Sea level is a natural integral indicator of climate variability. It reflects changes in practically all dynamic and thermodynamic processes of terrestrial, oceanic, atmospheric, and cryospheric origin. The use of estimates of sea level rise as an indicator of climate change therefore incurs the difficulty that the inferred sea level change is the net result of many individual effects of environmental forcing. Since some of these effects may offset others, the cause of the sea level response to climate change remains somewhat uncertain. This paper is focused on an attempt to provide first-order answers to two questions, namely, what is the rate of sea level change in the Arctic Ocean, and furthermore, what is the role of each of the individual contributing factors to observed Arctic Ocean sea level change? In seeking answers to these questions we have discovered that during the period 1954--1989 the observed sea level over the Russian sector of the Arctic Ocean is rising at a rate of approximately 0.123 cm yr-1 and that after correction for the process of glacial isostatic adjustment this rate is approximately 0.185 cm yr-1. There are two major causes of this rise. The first is associated with the steric effect of ocean expansion. This effect is responsible for a contribution of approximately 0.064 cm yr-1 to the total rate of rise (35%). The second most important factor is related to the ongoing decrease of sea level atmospheric pressure over the Arctic Ocean, which contributes 0.056 cm yr-1, or approximately 30% of the net positive sea level trend. A third contribution to the sea level increase involves wind action and the increase of cyclonic winds over the Arctic Ocean, which leads to sea level rise at a rate of 0.018 cm yr-1 or approximately 10% of the total. The combined effect of the sea level rise due to an increase of river runoff and the sea level fall due to a negative trend in precipitation minus evaporation over the ocean is close to 0. For the Russian sector of the Arctic Ocean it therefore appears that approximately 25% of the trend of 0.185 cm yr-1, a contribution of 0.048 cm yr-1, may be due to the effect of increasing Arctic Ocean mass.