Uranium ore

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https://en.wikipedia.org/wiki/Uranium_ore 

 

Sample of uranium ore

Uranium ore deposits are economically recoverable concentrations of uranium within the Earth's crust. Uranium is one of the more common elements in the Earth's crust, being 40 times more common than silver and 500 times more common than gold. It can be found almost everywhere in rock, soil, rivers, and oceans. The challenge for commercial uranium extraction is to find those areas where the concentrations are adequate to form an economically viable deposit. The primary use for uranium obtained from mining is in fuel for nuclear reactors.

Globally, the distribution of uranium ore deposits is widespread on all continents, with the largest deposits found in Australia, Kazakhstan, and Canada. To date, high-grade deposits are only found in the Athabasca Basin region of Canada.

Uranium deposits are generally classified based on host rocks, structural setting, and mineralogy of the deposit. The most widely used classification scheme was developed by the International Atomic Energy Agency (IAEA) and subdivides deposits into 15 categories.

Uranium

Main article: Uranium

Uranium is a silvery-gray metallic weakly radioactive chemical element. It has the chemical symbol U and atomic number 92. The most common isotopes in natural uranium are ²³⁸U (99.27%) and ²³⁵U (0.72%). All uranium isotopes present in natural uranium are radioactive and fissionable, and ²³⁵U is fissile (will support a neutron-mediated chain reaction). Uranium, thorium, and one radioactive isotope of potassium (⁴⁰
K) as well as their decay products are the main elements contributing to natural terrestrial radioactivity. Cosmogenic radionuclides are of less importance but unlike the aforementioned primordial radionuclides, which date back to the formation of the planet and have since slowly decayed away, they are replenished at roughly the same rate they decay by the bombardment of earth with cosmic rays.

Uranium has the highest atomic weight of the naturally occurring elements and is approximately 70% denser than lead, but not as dense as tungsten, gold, platinum, iridium, or osmium. It is always found combined with other elements. Along with all elements having atomic weights higher than that of iron, it is only naturally formed in supernova explosions.

Uranium minerals

Uraninite, also known as pitchblende

 

Autunite, a secondary uranium mineral named after Autun in France

 

Torbernite, an important secondary uranium mineral

The primary uranium ore mineral is uraninite (UO₂) (previously known as pitchblende). A range of other uranium minerals can be found in various deposits. These include carnotite, tyuyamunite, torbernite and autunite. The davidite-brannerite-absite type uranium titanates, and the euxenite-fergusonite-samarskite group are other uranium minerals.

A large variety of secondary uranium minerals are known, many of which are brilliantly coloured and fluorescent. The most common are gummite (a mixture of minerals), autunite (with calcium), saleeite (magnesium) and torbernite (with copper); and hydrated uranium silicates such as coffinite, uranophane (with calcium) and sklodowskite (magnesium).

Uranium Minerals
Primary uranium minerals
Name	Chemical Formula
uraninite or pitchblende	UO2
coffinite	U(SiO4)1–x(OH)4x
brannerite	UTi2O6
davidite	(REE)(Y,U)(Ti,Fe3+)20O38
thucholite	Uranium-bearing pyrobitumen
Secondary uranium minerals
Name	Chemical Formula
autunite	Ca(UO2)2(PO4)2 x 8-12 H2O
carnotite	K2(UO2)2(VO4)2 x 1–3 H2O
gummite	gum like mixture of various uranium minerals
saleeite	Mg(UO2)2(PO4)2 x 10 H2O
torbernite	Cu(UO2)2(PO4)2 x 12 H2O
tyuyamunite	Ca(UO2)2(VO4)2 x 5-8 H2O
uranocircite	Ba(UO2)2(PO4)2 x 8-10 H2O
uranophane	Ca(UO2)2(HSiO4)2 x 5 H2O
zeunerite	Cu(UO2)2(AsO4)2 x 8-10 H2O

Ore genesis

Wood fragment in a conglomerate from Utah, which has been partially replaced by pitchblende (black) and surrounded by carnotite (yellow)

There are several themes of uranium ore deposit formation, which are caused by geological and chemical features of rocks and the element uranium. The basic themes of uranium ore genesis are host mineralogy, reduction-oxidation potential, and porosity.

Uranium is a highly soluble, as well as a radioactive, heavy metal. It can be easily dissolved, transported and precipitated within ground waters by subtle changes in oxidation conditions. Uranium also does not usually form very insoluble mineral species, which is a further factor in the wide variety of geological conditions and places in which uranium mineralization may accumulate.

Uranium is an incompatible element within magmas, and as such it tends to become accumulated within highly fractionated and evolved granite melts, particularly alkaline examples. These melts tend to become highly enriched in uranium, thorium and potassium, and may in turn create internal pegmatites or hydrothermal systems into which uranium may dissolve.

Classification schemes

IAEA Classification (1996)

The International Atomic Energy Agency (IAEA) assigns uranium deposits to 15 main categories of deposit types, according to their geological setting and genesis of mineralization, arranged according to their approximate economic significance.

1. Unconformity-related deposits
2. Sandstone deposits
3. Quartz-pebble conglomerate deposits
4. Breccia complex deposits
5. Vein deposits
6. Intrusive deposits (Alaskites)
7. Phosphorite deposits
8. Collapse breccia pipe deposits
9. Volcanic deposits
10. Surficial deposits
11. Metasomatite deposits
12. Metamorphic deposits
13. Lignite
14. Black shale deposits
15. Other types of deposits

Alternate scheme

The IAEA classification scheme works well, but is far from ideal, as it does not consider that similar processes may form many deposit types, yet in a different geological setting. The following table groups the above deposit types based on their environment of deposition.

Uranium Deposit Classification
Uranium Transport / Precipitation Conditions	Deposit Type
Surface Processes / synsedimentary	Surficial deposits
	Quartz-pebble conglomerate deposits
	Phosphorite deposits
	Lignite
	Black shales
Diagenetic	Sandstone deposits
Diagenetic – Hydrothermal?	Unconformity-related deposits
	Vein deposits
	Collapse breccia pipe deposits
Magmatic – Hydrothermal?	Breccia complex deposits
	Volcanic deposits
	Metasomatite deposits
	Vein deposits
	Intrusive deposits
Metamorphic – Hydrothermal?	Metamorphic deposits

Deposit types (IAEA Classification)

Unconformity-related deposits

Ranger 3 open pit, Northern Territory, Australia: Uranium mineralised Cahill Formation as visible in the pit is unconformably overlain by Kombolgie sandstone forming the mountains in the background

Unconformity-type uranium deposits host high grades relative to other uranium deposits and include some of the largest and richest deposits known. They occur in close proximity to unconformities between relatively quartz-rich sandstones comprising the basal portion of relatively undeformed sedimentary basins and deformed metamorphic basement rocks. These sedimentary basins are typically of Proterozoic age, however some Phanerozoic examples exist.

Phanerozoic unconformity-related deposits occur in Proterozoic metasediments below an unconformity at the base of overlying Phanerozoic sandstone. These deposits are small and low-grade (Bertholene and Aveyron deposits, in France).

The two most significant areas for this style of deposit are currently the Athabasca Basin in Saskatchewan, Canada, and the McArthur Basin in the Northern Territory, Australia.

Main article: Cigar Lake Mine

Athabasca Basin

Main article: Athabasca Basin

The highest grade uranium deposits are found in the Athabasca Basin in Canada, including the two largest high grade uranium deposits in the world, Cigar Lake with 217 million pounds (99,000 t) U₃O₈ at an average grade of 18% and McArthur River with 324 million pounds (147,000 t) U₃O₈ at an average grade of 17%. These deposits occur below, across and immediately above the unconformity. Additionally, another high grade discovery is in the development stage at Patterson Lake (Triple R deposit) with an estimated mineral resource identified as; "Indicated Mineral Resources" estimated to total 2,291,000 tons at an average grade of 1.58% U₃O₈ containing 79,610,000 pounds of U₃O₈. "Inferred Mineral Resources" are estimated to total 901,000 tons at an average grade of 1.30% U₃O₈ containing 25,884,000 pounds of U₃O₈.

