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ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-22256-3 operations, which is inappropriate for long-term assessment in the BBCE model. Referring to the historical Bitcoin price data, we assume that the long-term Bitcoin price is mainly affected by the halving mechanism of Bitcoin mining rewards. (3) Miners gradually stop or choose other destinations for mining if the Bitcoin mining process is no longer profitable in China. (4) Bitcoin policies are consistent with the overall carbon emission flows in China. In other words, policies such as market access of Bitcoin miners and carbon tax of the Bitcoin blockchain operations can be rejiggered for different emission intensity levels. (5) Miners maintain full invest- ment intensity while in operation, as any reduction in individual investment intensity would put miners in disadvantage and jeopardize their chances of mining new blocks and receiving the reward. By investigating the inner feedback loops and causalities of the systems, BBCE modeling is able to capture the corresponding dynamic behaviors of system vari- ables based on proposed scenarios33,34. Supplementary Fig. 1 shows the complete structure of BBCE modeling. The whole quantitative relationships of BBCE para- meters are demonstrated in Supplementary Methods. Utilizing the flow diagram of BBCE systems illustrated in Supplementary Fig. 1, detailed feedback loops and flows of Bitcoin blockchain subsystems are discussed and clarified. The types, definitions, units, and related references of each variable in Supplementary Fig. 1 are reported in Supplementary Table 1. Bitcoin mining and transaction subsystem. The Bitcoin blockchain utilizes Proof-of-Work (PoW) consensus algorithm for generating new blocks and vali- dating transactions. Bitcoin miners earn a reward if the hash value of target blocks computed by their hardware is validated by all network participants. On the other hand, transactions packaged in the block are confirmed when the block is formally broadcasted to the Bitcoin blockchain. To increase the probability of mining a new block and getting rewarded, the mining hardware will be updated continuously and invested by network participants for higher hash rate, which would cause the hash rate of the whole network to rise. In order to maintain the constant 10-minute per new block generation process, the difficulty of generating a new block is adjusted based on the current hash rate of the whole Bitcoin network. The halving mechanism of block reward is designed to control the total Bitcoin circulation (maximum of 21 million Bitcoins) and prevent inflation. Reward halving occurs every four years, which means that the reward of broadcasting a new block in Bitcoin blockchain will be zero in 2140. As a result, the Bitcoin market price increases periodically due to the halving mechanism of Bitcoin blockchain. With the growing popularity and broadened transaction scope of Bitcoin, the total transactions and transaction fee per block may steadily grow, which drive the other source of Bitcoin miner’s profit rate. Overall, the profit of Bitcoin mining can be calculated by subtracting the total cost of energy consumption and carbon emissions from block reward and transaction fees. Miners will stop investing and updating mining hardware in China when the total cost exceeds the profit rate. Consequently, the whole network hash rate receives a negative feedback due to the investment intensity reductions. Bitcoin energy consumption subsystem. The network mining power is deter- mined by two factors: first, the network hash rate (hashes computed per second) positively accounts for the mining power increase in Bitcoin network when high hash rate miners are invested. However, the updated Bitcoin miners also attempt to reduce the energy consumption per hash, i.e., improve the efficiency of Bitcoin mining process, which helps to reduce the network mining power consumption. In addition, policy makers may raise the market access standard and create barriers for the low- efficiency miners to participate in Bitcoin mining activities in China. In terms of the energy consumption of the whole network, the power usage effectiveness is intro- duced to illustrate the energy consumption efficiency of Bitcoin blockchain as sug- gested by Stoll13. Finally, the network energy cost of Bitcoin mining process is determined by the network energy consumption and average electricity price, which further influences the dynamics behaviors of Bitcoin miner’s investment. Bitcoin carbon emission subsystem. The site selection strategies directly deter- mine the energy types consumed by miners. Although the electricity cost of dis- tinctive energies is more or less the same, their carbon emission patterns may vary significantly according to their respective carbon intensity index. In comparison to miners located in hydro-rich regions, miners located in coal-based regions generate more carbon emission flows under the similar mining techniques and energy usage efficiency due to the higher carbon intensity of coal-based energy17. The proposed BBCE model collects the carbon footprint of Bitcoin miners in both coal-based and hydro-based energy regions to formulate the overall carbon emission flows of the whole Bitcoin blockchain in China. The level variable GDP consists of Bitcoin miner’s profit rate and total cost, which suggests the productivity of the Bitcoin blockchain. It also serves as an auxiliary factor to generate the carbon emission per GDP in our model, which provides guidance for policy makers to implement