# SPAM: Solar Spectrum Prediction for Applications and Modeling

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## Abstract

**:**

## 1. Introduction

**S**olar

**S**pectrum

**P**rediction for

**A**pplications and Modeling), parameterized by a single ground-based F${}_{10.7}$ solar activity index. The model is based on 14 years of TIMED measurements and divided into two separate submodels: the Solar-SPAM model of the photon energy flux spectrum for the wavelength range of 0–190 nm with an initial TIMED resolution of 1 nm; and the Aero-SPAM model of photon flux in 37 wavelength intervals, including 20 wave bands and 16 separate spectral lines within the range of 5–105 nm, with an additional Ly-alpha line 121.5 nm, intended for aeronomic calculations.

## 2. Data

#### 2.1. F${}_{10.7}$ Index

#### 2.2. TIMED Spacecraft Data

## 3. Solar-SPAM: Shortwave Energy Spectrum Model

## 4. Aero-SPAM: EUV Photon Flux Model for Aeronomic Applications

## 5. Discussion

## 6. Conclusions

- 1.
- The F${}_{10.7}$ index is an excellent indicator of solar activity (Tapping, 2013) and may serve as a reliable proxy for the solar spectrum variations within the limits of the SPAM model applicability 65 < F${}_{10.7}$ < 200 s.f.u.
- 2.
- Since the atmosphere is transparent to radiation at a wavelength of 10.7 cm, the F${}_{10.7}$ radio flux can be reliably measured from the Earth’s surface in any weather. The time series of the daily F${}_{10.7}$ has been available continuously since 1947 for seven solar cycles, so the SPAM model can be applied to large-scale retrospective studies that require solar radiation data.
- 3.
- The F${}_{10.7}$ index is predictable, which allows SPAM to forecast the solar spectrum for various operational tasks. There are a number of services providing the forecast of the daily averaged F${}_{10.7}$ index, e.g., up to 55 days ahead (http://spaceweather.izmiran.ru/eng/forecasts.html, accessed on 20 November 2022), up to 27 days ahead with open-access forecast (https://www.swpc.noaa.gov/products/27-day-outlook-107-cm-radio-flux-and-geomagnetic-indices, accessed on 20 November 2022) and up to 45 days ahead with 5-day resolution (https://www.swpc.noaa.gov/products/usaf-45-day-ap-and-f107cm-flux-forecast, accessed on 20 November 2022). In addition, there is a long-term monthly average F${}_{10.7}$ forecast up to 20 years, including the next solar activity cycle, that can be used for future aeronomy estimations. (https://www.swpc.noaa.gov/products/predicted-sunspot-number-and-radio-flux, accessed on 20 November 2022).
- 4.
- SPAM’s single-variable parameterization is easy to implement. Despite the model simplicity, our results are in good agreement with the measurements.

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Table A1.**The Solar-SPAM model describing the solar irradiance spectrum (F, W·m${}^{-2}\xb7$ nm${}^{-1}$) depending on the daily F${}_{10.7}$ index, $F={P}_{1}\xb7{F}_{10.72}+{P}_{2}\xb7{F}_{10.7}+{P}_{3}$. ${P}_{1}$, ${P}_{2}$ and ${P}_{3}$ are the regression coefficients for the X-ray, EUV and FUV spectral intervals ($\lambda $) with 1 nm resolution. R is a correlation coefficient between F${}_{10.7}$ index and measured photon energy flux, RMSE: root-mean-square error calculated for each wavelength $\lambda $.

$\mathit{\lambda}$ | ${\mathit{P}}_{1}$ | ${\mathit{P}}_{2}$ | ${\mathit{P}}_{3}$ | R | RMSE |
---|---|---|---|---|---|

1.5 | −4.94024181$\times {10}^{-09}$ | 3.22175699$\times {10}^{-06}$ | −1.80553335$\times {10}^{-04}$ | 0.93 | 2.67305197$\times {10}^{-05}$ |

2.5 | −1.51234762$\times {10}^{-09}$ | 8.72873177$\times {10}^{-07}$ | −3.59300652$\times {10}^{-05}$ | 0.96 | 4.64649582$\times {10}^{-06}$ |

3.5 | −8.19051896$\times {10}^{-10}$ | 4.76131943$\times {10}^{-07}$ | −1.75069528$\times {10}^{-05}$ | 0.96 | 2.57208191$\times {10}^{-06}$ |

4.5 | −1.25299002$\times {10}^{-09}$ | 7.18966612$\times {10}^{-07}$ | −2.30913459$\times {10}^{-05}$ | 0.96 | 3.78321360$\times {10}^{-06}$ |

5.5 | −1.05306909$\times {10}^{-09}$ | 6.00386365$\times {10}^{-07}$ | −1.72945105$\times {10}^{-05}$ | 0.96 | 3.13381799$\times {10}^{-06}$ |

6.5 | −1.24449248$\times {10}^{-09}$ | 7.07626722$\times {10}^{-07}$ | −2.22302072$\times {10}^{-05}$ | 0.96 | 3.69094684$\times {10}^{-06}$ |

7.5 | −2.59694610$\times {10}^{-09}$ | 1.45374662$\times {10}^{-06}$ | −6.31698909$\times {10}^{-05}$ | 0.96 | 7.43469515$\times {10}^{-06}$ |

8.5 | −2.16866639$\times {10}^{-09}$ | 1.21455389$\times {10}^{-06}$ | −4.6505577$\times {10}^{-05}$ | 0.96 | 6.21501074$\times {10}^{-06}$ |

9.5 | −1.52361462$\times {10}^{-09}$ | 8.68533191$\times {10}^{-07}$ | −3.0246892$\times {10}^{-05}$ | 0.96 | 4.53196359$\times {10}^{-06}$ |

10.5 | −1.01521500$\times {10}^{-09}$ | 5.78430109$\times {10}^{-07}$ | −1.79161041$\times {10}^{-05}$ | 0.96 | 3.02874105$\times {10}^{-06}$ |

11.5 | −5.92986152$\times {10}^{-10}$ | 3.39846459$\times {10}^{-07}$ | −7.46323908$\times {10}^{-06}$ | 0.96 | 1.86757596$\times {10}^{-06}$ |

12.5 | −3.91620799$\times {10}^{-10}$ | 2.22633150$\times {10}^{-07}$ | −6.85281881$\times {10}^{-06}$ | 0.96 | 1.16787269$\times {10}^{-06}$ |

13.5 | −3.68662392$\times {10}^{-10}$ | 2.14384736$\times {10}^{-07}$ | −5.53046688$\times {10}^{-06}$ | 0.96 | 1.20433914$\times {10}^{-06}$ |

14.5 | −8.15473279$\times {10}^{-10}$ | 4.56904530$\times {10}^{-07}$ | −1.28641555$\times {10}^{-05}$ | 0.96 | 2.34443139$\times {10}^{-06}$ |

15.5 | −1.05314223$\times {10}^{-09}$ | 5.90337830$\times {10}^{-07}$ | −2.51992115$\times {10}^{-05}$ | 0.96 | 3.02143819$\times {10}^{-06}$ |

16.5 | −1.71833912$\times {10}^{-09}$ | 9.58528730$\times {10}^{-07}$ | −2.37694140$\times {10}^{-05}$ | 0.96 | 4.91384954$\times {10}^{-06}$ |

