Development of a new metrological model for measuring of the water surface evaporation Tovmach L. Tovmach Yr. Abstract Introduction

Transcription

1 Developmen of a new merological model for measuring of he waer surface evaporaion Tovmach L. Tovmach Yr. Sae Hydrological Insiue 23 Second Line, S. Peersburg, Russian Federaion Telephone (812) , Fax (812) , Е-mail : TOVMACHYV@MAIL.RU Absrac The waer surface evaporaion is one of he major members of he waer balance equaion. So, evaluaion of he measuremen error of he waer surface evaporaion is an imporan mehodological and merological ask. For an open-air 20 square meer pool, he sysemaic componen is small, which has been proved by he resuls of many observaions. A he same ime, an accidenal componen of measuremen errors for evaporaing pools is sufficienly big. Under invesigaion were he readings of several evaporaes saioned on he evaporaing plaform of he VALDAI branch of he GGI, where a 20 square meer pool and hree evaporaors of he GGI-3000 model are siuaed. By he use of he comparison mehod, hey received evaluaions of he accidenal componen error for he hree GGI-3000 evaporaors. They worked ou a physicalmahemaical model, which allowed o receive daa on he funcions influencing he degree of he measuremen error. They suggesed ha he pool and is hree GGI-3000 evaporaors in complex wih he funcions of influence can be used as he iniial model for evaporaion measuring devices. Inroducion Waer surface evaporaion is one of he basic parameers of he waer balance equaion used o calculae all major hydrological values. In his procedure, evaluaion of he evaporaion measuremen error is an imporan mehodological and merological ask. The RosHydroMe organizaion uses evaporaion gauges of he GGI-3000 ype o esimae he waer surface evaporaion on is hydrological field. Bu hey can' appreciae he error values wih a classic mehod, since he sandard means of measuremen are unavailable (do no exis). By way of comparing he readings of one GGI-3000 gauge wih hose of anoher one, hey can only evaluae he accidenal componen of he measuremen error, which is comparaively small, while he sysem componen of error remains raher big. Bu he resuls of numerous observaions proved ha he sysem componen of error was small for an evaporaion-measured 20m 2 pool. So, a 20m 2 pool was aken as a emporary sandard of VMO. A he same ime, as we'll show furher, an accidenal componen of error for evaporaing pools is sufficienly big as compared wih ha of he GGI In connecion wih his, he following asks were se: - o minimize he error sysem componen of GGI-3000, - o deermine he error accidenal componen of an evaporaion-measured pool.

2 To solve hese asks, we worked ou a physical-mahemaical model for evaluaion of errors of evaporaion gauges. To build up he model, we used he parameers shown in Table 1. Table 1 Convenional Measuremen Parameer measured sign Uni 1 bs20-evp Level of waer evaporaed from he surface of a 20m 2 pool E, mm 2 bs20-wm Temperaure of waer in he 20m 2 pool -0 C 3 bs20-ew Resilience of waer vapour a a given waer emperaure in a 20m 2 pool 4 bs20-dw absolue humidiy a he 2m heigh for a 20m 2 pool 5 bas5-evp Level of waer evaporaed from he surface of a 5m 2 pool E, mm 6 bas5-wm Temperaure of waer in he 5m 2 pool -0 C 7 bas5-ew Resilience of waer vapour a a given waer emperaure in a 5m 2 pool 8 bas5-dw absolue humidiy a he 2m heigh for a 5m 2 pool 9 bas3-evp Level of waer evaporaed from he surface of a 3m 2 pool E, mm 10 bas3-wm Temperaure of waer in he 3m 2 pool -0 C 11 bas3-ew Resilience of waer vapour a a given waer emperaure in a 3m 2 pool 12 bas3-dw absolue humidiy a he 2m heigh for a 3m 2 pool 13 p031-evp Level of waer evaporaed from GGI E, mm 14 p031-wm Temperaure of waer in GGI C 15 p031-ew Resilience of waer vapour a a given waer emperaure in GGI p031-dw absolue humidiy a he 2m heigh for GGI p032-evp Level of waer evaporaed from GGI E, mm 18 p032-wm Temperaure of waer in GGI C 19 p032-ew Resilience of waer vapour a a given waer emperaure in GGI p032-dw absolue humidiy a he 2m heigh for GGI p033-evp Level of waer evaporaed from GGI E, mm 22 p033-wm Temperaure of waer in GGI C 23 p033-ew Resilience of waer vapour a a given waer emperaure in GGI p033-dw absolue humidiy a he 2m heigh for GGI am-am Air emperaure a he 2m heigh air C 26 ame-ea2 Air absolue humidiy a he 2m heigh e wnd2-wd2 Wind speed a he 2m heigh U-200 м/с 28 prcp-prc Precipiaions by he readings of he evaporaion gauge precip., mm 29 rele-rle Air relaive humidiy a he 2m heigh f,% 30 defe-def Air humidiy deficiency a he 2m heigh Def 31 g20-gm Soil emperaure a he 20cm deep soil C 32 magnus Value of he sauraion resilience a a given emperaure, calculaed by he Magnus formula е-0 33 e-max2 Value of he sauraion resilience a a given emperaure, according o he readings of psychomerical ables е-0 34 def1 Air humidiy deficiency, by he Magnus formula е-0 35 def2 Air humidiy deficiency, by he psychomerical ables е-0 36 dae Number of days before/afer he summer solsice days

