New Developments in Environmental Science and Geoscience THE WATER TEMPERATURE SIMULATION IN THE MORAVA RIVER BASIN WATERCOURSES Dana Halmova, Pavla Pekarova, Jan Pekar, Katarina Kucarova wind speed, precipitation, evaporation, condensation... Abstract— The study is focused on water temperature simulation 2. Topographic conditions - altitude, latitude basin, flow in watercourses in the Morava River basin and its dependence on orientation, coastal vegetation, subsoil... expected increase of maximum daily air temperature. Our aim is to 3. The hydrological regime of flow - discharge, flow assess influence of possible air warming on water temperature increase in watercourses. In the process of data handling have used: velocity and depth of stream, level and temperature of series of average daily water temperature measured in groundwater... 21 watercourses in the Morava River basin and mean daily air 4. Anthropogenic activities in the basin - discharge of urban temperature series at Bratislava Airport, period 2006–2011. and industrial waste water, flow reduction [3], artificial Scenarios for extreme monthly air temperatures at station Bratislava reservoirs [4] and diversion canals and removal of riparian Airport have been calculated on the basis of statistical analysis of vegetation [5]. daily air temperatures for period 1951–2011. Extreme water temperatures have been simulated from the scenario of air Some Slovak hydrologists dealt with statistical analysis of temperatures by calibrated ARIMA models. Results of simulations low flows in water streams in Eastern Slovakia, to which is show, that in case of maximum air temperature increase by 1°C the attached the low water level in the stream [6]. The main water temperature will rise by 0.7°C–0.9 °C, depending on models objective of their work was to identify low flow trends in used. the selected 63 river stations in Eastern Slovakia in time period 1975–2012. Keywords— autoregressive models, ARIMA models, water temperature simulation, climate change. II. MORAVA RIVER BASIN CHARACTERISTIC I. INTRODUCTION The Morava River is a left tributary of the Danube and Morava basin is mostly located in the Czech Republic. HE water temperature is one of the main physical Catchment area of Morava River in estuary into the Danube is characteristics of the surface water. It directly influences T about 26 580 km2, of which in Slovakia is only 2 282 km2, the biota of the streams and adjacent land. The water representing 8.6% of the whole catchment area and 4.65% of temperature significantly influences other physical and the Slovak Republic area, (Fig. 1). chemical properties of the water. The productivity of the total water ecosystem does not only depend on the water temperature, but it is in great extend limited by the water Morava River basin temperature [1]. The factors that affect the water temperature can be generally divided into four groups [2]: 1. Atmospheric conditions - solar radiation, air temperature, This work was supported in part by Agency VEGA under the contract VEGA 2/0009/15 and results from the project implementation of the “Centre of excellence for integrated flood protection of land” (ITMS 26240120004) Slovakia supported by the Research & Development Operational Programme funded by the ERDF. D. Halmova is with Institute of Hydrology Slovak Academy of Sciences, Racianska 75, 831 02 Bratislava, Slovakia, (e-mail: [email protected]). P. Pekarova is with Institute of Hydrology Slovak Academy of Sciences, Racianska 75, 831 02 Bratislava, Slovakia (phone: +4212 44259311, Fax: Fig. 1 Morava River basin at the national level +4212 44259311, e-mail: [email protected]). J. Pekar is with the Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia (e-mail: [email protected]) In terms of water balance, sub-basin of Moravia is K. Kucarova is with Ministry of Environment of the Slovak Republic, (e- the catchment lowest rainfall (614 mm) as well as outflow mail: [email protected]) (109 mm). The Morava River basin is characterized by ISBN: 978-1-61804-283-5 53 New Developments in Environmental Science and Geoscience 40 a drainage system with a maximum average monthly flows P1M Mociarka: Láb K2M Stupávka: Borinka P1S Malina: Jakubov K2M Malina: Kuchyna P2M Chvojnica: Lopasov P1V Morava: Moravsky sv. Jan 35 K2M Myjava: Myjava P1M Oliva: Láb P1M Rudavka: Rohoznik during the spring season (March and April) and smallest K2M Teplica: Sobotiste K2M Solosnický p.: Solosnica P1S Rudava: Studienka 30 P1S Myjava: Sastin P1V Morava: Zahorska Ves P1M Suchy P. : Zohor average monthly discharges in the summer - autumn (August Ta Bratislava, air tempersture and September). The regime of small water levels is an 25 20 important phase of the hydrological cycle, which is associated C] ° 15 with the occurrence of minimum flows. Low flows are T [ 10 concentrated during two periods: summer-autumn period with 5 a minimum in the months of August to October, and in winter 0 depression usually