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.

Bounding the role of black carbon in the climate system: a scientific assessment

Black carbon aerosol plays a unique and important role in Earth’s climate system. Black carbon is a type of carbonaceous material with a unique combination of physical properties. This assessment provides an evaluation of black-carbon climate forcing that is comprehensive in its inclusion of all known and relevant processes and that is quantitative in providing best estimates and uncertainties of the main forcing terms: direct solar absorption; influence on liquid, mixed phase, and ice clouds; and deposition on snow and ice. These effects are calculated with climate models, but when possible, they are evaluated with both microphysical measurements and field observations. Predominant sources are combustion related, namely, fossil fuels for transportation, solid fuels for industrial and residential uses, and open burning of biomass. Total global emissions of black carbon using bottom-up inventory methods are 7500 Gg yr�-1 in the year 2000 with an uncertainty range of 2000 to 29000. However, global atmospheric absorption attributable to black carbon is too low in many models and should be increased by a factor of almost 3. After this scaling, the best estimate for the industrial-era (1750 to 2005) direct radiative forcing of atmospheric black carbon is +0.71 W m�-2 with 90% uncertainty bounds of (+0.08, +1.27)Wm�-2. Total direct forcing by all black carbon sources, without subtracting the preindustrial background, is estimated as +0.88 (+0.17, +1.48) W m�-2. Direct radiative forcing alone does not capture important rapid adjustment mechanisms. A framework is described and used for quantifying climate forcings, including rapid adjustments. The best estimate of industrial-era climate forcing of black carbon through all forcing mechanisms, including clouds and cryosphere forcing, is +1.1 W m�-2 with 90% uncertainty bounds of +0.17 to +2.1 W m�-2. Thus, there is a very high probability that black carbon emissions, independent of co-emitted species, have a positive forcing and warm the climate. We estimate that black carbon, with a total climate forcing of +1.1 W m�-2, is the second most important human emission in terms of its climate forcing in the present-day atmosphere; only carbon dioxide is estimated to have a greater forcing. Sources that emit black carbon also emit other short-lived species that may either cool or warm climate. Climate forcings from co-emitted species are estimated and used in the framework described herein. When the principal effects of short-lived co-emissions, including cooling agents such as sulfur dioxide, are included in net forcing, energy-related sources (fossil fuel and biofuel) have an industrial-era climate forcing of +0.22 (�-0.50 to +1.08) W m-�2 during the first year after emission. For a few of these sources, such as diesel engines and possibly residential biofuels, warming is strong enough that eliminating all short-lived emissions from these sources would reduce net climate forcing (i.e., produce cooling). When open burning emissions, which emit high levels of organic matter, are included in the total, the best estimate of net industrial-era climate forcing by all short-lived species from black-carbon-rich sources becomes slightly negative (�-0.06 W m�-2 with 90% uncertainty bounds of �-1.45 to +1.29 W m�-2). The uncertainties in net climate forcing from black-carbon-rich sources are substantial, largely due to lack of knowledge about cloud interactions with both black carbon and co-emitted organic carbon. In prioritizing potential black-carbon mitigation actions, non-science factors, such as technical feasibility, costs, policy design, and implementation feasibility play important roles. The major sources of black carbon are presently in different stages with regard to the feasibility for near-term mitigation. This assessment, by evaluating the large number and complexity of the associated physical and radiative processes in black-carbon climate forcing, sets a baseline from which to improve future climate forcing estimates.

