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ContentslistsavailableatScienceDirect

International Journal of Critical Infrastructure Protection

journalhomepage:www.elsevier.com/locate/ijcip

Changes in inoperability for interdependent industry sectors in Norway from 2012 to 2017

Stig Rune Sellevåg

Norwegian Defence Research Establishment (FFI), P.O. Box 25, 2027 Kjeller, Norway

a rt i c l e i nf o

Article history:

Received 27 May 2020 Revised 14 August 2020 Accepted 10 December 2020 Available online 19 December 2020 Keywords:

Inoperability input-output model National security

Critical infrastructure protection Resilience

a b s t r a c t

ThepurposeofthisworkhasbeentoinvestigatechangesininterdependenciesbetweenNorway’smain- landindustrysectorsandhowitmightaffectnationalsecurity.Tothisend,theinterdependencieswere analysedbyusingthedemand-reductioninoperabilityinput-outputmodelandnationalaccountdatafor thetimeperiod2012–2017.Theconstructionsectorandthefoodindustrysectorareveryimportantin- dustriesformainlandNorway.Theconstructionsectorhasalsoincreaseditsinfluencefrom2012to2017.

Becauseofthelargeinfluencethesesectorsexerciseonothersectors,disruptionstotheconstructionsec- tororthefoodindustrymayseriouslyimpactthenationalsecurityofNorway.Norway’sagriculturalsec- tor,inparticular,isveryfragiletowardsdisruptionstothefoodindustry.Effortstoenhancetheresilience oftheagricultureandthefoodindustryshouldthereforecontinue.Withincreasingdigitisationandau- tomationoftheconstructionindustry,itisnecessarytogetmoreknowledgeonhowthiswillaffectthe interdependenciesbetweentheconstructionindustryandothersectors,andthepotentialvulnerabilities thatfollows.Itisalsorecommendedtogainmoreknowledgeabouttheimportanceoftheconstruction sectorandconstructionworkersformaintainingcriticalnationalinfrastructuresduringcrises.

© 2020TheAuthor(s).PublishedbyElsevierB.V.

ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/)

1. Introduction

The COVID-19 pandemic has shown that supply of services by criticalnationalinfrastructures(CNI)underpressingconditions and without major failure is of utmost importance to our soci- ety.Infrastructuredisruptionscandirectlyorindirectlyaffectother infrastructures through a complicated web of interdependencies across differentindustriesandbusinesssectors. Theeffectsofthe disruptions mayimpact large geographical regions and send rip- plesthroughoutthenationalandglobaleconomyaswellasaffect nationalsecurity[1].Understandingthefragilityinducedbymulti- pleinterdependenciesisthereforeconsideredasoneofthemajor challengeswhenitcomestoprotectionofCNIs[2–4].

The situation is exacerbated by the proliferation of digital technologies and increased electrification which continueto add complexity to our CNIs [5,6]. Furthermore, CNIs in free market economies do not have one single entity in control of the sys- tem. CNIs are therefore open sociotechnical systems that are in- fluenced byinwardandoutwardflowofgoods,servicesandcapi- tal,aswell asundergoingconstant interactionandexchangewith their economic,social and naturalenvironments [5].CNIs should

E-mail address: stig-rune.sellevag@ffi.no

thereforebecharacterisedascomplexadaptivesystems[2,5].Con- sequently,understanding the propertiesof complexadaptive sys- temsisofimportancewheninformingpolicymakersanddecision makersonnationalsecurityissuesrelatedtoCNIs[5].Inaddition, effectivecrisismanagement ofdisruptionsofCNIs atthe national levelrequiressituationalawarenessacrossallCNIsectors[7].

ImprovingtheresilienceofourCNIsectorsisthereforeaprior- ityofnationalsecurity.However,inordertoassessthefuturena- tionalsecurityimplicationsofdigitaltransformationandincreased electrification,itisnecessarytogainbetterunderstandingofhow interdependenciesbetweenCNIsectorshavechangeduptillnow.

Thepurposeofthisworkhasbeentoinvestigatechangesinin- terdependenciesbetweenCNIsectorsatthe nationallevel. Inthe literature,severalframeworksandmodellingapproacheshavebeen proposed fordescribing interdependenciesbetweenCNIs; seee.g.

Ouyang[8]andreferences therein.Forthepurpose ofthisstudy, theinoperabilityinput-output model(IIM) waschosen.TheIIMis aneconomictheory-basedapproachthatassumesthatthelevelof economicinterdependenciesbetweenCNIsectorsisalsorepresen- tativetotheflowofcommodities(goodsandservices),byphysical and/or cyberinterconnections[2,8],betweentheCNIsectors. The riskoffailure foraCNIandthecascadingeffectsfollowingaper- turbationthatistriggeredby,e.g.,anaccident,anaturaldisasteror

https://doi.org/10.1016/j.ijcip.2020.100405

1874-5482/© 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

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amaliciousattack,ismeasuredintermsofthesystem’sinoperabil- ity, whereinoperability isdefinedas “theinability ofthe system toperformitsintendednaturalorengineeredfunctions”[9].Thus, theinoperabilitymeasuresthenormalisedproductionlossgivenas theratioofunrealisedproductionwithrespecttothe“as-planned”

production level[9]. Byexploitingnationalinput-output (I-O) ac- counts for describing interconnections between different sectors, the IIMoffers an easy andintuitive model foranalysing interde- pendencies betweenCNIsectorsatthenationallevelfordifferent types of perturbations. The IIM is therefore useful for industry- level interdependencyanalysisof natural,accidental ordeliberate events [8],andhas beensuccessfully applied to casesrelated to, e.g.,terrorism[10,11],the impactofhigh-altitude electromagnetic pulse [12],blackouts [13], hurricanes [14]andcyber-attacks [15], as well asanalysing interdependencies betweenItaly’s economic sectors[16](seealsoref.[17]).

Inthisworkwehave,forthefirsttime,analysedchangesinin- terdependenciesbetweenNorway’smainlandindustrysectorsover thetimeperiod2012–2017.FollowingSetola’sstudyofItaly’s eco- nomic sectors [16], the demand-reduction IIM of Haimes et al.

