HYDROMAX : A Real-Time Application for River Flow Forecasting. G. Bastin, L. Moens

Transcription

1 HYDROMAX : A Real-Tme Applcato for Rver Flow Forecastg G. Bast, L. Moes Proceedgs Iteratoal Symposum o Flood Defece, Vol., pp. D-33-40, Kassel Reports of Hydraulc Egeerg, N 9/2000, Hercules Verlag Kassel, Germay, September 2000

2 Hydromax : A Real-Tme Applcato for Rver Flow Forecastg. Itroducto G. Bast, L. Moes Cetre for Systems Egeerg ad Appled Mechacs (Cesame UCL) Bâtmet Euler Aveue Lemaître, LOUVAIN-la-NEUVE - BELGIUM Fax : + 32 /(0)0 / Emal : moes@auto.ucl.ac.be Hydromax s a applcato for rver flow forecastg ad flood alarms whch provdes real-tme short-term predctos of rver flows based o rafall ad past rver flow measuremets, ad log-term flood forecastg based o meteorologcal forecasts. The purpose of ths bref paper s to gve a geeral descrpto of Hydromax ad to demostrate ts performace wth typcal expermetal examples ad statstcal assessmets. For each rver bas, the forecasted rver flows are produced by a mathematcal model whch volves four parts: ) A optmal mmum varace terpolator whch computes the mea areal rafall o the watershed. 2) A o-lear coceptual producto fucto whch descrbes the water storage the watershed ad computes the effectve rafall from the mea areal rafall. 3) A lear ARX trasfer fucto whch descrbes the superfcal ruoff of the et rafall towards the watershed outlet ad computes the short term rver flow forecastg. 4) A smulato model whch produces log term rver flow forecasts from meteorologcal data. The detfcato of the model s qute data savg because oly rafall ad rver flow measuremets are requred whle a detaled physcal descrpto of the bas s ot eeded. Hydromax has bee developed to be user fredly ad to fulfll the real-tme forecastg requremets. It s successfully route operato for more tha fve years the Meuse rver (Walloo rego, Belgum) ad ts ma trbutares. 2 Telemeterg ad data acqusto To be operatoal, Hydromax must be coected to a relable telemeterg etwork ad a data acqusto system accessble from the forecastg ceter ad able to acheve frequet o-le feld measuremets of both rafall depths ragauges ad water levels rvers. I ths paper, the Hydromax performace wll be llustrated wth data from the telemeterg system of Sethy (Servce d'études hydrologques, Walloo Mstry of Publc Works - Belgum). Hydromax uses about 60 statos scattered the Meuse rver bas as show Fg..

3 Fg. : The telemeterg etwork of Sethy the Meuse rver bas The data are collected wth a basc tme-step ( t =. Hourly rafall ad rver flow measuremets over a perod of several years (cludg bg floods) were thus avalable for the model developmet. Obvously, the basc tme-step t must be much smaller tha the mea cocetrato tme of the cosdered rver bass. 3 Estmato of the mea areal rafall The put of the model s the mea areal rafall over the cosdered watershed. The possble spatal heterogeety of the rafall s thus ot take to accout here. The pot rafall depth s deoted P(z) wth z=(x,y)!², the Cartesa coordates. It s assumed to be a realzato of a two-dmesoal radom feld wth costat mea ad lear varogram. The rafall measuremets are avalable at measuremet statos ad deoted: P = P z ), P = P( z ), P = P( z ( 2 2 ) The average areal rafall PB over a catchmet area Ω!² s the defed as: PB = Ω! P( z) dz Ω

4 As s well kow, a optmal (lear, ubased, mmum varace) estmato of PB ca be computed from the set of rafall observato {P,,,} as : PB = λ P wth the λ solutos of the so-called krgg system: λ e( z, z j ) + µ = (, ) =,, Ω! e z z j dz j! Ω λ = where µ s a Lagrage multpler ad e(z,z j ) deotes the Eucldea dstace betwee the pots z ad z j!². 4 Computato of the effectve rafall wth the producto fucto The role of the producto fucto s to trasform the mea areal rafall PB to a effectve rafall PN whch s supposed to reach the bas outlet as surface ruoff. The model descrbes the balace of water volumes durg tme tervals t. Durg each tme terval the amout of precptated water s decomposed as follows: PB ( = PN( + E( + W ( wth t the dscrete tme dex. E ( represets the part of the rafall PB( that drectly evaporates durg the curret tme terval. W( represets the amout of water that wll ot partcpate the ruoff but wll be stored the bas uder varous forms (vegetato tercepto, superfcal depressos, sol mosture, etc ). The storage of the water the rver bas s the represeted by a lear reservor wth flow W( descrbed by the dfferece equato: S( = S( t ) + W ( E2 ( I( where S( deotes the stock of water the rver bas, I( s the amout of water draed by percolato ad E 2 ( s the part of stored water evapotraspratg durg the curret tme terval. The percolato term I( s represeted by a lear fucto of the avalable water stock: I ( = α ( S( t ) + W ( ) wth α a specfc percolato parameter. The evapotrasprato terms E ( ad E 2 ( are computed as: E ( = m ( PB(, ETP( ) E ( = max (0, m ( ETP( PB(, S( t ) + W ( I( )) 2 where ETP( represets a estmate of the seasoal potetal evapotrasprato for the cosdered bas. It s furthermore assumed that there s a physcal upper lmt Smax of the amout of stored water S( the rver bas. The water storage W( s the expressed as a fucto of S( ad PB( order to: - guaratee the codto 0 S( Smax t