3 To compare he influence of various parameers on he value of an error, we recouned he parameers' meanings ino relaive unis using he following formula: i = measured average average The only excepion is he parameer referring o he maximal heigh of he sun above he horizon and he lengh of he day. I was proved ha he evaporaion measuremen error depended on hese daa [1]. To make our calculaions of he influence of hese facors more accurae, we inroduced a new parameer, namely, he number of days before/afer he summer solsice. For example, on April 23 and on Augus 23, he lengh of he day and he maximal heigh of he sun above he horizon are equal. Bu from he poin of view of he amoun of waer evaporaion, hey are differen. Physical-mahemaical model. Descripion To build our physical-mahemaical model for waer evaporaion measuremen, we used he iniial daa hey had been receiving a he Valdai GGI experimenal field since A he Valdai field, hey have hree measuremen grounds: - on he shore, - on he coninen, - and on he waer surface (on a raf in he Valdai lake). On each ground, here is a 20m 2 evaporaion measuremen pool and a GGI-3000 gauge. The shore ground is beer equipped han he ohers, and observaions on i, pracically, have never been inerruped. So, he daa received from his ground were used as he basic ones for building our new model for waer evaporaion measuremen. The shore ground is equipped wih a 20m 2 -, a 5m 2 -, and a 3m 2 evaporaion measuring pool. Besides, on he ground, here are hree evaporaion gauges of he GGI-3000 ype, one of which is hea-insulaed. In his aricle, i is furher referred o as gauge No.3. Thus, we have o analyze he readings of six evaporaion gauges, hree of which are of he same GGI-3000 ype. In his case, we can apply a well-known mehod of comparison [2]. We eliminae he error sysem componen as mahemaically expeced difference in readings of he 2 evaporaion gauges. As a resul, we receive he following values of σ : GGI-3000 No.1 0,009mm 2 GGI-3000 No.2 0,056mm 2 GGI-3000 No.3 (hea-insulaed) 0,090mm 2 3m 2 pool 0,148mm 2 5m 2 pool 0,200mm 2

4 20m 2 pool 0,295mm 2 These resuls show ha he error accidenal componen for he GGI-3000 evaporaion gauges is close o a one poin error in he indicaor panel of a waer-level gauge used for he GGI funcioning. Cerain deviaions in he values of he error accidenal componen of he GGI gauges were condiioned by he fac ha GGI-3000 No.2 and No.3 had been wihdrawn from he observaion process for some ime, o be pained, and hus, he homogeneiy of he observaion process was broken. Besides, he value of he error accidenal componen of he hea-insulaed GGI (gauge No.3) could be influenced by a negleced error sysem componen. Thus, for he GGI gauges, he error accidenal componen ranges from 0,1mm o 0,3mm. The error accidenal componen for he 20m 2 evaporaion-measured pool is, on he average, by hree or four imes bigger, and makes, approximaely, 0,54mm. When deermining he error sysem componen, we assume ha i is insignifican for he 20m 2 pool. As for he res of he observaion objecs, here are heir values of he error sysem componen - Δ: GGI-3000 No.1 0,111mm GGI-3000 No.2 0,134mm GGI-3000 No.3 (hea-insulaed) 0,022mm 3m 2 pool 0,052mm 5m 2 pool 0,004mm The resuls of observaion proved our supposiion abou he ignorably small value of he error sysem componen for he 20m 2 pool. For he 5m 2 pool, he error sysem componen is insignificanly small. For he 3m 2 pool, i is smaller han one poin in he indicaor panel of he waer-level gauge. For he GGI-3000 evaporaor measuring gauges, he error sysem componen is significanly big, excep for he hea-insulaed one which was creaed especially o minimize he value of he error sysem componen [3]. So, we see ha he error accidenal componen for GGI-3000 gauges is small as compared wih ha of he evaporaion measured pools, and, on he conrary, he error sysem componen for GGI-3000 is big as compared wih ha of he evaporaion measured pools. On he basis of he aforesaid, we creae a linear dependency model for evaluaion of he sysem error for GGI-3000 and he error accidenal componen for he 20m 2 evaporaion-measured pool, as follows: N Δ = Δ0 + a i * i i= 1 N 2 2 σ =σ 0 + b i * i, i= 1 Where Δ 0 is he value of he error sysem componen for GGI-3000, a he average values of all he parameers on he day of he summer solsice,

