Adjoint methods in data assimilation for estimating model error

Data assimilation aims to incorporate measured observations into a dynamical system model in order to produce accurate estimates of all the current (and future) state variables of the system. The optimal estimates minimize a variational principle and can be found using adjoint methods. The model equations are treated as strong constraints on the problem. In reality, the model does not represent the system behaviour exactly and errors arise due to lack of resolution and inaccuracies in physical parameters, boundary conditions and forcing terms. A technique for estimating systematic and time-correlated errors as part of the variational assimilation procedure is described here. The modified method determines a correction term that compensates for model error and leads to improved predictions of the system states. The technique is illustrated in two test cases. Applications to the 1-D nonlinear shallow water equations demonstrate the effectiveness of the new procedure.

Simulated variations in atmospheric CO2 over a Wisconsin forest using a coupled ecosystem-atmosphere model

Ecosystem fluxes of energy, water, and CO2 result in spatial and temporal variations in atmospheric properties. In principle, these variations can be used to quantify the fluxes through inverse modelling of atmospheric transport, and can improve the understanding of processes and falsifiability of models. We investigated the influence of ecosystem fluxes on atmospheric CO2 in the vicinity of the WLEF-TV tower in Wisconsin using an ecophysiological model (Simple Biosphere, SiB2) coupled to an atmospheric model (Regional Atmospheric Modelling System). Model parameters were specified from satellite imagery and soil texture data. In a companion paper, simulated fluxes in the immediate tower vicinity have been compared to eddy covariance fluxes measured at the tower, with meteorology specified from tower sensors. Results were encouraging with respect to the ability of the model to capture observed diurnal cycles of fluxes. Here, the effects of fluxes in the tower footprint were also investigated by coupling SiB2 to a high-resolution atmospheric simulation, so that the model physiology could affect the meteorological environment. These experiments were successful in reproducing observed fluxes and concentration gradients during the day and at night, but revealed problems during transitions at sunrise and sunset that appear to be related to the canopy radiation parameterization in SiB2.

An urban parameterization for a global climate model. Part I: Formulation and evaluation for two cities

Urbanization, the expansion of built-up areas, is an important yet less-studied aspect of land use/land cover change in climate science. To date, most global climate models used to evaluate effects of land use/land cover change on climate do not include an urban parameterization. Here, the authors describe the formulation and evaluation of a parameterization of urban areas that is incorporated into the Community Land Model, the land surface component of the Community Climate System Model. The model is designed to be simple enough to be compatible with structural and computational constraints of a land surface model coupled to a global climate model yet complex enough to explore physically based processes known to be important in determining urban climatology. The city representation is based upon the “urban canyon” concept, which consists of roofs, sunlit and shaded walls, and canyon floor. The canyon floor is divided into pervious (e.g., residential lawns, parks) and impervious (e.g., roads, parking lots, sidewalks) fractions. Trapping of longwave radiation by canyon surfaces and solar radiation absorption and reflection is determined by accounting for multiple reflections. Separate energy balances and surface temperatures are determined for each canyon facet. A one-dimensional heat conduction equation is solved numerically for a 10-layer column to determine conduction fluxes into and out of canyon surfaces. Model performance is evaluated against measured fluxes and temperatures from two urban sites. Results indicate the model does a reasonable job of simulating the energy balance of cities.

