- Email: [email protected]
Finding better B0 and B1 parameters for the IRI F2-profile function
1998 Science LIP. All rights reserved Printed in Great Britain 0273-I 177/98 $19.00 + 0.00
Adv. Space Rex Vol. 22, No. 6. pp. 741-747, 0 1998 COSPAR.
Pergamon
Published
by Elsevier
PII: SO273-1177(98)00092-l
FINDING BETTER B, AND B, PARAMETERS FOR THE IRI FZPROFILE FUNCTION Bodo W. Rein&h and Xueqin Huang Center for Atmospheric Research, University of Massachusetts, 600 Sufsolk Street, Lowell, MA 01854, USA, [email protected]
ABSTRACT
Deficiencies in the IRI profile specifications for the bottomside F2 layer required a review of the IRI profile parameters Bu and Bi. Using the available database of measured electron density profiles from several Digisonde stations, the IRI proftie model is assessed. The paper describes a new technique to calculate the Bu and Br parameters that “best” reproduce the measured profiles. The use of the Digisonde’s Chebyshev polynomial presentation of the profiles offers a unique advantage for calculating the best Bu and Bl. 0 1998 COSPAR. Published by Elsevier Science Ltd.
INTRODUCTION
The IRI electron density profile N(h) for the bottomside of the F2 layer is described in terms of the peak density NmF2 by an analytic function (Bilitza, 1990) ~(h)/~mF2
= exp(-XB1)/cosh(X)
(1)
with X = (hmF2-h)/Bo
(2)
The entire profile is specified by only two parameters, B. and B 1, an ingenious approach as long as equation (1) accurately represents the vertical electron density distribution in the F2 region. The performance of the IRI profile function is discussed in the next section by comparing measured profiles from low latitude stations withthe IRI function. The currently used parameters Bo and I31have been described in the literature (Ramakrishnan and Rawer, 1972; Bilitza, 1990; Gulyaeva, 1987; Gulyaeva et al., 1996). The last section shows how the “best” Bc and B1 parameters for a given profile can be calculated in a least-squares fitting approach. At an IRI Task Force Meeting at the International Center for Theoretical Physics (ICTP) in Trieste in 1995, Reinisch and Huang (1997) had introduced a simple technique of calculating directly from the ionogramderived profiles Bu and B1 values that match the IRI profile to the ionogram profile. A plot of the normalized electron density versus X (Figure 1) shows the behavior of the IRI profile for different values of The values of electron density N and corresponding plasma frequency fN at X=1 are Bl. N=N1=0.2384NmF2, and f=f1=0,4883foF2 independent of B,. At X = 1, equation (2) gives h=hmF2-Be, hence Bo is the width between hmF2 and h=h(Nl), and B1 controls the profile shape in this height interval as seen from Figure 1. For any value of B1 (for example B1 = 3.0, the usual value in IRI), the X functions of the measured profile and the IRI profile can be compared to determine the best Bo for the IRI profile. This is described in Section 741
B. W. Reinisch and X. Huang
142
3. It is reasonable to extend the profile fitting from foF2 down to f, = 0.4883foF2 when the latter frequency is larger than foE or foF,, otherwise the fitting can only be done down to the critical frequency of the underlying layer.
011
N(h)/NmF2 Fig, 1. IRI function X for different values of B 1 IRI
F2-PROFILE
ASSESSMENT
For performance evaluation the lRl profiles are best compared with monthly average representative profiles (ARP), rather than with individual profiles. We have made such comparisons for three low latitude Digisonde sites: Barney (Puerto Rico), Jicamarca (Peru), and Puerto Madryn (Argentina) for summer and winter seasons (Reinisch and Huang, 1996). No winter 1993 data were available for Puerto Madryn, and
March data are used instead for the discussion. The method of calculating monthly ARPs is described in Huang and Reinisch (1996a). As an example, Figure 2 illustrates the differences between the measurementderived monthly ARP profiles and the IRI profile predictions for Jicamarca for the month of August 1993. The height differences of the profile points for 24 hourly profiles are shown comparing the IRI and ARP profiles. The top panel contains the nighttime profiles (Jicamarca standard local time is SLT=UT-5 hours), the bottom panel the daytime profiles. All IRI profiles were adjusted to the ARP peak coordinates (foF2,hmF2). At nighttime, h(IRI) - h(ARP) varies from 0 to +18 km which means that the IRI bottomside profiles are slightly too thin. The daytime curves are more complicated because of the occasional presence of an Fl layer. Limiting the comparison to the neighborhood of the F2 peak, say from foF2 to 0.7 foF2, the
differences reach values of 40 km, i.e. the IRI profile is much too thin. Since IRI 90 does not predict any F 1 occurrence for Jicamarca in August (Radicella et al., 1998) the height differences become large when F 1 is observed. This explains the large deviations at daytime below 0.7 foF2.
