Model

ЧИ И ИЧ Ь Х И. .1, П 12- ЬЧ И ИЩ . И. .2, . .3, К . .2, .И.2, - . .3, . .3 , - - , . . . , 3- , -1430, , , ( …; , …, ., , …; ., – ). , , . . , , . ( ). я я – , – – – ( . 1): – – - - - , - , - ; - ; . - . , . - , . . ё - - , - , . , , . . , – II ( Q = 0, ). , Shuttle Radar Topography Mission (SRTM). 135 0 30 km 1000 800 2000 1500 3000 2500 4000 3500 4500 . 1. . К , . . , . , , . . ( . 2). , . 8 5.0 6 4.5 Part of watershed area, % Temperature, oC 4 2 0 -2 -4 -6 -8 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 3900 3600 3300 3000 2700 2400 2100 1800 1500 1200 900 -10 0.0 -9 Altitude, m ) ( -5 -3 -1 1 3 5 7 9 Annual air tempereture, °C ) . 2. -7 ( ) , 2008). 136 ( ) ( ). . , 80 % 3-5 ). 250-300 1200 ( . 3, 4). 8-10 % ( – , 1400 Precipitations, mm 1200 1000 800 600 400 3900 3600 3300 3000 2700 2400 2100 1800 1500 900 1200 200 Altitude, m . 3. ( . 4. (P) , 2008). , ( ( , 2008). ). , , . . 137 . 2400 ( . 5, 6). ( 2000 . 2). 1800- , , , . 500 Evaporation, mm 450 400 350 300 250 3900 3600 3300 3000 2700 2400 2100 1800 1500 1200 900 200 Altitude, m . 5. . 6. ( (ET) , 2008). , 138 ( , 2008). щ - . , 720 903 . . , 85 % - , . . , – 1964-2006 . . 1. . 1. – 1964-2006 I – II III IV V VI 9.96 9.06 9.32 23.9 60 + 5.49 4.98 4.9 . ., VII 3 / . VIII 78.8 57.8 33 IX X XI XII 20 15.2 13.3 11.4 28.5 10.5 31.7 56.8 43.6 22.2 11.1 7.8 6.55 5.82 17.6 3.11 3.11 3.28 8.49 22.2 38.1 23.1 8.67 4.41 4.1 3.83 3.32 10.5 136 175 136 152 261 511 819 711 504 2000-3000 , 286 207 147 337 . . . ( , ) . , . , « » hRIV. « ». « « hRIV. », », , « ». « ( ) ё ( ). 139 », « ». . , . ( , ) ». ё « , « ». . « ё ». », « » « , , « III ». ( Q = f(Δh) – ). , – kf = 0.1-0.3 / . , « », w, . я. - . ( ., - …, , , ) , . . , -1 n10 / . 150-300 . ( ) , - . n10-1 , . . , . , 0,5 %. , . , . . , ), , , ( . 7. 140 ., , З . . З . З . З . – – ; ; – – ; . 7. . - , , - . - . . - - . , . . , . , 0.4 %. Snow-melt Run-off Model ( ) , , , k ε. . ( - ) ( ). ( ). , – : – ; 141 – – , , , ( ) . .; – , – ; – – , , , . . , . , , , 1800-2000 . , . , , , , . , , , . . 2700 ( . 8). . , . 18 16 Angle of slope, ° 14 12 10 8 6 3900 3600 3300 3000 2700 2400 2100 1800 1500 1200 900 4 Altitude, . 8. ( , 2008). . ( ) ( , , 2008). , , , 142 . . ε = kεP, , / ; kε – : ε– , ;P– , w– ), ( / , P = w + ET + ε = w + (1 – kε)P + kεP, , / ; ET – / . ( P , . : (1) ( E = ET, , 2008). , 2008). . , 2000-2100 , . 9. Precipitatopns,mm per month 70 – Suusamyr; 60 – Naryn; 50 – At-Bashy 40 30 20 10 0 I II III IV V VI VII VIII IX X XI XII Month . 9. 1964-2000 .( ). w , SRTM, : w = QRIV/SRIV, QRIV SRIV – . , kε ( P ) w , . SRTM ( . 10). 143 я. , ET . 10 ( SRTM). . : – ; , , , – - - , ; – , . : – , ; – – ; . . - . . ( ) - . , :   Z  Z  C1 Z  C 2 , mZ MAX   mZ MIN  , C1  Z MAX  Z MIN Z MAX C 2  mZ MAX   C1 Z MIN , 144 Z – , ; Z– – ( ; m(ZMAX), m(ZMIN) – , , . ), ( ) « , - ». . . . – Small Chychkan), . - (Usun-Akhmat), (Chychkan + (Torkent) SRTM . . , . SRIV (Torkent), (Chychkan + Small Chychkan), . - . (Usun-Akhmat), , . . , (P) .4 (E) , 6. ( w , 2008), : w = P – E. w ( , P ) = w. , . P w =w +ε : = (1 – kε)P + kεP , , / ; ε ; kε – – , / , , – : P = P – E = w, 145 – . w – 2008). , ( . P w =w +ε = (1 – kε)P – , ) + kεP , / ( , : , ; ε – ; kε – / . w . w ( , , 2008). ( ). / III , / – k f. , , . , kf = 1 / . III ( ), . (QRIV) , (HWSR – water table in water-storage reservoir) (VWVR –water volume in reservoir). , – . (QRD – reservoir discharge): HWSR = f(VWVR), , – (QRD – reservoir discharge). . (QRIV). ( QSURF) (QGW). . VWVR , , , f(VWVR) = (QRIV + QSURF + QGW – QRD.)×t. H , , t: ( . 10, …, 2010 ; ., …, ): VWVR = 4.7735×10–9×H6 –2.3103×10–5×H5 + 4.6499×10–2×H4 – 49.813×H3 + 29955.96×H2 – 9588308×H + 1276190130 (1) 2 R = 0.999993. (1) H, QRIV, QSURF QGW , QRD , . (1) . H ÷ VWVR 1 , , . 146 25 350 300 20 ) ( 3 15 200 150 10 100 5 50 я 910 900 890 880 870 860 850 840 830 820 810 800 790 780 770 760 750 740 730 720 0 710 0 700 ( 2 ) 250 ( ) . 11. , . Ф . . ( . 2). , - , . , ( ) . , ( . 12). ( . 13). , , , . 147 .2 - ( ). - № . . - ,/ , ( 1 ), 9 1,2 . . 920 1094,5 . 10 2 . , 1,2 . 1420 1795 (8) 942 . 1450 . 952,9, 1550 . 925,7 . 1220 , 0,4 22,7 , 296/(148-228) ,% 5 1,25 9,1 / SO446 HCO342 Cl10 NO32 Ca35 Mg34 Na30 K1 , 0,75 N2-QI - / QII-IV , 250/(149-161), 15,5 1,8 13,3 0,3 , 200/(147-178) 0,57 , (230-239) . N2-QI , , 19,9 2,5 1,7 5,6 SO457 HCO332 Cl9 NO32 SO448 HCO342 Cl8 NO32 Ca41 Na33 Mg25 K1 - . 0,4 QII-III 10,1 2,8 2,5 0,87 SO443 HCO342 Cl12 NO33 Na48 Ca36 Mg12 K4 . . 4 Mg39 Ca31 Na28 K2 , 0,6 . . 1551,5 . 976 1935 (1) . . . , (232-282) , 0,75 . 1164,3 . 100 . 1819 (5) S3 , N2-QI 1150 1788 (11) Q2, / 300/(116-140) . , , 850 . . 956,8 . , 2,5 , 1,7 1316,1 , 0,35 1338,9 ., 172/(130-145) , N2-QI +2,4 1,0 13,85 0,36 N2-QI 35 0.15 102 0.005 0,46 SO4 70 Cl 19 HCO311 Na54 Mg23 Ca21 K2 250/(203-239) 148 1,12 SO4 69 Cl 18 HCO313 Na58 Ca20 Mg15 K7 № . . - ,/ , ( 1 ), 1940 (2) 600 1056 , 1,1 . 1254,1 . 1485,9 . 1954 (4) 950 . 1527,1 . 1979 (12) 2,3 1624,5 1983 (14) 1991 (13) 1618 2003 (15) 261/(197-236) . 950 . ,% 11,3 2,5 - / / 15,7 0,54 , SO4 60 HCO327 Cl18 NO39 1,01 22,3 0,8 1,09 2,67 SO4 65 HCO317 Cl 16 NO31 Na54 Mg23 Ca20 K2 . , 248/(163-178) . N2-QI 180/(145-172) 43,8 0,008 1,01 SO4 68 HCO317 Cl 15 Na62 Ca21 Mg14 K3 N2-QI 50,5 3,0 1,2 7,8 HCO371 SO425 Cl3 NO31 Ca44 Na35 Mg19 K2 200/(162-181) - - 0,24 QII-IV 22,5 2,3 5,4 0,21 HCO378 SO410 C7 NO35 Ca75 Mg17 Na6 K2 . ,2 0,1 0,98 , . . 59,5 , , 2,75 . . 1802,7 . 0,5 , Ca67 Na16 Mg15 K2 . 1673 4 1,04 N2-QI . . 