1. Introduction

The amount of precipitation intercepted and subsequently evaporated from a forest canopy is considerable, accounting for 29% of the incident precipitation at Plynlimon Forest, United Kingdom (Calder 1990). Canopy interception is a critical component of a forest’s water budget, affecting the amount of water available to the understory and soil. The structural characteristics of the forest canopy reduce and spatially redistribute the overall water input to the underlying area (Lloyd and Marques 1988; Herwitz and Slye 1995; Loescher et al. 2002; Abrahams et al. 2003). Canopy structure has been documented to be a key control on the subcanopy water flux, affecting mineral and trace-gas fluxes, surface runoff, and erosion (Whelan and Anderson 1996; Levia and Frost 2003).

The amount of precipitation lost to canopy interception and evaporation is important in determining the water balance of a forested area (Calder 1976, 1977; Stewart 1977; Dolman 1987). Many forest canopies are highly coupled to the overlying atmosphere, which enhances moisture exchange; a moist canopy will readily evaporate water into the surrounding air (Rutter 1967; Stewart 1978; Harwood et al. 1999). Several recent studies have suggested that certain canopies, particularly those in tropical climates, may be decoupled to the atmospheric boundary layer (e.g., Derbyshire 1999; Kruijt et al. 2000; Delage et al. 2002). The precise mechanism behind this decoupling is still unclear, as is its applicability to canopies other than those in the above studies. Since interception loss varies with species (Lankreijer et al. 1993; Liu 1998; Wei et al. 2005), accurate measurements can aid predictions of the consequences of land-cover changes. Tree growth, streamflow, groundwater recharge, and water stress are closely related to evaporation, which is in turn strongly correlated to the canopy storage capacity (Halldin et al. 1984).

While one can use throughfall and stemflow measurements to calculate interception loss, this requires frequent data collection and offers few opportunities to extrapolate results to other species or locations. To create more applicable formulas, researchers have constructed dynamic, analytic, and numerical models of interception loss. Rutter et al. (1971) was among the first to derive an interception-loss model, which was based on observations of a Corsican pine (Pinus nigra) stand. The Rutter et al. (1971) model was later generalized and provided accurate interception estimates for two coniferus (Douglas fir and Norway spruce) and three hardwood (one hornbeam and two oak) stands (Rutter et al. 1975). Domingo et al. (1998) found that the Rutter model’s estimates of interception agreed with measured values for several semiarid species. While a significant advance, the Rutter model requires a substantial number of input fields, making it difficult to use with routine meteorological data.

Several models developed more recently have overcome the limitations of the Rutter model. This study compares the results from three such canopy interception models against measured interception for a leafless deciduous stand in the mid-Atlantic region of the United States. The three models used are the Mulder (1985) model, the Gash et al. (1995) model, and the WiMo model of Hörmann et al. (1996). The Gash et al. (1995) model is an updated version of the Gash (1979) model that has been reformulated for sparse canopies. By comparing measured and modeled interception, this study will determine the degree to which each model may be generalized to leafless deciduous stands in a temperate winter climate.

Many studies have compared the performance of the Mulder (1985) model and the older Gash (1979) model. Lankreijer et al. (1993) ascertained that both models overestimated interception for a deciduous forest in the Netherlands and a coniferous forest in France. Dolman (1987) compared these models for an oak forest in the Netherlands and found that the Mulder model overestimated interception relative to both the Gash (1979) model and measured values. Hutjes et al. (1990) concluded that both models accurately predicted interception for an evergreen forest in the Ivory Coast. Liu (2001) compared the Liu (1997) model against the Gash (1979) and Rutter models. The Liu model performed favorably in the more than 20 canopies considered, yet required fewer input variables and contained simpler formulas than either the Gash or Rutter model. The WiMo model has received relatively little attention in the literature and has seldom been compared with other interception models. Few studies have compared interception models against measurements taken in a deciduous stand in the leafless season. The canopy intercepts a far lower fraction of the incident precipitation during the leafless season, yet interception in this season is still a critical component of the water balance. Therefore, whether existing interception models can provide accurate predictions during the leafless season is of importance.

