#
Estimating Carbon Dioxide (CO_{2}) Emissions from Reservoirs Using Artificial Neural Networks

^{*}

## Abstract

**:**

_{2}) flux emissions from reservoirs based on the published data. Input variables, which were latitude, age, the potential net primary productivity, and mean depth, were selected by Spearman correlation analysis, and then the rationality of these inputs was proved by sensitivity analysis. Besides this, a Multiple Non-Linear Regression (MNLR) and a Multiple Linear Regression (MLR) were used for comparison with ANNs. The performance of models was assessed by statistical metrics both in training and testing phases. The results indicated that ANNs gave more accurate results than regression models and GRNN provided the best performance. With the help of this GRNN, the total CO

_{2}emitted by global reservoirs was estimated and possible CO

_{2}flux emissions from a planned reservoir was assessed, which illustrated the potential application of GRNN.

## 1. Introduction

_{2}) emissions, the hydroelectric reservoirs were responsible for emitting 48 Tg C yr

^{−1}as CO

_{2}[11], while Demmer et al. [12] estimated that GHG emissions accounted for 36.8 Tg C yr

^{−1}as CO

_{2}ignoring the types of reservoirs. These estimates corresponded roughly to 2% of global carbon emissions from inland waters that reported a flux of 2100 Tg C yr

^{−1}as CO

_{2}[13]. Although there was a minor difference between the estimated global CO

_{2}flux from hydroelectric systems and all reservoir systems, any significant difference between the areal emissions of CO

_{2}from hydroelectric and non-hydroelectric reservoirs was not detected by statistical analysis [12]. Depending on reservoir type, GHG emissions from reservoirs are related to various factors, which is crucial for understanding the mechanism and the control over GHG emissions. In a single reservoir system, both depth and temperature might be the important predictors of carbon emissions, and also reflect the spatial and seasonal variability [5,14]. GHG emissions tend to decrease with the increase of reservoirs’ latitude and age [11]. Considering the internal source of carbon emissions, the initial organic carbon in the flooded area is another key factor, especially in the young reservoirs [15,16]. Besides, the GHG emissions are also related to dam operation regime [5] and water quality, such as pH [17] and Chlorophyll-a [18,19].

_{2}emissions from reservoirs in many regions, which leaves a critical gap in the global CO

_{2}budgets. To resolve this problem, statistical models are the appropriate methods to extrapolate the flux of reservoirs without measured data and then derive regional or global estimations relying on a limited number of measurements [20]. One of the most common models is the statistical regression model, which can demonstrate the relationship between CO

_{2}emissions and one [9] or several [11,16] factors by the regression equations. Other models that can identify more complex non-linear responses, such as Random Forests [6] and Monte Carlo simulation [21], were also used to elucidate the relationship between CO

_{2}emissions and the factors of environment or dams, and also to predict CO

_{2}emissions from other under-sampled reservoirs in the nearby geographic region. Unlike these models with the inputs of environmental factors, a mathematical model with the theory of Self-Organized Criticality (SOC) was employed to extrapolate values from one reservoir to another directly without any other features [22]. These pioneering models showed a low degree of precision and regional limitations; therefore, developing and optimizing models of reservoir CO

_{2}emissions is still one of the future research directions [6,12].

_{2}fluxes have been measured in at least 229 reservoir systems in the world until 2016 [12], which supplies the sufficient amount of data for ANNs. Besides, many commonly employed techniques for measurement focus on quantifying the diffusive flux of gases across the air–water interface, which is suitable for CO

_{2}because of its solubility [12]. There are some other key factors that affect model performance, such as the architecture selection and parameter settings [28]. However, it is difficult to reach any conclusion of which model architecture is absolutely suitable to a particular circumstance. Therefore, ad hoc approaches, such as a trial-and-error approach, might be acceptable to determine the parameters, following the principle that the optimal network structure generally keeps a balance between generalization ability and network complexity [31].

_{2}flux emission from reservoirs by ANNs, back propagation neural network (BPNN) and general regression neural network (GRNN), based on the published data from various types of reservoirs with a global distribution. The input variables of models is selected through both the correlation analysis and domain knowledge. The rationality of selected sets of inputs is tested by sensitivity analysis. The model parameters selection are described in detail and the model performance is evaluated using statistical indices. Since the models have the ability to predict CO

_{2}fluxes from a reservoir without measurements, the global fluxes of CO

_{2}emissions from reservoirs can be estimated. Besides this, the possible magnitude of CO

_{2}emissions from a planned reservoir can also be assessed by models based on some reservoirs’ features, which gives guidance for dam’s construction.

