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141 Anthocyanins
65 Malvidin
64 Cyanidin
62 Delphinidin
43 Peonidin
33 Anthocyanidins
30 Grape
25 wine
20 Flavonoids
19 Flavonols
18 Pelargonidin
18 grapes
16 skin
15 cancer
14 Quercetin
14 Bilberry
14 Polyphenols
12 red wine
12 Blueberry
12 ethanol
11 beans
11 Sugar
10 Catechin
9 Soybean
8 blueberries
8 Kaempferol
7 Pea
7 breast cancer
7 Iron
7 Phytochemicals
6 black soybean
6 potato
6 Enzymes
6 Glycine
6 Phenolic acids
6 Seeds
6 Galactose
6 Horse gram
6 Insulin
6 nuts
6 Gallocatechin
6 Currant
6 Digestion
6 blood
5 Isorhamnetin
5 Glucose
5 Vegetables
5 Antioxidants
5 Chlorogenic Acid
5 Nutrition
5 agriculture
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Councils, education and the arts: new alliances
July 28, 2020 @ 8:30 am – 9:30 am
Due to social distancing, many UK children have missed a chunk of their schooling. When they return, educational priorities for them will be in maths and science, rather than the arts. Meanwhile, arts organisations have worked with local authorities to reach out to local communities – including youth – in new and compelling ways. Can these new alliances be a force for good?

subset: commoncrawl


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Wednesday, March 25, 2020
Benedicts Rule free essay sample
Ethics directs our attention to what it is to do good and to be called good. It studies activity, whether personal or institutional, in particular its significance for character and human flourishing. Doing Business with Benedict: The Rule of Saint Benedict and Business Management A Conversation [Illustrated] [Paperback] Marret Crosby Dollard (Author) Synopisis In the world of business where it has become fashionable to apply rules from other walks of life to the boardroom, the application of spiritual rules within business has become extremely popular. It also provides business with an alternative to whiteboard briefings and management spiel. The Rule of St Benedict is both spiritually enhancing and widely applicable. Managing permanent rapid change is the ultimate task for business from now on. The Rules stress on realism, vision and perseverance in the context of strong communities provides business large and small with a way forward to survival and success. We will write a custom essay sample on Benedicts Rule or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page The book also serves as a guide for people who run religious communities and indeed communities of any kind. For example, faced with the issue of whether monks should drink alcohol, Benedict admitted that it would be better if they did not. But he mused that nowadays (meaning the 5th century), it has become commonplace for beer and wine to be drunk at meals. And this is good. So, he sanctioned drinking moderately. It is true that Benedict penalized for lack of obedience, but the rationalization was to maintain order and, ultimately, to foster harmony within the community. Harmony cannot coexist with negativity. No organization can achieve its maximum efficiency if grumbling is wide-spread. Benedict did not suppress problems or personal freedom, but required that they be channeled properly through the organization via the daily employee chapter meeting, through mentors or the fatherly advice of the abbott (from the root abba meaning father). Benedict focuses in on what most managers avoidââ¬âaddressing negativity at a personal level. What is lost to todays managers is the impact on productivity and profitability. Any manager who has tried to change knows the crippling power of negativity to bind organizations. Stability is at the heart of Benedictine community. Through mutual obedience, a family is created that is the infrastructure of Benedictine community. Community, as a word, has Latin roots meaning, to eat bread together. The Rule of St. Benedict stresses the importance of coming together on a daily basis. This type of bonding was the foundation of community. Even business organizations require a measure of bonding to be successful. Long term successful organizations have strong social ties among their members. So many times business people overlook this key organizational facet. Socialization is bonding. The Benedictine team allows for individuality but is focused on the community. The virtue of humility is much lost today. It does not suppress individual achievement but does suppress the use of achievement to control and use as power. Some of the greatest individual craftsmen arose from the Benedictine community. It is humility that gives the individual a perspective of self and a role to build community. Individual ideas are fostered, but ultimately the good of the community is the rule by individual choice. Another characteristic of Benedictine teams is that they equate to community. The push today is to form multiple teams within an organization, which actually can lead to a breakdown in community and overall teamwork. Benedictine teams are totally integrated using committees for more specific problem solving, employee involvement, and administration. Benedictine communities used the daily team or chapter meeting to focus on one rule, one community. Committees were used to involve employees and develop a specific focus on an issue. Committees were part of the community, not separate teams as we see in many of todays structures.
Friday, March 6, 2020
Practice Identifying Subject and Object Complements
Practice Identifying Subject and Object Complements In our article on complements, we discussed subject complements, which follow a linking verb and provide additional information about the subject of the sentence. The subject complement is normally a noun or an adjective that defines or renames the subject in some way. We also learned about object complements, which follow and modify a direct object and provide additional information about it. An object complement can be a noun or adjective or any word acting as a noun or adjective. To easily understand it, think of it this way: Subject complements and object complements fill out and complete our sentences. Object complements provide more detail about the object of a sentence, while subject complements provide information about the subject to a sentence. In this exercise, you will learn to identify subject complements and object complements in sentences. Instructions for Practice Exercise Identify the complement in each of the following sentences, and note whether it is a subject complement or an object complement. When you are done, compare your answers, which appear below the test. Pablo is extremely intelligent.I find him intelligent.Shyla eventually became my best friend.Our neighbors dogs are very dangerous.Gingers hair dye turned the water pink.After our disagreement on the first day of school, Jenny became my friend for life.We painted the ceiling blue.You are making me sad.Paula is a good dancer.Dorothy named her parakeet Onan.Known as the father of the Texas blues, Blind Lemon Jefferson was a popular entertainer in the 1920s.The gift Karen gave her brother was a hamster.Buck grew up in Oklahoma and became an expert horse rider before reaching his 18th birthday.à I once considered Nancy my fiercest enemy.After reviewing the detailsà of the case, theà court pronounced the boy not guilty.By the second month of the drought, the river had run dry. Answers Pablo is extremelyà intelligent. (subject complement)I find himà intelligent. (object complement)Shyla eventually became my bestà friend.à (subject complement)Our neighbors dogs are very dangerous. (subject complement)Gingers hair dye turned the waterà pink. (object complement)After our disagreement on the first day of school, Jenny became myà friendà for life. (subject complement)We painted the ceilingà blue. (object complement)You are making meà sad. (object complement)Paula is a goodà dancer. (subject complement)Dorothy named her parakeetà Onan. (object complement)Known as the father of the Texas blues, Blind Lemon Jefferson was a popularà entertainerà in the 1920s. (subject complement)The gift Karen gave her brother was aà hamster. (subject complement)Buck grew up in Oklahoma and became an expertà horse riderà before reaching his 18th birthday.à (subject complement)I once considered Nancy my fiercestà enemy.à (object complement)After reviewin g the details of the case, theà court pronounced the boyà not guilty.à (object complement) By the second month of the drought, the river had runà dry. (subject complement)ââ¬â¹
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This is my Moving Timelapse Mantra - Follow your Creativity.
It is a collection of shots and thoughts from my life.
Thank you to the many people who helped me along the way.
Please check out my Youtube page for more.
Thanks for commenting. The drone is actually not mine. I am a cameraman, so had access to one on a couple of jobs. And made the most of my time with it! They really are great fun to shoot with. Hope to produce many more films like this one over the years. All the bestI think this is very professionnal and beautiful. Great job.
Now, I want a drone
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text: Arkansas State Parks Trip Ideas Filter Park Historic Washington State Park Ozark Folk Center Region Central North Central Southwest Lower Delta Northwest Upper Delta Park Activity Fishing Hiking Mountain Biking Watchable Wildlife Trail Type Trail Difficulty Author Matt Manos Meg Matthews Paul Butler Robin Gabe [X] Monika Rued Date Published April 2020 March 2020 January 2019 November 2018 September 2018 March 2018 [X] November 2017 October 2017 September 2017 [X] July 2017 June 2017 May 2017 [X] January 2017 December 2016 November 2016 October 2016 August 2016 Christmas and Candlelight at Historic Washington State Park Nov 2017 ⁄ Monika Rued Christmas and Candlelight at Historic Washington State Park in Washington, Ark., is a delightful time to connect with our rich Arkansas history and experience Historic Washington at its finest. Let's Ride: Mountain Biking Exhibit at State Capitol Jul 2017 ⁄ Monika Rued "Let's Ride: Mountain Biking in the State Parks of Arkansas" is a biking exhibit at the Arkansas Capitol, celebrating mountain biking in Arkansas State Parks. Music Roots Hits All the Right Notes Jul 2017 ⁄ Monika Rued The Music Roots Program in Stone County provides traditional folk music instruction in local schools. Skilled musicians provide youth with classes in traditional folk instruments. Winter To Do List Jan 2017 ⁄ Monika Rued If you're looking for ways to come out of hibernation this winter, we have plenty of fun things to do. Here are 10 ideas we rounded up from our Arkansas State Parks team.


