Optimal estimation of atmospheric 14 C production over the Holocene: paleoclimate implications

A tree-ring Δ14C record and a simple box model of the global 14C cycle are combined using a method of optimal estimation theory (Rauch-Tung-Striebel smoother). The combination is used to infer information about the time evolution of 14C production in the atmosphere % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiGabGEbbWUcca % GGOaWefv3ySLgznfgDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWF % pepucaGGPaaaaa!448D! $$(\mathcal{P})$$ for the period 9400 year BC to AD 1900 year. Unlike previous attempts to infer % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiGabGEbbWUctu % uDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wzaGqbaiab-9q8qbaa % !4334! $$\mathcal{P}$$ changes from the tree-ring record, the errors in both the Δ14C data and the model, which are assumed to be purely random (not systematic), are formally considered. The optimal time evolution of % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiGabGEbbWUctu % uDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wzaGqbaiab-9q8qbaa % !4334! $$\mathcal{P}$$ is compared to independent evidence of changes in cosmogenic nuclide production over the Holocene from a variety of records on their original chronology, e.g., a record of the virtual axial dipole moment (VADM) based on a compilation of archeomagnetic data, the record of 10Be concentration from the GISP2 ice core (Central Greenland), and the record of 10Be concentration from the PS1 ice core (South Pole). The rank correlations between % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf % gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFpepucaqGTaGaaeOv % aiaabgeacaqGebGaaeytaiaacYcacaaMe8Uae83dXdLaaeylamaaCa % aaleqabaGaaGymaiaaicdaaaGccaaMb8UaaeOqaiaabwgacaGGOaGa % ae4raiaabMeacaqGtbGaaeiuaiaaikdacaGGPaGaaiilaaaa!54D9! $$ \mathcal{P}{\text{ - VADM}},\;\mathcal{P}{\text{ - }}^{{10}} {\text{Be}}({\text{GISP}}2), $$ and % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf % gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFpepucaqGTaWaaWba % aSqabeaacaaIXaGaaGimaaaakiaaygW7caqGcbGaaeyzaiaacIcaca % qGqbGaae4uaiaaigdacaGGPaaaaa!4A9C! $$ \mathcal{P}{\text{ - }}^{{10}} {\text{Be}}({\text{PS}}1) $$ are highly significant (p < 0.01), indicating that geomagnetic field intensity and 10Be concentration in GISP2 and PS1 changed monotonically with 14C production. The linear correlation coefficients between % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiGabGEbbWUctu % uDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wzaGqbaiab-9q8qjaa % b2cacaqGwbGaaeyqaiaabseacaqGnbGaaiilaiaaysW7cqWFpepuca % qGTaWaaWbaaSqabeaacaaIXaGaaGimaaaakiaaygW7caqGcbGaaeyz % aiaacIcacaqGhbGaaeysaiaabofacaqGqbGaaGOmaiaacMcacaGGSa % GaaGjbVlaabggacaqGUbGaaeizaiaaysW7cqWFpepucaqGTaWaaWba % aSqabeaacaaIXaGaaGimaaaakiaaygW7caqGcbGaaeyzaiaacIcaca % qGqbGaae4uaiaaigdacaGGPaaaaa!67BE! $$\mathcal{P}{\text{ - VADM}},\;\mathcal{P}{\text{ - }}^{10} {\text{Be}}({\text{GISP}}2),\;{\text{and}}\;\mathcal{P}{\text{ - }}^{10} {\text{Be}}({\text{PS}}1)$$ are also highly significant (p<0.01) but relatively small (−0.76, 0.48, and 0.60, respectively). Thus, an important fraction (42–77%) of the variance in the geomagnetic and 10Be data is not accounted for by linear regression on the 14C productions implied by the tree-ring record. The % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiGabGEbbWUctu % uDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wzaGqbaiab-9q8qbaa % !4334! $$\mathcal{P}$$ variance near the 1500 yr period, which previous authors interpreted as solar variability, represents a small fraction of the total variance in the % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiGabGEbbWUctu % uDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wzaGqbaiab-9q8qbaa % !4334! $$\mathcal{P}$$ time series (<15% for the band 1200–1800 yr) and does not correspond to a spectral peak. Hence, the hypothesis of a direct solar forcing mechanism for the postulated millennial climate variability during the Holocene is not supported.