17.5 | −7.84248508$\times {10}^{-09}$ | 4.35156360$\times {10}^{-06}$ | −6.77832612$\times {10}^{-05}$ | 0.96 | 2.24071577$\times {10}^{-05}$ |

18.5 | −5.35989584$\times {10}^{-09}$ | 2.98171616$\times {10}^{-06}$ | −7.78638812$\times {10}^{-05}$ | 0.96 | 1.53019138$\times {10}^{-05}$ |

19.5 | −5.64009182$\times {10}^{-09}$ | 3.15119971$\times {10}^{-06}$ | −1.24435988$\times {10}^{-04}$ | 0.96 | 1.61351843$\times {10}^{-05}$ |

20.5 | −4.90601610$\times {10}^{-09}$ | 2.74377445$\times {10}^{-06}$ | −1.31174042$\times {10}^{-04}$ | 0.96 | 1.40380060$\times {10}^{-05}$ |

21.5 | −4.26086127$\times {10}^{-09}$ | 2.38514084$\times {10}^{-06}$ | −1.14409417$\times {10}^{-04}$ | 0.96 | 1.22091037$\times {10}^{-05}$ |

22.5 | −3.19159017$\times {10}^{-09}$ | 1.77982999$\times {10}^{-06}$ | −5.49342607$\times {10}^{-05}$ | 0.96 | 9.12119600$\times {10}^{-06}$ |

23.5 | −1.75266637$\times {10}^{-09}$ | 9.77475268$\times {10}^{-07}$ | −2.67796958$\times {10}^{-05}$ | 0.96 | 5.01372608$\times {10}^{-06}$ |

24.5 | −2.43810818$\times {10}^{-09}$ | 1.36192347$\times {10}^{-06}$ | −4.57043670$\times {10}^{-05}$ | 0.96 | 6.97290978$\times {10}^{-06}$ |

25.5 | −3.98387625$\times {10}^{-09}$ | 2.22551933$\times {10}^{-06}$ | −7.70072803$\times {10}^{-05}$ | 0.96 | 1.13958300$\times {10}^{-05}$ |

26.5 | −2.00773403$\times {10}^{-09}$ | 1.12849376$\times {10}^{-06}$ | −5.67602506$\times {10}^{-05}$ | 0.96 | 5.77108499$\times {10}^{-06}$ |

27.5 | −1.19730867$\times {10}^{-09}$ | 5.65394676$\times {10}^{-07}$ | −5.85964757$\times {10}^{-06}$ | 0.94 | 3.19981683$\times {10}^{-06}$ |

28.5 | −1.46295195$\times {10}^{-09}$ | 1.01404261$\times {10}^{-06}$ | −3.58365291$\times {10}^{-05}$ | 0.93 | 8.68678105$\times {10}^{-06}$ |

29.5 | −8.15084563$\times {10}^{-10}$ | 4.34467210$\times {10}^{-07}$ | 3.65433670$\times {10}^{-06}$ | 0.93 | 3.03848274$\times {10}^{-06}$ |

30.5 | −7.05077152$\times {10}^{-09}$ | 4.04741769$\times {10}^{-06}$ | 1.43586031$\times {10}^{-04}$ | 0.94 | 2.75155631$\times {10}^{-05}$ |

31.5 | −7.77266741$\times {10}^{-10}$ | 4.68802536$\times {10}^{-07}$ | 1.08074811$\times {10}^{-05}$ | 0.93 | 3.64885891$\times {10}^{-06}$ |

32.5 | −5.61602010$\times {10}^{-10}$ | 2.83431306$\times {10}^{-07}$ | −3.27491491$\times {10}^{-06}$ | 0.92 | 2.03502960$\times {10}^{-06}$ |

33.5 | 6.11880133$\times {10}^{-10}$ | 6.52060422$\times {10}^{-07}$ | −2.90103367$\times {10}^{-05}$ | 0.91 | 1.14428500$\times {10}^{-05}$ |

34.5 | −2.13887412$\times {10}^{-09}$ | 9.00810935$\times {10}^{-07}$ | −1.41575668$\times {10}^{-05}$ | 0.93 | 5.08999204$\times {10}^{-06}$ |

35.5 | −2.29655541$\times {10}^{-09}$ | 1.06445240$\times {10}^{-06}$ | −3.23960927$\times {10}^{-05}$ | 0.94 | 6.31089521$\times {10}^{-06}$ |

36.5 | −1.69356060$\times {10}^{-09}$ | 1.14642019$\times {10}^{-06}$ | −1.49427472$\times {10}^{-05}$ | 0.93 | 9.15296502$\times {10}^{-06}$ |

37.5 | −4.44754965$\times {10}^{-10}$ | 2.24144087$\times {10}^{-07}$ | 2.29852502$\times {10}^{-06}$ | 0.94 | 1.39955751$\times {10}^{-06}$ |

38.5 | −2.57264554$\times {10}^{-10}$ | 1.20451838$\times {10}^{-07}$ | 1.08315857$\times {10}^{-07}$ | 0.95 | 6.47189724$\times {10}^{-07}$ |

39.5 | −1.90799471$\times {10}^{-10}$ | 8.54129718$\times {10}^{-08}$ | −3.66570920$\times {10}^{-07}$ | 0.95 | 4.29404481$\times {10}^{-07}$ |

40.5 | −1.63110170$\times {10}^{-10}$ | 7.67917532$\times {10}^{-08}$ | 2.48479107$\times {10}^{-06}$ | 0.94 | 4.43317217$\times {10}^{-07}$ |

41.5 | −2.64676272$\times {10}^{-10}$ | 1.61050402$\times {10}^{-07}$ | −5.64014188$\times {10}^{-06}$ | 0.94 | 1.09306430$\times {10}^{-06}$ |

42.5 | −8.80727378$\times {10}^{-11}$ | 5.09406819$\times {10}^{-08}$ | 1.64104876$\times {10}^{-06}$ | 0.94 | 3.40898878$\times {10}^{-07}$ |

43.5 | −1.29810569$\times {10}^{-11}$ | 3.70763160$\times {10}^{-08}$ | 8.20072441$\times {10}^{-06}$ | 0.82 | 7.51972352$\times {10}^{-07}$ |

44.5 | −1.92736419$\times {10}^{-10}$ | 9.35286333$\times {10}^{-08}$ | 2.78944317$\times {10}^{-08}$ | 0.95 | 5.03560346$\times {10}^{-07}$ |

45.5 | −1.07354187$\times {10}^{-10}$ | 5.33853880$\times {10}^{-08}$ | 3.23226206$\times {10}^{-06}$ | 0.94 | 3.25167635$\times {10}^{-07}$ |

46.5 | 7.14925370$\times {10}^{-11}$ | 2.28505089$\times {10}^{-08}$ | 1.60620921$\times {10}^{-05}$ | 0.85 | 7.85818717$\times {10}^{-07}$ |

47.5 | −1.65354143$\times {10}^{-10}$ | 7.61012429$\times {10}^{-08}$ | 3.10560608$\times {10}^{-06}$ | 0.95 | 3.96736808$\times {10}^{-07}$ |

48.5 | −3.12973348$\times {10}^{-10}$ | 1.39150026$\times {10}^{-07}$ | 3.17305408$\times {10}^{-06}$ | 0.95 | 6.77782659$\times {10}^{-07}$ |

49.5 | −8.48676578$\times {10}^{-10}$ | 3.82780831$\times {10}^{-07}$ | −8.99955570$\times {10}^{-06}$ | 0.95 | 1.84750385$\times {10}^{-06}$ |

