Arithmetic Average: Sum of all precipitation values divided by the number of stations 1 n

Transcription

1 Char of ssgnment Suggested soluton PRCIPITTION Task (Charactersaton of the study area) rea: 43.3 km 2 Rver length: km Hghest pont: 346 m a.s.l. Lowest pont (staton elevaton): 668 m a.s.l. Domnant landuse: alpne farmland, pasture (37.8%), vegetaton-free area (33.5%) glacerzed area: 2.06% (2.0% also correct) Retenton capacty: sol type not defned (4.6%); very low (35.8%) extreme low (20.5%) Permeablty: sol type not defned (4.6%); excessve (48.9%) verage dscharge :.75 m³/s (verage annual flood :.4 m 3 /s!) Hghest flood: 9. m³/s (July 975) Task 2 (Methodology) 2. rthmetc verage: Sum of all precptaton values dvded by the number of statons n P = P = n where P areal ranfall [mm] n number of statons [-] P precptaton sum of statons per tme nterval [mm] Thessen-Polygons: - measurement value of each staton gets an area weght - each pont n the catchment s assgned to the nearest staton n = P = P where P areal ranfall [mm] n number of statons [-] catchment area [L 2 ] area whch s assgned to staton [L 2 ] P precptaton sum of staton for a gven tme nterval HS 7, Hydrology I, ssgnment Page

2 Char of Isohyets: - nterpolatng the precptaton depth of neghbourng statons result n lnes wth the same precptaton depth - accountng for the orography n = P = P * where P areal ranfall [mm] n number of subareas [-] catchment area [L 2 ] area between two sohyets [L 2 ] P average precptaton n subarea [mm] rthmetc verage: + smple - does not account for spatal dstrbuton of the statons -> evenly dstrbuted statons necessary - orographc effects neglected Thessen-Polygons: + accounts for uneven dstrbuton of the statons + for the same choce of statons polygons need to be derved just once relatvely smple - orographc effects neglected Isohyets: + spatal dstrbuton of the statons taken nto account + orographc effects taken nto account - work ntensve - meteorologcal experence needed 2.2 Catchment I: Methods: rthmetc verage, Thessen-Polygons or Isohyets Reasons: Statons evenly dstrbuted and relatve homogeneous topography rthm. verage: Statons B, C, D - statons wthn the catchment suffcent, statons evenly dstrbuted, n prncple also statons outsde of the catchment can be consdered. Thessen-Polygons:, B, C, D, catchment s not clearly bounded; therefore statons and can be assumed to be representatve as well. Isohyets:, B, C, D, due to the locaton n the lowland all statons can be used. Catchment II: Methods: Isohyets (opt. Thessen-Polygons) Isohyets are preferable for alpne catchments snce the nfluence of the topography s ncluded n drawng the sohyets. Thessen-Polygons are also often used, but orographc effects are not taken nto account. The results should be assessed crtcally. HS 7, Hydrology I, ssgnment Page 2

3 Char of, D, the catchment s bordered by mountan ranges, therefore the statons outsde can be assumed not to be representatve. They have also no relevant nformaton for the sohyets method. Task 3 (Computaton of the real Ranfall) 3. real Ranfall (mm) Tme real Ranfall Thessen-Polygons boxes fracton area # [-] km 2 Polygon Staton Polygon Staton B Polygon Staton C Polygon Staton D : : : : : : : : : : : : : Σ Gebetsnederschlag [mm] :30 9:00 9:30 20:00 20:30 2:00 2:30 22:00 22:30 23:00 23:30 00:00 00:30 Uhrzet HS 7, Hydrology I, ssgnment Page 3

4 Char of Task 4 (DDF-Curve) 4. Statstcal test: Kolomogorov-Smrnov, Ch-square-test Graphcal test: probablty paper 4.2 Sample moments Duraton (h) verage m T Varance s 2 T Parameters of the Gumbel dstrbuton: 4.4 Duraton (h) α T u T Precptaton depth h T (R) Precptaton depth h T (R) return perode R Duraton (h) HS 7, Hydrology I, ssgnment Page 4

5 Char of Data only avalable for 30 years. - xtrapolaton necessary to estmate extreme events wth large return perod (> 00 years) results afflcted wth large uncertanty. - It s not clear whether the extreme events really follow the chosen dstrbuton or f another dstrbuton wth other parameters mght be more sutable. HS 7, Hydrology I, ssgnment Page 5