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A detailed reanalysis is presented of a "Bayesian" climate parameter study (as exemplified by Forest et al.) that estimates climate sensitivity (ECS) jointly with effective ocean diffusivity and aerosol forcing, using optimal fingerprints to compare multidecadal observations with simulations by the Massachusetts Institute of Technology 2D climate model at varying settings of the three climate parameters. Use of improved methodology primarily accounts for the 90% confidence bounds for ECS reducing from 2.1–8.9 K to 2.0–3.6 K. The revised methodology uses Bayes's theorem to derive a probability density function (PDF) for the whitened (made independent using an optimal fingerprint transformation) observations, for which a uniform prior is known to be noninformative. A dimensionally reducing change of variables onto the parameter surface is then made, deriving an objective joint PDF for the climate parameters. The PDF conversion factor from the whitened variables space to the parameter surface represents a noninformative joint parameter prior, which is far from uniform. The noninformative prior prevents more probability than data uncertainty distributions warrant being assigned to regions where data respond little to parameter changes, producing better-constrained PDFs. Incorporating 6 years of unused model simulation data and revising the experimental design to improve diagnostic power reduces the best-fit climate sensitivity. Employing the improved methodology, preferred 90% bounds of 1.2–2.2 K for ECS are then derived (mode and median 1.6 K). The mode is identical to those from Aldrin et al. and [using the same Met Office Hadley Centre Climate Research Unit temperature, version 4 (HadCRUT4), observational dataset] from Ring et al. Incorporating nonaerosol forcing and observational surface temperature uncertainties, unlike in the original study, widens the 90% range to 1.0–3.0 K.
1. Introduction
Key climate system parameters—in particular equilibrium climate sensitivity (Seq), effective vertical deep-ocean diffusivity (Kυ), and total aerosol forcing (Faer)—are often estimated by studies (usually formulated in Bayesian terms) that compare simulations by adjustable parameter climate models with observations. Examples of such studies include Forest et al. (2000, 2001, 2002, 2006, 2008, hereafter F00, F01, F02, F06, and F08, respectively; collectively the Forest studies), Andronova and Schlesinger (2001), Frame et al. (2005), Hegerl et al. (2006), Knutti et al. (2002), Sansó et al. (2008, hereafter SFZ08), Sansó and Forest (2009, hereafter SF09), Aldrin et al. (2012), and Ring et al. (2012). These studies provided six of the eight probability density functions (PDFs) given in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) for equilibrium climate sensitivity inferred from observed changes in climate [Hegerl et al. (2007), see their appendix 9.B for an explanation of such studies].
The Forest studies are excellent examples since they used a wide spread of instrumental observations and avoided dependence on existing ill-constrained estimates of Kυ and Faer by jointly estimating them with Seq. Using for this reason F06 as a starting point, this paper derives and implements an improved, objective Bayesian, methodology, which provides better defined PDFs for Seq in particular. Further, by taking advantage of the final 6 years of model simulation data, unused in F06, and revising the experimental design to improve diagnostic power, an updated closely constrained estimate for Seq is obtained.
F06 and similar studies involve comparisons between observed temperatures at various spatiotemporal coordinates and climate model simulations. The models have adjustable calibrated parameters controlling key climate properties and are more suited than atmosphere–ocean general circulation models (AOGCMs) for exploring the entire parameter space and running multiple simulations at varying parameter settings.
F06 used the Massachusetts Institute of Technology (MIT) 2D climate model (2DCM) (Sokolov and Stone 1998; F06). Forcings from all greenhouse gases (specified explicitly), sulfate aerosols (calculated from emissions), stratospheric and tropospheric ozone, land use, solar irradiance, and volcanism (specified as stratospheric aerosol optical depth) (collectively referred to as GSOLSV) were included: see the F06 auxiliary material for details. To place F06 in context, it represented an update of F02 using more comprehensive forcings; F08 used the same methods and data as F06 except for its model simulations, which employed a later version of the MIT 2DCM, while Libardoni and Forest (2011) investigated sensitivities to the surface temperature dataset. Drignei et al. (2008) used a statistical model as a nonlinear regression surrogate to estimate the same parameters using F02's data and alternative correlation structures. SFZ08 and SF09 used F06 data but employed more complex hierarchical Bayesian methods, unlike the approaches used in F06 and this paper, which differ principally in the prior distribution used. The SFZ08 and SF09 posterior PDFs for Seq and substantially reflected the chosen priors and, using uniform priors, were poorly constrained.
F06 used three "diagnostics" (groups of variables whose observed values are compared to model simulations):
Surface-air temperatures [surface (sfc)]: These are four equal-area latitude averages for each of the 5 decades comprising 1946–95, referenced to 1905–95 climatology (Jones et al. 1999).
Deep-ocean temperatures [deep ocean (do)]: This is the trend in global mean 0–3-km-deep-layer pentadal averages ending in 1959–95 (Levitus et al. 2005).
Upper-air temperatures [upper air (ua)]: These are the differences between 1986–95 and 1961–80 averages at eight standard pressure levels from 850 to 50 hPa on a 5° grid (Parker et al. 1997).
Simulations were run from 1860 to 2001 using 499 parameter combinations, with Seq ranging from 0.5 to 15 K, Kυ from 0 to 64 cm2 s−1, and Faer from −1.5 to +0.5 W m−2. (Units for these parameters are generally omitted from here on.) Cases with Seq > 10 were discarded. For estimation, Kυ was parameterized as its square root (Sokolov et al. 2003), ocean heat uptake being proportional thereto. The term Faer represents net forcing (direct and indirect) during the 1980s relative to pre-1860 levels and implicitly includes omitted forcings with patterns similar to those of sulfate aerosols. Means of four-member initial condition ensembles were used at each parameter combination to reduce the impact of internal variability. The diagnostics ended in 1995, matching F02 to enable the effects of including a more complete set of forcings to be illustrated, so the final six simulation years were not used. Reference should be made to F06 and F02 for a fuller description of the MIT2DCM and simulation runs, applied climate forcings, and methods used.
F06 uses an optimal fingerprint method involving comparing the modeled Tm(θm) and observed spatiotemporal patterns of temperature change for each diagnostic, where represents the three climate parameters being estimated. These are idealized parameters and, in practice, Seq changes somewhat with time as additional feedbacks are activated. Simulation variability and model error are ignored.
AOGCM control run data provide an estimate of the natural variability (climate noise) covariance matrix CN for each diagnostic. The estimated noise covariance matrix will be inaccurate, since AOGCM control runs are of limited length and imperfectly simulate natural variability. Regularization is applied to obtain an approximate but more robust inverse covariance matrix estimate. The usual truncated eigen-decomposition regularization method is employed in F06, with only the largest κ eigenfunctions (EOFs), or modes of variability, being retained in the estimate, . Sensitivity to the truncation parameter is a known problem with optimal fingerprint methods (Allen and Tett 1999, hereafter AT99).
Measurement error for the surface and upper-air diagnostics is small compared to estimated internal climate variability and is therefore ignored. For the univariate deep-ocean diagnostic, neither observational measurement error nor control run variance dominates. The two variances are added to give , κ being irrelevant here since has only one element.
For each diagnostic, goodness-of-fit statistics are computed. From r2 F06 compute a joint likelihood for each Tm(θm), representing the relative probability of that diagnostic's observations as a function of the candidate parameter value θm. The likelihood function is based on Δr2, the excess of over the minimum r2 value, having a distribution: m being the number of parameters being estimated and ν the degrees of freedom (DF) available for estimating N (see supplemental material for additional discussion). The minimum r2 is checked for consistency with the errors being generated by internal variability.
F06 uses a Bayesian paradigm, whereby probability distributions can be estimated for unknown parameters. Applying Bayes's theorem, F06 derives a joint posterior PDF for the parameter vector θ as the normalized product of the likelihood function from one diagnostic and a "prior" probability distribution consisting of the product of separate uniform priors for each parameter. Bayes's theorem is then applied twice more, each time multiplying the previous posterior PDF for θ, used as the prior, by the likelihood function from another diagnostic to obtain an updated posterior PDF. Marginal PDFs for individual climate system parameters are obtained by integrating out the other parameters from the final joint parameter posterior PDF. Although such PDFs may appear to provide precise probabilistic information, they are perhaps better viewed as indicating how likely it is that any chosen range brackets the parameter value.
Inferences as to climate system parameter values will be affected by the data used. The choice of data (and parameterizations) may be guided by the physics of the climate system but remains somewhat subjective. There is merit in seeking data that well constrain parameter values, but there may be a trade-off with data quality and coverage. Surface, upper-air, and/or deep-ocean temperature data spanning much of the instrumental period are typically used. Using other data types or periods may give rise to significantly different parameter estimates, as can detailed data processing choices. The selection of data types to compare to model simulations is a key decision; in this paper we work from the F06 data choices.
