The formation of vertical sedimentary succession of a delta in the arid and semi-arid basin-margin progradation dramatically depends on the variation of sediment flux and accommodation, but the discontiguous record of signals tends to exist enormously variable, which renders the bulk record of microfacies difficult to quantify from the vertical sedimentary succession. We analyzed the 18 vertical sedimentary successions collected from 18 field trenches of a lake delta by the cusp-catastrophe model, allowing detailed mapping of microfacies. The present detailed study indicates the suitability of cusp-catastrophe theory for explaining vertical sedimentary succession in the BWH (Bawanghe) delta. Three equilibrium states of processes responsible for the deposition of the BWH delta's evolution were established: sandy-dominated upper leaves primarily exhibit the delta plain; sandy/muddy-dominated lower leaves present the delta plain and pro-delta; and sandy-dominated middle leaves which commonly developed the delta front. The result of analysis shows that the reliability of the cusp-catastrophe model to identity mutation of vertical sedimentary succession exceeds 50 %, and to identity microfacies transitions with a precipitation periodicity exceeds 70 %. These cognitions support the previous view that changing precipitation results in an abrupt change in margin progradation. Simultaneously, the study gives new insights into the microfacies quantification of lake deltas and reveals the influence of crest value changes of precipitation on vertical sedimentary succession can be understood from the dependence of microfacies distribution on the change of sediment flux and accommodation.