1653,6, 1,75 . . 1618 0,45 S3 , , N2-QI 1362 Q2, / 200/(140-191) - . 1953 (3) 1327 . , 200/(162-193) . , . , 1764,4 . 0,81 N2-QI +0,9 2,5 26,4 0,32 SO4 40 HCO338 Cl 20 NO32 Na41 Mg40 Ca19 . , 0,25 . 1864,1 . . 235/(145-171) - 0,21 pQIII-IV 1847 53.95 3.3 3.85 0.55 HCO374 SO410 C10 NO36 Ca65 Mg25 Na11 K2 149 № . . - ,/ , ( 1 ), 2500 (7) 976 2501 (20) 982 2503 (17) 800 . 1,2 . 1067,4 . . . . . . 908 S3 , 4 , 250/(166-177), 100/(27-31), N2 47,1 3,8 3,9 4,0 N2-QI 66,5 1,5 22,0 0,2 , - (48-63), QII-IV 3,44 23,1 2,5 . . , 2,6 2,55 . SO4 53 Cl32 HCO315 1,1 Na60 Ca23 Mg17 SO4 41 Cl 41 HCO315 NO33 0,31 - , 3,3 . . 1320 . Ca55 Mg35 Na10 K3 8,1 QIV . 1088 . 2504 (18) / Ca46 Na43 Mg11 25/(14-24) . 907 - SO4 79 HCO316 Cl 2 1,0 0,85 (74-80) 2503(17 ) ,% / 250/(184-238) (210-233) , 2,65 . . 1088 . Q2, / . 3,05 . 1028,1 ., 0,45 . 945,5 . 2.15 , , 2,65 14,8 2,89 21,3 HCO383 SO410 NO34 CI3 Ca67 Mg23 Na9 K1 58/(22-38) , 0,17 N2-QI 935 3,35 7,8 11,37 3,1 HCO375 CI12 SO410 NO33 Ca60 Mg30 Na9 K1 2505 (19) 1020 . 0,9 . . , , 1,45 . . 994,4 . 72/(21-27), 0,17 N2-QI (40-46), 3,24 3,8 2,15 Ca59 Mg31 Na9 K1 (62-65) 1– 9,2 HCO375 SO411 CI10 NO34 , 150 «+» , . 12. . 151 . 13. 152 . ( - ) . , . 1. . QRIV   Qi , : . ( . 1). 2. w ( . / ; . 14). . 14. , ( . . ( w , , 2008). , , 2008): P P – E – , / , / =w ; w +E – , , . w <w , : – w , , 153 ε – , , . , w w ÷w , w . . 1:1, . . 3. . : , / / , . h . ÷ Alt; , 1:1 . / . , / , , ( h ). 1:1 ÷h . , , / . . , / , , h ÷h . . , 1:1, . / . . I I h2 h1 – / , I . ÷I : =(h2 – h1)/l, : =(Alt2 – Alt1)/l ; Alt2 Alt1 – . , . , , , , I = 0. h . ; l– , , , . ( k f) (ε). , . . . P, E ε . . - . , , . 154 . ( . 15). 1500 1000 500 Water flow discharge, m3/s – data 0 50 100 150 200 250 300 Month . 15. 1964-2006 я . щ . . , 85 %. - a - ) - ( - 1 ( ), . . -1430 .( , . …, ). , a ( , - ) 300 / . . , 5 / , a – , 30 / . ( . 16). 1.2 y = -0.0201x + 0.7417 R2 = 0.0942 Salinity, g/l 1 0.8 0.6 0.4 0.2 0 0 5 10 15 20 25 Permeability, m/day . 16. . 1 – a . 155 3- Ч я я. a , « « », ». . . . ( ). , , « » ». « , , » « », .( - . . . ). , . - , 2008, 237 c. . № -3-1103-44/143 , 2010- 58 . 156 : NUMERICAL HYDROLOGICAL MODEL OF THE TOKTOGUL WATER RESERVOIR SPECIFIC CATCHMENT AREA Tokarev I.V.1, Glazunov V.N.2, Gorev I.V.2, Nikulichev V.B.3, Panov A.I.2, Samsonova A.A.3, Kuzmichonok V. A.3 1 – Saint Petersburg Branch of the Geoecology Institute under the Russian Academy of Sciences, Saint Petersburg. 2 – All-Russian Research Institute of Experimental Physics, RFNC-VIIEF, Sarov 3 – Institute of Water Problems and Hydropower NAS KR Hydrological and hydrogeological investigations performed in the frames of the ISTC Project #KR-1430 have demonstrated that the Toktogul Reservoir water balance is formed on the basis of river run-off, while the water quality is determined by the interaction of the surface run-off with the groundwater flow (Savel‟ev and Tokarev; Tolstikhin et al.; both in this collection of papers). The main natural factor which determines the possibility of required water volume accumulation in the Reservoir is the Naryn River run-off. The natural factor which changes the water quality is the evaporite solution and the consequent high-salinity water flow into the Reservoir. The numerical hydrological model of the Toktogul Reservoir specific catchment area was made for the estimation of the surface water balance items and for the realization of the Constantly Functioning Model (CFM). Natural conditions analysis and schematization for the accounting in the numerical model Geographical boundaries of the simulated area – Toktogul Reservoir specific catchment area within the ridges‟ watersheds (Fig. 4.1): – Talass Ala-Too, Suusamyr-Too – on the North; – Kem-Irim-Too and northern prongs of the Fergan ridge, Babash-Ata – on the South; – At-Oynok – on the west. The Model includes the Ket‟men‟-Tyube Depression as the Reservoir riparian area. The southern slopes of the Talass and Suusamyr ridges are wide, slanting and are divided into separate big prongs. In this area of the Depression the main volumes of the sedimentary NeogenicQuarternary rocks, which fill the river valleys are present. These loose sediments are rich with water and, thus, the main groundwater sources are formed there. The northern slopes of the Kyok-Irim-Too, At-Oynok and Fergan ridges are short, intensely fragmented and are composed, mainly, of crystalline rocks. Loose rocks are purely present or are not present at all; due to this fact the southern edge of the Depression does not bear water. Numerical realization. Since the simulated area is a closed water-catchment basin the contour of the grid area is realized as tight boundaries – type II boundary condition (the flow Q = 0, Neumann condition). The ground surface is described with the digital relief model made basing on the Shuttle Radar Topography Mission (SRTM) data. 130 0 30 km 1000 800 2000 1500 3000 2500 4000 3500 4500 m Fig. 1. Geographical boundaries of the simulated area. Climatic factors. The climate here is sharply continental and dry. The spring, autumn and winter seasons are characterized by air intrusion from the west, which brings the major volume of moisture. In summer the mountain-valley wind prevails. Temperature. Because of considerable altitude variability the temperatures between the Ket‟men-Tyube Depression at the Reservoir water level and the watersheds differ significantly (see Fig.2). This regularity influences all the water balance items; each has its own functional dependence on the altitude. 