2. Study area

The experimental forest plot (800 m²) was located in the Fair Hill Natural Resource Management Area in Fair Hill, Maryland (39°42′N, 75°50′W) at an elevation of 72 m above sea level (Fig. 1). The rectangular study plot was nearly level with a stand density of 225 trees ha⁻¹ and a stand basal area of 36.8 m² ha⁻¹, indicating that there were relatively few but large trees within the study plot. The canopy trees had a mean diameter at breast height (dbh, 1.37 m above ground level) of 40.8 cm and a mean height of 27.8 m. The mean bark thickness of the canopy trees was 7.0 mm. Fagus grandifolia Ehrh. (American beech) was the most common tree species within the plot, accounting for approximately 50% of the canopy trees. Liriodendron tulipifera L. (yellow poplar) was the second most common species, constituting approximately 25% of the canopy trees. The remaining 25% of canopy trees were composed of Quercus velutina Lam. (black oak), Acer rubrum L. (red maple), and Acer saccharinum L. (silver maple).

The Fair Hill Natural Resource Management Area is close to the Atlantic coast and experiences a temperate climate. The mean annual precipitation is 1221.5 mm and precipitation does not vary greatly with season. Summer is the wettest season (324.1 mm total for June, July, and August) and winter the driest (274.1 mm for December, January, and February). Snowfall occurs almost exclusively in winter, and the annual total (350.5-mm depth on average) is often dominated by only a few storms. The mean January (July) air temperature is −0.6°C (24.6°C). The growing season averages 191 days in April through October.

3. Materials and methods

c. Wet-canopy evaporation

In this and all subsequent equations, a horizontal line over a quantity X (i.e., X) denotes a time average of that quantity. Values for all parameters and constants are given in Table 2. We used the Penman–Monteith equation given in Lankreijer et al. (1993) to calculate the wet-canopy evaporation as

where E′ is the evaporation rate (kg m⁻² s⁻¹), D is the slope of the saturated water vapor pressure curve at the hourly mean air temperature (T) (Pa K⁻¹), R_n is the hourly mean net radiation (W m⁻²), C_p is the specific heat of the atmosphere at constant pressure (J kg⁻¹ C⁻¹), e_s and e_a are the saturation and actual vapor pressure (Pa), respectively, r_a is the aerodynamic resistance (s m⁻¹), γ is the psychrometric constant (Pa K⁻¹), and λ is the latent heat of vaporization (J kg⁻¹). Here R_n was estimated from measured shortwave radiation values and longwave radiation calculated from the Angstrom equations.

The r_a, term in Eq. (1) has traditionally been approximated as the aerodynamic resistance for momentum

where r_a,_M is the aerodynamic resistance for momentum (s m⁻¹), k is the von Kármán constant, u is the wind speed (m s⁻¹), z is the measurement height (m), d is the zero-plane displacement height (m), and z₀,_M is the roughness length for momentum (m). Rutter et al. (1975) used this equation to estimate r_a for both leafed and leafless canopies. Lankreijer et al. (1993) found that using the aerodynamic resistance for heat (r_a,H) instead of r_a,_M improved estimates of interception in both the Mulder (1985) and Gash (1979) models for an oak canopy in the Netherlands. Lankreijer et al. (1993) calculated the r_a,_H as

where z₀,_H is the roughness length for heat (m). We believe that using Eq. (3) instead of Eq. (2) to approximate r_a in Eq. (1) is appropriate for our leafless mixed deciduous canopy and will improve all three models’ results.