IRI Profile
0.0
0.1
0.2
0.3
Parameters
0.3
743
Bo and B,
(1.5
0.6
0.8
0.9
1.0
0.8
0.9
1.0
fN/foF2 E lx
a ’ s
120 tit? 100
40 30 20
0.0
0.1
0.2
0.3
03
0.6
0.7
fN/foF2 Fig. 2. ProfIle height differences between IRI and monthly ARP for hourly profiles at Jicamarca, August 1993 (Rl2=52). Jicamarca standard local time is SLT=tJT-5. Table 1 summarizes the results of the study by Reinisch and Huang (1996) for three low latitude stations: Jicamarca, Ramey and Puerto Madryn. The IRI daytime summer profiles are all too thick while the winter profiles seem to be too thin near the equator.
St&iOIl
Jicamarca, Peru
Ramey, Puerto RiCO
67.lW, 18.5N Puerto Madryn, Argentina 65.3W,
42.78
Table I. IRI F2-I rofrle Assessment Daytime MO&l December 1993 Too thick (-15 km) CR12 = 39)
Ni~h~ime Too thick (*IO km)
August 1993 (Riz = 52) December 1992 CR12 = 73)
Too thin (-15 km) Good (+5 km)
Slightly thin (-8 km) Slightly thin (+9 km)
June 1993
Too (-18 Too (-20
Good
CR12
= 67)
December 1993 (Rtz = 39) Mamh 1993 (Rtz = 67)
thick km) thick km)
Good
Too thick (-10 km) Slightly thick (-10 km)
We speculated that wrong values of B, and B, are the reason for the large differences, rather than limitations in the functional description of the profile by Eq. (1). To test this assumption we calculated the best Be and
744
3. W. Reinisch and X. i-hung
B1 (solid lines) for each of these stations and months and compared them with the W (dashed) parameters (Figures 3a, b, c). The IRI recommended “Gulyaeva Be” was used throughout this study. Clearly the biggest differences in 30 occur for Jicamarca in winter (August) reaching a value of 70 km at noon (17 UT). At other s~t~on~mon~s the differences stay mostly below 20 km. An unexpected result is the often observed diurnal variation of&. FITTING THE IRI
FUNCTION TO THE MEASURED PROFILE
If the electron density profile between the base and the peak of the F2 layer, with plasma frequencies fs to fn = foF2 respectively, is given in terms of Chebyshev polynomials (Huang and Reinisch, 1996b) then
with
where f = 80.6m in SI units, A are the Chebyshev coefficients, and the Tei the shifted Chebyshev polynomials. It is advantageous to also express the IR.l function in the same form. Replacing (1) by
( 2 exp (-X”‘) -_= fFn ex + eax
(5)
or Tm
one obtains 2 g In + = in 2 -x”’ - tnfe” + e”x) m
(7)
The plasma frequency f, of the base of the FZIayer is taken either as the fowest frequency of the F2 trace or 0.4883fm, whichever is the larger. From (7) for any value of Bl one can obtain X(g, B,) and expand this function as a sum of Chebyshev polynomials with coefficients Ci: XlRtfg,
81)= ,‘9
c fCi0%)fi (&I
@>
Solving (2) for h and substi~ting (8) yields: hlni = hmF2 - @ C [Bo G(b) Of
T (S)I
bl = hmF2 - a C[Dj0% St> Ti(g)]
The unknown coefficients Di are dete~ined by rnin~rni~~g the least-squares error:
Pb)
IRI Profile Parameters BO and El
B. W. Rernisch and
746
X.
