Mathematical Methods and Tools in Water Resources Management

Including Some Environmental Problems

Krasimira Nikolova, Institute of Water Problems, BAS

Nikolay Kirov, Institute of Mathematics and Informatics, BAS

Irena Ilcheva, Institute of Water Problems, BAS

1.4 billion people live around river basins where current water usage is in conflict with environmental requirements

The basic dilemma is how to provide water for human needs in the face of increasing population pressures and the environmental needs of water. If water is reserved in some way for the environment, the availability of water for human usage is reduced.

Many regions in the world are in state of water stress because of scarcity of water resources

• Water availability is projected to increase in northern regions of Europe.

• Southern and southeastern parts of Europe, which already suffer from water stress, could experience reductions in water resources due to increased frequency and intensity of droughts.

The global climatic changes – the increase of frequency and intensity of extreme phenomena such as floods and droughts hardens the problems.

• The EU Floods Directive• The Water Scarcity and Droughts EU Policy as well as

the EC’s White Paper on Adaptation

The main objectives of WFD are: • Provision of enough water resources for satisfaction of the basic human needs• Minimizing the negative effects on the ecological river runoff and groundwater resources• Minimizing the negative effects on economics

The Water Framework Directive (WFD) establishes a legal framework to protect and restore the water environment across Europe and to ensure the long-term sustainability

of water usage

Several existing EU policies and initiatives contribute to the efforts for adaptation to climate change with regard to water issues such as:

Peculiarities of the water resource systems• Water resource systems (WRS) are the tool through which the river runoff has been used and

managed. They consist of one or more reservoirs as water sources and many hydraulic structures such as dams, canals, tunnels, irrigation systems (IRS), hydropower plants (HPP), water supply systems, etc. Their water resources are used to satisfy multiple objectives – irrigation water demand, industrial demand, drinking and municipal water demand, hydropower production, low flow augmentation, recreation, fishery demand, provision of minimum river flow needed for ecosystems. So a great number of these objectives – natural, engineering, social, ecological, etc. – have stochastic nature like river runoff. Others are not commensurable, often not quantifiable and some have conflicting demands to the water use.

• WRS are complex systems with stochastic and dynamic character and include a great number of mutually joined and interacted elements. The main difficulty in the process of WRS operation and planning is to obtain determinate rules for their management because some water demands and river runoff are random variables. This makes the mathematical description and modeling a difficult task which can be solved by the successfully application of probability theory and statistics, mathematical programming, simulation technique and multiple-objective optimization.

• Water demand increase

• The available water resources decrease

• The conflicts become deeper:

- between the priority water user – drinking water supply and ecological needs;

- between water users located in the upper and lower parts of the river basins;

- between river basins from which water is taken and other basins where water is transferred.

The conflict for water usage deepens

The management of water resource systems (WRS) represents a key element in achieving the balance between social-economic and ecological objectives of water usage.

• In this report are presented some mathematical models and tools for assessment and analysis of WRS developed in the Institute of Water Problems and the Institute of Mathematics and Informatics.

• The study is connected with the WFD implementation. The results are obtained from water resource balances (WRB) for two real WRS in Bulgaria with the use of multiple-objective optimization and simulation technique. These two methods are applied: on local level where separate WRS are considered, and on global level where WRS are in the scope of the whole river basin.

Multiple objective optimization application

The numerous objectives in water management are: - hydropower generation, - recreation, - regional development, - irrigation, - environmental conservation, - pollution control, - wild life preservation, - flood control, - fishing opportunities, etc.

but are also: - competitive, non commensurable and often non quantifiable

A reasonable compromise decision should be found. Multiple criteria decision making is an appropriate technique to

identify the trade-offs among the conflicting objectives and to choose the best possible solution.

Николай напиши нещо за SWTM

Case study – mathematical model of WRS “Koprinka” based on SWT

method • The WRS “Koprinka” is created on the river Tundja and includes the res. “Koprinka”, two HPPs, two IRSs –

IRS “St. Zagora” and IRS “Kazanluk”. It is necessary to satisfy the irrigation water demand and industrial water demand to produce maximum electricity and to provide the ecological flow in the river after the dam.