## 2. Materials and Methods

#### 2.1. Data Collection

_{2}emission fluxes from reservoir surface were based on data collection by Barros et al. [11] in 2011 and Deemer et al. [12] in 2016. CO

_{2}emission monitoring data from reservoirs in some latest literature were also assembled. Some essential parameters about reservoirs and monitoring were collected from the relevant literature and part of missing values were completed from Global Reservoir and Dam (GRanD) database [19]. Another important parameter, the primary productivity of potential vegetation (NPP0) in the reservoir’s location, was extracted from the map of the human appropriation of net primary production (HANPP) [32]. In cases where more than one study measured CO

_{2}fluxes from the system in the same year, the arithmetic mean of these parameters was used for statistic, and CO

_{2}fluxes from same reservoir measured in different years were kept at the original values. Therefore, 277 data sets were collected based on the studies in 235 reservoirs, and the information of data set can be found in supplementary Table S1.

_{2}flux. CO

_{2}flux was used as the output of models in this study. The statistical parameters including minimum value, maximum value, mean value, median, standard deviation, and variation coefficient are given in Table 1.

#### 2.2. Input Variables and Data Processing

_{2}emissions data set comprises 235 reservoirs in 21 countries. In this study, 70% of samples with the whole selected input variables were randomly chosen to build and train models, while the remaining data was used to test the models.

#### 2.3. Artificial Neural Networks (ANNs)

#### 2.3.1. Back Propagation Neural Networks (BPNNs)

#### 2.3.2. General Regression Neural Networks (GRNNs)

#### 2.4. Statistical Regression Models

#### 2.5. Performance Metrics

^{2}) is identical to the square of the correlation coefficient (R) in some cases, which evaluates the degree of variability that can be explained by the model. Nash–Sutcliffe efficiency (NSE) [40] is a popular likelihood function to define the goodness of fit between monitoring data and model outputs. Smaller RMSE and MAE values and larger R

^{2}and NSE values indicate better model performance.

## 3. Results

#### 3.1. Alternative Input Variable Selection

_{2}flux and other nine variables of these reservoirs. Spearman correlation coefficient was selected because the data of CO

_{2}flux was not normally distributed (Kolmogorov–Smirnov test, p < 0.001), even after several different attempts at transformation. Some reservoirs were measured many times in different years, which means these reservoirs have more than one set of data with the same parameters except age and CO

_{2}flux. Therefore, Spearman correlation analysis between CO

_{2}flux and age was carried out by the original values, while Spearman correlation analysis between CO

_{2}flux and other parameters (Lat, Chl-a, WT, MD, RT, DOC, TP, and NPP0) was made based on the arithmetic mean.

_{2}prediction. Only the reservoir data where the four parameters’ records are effective and available were used, otherwise, this set of data would be removed. After deleting the invalid data, a dataset containing 251 sets of data was selected for simulation.

#### 3.2. Model Parameters Selection

^{−2}d

^{−1}). As a result, the topology of BPNN used in this study has four input neurons, nine hidden neurons, and one output neuron.

^{−2}d

^{−1}).

#### 3.3. Model Performances

_{2}flux for training and testing are given in Table 3.

_{2}flux values by MLR, MNLR, BPNN, and GRNN models in training and testing stages are plotted in Figure 3. Comparisons among three models above indicate that GRNN generally gives better accuracy than the BPNN, MNLR, and MLR models. This can also be clearly observed from the fit line equations.

#### 3.4. Sensitivity Analysis

_{2}flux. We built new models based on different combination of input variables and compared their RMSE and R

^{2}values. These four sets of inputs were made up by omitting a parameter on each run. It was obvious that the omission of the most important parameter could have the highest influence on model performance, which was reflected in higher RMSE values and lower R

^{2}values [41]. Results of sensitivity analysis are presented in Table 5. The results demonstrated that the performance of the models with four input variables is better than other models’, and the latitude parameter is an essential input for GRNN, BPNN, and MNLR.

## 4. Discussion

#### 4.1. Comparison of Results Obtained by Models

_{2}emission from reservoirs.

_{2}flux in training and testing data sets, which is general in statistical prediction models [24,45]. Because the inputs cannot totally explain the outputs especially for extreme values, this tendency can also partly attribute to the non-homogeneous nature of data. Since CO

_{2}fluxes were measured from various reservoirs in different years, the lower slope in testing phases is due to the differences in training and testing data ranges. As listed in Table 3, the median and standard deviation of the testing data set were higher than those of the training data set.