Climate and carbon cycle changes from 1850 to 2100 in MPI-ESM simulations for the Coupled Model Intercomparison Project phase 5

The new Max-Planck-Institute Earth System Model (MPI-ESM) is used in the Coupled Model Intercomparison Project phase 5 (CMIP5) in a series of climate change experiments for either idealized CO2-only forcing or forcings based on observations and the Representative Concentration Pathway (RCP) scenarios. The paper gives an overview of the model configurations, experiments related forcings, and initialization procedures and presents results for the simulated changes in climate and carbon cycle. It is found that the climate feedback depends on the global warming and possibly the forcing history. The global warming from climatological 1850 conditions to 2080–2100 ranges from 1.5°C under the RCP2.6 scenario to 4.4°C under the RCP8.5 scenario. Over this range, the patterns of temperature and precipitation change are nearly independent of the global warming. The model shows a tendency to reduce the ocean heat uptake efficiency toward a warmer climate, and hence acceleration in warming in the later years. The precipitation sensitivity can be as high as 2.5% K−1 if the CO2 concentration is constant, or as small as 1.6% K−1, if the CO2 concentration is increasing. The oceanic uptake of anthropogenic carbon increases over time in all scenarios, being smallest in the experiment forced by RCP2.6 and largest in that for RCP8.5. The land also serves as a net carbon sink in all scenarios, predominantly in boreal regions. The strong tropical carbon sources found in the RCP2.6 and RCP8.5 experiments are almost absent in the RCP4.5 experiment, which can be explained by reforestation in the RCP4.5 scenario.

Climatic impacts of land-use change due to crop yield increases and a universal carbon tax from a scenario model*

Future land cover will have a significant impact on climate and is strongly influenced by the extent of agricultural land use. Differing assumptions of crop yield increase and carbon pricing mitigation strategies affect projected expansion of agricultural land in future scenarios. In the representative concentration pathway 4.5 (RCP4.5) from phase 5 of the Coupled Model Intercomparison Project (CMIP5), the carbon effects of these land cover changes are included, although the biogeophysical effects are not. The afforestation in RCP4.5 has important biogeophysical impacts on climate, in addition to the land carbon changes, which are directly related to the assumption of crop yield increase and the universal carbon tax. To investigate the biogeophysical climatic impact of combinations of agricultural crop yield increases and carbon pricing mitigation, five scenarios of land-use change based on RCP4.5 are used as inputs to an earth system model [Hadley Centre Global Environment Model, version 2-Earth System (HadGEM2-ES)]. In the scenario with the greatest increase in agricultural land (as a result of no increase in crop yield and no climate mitigation) there is a significant -0.49 K worldwide cooling by 2100 compared to a control scenario with no land-use change. Regional cooling is up to -2.2 K annually in northeastern Asia. Including carbon feedbacks from the land-use change gives a small global cooling of -0.067 K. This work shows that there are significant impacts from biogeophysical land-use changes caused by assumptions of crop yield and carbon mitigation, which mean that land carbon is not the whole story. It also elucidates the potential conflict between cooling from biogeophysical climate effects of land-use change and wider environmental aims.

Including an ocean carbon cycle model into iLOVECLIM (v1.0)

The atmospheric carbon dioxide concentration plays a crucial role in the radiative balance and as such has a strong influence on the evolution of climate. Because of the numerous interactions between climate and the carbon cycle, it is necessary to include a model of the carbon cycle within a climate model to understand and simulate past and future changes of the carbon cycle. In particular, natural variations of atmospheric CO2 have happened in the past, while anthropogenic carbon emissions are likely to continue in the future. To study changes of the carbon cycle and climate on timescales of a few hundred to a few thousand years, we have included a simple carbon cycle model into the iLOVECLIM Earth System Model. In this study, we describe the ocean and terrestrial biosphere carbon cycle models and their performance relative to observational data. We focus on the main carbon cycle variables including the carbon isotope ratios δ13C and the Δ14C. We show that the model results are in good agreement with modern observations both at the surface and in the deep ocean for the main variables, in particular phosphates, dissolved inorganic carbon and the carbon isotopes.