Formulation and implementation of a residual-mean ocean circulation model

A parameterization of mesoscale eddies in coarse-resolution ocean general circulation models (GCM) is formulated and implemented using a residual-mean formalism. In that framework, mean buoyancy is advected by the residual velocity (the sum of the Eulerian and eddy-induced velocities) and modified by a residual flux which accounts for the diabatic effects of mesoscale eddies. The residual velocity is obtained by stepping forward a residual-mean momentum equation in which eddy stresses appear as forcing terms. Study of the spatial distribution of eddy stresses, derived by using them as control parameters to ‘‘fit’’ the residual-mean model to observations, supports the idea that eddy stresses can be likened to a vertical down-gradient flux of momentum with a coefficient which is constant in the vertical. The residual eddy flux is set to zero in the ocean interior, where mesoscale eddies are assumed to be quasi-adiabatic, but is parameterized by a horizontal down-gradient diffusivity near the surface where eddies develop a diabatic component as they stir properties horizontally across steep isopycnals. The residual-mean model is implemented and tested in the MIT general circulation model. It is shown that the resulting model (1) has a climatology that is superior to that obtained using the Gent and McWilliams parameterization scheme with a spatially uniform diffusivity and (2) allows one to significantly reduce the (spurious) horizontal viscosity used in coarse resolution GCMs.

Intercomparison of radiative forcing calculations of stratospheric water vapour and contrails

Seven groups have participated in an intercomparison study of calculations of radiative forcing (RF) due to stratospheric water vapour (SWV) and contrails. A combination of detailed radiative transfer schemes and codes for global-scale calculations have been used, as well as a combination of idealized simulations and more realistic global-scale changes in stratospheric water vapour and contrails. Detailed line-by-line codes agree within about 15 % for longwave (LW) and shortwave (SW) RF, except in one case where the difference is 30 %. Since the LW and SW RF due to contrails and SWV changes are of opposite sign, the differences between the models seen in the individual LW and SW components can be either compensated or strengthened in the net RF, and thus in relative terms uncertainties are much larger for the net RF. Some of the models used for global-scale simulations of changes in SWV and contrails differ substantially in RF from the more detailed radiative transfer schemes. For the global-scale calculations we use a method of weighting the results to calculate a best estimate based on their performance compared to the more detailed radiative transfer schemes in the idealized simulations.

Using idealized snow forcing to test teleconnections with the Indian summer monsoon in the Hadley Centre GCM

Anomalous heavy snow during winter or spring has long been regarded as a possible precursor of deficient Indian monsoon rainfall during the subsequent summer. However previous work in this field is inconclusive, in terms of the mechanism that communicates snow anomalies to the monsoon summer, and even the region from which snow has the most impact. In this study we explore these issues in coupled and atmosphere-only versions of the Hadley Centre model. A 1050-year control integration of the HadCM3 coupled model, which well represents the seasonal cycle of snow cover over the Eurasian continent, is analysed and shows evidence for weakened monsoons being preceded by strong snow forcing (in the absence of ENSO) over either the Himalaya/Tibetan Plateau or north/west Eurasia regions. However, empirical orthogonal function (EOF) analysis of springtime interannual variability in snow depth shows the leading mode to have opposite signs between these two regions, suggesting that competing mechanisms may be possible. To determine the dominant region, ensemble integrations are carried out using HadAM3, the atmospheric component of HadCM3, and a variety of anomalous snow forcing initial conditions obtained from the control integration of the coupled model. Forcings are applied during spring in separate experiments over the Himalaya/Tibetan Plateau and north/west Eurasia regions, in conjunction with climatological SSTs in order to avoid the direct effects of ENSO. With the aid of idealized forcing conditions in sensitivity tests, we demonstrate that forcing from the Himalaya region is dominant in this model via a Blanford-type mechanism involving reduced surface sensible heat and longwave fluxes, reduced heating of the troposphere over the Tibetan Plateau and consequently a reduced meridional tropospheric temperature gradient which weakens the monsoon during early summer. Snow albedo is shown to be key to the mechanism, explaining around 50% of the perturbation in sensible heating over the Tibetan Plateau, and accounting for the majority of cooling through the troposphere.