50.5 | −6.92148698$\times {10}^{-10}$ | 3.05273387$\times {10}^{-07}$ | −2.21022224$\times {10}^{-06}$ | 0.95 | 1.42588987$\times {10}^{-06}$ |

51.5 | −3.52451773$\times {10}^{-10}$ | 1.49567940$\times {10}^{-07}$ | −2.77810793$\times {10}^{-06}$ | 0.95 | 6.67205223$\times {10}^{-07}$ |

52.5 | −4.88285423$\times {10}^{-10}$ | 2.06597500$\times {10}^{-07}$ | −5.71616451$\times {10}^{-06}$ | 0.95 | 9.23676788$\times {10}^{-07}$ |

53.5 | −1.51950475$\times {10}^{-10}$ | 6.22135728$\times {10}^{-08}$ | 4.00946070$\times {10}^{-06}$ | 0.92 | 3.69972956$\times {10}^{-07}$ |

54.5 | −1.47270077$\times {10}^{-10}$ | 5.88009296$\times {10}^{-08}$ | 1.18884773$\times {10}^{-06}$ | 0.95 | 2.61720547$\times {10}^{-07}$ |

55.5 | −2.67639507$\times {10}^{-10}$ | 9.72464276$\times {10}^{-08}$ | 2.22162082$\times {10}^{-05}$ | 0.63 | 1.37799232$\times {10}^{-06}$ |

56.5 | −1.01960607$\times {10}^{-10}$ | 4.67610258$\times {10}^{-08}$ | 3.41494514$\times {10}^{-06}$ | 0.93 | 2.80937628$\times {10}^{-07}$ |

57.5 | −1.61974440$\times {10}^{-10}$ | 6.72143036$\times {10}^{-08}$ | 1.17127082$\times {10}^{-06}$ | 0.95 | 3.07827728$\times {10}^{-07}$ |

58.5 | −1.01763203$\times {10}^{-09}$ | 4.54759489$\times {10}^{-07}$ | 1.65241671$\times {10}^{-05}$ | 0.91 | 3.09599754$\times {10}^{-06}$ |

59.5 | −1.56307209$\times {10}^{-10}$ | 6.36007172$\times {10}^{-08}$ | 3.86630485$\times {10}^{-06}$ | 0.92 | 3.58530411$\times {10}^{-07}$ |

60.5 | −6.00806861$\times {10}^{-10}$ | 2.63372194$\times {10}^{-07}$ | 5.64617215$\times {10}^{-07}$ | 0.94 | 1.45080898$\times {10}^{-06}$ |

61.5 | −6.04959878$\times {10}^{-10}$ | 2.45041951$\times {10}^{-07}$ | −1.62883930$\times {10}^{-06}$ | 0.94 | 1.21428067$\times {10}^{-06}$ |

62.5 | −6.49554222$\times {10}^{-10}$ | 2.79301792$\times {10}^{-07}$ | 1.91126658$\times {10}^{-05}$ | 0.89 | 2.08911118$\times {10}^{-06}$ |

63.5 | −4.82850036$\times {10}^{-10}$ | 1.71382019$\times {10}^{-07}$ | 2.02470800$\times {10}^{-05}$ | 0.75 | 1.67842699$\times {10}^{-06}$ |

64.5 | −1.06653492$\times {10}^{-10}$ | 4.22914685$\times {10}^{-08}$ | 1.50553273$\times {10}^{-06}$ | 0.94 | 2.03369385$\times {10}^{-07}$ |

65.5 | −8.18714565$\times {10}^{-11}$ | 3.40516816$\times {10}^{-08}$ | 1.66550540$\times {10}^{-06}$ | 0.94 | 1.76539694$\times {10}^{-07}$ |

66.5 | −9.90389288$\times {10}^{-11}$ | 4.04518744$\times {10}^{-08}$ | 1.56394010$\times {10}^{-06}$ | 0.94 | 1.96591466$\times {10}^{-07}$ |

67.5 | −9.41472141$\times {10}^{-11}$ | 3.78395774$\times {10}^{-08}$ | 8.82049866$\times {10}^{-07}$ | 0.94 | 1.80481835$\times {10}^{-07}$ |

68.5 | −8.29145674$\times {10}^{-11}$ | 3.45290364$\times {10}^{-08}$ | 5.19960242$\times {10}^{-06}$ | 0.82 | 3.44043640$\times {10}^{-07}$ |

69.5 | −1.37956080$\times {10}^{-10}$ | 5.60239688$\times {10}^{-08}$ | 1.65024766$\times {10}^{-06}$ | 0.94 | 2.65869617$\times {10}^{-07}$ |

70.5 | −1.01440668$\times {10}^{-10}$ | 4.37751602$\times {10}^{-08}$ | 9.44754103$\times {10}^{-06}$ | 0.79 | 4.90083335$\times {10}^{-07}$ |

71.5 | −8.82187053$\times {10}^{-11}$ | 3.44490090$\times {10}^{-08}$ | 2.44945919$\times {10}^{-06}$ | 0.92 | 1.89763276$\times {10}^{-07}$ |

72.5 | −1.38052514$\times {10}^{-10}$ | 5.94292750$\times {10}^{-08}$ | 4.19292916$\times {10}^{-07}$ | 0.95 | 2.87817244$\times {10}^{-07}$ |

73.5 | −4.91176916$\times {10}^{-11}$ | 2.32864269$\times {10}^{-08}$ | 1.44437460$\times {10}^{-06}$ | 0.94 | 1.39806401$\times {10}^{-07}$ |

74.5 | −6.46953103$\times {10}^{-11}$ | 2.83325477$\times {10}^{-08}$ | 2.59377737$\times {10}^{-06}$ | 0.93 | 1.66218244$\times {10}^{-07}$ |

75.5 | −7.34309741$\times {10}^{-11}$ | 3.29461087$\times {10}^{-08}$ | 4.00460892$\times {10}^{-06}$ | 0.90 | 2.45820894$\times {10}^{-07}$ |

76.5 | −3.05657856$\times {10}^{-11}$ | 2.93068006$\times {10}^{-08}$ | 1.40723930$\times {10}^{-05}$ | 0.74 | 6.32637967$\times {10}^{-07}$ |

77.5 | 5.43557600$\times {10}^{-11}$ | 2.19484499$\times {10}^{-08}$ | 1.18134495$\times {10}^{-05}$ | 0.89 | 5.64382540$\times {10}^{-07}$ |

78.5 | −8.51779066$\times {10}^{-11}$ | 5.79401798$\times {10}^{-08}$ | 1.63692915$\times {10}^{-05}$ | 0.82 | 8.43951888$\times {10}^{-07}$ |

79.5 | −2.21722606$\times {10}^{-10}$ | 8.88851417$\times {10}^{-08}$ | 8.27783879$\times {10}^{-06}$ | 0.89 | 6.07167204$\times {10}^{-07}$ |

80.5 | −1.65576278$\times {10}^{-10}$ | 7.79627572$\times {10}^{-08}$ | 5.66367756$\times {10}^{-06}$ | 0.94 | 4.44114376$\times {10}^{-07}$ |

81.5 | −1.92487027$\times {10}^{-10}$ | 8.70304770$\times {10}^{-08}$ | 5.81788594$\times {10}^{-06}$ | 0.93 | 5.12896384$\times {10}^{-07}$ |

