# Parameter Uncertainty Analysis of the Life Cycle Inventory Database: Application to Greenhouse Gas Emissions from Brown Rice Production in IDEA

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## Abstract

**:**

## 1. Introduction

- assess the applicability of the semi-quantitative DQI approach and the stochastic modeling approach to the parameter uncertainty analysis of the brown rice production and compare the uncertainty analysis results from both approaches;
- develop a method for the parameter uncertainty analysis of the agricultural DB in the IDEA.

## 2. Materials and Methods

#### 2.1. Brown Rice Production in the IDEA

_{4}, N

_{2}O from the agricultural land were included, but emissions from buildings and equipment and the CO

_{2}sinking of rice production (plants) were excluded. The allocation of the rice straw was not considered because of its low economic value.

#### 2.2. Overview of the Parameter Uncertainty Analysis

#### 2.3. Stochastic Modeling Approach

#### 2.3.1. Step 1. Contribution Analysis

#### 2.3.2. Step 2. Choosing Probability Density Function

_{4}from land) of input parameter contribute about 80% to the GHG (Greenhouse Gas) emissions produced from brown rice production (see case study; Section 3). Here, as an example, we defined three formulas that were related on the input parameter; energy, pesticide use, and CH

_{4}from land for the brown rice production (kth product) as shown in Equations (1)–(3).

_{4}/m

^{2}[38]; $Area\text{}of\text{}Rice\text{}padd{y}_{\left(i,k\right)}$: area of the ith type (dry-field plant and deep water) in the kth product production, m

^{2}; ${W}_{\left(i\right)}$: contribution of ith type (dry-field plant and deep water), 1993–2007, % [35].

#### 2.3.3. Step 3. Monte Carlo Simulation

_{i}, followed by generating the random deviate from the PDF of X

_{i}. Here, the transformation method that transforms the uniform deviate of the uniform distribution to the random deviate of the assumed distribution is used. The next step is to compute the model output using the random deviates, to obtain the relevant statistics [39]. The model output, z, from the Monte Carlo simulation can be expressed as shown in Equation (5):

#### 2.4. Semi-Quantitative DQI Approach

#### 2.4.1. Step 1. Data Quality Assessment (DQA)

#### 2.4.2. Step 2. Aggregated DQI (ADQI)

#### 2.4.3. Step 3. Uncertainty Analysis Using the Transformation Matrix

#### 2.5. Modification of the Semi-Quantitative DQI Approach for IDEA

## 3. Results

#### 3.1. Stochastic Modeling Approach

_{2}eq/f.u., 1.24~1.43 kg CO

_{2}eq/f.u., 0.05 kg CO

_{2}eq/f.u., and 3.95%, respectively, as shown Figure 3.

#### 3.2. Semi-Quantitative DQI Approach

_{2}eq/f.u. (functional unit), 1.07~1.62 kg CO

_{2}eq/f.u., 0.15 kg CO

_{2}eq/f.u., and 11.2%, respectively. The 95% confidence interval of the stochastic approach and that of the semi-quantitative DQI approach around the mean were (1.24 < mean = 1.32 < 1.43) and (1.07 < mean = 1.34 < 1.62), respectively. The relative difference in the absolute value between the single value (point estimate value) (1.35 kg CO

_{2}eq/f.u., see Figure 3) and the upper and lower bounds of the confidence interval were 5.9% (0.08 kg CO

_{2}eq/f.u.), 8.2% (0.11 kg CO

_{2}eq/f.u.) in the stochastic modeling approach, and 20.7% (0.27 kg CO

_{2}eq/f.u.), 20.0% (0.28 kg CO

_{2}eq/f.u.) in the semi-quantitative DQI approach, respectively. This result indicates that point estimate cannot represent the true mean, but rather the confidence interval of the two approaches should be discussed for the development of the simple method for the parameter uncertainty analysis of the agricultural dataset in the IDEA.