Resolution of the uncertainties in the radiative forcing of HFC-134a

HFC-134a (CF3CH2F) is the most rapidly growing hydrofluorocarbon in terms of atmospheric abundance. It is currently used in a large number of household refrigerators and air-conditioning systems and its concentration in the atmosphere is forecast to increase substantially over the next 50–100 years. Previous estimates of its radiative forcing per unit concentration have differed significantly 25%. This paper uses a two-step approach to resolve this discrepancy. In the first step six independent absorption cross section datasets are analysed. We find that, for the integrated cross section in the spectral bands that contribute most to the radiative forcing, the differences between the various datasets are typically smaller than 5% and that the dependence on pressure and temperature is not significant. A “recommended'' HFC-134a infrared absorption spectrum was obtained based on the average band intensities of the strongest bands. In the second step, the “recommended'' HFC-134a spectrum was used in six different radiative transfer models to calculate the HFC-134a radiative forcing efficiency. The clear-sky instantaneous radiative forcing, using a single global and annual mean profile, differed by 8%, between the 6 models, and the latitudinally-resolved adjusted cloudy sky radiative forcing estimates differed by a similar amount.

Changes of interannual NAO variability in response to greenhouse gases forcing

Observations show that there was change in interannual North Atlantic Oscillation (NAO) variability in the mid-1970s. This change was characterized by an eastward shift of the NAO action centres, a poleward shift of zonal wind anomalies and a downstream extension of climate anomalies associated with the NAO. The NAO interannual variability for the period after the mid-1970s has an annular mode structure that penetrates deeply into the stratosphere, indicating a strengthened relationship between the NAO and the Arctic Oscillation (AO) and strengthened stratosphere-troposphere coupling. In this study we have investigated possible causes of these changes in the NAO by carrying out experiments with an atmospheric GCM. The model is forced either by doubling CO2, or increasing sea surface temperatures (SST), or both. In the case of SST forcing the SST anomaly is derived from a coupled model simulation forced by increasing CO2. Results indicate that SST and CO2 change both force a poleward and eastward shift in the pattern of interannual NAO variability and the associated poleward shift of zonal wind anomalies, similar to the observations. The effect of SST change can be understood in terms of mean changes in the troposphere. The direct effect of CO2 change, in contrast, can not be understood in terms of mean changes in the troposphere. However, there is a significant response in the stratosphere, characterized by a strengthened climatological polar vortex with strongly enhanced interannual variability. In this case, the NAO interannual variability has a strong link with the variability over the North Pacific, as in the annular AO pattern, and is also strongly related to the stratospheric vortex, indicating strengthened stratosphere-troposphere coupling. The similarity of changes in many characteristics of NAO interannual variability between the model response to doubling CO2 and those in observations in the mid-1970s implies that the increase of greenhouse gas concentration in the atmosphere, and the resulting changes in the stratosphere, might have played an important role in the multidecadal change of interannual NAO variability and its associated climate anomalies during the late twentieth century. The weak change in mean westerlies in the troposphere in response to CO2 change implies that enhanced and eastward extended mid-latitude westerlies in the troposphere might not be a necessary condition for the poleward and eastward shift of the NAO action centres in the mid-1970s.

Ozone database in support of CMIP5 simulations: results and corresponding radiative forcing