Huang
[h - hddg
(10)
where h is the Digisonde profile height. B 1 is incremented from 1.O to 6.0 in steps of 0.01, and the Bl value producing the smallest error in (10) is selected. Once Bl is known, the coefficients Ci in Eq. (8) can be calculated using least-squares fitting:
(11) where X is obtained from the Digisonde profile. B0 is now simply Be = DilCi, It is easy to show that in terms of Ai and Ci the parameter Bo becomes ZiTilAiSijCj B, = EcCCiSijCj with
=I
(12)
1
Sij
d’(g)f;(g)dg
0
(13)
Figure 4 illustrates the improvement that can be obtained when the best Be and Br parameters are used in the IRI F2 profile equation. The figure shows the Jicamarca ARP profile (solid line} for 13 SLT in August 1993 together with the lRI 90 prediction (long dashes). Clearly the IRI profile is much too thin with the
Fig. 4. The “best” IRI F2-profile (short dashes) is compared with the standard IRI profile (long dashes). The best IRI profile is a good fit to the monthly ARP (solid line). Jicamarca, August 1993, 13 SLT.
IRI Profile Parameters Bo and BI
141
standard Bo, Bt parameters. The short dashes represent the IRI profile with the calculated best B. and Bt parameters reproducing the experimental F2 profile very accurately. The profile fit was performed between N = NmF2 and N = NmFl. To read the Ba values from the figure requires extrapolating the IRI FZprofiles down to Nt = 1.7~10~~ m-3 yielding Bc(standard) = 130 km and Be(best) = 200 km. The Bt(best) is 1.6 rather then 3.0 as used by IRI (see Figure 3a). SUMMARY Comparison with profile data from ionosondes shows that the IRI bottomside FZprofiles can be improved The best (in a least-squares sense) parameters can easily be by using better Ba and Bt parameters. calculated from measured profiles presented as a sum of Chebyshev polynomials. Although the procedure is applicable to individual or to monthly average representative profiles, it is recommended to use the latter when calculating the best Bc, B 1. The ideas and techniques described in this paper were developed using Digisonde ionograms, however they are directly applicable to any type ionograms. The required software is available from the authors. Digisonde stations running version 4 of ARTIST (Automated Real Time Ionogram Scaling and True height) software, calculate B, and B, values for each ionogram in real time. Now that a standard technique of calculating B, and B, from ionogram profiles is established, it can be used to determine a tabular or functional description of the variations of the B,, B, parameters as function of latitude, time of day, season and solar activity. First results of this effort have been reported by Radicella et al. (1998). A task remaining on the way to a better IRI model is the development of a seamless transition to the Fl and E layer profiles. This task will be addressed in 1998. ACKNOWLEDGMENT This work was in part supported by US Air Force contracts F19628-90-K-0029
and F1962896-C-0159.
REFERENCES Bilitza, D., The International Reference Ionosphere, 1990, National Space Science Data Center, NSSDC/WDC-A-R&S Report 90-22, Greenbelt, Maryland, November (1990). Gulyaeva, T.L., Adv. Space Res., 7(6), 39-48, (1987). Gulyaeva, T.L., K.K. Mahajan, and N.K. Sethi, Modification of IRI half-density option for low latitudes, Adv. Space Res., 18(6), 149-152, (1996). Huang, X. and B.W. Reinisch, Vertical electron density profiles from Digisonde ionograms; the average representative profile, Annuli Geofisicu XXXIX, 4,75 l-756, August (1996a). Huang, X. and B.W. Reinisch, Vertical electron density profiles from the Digisonde network, Adv. Space Res., 18(6), 121-129, (1996b). Radicella, S. M., D. Bilitza, B.W. Reinisch, J.O. Adeniyi, M.E. Mosert Gonzalez, B. Zolesi, M.L. Zhang and S.R. Zhang, IRI Task Force Activity at ICTP: proposed improvements for the IRI region below the F peak, Adv. Space Res., this issue, (1998). Ramakrishnan, S. and K. Rawer, Space Research XII, 1253-1259, Akademie-Verlag, Berlin, (1972). Reinisch, B.W. and X. Huang, Low latitude Digisonde measurements and comparison with IRI, Adv. Space Res., 18(6), 5-12, (1996). Reinisch, B.W. and X. Huang, Fitting the IRI F2-Profile function to measured profiles, Proceedings IRI Task Force Activity 1996, Intl. Ctr. Theoretical Phys., Rep. IC/IR/97/11,62-70 (1997).
