An Empirical Relationship Between Coronal Density and Solar Wind Velocity in the Middle Corona With Applications to Space Weather

Accurate predictions of ambient solar wind conditions are a central component of space weather forecasting. A recent advancement is to use the distribution of electron density at a heliocentric distance of 8 R-?, gained by applying coronal rotational tomography to coronagraph data, as an inner boundary condition for the time-dependent Heliospheric Upwind eXtrapolation solar wind model. This approach requires conversion of densities into solar wind velocity at the inner boundary. Based on comparison of the distribution of in situ measurements of density and velocities, this work finds a scaled exponential equation relating the density and outflow velocity at 8 R-?, with three key parameters found as a function of time between years 2007-2021. Based on this relationship, comparison of modeled and in situ measurements of velocities at Earth, STEREO A and STEREO B over the past solar cycle give a mean absolute error of 61.2, 69.0, and 66.1 km s(-1) respectively. An analysis of thousands of events (defined as solar wind streams above 450 km s(-1)) gives an accuracy score of 76%. This agreement validates the density-velocity relationship, and shows that an inner boundary based on coronagraph observations is a robust complement, or alternative, to commonly-used magnetic model constraints for solar wind modeling and forecasting.