• A contradiction arises between irrigation and hydropower output on the one hand and between minimum river flow and irrigation on the other hand. A calculation scheme is created and the following trade-off curves were obtained by making use of the SWT method.

The relationship analysis of WRS-environment includes two levels of decision making (DM): •Assessment and DM on local level in the design stage – environmental impact assessment (EIA)

•Assessment and strategic DM in the planning stage – strategic environmental assessment (SEA)

A model base and software for multiple-objective analysis at EIA is used for:

• Creation of worth functions

• Cumulative impact assessment

• Ranking checklists and matrices

• Expert estimations

• Principle of dominance and rank theory for DM

ОЦЕНКИ НА ПЛАНОВЕТЕ ПО ОТДЕЛНИТЕ КРИТЕРИИ\ критерии 1 2 3 4 5 6 7

план \1 1.00 1.00 1.00 2.00 3.00 3.00 1.002 3.00 3.00 3.00 3.00 3.00 3.00 2.003 3.00 3.00 3.00 3.00 3.00 3.00 3.004 3.00 3.00 3.00 3.00 3.00 3.00 4.005 2.00 2.00 2.00 3.00 3.00 3.00 3.006 2.00 2.00 2.00 3.00 3.00 3.00 4.00

РАЗГЛЕЖДАНЕ ПРИ ВСИЧКИ КРИТЕРИИплан 2 доминира над план 1,план 3 доминира над план 1,

и над план 2,и над план 5,

план 4 доминира над план 1,и над план 2,и над план 3,и над план 5,и над план 6,

план 5 доминира над план 1,план 6 доминира над план 1,

и над план 5,ИЗКЛЮЧВАНЕ НА ЕДИН КРИТЕРИЙ

Program EXPERT – worth functions

Program KSPIS – ranking checklists

Program DOMINI – method of dominance

ENVIRONMENTAL IMPACT ASSESSMENT

The ecological runoff is a part of the river runoff that should not be completely taken away from the river and the environment. In order to ensure this, an assessment has to be made of the extent to which natural runoff regime could be changed without affecting the sustainable functioning of the environment. The necessity of new management methods aimed at guaranteeing the ecological runoff becomes more important.

There are various methods for determining of the minimum permissible flow. Most of them are based on the main hypothesis, which states that the fluctuations of the river runoff are the most important abiotic factor, determining the quality of living environment – a decisive factor for development of a biocenosis.

ECOLOGICAL RIVER FLOW

The developed models and software are applied in the case study of EIA of the “Project for water transfer from derivation Maritsa 1200 of cascade Belmeken–Sestrimo towards Sofia town” according to the criteria of the “Law of Environmental Protection”

Степенна възд.

Време-траене

Обхват Честота

Куму-латив-ни

Компл. Ефект

Компл. Функция на

ц.I

Ефект1 матрица 1

Ефект2 матрица 2

Реалнаоценка

1 2 3 4 5 6 7 8 9 10 11 12

ВЪЗДУХ Строителство -3 -1 -1 -1 0 -6 -2 -1 -2 -3Експлоатация 0 0 0 0 0 0 0 0 0 0

ВОДИ Строителство -1 -1 -1 -1 0 -4 -1 -1 -1 -1Експлоатация -3 -3 -3 -2 0 -11 -2 -3 -3 -3

ПОЧВИ Строителство -3 -1 -2 -2 0 -8 -2 -2 -3 -3Експлоатация 0 0 0 0 0 0 0 0 0 0

ФЛОРА Строителство -3 -3 -1 -2 0 -9 -2 -2 -3 -3Експлоатация 0 0 0 0 0 0 0 0 0 0

ФАУНА Строителство -1 -1 -1 -2 0 -5 -1 -1 -1 -3Експлоатация 0 0 0 0 0 0 0 0 0 0

ЛАНДШАФТ Строителство -2 -3 -2 -2 0 -9 -2 -2 -3 -3Експлоатация -3 -1 -1 -2 0 -7 -2 -1 -2 -2

КУЛТУРНОН.

