1. Conditions Leading to Anomalously Early Loran-C Signal Skywave

2. Components of the Transmitted Loran-C Signal Loran-C Transmitter Normally, the skywave pulse is well-separated in time from the groundwave For longer ranges and lower ionospheres, however, the skywave is nearly aligned with the groundwave If, under these conditions, skywave signal strength  groundwave signal strength, correct cycle identification becomes a major problem

3. Outline Calculation of ionospheric height profiles Profiles under day, night, and anomalous conditions Skywave signal group delay and amplitude relative to groundwave Anomalous Conditions: Origins and their Footprint on the Ionosphere Effects on Loran –Integrity vs. Availability –Strategies to avoid/minimize effects

4. Groundwave/Skywave Geometry h RERE R E + h R/2 (arc length)  / 2  = R / R E Skywave Groundwave   = incidence angle Group delay between groundwave and skywave components:

5. Effective Ionospheric Heights The ionospheric height depends not only on solar zenith angle (which includes day and night as extremes), but also on incidence angle Consider a height profile over path length that yields greater heights for low incidence angles (short path lengths/ranges) and smaller heights for higher incidence angles (greater ranges), viz. where h = ionospheric height and  = incidence angle

6. Although the greatest ionospheric height would be expected at range R = 0 (where  = 0), Loran transmitting antennas have an effective dipole pattern, with a null vertically upward The peak ionospheric height thus occurs at a non-zero range (typically 50 – 100 km) The functional form for h follows this expected behavior for a dipole-pattern type antenna Effective Ionospheric Heights (Cont’d)

7. Profile Calibration Procedure Pick the extreme effective ionospheric reflection heights at –a short range (maximum height) –the maximum range: 90° (grazing) launch angle for a one-hop skywave (minimum height) or –pick one of the extreme heights and assume the other extreme differs from it by: 12 km for day and 10 km for night Solve for  and  Solve the implicit equation for ionospheric height, i.e., at each point along the path

8. Profile Calibration Procedure (Cont’d) Since skywave delay depends on mid-path ionospheric height, incidence angle, and range, one can fit a profile to existing skywave delay data* at several ranges along a given great- circle path At this time, we have not included the variable daytime solar zenith angle over the path but that will be included in our final product * Last, J., R. Farnworth, M. Searle, Effect of Skywave Interference on the Coverage of Loran-C, IEE Proceedings-F, Vol. 139, No. 4, August 1992 (data taken from DMA groundwave/skywave correction tables that are purportedly based on measurement data

9. Skywave Delay Relative to Groundwave DOTDMA Data

10. Ionospheric Height and Incidence Angle Profiles Day Night

11. Polar Ionosphere Polar Cap Disturbances (PCDs) are caused by solar proton events The effective height for the ionosphere during a polar cap disturbance event can be as low as 50 km (Davies, Ionospheric Radio) Using the model described earlier, we assign a maximum ionospheric height of 56 km and a minimum ionospheric height of 44 km

12. Skywave Amplitude The skywave amplitude for a ground-based vertical E-field receiver antenna is where P t = transmitting station power  = launch/receive elevation angle  R  =parallel-to-parallel reflection coefficient D = ionospheric convergence factor F t, F r = transmit/receive antenna factors s = signal path length

13. Skywave Amplitude (cont’d) The reflection coefficients are a key part of the skywave amplitude calculation – all other parts of the expression depend on geometry and antenna configuration/type. Reflection coefficients for PCD ionospheres were extrapolated from values measured during “normal” ionospheric conditions Reflection coefficients are complex and therefore introduce a phase shift as well as reduction in amplitude

14. Reflection Coefficients Assumed Magnitude only – based on measurements Loran propagation is within this region

15. Groundwave and Skywave Amplitudes 1 kW Transmitter Assumed

16. Skywave Group Delay Skywave group delay relative to Groundwave pulse onset is calculated for –the skywave interacting with the PCD ionosphere described earlier –groundwave propagating over 10 -3 mho/m earth –group delay introduced by dispersive ionosphere (reflection coefficient)

17. Skywave Delay relative to Groundwave

18. Skywave Group Delay and SGR Both skywave group delay and signal level relative to groundwave are important in calculating the probability of incorrect cycle identification In developing strategies to maximize cycle detection probability, we must determine “worst-case” combinations of these parameters

19. Challenging Cycle Identification Region

20. Origin of PCDs Solar Proton Events occur as the result of complex plasma processes on the sun that cause excessive fluxes of protons traveling outward from the sun along interplanetary magnetic field (IMF) lines, some of which hit the earth’s magnetosphere The earth’s high-latitude geomagnetic field lines parallel the IMF so the protons are less deflected from this region Protons cause Polar Cap Disturbances (PCDs) that result from excess ionization in the ionospheric D- regions poleward of the auroral zones