#### 3.3. Modification of the Semi-Quantitative DQI Approach for the Agriculture Dataset in the IDEA

_{2}eq/f.u. and 1.24 kg CO

_{2}eq/f.u.) at the lower bounds and 13.29% (1.62 kg CO

_{2}eq/f.u. and 1.43 kg CO

_{2}eq/f.u.) at the upper bounds. A similar observation has been made in other research works as well, where the semi-quantitative DQI approach overestimated the uncertainty [29,48,49]. In particular, the shape parameter and range endpoint appearing in the beta distribution may not be universally applicable; therefore, the beta distribution parameters (shape parameter and range endpoint) should be determined for the agricultural LCI dataset in the IDEA. The two alternative approaches (modification of semi-quantitative DQI approach), alternative approach A and B, were proposed in order to reduce the difference between the two approaches.

## 4. Discussion

_{2}eq/f.u.), 13.71% (0.17 kg CO

_{2}eq/f.u.) in the initial approach, −4.20% (0.06 kg CO

_{2}eq/f.u.), 8.06% (0.10 kg CO

_{2}eq/f.u.) in alternative approach A, and −1.40% (0.02 kg CO

_{2}eq/f.u.), 3.23% (0.04 kg CO

_{2}eq/f.u.) in alternative approach B; (ii) the difference of standard deviation is 200% (initial approach), 80% (alternative approach A), and 20% (alternative approach B), respectively. In addition, the difference of CV (Coefficient Variation) presents similar results, as shown Figure 4. This indicates that alternative B is closest to the stochastic modeling of the brown rice production.

_{4}emissions as stipulated in the guide for the agriculture datasets in the IDEA, shown in Figure 1, and thus same empirical equations such as Equations (1)–(3) can be applicable to other types of agricultural products.

## 5. Conclusions

- A simple method for the parameter uncertainty analysis of the agriculture industry dataset was proposed by modifying the beta distribution parameters (transformation matrix including the endpoint range, shape parameter, and aggregated DQI (ADQI) scales) in the semi-quantitative DQI approach based on the stochastic modeling result.
- The stochastic modeling approach provides the best estimate of the true mean of the sample space; however, because of the excessive requirements for the number of data points, its use in uncertainty analyses is not practical.

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**The hierarchical structure of the IDEA (inventory database for environmental analysis) and input parameters of brown rice production.

**Figure 2.**Flow of the stochastic modeling, the semi-quantitative DQI (data quality indicator) approach, and modification of the semi-quantitative DQI approach.

**Figure 3.**Comparison of the probability distribution of the GHG (greenhouse gas) emissions between the semi-quantitative DQI approach and the stochastic modeling approach.

**Figure 4.**Comparison between the stochastic modeling approach and three semi-quantitative DQI approaches of the brown rice production in the IDEA (kg CO

_{2}-eq/f.u.), SD: Standard Deviation, kg CO

_{2}eq/f.u.; CV: Coefficient Variation, %.

Aggregated DQI Scores | Beta Distribution Parameter | |
---|---|---|

Shape Parameters (α, β) | Range Endpoints (%) | |

1 | 5, 5 | 10 |

1.5 | 4, 4 | 15 |

2 | 3, 3 | 20 |

2.5 | 2, 2 | 25 |

3 | 1, 1 | 30 |

3.5 | 1, 1 | 35 |

4 | 1, 1 | 40 |

4.5 | 1, 1 | 45 |

5 | 1, 1 | 50 |

**Table 2.**The data points of parameters in Equations (1)–(3) for estimating the PDF (probability density function).

Parameters in Equations (1)–(3) | Number of Data Points | Range of Value | Reference | ||
---|---|---|---|---|---|

Energy | $Energ{y}_{farm\left(k\right)}$ | 15 | 5.57–7.75 yen/kg | [35,36] | |

$Energ{y}_{cost\left(i\right)}$ | Diesel | 15 | 19.09–81.11 yen/L | [35,36] | |

Kerosene | 15 | 15.15–88.43 yen/L | [35,36] | ||

Electricity | 15 | 14.01–16.30 yen/kwh | [35,36] | ||

LPG | 15 | 39.06–72.85 yen/kg | [35,36] | ||

Pesticides | ${\begin{array}{c}Pesticide\\ consumption\end{array}}_{\left(i,\text{}k\right)}$ | Miscellaneous chemicals | 15 | 13,344–37,000 ton/year | [37] |

Pesticides | 15 | 47,459–75,000 ton/year | [37] | ||

Rice production | Amount of brown rice production | 18 | 7,791,500–11,980,700 ton/year | [35] | |

Methane (land) | $C{H}_{4\left(k\right)}$ | 9 | 15.85–16.17 g CH_{4}/m^{2}·year | [38] |