A continuous tropospheric and stratospheric vertically resolved ozone time series, from 1850 to 2099, has been generated to be used as forcing in global climate models that do not include interactive chemistry. A multiple linear regression analysis of SAGE I+II satellite observations and polar ozonesonde measurements is used for the stratospheric zonal mean dataset during the well-observed period from 1979 to 2009. In addition to terms describing the mean annual cycle, the regression includes terms representing equivalent effective stratospheric chlorine (EESC) and the 11-yr solar cycle variability. The EESC regression fit coefficients, together with pre-1979 EESC values, are used to extrapolate the stratospheric ozone time series backward to 1850. While a similar procedure could be used to extrapolate into the future, coupled chemistry climate model (CCM) simulations indicate that future stratospheric ozone abundances are likely to be significantly affected by climate change, and capturing such effects through a regression model approach is not feasible. Therefore, the stratospheric ozone dataset is extended into the future (merged in 2009) with multimodel mean projections from 13 CCMs that performed a simulation until 2099 under the SRES (Special Report on Emission Scenarios) A1B greenhouse gas scenario and the A1 adjusted halogen scenario in the second round of the Chemistry-Climate Model Validation (CCMVal-2) Activity. The stratospheric zonal mean ozone time series is merged with a three-dimensional tropospheric data set extracted from simulations of the past by two CCMs (CAM3.5 and GISSPUCCINI)and of the future by one CCM (CAM3.5). The future tropospheric ozone time series continues the historical CAM3.5 simulation until 2099 following the four different Representative Concentration Pathways (RCPs). Generally good agreement is found between the historical segment of the ozone database and satellite observations, although it should be noted that total column ozone is overestimated in the southern polar latitudes during spring and tropospheric column ozone is slightly underestimated. Vertical profiles of tropospheric ozone are broadly consistent with ozonesondes and in-situ measurements, with some deviations in regions of biomass burning. The tropospheric ozone radiative forcing (RF) from the 1850s to the 2000s is 0.23Wm−2, lower than previous results. The lower value is mainly due to (i) a smaller increase in biomass burning emissions; (ii) a larger influence of stratospheric ozone depletion on upper tropospheric ozone at high southern latitudes; and possibly (iii) a larger influence of clouds (which act to reduce the net forcing) compared to previous radiative forcing calculations. Over the same period, decreases in stratospheric ozone, mainly at high latitudes, produce a RF of −0.08Wm−2, which is more negative than the central Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) value of −0.05Wm−2, but which is within the stated range of −0.15 to +0.05Wm−2. The more negative value is explained by the fact that the regression model simulates significant ozone depletion prior to 1979, in line with the increase in EESC and as confirmed by CCMs, while the AR4 assumed no change in stratospheric RF prior to 1979. A negative RF of similar magnitude persists into the future, although its location shifts from high latitudes to the tropics. This shift is due to increases in polar stratospheric ozone, but decreases in tropical lower stratospheric ozone, related to a strengthening of the Brewer-Dobson circulation, particularly through the latter half of the 21st century. Differences in trends in tropospheric ozone among the four RCPs are mainly driven by different methane concentrations, resulting in a range of tropospheric ozone RFs between 0.4 and 0.1Wm−2 by 2100. The ozone dataset described here has been released for the Coupled Model Intercomparison Project (CMIP5) model simulations in netCDF Climate and Forecast (CF) Metadata Convention at the PCMDI website (http://cmip-pcmdi.llnl.gov/).

The Empirical Forcing Function as a tool for the diagnosis of large-scale atmospheric anomalies

The time-mean quasi-geostrophic potential vorticity equation of the atmospheric flow on isobaric surfaces can explicitly include an atmospheric (internal) forcing term of the stationary-eddy flow. In fact, neglecting some non-linear terms in this equation, this forcing can be mathematically expressed as a single function, called Empirical Forcing Function (EFF), which is equal to the material derivative of the time-mean potential vorticity. Furthermore, the EFF can be decomposed as a sum of seven components, each one representing a forcing mechanism of different nature. These mechanisms include diabatic components associated with the radiative forcing, latent heat release and frictional dissipation, and components related to transient eddy transports of heat and momentum. All these factors quantify the role of the transient eddies in forcing the atmospheric circulation. In order to assess the relevance of the EFF in diagnosing large-scale anomalies in the atmospheric circulation, the relationship between the EFF and the occurrence of strong North Atlantic ridges over the Eastern North Atlantic is analyzed, which are often precursors of severe droughts over Western Iberia. For such events, the EFF pattern depicts a clear dipolar structure over the North Atlantic; cyclonic (anticyclonic) forcing of potential vorticity is found upstream (downstream) of the anomalously strong ridges. Results also show that the most significant components are related to the diabatic processes. Lastly, these results highlight the relevance of the EFF in diagnosing large-scale anomalies, also providing some insight into their interaction with different physical mechanisms.

