Quantitative delimitation of radiant belt toward lake of lake-terrestrial ecotone

Abstract

Background

Lake-terrestrial ecotone is a transition zone between terrestrial and aquatic ecosystems. Linking land and lake, it is thus highly sensitive and vulnerable to disturbances. It includes three parts, namely, radiant belt toward land, shoreline zone and radiant belt toward lake. Extending from multi-year average low water level line to open water, radiant belt toward lake is a key part of lake-terrestrial ecotone. However, the delimitation method for radiant belt toward is unsolved, which is a big obstacle to protecting lake-terrestrial ecotone effectively. Wave is a major hydrodynamic factor in lakes, especially large shallow lakes. For linking landward and waterward directions, the boundary of radiant belt toward lake may be affected by waves. Hence, exampled as Lake Taihu, this research was carried out from wave perspective.

Results

In July 2021, a total of 12 species aquatic macrophyte were collected, including 3 species of floating-leaved and 9 submerged macrophyte within radiant belt toward lake of Lake Taihu. Aquatic macrophyte were incorporated into calibrated wave models driven by constant winds via MIKE21 SW. Wave height attenuation was successfully simulated, ranging − 0.19% ~ 8.89% under eastern-wind condition and − 0.08% ~ 23.37% under western-wind condition. In general, wave height gradually attenuates from shore to water. The abrupt change point in relative wave height was used as the boundary of the radiant belt toward lake. A total of 26 sampling lines from bank to water around the whole lake of Lake Taihu were set, ranging 701 ~ 2155 m. Based on the setups of sampling lines, the delimitation range of Lake Taihu is about 1 ~ 2 km.

Conclusions

A novel approach was developed for quantitative delimitation of radiant belt toward lake. Both wind forcing and aquatic vegetation has slight impact on results of delimitation, indicating the feasibility of this approach. It determines a theoretical boundary of lake-terrestrial ecotone, which is helpful to a more precise protection and restoration of large shallow lakes. Moreover, it could provide a potential method for quantitative delimitation for large shallow lakes with similar conditions.

Background

Lake-terrestrial ecotone is an indispensable part of aquatic ecosystem. It has a number of ecological functions, i.e., pollutant interception and purification, improving lake biodiversity and providing habitat for wildlife. However, as the result of its special structure and geographical location, lake-terrestrial ecotone is highly vulnerable to human activities. With the rapid ecological degradation and loss of ecological functions, hence, the protection and restoration of lake-terrestrial ecotone is of extraordinary significance to healthy lakes. Radiant belt toward lake is an important part of lake-terrestrial ecotone (Fig. 1). It is a transitional zone extending from the multi-year average low water level line to open water. On one hand, it is affected by waves and currents from lake, on the other hand, by land. Radiant belt toward lake is the main distribution area for floating-leaved and submerged macrophyte [1]. Ye et al. [1] had systematically and clearly defined the structure and functions of lake-terrestrial ecotone. Zheng et al. [2] delimited radiant belt toward land by moving split-window technology (MSWT) in lakes of lower Yangze River basin. In terms of prior studies in lake-terrestrial ecotone [1, 2], the quantitative delineation, especially radiant belt toward lake, still remains unclear. The lack in accurate quantitative delimitation poses a challenge to researchers and government in effective protection and restoration for lakes. Kalff [3] suggested that lake-terrestrial ecotone is the area covered or likely to be covered by aquatic macrophyte. For deep lakes, with light as the limiting factor, it is feasible to define the boundary of radiant belt toward lake as the boundary of aquatic macrophyte growth. However, simply by the disappearance of aquatic macrophyte, mostly submerged ones, it is not applicable for some large shallow lakes, i.e., Lake Taihu, for conditions of aquatic macrophyte spreading into the center of lake or no macrophyte covered in some areas [4, 5]. Thus, a new delimitation method is of urgent need to be developed to not only meet accuracy, but also to guide large shallow lakes with similar conditions. As the basis of ecological restoration for lake-terrestrial ecotone, the quantitative delineation is the primary issue for more targeted and precise control, thus it has significance in making scientific support for spatial management and ecological restoration of lakes.