Строителство -3 -1 -1 -2 0 -7 -2 -1 -2 -3Експлоатация 0 0 0 0 0 0 0 0 0 0

ЗДРАВЕ Строителство -1 -1 -1 -1 0 -4 -1 -1 -1 -1Експлоатация 3+ 3+ 3+ 3+ N +12 +3 +3 +3 +3

СОЦ-ИКОНОМИЧЕСКИ 3+ 3+ 3+ 3+ N +12 +3 +3 +3 +3

Степенна възд.

Време-траене

Обхват Честота

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Компл. Ефект

Компл. Функция на

ц.I

Ефект1 матрица 1

Ефект2 матрица 2

Реалнаоценка

1 2 3 4 5 6 7 8 9 10 11 12

ВЪЗДУХ Строителство -3 -1 -1 -1 0 -6 -2 -1 -2 -3Експлоатация 0 0 0 0 0 0 0 0 0 0

ВОДИ Строителство -1 -1 -1 -1 0 -4 -1 -1 -1 -1Експлоатация -3 -3 -3 -2 0 -11 -2 -3 -3 -3

ПОЧВИ Строителство -3 -1 -2 -2 0 -8 -2 -2 -3 -3Експлоатация 0 0 0 0 0 0 0 0 0 0

ФЛОРА Строителство -3 -3 -1 -2 0 -9 -2 -2 -3 -3Експлоатация 0 0 0 0 0 0 0 0 0 0

ФАУНА Строителство -1 -1 -1 -2 0 -5 -1 -1 -1 -3Експлоатация 0 0 0 0 0 0 0 0 0 0

ЛАНДШАФТ Строителство -2 -3 -2 -2 0 -9 -2 -2 -3 -3Експлоатация -3 -1 -1 -2 0 -7 -2 -1 -2 -2

КУЛТУРНОН.

Строителство -3 -1 -1 -2 0 -7 -2 -1 -2 -3Експлоатация 0 0 0 0 0 0 0 0 0 0

ЗДРАВЕ Строителство -1 -1 -1 -1 0 -4 -1 -1 -1 -1Експлоатация 3+ 3+ 3+ 3+ N +12 +3 +3 +3 +3

СОЦ-ИКОНОМИЧЕСКИ 3+ 3+ 3+ 3+ N +12 +3 +3 +3 +3

Степенна възд.Степенна възд.Степенна възд.

Време-траенеВреме-траенеВреме-траене

ОбхватОбхватОбхват Честота

Честота

Честота

Куму-латив-ни

Куму-латив-ни

Куму-латив-ни

Компл. ЕфектКомпл. ЕфектКомпл. Ефект

Компл. Функция на

ц.I

Компл. Функция на

ц.I

Компл. Функция на

ц.I

Ефект1 матрица 1

Ефект1 матрица 1

Ефект1 матрица 1

Ефект2 матрица 2

Ефект2 матрица 2

Ефект2 матрица 2

РеалнаоценкаРеалнаоценкаРеалнаоценка

111 222 333 444 555 666 777 888 999 101010 111111 121212

ВЪЗДУХВЪЗДУХ СтроителствоСтроителство -3-3 -1-1 -1-1 -1-1 00 -6-6 -2-2 -1-1 -2-2 -3-3ЕксплоатацияЕксплоатацияЕксплоатация 000 000 000 000 000 000 000 000 000 000

ВОДИВОДИ СтроителствоСтроителство -1-1 -1-1 -1-1 -1-1 00 -4-4 -1-1 -1-1 -1-1 -1-1ЕксплоатацияЕксплоатацияЕксплоатация -3-3-3 -3-3-3 -3-3-3 -2-2-2 000 -11-11-11 -2-2-2 -3-3-3 -3-3-3 -3-3-3

ПОЧВИПОЧВИ СтроителствоСтроителство -3-3 -1-1 -2-2 -2-2 00 -8-8 -2-2 -2-2 -3-3 -3-3ЕксплоатацияЕксплоатацияЕксплоатация 000 000 000 000 000 000 000 000 000 000