8 5.0 6 4.5 Part of watershed area, % Temperature, oC 4 2 0 -2 -4 -6 -8 3.5 3.0 2.5 2.0 1.5 1.0 0.5 3900 3600 3300 3000 2700 2400 2100 1800 1500 1200 900 -10 0.0 -9 Altitude, m а) 4.0 -7 -5 -3 -1 1 3 5 7 9 Annual air tempereture, °C b) Fig. 2. Height-wise distribution of annual average temperatures, mm (а) and the temperature frequency diagram (b) (Кuzmichenok, 2008). 131 Precipitations (water balance augmentation part). The main portion of water resources is formed on the windward slopes of the ridges. Within the Ket‟men‟-Tyube Depression the average annual amount of precipitations is 250-300 mm, in the mountains the amount of precipitations grows up to 1200 mm (Fig. 3, 4). In the period from May to November the amount of precipitations makes 80% of the whole amount, the whole summer share is 8-10% (the minimum is in August – 3-5 mm). 1400 Precipitations, mm 1200 1000 800 600 400 3900 3600 3300 3000 2700 2400 2100 1800 1500 900 1200 200 Altitude, m Fig. 3. Annual precipitations distribution (mm) versus height (Кuzmichenok, 2008). Fig. 4. Annual rainfall (mm) within the specific water catchment of the Toktogul Reservoir (Kuzmichenok, 2008). 132 Evaporation (water balance diminution part). The amount of evaporation in each point is mainly determined as the ratio of precipitations volume to the air temperature, as well as the slopes‟ exposure to the sun and prevailing winds. Because of the sub-latitudinal location of the ridges the growth of evaporation at the northern and southern exposure slopes is described with different functions. In the result, for the simulated area the general trend is the growth of evaporation up to 2400 m (Fig. 5, 6). At higher places the evaporation decreases due to the annual average temperature decrease (Fig. 2). At the altitudes under 1800-2000 m the evaporation nearly completely compensates the precipitations, which means that nearly all the moisture falling in the form of rain or snow evaporates. 500 Evaporation, mm 450 400 350 300 250 3900 3600 3300 3000 2700 2400 2100 1800 1500 900 1200 200 Altitude, m Fig. 5. Annual evaporation distribution (mm) versus height. (Kuzmichenok, 2008). Fig. 6. Distribution of annual evaporation (mm) within the specific water catchment of the Toktogul Reservoir (Kuzmichenok, 2008). 133 Reservoir and rivers. The Reservoir occupies a considerable part of the Ket‟men-Tyube Depression with the absolute water level mark from 720 to 903 m above sea level. The main artery of the Reservoir is the Naryn River, which provides about 85 % of the water supply to the Reservoir. Within the simulated area we can also detach the water catchment areas of minor rivers, of which the most important are the Uzun-Akhmat, the Chychkan and the Torkent. The annual and monthly average values of the main rivers‟ run-offs, basing on the 1964-2006 observation data, are shown below in Table 1. Table 1. Annual and monthly average river run-offs within the Ket‟men-Tyube Depression in the period from 1964 to 2006, m3/s. Month I II III IV V VI VII VIII IX X XI XII Uzun9.96 9.06 9.32 23.9 60 78.8 57.8 33 20 15.2 13.3 11.4 28.6 Akhmat Chychkan 5.49 4.98 4.9 10.5 31.7 56.8 43.6 22.2 11.1 7.8 6.55 5.82 17.6 Torkent 3.11 3.11 3.28 8.49 22.2 38.1 23.1 8.67 4.41 4.1 3.83 3.32 10.3 Naryn 136 136 152 261 511 819 711 504 286 207 175 147 323 The height difference between the watersheds and the sea level in the Reservoir is 2000-3000 m, therefore all the rivers are torrents. Numerical realization. The altitude position of the rivers within the simulated area is set according to the relief digital model. Macro-convolutions of the riverbeds (the riverbed convolutions are longer than the dimensions of the numerical model blocks) are described by means of setting the rivers‟ reaches. The reaches‟ inclinations are calculated automatically basing on the grid approximation of the relief digital model. For each elbow the river geometry is described by the relief surface basing on which the parameter “water level” in the river, hRIV, is calculated. The water level in the river is determined as the difference between the relief surface in the point and the parameter “river bank height”. The river bed location is determined via the parameter „river depth” which is deducted from hRIV. The bottom sediment thickness is characterized by the parameter “screen thickness” with its own parameter “hydraulic conductivity”. For each river the area called “river basin” is set-up. In fact, this area is the river water catchment area. When the seepage with the function name “atmospheric precipitations” is set-up, the volume of atmospheric precipitations in the river basin is taken into account within the parameter “river flow”. When the model is calibrated, the corresponding quantity is compared with the data on the real gage lines. For each river reach the river geometry is described by the relief surface from which the “river depth” is counted. So the river bottom mark is determined. The water level in the river is determined as the difference between the relief level in the point and the “river bank height”. The parameter called “screen thickness” which characterizes the bottom sediments thickness with their “hydraulic conductivity” is added to the river bottom. The connection between the surface water and groundwater is realized using the III type BC (the flow Q = f(Δh) is the Cauchy condition). Since