Jicamarca Topside Electron Temperature Measurements: Sep 16-19, 1994

Information on Analysis

Fitting Strategy

Two different integration times (15 minutes and 60 minutes) were used on the original raw data, and two analysis schemes were applied to these two times, making a total of four permutations.

The data begins at 969 km altitude, and results are available in 75 km steps (1/4 of the pulse length, 300 km). I have used a trapezoidal summation rule which guarantees equal height resolution at all lags (and much better statistics at long lags). This decision sets the first altitude available to 969 km, although the sampling raster actually begins at 600 km.

The fitting strategies used were as follows:

("15 min", "60 min" plot labels):
- Tr = 1 at all heights
- 100 percent H+ and 0 percent He+ above a time-varying height as follows: (all times EST)
  - 1130 - 1959: all H+ >= 1550 km
  - 2000 - 0159: all H+ >= 1200 km
  - 0200 - 0559: all H+ >= 1000 km
  - 0600 - 1129: all H+ >= 1400 km
  The heights were determined in an ad-hoc fashion, by looking at the fit results.
- The altitude gradients on H+ and He+ are encouraged (but not strictly required) to be smaller than a set number through constrained NLLS analysis. The values for gradients are:
  - H+: (-1e-3, 6e-3) fraction / km
  - He+: (-6e-4, 6e-4) fraction / km
  Again, these gradient limits are ad-hoc, but encompass a full "reasonable" gradient range.
("15 min All H+", "60 min All H+" plot labels):
- Tr = 1 at all heights
- 100 percent H+ and 0 percent He+ at all heights

Data Filtering

In making the plots, all data with the following criteria were rejected:

Te > 5000 K
dTe > 300 K
frac H+ < 0.5

Only nighttime data from 19 EST to 05 EST was plotted.

Fitting Results

Preliminary Conclusions

Past 20 EST, the assumption of 100 percent H+ and 0 percent He+ seems to be valid, and results in a much cleaner set of temperature results. (Examine the plots of light ion fractions for the "15 min" and "60 min" cases - they show a definite clustering of H+ toward 100 percent and He+ toward 0 percent.)
A reason for this (besides the fact that the assumption removes two degrees of freedom from the fit) is that, with Te = Ti enforced, there seems to be a nighttime fitting ambiguity at 50 MHz between
- 100% H+, Te = Ti = 500 K
- 65-75% H+, 25-35% He+, Te = Ti = 700 - 750 K
The latter solution is occasionally chosen in the "15 min" and "60 min" cases, and can lead to some hopping around in temperatures on the order of 200 K. You can see the "75 percent H+" results appearing on the "15 min" light ion fraction scatter plot for 1041 km , for example.
Below are two examples of this ambiguity in action. The top panel shows the two theoretical ACFs from the "15 min" and the "15 min All H+" case, while the bottom panel adds the data. Notice that in each case, the "all H+" solution has significantly lower error bars, as one would expect from a fit ambiguity.
This is 969 km; the parameter values and uncertainties associated with these two fit solutions are
```
 15 minute:          Ne 6.54e3 (1.37e2)  Te=Ti 822 (149)  frac H+: 0.653 (0.156)  frac He+: 0.348 (0.160)
 15 minute, all H+:  Ne 6.50e3 (1.24e2)  Te=Ti 576 (23)   frac H+: 1.000 (-----)  frac He+: 0.000 (-----)
       
```
Click here for Postscript.
This is 1113 km; the parameter values and uncertainties associated with these two fit solutions are
```
 15 minute:          Ne 5.57e3 (1.52e2)  Te=Ti 872 (67)   frac H+: 0.612 (0.091)  frac He+: 0.419 (0.119)
 15 minute, all H+:  Ne 5.57e3 (1.46e2)  Te=Ti 595 (33)   frac H+: 1.000 (-----)  frac He+: 0.000 (-----)
       
```
Click here for Postscript.
Concentrating on the "all H+" fits, I don't see any evidence of post-midnight Te increases around 300 - 400 K (or higher) on any of the three nights shown. At the lower altitudes, things are either varying by about +/- 100 K (Sep 16-17), or monotonically decreasing (Sep 17-18) after midnight. The error bars on the temperatures are small enough to be able to detect any large increases.
Here's one example of the temperature behavior ("15 min all H+", 1113 km), but I recommend leafing through the individual plots tabulated below.
There are some temperature variations in the data > 1200 km, but again, these seem to stay below 300 K in their oscillations.
Up to about 1275 km, the 15 minute data seems to be good enough to use. Past that, the 60 minute data is good to 1500? km (and maybe beyond that).

Plots

You can see either a GIF version or a Postscript version of the individual plots by selecting the "G" or "P" links, respectively.

15 minute

 969 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P   
1041 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1113 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1185 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1257 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1329 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1401 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1473 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1545 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1842 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P

60 minute

 969 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P   
1041 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1113 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1185 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1257 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1329 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1401 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1473 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1545 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1842 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P

15 minute, All H+

 969 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P   
1041 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1113 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1185 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1257 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1329 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1401 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1473 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1545 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1842 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P

60 minute, All H+

 969 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P   
1041 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1113 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1185 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1257 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1329 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1401 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1473 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1545 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P 
1842 km:    All days:  G / P   Individual days:  G / P   Light ion frac:  G / P

Additional Work

I can squeeze out altitudes beginning at 784 km by using a rectangular summation rule rather than a trapezoidal one. This would add 200 km of coverage to the bottom of the available data. However, the analysis appears to be somewhat trickier as H+ is definitely not 100% all the time (for example) and some assumptions have to be carefully adjusted. Perhaps we can make the point about midnight temperature increases without this data, since it requires extra effort.

Philip Erickson <pje@hyperion.haystack.edu>

Last modified: Thu Oct 2 08:36:32 1997