82.5 | −2.51845067$\times {10}^{-10}$ | 1.14456368$\times {10}^{-07}$ | 6.30086163$\times {10}^{-06}$ | 0.94 | 6.49515749$\times {10}^{-07}$ |

83.5 | −4.38140196$\times {10}^{-10}$ | 1.97591643$\times {10}^{-07}$ | 1.99037756$\times {10}^{-05}$ | 0.90 | 1.48395770$\times {10}^{-06}$ |

84.5 | −3.73488547$\times {10}^{-10}$ | 1.70436208$\times {10}^{-07}$ | 8.14608828$\times {10}^{-06}$ | 0.94 | 9.68131273$\times {10}^{-07}$ |

85.5 | −4.33366783$\times {10}^{-10}$ | 2.09399580$\times {10}^{-07}$ | 9.28690005$\times {10}^{-06}$ | 0.94 | 1.21724813$\times {10}^{-06}$ |

86.5 | −4.84412766$\times {10}^{-10}$ | 2.36665683$\times {10}^{-07}$ | 1.09788284$\times {10}^{-05}$ | 0.94 | 1.44126953$\times {10}^{-06}$ |

87.5 | −4.83254202$\times {10}^{-10}$ | 2.68350608$\times {10}^{-07}$ | 1.39973835$\times {10}^{-05}$ | 0.94 | 1.85920378$\times {10}^{-06}$ |

88.5 | −6.21282703$\times {10}^{-10}$ | 3.37561898$\times {10}^{-07}$ | 1.45738166$\times {10}^{-05}$ | 0.94 | 2.27765383$\times {10}^{-06}$ |

89.5 | −6.68966301$\times {10}^{-10}$ | 3.86462205$\times {10}^{-07}$ | 1.63709915$\times {10}^{-05}$ | 0.93 | 2.80715372$\times {10}^{-06}$ |

90.5 | −9.40447671$\times {10}^{-10}$ | 4.91524881$\times {10}^{-07}$ | 1.81668436$\times {10}^{-05}$ | 0.93 | 3.38519060$\times {10}^{-06}$ |

91.5 | −7.89804624$\times {10}^{-10}$ | 4.23827993$\times {10}^{-07}$ | 1.56806295$\times {10}^{-05}$ | 0.94 | 2.81369582$\times {10}^{-06}$ |

92.5 | −2.51717440$\times {10}^{-10}$ | 1.25207391$\times {10}^{-07}$ | 7.46452895$\times {10}^{-06}$ | 0.95 | 7.21226067$\times {10}^{-07}$ |

93.5 | −2.52576412$\times {10}^{-10}$ | 1.27365730$\times {10}^{-07}$ | 7.86103295$\times {10}^{-06}$ | 0.95 | 7.08295267$\times {10}^{-07}$ |

94.5 | −1.68630601$\times {10}^{-10}$ | 8.97996451$\times {10}^{-08}$ | 6.01452925$\times {10}^{-06}$ | 0.95 | 5.30470738$\times {10}^{-07}$ |

95.5 | −1.71120327$\times {10}^{-10}$ | 8.22690427$\times {10}^{-08}$ | 4.20933726$\times {10}^{-06}$ | 0.95 | 4.36420483$\times {10}^{-07}$ |

96.5 | −1.16976002$\times {10}^{-10}$ | 5.79214134$\times {10}^{-08}$ | 3.16068207$\times {10}^{-06}$ | 0.95 | 3.17857028$\times {10}^{-07}$ |

97.5 | −9.42103907$\times {10}^{-10}$ | 7.84156346$\times {10}^{-07}$ | 6.35681772$\times {10}^{-05}$ | 0.89 | 9.05302834$\times {10}^{-06}$ |

98.5 | −1.74979936$\times {10}^{-10}$ | 9.39505851$\times {10}^{-08}$ | 8.37957920$\times {10}^{-06}$ | 0.94 | 6.18586716$\times {10}^{-07}$ |

99.5 | −3.06874683$\times {10}^{-10}$ | 1.63261897$\times {10}^{-07}$ | 1.00132945$\times {10}^{-05}$ | 0.95 | 9.92576035$\times {10}^{-07}$ |

100.5 | −2.08354284$\times {10}^{-10}$ | 1.12300476$\times {10}^{-07}$ | 1.82943275$\times {10}^{-06}$ | 0.95 | 6.70876385$\times {10}^{-07}$ |

101.5 | −2.22515562$\times {10}^{-10}$ | 1.04514427$\times {10}^{-07}$ | 5.86589870$\times {10}^{-06}$ | 0.95 | 5.33557018$\times {10}^{-07}$ |

102.5 | −1.34390246$\times {10}^{-09}$ | 8.98461854$\times {10}^{-07}$ | 3.81054263$\times {10}^{-05}$ | 0.92 | 7.66619612$\times {10}^{-06}$ |

103.5 | −1.01901721$\times {10}^{-09}$ | 6.79827099$\times {10}^{-07}$ | 4.51530159$\times {10}^{-05}$ | 0.94 | 5.22679531$\times {10}^{-06}$ |

104.5 | −4.18859821$\times {10}^{-10}$ | 1.89817197$\times {10}^{-07}$ | 3.18890523$\times {10}^{-06}$ | 0.95 | 9.38122529$\times {10}^{-07}$ |

105.5 | −2.54275033$\times {10}^{-10}$ | 1.20088332$\times {10}^{-07}$ | 6.60009868$\times {10}^{-06}$ | 0.96 | 5.89125254$\times {10}^{-07}$ |

106.5 | −2.43809593$\times {10}^{-10}$ | 1.18160635$\times {10}^{-07}$ | 7.74794070$\times {10}^{-06}$ | 0.96 | 5.90449142$\times {10}^{-07}$ |

107.5 | −2.33163874$\times {10}^{-10}$ | 1.20516330$\times {10}^{-07}$ | 9.87441885$\times {10}^{-06}$ | 0.95 | 6.87291920$\times {10}^{-07}$ |

108.5 | −3.69477413$\times {10}^{-10}$ | 2.17542411$\times {10}^{-07}$ | 1.10904940$\times {10}^{-05}$ | 0.96 | 1.26819431$\times {10}^{-06}$ |

109.5 | −2.81707873$\times {10}^{-10}$ | 1.45887138$\times {10}^{-07}$ | 9.82531461$\times {10}^{-06}$ | 0.95 | 7.99552250$\times {10}^{-07}$ |

110.5 | −9.10934796$\times {10}^{-11}$ | 1.04423228$\times {10}^{-07}$ | 1.44644224$\times {10}^{-05}$ | 0.92 | 1.08652364$\times {10}^{-06}$ |

111.5 | −1.66854605$\times {10}^{-10}$ | 1.18197160$\times {10}^{-07}$ | 1.27341149$\times {10}^{-05}$ | 0.95 | 8.46551633$\times {10}^{-07}$ |

112.5 | −1.97256040$\times {10}^{-10}$ | 1.22023811$\times {10}^{-07}$ | 1.39870362$\times {10}^{-05}$ | 0.95 | 8.24895534$\times {10}^{-07}$ |

113.5 | −1.84532308$\times {10}^{-10}$ | 1.04923564$\times {10}^{-07}$ | 7.42101884$\times {10}^{-06}$ | 0.95 | 6.63927760$\times {10}^{-07}$ |

114.5 | −1.82255068$\times {10}^{-10}$ | 1.00964734$\times {10}^{-07}$ | 1.09676338$\times {10}^{-05}$ | 0.95 | 5.83301149$\times {10}^{-07}$ |