McArthur Basin

Main article: McArthur Basin

The deposits of the McArthur River basin in the East Alligator Rivers region of the Northern Territory of Australia (including Jabiluka, Ranger, and Nabarlek) are below the unconformity and are at the low-grade end of the unconformity deposit range but are still high grade compared to most uranium deposit types. There has been very little exploration in Australia to locate deeply concealed deposits lying above the unconformity similar to those in Canada. It is possible that very high grade deposits occur in the sandstones above the unconformity in the Alligator Rivers/Arnhem Land area.

Sandstone deposits

A uranium mine, near Moab, Utah. Note alternating red and white/green sandstone. This corresponds to oxidized and reduced conditions in groundwater redox chemistry. The rock forms in oxidizing conditions, and is then "bleached" to the white/green state when a reducing fluid passes through the rock. The reduced fluid can also carry uranium-bearing minerals.

Sandstone deposits are contained within medium to coarse-grained sandstones deposited in a continental fluvial or marginal marine sedimentary environment. Impermeable shale or mudstone units are interbedded in the sedimentary sequence and often occur immediately above and below the mineralised horizon. Uranium is mobile under oxidising conditions and precipitates under reducing conditions, and thus the presence of a reducing environment is essential for the formation of uranium deposits in sandstone.

Primary mineralization consists of pitchblende and coffinite, with weathering producing secondary mineralization. Sandstone deposits constitute about 18% of world uranium resources. Orebodies of this type are commonly low to medium grade (0.05–0.4% U₃O₈) and individual orebodies are small to medium in size (ranging up to a maximum of 50,000 t U₃O₈).

Sandstone hosted uranium deposits are widespread globally and span a broad range of host rock ages. Some of the major provinces and production centers include:

1. the Wyoming basins
2. the Grants District of New Mexico
3. deposits in Central Europe and
4. Kazakhstan

Significant potential remains in most of these centers as well as in Australia, Mongolia, South America, and Africa.

This model type can be further subdivided into the following sub-types:

• tabular
• roll front
• basal channel
• structurally related

Many deposits represent combinations of these types.

Tabular

Tabular deposits consist of irregular tabular or elongate lenticular zones of uranium mineralisation within selectively reduced sediments. The mineralised zones are oriented parallel to the direction of groundwater flow, but on a small scale the ore zones may cut across sedimentary features of the host sandstone. Deposits of this nature commonly occur within palaeochannels cut in the underlying basement rocks.

Tabular sandstone uranium deposits contains many of the highest grades of the sandstone class, however the average deposit size is very small.

Roll front

Structures interpreted as Palaeo-rollfronts in South Australia

Roll-front uranium deposits are generally hosted within permeable and porous sandstones or conglomerates. The mechanism for deposit formation is dissolution of uranium from the formation or nearby strata and the transport of this soluble uranium into the host unit. When the fluids change redox state, generally in contact with carbon-rich organic matter, uranium precipitates to form a 'front'.

The Rollfront subtype deposits typically represent the largest of the sandstone-hosted uranium deposits and one of the largest uranium deposit types with an average of 21 million lb (9,500 t) U₃O₈. Included in this class are the Inkai deposit in Kazakhstan and the Smith Ranch deposit in Wyoming. Probably more significant than their larger size, rollfront deposits have the advantage of being amenable to low cost in-situ leach recovery.

Typical characteristics:

• roll-front deposits are crescent-shaped bodies that transect the host lithology
• typically the convex side points down the hydraulic gradient.
• the limbs or tails tend to be peneconcordant with the lithology.
• most ore-bodies consist of several interconnected rolls.
• individual roll-front deposits are quite small but collectively can extend for considerable distances.

Basal channel (palaeochannel)

Basal channel deposits are often grouped with tabular or rollfront deposits, depending on their unique characteristics. The model for formation of palaeochannel deposits is similar to that for roll-front deposits, above, except that the source of uranium may be in the watershed leading into a stream, or the bed load of the palaeochannel itself. This uranium is transported through the groundwaters and is deposited either at a reduced boundary, or in ephemeral drainage systems such as those in deserts of Namibia and Australia, it is deposited in calcretised evaporation sites or even in saline lakes as the ground water evaporates.

Some particularly rich uranium deposits are formed in palaeochannels which are filled in the lower parts by lignite or brown coal, which acts as a particularly efficient reductive trap for uranium. Sometimes, elements such as scandium, gold and silver may be concentrated within these lignite-hosted uranium deposits.

The Frome Embayment in South Australia hosts several deposits of this type including Honeymoon, Oban, Beverley and [Four-Mile] (which is the largest deposit of this class). These deposits are hosted in palaeochannels filled with Cainozoic sediments and sourced their uranium from uranium-rich Palaeo- to Mesoproterozoic rocks of the Mount Painter Inlier and the Olary Domain of the Curnamona Province.

Structurally related

Westmoreland uranium deposit, Queensland, Australia: most of the orebodies (position of two of them marked) are hosted along the Redtree dolerite dyke (broken line) within the Paleoproterozoic Westmoreland conglomerate

Tectonic-lithologic controlled uranium deposits occur in sandstones adjacent to a permeable fault zone which cuts the sandstone/mudstone sequence. Mineralisation forms tongue-shaped ore zones along the permeable sandstone layers adjacent to the fault. Often there are a number of mineralised zones 'stacked' vertically on top of each other within sandstone units adjacent to the fault zone.

Quartz-pebble conglomerate deposits

Quartz pebble conglomerate hosted uranium deposits are of historical significance as the major source of primary production for several decades after World War II. This type of deposit has been identified in eight localities around the world, however the most significant deposits are in the Huronian Supergroup in Ontario, Canada and in the Witwatersrand Supergroup of South Africa. These deposits make up approximately 13% of the world's uranium resources.

Two main sub-types have been identified:

• Elliot Lake
• Witwatersrand

Quartz pebble conglomerate hosted uranium deposits formed from the transport and deposition of uraninite in a fluvial sedimentary environment and are defined as stratiform and stratabound paleoplacer deposits. Host rocks are typically submature to supermature, polymictic conglomerates and sandstones deposited in alluvial fan and braided stream environments. The host conglomerates of the Huronian deposits in Canada are situated at the base of the sequence, whereas the mineralized horizons in the Witwatersand are arguably along tectonized intraformational unconformities.

Uranium minerals were derived from uraniferous pegmatites in the sediment source areas. These deposits are restricted to the Archean and early Paleoproterozoic and do not occur in sediments younger than about 2,200 million years when oxygen levels in the atmosphere reached a critical level, making simple uranium oxides no longer stable in near-surface environments.

Quartz pebble conglomerate uranium deposits are typically low grade but characterized by high tonnages. The Huronian deposits in Canada generally contain higher grades (0.15% U₃O₈) and greater resources (as shown by the Denison and Quirke mines), however some of the South African gold deposits also contain sizeable low grade (0.01% U₃O₈) uranium resources.

Witwatersrand sub-type

In the Witwatersrand deposits ores are found along unconformities, shale and siltstone beds, and carbonaceous seams. The West Rand Group of sediments tend to host the most uranium within the Witwatersrand Supergroup. The uranium rich Dominion Reef is located at the base of the West Rand Supergroup. The Vaal Reef is the most uranium rich reef of the Central Rand Group of sediments. Structural controls on the regional scale are normal faults while on the deposit scale are bedding parallel shears and thrusts. Textural evidence indicates that the uranium and gold have been remobilized to their current sites; however the debate continues if the original deposition was detrital or was entirely hydrothermal, or alternatively related to high grade diagenesis.

