A Simplified Method of True Height Analysis to Estimate the Real Height of Sporadic E Layers

The sporadic E (Es) layer virtual height h ' Es ${h}<^>{\prime }Es$ and the ordinary wave critical frequency foEs $foEs$ are routinely measured ionogram parameters, used to characterize the Es altitude occurrence and intensity. It has become common practice to take the real height hEs $hEs$ to be about equal to h ' Es ${h}<^>{\prime }Es$ by assuming that signal propagation delays in the E region plasma below the layer are small and can be neglected. Although this applies for nighttime, during daytime it may overestimate hEs $hEs$ significantly. The present paper relies on true height analysis theory to devise a simplified method and propose an algorithm that can estimate Es real heights reasonably well. The method relies on h ' Es ${h}<^>{\prime }Es$ and foEs $foEs$ ionosonde measurements and E region electron density profiles obtained from the International Reference Ionosphere model. The algorithm is applied to a typical set of Digisonde observations to compute hEs $hEs$ and examine real height variations and functional dependencies. Whereas hEs $hEs$ similar or equal to h ' Es ${h}<^>{\prime }Es$ at nighttime, during daytime there are notable h ' Es ${h}<^>{\prime }Es$ - hEs $hEs$ differences taking values less than 10 km for most of the observed layers. During the early morning and early afternoon hours, however, when weak layers appear at upper heights, the virtual to real height differences become larger reaching 20-25 km. The method proposed here for the estimation of hEs $hEs$ can be easily applied to improve the accuracy of the results of sporadic E layer studies. Sporadic E (Es) refers to layers of enhanced electron density in the E region ionosphere between similar to 90 and 120 km. They have been studied with ionosondes extensively. The ionogram key parameters related to sporadic E are the ordinary wave critical frequency foEs $foEs$ and the layer virtual height h ' Es ${h}<^>{\prime }Es$. The virtual height is half the elapsed time from the ionosonde to the reflecting layer and back, multiplied by the speed of light. Since the true Es height hEs $hEs$ is not measured, it has become common practice to set hEs $hEs$ similar or equal to h ' Es ${h}<^>{\prime }Es$ by assuming that the ionosonde signal suffers negligible retardation in the lower E region below the layer. This approximation is valid during nighttime but not during daytime, especially for weak layers in upper altitudes. This problem has been recognized for a long time but was downplayed. The present paper provides a method and an algorithm that can estimate sporadic E real heights hEs $hEs$. It relies on theoretical principles and uses the ionosonde-measured Es parameters and E region electron density profiles from the International Reference Ionosphere (IRI) model. The results suggest that the proposed hEs $hEs$ algorithm is a useful tool that improves the accuracy of the ionosonde-based Es studies. Ionosondes measure the sporadic E layer virtual height h ' Es $Es$ but not the real layer height hEs $hEs$ which needs to be estimated A method and an algorithm are proposed to compute hEs $hEs$ from the ionosonde-measured h ' Es $Es$ and foEs $foEs$ parameters, and IRI-modeled Ne ${N}_{e}$(h) profiles The method is applied to ionosonde measurements to compute hEs $hEs$ and search for diurnal variations and functional dependences on h ' Es $Es$ and foEs $foEs$