the rivers have torrential characters, the set penetrability of the bottom sediments is rather high – kf = 0.1-0.3 m/day. The water flows calculated for the “River”-type object are recalculated for the surface run-off. 134 Geological-hydrogeological conditions. The waterbearing strata within the specific water catchment area of the Toktogul Reservoir can be divided into two groups. The first group includes fractured grounds presented mainly by igneous rock and strongly metamorphosed formations mainly of the Pre-Cainozoic period. The second group includes loose sediments of the Neogenic and Quaternary periods. Fractured grounds are characterized by noticeable penetrability only through cuts in the vicinity of day, where the filtration coefficients reach n10-1 m/day. The thickness of the active fractured zone evidently, does not exceed 150-300 m down from the grounds surface. These geological formations play the roles of conductors only. Porous rocks are characterized by rather wide spread of the hydraulic conductivity from n10-1 to first meters per day. These geological formations play the roles of conductors because they have considerable capacitance. All watersheds within the simulated area are composed of fractured rocks, therefore the water reserve there exists only as season-depending snow and glaciers. The glacier area within the specific water catchment area of the Toktogul Reservoir is negligible, because it makes less than 0.5 %. The groundwater is fed both by direct seepage of atmospheric precipitations and by absorbed flat surface run-off in the mid mountains. Considerable role is also played by the groundwater underflow, however we do not have data on the river flow variation from the river heads down to estuaries. Numerical realization. The concept model of the groundwater flow formation is shown in Fig. 7. The information presented above, as well as the data obtained during the Project realization allow us to formulate the concept model of the groundwater and run-off formation, which presented in Fig. 7. Zone of direct precipitations absorption and surface flow transit to the underground flow Water transit zone to the underground conditions – crystalline weakly penetrable strata; Zone of groundwater discharge to the river network Resources formation zone – loose sandy-argillaceous sediments, relatively poor filtering; – argillaceous impervious sediments – loose sediments (mainly sand), well filtering; Fig. 7. Conceptual model of the groundwater flow and run-off formation in the Naryn and Toktogul Reservoir catchments area. The water resources formation zone is in the mid and high mountains; the main groundwater 135 reserve is accumulated due to the snow melting and spring rainfalls, since the maximum precipitations are in February-April. The water transit from snow and rains into the surface and groundwater run-offs takes place at the end of April and in May. In the mid-mountains the zone of direct precipitations absorption and of surface run-off transit to the groundwater is located in the near-rim zones. Within the Ket‟men-Tyube Depression water resources are not replenished because of the relatively low volume of precipitations and high evaporation. However, this is the part of the geological structure of the Ket‟men-Tyube Depression, where the main groundwater reserves are located. The groundwater discharges into the local river net and into the Toktogul Reservoir. The real distribution of the sediments filtration, gravitation and elastic capacity coefficients determines the quantity of atmospheric precipitations inflow into the water catchment area in comparison with the snow melting period. In the numerical model the glacier-based river feeding is not taken into account because the area covered with glaciers in the Reservoir catchment area does not exceed 0.4 %. The calculation results on the Snow-melt Run-off model (Tokarev, Savel‟ev, - in this collection of papers) allow us to deem that the groundwater feeding depends on the season-depending snow melting dynamics and is characterized by the time varying seepage coefficient, kε. The filtration coefficients of the surrounding rock are pre-set basing on the development work data (northern edge of the Ket‟men‟-Tyube Depression) and basing on expert estimations (mountain enclosure). See page (water balance diminution part). The volume of the groundwater seepage feeding is rather a complicated function, which includes the following parameters: – the main meteorological parameters specified above – the volume of precipitations and evaporation; – auxiliary meteorological factors – type of precipitations, their seasonal distribution, winds, tempo of transition through zero in spring (spring harmony), etc. – geological parameters – steepness of slopes, granulometric composition of the soil substratum, type and degree of bedrock penetrability, aeration zone capacities and other less significant aspects. Because of the presence of a big complex of influencing factors, during the Project we were unable to determine this parameter directly experimentally. The expert judgment of the seepage intensity can be determined basing on general consideration, as well as on the data on the groundwater isotope composition.According to this data the lower boundary of the groundwater seepage feeding is located higher than 1800-2000 m. At the same altitudes we observe considerable loose rock sediments