## Abstract

Evapotranspiration (ET) is the major cause of wetland water loss. The Penman–Monteith model is the most suitable ET model for wetlands. However, its accuracy depends on canopy resistance. Here, we studied the *Phragmites australis* community in the Liaohe Delta, northeastern China. We used flux and environmental data from the Panjin Wetland Ecosystem Research Station, and physiological and ecological parameters. Canopy resistance was calculated by the Penman–Monteith model, and canopy resistance and its influencing factors were analyzed. We created a canopy resistance model, named the *Phragmites australis* wetland (PW) model, using leaf stomatal resistance, leaf area index (LAI) and environmental factors. The PW model differed from the traditional Jarvis model in that the effective LAI was added, and the stomatal resistance was changed from a fixed to dynamic value and the environmental factors only contained two items: solar radiation and water vapor pressure difference. The PW model allowed the conversion from leaf scale to canopy scale. A comparison of the PW model with the Jarvis model parameters showed that accuracy improved significantly: *R*^{2} values increased from 0.56 to 0.74. The model can provide parameters for *P. australis* ET models and provide a new method for accurate estimation of wetland ET.

## INTRODUCTION

Evapotranspiration (ET) is the major cause of wetland water loss and its accurate estimation is of prime interest for understanding wetland water balance and water transport in a soil–plant–atmosphere continuum (SPAC) system (Yu *et al.* 2008). The *Phragmites australis* ET process can be divided into leaf, plant, canopy, ecosystem, and regional and other spatial scales. It is important, although difficult, to achieve accurate process parameters at different scales to simulate wetland ET (Yu *et al.* 2014). There are significant differences in the daily ET of *P. australis* in different locations. For example, daily ET ranged between 0.5 and 6.5 mm d^{−1} in a reed prairie wetland of northcentral Nebraska, USA (Burba *et al.* 1999); the mean daily ET during the growing season was 2.32 mm d^{−1} in Liaohe Delta, China (Zhou *et al.* 2010); ET exceeded 20 mm d^{−1} under extreme weather conditions in the Baiyangdian wetland, China (Xu *et al.* 2011); the average ET rate during the growing season was 4.4 mm d^{−1}, with a maximum daily rate of 8.2 mm d^{−1}, in a riparian wetland of the Republican River basin of south-central Nebraska, USA (Lenters *et al.* 2011); and the mean annual wetland ET was 7.0–10.6 mm d^{−1} in subtropical Australia (Headley *et al.* 2012). Coupling parameters in the SPAC system is key to accurately simulating ET at different scales in a reed wetland. Previous studies of surface parameterization of the reed wetland to estimate ET at different spatial scales are insufficient. Further exploration of the methods and the parameterization of ET modeling can provide an accurate assessment of wetland water loss and its changes in a *P. australis* community.

Canopy resistance (*r*_{c}) reflects the resistance to vapor flow through the canopy total leaf area required to oppose the process of water transition from the vegetation canopy to the reference height of the atmosphere. The *r*_{c} value depends on factors such as the plant genotype, climate, air resistance, and soil evaporation (Gharsallah *et al.* 2013). Canopy resistance has been often used to simulate ET in the Penman–Monteith model (Whitley *et al.* 2009); the accuracy of that model depends on canopy resistance and aerodynamic resistance (Yan *et al.* 2015), but there are no direct measurements and methods for calculating *r*_{c}. Three methods have been used to simulate the canopy resistance of plants in previous studies: (1) back-calculating from the Penman–Monteith model (Liljedahl *et al.* 2011); (2) scaling-up leaf stomatal resistance to canopy resistance based on leaf area index (LAI) or effective LAI (Zhang *et al.* 2011; Wei *et al.* 2013); and (3) simulating canopy resistance with the environmental factors such as solar radiation, air temperature, relative humidity (RH), vapor pressure deficit, and soil water content (Jarvis 1976; Noilhan & Planton 1989; Sun 1996; Leuning *et al.* 2008; Hua *et al.* 2015). The Jarvis model is the most widely used method for estimating canopy resistance (Alfieri *et al.* 2008). However, the applicability of models must be considered because of the differences in vegetation and geographical locations. Since few studies have assessed the adaptation of the models to canopy resistance in *P. australis* wetlands, and the accuracy of ET is determined by the canopy resistance of different ecosystems and environments, it is very important to simulate the regional ET in *P. australis* communities.

