Addressing the Modelling Precision in Evaluating the Ecosystem Services of Coastal Wetlands

: Wetlands are one of the world’s most productive ecosystems, and therefore it is crucial that management decisions regarding wetlands incorporate awareness of accurate assessments of the value of their respective ecosystem services. In this paper, we seek to improve the modelling precision in the scale transform process of ecosystem service evaluation. Firstly, we selected eight services as the criteria to calculate wetland ecosystem values: substance production, ﬂood control, carbon sequestration, gas regulation, climate regulation, wave reduction, adding new lands, recreation and education. Then, six coastal wetlands of Liaoning province were chosen as the case study areas, and their ecosystem values were calculated by empirical method. Next, we simulated ecosystem values of the six cases by two spatial-scales transform methods named meta-analysis and wavelet transform. Finally, we compared the two groups of simulated values with the empirical measured values to examine their evaluation precisions. The results indicated that the total precision of the wavelet transform model (0.968) was higher than that of meta-analysis (0.712). In addition, the simulated values of single services such as substance production, ﬂood control, carbon sequestration, gas regulation, and climate regulation were closer to the measured values using wavelet transform model. This research contributes to identifying an evaluation model with higher precision for evaluating wetland ecosystem services in the process of scale transform.


Introduction
Increasing attention has been paid to the evaluation of wetland ecosystem services from resource managers, researchers, and the wider public [1][2][3][4][5]. The evaluation can monetize and quantitatively illustrate the values of wetland ecosystem services, strengthening the public's awareness of protecting wetlands [6,7]. Located in the confluence of fresh and saltwater ecological systems, coastal wetlands with high productivity and biodiversity provide rich material and a number of ecosystem services for human beings, such as raw materials, food production, carbon sequestration, wave reduction, climate regulation, and gas regulation, etc. [6,[8][9][10]. Moreover, some coastal wetlands located along bird migratory routes, such as the large tidal flats of the Chinese coastal wetlands, supply food for millions of birds travelling across East Asia and Australia [11,12]. Thus, coastal wetlands are not only important for human survival, in particular for those relying on local fish, but also for the survival of millions of migratory birds and other organisms. However, the ecosystem services provided by coastal wetlands vary according to special scales when calculating the ecological and geographical processes [13,14]. Errors exist when evaluating the ecological services of large-scale coastal wetlands since they are not as simple as the sum of small pieces of coastal wetlands [15]. Thus, methods for scale transformation of coastal wetland ecosystem service evaluation are particularly urgently needed [16,17].
Two methods, named meta-analysis and wavelet transform, are actively used for larger scale wetland ecosystem service estimation in contemporary research [18][19][20][21][22]. Meta-analysis is a commonly used scale transform method that can attain the value per unit area by adjusting the function [23,24]. Through statistical integration and systematic reviews of previous research, meta-analysis can obtain comparatively accurate values on large scales by value transfer functions [19]. However, meta-analysis is still criticized for its credibility for the extraction and analysis of spatial information since the results generated by its value transfer functions are still services value per unit [15,25]. By contrast, wavelet transform can localize the space scales (i.e., it has the performance to localize large-scale wetlands) to balance the wavelet coefficients of the localization space. It can also provide multi-scales of resolution from large to small and an arbitrary direction of rotation, which can be used to extract the directional characteristics of wetlands [26,27]. Clustering aims to detect groups and assign labels to the objects based on the cluster that they belong to. The grid based algorithm quantizes the space into a finite number of cells and then carries out operations on this space.
Some previous research has used meta-analysis and wavelet transform for wetland ecosystem service estimation [19,23]; however, few of them compared the model precisions of these two methods. Thus, in this paper, we seek to explore whether these two methods give consistent results when assessing the ecosystem services values of the same wetland. This research contributes to identifying a more accurate and efficient scale transform method for wetland evaluation at a larger space-scale, providing a technique tool for establishing wetland ecological compensation systems at different spatial patterns, conducting large-scale wetland protection projects, and accounting for green GDP [28][29][30][31].
The high-precision model can also be used in evaluating the ecological services of cross-regional, national and even international wetlands in further application.

Study Site Description
The study sites are located along the northeast coast of China, delimited by Yalujiang Estuary to the east and Shanhaiguan Old Faucet to the west. The study contains approximately 2920 km of coastline ( Figure 1). The coastal wetland area in Liaoning province is nearly 713,200 ha, which constitutes 51.10% of the total wetlands in Liaoning Province. Liaoning Province is the only coastal province in northeast China. The mainland coastline within the territory accounts for 12% of the total length of the coastline through the whole nation [32].
Six wetlands in Liaojing province, named Liuguhe wetland, Linghe estuary wetland, Shuangtai estuary wetland, Yongyuanjiao wetland, Banhaibao wetland and Yalujiang estuary wetland, were selected as case study areas ( Figure 1). Those cases were designed to cover as many types of coastal wetland as possible. Table 1 illustrates how each case represents specific types of coastal wetlands, including shallow marine waters, rocky coast, sandy stone sea beaches, sludge sea beaches, intertidal salt marshes, estuarine waters, and estuarine delta.