thinning, which fill the river valleys in the Toktogul Reservoir specific catchment area. In the mountain countries the upper boundary of the groundwater feeding area, as a rule, is located at the altitudes where the surface steepness increases considerably, which forms the conditions for the complete transit of precipitations into the surface run-off. Apart from this the presence of the subrock – low fissured difference of crystalline rocks – also decreases the seepage feeding intensity. At last during cold seasons the ground and soil freezing has its contribution to this process, as well. In the case of the Toktogul Reservoir specific catchment area, the watersheds are located at the altitudes over 2700 m and have mainly flat tops (see Fig. 8). Therefore the water flowing from the watersheds is relatively slow. Thus, the area of the seepage feeding within the simulated area stretches up to the watersheds. 136 18 16 Angle of slope, ° 14 12 10 8 6 3900 3600 3300 3000 2700 2400 2100 1800 1500 1200 900 4 Altitude, м Fig. 8. Steepness distribution (°) versus altitude (Kuzmichenok, 2008). Numerical description of the groundwater feeding. Distribution of the annual rainfall and evaporation within the simulated area is estimated according to the digital (statistical) model of Kyrgyzstan moistening built basing on the data from weather stations (Kuzmichenok, 2008). Since the major parameter which controls the precipitations and evaporation is the altitude, then the maps of the annual rainfall and evaporation, on the whole, replicate the relief map. In the numerical model we use the grid approximation of annual rainfall and evaporation distribution. The volume of the seepage feeding in each grid node is calculated basing on the relation: ε = kεP, where ε is the seepage feeding layer, mm/year; kε is the seepage coefficient, parts of unity; P is the layer of precipitations in a certain point of the simulated area, mm/year The model calibration is performed basing on the balance equation: P = w + ET + ε = w + (1 – kε)P + kεP, (1) where w is the layer of the surface run-off, mm/year; ET is the layer of evapotranspiration (evaporation and transpiration by vegetation), mm/year. In the case under consideration evaporation is E = ET, since the layer of vegetation transpiration turns out to be insignificant.(Kuzmichenok, 2008). The spatial distribution of the quantity P is set basing on the digital moistening model of the Toktogul Reservoir specific catchment basin (Kuzmichenok, 2008). When solving the nonstationary problem we use the data on the annual rainfall. The characteristic image of the precipitations annual distribution graph for the stations located at the altitudes about 2000-2100 m, is shown in Fig. 9. The check quantity, w, is calculated basing on the data about the sizes of the water catchment areas of some rivers, determined over the relief digital model SRTM, as well as from the observations at hydrologic section: w = QRIV/SRIV, where QRIV and SRIV measured flow and water catchment area of the corresponding river. The quantity kε is selected in the course of the model calibration; at that the controlling (calibrating) parameters are the model values of wMOD, ETMOD and P MOD, calculated basing on the numerical solution. Geometrical description of the simulated area. The relief model is made basing on the data of SRTM (Fig. 10). 137 Precipitations,mm per month 70 – Suusamyr; 60 – Naryn; 50 – At-Bashy 40 30 20 10 0 I II III IV V VI VII VIII IX X XI XII Month Fig. 9. Monthly average precipitations based on the weather-station data in the period from 1964 to 2006. Fig. 10. Relief within the Toktogul Reservoir water catchment area (SRTM data). Then supporting design has been made. The concept developed at the preliminary Project phases provides for the geological environment approximation in six layers: – the three upper layers correspond to porous collectors: in the mountains they are alluvialdealluvial sediments, in the valleys they are loose neogenic and Quaternary sediments filling 138 the Ket‟men-Tyube Depression and the valleys of the Uzun-Akhmat, Chychkan, Torkent and Saragata rivers; – the three lower levels correspond to the zones of active, diminishing and low fissuring of the mountain ridge crystalline rocks. Within the Reservoir water area another layers identification is used for the approximation of the geological environment: – the two upper layers are used for the description of loose drifts formed after the Reservoir was filled with water; – the three mid layers correspond to loose neogenic and Quaternary sediments; – the one lower layer corresponds to the crystalline rocks of the Reservoir bed. The data on the geometry of separate strata within the simulated area are very scarce. During the analysis of the archival information we have discovered the description of the geological section in the proper scale for the Ket‟men-Tyube Depression only. In view of this fact we have decided to add the needed scope of data basing on the following consideration. The thickness of the loose rock sediments grows in the direction from the watershed towards the valleys of the rivers and the Depression itself. This growth has clear nonlinear character, therefore we propose using the following dependence for the reconstruction of the watershed surfaces:  Z  Z  C1 Z  C2 C1   ZM AX mZ MAX   mZ MIN  Z MAX  Z MIN C2  mZMAX   C1 ZMIN , , , where Z is the calculated