Adv. Space Rex Vol. 22, No. 6. pp. 741-747, 0 1998 COSPAR.
Pergamon
Published
by Elsevier
PII: SO273-1177(98)00092-l
FINDING BETTER B, AND B, PARAMETERS FOR THE IRI FZPROFILE FUNCTION Bodo W. Rein&h and Xueqin Huang Center for Atmospheric Research, University of Massachusetts, 600 Sufsolk Street, Lowell, MA 01854, USA, [email protected]
ABSTRACT
Deficiencies in the IRI profile specifications for the bottomside F2 layer required a review of the IRI profile parameters Bu and Bi. Using the available database of measured electron density profiles from several Digisonde stations, the IRI proftie model is assessed. The paper describes a new technique to calculate the Bu and Br parameters that “best” reproduce the measured profiles. The use of the Digisonde’s Chebyshev polynomial presentation of the profiles offers a unique advantage for calculating the best Bu and Bl. 0 1998 COSPAR. Published by Elsevier Science Ltd.
INTRODUCTION
The IRI electron density profile N(h) for the bottomside of the F2 layer is described in terms of the peak density NmF2 by an analytic function (Bilitza, 1990) ~(h)/~mF2
= exp(-XB1)/cosh(X)
(1)
with X = (hmF2-h)/Bo
(2)
The entire profile is specified by only two parameters, B. and B 1, an ingenious approach as long as equation (1) accurately represents the vertical electron density distribution in the F2 region. The performance of the IRI profile function is discussed in the next section by comparing measured profiles from low latitude stations withthe IRI function. The currently used parameters Bo and I31have been described in the literature (Ramakrishnan and Rawer, 1972; Bilitza, 1990; Gulyaeva, 1987; Gulyaeva et al., 1996). The last section shows how the “best” Bc and B1 parameters for a given profile can be calculated in a least-squares fitting approach. At an IRI Task Force Meeting at the International Center for Theoretical Physics (ICTP) in Trieste in 1995, Reinisch and Huang (1997) had introduced a simple technique of calculating directly from the ionogramderived profiles Bu and B1 values that match the IRI profile to the ionogram profile. A plot of the normalized electron density versus X (Figure 1) shows the behavior of the IRI profile for different values of The values of electron density N and corresponding plasma frequency fN at X=1 are Bl. N=N1=0.2384NmF2, and f=f1=0,4883foF2 independent of B,. At X = 1, equation (2) gives h=hmF2-Be, hence Bo is the width between hmF2 and h=h(Nl), and B1 controls the profile shape in this height interval as seen from Figure 1. For any value of B1 (for example B1 = 3.0, the usual value in IRI), the X functions of the measured profile and the IRI profile can be compared to determine the best Bo for the IRI profile. This is described in Section 741
B. W. Reinisch and X. Huang
142
3. It is reasonable to extend the profile fitting from foF2 down to f, = 0.4883foF2 when the latter frequency is larger than foE or foF,, otherwise the fitting can only be done down to the critical frequency of the underlying layer.
011
N(h)/NmF2 Fig, 1. IRI function X for different values of B 1 IRI
F2-PROFILE
ASSESSMENT
For performance evaluation the lRl profiles are best compared with monthly average representative profiles (ARP), rather than with individual profiles. We have made such comparisons for three low latitude Digisonde sites: Barney (Puerto Rico), Jicamarca (Peru), and Puerto Madryn (Argentina) for summer and winter seasons (Reinisch and Huang, 1996). No winter 1993 data were available for Puerto Madryn, and
March data are used instead for the discussion. The method of calculating monthly ARPs is described in Huang and Reinisch (1996a). As an example, Figure 2 illustrates the differences between the measurementderived monthly ARP profiles and the IRI profile predictions for Jicamarca for the month of August 1993. The height differences of the profile points for 24 hourly profiles are shown comparing the IRI and ARP profiles. The top panel contains the nighttime profiles (Jicamarca standard local time is SLT=UT-5 hours), the bottom panel the daytime profiles. All IRI profiles were adjusted to the ARP peak coordinates (foF2,hmF2). At nighttime, h(IRI) - h(ARP) varies from 0 to +18 km which means that the IRI bottomside profiles are slightly too thin. The daytime curves are more complicated because of the occasional presence of an Fl layer. Limiting the comparison to the neighborhood of the F2 peak, say from foF2 to 0.7 foF2, the
differences reach values of 40 km, i.e. the IRI profile is much too thin. Since IRI 90 does not predict any F 1 occurrence for Jicamarca in August (Radicella et al., 1998) the height differences become large when F 1 is observed. This explains the large deviations at daytime below 0.7 foF2.