Fig. 1

Comparison of structures of lake-terrestrial ecotone and coastal zone [1]

With reference to coastal zone (Fig. 1), wave conditions were chosen to quantitatively delineate radiant belt toward lake of Lake Taihu, a typical large shallow lake in China. As an important hydrodynamic factor in large shallow lakes, wave conditions are vital in shaping lake basin formation and shoreline morphology [6, 7], as well as pollutant release [8], dispersion and elimination [9]. Moreover, wave conditions are active dynamic factors within radiant belt toward lake for linking landward and waterward directions, as well [1]. The wave growth could be directly influenced by wind forcing, water depth and shoreline morphology [10], as well as aquatic macrophyte, which may lead to wave height attenuation and energy dissipation [11, 12]. At present, waves are mainly presented by empirical formulas, field observations, flume experiments and numerical simulations [13]. Numerical simulations are widely used for its high precision and low labor costs. In terms of wave numerical simulation, WAVEWATCH III, SWAN and MIKE21 SW models are mostly used. Among them, WAVEWATCH III model is mainly used in the simulation of large-scale sea area, such as the Mediterranean Sea [14], East Sea [15], Red Sea [16], and Indian Ocean [17]. SWAN and MIKE21 SW models can be used in wave simulation of nearshore and lakes, such as Black Sea [18], UK Coastal [19], Lake Taihu [20, 21]. Fonseca [22] compared the coastal spectral wave model performances, found that the grids of MIKE21 SW are better adjusted than the ones of SWAN. Hence, in this study MIKE21 SW is used to project the wave field of Lake Taihu based on the wind field information.

The aims of this study were to (i) research the distribution characteristic of aquatic macrophyte within radiant belt toward lake of Lake Taihu, (ii) simulate wave fields of Lake Taihu driven by constant winds via MIKE21 SW, (iii) incorporate aquatic macrophyte obtained by field survey into calibrated models according to definition of radiant belt toward lake, (iv) develop a delimitation method for radiant belt toward lake, (v) delimit the boundary of radiant belt toward lake of Lake Taihu, and investigate the influencing factors of the delimitation results.

Materials and methods

Study area

The study area is Lake Taihu(30° 55′ 40″–31° 32′ 58″ N, 119° 52′ 32″–120° 36′ 10″ E) in Jiangsu Province, China. It is the third largest freshwater lake in China. Lake Taihu has a current surface area of 2338.11 km², and a shoreline in total length is about 405 km. The average water depth is 1.9 m, and the maximum water depth is 2.6 m, Lake Taihu is a typical large shallow lake. This region has a subtropical monsoon climate with four distinct seasons, abundant rainfall and heat. The average annual precipitation of the Lake Taihu basin is 1177 mm, and the average annual temperature of Lake Taihu basin is 15–17 ℃. As the catchment center of the basin, a large amount of pollutants were carried into Lake Taihu with inflowing water, leading to a rapid decline in water quality and ecosystem degradation.

Lake Taihu has experienced a rapid ecosystem degradation since the explosive development in surrounding area. Aquatic macorphyte could reflect the health of lakes, especially ones in radiant belt toward lake. From 1960s to 2014, a total of 8 species aquatic macrophytes had disappeared, such as Callitriche stangnalis, Utricularia minor, the dominant species of aquatic plants show a monoculture trend, as well [23].

Field survey

In consider of the wave height attenuation that caused by aquatic macrophyte within radiant belt toward lake, a field survey was conducted in July 2021 (Additional file 1). Aquatic macrophyte were collected by a self-made sampler. The distribution of aquatic macrophyte, species, height (m), diameter (m) and density (units/m²) were recorded in-site for further analysis and processing.

IV (important value) was used to tell the dominant species in each layer, and the aquatic macrophyte associations were named by the dominant species of each layer, respectively. The IV calculation formula, given by

$${\text{IV}}_{1} = \left( {\frac{{D_{1} }}{\sum D} + \frac{{C_{1} }}{\sum C} + \frac{{F_{1} }}{\sum F}} \right) \div 3{ ,}$$

(1)

where ${\text{IV}}_{1}$ is the important value of species1 in sampling point, $D_{1}$ is the density of species1 in sampling point, $\sum D$ is the total density of vegetation in sampling point, $C_{1}$ is the coverage of species1 in sampling point, $\sum C$ is the total coverage of species1 in sampling point, ${\text{F}}_{1}$ is the frequency of species1 in sampling point, $\sum F$ is the total frequency in sampling point.

