1. In Jean’s escape, particles at the exobase moving in the outward direction with sufficient velocity (i.e. high enough kinetic energy) can escape from the planet…typically the vertical flow from the atmosphere is small HDE arises when the flow speed becomes large Hydrodynamic Escape from Planetary Atmospheres

2. HDE also differs from gas-kinetic evaporation in that in some circumstances a substantial fraction of the entire thermospheric energy budget is used to power escape of gas from the atmosphere; it is possible that heavier species can be “dragged” along during HDE Under this circumstance, it is expected that atmospheric expansion due to HDE will be the dominant loss process

3. HDE is an important process in atmospheric evolution of the terrestrial planets and CEGPs and can change the composition of planetary atmospheres from primordial values irreversibly hydrogen escape is of particular importance as it affects the oxidation state of the atmosphere and because it results in the loss of water vapour

4. For Instance…(outstanding problems) Did early Venus initially have an ocean? HDE modelling using a water-rich atmosphere on Venus can help assess this problem (Kasting and Pollack, 1983) Isotopic ratios (i.e. fractionation: D/H, N, and noble gases) are very different on terrestrial planets even though they are believed to be formed from similar material (Hunten et al., 1987; Pepin, 1991)

5. and… Greenhouse warming by methane in the atmosphere of the early Earth? CH 4 density on early Earth dependent on HDE, strongly influencing its atmospheric climate and composition, i.e. (Pavlov et al., 2000; 2001) “blow-off” on HD209458b (Osiris) (Vidal-Madjar et al., 2003; 2004)

6. HD Escape Equations

7. Watson et al. (1981): shooting method or trial-and-error method to solve steady state HDE equation for early Earth and Venus Set of solutions at the critical point (exobase) selected which can match the zero temperature at infinity and set temperature at the lower boundary. Calculated temperature and density at the boundary very sensitive to initial settings and I couldn’t reproduce cases using that method Some Previous Models

8. Kasting and Pollack (1983) numerically solve the steady state HDE problem for Venus Use an iterative method in which the momentum and energy equations are simultaneously solved Not able to get an exact sol’n at the critical point obtaining the supersonic solution Instead, they obtained subsonic solutions and argued that the escape flux can be close to the critical escape flux Method included infrared cooling by H 2 O and CO 2 while only EUV absorption considered by Watson

9. Chassefiere (1996) solves steady state HDE problem from lower boundary to exobase level Position of exobase level is determined when the mean free path becomes greater than the scale height Outgoing flow at exobase is set to be equivalent to a modified Jean’s escape (ionization and interaction between escaping particles and solar wind considered) Application to water-rich early Cytherian atmosphere

10. Using the equations 1, 2, and 3 with B.C.’s etc, the HD equations can be solved using 1st order Lax- Friedriechs scheme, Godunov method, or Finite Difference scheme since these are linear advection equations (hyperbolic)