[9,11]waschosen.Thetimeframewasselectedonthebasisofthe availabilityofcomparablenationalI-Oaccountsdata.Onthebasis ofthefindings,implicationsforthenationalsecurityofNorwayare discussed. Data fortheUnited Kingdom(UK) havebeenincluded forcomparison.

2. Methods

IIMforinterdependentinfrastructuresectorsisdescribedelse- where [9,11,18], so only brief details will be given. The Leontief input-outputmodelisgiveninEq.(1).Inthisformulation,xiisthe total production output ofindustry i, aij is theLeontief technical coefficient,i.e.theproportionofindustryi’sinputtojwithrespect to the “as-planned” total productionof j (xj), and ci is the final demandfori’soutput[9,11].

x=Ax+c

xi=

j

ai jxj+ ci

i (1)

In the demand-reduction IIM, Eq. (1) is transformed into Eq.(2)[9,11]:

q=Aq+cq= [IA]1c=Sc (2) Here,theinoperabilityq∈[0, 1]nisavectorspecifyingthenor- malisedproductionlossesforeachoftheninfrastructuresthatcan bepotentiallyrealisedafteraprolongeddemand-sideperturbation c[9,11].Aninoperabilityofqi=0meansthattheproductionout- putofi is“asplanned”,whileqi= 1impliesthat iis100%inop- erable [11].The n×n matrix A describes the interdependencies betweenindustry sectorsandrelatestotheLeontieftechnicalco- efficientsasgiveninEq.(3)[9,11]:

ai j=ai j

xj xi

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In order to quantify the role of each infrastructure sector, the dependency index(

δ

i) andthe influence gain (

ρ

j) have also been calculated. The dependency index is defined as given in Eq.(4)[19]:

δ

i= 1 n−1

n

j=i

ai j (4)

whiletheinfluencegainisdefinedas(Eq.(5))[19]:

ρ

j= 1 n−1

n

i=j

ai j (5)

The dependency index measures the exposure of the i-th in- frastructuresectortofailuresintheothersectors,whiletheinflu- encegainexpressesthej’sabilitytopropagateinoperabilitytothe othersectors.AsdiscussedbySetolaetal.[19],

δ

iand

ρ

jdoesnot take intoaccount second-orhigher-order dependencies.This can bedonebyevaluatingthenormalisedrowandcolumnsumofthe Smatrixcoefficientssince[19]:

S= [IA]1=I+A+A2+A3+· · · (6) Analogously to Eqs. (4) and (5), the overall dependency in- dex(

δ

overalli ) andinfluencegain (

ρ

overallj )are definedaccordingto

Eqs.(7)and(8),respectively[19]:

δ

ioverall= 1 n−1

n

j=i

si j (7)

ρ

overallj = 1 n−1

n

i=j

si j (8)

Bycomparingthe

δ

ioveralland

δ

i (orthe

ρ

overallj and

ρ

j)values, informationabouttheimportance ofsecond-andhigher-orderin- terdependenciescanbeobtained.Thevalueforthemaximumn-th order interdependency ofi can be calculated in accordancewith Eq.(9):

γ

i(n)=maxj

ai jn

i,j (9)

AccordingtoSetola etal.[19],

δ

overalli and

ρ

overallj expressesthe resilienceofthe i-thinfrastructuresectorandtheinfluencethatj exercisesontheentiresystem.However,giventhatresilienceisof- teninterpretedas“theabilityofthesystemtosustainorrestoreits basicfunctionalityfollowingarisksourceoranevent”[20],itcan bearguedthatamoresuitable,yetrelated,interpretationof

δ

overalli

isthatitexpressesthefragilityofithatisinducedbythemultiple interdependenciestoothersectors[2–4].Underthisinterpretation, alargevalueof

δ

overalli wouldimplythatiismorefragile(lessre-

silient) towards disruptionsofother sectorsthan asector with a low

δ

overallvalue.

Following Haimes etal. [9],the Leontief technicalcoefficients (ai j) were obtained from the Norwegian national accounts I-O tables for domestic use (industry-by-industry; ESA Questionnaire 1850)thatarepublishedbyStatisticsNorway(SSB)[21].According toSSB,theI-O tablesarederived fromthesupplyandusetables undertheassumption ofafixed productsalesstructure [21].The I-O tables consist of 64 different mainland industry sectorsthat representalldomesticproductionactivityexcepttheshippingand petroleumsectors.Theirdescriptionsandaccompanyingcodesare giveninref.[22](TableS1).Basedontheobtainedai jcoefficients, the A matrix wascalculated in accordance with Eq.(3) for the years2012–2017. Thistime frame wasselected becausecompara- bleI-O tables havebeenmade available by SSBover thisperiod.

Caveat:Forconfidentialityreasons,thedataforR19,R20 andR21 havebeenpresentedtogetherinthecolumnforR21inthedatasets providedbySSB.

3. Resultsanddiscussions 3.1. Dependencyandinfluence

As a first exploration ofthe datasets,

δ

i (Eq.(4)) values have beencalculated forthe differentsectorsforthe years2012–2017.

The

δ

i values for 2012 and 2017 are displayed in Fig. 1 (a plot of

δ

i(2017)

δ

i(2012) valuesis giveninref.[22],Fig.S1). Ofpar- ticular interest to CNIs in Norway [23], is “Products of agricul- ture, hunting andrelated services (R01)” since the sector relates to the security offood supply andit has a highdependency in- dex comparedto the other sectors. Taking 2012as thereference

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Fig. 1. Dependency indices for different Norwegian industry sectors for the years 2012 and 2017. A description of the different sectors is given in ref. [22] (Table S1).

Fig. 2. Influence gains for different Norwegian industry sectors for the years 2012 and 2017. A description of the different sectors is given in ref. [22] (Table S1).

year, a one-sample t-test on the

δ

R01 values from 2013 to 2017 showsthatthemean

δ

R01value(0.016)isdifferentfromthe2012 value (

δ

R01 = 0.017) (statistically significant with p = 0.015 for N=5and

α

=0.05).Furthermore,linearregressionshowsthatthe slope is significantly different from zero (

β

δ=−3.7×10−4, p= 0.04). Thus, R01’sdependency to other sectorshas declinedover the time period 2013–2017compared to 2012. If we look atthe

δ

overallR01 values,ontheotherhand,nosuchchangeisobserved.