ФЛОРАФЛОРА СтроителствоСтроителство -3-3 -3-3 -1-1 -2-2 00 -9-9 -2-2 -2-2 -3-3 -3-3ЕксплоатацияЕксплоатацияЕксплоатация 000 000 000 000 000 000 000 000 000 000

ФАУНАФАУНА СтроителствоСтроителство -1-1 -1-1 -1-1 -2-2 00 -5-5 -1-1 -1-1 -1-1 -3-3ЕксплоатацияЕксплоатацияЕксплоатация 000 000 000 000 000 000 000 000 000 000

ЛАНДШАФТЛАНДШАФТ СтроителствоСтроителство -2-2 -3-3 -2-2 -2-2 00 -9-9 -2-2 -2-2 -3-3 -3-3ЕксплоатацияЕксплоатацияЕксплоатация -3-3-3 -1-1-1 -1-1-1 -2-2-2 000 -7-7-7 -2-2-2 -1-1-1 -2-2-2 -2-2-2

КУЛТУРНОН.КУЛТУРНОН.

СтроителствоСтроителство -3-3 -1-1 -1-1 -2-2 00 -7-7 -2-2 -1-1 -2-2 -3-3ЕксплоатацияЕксплоатацияЕксплоатация 000 000 000 000 000 000 000 000 000 000

ЗДРАВЕЗДРАВЕ СтроителствоСтроителство -1-1 -1-1 -1-1 -1-1 00 -4-4 -1-1 -1-1 -1-1 -1-1ЕксплоатацияЕксплоатацияЕксплоатация 3+3+3+ 3+3+3+ 3+3+3+ 3+3+3+ NNN +12+12+12 +3+3+3 +3+3+3 +3+3+3 +3+3+3

СОЦ-ИКОНОМИЧЕСКИСОЦ-ИКОНОМИЧЕСКИ 3+3+ 3+3+ 3+3+ 3+3+ NN +12+12 +3+3 +3+3 +3+3 +3+3

Matrix of environmental impacts assessment

In the Institute of Water Problems in connection with the River Basin Management Plans (RBMP) development and according to the requirements of the WFD some investigations are carried out related to the assessment of water demand satisfaction in different economic and climatic scenarios.

Water resource system balances for four river basins in Bulgaria are developed – the rivers Tundja, Struma, Ogosta and Kamchia.

SIMULATION MODELING APPLICATION IN WATER RESOURCE BALANCE OF RIVER BASINS

The WRS balance represents a comparison between the available water resources and water demand of all water users and consumers.

The simulation model SIMYL was used for balance calculation. It is developed in IWP and allocates water on the basis of priorities at given scheme of water usage in the river basin.

A network flow model is created – the nodes indicate water reservoirs, water intakes, water users, etc. and the arcs are elements of the connections – river course, derivations, channels, etc.

• Computer program is based on the description of water resources scheme by network flow models. A distribution of water between the water users and water consumers is made taking into account the functional characteristics of the system “water source - water user“.

• Current balance for two scenarios of climatic conditions – for the periods 1961-2004 and 1985-1994 – considered as a scenario of possible drought.

• The obtained results are a set of data: reliability water demand satisfaction by years, months, volumes show for the first calculated period that almost water users’ demands are satisfied. Several of them do not meet the normative reliability. Generalized indexes for satisfaction of water users and complete data base are obtained, which could be used for more detailed analyses.

• The water resource balance determined for the dry period 1985-1994 demonstrates deepening of water shortage in irrigation, drinking and industrial water supply as well as some impossibility for the necessary minimum flow provision in several sites of the rivers.

Case study – the Tundja river basinA graphical-space information system is created as GIS containing the necessary main data for the existing water resource infrastructure, river runoff and water

demand which give an easy access to them of the end user.

