Improvement on Kp derived Solar Wind Parameters

[twfang]

Our current forecast uses Kp to derive solar wind parameters. Calculations for the forecasted values of Bz, By, angle, and velocity are based on the following relationships (code can be found here).

SW_By = 0.0
SW_Bt = SW_Bz
If (Bz .ge. 0.0) SW_Angle = 0.0
If (Bz .lt. 0.0) SW_Angle = 180.
SW_Velocity = 317.0 + 55.84 * Kp - 2.71 * Kp_squared
SW_Bz = -0.085 * Kp_squared - 0.081* Kp + 0.434 + 0.0079 * F10.7(daily) - 0.0022 * Kp *
F10.7(daily)

The SW_Bz is really wimpy, especially at low F10.7:
-0.4 for Kp 3 at F10.7=100
-3.6 for Kp 6 at F10.7=100
-8.4 for Kp 9 at F10.7=100

Dan Weimer developed a relationship between the solar wind electric field and Kp:
Esw = 0.1455 + 0.4675 * Kp - 0.1446 * Kp_squared + 0.0276 * Kp_cubed

We assume no information on By in the forecast, the solar wind electric field becomes the product of the solar wind velocity and Bz, then we can get Bz through Esw and Vsw:
Esw = - Vsw * Bz

The Goncharov paper has a relationship between Kp and Bz :
Bz = - Kp * 2.27 (or -Kp / .44 as in equation 5, but only above Kp 2). This is hard to interpret given Figure 1a in their paper. Which gives the values in the second column below. The values from Weimer's SW electric field formula (3rd column) divided by the Vsw (5th column) from our expression, are fairly consistent with Goncharov, at the high Kp levels, and lower for the mid-range Kp levels.

We need to try out the new estimation in the WAM-IPE to see the impact of these values.

[twfang]

The complete set of Kp and Bz, which are derived based on Weimer's Esw and our original Vsw are listed below.

KP Index , SWE , SW Vel. , IMF Bz
0.000 , 0.15 , 317.0 , -0.46
0.300 , 0.27 , 333.5 , -0.82
0.700 , 0.41 , 354.8 , -1.16
1.000 , 0.50 , 370.1 , -1.34
1.300 , 0.57 , 385.0 , -1.48
1.700 , 0.66 , 404.1 , -1.63
2.000 , 0.72 , 417.8 , -1.73
2.300 , 0.79 , 431.1 , -1.84
2.700 , 0.90 , 448.0 , -2.00
3.000 , 0.99 , 460.1 , -2.16
3.300 , 1.11 , 471.8 , -2.34
3.700 , 1.29 , 486.5 , -2.66
4.000 , 1.47 , 497.0 , -2.96
4.300 , 1.68 , 507.0 , -3.31
4.700 , 2.02 , 519.6 , -3.88
5.000 , 2.32 , 528.5 , -4.39
5.300 , 2.67 , 536.8 , -4.98
5.700 , 3.23 , 547.2 , -5.90
6.000 , 3.71 , 554.5 , -6.69
6.300 , 4.26 , 561.2 , -7.59
6.700 , 5.09 , 569.5 , -8.94
7.000 , 5.81 , 575.1 , -10.10
7.300 , 6.60 , 580.2 , -11.37
7.700 , 7.78 , 586.3 , -13.27
8.000 , 8.77 , 590.3 , -14.86
8.300 , 9.86 , 593.8 , -16.60
8.700 , 11.46 , 597.7 , -19.17
9.000 , 12.78 , 600.0 , -21.29

[twfang]

Here are some results from the 2013 and 2015 storms. Three tests were carried out. IPE outputs can be found in this google drive folder.

time obs (all the solar wind parameters are from the observations)
time derived (all the solar wind parameters are derived from the observed Kp and F10.7 using the default Bz equation)
newdrivers (using the timederive model and observed Kp and F10.7, but use the Esw and Vsw to obtain new Bz)

2013/03/17 time obs

2013/03/17 time derived

2013/03/17 newdrivers

2015/03/17 time obs

2015/03/17 time derived

2015/03/17 newdrivers

[twfang]

Tim has looked into several different plots for 2013 and 2015 St. Patrick Day's storms and can be found here. Results from these runs look good!