The aquatic macrophyte associations were named after by the dominant species in each layer, which the dominant species were determined by the IV. Same layer was connected by ‘+’, different layer was connected by ‘−’.

Wave model application

MIKE21 SW introduction

MIKE21 SW spectral wave model is a third-generation wave model that simulates the growth, decay and transformation of wind-generated waves and swells in offshore and coastal areas, has been widely used [24]. It is based on the finite volume technique to solve the governing equations, taking into account the following physical phenomena: wind wave generation, refraction, shoaling, white-capping, bottom friction, wave breaking dissipation, nonlinear wave–wave and wave–current interactions [24]. Two formulations are available: directional decoupled parametric formulation and fully spectral formulation. The latter is used in this study and the governing equation is the wave action balance equation, given by

$$\frac{\partial }{\partial t}N + \frac{\partial }{\partial x}N.C_{g.x} + \frac{\partial }{\partial y}N.C_{g.y} + \frac{\partial }{\partial \theta }N.C_{\theta } + \frac{\partial }{\partial \sigma }N.C_{\sigma } = \frac{S}{\sigma }$$

(2)

$$S = S_{{{\text{in}}}} + S_{{{\text{nl}}4}} + S_{{{\text{ds}}}} + S_{{{\text{nl}}3}} + S_{{{\text{bot}}}} + S_{{{\text{surf}}}} .$$

(3)

In Eq. (2), where N $({\upsigma },{\uptheta }$) is the action density spectrum, $\sigma$ is the relative radian frequency and $\theta$ is the wave direction. The first term represents the local rate of change of action density in time. The second and the third ones are action density propagation in x and y geographic spaces with propagation velocities $C_{g.x}$ and $C_{g.y}$, respectively. The fourth term is related to the depth-induced and current-induced refraction with propagation velocity $C_{\theta }$ in $\theta$-space. The fifth term represents shifting of the relative frequency due to variations in depth and currents with propagation velocity $C_{\sigma }$ in ${\upsigma }$-space. In Eq. (3), S is the energy source term that contains a superposition of source functions which represent relevant physical phenomena. $S_{{{\text{in}}}}$ represents the generation of wind energy, $S_{{{\text{nl}}4}}$ is the wave energy transfer due to quadruple wave-wave interaction, $S_{{{\text{ds}}}}$ is the dissipation of wave energy due to white-capping, $S_{{{\text{nl}}3}}$ is the wave energy transfer due to triple wave–wave interaction, $S_{{{\text{bot}}}}$ is the dissipation of wave energy due to bottom friction and $S_{{{\text{surf}}}}$ is the dissipation due to depth-induced breaking.

According to definition of radiant belt toward lake, this research thus only took wind forcing as the driving force (wind speed: 5 m/s, wind direction: north, east, south, west) and bottom friction representing the presence of aquatic macrophyte into account. The bottom friction was selected as Nikuradse roughness at present research. All other parameters were set as default value according to MIKE21 SW manual [24], as well.

Model establishment and validation

For constant wind forcing, Putian Formula from “Code for design of levee project” (GB50286-2013) [25] has been proved applicable for Lake Taihu [21], in which specifies an approach to calculating wave conditions in inland lakes. Given the irregular shape of the boundary of Lake Taihu, it is necessary to introduce the equivalent fetch length for wave calculation:

$$F_{e} = \frac{{\mathop \sum \nolimits_{i} r_{i} \times \cos^{2} \alpha_{i} }}{{\mathop \sum \nolimits_{i} \cos \alpha_{i} }},$$

(4)

where r_i is the length of the ray led from the calculation point to the opposite bank at every $\Delta$ α angle within 45° on each side of the main wind direction (m), α_i is the angle between the r_i ray and the r₀ ray on the main wind direction (°). which α_i = i*$\Delta$ α, $\Delta$ α = 15°, i = 0, ± 1, ± 2, ± 3. (Additional file 2).

