# Two-Dimensional Mapping of Ionospheric Total Electron Content over the Philippines Using Kriging Interpolation

^{*}

## Abstract

**:**

## 1. Introduction

_{4}) using kriging. They used the maps to describe the ionospheric features in India observed from 15 to 20 March 2015.

## 2. Materials and Methods

#### 2.1. GNSS Receiver Stations and Receiver Data

#### 2.2. Developing Regional TEC Maps Using Kriging Interpolation

^{16}electrons per square meter. For kriging, the mapping involves the use of TEC and its location of observation.

_{s}), and $c$ is the speed of light.

#### 2.3. Finding the Optimum Parameters for Kriging Interpolation

#### 2.4. Analysis of TEC Maps

## 3. Results

#### 3.1. Optimum Parameters for Kriging

#### 3.2. GNSS VTEC Maps over the Philippines

_{2}and N

_{2}increases while atomic oxygen density decreases. This causes the ionosphere to be composed of more neutrals than ions, hence a depletion of TEC [21]. It has also been confirmed that O/N

_{2}decreased in Asian sectors the day after the storm [38]. This storm was caused by a coronal mass ejection (CME) from the Sun that occurred on March 15. It reached Earth on St. Patrick’s Day, 17 March, creating the strongest geomagnetic storm of Solar Cycle 24 [38,39].

#### 3.3. Spatial and Temporal Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Distribution of GNSS receiver stations in the Philippines used. All these stations are from PAGeNet except for PIMO, which is part of IGS.

**Figure 2.**Sample of the semivariogram as function of the lag distance. Scattered points represent the experimental semivariogram. The fitted line is the theoretical semivariogram.

**Figure 3.**Distribution of variable GNSS receiver stations used. Stations in green indicate the additional stations for that parameter. 9 stations include PBAS, PGEN, PILC, PIMO, PLEG, PPPC, PTAC, PTUG and PZAM. 12 stations include the 9 stations plus PMAS, PSUR and PURD. 15 stations include the 12 stations plus PDAV, PMOG and PNDO. 18 stations include all receiver stations initially considered for this study based on Figure 1.

**Figure 4.**(

**a**) A GIM map is taken from the IONEX file. (

**b**) VTEC values from different points of the GIM map were taken. The points were chosen from the varying number of chosen GNSS stations based on Figure 3. (

**c**) The map is recreated using kriging based on (

**b**).

**Figure 5.**Frequency of the best-performing number of station parameters together with the linear model across 12 days in terms of mean and standard deviation.

**Figure 6.**Comparing IGS GIM (

**left**) and a VTEC map based on PAGeNet GNSS data and mapped using kriging interpolation (

**right**).

**Figure 7.**(

**a**) 1-dimensional VTEC timeseries of 30 March (quiet), 17 March (active), 5 March (scintillated) and the average quiet day VTEC of March 2015 observed by PIMO station and (

**b**) difference between the average quiet day and the three dates. Positive values denote higher VTEC levels than average and vice versa. This shows the variation in VTEC during different geomagnetic and ionospheric conditions.

**Figure 8.**The planetary K (Kp) and the solar flux indices of the dates based on Figure 7.

**Figure 9.**2-dimensional map of VTEC on an average quiet day of March 2015 at 0 UT, 8 UT, 13 UT and 21 UT.

**Figure 10.**2-dimensional map of VTEC on 30 March (quiet), 5 March (scintillated), 17 March (active) 2015 at 0 UT, 8 UT, 13 UT and 21 UT.

**Figure 11.**2-dimensional map of differential VTEC between the average quiet day VTEC and VTEC on the indicated dates.

**Figure 13.**Latitude profiles of 30 March, 5 March and 17 March with the difference between them and the latitude profiles of quiet day VTEC plus Kp-index bar graph.

**Figure 14.**Longitude profiles of 30 March, 5 March and 17 March with the difference between them and the latitude profiles of quiet day VTEC plus Kp-index bar graph.

**Table 1.**Mean normalized error (MNE) values throughout 12 days of March 2015. Values in bold and in green indicate the best-performing parameter set on that day. The worst-performing sets are in red.

