Modeling of ground water table depth response to precipitation on the drainage areas

Abstract

Modeling of ground water table depth response to precipitation was based on data obtained from the drainage field Radmilovac near Belgrade. Drainage field was consisted of drainage treatment I and II representing drain spacing of L;=l0 m and L2= 30 m, respectively. For the modeling of stochastic process, moving average model (MA) was used. Assuming that rank of the model n was known, estimation of the MA parameters was carried out. Obtained data were used for calculation of the criterion J. Then, criterion J response to parameter n was plotted. Obtained values range from 1 to 35. Starting from the lower value of the parameter n and by increasing it gradually value of the criterion was significantly reducing until the moment when further increment had neglected influence. Plateau of the function was established on n=27 and this value can be assumed for the responding rank of the model. Such a great rank of the model could be explained by the lowest topography of the drainage field regarding the whole catchments area, to whom surface and groundwater runoff gravitate. The value of the mean square error was significantly lower on the drainage treatment I with narrower drain spacing (L/=10m). Logically, groundwater table depth cannot response to precipitation simultaneously. Therefore, certain delay caused by filtration characteristics of the soil was assumed to be in the range from 0 to 5 days in order to estimate its influence on value of the criterion 7. However, results show that assumption of significant delay on groundwater depth variation is not sustainable. Assuming the rank value of the model and rank of the delay (n=27, d=0) theirs responses to groundwater table depths above the drains (h) both by measurement and by model estimation are represented. Mainly, MA model can be used for multistage prediction of the process consequence y (groundwater table depth) based on the measurement of the process cause x (precipitation).

U radu je izvršeno modeliranje zavisnosti dubine podzemne vode od padavina na dreniranom području na kome su rastojanja između drenova 10 i 30 m. U cilju modeliranja stohastičkih procesa koji su u ovom radu od interesa upotrebljen je MA (Moving Average) model. Pretpostavljeno je da je red modela n poznat procenjeni su parametri tako usvojenog MA modela i sračunata je vrednost kriterijuma. Zatim je skicirana zavisnost kriterijuma J od vrednosti parametra n koji se kretao u opsegu od 1 do 35. Polazeći od malih vrednosti parametra n i njegovim postepenim povećavanjem vrednost kriterijuma značajno smanjuje sve do trenutka kada se daljim povećavanjem efekat na kriterijumu ne vidi. Plato funkcije se uspostavlja na n=27, i ova vrednost se može usvojiti za odgovarajući red modela. Ovako veliki red modela može se objasniti topografskim položajem dreniranog područja, ka kome gravitiraju vode sa okolnih viših terena. Vrednost srednje kvadratne greške značajno manja za drenažni sistem za manjim međudrenskim rastojanjem (L;=10m) Logično je očekivati da padavine ne utiču na nivo podzemnih voda momentalno, već da postoji izvesno kašnjenje, uslovljeno filtracionim karakteristikama zemljišta, pa je u analizu uvedeno kašnjenje 0-5 dana da bi se procenilo koliko ono utiče na vrednost kriterijuma /. Međutim, rezultati pokazuju da pretpostavka o značajnom uticaju kašnjenja na promenu nivoa podzemnih voda nije održiva. Za vrednosti koje su usvojene kao red modela i red kašnjenja (n=27, d=0) prikazane su vrednosti visine vode iznad drena (h), i to vrednosti dobijene merenjem i vrednosti koje sračunava model. Ovako dobijen MA model se prvenstveno može iskoristiti za višekoračnu predikciju procesa posledice y (nivo podzemnih voda) na osnovu merenja procesa uzroka x (padavine).