Finally, we converted E′ to a value of millimeters per hour to match our precipitation measurements. The storm-averaged evaporation rate (E′) was quite low for the December and January storms because of the low values of incident shortwave radiation during the winter season (Table 1). The average evaporation rate increased rapidly in February and March as more energy became available to evaporate water from the canopy. The seasonal trend in R_n accounted for approximately 70% of the variance in E′. This indicates that the wet-canopy evaporation during these storms depended primarily on the seasonal cycle of solar irradiance and not on other meteorological variables (e.g., relative humidity or wind speed). Averaged over 1 December 2004–30 April 2005, E′ was 0.07 mm h⁻¹, which is equivalent to 613 mm yr⁻¹ or 50% of the mean annual precipitation at the site.

4. Model descriptions

a. Common terms

We define c to be the fraction of the canopy covered, or

Gash et al. (1995) used this relationship to convert a measured value of canopy cover to a coefficient of free throughfall. Each of the models calculates E′ as in Eq. (1). The amount of precipitation striking the canopy during each storm is

For the Gash et al. (1995) and WiMo models, the amount of precipitation diverted to stemflow is

for those storms that saturate the canopy. Stemflow is neglected for all storms in the Mulder (1985) model and for storms that do not saturate the canopy in the Gash et al. (1995) and WiMo models.

b. Mulder (1985) model

Mulder (1985) developed a numerical model (hereafter the “Mulder model”) notable both for its use of standard meteorological variables to derive interception loss, as well as its ability to maintain a moist canopy between storms by calculating a running water balance. For each day, separate averages of hourly R_n and E′ are maintained for rainy and dry periods. Rainy periods are defined as those hours when the Geonor gauge recorded more than 0.1 mm of precipitation. The ability to distinguish between rainy and dry conditions is a key difference between the Mulder model and the Gash and WiMo models.

Precipitation is summed over the day and then evenly divided into small showers of equal duration (t_shw). The number of showers is defined as the number of rainy periods bounded by at least 2 h of dry conditions. Showers continuing through the end of the day are considered to have stopped at midnight. Showers beginning in the first (final) two hours of a day are (are not) counted. The model distributes the showers and dry intervals evenly throughout the day. All dry intervals are initially of equal duration (t_dry). The length of the last dry interval in each day is averaged with the first dry interval in the following day. Half of the averaged dry interval is placed in each day, so that every day effectively begins and ends with a shortened dry interval.

All showers in the same day have a constant hourly precipitation rate, equal to the mean hourly precipitation rate during rainy periods (P′_r). The mean hourly rate of precipitation striking the canopy is therefore

consistent with Eq. (5).

Each shower begins with the canopy in the wetting-up phase. The canopy can only become saturated if P′_υ is greater than the mean evaporation rate during rainy periods (E′_r). If this condition is met, the model calculates the time required for the canopy to reach saturation (t_sat), given the amount of water initially on the canopy (C_wi) (Table 3). If t_sat > t_shw or if P′_υ ≤ E′_r, the canopy does not become saturated and the total interception for the shower is given by the interception for the wetting-up phase (I_w); C_wf represents the amount of water on the canopy at the end of the shower. If the canopy reaches saturation, the canopy spends the remaining time (i.e., t_shw-t_sat) in the saturation phase. In this case, C_wf is equal to S_c and the total interception for the shower is the sum of I_w and the interception during the saturation phase (I_s).

After the shower ends, the canopy moves into the drying-out phase. The canopy water at the end of the drying-out phase is calculated by C_wd, given C_wf and the mean evaporation rate during dry intervals (E′_d). The value C_wd becomes C_wi at the beginning of the next shower, so that a running water balance is maintained over the entire simulation period.