2. Objective Bayesian inference
In order for Bayesian inference to reflect, insofar as possible, only the data from which it is derived—as is appropriate when reporting objectively stand-alone scientific results—a noninformative prior must be used (Bernardo and Smith 1994; Kass and Wasserman 1996). If the prior is informative, and not overwhelmed by the data, a Bayesian posterior density is unlikely to approximate the density arising if, hypothetically, the experiment(s) concerned were to be repeated indefinitely, so valid frequentist confidence intervals cannot be estimated. Since the available data are insufficient to constrain climate parameters narrowly, an informative prior exerts strong influence.
Typically, scientific studies not expressed in Bayesian terms implicitly use a noninformative prior when considered from a Bayesian perspective. That occurs when observables are sampled according to their probability distributions. Gregory et al. (2002) estimated the change in global mean temperature between two periods and the corresponding change in forcing net of ocean heat uptake. They repeatedly sampled the probability distributions for those estimated changes, assuming independent normal error distributions, to derive a PDF for the ratio of the changes, which gives Seq. The resulting PDF effectively embodies a noninformative prior. Similarly, Forster and Gregory (2006) diagnosed Seq by ordinary least squares regression of changes in forcing net of radiative flux on changes in surface temperature, all errors being assumed Gaussian. They stated that this was equivalent to assuming uniform priors in the data (observables), which is noninformative given Gaussian errors.
Explicitly Bayesian climate sensitivity studies have commonly used uniform priors, or sometimes deliberatively informative "expert" priors, for the parameters being estimated. Frame et al. (2005) advocated sampling a flat prior distribution in Seq if that is the target of the estimate and did not mention noninformative priors, but nevertheless derived PDFs for Seq using various different sampling methods. Their uniform sampling-of-observables method, which they stated was appropriate for and gave an objective range for Seq relevant to twenty-first-century warming forecasts, is very similar to the one we propose, although their implementation requires equal numbers of observables and parameters, and likelihood skewness may mean the prior involved was only approximately noninformative. Pueyo (2012) asserted that the problems of estimating Seq and its reciprocal, the climate feedback parameter, were equivalent, and hence their priors should have the same form, implying a uniform-in-log(Seq) prior. However, it is not clear that in practice the two problems have the same characteristics. In any event, Pueyo's arguments are not applicable where, as here, the prior is for jointly estimating Seq and other parameters and is a function of all those parameters.
When data affected by random errors bear strongly nonlinear relationships to parameters upon which the (hypothetical) true data values depend, as with Seq and Kυ in particular, a uniform prior is only noninformative if applied to the true data, the likelihood functions for which are of known form, centered on the observations (Box and Tiao 1973). Applied to the model parameters, as in F06, a uniform prior will be informative and may lead to substantially erroneous estimated parameter PDFs. Many parameterizations are possible. In this paper, a uniform prior is applied to the true data, a parameterization in which a uniform prior is noninformative.
Correct inference about parameters that have nonlinear relationships with data is impossible when, as in F06, only a sum of squared whitened differences (r2) is computed. The sum of squares suffices to derive a probability density in data space but not to map that density into a density in parameter space. To estimate objectively a joint probability density for the parameters, the relationship between natural volume elements in data space and in parameter space must be computed. Determining a noninformative prior for the parameters is intimately bound up with that metric relationship (Kass 1989). Computing it requires information on how each whitened difference changes with model parameter values. Without such information, there is no way of correctly allocating probability mass between different locations in parameter space with identical sums of squared differences. For example, if the position of a point in 3D relative to an origin is measured with error in Cartesian coordinates but the parameters to be estimated are distance, azimuth, and elevation (spherical coordinates), knowing provides no information as to , and the relationship between the data space and parameter space volume elements and varies with location.
Furthermore, Bayesian updating cannot provide objective inference when the data used in deriving the posterior to be updated (forming the prior) and the data from which the updating likelihood function is derived have differing nonlinear relationships with the parameters, as the sets of diagnostic data in F06 do. In that case, the noninformative parameter priors required for objective Bayesian inference from the two datasets individually would differ. Using the appropriate individually noninformative prior, Bayesian updating would produce a different result according to the order in which Bayes's theorem was applied to the two datasets (see supplemental material for additional discussion). That noninformative priors and Bayesian updating conflict is a known problem (Kass and Wasserman 1996).
Noninformative priors vary with the experiment involved; they cannot be directly interpreted in probabilistic terms (Bernardo and Smith 1994). In order for the posterior to be dominated to the greatest possible extent by the data, however weak, and thereby for the prior to convey no particular knowledge as to the parameters, a noninformative prior must differ according to what nonlinear relationships the data has with the parameters.
3. Data
a. Data sources
The raw surface and upper-air observational datasets employed in F06 were revised subsequent to use in F06 and are no longer online. Only partial AOGCM control run data still exist. We were initially unable to obtain original data for F06 and instead obtained archives of processed diagnostic data for two related studies: Curry et al. (2005, hereafter CSF05) and SFZ08. F06 stated that CSF05 used its data, while SFZ08 stated that it used F06 data. An archive of F06's computer code and partially processed annual and decadal data (GRL06_reproduce) was subsequently made available, with model simulation data verified against partially extant raw data. Analysis showed that the SFZ08 surface and upper-air diagnostic data were essentially identical to that generated by GRL06_reproduce and that the significantly different CSF05 data were misprocessed.
The GRL06_reproduce MIT model data ended in November 2001, with the last 6 years' data being discarded since the F06 diagnostics ended in 1995, but the surface observational data used ran to August 1996. Dr. Forest has confirmed (C. E. Forest 2012, personal communication) that there is thus a 9-month discrepancy between the F06/SFZ08 model simulation and observational surface diagnostic data and also that the forcings used were valid through to 2001. The timing mismatch has little impact on results.
We present results using the F06/SFZ08 5-decade to 1995/96 surface diagnostic data so as to provide accurate comparisons with the F06 results. We also present results using a revised extended surface diagnostic with correctly matched model and observational data for the 6 decades to 2001, using a 9-decade climatology to 1991 to compute temperature anomalies. Doing so substantially improves the constraint provided by the surface diagnostic. With a surface diagnostic comprising 5 decades, all included in the climatology, greater model simulation temperature increases at higher Seq settings are more heavily diluted by deduction of increased model simulation climatological means. This effect may be illustrated by calculating, for both surface diagnostics, what proportion of the difference between the global mean model-simulated temperatures in the key final diagnostic decade at settings of and , before deduction of the climatological mean, remains after its deduction. Settings of and are used. For the revised diagnostic, that proportion is over 1.3 times as great as it is for the F06 diagnostic. Over the lower half of the Faer range, the F06 surface diagnostic is unable to provide any significant constraint on Seq when , while the deep-ocean diagnostic cannot do so until is higher—greatly higher when (see Fig. S2 of the supplemental material). Use of the revised surface diagnostic remedies this weakness in constraining Seq.
For surface observational data to 2001, to which the original Met Office Hadley Centre Climate Research Unit temperature (HadCRUT) dataset does not extend, we use the latest version, HadCRUT4 (Morice et al. 2012). Otherwise, we use GRL06_reproduce data (for the F06 surface and upper-air diagnostics, the essentially identical SFZ08 data), save for using third climate configuration of the Met Office Unified Model (HadCM3; Gordon et al. 2000) control run deep-ocean data.
When employing the surface diagnostic extending to 2001, we use the full Levitus et al. (2005) deep-ocean observational dataset, matching the model simulation data for 40 pentads ending 1998 rather than 37 ending in 1995. The periods covered by the various diagnostics did not match in F06 and need not do so, but it is preferable that they be broadly similar.
b. Issues with the upper-air diagnostic
The Bayesian inference in both our and F06's method involves multiplying probability densities relating to the three diagnostics' whitened differences. Doing so will only be valid if errors in those differences are independent. If the errors are positively correlated, multiplying the diagnostic likelihood functions will overstate statistical significance. Covariance of the temperature change variables within the individual diagnostics is addressed by regularized whitening, resulting in a reduced number of variables, which should be independent provided AOGCM control run simulations represent natural variability sufficiently accurately. This issue is discussed in AT99, where a consistency criterion is proposed based (in the F06 case and our case) on , using truncation parameter κ, lying within the 5%–95% points of the or, more cautiously, distribution.
However, whitening does not address interdiagnostic correlations. Nonindependence of observational variability is not a particularly serious concern regarding the deep-ocean diagnostic, where natural variability is only moderately correlated with surface temperature variability and most variance comes from measurement/analysis error. However, it is a concern between the surface and upper-air diagnostics, where no dilution of correlations by added measurement/analysis error occurs. Because of linkage via the lapse rate, fluctuations in surface and tropospheric temperatures are likely to be highly correlated. In the tropics, the tropopause is generally above the 150-hPa level. Figure 1 shows that the decadal-scale correlation of natural variability of upper air with surface temperatures, as simulated by the second climate configuration of the Met Office Unified Model (HadCM2; Johns et al. 1997) control run, is close to one from 20°S–20°N except at 100- and 50-hPa pressure levels. Outside the tropics, these correlations remain generally high for the 850–300-hPa levels.