5 - verfy the hydrologcal prcple that the effectve rafall PN( creases wth both rafall testy PB( ad sol mosture S(. The followg fucto satsfes these requremets: W ( = ( PB( E( % [ S max S( ] exp ( β # $ wth β a specfc ruoff coeffcet. & ' S max S( The producto fucto model the volves three parameters (α, β, Smax) that have to be calbrated from expermetal data for each cosdered rver bas. 5 Computato of the short term rver flow forecastg wth a lear trasfer fucto At each tme t, a forecastg Qˆ (t+ s computed for the future tme stat (t+(.e. wth a predcto horzo of h measuremet tme steps) as a lear combato of past rver flow measuremets ad past effectve rafall values, wth a lear regresso model (ARX model) of the form: Qˆ( t + = a Q( t ( ) + m j= b j PN( t ( j ) where Q(t-(-) deotes the rverflow measuremets at the past tme stats (t-(-) whle PN(t-(j-) represets the effectve rafall cumulated over h successve tme steps ad computed wth the producto fucto. For each rver bas, the values of the predcto horzo h ad the coeffcet a, b j are determed from expermetal data. To get accurate forecasts, the predcto horzo h must obvously be smaller tha the atural respose tme of the rver bas. As a rule of thumb, t s selected betwee the oe ffth ad the oe thrd of the peak tme of the ut hydrograph. The dmesos ad m of the regresso terms the model are selected usg classcal statstcal tools of system detfcato theory (correlogram of predcto errors, Bayeso Iformato Crtero, etc ) accordg to a parsmoy prcple. The parameters a ad b j are calbrated by lear regresso. 6 Computato of log term rver flow forecasts from meteorologcal data The goal here s to compute rver flow forecasts over predcto horzos that are sgfcatly larger tha the atural respose tme of the rver bas. Ths obvously requres to atcpate the future rafalls by meteorologcal formatos. Such log-term rverf low forecasts may be computed by teratg the short-term predcto model as follows: Qˆ( t + k = + k k a Qˆ ( t + ( ) + b PN( t + ( ) + j= k a Q( t + ( j ) m j= b PN( t + ( j ) where Qˆ (t+(-) represet successve terated rver flow forecasts ad PN( t + ( )

6 effectve rafall forecasts to be provded by the user. 7 A example : the flood of Jauary 995 I ths last secto, the Hydromax performace s llustrated wth a typcal forecastg example the Ourthe rver bas. The outlet of the rver bas s located at Tabreux (607 Km²) ad four ragauges are avalable (see map Fg. ). Hourly rafall-rverflow data durg 2 years ( ) have bee used to calbrate the model. The estmated model parameters are gve Table. The ut hydrograph of the rver s also show Fg. 2. The selected predcted horzo s h=6 hours. Fg. 2 : Tabreux Ut hydrograph Table : Tabreux - Parameters of the model α β Smax a a 2 b b 2 b 3 b The predctve capablty of the model s here llustrated wth the bg flood of Jauary 995 (whch s ot data set for model costructo). I Fg. 3, a typcal example of o-le forecastg wth Hydromax s show. We ca see that Hydromax computes a short term predcto for 8 p.m. of 98 m³/s (bg blue dot o the fgure), whch s to be compared to the actual value of 200 m³/s. Hydromax also computes a log term predcto over a horzo of 42 hours (+ le) for the gve scearo of future rafalls ad a optmstc predcto (o le) uder the assumpto that the rafall wll deftely stop.

7 I Fg. 4, a comparso betwee the observed rver flow dscharges ad the short-term predctos all alog ths bg flood of Jauary 995 s preseted. Fally the statstcal accuracy of Hydromax at a level of 90 % s llustrated Table 2. Table 2 : Upper boud of the relatve forecastg error at a level of 90 % Horzo 6 hours ahead 2 hours ahead 8 hours ahead 24 hours ahead 30 hours ahead Qˆ Q Characterstcs of the rverflow stato Meteorologcal forecasts wdow Measured dscharge Measured rafall Meteorologcal forecasts Forecastg wthout rafall Forecasted dscharge Forecastg based o meteorologcal forecasts Fg. 3: Example of Hydromax wdows : forecastg of Ourthe (a Meuse trbutary) flow rate durg the bg flood of Jauary 995

8 Fg. 4 : Tabreux Comparso betwee observed ad forecasted dscharges durg the bg flood of Jauary Ackowledgemets Hydromax has bee developed by the authors at Cesame (Ceter for Systems Egeerg ad Appled Mechacs, Uversty of Louva-la-Neuve). The krgg computato of the mea areal rafall follows the les of []. The structure of the shortterm forecastg model was tally sketched [2] ad further vestgated the Ph.D. Thess of B. Wéry [3]. The expermetal data were provded by Sethy (Servce d'études hydrologques, Walloo Mstry of Publc Works - Belgum) whch s also gratefully ackowledged for ts warm collaborato ad facal support.

9 9 Bblography [] G. Bast, B. Loret, C. Duqué ad M. Gevers. Optmal Estmato of the Average Areal Rafall ad Optmal Selecto of Ragauge Locatos Water Resources Research, Vol. 20 (4), pp , Aprl 984. [2] B. Loret ad M. Gevers. Idetfcato of Rafall-Ruoff Process 4 th IFAC Symposum o Idetfcato ad System Parameter Estmato, Tblss, USSR, North-Hollad, pp , 974. [3] B. Wéry. Idetfcato des systèmes hydrologques Applcato à la prévso des crues Ph.D. Thess, Uversty of Louva-la-Neuve, March 990.