TCA Evaluation : Lab Measurements, Modelling and System Simulations

The study reported here is part of a large project for evaluation of the Thermo-Chemical Accumulator (TCA), a technology under development by the Swedish company ClimateWell AB. The studies concentrate on the use of the technology for comfort cooling. This report concentrates on measurements in the laboratory, modelling and system simulation. The TCA is a three-phase absorption heat pump that stores energy in the form of crystallised salt, in this case Lithium Chloride (LiCl) with water being the other substance. The process requires vacuum conditions as with standard absorption chillers using LiBr/water. Measurements were carried out in the laboratories at the Solar Energy Research Center SERC, at Högskolan Dalarna as well as at ClimateWell AB. The measurements at SERC were performed on a prototype version 7:1 and showed that this prototype had several problems resulting in poor and unreliable performance. The main results were that: there was significant corrosion leading to non-condensable gases that in turn caused very poor performance; unwanted crystallisation caused blockages as well as inconsistent behaviour; poor wetting of the heat exchangers resulted in relatively high temperature drops there. A measured thermal COP for cooling of 0.46 was found, which is significantly lower than the theoretical value. These findings resulted in a thorough redesign for the new prototype, called ClimateWell 10 (CW10), which was tested briefly by the authors at ClimateWell. The data collected here was not large, but enough to show that the machine worked consistently with no noticeable vacuum problems. It was also sufficient for identifying the main parameters in a simulation model developed for the TRNSYS simulation environment, but not enough to verify the model properly. This model was shown to be able to simulate the dynamic as well as static performance of the CW10, and was then used in a series of system simulations. A single system model was developed as the basis of the system simulations, consisting of a CW10 machine, 30 m2 flat plate solar collectors with backup boiler and an office with a design cooling load in Stockholm of 50 W/m2, resulting in a 7.5 kW design load for the 150 m2 floor area. Two base cases were defined based on this: one for Stockholm using a dry cooler with design cooling rate of 30 kW; one for Madrid with a cooling tower with design cooling rate of 34 kW. A number of parametric studies were performed based on these two base cases. These showed that the temperature lift is a limiting factor for cooling for higher ambient temperatures and for charging with fixed temperature source such as district heating. The simulated evacuated tube collector performs only marginally better than a good flat plate collector if considering the gross area, the margin being greater for larger solar fractions. For 30 m2 collector a solar faction of 49% and 67% were achieved for the Stockholm and Madrid base cases respectively. The average annual efficiency of the collector in Stockholm (12%) was much lower than that in Madrid (19%). The thermal COP was simulated to be approximately 0.70, but has not been possible to verify with measured data. The annual electrical COP was shown to be very dependent on the cooling load as a large proportion of electrical use is for components that are permanently on. For the cooling loads studied, the annual electrical COP ranged from 2.2 for a 2000 kWh cooling load to 18.0 for a 21000 kWh cooling load. There is however a potential to reduce the electricity consumption in the machine, which would improve these figures significantly. It was shown that a cooling tower is necessary for the Madrid climate, whereas a dry cooler is sufficient for Stockholm although a cooling tower does improve performance. The simulation study was very shallow and has shown a number of areas that are important to study in more depth. One such area is advanced control strategy, which is necessary to mitigate the weakness of the technology (low temperature lift for cooling) and to optimally use its strength (storage).

Ability of Gutta-Percha and Resilon to Fill Simulated Lateral Canals by Using the Obtura II System

Introduction: The aim of this study was to evaluate the ability of Resilon (Resilon Research, LLC, North Branford, CT) and 2 types of gutta-percha to fill simulated lateral canals when using the Obtura II system (Model 823-700; Obtura Spartan, Fenton, MO). Methods: Forty-five human single-rooted teeth were selected and subjected to root canal preparation. After that, simulated lateral canals were made at 2, 5, and 8 mm from the working length (WL). The specimens were divided into 3 groups (n = 15) according to the filling material used: Obtura Flow 150 gutta-percha (Obtura flow), Odous Endo Flow gutta-percha (Odous; Odous de Deus Ind e Corn. Ltda Belo Horizonte, MG, Brazil), and Resilon pellets (Resilon). Root canals were filled using the Obtura II system with the tip inserted to 3 mm from the WL. No sealer was used for root canal obturation. Specimens were subjected to a tooth decalcification and clearing method, and filling of the lateral canals was analyzed by digital radiography and photographs. The measurement of lateral canal filling was done using Image Tool software (UTHSCSA Image Tool for Windows version 3.0, San Antonio, TX). Data were statistically analyzed with the Kruskal-Wallis test at 5% significance. Results: All materials showed an ability to penetrate into the simulated lateral canals, with a minimum percentage of 73% in all thirds of the root canal. Conclusions: It was concluded that gutta-percha and Resilon are solid core materials with a lateral canal filling ability when used with the Obtura II system. (J Endod 2012;38:676-679)