The Liaohe Delta wetland in northeastern China is covered by an area of approximately 900 km^{2} of *P. australis*, believed to be the largest reedfield in the world (Zhou *et al.* 2009). The study took the *P. australis* community as its research object in the Liaohe Delta wetland and considered the key scientific problem of how to achieve an accurate estimation of canopy resistance. Observations of ecophysiological characteristics of the *P. australis* community and environmental factors were analyzed, combining micrometeorological and vapor flux data with the microclimate gradient observation system and the eddy covariance system in the Panjin Wetland Ecosystem Research Station. The canopy resistance of *P. australis* was established with leaf stomatal resistance, LAI, and environmental factors and compared with the value calculated by the back-calculating of the Penman–Monteith model. The objective of the research was to provide a fitting method of canopy resistance, which allowed scaling-up from leaf to canopy level and the evaluation of accurate ET of *P. australis* in the wetland.

## METHODS

### Experimental site and data

The research site was located at 40°56′N, 121°57′E, at the Panjin Wetland Ecosystem Research Station, Institute of Atmospheric Environment, China Meteorological Administration, Shenyang, China. The station is located in the Liaohe Delta wetland (40°41′–41°27′N, 121°30′–122°41′E), northeast China (Figure 1) in a warm temperate zone with a monsoon climate. The *P. australis* at the research station is in good condition; the growing season and flooding time are from April to October; and in July, the height of *P. australis* is at its greatest, averaging 200–300 cm (Jia *et al.* 2016).

The station is equipped with a microclimate gradient observation system and an eddy covariance system. The eddy covariance system is installed at a height of 4 m. Its main features are a dimensional supersonic anemoscope, an open path CO_{2}/H_{2}O analyzer (Li-7700, Li-cor Inc., USA), and a data logger (Li-7550, Li-cor Inc., USA) with a sampling frequency of 10 Hz. The observation heights of the microclimate gradient system are at 1, 2, 4, 8, 16, and 30 m, and the observation terms include wind speed, air temperature, and RH at a sampling frequency of 10 min (Jia *et al.* 2017).

Data from 2015 and 2016 were used in this research and included the microclimate gradient data and 30 min flux data. The raw data from the eddy covariance system was converted to 30 min flux data by removing noise, revolving coordinates, WPL (Webb–Pearman–Leuning, Webb *et al*. 1980) adjustment and declining tendency with Eddypro 5.0.1 software (Li-cor Inc., USA). The latent heat flux (*λE*) was used for the ET flux.

### Measurement of leaf stomatal resistance and LAI

The diurnal photosynthetic and stomatal conductance dynamics of *P. australis* leaves were measured on sunny days from 08:00 to 18:00 at 1–2 h intervals in July and August 2015 and 2016. Each individual plant was delimited into five vertical layers and measured from the base to the top of the stem in height ranges 0–60, 60–120, 120–180, 180–240, and 240–300 cm, respectively (Figure 2). We selected three plants representative of the average growth of the *P. australis* community to measure leaf stomatal conductance (*g*_{s}) in each layer, using a portable photosynthesis system (Li-COR 6400, Lincoln, NE, USA). Three blades were selected in each layer for measurement, and the average value was the layer *g*_{s}. We also measured photosynthetically active radiation (PAR), atmospheric temperature (*T*_{a}), RH, saturated vapor pressure difference (VPD), and air CO_{2} concentration. The LAI was observed in the five layers of the *P. australis* community with a plant canopy analyzer (Lai2000, Li-cor, Inc., USA) on the same day. When the LAI was observed in each layer, it included the canopy LAI above this layer.

The leaf stomatal resistance (*r*_{s}) is the reciprocal of the leaf stomatal conductance (*g*_{s}):.

