Let's use solar energy! How large does the area need to be?

Our society consumes quite large amount of energy, mostly relying on fossil-fuels, and our demand of energy shall keep increasing as a whole. To supply the energy demand in coming future, renewable energy needs to be utilized (see The amount of energy we consume). Thinking of sunlight as a model, one may notice that energy amount depends on the area of irradiation. Let's see in this post how large the area needs to be to supply the energy to the world.

Is it possible to support the world energy consumption by solar light?

Let me consider a scenario in which the total energy demand in the world is supplied by the sunlight.
... is it really possible to do that to begin with?
Quantitatively addressing such a scenario would require three key information of (1) energy density of sunlight, (2) duration of irradiation, and (3) energy conversion efficiency.

(1) energy density of sunlight

Actually, the energy density of sunlight vaires wiht the latitude. While regions around the equator recieve stronger sunlight, the polar regions recieve the weaker ones because the sunlight needs to travel through larger volume of air. At Air mass of 1.5 (around the average latitude of US^[1]) the sunlight irradiation energy at full wave length is 1003 [W m^-2].

(2) duration of sunlight irradiation

The duration of sunlight also varies with the location.^[2] In USA, most locations recieve the sunlight 2,000s [h] annually.^[3] As a representative value, 2,500 [h] is adopted here.

(3) energy conversion efficiency

We have to accept some losses because we cannot convert the solar energy into the form of energy that we use. I consider here a value of 10% as the conversion efficiency from sunlight to electric power. This value is slightly smaller than the typical photovoltaic (PV) cells of 14-20%.^[4] The highest reported under development is 47.1% according to the National Renewable Energy Laboratory (NREL).^[5]

The world primary energy consumption was approximately 5.6*10²⁰ [J year^-1] as seen in another post (The amount of energy we consume). Therefore, the total area needed to support the world energy consumption is approximately 620,000 km²(=5.6*10²⁰ [J y^-1] / 1003 [W m^-2] / 2,500 [h y^-1] /10 [%]), corresponding to 790 [km] square.

Because the land area of Japan is 378,000 [km²],^[6] the world needs 1.6 times larger area than Japan to support its energy demand. In the case of USA, because its land area is 9,628,000 [km²],^[7] just 6.4% of area is sufficient.

How large does the area need to be to support Japan's energy demand?

What would be the needed area in the case of Japan' energy demand?

Because the primary energy consumption of Japan amounts to 1.9*10¹⁹ J,^[8] an area of 21,194 [km²] is needed to support it. Among preferctures in Japan, the largest one is Hokkaido with 83,457 [km²], followed by Iwate with 15,279 [km²].^[9] A quarter of Hokkaido is more than enough, but larger area than Iawte is needed, in the case of Japan.

References

1. National Renewable Energy Laboratory (NREL), Statistical Review of World Energy, “Reference Air Mass 1.5 Spectra”, https://www.nrel.gov/grid/solar-resource/spectra-am1.5.html (accessed on 2022/02/03).
2. How To Journey.com, “［統計］世界・日本の主要都市の日照時間ランキング”, https://howtojourney.com/8657/ (accessed on 2022/02/3)
3. Current Results Publishing Ltd., “Average Annual Sunshine by State”, https://www.currentresults.com/Weather/US/average-annual-state-sunshine.php (accessed on 2022/02/03)
4. 国立研究開発法人 新エネルギー・産業技術総合開発機構, "世界一のモジュール変換効率40％超を目指す、太陽電池開発中", https://www.nedo.go.jp/hyoukabu/articles/201111sharp/index.html (accessed on 2022/02/08)
5. National Renewable Energy Laboratory (NREL), "Best Research-Cell Efficiency Chart", https://www.nrel.gov/pv/cell-efficiency.html (accessed on 2022/02/08)
6. 外務省, “日本の領土をめぐる情勢”, https://www.mofa.go.jp/mofaj/territory/page1w_000011.html (accessed on 2022/02/03)
7. 外務省, “アメリカ合衆国（United States of America）基礎データ”, https://www.mofa.go.jp/mofaj/area/usa/data.html (accessed on 2022/02/03)
8. 経済産業省 資源エネルギー庁, “総合エネルギー統計”, https://www.enecho.meti.go.jp/statistics/total_energy/results.html#headline2 (accessed on 2022/02/03)
9. 国土交通省 国土地理院, “都道府県別面積の順位”, https://www.gsi.go.jp/common/000077733.pdf (accessed on 2022/02/03)