Another industry of interest is “Services auxiliary to financial servicesandinsuranceservices(R66)” sincefinancialservicesisa CNI [23]. Here,we findthat the dependencyindexhas increased from0.006in2012to0.011in2017.Theslopeoftheincreasewas 7.3 × 104 (p = 0.01) (see also ref. [22], Fig. S1). No change is foundfor

δ

overallR66 overtheperiod2013–2017comparedtothe2012 value(0.018).

The

ρ

j (Eq. (5)) values forthe industry sectors for 2012 and 2017 are plotted in Fig. 2 (a plot of

ρ

j(2017)

ρ

j(2012) values is given inref. [22], Fig. S2). As can be seen, “Constructions and construction works(RF)” isthesectorthat exerciseslargestinflu- enceontheother sectors.LinearregressionshowsthatRFhasin- creaseditsinfluencegainfrom0.046in2012to0.056in2017with

β

ρ=3×104 (p = 0.009 for N = 5). The same trend is found for

ρ

RFoverall.Furthermore,the

ρ

RFoverallvaluesaresubstantiallylarger (0.114 for 2017 and 0.097 for 2012), implying that second- and

higher-order dependencies are of importance (see

γ

i(2) and

γ

i(3)

valuesinvolvingRFinref.[22],TableS2).

From Fig. 2, we also seethat the sector “Foodproducts, bev- erages andtobacco products (R10_12)” hasa large influencegain value(0.054and0.055for2012and2017,respectively).Nochange in influence gain was observed over the period 2012–2017 (ref.

[22], Fig. S2), neither for the

ρ

R10_12 nor the

ρ

R10overall_12 values. The largeinfluenceofR10_12inviewofthelargedependencyindexof R01,isofinterestintheperspectiveofsecurityoffoodsupplyand willbeinvestigatedinthefollowingofthispaper.

In a CNI perspective, it is interesting to note that the sector

“Publicadministrationanddefenceservices;compulsorysocialse- curity services(R84)” hasgainedinfluence overtheperiodinves- tigated.From 2012to 2017,

ρ

R84 hasincreasedfrom0.016 (0.028) for2012to0.022(0.037)for2017with

β

ρ=1.4×103(p= 0.02 forN=5);the

ρ

R84overallvaluesaregiveninparenthesis.

3.2. Changesininoperability

In order to gain insight into the interdependencies between Norwegian infrastructure sectors, inoperabilities associated with perturbationsofsectorsofinterest havebeencalculated (Eq.(2)).

Thelistofperturbedsectorstobeinvestigated,wasselectedonthe basisofthe sectors’dependencyindexandinfluencegain aswell

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Table 1

List of perturbed Norwegian industry sectors for domestic use of products.

Code Industry sector

R01 Products of agriculture, hunting and related services R10_12 Food products, beverages and tobacco products RD Electricity, gas, steam and air-conditioning RF Constructions and construction works

R49 Land transport services and transport services via pipelines R50 Water transport services

R51 Air transport services R61 Telecommunications services

R64 Financial services, except insurance and pension funding R84 Public administration and defence services; compulsory

social security services R86 Human health services

as their relevance to Norwegian CNIs [23]. From this, 11 sectors wereselected(Table1).Thesesectorsarerelatedtomanufactureof foodstuff, electricitysupply,telecommunicationsservices,financial services,transport services,humanhealth services,publicadmin- istration anddefenceservices,andconstructionsandconstruction works.Supplyofwaterwasexcluded fromthisstudyonthebasis ofsmall

δ

iand

ρ

jvaluesfortheR36sector(“Naturalwater;water treatmentandsupplyservices).

Since thepurposeofthisworkistoinvestigatehowtheinter- dependencies mayhavechanged from2012to 2017, thesector k selectedforexperimentationwasperturbedbyanotional10%de- mandreduction(ck=0.1).Onlyone sectorwasperturbed ineach experiment (ci

=k=0.0).The demand reductioncan be causedby, e.g.,failures,accidents, natural hazardsormalicious actslike ter- rorism [10–15]. The main resultsfromthe experiments are sum- marisedinTable2anddiscussedinthefollowing.Additionaldata fromtheexperimentsareprovidedinref.[22](Fig.S3).

3.2.1. Manufactureoffoodstuff

Theinoperabilitiescausedbyanotional10%demandreduction for sector R10_12 (“Food products etc.”; cR10_12=0.1) are sum- marisedin Table2.Some notableeffects canbe observed.Firstly, theinoperabilityofR10_12isamplifiedfrom0.1to0.13.Secondly, R01 (“Productsofagriculture etc.”) ishighly affectedwith an in- operabilityof0.12.Thatis,theinoperabilityofR01isofthesame orderofmagnitudeastheinitially perturbed sector(R10_12) due to cascadingeffects.Thiscan beunderstoodintermsofthelarge

γ

i(1),

γ

i(2) and

γ

i(3) valuesbetweenR01andR10_12(ref.[22],Ta-

bleS2).Thirdly,thesector“Fishandotherfishing products;aqua- culture products; support services to fishing (R03)” is also sub- stantially affectedwithan inoperabilityof0.04. Ifwelookatthe change in inoperability (qi=qiqi(2012)) for the sectors R01,

R03andR10_12overtheyears2013–2017relativeto2012,nosig- nificantchangeisobserved(ref.[22],Fig.S4).

IftheR01sectorisperturbedbyanotional10%demandreduc- tion(cR01=0.1),theinoperabilityofR10_12isonlyaround0.005 whiletheinoperabilityofR01isaround0.11(Table2).Therehas, however,beenaslightyetstatisticallysignificantdeclineinqR01

(slope

β

q =−2.4× 104;p= 0.005forN= 5)andforqR10_12

(

β

q =−1.5×104;p=0.04)overtheyears2013–2017compared to2012(ref.[22],Fig.S4).Thus,bothR01andR10_12havebecome lessfragiletowardsdisruptionsoftheR01sector.