The method for Empirical Measurement
Based on the Millennium Ecosystem Assessment and double accounting [33][34][35], the dominant ecosystem services of the six cases can be classified as provisioning, regulating, and cultural services, containing eight more specific services: substance production, flood control, carbon sequestration, gas regulation, climate regulation, wave reduction, the addition of new land, recreation and scientific research [9,11,36]. The gross and separating ecosystem service value of each case was evaluated by empirical evaluation methods, which provide a control group for later model precision comparison. The economic values of substance production, gas regulation and the addition of new land in the coastal wetlands of Liaoning were calculated using the market price method [23]. The economic values of flood control and climate regulation were calculated using the replacement cost method [2], the economic value of water conservation was calculated by the shadow price method [37][38][39], the economic value of carbon sequestration was calculated using the carbon tax method [40,41], the economic value of wave reduction was calculated using the expert evaluation method [42,43], and finally the economic values of recreation and scientific research were calculated using the travel cost and the simulate market methods [44,45].

The Methods for Space-Scale Transform
The techniques of scale transformation applied in this research belong to scaling up, which means estimating the ecological services of a large-scale wetland based on those of some small-scale wetlands that are more prone to be evaluated. We selected meta-analysis as one scaling up model because it is a useful tool to account the total value of the coastal wetland ecosystem services. Meanwhile, we used the method of wavelet transform to interpret multi-scale and non-stationary space-series data and reveal the features of coastal wetlands that are not apparent.

The Meta-Analysis Method
The process of meta-analysis includes three steps. The first step is related to data preparation: we carefully selected primary studies on the theme of coastal wetland evaluation (including both peer reviewed and non-peer reviewed studies) to populate our meta-analysis database. In the second step, we statistically estimated the impact of geospatial, environmental and socio-economic characteristics on coastal wetland ecosystem services. In the final step, the fitted model was used with the specific characteristics of the test areas in the typical cases to estimate the value of coastal wetland ecosystem services provided by each typical case.
A multi-variable model for the meta-regression analysis was conducted using a weighted least square (WLS) model in Equation (1): where subscripts i and j refer to the ith observation in the jth study. The dependent variable Vij is the value of the coastal wetland ecosystem service for observation i in study j, measured in 2013 USD per ha per year. β 0 is the intercept and β w , β m and β c are the coefficients to be estimated for the explanatory (independent) variables including wetland characteristics, the evaluation techniques and environmental characteristics. As is the case for most meta-analyses on wetland ecosystem service values [18,46], the economic values (Vij) were natural-log-transformed prior to analysis. Xw represents wetland characteristics. Xm represents the evaluation techniques, Xc represents environmental characteristics.

The Wavelet Transform Method
Based on spatial scale analysis and WaveCluster, we clustered the different geographic units of the coastal wetland in typical cases, and then transformed the value of the same cluster of the coastal wetland ecosystem services using layers of scales to account for the up-scaled values. Finally, we calculated each value of the coastal wetland ecosystem services in six typical cases. Because the number of data was small and the wavelet coefficients of each scale had strong correlations in each typical case, we used continuous wavelet transform. In this description, f (x) denotes the spatial evolution results of coastal wetland ecosystem services. We can define continuous wavelet transform, which we denote by W(s, τ), as the complex conjugation of f (x) with a detailed and translated "mother" wavelet function Ψs, τ(x) [47]: where s represents the dilation (scale) of the wavelet function and τ represents the degree of distance translation along the series. The term 1/ √ s normalises the wavelet function energy at each scale. Equation (2) emphasizes that the wavelet function is in fact a "basis" function. W(s,τ) in Equation (3) represents the coefficients of wavelet transform at different scales.

The Method for Precision Comparison
Three indicators were selected to verify the consistency between the simulation values and the empirical measured values, including the determination coefficient (R 2 ), the root-mean-square error (RMSE), and the relative mean deviation (RMD). R 2 , also called goodness-of-fit, represents the interpretive degree of independent variables to the dependent variable. Thus, the higher the value of R 2 , the higher the precision. RMD was used to measure the deviation between simulated values and measured values. The smaller the value of RMD, the higher the precision. Further, RMD refers to the outcome of mean variation divided by average value. The smaller RMD means closer repeated measured values. The equations of R 2 , RMSE and RMD can be seen in Equations (4)-(6) below.
where O i and P i represents the empirical measured values and simulated values, while O and P represents the average values of the empirical measured values and simulated values. n represents the observation frequency.

