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Based on the work of Itzykson and Zuber on Kontsevich's integrals, we give ageometric interpretation and a simple proof of Zhou's explicit formula for theWitten-Kontsevich tau function. More precisely, we show that the numbers$A_{m,n}^{Zhou}$ defined by Zhou coincide with the affine coordinates for thepoint of the Sato Grassmannian corresponding to the Witten-Kontsevich taufunction. Generating functions and new recursion relations for $A_{m,n}^{Zhou}$are derived. Our formulation on matrix-valued affine coordinates and on taufunctions remains valid for generic Grassmannian solutions of the KdVhierarchy.  A by-product of our study indicates an interesting relation between thematrix-valued affine coordinates for the Witten-Kontsevich tau function and the$V$-matrices associated to the $R$-matrix of Witten's $3$-spin structures.

Geometric interpretation of Zhou's explicit formula for the Witten-Kontsevich tau function