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The vertical temperature gradient is an important indicator of atmospheric stratification, and the horizontal temperature gradient describes the variation in atmospheric temperature in a given horizontal direction. In the meanwhile, Temperature advection is a phenomenon whereby the temperature changes as a result of the horizontal air movements that plays an important role in the development of weather systems and weather phenomena. In this paper, a one-dimensional numerical differentiation algorithm is applied to calculate the temperature gradient and temperature advection from the temperature and wind fields obtained from flat-floating sounding data, and the results are compared with those of the central difference method. The comparison shows that the one-dimensional numerical differentiation algorithm is stable and feasible. However, in the calculation of the vertical temperature gradient, the advantages of the one-dimensional numerical differentiation algorithm are not apparent because of the high accuracy of the flat-floating sounding data. The relative error of the temperature-advection associated with the one-dimensional numerical differentiation algorithm is two orders of magnitude less than that associated with the central difference method. In addition, the relative error of the one-dimensional numerical differentiation algorithm is more stable. These results show that the issue of calculating partial derivatives based on observation data is ill-posed in mathematics and that the one-dimensional numerical differentiation algorithm is better suited to solve such issues than is the central difference method.
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