### Back-calculating from the Penman–Monteith model

The latent heat flux (*λE*) was measured with the eddy covariance system in *P. australis* wetland. The canopy resistance was obtained by reversing the Penman–Monteith model, using the measured *λE*, and the calculated value was taken as the measured value for testing the accuracy of the simulation.

*r*

_{c}is the canopy resistance (s/m),

*λE*is the ET flux (W/m

^{2}), Δ is the slope of the saturation vapor pressure curve (kPa/°C),

*e*

_{s}and

*e*

_{a}are the saturated vapor pressure and actual vapor pressure, respectively (kPa),

*ρ*is the air density (kg/m

^{3}),

*r*

_{a}is the aerodynamic resistance (s/m),

*γ*is the psychometric constant (kPa/°C),

*R*

_{n}is the net radiation (W/m

^{2}),

*G*is the ground heat flux (W/m

^{2}) and

*C*

_{p}is the specific heat of dry air at constant pressure (J/kg/°C).

*r*

_{a}with the Monteith–Obukhov model: where

*u*is the wind speed (m/s),

*Z*is the wind speed sensor height (m),

*d*is the zero plane displacement (m),

*d*= 0.63

*h*,

*h*is the plant height (m),

*Z*

_{0}is the surface roughness (m),

*Z*

_{0}= 0.3 (

*h*−

*d*),

*k*is the Karman constant and the general value is 0.4.

### Canopy resistance simulation methods

The reed wetland in the Liaohe Delta is flat with relatively homogeneous vegetation; the surface is fully covered with *P. australis* in July and August, which can be regarded as the single cover. In this paper, the canopy of *P. australis* was regarded as a ‘big leaf’, and the data selected for model establishment were under the conditions of LAI ≥3. A single source model for estimating canopy resistance was established, ignoring soil evaporation and assuming that the latent heat flux was mainly derived from the contribution of the vegetation canopy (Huang *et al.* 2007).

Jarvis (1976) considered the influence of environmental factors such as radiation, VPD, temperature, and soil water content to establish a canopy resistance model.

*r*

_{min}is the minimum stomatal resistance, canopy resistance,

*r*

_{s,i}is the stomatal resistance of each layer,

*F*

_{1}(

*X*

_{1}),

*F*

_{2}(

*X*

_{2}),

*F*

_{3}(

*X*

_{3}), and

*F*

_{4}(

*X*

_{4}) are environmental factors function (radiation, VPD, temperature, and soil water content, respectively) (Jarvis 1976).

In this paper, based on the Jarvis model, the canopy resistance was constructed as follows.

As stomatal resistance and LAI are measured in each layer of the plant, canopy resistance can be calculated by scaling-up leaf stomatal resistance to canopy resistance based on the effective LAI.

*r*

_{c}with measured data: where

*r*

_{c}is the canopy resistance,

*r*

_{s,i}is the stomatal resistance of each layer,

*R*(

*X*

_{f}) is the environmental factor function, and LAI

_{eff}is effective LAI.

Other meteorological data at the 4 m height of the microclimate gradient system are used in Equation (1).

## RESULTS

### Diurnal variation in stomatal resistance and environmental factors in leaves of *P. australis*

The diurnal variation in *r*_{s} of *P. australis* (observations on 3 July 2015 are used as an example) showed a vertical distribution, with lower *r*_{s} in the upper layers, gradually rising with proximity to the plant base; the *r*_{s} in layer A5 was the highest (Figure 3). The diurnal variation in PAR and VPD of *P. australis* in each layer generally showed single-peak curves, with lower values in the morning and evening and higher values at noon (Figure 4(a) and 4(b)). The higher PAR and lower VPD values were in the upper layers. Because of the shade cast by the upper leaves, PAR decreased and VPD increased in proximity to the plant base. The diurnal variation in *T*_{a} in each layer showed single-peak curves, with lower values in the morning and evening and higher values at noon (Figure 4(c)); the diurnal variation in RH showed ‘V’-shaped curves in each layer, with higher values in the morning and evening and lower values at noon (Figure 4(d)). Differences in *T*_{a} and RH among the five layers were, however, smaller.