115.5 | −1.79977830$\times {10}^{-10}$ | 9.70059057$\times {10}^{-08}$ | 1.45142487$\times {10}^{-05}$ | 0.95 | 5.79507535$\times {10}^{-07}$ |

116.5 | −1.14063699$\times {10}^{-10}$ | 6.14789756$\times {10}^{-08}$ | 2.11095772$\times {10}^{-05}$ | 0.95 | 3.67271760$\times {10}^{-07}$ |

117.5 | −1.19813939$\times {10}^{-09}$ | 5.28441463$\times {10}^{-07}$ | 5.22879409$\times {10}^{-05}$ | 0.95 | 2.46827715$\times {10}^{-06}$ |

118.5 | −3.17606335$\times {10}^{-10}$ | 1.43250820$\times {10}^{-07}$ | 2.42879319$\times {10}^{-05}$ | 0.95 | 6.91404625$\times {10}^{-07}$ |

119.5 | −5.07968379$\times {10}^{-10}$ | 2.73788903$\times {10}^{-07}$ | 3.79524397$\times {10}^{-05}$ | 0.95 | 1.63559867$\times {10}^{-06}$ |

120.5 | −3.91694650$\times {10}^{-09}$ | 1.76667070$\times {10}^{-06}$ | 4.67276673$\times {10}^{-05}$ | 0.95 | 8.52689227$\times {10}^{-06}$ |

121.5 | −2.10473407$\times {10}^{-08}$ | 3.12348452$\times {10}^{-05}$ | 4.59160841$\times {10}^{-03}$ | 0.91 | 3.68717499$\times {10}^{-04}$ |

122.5 | −9.24069369$\times {10}^{-10}$ | 4.16785440$\times {10}^{-07}$ | 4.09787537$\times {10}^{-05}$ | 0.95 | 2.01162816$\times {10}^{-06}$ |

123.5 | −6.22067015$\times {10}^{-10}$ | 2.80572523$\times {10}^{-07}$ | 2.53756139$\times {10}^{-05}$ | 0.95 | 1.35419220$\times {10}^{-06}$ |

124.5 | −4.72854326$\times {10}^{-10}$ | 2.13272731$\times {10}^{-07}$ | 1.79398692$\times {10}^{-05}$ | 0.95 | 1.02936761$\times {10}^{-06}$ |

125.5 | −2.37088928$\times {10}^{-10}$ | 1.27788104$\times {10}^{-07}$ | 2.05651276$\times {10}^{-05}$ | 0.95 | 7.63398559$\times {10}^{-07}$ |

126.5 | −7.26808556$\times {10}^{-10}$ | 3.27814376$\times {10}^{-07}$ | 1.76920985$\times {10}^{-05}$ | 0.95 | 1.58220650$\times {10}^{-06}$ |

127.5 | −1.57815999$\times {10}^{-10}$ | 8.50609426$\times {10}^{-08}$ | 1.52935833$\times {10}^{-05}$ | 0.95 | 5.08149030$\times {10}^{-07}$ |

128.5 | −1.17377545$\times {10}^{-10}$ | 6.32650980$\times {10}^{-08}$ | 1.23296767$\times {10}^{-05}$ | 0.95 | 3.77941945$\times {10}^{-07}$ |

129.5 | −5.73834119$\times {10}^{-11}$ | 7.57079693$\times {10}^{-08}$ | 1.75886126$\times {10}^{-05}$ | 0.93 | 7.63296694$\times {10}^{-07}$ |

130.5 | −1.24053248$\times {10}^{-09}$ | 5.70638506$\times {10}^{-07}$ | 1.20965081$\times {10}^{-04}$ | 0.91 | 4.16222369$\times {10}^{-06}$ |

131.5 | −2.12721218$\times {10}^{-10}$ | 9.61118248$\times {10}^{-08}$ | 1.95150657$\times {10}^{-05}$ | 0.91 | 6.62435421$\times {10}^{-07}$ |

132.5 | −1.07001857$\times {10}^{-10}$ | 6.29334120$\times {10}^{-08}$ | 1.62571838$\times {10}^{-05}$ | 0.90 | 5.67873985$\times {10}^{-07}$ |

133.5 | −8.94382834$\times {10}^{-10}$ | 8.71939234$\times {10}^{-07}$ | 1.31975911$\times {10}^{-04}$ | 0.94 | 7.54203153$\times {10}^{-06}$ |

134.5 | −8.35494200$\times {10}^{-11}$ | 6.28665121$\times {10}^{-08}$ | 1.35754292$\times {10}^{-05}$ | 0.88 | 7.29144198$\times {10}^{-07}$ |

135.5 | −1.25088026$\times {10}^{-10}$ | 8.54845405$\times {10}^{-08}$ | 3.77824430$\times {10}^{-05}$ | 0.90 | 8.81264590$\times {10}^{-07}$ |

136.5 | −9.79967900$\times {10}^{-11}$ | 7.22954986$\times {10}^{-08}$ | 2.10731394$\times {10}^{-05}$ | 0.90 | 7.68205303$\times {10}^{-07}$ |

137.5 | −1.24013546$\times {10}^{-10}$ | 7.97949440$\times {10}^{-08}$ | 2.37165611$\times {10}^{-05}$ | 0.91 | 7.11357554$\times {10}^{-07}$ |

138.5 | −7.39876006$\times {10}^{-11}$ | 5.55570063$\times {10}^{-08}$ | 2.54832371$\times {10}^{-05}$ | 0.87 | 6.99090195$\times {10}^{-07}$ |

139.5 | −9.49205508$\times {10}^{-10}$ | 4.89958571$\times {10}^{-07}$ | 4.33705249$\times {10}^{-05}$ | 0.96 | 2.54613277$\times {10}^{-06}$ |

140.5 | −$5.67937224\times {10}^{-10}$ | 3.05432744$\times {10}^{-07}$ | $4.62582464\times {10}^{-05}$ | 0.95 | 1.88073609$\times {10}^{-06}$ |

141.5 | −$2.43621952\times {10}^{-10}$ | 1.13736869$\times {10}^{-07}$ | $3.27628394\times {10}^{-05}$ | 0.90 | 8.95784614$\times {10}^{-07}$ |

142.5 | −$1.95955912\times {10}^{-10}$ | 1.01825495$\times {10}^{-07}$ | $3.75119030\times {10}^{-05}$ | 0.83 | 1.18926525$\times {10}^{-06}$ |

143.5 | −$2.46624207\times {10}^{-10}$ | 1.15175318$\times {10}^{-07}$ | $4.23845795\times {10}^{-05}$ | 0.88 | 1.00877166$\times {10}^{-06}$ |

144.5 | −$1.61278923\times {10}^{-10}$ | 8.93582633$\times {10}^{-08}$ | $4.38438448\times {10}^{-05}$ | 0.86 | 9.81989792$\times {10}^{-07}$ |

145.5 | −$2.75726953\times {10}^{-10}$ | 1.38512452$\times {10}^{-07}$ | $4.32208222\times {10}^{-05}$ | 0.89 | 1.19372564$\times {10}^{-06}$ |

146.5 | −$2.43757781\times {10}^{-10}$ | 1.36559581$\times {10}^{-07}$ | $5.45324615\times {10}^{-05}$ | 0.89 | 1.27366067$\times {10}^{-06}$ |