Uranium minerals in the Witwatersrand deposits are typically uraninite with lesser uranothorite, brannerite, and coffinite. The uranium is especially concentrated along thin carbonaceous seams or carbon leaders. Strong regional scale alteration consists of pyrophyllite, chloritoid, muscovite, chlorite, quartz, rutile, and pyrite. The main elements associated with the uranium are gold and silver. Gold contents are much higher than in the Elliot Lake type with U:Au ranging between 5:1 and 500:1, which indicates that these gold-rich ores are essentially very low grade uranium deposits with gold.

Elliot Lake sub-type

Sedimentological controls on the Huronian deposits of the Elliot Lake district appear to be much stronger than in the Witwatersrand deposits. Ores grade from uranium through thorium to titanium-rich with decreasing pebble size and increasing distance from their source. While evidence of post-diagenetic remobilization has been identified, these effects appear far subordinate to the sedimentological controls.

Ore consists of uraninite with lesser brannerite and thucholite. These occur in thin beds exhibiting graded bedding reminiscent of placer sorting. Alteration is nonexistent to very weak at best and the weak chlorite and sericite are believed to be mainly post-ore effects. Other post-depositional alteration includes pyritization, silicification, and alteration of titanium minerals. The most prominent geochemical associations with the uranium are thorium and titanium.

This schematic model represents the original depositional setting. The Huronian underwent mild post-depositional folding during the Penokean orogeny around 1.9 billion years. The main regional structure is the Quirke syncline along the margins of which the majority of the known deposits are situated. Due to this structural overprint ore bodies range from subhorizontal to steeply dipping.

Breccia complex deposits (IOCG-U)

See also: Iron oxide copper gold ore deposits

 

Chalcopyrite-rich ore specimen from Olympic Dam: copper-rich sections of the deposits are usually also rich in uranium

 

Uranium-rich breccia at Mount Gee, Mount Painter Inlier, South Australia

Only one iron-ore-copper-gold (IOCG) deposit of this type is known to contain economically significant quantities of uranium. Olympic Dam in South Australia is the world's largest resource of low-grade uranium and accounts for about 66% of Australia's reserves plus resources.

Uranium occurs with copper, gold, silver, and rare earth elements (REE) in a large hematite-rich granite breccia complex in the Gawler Craton overlain by approximately 300 metres of flat-lying sedimentary rocks of the Stuart Shelf geological province.

Another example for the Breccia type is the Mount Gee area in the Mount Painter Inlier, South Australia. Uranium mineralised quartz-hematite breccia is related to Palaeoproterozoic granites with uranium contents of up to 100 ppm. Hydrothermal processes at about 300 million years ago remobilised uranium from these granites and enriched them in the quartz-hematite breccias. The breccias in the area host a low grade resource of about 31,400 t U₃O₈ at 615 ppm in average.

Vein deposits

Uranium ore (pitchblende in dolomite) from the vein-type deposit Niederschlema-Alberoda

 

Polymetallic uranium ore, Marienberg, Erzgebirge Mts, Germany

Vein deposits play a special role in the history of uranium: the term "pitchblende" ("Pechblende") originates from German vein deposits when they were mined for silver in the 16th century. F.E. Brückmann made the first mineralogical description of the mineral in 1727 and the vein deposit Jachymov in the Czech Republic became the type locality for uraninite. In 1789 the German chemist M. H. Klaproth discovered the element of uranium in a sample of pitchblende from the Johanngeorgenstadt vein deposit. The first industrial production of uranium was made from the Jachymov deposit and Marie and Pierre Curie used the tailings of the mine for their discovery of polonium and radium.

Vein deposits consist of uranium minerals filling in cavities such as cracks, veins, fractures, breccias, and stockworks associated with steeply dipping fault systems. There are three major subtypes of vein style uranium mineralisation:

• intragranitic veins (Central Massif, France)
• veins in metasedimentary rocks in exocontacts of granites
  • quartz-carbonate uranium veins (Erzgebirge Mts, Germany/Czech Republic; Bohemian Massif, Czech Republic)
  • uranium-polymetal veins (Erzgebirge Mts, Germany/Czech Republic; Saskatchewan, Canada)
• mineralised fault and shear zones (central Africa; Bohemian Massif, Czech Republic)

Intragranitic veins form in the late phase of magmatic activity when hot fluids derived from the magma precipitate uranium on cracks within the newly formed granite. Such mineralisation contributed much to the uranium production of France. Veins hosted by metasedimentary units in the exocontact of granites are the most important sources of uranium mineralisation in central Europe including the world class deposits Schneeberg-Schlema-Alberoda in Germany (96,000 t uranium content) as well as Pribram (50,000 t uranium content) and Jachymov (~10,000 t uranium content) in the Czech Republic. Also they are closely related to the granites, the mineralization is much younger with a time gap between granite formation and mineralisation of 20 million years. The initial uranium mineralisation consists of quartz, carbonate, fluorite and pitchblende. Remobilisation of uranium occurred at later stages producing polymetal veins containing silver, cobalt, nickel, arsenic and other elements. Large deposits of this type can contain more than 1,000 individual mineralized veins. However, only 5 to 12% of the vein areas carry mineralization and although massive lenses of pitchblende can occur, the overall ore grade is only about 0.1% uranium.

The Bohemian Massif also contains shear zone hosted uranium deposits with the most important one being Rozna-Olsi in Moravia northwest of Brno. Rozna is currently the only operating uranium mine in central Europe with a total uranium content of 23,000 t and an average grade of 0.24%. The formation of this mineralisation occurred in several stages. After the Variscan Orogeny, extension took place and hydrothermal fluids overprinted fine grained materials in shear zones with a sulfide-chlorite alteration. Fluids from the overlying sediments entered the basement mobilising uranium and while uprising on the shear zone, the chlorite-pyrite material caused precipitation of uranium minerals in form of coffinite, pitchblende and U-Zr-silicates. This initial mineralisation event took place at about 277 million to 264 million years. During the Triassic a further mineralisation event took place relocating uranium into quartz-carbonate-uranium veins. Another example of this mineralisation style is the Shinkolobwe deposit in Congo, Africa, containing about 30,000 t of uranium.

Intrusive associated deposits

Intrusive deposits make up a large proportion of the world's uranium resources. Included in this type are those associated with intrusive rocks including alaskite, granite, pegmatite and monzonites. Major world deposits include Rossing (Namibia), Ilimaussaq intrusive complex (Greenland) and Palabora (South Africa).

Phosphorite deposits

Marine sedimentary phosphorite deposits can contain low grade concentrations of uranium, up to 0.01–0.015% U₃O₈, within fluorite or apatite. These deposits can have a significant tonnage. Very large phosphorite deposits occur in Florida and Idaho in the United States, Morocco, and some middle eastern countries.

Collapse breccia pipe deposits

Collapse breccia pipe deposits occur within vertical, circular solution collapse structures, formed by the dissolution of limestone by groundwater. Pipes are typically filled with down-dropped coarse fragments of limestone and overlying sediments and can be from 30 to 200 metres (100 to 660 ft) wide and up to 1,000 metres (3,300 ft) deep.

Primary ore minerals are uraninite and pitchblende, which occur as cavity fills and coatings on quartz grains within permeable sandstone breccias within the pipe. Resources within individual pipes can range up to 2500 tonnes U₃O₈ at an average grade of between 0.3 and 1.0% U₃O₈.

The best known examples of this deposit type are in the Arizona breccia pipe uranium mineralization in the US, where several of these deposits have been mined.

Volcanic deposits

Volcanic deposits occur in felsic to intermediate volcanic to volcaniclastic rocks and associated caldera subsidence structures, comagmatic intrusions, ring dykes and diatremes.

Mineralization occurs either as structurally controlled veins and breccias discordant to the stratigraphy and less commonly as stratabound mineralization either in extrusive rocks or permeable sedimentary facies. Mineralization may be primary, that is magmatic-related or as secondary mineralization due to leaching, remobilization and re-precipitation. The principal uranium mineral in volcanic deposits is pitchblende, which is usually associated with molybdenite and minor amounts of lead, tin and tungsten mineralization.