We stipulated that the canopy was completely dry at the beginning of the simulation period (1 December), such that for the very first shower C_wi was equal to zero. Sufficient wetting and drying cycles occurred before the beginning of our first storm (7 December) that the initial condition of the canopy is of little consequence.

d. WiMo model

Herwitz and Slye (1995) recognized the effect of wind-driven precipitation on interception, a factor that neither the Gash nor the Mulder model takes into account. Hörmann et al. (1996) presented a model that does incorporate the influence wind-driven precipitation, named “WiMo.” As described in that study, the WiMo model uses the same underlying equations as the Gash (1979) model, but adds the ability to vary S_c with the maximum sustained wind speed during a rainstorm (u_max). Hörmann et al. (1996) found that WiMo proved more accurate than the Gash (1979) model for a beech forest in northern Germany.

We have updated the WiMo model’s physics to match the equations in Gash et al. (1995), which are better optimized for our sparse canopy. The WiMo model calculates the S_c for each storm as a function of u_max via a regression equation linking the optimum storage capacity (S_o) and u_max. We obtained u_max from our 5-min meteorological observations. To find the S_o for each storm, WiMo employs a “bucket model” that calculates throughfall at each hourly time step i (Tⁱ_f) during the storm as

where Cⁱ_w is

If Cⁱ_w exceeds S_c, it is reset to S_c at the end of the time step, after the excess has been added to the throughfall term.

A computer program found S_o for each storm by running the above bucket model for each S_c between 0.1 and 4.0 mm, in increments of 0.01 mm. For each S_c, T_f was compared against the measured value from our stand. The S_c that produced the lowest absolute difference between T_f and the measured value was judged to be the S_o for that storm. Ordered pairs of S_o and u_max from each storm were used to generate a regression equation for S_c as a function of u_max.

5. Results

We derived a logarithmic regression equation (r² = 0.586, p < 0.05) from the output of the WiMo bucket model:

The boundary conditions of this equation and its implications for the response of a leafless canopy to wind-driven precipitation will be discussed in section 6.

We obtained interception values from each model for each storm in Table 1. There is little explanation for the models’ pattern of over- and underprediction for individual storms (Table 4). All three models twice overpredicted interception during high-volume events (22 March, 1 April), while underpredicting interception for two others (9 December, 11 January). During these four storms, the high precipitation rate quickly saturated the canopy, which remained saturated for the duration of the event. This reduced the total interception, as a saturated canopy can intercept at most the amount of water that evaporates from it, and during these storms P′ was much greater than E′. Similarly, the models both overpredicted (7 January) and underpredicted (9 February) interception for low-volume storms, in which the canopy was either slow to reach or never reached its storage capacity. No significant correlation was found between the models’ differences for individual storms and any single meteorological variable in Table 1.

All models tended to overestimate interception during January, March, and April, while underestimating interception for the February storm and one of the December storms (9 December). The models showed the greatest overestimates when the measured percentage of P_g was low (3 January, 1 April, 6 April) and the greatest underestimates when the measured percentage was high (9 December, 9 February). These overestimates and underestimates indicate a lack of flexibility in each model, which will be discussed further in section 6.

We define P_G to be the total precipitation summed over all 11 storms (i.e., ΣP_g). To evaluate each model’s overall performance, we calculated 1) the total interception over the study period for models and measurements; 2) the percent error from the total measured interception; 3) the percentage of P_G intercepted; and 4) the difference in this percentage between measured and modeled values. We also calculated the percentage of P_g intercepted for each storm and computed the difference between measured and modeled values. We used the difference (in millimeters) between measured and modeled values for each storm to calculate the standard deviation, skewness, kurtosis, and Nash–Sutcliffe model efficiency (Nash and Sutcliffe 1970) (Table 4). A normal Gaussian distribution was assumed to have a kurtosis of zero. The Nash–Sutcliffe efficiency does not include the 9 February storm. The models performed equally poorly for this storm and its inclusion would have resulted in negative Nash–Sutcliffe model efficiencies for all models. Removing this storm adds an equal amount to each model’s efficiency value.

