Dogs are sensitive to small variations of the Earth's magnetic field

I don't know - for my taste, to exclude alignment to the sun they would have had to keep the dogs in a closed environment with an artificial light source. After all, even with clouds present you know where the sun is (and you can still get sunburned etc.)

It also rings my "skeptical" alarm bells when they cite the "original" evidence that cattle aligns along the N-S axis, but they don't cite the paper that fails to replicate the "original" findings in cattle: http://link.springer.com/article/10.1007%2Fs00359-011-0628-7

Not that I know what calm vs stable MF would be. I wonder if it correlates with something else other than sun's position?

Typically, the daily declination comprises westward-shifts in the morning and eastward-shifts in the afternoon, while the magnetic field is rather stable at night [21,22]. This calls for necessity to test whether the dog alignment is not actually influenced primarily by time of the day and most probably by position of the sun on the sky. We can, however, exclude this alternative. First, days when the magnetic field parameters change erratically and unpredictably (i.e., magnetic storms) are quite frequent. These changes have been well studied by others and are described in the literature (cf. [21,22] for reviews). Second, the data collection was not biased to either morning or afternoon (Table 8). Third, periods of sampling under conditions of quiet magnetic field were rather evenly distributed in the course of the day. Fourth, and most importantly, alignment during excreting was apparent under conditions of quiet magnet field, irrespective of the time of day or month. Time of day per se was not a reliable predictor of expression of alignment (Figure 2, Tables 3, 9). Fifth, generally, there are on average 1,450 sunshine hours per year at maximum in the Czech Republic and in Germany, on localities where measurements were done. Even if we would assume that these sunshine hours were evenly distributed over the daylight period and the year (as our observations were), there would only be a probability of 33 % that the observation was made when the sun was visible. Hence, with high probability (67 %) most walks during the daylight period were made when it was cloudy.