Volcanic hosted uranium deposits occur in host rocks spanning the Precambrian to the Cenozoic but because of the shallow levels at which they form, preservation favors younger age deposits. Some of the more important deposits or districts are Streltsovskoye, Russia; Dornod, Mongolia; and McDermitt, Nevada.

The average deposit size is rather small with grades of 0.02% to 0.2% U₃O₈. These deposits make up only a small proportion of the world's uranium resources. The only volcanic hosted deposits currently being exploited are those of the Streltsovkoye district of eastern Siberia. This is in fact not a single stand-alone deposit, but 18 individual deposits occurring within the Streltsovsk caldera complex. Nevertheless, the average size of these deposits is far greater than the average volcanic type.

Surficial deposits (calcretes)

Surficial deposits are broadly defined as Tertiary to Recent near-surface uranium concentrations in sediments or soils. Mineralization in calcrete (calcium and magnesium carbonates) are the largest of the surficial deposits. They are interbedded with Tertiary sand and clay, which are usually cemented by calcium and magnesium carbonates. Surficial deposits also occur in peat bogs, karst caverns and soils.

Surficial deposits account for approximately 4% of world uranium resources. The Yeelirrie deposit is by far the world's largest surficial deposit, averaging 0.15% U₃O₈. Langer Heinrich in Namibia is another significant surficial deposit.

Metasomatite deposits

Metasomatite deposits consist of disseminated uranium minerals within structurally deformed rocks that have been affected by intense sodium metasomatism. Ore minerals are uraninite and brannerite. Th/U ratio in the ores is mostly less than 0.1. Metasomatites are typically small in size and generally contain less than 1000 t U₃O₈. Giant (up to 100 thousands t U) U deposits in sodium metasomatites (albitites) are known in Central Ukraine and Brazil.

Two subtypes are defined based on host lithologies:

• metasomatized granite; ex. Ross Adams deposit in Alaska, United States, Novokostantynivka deposit in Kirovogradska oblast, Ukraine.
• metasomatised metasediment; ex. Zhovta Richka and Pervomayske deposits in Dnipropetrovska oblast, Ukraine and Valhalla deposit in northwestern Queensland, Australia.

Metamorphic deposits

Abandoned open pit of Mary Kathleen uranium mine; the orebody is a skarn mineralisation enriched in U, Cu, Th and REE

Metamorphic deposits those that occur in metasediments or metavolcanic rocks where there is no direct evidence for mineralization post-dating metamorphism. These deposits were formed during regional metamorphism of uranium bearing or mineralized sediments or volcanic precursors.

The most prominent deposits of this type are Mary Kathleen, Queensland, Australia, and Forstau, Austria.

Lignite

Lignite deposits (soft brown coal) can contain significant uranium mineralization. Mineralization can also be found in clay and sandstone immediately adjacent to lignite deposits. Uranium has been adsorbed onto carbonaceous matter and as a result no discrete uranium minerals have formed. Deposits of this type are known from the Serres Basin, in Greece, and in North and South Dakota in the USA. The uranium content in these deposits is very low, on average less than 0.005% U₃O₈, and does not currently warrant commercial extraction.

Black shale deposits

Black shale mineralisations are large low-grade resources of uranium. They form in submarine environments under oxygen-free conditions. Organic matter in clay-rich sediments will not be converted to CO₂ by biological processes in this environment and it can reduce and immobilise uranium dissolved in seawater. Average uranium grades of black shales are 50 to 250 ppm. The largest explored resource is Ranstad in Sweden containing 254,000 t of uranium. However, there are estimates for black shales in the US and Brazil assuming a uranium content of over 1 million tonnes, but at grades below 100 ppm uranium. The Chattanooga Shale in the southeastern USA for example is estimated to contain 4 to 5 million tonnes at an average grade of 54 ppm.

Because of their low grades, no black shale deposit ever produced significant amounts of uranium with one exception: the Ronneburg deposit in eastern Thuringia, Germany. The Ordovician and Silurian black shales at Ronneburg have a background uranium content of 40 to 60 ppm. However, hydrothermal and supergene processes caused remobilsation and enrichment of the uranium. The production between 1950 and 1990 was about 100,000 t of uranium at average grades of 700 to 1,000 ppm. Measured and inferred resources containing 87,000 t uranium at grades between 200 and 900 ppm are left.

Other types of deposits

• There are also uranium deposits, of other types, in the Jurassic Todilto Limestone in the Grants District, New Mexico, USA.
• The Freital/Dresden-Gittersee deposit in eastern Germany produced about 3.700 t of uranium from Permian hard coal and its host rocks. The average ore grade was 0.11%. The deposit formed in a combination of syngenetic and diagenetic processes.
• In some countries, for example China, trials are underway to extract uranium from fly ash.

Boolean algebra (structure)

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Boolean_algebra_(structure) 

In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties of both set operations and logic operations. A Boolean algebra can be seen as a generalization of a power set algebra or a field of sets, or its elements can be viewed as generalized truth values. It is also a special case of a De Morgan algebra and a Kleene algebra (with involution).

Every Boolean algebra gives rise to a Boolean ring, and vice versa, with ring multiplication corresponding to conjunction or meet ∧, and ring addition to exclusive disjunction or symmetric difference (not disjunction ∨). However, the theory of Boolean rings has an inherent asymmetry between the two operators, while the axioms and theorems of Boolean algebra express the symmetry of the theory described by the duality principle.

Boolean lattice of subsets

History

The term "Boolean algebra" honors George Boole (1815–1864), a self-educated English mathematician. He introduced the algebraic system initially in a small pamphlet, The Mathematical Analysis of Logic, published in 1847 in response to an ongoing public controversy between Augustus De Morgan and William Hamilton, and later as a more substantial book, The Laws of Thought, published in 1854. Boole's formulation differs from that described above in some important respects. For example, conjunction and disjunction in Boole were not a dual pair of operations. Boolean algebra emerged in the 1860s, in papers written by William Jevons and Charles Sanders Peirce. The first systematic presentation of Boolean algebra and distributive lattices is owed to the 1890 Vorlesungen of Ernst Schröder. The first extensive treatment of Boolean algebra in English is A. N. Whitehead's 1898 Universal Algebra. Boolean algebra as an axiomatic algebraic structure in the modern axiomatic sense begins with a 1904 paper by Edward V. Huntington. Boolean algebra came of age as serious mathematics with the work of Marshall Stone in the 1930s, and with Garrett Birkhoff's 1940 Lattice Theory. In the 1960s, Paul Cohen, Dana Scott, and others found deep new results in mathematical logic and axiomatic set theory using offshoots of Boolean algebra, namely forcing and Boolean-valued models.

Definition

A Boolean algebra is a six-tuple consisting of a set A, equipped with two binary operations ∧ (called "meet" or "and"), ∨ (called "join" or "or"), a unary operation ¬ (called "complement" or "not") and two elements 0 and 1 in A (called "bottom" and "top", or "least" and "greatest" element, also denoted by the symbols ⊥ and ⊤, respectively), such that for all elements a, b and c of A, the following axioms hold:

a ∨ (b ∨ c) = (a ∨ b) ∨ c	a ∧ (b ∧ c) = (a ∧ b) ∧ c	associativity
a ∨ b = b ∨ a	a ∧ b = b ∧ a	commutativity
a ∨ (a ∧ b) = a	a ∧ (a ∨ b) = a	absorption
a ∨ 0 = a	a ∧ 1 = a	identity
a ∨ (b ∧ c) = (a ∨ b) ∧ (a ∨ c)	a ∧ (b ∨ c) = (a ∧ b) ∨ (a ∧ c)	distributivity
a ∨ ¬a = 1	a ∧ ¬a = 0	complements

Note, however, that the absorption law and even the associativity law can be excluded from the set of axioms as they can be derived from the other axioms (see Proven properties).