The correlation between *r*_{s} and PAR and VPD was significant; the correlation coefficients were −0.694 and 0.528, respectively. The *r*_{s} decreased as PAR rose and increased as VPD rose in hourly scale (Figure 5(a) and 5(b)). The correlation between *r*_{s} and *T*_{a} and RH was not significant (Figure 5(c) and 5(d)). Previous studies showed that radiation and saturated VPD were key factors affecting *r*_{s} when the soil moisture was sufficient (Zhang *et al.* 2011). As the base of *P. australis* is covered with water in the growing season, PAR and VPD were the two main environmental factors affecting *r*_{s}.

### Relationship between canopy resistance and environmental factors

The diurnal variation in *r*_{c} calculated by the Penman–Monteith formula showed a trend of lower values in the morning and evening and higher values at noon, with a sudden increase in the evening. Solar radiation (*R*_{n}) showed higher values at noon and lower values in the morning and evening, and VPD showed an increasing trend or higher values at noon and lower values in the morning and evening (Figure 6(a)–6(d)). The correlation between *r*_{c} and solar radiation and VPD in hourly scale was significant (Figure 7(a)), and the correlation coefficients were −0.826 and 0.497, respectively. The trend in *r*_{c} decreased as solar radiation increased and rose as VPD decreased (Figure 7(b)).

### Simulation of canopy resistance based on leaf stomatal resistance

The correlation between *r*_{c} (calculated by the Penman–Monteith formula) and average *r*_{s} (observed at the same time in July and August 2015 and 2016) of each layer is shown in Table 1. The result showed that the correlation coefficient in layer A1 was the greatest at 0.731; therefore, the *r*_{s} of layer A1 was chosen as the input variable of the model for simulating canopy resistance.

Layer | A1 | A2 | A3 | A4 | A5 | Minimum | Average |
---|---|---|---|---|---|---|---|

Correlation coefficient | 0.731** | 0.457* | 0.169 | 0.116 | 0.132 | 0.508** | 0.321 |

Layer | A1 | A2 | A3 | A4 | A5 | Minimum | Average |
---|---|---|---|---|---|---|---|

Correlation coefficient | 0.731** | 0.457* | 0.169 | 0.116 | 0.132 | 0.508** | 0.321 |

**P* < 0.01 level significantly correlated.

***P* < 0.05 level significantly correlated.

It is very difficult to obtain the actual *r*_{c} value because differences in lighting conditions in the canopy were great. Because of this, we used *r*_{s} and the LAI to simulate *r*_{c} and so expand from a leaf to the canopy scale. We constructed a canopy resistance (*r*_{c}) model, with the leaf stomatal resistance (*r*_{s}) and effective LAI (LAI_{eff}) in the top layer of *P. australis* as input variables, and *R*_{n} and VPD as environmental stress factors (observed on sunny days from July to August in 2015–2016).

*P. australis*wetland (the ‘PW’ model) was established (Jarvis 1976; Hua

*et al.*2015)

Model fitting parameters were calculated by the iterative method: *a*_{1} = 127.38, *a*_{2} = 0.001.

A comparison of the actual value and simulated value in canopy resistance showed that the decisive factor *R*^{2} was 0.78 (Figure 8).

## DISCUSSION

Coupling parameters in the atmosphere–vegetation–soil interface are key to accurately simulating ET at different temporal and spatial scales in reed wetland. Expanding the spatial scale mainly depends on the conversion of stomatal resistance at different scales, so stomatal resistance simulation at different scales (single leaf, plant, canopy, and regional) becomes the key to scaling-up (Li *et al.* 2012). Canopy structure characteristics are the main factors affecting the internal environment of the plant, and the LAI is the most important parameter for analyzing the structure of plant communities (Zhang & Yao 2000; Yu 2001). Because the stomatal resistance of different species responds differently to environmental factors, the scaled conversion can reflect the different responses of canopy transpiration to environmental factors.

The Jarvis (1976) model of canopy resistance contains three factors: soil, plant, and atmosphere, and the mechanisms of many models of canopy resistance have been derived from it. The Jarvis model is the most commonly used model and includes solar radiation, saturated VPD, air temperature, CO_{2} concentration and soil moisture conditions, and other environmental response functions. We established the PW model in this paper based on the Jarvis model. The difference between our PW model and the Jarvis model is that the PW model added the effective LAI, the stomatal resistance was changed from a fixed to a dynamic value and the environmental factors only contained two items: solar radiation and water VPD.