Even ignoring the correlation issue, inferences from the upper-air diagnostic are problematic. Parameter inference from the upper-air diagnostic varies greatly as κua and/or the weighting of levels is changed and is also somewhat sensitive to the smoothness of interpolation. Mass weighting of upper-air data was employed in F06, treating each pressure level as extending halfway toward the next, and toward 1000 hPa (surface pressure) at the bottom and 30 hPa at the top. If alternatively the top (50 hPa) level is treated as extending halfway toward zero pressure—increasing its weight modestly, from 4.0% to 5.6%—parameter inference in the Seq–Kυ plane from the fit between the model and observational upper-air data changes dramatically when , as in F06. The F06 weighting is perhaps preferable, but sensitivity to minor reweighting is worrying. The possibility of inference being sensitive to fairly arbitrary choices of weightings and truncation parameters is inherent in optimal fingerprint methods.
Figure 2a replicates the AT99 statistical consistency test on the sum of squares of whitened differences between best-fit modeled and observed upper-air diagnostic temperatures. At F06's selection of , the minimum r2 with the top level weighted toward 0 hPa is 10.2, easily satisfying the AT99 consistency test; whereas with the F06 weightings it is 20.2, failing the stricter test version. This high value is not apparent from the interpolated r2 values produced by the GRL06_reproduce code, which do not accurately reflect the F06 method and have a much lower and incorrect minimum of 11.4. On both weightings, at the AT99 consistency test is well satisfied, and parameter inference is similar to that at with the alternative mass weighting. This (along with it failing the AT99 , test) strongly suggests that it is the F06 weighting–truncation combination that produces invalid inference. We validated the weighting–truncation combinations by recomputing values using leave-one-out subsampling, omitting each row of the control data matrix in turn. At , over half these subsampled values failed the AT99 , consistency test when using F06 50-hPa-level weighting, and over a quarter failed when using the alternative weighting. At , all of the values passed it, irrespective of weighting. We therefore prefer , but retain F06's 50-hPa-level weighting.
Given high correlations and sensitivity to weightings, the validity of inference based on inclusion of information from the upper-air diagnostic is questionable. Fortunately, the upper-air diagnostic is considerably less informative than the surface diagnostic in constraining parameter values. The results using the extended surface diagnostic avoid the problematic upper-air diagnostic by employing only surface and deep-ocean diagnostics; adding the upper-air diagnostic, using the preferred , hardly changes parameter inference.
4. Method
a. Introduction
We retain the F06 approach of whitening diagnostic variables, using the same regularized inverse climate noise covariance matrix estimates. As discussed in section 3, whitening does not remove interdiagnostic noise correlations, which appear substantial as regards the upper-air diagnostic but tolerably low between the surface and deep-ocean diagnostics. We remove dependence on parameter surface flatness by working with the full set of whitened variables , a vector of length (where ), rather than using the F06 , method—the mathematical basis of which requires the whitened variables to be linear functions of the parameters, which they are not. Accordingly, the F distribution we use relates to r2, not . We adjust the F distribution for the geometry involved; the unadjusted density goes to zero at the best-fit point (see supplemental material for additional discussion). This step appears to have been omitted in F06: its effects increase with dimensionality and are modest when using the method. We undertake only a single Bayesian step, in whitened variables space, at which point the likelihood function is a radially symmetric multidimensional Gaussian and a joint uniform prior—corresponding to uniform sampling over the whitened variables —is the so-called Jeffreys' prior (Jeffreys 1946) and is known to be noninformative. We then convert the thus-derived joint PDF for the "true" whitened diagnostic variables (hypothetical observations excluding climate noise) into a joint PDF for the true model parameters , which, assuming model accuracy, equal the true climate system parameters.
Although working with full sets of whitened differences, rather than just their sum of squares, is much more computationally demanding than the F06 method, given the large number of parameter combinations involved, we thereby retain the information required to derive a PDF conversion factor [] equating to a noninformative joint parameter prior. F06's choice of uniform parameter priors was made in the absence of such information. We avoid use of Bayesian updating, with its known incompatibility with noninformative priors, by working with a single set of combined whitened differences from all the diagnostics.
b. Derivation and interpretation of the PDF conversion factor
Mathematical details of F06's method and of the objective Bayesian method, including derivation of the conversion factor from probability density in whitened observation space to that in parameter space, are given in appendixes A and B respectively. (The term is the Jacobian matrix of partial derivatives of the whitened modeled diagnostic temperatures with respect to the model parameters.) The resulting inferential equation is
This implies that can alternatively be viewed as the joint parameter prior when applying Bayes's theorem to derive a posterior joint parameter PDF from the combined diagnostics likelihood, being as a function of θt. This will be a noninformative Jeffreys' prior, since the prior used when applying Bayes's theorem to the whitened temperatures was a noninformative Jeffreys' prior, and Jeffreys' priors are invariant under reparameterization.
The standard Jeffreys' noninformative prior for parameters related to normally distributed whitened variables, derived in Jewson et al. (2009), is indeed identical to . An alternative derivation of the same posterior using a result in a differential geometry approach to conditional probability (Mosegaard and Tarantola 2002) is outlined in the supplemental material. A joint posterior can also be derived using our method on the assumption, implicit in F06, that the parameter surface is flat. On that assumption, the combined likelihood for each diagnostic agrees to that using the F06 method, where , after the geometrical volume correction, which converts a PDF for into a joint PDF for the three underlying error variables (see supplemental material for additional discussion).
The detailed analysis has been undertaken with uncertainty in the variance of the whitened differences ignored. On that basis, noting from (B6) that the right-hand side of (B8) is proportional to ,
This represents the product of likelihood functions for the individual diagnostics, its form for each of them equating, after multiplying by a (r2)κ/2−1 geometric volume adjustment (see supplemental material for additional discussion), to a distribution for the sum of squares r2 of the κ whitened differences. To allow for variance uncertainty, we replace distributions with distributions (a t distribution for the deep-ocean diagnostic), as in the F06 method, giving the combined likelihood as
To simplify the mathematics, the derivation of the PDF conversion factor from whitened variables to parameter space—which allocates probability according to relative volumes in those spaces—ignores uncertainty in the variance of the whitened differences arising from CN being estimated with only ν DF. Such variance uncertainty has little effect on the calculation involved, and the conversion factor has much less influence than the joint likelihood (where variance uncertainty is allowed for). Variance uncertainty is small for the surface diagnostic since νsfc is large. We take for respectively the 5- and 6-decade surface diagnostics, reflecting the numbers of samples with nonoverlapping diagnostic periods obtainable from the control data, increased by 50% for overlapping samples (see AT99). Variance uncertainty for the upper-air diagnostic has little influence on the conversion factor. Uncertainty in the deep-ocean trend variance estimate, which is large and estimated with fewer DF, is explicitly allowed for. A more detailed justification for the approach adopted, including for the deep-ocean diagnostic, is set out in the supplemental material.
5. Implementation
a. Interpolation
F06 computed r2 for each of the modeled parameter combinations and interpolated it to a fine parameter grid spanning their range in two stages. Interpolation was first to a spacing of ΔSeq = 0.1 K and and then to . Our method requires separate interpolation of all model diagnostic variables. Interpolation of model data is preferable as it is less nonlinear in the parameters than is r2, and model simulation variability can be allowed for.
We follow Curry (2007) in using a thin plate spline (TPS) single-stage interpolation. For convenience we extrapolate Seq into the range 0–0.5; as likelihood is extremely low there, this has negligible impact. The interpolation fits a TPS, separately for each variable, so as to best match actual values at all model run parameter combinations. The total squared misfits are minimized subject to a smoothness constraint, which by giving influence to all actual values in a neighborhood restricts the impact of distortions in individual values caused by model simulation variability. The F06 method is less able to reduce the effects of model simulation variability both because it uses two steps and because the relationship between the quantity being interpolated and model simulation variability is indirect.
Since we compute derivatives of the whitened interpolated variables with respect to the parameters—and from that (Jacobian) matrix the PDF conversion factor/noninformative prior—by differencing across adjacent fine grid cells, reasonably smooth interpolation is preferable. We achieve this by restricting the DF used in interpolation to below that resulting from the default smoothness constraint. With 256 DF for all diagnostics, the noninformative prior remains somewhat artifacted, particularly at model run locations. Using 128 DF instead for all diagnostics produced less artifaction, while still departing only modestly from model ensemble values.
However, the interpolation should depart from model ensemble values on account of model simulation variability (Curry 2007). Using 128 DF, interpolation error at model run locations averages 60%–100% of estimated model ensemble variability for the surface diagnostic, confirming that choice is reasonable. Similar comparisons suggest that 64 DF would be appropriate for the upper-air diagnostic interpolation and 256 DF for the deep-ocean diagnostic. These values are used for all results. The parameter marginal posterior PDFs using our method are very similar with 64, 128, or 256 DF interpolation.