A Boolean algebra with only one element is called a trivial Boolean algebra or a degenerate Boolean algebra. (In older works, some authors required 0 and 1 to be distinct elements in order to exclude this case.)

It follows from the last three pairs of axioms above (identity, distributivity and complements), or from the absorption axiom, that

a = b ∧ a     if and only if     a ∨ b = b.

The relation ≤ defined by a ≤ b if these equivalent conditions hold, is a partial order with least element 0 and greatest element 1. The meet a ∧ b and the join a ∨ b of two elements coincide with their infimum and supremum, respectively, with respect to ≤.

The first four pairs of axioms constitute a definition of a bounded lattice.

It follows from the first five pairs of axioms that any complement is unique.

The set of axioms is self-dual in the sense that if one exchanges ∨ with ∧ and 0 with 1 in an axiom, the result is again an axiom. Therefore, by applying this operation to a Boolean algebra (or Boolean lattice), one obtains another Boolean algebra with the same elements; it is called its dual.

Examples

• The simplest non-trivial Boolean algebra, the two-element Boolean algebra, has only two elements, 0 and 1, and is defined by the rules:

∧ 0 1 0 0 0 1 0 1

∨ 0 1 0 0 1 1 1 1

a 0 1 ¬a 1 0

• It has applications in logic, interpreting 0 as false, 1 as true, ∧ as and, ∨ as or, and ¬ as not. Expressions involving variables and the Boolean operations represent statement forms, and two such expressions can be shown to be equal using the above axioms if and only if the corresponding statement forms are logically equivalent.

• The two-element Boolean algebra is also used for circuit design in electrical engineering; here 0 and 1 represent the two different states of one bit in a digital circuit, typically high and low voltage. Circuits are described by expressions containing variables, and two such expressions are equal for all values of the variables if and only if the corresponding circuits have the same input-output behavior. Furthermore, every possible input-output behavior can be modeled by a suitable Boolean expression.

• The two-element Boolean algebra is also important in the general theory of Boolean algebras, because an equation involving several variables is generally true in all Boolean algebras if and only if it is true in the two-element Boolean algebra (which can be checked by a trivial brute force algorithm for small numbers of variables). This can for example be used to show that the following laws (Consensus theorems) are generally valid in all Boolean algebras:
  • (a ∨ b) ∧ (¬a ∨ c) ∧ (b ∨ c) ≡ (a ∨ b) ∧ (¬a ∨ c)
  • (a ∧ b) ∨ (¬a ∧ c) ∨ (b ∧ c) ≡ (a ∧ b) ∨ (¬a ∧ c)

• The power set (set of all subsets) of any given nonempty set S forms a Boolean algebra, an algebra of sets, with the two operations ∨ := ∪ (union) and ∧ := ∩ (intersection). The smallest element 0 is the empty set and the largest element 1 is the set S itself.

• After the two-element Boolean algebra, the simplest Boolean algebra is that defined by the power set of two atoms:

∧ 0 a b 1 0 0 0 0 0 a 0 a 0 a b 0 0 b b 1 0 a b 1

∨ 0 a b 1 0 0 a b 1 a a a 1 1 b b 1 b 1 1 1 1 1 1

x 0 a b 1 ¬x 1 b a 0

• The set ${\displaystyle A}$ of all subsets of ${\displaystyle S}$ that are either finite or cofinite is a Boolean algebra and an algebra of sets called the finite–cofinite algebra. If ${\displaystyle S}$ is infinite then the set of all cofinite subsets of ${\displaystyle S,}$ which is called the Fréchet filter, is a free ultrafilter on ${\displaystyle A.}$ However, the Fréchet filter is not an ultrafilter on the power set of ${\displaystyle S.}$
• Starting with the propositional calculus with κ sentence symbols, form the Lindenbaum algebra (that is, the set of sentences in the propositional calculus modulo logical equivalence). This construction yields a Boolean algebra. It is in fact the free Boolean algebra on κ generators. A truth assignment in propositional calculus is then a Boolean algebra homomorphism from this algebra to the two-element Boolean algebra.
• Given any linearly ordered set L with a least element, the interval algebra is the smallest algebra of subsets of L containing all of the half-open intervals [a, b) such that a is in L and b is either in L or equal to ∞. Interval algebras are useful in the study of Lindenbaum–Tarski algebras; every countable Boolean algebra is isomorphic to an interval algebra.

Hasse diagram of the Boolean algebra of divisors of 30.

• For any natural number n, the set of all positive divisors of n, defining ${\displaystyle a\le b}$ if a divides b, forms a distributive lattice. This lattice is a Boolean algebra if and only if n is square-free. The bottom and the top element of this Boolean algebra is the natural number 1 and n, respectively. The complement of a is given by n/a. The meet and the join of a and b is given by the greatest common divisor (gcd) and the least common multiple (lcm) of a and b, respectively. The ring addition a+b is given by lcm(a,b)/gcd(a,b). The picture shows an example for n = 30. As a counter-example, considering the non-square-free n=60, the greatest common divisor of 30 and its complement 2 would be 2, while it should be the bottom element 1.
• Other examples of Boolean algebras arise from topological spaces: if X is a topological space, then the collection of all subsets of X which are both open and closed forms a Boolean algebra with the operations ∨ := ∪ (union) and ∧ := ∩ (intersection).
• If ${\displaystyle R}$ is an arbitrary ring then its set of central idempotents, which is the set
  $${\displaystyle A=\left\{e\in R:e^2=e\text{ and }ex=xe\text{ for all }x\in R\right\},}$$

  
  becomes a Boolean algebra when its operations are defined by ${\displaystyle e\vee f:=e+f-ef}$ and ${\displaystyle e\wedge f:=ef.}$

Homomorphisms and isomorphisms

A homomorphism between two Boolean algebras A and B is a function f : A → B such that for all a, b in A:

f(a ∨ b) = f(a) ∨ f(b),

f(a ∧ b) = f(a) ∧ f(b),

f(0) = 0,

f(1) = 1.

It then follows that f(¬a) = ¬f(a) for all a in A. The class of all Boolean algebras, together with this notion of morphism, forms a full subcategory of the category of lattices.

An isomorphism between two Boolean algebras A and B is a homomorphism f : A → B with an inverse homomorphism, that is, a homomorphism g : B → A such that the composition g ∘ f: A → A is the identity function on A, and the composition f ∘ g: B → B is the identity function on B. A homomorphism of Boolean algebras is an isomorphism if and only if it is bijective.

Boolean rings

Main article: Boolean ring

Every Boolean algebra (A, ∧, ∨) gives rise to a ring (A, +, ·) by defining a + b := (a ∧ ¬b) ∨ (b ∧ ¬a) = (a ∨ b) ∧ ¬(a ∧ b) (this operation is called symmetric difference in the case of sets and XOR in the case of logic) and a · b := a ∧ b. The zero element of this ring coincides with the 0 of the Boolean algebra; the multiplicative identity element of the ring is the 1 of the Boolean algebra. This ring has the property that a · a = a for all a in A; rings with this property are called Boolean rings.

Conversely, if a Boolean ring A is given, we can turn it into a Boolean algebra by defining x ∨ y := x + y + (x · y) and x ∧ y := x · y. Since these two constructions are inverses of each other, we can say that every Boolean ring arises from a Boolean algebra, and vice versa. Furthermore, a map f : A → B is a homomorphism of Boolean algebras if and only if it is a homomorphism of Boolean rings. The categories of Boolean rings and Boolean algebras are equivalent.

Hsiang (1985) gave a rule-based algorithm to check whether two arbitrary expressions denote the same value in every Boolean ring. More generally, Boudet, Jouannaud, and Schmidt-Schauß (1989) gave an algorithm to solve equations between arbitrary Boolean-ring expressions. Employing the similarity of Boolean rings and Boolean algebras, both algorithms have applications in automated theorem proving.

