Aiviekstes Baseina Hidroloģijas Matemātiskā Modelēšana

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Aiviekstes Baseina Hidroloģijas Matemātiskā Modelēšana Aiviekstes baseina hidroloģijas matemātiskā modelēšana Juris Senņikovs Vides un tehnoloģisko procesu matemātiskās modelēšanas laboratorija, Fizikas un matemātikas fakultāte, Latvijas Universitāte Laikā un telpā sadalīts Aiviekstes ūdensbaseina hidroloģijas un hidraulikas modelis ir izveidots un kalibrēts tipiskam, sausam un slapjam hidroloģiskajiem režīmiem Vairāku klimata izmaiņu scenāriju ietekme uz baseina hidroloģisko režīmu aprēķināta ar izveidoto modeli. Īsumā par Aiviekstes noteces baseinu •Atrodas Latvijas ziemeļaustrumu daļā •Ir Daugavas baseina sastāvdaļa •Baseina laukums ir aptuveni 9000 km2 •Aiviekstes vidējais caurplūdums pie ietekas Daugavā ir aptuveni 60 m3/s •Aiviekste iztek no Lubānas ezera, kas atrodas noteces baseina vidusdaļā Mūsu pieeja hidroloģiskajai modelēšanai Laikā un telpā sadalīts uz fizikāliem apsvērumiem balstīts modelis Iepriekšminētais nozīmē, ka viss baseins ir sadalīts [trijstūra] galīgajos elementos, katrā elementā tiek rēķināta hidroloģiskāūdens bilance. Upju tīkls ir sadalīts galīgajos elementos – nogriežņos, upēm piegulošie virsmas ūdens elementi veido upju noteci, kuras transformācija [sadalījums pa] upju tīklā tiek aprēķināta ar hidraulikas modeli. Modeļa galvenās sastāvdaļas ir •Virsmas ūdens modelis – būtiskākais aprēķināmais mainīgais tajā ir ūdenssaturs. •Grunts un pazemes ūdens modelis, aprēķināmais mainīgais – gruntsūdens līmenis. •Upju hidraulikas modelis – aprēķina upju ūdenslīmeni un caurplūdumu •Ezeru modelis, kas aprēķina ezera ūdenslīmeni Hidroloģiskā modeļa vienkāršota diagramma Atmosfēra Ezeri Sniegs Virsmas ūdens Upes Komponentes Pazemes ūdens Nokrišņi Iztvaikošana Infiltrācija Virszemes notece Kušana Barošanās no pazemes ūdeņiem Procesi Virsmas ūdens plūsmas virziens Upes Režģa elements Režģa punkts lout Ezers Apatch Aelem Upes nogrieznis Virsmas ūdens modelis Galvenās sastāvdaļas: •Nokrišņi (lietus) •Sniega kušana •Iztvaikošana un transpirācija •Infiltrācija •Barošanās no pazemes ūdeņiem •Virsūdens plūsma Galīgo tilpumu modelis trijstūra elementos (aprēķināmie mainīgie uzdoti trijstūros) Virsūdens plūsma notiek virsmas līmeņa negatīvā gradienta virzienā (“pa visstāvāko nogāzi”) dw −(i) +(i) = P − E −Vinf iltr +Vsurface − ∑Vrunoff + ∑Vrunoff +Vsnow dt i i P – nokrišņi (lietus) w – ūdenssaturs (=wintercepted+wponded) E – iztvaikošana Vsurface – barošanās no pazemes ūdeņiem - + V runoff, V runoff -virsūdens plūsma Vsnow – sniega kušana Ja w>wintercepted 1 2/3 1/ 2 lout Vrunoff = ()w − wint ercepted S0 ⋅ n – berzes koeficients virsūdens n Aelem plūsmai (atkarīgs no zemes lietojuma veida) S0 –virsmas slīpums Iztvaikošanas uzdošanas veids E = Ke (w)()()esat T − e Sniega kušanas modelis Aprēķināmais mainīgais – ūdenssaturs sniega formā dS S – ūdenssaturs sniega formā = P −V P – nokrišņi (sniegs) dt s snow s Vsnow = CMELT (T-T2) – sniega kušanas ātrums T2 –bāzes temperatūra (>0ºC) Pazemes ūdens modelis Aprēķina pazemes ūdens līmeni Sastāvdaļas: •Darsī filtrācijas plūsma •Infiltrācija •Virsmas ūdens un upju barošanās no pazemes ūdens •Plūsma uz/no ezeriem Galīgo elementu modelis, mainīgie trijstūra režģa