Study on prediction of snowmelt using energy balance equations and comparing with regression method in the Eastern part of Turkey

Transcription

1 Journl o Scientiic & Indutril Reerch Vol. 64, July 2005, pp Study on prediction o nowmelt uing energy blnce eqution nd compring with regreion method in the Etern prt o Turkey Chit Yerdelen nd Reşt Acr Deprtment o Civil Engineering, Atturk Univerity, Erzurum, Turkey Received 28 July 2004; revied 16 Mrch 2005; ccepted 16 My 2005 Thi pper preent two nowmelt model: i) Energy blnce model (EBM); nd ii) Liner regreion model (LRM). To decide uitble model or the bin, dily men low dt o Kırkgöze dichrge guging ttion o Stte Hydrulic Work (DSİ) w pplied to Kru-Kırkgöze mountinou bin tht h km 2 wterhed dringe bin nd elevtion rnge o m in the etern prt o Turkey. EBM w pplied during now melting period, in Mrch-My or Hourly temperture (T), wind velocity (V), hortwve rdition (Rd), reltive humidity (RH) nd intenity o rinll (Y) were ued input prmeter. Intervl o contnt in EBM tht re now urce conductnce (K S ), now urce turted conductnce (K St ), liquid holding cpcity o now (L k ), reh now viible bnd relectnce (α vo ) nd reh now ner inrred bnd relectnce (α iro ) were determined or ech period. The coeicient o correltion (R) between now melting dt clculted by EBM nd guging dt were in the rnge o or ech yer (R 2 = ). Moreover, LRM i etblihed or the only period o 1987 uing oberved dichrge o bin nd meteorologicl vrible. The computed coeicient o correltion (R) between regreion model including ive predictor vrible (T, Rd, RH, V & Y) nd guging dt w obtined 0.87 (R 2 =0.757). Two model re then compred in term o coeicient o correltion. EBM w ound more repreenttive thn LRM to predict nowmelt in etern prt o Turkey due to high coeicient o correltion. Keyword: Energy blnce, M blnce, Snow, Snowmelt model, Regreion, Hydrology Introduction Snow i complicted nd rpidly evolving mteril, which my hve igniicnt verticl nd horizontl vrition in it therml, hydrulic nd mechnicl propertie. Snowmelt i igniicnt urce wter input o importnce to mny pect o hydrology including wter upply, eroion nd lood control 1. Modeling nowmelt in hydrologicl model i epecilly problemtic becue n incorrectly imulted melt event not only incorrectly predict low on tht dy, but lo on the dy when the ctul melt occur 2. Snowmelt i driven primrily by energy exchnge t the now-ir interce. The rte o nowmelt depend on the vilbility o energy to nowpck nd i uully dominted by net rdition nd temperture. Cold nowpck (< 0 C) hve negtive energy blnce. Wrming cue the pck to become iotherml (=0 C) nd dditionl energy reult in ppoitive energy blnce nd melt 3. Etimting wterhed runo in re with eonl now cover *Author or correpondence E-mil: rcr@tuni.edu.tr require nowmelt lgorithm be prt o the modeling ytem. Generlly, computtion o nowmelt rom wterhed i mde uing either n energy blnce pproch or ome index pproch. The energy blnce, employed in the preent work, require inormtion rdition energy, enible nd ltent het, energy trnerred through rinll over now nd het conduction rom ground to nowpck. An extenive review on thi topic i vilble 4. HEC-1, ingle-event model, ue either degree-dy temperture index method or impliied energy blnce pproch 5. SSARR (Stremlow Synthei nd Reervoir Regultion) w developed by the North Pciic Diviion (NPD) Corp o Engineer in 1956 to provide hydrologic imultion on nowmeltdominted river ytem or plnning, deign, nd opertion o wter control work 6. The Generlized Stremlow Simultion Sytem, requently identiied the Scrmento Ctchment Model, i mjor component o the Ntionl Wether Service River Forect Sytem (NWSRFS) 7. The now ccumultion nd bltion routine ued in NWSRFS re bed primrily on the eort o Anderon 8, who developed combined energy nd temperture index

