You are mistaken in virtually everything you say here. I shall take a single instance, as per the highlighted text. Here are a couple of papers that illustrate the techniques. (Many, many more could be provided. I'm sure you can search for these yourself.) These and the associated technology continue to advance so that the determinations are refined and extended.
Here’s an excerpt from the first couple paragraphs of your first link. I must admit that about the only things I understand are "highlighted."
“[1]
We estimate tropical Atlantic upper ocean temperatures using oxygen isotope and Mg/Ca ratios in well‐preserved planktonic foraminifera extracted from Albian through Santonian black shales recovered during Ocean Drilling Program Leg 207 (North Atlantic Demerara Rise).
On the basis of a range of plausible assumptions regarding seawater composition at the time the data support temperatures between 33° and 42°C. In our low‐resolution data set spanning ∼84–100 Ma a local temperature maximum occurs in the late Turonian, and
a possible minimum occurs in the mid to early late Cenomanian. The relation between single species foraminiferal δ18O and Mg/Ca suggests that the ratio of magnesium to calcium in the Turonian‐Coniacian ocean
may have been lower than in the Albian‐Cenomanian ocean,
perhaps coincident with an ocean 87Sr/86Sr minimum. The carbon isotopic compositions of distinct marine algal biomarkers were measured in the same sediment samples. The δ13C values of phytane, combined with foraminiferal δ13C and
inferred temperatures,
were used to estimate atmospheric carbon dioxide concentrations through this interval.
Estimates of atmospheric CO2 concentrations range between 600 and 2400 ppmv.
Within the uncertainty in the various proxies,
there is only a weak overall correspondence between higher (lower) tropical temperatures and
more (less) atmospheric CO2. The GENESIS climate model underpredicts tropical Atlantic temperatures
inferred from ODP Leg 207 foraminiferal δ18O and Mg/Ca
when we specify approximate CO2 concentrations
estimated from the biomarker isotopes in the same samples. Possible errors in the temperature and CO2
estimates and
possible deficiencies in the model are discussed. The
potential for and effects of substantially higher atmospheric methane during Cretaceous anoxic events,
perhaps derived from high fluxes from the oxygen minimum zone, are considered in light of recent work that shows a quadratic relation between increased methane flux and atmospheric CH4concentrations. With 50 ppm CH4, GENESIS sea surface temperatures
approximate the minimum upper ocean temperatures
inferred from proxy data when CO2 concentrations specified to the model are near those
inferred using the phytane δ13C proxy. However, atmospheric CO2 concentrations of 3500 ppm or more are still required in the model in order to reproduce
inferred maximum temperatures.
1. Introduction
[2] The concentration of carbon dioxide in the atmosphere
is believed to be a primary determinant of climate [
Royer et al., 2004]. Model studies indicate that the direct radiative effects and water vapor feedbacks accompanying a change from 500 to 1000 ppm CO2(values at the lower end of mid‐Cretaceous CO2
estimates) have a greater effect on Earth's surface temperature than the combined temperature effects of paleogeographic and solar luminosity changes over the past 90 million years [
Bice et al., 2000;
Bice and Norris, 2002].
Estimates of Cretaceous CO2 concentrations have been made using a variety of terrestrial and marine proxies, including the carbon isotopic composition of specific organic compounds.
The resulting estimates for an individual geologic stage can vary widely [
Royer et al., 2001;
Bice and Norris, 2002, and references therein]. In a model‐data study,
Bice and Norris [2002] suggested that in the mid‐Cretaceous at least, this variability
may be real, which points out the need for a multiple proxy approach in order to more reliably constrain paleo‐CO2 concentrations.”
