In the literature, we found 15 references showing that the sunspot photospheric magnetic field vertical gradient is on the order of 3-4？G/km, with field strength decreasing with height, whereas the horizontal gradient is nine times weaker on the order of 0.4-0.5？G/km. This is confirmed by our recent THEMIS observations. As a consequence, the vanishing of is not realized. In other words, a loss of magnetic flux is observed with increasing height, which is not compensated for by an increase of the horizontal flux. We show that the lack of spatial resolution, vertical as well as horizontal, cannot be held responsible for the nonvanishing observed . The present paper is devoted to the investigation of this problem. We investigate how the magnetic field is influenced by the plasma anisotropy due to the stratification, which is responsible for an “aspect ratio” between horizontal and vertical typical lengths. On the example of our THEMIS observations, made of two spectral lines formed at two different depths, which enables the retrieval of the three components entering , it is shown that once this aspect ratio is applied, the rescaled vanishes, which suggests a new methodology for MHD modeling in the photosphere. 1. Introduction In the literature, we found 15 references reporting magnetic field gradient measurements in sunspots, with various lines, instruments, and interpretation methods. We restricted to references later than 1983. A detailed study of the references shows that they may be classified into two types: those where the vertical gradient is measured, which is found on the order of 3-4？G/km with the field strength decreasing with height, and those where alternatively the horizontal gradient is obtained, which is found on the order of 0.4-0.5？G/km. These orders of magnitude were completely retrieved in our recent THEMIS observations. This classification does not suffer any exception. The two gradients differ by a factor of nine. This problem was pointed out by other authors. Solanki [1] investigated the problem and concluded that “no satisfactory solution has been found as yet for the unexpectedly small (horizontal) gradients.” As a consequence, the vanishing of is not realized, and the present paper is devoted to the investigation of this problem. In Section 2, we report in details about these observations, and we discuss different possible causes on the observational side of the question. We consider the noise effect, the unresolved structure effect, and the line-of-sight and pixel integration effects. As none of these effects has brought the
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