Representation of the Weddell Sea deep water masses in the ocean component of the NCAR-CCSM model

We examine Weddell Sea deep water mass distributions with respect to the results from three different model runs using the oceanic component of the National Center for Atmospheric Research Community Climate System Model (NCAR-CCSM). One run is inter-annually forced by corrected NCAR/NCEP fluxes, while the other two are forced with the annual cycle obtained from the same climatology. One of the latter runs includes an interactive sea-ice model. Optimum Multiparameter analysis is applied to separate the deep water masses in the Greenwich Meridian section (into the Weddell Sea only) to measure the degree of realism obtained in the simulations. First, we describe the distribution of the simulated deep water masses using observed water type indices. Since the observed indices do not provide an acceptable representation of the Weddell Sea deep water masses as expected, they are specifically adjusted for each simulation. Differences among the water masses` representations in the three simulations are quantified through their root-mean-square differences. Results point out the need for better representation (and inclusion) of ice-related processes in order to improve the oceanic characteristics and variability of dense Southern Ocean water masses in the outputs of the NCAR-CCSM model, and probably in other ocean and climate models.

Development of human visual system analysis for the implementation of a new instrument for flicker measurement

Flicker is a power quality phenomenon that applies to cycle instability of light intensity resulting from supply voltage fluctuation, which, in turn can be caused by disturbances introduced during power generation, transmission or distribution. The standard EN 61000-4-15 which has been recently adopted also by the IEEE as IEEE Standard 1453 relies on the analysis of the supply voltage which is processed according to a suitable model of the lamp – human eye – brain chain. As for the lamp, an incandescent 60 W, 230 V, 50 Hz source is assumed. As far as the human eye – brain model is concerned, it is represented by the so-called flicker curve. Such a curve was determined several years ago by statistically analyzing the results of tests where people were subjected to flicker with different combinations of magnitude and frequency. The limitations of this standard approach to flicker evaluation are essentially two. First, the provided index of annoyance Pst can be related to an actual tiredness of the human visual system only if such an incandescent lamp is used. Moreover, the implemented response to flicker is “subjective” given that it relies on the people answers about their feelings. In the last 15 years, many scientific contributions have tackled these issues by investigating the possibility to develop a novel model of the eye-brain response to flicker and overcome the strict dependence of the standard on the kind of the light source. In this light of fact, this thesis is aimed at presenting an important contribution for a new Flickermeter. An improved visual system model using a physiological parameter that is the mean value of the pupil diameter, has been presented, thus allowing to get a more “objective” representation of the response to flicker. The system used to both generate flicker and measure the pupil diameter has been illustrated along with all the results of several experiments performed on the volunteers. The intent has been to demonstrate that the measurement of that geometrical parameter can give reliable information about the feeling of the human visual system to light flicker.

