The K indices have long been a very important way to estimate geomagnetic activity. However, they have some basic and practical problems which restrict their reliability and applicability for long-term (centennial) studies. Here we discuss these problems, modify the K method and construct a new, straightforward, easily verifiable and homogeneous index, the so called Ah index, which is based on digital, hourly data and is dedicated for centennial studies. The local Ah indices correlate with the local K and ak indices very well and extend them typically by several decennia. Ah indices at all studied stations verify that geomagnetic activity has increased during the last century. However, the amount of centennial increase varies greatly with latitude, being largest at high latitudes, smaller at low latitudes and, unexpectedly, smallest at mid-latitudes. The centennial increase in the aa index is roughly twice larger than in the Ah index at similar mid-latitudes. This is due to the erroneous scaling of the aa index in the late 1950s, requiring aa to be revised. The global Ah index correlates uniquely well with the Ap index, better than aa or the not-K based IHV (Inter-Hourly Variability) index. Thus Ah yields the most accurate extension of the Ap index by roughly 30 years.