punktos ∂h ()h − z S = ∇ ⋅(K(h − z )∇h)+V −V −V g s ∂t g inf iltr river surface h – ūdenslīmenis zg –efektīvā sprostslāņalīmenis K – filtrācijas koeficients Ezerā h=hlake Upju barošanās K()h − h river Ja h>hriver Vriver = Δlriver ∆lriver –empīrisks Virsmas ūdens barošanās K(h − (hsurface − Δhsurface )) V = Ja h>(hsurface- ∆hsurface) surface Δl surface ∆lsurface –empīrisks ∆hsurface –virsmas līmeņa korekcija Upju hidraulikas modelis Aprēķināmie mainīgie – ūdenslīmenis un caurplūdums Sen-Venāna vienādojumi Nobīdīto galīgo diferenču metode (līmenis punktos, caurplūdums nogriežņos) Ieejas dati – upes grunts slīpums un šķērsgriezumi Ūdens avoti – virsūdens plūsma, barošanās no pazemes ūdens Ezeru modelis Aprēķina ezera ūdenslīmeni un no ezera izplūstošo upju caurplūdumu Ūdens avoti – virsmas ūdens, upes, pazemes ūdens Ūdens noteces – upes, pazemes ūdens dhlake (i) (i) (i) (i) (i) Alake = ∑Qriverin − ∑Qriverout + ∑Vrunoff lout (w − wintercept ) dt i i i ∂h + K (h − z )dΓ {+P − E} ∫ g Γ ∂n Modeļa ieejas dati •Zemes virsmas topogrāfija [augstumi] + upju tīkls => modeļa režģis, modeļa upju tīkls, modeļa ezeru robežas •Zemes lietojuma dati [National CORINE Land Cover 2000 in Latvia ] =>sagrupēti 6 galvenajos tipos (no hidroloģijas modeļa viedokļa) (lauksaimniecības zeme, meži, pļavas/krūmi (dabiskie), purvi, ūdenstilpnes), modelis ņem vērā katra zemes lietojuma proporcijas katra no virsmas ūdens aprēķina elementiem •Upju caurplūduma novērojumi 7 stacijās [A.Zīverts] •Ikdienas meteoroloģiskie dati (nokrišņi un gaisa temperatūra) Rēzeknē, Zīlānos un Gulbenē [LVĢMA] Modeļrežģis un modeļa upju tīkls 6380000 240 231.5 6360000 223 214.5 206 6340000 197.5 189 180.5 6320000 172 163.5 155 6300000 146.5 138 129.5 6280000 121 112.5 104 6260000 95.5 87 6240000 78.5 70 610000 620000 630000 640000 650000 660000 670000 680000 690000 700000 710000 720000 Zemes lietojums no CORINE Zemes lietojuma procentuālais dalījums pa modeļa elementiem 6380000 6380000 6360000 6360000 1 1 Gulbene Gulbene 6340000 6340000 6320000 6320000 0.67 0.67 6300000 6300000 0.33 0.33 6280000 6280000 Rēzekne Rēzekne Zīlāni Zīlāni 6260000 6260000 0 0 6240000 6240000 6220000 6220000 600000 620000 640000 660000 680000 700000 720000 740000 600000 620000 640000 660000 680000 700000 720000 740000 Meži Lauksaimniecība Caurplūduma novērojumu stacijas 300 270 Pededze 240 210 180 Kuja Aiviekste-Lubāna 150 Iča 120 Aiviekste-HES 90 Malta Rēzekne 60 30 0 Kalibrācijas scenāriju izvēle Tika aplūkoti trīs dažādi gadi ¾ Laika periods no Jūl/76 līdz Jūn/77 tika pieņemts kā “sauso” gadu reprezentējošs, gada nokrišņu summa 518 mm, gada vidējais caurplūdums 35 m3/s ¾ Laika periods no Jūl/77 līdz Jūn/78 tika pieņemts kā “vidējo” gadu reprezentējošs, gada nokrišņu summa 660 mm, gada vidējais caurplūdums 57 m3/s ¾ Laika periods no Jūl/79 līdz Jūn/80 tika pieņemts kā “slapjo”, gadu reprezentējošs, gada nokrišņu summa 762 mm , gada vidējais caurplūdums 92 m3/s Kalibrācijas scenāriju izvēle, caurplūdumu novērojumi “Sausais” “Vidējais” “Slapjais” Noteces baseina 1976/77 1977/78 1978/79 Stacija laukums, km2 Q, m3/s Q, m3/s Q, m3/s Aiviekste HES 8660 34.85 58.60 91.75 Aiviekste Lubāna 7200 24.18 42.57 62.81 Kuja, Aizkuja 268 1.47 2.82 3.65 Pededze, Litene 978 4.67 7.24 12.95 Iča, Kuderi 674 2.37 5.76 