Using a sample of over 70, 000 red clump (RC) stars with $5$-$10$% distance accuracy selected from the LAMOST Spectroscopic Survey of the Galactic Anti-center (LSS-GAC), we study the radial and vertical gradients of the Galactic disk(s) mainly in the anti-center direction, covering a significant disk volume of projected Galactocentric radius $7 \leq R_{\rm GC} \leq 14$ kpc and height from the Galactic midplane $0 \leq |Z| \leq 3$ kpc. Our analysis shows that both the radial and vertical metallicity gradients are negative across much of the disk volume probed, and exhibit significant spatial variations. Near the solar circle ($7 \leq R_{\rm GC} \leq 11.5$ kpc), the radial gradient has a moderately steep, negative slope of $-0.08$ dex kpc$^{-1}$ near the midplane ($|Z| < 0.1$ kpc), and the slope flattens with increasing $|Z|$. In the outer disk ($11.5 < R_{\rm GC} \leq 14$ kpc), the radial gradients have an essentially constant, much less steep slope of $-0.01$ dex kpc $^{-1}$ at all heights above the plane, suggesting that the outer disk may have experienced an evolution path different from that of the inner disk. The vertical gradients are found to flatten largely with increasing $R_{\rm GC}$. However, the vertical gradient of the lower disk ($0 \leq |Z| \leq 1$ kpc) is found to flatten with $R_{\rm GC}$ quicker than that of the upper disk ($1 < |Z| \leq 3$ kpc). Our results should provide strong constraints on the theory of disk formation and evolution, as well as the underlying physical processes that shape the disk (e.g. gas flows, radial migration, internal and external perturbations).
Comment: 24 pages, 12 figures, 1 table, Accepted for publication in a special issue of Research in Astronomy and Astrophysics on LAMOST sciences