3.2.2. Electricity,gas,steamandairconditioningsupply

In Norway, production and distribution of electricity are the principal parts of the sector “Electricity, gas, steam and air- conditioning (RD)”.As can be seen fromTable 2, the inoperabil- ityof RD following a notional10% demand reduction (cRD=0.1) is0.104whichimpliesthatRDisonlyslightlyaffectedbyinterde- pendenciestoothersectors(the

γ

RD(n)valuesaresmall;seeref.[22], TableS2). Furthermore,theimpactonothersectorsisalsolimited withinoperabilityvaluesbeing0.002orless.

Therehasbeena small,yet statisticallysignificant dropinthe meanqRD (qRD=−6.7×104;p =0.003 forN = 5)over the period 2013–2017 compared to 2012. However, linear regression showsthat the slope is not significantly different fromzero (ref.

[22], Fig.S4). Furthermore,the dependencyindex forRDhas not changed significantly over the time period. It is therefore to be seenwhetherRDhasbecomelessfragiletowardscascadingeffects.

3.2.3. Telecommunicationsservices

Turning to the telecommunications services sector (R61), qR61 causedbyanotional10%demandreduction(cR61=0.1)was0.128 fortheyear2017(0.139in2012).R61hasaquitelargefirst-order self-dependency (

γ

R61(1)=0.22 [22]), which explainsthe amplifica- tionoftheinoperabilityforR61.Bycomparingthe

δ

R61(0.005)and

δ

R61overall(0.014)values,theinoperabilityforR61isalsosubstantially affected by second- and higher-order dependenciesto other sec- tors.Furthermore,theinoperabilityofR61hasalsoaconsiderable impactonthesectorsR58(“Publishingservices”)andR73(“Adver- tisingandmarketresearchservices”);seeTable2.

Ifwelookatthetrendovertheyears2013–2017comparedto 2012,qR61hassignificantlydeclined(

β

q=−3×103;p=0.027 forN=5;seeref.[22],Fig.S4).AdeclineinqR73isalsoobserved (

β

q=−4×10−4;p=0.004).Nosignificantchangeisobservedfor R58.

3.2.4. Financialservices

Theinoperabilitiescausedbyanotional10%demandreduction for the sector “Financial services, except insurance and pension

Table 2

Inoperabilities ( q k) for different Norwegian industry sectors that are caused by a notional 10% demand reduction for the sectors, together with cascading effects to other sectors (year 2017) a.

Perturbed sector ( k ) Inoperability perturbed sector ( q k) Cascading effects to other sectors ( q i=k)

Most affected bsector Second-most affected sector b All other sectors

R10_12 0.130 R01 (0.115) R03 (0.04) < 0.02

R01 0.106 R10_12 (0.0042) R02 (0.0036) < 0.0035

RD 0.104 R73 (0.0025) R53 (0.0022) < 0.0022

R61 0.128 R58 (0.006) R73 (0.005) < 0.004

R64 0.110 R66 (0.043) R62_63 (0.008) < 0.008

R49 0.105 R77 (0.008) R33 (0.007) < 0.005

R50 0.106 R52 (0.016) R65 (0.011) < 0.008

R51 0.101 R52 (0.007) R77 (0.005) < 0.004

R86 0.100 R96 (0.006) R62_63 (0.004) < 0.003

R84 0.101 R95 (0.028) R49 (0.017) < 0.01

RF 0.129 R16 (0.101) R23 (0.071) < 0.04

a See ref. [22] (Table S1) for a description of the sectors.

bInoperabilities are given in parenthesis.

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funding (R64)” (cR64=0.1) for the year 2017 are summarised in Table2.Severalimpactscanbe observed.Firstly, theinoperability ofR64isamplifiedto0.11.Secondly,thesector“Servicesauxiliary to financialservicesandinsuranceservices(R66)” issubstantially affected with an inoperability of 0.04. Lastly, the sectors “Postal andcourierservices(R53)”,“Publishingservices(R58)”,“Computer programming, consultancy and related services; information ser- vices (R62_62)” and R73 all suffer inoperabilities in the order of 0.006−0.008.

When it comes to changes in inoperabilities over the years 2013–2017comparedto2012,one-samplet-testsshowthatseveral qivaluesaresignificantlydifferentfromzero:qihasincreased for R53 (qR53=0.0012, p=0.003), R58 (qR58=0.0012, p= 0.029), R62_63 (qR62_63=0.0029, p=0.006), R64 (qR64= 0.0022, p=0.003) and R73 (qR73=0.0014, p=0.008). The qR66 value is not differentfromzeroover the years2013–2017, butqR66=−0.011over theyears2014–2017 (p< 0.001,N =4) (seeref.[22]fordetails).

3.2.5. Transportservices

The effects of a notional 10% demand reduction for the sec- tors “Landtransport services andtransport services via pipelines (R49)”,“Watertransportservices(R50)” and“Airtransportservices (R51)” aresummarised inTable2(year2017). Ofthethree trans- port services, disruption of R50 has the greatest impact on the other sectors,followedbyR49.AscanbeseeninTable2,thedis- ruption ofR50 causes inoperabilities ofaround 0.02and0.01 for the sectors“Warehousing andsupport services fortransportation (R52)” and “Insurance,reinsurance andpension fundingservices, exceptcompulsorysocialsecurity(R65)”,respectively.

Data on changesin inoperabilitiesforthe threetransport sec- tors R49, R50andR51 over theyears 2013–2017relativeto 2012 are given in ref. [22] (Fig. S4). Only a few significant changes are observed for the sectors that are substantially affected by the perturbation. Starting with the perturbation of R49 experi- ment,one-samplet-testshowsthatqR45 forthesector “Whole- sale and retail trade and repair services of motor vehicles and motorcycles (R45)” is lower comparedto the qR45 value for 2012 (qR45=−5.3×10−4, p=0.009). If we look at the R51 exper- iment, qR77=4.7×10−3 (p=0.02) for the sector “Rental and leasingservices(R77)”.Nosignificantchangesareobservedforthe R50experiment.