147.5 | −$2.46147842\times {10}^{-10}$ | 1.39066818$\times {10}^{-07}$ | $7.11427892\times {10}^{-05}$ | 0.89 | 1.35250470$\times {10}^{-06}$ |

148.5 | −$3.12927956\times {10}^{-10}$ | 1.56053330$\times {10}^{-07}$ | $7.20397030\times {10}^{-05}$ | 0.87 | 1.51332205$\times {10}^{-06}$ |

149.5 | −$2.31230729\times {10}^{-10}$ | 1.24944106$\times {10}^{-07}$ | $6.58375866\times {10}^{-05}$ | 0.83 | 1.51364906$\times {10}^{-06}$ |

150.5 | −$2.43791216\times {10}^{-10}$ | 1.21205065$\times {10}^{-07}$ | $7.57760769\times {10}^{-05}$ | 0.80 | 1.52268475$\times {10}^{-06}$ |

151.5 | −$1.94987017\times {10}^{-10}$ | 1.16236962$\times {10}^{-07}$ | $8.38650446\times {10}^{-05}$ | 0.80 | 1.65675848$\times {10}^{-06}$ |

152.5 | −$4.33361801\times {10}^{-10}$ | 2.37558655$\times {10}^{-07}$ | $9.63535070\times {10}^{-05}$ | 0.91 | 2.01495486$\times {10}^{-06}$ |

153.5 | −$1.73871412\times {10}^{-10}$ | 1.71988954$\times {10}^{-07}$ | $1.12191003\times {10}^{-04}$ | 0.88 | 2.21903105$\times {10}^{-06}$ |

154.5 | −$1.16988909\times {10}^{-09}$ | 6.16487236$\times {10}^{-07}$ | $1.70987119\times {10}^{-04}$ | 0.93 | 4.36900801$\times {10}^{-06}$ |

155.5 | −$2.55020760\times {10}^{-10}$ | 2.92214578$\times {10}^{-07}$ | $1.64242591\times {10}^{-04}$ | 0.92 | 3.20494890$\times {10}^{-06}$ |

156.5 | −$4.53027932\times {10}^{-10}$ | 2.51428725$\times {10}^{-07}$ | $1.68458783\times {10}^{-04}$ | 0.85 | 2.85808410$\times {10}^{-06}$ |

157.5 | −$1.72784194\times {10}^{-10}$ | 1.48582781$\times {10}^{-07}$ | $1.57486859\times {10}^{-04}$ | 0.77 | 2.79008511$\times {10}^{-06}$ |

158.5 | −$2.29772147\times {10}^{-10}$ | 1.46877406$\times {10}^{-07}$ | $1.54423418\times {10}^{-04}$ | 0.74 | 2.69140338$\times {10}^{-06}$ |

159.5 | −$9.39400590\times {10}^{-11}$ | 1.10698536$\times {10}^{-07}$ | $1.54968996\times {10}^{-04}$ | 0.73 | 2.59598688$\times {10}^{-06}$ |

160.5 | −$8.39077851\times {10}^{-11}$ | 1.26638098$\times {10}^{-07}$ | $1.71073746\times {10}^{-04}$ | 0.77 | 2.80522066$\times {10}^{-06}$ |

161.5 | −$1.98721268\times {10}^{-10}$ | 1.37610016$\times {10}^{-07}$ | $2.05647262\times {10}^{-04}$ | 0.65 | 3.39322701$\times {10}^{-06}$ |

162.5 | −$4.73652596\times {10}^{-10}$ | 2.82618134$\times {10}^{-07}$ | $2.23170447\times {10}^{-04}$ | 0.82 | 3.76275218$\times {10}^{-06}$ |

163.5 | −$1.55191039\times {10}^{-10}$ | 2.30331717$\times {10}^{-07}$ | $2.39080251\times {10}^{-04}$ | 0.83 | 4.07902394$\times {10}^{-06}$ |

164.5 | −$4.04165128\times {10}^{-10}$ | 3.37772150$\times {10}^{-07}$ | $2.81318936\times {10}^{-04}$ | 0.86 | 4.56771102$\times {10}^{-06}$ |

165.5 | −$7.73823055\times {10}^{-12}$ | 2.97227900$\times {10}^{-07}$ | $4.63250839\times {10}^{-04}$ | 0.76 | 7.93202201$\times {10}^{-06}$ |

166.5 | $4.07530120\times {10}^{-11}$ | 8.57496540$\times {10}^{-08}$ | $3.29404588\times {10}^{-04}$ | 0.51 | 5.05815432$\times {10}^{-06}$ |

167.5 | −$2.04674881\times {10}^{-10}$ | 3.39319234$\times {10}^{-07}$ | $3.67674446\times {10}^{-04}$ | 0.81 | 6.73876290$\times {10}^{-06}$ |

168.5 | −$4.43360209\times {10}^{-10}$ | 2.79935936$\times {10}^{-07}$ | $4.04891772\times {10}^{-04}$ | 0.66 | 6.38829474$\times {10}^{-06}$ |

169.5 | $1.21153174\times {10}^{-10}$ | 2.01744392$\times {10}^{-07}$ | $5.46199225\times {10}^{-04}$ | 0.64 | 8.70736220$\times {10}^{-06}$ |

170.5 | −$5.85190609\times {10}^{-10}$ | 4.32779772$\times {10}^{-07}$ | $6.13206686\times {10}^{-04}$ | 0.68 | 1.01094842$\times {10}^{-05}$ |

171.5 | −$5.06522331\times {10}^{-10}$ | 4.47020613$\times {10}^{-07}$ | $6.17992427\times {10}^{-04}$ | 0.70 | 1.06043009$\times {10}^{-05}$ |

172.5 | −$3.24768827\times {10}^{-10}$ | 3.72615949$\times {10}^{-07}$ | $6.98235220\times {10}^{-04}$ | 0.60 | 1.23238287$\times {10}^{-05}$ |

173.5 | $5.76888817\times {10}^{-11}$ | 2.79814116$\times {10}^{-07}$ | $6.97522794\times {10}^{-04}$ | 0.61 | 1.18627791$\times {10}^{-05}$ |

174.5 | −$1.17218795\times {10}^{-10}$ | 3.92089797$\times {10}^{-07}$ | $8.58418577\times {10}^{-04}$ | 0.61 | 1.50705494$\times {10}^{-05}$ |

175.5 | −$1.37607193\times {10}^{-10}$ | 5.06896902$\times {10}^{-07}$ | $1.04781557\times {10}^{-03}$ | 0.60 | 1.97468460$\times {10}^{-05}$ |

176.5 | −$8.96657609\times {10}^{-10}$ | 6.78269058$\times {10}^{-07}$ | $1.12910891\times {10}^{-03}$ | 0.59 | 2.01888857$\times {10}^{-05}$ |

177.5 | $1.32627992\times {10}^{-09}$ | 1.79727927$\times {10}^{-07}$ | $1.42010797\times {10}^{-03}$ | 0.47 | $2.90878237\times {10}^{-05}$ |

178.5 | $1.98167580\times {10}^{-09}$ | $8.00937083\times {10}^{-08}$ | $1.59925973\times {10}^{-03}$ | 0.48 | $3.18302836\times {10}^{-05}$ |

179.5 | $1.18969584\times {10}^{-09}$ | $3.52847586\times {10}^{-07}$ | $1.62399680\times {10}^{-03}$ | 0.54 | $3.13644235\times {10}^{-05}$ |