punitive carbon taxation on Bitcoin industry. Finally, by combining both carbon cost and energy cost, the total cost of Bitcoin mining process provides a negative feedback for miner’s profit rate and their investment strategies. BBCE model parameterizations and quantitative settings. Our BBCE model has been constructed in Vensim software (PLE version 8.2.1). The time-related Bitcoin blockchain time-series data are obtained from www.btc.com, including network hash rate, block size, transaction fee, and difficulty. In addition, the auxiliary parameters and macroenvironment variables for network carbon emission flows assessment are set and considered through various guidelines. For example, the carbon intensities of different energies are suggested by Cheng et al.35. The average energy cost in China and carbon taxation are collected from the World Bank. The site proportion of Bitcoin miners in China are set based on the regional statistics of Bitcoin mining pools in www.btc.com. Moreover, the monthly historical data of Bitcoin blockchain are utilized for time-related parameter regression and simulation from the period of January 2014 to January 2020 through Stata software (version 14.1). Based on the regressed parameters, the whole sample timesteps of network carbon emission assessment cover the period from January 2014 to January 2030 in this study, which is available for scenario investigations under different Bitcoin policies. The initial value of static parameters in BBCE model are shown in Supplementary Table 2, the actual values of the parameterizations adopted are reported in Supplementary Methods, and the key quantitative settings of each subsystem are, respectively, run as follows: According to the guidance of the Cambridge Bitcoin Electricity Consumption Index (https://www.cbeci.org) and Küfeoğlu and Özkuran16, Bitcoin mining equipment is required to update and invest for remaining profitability. It is clear that mining hardware in the Bitcoin network consists of various equipments and their specifications. As a result, the investment intensity in Bitcoin blockchain is computed by the average price of a profitable mining hardware portfolio. The quantitative relationship between investment intensity and time can be expressed as the following form: Investment intensity 1⁄4 α1 ́ Time ́ Proportion of Chinese miners ð1Þ In Eq. (1), the parameter α1 serves as the investment intensity function coefficient on time and the proportion of Chinese miners, which is estimated and formulated by the historical data of Bitcoin blockchain operation from the period of January 2014–January 2020. Then the Bitcoin miner profits are accumulated by profit rate and investment intensity flows, which can be obtained as follows: Mining power 1⁄4 Mining hash rate ́ Mining efficiency ð7Þ 8 NATURE COMMUNICATIONS | (2021)12:1938 | https://doi.org/10.1038/s41467-021-22256-3 | www.nature.com/naturecommunications Miner cumulative profitst 1⁄4 Zt 0 ðMiner profit rate Investment intensityÞdt ð2Þ As discussed above, the aim of Bitcoin mining hardware investment is to improve the miner’s hash rate and the probability of broadcasting a new block. Utilizing the statistics of Bitcoin blockchain, the hash rate of the Bitcoin network is regressed, and the equation is: Mining hash rate 1⁄4 eβ1 þα2 Investment intensity ð3Þ Where β1 and α2 represent the network hash rate constant function coefficient and coefficient on investment intensity, respectively. Similarly, the average block size of Bitcoin is consistent with time due to the growing popularity of Bitcoin transactions and investment. The block size is estimated by time and is illustrated as below: Block size 1⁄4 eβ2 þα3 Time ð4Þ Where β2 and α3 indicate the block size function constant coefficient and coefficient on time, respectively. The proportion of Chinese miners in the Bitcoin mining process will gradually decrease if mining Bitcoin in China is not profitable. So, the proportion parameter in the BBCE model is set as follows: Proportion of Chinese miners 1⁄4IF THEN ELSEðMiner cumulative Profits <0;0:70:01 ́Time; 0:7Þ ð5Þ Suggested by the mining pool statistics obtained from BTC.com, China accounts for approximately 70% of Bitcoin blockchain operation around the world. As a result, we set the initial proportion of Chinese Bitcoin miners as 70%. In addition, the proportion of Chinese Bitcoin miners will gradually decrease if the Bitcoin mining process is no longer profitable in China. The energy consumed per hash will reduce, i.e., the mining efficiency of the Bitcoin blockchain will improve, when updated Bitcoin hardware is invested and introduced. Moreover, the market access standard for efficiency proposed by policy makers also affects network efficiency. Consequently, the mining efficiency can be calculated as follows: Mining efficiency 1⁄4 eβ3 þα4 ́ Investment intensity ́ Market assess standard for efficiency ð6Þ Where β3 and α4 act as the mining efficiency function constant coefficient and coefficient on investment intensity and market access standard for efficiency, respectively. The above function coefficients of BBCE parameters are regressed and formulated based on the actual Bitcoin blockchain operation data from the period of January 2014 to January 2020, and the specific value of each parameter is reported in Supplementary Methods. The mining power of the Bitcoin blockchain can be obtained by network hash rate and mining efficiency. The equation of mining power is shown as follows:PDF Image | carbon emission flows and sustainability of Bitcoin blockchain
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