The Measured Ecosystem Service Values of the Six Cases
The various types of ecosystem service values of the six cases in Liaoning coastal wetlands were calculated based on the empirical measurement methods listed in Section 2.2. The detailed results are shown in Table 2. It can be seen that Yalujiang estuary had the highest gross ecosystem service value (3,464,077,670 USD), followed by Linghe estuary (3,397,896,440 USD). In contrast, Yongyuanjiao wetland had the lowest ecosystem service value (9,708,738 USD), which was only 0.2% of that of Yalujiang estuary. However, the great disparity in value was related to the measured areas of cases rather than the wetland quality. The results of value on per unit area confirmed this deduction. The highest value on per unit area belonged to Yongyuanjiao (965,372,168 USD/10 4 ha), while the lowest value on per unit area belonged to Banhaibao estuary (374,433,657 USD/10 4 ha). In terms of the single ecological value, the average value peaked at 437,378,641 USD in the value of carbon sequestration and reaches to the bottom at 62,297,735 USD in the value of recreation and education.  Meanwhile, the data analysis results suggested generally that the simulated values of the six cases by meta-analysis were slightly lower than the empirical measured values. The model of meta-analysis was constructed based on the nation-wide cases and then implemented at the provincial level-Liaoning province. This process lowered the ecological values of the selected cases. The detailed comparisons between simulated values and measured values suggest differences exist in the veracity of simulation, either in different cases or targeting different single ecological values (see Figure 2). The smallest difference existed in the case of Shuangtai estuary wetland (Figure 2c) while the largest difference existed in Yongyuanjiao wetland (Figure 2d). From the aspect of wetland types, the method of meta analysis collected all the coastal wetland types to establish the database, so the wetlands had more types and the simulated values would be more closer to the measured values. Among six cases, Shuangtai estuary wetland included five coastal wetland types and Yongyuanjiao wetland included only one coastal wetland type (see Table 1).

The Ecosystem Service Values Stimulated by Wavelet Transform and Their Differences from Measured Values
The ecosystem service values of the six cases were stimulated by wavelet transform based on the methods presented in Section 2.3.2, and the results are shown in Table 4. The simulated values showed a slight difference from both the measured values and values simulated by wavelet transform. The Linghe estuary had the highest gross ecosystem service value (3,199,676,375 USD), followed by Yalujiang estuary (3,193,851,133 USD) with a narrow margin. The Yongyuanjiao wetland remained the lowest ecosystem service value (8,414,239 USD). The highest value on per unit area also belonged to Yongyuanjiao (841,423,948 USD/10 4 ha), which was more than twice as much as the lowest value (Banhaibao, 334,304,207 USD/10 4 ha). The average value peaked at 421,359,223 USD/10 4 ha in the value of substance production and reaches to the bottom at 37,864,078 USD/10 4 ha in the value of adding new lands. The detailed comparisons between simulated values and measured values suggested differences exist in the veracity of simulation, either in different cases or targeting different single ecological values (see Figure 4). The smallest difference existed in the case of Linghe estuary wetland (Figure 4b) while the largest difference existed in Liuguhe wetland and Yongyuanjiao wetland (Figure 4a,d). From the aspect of wetland areas, the method of wavelet transform adopted belt transect lines for sampling, so the wetlands had more areas, and the simulated values would be more close to the measured values. Among six cases, Linghe estuary wetland had the largest areas (6.77 × 10 4 ha), Liuguhe wetland and Yongyuanjiao wetland had relatively smaller areas (0.04 × 10 4 ha & 0.01 × 10 4 ha). Figure 5 illustrates the dispersion of the conserved simulated values from 48 groups of data. It can be seen that the distinction between simulated values and measured values varied from −0.65 × 10 8 USD/10 4 ha to 0.16 × 10 8 USD/10 4 ha. The percentage of distinction between −0.16 × 10 8 USD/10 4 ha and 0.16 × 10 8 USD/10 4 ha reaches to 81.25%, which is far more than that of meta-analysis.

The Precision Comparison between Meta-Analysis and Wavelet Transform
The simulated values by meta-analysis and wavelet transform were correlated to the measured values, respectively, and the results are presented in Figure 6. The results showed both values simulated by meta-analysis and wavelet transform illustrate significant correlativity with the measured values. However, the R 2 of wavelet transform reached to 0.968, which was higher than that of metaanalysis (0.712). The values of eight single ecological services simulated by meta-analysis and wavelet transform were compared with the corresponding measured values (see Table 5). The data from the meta-analysis indicated that the simulated value of substance production, flood control, carbon sequestration, climate regulation and gas regulation had significant correlations with the measured values. The R 2 are 0.945, 0.880, 0.933, 0.891 and 0.853 (p < 0.01), RMSE were 9.96%, 5.67%, 5.50%, 5.75% and 4.05%, while RMD were −27.08%, 13.80%, 3.60%, −20.08% and 3.74%. The simulated value of wave reduction showed a certain correlation with the measured values. Note: *** stands for p < 0.001, ** stands for p < 0.01, * stands for p < 0.05.