2 YERDELEN & ACAR: STUDY ON PREDICTION OF SNOWMELT USING ENERGY BALANCE EQUATIONS 521 method tht ued only temperture nd precipittion input meteorology. A dierence rom other temperture index method i tht ech phyicl proce i repreented eprtely, rther thn uing ingle melt index. Procee re conceptully modeled nd include nowpck ccumultion, het exchnge t the ir/now interce, rel extent o now cover, het torge within the nowpck, liquid wter retention, lgged trnmiion o melt through the pck, nd het exchnge t the ground/now interce. SNTHERM 9, one-dimenionl m nd energy blnce model tht conider the procee occurring within multi-lyered nowpck, include now ccumultion, compction, grin growth, melt, condention melt, dvection, pore wter retention, nd wter low through the pck. SNTHERM, being the mot comprehenive o the model reviewed, h the mot divere cientiic vlidtion. In the preent pper, n Energy Blnce Model (EBM) nd Liner Regreion Model (LRM) or nowmelt in etern prt o Turkey re developed. Conidering energy blnce or mount o now correponding to unit re, two dierentil eqution re obtined. Reulting dierentil eqution ytem i olved numericlly by uing the Runge-Kutt method. LRM i etblihed uing let qure method. Both model re compred to decide which model i uitble or Kırkgöze bin. Fig. 1 Mp o Turkey nd Kru-Kırkgöze bin Bin nd Dt The model re pplied to Kru-Kırkgöze bin hevy nowll region (re, km 2 ; elevtion, m), which reche nnul men now depth o 2 m during winter. Kru- Kırkgöze bin h mountinou nd oretle re nd h been derived by 7 tributrie nd Kırkgöze River, which i one o the mjor contributor o wter. Snowmelt rom mid-mrch to June contribute percent o the nnul runo o Kru bin. Dt o thi model w obtined rom Erzurum Meteorology Sttion tht i elevted 1869 m nd locted on 39º 57 ltitude, 41º 10 longitude. Precipittion dt w obtined rom Şenyurt Meteorology Sttion tht i elevted 2160 m nd locted on 40º 11 ltitude, 41º 29 longitude. Energy content nd wter equivlence vlue were tken rom Güzelyyl now obtining ttion tht i elevted 2070 m nd locted on 40º 12 ltitude, 41º 29 longitude (Fig 1). Energy Blnce Model The energy blnce or the het budget o nowpck govern the production o melt wter. Thi method involve n ccounting o incoming energy, outgoing energy nd the chnge in energy torge or nowpck or given time. The energy i then expreed the het equivlent o nowmelt. The preence o cloud cover nd vegettion cover

3 522 J SCI IND RES VOL 64 JULY 2005 igniicntly ect the energy blnce o now urce. The nowpck i chrcterized by: Wter equivlence, W (m); Energy content, U (kj.m -2 ); nd, Age o now, which i only ued or lbedo clcultion. Wter equivlence include ny liquid wter preent in the nowpck. The energy content (U) i reltive to reerence tte o wter t 0ºC in the ce phe. U (>0) men the nowpck (i ny) i iotherml with ome liquid content nd U (<0) cn be ued to clculte the nowpck verge temperture T (ºC). The model i deigned by ollowing input: Air temperture, T (ºC); Wind peed, V (m/); Reltive humidity, RH (%); Precipittion, Y (m/h); nd Incoming olr rdition; Q i (kj m -2 h -1 ). Given the tte vrible U nd W, their evolution in time i determined by olving the ollowing energy nd m blnce eqution: du = Qn + Qli