absolute mark of the model strata bottom, m; Z is the absolute mark of the overlaying model strata (for the upper strata this is the relief mark); m(ZMAX), m(ZMIN) is the thickness of the strata on the watershed and at the Reservoir shore line, respectively, m. The proposed mathematical model will also allow calculation of the thickness growth of the active jointing zone of the crystalline strata in the direction from the valleys towards the watersheds and to predetermine the corresponding thicknesses of the model “formations”. Within the Ket‟men-Tyube Depression the calculated marks are adjusted according to the available information on the Neogenic and Quarterly deposits geometry known from the wells‟ boring data. At the phase of the data preparation to the calculation the pre-processor determined the grid approximation of the relief and separating surfaces. The external boundaries of the simulated area are externally indeterminate. The rivers Usun-Akhmat, Chychkan, Torkent are traced in the automated regime with further manual correction. At that the spatial position of the rivers and the correspondence of the water levels to the SRTM data and topographical maps are checked. The data on the water levels in the rivers are also used for the model calibration. The water catchment areas of the mentioned rivers were detached, as well as those of temporary water flows and dry valleys. The detachment was made automatically with manual correction. The water catchment areas, SRIV, were calculated for the rivers Usun-Akhmat, Chychkan, Torkent, as well as the areas of temporal water flows and dry valleys. 139 Parametrical model filling; setting boundary conditions The non-homogeneity zones are manually detached over parameters with account for all earlier obtained data and according to the accepted schematization. The detached non-homogeneity zones are approximated by the processor on the grid layout. For example, the grid approximation of the precipitations and evaporation (E) layer spatial distribution (P) is performed basing on the distributions presented in Figs. 4 and 6. According to the moistening balance model (Kuzmichenok, 2008) the surface run-off, w, is the difference between the precipitations and the evaporation: w = P – E. In the numerical hydro-geological model of the Toktogul Reservoir catchment area the quantity w (the part of the precipitations layer feeding the surface run-off) is taken as the augmenting part of the water balance P MOD = w. This is done to exclude the necessity to simulate evaporation. In this case the atmospheric feeding in the model falls into the direct surface run-off to the rivers and the seepage: P MOD  wMOD   MOD  (1 k )  P MOD  k  P MOD , where wMOD is the surface run-off model layer, mm/year; εMOD is the model layer of the groundwater seepage feeding, mm/year; kε is the seepage coefficient. In each calculation point the precipitations layer which goes to the balance augmenting part of the Toktogul Reservoir specific catchment area is the difference between the precipitations and the evaporation: P MOD  P  E  w , where w is the surface run-off, according to the statistics (balance) model (Kuzmechenok, 2008). In this case the atmospheric feeding in the model falls into the direct surface run-off to the rivers and the seepage. The simplified description of the summarized water balance in the model is as follows: P MOD  wMOD   MOD  (1 k )  P MOD  k  P MOD where wMOD is the model layer of the direct surface run-off, mm/year; εMOD is the model layer of the groundwater seepage feeding, mm/year; kε is the seepage coefficient. MOD The spatial distribution of the surface run-off, w , is calculated during the model solving and MOD is used during calibration. For this purpose the model layer of the surface run-off, w , is compared with the value obtained when the statistics moistening model of the Toktogul Reservoir catchment basin (Kusmichenok, 2008) was developed. Boundary conditions at the rivers were determined as the third-type condition (type III BC – Cauchy condition). This condition is determined as the dependence of the cross-flow to/from the river on the pressure, thickness and filtration coefficient gradients of the screen in the river bed – kf . Within the simulated area all the rivers have a torrential character, therefore there should be tight connection with the rivers. In view of this the initial values of the bottom sediments filtration coefficient are taken equaling kf = 1 m/day. Boundary conditions at the Reservoir are also set using the type III BC (Cauchy condition), 140 specially modified for the water level setting in the Reservoir. The difficulty of the program realization of this boundary is that the water level in the Reservoir (HWSR – water table in water-storage Reservoir) depends on the volume of the accumulated water (V WVR –water volume in Reservoir). The volume of the accumulated water, in its turn, depends on the combination of two balance constituents – the Naryn river flow together with the flows of minor rivers (QRIV) and the water discharge from the Reservoir (QRD – reservoir discharge): HWSR = f(VWVR), The water flow in the Reservoir is mainly determined by the contribution of Naryn and minor rivers (QRIV). To less extent the Reservoir water balance depends on the flat-bed flow (the surface constituent of QSURF) and the groundwater discharge directly into the Reservoir (QGW). However, the latter two quantities are quite important when simulating the water quality variation in the Reservoir. Thus, the volume of the water accumulated in the Reservoir is determined by the relation of the balance items at the time interval t: f(VWVR) = (QRIV + QSURF + QGW – QRD.)