The Mulder model was the most accurate in terms of the total interception, overestimating the measured value by only 3.2%. The WiMo model underestimated the total measured value by 9.5%. The Gash model lagged the other two, underestimating the total measured interception by 17.8%. All models predicted the percentage of P_G intercepted to within 1.1% of P_G of the measured value (5.7%). Each model’s differences formed a negatively skewed distribution, due to the 9 February outlier. It is interesting to note that while the Mulder model was the most accurate overall, it had the highest standard deviation, the lowest skewness, and a low kurtosis for its differences for individual storms. The Mulder model also had the lowest Nash–Sutcliffe model efficiency. These statistics imply that the Mulder model’s differences for individual storms were typically larger than the other two models’ differences.

When running sums of interceptions were considered, the models tracked the measured values relatively well (Fig. 2). The models oscillated between overestimating the measured running total during late December and January and underestimating it during February and March. It was only in April that the models converged toward to the measured total.

In section 3d, we noted that some of our stand and canopy parameters were adapted from previous studies. While we believe that these parameters are valid for our stand, we conducted a sensitivity analysis to examine whether the assumed parameter values had affected the models’ estimates. We conducted additional runs of each model with modified values of each parameter that was inferred or derived from a previous study. The modified values represent the bounds of a reasonable error range for the parameter in question. The parameters in the Penman–Monteith equation were multiplied and divided by 2, as were the stemflow parameters c_s and S_t; S_c(c_t) was modified by adding or subtracting 0.5 (0.05). Only one parameter was changed at a time, as nonlinear interactions between parameters were estimated to be negligible.

The results of the sensitivity analysis are expressed as a ratio (Table 5),

where F is the ratio, I_new is the total interception after the modification, and I is the total interception before the modification. All three models were most sensitive to changes in c_t. The WiMo model was not tested for changes in S_c because the model calculates S_c itself. The Gash and WiMo models showed no sensitivity to changes to c_s because all rainstorms provided sufficient precipitation to saturate the trunks even at half of our original value of c_s, leaving stemflow to equal S_t (Table 3).

We note that changes to individual evaporation parameters had little or no effect on the models’ estimates of total interception. Therefore, the differences between measured and modeled values (Table 4) are not due to our assumed values for the evaporation parameters. The models were more sensitive to changes in S_c and c_t. Our values for these two parameters are potentially a significant source of error. We continue to believe that the values specified for S_c and c_t are appropriate for our canopy, for the reasons given in section 3d.

6. Discussion

A mixed deciduous forest is naturally more susceptible to small-scale variations in throughfall than a homogeneous stand (Jackson 1971; Lloyd and Marques 1988; Lloyd et al. 1988). Throughfall can vary across a mixed stand by a considerable percentage of P_g, particularly for small storms, and this must be taken into account when model predictions are compared against “actual” values (Lloyd and Marques 1988; Carlyle-Moses et al. 2004). While we randomly redistributed the throughfall gauges in the plot after each rainstorm to minimize any spatial throughfall variability, our gauges covered less than 1% of the stand area. Lloyd and Marques (1988) defined the probable standard error of estimating throughfall using this roving gauge method as

where σ is the probable standard error of the measured values as a percentage of P_G, σ_i is the standard error of the measured values as a percentage of P_G, N is the total number of sampling points (304), n is the number of gauges (30), and m is the number of times the gauges were relocated (11). The probable standard error for this study is 8.1% of P_G, which is abnormally high due to the 9 February event; without this event σ would be 4.1% of P_G, which agrees with the values given in Lloyd and Marques (1988) and Bryant et al. (2005). All three models’ predictions of the percentage of P_G intercepted (Table 4) are within the probable standard error of our measurements.