180.5 | −$1.61188575\times {10}^{-09}$ | $1.46962414\times {10}^{-06}$ | $2.01940644\times {10}^{-03}$ | 0.62 | $4.36405768\times {10}^{-05}$ |

181.5 | −$3.61654690\times {10}^{-09}$ | $2.50708549\times {10}^{-06}$ | $2.31968020\times {10}^{-03}$ | 0.66 | $5.98817371\times {10}^{-05}$ |

182.5 | $1.44002194\times {10}^{-10}$ | $8.58952566\times {10}^{-07}$ | $2.34991118\times {10}^{-03}$ | 0.46 | $5.34544458\times {10}^{-05}$ |

183.5 | −$5.43430484\times {10}^{-10}$ | $9.53841592\times {10}^{-07}$ | $2.52448745\times {10}^{-03}$ | 0.45 | $5.15037308\times {10}^{-05}$ |

184.5 | −$1.30322879\times {10}^{-09}$ | $9.76484389\times {10}^{-07}$ | $2.20300301\times {10}^{-03}$ | 0.47 | $3.95649715\times {10}^{-05}$ |

185.5 | −$1.62506964\times {10}^{-09}$ | $1.13882183\times {10}^{-06}$ | $2.50603519\times {10}^{-03}$ | 0.44 | $4.83075423\times {10}^{-05}$ |

186.5 | −$1.89245396\times {10}^{-09}$ | $1.37388136\times {10}^{-06}$ | $2.88406355\times {10}^{-03}$ | 0.44 | $5.91202561\times {10}^{-05}$ |

187.5 | $6.84720021\times {10}^{-10}$ | $6.10050906\times {10}^{-07}$ | $3.29718092\times {10}^{-03}$ | 0.35 | $6.56653209\times {10}^{-05}$ |

188.5 | $1.53237630\times {10}^{-09}$ | $8.38490308\times {10}^{-07}$ | $3.18211645\times {10}^{-03}$ | 0.46 | $7.35219971\times {10}^{-05}$ |

189.5 | $7.23049173\times {10}^{-09}$ | −$4.24163156\times {10}^{-07}$ | $2.42571457\times {10}^{-03}$ | 0.51 | $6.85476734\times {10}^{-05}$ |

**Table A2.**The Aero-SPAM model describing the photon flux (I, m${}^{-2}\xb7$s${}^{-1}\xb7$nm${}^{-1}$) in 37 specified spectral channels depending on the daily ${F}_{10.7}$ index, $I={P}_{1}\xb7{F}_{10.7}^{2}+{P}_{2}\xb7{F}_{10.7}+{P}_{3}$. ${P}_{1}$, ${P}_{2}$ and ${P}_{3}$ are the regression coefficients for the 37 EUV spectral intervals ($\lambda $), including 17 lines and 20 bands. R is a correlation coefficient between ${F}_{10.7}$ and photon flux. RMSE is the root-mean-square error for the measured and simulated I values.

N^{o} | ${\mathit{\lambda}}_{\mathbf{min}}$, nm | ${\mathit{\lambda}}_{\mathbf{max}}$, nm | ${\mathit{P}}_{1}$ | ${\mathit{P}}_{2}$ | ${\mathit{P}}_{3}$ | R | RMSE |
---|---|---|---|---|---|---|---|

1 | 5 | 10 | −$7.22814128\times {10}^{+06}$ | $4.34844365\times {10}^{+09}$ | −$1.63154083\times {10}^{+11}$ | 0.96 | $2.49833157\times {10}^{+10}$ |

2 | 10 | 15 | −$1.72793713\times {10}^{+08}$ | $1.06538527\times {10}^{+11}$ | −$2.83695953\times {10}^{+12}$ | 0.96 | $6.38391466\times {10}^{+11}$ |

3 | 15 | 20 | −$1.79873111\times {10}^{+09}$ | $1.05716281\times {10}^{+12}$ | −$2.74337230\times {10}^{+13}$ | 0.96 | $6.09484906\times {10}^{+12}$ |

4 | 20 | 25 | −$1.67014302\times {10}^{+09}$ | $9.88384185\times {10}^{+11}$ | −$3.90160466\times {10}^{+13}$ | 0.96 | $5.65031654\times {10}^{+12}$ |

5 | 25.6 | −$2.42136993\times {10}^{+08}$ | $1.44676220\times {10}^{+11}$ | −$7.27167455\times {10}^{+12}$ | 0.96 | $8.22340432\times {10}^{+11}$ | |

6 | 28.4 | −$2.15749026\times {10}^{+08}$ | $1.47186233\times {10}^{+11}$ | −$5.25550336\times {10}^{+12}$ | 0.92 | $1.36257538\times {10}^{+12}$ | |

7 | 25 | 30 | −$8.49047253\times {10}^{+08}$ | $4.39836923\times {10}^{+11}$ | −$1.07767192\times {10}^{+13}$ | 0.96 | $2.37564549\times {10}^{+12}$ |

8 | 30.3 | −$1.05374887\times {10}^{+09}$ | $6.15749059\times {10}^{+11}$ | $2.21870265\times {10}^{+13}$ | 0.94 | $4.36129879\times {10}^{+12}$ | |

9 | 30 | 35 | −$5.78821182\times {10}^{+08}$ | $4.09300016\times {10}^{+11}$ | −$7.39277758\times {10}^{+12}$ | 0.93 | $3.67860958\times {10}^{+12}$ |

10 | 36.8 | −$3.67641064\times {10}^{+08}$ | $2.23500665\times {10}^{+11}$ | −$3.44107714\times {10}^{+12}$ | 0.93 | $1.76712865\times {10}^{+12}$ | |

11 | 35 | 40 | −$5.27393084\times {10}^{+08}$ | $2.60815376\times {10}^{+11}$ | −$4.81963679\times {10}^{+12}$ | 0.94 | $1.61468490\times {10}^{+12}$ |

12 | 40 | 45 | −$1.76485806\times {10}^{+08}$ | $9.43602417\times {10}^{+10}$ | $1.20746026\times {10}^{+12}$ | 0.95 | $5.78446944\times {10}^{+11}$ |

13 | 46.5 | −$9.16428947\times {10}^{+06}$ | $1.10576870\times {10}^{+10}$ | $3.46127070\times {10}^{+12}$ | 0.84 | $1.99324850\times {10}^{+11}$ | |

14 | 45 | 50 | −$3.28417068\times {10}^{+08}$ | $1.54464379\times {10}^{+11}$ | $2.70338559\times {10}^{+11}$ | 0.96 | $7.65976697\times {10}^{+11}$ |

15 | 50 | 55 | −$4.35029980\times {10}^{+08}$ | $1.94267789\times {10}^{+11}$ | −$9.12633707\times {10}^{+11}$ | 0.96 | $9.17807984\times {10}^{+11}$ |

16 | 55.4 | −$7.45540942\times {10}^{+07}$ | $2.70143268\times {10}^{+10}$ | $6.20498828\times {10}^{+12}$ | 0.60 | $4.21493552\times {10}^{+11}$ | |

17 | 58.4 | −$2.67242090\times {10}^{+08}$ | $1.26513904\times {10}^{+11}$ | $5.22846617\times {10}^{+12}$ | 0.91 | $9.60988214\times {10}^{+11}$ | |

18 | 55 | 60 | −$1.11331394\times {10}^{+08}$ | $4.91943896\times {10}^{+10}$ | $2.59480808\times {10}^{+12}$ | 0.94 | $2.86378660\times {10}^{+11}$ |