Qle + Qp + Qg + Qh + Qe Q (1) m dt dw = Y M r E (2) dt where Q n, net hortwve rdition; Q li, incoming longwve rdition; Q le, outgoing longwve rdition; Q p, dvected het rom precipittion; Q g, ground het lux; Q h, enible het lux; Q e, ltent het lux due to ublimtion/ condention; nd Q m, dvected het removed by melt wter. In Eq. (2) (ll in m h -1 o wter equivlence); Y=precipittion rte, M r =meltwter outlow rom nowpck nd E=ublimtion rom the nowpck. A computer code w mde bed on Runge-Kutt method to olve et o non-liner Eq (1) nd (2). Time tep w choen one hour in the numericl olution. Shortwve Rdition Net hortwve rdition i clculted : Q Q ( 1 α) (3) n = i where Q i i the incoming hortwve rdition tht i directly meured nd α i now lbedo, which i clculted 10 unction o now urce ge nd olr illumintion ngle. The ge o the now urce i retined tte vrible, nd i updted with ech time tep, dependent on now urce temperture nd nowll. Relectnce i computed or two bnd; viible (< 0.7 µm) nd ner inrred (> 0.7 µm). Then lbedo i tken the verge o the two relectnce: α vd + α α = ird (4) 2 Where; α = ( 1 C F ) α (5) vd ird v ir ge ge vo α = ( 1 C F ) α (6) iro α vd nd α ird repreent diue relectnce in the viible nd ner inrred bnd repectively. F ge i unction to ccount or ging o the now urce. C v (=0.2) nd C ir (=0.5) re prmeter tht quntiy the enitivity o repective bnd lbedo to now urce ging (grin ize growth), nd α vo nd α ird re reh now relectnce in ech bnd. F = τ /( 1+ τ ) (7) ge where τ i non-dimenionl now urce ge tht i incremented t ech time tep by quntity deigned to emulte the eect o growth o urce grin ize: r1 + r2 + r3 τ = t (8) τ 0 Here t i the time tep in econd with τ 0 =10 6. The r 1 i prmeter dependent on now urce temperture, T (ºK), which repreent the eect o grin growth to vpor diuion. r 1 = exp T (9) r 2 repreent the dditionl eect ner nd t reezing point due to melt nd rereeze: r min( 10 2 = r 1,1) (10) r 3 =0.03, which repreent the eect o dirt nd oot. Longwve Rdition Incoming long wve rdition i intended to be model input. However, where thi i not vilble it i etimted bed on ir temperture (T in K) uing the Sten-Boltzmnn eqution with ir emiivity (ε ) bed on ir vpor preure (e in P), ir temperture nd cloud cover.

4 YERDELEN & ACAR: STUDY ON PREDICTION OF SNOWMELT USING ENERGY BALANCE EQUATIONS 523 Q li = ε σt (11) 4 Outgoing long wve rdition i Q lo = ε σt (12) 4 where ε (0.97-1, here 0.99) i emiivity, σ the Sten Boltzmnn contnt nd T i now urce temperture (K). Advected Het rom Precipittion Meured precipittion rte Y (=Y y +Y k ), i prtitioned into rin Y y (T T y =3ºC), nd now Y k (T T y =-1ºC), (both in term o wter equivlence depth) uing the ollowing rule bed on ir temperture T, where T y i threhold ir temperture, bove which ll precipittion i rin, nd T k threhold ir temperture, below which ll precipittion i now 11. The temperture o rin i tken the greter o the ir temperture nd reezing point nd the temperture o now i the leer o ir temperture nd reezing point. The dvected het i the energy required to convert thi precipittion to the reerence tte (0 C ice phe). ( ) ( ) Qp = Y y h ρw + Cw ρw mx T,0 + Yk C ρw min T,0 (13) Ground Het Flux Since ground het lux i not known, it i tken to be zero. Senible Het Flux Senible het lux i given ollow. Q h = KVρ C T T ) (14) ( Senible het lux between the now urce nd ir bove i modeled uing the concept o lux proportionl to temperture grdient. Conidering unit volume o ir, the het content i ρ C T, where ρ i ir denity (determined