When using the F06 method, parameter PDFs exhibit more sensitivity to the DF used in interpolation, principally for the upper-air diagnostic. TPS upper-air interpolation with unrestricted DF results in a flattening—starting at Seq approaching 4—appearing in the Seq PDF. Investigation reveals that the flattening is only noticeable when unrestricted DF interpolation is used for the 0°–5°S latitude band, where it appears that some data misprocessing may have occurred. The even more limited reduction of model simulation variability with the F06 interpolation method may account for such flattening being more pronounced in the published F06 Seq PDF.
b. Whitening the diagnostic variables
We follow F06's use of surface and upper-air data from the 1691-yr HadCM2 control run, masking for observational availability. F06 found that PDFs resulting from use of surface control run data from different AOGCMs did not differ qualitatively. Before generating the new 6-decade surface diagnostic, we verified that, using the F06 diagnostic periods, our code accurately generated the F06/SFZ08 surface diagnostic from model, observational, and control data extracted from the GRL06_reproduce archive.
Figure 2b replicates the AT99 consistency test on the sum of squares of whitened differences between best-fit modeled and observed surface diagnostic temperatures. Using the GRL06_reproduce HadCM2 control data, the 5- and 6-decade diagnostic data fail the AT99 consistency test beyond and 17, respectively. Using the 5-decade to 1995/96 diagnostic, inferred parameter PDFs are almost identical between and and differ only slightly at . Using the revised 6-decade to 2001 diagnostic, parameter PDFs differ little between . We therefore emphasize use of , as in F06, for both the original F06 and the revised surface diagnostics. Stability was tested by recomputing values with varying segments of the control data omitted. For both diagnostic versions the AT99 test was satisfied in all cases at .
In view of the significant difference in inference as to Seq arising from use of the revised surface diagnostic and the danger that this might arise from a particular EOF correlating with some noise pattern in the observations, we have examined the effects of excluding one EOF at a time. Since the AT99 consistency test is only satisfied up to for the revised surface diagnostic, we took the first 17 EOFs, calculated r2 values with the contribution thereto from each EOF in turn removed, and derived parameter PDFs for each case, using the same 40-yr revised deep-ocean diagnostic throughout. No major differences emerged, with the mode of all the PDFs for Seq being within ±0.2 K of that at with no EOFs excluded. Similar variation occurred using the original diagnostic.
As shown in Fig. 3, using the revised diagnostics, parameter PDFs become less well constrained at , but not materially so when using the objective Bayesian method. Below , parameter PDFs become increasingly poorly constrained using either the original or revised surface and deep-ocean diagnostics, as insufficient information is then retained to discriminate adequately between differing regions in parameter space.
We use the F06/SFZ08 HadCM2 upper-air control data matrix, containing 40 nonoverlapping samples, and take , one DF being lost in estimating a mean.
Whitening the deep-ocean diagnostic differences involves no truncation but necessitates aggregating climate noise and estimated uncertainty in the observational temperature trend. Weighted linear least squares regression is used, as in F06, giving observational trend estimates for the 37 years to 1995 (40 years to 1998) of 0.70 (0.68) mK yr−1, with unadjusted standard error (SE) of 0.08 (0.07) mK yr−1. However, the regression residuals are highly autocorrelated, largely because of the 80% overlap of adjacent pentads. Adjusted, approximately twice as high, SEs estimated from regressions on nonoverlapping pentadal data were therefore used. This ignores the previously discussed gain in effective DF resulting from using overlapping samples. Most remaining autocorrelation is probably because of slow natural variability in ocean temperature, which is accounted for by adding climate noise rather than measurement error correlation. To test sensitivity to observational trend SEs, variants of the main results using 50% higher SEs were generated. These variants also serve to test the impact of climate noise correlation between the surface and deep-ocean diagnostics since the higher SEs reduce (to below 15%) the noise contribution to total deep-ocean whitening variance. In each case, the effective DF used for the t distribution was adjusted to reflect the adjustments made to the SEs.
We obtained deep-ocean control data from the 6100-yr HadCM3 control run, whereas F06 used years 1–900 of the Geophysical Fluid Dynamics Laboratory (GFDL) R30 spectral resolution control run (Delworth et al. 2002). Trend variability in the first one-third of these control runs greatly exceeds that in the middle and final thirds, with the models appearing to be adjusting nonmonotonically toward dynamic equilibrium during the first one-third, perhaps because of dynamically inconsistent initial conditions. We therefore use the final two-thirds of the HadCM3 data; the corresponding segments of GFDL R30 data yield a similar estimate. Our deep-ocean climate noise estimate is accordingly only about half F06's. Conversely, our observational trend SE is about double F06's since F06 made no autocorrelation adjustment. The aggregate climate noise and observational estimate SE deep-ocean trend variance used, without a further 50% increase in SE, is close to that in F06.
c. Off-grid probability mass
We adopt the F06 approach of assigning zero probability to off-grid regions and normalizing to unit total probability. The joint parameter posterior PDFs are low at all grid boundaries except (when using the objective Bayesian method with the original F06 diagnostics) to a modest extent at the boundary—which the true value must lie above—for below-average Seq values. If substantial parts of the likelihood lay in infeasible parameter regions, parameter inference would be problematic.
6. Results
The left-hand panels in Fig. 3 show marginal posterior PDFs for Seq, Kυ, and Faer obtained with the original diagnostics, at the preferred and , using both the F06 method with uniform priors and our new objective Bayesian method. For the F06 method, PDFs are also shown using . PDFs using the new method are insensitive to the choice of . Identical diagnostic whitened differences are used for both methods. F06 employed different DF for the three diagnostics, but on both methods results are insensitive to adopting the DF used in F06.
Using the F06 method, PDFs for Seq are much worse constrained than when using our new method, particularly at the deprecated . The Seq PDF using our method has a shape approximating that expected theoretically (Roe and Baker 2007): when converted into a PDF for the climate feedback parameter, which is reciprocally related to Seq, its distribution is close to normal. The Seq PDFs using the F06 method, when so converted, are much less symmetric.
The PDFs for are also better constrained using our method and the already well constrained PDFs for Faer become more so.
The F06 main result PDFs based on uniform priors are shown for comparison. They differ slightly from the PDFs we compute using the F06 method and , partly because of differences in interpolation and partly because of various errors in F06's implementation of its method. In addition to its upper-air r2 values not according with its method, as already mentioned, the GRL_reproduce code shows that in computing likelihoods the F distribution's cumulative distribution function (CDF), was erroneously used, rather than its PDF, and the univariate deep-ocean diagnostic was treated as trivariate, its r2 value being wrongly divided by 3.
At , using our method the 5%–95% bounds for Seq, , and Faer are respectively 2.0–3.6 K, 0.1–1.3 cm s−½, and −0.6 to −0.15 W m−2. Using the F06 method (in parentheses: as reported in F06) the corresponding ranges are 2.0–6.5 (2.1–8.9) K, 0.2–1.7 (0.2–2.0) cm s−½, and −0.75 to −0.2 (−0.74 to −0.14) W m−2. The modes using our and the F06 method are respectively 2.4 and 2.5 (2.9) K for Seq, 0.6 and 0.7 (0.8) cm s−½ for , and −0.4 and −0.5 (−0.5) W m−2 for Faer.
Imposing the assumption implicit in the F06 method that the parameter surface is flat, but otherwise using our new method, reduces the upper 95% bound on Seq but only by 0.3 K even in the 50% higher than standard deep-ocean observational trend SE case. This confirms that assuming flatness is inappropriate, although the effects are modest here.
The right-hand panels in Fig. 3 show PDFs corresponding to those in the left-hand panels but using the revised diagnostics: longer 6-decade to 2001 surface diagnostic, 40-yr to 1998 deep-ocean diagnostic, and no upper-air diagnostic. The shapes of the PDFs are broadly similar to those using the original F06 diagnostics, but those for Seq are narrower and have lower modes, while those for and Faer are wider, particularly when using the F06 method. Varying or Faer has only a small effect on model-simulated surface temperatures and hence on the diagnostic fit when model climate sensitivity is low. Therefore, looser constraint on and Faer is a counterpart of Seq being tightly constrained at lower levels.
As when using the F06 diagnostics, we emphasize results using where consistency with the statistical model, per the test in AT99, is good. We show PDFs at for comparison. Those using our new method differ relatively little from PDFs at , save for the Faer PDF shifting slightly. However, PDFs using the F06 method become substantially less well constrained.
At , using our method the 5%–95% bounds for Seq, , and Faer are respectively 1.2–2.2 K, 0.3–2.1 cm s−½, and −0.55 to 0.0 W m−2. Using the F06 method the corresponding ranges are 1.1–2.9 K, 0.5–4.4 cm s−½, and −0.8 to −0.05 W m−2. The modes (medians) using our and the F06 method are, respectively, 1.6 and 1.5 K (both 1.6 K) for Seq, 0.9 and 1.0 (1.0 and 1.3) cm s−½ for , and −0.25 and −0.4 (−0.3 and −0.35) W m−2 for Faer.