Putian formula can be used to calculate average wave height and significant wave height, respectively:

$$\frac{{g\overline{H}}}{{{\text{v}}^{2} }} = 0.13\tanh \left[ {0.7\left( {\frac{gd}{{{\text{v}}^{2} }}} \right)^{0.7} } \right]\tanh \left\{ {\frac{{0.0018\left( {\frac{{gF_{{\text{e}}} }}{{v^{2} }}} \right)^{0.45} }}{{0.13\tanh \left[ {0.7\left( {\frac{gd}{{v^{2} }}} \right)^{0.7} } \right]}}} \right\}$$

(5)

$$h_{m} = 1.21\overline{H} ,$$

(6)

where g is gravity acceleration (m/s²), $\overline{H}$ is average wave height (m), v is computational wind speed (m/s), d is the average water depth(m), $F_{{\text{e}}}$ is equivalent fetch length (m), $h_{m}$ is significant wave height (m).

To quantify computational and numerical difference of $h_{m}$, a statistical analysis and uncertainty analysis was conducted with 2 parameters: relative bias (R.bias) and root mean square error (RMSE/m), given by

$${\text{R}}.{\text{bias}} = \frac{{{\raise0.7ex\hbox{${\left( {\mathop \sum \nolimits_{i = 1}^{n} \left| {s_{{\text{i}}} - m_{i} } \right|} \right)}$} \!\mathord{\left/ {\vphantom {{\left( {\mathop \sum \nolimits_{i = 1}^{n} \left| {s_{{\text{i}}} - m_{i} } \right|} \right)} n}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$n$}}}}{{\overline{m}}}{ }$$

(7)

$${\text{RMSE}} = \sqrt {{\raise0.7ex\hbox{${\left[ {\mathop \sum \nolimits_{{{i} = 1}}^{{n}} \left( {s_{{i}} - m_{{\text{i}}} } \right)^{2} } \right]}$} \!\mathord{\left/ {\vphantom {{\left[ {\mathop \sum \nolimits_{{{i} = 1}}^{{n}} \left( {s_{{\text{i}}} - m_{{\text{i}}} } \right)^{2} } \right]} n}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$n$}}} ,$$

(8)

where $s_{i}$ are values obtained by numerical simulation (m), $m_{i}$ are values calculated by Putian formula (m) and n is the sample size, in present research, n = 5.

Numerical simulation of generalized aquatic macrophyte in MIKE21 SW

For attenuation in significant wave height that may be caused by aquatic macrophyte, the physical properties obtained from field survey were transferred into equivalent sand heights [26] with reference to aforementioned Nikuradse roughness by Manning’s coefficient support [27,28,29] [Eqs. (9)–(11)], given by

$$n_{v} = \sqrt {\left( \frac{1}{M} \right)^{2} + \frac{{C_{D} m_{i} Dmin\left( {h_{v} ,h} \right)h^{\frac{1}{3}} }}{2g} }$$

(9)

$$K_{{S_{i} }} = \left( {\frac{8.25\sqrt g }{{n_{v} }}} \right)^{6}$$

(10)

$$K_{s\_all} = \mathop \sum \limits_{i} K_{{s_{i} }} \times \frac{{m_{i} }}{m} ,$$

(11)

where n_v is vegetated Manning’s coefficient, M is bottom Manning’s coefficient, equals 50, C_D is vegetation drag coefficient, C_D equals 0,0.1,0.2,0.3 in present research, m_i is the density of the ith species (stems/m²), h_v is height of vegetation (m), h is average water depth of each lake area (m), g is gravity acceleration (m/s²), K_si is equivalent sand roughness height of each species(m), K_{s_all} is equivalent sand roughness height of each aquatic macrophyte association (m), i is the ith species of the association, K_Si is the ith K_S calculated by Eq. (10) (m), m is the density of the association (stems/m²).

