2016). This implies that there is variability in rainfall patterns across years and seasons in the study area, but we speculated that as long as the climate of the study area was characterized by simultaneous rain and hot climate during the study period, the complementary effect between and would be maintained and the conclusions of this study could be considered effective. Therefore, it is beneficial to encourage argumentation of these findings in different climate-type regions for the application and development of the model. However, these should not affect the primary goal of the study, which explored the effect of time-step variability in climatic parameters on modeling accuracy, rather than the modeling diversity among different tree species.

This study was conducted to examine the reasonableness of the assumption in the RSGM that the meteorological parameters are the same for all storms, and to explore the differences in the estimation results for single storms when the RSGM was driven by three time-step climate parameters, respectively. The obtained results indicated that all the indicators used to evaluate the model's accuracy were improved if the time step of the climatic parameters (⁠ and ⁠) involved in the modeling were increased when the models were run on an event basis, regardless of whether the model was run for Pt, Po, or At. This indicates that the assumption in the RSGM is correct in the study region during the growing season. Fixed climatic parameters were more suitable for predicting cumulative interception in Pt, Po, and At during the growing season in the studied region, whereas meteorological parameters, when averaged for a single event, cannot be usefully applied in the RSGM to obtain satisfying estimations. Nonetheless, the prediction accuracy of the RSGM for individual intercepted events was poor regardless of the time-step variability used. The satisfactory performance obtained using fixed climatic parameters can be associated with a compensation between the overestimation of small rainfall events and the underestimation of large rainfall events. These results indicate that when planning forest restructuring and water resources rational allocation initiatives, it is more appropriate to use fixed climatic parameters to run the RSGM to estimate I for Pt, Po, or At in Northern China during the growing season. Further studies are required to confirm this conclusion across the widest possible range of species, regions, and temporal scales to clarify the detailed reasons for this effect. Moreover, future studies could attempt to prove a conjecture that unknown complementary effects between climate parameters on long time scales may have contributed to such better model performance when fixed climate parameters are used, which would lead a better understanding and application of the relevant assumptions in the RSGM.

This work was funded by a project of the Key Laboratory of Water Saving Irrigation Project of the Ministry of Agriculture (Farmland Irrigation Research Institute of Chinese Academy of Agricultural Sciences, No. FIRI2018-04). We appreciate the constructive comments from the editors and anonymous reviewers that helped to improve the quality of this paper.

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