at its new, higher value. Positive climate change feedbacks amplify changes in the climate system, and can lead to destabilizing effects for the climate. An increase in temperature from greenhouse gases leading to increased water vapor (which is itself a greenhouse gas) causing further warming is a positive feedback, but not a runaway effect, on Earth. Positive feedback effects are common (e.g. ice–albedo feedback) but runaway effects do not necessarily emerge from their presence. Though water plays a major role in the process, the runaway greenhouse effect is not a result of water vapor feedback. The runaway greenhouse effect can be seen as a limit on a planet's outgoing longwave radiation that, when surpassed, results in a state where water cannot exist in its liquid form (hence, the oceans have all "boiled away"). A planet's outgoing longwave radiation is limited by this evaporated water, which is an effective greenhouse gas and blocks additional infrared radiation as it accumulates in the atmosphere. Assuming radiative equilibrium, runaway greenhouse limits on outgoing longwave radiation correspond to limits on the increase in stellar flux received by a planet to trigger the runaway greenhouse effect. Two limits on a planet's outgoing longwave radiation have been calculated that correspond with the onset of the runaway greenhouse effect: the Komabayashi–Ingersoll limit and the Simpson–Nakajima limit. At these values the runaway greenhouse effect overcomes the Stefan–Boltzmann feedback so an increase in a planet's surface temperature will not increase the outgoing longwave radiation. The Komabayashi–Ingersoll limit was the first to be analytically derived and only considers a grey stratosphere in radiative equilibrium. A grey stratosphere (or atmosphere) is an approach to modeling radiative transfer that does not take into account the frequency-dependence of absorption by a gas. In the case of a grey stratosphere or atmosphere, the Eddington approximation can be used to calculate radiative fluxes. This approach focuses on the balance between the outgoing longwave radiation at the tropopause,, and the optical depth of water vapor, , in the tropopause, which is determined by the temperature and pressure at the tropopause according to the saturation vapor pressure. This balance is represented by the following equationsWhere the first equation represents the requirement for radiative equilibrium at the tropopause and the second equation represents how much water vapor is present at the tropopause. Taking the outgoing longwave radiation as a free parameter, these equations will intersect only once for a