Yu *et al.* (2008) found that the correlation coefficient between LAI and ET of reed wetlands was 0.728, indicating that the influence of LAI on ET was significant. It appears that adding LAI, as in this study, may better reflect the plant factors. The study suggested that the dominant factors influencing canopy resistance varied at different time scales (Huang *et al.* 2007). The leaf stomatal resistance cannot be represented by a fixed value, because the daily variation in leaf stomatal resistance is great (Li *et al.* 2013), so using dynamic values may better represent the actual situation. The *P. australis* community studied in this paper is flooded in the growing season: soil moisture is sufficient, and the CO_{2} concentration is stable. It is unnecessary to consider the soil moisture conditions, and air temperature is not a major factor. Therefore, the reduction in environmental factors can simplify the input to the model.

The canopy resistance parameters calculated by the PW model were substituted into the Penman–Monteith model to estimate the ET of the reed wetland in Liaohe Delta (Figure 9). A comparison of the PW model with the Jarvis model parameters shows that accuracy improved significantly, with *R*^{2} values of 0.74 and 0.56, respectively (Figure 10). Therefore, the PW model constructed in this paper is suitable for the *P. australis* wetland in the Liaohe Delta.

Among the numerous ET models, the Penman–Monteith model is most suitable for wetlands, but its accuracy depends on canopy resistance. The PW model realized the conversion from leaf scale to canopy scale. Compared with canopy resistance parameter calculations based on the Jarvis model, ET calculated by the Penman–Monteith model and the PW model was more suitable for the *P. australis* of the Liaohe Delta wetland.

Some studies have reported that canopy resistance could be regarded as the sum of stomatal resistance of each leaf (Szeicz 1969); other studies believed that the canopy resistance combined with the stomatal resistance of the upper, middle, and lower layers, and effective LAI was the best (Chu *et al.* 1995); yet other research suggested that the minimum or maximum stomatal resistance and the LAI can be combined in canopy resistance (Kelliher *et al.* 1995, Li *et al.* 2015). Our study suggests that the canopy resistance has a high correlation with the upper layer stomatal resistance. Considering that the water vapor in the canopy of the crop is mainly derived from the upper leaves of the canopy, this is consistent with Lu *et al.*'s (1988) study. However, for the day and hour scales, the factors affecting canopy resistance were different (Huang *et al.* 2007), and the daily variation in stomatal resistance was large (Li *et al.* 2013). Calculating the canopy resistance on an hourly scale requires additional factors such as LAI and environmental factors.

Due to the data deviation caused by changes in environmental factors and the limitations of the model itself (Zhao *et al.* 2015), there are still errors in the model. Further research is needed to improve the model and better simulate canopy resistance. In addition, in the process of canopy resistance calculation using the Penman–Monteith formula, some irregular and mutated values were found especially in night-time data, which may affect the accuracy of the canopy resistance model. These questions should be explored and corrected in further research.

## CONCLUSION

We selected the *P. australis* community in the Liaohe Delta wetland as the research object for this paper. Using data from the Panjin Wetland Ecosystem Research Station, the flux data observed from the eddy covariance system were converted to ET values, and canopy resistance was calculated by the Penman–Monteith model as an actual value. Canopy resistance and its influences, including physiological and environmental factors, were analyzed. Based on the physiological and environmental factors and leaf stomatal resistance, we established a canopy resistance model of *P. australis* (the PW model) and realized the conversion from the leaf to the canopy scale. The model can provide parameters for *P. australis* ET models and provides a new method for the accurate estimation of wetland ET.

## ACKNOWLEDGEMENTS

This study was financially supported by the Institute of Atmospheric Environment, China Meteorological Administration, Shenyang (grant no. 2017SYIAEMS4), the National Natural Science Foundation of China (grant no. 41405109) and Department of Science & Technology of Liaoning Province (grant no. 2018108004).