No. ofStations | Model | DOY 60 | DOY 61 | DOY 62 | DOY 64 | DOY 65 | DOY 76 |

9 | linear | 0.00442 | 0.00437 | 0.00436 | 0.00450 | 0.00567 | 0.00435 |

spherical | 0.00475 | 0.00471 | 0.00468 | 0.00488 | 0.00584 | 0.00460 | |

exponential | 0.00554 | 0.00560 | 0.00566 | 0.00582 | 0.00676 | 0.00545 | |

12 | linear | 0.00414 | 0.00425 | 0.00431 | 0.00443 | 0.00546 | 0.00432 |

spherical | 0.00434 | 0.00451 | 0.00457 | 0.00472 | 0.00562 | 0.00454 | |

exponential | 0.00498 | 0.00524 | 0.00539 | 0.00554 | 0.00640 | 0.00528 | |

15 | linear | 0.00402 | 0.00417 | 0.00420 | 0.00438 | 0.00569 | 0.00414 |

spherical | 0.00418 | 0.00436 | 0.00440 | 0.00460 | 0.00582 | 0.00434 | |

exponential | 0.00472 | 0.00498 | 0.00508 | 0.00528 | 0.00647 | 0.00499 | |

18 | linear | 0.00403 | 0.00418 | 0.00421 | 0.00440 | 0.00566 | 0.00415 |

spherical | 0.00418 | 0.00435 | 0.00438 | 0.00461 | 0.00579 | 0.00433 | |

exponential | 0.00468 | 0.00493 | 0.00502 | 0.00525 | 0.00644 | 0.00493 | |

No. ofStations | Model | DOY 77 | DOY 84 | DOY 85 | DOY 86 | DOY 87 | DOY 89 |

9 | linear | 0.00492 | 0.00360 | 0.00320 | 0.00391 | 0.00332 | 0.00300 |

spherical | 0.00539 | 0.00387 | 0.00342 | 0.00418 | 0.00357 | 0.00324 | |

exponential | 0.00672 | 0.00438 | 0.00406 | 0.00486 | 0.00428 | 0.00381 | |

12 | linear | 0.00516 | 0.00352 | 0.00314 | 0.00387 | 0.00331 | 0.00301 |

spherical | 0.00557 | 0.00377 | 0.00333 | 0.00410 | 0.00351 | 0.00320 | |

exponential | 0.00678 | 0.00424 | 0.00391 | 0.00472 | 0.00419 | 0.00371 | |

15 | linear | 0.00531 | 0.00347 | 0.00315 | 0.00399 | 0.00336 | 0.00304 |

spherical | 0.00565 | 0.00363 | 0.00332 | 0.00416 | 0.00353 | 0.00319 | |

exponential | 0.00671 | 0.00407 | 0.00383 | 0.00469 | 0.00413 | 0.00361 | |

18 | linear | 0.00539 | 0.00343 | 0.00315 | 0.00398 | 0.00336 | 0.00305 |

spherical | 0.00571 | 0.00359 | 0.00331 | 0.00414 | 0.00352 | 0.00319 | |

exponential | 0.00671 | 0.00401 | 0.00380 | 0.00466 | 0.00410 | 0.00358 |

**Table 2.**Standard deviation values of the mean normalized error throughout 12 days of March 2015. Values in bold and in green indicate the least value on that day. The worst-performing sets are in red.

No. ofStations | Model | DOY 60 | DOY 61 | DOY 62 | DOY 64 | DOY 65 | DOY 76 |

9 | linear | 0.00502 | 0.00436 | 0.00531 | 0.00469 | 0.00338 | 0.00252 |

spherical | 0.00527 | 0.00455 | 0.00551 | 0.00495 | 0.00346 | 0.00272 | |

exponential | 0.00593 | 0.00528 | 0.00627 | 0.00561 | 0.00412 | 0.00343 | |

12 | linear | 0.00495 | 0.00418 | 0.00529 | 0.00466 | 0.00326 | 0.00250 |

spherical | 0.00506 | 0.00429 | 0.00542 | 0.00484 | 0.00332 | 0.00265 | |

exponential | 0.00550 | 0.00479 | 0.00592 | 0.00531 | 0.00374 | 0.00318 | |

15 | linear | 0.00507 | 0.00421 | 0.00538 | 0.00476 | 0.00349 | 0.00246 |

spherical | 0.00513 | 0.00428 | 0.00546 | 0.00487 | 0.00353 | 0.00259 | |

exponential | 0.00539 | 0.00460 | 0.00580 | 0.00523 | 0.00386 | 0.00297 | |

18 | linear | 0.00501 | 0.00418 | 0.00532 | 0.00473 | 0.00341 | 0.00238 |

spherical | 0.00506 | 0.00423 | 0.00538 | 0.00483 | 0.00348 | 0.00247 | |

exponential | 0.00532 | 0.00452 | 0.00569 | 0.00516 | 0.00385 | 0.00280 | |

No. ofStations | Model | DOY 77 | DOY 84 | DOY 85 | DOY 86 | DOY 87 | DOY 89 |

9 | linear | 0.00330 | 0.00206 | 0.00285 | 0.00232 | 0.00231 | 0.00357 |

spherical | 0.00359 | 0.00220 | 0.00308 | 0.00243 | 0.00256 | 0.00380 | |

exponential | 0.00450 | 0.00225 | 0.00371 | 0.00275 | 0.00300 | 0.00433 | |

12 | linear | 0.00321 | 0.00203 | 0.00285 | 0.00231 | 0.00232 | 0.00354 |

spherical | 0.00347 | 0.00216 | 0.00304 | 0.00240 | 0.00249 | 0.00372 | |

exponential | 0.00428 | 0.00223 | 0.00360 | 0.00271 | 0.00295 | 0.00416 | |

15 | linear | 0.00337 | 0.00203 | 0.00281 | 0.00244 | 0.00235 | 0.00354 |

spherical | 0.00358 | 0.00209 | 0.00300 | 0.00251 | 0.00251 | 0.00368 | |

exponential | 0.00428 | 0.00221 | 0.00351 | 0.00280 | 0.00296 | 0.00405 | |

18 | linear | 0.00340 | 0.00201 | 0.00279 | 0.00242 | 0.00233 | 0.00357 |

spherical | 0.00361 | 0.00208 | 0.00297 | 0.00250 | 0.00249 | 0.00370 | |

exponential | 0.00427 | 0.00220 | 0.00345 | 0.00279 | 0.00294 | 0.00403 |

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**MDPI and ACS Style**

Maglambayan, V.L.L.; Macalalad, E.P. Two-Dimensional Mapping of Ionospheric Total Electron Content over the Philippines Using Kriging Interpolation. *Atmosphere* **2022**, *13*, 1626.
https://doi.org/10.3390/atmos13101626

**AMA Style**

Maglambayan VLL, Macalalad EP. Two-Dimensional Mapping of Ionospheric Total Electron Content over the Philippines Using Kriging Interpolation. *Atmosphere*. 2022; 13(10):1626.
https://doi.org/10.3390/atmos13101626

**Chicago/Turabian Style**

Maglambayan, Vincent Louie L., and Ernest P. Macalalad. 2022. "Two-Dimensional Mapping of Ionospheric Total Electron Content over the Philippines Using Kriging Interpolation" *Atmosphere* 13, no. 10: 1626.
https://doi.org/10.3390/atmos13101626