C_D is a crucial parameter related to hydrodynamic conditions and plant characteristics, including rigidity and submergence [30]. Flexibility and submergence of aquatic vegetation can reduce the values of C_D [31]. Previous studies proposed empirical equations in related to Reynolds number(Re) or Keulegan–Carpenter number (KC) [31]. Despite all the uncertainties and challenges posed by assessing in field. In present work constant values, C_D = 0 and C_D = 0.1, 0.2, 0.3 were used, with reference to Oude’s research [32] (Echinodorus grandiflorus C_D = 0.06–0.13, Cabomba caroliniana C_D = 0.07–0.12, Nymphaea rubra C_D = 0.11–0.23). In which, the C_D = 0 represents no aquatic macrophyte on lake bed, and C_D = 0.1,0.2,0.3 represents the different degrees in roughness caused by aquatic macrophyte on lake bed.

Wave height attenuation

To quantify the wave height attenuation caused by aquatic macrophyte incorporation, this research hereby introduce the wave height attenuation rate, given by

$${\text{Wave height attenuation rate}} = \frac{{\left( {h_{m1} - h_{m2} } \right)}}{{h_{m1} }} \times 100\% ,$$

(12)

where $h_{m1}$ is the significant wave height simulated, $h_{m2}$ is the significant wave height simulated after aquatic macrophyte incorporation.

Delimit range method and sampling design

Due to the dense distribution of aquatic macrophyte in lake-terrestrial ecotone [1, 3,4,5] and its potential in wave height attenuation nearshore [11, 12], field survey data obtained in July 2021 were incorporated into numerical simulation in this study. Extending from multi-year average low water level line to the center of the lake [1], in total of 26 sampling lines were made perpendicular to shoreline with 500 sampling points evenly distributed (Fig. 2). In comparison of lake-terrestrial ecotone and coastal zone, it shows great similarities in profile structure. Bounded by breaking point, the sea area can be divided to offshore and coastal zone. In which, the inshore area is extending from low tide level to breaking point. The breaking point is determined by relative wave height. Hence, with reference to coastal zone [10], relative wave height (ratio of significant wave height to water depth) is selected as the indicator. The boundary of radiant belt toward lake is the end point in water area which is affected by landward according to the definition. Thus, by plotting curves between relative wave height and distance to lake shore, sampling points with abrupt change of the slope of the tangent line within curves were selected as the boundary of the radiant belt toward lake of lake-terrestrial ecotone. Since the abrupt change point whose second-order derivative is discontinuous, which is the end point of terrestrial impact on water area in mathematical expression. From wave perspective, the wave height can be influenced by wind forcing, water depth, shoreline morphology and aquatic macrophyte. In this research, the wave models were set up at certain water level. However, it is unknown that the variance of wind forcing and aquatic macrophyte would deviate the delimitation result or not due to lack of reference. To find out the boundary of radiant belt toward lake, and investigate the influencing factors of the delimitation result. The delimiting method for the boundary of radiant belt toward lake used in the present research is developed by adjusting the relative parameters, such as vegetation drag coefficients and wind directions.

Fig. 2

Schematic of location and setup of sampling lines. In which, red dot represents the sampling line starting point, and the black line represents the boundary of lake. The right one is a scope into the setup of sampling lines, where the sampling line is made perpendicular to shoreline and extending to the lake center

Data analysis

MIKE21 SW was used to simulate the wave field of Lake Taihu. Microsoft Excel was used for data processing and analyzing, QGIS3.12 was used for plotting.

Results

Field survey

A total of 12 species aquatic macrophyte were collected in field survey in July, 2021. A total of 3 species of floating-leaved macrophyte were collected, namely, Nymphoieds peltatum, N. indica and Trapa maximowiczii. A total of 9 species of submerged macrophyte were collected, namely, Potamogeton crispus, P. malainus, P. maackianus, Myriophyllum spicatum, Ceratophyllum demersum, Hydirlla verticillata, Vallisneria natans, Elodea nuttali and Najas marina. In total of 263.06 km² water area was covered by aquatic macrophyte, occupying 11.25% of the total water surface area. According to the calculation of IV (Additional file 3), a total of 6 aquatic macrophyte associations were classified, respectively (Fig. 3); the composition of each macrophyte associations and the parameters obtained in field survey are listed in Additional file 4.

