Sensitivity of the Eocene climate to CO₂ and orbital variability

The early Eocene, from about 56 Ma, with high atmospheric CO2 levels, offers an analogue for the response of the Earth’s climate system to anthropogenic fossil fuel burning. In this study, we present an ensemble of 50 Earth system model runs with an early Eocene palaeogeography and variation in the forcing values of atmospheric CO2 and the Earth’s orbital parameters. Relationships between simple summary metrics of model outputs and the forcing parameters are identified by linear modelling, providing estimates of the relative magnitudes of the effects of atmospheric CO2 and each of the orbital parameters on important climatic features, including tropical–polar temperature difference, ocean–land temperature contrast, Asian, African and South (S.) American monsoon rains, and climate sensitivity. Our results indicate that although CO2 exerts a dominant control on most of the climatic features examined in this study, the orbital parameters also strongly influence important components of the ocean–atmosphere system in a greenhouse Earth. In our ensemble, atmospheric CO2 spans the range 280–3000 ppm, and this variation accounts for over 90 % of the effects on mean air temperature, southern winter high-latitude ocean– land temperature contrast and northern winter tropical–polar temperature difference. However, the variation of precession accounts for over 80 % of the influence of the forcing parameters on the Asian and African monsoon rainfall, and obliquity variation accounts for over 65 % of the effects on winter ocean–land temperature contrast in high northern latitudes and northern summer tropical–polar temperature difference. Our results indicate a bimodal climate sensitivity, with values of 4.36 and 2.54 ◦C, dependent on low or high states of atmospheric CO2 concentration, respectively, with a threshold at approximately 1000 ppm in this model, and due to a saturated vegetation–albedo feedback. Our method gives a quantitative ranking of the influence of each of the forcing parameters on key climatic model outputs, with additional spatial information from singular value decomposition providing insights into likely physical mechanisms. The results demonstrate the importance of orbital variation as an agent of change in climates of the past, and we demonstrate that emulators derived from our modelling output can be used as rapid and efficient surrogates of the full complexity model to provide estimates of climate conditions from any set of forcing parameters

Assimilation of temperature and hydraulic gradients for quantifying the spatial variability of streambed hydraulics

Understanding the spatial and temporal characteristics of water flux into or out of shallow aquifers is imperative for water resources management and eco-environmental conservation. In this study, the spatial variability in the vertical specific fluxes and hydraulic conductivities in a streambed were evaluated by integrating distributed temperature sensing (DTS) data and vertical hydraulic gradients into an ensemble Kalman filter (EnKF) and smoother (EnKS) and an empirical thermal-mixing model. The formulation of the EnKF/EnKS assimilation scheme is based on a discretized 1D advection-conduction equation of heat transfer in the streambed. We first systematically tested a synthetic case and performed quantitative and statistical analyses to evaluate the performance of the assimilation schemes. Then a real-world case was evaluated to calculate assimilated specific flux. An initial estimate of the spatial distributions of the vertical hydraulic gradients was obtained from an empirical thermal-mixing model under steady-state conditions using a constant vertical hydraulic conductivity. Then, this initial estimate was updated by repeatedly dividing the assimilated specific flux by estimates of the vertical hydraulic gradients to obtain a refined spatial distribution of vertical hydraulic gradients and vertical hydraulic conductivities. Our results indicate that optimal parameters can be derived with fewer iterations but greater simulation effort using the EnKS compared with the EnKF. For the field application in a stream segment of the Heihe River Basin in northwest China, the average vertical hydraulic conductivities in the streambed varied over three orders of magnitude (5 x 10(-1) to 5 x 10(2) m/d). The specific fluxes ranged from near zero (q(z)<0.05 m/d) to 1.0 m/d, while the vertical hydraulic gradients were within the range of -0.2 to 0.15 m/m. The highest and most variable fluxes occurred adjacent to a debris-dam and bridge pier. This phenomenon is very likely the result of heterogeneous streambed hydraulic characteristics in these areas. Our results have significant implications for hyporheic micro-habitats, fish spawning and other wildlife incubation, regional flow and hyporheic solute transport models in the Heihe River Basin, as well as in other similar hydrologic settings.National Natural Science Foundation of China [91225301, 91425303]; Ministry of Environmental Protection of China [201309005]; Microsoft Azure research award [RFPs 201406]SCI(E)[email protected]