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Solving the time-dependent Schrödinger equation is an important application area for quantum algorithms. We consider Schrödinger's equation in the semi-classical regime. Here the solutions exhibit strong multiple-scale behavior due to a small parameter ℏ , in the sense that the dynamics of the quantum states and the induced observables can occur on different spatial and temporal scales. Such a Schrödinger equation finds many applications, including in Born-Oppenheimer molecular dynamics and Ehrenfest dynamics. This paper considers quantum analogues of pseudo-spectral (PS) methods on classical computers. Estimates on the gate counts in terms of ℏ and the precision ε are obtained. It is found that the number of required qubits, m , scales only logarithmically with respect to ℏ . When the solution has bounded derivatives up to order ℓ , the symmetric Trotting method has gate complexity O ( ( ε ℏ ) − 1 2 p o l y l o g ( ε − 3 2 ℓ ℏ − 1 − 1 2 ℓ ) ) , provided that the diagonal unitary operators in the pseudo-spectral methods can be implemented with p o l y ( m ) operations. When physical observables are the desired outcomes, however, the step size in the time integration can be chosen independently of ℏ . The gate complexity in this case is reduced to O ( ε − 1 2 p o l y l o g ( ε − 3 2 ℓ ℏ − 1 ) ) , with ℓ again indicating the smoothness of the solution. 

A longstanding question for scientists has been whether or not any observable trends or shifts in global lightning activity have occurred since the Industrial Revolution. This study utilized over 8,000 certified ground‐based stations over a 43‐year period, as well as 16 years of Tropical Rainfall Measuring Mission (TRMM) Lightning Imaging Sensor (LIS) data, to provide a better understanding of the processes behind these trends. Ground station results show that many global regions have observed significant increases or decreases in thunder day occurrence. The Amazon, Maritime Continent, India, Congo, Central America, and Argentina display increases in annual thunder days since the 1970s, whereas China, Australia, and the Sahel among others observe decreases in the number of thunder days. The corresponding change in lightning flash density from the TRMM‐LIS, as well as the number of thunderstorm features and lightning flashes per thunderstorm feature, is compared to the thunder day trends during the TRMM lifespan. Results show a positive correlation between the changes of thunder day occurrence and flash density over most regions of the TRMM domain, including the Maritime Continent, China, South Africa, and Argentina. However, there are several regions with disagreements between the flash density and thunder day trends, such as India and Western Africa. The disagreements are related to the changes in the number of flashes per thunderstorm, which suggest other reasons to interpret the long term trends in thunder day occurrence over various regions. Understanding these regional trends in lightning activity is important in understanding the changes of precipitation systems under a varying climate.