21. Origin of PCDs (Cont’d) The same processes leading to SPEs also cause shock waves to propagate along the IMF and eventually hit the geomagnetic field causing –geomagnetic storms –the auroral zone to move equatorward This latter phenomenon causes the continuing proton flux to excessively ionize lower-latitude ionospheres

22. POLAR IONOSPHERIC DISTURBANCES GPS EQUATORIAL IONOSPHERIC DISTURBANCES UFO & FLTSATCOM MAGNETIC EQUATOR SPACE BASED RADAR Active sun is source of excessive radiation and particles that disturb Earth’s “geospace” Solar-induced geomagnetic storms lead to disturbances in the polar and equatorial ionosphere Anomalous Solar Events Affect the Earth

23. Solar ProtonEvent Determination Obtain solar proton event (SPE) data from Space Environment Lab (SEL) for 1976- 2002 Determine the position of the Auroral Zone (AZ) boundary for each of major SPE events

24. Effect of Accompanying Geomagnetic Storm The position of the AZ boundary is very sensitive to geomagnetic storms and is measured by the ring current index, Dst In a recent paper*, a relationship between the plasmapause L-shell and Dst was derived: [  = geomagnetic latitude of AZ ; Dst has units of nT] *Yokoyama, N., Y. Kamide, and H. Miyaoka, The size of the auroral belt during magnetic storms, Ann. Geophysicae 16: 566-573 (1998)

25. Event Characteristics Dst data is compiled by the World Data Center (C2) at Kyoto University (web- accessible) For each SPE event, Dst data was analyzed for the corresponding date and time –for nearly every event, a precipitous drop in Dst occurred 2 – 4 days after the event onset time –the duration of the anomalously low Dst condition was typically 2 hours

26. Examples of SPE-associated Dst Excursions SPE Onset Max Dst drop SPE Onset Dst drop

27. Temporal/Spatial Effects on the Loran User For user-station paths having mid-points: Poleward of the “nominal” AZ boundary (~60° Geomagnetic North), the SPE effect persists for 2 – 4 days, depending on the event and the local geospace conditions Equatorward of the AZ boundary, the SPE effect lasts only a few hours, near the end of the event, and only then if the geomagnetic storm drives the AZ boundary sufficiently far south

28. Impact on Loran Conditions for anomalous skywave propagation occur when 1.Groundwave Path Length > 800 - 1000 km 2.Groundwave Path Length < 2R e arc cos ((R e /(R e + h)) 3.Ionospheric Height : 44 -56 km How often and where do these conditions occur in the U.S.?

29. Anomalous Region for a Single Station Auroral Zone Boundary Loran Station 800 km 1600 km Anomalous Region for a User Receiver The Anomalous Region includes those receiver locations whose path mid-points are poleward of the AZ boundary

30. Affected CONUS Area vs. AZ Boundary GM Lat

31. Solar Proton Event Histogram - 2001

32. Event Probability Calculation Find the probability that any eLoran user, with a receiver located anywhere in the contiguous 48 states will use a Loran station with a range between 800 and 1600 km and having a path mid-point that is poleward of the AZ boundary at any time during a year at the peak of the solar cycle

33. Individual Station Results - 2001

34. Station Event Probabilities

35. Discussion Probabilities of the anomalously early skywave delay condition are between 2x10 -4 and 2x10 -3 Probabilities are certainly higher in Alaska and Canada

36. Methods to alleviate early skywave problems: –Shape pulse for earlier rise time –Receiver techniques identify/remove through prediction and correlation antenna polarization techniques –Warning systems endemic monitors external monitors Discussion (Cont’d)

37. Implications of these Results If warnings are issued prior to, or at the onset of, these events, the resulting lack of coverage reduces the availability of the signal Warning systems must be designed so that the overall level of integrity < 10 -7 / hour

38. SEL provides probabilities for occurrence of high activity, e.g., solar proton events (SPE) SEL also provides notices of these events essentially at onset Mechanisms that lead to equatorward movement of the auroral zone (AZ) boundary follow the SPE by a few hours to ~ 5 days Implications of these Results (Cont’d)

39. The AZ boundary movement eventually occurs following the SPE, but the exact time cannot be forecast precisely Thus, advance warnings in the uncertain range of ~ 10 hours - 5days can be given regarding the occurrence of these events in the contiguous 48 states Monitor sites can detect these events by monitoring stations at ranges between ~ 1000 and 1500 km whose path mid-points have geomagnetic latitudes between 40° and 60°