A reconstruction of radiocarbon production and total solar irradiance from the Holocene ¹⁴C and CO₂ records: implications of data and model uncertainties

Radiocarbon production, solar activity, total solar irradiance (TSI) and solar-induced climate change are reconstructed for the Holocene (10 to 0 kyr BP), and TSI is predicted for the next centuries. The IntCal09/SHCal04 radiocarbon and ice core CO2 records, reconstructions of the geomagnetic dipole, and instrumental data of solar activity are applied in the Bern3D-LPJ, a fully featured Earth system model of intermediate complexity including a 3-D dynamic ocean, ocean sediments, and a dynamic vegetation model, and in formulations linking radiocarbon production, the solar modulation potential, and TSI. Uncertainties are assessed using Monte Carlo simulations and bounding scenarios. Transient climate simulations span the past 21 thousand years, thereby considering the time lags and uncertainties associated with the last glacial termination. Our carbon-cycle-based modern estimate of radiocarbon production of 1.7 atoms cm−2 s−1 is lower than previously reported for the cosmogenic nuclide production model by Masarik and Beer (2009) and is more in-line with Kovaltsov et al. (2012). In contrast to earlier studies, periods of high solar activity were quite common not only in recent millennia, but throughout the Holocene. Notable deviations compared to earlier reconstructions are also found on decadal to centennial timescales. We show that earlier Holocene reconstructions, not accounting for the interhemispheric gradients in radiocarbon, are biased low. Solar activity is during 28% of the time higher than the modern average (650 MeV), but the absolute values remain weakly constrained due to uncertainties in the normalisation of the solar modulation to instrumental data. A recently published solar activity–TSI relationship yields small changes in Holocene TSI of the order of 1 W m−2 with a Maunder Minimum irradiance reduction of 0.85 ± 0.16 W m−2. Related solar-induced variations in global mean surface air temperature are simulated to be within 0.1 K. Autoregressive modelling suggests a declining trend of solar activity in the 21st century towards average Holocene conditions.

Paleoclimate data-model comparison and the role of climate forcings over the past 1500 years

The past 1500 years provide a valuable opportunity to study the response of the climate system to external forcings. However, the integration of paleoclimate proxies with climate modeling is critical to improving the understanding of climate dynamics. In this paper, a climate system model and proxy records are therefore used to study the role of natural and anthropogenic forcings in driving the global climate. The inverse and forward approaches to paleoclimate data–model comparison are applied, and sources of uncertainty are identified and discussed. In the first of two case studies, the climate model simulations are compared with multiproxy temperature reconstructions. Robust solar and volcanic signals are detected in Southern Hemisphere temperatures, with a possible volcanic signal detected in the Northern Hemisphere. The anthropogenic signal dominates during the industrial period. It is also found that seasonal and geographical biases may cause multiproxy reconstructions to overestimate the magnitude of the long-term preindustrial cooling trend. In the second case study, the model simulations are compared with a coral δ18O record from the central Pacific Ocean. It is found that greenhouse gases, solar irradiance, and volcanic eruptions all influence the mean state of the central Pacific, but there is no evidence that natural or anthropogenic forcings have any systematic impact on El Niño–Southern Oscillation. The proxy climate relationship is found to change over time, challenging the assumption of stationarity that underlies the interpretation of paleoclimate proxies. These case studies demonstrate the value of paleoclimate data–model comparison but also highlight the limitations of current techniques and demonstrate the need to develop alternative approaches.

Influence of the Central American Seaway and Drake Passage on ocean circulation and neodymium isotopes: A model study

