Table of contents 1 Introduction 2 NAM model 2 Purpose of study 2 NAN basin characteristic 2 Theoretical considerations 3 Methodology 3 The

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1 Table of cotets Table of cotets 1 Itroducto 2 NAM model 2 Purpose of study 2 NAN bas characterstc 2 Theoretcal cosderatos 3 Methodology 3 The calculato sequece NAM 3 Statstcal measuremets: 7 Calbrato of the NAM model. 8 Valdato of the model 9 Falzato 11 Cocluso 11 Sestvty Aalyss 11

2 Itroducto NAM model NAM s ad abbrevato of the Dash Nedbor-Afstromgs-Model, meag precptato-ruoff model. Ths was orgally developed by the Hydrologcal Secto of the Isttute of Hydrodyamcs ad Hydraulc Egeerg at the Techcal Uversty of Demark, (Nelse ad Hase, 1973). Durg the past decade t has bee extesvely appled ad modfed by the Dash Hydraulc Isttute a large umber of projects. A mathematcal hydrologcal model lke NAM s a set of lked mathematcal statemets descrbg, a smplfed quattatve form, the behavor of the lad phase of the hydrologcal cycle. Numerous hydrologcal models exst. NAM smulates the rafall-ruoff process rural catchmet. It operates by cotuously accoutg for the mosture cotet four dfferet ad mutually terrelated storages, whch represet physcal elemets of the catchmet. The put data to the model are precptato, potetal evapotrasprato ad temperature (oly f the sow route s used). O ths bass, t produces, as ma results, ruoff ad groudwater level values as well as formato about other elemets of the lad phase of the hydrologcal cycle, such as the temporal varato of the sol mosture cotet ad the groudwater recharge. A coceptual model lke NAM s based o physcal structures ad equatos used together wth sem-emprcal oes. Thus, some of the parameters ca be evaluated from physcal catchmet data, but the fal parameter estmato must be performed by calbrato applyg cocurret put ad output tme seres. The model structure s show Fg. 1. It s ad mtato of the lad phase of the hydrologcal cycle. Water s stored four storages. Purpose of study The purpose of ths exercse s to buld a NAM model Excel. It s set up, calbrated ad valdated for real data from the NAN catchmet Thalad so wth a catchmet area of 10,335 km 2. NAN bas characterstc Na Rver Bas s located orther part of Thalad. It shows moutaous ad forest area ad also t s oe of four rvers cotrbutg flow to the Chao-Phra-Ya Rver. Na bas lkewse shows a steep bas wth flash floods therefore, Na Cty frequetly flooded. Furthermore, there s a Srkt Dam dow to Na Rver.

3 Theoretcal cosderatos Methodology Frst, we start at part of model bult wth kow model parameters, tal codto ad observed dscharge, the try to buld NAM model excel ad check the result of model calculato wth NAM had calculato After ths we apply ths mathematcal model to the actual stuato of NAN rver catchmet area Thalad wth kow observed dscharge data ad meteorologcal data (rafall data, potetal evaporato.). I ths part, t wll be dvded to 2 parts: Calbrato of model to NAN rver bas by usg 3 years data to calculate the most approprate parameters of model that wll gve the smulated result best matchg to the actual observed data. Checkg that the valdato of ths mathematcal NAM model ad the parameters of ths model ca be appled to use wth aother perod of NAN catchmet. I ths step, 2 years rafall data s the put of the model wthout chagg parameters. From the same area as the oe used for calbrato, we compare the smulated dscharge to the observed dscharge to check valdato of model. For checkg effcecy of NAM model to NAN catchmet area, t ca be observed from graph ad usg coeffcet of determato R 2 (square of Pearso product momet correlato) The calculato sequece NAM Add the rafall (the precptato) to the upper storage..e. add P to U: U t =U t-1 +P Calculate the actual evaporato (E a ) f the upper storage s full the the actual Evaporato = Potetal evaporato otherwse apply the lear varato. Adjust the upper storage (U) for the actual evaporato (E a ). If the actual evaporato (E a ) s take from the upper storage (U) the U t = U t - E a Calculate the terflow (Q f ). Remember that QIF max = U max / CKIF where CKIF s the tme costat for terflow Subtract the Iterflow (Q f ) from the upper storage (U);.e. U t =U t -Q f Calculate the excess precptato P : P = U t -U max f U t > U max P = 0 f U t U max If the excess precptato P > 0 the set U t U max meag tat the upper storage s full.