Fig. 3

Aquatic macrophyte associations classification in different lake area. In which, a represents Gonghu Bay, b represents Zhenhu Bay, c represents Xuhu Bay, d represents Xiaobai Lake, e represents Area between Xishan and Dongshan, f represents East Taihu

Model establishment and validation

The model area is dissected using a triangular mesh of 31,611 grid cells, 16,484 grid nodes, and the grid side length is between 200 and 1000 m. Simulated by triangular mesh as a basic unit, all sides of the triangular mesh are linearly interpolated. The boundary condition is set as land boundary, constant winds are chosen as the driving force of the models. The bottom friction is selected as Nikuradse roughness, which is taken as 0.015–0.020 m. In total of 5 calibration sampling point (Additional file 5) were selected to validate the credibility of established models. The multi-year average water level of Lake Taihu, 2.99 m (Wusong Zero Datum) [33] was used in Putian formula. The computational and simulated values are listed in Table 1.

Table 1 Results of empirical formula and model simulation

Calculated by Eqs. (7, 8), the Nikuradse roughness and the R.bias and RMSE of each model driven by different wind forcing are listed in Table 2, respectively.

Table 2 Statistical and uncertainty analysis of models established

Wave height attenuation caused by aquatic macrophyte

Numerical simulation of sampling lines driven by different wind directions

In this section, GH2, GH3, ZH1, ZH2, XH1, XH2, EC2, EC3 and EC4 in vegetated eastern lake areas were analyzed to investigate significant wave height simulations driven by wind from different directions. It is worth mentioning each sampling line has different lengths as a result of different scales of lake areas (Table 3).

Table 3 Simulation of significant wave heights driven by constant winds

Due to the differences in fetch length, different wind directions appear to have influence on significant wave height simulated within same sampling line. For the sampling lines selected, significant wave heights simulated driven by western wind appear to be higher than ones driven by eastern wind. Respectively, the significant wave heights of East Taihu appear to be lower than other lake areas’, it could be the result of narrow shape of bathmetry of East Taihu.

Wave attenuation caused by aquatic macrophyte

The vegetation-induced wave attenuation and changes in flow patterns had been observed and confirmed in prior research [34,35,36,37,38,39,40,41,42,43,44,45,46]. The attenuation in significant wave height for different vegetation drag coefficients within sampling line driven by both eastern and western wind conditions were investigated, respectively. By Eq. (12), the wave height attenuation rates are listed in Table 4 and 5, respectively.

Table 4 Wave height attenuation rate ranges driven by eastern wind %

Table 5 Wave height attenuation rate ranges driven by western wind %

Delimitation results of radiant belt toward lake

Based on setups of sampling lines and sampling points, along with the mathematical expressions, in total of 26 sampling lines located in all lake areas of Lake Taihu were delimited, as shown in Table 6.

Table 6 Results of delimitation of 26 sampling lines

A total of 26 sampling lines were delimited, ranging 701–2155 m. Hereby, based on the setups of all sampling lines, the radiant belt toward lake of Lake Taihu ranges about 1–2 km.

Discussion

Statistical and uncertainty analysis of models established

Putian formula is an empirical formula based on long-term wind waves observation data, presented as a common method of wind waves calculation in China. R.bias and RMSE can be used to evaluate the accuracy of models established, the smaller the values are, the more accurate the models established. With an average R.bias at 0.0331 and an average RMSE at 0.0075 m, shows that the simulated wave heights are very close to computational results from Putian formula, which indicates that MIKE21 SW can simulate well in wave activities of Lake Taihu. Moreover, as listed in Table 1, the values simulated by MIKE21 SW are always slightly higher than ones by Putian formula, the same phenomenon were observed in similar research, as well [21, 47]. Hereby, it could be inferred as the computational biases caused by grid dissections of wave models. Nevertheless, the established models could be considered as accurate.