Чt. The ration of the water level in the Reservoir, H, and the accumulated water volume, VWVR, is known in advance or is adjusted in the course of the bathymetrical and topographical survey ordered by the Toktogul HPS Cascade Administration (Fig.10. Adjustment…, 2010; Shabunin et al. Calculation…, in this collection of papers): VWVR = 4.7735Ч10–9ЧH6 –2.3103Ч10–5ЧH5 + 4.6499Ч10–2ЧH4 – 49.813ЧH3 + 29955.96ЧH2 – 9588308ЧH + 1276190130 (1) the approximation accuracy is R2 = 0.999993. For the use in the numerical model the equation (1) is solved with the reference to the parameter H, since the quantities QRIV, QSURF and QGW are under the determination, and QRD was set by the user basing on the data of the Toktogul HPS Cascade Administration. The equation (1) is solved with iterations in the course of the data preparation by the pre-processor. Basing on the obtained solutions the H ч VWVR is tabulated with the step approximately 1 m, after which the approximation function used during the process of solving is built. Filtration parameters. At present one of the most complicated issues is the evaluation of the strata filtration parameters. The archival data about experimental-filtration sampling concerning the investigated area are very poor. At that, the earlier bored wells characterize the loose sediments of the Ket‟men-Tubinskaya Depression only, because they have been bored for the purposes of groundwater operation. The wells which could characterize the groundwater within the mountain enclosure (areas of fractured ground development) are practically unavailable. The relief model, the data on the groundwater filtration parameters allow us to split the simulated model into fragments within which different grid fragmentation density is realized. (Fig. 12). The approximation of the model area itself by the grid fragmentation is shown on Fig. 13. The grid fragmentation density is selected so that within the loose sediments distributions which are better characterized by the filtration parameters, the model representation of the environment is the most detailed one. 141 25 350 300 20 15 200 150 10 Volume (km3) Area (km2) 250 100 5 50 0 910 900 890 880 870 860 850 840 830 820 810 800 790 780 770 760 750 740 730 720 710 700 0 Water level height (m) area volume Fig. 11. Measurement results of water levels and volume calculation, and of the Toktogul Reservoir water. Fig. 12. Presentation of the Toltogul Reservoir catchment area by the fragments with different grid discretization. 142 Fig. 13. Grid approximation of the Toktogul Reservoir catchment area. Model calibration Filtration calculation in stationary set-up. Calculation of the saturated-non-saturated filtration in stationary set-up was performed for the calibration of the penetrability parameters (filtration coefficients) and the model balance check. At the calibration a number of model quantities with their values obtained according to the observations were compared. 1. Checking over the mean river flows. The model flow volume was calculated for each river; for this purpose the water flows at all elbows were summarized: MOD   QiMOD QRIV . The simulation results were compared with the initial data (Table 1). MOD 2. Checking over the spatial distribution of the surface run-off layer, w . The spatial KUZMICH . approximation of the surface run-off w , built with account for the observations is known (Fig. 14). 143 Fig. 14. Annual recharge flow layer (mm) within the specific water catchments area of the Toktogul reservoir.(Kuzmichenok, 2008). Kuzmichenok V.A. used a simple model where the groundwater run-off is not present (Kuzmichenok, 2008): P KUZMICH  wKUZMICH  E KUZMICH , KUZMICH KUZMICH is the precipitations level, mm/year; w is the surface run-off level, mm/year; where P KUZMICH E is the evaporation level, mm/year. MOD  wKUZMICH by default, since in the model the When solving the non-stationary problem, w atmospheric feeding level is split into: MOD – the constituent w , which describes the direct run-off to the rivers; – the seepage constituent,  , which forms the groundwater discharge into the river net taking place with time delay. When the problem is solved with the stationary set-up, when the strata capacity is not taken into MOD KUZMICH account, one can use the comparison of w with w for the model calibration. For this purpose MOD MOD KUZMICH the graph w ч w was built. In the graph dots form a line with the inclination 1:1 starting from the coordinate origin. There were no surges there. 3. Apart from this a number of other checks should be applied. A. The condition is checked, according to which in the area of groundwater feeding and transit the levels/pressures cannot be higher than the ground surface mark. The exclusion is the river valleys. 