_{2}and age based on datasets of 15 reservoirs (R

^{2}= 0.35), and Deemer et al. [12] built the relationship between CO

_{2}and mean annual precipitation based on datasets of 31 reservoirs (R

^{2}= 0.11). Barros et al. [11] used the multiple regression analysis to describe the relationship between three dependent variables (age, latitude, and DOC) and CO

_{2}flux based on datasets of 73 reservoirs (R

^{2}= 0.40). Compared with these regression models, our GRNN showed higher R

^{2}in both training (R

^{2}= 0.61) and testing (R

^{2}= 0.76) phases. The superior performance benefits from not only the advantages of GRNN, but also the larger database. Besides, without a testing process in the previous regression models, it is difficult to evaluate their generalization ability and apply in other reservoirs credibly. This study demonstrates that GRNN models could be an appropriate approach for prediction CO

_{2}emissions from reservoirs in other study systems.

#### 4.2. Sensitivity Analysis

_{2}flux was not reflected adequately in the results of Spearman correlation analysis. The possible reason is that the relationship between latitude and CO

_{2}flux is non-linear. Consequently, the use of non-linear statistical dependence measures is more appropriate for determining inputs to ANN models [31].

#### 4.3. Application of Established Model

#### 4.3.1. Estimation of the Global Magnitude of the CO_{2} Fluxes from Reservoirs

_{2}emissions from documented reservoirs can be estimated. This estimation was based on the GRanD, which contains 6862 records of reservoirs updated in 2011 [19], and HANPP [32]. We selected latitude, the year of construction and the average depth from GRanD and extracted NPP0 from HANPP following the site of these reservoirs.

_{2}fluxes from global reservoirs by the tested GRNN, the confidence interval should be given together. However, ANNs are black box models that cannot be described as particular equations. Therefore, the potential predictive confidence interval was given based on the statistical analysis between observed and predicted CO

_{2}fluxes in testing phase. The methods to calculate confidence interval are as follows [46]: (a) the errors between observed and predicted values in testing phase were calculated; (b) the Bootstrap samples were created by resampling from the errors on 100,000 replicates; (c) the medians of Bootstrap error samples are computed; (d) the $1-\alpha $ Bootstrap Pivotal Confidence Intervals (CIs) for median of errors are estimated by Equation (10):

_{2}emission fluxes from 6862 reservoirs in 2011. Because 95% CI of error from GRNN is (−68.11, 60.86), these fluxes were updated into intervals for subsequent estimations. Then we multiplied these fluxes, corresponding area, and the number of days in a year that CO

_{2}can diffuse on the surface of reservoirs. Considering the influence of seasonality, especially the ice cover, we made an assumption that the temperate reservoirs which located higher than 30° N or 30° S latitudes are ice-free for 200 days on average. This refers to the one of the study in St. Louis et al. [8], since only this study takes ice cover into account among pervious estimations listed in Table 6. As a result, we estimate that global reservoirs emit 40.03 Tg C yr

^{−1}as CO

_{2}(5th and 95th confidence interval: 32.03–47.18 Tg C yr

^{−1}as CO

_{2}).

_{2}flux estimated by St. Louis et al. [8] is larger, which might be caused by the overestimation of global reservoirs’ area and the young age of sampled reservoirs. Only three tropical reservoirs with the average age of 7.70 years were used to estimate CO

_{2}fluxes from all tropical reservoirs. The estimation by Hertwich [16] is also a little larger, because CO

_{2}flux is multiplied by an uncertainty factor of 2. The previous estimations derived from the product of the average of CO

_{2}flux in database multiplied with the global surface area of reservoirs, while the estimation in this study took into account the annual-scale flux variability of a special reservoir and the difference in geographical position among global reservoirs. However, further refinement is still required for more precise estimates. Since there are no real data of time-series, this model cannot predict potential CO

_{2}fluxes in long temporal scale. The cause–effect relationships between water quality and CO

_{2}flux received little attention in this study because of the limited data. The direct and indirect influences from ice cover especially in the boreal region should be fully studied and accurately calculated in future estimations.

#### 4.3.2. Estimations of CO_{2} Emissions from a Planned Reservoir

_{2}emission flux during a fixed period of time from a proposed reservoir with planned location and depth can be estimated by this model. Therefore, it is possible to give guidance for dam construction. A hypothetical case, which was not based on any actual events, was used to show this potential utilization of GRNN in this study. We assumed that a reservoir would be constructed, and the geographical coordinates could be selected from 23.5° N to 26.4° N with the same longitude (115° E), and the mean depth could vary from 5 m to 34 m. The possible CO

_{2}fluxes emission from this reservoirs in the first 20 years with different features were shown in Figure 4. Although the construction of reservoirs should consider many realistic questions, the possible carbon emissions from new reservoirs might also be used as an important index of reservoir construction in the future.