Calculation scheme

Graphical calculation scheme of the basin is made reflecting the river network with the direction of water movement, location of the physical structures, water abstraction points, connections between the separate objects and the way for water resources usage. Based on this scheme a network mathematical model (containing 135 nodes) is developed for WRS balance calculation.

The obtained results show that:• The estimated water resources meet the present water demand.• Because of the considerable reduction of irrigation areas at present time and

the pessimistic prognoses related to the land reclamation development in the near future, one part of the reservoir usable storage could be kept empty for water retaining during the summer floods which occur in the past years. This result could be considered as a measure to achieve some of the Directive’s environmental objectives, e.g. flood control.

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indexby

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yearsby

volumeAverageshortage

initialvolume in

the reservoir

Annual water

demands Water users

Node №

reliability %

Period 1961-2004

variant I.1data

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0.04299.0590.9199.52404846W.S.25112

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volumeAverageshortage

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the reservoir

Annual water

demands Water users

Node №

reliability %

Period 1961-2004

variant I.1data

Scenarios “Drought” – the ecological river flow of the Tundja river at the border is not provided ????

• The red line is the required ecological flow

• Here are presented the three driest years

Calculating water resources scheme, simulation model and GIS for the transboundary river basin of Struma have been developed as a part of the River Basin Management Plans (RBMP).

The calculating scheme is based on the water recourse system. The following objects were taken into account: 50 irrigation fields, 44 water supply groups, 33 industry points, and 188 points of water abstraction, 37 reservoirs; 25 pumping stations; 3 cascades and 32 operating Small Hydroelectric Power Plants (SHPP); 5 fish breeding ponds; 8 water derivations, points for ecological water quantities etc. The scheme is integrated in GIS.

Case study – the Struma river basin

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Fragment of the graphic presentation of the water use scheme of the river Blagoevgradska Bistritza and a section of the river Struma up to HMS15800/ Krupnik.

The developed calculating scheme based on the graphical scheme of the watershed includes 140 hydro nodes and 150 arcs.

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Text

The accent of modeling and analysis is on the critical river sections, which are subject to risk of failure in achieving the ecological requirements.

SCENARIO I.2

Node Name Inflow Demands Shortages

Reliability

Reliability index

by volumesby

yearsby

months

21 irrig.29 0 57668 3116 94.60 80.00 91.94 .890

22 Ind Blag 0 5800 0 100.00 100.00 100.00 .000

23 Rubarnik 0 13372 0 100.00 100.00 100.00 .000

24 iaRakochevica 0 0 0 0 0 0 0

50 Eko 5 rB 0 97956 19966 79.62 .00 60.00 5.829

97 irrig.28 0 15411 0 100.00 100.00 100.00 .000

98 prehBla 468935 50949 0 100.00 100.00 100.00 .000

99 irrig.27 0 13362 3929 70.60 10.00 71.43 15.671

100 WS 27 0 63701 4485 92.96 20.00 80.00 .933

101 WS 29 143973 742 0 100.00 100.00 100.00 .000

102 Ws 28 117569 980 0 100.00 100.00 100.00 .000

103 Ind 23 161985 810 0 100.00 100.00 100.00 .000

Table 1 shows the expected reliability in percentages by years, months and volume for different water users in a dry future 10 years period.

These figures show the calculated by SIMYL disturbed monthly average river flow hydograph in two points – one on Struma river under the Krupnik village, and the other on the Sandanska Bistritsa river at the town of Sandanski. On these graphics a comparison is made between the monthly average discharge and the ecologically necessary minimum during the dry years.

Struma river, Krupnik

0,00

50,00

100,00

150,00

200,00

250,00

300,00

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1 2 3 4 5 6 7 8 9 10 11 12m onths

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ecological minsimulated 1986simulated 1988simulated 1994undisturbed 1986

Sandanska Bistrica river

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ecological minsimulated 1986simulated 1988simulated 1994

An analysis is made of the cumulative impact due to the water shortage, water pollution, small hydropower plants, etc. These are the so called “critical sections”.