Rēzekne, Griškāni 505 1.49 3.37 5.06 Malta, Viļāni 782 2.71 6.14 8.29 Izmērītā Aiviekstes caurplAivieksteūduma discharge. laika Dry grafiksYear. “sausā” gadā 250.00 25 200.00 20 AivHES AivLub W 150.00 15 Discharge 100.00 10 50.00 5 0.00 0 01.Jūl.76 31.Jūl.76 30.Aug.76 30.Sep.76 30.Okt.76 30.Nov.76 30.Dec.76 29.Jan.77 01.Mar.77 31.Mar.77 01.Mai.77 31.Mai.77 30.Jūn.77 Time Izmērītā Aiviekstes caurplAivieksteūduma discharge. laika Wet grafiks Year. “slapjā” gadā 300.00 35 30 250.00 25 AivHES 200.00 AivLub W 20 150.00 Discharge 15 100.00 10 50.00 5 0.00 0 01.Jūl.78 31.Jūl.78 30.Aug.78 30.Sep.78 30.Okt.78 30.Nov.78 30.Dec.78 29.Jan.79 01.Mar.79 31.Mar.79 01.Mai.79 31.Mai.79 30.Jūn.79 Time Izmērītā Kujas un RēzeknesKuja and R ēcaurplzekne discharge.ūduma Average laika Year. grafiks “tipiskā” gadā 30.00 25.00 20.00 Kuja-Aizkuja Rēzekne 15.00 Discharge 10.00 5.00 0.00 01.Jūl.77 31.Jūl.77 30.Aug.77 30.Sep.77 30.Okt.77 30.Nov.77 30.Dec.77 29.Jan.78 01.Mar.78 31.Mar.78 01.Mai.78 31.Mai.78 30.Jūn.78 Time Kalibrācijas stratēģija • Kalibrācijas mērķis – novērojumu un modeļa caurplūdumu kvadrātiskās standartnovirzes minimizēšana. To panāk mainot empīriskos modeļa parametrus – (1) pazemes ūdens modeļa parametrus, (2) no zemes lietojuma atkarīgos virsmas ūdens berzes, iztvaikošanas, kušanas un infiltrācijas parametrus • Pirms katra no trīs gadu garajiem kalibrācijas aprēķiniem modelis “ieskriešanās” režīmā darbināts 90 gadu ilgam laika periodam, nostabilizējot pazemes ūdens līmeni kvazi- periodiskā režīmā Virsmas līmenis Tipisks pazemes ūdens līmenis 240 240 6380000 6380000 235 235 230 230 225 225 220 220 6360000 215 6360000 215 210 210 205 205 200 200 195 195 6340000 6340000 190 190 185 185 180 180 175 175 6320000 170 6320000 170 165 165 160 160 155 155 150 150 6300000 6300000 145 145 140 140 135 135 130 130 6280000 125 6280000 125 120 120 115 115 110 110 105 105 6260000 6260000 100 100 95 95 90 90 85 85 6240000 80 6240000 80 75 75 70 70 600000 620000 640000 660000 680000 700000 720000 600000 620000 640000 660000 680000 700000 720000 Kalibrācijas rezultāts, izmērītie un aprēķinātie caurplūdumi kalibrācijas periodā 300 Model - Aiviekste@HPP AivHES 280 Aiviekste - HES 260 240 220 200 180 160 140 m^3/s, m^3/s m^3/s, 120 100 80 60 40 20 0 01.09.1976 01.03.1977 01.09.1977 01.03.1978 01.09.1978 01.03.1979 Kalibrācijas rezultāts, izmērītie un aprēķinātie caurplūdumi kalibrācijas periodā 200 Model - Aiviekste@Lubāna Aiviekste - Lubāna AivLub 180 160 140 120 100 m^3/s, m^3/s m^3/s, 80 60 40 20 0 01.09.1976 01.03.1977 01.09.1977 01.03.1978 01.09.1978 01.03.1979 Kalibrācijas rezultāts, izmērītie un aprēķinātie caurplūdumi kalibrācijas periodā 50 Model Malta Malta – Viļāni Malta 45 40 35 30 25 m^3/s, m^3/s m^3/s, 20 15 10 5 0 01.09.1976 01.03.1977 01.09.1977 01.03.1978 01.09.1978 01.03.1979 Kalibrācijas rezultāts, izmērītie un aprēķinātie caurplūdumi kalibrācijas periodā 80 Model - Iča Iča - Kuderi Iča 70 60 50 40 m^3/s, m^3/s m^3/s, 30 20 10 0 01.09.1976 01.03.1977 01.09.1977 01.03.1978 01.09.1978 01.03.1979 Kalibrācijas rezultāts, izmērītie un aprēķinātie caurplūdumi kalibrācijas periodā 90 Model - Pededze Pededze - Litene Pededze 80 70 60 50 m^3/s, m^3/s m^3/s, 40 30 20 10 0 01.09.1976
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