5 2 σ 0 he value of he error accidenal parameer for he 20m 2 pool a he average values of all he parameers on he day of he summer solsice, N he number of parameers, a i and b i coefficiens. Thus, he sysem- and he accidenal componens of error are supposed o be regarded as a plane in he N-space. Table 1 shows ha all he 36 parameers can be used for he calculaion, hough i is no absoluely necessary o do. For example, when you evaluae he error sysem componen for GGI- 3000, i is advisable o use only such parameers as he level of he evaporaed waer, he waer emperaure, resilience of he waer vapour a he given waer emperaure and he difference beween he resilience of sauraion and he air absolue humidiy a he 2m heigh. All he readings should be aken from a cerain evaporaion measuring gauge, and should no be conneced wih he evaporaion-measured pools. You should use he same procedure o evaluae he error accidenal componen of he evaporaion-measured pools. Similarly, here is no sense in simulaneous usage of he daa on he resilience of sauraion and he deficiency of humidiy calculaed wih he help of he empirical Magnus formula and he same daa received wih he help of he psychomerical ables. The planes are drawn wih he help of he smalles squares mehod. By calculaing he dispersion of deviaions, from hese planes, of he resuls of your measuremens, you can appreciae he level of accuracy of your evaluaions. 3000: Resuls Finally, we received he following dependencies of he error sysem componen for GGI- Δ = 0,09 + 0,61 3,99 + 4,50 1,44 + 3,54 2,61 0,57 + 0,20 0,35 1, and he error accidenal componen for he 20m 2 evaporaing pool: σ 2 = 0,38-0,53 + 1,76 0,92 + 0,23 0,12 0,09 0,74 0, As aforesaid, all he parameers of i are given in relaive unis. Thus, he coefficiens for he error sysem componen are expressed in mm, and hose for 2 σ are expressed in mm 2. And only he parameer 36, denoing he number of days before/afer he summer solsice, is expressed in days. Now we'll analyze he influence of various parameers on he error sysem and accidenal componens, in order of decrease of heir influence. In he influence on he error sysem componen, he firs place akes resilience of he waer vapour calculaed by he waer emperaure. The second place akes he waer emperaure. Then goes he air emperaure, and hen he air humidiy, he difference beween he resilience of sauraion and he air absolue humidiy, resilience of sauraion a a given air emperaure, he level

6 of he evaporaed waer, he wind speed, he soil emperaure, relaive humidiy. To sum up he aforesaid, he value of he error sysem componen is influenced mainly by he parameers referring o he speed of evaporaion, hen go he emperaure parameers, and hen he wind speed and air humidiy. In he influence on he error accidenal componen, he firs place akes he air emperaure. Then go absolue humidiy, he value of he resilience of sauraion a a given air emperaure, resilience of he waer vapour a a given waer emperaure, relaive humidiy, he soil emperaure and he number of days before/afer he summer solsice. I is imporan o mark ha he value of he error accidenal componen depends mainly on he coefficien independen of he parameers. The mos imporan role in he error acciden componen and, alike, in he error sysem componen, is played by he parameers conneced wih evaporaion speed. Parameers conneced wih absorpion of he hea energy are also imporan in his process. Conclusion The 20m 2 evaporaing pool in combinaion wih he hree GGI-3000 evaporaion gauges, se side by side, can serve as an iniial sandard model for evaporaion measuremen. This sandard model is capable of self-conrolling, using he described above mehod. The hea-insulaed GGI TM can serve as a secondary sandard model afer is error sysem componen is correced wih he help of his newly developed mehod. References 1. Golubev V.S. Influence of evaporaor side on he direc sun radiaion absorbed by waer.//works GGI, 1988, issue 331, pp (in Russian) 2. Golubev V.S., Konovalov D.A., Simonenko A.Y., Tovmach Y.V. Evaluaion of measuremen errors of amospheric precipiaions wih he Valdai conrol sysem.//merology and Hydrology, 1997, No.7, pp (in Russian) 3. Golubev V.S., Kaluzhny I.L., Fedorova T.G. Hea-insulaed evaporaor GGI-3000-TM and is esing.//works GGI, 1980, issue 226, pp (in Russian)