Highly contrasting effects of different climate forcing agents on terrestrial ecosystem services

Many atmospheric constituents besides carbon dioxide (CO2) contribute to global warming, and it is common to compare their influence on climate in terms of radiative forcing, which measures their impact on the planetary energy budget. A number of recent studies have shown that many radiatively active constituents also have important impacts on the physiological functioning of ecosystems, and thus the ‘ecosystem services’ that humankind relies upon. CO2 increases have most probably increased river runoff and had generally positive impacts on plant growth where nutrients are non-limiting, whereas increases in near-surface ozone (O3) are very detrimental to plant productivity. Atmospheric aerosols increase the fraction of surface diffuse light, which is beneficial for plant growth. To illustrate these differences, we present the impact on net primary productivity and runoff of higher CO2, higher near-surface O3, and lower sulphate aerosols, and for equivalent changes in radiative forcing.We compare this with the impact of climate change alone, arising, for example, from a physiologically inactive gas such as methane (CH4). For equivalent levels of change in radiative forcing, we show that the combined climate and physiological impacts of these individual agents vary markedly and in some cases actually differ in sign. This study highlights the need to develop more informative metrics of the impact of changing atmospheric constituents that go beyond simple radiative forcing.

Sensitivity of direct radiative forcing by mineral dust to particle characteristics

Airborne dust affects the Earth's energy balance — an impact that is measured in terms of the implied change in net radiation (or radiative forcing, in W m-2) at the top of the atmosphere. There remains considerable uncertainty in the magnitude and sign of direct forcing by airborne dust under current climate. Much of this uncertainty stems from simplified assumptions about mineral dust-particle size, composition and shape, which are applied in remote sensing retrievals of dust characteristics and dust-cycle models. Improved estimates of direct radiative forcing by dust will require improved characterization of the spatial variability in particle characteristics to provide reliable information dust optical properties. This includes constraints on: (1) particle-size distribution, including discrimination of particle subpopulations and quantification of the amount of dust in the sub-10 µm to <0.1 µm mass fraction; (2) particle composition, specifically the abundance of iron oxides, and whether particles consist of single or multi-mineral grains; (3) particle shape, including degree of sphericity and surface roughness, as a function of size and mineralogy; and (4) the degree to which dust particles are aggregated together. The use of techniques that measure the size, composition and shape of individual particles will provide a better basis for optical modelling.

Global-scale climate impact functions: the relationship between climate forcing and impact

Although there is a strong policy interest in the impacts of climate change corresponding to different degrees of climate change, there is so far little consistent empirical evidence of the relationship between climate forcing and impact. This is because the vast majority of impact assessments use emissions-based scenarios with associated socio-economic assumptions, and it is not feasible to infer impacts at other temperature changes by interpolation. This paper presents an assessment of the global-scale impacts of climate change in 2050 corresponding to defined increases in global mean temperature, using spatially-explicit impacts models representing impacts in the water resources, river flooding, coastal, agriculture, ecosystem and built environment sectors. Pattern-scaling is used to construct climate scenarios associated with specific changes in global mean surface temperature, and a relationship between temperature and sea level used to construct sea level rise scenarios. Climate scenarios are constructed from 21 climate models to give an indication of the uncertainty between forcing and response. The analysis shows that there is considerable uncertainty in the impacts associated with a given increase in global mean temperature, due largely to uncertainty in the projected regional change in precipitation. This has important policy implications. There is evidence for some sectors of a non-linear relationship between global mean temperature change and impact, due to the changing relative importance of temperature and precipitation change. In the socio-economic sectors considered here, the relationships are reasonably consistent between socio-economic scenarios if impacts are expressed in proportional terms, but there can be large differences in absolute terms. There are a number of caveats with the approach, including the use of pattern-scaling to construct scenarios, the use of one impacts model per sector, and the sensitivity of the shape of the relationships between forcing and response to the definition of the impact indicator.