with a minimum in January. -5 Fig. 2 shows the relation between the mean annual water -10 temperature (To) of the Morava River at station Záhorská Ves 01/01/2010 01/04/2010 01/07/2010 01/10/2010 and the mean annual air temperature (Ta) in station Bratislava Fig. 3 Measured water temperature T during the year 2010 Airport, 1956–2011. In Fig. 2a we can see that the mean at chosen gauging stations in the Morava River basin, Ta- air temperature - Bratislava annual temperatures of both series are identical since the year 1991. The mean annual water temperature corresponds to the mean annual temperature of the environment through which III. THE SIMULATION OF THE WATER TEMPERATURE the river flows. The air temperature increased in the period DEVELOPMENT 1971–1998. In case of water temperature the increase was much more moderate in last twenty years. A. Autoregressive Models Linear autoregressive models represent the very suitable means to describe the periodic time series with strong y = 0.998x 13 13 To, Morava R² = 0.710 stochastic character. They are simple autoregressive models of 12 12 the processes AR (p), MA (q) and the combination of ARMA 11 C] 11 ° 10 (p, q) as well as the integrated form ARIMA (p, d, q). ARIMA T [ C], Morava 10 model has several advantages. It is highly flexible, fast 9 ° 1998-2011 8 Ta, Bratislava To [ 9 responds and adapts to changing the nature of the test process. 9 10 11 12 13 7 The model is able to model the stochastic seasonality even 1931 1951 1971 1991 2011 ° Ta [ C], Bratislava trend better than the classical time series analysis [8]–[14]. a) b) In this work we have used several types of ARIMA models Fig. 2 a) Long-term trend of the mean annual air temperature (Ta) with additional regression component - the air temperature. in Bratislava (1931–2011) and of the mean annual water temperature (To) of the Morava River at station Záhorská Ves (1955–2011). b) B. Input data Relation between mean annual water temperature (To) of the Morava Input data for autoregressive models testing are monthly River at station Záhorská Ves and the air temperature (Ta) in series of the maximum average daily water temperature in Bratislava, period 1998–2011. selected rivers in the Morava River basin (Myjava: Šaštín– Stráže, Močiarka: Láb, Morava: Záhorská Ves and Stupávka: Since the period of introducing the automatic measuring Borinka), Fig. 4. stations the mean annual air and water temperatures are 30 identical and the relation between them is very close (Fig. 2b). 25 P1S Myjava: Sastin 20 C] The long-term water temperature trend of the Morava river ° 15 T [ T 10 was evaluated from the series of mean annual water 5 0 temperature (To) and maximal annual water temperature 01.01.2006 02.01.08 02.01.10 (To, max) in the period 1956–2010. The mean annual water 30 P1M Mociarka: Láb 25 temperature of the Morava River was decreasing in 1956– 20 C] ° 15 1996, but since 1996 the trend is increasing. The series of [ T 10 maximal annual water temperature does not show neither 5 0 increasing nor decreasing trend, [7]. 01.01.2006 02.01.08 02.01.10 Average daily water temperature at selected stations Morava 30 K2M Stupávka: Borinka 20 C] River basin indicate the type-specific and seasonal course of ° temperature (Fig. 3). [ T 10 Specific decreasing trend in water temperature was observed 0 01.01.2006 02.01.08 02.01.10 at the gauging station Myjava: Myjava (dark green) in Fig. 4 Measured water temperature T at station Myjava: Šaštín– the period 2009–2011. Stráže, Močiarka: Láb and Stupávka: Borinka in the Morava River basin. (Axis-x period 2006–2011). ISBN: 978-1-61804-283-5 54 New Developments in Environmental Science and Geoscience Selected hydrometric stations represent three types of rivers Table 2 Comparison of predictions for the 5 selected models (small, medium and large) and in their surrounding area was Model RMSE RUNS RUNM AUTO MEAN VAR not located significant source of anthropogenic effects. As a (A) 1.11349 OK OK ** OK OK regressor the monthly series of maximum average daily air (B) 1.58388 OK ** *** OK *** (C) 1.45784 OK ** OK OK ** temperature in the Bratislava Airport station were used. For (D) 1.43085 OK OK ** OK OK the statistics processing the average daily water temperatures (E) 1.38074 OK OK OK OK OK series, calculated from hourly data, are used. Where: RMSE = residual standard deviation; RUNS = number of rising and falling courses; Runm = number of traces above and below the median; C. Model calibration and verification AUTO = Box-Pierce test of auto-correlative course; MEAN = t-test; VAR = Six years period 2006–2011 was used for calibration. F-test; OK = not significant (p ≥ 0.10), * = 90% limit/interval of The choice of the time period was associated with a gradual reliability/confidence interval, ** = 95% limit/interval of reliability/confidence interval, *** = 99% limit/interval of transition to the automatic hourly hydrological data collection reliability/confidence interval.