Ideals and filters

Main articles: Ideal (order theory) and Filter (mathematics)

An ideal of the Boolean algebra A is a subset I such that for all x, y in I we have x ∨ y in I and for all a in A we have a ∧ x in I. This notion of ideal coincides with the notion of ring ideal in the Boolean ring A. An ideal I of A is called prime if I ≠ A and if a ∧ b in I always implies a in I or b in I. Furthermore, for every a ∈ A we have that a ∧ -a = 0 ∈ I and then a ∈ I or -a ∈ I for every a ∈ A, if I is prime. An ideal I of A is called maximal if I ≠ A and if the only ideal properly containing I is A itself. For an ideal I, if a ∉ I and -a ∉ I, then I ∪ {a} or I ∪ {-a} is properly contained in another ideal J. Hence, that an I is not maximal and therefore the notions of prime ideal and maximal ideal are equivalent in Boolean algebras. Moreover, these notions coincide with ring theoretic ones of prime ideal and maximal ideal in the Boolean ring A.

The dual of an ideal is a filter. A filter of the Boolean algebra A is a subset p such that for all x, y in p we have x ∧ y in p and for all a in A we have a ∨ x in p. The dual of a maximal (or prime) ideal in a Boolean algebra is ultrafilter. Ultrafilters can alternatively be described as 2-valued morphisms from A to the two-element Boolean algebra. The statement every filter in a Boolean algebra can be extended to an ultrafilter is called the Ultrafilter Theorem and cannot be proven in ZF, if ZF is consistent. Within ZF, it is strictly weaker than the axiom of choice. The Ultrafilter Theorem has many equivalent formulations: every Boolean algebra has an ultrafilter, every ideal in a Boolean algebra can be extended to a prime ideal, etc.

Representations

It can be shown that every finite Boolean algebra is isomorphic to the Boolean algebra of all subsets of a finite set. Therefore, the number of elements of every finite Boolean algebra is a power of two.

Stone's celebrated representation theorem for Boolean algebras states that every Boolean algebra A is isomorphic to the Boolean algebra of all clopen sets in some (compact totally disconnected Hausdorff) topological space.

Axiomatics

Proven properties

Huntington 1904 Boolean algebra axioms

The first axiomatization of Boolean lattices/algebras in general was given by the English philosopher and mathematician Alfred North Whitehead in 1898. It included the above axioms and additionally x∨1=1 and x∧0=0. In 1904, the American mathematician Edward V. Huntington (1874–1952) gave probably the most parsimonious axiomatization based on ∧, ∨, ¬, even proving the associativity laws (see box). He also proved that these axioms are independent of each other. In 1933, Huntington set out the following elegant axiomatization for Boolean algebra. It requires just one binary operation + and a unary functional symbol n, to be read as 'complement', which satisfy the following laws:

1. Commutativity: x + y = y + x.
2. Associativity: (x + y) + z = x + (y + z).
3. Huntington equation: n(n(x) + y) + n(n(x) + n(y)) = x.

Herbert Robbins immediately asked: If the Huntington equation is replaced with its dual, to wit:

4. Robbins Equation: n(n(x + y) + n(x + n(y))) = x,

do (1), (2), and (4) form a basis for Boolean algebra? Calling (1), (2), and (4) a Robbins algebra, the question then becomes: Is every Robbins algebra a Boolean algebra? This question (which came to be known as the Robbins conjecture) remained open for decades, and became a favorite question of Alfred Tarski and his students. In 1996, William McCune at Argonne National Laboratory, building on earlier work by Larry Wos, Steve Winker, and Bob Veroff, answered Robbins's question in the affirmative: Every Robbins algebra is a Boolean algebra. Crucial to McCune's proof was the computer program EQP he designed. For a simplification of McCune's proof, see Dahn (1998).

Further work has been done for reducing the number of axioms; see Minimal axioms for Boolean algebra.

Generalizations

Removing the requirement of existence of a unit from the axioms of Boolean algebra yields "generalized Boolean algebras". Formally, a distributive lattice B is a generalized Boolean lattice, if it has a smallest element 0 and for any elements a and b in B such that a ≤ b, there exists an element x such that a ∧ x = 0 and a ∨ x = b. Defining a ∖ b as the unique x such that (a ∧ b) ∨ x = a and (a ∧ b) ∧ x = 0, we say that the structure (B,∧,∨,∖,0) is a generalized Boolean algebra, while (B,∨,0) is a generalized Boolean semilattice. Generalized Boolean lattices are exactly the ideals of Boolean lattices.

A structure that satisfies all axioms for Boolean algebras except the two distributivity axioms is called an orthocomplemented lattice. Orthocomplemented lattices arise naturally in quantum logic as lattices of closed subspaces for separable Hilbert spaces.

Climate resilience

From Wikipedia, the free encyclopedia

 

 

A graphic displaying the inter-connectivity between climate change, adaptability, vulnerability, and resilience.

Climate resilience is defined as the "capacity of social, economic and ecosystems to cope with a hazardous event or trend or disturbance". This is done by "responding or reorganising in ways that maintain their essential function, identity and structure (as well as biodiversity in case of ecosystems) while also maintaining the capacity for adaptation, learning and transformation". The key focus of increasing climate resilience is to reduce the climate vulnerability that communities, states, and countries currently have with regards to the many effects of climate change. Currently, climate resilience efforts encompass social, economic, technological, and political strategies that are being implemented at all scales of society. From local community action to global treaties, addressing climate resilience is becoming a priority, although it could be argued that a significant amount of the theory has yet to be translated into practice. Despite this, there is a robust and ever-growing movement fueled by local and national bodies alike geared towards building and improving climate resilience.

Climate resilience is related to climate change adaptation efforts. It aims to reduce climate change vulnerability and includes considerations of climate justice and equity. Practical implementations include climate resilient infrastructure, climate resilient agriculture and climate resilient development. Most objective approaches to measuring climate resilience use fixed and transparent definitions of resilience, and allow for different groups of people to be compared through standardised metrics.

Definition

Climate resilience is generally considered to be the ability to recover from, or to mitigate vulnerability to, climate-related shocks such as floods and droughts. It is a political process that strengthens the ability of all to mitigate vulnerability to risks from, and adapt to changing patterns in, climate hazards and variability.

The IPCC Sixth Assessment Report defines climate resilience as follows: "Resilience in this report is defined as the capacity of social, economic and ecosystems to cope with a hazardous event or trend or disturbance, responding or reorganising in ways that maintain their essential function, identity and structure as well as biodiversity in case of ecosystems while also maintaining the capacity for adaptation, learning and transformation. Resilience is a positive attribute when it maintains such a capacity for adaptation, learning, and/or transformation."

Resilience is a useful concept because it speaks across sectors and disciplines but this also makes it open to interpretation resulting in differing, and at times competing, definitions. The definition of climate resilience is heavily debated, in both conceptual and practical terms.

Related concepts

United Nations Environment Programme Adaptation Gap Report 2020

Climate change adaptation

The fact that climate resilience encompasses a dual function, to absorb shock as well as to self-renew, is the primary means by which it can be differentiated from the concept of climate adaptation. In general, adaptation is viewed as a group of processes and actions that help a system absorb changes that have already occurred, or may be predicted to occur in the future. For the specific case of environmental change and climate adaptation, it is argued by many that adaptation should be defined strictly as encompassing only active decision-making processes and actions – in other words, deliberate changes made in response to climate change.

Of course, this characterization is highly debatable: after all, adaptation can also be used to describe natural, involuntary processes by which organisms, populations, ecosystems and perhaps even social-ecological systems evolve after the application of certain external stresses. However, for the purposes of differentiating climate adaptation and climate resilience from a policymaking standpoint, we can contrast the active, actor-centric notion of adaptation with resilience, which would be a more systems-based approach to building social-ecological networks that are inherently capable of not only absorbing change, but utilizing those changes to develop into more efficient configurations.