Global analysis of radiative forcing from fire-induced shortwave albedo change

Land surface albedo, a key parameter to derive Earth's surface energy balance, is used in the parameterization of numerical weather prediction, climate monitoring and climate change impact assessments. Changes in albedo due to fire have not been fully investigated on a continental and global scale. The main goal of this study, therefore, is to quantify the changes in instantaneous shortwave albedo produced by biomass burning activities and their associated radiative forcing. The study relies on the MODerate-resolution Imaging Spectroradiometer (MODIS) MCD64A1 burned-area product to create an annual composite of areas affected by fire and the MCD43C2 bidirectional reflectance distribution function (BRDF) albedo snow-free product to compute a bihemispherical reflectance time series. The approximate day of burning is used to calculate the instantaneous change in shortwave albedo. Using the corresponding National Centers for Environmental Prediction (NCEP) monthly mean downward solar radiation flux at the surface, the global radiative forcing associated with fire was computed. The analysis reveals a mean decrease in shortwave albedo of −0.014 (1σ = 0.017), causing a mean positive radiative forcing of 3.99 Wm−2 (1σ = 4.89) over the 2002–20012 time period in areas affected by fire. The greatest drop in mean shortwave albedo change occurs in 2002, which corresponds to the highest total area burned (378 Mha) observed in the same year and produces the highest mean radiative forcing (4.5 Wm−2). Africa is the main contributor in terms of burned area, but forests globally give the highest radiative forcing per unit area and thus give detectable changes in shortwave albedo. The global mean radiative forcing for the whole period studied (~0.0275 Wm−2) shows that the contribution of fires to the Earth system is not insignificant.

Radiative forcing and climate metrics for ozone precursor emissions: the impact of multi-model averaging

Multi-model ensembles are frequently used to assess understanding of the response of ozone and methane lifetime to changes in emissions of ozone precursors such as NOx, VOCs (volatile organic compounds) and CO. When these ozone changes are used to calculate radiative forcing (RF) (and climate metrics such as the global warming potential (GWP) and global temperature-change potential (GTP)) there is a methodological choice, determined partly by the available computing resources, as to whether the mean ozone (and methane) concentration changes are input to the radiation code, or whether each model's ozone and methane changes are used as input, with the average RF computed from the individual model RFs. We use data from the Task Force on Hemispheric Transport of Air Pollution source–receptor global chemical transport model ensemble to assess the impact of this choice for emission changes in four regions (East Asia, Europe, North America and South Asia). We conclude that using the multi-model mean ozone and methane responses is accurate for calculating the mean RF, with differences up to 0.6% for CO, 0.7% for VOCs and 2% for NOx. Differences of up to 60% for NOx 7% for VOCs and 3% for CO are introduced into the 20 year GWP. The differences for the 20 year GTP are smaller than for the GWP for NOx, and similar for the other species. However, estimates of the standard deviation calculated from the ensemble-mean input fields (where the standard deviation at each point on the model grid is added to or subtracted from the mean field) are almost always substantially larger in RF, GWP and GTP metrics than the true standard deviation, and can be larger than the model range for short-lived ozone RF, and for the 20 and 100 year GWP and 100 year GTP. The order of averaging has most impact on the metrics for NOx, as the net values for these quantities is the residual of the sum of terms of opposing signs. For example, the standard deviation for the 20 year GWP is 2–3 times larger using the ensemble-mean fields than using the individual models to calculate the RF. The source of this effect is largely due to the construction of the input ozone fields, which overestimate the true ensemble spread. Hence, while the average of multi-model fields are normally appropriate for calculating mean RF, GWP and GTP, they are not a reliable method for calculating the uncertainty in these fields, and in general overestimate the uncertainty.