rom tmopheric preure nd temperture), C ir peciic het cpcity, nd V wind peed. P ρ = (15) RdT K, turbulent trner coeicient re unction o urce roughne nd nominl meurement height or ir temperture nd wind peed. On compring the uul expreion or turbulent trner in logrithmic boundry lyer proile or neutrl condition, the ollowing expreion i obtined: 2 K k ln( / 0 ) = (16) Z z where Z i height tht i meure wind peed; z o i roughne height t which the logrithmic boundry lyer proile predict zero velocity; nd k i von Krmn contnt 12. Ltent Het Flux Ltent het luxe between the now urce nd ir re modeled uing the concept o lux proportionl to vpor preure grdient ollow: 0.622hv Qe = K V ( e e ) (17) R T d where e i vpor preure t now urce, now umed turted t T nd clculted uing polynomil pproximtion; e i ir vpor preure, R d i dry g contnt, nd h v ltent het o ublimtion 13. ((17.27T ) /( + 237,3) ) = T e e (18) e = erh (19) Snow Surce Temperture Since now i reltively good inultor, T i in generl dierent rom T. Thi dierence i ccounted or uing n equilibrium pproch tht blnce energy luxe t the now urce. Het conduction into the now i clculted uing the temperture grdient nd therml diuivity o now. Q = K ρ C T T ) (20) ( where K nd termed now urce conductnce re nlogou to the het nd vpor conductnce. A vlue o K i obtined by uming contnt. Then uming equilibrium t the urce, the urce energy blnce give: Q = Q + Q + Q + Q T ) + Q ( T ) Q ( T ) (21) n li p h ( e le Anlogou to the derivtion o Penmn eqution or evportion, the unction o T in thi energy blnce eqution re linerized bout reerence temperture T*, nd eqution i olved or T : * * *4 Qn + Qli + Qp + KT ρc Khv ρ( e ( T ) e T / P + 3ε T + ρct K T = *3 ρc K + ρc K h vρ / P + 4ε T (22)

5 524 J SCI IND RES VOL 64 JULY 2005 Tble 1 Vlue o intervl o the K S, K St, L k, α vo, α iro contnt Vlue K S K St L k α vo α iro Reported in literture Clculted or EBM where = de /dt nd ll temperture re bolute. Thi eqution i ued in n itertive procedure with n initil etimte T* = T, in ech itertion replcing T* by the ltet T. The procedure converge to inl T, which, i le thn reezing, i ued to clculte urce energy luxe. I the inl T i greter thn reezing, it men tht the energy input to the now urce cnnot be blnced by therml conduction into the now. Surce melt will occur nd the iniltrtion o melt wter will ccount or the energy dierence nd T i then et to 0 C 13. Advected Het Removed by Melt Wter The energy content tte vrible U determine the liquid content o the nowpck. Thi reult, together with Drcy lw or low through porou medi, i ued to determine the outlow rte. 3 M r = K t S (23) where K t i the now turted hydrulic conductivity nd S i the reltive turtion in exce o wter retined by cpillry orce. S i given by: S L L 1 L ρ w ρ w L c / L ρ ρ = c (24) = U /( h W ) (25) ρ w where L denote the m rction o totl nowpck (liquid nd ice) tht i liquid, L c the cpillry retention rction o the olid mtrix wter equivlence nd ρ i the denity o ice 14. Q m = ρ h M (26) w r Reult o the Energy Blnce Model EBM w run or nine eon (1 Mrch - 31 My) o , the nowmelt eon or thi re. Intervl o EBM contnt tht re now urce conductnce (K S ), now urce turted conductnce (K St ), liquid holding cpcity o now (L k ), reh now relectnce in viible bnd (α vo ), nd diue relectnce in the ner inrred bnd (α iro ), re determined or ech period. Vlue o intervl o K S, K St, L k, α vo, α iro re clibrted with dily men low dt o Kırkgöze dichrge guging ttion o Stte Hydrulic Work (DSİ) or ll period (Tble 