3.2.6. Humanhealthservices

Anotional10%demandreductioninthesector“Humanhealth services (R86)” does not yield a substantial amplificationof qR86 because ofsmallinterdependenciesto othersectors(ref. [22],Ta- ble S2). Furthermore,only very smallinoperabilities are induced in other sectors(Table2). The sector that isaffected themost is

“Otherpersonalservices(R96)”,sufferinganinoperabilityof0.006 (year 2017).When itcomestochanges ininoperabilitiesoverthe period2013–2017, qR96 hasdropped from0.012 in2012toanav- eragevalueof0.006from2015onwardsto2017(ref.[22],Fig.S4).

NosignificantchangeininoperabilityforR86isseenfrom2012to 2017.

3.2.7. Publicadministrationanddefenceservices

Several effects are seen following a notional 10% demand re- duction inthesector“Publicadministrationanddefenceservices;

compulsory socialsecurity services(R84)” for2017 (Table 2).The sector thatsuffersthe greatestimpactduetocascadingeffects,is

“Repair services ofcomputers andpersonal andhouseholdgoods (R95)” with qR95 = 0.028, followed by R49 (qR49 = 0.017) and R66 (qR66 = 0.01). Impacts on other sectors of interest include:

RD (qRD = 0.007), R36 (qR36 = 0.008), RF (qRF = 0.006), R53 (qR53=0.007)and“Securityandinvestigationservices;servicesto

buildings andlandscape; officeadministrative, officesupport and otherbusinesssupportservices(R80_82)” (qR80_82 =0.009).

Dataonchanges intheinoperabilitiesfortheabovementioned sectors over the period 2013–2017 compared to 2012 values are reported in ref. [22] (Fig. S4). First of all, qR36 has reduced slightly over the period (qR36=−5.0×10−4, p=0.009). The sectors R53, R66, R80_82 and R95 have become more affected by cascading effects following the perturbation of the R84 sec- tor with

β

q(R53)=6.6×104 (p = 0.027),

β

q(R66)=1.0×103 (p =0.045),

β

q(R80_82)=3.5×10−4 (p< 0.001)and

β

q(R95)= 3.8×103(p=0.009).ForthesectorsRD,RF,R49andR84nosig- nificantchangesareobserved,buttheinoperabilityofR49changed substantiallyfrom0.0023in2016 to0.017in 2017.Itisyetto be seenifthistrendcontinues.

3.2.8. Constructionsandconstructionworks

Aspreviouslydiscussed,RFisthesectorwiththelargestinflu- encegain.Thecascadingeffectsfollowinganotional10% demand reductioninRFhavesubstantialimpactsonanumberofothersec- tors(Table2).Mostnotablyarethesectors“Woodandofproducts ofwoodandcork, exceptfurniture;articlesof strawandplaiting materials (R16)” and“Othernon-metallicmineralproducts (R23)”

with inoperabilities of 0.101 and 0.07, respectively. Other sectors that experience qi > 0.02 are [22]: “Products of forestry, log- gingandrelatedservices(R02)” (qR02 =0.03); “Rubberandplas- tics products (R22)” (qR22 = 0.037); “Electrical equipment (R27)”

(qR27 = 0.028); “Architecturaland engineeringservices; technical testingandanalysis services(R71)” (qR71 = 0.029); “Employment services(R78)” (qR78=0.033).DuetoRF’sself-dependencyaswell asitsdependenciestoothersectors,theinoperabilityofRFisam- plifiedto0.129.

The changes in inoperabilities for the sectors with qi > 0.02 are reportedin ref.[22] (Fig. S4)andsummarised in thefollow- ing.Starting withR02,qR02 dropped from0.047in2013to0.032 in 2014. From 2014 onwards to 2017, the R02 sector is less af- fectedby thecascading effectsfrom the perturbation ofRF with qR02 = −0.012 (p = 0.001) compared to the 2012 value. The qR16 andqR78 valueshaveincreasedby 0.009(p=0.009)and 0.008 (p = 0.024), respectively, while no significant changes are observed forR22 andR27 over the period2012–2017. Linear re- gressionsoftheqR23 andqR71valuesshowthat bothR23and R71are becoming more affectedby the perturbation ofRF; both sectorswithaslopeof

β

q=3×10−3 (p<0.02).

3.3. Effectsofperturbationstomultiplesectors

The sectors R01, R03 and R10_12 were selected for experi- mentation in order to investigate the effects of perturbations to multiplesectors. R01andR10_12werechosen becausethey have largedependencyindexandinfluencegainvalues,respectively.In addition, both R01 and R03 are highly dependant upon R10_12 (ref. [22], Table S2). Obviously, the inoperabilities for the dif- ferent sectors will increase if the c values increase. We have therefore kept ctot=

ici constant in the different experiments, whilevaryingthecivalues.Eightdifferentexperimentswere car- ried out where R01, R03 and R10_12 were perturbed by ci

{

0.0, 0.01, 0.025, 0.04, 0.05, 0.10

}

,while maintainingctot=0.1. Asametricforthetotalimpactoftheperturbationsonallsectors, wehaveusedqtot=

iqi.The I-Otablefor2017wasusedinthe experiments.

The results fromthe experiments are summarised in Table 3. IfonlyR01is perturbed (experiment1),R01 suffersa substantial inoperability, but qtot is the lowest for all experiments. On the other hand,ifR10_12isperturbed bya notional10% demandre- duction(experiment3),bothqR01andqtothavethelargestvalues forall experimentsinvestigated.The experiments1 and3clearly

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Table 3

Inoperabilities ( q k) resulting from perturbations ( c ) of the Norwegian R01, R03 and R10_12 sectors for domestic use (2017 data) a.