4 Calculate the overlad flow volume OF Calculate the groudwater recharge G Calculate the chage the lower storage DL Adjust the lower storage (L) wth DL Routg of the flow Calculate the overlad flow OF: OF = QOF ( 24/ overladfl ow routgtme) ( 24/ overladfl ow routgtme) ( 1 e ) + Of e tme 1 Calculate the base flow BF: ( 24/ baseflowroutgtme) ( 24/ Baseflowroutg tme) ( 1 e ) + BF e BF = G Calculate the total Q tot tme 1

5 Table 1 NAM model parameters Parameter Rage of value Umax [mm] Lmax [mm] CQOF [-] TOF [-] TIF [-] TG [-] CKIF [hours] CK1,2 [hours] CKBF [hours] Descrpto Maxmum water cotet the surface storage. Ths storage ca be terpreted as cludg the water cotet the tercepto storage, surface depresso storages, ad the uppermost few cm s of the sol Maxmum water cotet the lower zoe storage. Lmax ca be terpreted as the maxmum sol water cotet the root zoe avalable for the vegetatve trasprato Overlad flow ruoff coeffcet. CQOF determes the dstrbuto of excess rafall to overlad flow ad fltrato Threshold value for overlad flow. Overlad flow s oly geerated f the relatve mosture cotet the lower zoe storage s larger tha TOF Threshold value for terflow. Iterflow s oly geerated f the relatve mosture cotet the lower zoe storage s larger tha TIF Threshold value for recharge. Recharge to the groudwater storage s oly geerated f the relatve mosture cotet the lower zoe storage s larger tha TG Tme costat for terflow from the surface storage. It s the domat routg parameter of the terflow because CKIF >> CK1, Tme costat for overlad flow ad terflow routg. Overlad flow ad terflow are routed through two lear reservors seres wth the same tme costat CK1, ,000 Baseflow tme costat. Baseflow from the groudwater storage s geerated usg a lear reservor model wth tme costat CKBF. Calbrato Large value causes less overlad flow ad fltrato, ad hgher evapotrasprato ad terflow. Large value causes hgher evapotrasprato ad fltrato, ad less overlad flow ad base flow. Large value causes hgh overlad flow, ad small fltrato. Large value causes the delay of the threshold of overlad flow wet perod, ad hgher fltrato. Large value causes the delay of the threshold of terflow wet perod, ad hgher fltrato ad overlad flow. Large value causes the delay of the threshold of groudwater flow wet perod, ad qucker fllg of root zoe. Large value causes hgher terflow, ad less fltrato ad overlad flow. Icreasg CK* cause loger durato ad lower peaks of flow compoets. Chagg CK* has o effect o geerated flow volumes over log tme but chagg the shape of hydrographs.

6 Fg. 1 The structure of NAM model CK BF

7 Statstcal measuremets: I ths study, we use mass balace cosderato for model bult. totalof observed flow Mass balace = total of smulated flow Goodess of ft ad accuracy crtera The square of the Pearso product momet correlato coeffcet, R 2 Where R = = 1 = 1 ( QOBS QOBS ) ( QSIM QSIM ) 2 ( ) ( ) 2 QOBS QOBS QSIM QSIM = 1 The Root Mea Square Error RMSE = 1 ( QOBS QSIM ) = 1 2 where QOBS QSIM QOBS QSIM observed smulated valueat tmestep average observed valueat tmestep average smulated value value umber of value tmestep

8 Calbrato of the NAM model. The calbrato of the model s very dffcult, because of the sze of the catchmet ad the durato of the tme perod. There are a lot of peaks that has to be ftted, ad at the same tme the rato of the smulated ad measured flow has to ft for matag the mass balace whch makes the calbrato eve more complcated. To cacel the mpact of tal values we use the frst year to fll the taks the model. Ths s oe of the advatages of the NAM modal, that t has a vrtual memory, but ths vrtual memory has to be flled up. The tal value therefore has a eglgble fluece o the fal results. To check ths we chaged the tal value of Lt the calbrated model from 20 to 500. Ths showed a cremet the water mass rato of The calbrato method we use s tral ad error. Smply adjust oe of the parameters ad see f the results get better. After a rough calbrato has bee made the calbrato s doe aga wth vary small chages. To check the qualty of the results we bult a graph over the smulated ruoff ad observed ruoff. Also a graph of the accumulated smulated ad observed ruoff s draw. The objectve of the calbrato we have chose to be water balace. Ths has the frst prorty. The purpose of makg water balace frst prorty of the calbrato s, eve though the NAN cty s frequetly flooded, to check or forecast the dmeso of the Srkt Dam ad operato of ths reservor. Also the square of the Pearso product momet correlato coeffcet method s looked upo to get a good calbrato. The same wth the root mea square. Calbratg wth above method ad objectves we get followg results: Umax 20 Lmax 133 CQOF 0.40 CKIF 400 TOF 0.60 TIF 0.30 TG 0.03 CK CKBF 1500 GWLBF These values are all coected some way so the calbrato s ot uque. That s the same smulato ca be obtaed wth combato of other values. To determe these values wth hgher accuracy we have to do more feld measuremets. The rato of smulated flow ad measured flow s, wth the values about: //TJEK DEN R 2 value s The mass balace s very good, sce we calbrated the model targetg the mass balace.