Imposing a 50% increase in the estimated deep-ocean observational trend SE (at ) marginally increases the widths of the parameter marginal PDFs when using our method, with the 95% bound on Seq rising to 2.3 K. Using the F06 method they increase somewhat more: most notably, the 95% bound for Seq becomes 4.4 K.
Figure 4 shows the computed PDF conversion factor from whitened difference to parameter space (or noninformative joint parameter prior) used to generate the new method revised diagnostics results, . Its shape varies little using and/or the F06 diagnostics. A PDF-weighted mean over Faer values has been shown. When instead conditioned on Faer, the prior retains its broad shape over the range where the Faer likelihood is significant but scales up by a factor of several times as Faer becomes less negative. The sharp decline in the prior with reflects reducing sensitivity of modeled temperatures to parameter changes as ocean heat uptake increases, so that volumes in parameter space correspond to progressively smaller volumes in whitened difference space.
Model-prediction variability remaining after interpolation accounts for departures from smoothness and monotonicity in the noninformative prior. The upturn in the low Seq, high corner is an artifact arising because at low Seq, where temperature changes are small, model variability results in some of the simulated surface diagnostic temperatures changing in the wrong direction from to 8, between which there are no modeled values.
Figure 5 shows marginal joint credible regions in space, using our method for both the F06 and revised diagnostics. The tongue of probability heading toward high Seq levels, using the F06 diagnostics, is only reduced to low levels (producing better-constrained PDFs, particularly for Seq) by the falling value of the noninformative prior. The other diagnostic likelihoods cannot by themselves sufficiently reduce the substantial surface diagnostic likelihood that exists at very high Seq, even at fairly low . The revised surface diagnostic discriminates more, so the Seq PDF is reasonably constrained even when employing the F06 uniform priors method.
7. Discussion
The Forest papers develop a powerful means of estimating climate sensitivity jointly with uncertain ocean diffusivity and aerosol forcing. We develop a revised, objective Bayesian, statistical inference approach that improves their methods, principally by use of a noninformative prior but also by the avoidance of Bayesian updating (which is incompatible therewith) and of dependence on parameter surface flatness, and by incorporating a geometric volume adjustment.
Using our objective Bayesian method, the F06 approach of comparing observed with model-simulated spatiotemporal surface temperature patterns fairly well constrains parameter estimates using the same diagnostics as in F06, whereas Seq is badly constrained using the F06 method and uniform priors. We find the upper-air diagnostic—which provides relatively weak inference—problematic, with natural variability in many of its variables likely highly correlated with that in surface diagnostic variables and sensitivity to the weightings and truncation used, with the weightings–truncation combination used in F06 seemingly producing unsatisfactory inference.
We resolve these issues by employing only surface and deep-ocean diagnostics, revising these to use longer diagnostic periods, taking advantage of previously unused post-1995 model simulation data and correctly matching model simulation and observational data periods (mismatched by 9 months in the F06 surface diagnostic). Using the revised diagnostics, estimates of Seq are lower and more tightly constrained, with a 1.1–2.9-K range obtained using the F06 method and 1.2–2.2 K using the new method. Switching from the original HadCRUT observational surface temperature dataset to the updated HadCRUT4 may have contributed significantly to this reduction: Ring et al. (2012) reported that doing so caused a 0.5-K reduction in their Seq estimate.
Comparison, at the best-fit parameter combinations, of the model-simulated and observed rises in global mean temperature between the first 20 and last 20 simulation years provides a key reality check for the validity of inference arising from the alternative diagnostics, testing all stages of the optimal fingerprint method. Taking the best-fit point at under the new method and using the revised diagnostics, the two temperature rises are virtually identical. Using the original F06 diagnostics, the model-simulated rise is one-third higher than observed. These test results, while not proving that parameter inference is correct using the revised diagnostics or incorrect using the original diagnostics, provide substantial support for preferring use of the revised diagnostics. However, the sensitivity of inference about Seq to the data used, its processing and analysis, indicates that results using the revised diagnostics should not be regarded as definitive.
Our method of converting directly from a PDF in whitened variable space to one in parameter space yields a conversion factor equating to a noninformative joint prior for the parameters. Its shape is far removed from the uniform priors mainly used in F06, substantially affecting results. Although, coincidentally, the central section of the shape of the F06 expert prior for Seq is broadly similar to a cross section of the noninformative joint prior at fixed Kυ and Faer, the expert prior declines much more rapidly at low and high Seq. Moreover, the noninformative joint prior is far from uniform in Kυ and Faer and is not a separable function of the three parameters. The shape of the noninformative prior reflects how informative the data are about the parameters as their values vary, rather than the preexisting information as to parameter values. Any such prior information is unlikely to be independent of information provided by the data, invalidating Bayesian inference. We recommend that a computed noninformative joint parameter prior, not separate uniform (or expert) priors, be used in future Bayesian climate parameter studies.
Using the same diagnostics and method as F06, we obtain tighter bounds (5%–95% points per marginal posterior PDFs) at than reported with uniform priors in F06. This is particularly so for Seq, the central estimate of which is, moreover, reduced by 0.4 K. This principally reflects use of a preferable upper-air truncation parameter and a corrected implementation of the F06 method. Our 90% range of 2.0–3.6 K for Seq, obtained using the new method with the F06 diagnostics, improves on the IPCC's 2–4.5-K "likely" range given in Hegerl et al. (2007). Our 90% range of 1.2–2.2 K for Seq, obtained using the preferred revised diagnostics and the new method, appears low in relation to that range, partly because uncertainty in nonaerosol forcings and surface temperature measurements is ignored. Incorporation of such uncertainties is estimated to increase the Seq range to 1.0–3.0 K, with the median unchanged (see supplemental material for derivation and additional discussion).
Our 1.6-K mode for Seq obtained with the objective Bayesian method and the preferred revised diagnostics is identical to that from the main results in two recent studies providing observationally constrained estimates of Seq: Aldrin et al. (2012) and (using the same HadCRUT4 dataset) Ring et al. (2012). Our 1.1–2.9-K 90% range for Seq obtained using the F06 method (uniform priors) and revised diagnostics compares with the 1.2–3.5 K obtained using a uniform prior for Seq in Aldrin et al. (2012).
The F06 Method and mFm,ν Distribution
Each F06 goodness-of-fit statistic is based on a vector of the p differences between observations and model predictions. Through premultiplication by a "whitening" matrix ( being the truncated eigen-decomposition of ), ũ is transformed into a set of error variables (whitened differences) that would, if inter alia the estimated noise covariance matrix and the model predictions were accurate, have independent N(0, 1) distributions when the model parameter settings equaled the climate system parameters' hypothetical true values.
Since only the largest covariance matrix EOFs are retained, there are only κ nonzero whitened differences. The whitened differences' sum of squares, r2, is computed for each parameter combination setting. AT99 states, in the context of climate change detection and attribution, that where m scaling factors for the ratios of observed to model-predicted pattern amplitudes are estimated before model minus observation differences are determined, ( from here on referring to the version retaining κ EOFs). When, as in F06, the aim is instead to estimate climate system parameters, the scaling factors are all set to unity rather than being estimated, as discussed in F01; so . Accordingly, assuming the model is accurate and uses the true parameter values (resulting in the underlying whitened differences being zero)
The realized differences at each candidate model parameter settings are whitened and the whitened sum of squares r2 computed. That sum represents the squared length of , a vector in a κ-dimensional whitened difference space, with origin where all those differences are zero:
It is argued in F01 [see Eq. (6) therein] that
where represents the actual differences at the true model parameter settings and the estimated differences, being the actual differences at the best-fit model parameters (where r2 is minimized), and m now represents the number of unknown model parameters. Here .
Defining as the minimum r2 as model parameters are varied and as the excess of r2 at an arbitrary location in parameter space over , it is asserted [F01, their Eq. (7)] that
Given known observational values, all realizable whitened difference vectors extend from the origin to a point on an dimensional hypersurface (the parameter surface) embedded in the κ-dimensional space, the location of that surface depending on the observational values. In the κ-dimensional space, is the squared length of , the vector ending at the point on the surface nearest to the origin, representing the best-fit estimated differences in (A3):
At this point, the parameter surface is orthogonal to (otherwise the minimum would lie elsewhere). An m-dimensional tangent hyperplane coincident with the parameter surface where it meets , and therefore also orthogonal to , can be constructed. If the parameter surface is flat, and so everywhere is coincident with the tangent hyperplane, will, as assumed in F06, have an mFm,ν distribution per (A4). However, the parameter surface is more likely to be convex, resulting in an mFm,ν distribution producing tighter bounds on the parameters than are justified (see supplemental material for additional discussion).
New Method
We start by defining whitened versions of the modeled, observed, and underlying surface diagnostic temperatures: , , and . The underlying temperatures are what the observed temperatures would have been in the absence of climate noise and on the assumption of model accuracy are functions of the true parameter vector θt.