Experiment c R01 c R03 c R10_12 q R01 q R03 q R10_12 q tot

#1 0.1 0.0 0.0 0.106 0.001 0.004 0.144

#2 0.0 0.1 0.0 0.011 0.116 0.012 0.213

#3 0.0 0.0 0.1 0.115 0.044 0.130 0.478

#4 0.05 0.05 0.0 0.059 0.059 0.008 0.178

#5 0.05 0.04 0.01 0.069 0.051 0.020 0.205

#6 0.05 0.025 0.025 0.085 0.041 0.038 0.244

#7 0.05 0.01 0.04 0.100 0.030 0.055 0.284

#8 0.05 0.0 0.05 0.111 0.023 0.067 0.311

a See ref. [22] (Table S1) for a description of the sectors.

demonstratethe differenceifa sector withhighinfluence gainis perturbed vs. a sector with a large dependency index. The same trendisobservedinexperiments4–8;themorethehigh-influence sector R10_12 is perturbed, the higher is the total inoperability of the whole system compared to experiment 1. However, qR01 was lower in the experiments 4–7 where cR01=0.05, than in

experiment 1 where cR01=0.1. Similar results are observed for perturbationsof,e.g.,RDandR61(resultsnotshown).

3.4. ComparisontoUnitedKingdom

UKwaschosen asthecountrytocomparewithforthefollow- ingreasons:Firstly,UKisoneofNorway’smostimportanttrading partners. Secondly,both countriesbeing NATOmembers, Norway andUK have a long-lastingdefence andnational security collab- oration.Thirdly,comparableinput-output tables fordomestic use areavailableforthetwocountries.Lastly,itisofinteresttocom- pareNorwayasasmallEuropeancountrywithanopen economy tothesecondlargesteconomyinEuropeintermsofGrossDomes- ticProduct(GDP).TheUK2016input-outputtablefordomesticuse wasusedintheanalysis[24].

Dependency indices (Eq.(4)) and influence gains(Eq.(5)) for thedifferent UK industry sectorsforthe year2016 are shownin Figs.3a andb,respectively.Norwegian 2016valueshavebeenin- cluded in the plots for comparison. The UK sectors with largest

δ

ivalue areR02(0.0145),“Repair andinstallation servicesofma- chineryandequipment(R33)” (0.0142)andR23(0.0137). Whenit

Fig. 3. Dependency indices (a) and influence gains (b) for Norwegian and UK industry sectors for the year 2016. A description of the different sectors is given in ref.

[22] (Table S1).

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comestoinfluencegain,theUKsectorsRF(0.047),R10_12(0.024),

“Wholesale tradeservices,exceptofmotorvehicles andmotorcy- cles (R46)” (0.021) andR84 (0.021) exercise largest influence on the othersectors. Afew notabledifferencesbetweenNorwayand UKcanbeseen.TheNorwegiansectorsR01andR66havelarger

δ

i

valuesthan inUK.Ontheoppositeside,the sectorsR02 andR24 (“Basicmetals”) in particular,havelarger

δ

i valuesinUK than in Norway.Ifwelookattheinfluencegain,RB(“Miningandquarry- ing”)exerciseslargerinfluenceinNorwaythanintheUK,whileRD andR86havesubstantiallylargerinfluencegainsintheUKthanin Norway.

Wehavealsocomparedtheinoperabilitiesfollowinganotional 10% demand reduction for the sectors enlisted in Table 1 (year 2016).SelectedresultswheresubstantialdifferencesbetweenNor- way and UK are found, are shown in Fig. 4a-e (the rest of the results are given in ref. [22]). Starting with the perturbation of R10_12,weseeinFig.4athattheinoperabilityofR01inNorwayis morethantwotimeslargerthanintheUK.Thisdifferencecanbe understood in termsof the

γ

R01(n) values forNorway andUK; R01 has a much larger first-order dependency on R10_12 in Norway (0.89) than inthe UK (0.39) [22]. Thisis also reflected indiffer- encesinexportsofproductsofagricultureforNorwayandtheUK, wherethefractionofexportsofproductsfromR01intheUK(rel- ativetothetotalexportsfromallsectors)isanorderofmagnitude largerthan thecorrespondingvaluefortheNorwegianR01sector [21,24].

Thesecondcasewheresubstantialdifferencesareseenbetween Norway and the UK, is perturbation of RD. As can be seen in Fig.4b,thecascadingeffectsfollowinganotional10% demandre- ductionforRDareminorinNorway,butsevereintheUK.Firstand foremost,weseethattheinoperabilityofRDinitsselfisamplified to0.203.Moreover,R02,RBandR33sufferinoperabilitiesof0.109, 0.04and0.026,respectively.Ifwecomparethe

γ

RD(n)valuesforNor- wayandtheUK,some notabledifferencesare seen(ref.[22];Ta- blesS2andS3,respectively).RDinNorwayhasasmallfirst-order interdependency withR24(0.08) andsecond-andthird-order in- terdependencieswithRFintheorderof0.03and0.01,respectively.

RDinUK,ontheother hand,hasstrongfirst-,second-andthird- orderself-dependencieswithvaluesof0.51,0.26and0.13,respec- tively.InNorway,productionanddistributionofelectricityarethe principal parts ofRD, whilethe useof gasis muchmore impor- tant in the UK [25]. Furthermore, electricity-intensive industries inNorway havefavourablelong-termelectricity contractsandre- ceivegovernmental supporttoinvestinenergy-efficient technolo- gies[26].

DifferencesbetweenNorwayandtheUKarealsoseenforper- turbation of R64 (Fig. 4c). Most noticeable is that R66 is much more dependant upon R64 inNorway than in theUK withfirst- orderinterdependenciesof0.38and0.06,respectively,andinoper- abilitiesof 0.044and0.008.However, ifwe lookatthetotal im- pactonallsectors,qtotisinfactslightlylargerforUK(0.25)than forNorway(0.22).

As seen inFig.4d, manufactureof basicpharmaceuticalprod- uctsandpharmaceuticalpreparations(R21)intheUKismorethan eighttimesmoreaffectedbyperturbationinR86thaninNorway.

This is causedby the strong first-orderdependency betweenthe pharmaceuticalindustry andthe human healthservices sectorin the UK [22]. Norway, on the other hand,is heavily reliant upon imports of pharmaceuticals.Furthermore,a notional10% demand reduction for R86 gives a higher qtot value in UK (0.29) than in Norway(0.17).