#### 4.4. Future Research Directions

_{2}emissions from existing reservoirs, ignoring the potential CO

_{2}emissions from that land before impoundment, which might overestimate greenhouse effect from reservoirs. Recent study shows that the net carbon emissions from reservoirs are determined by different types of areas before flooding and provides a simple approach to quantify the net CO

_{2}emissions [47]. Future studies are therefore necessary to simulate and predict net CO

_{2}flux emits from reservoirs. Moreover, the combination of classification and regression machine learning can be a promising approach.

_{2}emission was chosen to simulate because of the quantity and quality of the monitoring data. However, CH

_{4}is a more powerful GHG than CO

_{2}[12]. Unlike CO

_{2}emissions, CH

_{4}emissions from reservoirs are new and anthropogenic [47]. Therefore, CH

_{4}footprint should be simulated and the magnitude needs to be estimated based on various released pathways in the future.

## 5. Conclusions

_{2}emissions from reservoirs based on data records collected from published various field studies. Input variables used in models were selected by both Spearman correlation analysis and domain knowledge. The performance of models and observation was compared and evaluated by the indexes of RMSE, MAE, R

^{2}, and NSE. It appears that the performance of ANNs is superior to the one of regression models. The GRNN’s performance is better than BPNN’s, while MNLR is superior to MLR. Sensitivity analysis of these four models confirmed that latitude-value is an important parameter in predicting CO

_{2}flux. The results demonstrate that GRNNs have great potential to estimate CO

_{2}emission from reservoirs when it is hard to acquire the monitoring data. The statistical models deserve more attention, because they are effective tools to assess global GHG emissions from reservoirs and provide new insights into the consideration of reservoir’s construction during the planning stage. However, since the accuracy and generalization of statistical models largely depend on the measured data, more monitoring will be required in global reservoirs systematically. For example, the global CO

_{2}flux can be predicted in a longer time scale with the data of continuous monitoring on special reservoirs located in different latitude. Moreover, the mechanism models should be built to understand the relationship between CO

_{2}emission and other environmental factors clearly in the future.

## Supplementary Materials

_{2}emission measurements and other data of reservoirs analyzed in the paper.

## Author Contributions

## Conflicts of Interest

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**Figure 4.**CO

_{2}emissions from reservoirs with different locations and depths in the first 20 years.

Parameters | Unit | Min | Max | Mean | Median | SD | VC |
---|---|---|---|---|---|---|---|

Lat | ° | −42.93 | 68.00 | 31.96 | 38.17 | 26.36 | 0.83 |

Age | yrs | 1.00 | 95.00 | 39.09 | 36.00 | 24.55 | 0.63 |

Chl-a | μg L^{−1} | 0.20 | 137.50 | 12.03 | 4.13 | 24.78 | 1.96 |

WT | °C | 6.30 | 35.00 | 17.88 | 17.40 | 5.52 | 0.30 |

MD | m | 0.30 | 400.00 | 26.58 | 15.00 | 40.26 | 1.52 |

RT | days | 1.25 | 13,140.00 | 665.75 | 180.00 | 1689.54 | 2.54 |

DOC | mg L^{−1} | 1.25 | 30.00 | 4.79 | 3.82 | 4.01 | 0.84 |

TP | μg L^{−1} | 1.40 | 500.00 | 62.61 | 29.00 | 96.89 | 1.55 |

NPP0 | mg C m^{−2} d^{−1} | 151.90 | 3200.68 | 1529.21 | 1574.50 | 604.70 | 0.40 |

CO_{2} flux | mg C m^{−2} d^{−1} | −356.00 | 3800.00 | 400.90 | 254.75 | 569.89 | 1.42 |

Variables | n | Correlation | Sig. | Variables | n | Correlation | Sig. |
---|---|---|---|---|---|---|---|

