The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

Drought is a complex and multivariate phenomenon influenced by diverse physical and biological processes. Such complexity precludes simplistic explanations of cause and effect, making investigations of climate change and drought a challenging task. Here, we review important recent advances in our understanding of drought dynamics, drawing from studies of paleoclimate, the historical record, and model simulations of the past and future. Paleoclimate studies of drought variability over the last two millennia have progressed considerably through the development of new reconstructions and analyses combining reconstructions with process-based models. This work has generated new evidence for tropical Pacific forcing of megadroughts in Southwest North America, provided additional constraints for interpreting climate change projections in poorly characterized regions like East Africa, and demonstrated the exceptional magnitude of many modern era droughts. Development of high resolution proxy networks has lagged in many regions (e.g., South America, Africa), however, and quantitative comparisons between the paleoclimate record, models, and observations remain challenging. Fingerprints of anthropogenic climate change consistent with long-term warming projections have been identified for droughts in California, the Pacific Northwest, Western North America, and the Mediterranean. In other regions (e.g., Southwest North America, Australia, Africa), however, the degree to which climate change has affected recent droughts is more uncertain. While climate change-forced declines in precipitation have been detected for the Mediterranean, in most regions, the climate change signal has manifested through warmer temperatures that have increased evaporative losses and reduced snowfall and snowpack levels, amplifying deficits in soil moisture and runoff despite uncertain precipitation changes. Over the next century, projections indicate that warming will increase drought risk and severity across much of the subtropics and mid-latitudes in both hemispheres, a consequence of regional precipitation declines and widespread warming. For many regions, however, the magnitude, robustness, and even direction of climate change-forced trends in drought depends on how drought is defined, with often large differences across indicators of precipitation, soil moisture, runoff, and vegetation health. Increasing confidence in climate change projections of drought and the associated impacts will likely depend on resolving uncertainties in processes that are currently poorly constrained (e.g., land-atmosphere interactions, terrestrial vegetation) and improved consideration of the role for human policies and management in ameliorating and adapting to changes in drought risk.

Climate Change and Drought: From Past to Future

By synthesizing recent studies employing a wide range of approaches (modern observations, paleo reconstructions, and climate model simulations), this paper provides a comprehensive review of the linkage between multidecadal Atlantic Meridional Overturning Circulation (AMOC) variability and Atlantic Multidecadal Variability (AMV) and associated climate impacts. There is strong observational and modeling evidence that multidecadal AMOC variability is a crucial driver of the observed AMV and associated climate impacts and an important source of enhanced decadal predictability and prediction skill. The AMOC‐AMV linkage is consistent with observed key elements of AMV. Furthermore, this synthesis also points to a leading role of the AMOC in a range of AMV‐related climate phenomena having enormous societal and economic implications, for example, Intertropical Convergence Zone shifts; Sahel and Indian monsoons; Atlantic hurricanes; El Nino–Southern Oscillation; Pacific Decadal Variability; North Atlantic Oscillation; climate over Europe, North America, and Asia; Arctic sea ice and surface air temperature; and hemispheric‐scale surface temperature. Paleoclimate evidence indicates that a similar linkage between multidecadal AMOC variability and AMV and many associated climate impacts may also have existed in the preindustrial era, that AMV has enhanced multidecadal power significantly above a red noise background, and that AMV is not primarily driven by external forcing. The role of the AMOC in AMV and associated climate impacts has been underestimated in most state‐of‐the‐art climate models, posing significant challenges but also great opportunities for substantial future improvements in understanding and predicting AMV and associated climate impacts.

A Review of the Role of the Atlantic Meridional Overturning Circulation in Atlantic Multidecadal Variability and Associated Climate Impacts

Earth’s climate history is often understood by breaking it down into constituent climatic epochs1. Over the Common Era (the past 2,000 years) these epochs, such as the Little Ice Age2–4, have been characterized as having occurred at the same time across extensive spatial scales5. Although the rapid global warming seen in observations over the past 150 years does show nearly global coherence6, the spatiotemporal coherence of climate epochs earlier in the Common Era has yet to be robustly tested. Here we use global palaeoclimate reconstructions for the past 2,000 years, and find no evidence for preindustrial globally coherent cold and warm epochs. In particular, we find that the coldest epoch of the last millennium—the putative Little Ice Age—is most likely to have experienced the coldest temperatures during the fifteenth century in the central and eastern Pacific Ocean, during the seventeenth century in northwestern Europe and southeastern North America, and during the mid-nineteenth century over most of the remaining regions. Furthermore, the spatial coherence that does exist over the preindustrial Common Era is consistent with the spatial coherence of stochastic climatic variability. This lack of spatiotemporal coherence indicates that preindustrial forcing was not sufficient to produce globally synchronous extreme temperatures at multidecadal and centennial timescales. By contrast, we find that the warmest period of the past two millennia occurred during the twentieth century for more than 98 per cent of the globe. This provides strong evidence that anthropogenic global warming is not only unparalleled in terms of absolute temperatures5, but also unprecedented in spatial consistency within the context of the past 2,000 years.