1). The curve o imulted nd oberved dily dichrge (Fig 2 & 3) re imilr but time lg re determined three dy dichrge due to prticulrly ctchment routing, wter retention nd movement, hydrulic conductivity, rerozen now nd oil condition tht chnge rom point to point in the re. High coeicient o correltion re computed or imulted nd oberved hydrogrph o dily dichrge or ech yer or the entire period. In ome prt o hydrogrph, dierent dily dichrge re determined, becue o dierent prmeter in dy. For 21, 24 nd 28 April 1987, dierent dily dichrge were obtined by EBM. Hourly chnging o rdition nd temperture o thee dy re plotted to evlute the dierence (Fig 4, b). Chnging o rdition i norml when it compred with other dy nd lo chnging temperture i norml. The reon or dierent clcultion o nowmelt my be the eect o topogrphic prmeter (elevtion, pect, lope) nd meteorologicl vrible (previling wind direction, temperture). In ddition to thee, dily men vlue o input prmeter or Mrch 1987 re ollow: temperture, -5.9 ºC; rdition, 705 kj/m 2 ; velocity o wind, km/h; humidity, 0.753; nd, rinll, m/dy. All thee vlue re too mll to produce nowmelt or thi month. Ater Mrch, beginning o the irt hl o the April 1987, the clculted nowmelt begin to incree. During April nd My (repectively), dily men vlue o input prmeter re ollow: temperture, 2.83, 12.16ºC; rdition, , kj/m 2 ; velocity o wind, 2.53, 2.88 km/h; humidity, 70, 51 %; nd, rinll, , m/dy 15. To judge ccurcy o imulted nd oberved tremlow, liner cle plot o imulted nd oberved hydrogrph o dily dichrge or ech yer or entire clibrtion nd veriiction period were mde (Fig 5). The high coeicient o correltion o nine eon were clculted (Tble 2).

6 YERDELEN & ACAR: STUDY ON PREDICTION OF SNOWMELT USING ENERGY BALANCE EQUATIONS 525 Fig 2 Simulted nd oberved dily dichrge Fig 3 Uing EBM comprion o computed nd oberved tremlow-wter (1987)

7 526 J SCI IND RES VOL 64 JULY 2005 Reult o the Regreion Model A multiple LRM i etblihed only or 1987 eon uing 552 dt point. The criterion vrible i the oberved dily dichrge (Q c ). Five predictor vrible re men dily temperture (T), wind velocity (V), reltive humidity (RH), rdition (Rd) nd precipittion (Y). The correltion mtrix (Tble 3) i 6x6 ymmetric mtrix. The determinnt i computed to be ; uch low vlue indicte tht intercoreltion i high. Stndrd error i 4.06 nd degree o reedom i 86. Regreion eqution i obtined uing the let qure method nd i ollow: Q c = 16, ,566T + 0,109V 18,388RH + 0,001593Rd + 220, 291Y (27) Oberved vlue nd predicted vlue rom LRM re plotted with time (Fig 6). The computed coeicient o correltion (R) i 0.87 (R 2 =0.757), which men tht the eqution involving ive predictor vrible explin 75.7 percent o the vrition in the nowmelt dichrge (Q c ). T i the mot eective vrible in the LRM (Tble 3). The Fig 4 Vrition in melt ctor on 21, 24, 28 April 1987: ) Temperture; b) Rdition Tble 2 Simulted nd oberved dichrge nd coeicient o determintion or Yer Totl imulted dichrge Totl oberved dichrge Coeicient o Determintion R Fig 5 Reltionhip o imulted totl dily dichrge nd oberved totl dily dichrge

