Fig. 9. Level curves of the cost function λ for an irreversible lake (b = 0.4) (left column) and for an hysteretic lake (b = 0.8) (right column). L_min = 0.1, L_max = 1, P_max = 0.5 and VL_max = 0.1). The cost function λ parameters c₁ and c₂ equal 0.3 and 17, respectively, in the first row and 1.5 and 5, respectively, in the second row. The values of the cost function of two states that belong to the same colored line are equal. Viab(K) (gray area) and the set of states where the cost is null merge. In the case of the hysteretic lake (b), the value of the cost function is finite for all states, whereas the cost function takes the infinite value in the case of the irreversible lake (left column).