Wave height attenuation caused by aquatic macrophyte

Numerical simulation has enabled a large scope into wave height attenuation caused by aquatic macrophyte. In prior studies, the vegetation incorporated waves can be simulated in 2 approaches: (i) by corresponding modules developed by original softwares, i.e., SWAN-VEG [32], Xbeach-VEG [48] (ii) by introducing terms into governing equations of energy dissipation due to vegetation [49, 50]. However, MIKE21 SW was rarely applied as a result of lacks in corresponding modules. Gui [51] pointed out that bottom friction could be increased as a result of presence of vegetation on lake bed. Hereby, combining field survey and mathematical formula, this research has developed a proper approach coupling aquatic macrophyte into wave models via MIKE21 SW.

Currently, aquatic vegetation on lake bed are treated as idealized cylinders in numerical simulation [52], which leads to a good agreement in rigid aquatic vegetation [53]. By introducing concession factor D in C_D to simulate the swaying of flexible vegetation, the agreement between experimental and simulation data were improved in SWAN-VEG [53]. With reference to Oude’s research [32], the C_D was properly decreased to 0.1 ~ 0.3. The wave attenuation rate ranges from − 0.19% ~ 8.89% by eastern wind, and − 0.08% ~ 23.37% by western wind, indicating the very need of aquatic vegetation incorporation. However, the minimum attenuation rate − 0.19% (in ZH2 eastern wind) indicates a slight increase in wave height, it is probably because that energy accumulation happening at some sampling point. In consider of the original simulation results in ZH2 (0.001 m–0.002 m), it could be the computational biases as the result of the small wave height, as well. Little of research had considered a large scale of vegetated-wave in numerical simulation [32]. In addition, the flow regime and species, rigidity and composition of aquatic vegetation were different case by case [32]. Hence, with an average attenuation rate of 4.95% driven by western wind, and ones driven by eastern wind is 2.17%, the wave height attenuation rate could be considered as appropriate.

The wave height attenuation is related to wave parameters and vegetation characteristics [35]. In Tables 4 and 5, the changes in wave height attenuation were observed as a result of changes in wind directions. Longer fetch makes it possible for wave grow adequately, thus a higher attenuation rate, similar conclusions were drawn out in Paquier’s [54] and Reidenbach’s [55] research, as well. By changing C_D, the wave height attenuation appears slight change. Similar results were found in Gui’s [51] study of parameter analysis in MIKE21 SW, when bottom friction increase to some specific value, the wave attenuation stops changing. Hereby, it could be inferred as a fully attenuation happened in present research. Smaller wave heights make it insignificant in wave height attenuation calculation process.

Delimitation of radiant belt toward lake

According to definition of radiant belt toward lake, the boundary of it is the end point of terrestrial impact on water area. With reference to coastal zone, abrupt change point of relative wave height was used to delimit the boundary. It was found in each sampling line of all lake areas. Exampled by GH1 (Fig. 4a), changes in wind forcing have shown slight impact on the abrupt change point (point 110 in GH1), same phenomena were observed at all other sampling lines. Changes in delimitation result were at most 116 m (in EC2) when wind direction changes. It can be recognized reasonable in consider of the large scale of Lake Taihu. As it is listed in Table 5, the curves of XH2 (Fig. 4b) whose wave attenuation is the highest are found the presence of aquatic macrophyte show no impact on the abrupt change point (point 225 in XH2). The delimitation results are barely influenced when wind and aquatic macrophyte parameters change. Hence, a novel approach has been developed for quantitative delimit radiant belt toward lake of Lake Taihu. The result of delimitation could provide a theoretical boundary for lake-terrestrial ecotone for more precise protection and restoration. Moreover, the approach this research developed could also provide a proper way to quantitative delimit for large shallow lakes with similar conditions, as well.

Fig. 4

a Delimitation of GH1 by different wind forcing. b Delimitation of XH2 by western wind

Conclusions

A novel approach was developed to quantitatively delimit the range of radiant belt toward lake of Lake Taihu from wave perspective via numerical simulation. According to the definition, aquatic macrophyte obtained by field survey were incorporated into wave models. As a result, the wave height attenuation was observed in present work. Based on the setups of sampling line and delimitation result, the range of radiant belt toward lake was identified as 1 ~ 2 km. The boundary this research delimit could provide a theoretical basis for more precise lake-terrestrial ecotone protection and restoration for Lake Taihu. Moreover, the approach this research developed could provide a method for quantitative delimitation of large shallow lake with similar conditions, as well.