Assessment of the ecological runoff and the extent of objective achievement

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0

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р. Струма при гр. Перник 51650

9,623

0,962 1,602 1,602

0

10

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р. Струма – c. Ръждавица 51700

26,164

2,616 4,465 4,465

0

10

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р. Струма Бобошево 51750

45,95

4,59510,724 10,724

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р. Струма Крупник 51800

75,57

7,55710,261 10,261

70

0

10

20

30

40

50

60

70

80

р. Струма Марино поле 518800

0,5

1

1,5

2

2,5

3

3,5

4

4,5

5

1

Q0

10%Q0

Qmin 95%

Qeco

П Е Р Н И К

Б Р Е З Н И К

РА Д О М И Р

Б О Б О В Д О Л

я з. С т уд е н а

я з . Д я к о в о

р . Д раго вищ ицар. Бистриц а р . Топ олн ица

р. Кръ чин ск а

р. Слатин ска

р. Р

е чи ц

а

р . Би ст рица

р. Х ър совска

р . С тара

р . Су ш и цка р. М ечкулска

р . Б реж анска

р . П ет ро вска

р . Кали ма н с ка

р . С еделска

р . Буди лска

р. С т рум ешн иц а

р. Ри бин а

я з. П ч е л и н а

Д У П Н И Ц А

Р И Л А

К О Ч Е Р И Н О В О

Б Л А Г О Е В Г РА Д

С И М И Т Л И

Б О Б О Ш Е В О

К Р Е С Н А

СА Н Д А Н С К И

С Т Р У М Я Н И

П Е Т Р И Ч

С А П А Р Е ВА Б А Н Я

К Ю С Т Е Н Д И Л

Т Р Е К Л Я Н О

З Е М Е Н

К О ВАЧ Е В Ц И

10

0

10

0

10

0

0

10

20

30

40

50

60

70

80

90

100

eco Pernik

обезп. по обемобезп. по месециобезп. по години

10

0

10

0

10

0

0

20

40

60

80

100

eco Per nik Перник

10

0

10

0

10

0

0

20

40

60

80

100

eco Per nik Ръждавица

93

,6 70

,8

10

0

20

40

60

80

100

eco 4 rR il Рилска

79

,62

60

0

0

10

20

30

40

50

60

70

80

1 Бл.Бистрица

91

72

20

0

20

40

60

80

100

1 Крупник

10

0

10

0

10

0

0

20

40

60

80

100

eco Pernik Марино поле

Зависимост дефицит ВС- екодефицит Крупник нормирани

сценарий засушаване

0.75

0.8

0.85

0.9

0.95

1

1.05

0.75 0.8 0.85 0.9 0.95 1 1.05

дефицит ВС

екод

ефиц

ит

компромиснирешения

Дефицити при различни варианти - сценарий засушаване

Qeco =1.6

m3/sQeco = 2.4

m3/sQeco = 3.2

m3/s0

5

10

15

20

25

1 2 3

QecoI - варианти екологичен отток

mln

m3

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

mln

m3

дефицит ВС

екодефицитРъждавица

• The “concept of addition” represents one possibility for ecological runoff provision. It consists of the runoff regulation within a certain interval in a given cross section of the river valley in order to guarantee the ecological runoff in other sections of this river valley.

• The results from the experiments are shown in the next figures.

Dependence between deficiency in WRS at the site over Rajdavitsa and eco-deficiency in the site at Krupnik

QecoI.1.+dQ

QecoI.2. Приоритет I

нужди в собствен водосбор - створI

QecoII

QecoI.1.

Lkr

QecoIV

QecoIII

WS I

WSII

WS III

Приоритет IV прехвърляне води съседен водосбор

Приоритет III прехвърляне води в собствен водосбор –

створ II

Приоритет II нужди в собствен водосбор створI –

створ II

II створ

I створ WS IV

Both people and their economies have benefited from water resource systems. Yet in many regions, water resource systems are neither able to meet the demands, or even the basic needs for fresh water, nor can they support and maintain resilient biodiversity ecosystems.

The developed mathematical models with both mentioned methods, assist the decision makers in their activity of WRS planning and management.

Thank you for your attention!