The Simulation of the Water Temperature Rising Using ARIMA Models

Dana Halmova, Pavla Pekarova, WSEAS TRANSACTIONS on HEAT and MASS TRANSFER Jan Pekar, Katarina Kucarova The Simulation of the Water Temperature Rising Using ARIMA Models DANA HALMOVA1, PAVLA PEKAROVA1, JAN PEKAR2, KATARINA KUCAROVA3 1 Institute of Hydrology Slovak Academy of Sciences Racianska 75, 831 02 Bratislava SLOVAKIA 2 Comenius University in Bratislava Faculty of Mathematics, Physics and Informatics SLOVAKIA 3 Ministry of Environment of the Slovak Republic Bratislava SLOVAKIA [email protected], http://www.ih.savba.sk/ Abstract: - The methodological approach to measuring the water temperature was historically developing. The economic importance of knowledge on flowing water temperature and thus the responsibility of the observer for the proper and reliable measurements has been known for over a century. In Slovakia, the water temperature in streams is measured according to sectorial technical environmental standards (Measurement of water levels, water temperature and ice phenomena on the surface flows) of 2005. Water temperature plays a key role from environmental, biochemical as well as chemical point of view. Increase in water temperature, e.g. during extreme and long-lasting heat waves and drought, can cause undesirable chemical and biochemical reactions. In the study we have focused on water temperature simulation in twenty one streams in the Slovak part of the Morava River basin. The aim was to assess the impact of the expected air temperature increase to a temperature rise of water in the streams. While processing the data, we used the time series of the average daily water temperature in selected gauging stations in the Morava River basin and the average daily air temperature measured in Bratislava-airport, for the period 2006–2011. Scenarios of extreme monthly air temperatures at the Bratislava-airport were compiled based on statistical analysis of daily air temperatures during 1951–2011. Extreme water temperatures were simulated based on a scenario of air temperature using several ARIMA models (Autoregressive Integrated models of Moving Averages). Results of the simulations show, that for increasing the maximum air temperature by 1°C, the water temperature may be increased by 0.7–0.9°C, depending on the model used. Key-Words: ARIMA models, water temperature simulation, Water Framework Directive, climate change 1 Introduction 2. Topographic conditions – altitude and latitude of The water temperature is one of the main physical characteristics of the surface water. It directly the basin, flow orientation, coastal vegetation, influences the biota of the streams and adjacent subsoil... land. The water temperature significantly influences 3. The hydrological regime of flow - discharge, flow other physical and chemical properties of the water. velocity and depth of stream, level and temperature The productivity of the total water ecosystem does of groundwater... not only depend on the water temperature, but it is 4. Anthropogenic activities in the basin - discharge in great extend limited by the water temperature [1]. of urban and industrial waste water, flow reduction The factors that affect the water temperature can be [3], artificial reservoirs [4] and diversion canals generally divided into four groups [2]: and removal of riparian vegetation [5]. 1. Atmospheric conditions - solar radiation, air Several Slovak hydrologists addressed the statistical temperature, wind speed, precipitation, evaporation, analysis of drought in watercourses in the East condensation... Slovakia, which are connected with the high water temperature in rivers [6]. The main objective of E-ISSN: 2224-3461 46 Volume 11, 2016 Dana Halmova, Pavla Pekarova, WSEAS TRANSACTIONS on HEAT and MASS TRANSFER Jan Pekar, Katarina Kucarova their work was to identify long-term trends in low • “Water body” may be representative of the entire flows in selected 63 stations in the East Slovakia section of a watercourse, or may be part of it (entity during the period 1975–2012. = less than or corresponding to watercourse). • “Stream type” is a grouping of watercourses into 1.1 Methodology of water temperature categories with similar internal characteristics measuring in Slovakia (= entity associating several streams). The methodological approach to measuring In the Slovak Republic (SR) there were defined the water temperature in Slovakia was historically 1763 surface water bodies and 22 stream types. developing. The first continual water temperature Identification of different types of flows includes: measurements started in 1921 on the Danube River the type of landscape (P - the Pannonian plain, K – at Bratislava. The water temperature was measured the Carpathians), the altitude (1–4) and the size of by observer. According to the source, the stream: M - small, S - middle and V - large flow. temperature of the water flow was measured daily, With increasing altitude in small streams (P1M, regularly at 