IRI Profile
0.0
0.1
0.2
0.3
Parameters
0.3
743
Bo and B,
(1.5
0.6
0.8
0.9
1.0
0.8
0.9
1.0
fN/foF2 E lx
a ’ s
120 tit? 100
40 30 20
0.0
0.1
0.2
0.3
03
0.6
0.7
fN/foF2 Fig. 2. ProfIle height differences between IRI and monthly ARP for hourly profiles at Jicamarca, August 1993 (Rl2=52). Jicamarca standard local time is SLT=tJT-5. Table 1 summarizes the results of the study by Reinisch and Huang (1996) for three low latitude stations: Jicamarca, Ramey and Puerto Madryn. The IRI daytime summer profiles are all too thick while the winter profiles seem to be too thin near the equator.
St&iOIl
Jicamarca, Peru
Ramey, Puerto RiCO
67.lW, 18.5N Puerto Madryn, Argentina 65.3W,
42.78
Table I. IRI F2-I rofrle Assessment Daytime MO&l December 1993 Too thick (-15 km) CR12 = 39)
Ni~h~ime Too thick (*IO km)
August 1993 (Riz = 52) December 1992 CR12 = 73)
Too thin (-15 km) Good (+5 km)
Slightly thin (-8 km) Slightly thin (+9 km)
June 1993
Too (-18 Too (-20
Good
CR12
= 67)
December 1993 (Rtz = 39) Mamh 1993 (Rtz = 67)
thick km) thick km)
Good
Too thick (-10 km) Slightly thick (-10 km)
We speculated that wrong values of B, and B, are the reason for the large differences, rather than limitations in the functional description of the profile by Eq. (1). To test this assumption we calculated the best Be and
744
3. W. Reinisch and X. i-hung
B1 (solid lines) for each of these stations and months and compared them with the W (dashed) parameters (Figures 3a, b, c). The IRI recommended “Gulyaeva Be” was used throughout this study. Clearly the biggest differences in 30 occur for Jicamarca in winter (August) reaching a value of 70 km at noon (17 UT). At other s~t~on~mon~s the differences stay mostly below 20 km. An unexpected result is the often observed diurnal variation of&. FITTING THE IRI
FUNCTION TO THE MEASURED PROFILE
If the electron density profile between the base and the peak of the F2 layer, with plasma frequencies fs to fn = foF2 respectively, is given in terms of Chebyshev polynomials (Huang and Reinisch, 1996b) then
with
where f = 80.6m in SI units, A are the Chebyshev coefficients, and the Tei the shifted Chebyshev polynomials. It is advantageous to also express the IR.l function in the same form. Replacing (1) by
( 2 exp (-X”‘) -_= fFn ex + eax
(5)
or Tm
one obtains 2 g In + = in 2 -x”’ - tnfe” + e”x) m
(7)
The plasma frequency f, of the base of the FZIayer is taken either as the fowest frequency of the F2 trace or 0.4883fm, whichever is the larger. From (7) for any value of Bl one can obtain X(g, B,) and expand this function as a sum of Chebyshev polynomials with coefficients Ci: XlRtfg,
81)= ,‘9
c fCi0%)fi (&I
@>
Solving (2) for h and substi~ting (8) yields: hlni = hmF2 - @ C [Bo G(b) Of
T (S)I
bl = hmF2 - a C[Dj0% St> Ti(g)]
The unknown coefficients Di are dete~ined by rnin~rni~~g the least-squares error:
Pb)
IRI Profile Parameters BO and El
B. W. Rernisch and
746
X.