Since the whitening operation is linear the whitening may be carried out before calculating differences or after, so
By supposition, variability in the whitened observed temperatures has a distribution:
Now consider the κc vectors of whitened observed , underlying , and modeled temperatures for all three diagnostics combined, where , and define . On the assumption, implicit in F06's use of Bayesian updating, that the whitened differences for the three diagnostics are independent, we can obtain equations corresponding to (B2) for the other diagnostics and then multiply them to obtain a PDF for :
The density for depends only on the pivot variable , so is a location parameter vector. The noninformative joint prior for estimating location parameters in the presence of independent normal errors of known variance is uniform (Datta and Sweeting 2005): . Applying Bayes's theorem at this point, we derive a posterior joint PDF for the underlying whitened temperatures as
Omitting constant values of the uniform prior and the denominator we obtain
which, substituting from (B4), becomes
This Bayesian posterior is identical to the error distribution PDF when estimating the underlying whitened temperatures using a frequentist approach.
Given the assumption of model prediction accuracy , we can, since (B1) extended to the combined diagnostics then implies , simplify (B7) to
The resulting joint posterior PDF for can now be converted into a joint PDF for the parameters using a standard generalization [Mardia et al. 1979, their Eq. (2.5.16)] of the usual formula for converting PDFs upon a change of variables with unchanged dimensionality. If is a parameterization of a m-dimensional hypersurface in and g(θ) is a PDF on , then x has a PDF on the hypersurface given by
is the Jacobian matrix evaluated at . Here, we take , the joint PDF for the true parameter vector, and so that and we make the PDFs conditional on (which does not affect D), with the result that (B9) becomes
Rearranging (B11),
By the presumed model prediction accuracy and (B1)
and noting that is not a function of θ we can therefore change (B12) to
Substituting now from Eq. (B6) in Eq. (B13), noting that conditionality on is the same as conditionality on θt, gives
where represents a conversion factor from probability density in whitened observation space to that in parameter space (i.e., on the parameter surface).
Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/JCLI-D-12-00473.s1.


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ABoR releases voter guide for November elections
Election Day is Tuesday, November 6! ABoR's Legislative Management Team (LMT) met with and vetted candidates running for Austin City Council. The LMT then made recommendations for candidate endorsements to the ABoR Board of Directors, which were approved. The Austin Board of REALTORS® is thrilled to put its support behindContinue Reading


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Floor plans for
3521 Blue Ridge Rd.
This home takes on a more modern, streamlined look. My goal with the design was to capture the current trends in a timeless design.
The exterior features white brick and over-sized black metal windows that allow incredible amounts of natural light. There is a large screened porch and patio in the rear with plenty of room to entertain while still having privacy. Mature trees provide shade and shield the neighbors. The lot also allows for a large outdoor entertaining area and pool, almost impossible to find in this part of town.
The ceilings are high and vaulted in the master to 18 feet and 20 feet in the main floor great room. Large fireplaces provide a warm ambiance. The circular staircase is a beautiful focal point from the moment you walk in the front door. The master bedroom features 18 ft vaulted ceilings, a balcony, a large modern bathroom with steam shower and massive closet.
Storage was not ignored with lots of closets, attic space and over 1500 sq ft unfinished above the garage and in the basement.
Entertaining was also considered with a large dining room, oversized common areas, screened porch, huge movie theater, large basement area with bar and card room.
There are just too many special details to mention! Contact us today for more information!


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able sisters
Animal Crossing
Awesome Game-Themed Animal Crossing: New Horizons Designs
It is likely painfully obvious that MyPotatoGames adores Animal Crossing. Additionally, as a website that provides wholesome video game news,…Read More »
Animal Crossing
Even More Fan-Made Custom Designs In Animal Crossing: New Horizons
Providing you have the Custom Designs app on your NookPhone, you can create your own designs (including transparent ones) and scan QR…Read More »
Animal Crossing
How To Meet Labelle In Animal Crossing: New Horizons
If you've unlocked the Able Sisters clothing shop, you may have wondered "Where's Labelle?". Labelle first appeared in Animal Crossing:…Read More »
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Amazing Fan-Made Custom Designs In Animal Crossing: New Horizons
Getting the custom designs app on your NookPhone will allow you to create your own designs and scan QR codes…Read More »


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Bad Kleinkirchheim, Austria
Bad Kleinkirchheim Wheelchair Enabled Accommodation
Bad Kleinkirchheim
Hotel Trattlerhof
Bad Kleinkirchheim Hotel
Sleeps 20
Hotel Trattlerhof enjoys a scenic location on the edge of the forest close to the centre of Bad Kleinkirchheim. Many hiking and biking trails pass by the...
- Wi-Fi
- Swimming Pool
- Pet Friendly
- On-site Parking
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Bad Kleinkirchheim Wheelchair Enabled Accommodation
If you are looking for Bad Kleinkirchheim accommodation , SafariNow has a selection of Hotel, accommodation in Bad Kleinkirchheim and surrounds. With 13 listings in Bad Kleinkirchheim, our handy Bad Kleinkirchheim map search and great low prices, it's easy to book the perfect holiday accommodation for your Bad Kleinkirchheim visit.


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Making Plans - Please prepare layout for your light weight aluminum railings. This means you will certainly not make any acquisitions that you do not need.
There are a wide range of gliders. A lot of gliders are offered with the choice to seat 2 or three people. You need to examine your needs and also comfort level for both to figure out which acquisition is the best for you.
The finest alternative for you is teak wood since it is the best quality wood to make use of for the Adirondack chair as well as it will use extremely well. Your Adirondack furnishings might get unclean, as will any kind of other furnishings, you will certainly obtain the advantages of durability as well as long-lasting reliability.
Benefits of an aluminum canopy consist of sturdiness and also low-maintenance, although form as well as color options are restricted. If the color is made of material, it would involve better treatment and also maintenance, although more colors as well as forms are readily available for this product type.
Preparation for barriers: After fixing the bottom assistance, prepare the full railing on a level floor as well as erect it in the bottom assistance just when it is totally ready
If you still aren't convinced that outdoor patio furniture is right for you, a final point I can recommend is to check it out. Most likely to a store or two as well as see what is available. Require time to sit in the chairs. I'm quite certain that when you see exactly how loaded with comfort outdoor patio furnishings really is, you'll be buying some for your home before you recognize it.
When acquiring exterior furniture such as Adirondack chairs or tables is their comfortability, another vital suggestion to keep in mind. You have to analyze whether it gives appropriate relaxation to your body or not. If you really feel comfy while sitting in Adirondack chair, after that it deserves purchasing.
Now after you have actually chosen the sort of chair, you can take into consideration Adirondack chair pillows to bring that magnificent shade to your valued belongings. It does not matter which Adirondack chair you are choosing, one point remains sure that you will certainly buy just the very best one that will certainly be based on your design and needs.
Top rail: The top rail will certainly have slots of the dimension of wood inserts as well as spaced to ensure that the leading railing enters into these slots easily. The leading barrier is to be fixed to the verticals with help of cleats. This will certainly ensure that the leading rail does stagnate and also the functional section of top rail does not have any kind of protruding bolts.
Be sure to select a design that will certainly last a long period of time which you'll enjoy for a while. Shy away from choosing a fashionable style or material pattern for your outdoor patio furniture. The more classic and fundamental you choose, the longer you will intend to keep it.
There is nothing even worse than holding an event as well as having no where for individuals to unwind and also rest. If you include small points like patio area furnishings to make your house more guest and party pleasant, you can host the ideal parties of the summer season.
Since canopy cuts vary in size, knowing the measurements of the area will help the proprietor choose the most affordable combinations. Some awning or cover makers provide track extenders to suit slight modifications in dimension. As soon as measurement problems are settled, the owner currently has the alternative to seek setup as a diy job or to seek specialist assistance from licensed dealers.
These troubles can be resolved using awnings or canopies. These safety tones are normally cost-efficient as well as attribute lightweight skeletal frames. An awning or canopy can be made from a composite product, textile or even aluminum, and some can be found in retractable versions with handbook or electric control.
The major parts of barriers are bottom articles, verticals, leading railings, and also center rails. All the parts are available from a DIY workshop or the parts can be individually bought as well as set up together. It is easy to make fine-looking railings. The initiative needed is additionally not very high.


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Te Matariki Clendon Library Second and fourth Monday of every month 10.30am to 11.30am Free
Te Matariki Clendon Library
Do you love talking about the books you've read? Would you like to hear about books others have enjoyed?
Come along and join our book club, where you can share your favourite reads, make friends with other enthusiastic readers and discover new titles and authors.
We meet on the second and fourth Mondays of the month, excepting school holidays, in the Peaceful Place.
We enjoy morning tea while we discuss books and occasionally have a special guest speaker join us.
We enjoy a new theme each book chat and have a newsletter to accompany the session.