Our stemflow measurements represent an additional source of measurement error. We measured stemflow from only one tree in the plot. This tree had a height and dbh near the stand average and was of the same species (American beech) as the majority of canopy trees. While one tree represents the smallest of samples, stemflow is not a critical component of interception in our stand. Kittredge (1948) and Hörmann et al. (1996) agree that the percentage of P_g diverted to stemflow in a beech forest is at most 10%. Kittredge (1948) found that for a storm with a P_g of 12 mm, only 7.5% became stemflow. Over all 11 storms, measured stemflow in our stand was 5% of P_G. While we acknowledge that our limited sample of one tree cannot properly represent the variability in stemflow across the stand, that variability is almost certainly a negligible portion of interception in this stand.

The discrepancies between the models’ predictions of interception must be a direct result of each model’s basic assumptions. The WiMo model uses the same underlying equations as the Gash model, yet it provided a more accurate estimate of the total interception. It is highly probable that this advantage is due to the WiMo’s ability to vary S_c with u_max. Whereas Hörmann et al. (1996) found that an increase in u_max caused a decrease in S_c, our study found that S_c increased logarithmically with u_max [Eq. (10)]. Hörmann et al. (1996) attributed their decrease in S_c to stronger winds shaking more water from the canopy leaves, an effect that is not present in our leafless stand. Instead, we believe that as u_max increases, precipitation falls at a lower angle relative to the horizontal, increasing the effective canopy area and allowing the canopy to intercept a greater percentage of the P_g (Herwitz and Slye 1995). Theoretically, the wind effects should be represented as an increased value of c (decreased value of c_t). The WiMo model varies S_c, not c, with u_max, and so the WiMo model represents the effect of wind speed on interception as an increased value of S_c for a constant c. The logarithmic relationship between S_c and u_max is physically reasonable: At low (high) wind speeds, a small increase in the wind speed will have a large (negligible) effect on the angle at which the rain falls relative to the horizontal.

The regression equation relating S_c and u_max has a nonsensible boundary condition, as S_c is negative for storms with u_max less than 3.1 m s⁻¹. None of the 11 storms considered had a u_max below 3.1 m s⁻¹, and so the regression equation in the Hörmann et al. (1996) bucket model fails to properly account for them. Hörmann et al. (1996) experienced similar problems, as their S_c grew improbably large for low values of u_max. Evidently, storms with u_max less than 3.1 m s⁻¹ are quite rare in this stand during the leafless season, and so this boundary condition is not of great concern.

The Mulder model predicted the total interception more accurately than either the Gash or the WiMo model, and so might be considered the best interception model for this canopy under these conditions. While Mulder (1985) provides a different parameterization than Gash et al. (1995), it is also important to note that the Mulder model maintains a running water balance between storms, while the Gash and WiMo models do not. It is possible that the Gash and WiMo models’ assumption that the canopy is always completely dry prior to each storm is not valid in this stand. An experiment that compared these models’ performance for a set of storms that occurred immediately after one another, such that the canopy would not have the opportunity to dry, would highlight the effects of this assumption.

While all three models predicted the percentage of P_G intercepted to within 1.1% of P_G of the measured value, it may be that their accuracy can be attributed to the particular set of rainstorms in this study. The models frequently overestimated or underestimated interception for individual events (Table 4). Only 23 December, 27 March, and 1 April were predicted with any real accuracy. The standard deviation of each model’s differences for individual storms is approximately 1 mm. This is quite high considering that the least accurate model overall (the Gash model) underestimated the total precipitation by only 3.4 mm. The WiMo model had the lowest standard deviation and the highest kurtosis value. These statistics indicate that the distribution of the WiMo model’s differences had a higher peak around zero, where zero is the measured value. The Mulder and Gash models’ differences, however, were more uniformly distributed across their space. The WiMo model also had the highest Nash–Sutcliffe model efficiency. The Nash–Sutcliffe efficiency compares the variance of the residuals (i.e., the variance of the difference between measured and modeled values) against the initial variance of the measured values. An efficiency score of unity represents identical measured and modeled values. A high score for the WiMo model indicates that the WiMo model’s estimates for individual storms were, when considered together, reasonably close to the measured values. The Mulder model had the lowest Nash–Sutcliffe efficiency, the highest standard deviation, and a low kurtosis. These metrics imply that the Mulder model’s accurate estimate of the total interception was a result of the offsetting of its inaccuracies for individual storms over the course of the study.

