Increasing headwind during climb does miracles to the climb rate.  Suppose you want to climb from sea level to 2000 feet while increasing the true airspeed from 140 to 160 knots (70 m/s to 80 m/s).  In steady wind conditions that means the aircraft needs to accelerate 20 knots during that climb, which consumes part of the energy available. 

But if there is a windshear and the headwind is increasing by 30 knots during that climb (not unreasonable in stormy conditions), the groundspeed will reduce by 10 knots. Instead of needing to add kinetic energy, the aircraft needs to reduces it. This means more energy is available for climbing and thus the climb rate is higher.