Authors:
(1) Michael Sorochan Armstrong, Computational Data Science (CoDaS) Lab in the Department of Signal Theory, Telematics, and Communications at the University of Granada;
(2) Jose Carlos P´erez-Gir´on, part of the Interuniversity Institute for Research on the Earth System in Andalucia through the University of Granada;
(3) Jos´e Camacho, Computational Data Science (CoDaS) Lab in the Department of Signal Theory, Telematics, and Communications at the University of Granada;
(4) Regino Zamora, part of the Interuniversity Institute for Research on the Earth System in Andalucia through the University of Granada. Table of Links Abstract & Introduction Optimization of the Optical Interpolation Materials and Methods Results and Discussion Conclusion Appendix A: Proof of Hermitian Self-Adjoint product identity for Equidistant Time-Domain Measurements Appendix B: AAH ̸= MIN I in the Non-Equidistant Case Acknowledgments & References 3 MATERIALS AND METHODS 3.0.1 Remote Sensor Data Soil temperature data were collected in the Sierra Nevada National Park in Andaluc´ıa, Spain, as part of the Smart EcoMountains program through the Lifewatch ERIC Program, from solar-powered remote multi-parametric micro-stations located within different environments (shrub, rock, and bare-earth) and altitudes (from 1500m to 2300m) from 29- 07-2020 until 04-05-2023. Measurements were continuously collected at a nominal 10 minute interval with micro-sensors (ibuttons, thermochron-type; Maxim integrated) connected to a network that transmits the collected information when connectivity is available. All the collected data were visually inspected for extreme values outside the normal ranges of the variable in the time series due to sensor failures, identifying a single sensor reporting erroneous values that were reported as NaNs. 3.0.2 Computational information All calculations were run with a B550 AORUS ELITE AX V2 motherboard with 128 GiB DDR4 RAM, an AMD Ryzen 9 5950x 32 core processor with an NVIDIA GeForce RTX 3080 graphics processor, and a 2 TB NVMe Samsung SSD 980. Software was installed on Ubuntu 22.04.3 LTS 64-bit operating system “Jammy Jellyfish”. Graphical inspections and data cleaning were conducted with the tidyverse 2.0.0 package [13] implemented in the R 4.3.1 software environment [14]. Calculations were performed using Python 3.10. Data was parsed and cleaned from the original .csv values using Pandas 2.0.3. Various numerical operations were performed using the vectorized functions available in NumPy 1.25 [15], with additional statistical functionality from SciPy 1.11 [16]. Graphics were created using Matplotlib 3.7.1 [17]. This paper is available on arxiv under CC 4.0 license. Authors: (1) Michael Sorochan Armstrong, Computational Data Science (CoDaS) Lab in the Department of Signal Theory, Telematics, and Communications at the University of Granada; (2) Jose Carlos P´erez-Gir´on, part of the Interuniversity Institute for Research on the Earth System in Andalucia through the University of Granada; (3) Jos´e Camacho, Computational Data Science (CoDaS) Lab in the Department of Signal Theory, Telematics, and Communications at the University of Granada; (4) Regino Zamora, part of the Interuniversity Institute for Research on the Earth System in Andalucia through the University of Granada. Authors: Authors: (1) Michael Sorochan Armstrong, Computational Data Science (CoDaS) Lab in the Department of Signal Theory, Telematics, and Communications at the University of Granada; (2) Jose Carlos P´erez-Gir´on, part of the Interuniversity Institute for Research on the Earth System in Andalucia through the University of Granada; (3) Jos´e Camacho, Computational Data Science (CoDaS) Lab in the Department of Signal Theory, Telematics, and Communications at the University of Granada; (4) Regino Zamora, part of the Interuniversity Institute for Research on the Earth System in Andalucia through the University of Granada. Table of Links Abstract & Introduction Abstract & Introduction Optimization of the Optical Interpolation Optimization of the Optical Interpolation Materials and Methods Materials and Methods Results and Discussion Results and Discussion Conclusion Conclusion Appendix A: Proof of Hermitian Self-Adjoint product identity for Equidistant Time-Domain Measurements Appendix A: Proof of Hermitian Self-Adjoint product identity for Equidistant Time-Domain Measurements Appendix B: AAH ̸= MIN I in the Non-Equidistant Case Appendix B: AAH ̸= MIN I in the Non-Equidistant Case Acknowledgments & References Acknowledgments & References 3 MATERIALS AND METHODS 3.0.1 Remote Sensor Data Soil temperature data were collected in the Sierra Nevada National Park in Andaluc´ıa, Spain, as part of the Smart EcoMountains program through the Lifewatch ERIC Program, from solar-powered remote multi-parametric micro-stations located within different environments (shrub, rock, and bare-earth) and altitudes (from 1500m to 2300m) from 29- 07-2020 until 04-05-2023. Measurements were continuously collected at a nominal 10 minute interval with micro-sensors (ibuttons, thermochron-type; Maxim integrated) connected to a network that transmits the collected information when connectivity is available. All the collected data were visually inspected for extreme values outside the normal ranges of the variable in the time series due to sensor failures, identifying a single sensor reporting erroneous values that were reported as NaNs. 3.0.2 Computational information All calculations were run with a B550 AORUS ELITE AX V2 motherboard with 128 GiB DDR4 RAM, an AMD Ryzen 9 5950x 32 core processor with an NVIDIA GeForce RTX 3080 graphics processor, and a 2 TB NVMe Samsung SSD 980. Software was installed on Ubuntu 22.04.3 LTS 64-bit operating system “Jammy Jellyfish”. Graphical inspections and data cleaning were conducted with the tidyverse 2.0.0 package [13] implemented in the R 4.3.1 software environment [14]. Calculations were performed using Python 3.10. Data was parsed and cleaned from the original .csv values using Pandas 2.0.3. Various numerical operations were performed using the vectorized functions available in NumPy 1.25 [15], with additional statistical functionality from SciPy 1.11 [16]. Graphics were created using Matplotlib 3.7.1 [17]. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

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