19 | 60.9 | −$1.75317009\times {10}^{+08}$ | $7.84311521\times {10}^{+10}$ | $2.56019089\times {10}^{+11}$ | 0.94 | $4.50958343\times {10}^{+11}$ | |

20 | 62.9 | −$1.95380036\times {10}^{+08}$ | $8.57116193\times {10}^{+10}$ | $6.10932407\times {10}^{+12}$ | 0.89 | $6.88675932\times {10}^{+11}$ | |

21 | 60 | 65 | −$3.18739604\times {10}^{+08}$ | $1.31380748\times {10}^{+11}$ | $7.10288562\times {10}^{+12}$ | 0.90 | $8.93006924\times {10}^{+11}$ |

22 | 65 | 70 | −$1.54464890\times {10}^{+08}$ | $6.57942854\times {10}^{+10}$ | $3.90335230\times {10}^{+12}$ | 0.93 | $3.82370215\times {10}^{+11}$ |

23 | 70.3 | −$3.92892316\times {10}^{+07}$ | $1.62255869\times {10}^{+10}$ | $3.31133072\times {10}^{+12}$ | 0.78 | $1.84543928\times {10}^{+11}$ | |

24 | 70 | 75 | −$1.17284653\times {10}^{+08}$ | $5.16415922\times {10}^{+10}$ | $2.62008424\times {10}^{+12}$ | 0.94 | $2.82746960\times {10}^{+11}$ |

25 | 76.5 | −$2.80655392\times {10}^{+07}$ | $1.48549365\times {10}^{+10}$ | $5.22726113\times {10}^{+12}$ | 0.72 | $2.63413854\times {10}^{+11}$ | |

26 | 77 | −$1.42682444\times {10}^{+07}$ | $1.64116032\times {10}^{+10}$ | $4.19804672\times {10}^{+12}$ | 0.88 | $2.42046487\times {10}^{+11}$ | |

27 | 78.9 | −$5.13752841\times {10}^{+07}$ | $2.67845754\times {10}^{+10}$ | $6.25669926\times {10}^{+12}$ | 0.81 | $3.56475663\times {10}^{+11}$ | |

28 | 75 | 80 | −$1.09163517\times {10}^{+08}$ | $4.63578518\times {10}^{+10}$ | $4.91238247\times {10}^{+12}$ | 0.89 | $3.39676578\times {10}^{+11}$ |

29 | 80 | 85 | −$5.71385988\times {10}^{+08}$ | $2.65288858\times {10}^{+11}$ | $1.93295978\times {10}^{+13}$ | 0.94 | $1.62478581\times {10}^{+12}$ |

30 | 85 | 90 | −$1.26716263\times {10}^{+09}$ | $6.53242857\times {10}^{+11}$ | $2.77927431\times {10}^{+13}$ | 0.94 | $4.18839876\times {10}^{+12}$ |

31 | 90 | 95 | −$1.14503862\times {10}^{+09}$ | $5.87977430\times {10}^{+11}$ | $2.50221903\times {10}^{+13}$ | 0.95 | $3.62200988\times {10}^{+12}$ |

32 | 97.8 | −$4.60750790\times {10}^{+08}$ | $3.84479195\times {10}^{+11}$ | $3.11115764\times {10}^{+13}$ | 0.90 | $4.64901797\times {10}^{+12}$ | |

33 | 95 | 100 | −$3.84402107\times {10}^{+08}$ | $1.97008185\times {10}^{+11}$ | $1.26370475\times {10}^{+13}$ | 0.95 | $1.14344491\times {10}^{+12}$ |

34 | 102.6 | −$7.45028477\times {10}^{+08}$ | $4.75205812\times {10}^{+11}$ | $1.89621526\times {10}^{+13}$ | 0.93 | $4.08952635\times {10}^{+12}$ | |

35 | 103.2 | −$6.18608147\times {10}^{+08}$ | $3.73585739\times {10}^{+11}$ | $2.24459796\times {10}^{+13}$ | 0.94 | $2.81357100\times {10}^{+12}$ | |

36 | 100 | 105 | −$4.16550795\times {10}^{+08}$ | $2.04940624\times {10}^{+11}$ | $5.82827246\times {10}^{+12}$ | 0.96 | $1.07697392\times {10}^{+12}$ |

37 | 121.6 | −$2.81408845\times {10}^{+10}$ | $2.25475006\times {10}^{+13}$ | $2.62203706\times {10}^{+15}$ | 0.92 | $2.35540620\times {10}^{+14}$ |

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**Figure 1.**Distribution of TIMED data used to develop the SPAM model against F${}_{10.7}$ solar activity index. Note that 5% of the data to the right of the red vertical line (over 200 s.f.u.) has been excluded due to its significant sparseness.

**Figure 2.**Panel (

**a**): Average energy spectrum in the range of 0–190 nm built on the TIMED SEE data. Standard deviation of measurement data is shown as a vertical line in each 1 nm wide spectral channel; Panel (

**b**): Relative standard deviation of measurement data, note the logarithmic scale; Panel (

**c**): correlation coefficients between the energy flux at a certain wavelength and the index F${}_{10.7}$.

**Figure 3.**The scatterplots of TIMED energy flux measurements F versus F${}_{10.7}$ index for 0.5, 2.5, 4.5, 58.5, 97.5, 102.5, 139.5, 150.5 and 189.5 nm. Black lines are the second order polynomial fitting functions.

**Figure 4.**Panel (

**a**): simulated differential photon flux using Aero-SPAM model during low solar activity in 20 June 2009 (blue line) and during high solar activity in 18 June 2015 (red line) and their relative difference (black line). Panels (

**b**,

**c**): vertical distribution of the photoionization rates between 90 and 250 km above the Gorkovskaya station (60.27${}^{\circ}$ N, 29.38${}^{\circ}$ E) during low and high solar activity. The calculations were carried out for the photoionization rates of molecular oxygen O${}_{2}$ (magenta), molecular nitrogen N${}_{2}$ (red), atomic oxygen O (blue) and nitric oxide NO (green), and total ionization rate (black) for the local noon during summer solstices.

**Figure 5.**Solar irradiance time series in different spectral lines: (

**a**) 3.5 nm; (

**b**) 53.5 nm; (

**c**) 97.5 nm; (

**d**) 159.5 nm. TIMED SEE measurements shown in red (before) and in green (after sensor degradation); black curve is the Solar-SPAM calculations. Blue vertical line denotes the date of the last absolute detector calibration on 1 June 2016. Panels (

**e**–

**h**) show scatterplots of the radiation flux versus the F${}_{10.7}$ solar activity index.

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**MDPI and ACS Style**

Nikolaeva, V.; Gordeev, E.
SPAM: Solar Spectrum Prediction for Applications and Modeling. *Atmosphere* **2023**, *14*, 226.
https://doi.org/10.3390/atmos14020226

**AMA Style**

Nikolaeva V, Gordeev E.
SPAM: Solar Spectrum Prediction for Applications and Modeling. *Atmosphere*. 2023; 14(2):226.
https://doi.org/10.3390/atmos14020226

**Chicago/Turabian Style**

Nikolaeva, Vera, and Evgeny Gordeev.
2023. "SPAM: Solar Spectrum Prediction for Applications and Modeling" *Atmosphere* 14, no. 2: 226.
https://doi.org/10.3390/atmos14020226