8 YERDELEN & ACAR: STUDY ON PREDICTION OF SNOWMELT USING ENERGY BALANCE EQUATIONS 527 Tble 3 Correltion mtrix T V RH Rd Y Q c T 1 V RH Rd Y Q c Fig 6 Uing LRM comprion o computed nd oberved tremlow-wter (1987) coeicient o correltion or temperture i It men tht T explin 69.6 percent o the vrition in Q c by itel. Thu, V, RH, Rd nd Y on nowmelt reult n incree o only 6.1 percent in Q c o the totl vrition (75.7%) 15. Concluion EBM nd LRM or prediction o dily dichrge o nowmelt were pplied in etern prt o Turkey (Kru-Kırkgöze Bin). Time dely in runo genertion i determined three dy due to ctchment routing, wter retention nd movement hydrulic conductivity, rerozen now nd oil condition, which chnge rom point to point in the re. Vlue o intervl o the model contnt (K S, K St, L k, α vo, α iro ) were determined or ll period or EBM. High correltion coeicient (R= R 2 = ) were computed or imulted nd oberved hydrogrph o dily dichrge or ech yer. In ome prt o hydrogrph, dierent dily dichrge were clculted due to the eect o topogrphic prmeter (elevtion, pect nd lope) nd meteorologicl vrible (previling wind direction, temperture). The chnging o dily temperture nd rdition i dicued. While temperture i under 0ºC in the middle o the night to erly noon, epecilly between 22 nd 10 h, there i no nowmelt nd the rdition doe not ect to produce nowmelt between 18 nd 5 h. Reltive humidity i invere eective prmeter to produce nowmelt. Wind velocity nd direction o wind re lo eective to produce nowmelt, epecilly rom outhweter. The computed coeicient o correltion or regreion model i 0.87 (R 2 =0.757), which men tht the eqution involving ive predictor vrible, which explin 75.7 percent o totl vrition in the nowmelt dichrge (Q c ). The order o importnce o

9 528 J SCI IND RES VOL 64 JULY 2005 the predictor vrible i obtined 0.84, -0.75, 0.47, 0.39 nd 0.02 or T, RH, Rd, V nd Y, repectively or the regreion model. Conequently, EBM i more ccurte thn LRM or prediction o nowmelt in etern prt o Turkey due to higher correltion coeicient. Reerence 1 Trboton D G & Luce C H, Uth energy blnce now ccumultion nd melt model (Uth Wter Reerch Lbortory, Uth Stte Univ, Uth) Wlter M T, Brook E S, McCool D K, King L G, Molnu M & Boll J, Proce-bed nowmelt modeling: doe it require more input dt thn temperture-index modeling, J Hydrology, 300 (2005) Dvie A S, Montly nowmelt modelling or lrge cle climte chnge tudie uing the degree dy pproch, Ecologicl Modelling, 101 (1997) Melloh R E, A Synopi nd comprion o elected nowmelt lgorithm, CRELL Rep, 99-8, Feldmn A D, HEC-1 lood hydrogrph pckge, in Computer Model o Wterhed Hydrology, edited by V Y Singh (Wter Reource Publiction, Highlnd Rnch) 1995, Smkhtin V U, Low low hydrology: A review, J Hydrology, 240 (2001) Tutej N K, Bele G, Dwe W, Vze J, Murphy B et l, Predicting the eect o lndue chnge on wter nd lt blnce - A ce tudy o ctchment ected by drylnd linity in NSW, Autrli, J Hydrology, 283 (2003) Anderon E A, Development nd teting o now pck energy blnce eqution, Wter Reource Re, 4 (1968) Jordn R, A one-dimenionl temperture model or now cover: Technicl documenttion or SNTHERM89, USA Cold Region Re & Engg Lb, Specil Report 91-16, Dickinon R E, Seller A H & Kennedy Y J, Biopheretmophere trner cheme (BATS) verion 1 e Coupled to the NCAR community climte model, Ntionl Center or Atmopheric Reerch, U.S. Army, Runo rom nowmelt, Deprtment o Army U.S. Army crop o engineer, , Whington DC Lee Y H & Mhrt L, An evlution o nowmelt nd ublimtion over hort vegettion in lnd urce modeling, Hydrologicl Procee, 18 (2004) Retrepo N C & Arin M A, Energy nd wter exchnge rom temperte pine plnttion oret, Hydrologicl Procee, 19 (2005) Singh Y & Singh V Y, Snow nd Glcier Hydrology (Kluwer Acdemic Publ., ) 2001, Yerdelen C, A Snow melting model or mountinou re nd pplying to Erzurum Kırkgöze Bin, Ph D Thei, Atturk Univerity Grdute School o Nturl And Applied Science, Erzurum, Turkey, 2003.