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The Carbon Footprint of Bitcoin

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with 𝑁 - 𝑒 = realistic energy efficiency of hardware [𝐽/𝐻] - π‘ƒπ‘ˆπΈπ‘ = π‘™π‘œπ‘ π‘ π‘’π‘  π‘“π‘Ÿπ‘œπ‘š π‘π‘œπ‘œπ‘™π‘–π‘›π‘” π‘Žπ‘›π‘‘ 𝐼𝑇 π‘’π‘žπ‘’π‘–π‘π‘šπ‘’π‘›π‘‘ [%] The realistic energy efficiency of the network can be determined using the market shares of ASIC producers and the energy efficiency of the hardware in operation. 𝑒 =[βˆ‘π‘› 𝑆 βˆ—π‘’ ]+[1βˆ’(βˆ‘π‘› 𝑆 )]βˆ—π‘’, (4) 𝑁 𝑖=1 𝐴𝑃𝑖 𝐴𝑃𝑖 𝑖=1 𝐴𝑃𝑖 𝑃 with- i=ASICProducer(1,...,n) - 𝑒𝑁 = realistic energy efficiency of hardware [𝐽/𝐻] - 𝑆 =𝑠hπ‘Žπ‘Ÿπ‘’π‘œπ‘“π΄π‘†πΌπΆπ‘π‘Ÿπ‘œπ‘‘π‘’π‘π‘’π‘Ÿπ‘–[%] 𝐴𝑃𝑖 - 𝑒𝐴𝑃𝑖 = energy efficiency of 𝐴𝑆𝐼𝐢 π‘π‘Ÿπ‘œπ‘‘π‘’π‘π‘’π‘Ÿ 𝑖 [𝐽/𝐻] - 𝑒𝑃 = energy efficiency π‘“π‘œπ‘Ÿ π‘§π‘’π‘Ÿπ‘œ π‘π‘Ÿπ‘œπ‘“π‘–π‘‘ [𝐽/𝐻] If some of the computing power cannot be assigned to one of the major ASIC producers, we assume this computing power originates from hardware, which generates zero profit. By equalizing EUB and ERM, we derive 𝑒𝑃 = (𝑅𝐡+𝑅𝑇)βˆ—π‘€ βˆ— 1 . (5) π‘ƒπ‘βˆ—π»βˆ—π‘ƒπ‘ˆπΈπ‘ 𝑑 In terms of the average losses from cooling and equipment, we differentiate between three types of mining facilities according to size, and weight them by their share in terms of computing power π‘ƒπ‘ˆπΈπ‘ =𝑆𝑆 βˆ—π‘ƒπ‘ˆπΈπ‘† +𝑆𝑀 βˆ—π‘ƒπ‘ˆπΈπ‘€ +𝑆𝐿 βˆ—π‘ƒπ‘ˆπΈπΏ. - 𝑗 = π‘“π‘Žπ‘π‘–π‘™π‘–π‘‘π‘¦ 𝑑𝑦𝑝𝑒 (π‘†π‘šπ‘Žπ‘™π‘™, π‘€π‘’π‘‘π‘–π‘’π‘š, πΏπ‘Žπ‘Ÿπ‘”π‘’) - 𝑆 =𝑠hπ‘Žπ‘Ÿπ‘’π‘œπ‘“π‘“π‘Žπ‘π‘–π‘™π‘–π‘‘π‘¦π‘‘π‘¦π‘π‘’π‘—[%] 𝑗 - π‘ƒπ‘ˆπΈ =π‘™π‘œπ‘ π‘ π‘’π‘ π‘“π‘Ÿπ‘œπ‘šπ‘π‘œπ‘œπ‘™π‘–π‘›π‘”π‘Žπ‘›π‘‘πΌπ‘‡π‘’π‘žπ‘’π‘–π‘π‘šπ‘’π‘›π‘‘π‘œπ‘“π‘“π‘Žπ‘π‘–π‘™π‘–π‘‘π‘¦π‘‘π‘¦π‘π‘’π‘—[%] 𝑗 The resulting carbon footprint of the Bitcoin network depends on the carbon intensity 𝐼𝑁 of the power mix: 𝐹 = 𝐸 βˆ— 𝐼𝑁 . In order to incorporate local differences in the carbon intensity of the power mix, we differentiate among regions and weight them by computing power share: 𝐼=βˆ‘π‘› 𝑆 βˆ—πΌ +β‹―+𝑆 βˆ—πΌ . 𝑁 𝑖=𝑅𝑒𝑔 1 𝑅𝑒𝑔 1 𝑅𝑒𝑔 1 𝑅𝑒𝑔 𝑛 𝑅𝑒𝑔 𝑛 17

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