The WiMo model’s ability to optimize S_c improves its predictions of interception, both for individual storms and the seasonal total, but restricts its use in stands where wind measurements are difficult to obtain. The WiMo model thus represents a definite improvement over the Gash model in this stand, but its applicability to other leafless stands is predicated upon the availability of wind data and the determination of a suitable regression equation between S_c and u_max.

As mentioned previously, the measured percentage of P_g intercepted varied greatly from storm to storm. The models overpredicted interception when this percentage was much lower than the fraction of canopy covered (c) and underpredicted interception when the percentage was much higher than c. Over all 11 storms, the canopy intercepted 5.8% of P_G, which is lower than c (10%) and closer to the models’ predictions. (The canopy should intercept somewhat less than c, since the canopy does not intercept all incident precipitation while saturated.) In other words, the percentage of P_g intercepted converged to a value less than c over the course of the study period. This is evident from Fig. 2. The fixed coefficient of free throughfall (c_t)—and consequently c [Eq. (4)]—constrained the models’ ability to accurately determine interception during storms such as 9 February, as the modeled canopy could not possibly intercept more precipitation than the models allowed to strike it [Eq. (5)]. The c_t establishes a hard upper boundary on interception in all three models. This limit does not exist in reality, as wind-driven events can increase the effective canopy area and allow the canopy to intercept more than P_υ (Herwitz and Slye 1995).

The models accurately predicted the total interception over the study period, but not the interception for the individual storms. The key difference between the total interception and the individual storms is that the measured percentage of P_g intercepted was less than (greater than) c for the total interception (individual storms). The percentage of P_G intercepted is the critical value here, since these models are most often used to estimate interception over an entire season rather than for a single storm. Since all three models predicted the percentage of P_G intercepted to within the probable standard error of the measurements, we believe that all three models will perform adequately for a leafless stand of this type in this climate, as long as c_t is appropriately specified.

7. Conclusions

This study compared the Mulder (1985), Gash et al. (1995), and WiMo (Hörmann et al. 1996) interception models for a leafless mixed deciduous forest in the eastern United States. Each model predicted interception for 11 rainstorms during the winter and early spring of 2004/05. These values were compared against measurements collected approximately 2 h after each storm.

All three models demonstrated large differences for individual storms (Table 4) that bore no relationship to any applicable meteorological variable (Table 1), but were connected to the measured percentage of P_g intercepted. The models underestimated interception when the percentage of P_g intercepted was much greater than the canopy cover c (10%) and overestimated interception when the percentage of P_g was much less than c. While the percentage of P_g intercepted varied for individual events—leading to the models’ differences—it converged to a value less than c as the sample size of storms grew, which allowed the models to accurately predict the total measured interception. This underscores the importance of selecting an appropriate value of c (or c_t) for these models.

The Mulder model overestimated the measured percentage of P_G intercepted by 0.1% of P_G; the WiMo model underestimated the measured percentage by 0.6% of P_G; and the Gash model underestimated by 1.1% of P_G. The WiMo model’s advantage over the Gash model is most likely due to the former’s ability to optimize the canopy storage capacity for the maximum sustained wind speed during a storm. In this stand, the storage capacity increased logarithmically with the maximum wind speed. The Mulder model gives the most accurate value of total interception, although its high standard deviation and low kurtosis imply that it was less accurate for individual storms. We hypothesize that the Mulder model’s accuracy is due at least in part to its ability to maintain a moist canopy between storms.

Despite differences in underlying assumptions and complexity, each model successfully predicted the percentage of P_G intercepted to within the probable standard error of our measurements. We therefore conclude that all three models are appropriate for use in predicting leafless-season interception in deciduous forests in the eastern United States.