7:00 am, or even in another time (hour) P2M, and K2M) average and maximum water to a specific provision. The mercury thermometer temperature decreases. The summary of numbers of with Celsius scale with a range from –12 to 40°C water bodies, types and data from the Morava River was used for the measurements of the water basin is given in Table 1. temperature in watercourses. Temperature was measured under the water surface, at a place designated for this purpose, at least 1.5 meters from Table 1 Summary of numbers of water bodies, types the banks. Sampling point should not be: shadowed and data from the Morava River basin type Number of Number of VS of Number of obtained by vegetation, too shallow or deep and water should water bodies particular type data sets of VS with flow slightly. In case the access to water is difficult of particular with TVO temperature or impossible, the measurement is carried out in type measurements measurements P1M 58 4 4 another suitable place, where it is necessary to P1S 4 6 5 observe at all times. The place of measurement must M1(P1V) 2 6 3 guarantee finding the average water temperature. P2M 18 3 3 K2M 20 6 6 Nowadays, the measurements are executed Total 102 25 21 according to the sectorial technical environmental standards [7]. According to that environmental TVO – water temperature, VS – gauging station standard, water temperature is measured usually in the morning at 7:00 am. Exception are the prognostic stations, where the water temperature is measured simultaneously with the water level at 2 Description of the Morava River 6:00 am. In some stations for special purpose, the basin water temperature can be implemented in other The Morava River is a left tributary of the Danube. terms or several times a day. A primary requirement The Morava River basin is mostly located in the for all measurements is to follow the frequency and Czech Republic. Catchment area of the Morava time of measurements throughout the whole year. River at estuary into the Danube is about In the context of sustainable protection and efficient 26 580 km2, of which is only 2 282 km2 in Slovakia, use of water, considerable attention has focused on representing 8.6% of the whole catchment area and extremality in the hydrological regime of water. 4.65% of the Slovak Republic area (Table 2), Sustainable protection and efficient use of water is (Fig. 1). based on the process of implementing the Water In terms of water balance, sub-basin of Morava is Framework Directive (WFD) [8] and is directly the catchment of lowest rainfall (614 mm) as well as related to water quality and quantity, which are lowest outflow (109 mm), in the Danube basin. affected by climate change, with a direct impact on The Morava River basin is characterized by the established environmental goals. WFD a drainage system with the maximum average introduced a new understanding and new monthly flows during the Spring season (March and terminology in the evaluation of water status. April), and the smallest average monthly discharges Evaluation of the status is not related to the entity in the Summer - Autumn seasons (August and "flow", but it is based on the evaluation of "water September). bodies" and "stream types": The regime of low water levels is an important phase of the hydrological cycle, which is associated E-ISSN: 2224-3461 47 Volume 11, 2016 Dana Halmova, Pavla Pekarova, WSEAS TRANSACTIONS on HEAT and MASS TRANSFER Jan Pekar, Katarina Kucarova with the occurrence of minimum flows. Low flows period 1971–1998. In case of water temperature the are concentrated during two periods: Summer- increase was much more moderate in last twenty Autumn period with a minimum in the months of years. August to October, and the winter depression 13 To, Morava usually with a minimum in January. 12 11 C] Table 2 Basic characteristics of the gauging profiles ° 10 T [ T 9 Gauging station Sastin- Myjava Borinka 8 Ta, Bratislava Straze 7 Catchment Morava Morava Morava 1931 1951 1971 1991 2011 River name Myjava Myjava Stupavka 2 Catchment area [km ] 640.04 32.53 35.74 Fig. 2 Long-term trend of the mean annual air Catchment altitude [m a.s.l.] temperature (Ta) in Bratislava (1931–2011) and of Min. 167.56 324.53 217.81 Max. 820 820 651.91 the mean annual water temperature (To) of the Average 303.62 472.54 462.67 Morava River at station Zahorska Ves (1955–2011). Average slope [°] 5.96 8.66 9.24 Density of the river network 1.22 1.48 1.38 Since the period of introducing the automatic [km.km2] Forest coverage [%] 34.92 41.4 84.66 measuring stations, the mean annual air and water Average annual discharge 2.51 0.22 0.35 temperatures are identical and the relation between [m3.s-1] them is very close (Fig. 2). The long-term water temperature trend of the Morava River was r e evaluated from the series of mean annual water iv R a v temperature (To) and maximal annual water ra Myjava o M Sastin temperature (To, max) in the period 1956–2010.

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