Parameter | Input | Stochastic Parameter | |
---|---|---|---|

Methane (land) | 0.03100 (kg/f.u.) | Beta | Minimum = 0.02793, Maximum = 0.03414, Alpha = 2.0, Beta = 3.0 |

Miscellaneous chemicals (insect-fungicide) | 0.01060 (kg/f.u.) | Beta | Minimum = 0.00645, Maximum = 0.015900, Alpha = 2.09, Beta = 4.28 |

Diesel | 0.04850 (L/f.u.) | Beta | Minimum = 0.03200, Maximum = 0.09100, Alpha = 0.64, Beta = 1.72 |

Kerosene | 0.02290 (L/f.u.) | Beta | Minimum = 0.02061, Maximum = 0.02520, Alpha = 2.0, Beta = 3.0 |

Pesticides | 0.00483 (kg/f.u.) | Lognormal | Mean = 0.00388, Std. Dev. = 0.00124, Location = 0.000270 |

Electricity | 0.07227 (kwh/f.u.) | Pareto | Location = 0.06456 Shape = 9.44472 |

Liquefied petroleum gas | 0.00008 (kg/f.u.) | Lognormal | Mean = 0.00008, Std. Dev. = 0.00001, Location = 0.00007 |

**Table 4.**The result of DQA (data quality assessment) and ADQI (aggregated data quality indicator) for the semi-quantitative DQI (data quality indicator) approach to the analysis of the brown rice production.

DQI | DQA | Weighting Factor | ADQI | Beta Distribution Parameter |
---|---|---|---|---|

Reliability | 3 | 0.473 | 2.615 (assume 2.5 to apply to the beta distribution) | Shape parameters (α, β; 2, 2); range endpoint, ±25%) |

Completeness | 2 | 0.241 | ||

Temporal correlation | 3 | 0.147 | ||

Geographical correlation | 1 | 0.072 | ||

Technological correlation | 3 | 0.067 |

**Table 5.**Two alternative approaches A and B for the semi-quantitative DQI approach for the agriculture DBs (data bases) in the IDEA.

Beta Distribution Parameter | ||||
---|---|---|---|---|

ADQI | Shape Parameters (α, β) | Initial Endpoint Range (%) | Alternative A (%) | Alternative B (%) |

1 | 4, 5 | 10.00 | 5.00 | 2.50 |

1.5 | 4, 5 | 15.00 | 7.50 | 3.75 |

2 | 3, 4 | 20.00 | 10.00 | 5.00 |

2.25 | 3, 4 | - | 12.50 | 7.50 |

2.5 | 3, 4 | 25.00 | 15.00 | 10.00 |

2.75 | 2, 3 | - | 17.50 | 12.50 |

3 | 2, 3 | 30.00 | 20.00 | 15.00 |

3.25 | 2, 3 | - | 22.50 | 17.50 |

3.5 | 1, 2 | 35.00 | 25.00 | 20.00 |

3.75 | 1, 2 | - | 27.50 | 22.50 |

4 | 1, 2 | 40.00 | 30.00 | 25.00 |

4.5 | 0, 1 | 45.00 | 35.00 | 30.00 |

5 | 0, 1 | 50.00 | 40.00 | 35.00 |

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**MDPI and ACS Style**

Baek, C.-Y.; Tahara, K.; Park, K.-H.
Parameter Uncertainty Analysis of the Life Cycle Inventory Database: Application to Greenhouse Gas Emissions from Brown Rice Production in IDEA. *Sustainability* **2018**, *10*, 922.
https://doi.org/10.3390/su10040922

**AMA Style**

Baek C-Y, Tahara K, Park K-H.
Parameter Uncertainty Analysis of the Life Cycle Inventory Database: Application to Greenhouse Gas Emissions from Brown Rice Production in IDEA. *Sustainability*. 2018; 10(4):922.
https://doi.org/10.3390/su10040922

**Chicago/Turabian Style**

Baek, Chun-Youl, Kiyotaka Tahara, and Kyu-Hyun Park.
2018. "Parameter Uncertainty Analysis of the Life Cycle Inventory Database: Application to Greenhouse Gas Emissions from Brown Rice Production in IDEA" *Sustainability* 10, no. 4: 922.
https://doi.org/10.3390/su10040922