Thelastcasewheresubstantialdifferencesareobserved,isdis- ruptionofRF(Fig.4e).Firstly,anotional10%demandreductionfor RF hasa substantialimpactonboththeUKandNorwaywithqtot

values of 0.74 and0.82, respectively. Secondly, sectors relatedto non-metallicmineralproducts(R23),basicmetals(R24)andelec-

trical equipment (R27)are more affected inthe UK than inNor- way(

|

q

|

>0.02).Lastly,manufactureofwoodandwoodproducts (R16)andemploymentservices(R78)aremoreaffectedinNorway thanintheUK(

|

q

|

>0.02).

3.5. ImplicationsforthenationalsecurityofNorway

Inorderto assesstheimplications forthenational securityof Norway,impactsintermsoftotaleconomiclosses(

δ

xtot)havealso

beencalculatedfromEq.(10)[11]:

δ

xtot=

i

qixi

i (10)

wheretheeconomic lossofsectori(

δ

xi)istheproductofthein- operabilityofsectori (qi)(triggeredbythe perturbationofsector k)andits“as-planned” production(xi).

ThetotaleconomiclossesforNorwayfollowinga notional10%

demand reduction for the sectors enlisted in Table 1, are sum- marisedinFig.5a(theqtotvaluesareshowninFig.5b).Thetotal economic lossesare by far the largestforperturbation of theRF sector (cRF=0.1),which amountedto morethan 110billion Nor- wegiankroner(NOK)forthe2017data.Thenextsectorsthattrig- gerlargeeconomiclossesareR84andR10_12with

δ

xtotvaluesin

the order of 50 billion NOK. Of the investigated sectors,

δ

xtot is

smallestfortheperturbationoftheR51sector(6.7billionNOK).If we comparetotheUK, we findagainthatRF triggers thelargest

δ

xtotvalue[22].

Onthebasis ofthefindings inthiswork, afew commentson theimplicationsforNorway’snationalsecuritycanbemade.Since 2000thesocietaldependencyonCNIserviceslikeelectricitysup- ply,telecommunicationsservicesandfinancialserviceshasgained increasedfocus inNorway andelsewhere. Theneed forreducing vulnerabilities in thesesectors has therefore been highlighted in severalcommissions on criticalinfrastructure security in Norway [27,28].Indeed,thisstudyfinds thatthecascadingeffects follow- ingadisruptioninelectricitysupply(theRDsector)orintelecom- municationsservices(the R61sector)havenotincreasedoverthe years 2013–2017compared to2012, neitherwith respectto

δ

xtot

or qtot (Fig. 5a and 5b, respectively). However, as mentioned in Section3.2.2fortheRDsector,itisyettobeseenifthissituation continues.Informationbeyond2017aboutcascadingeffectsfollow- ing disruption of the RD or the R61sectors is therefore needed.

Whenitcomestofinancial services(R64),adeclineinqtotvalues followingdisruptionoftheR64sectorisobservedforthetimepe- riodinvestigated(Fig.5b).Despitethisdecline,thetotaleconomic lossfollowingdisruptionoftheR64sectorhasincreasedoverthe sametimeperiod(Fig.5a).Efforts toimprovetheresilienceoffi- nancialservicesandtominimisecascadingeffectsshouldtherefore continue.

Moving to the RF sector, this sector is not defined as a CNI sector in Norway [23], in the UK [29] or in the United States (US)[30].In ordertoassesstheimpact ofperturbationofthe RF sectoronnationalsecurity,itisofusetorevisit thedefinitionfor criticalinfrastructure.Acknowledgingthatseveraldefinitionsexist, itishelpfulforthisworktousetheUKdefinition:“Thosecritical elementsofInfrastructure(facilities,systems,sites,property,infor- mation,people, networksandprocesses),the lossorcompromise ofwhich would resultinmajor detrimental impact on the avail- ability,deliveryorintegrityofessentialservices,leadingtosevere economic or social consequences or to loss of life” [29]. Thus, CNInotonlyincludes,e.g.,facilities,systemsandinformation,but also the essential CNI workers. Although RF is not a CNI sector in itself, it is an underpinning function for the construction and maintenance of CNIs. Construction workers have therefore been included in the list of essential critical infrastructure workers in the US related to the COVID-19 response [31]. However, this is

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Fig. 4. Comparison of inoperabilities in Norway and United Kingdom (UK) that are caused by a notional 10% demand reduction for the sectors (year 2016): (a) R10_12, (b) RD, (c) R64, (d) R86 and (e) RF.

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Fig. 5. (a) Total economic losses and (b) cumulative inoperabilities ( q tot) for all sectors following a notional 10% demand reduction for the Norwegian industry sectors RF, R84, R10_12, R86, R64, R50, R49, R61, RD, R01 and R51 (see Table 1 for a description).

not the caseforNorway [32], whichis likelyrelatedto how CNI sectorsare identifiedinNorway [23].Withincreasing digitisation and automation of the construction industry [33,34], there is a need formoreknowledge onhowthiswillaffecttheinterdepen- denciesbetweentheconstruction industryandother sectors, and the potential vulnerabilitiesthat follows.There isalso aneed for more informationontheimportance oftheconstruction industry and construction workers for maintaining CNIs during crises, to betterinformcivilcontingencyplanning.

Lastly, the food supply chain is vulnerable to a multitude of threats and hazards [35–37]. Contamination of the food supply chain oroutbreaks in the agricultural sector can not only cause productionlossesandreducedexports,butalsotemporalchanges inconsumers’demandfortheaffectedproducts[38,39].Thus,pre- viousEuropeanincidentsthathaveaffectedthefoodsupplychain,

havenotonlyhadsignificanteconomicimpactonthefoodindus- try, but also led to consumers’ questioning the food safety [36]. AlthoughfooddefencehasgainedincreasedawarenessinEurope, thereare still shortcomingswithrespectto incorporationoffood defence principlesin legal frameworks[37] aswell astools and methodsforensuringfoodsupplychainintegrity[36].Inaddition, foodavailability,access,utilisationandstabilitymaybeaffectedby climate change[35,40]. Giventhe significant impact triggered by disruptionoftheNorwegianfoodindustry,alsotakingintoaccount thatthefoodindustryisthelargestmainlandindustryinNorway, enhancingtheresilienceofthefoodindustryshouldcontinue.Fur- thermore,giventhatNorwayisanetimporterofagriculturalprod- uctsandthatthevastmajorityofNorway’sagriculturalproduction isconsumeddomesticallywithverylittleexports[41],thefragility oftheagriculturalsectorshouldcontinuetobereduced.