Huang
[h - hddg
(10)
where h is the Digisonde profile height. B 1 is incremented from 1.O to 6.0 in steps of 0.01, and the Bl value producing the smallest error in (10) is selected. Once Bl is known, the coefficients Ci in Eq. (8) can be calculated using least-squares fitting:
(11) where X is obtained from the Digisonde profile. B0 is now simply Be = DilCi, It is easy to show that in terms of Ai and Ci the parameter Bo becomes ZiTilAiSijCj B, = EcCCiSijCj with
=I
(12)
1
Sij
d’(g)f;(g)dg
0
(13)
Figure 4 illustrates the improvement that can be obtained when the best Be and Br parameters are used in the IRI F2 profile equation. The figure shows the Jicamarca ARP profile (solid line} for 13 SLT in August 1993 together with the lRI 90 prediction (long dashes). Clearly the IRI profile is much too thin with the
Fig. 4. The “best” IRI F2-profile (short dashes) is compared with the standard IRI profile (long dashes). The best IRI profile is a good fit to the monthly ARP (solid line). Jicamarca, August 1993, 13 SLT.
IRI Profile Parameters Bo and BI
141
standard Bo, Bt parameters. The short dashes represent the IRI profile with the calculated best B. and Bt parameters reproducing the experimental F2 profile very accurately. The profile fit was performed between N = NmF2 and N = NmFl. To read the Ba values from the figure requires extrapolating the IRI FZprofiles down to Nt = 1.7~10~~ m-3 yielding Bc(standard) = 130 km and Be(best) = 200 km. The Bt(best) is 1.6 rather then 3.0 as used by IRI (see Figure 3a). SUMMARY Comparison with profile data from ionosondes shows that the IRI bottomside FZprofiles can be improved The best (in a least-squares sense) parameters can easily be by using better Ba and Bt parameters. calculated from measured profiles presented as a sum of Chebyshev polynomials. Although the procedure is applicable to individual or to monthly average representative profiles, it is recommended to use the latter when calculating the best Bc, B 1. The ideas and techniques described in this paper were developed using Digisonde ionograms, however they are directly applicable to any type ionograms. The required software is available from the authors. Digisonde stations running version 4 of ARTIST (Automated Real Time Ionogram Scaling and True height) software, calculate B, and B, values for each ionogram in real time. Now that a standard technique of calculating B, and B, from ionogram profiles is established, it can be used to determine a tabular or functional description of the variations of the B,, B, parameters as function of latitude, time of day, season and solar activity. First results of this effort have been reported by Radicella et al. (1998). A task remaining on the way to a better IRI model is the development of a seamless transition to the Fl and E layer profiles. This task will be addressed in 1998. ACKNOWLEDGMENT This work was in part supported by US Air Force contracts F19628-90-K-0029
and F1962896-C-0159.
REFERENCES Bilitza, D., The International Reference Ionosphere, 1990, National Space Science Data Center, NSSDC/WDC-A-R&S Report 90-22, Greenbelt, Maryland, November (1990). Gulyaeva, T.L., Adv. Space Res., 7(6), 39-48, (1987). Gulyaeva, T.L., K.K. Mahajan, and N.K. Sethi, Modification of IRI half-density option for low latitudes, Adv. Space Res., 18(6), 149-152, (1996). Huang, X. and B.W. Reinisch, Vertical electron density profiles from Digisonde ionograms; the average representative profile, Annuli Geofisicu XXXIX, 4,75 l-756, August (1996a). Huang, X. and B.W. Reinisch, Vertical electron density profiles from the Digisonde network, Adv. Space Res., 18(6), 121-129, (1996b). Radicella, S. M., D. Bilitza, B.W. Reinisch, J.O. Adeniyi, M.E. Mosert Gonzalez, B. Zolesi, M.L. Zhang and S.R. Zhang, IRI Task Force Activity at ICTP: proposed improvements for the IRI region below the F peak, Adv. Space Res., this issue, (1998). Ramakrishnan, S. and K. Rawer, Space Research XII, 1253-1259, Akademie-Verlag, Berlin, (1972). Reinisch, B.W. and X. Huang, Low latitude Digisonde measurements and comparison with IRI, Adv. Space Res., 18(6), 5-12, (1996). Reinisch, B.W. and X. Huang, Fitting the IRI F2-Profile function to measured profiles, Proceedings IRI Task Force Activity 1996, Intl. Ctr. Theoretical Phys., Rep. IC/IR/97/11,62-70 (1997).