Climate change vulnerability

If the definition of resiliency is the ability to recover from a negative event, in this case climate change, then talking about preparations beforehand and strategies for recovery (aka adaptations), as well as populations that are more or less capable of developing and implementing a resiliency strategy (aka vulnerable populations) are essential. This is framed under the assumed detrimental impacts of climate change to ecosystems and ecosystem services.

It is important to note that efforts to enhance resiliency can result in outcomes that are adaptive, maladaptive, or even both. When considering inequality with adaptation we can focus on distributive justice, the intent of which is to maximize benefits for and promote the engagement of the most disadvantaged communities. Identifying a community or population as vulnerable can lead to biases due to the different factors negotiated in the term vulnerable. Outcome vulnerability (focusing on quantitative measures) and contextual vulnerability (focusing on qualitative measures) are two aspects that must be thought of in unison to achieve a wholistic understanding of a community's vulnerable state. Because one population's level of vulnerability is constantly shifting (as are the threats and impacts of climate change) the efforts to provide adaptive strategies must offer multiple opportunities and outcomes.

Climate change vulnerability (or climate vulnerability or climate risk vulnerability) is defined as the "propensity or predisposition to be adversely affected" by climate change. It can apply to humans but also to natural systems (ecosystems). Human and ecosystem vulnerability are interdependent. Climate change vulnerability encompasses "a variety of concepts and elements, including sensitivity or susceptibility to harm and lack of capacity to cope and adapt". Vulnerability is a component of climate risk. Vulnerability differs within communities and across societies, regions and countries, and can change over time. Approximately 3.3 to 3.6 billion people live in contexts that are highly vulnerable to climate change in 2021.

Vulnerability of ecosystems and people to climate change is driven by certain unsustainable development patterns such as "unsustainable ocean and land use, inequity, marginalization, historical and ongoing patterns of inequity such as colonialism, and governance". Therefore, vulnerability is higher in locations with "poverty, governance challenges and limited access to basic services and resources, violent conflict and high levels of climate-sensitive livelihoods (e.g., smallholder farmers, pastoralists, fishing communities)".

Components

Currently, the majority of work regarding climate resilience has focused on actions taken to maintain existing systems and structures. This largely relates to the capacity of social-ecological systems to sustain shocks and maintain the integrity of functional relationships in the face of external forces. However, there is a growing consensus in the academic literature that actions taken to induce structural changes must also be recognized within the definition of resilience. The three basic capacities that are understood under the common definition are absorptive, adaptive, and transformative, each of which contributes different factors to the efforts of resilience work. This includes the capacity of social-ecological systems to renew and develop, and to utilize disturbances as opportunities for innovation and evolution of new pathways that improve the system's ability to adapt to macroscopic changes.

Key aspects include: how resilience relates to climate change adaptation; the extent to which it should encompass actor-based versus systems-based approaches to improving stability; and its relationship with the balance of nature theory or homeostatic equilibrium view of ecological systems.

The building of climate resilience is a highly comprehensive undertaking that involves of an eclectic array of actors and agents: individuals, community organizations, micropolitical bodies, corporations, governments at local, state, and national levels as well as international organizations. In essence, actions that bolster climate resilience are ones that will enhance the adaptive capacity of social, industrial, and environmental infrastructures that can mitigate the effects of climate change. Currently, research indicates that the strongest indicator of successful climate resilience efforts at all scales is a well-developed, pre-existing network of social, political, economic and financial institutions that is already positioned to effectively take on the work of identifying and addressing the risks posed by climate change. Cities, states, and nations that have already developed such networks are, as expected, to generally have far higher net incomes and GDP.

Therefore, it can be seen that embedded within the task of building climate resilience at any scale will be the overcoming of macroscopic socioeconomic inequities: in many ways, truly facilitating the construction of climate resilient communities worldwide will require national and international agencies to address issues of global poverty, industrial development, and food justice. However, this does not mean that actions to improve climate resilience cannot be taken in real time at all levels, although evidence suggests that the most climate resilient cities and nations have accumulated this resilience through their responses to previous weather-based disasters. Perhaps even more importantly, empirical evidence suggests that the creation of the climate resilient structures is dependent upon an array of social and environmental reforms that were only successfully passed due to the presence of certain sociopolitical structures such as democracy, activist movements, and decentralization of government.

An aerial view of Delhi, India where urban forests are being developed to improve the weather resistance and climate resilience of the city

By sector

Climate resilient development

Climate resilient development has become the new paradigm for sustainable development influencing theory and practice across all sectors globally. This is particularly true in the water sector, since water security is intimately connected to climate change. On every continent, governments are adopting policies for climate resilient economies, driven in part by international frameworks such as the Paris Agreement and the Sustainable Development Goals.

Climate resilient development "integrates adaptation measures and their enabling conditions with mitigation to advance sustainable development for all". It involves questions of equity and system transitions, and includes adaptations for human, ecosystem and planetary health. Climate resilient development is facilitated by developing partnerships with traditionally marginalised groups, including women, youth, Indigenous Peoples, local communities and ethnic minorities.

To achieve climate resilient development, the following actions are needed: increasing climate information, and financing and technical capacity for flexible and dynamic systems. This needs to be coupled with greater consideration of the socio-ecological resilience and context-specific values of marginalised communities and meaningful engagement with the most vulnerable in decision making.

Climate resilient infrastructure

Infrastructure failures can have broad-reaching consequences extending away from the site of the original event, and for a considerable duration after the immediate failure. Furthermore, increasing reliance infrastructure system interdependence, in combination with the effects of climate change and population growth all contribute to increasing vulnerability and exposure, and greater probability of catastrophic failures. To reduce this vulnerability, and in recognition of limited resources and future uncertainty about climate projections, new and existing long-lasting infrastructure must undergo a risk-based engineering and economic analyses to properly allocate resources and design for climate resilience.

Incorporating climate projections into building and infrastructure design standards, investment and appraisal criteria, and model building codes is currently not common. Some resilience guidelines and risk-informed frameworks have been developed by public entities. Such manuals can offer guidance for adaptive design methods, characterization of extremes, development of flood design criteria, flood load calculation and the application of adaptive risk management principals account for more severe climate/weather extremes. One example is the "Climate Resiliency Design Guidelines" by New York City.

Climate resilient agriculture

Main articles: Effects of climate change on agriculture, Climate change adaptation § Agriculture, and Climate-smart agriculture

Multiple returns of climate resilient agriculture will be delayed. One of India's strategies, responsive crop monitoring, cannot be planned. While the government is working to create systems to guide farmers in specific situations, response farming depends on the direction of climate change. Additionally, investing in tolerant livestock breeds will decrease production in the short term. Tolerant livestock's appeal lies in their ability to resist changes to the environment as climate change worsens. These immediate uncertainties are part of India's goal of promoting environmental health to support agricultural production long term.

Similar initiatives are implemented on local scales around the world. In the United States, the state of New York's Department of Agriculture started its Climate Resilient Farming program. This program aims to reduce the impact of climate change on agriculture and mitigate agriculture's impact on climate change. It promotes similar ideas to India's, including water management and the promotion of soil health. The climate-resilient programming also provides funds to help farmers reduce methane and properly store agricultural waste. New York state's focus on reducing greenhouse gas emissions balances developing climate-resilient agriculture and the slowing of climate change.

Government support of this intersection is used to support change amongst individual farmers. As climate variability increases, the costs associated with promoting climate resilience become larger in comparison. The risk of investing in tolerant breeds, soil management, and proper environmental care can also be daunting to small farmers. Such individuals have reported hesitation to implement suggested practices like reducing herd size to promote soil-healthy grazing. The popularity of climate resilient farming amongst subsistence farmers helps ease the transition to a climate-resilient system. Alongside developing new techniques, farmers can use techniques they already knew, such as no-till farming and cover cropping.