Discussion
In this paper, we compared simulated values calculated by two transform scale methods. Data was acquired from six coastal wetlands in Liaoning province. The obtained results showed that the precision of the wavelet transform model was higher than that of meta analysis.
By analysing those two space-scale methods, it can be found that the important step of meta analysis is determined by data collection. Thus, the themes of coastal wetland evaluation were carefully selected based on the previous studies [46,[48][49][50]. Finally, a model based on the impact of geospatial, environmental and socio-economic characteristics on coastal wetland ecosystem services was constructed to calculate the value of each wetland type [36,51]. While wavelet transform is a relatively new and precise method for space series processing, wavelet transform allows for a completely flexible window function (called the mother wavelet), which can be changed over space based on scale and distance factors [20]. As the mother wavelet moves across space during the wavelet transform process, it generates several coefficients that represent the similarity between the space and mother wavelet at any specific scale [21,52]. Therefore, the wavelet transform method can identify nonlinear changes of values in different geographical spaces for coastal wetland ecosystem services in Liaoning province, China.
Thus, according to the theory of each method (Equations (1) and (3)), meta analysis would be affected by ecological factors and some other related environmental characteristics including wetland area, the GDP per capita, the population density, latitude, the distance from the wetland to the city centre and the evaluation year, while the wavelet transform would be mainly affected by two parameters including scale factors and distance factors. In order to precisely analyze the influence of each factor for two methods, sensitivity analysis method was used to test each possible parameter that affected the simulated result [53][54][55]. The sensitivity of parameter variables is the variation with the corresponding parameters, which increased by 10% [56][57][58]. This step is called local sensitivity analysis: total parameter variables are the changes with all parameters increased by 10% at the same time [59], and this step is called global sensitivity analysis. Through the model computation (Table 6), the random error from the affected factors with the method of meta analysis attained +14.60%, and +8.70% for wavelet transform, which further proved that wavelet transform has higher simulation precision than meta analysis. Note: The sensitivity of parameter variables was the change proportion with the corresponding parameters, which increased by 10%; total parameter variables were the change proportion with all parameters, which increased by 10% at the same time. V Size stands for the variable of wetland size, V GDP stands for the variable of the GDP per capita, V Density stands for the variable of the population density, V Latitude stands for the variable of Latitude, V Distance stands for the variable of the distance from the wetland to the city center, V Year stands for the variable of the evaluation year. Values for all important factors were printed in italics, with the most important factor being underlined. "+" stands for the increased change of sensitivity, also called the increased ratio of the wetland per unit value, "−" stands for the decreased change of sensitivity, also called the decreased ratio of the wetland per unit value.
By applying the meta analysis to simulate the whole provincial coastal wetland values, the results indicated that three services, named adding new lands, wave reduction, recreation and educationm had relatively lower precision (the R 2 were 0.612, 0.712 and 0.646). The analysis of the database revealed the reasons for the lower precision may be the absence of raw data, which was also different from previous research [19,60]. Meanwhile, for the value of recreation and education, distinctions would exist between different coastal wetlands because of geomorphology and tourist attraction etc. [61][62][63][64]. There was no relationship between the value of recreation and education and wetland area, and social-economic characteristics around the wetlands. Thus, if we use the Meta analysis to evaluate a larger scale of wetlands, the ecosystem services with higher precision can directly apply the model. However, three services with relatively lower precision can combine with some other methods such as the method of direct extrapolation [65][66][67][68][69] to achieve better evaluation results.
This study contributes to a more precise evaluation model of wetland ecosystem services in the process of scale transform, providing information on wetland valuation and guidance on how evaluation should be conducted in larger wetlands. The accurate economic valuation of wetlands helps policy makers and planners realize the significant values of wetlands. It could also be necessary for wetland planning, conservation projects, and generally wise use. However, this study still has some limitations. For example, all types of coastal wetland should be selected in Liaoning province. Due to restrictions of labor inputs, the six cases we selected can only cover some types of coastal wetland. We hope that there will be some other more reasonable methods to resolve this limitation in the future.

Conclusions
In this paper, we compared the simulated values provided by two scale transform methods with the measured values in six typical coastal wetlands in Liaoning province, in order to acquire the precision of both methods. The total precision of the wavelet transform model (0.968) was higher than that of meta-analysis (0.712). In addition, the simulated values of single services such as substance production, flood control, carbon sequestration, gas regulation, and climate regulation were closer to the measured values using wavelet transform model. Therefore, this information could be useful for relevant decision makers to select appropriate methods in wetland evaluation projects at larger scales. The wavelet transform method would be helpful to calculate budgets and optimize project coats by providing more efficient and precise results.