Situations when it is better to do a static run up
1> In icing conditions it is usually specified.
2> If you have on an aft C of G and low gross weight, conditions which can lead to very low nose wheel sterring effectiveness.
3> If take off performance is critical. However for aircraft such as the 747-400 the performance difference between a rolling and a static take off is minimal.
4> If FOD is a concern.
5> Slippery runway conditions.
On certain engines / aircraft you are also strongly advised NOT to do a static run up if the crosswind component is greater than 20 kts due to the increased possibility of engine surge.