Book chat
Book clubs
Book club
Book club at Kumeū
Adult book group
Book club
Tamil book club
Book chat
Literatea book chat
Weekend book chat
Talking poetry
Crafts & hobbies, Book clubs
Reading Revolution
Classes & workshops, Book clubs
17 Palmers Rd
9am - 5.30pm
9am - 6.30pm
9am - 5.30pm
9am - 7pm
9am - 5.30pm
9am - 4pm
Phone: 09 377 0209
Shine bright these school holidays from 4 July - 19 July with fun activities and events for tamariki.
Pīataata mai! Shine your light on Matariki with us from 20 Pipiri - 15 Hōngongoi
Our resources can help you with job-seeking, upskilling and changing careers.
Was this page useful?
To ask for help or information, contact us.


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Now Viewing:Belmont, MA
If you purchase products that are not avaiable today, we'll reach out within four hours about delivery or pickup in a few days.
Coolship Pêche marries the delicate flavor of farm-fresh peaches with their Coolship beer's signature notes of tart funk, apricot, and oak. In line with traditional Belgian brewing methods, this beer starts with Pilsner malt, 40% raw wheat, and aged whole-leaf hops. The unfermented wort is then transferred to a large shallow pan called a coolship, which allows the wort to mingle with wild yeast and souring microbiota in the Maine air. The beer then ferments and ages in French oak wine barrels for roughly two years. To finish, we add fresh, Maine-grown peaches and let the barrels rest for another five months before the beer is ready for bottles; 6.8% abv


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Deep learning teams up with robotics
6. February 2020
EVK, the image processing specialist, and the Swedish company OP Teknik have jointly developed a solution for the efficient sorting of construction and demolition waste. By combining hyperspectral imaging technology with a deep learning approach from EVK together with robot technology from OP Teknik, a flexible system has been created for high material throughput with high sorting accuracy.
By combining EVK Hyperspectral Imaging Technology with a deep learning approach and robotics technology from OP Teknik, the two companies developed a flexible, high- throughput system SELMA for accurate sorting of selected fractions in C&D waste. The system combines EVK HELIOS imaging platform with robotics-based sorting and is characterized by the ability to accurately differentiate between many heterogeneous materials, such as paper, cartonnage, wood or even light bulbs. The stand-alone sorting system SELMA can be rapidly deployed to remote demolition sites and addresses recyclers to whom high C&D sorting accuracy and high throughput is of high importance.
Dr. Matthias Kerschhaggl, Chief Technology Officer at EVK, explains: "Providers of sorting systems like OP Teknik benefit from a company like EVK because it offers not only imaging sensing technology but also analytics software and domain relevant application knowhow. The EVK HELIOS platform, for instance, helps machine builders like OP Teknik in developing their solutions within shortest time, thus giving them a time to market advantage".
Fredrik Brandt, CTO, OP Teknik explains: "The classification enables the handling of complex material flows, as they occur in CnD waste sorting". He adds: "The provided sorting system SELMA can be used anywhere and is ideally suited for large sorting plants which handle industrial waste".
Alexander Fetz
+43 316 461 664
More news on this topic
Smart metal recycling
A successful collaboration of cluster partners: For digitisation of all its recycling systems, the metal recycling specialist ATM has put its trust in high-performance technology from t-matix. The technology captures data in real time on usage patterns, product optimisation, utilisation and maintenance and makes it available to the client in a simplified and prepared format. The resulting data analysis allows, for example, greatly simplified maintenance and servicing of plant and equipment and improved planning for sustainable savings in resources. More →
One-Stop-Shop-Recycling-Solutions for metals
Experts offer individual solutions for metal recycling under the platform don't waste//invest. More →
From the mixed waste stream to valuable secondary materials
One-stop-shop recycling solutions are offered by experts on the don't waste // invest platform for domestic waste. More →


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About 3 results.
Austin Watson (born September 4, 1986), is an American professional wrestler. He is currently signed to WWE, where he performs on the SmackDown brand under the ring name Xavier Woods. He is currently inactive due to an achilles injury, but is still one-third of the current SmackDown Tag Team Champions. Watson also makes public appearances outside of wrestling under the name Austin Creed, a ring name he used as a wrestler during his first years.Watson previously worked for Total Nonstop Action Wrestling (TNA) as Consequences Creed, and was a one-time TNA World Tag Team Champion with Jay Lethal as Lethal Consequences. After signing with WWE in 2010, he was assigned to its developmental territory Florida Championship Wrestling (FCW) under the ring name Xavier Woods. FCW was later rebranded into NXT, where Woods worked until he was called up to the main roster in 2013. In 2014, Woods formed The New Day alongside Big E and Kofi Kingston, and have since become six-time SmackDown Tag Team Champions and two-time Raw Tag Team Champions, with their second reign being the longest tag team title reign in WWE history.
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Hans Wegner Ch34 "Yoke" Chair For Carl Hansen, Denmark, 1959
Hans Wegner Ch34 "Yoke" Chair For Carl Hansen, Denmark, 1959
For this location please request a delivery quote from the seller
The above information is an estimate only, and is based upon front-door delivery. Final rates vary by destination and complexity. To get an accurate delivery quote suited to your needs, please request a quote
Can't find the information you're looking for?
About this item
Armchair model CH34 or "Yoke" chair, designed by Hans J. Wegner and manufactured by Carl Hansen & Son, Denmark, 1959. Rare early edition of an iconic Wegner design in perfect original condition. This chair model CH34 has only been in production from 1959 until 1964.
The rotating backrest makes this chair highly comfortable and suitable as an everyday desk chair. Solid oak frame and original soft black leather with great patina. Beautiful detailing. Signed with manufacturers' stamp at the underside of the seat.
Wear consistent with age and use.
Wear condition
Date of manufacture
Place of origin
VAT status
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Warburton Circuit
|Distance: 13km
Bookings are not required for this walk, just turn up at: 9:45am Ringwood station, in front of the Ringwood RSL, on Station St.
The leader will organise car-pooling and provide directions to the location of the walk. Drivers are really appreciated to help car-pool walkers between the meeting point and the walk location. There is free all-day parking nearby if your vehicle isn't needed for transport, but please check parking signs.
The drive from the meeting point to the starting point of the walk will take about 50 minutes and is 100 km return.
The walk will take around 4.5 hours including breaks.
Expect to return to the meeting point around 6.00pm.
Walk Description
A circuit walk around Warburton that includes the Backstairs Track, La La Falls and a section along the Yarra River. Some steep climbs.
What to bring
• Day pack
• Sufficient water (2 litres, more on hot summer days)
• Lunch and snacks
• Hat, sun screen
• Suitable outdoor clothing (no jeans/sneakers!)
• Rainwear & warm jacket
• Proper walking shoes/boots
Refer to our Gear Checklist page for more details. If you are not properly equipped, the walk leader can decide not to let you participate on this walk.
Booking Fee:
YHA Bushwalking Victoria Members: Free
Non-members: $7 (please pay the leader CASH at the start of the walk, no credit cards)
Passengers must pay the driver their share of car-pooling costs as described on the Car-pooling page. Please bring cash for this purpose.
Still have questions?
Check out What happens on a walk.
Check out Day walks and social activities.
Contact the leader using the "Enquiry" button below BEFORE 8 pm on the preceding Wednesday.
Activity Date(s)
December 15, 2019 9:45 am
December 15, 2019 6:00 pm
Sonya R
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Lupin And Lilly Expand Partnership In India
Lupin Limited has launched Galls' (tadalafil), an oral PDE5 inhibitor, for the treatment of erectile dysfunction (ED) in adult males. Cialis was shown to improve erectile function compared to placebo up to 36 hours following dosing. Cialisx tablet is available in 10 mg and 20 mg strengths. The product is currently marketed in over 100 countries.
Lupin has acquired the rights to market, promote and distribute Lilly's Erectile Dysfunction (ED) product, Cialis"through its specialty field force while Lilly will be responsible for manufacturing and importing the product. Lupin is already promoting and distributing Lilly's Huminsulin range of products and rapid acting insulin analog under the brand names Lispro and Eglucene.
The PDE-5 market in India is valued at around IN R 390 crore, out of which Tadalafi I contributes around 23%. The market size has doubled since 2012 and is growing annually at 15%. As per a study", 52% men between the age40 to 70 years suffer from erectile dysfunction (ED) of various type ranging from mild to severe. ED causes depression, low self-esteem and affects the quality of life.
Commenting on the launch, Mr Rajeev Sibal, President - India Region Formulations, Lupin said, "We are very happy with the addition of Galls° to our business portfolio. It heralds Lupin's entry into the fast growth PDE-5 inhibitors market which will address the unmet medical need in ED space in India. The launch demonstrates Lupin's commitment to grow its brand franchise in India and bring meaningful products to patients in the country.
"We are pleased to expand our relationship with Lupin, with whom we have successfully partnered in the past. Cialis is a new treatment option for men with ED. Today, Erectile dysfunction is a significant medical condition affecting large number of Indian men, this partnership will help expand our reach to more patients. Lilly is committed to bringing innovative products to India" said Edgard Olaizola, Managing Director, Eli Lilly and Company (India) Pvt. Ltd.