The sensitivity of the neodymium isotopic composition (ϵNd) to tectonic rearrangements of seaways is investigated using an Earth System Model of Intermediate Complexity. The shoaling and closure of the Central American Seaway (CAS) is simulated, as well as the opening and deepening of Drake Passage (DP). Multiple series of equilibrium simulations with various intermediate depths are performed for both seaways, providing insight into ϵNd and circulation responses to progressive throughflow evolutions. Furthermore, the sensitivity of these responses to the Atlantic Meridional Overturning Circulation (AMOC) and the neodymium boundary source is examined. Modeled ϵNd changes are compared to sediment core and ferromanganese (Fe-Mn) crust data. The model results indicate that the North Atlantic ϵNd response to the CAS shoaling is highly dependent on the AMOC state, i.e., on the AMOC strength before the shoaling to shallow depths (preclosure). Three scenarios based on different AMOC forcings are discussed, of which the model-data agreement favors a shallow preclosure (Miocene) AMOC (∼6 Sv). The DP opening causes a rather complex circulation response, resulting in an initial South Atlantic ϵNd decrease preceding a larger increase. This feature may be specific to our model setup, which induces a vigorous CAS throughflow that is strongly anticorrelated to the DP throughflow. In freshwater experiments following the DP deepening, ODP Site 1090 is mainly influenced by AMOC and DP throughflow changes, while ODP Site 689 is more strongly influenced by Southern Ocean Meridional Overturning Circulation and CAS throughflow changes. The boundary source uncertainty is largest for shallow seaways and at shallow sites.

Earth system commitments due to delayed mitigation

As long as global CO₂ emissions continue to increase annually, long-term committed Earth system changes grow much faster than current observations. A novel metric linking this future growth to policy decisions today is the mitigation delay sensitivity (MDS), but MDS estimates for Earth system variables other than peak temperature (ΔT max) are missing. Using an Earth System Model of Intermediate Complexity, we show that the current emission increase rate causes a ΔT max increase roughly 3–7.5 times as fast as observed warming, and a millenial steric sea level rise (SSLR) 7–25 times as fast as observed SSLR, depending on the achievable rate of emission reductions after the peak of emissions. These ranges are only slightly affected by the uncertainty range in equilibrium climate sensitivity, which is included in the above values. The extent of ocean acidification at the end of the century is also strongly dependent on the starting time and rate of emission reductions. The preservable surface ocean area with sufficient aragonite supersaturation for coral reef growth is diminished globally at an MDS of roughly 25%–80% per decade. A near-complete loss of this area becomes unavoidable if mitigation is delayed for a few years to decades. Also with respect to aragonite, 12%–18% of the Southern Ocean surface become undersaturated per decade, if emission reductions are delayed beyond 2015–2040. We conclude that the consequences of delaying global emission reductions are much better captured if the MDS of relevant Earth system variables is communicated in addition to current trends and total projected future changes.

Past and future evolution of Abies alba forests in Europe - comparison of a dynamic vegetation model with palaeo data and observations

Information on how species distributions and ecosystem services are impacted by anthropogenic climate change is important for adaptation planning. Palaeo data suggest that Abies alba formed forests under significantly warmer-than-present conditions in Europe and might be a native substitute for widespread drought-sensitive temperate and boreal tree species such as beech (Fagus sylvatica) and spruce (Picea abies) under future global warming conditions. Here, we combine pollen and macrofossil data, modern observations, and results from transient simulations with the LPX-Bern dynamic global vegetation model to assess past and future distributions of A. alba in Europe. LPX-Bern is forced with climate anomalies from a run over the past 21 000 years with the Community Earth System Model, modern climatology, and with 21st-century multimodel ensemble results for the high-emission RCP8.5 and the stringent mitigation RCP2.6 pathway. The simulated distribution for present climate encompasses the modern range of A. alba, with the model exceeding the present distribution in north-western and southern Europe. Mid-Holocene pollen data and model results agree for southern Europe, suggesting that at present, human impacts suppress the distribution in southern Europe. Pollen and model results both show range expansion starting during the Bølling–Allerød warm period, interrupted by the Younger Dryas cold, and resuming during the Holocene. The distribution of A. alba expands to the north-east in all future scenarios, whereas the potential (currently unrealized) range would be substantially reduced in southern Europe under RCP8.5. A. alba maintains its current range in central Europe despite competition by other thermophilous tree species. Our combined palaeoecological and model evidence suggest that A. alba may ensure important ecosystem services including stand and slope stability, infrastructure protection, and carbon sequestration under significantly warmer-than-present conditions in central Europe.