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No evidence for globally coherent warm and cold periods over the preindustrial Common Era

The measurement and simulation of water vapor isotopic composition has matured rapidly over the last decade, with long-term datasets and comprehensive modeling capabilities now available. Theories for water vapor isotopic composition have been developed by extending the theories that have been used for the isotopic composition of precipitation to include a more nuanced understanding of evaporation, large-scale mixing, deep convection, and kinetic fractionation. The technologies for in-situ and remote sensing measurements of water vapor isotopic composition have developed especially rapidly over the last decade, with discrete water vapor sampling methods, based on mass spectroscopy, giving way to laser spectroscopic methods and satellite- and ground-based infrared absorption techniques. The simulation of water vapor isotopic composition has evolved from General Circulation Model (GCM) methods for simulating precipitation isotopic composition to sophisticated isotope-enabled microphysics schemes using higher-order moments for water- and ice-size distributions. The incorporation of isotopes into GCMs has enabled more detailed diagnostics of the water cycle and has led to improvements in its simulation. The combination of improved measurement and modeling of water vapor isotopic composition opens the door to new advances in our understanding of the atmospheric water cycle, in processes ranging from the marine boundary layer, through deep convection and tropospheric mixing, and into the water cycle of the stratosphere. Finally, studies of the processes governing modern water vapor isotopic composition provide an improved framework for the interpretation of paleoclimate proxy records of the hydrological cycle.

Stable isotopes in atmospheric water vapor and applications to the hydrologic cycle

An “offline” approach to DA is used, where static ensemble samples are drawn from existing CMIP climate-model simulations to serve as the prior estimate of climate variables. We use linear, univariate forward models (“proxy system models (PSMs)”) that map climate variables to proxy measurements by fitting proxy data to 2 m air temperature from gridded instrumental temperature data; the linear PSMs are then used to predict proxy values from the prior estimate. Results for the LMR are compared against six gridded instrumental temperature data sets and 25% of the proxy records are withheld from assimilation for independent verification. Results show broad agreement with previous reconstructions of Northern Hemisphere mean 2 m air temperature, with millennial-scale cooling, a multicentennial warm period around 1000 C.E., and a cold period coincident with the Little Ice Age (circa 1450–1800 C.E.). Verification against gridded instrumental data sets during 1880–2000 C.E. reveals greatest skill in the tropics and lowest skill over Northern Hemisphere land areas. Verification against independent proxy records indicates substantial improvement relative to the model (prior) data without proxy assimilation. As an illustrative example, we present multivariate reconstructed fields for a singular event, the 1808/1809 “mystery” volcanic eruption, which reveal global cooling that is strongly enhanced locally due to the presence of the Pacific-North America wave pattern in the 500 hPa geopotential height field.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2016JD024751

The last millennium climate reanalysis project: Framework and first results

Initial skill assessment of the California Harmful Algae Risk Mapping (C-HARM) system.

A potential consequence of climate change is global decrease in dissolved oxygen at depth in the oceans due to changes in the balance of ventilation, mixing, respiration, and photosynthesis. We present hydrographic cruise observations of declining dissolved oxygen collected along CalCOFI Line 66.7 (Line 67) off of Monterey Bay, in the Central California Current region, and investigate likely mechanisms. Between 1998 and 2013, dissolved oxygen decreased at the mean rate of 1.92 µmol kg−1 year−1 on σθ 26.6–26.8 kg m−3 isopycnals (250–400 m), translating to a 40% decline from initial concentrations. Two cores of elevated dissolved oxygen decline at 130 and 240 km from shore, which we suggest are a California Undercurrent and a California Current signal respectively, occurred on σθ ranges of 26.0–26.8 kg m−3 (100–400 m). A box model suggests that small annual changes in dissolved oxygen in source regions are sufficient to be the primary driver of the mid-depth declines. Variation in dissolved oxygen at the bottom of the surface mixed layer suggests that there is also a signal of increased local remineralization.

/pdf/a-sixteen-year-decline-in-dissolved-oxygen-in-the-central-2clog71rod.pdf

David M. Anderson

Papers

The last millennium climate reanalysis project: Framework and first results

Initial skill assessment of the California Harmful Algae Risk Mapping (C-HARM) system.

A Sixteen-year Decline in Dissolved Oxygen in the Central California Current.