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3.6. Limitations

Mostofthe limitationstothisstudypertainto theapplicabil- ityoftheIIMitself[42,43];themainlimitationbeingtheassump- tionthateconomicchangeisrepresentativefortheinterdependen- cies betweenthe industrysectors(eq.(3)). Still,economicfactors are importantbecause such factors play a major role in shaping theoperatingenvironmentofCNIs[2].Secondly,theIIMonlycov- ersparts ofthe sixdimensionsproposed by Rinaldiet al.[2]for analysing infrastructureinterdependencies.GiventhattheIIMap- plied in this work is a static, linear model, temporal and non- linear behaviours are for example not addressed. However, since the purpose ofthis work is togain insightinto interdependency changes over the period 2012–2017, the use of a static modelis considered sufficient. Furthermore,asargued by Kelly[42],large, widespread disasters maychange the underlyingstructure ofthe economyandconsequentlyalsothetechnicalcoefficients.Toavoid problemsassociatedwithlargeperturbations,theupperlimitofc has beenrestrictedto a maximumof10% as usedin other stud- ies [11,16].Thisleads, however,toother limitations.Inparticular, theeffectsof,e.g.,large-scalepoweroutagesorlossoftelecommu- nication services are not properlyaddressed inthis study.Lastly, infrastructuredisruptionstypicallyoccuronthesupply-sideofthe economy[42],whichinthedemand-reduction IIMismodelledas aforceddemand-reductionwithimpactscascadingtoothersectors bybackwardslinkages[42,43].However,asarguedbyOosterhaven [43], the use of the supply-driven IIM is more problematicthan the demand-reductionIIM. Thedemand-reduction IIMwasthere- fore applied inthis work, alsotaking intoconsideration that the public’s securityconcernsrelatedto,e.g.,terrorismmaycausede- mandperturbations[11,44].

Onthebasisoftheselimitations,careshouldbeexercisedwhen interpretingtheresults.FollowingargumentsbyOosterhaven[43], the results cannot be used to prioritise CNI resilience initiatives at the national level, nor can the results be used to assess the widereconomicimpactsafterCNIdisruptions.Theresultsdo,how- ever,provideinsightintotheinterdependencytrendsforNorway’s mainlandindustry sectorsinviewofnationalsecurity. Theresults canalsoinformresearchers,stakeholdersandpolicymakersonCNI sectorsthatshouldreceivemoreattentioninfuturestudies.

4. Conclusions

Forthe first time,changes ininterdependencies betweenNor- way’s mainland industry sectors havebeen analysed in terms of thedemand-reductioninoperabilityinput-outputmodel[9,11].The timeperiod2012–2017wasselectedonthebasisoftheavailability ofcomparablenationalI-Oaccountsdata.

The sectors RF (constructions and construction works) and R10_12(manufactureoffoodproducts)areveryimportantindustry sectorsformainlandNorway.Becauseofthelargeinfluencethese sector exercise onother sectors,disruptionsofRF orR10_12may have significant effects on the national security of Norway. Nor- way’sagriculturalsector, inparticular,isvery fragiletowardsdis- ruptions tothe foodindustry.Furthermore, theRF sector has in- creaseditsinfluencegainfrom2012to2017.

The inoperability of the telecommunication services sector (R61) has significantly declined over the years 2013–2017 com- paredto2012.Financialservices(R64),ontheotherhand,hasbe- come more fragile towards cascadingeffects over the same time period.Forthe electricitysupplysector (RD),onlyminorchanges areobserved.

If we look at land (R49), water (R50) andair (R51) transport services,disruptionofwatertransportserviceshasthegreatestim- pactontheothersectorsfollowedbylandtransportservices.Only minorchangesininoperabilitiesareobservedfrom2012to2017.

Perturbation of public administration and defence services (R84)hassubstantialimpact onmanyoftheother sectors. Inad- dition,severalsectorshavebecomemoreaffectedbytheperturba- tionofthe R84sector overthetime period2012–2017, whilethe inoperabilities ofRD, RF,R49 andR84 haveremainedunchanged over the sametime period. Ifwe look at perturbationof human healthservices(R86),nosignificantchangesareseenfrom2012to 2017.

On the basis of the results in this work, it is recommended to gain more knowledge about the importance of the construc- tionindustry andconstruction workersformaintainingCNIsdur- ing crises. In addition, with increasing digitisation and automa- tionoftheconstructionindustry [33,34],thereisaneedformore knowledgeonhowthiswillaffecttheinterdependenciesbetween theconstructionindustryandothersectors,andthepotentialvul- nerabilitiesthat follows.Norwayshouldalsocontinueto enhance theresilienceofitsagricultureandfoodindustry.

DeclarationofCompetingInterest None.

Acknowledgements

This work wasfunded by the Norwegian Ministry of Defence throughprojectgrant1539.

Supplementarymaterials

Supplementary material associated with this article can be found,intheonlineversion,atdoi:10.1016/j.ijcip.2020.100405. References

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[2] S.M. Rinaldi , J.P. Peerenboom , T.K. Kelly , Identifying, understanding, and an- alyzing critical infrastructure interdependencies, IEEE Control Syst. Mag. 21 (2001) 11–25 .

[3] S.E. Chang , Infrastructure resilience to disasters, Bridge (Kans City) 39 (2009) 36–41 .

[4] A. Vespignani , The fragility of interdependency, Nature 464 (2010) 984–985 . [5] E.J. Oughton, W. Usher, P. Tyler, J.W. Hall, Infrastructure as a complex adaptive

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