BOD sag is a typical DO pattern followed in an aerated aqueous system (with time). When any organic load comes into the water body, the aerobic microbes decompose it using the oxygen of water and thus depletion of DO occurs in the water body. At the same time, re-aeration provides oxygen to the water body. The rate of oxygenation is proportional to the deficit of oxygen from the saturation value. The rate of depletion of DO and the rate of oxygenation is equal at a point where the O2 deficiency is maximum. After the point rate of oxygenation overcomes the O2 depletion rate.
dD/dt=k1L-k2D
dD/dt= Rate of change in oxygen deficit.
L= BOD at that time
k1= deoxygenation rate const.
D=oxygen deficit.
k2= reaeration constant.
For details, you can study any good environmental water chemistry book.