Tools

Climate resilience framework

A climate resilience framework can better equip governments and policymakers to develop sustainable solutions that combat the effects of climate change. To begin with, climate resilience establishes the idea of multi-stable socio-ecological systems (socio-ecological systems can actually stabilize around a multitude of possible states). Secondly, climate resilience has played a critical role in emphasizing the importance of preventive action when assessing the effects of climate change. Although adaptation is always going to be a key consideration, making changes after the fact has a limited capability to help communities and nations deal with climate change. By working to build climate resilience, policymakers and governments can take a more comprehensive stance that works to mitigate the harms of climate change impacts before they happen. Finally, a climate resilience perspective encourages greater cross-scale connectedness of systems. Creating mechanisms of adaptation that occur in isolation at local, state, or national levels may leave the overall social-ecological system vulnerable. A resilience-based framework would require far more cross-talk, and the creation of environmental protections that are more holistically generated and implemented.

One weakness of centralized organisations is their lack of adaptation to climate change issues specific to territories. To overcome it, a new concept called the "mistletoe ball" society (la société "boule de gui" in French) is emerging. States can provide resources (financial, empowerment, skills) to territories so they can provide a safety net to inhabitants, companies and public organizations. In addition, each territory is linked to each other through cooperation and solidarity ties. This safety net encompasses access to energy, food, mobility, health and education, among others. It doesn't provide full services but minimum services to survive the time needed to come back to a better situation. Compared to a full autonomous territory, it brings more resilience because a territory can be overwhelmed by a natural disaster and so needs help from other areas that are not affected. In addition, it needs less resources to create a safety net rather than a full autonomous system.

Disaster preparedness protocols

Main article: Disaster risk reduction

At larger governmental levels, general programs to improve climate resiliency through greater disaster preparedness are being implemented. For example, in cases such as Norway, this includes the development of more sensitive and far-reaching early warning systems for extreme weather events, creation of emergency electricity power sources, enhanced public transportation systems, and more.

Measurements

Governments and development agencies are spending increasing amounts of finance to support resilience-building interventions. Resilience measurement can make valuable contributions in guiding resource allocations towards resilience-building. This includes targeted identification of vulnerability hotspots, a better understanding of the drivers of resilience, and tools to infer the impact and effectiveness of resilience-building interventions. In recent years, a large number of resilience measurement tools have emerged, offering ways to track and measure resilience at a range of scales - from individuals and households to communities and nations.

Efforts to measure climate resilience currently face several technical challenges. Firstly, the definition of resilience is heavily contested, making it difficult to choose appropriate characteristics and indicators to track. Secondly, the resilience or households or communities cannot be measured using a single observable metric. Resilience is made up of a range of processes and characteristics, many of which are intangible and difficult to observe (such as social capital). As a result, many resilience toolkits resort to using large lists of proxy indicators.

Most of the recent initiatives to measure resilience in rural development contexts share two shortcomings: complexity and high cost. USAID published a field guide for assessing climate resilience in smallholder supply chains.

Most objective approaches use fixed and transparent definitions of resilience and allow for different groups of people to be compared through standardized metrics. However, as many resilience processes and capacities are intangible, objective approaches are heavily reliant on crude proxies. Examples of commonly used objective measures include the Resilience Index Measurement and Analysis (RIMA) and the Livelihoods Change Over Time (LCOT).

Subjective approaches to resilience measurement take a contrasting view. They assume that people have a valid understanding of their resilience and seek to factor perceptions into the measurement process. They challenge the notion that experts are best placed to evaluate other people's lives. Subjective approaches use people's menu of what constitutes resilience and allow them to self-evaluate accordingly. An example is the Subjectively-Evaluated Resilience Score (SERS)

History

The theoretical basis for many of the ideas central to climate resilience have actually existed since the 1960s. Originally an idea defined for strictly ecological systems, resilience in ecology was initially outlined by C.S. Holling as the capacity for ecological systems and relationships within those systems to persist and absorb changes to "state variables, driving variables, and parameters." This definition helped form the foundation for the notion of ecological equilibrium: the idea that the behavior of natural ecosystems is dictated by a homeostatic drive towards some stable set point. Under this school of thought (which maintained quite a dominant status during this time period), ecosystems were perceived to respond to disturbances largely through negative feedback systems – if there is a change, the ecosystem would act to mitigate that change as much as possible and attempt to return to its prior state.

As greater amounts of scientific research in ecological adaptation and natural resource management was conducted, it became clear that oftentimes, natural systems were subjected to dynamic, transient behaviors that changed how they reacted to significant changes in state variables: rather than work back towards a predetermined equilibrium, the absorbed change was harnessed to establish a new baseline to operate under. Rather than minimize imposed changes, ecosystems could integrate and manage those changes, and use them to fuel the evolution of novel characteristics. This new perspective of resilience as a concept that inherently works synergistically with elements of uncertainty and entropy first began to facilitate changes in the field of adaptive management and environmental resources, through work whose basis was built by Holling and colleagues yet again.

By the mid 1970s, resilience began gaining momentum as an idea in anthropology, culture theory, and other social sciences. There was significant work in these relatively non-traditional fields that helped facilitate the evolution of the resilience perspective as a whole. Part of the reason resilience began moving away from an equilibrium-centric view and towards a more flexible, malleable description of social-ecological systems was due to work such as that of Andrew Vayda and Bonnie McCay in the field of social anthropology, where more modern versions of resilience were deployed to challenge traditional ideals of cultural dynamics.

Eventually by the late 1980s and early 1990s, resilience had fundamentally changed as a theoretical framework. Not only was it now applicable to social-ecological systems, but more importantly, resilience now incorporated and emphasized ideas of management, integration, and utilization of change rather than simply describing reactions to change. Resilience was no longer just about absorbing shocks, but also about harnessing the changes triggered by external stresses to catalyze the evolution the social-ecological system in question.

Examples

Improving climate resilience of water and sanitation services

Climate resilience is the ability to recover from, or to mitigate vulnerability to, climate-related shocks such as floods and droughts. Climate resilient development has become the new paradigm for sustainable development influencing theory and practice across all sectors globally. This is particularly true in the water sector, since water security is intimately connected to climate change. On every continent, governments are adopting policies for climate resilient economies. International frameworks such as the Paris Agreement and the Sustainable Development Goals are drivers for such initiatives.

Climate-resilient water services (or "climate-resilient WASH") provide access to high quality drinking water during all seasons and even during extreme weather events. The right infrastructure and management choices are important at the community and household levels in order to achieve climate resilience for water supply.

To put climate resilience into practice and to engage better with politicians, the following questions need to be addressed on a case by case basis: "resilience of what, to what, for whom, over what time frame, by whom and at what scale?":

• "Resilience of what?" means thinking beyond infrastructure but to also include resilience of water resources, local institutions and water users.
• "Resilience to what?" means that smaller variations in water quantity and quality are as important as extreme events: smaller changes in seasonal rainfall variability can have devastating impacts on rainfall-dependent communities. Moreover, those without access to safe, reliable domestic water supplies face heightened water insecurity at specific times throughout the year due to cyclical changes in water quantity or quality. For example, where access to water on-premises is not available, drinking water quality at the point of use (PoU) can be much worse compared to the quality at the point of collection (PoC). Correct household practices around hygiene, storage and treatment are therefore important. There are interactions between weather, water source and management, and these in turn impact on drinking water safety.
• "Resilience over what time frame?" refers to short term or longer-term investments.
• "Resilience for whom?" speaks about reducing vulnerability and preventing maladaptation: For instance, top-down, technocratic interventions that attempt to work around power and politics undermine indigenous knowledge and compromise community resilience.
• "Resilience by whom?" refers to the fact that including diverse actors can expose, and allow operation within, power imbalances across scales.
• And finally, "Resilience at what scale?" reminds decision makers to scale-up solutions while maintaining context specificity.