Lat | 236 | −0.025 | 0.69 | RT | 98 | 0.055 | 0.59 |

Age | 266 | −0.307 | 0.00 | DOC | 51 | 0.129 | 0.36 |

Chl-a | 69 | −0.115 | 0.35 | TP | 47 | 0.005 | 0.98 |

WT | 158 | −0.118 | 0.13 | NPP0 | 234 | 0.153 | 0.02 |

MD | 217 | −0.151 | 0.02 |

Statistical Parameters | Unit | Training Set | Testing Set |
---|---|---|---|

n | 76 | 175 | |

Min | mg C m^{−2} d^{−1} | −325.90 | −356.00 |

Max | mg C m^{−2} d^{−1} | 3776.00 | 3800.00 |

Mean | mg C m^{−2} d^{−1} | 390.82 | 486.40 |

Median | mg C m^{−2} d^{−1} | 243.29 | 312.03 |

SD | mg C m^{−2} d^{−1} | 549.75 | 664.02 |

Model | Training Data Set | Testing Data Set | ||||||
---|---|---|---|---|---|---|---|---|

RMSE | MAE | R^{2} | NSE | RMSE | MAE | R^{2} | NSE | |

MLR | 476.42 | 313.22 | 0.25 | 0.25 | 625.36 | 429.96 | 0.12 | 0.11 |

MNLR | 417.26 | 282.00 | 0.43 | 0.42 | 529.53 | 391.46 | 0.40 | 0.36 |

BPNN | 396.59 | 268.53 | 0.52 | 0.48 | 505.43 | 395.33 | 0.47 | 0.42 |

GRNN | 272.50 | 147.62 | 0.76 | 0.75 | 418.48 | 295.34 | 0.61 | 0.60 |

^{−1}d

^{−1}; the unit of MAE is mg C m

^{−1}d

^{−1}. RMSE, root mean squared error; MAE, mean absolute error; NSE, Nash–Sutcliffe efficiency; MLR, multiple linear regression; MNLR, multiple non-linear regression; BPNN, Back Propagation Neural Network; GRNN, Generalized Regression Neural Network.

Model | RMSE (mg C m^{−2} d^{−1}) | R^{2} | ||||||
---|---|---|---|---|---|---|---|---|

GRNN | BPNN | MNLR | MLR | GRNN | BPNN | MNLR | MLR | |

All | 418.48 | 505.43 | 529.53 | 625.36 | 0.61 | 0.47 | 0.40 | 0.12 |

Skip MD | 432.14 | 552.55 | 530.95 | 629.10 | 0.59 | 0.35 | 0.39 | 0.11 |

Skip NPP0 | 463.63 | 567.08 | 532.26 | 635.25 | 0.52 | 0.38 | 0.38 | 0.09 |

Skip Age | 462.65 | 519.62 | 535.68 | 633.44 | 0.57 | 0.45 | 0.39 | 0.10 |

Skip Lat | 469.06 | 555.51 | 628.93 | 620.69 | 0.51 | 0.32 | 0.11 | 0.13 |

Studies | Sample Size | Type of Dataset | Method | Area (10^{5} km^{2}) | CO_{2} (Tg C yr^{−1}) | |
---|---|---|---|---|---|---|

This study | 251 | All reservoirs | Individual ^{1} | 4.47 | 40.03 ^{3} | |

Previous studies | Deemer et al. [12] | 229 | All reservoirs | Average ^{2} | 3.1 | 36.8 |

Hertwich [16] | 142 | Hydroelectric | Average ^{2} | 3.3 | 76 | |

Barros et al. [11] | 85 | Hydroelectric | Average ^{2} | 3.4 | 48 | |

St. Louis et al. [8] | 19 | All reservoirs | Average ^{2} | 15.0 | 272.2 |

^{1}Individual method, calculated by the sum of CO

_{2}flux from each individual reservoir;

^{2}Average method, calculated by the multiplication of average CO

_{2}flux of database and total reservoirs area. (2)

^{3}The 95% confidence interval is (32.03, 47.18) Tg C yr

^{−1}.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chen, Z.; Ye, X.; Huang, P.
Estimating Carbon Dioxide (CO_{2}) Emissions from Reservoirs Using Artificial Neural Networks. *Water* **2018**, *10*, 26.
https://doi.org/10.3390/w10010026

**AMA Style**

Chen Z, Ye X, Huang P.
Estimating Carbon Dioxide (CO_{2}) Emissions from Reservoirs Using Artificial Neural Networks. *Water*. 2018; 10(1):26.
https://doi.org/10.3390/w10010026

**Chicago/Turabian Style**

Chen, Zhonghan, Xiaoqian Ye, and Ping Huang.
2018. "Estimating Carbon Dioxide (CO_{2}) Emissions from Reservoirs Using Artificial Neural Networks" *Water* 10, no. 1: 26.
https://doi.org/10.3390/w10010026