Pinatubo Study (Atmospheric Carbon Dioxide Reservoir)
Notes Accompanying Referenced PowerPoint Slides
©EnergyCite Inc./ClimateCite Corp. Intellectual Property;
Not for release to third parties without prior permission
March 12, 2022
In November 2021, ClimateCite Corp, a non-profit 501(c)(3)compliant educational and research entity and its sister company EnergyCite, Inc. engaged two Stanford educated Ph.D. physicists, Dr. Shahar Ben-Menahem and Dr. Abraham Ishihara through the research company, MODOC Analytics, to conduct an analysis of the atmospheric reservoir of Carbon Dioxide (CO2) and the effect the June 15, 1991 volcanic eruption of Pinatubo had on the rate of change of the CO2 quantity.
The first phase of this study used software to determine if we could detect inflection points (defined as changes in sign of established trend) that corresponded to a single major climate event within a data set of daily CO2 concentration measurements; the event was the 1991 explosive volcanic eruption of Pinatubo in the Philippine Islands. The data set was the daily CO2 concentrations reported by NOAA Mauna Loa. Hypothetically, if we were able to detect this event with statistical confidence, then we could use the same data set and software to produce evidence that Henry’s Law controls CO2 atmospheric concentrations due to the solubility of CO2 gas in the Earth’s hydrosphere. This example would be the first case which then would be expanded by looking at many different types of climate, weather and environmental events, such as human CO2 emissions which are presumed and widely reported to affect global CO2 concentration.
An inflection point in this context means a definitive, statistically significant, change in the rate of change of the amount of CO2 gas in air as reported by the laboratory of the U.S. National Atmospheric and Oceanic Administration (NOAA) located about 11,000 feet above sea level on Mauna Loa volcano on the Big Island of Hawaii. The software tool for this initial phase was designed by S. Ben-Menahem, PhD and A. Ishihara, PhD.
The Mauna Loa data set was selected by ClimateCite and its principal scientist, C. Bromley, because it is widely recognized and reported and widely but not universally assumed to be the gold standard representing the net global average CO2 gas concentration in the atmosphere. This data set was also selected because the data are readily accessible and have been measured since the 1970s
The deliverables of Modoc Analytics to ClimateCite/EnergyCite in connection with the undertaken NOAA Mauna Loa CO2 level time-series with their descriptions — as well as brief explanation of the computations that went into producing them — are as follows:
1. Block Diagram:
The raw (or at least as raw as we are able to publically obtain) daily Mauna Loa (hereinafter ML) CO2 data, from the early 70s through 2020, is used as input for our sequence of algorithms. This time-series data — although we refer to it as “raw” — has been slightly processed by us as follows:
1.a. Data for days for which no real CO2 data was available from ML, but for which data were available for days both preceding and following the block of missing-data day(s), were interpolated accordingly.
1.b. Data for days (at the beginning of the recording period — early 1970s) for which no real data was available and no earlier data with valid data were available — were replaced by constant nominal values in the low 300’s. This block of data is limited to the early 1970s and does not affect our results for the period surrounding the Pinatubo event.
The following mathematical procedures (as summarized by boxes in the Block Diagram) are then applied to this “raw CO2 level data” time series (wherein time is given in fractional Gregorian years and CO2 levels are given in ppm units):
1.c. A JTFA (“Joint Time Frequency Analysis”) is performed. Those skilled in the art of time-series DSP will recognize that this term refers to a class of methods, wherein a quantity-vs-time series is analyzed for its frequency content (such as PSD = Power Spectrum Density) as a function of time. While there are many JTFA techniques, the simplest one is performing a Fast Fourier Transform analysis (FFT) in a moving (“swept”) time window, and computing the complex FFT coefficients as a function of both window start-time and in-window frequency index. This type of JTFA transformation, however, is not easily invertible (and we need inversion, as explained below).
One of the simplest sub-classes of JTFA methods which is easily invertible is the Gabor Transform.
The Ben-Menahem-Ishihara proprietary analysis method used in this investigation was based on combining the above two methods.
1.d. In the quantity-vs-(t, freq) ( time-frequency analyzes raw data) result of our JTFA, we then remove the seasonal (1-year period) frequency-band peak via a notch filter, and also suppress the high-frequency band (“low-pass filtering”). [Those skilled in the art of DSP or analog filtering in EE and other branches of physics-based engineering will readily recognize these terms and techniques.]
1.e. After the notch-and low-pass filtering of the JTFA-produced data — represented by the relevant boxes in the Block Diagram — the filtered JTFA transform is then inverted. This computation yields the output (lower-left) box of the Block Diagram — the processed CO2 vs. time signal (and its time derivative).
2. Raw & Processed Data Files:
2.a. Our interpolated “raw” CO2 vs. time data file Is described above. It is provided in two-column ‘.csv’ file format, with Column 1 representing ML measurement time (in fractional Gregorian years), and Column 2 representing CO2 levels in ppm units.
2.b. The processed CO2 levels file, as well as its time-derivative files (in units ppm and ppm/year, respectively). These files are again in 2-column ‘.csv’ format; they are referred to in the output (lower-left) block of the Block Diagram.
2.c. JTFA file: this is a 3-column ‘.csv’ file. Column 1 represents time (again in Gregorian date fractional years); Column 2 represents frequency (in units of cycles-per-year); Column 3 represents the JTFA-PSD (Power Spectrum Density), which is the squares modulus of the complex JTFA signal at the time and frequency corresponding to the given row.
3. Raw & Processed Plots:
3.a. Plot over the entire ML recording epoch (circa 5 decades) of both the “raw” (as defined in 1 above) and processed (as defined in 2.b above) CO2 levels, vs. time, with slanted DD/MM/YY date markers provided on the x-axis (time axis).
3.b. Two plots as in the previous sub-deliverable, but zoomed in to cover only the Pinatubo decade: 1990-2000.
3.c. Plot of time derivative of the processed CO2 time derivative vs. time (from 2.b above), with the estimated “would-be inflection” times bracketing the detected “Pinatubo Event” indicated by arrows and DD/MM/YY date markers.
On this plot, the mean baseline pre- and post-Pinatubo CO2 derivative values are indicated as horizontal lines.