144 MOD The graph h ч Alt is built for the checking purposes. The correctness of the initial data setting and/or the calculation correctness are checked for the areas where the dots swing to the right from the line 1:1. B. The condition is checked, according to which the groundwater levels/pressures in the cells with the river elbows must be close to the water levels in the rivers (obtained according to the MOD RIVER topographical map). For the checking purposes the graphs h чh are built. The correctness of the initial data setting and/or the calculation correctness were checked for the areas where the dots swing to the right from the line 1:1. C. The condition is checked, according to which the groundwater levels/pressures in the cells located near the Reservoir must be close to the water level in it. For the checking purposes the graph hMOD ч h RESERVOIR is built. The correctness of the initial data setting and/or the calculation correctness are checked for the areas where the dots swing to the right or to the left from the line 1:1. D. The solution is checked for the absence of surges. For this purpose the hydraulic gradient between adjacent cells: I MOD  (h2  h1 ) / l , and the relief rake between the same cells : I RELIEF  ( Alt 2  Alt1 ) / l are calculated, where h2 and h1 are the levels/pressures in the cells, m; Alt2 and Alt1 are the relief marks in the cells, m; l is the distance between the geometrical centers of the cells. MOD RELIEF чI were drawn, which had to be straight lines without surges and swings The graphs I of separate dots. The following feature of the hydrogeological model of the simulated area is used. Significant MOD  0 across the filtration flows towards the Reservoir, hydraulic gradients should not be present I between the cells located along the Reservoir shore. MOD E. The model pressures ( h ) were compared with the data of the hydrogeological map, because this is the only factual material available for us, though fragmentary. The filtration (kf) and seepage (ε) coefficients are varied for the correction of the model solution. After the mentioned parameters are changed, all the calculations and the controlling graphs are made again until the desired result is achieved. Filtration calculation in non-standard set-up. The model of the saturated-non-saturated filtration of the Toktogul Reservoir specific catchment area in the non-stationary set-up is the complete solution of one the Project tasks. For the realization of this model the feeding is made non-stationary. For this purpose the time dependences of P, E and ε are set. At the phase of the saturated-non-saturated filtration calculation in the non-stationary set-up the capacity parameters are calibrated and the model balance is adjusted. The model calibration is made using the scheme described above; for which a number of calculated model values are compared with the values obtained due to observations. In addition to the used calibration criteria we use the factual data on the Naryn run-off (Fig. 15). 145 1500 1000 500 Water flow discharge, m3/s – data 0 50 100 150 200 250 300 Month Fig. 15. Factual run-off the Naryn river in the period from 1976 to 2006. Simulation of the water quality variation in the Reservoir. The background of the water quality formation in the Reservoir is the Naryn river flow, which contributes about 85 % of water into the Reservoir water balance. Within the Ket‟men‟-Tyube Depression we can detach the ridges Shamshykal-Ata (on the northeastern shore of the Reservoir) and Ortok-Too (on the south-eastern shore), where evaporites are spread. Because of the presence of easily soluble salt sediments these areas are the sources of additional saline load for the Reservoir. During the Project#KR-1430 we managed to show that the main ion flow is caused by the surface wash-out. Basing on the results of in-situ observations we discovered that mineralization of the surface water flowing from the Shamshykal-Ata mountains (the north-eastern shore of the Reservoir) during winter time reaches 300 g/l. The salt supply to the Reservoir less depends on the groundwater discharge, which mineralization, according to the measurements, can be 3-5 g/l. For the groundwater weak dependence of water salinity on rock permeability takes place (Fig. 16). 1.2 y = -0.0201x + 0.7417 R2 = 0.0942 Salinity, g/l 1 0.8 0.6 0.4 0.2 0 0 5 10 15 20 25 Permeability, m/day Fig. 16. Relation between the rock permeability and groundwater mineralization in the Toktogul Reservoir basin 146 Numerical realization. For the solution of the problem of mass transport in the region of Shamshykal-Ata mountains for the simulated periods determined as “winter time” we set the increased mineralization of the water balance constituent controlled by the parameter “atmospheric precipitations”. Conclusions. The built model can be used for the forecasting at water discharge from the Toktogul Reservoir. For this purpose the regional weather model should be built. In this model basing on the probabilistic analysis the scenarios of normal weather conditions must be taken into account (a number of years with normal mean annual supply with precipitations). Apart from this the probability of extreme conditions such as low-water and high-water years must be estimated. The series lengths, frequency and sequence of “normal”, “low-water” and “high-water” years must be set basing on the analysis of the available hydrometeorological material of the regression models. Reference Kuzmichenok V.A. Digital models of humid characteristics of Kyrgyzstan. (Mathematical and cartographic modelling). Bishkek, publication of the Kyrgyz-Russian Slavic University, 2008, p. 237. Adjustment of the Toktogul Reservoir useful capacity. Report on the research under the topic # D-31103-44/143 - Bishkek: IWP and HP KAS, 2010, p. 70. 147