9 R 2 s ot good, but ths value s ot trustable ths case. A lttle tme delay of a peak wll have a very large fluece o R 2. The graph of accumulated water mass balace s very good ftted. The graph s ftted OK. Not as good as the water balace though. Especally the large peak the frst year s ftted perfectly. The rest of the peaks are ether a lttle bt above or a lttle bt below. Both s cluded appedx. Valdato of the model The valdato of the model meas that the calbrated model ca be used approprately ot oly the usg the calbrato data perod but stll work rghtly aother tme. I ths study, the effectve model parameters are obtaed from the calbrato process. The frst year (1987), secod year (1988) ad thrd year data (1989) remas the model. These have to be the model to keep t warm. That s, they are used to fll up the vrtual memory. The fourth (1990) ad the ffth (1991) are used for checkg the model ad the calbrato of the model. The crtera used for cosderg the valdato are mass balace ad the statstcal measuremet are The square of the Pearso product momet correlato coeffcet, R 2 ad the root mea square error, RMSE as show below: year Mass balace factor R 2 RMSE Fourth year (1990) Ffth year (1991) It s otced that the rato of measured flow ad smulated s very hgh as 1.17 for the fourth year. For valdato of the ffth year the rato s: Therefore t s see that the producto of ruoff creases as tme goes. Ths could dcate that there are some chages the catchmet area. Urbasato or chagg of lad use may be occurred ad may cause of ths creasg ruoff. E.g. cuttg dow trees ca crease the ruoff because the trees wll ot cosume the ad cotrbute to the evaporato of the water. Urbazato decreases the amout of fltrato because of the mpermeable surface. It could also mea that we dd ot calbrate the model properly. To determe, f there s a tedecy to more ruoff we would eed a loger perod of data, or data of cuttg dow trees the catchmet area for the observed tme perod. I addto, NAN catchmet area s the steep bas ad flash flood ad there s a Srkt Dam dow to Na Rver. So actually the observed flow s greater tha smulated flow ad for usg oly mass balace cosderato (sgle objectve), t caot ft the peak of the hydrograph of observed ad smulated flow. Mass balace cosderato s used for water resource plag log term perod.

11 Falzato Cocluso The model that we have buld would descrbe as a good model. The valdato of the model s show a rather large dfferece betwee the observed ad smulated flow. But because of the systematc error we are able to coclude that there has bee a chage the propertes of the catchmet area. The R 2 (square of Pearso product momet correlato) value eve creases the valdato. Ths meas that the shape of the valdato curve actually comes closer to the curve represetg measured data. Oly the dfferece betwee the mass of water s very accurate. Sestvty Aalyss All parameters are chaged wth ther rages ad the compare accumulated smulated flows from both upper rage ad lower values wll be compare as show appedx. Therefore, the sgfcat parameters are U max, L max ad CK BF because they result the hgh dffereces of flow. Ths aalyss helps very much mprovemet calbrato o whch parameters have to be focused o. It s otce that the way to aalyze sestvty depeds o the restrcted rages of each parameter. Actually the rage must be carry out from characterstcs of bas by feld measuremet. It s also otced that the peak ad tmg of peak are ot cocered ths aalyss by the reaso of large scale of tme seres.

Functions of Random Variables

Functions of Random Variables Fuctos of Radom Varables Chapter Fve Fuctos of Radom Varables 5. Itroducto A geeral egeerg aalyss model s show Fg. 5.. The model output (respose) cotas the performaces of a system or product, such as weght,