ISSN: 2641-3078
Annals of Limnology and Oceanography
Research Article       Open acess      Peer-Reviewed

High-frequency modeling of dissolved oxygen and net ecosystem metabolism using STELLA

Miraç Eryiğit*, Fatih Evrendilek and Nusret Karakaya

Department of Environmental Engineering, Bolu Abant Izzet Baysal University, Bolu, 14030, Turkey
*Corresponding author: Dr. Miraç Eryiğit, Instructor, Department of Environmental Engineering, Bolu Abant Izzet Baysal University, Bolu, 14030, Turkey, Tel: +90 535 329 89 25; E-mail: miraceryigit@hotmail.com
Received: 02 January, 2023 | Accepted: 10 January, 2023 | Published: 11 January, 2023
Keywords: Dissolved oxygen modelling; Stream; Ecosystem metabolism; High frequency; Two-station method

Cite this as

Eryiğit M, Evrendilek F, Karakaya N (2023) High-frequency modeling of dissolved oxygen and net ecosystem metabolism using STELLA Ann Limnol Oceanogr 8(1): 001-008. DOI: 10.17352/alo.000013

Copyright

© 2023 Eryiğit M, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

This paper proposes a high-frequency process model for estimating Dissolved Oxygen (DO) and net ecosystem metabolism (NEM) in streams. The model was implemented by using STELLA to predict DO concentrations at one-minute intervals downstream of a 150-m headwater reach of the Abant Creek (Bolu, Turkey). NEM was also predicted at each interval by using a two-station method along the reach. DO, water temperature and other environmental variables used in the model were measured during 17 months between August 2015 and December 2016. The model was run for a day representing every month of the year. Model parameters were calibrated and validated according to mean absolute error (MAE) between measured and simulated values of DO and NEM. The results showed that the model appeared to be promising in terms of high-frequency estimations of DO.

Introduction

Dissolved oxygen (DO) is vital for aquatic life. Therefore, DO lack or extreme oscillations of DO affect all creatures living in the water [1-4]. In general, these issues occur due to human activities (discharges, agriculture, etc.) causing variations in DO concentrations shortly [5-9]. Also, natural events such as instantaneous temperature waves, heavy rainfalls and storms may influence DO concentrations in the water [10,11]. Thus, high-frequency DO data are required in order to evaluate sudden reactions of stream and lake ecosystems against extreme events and human activities. In addition, to DO, stream metabolism is also important as one of the fundamental indicators of nutrient, organic matter cycling, and stream health [12-15]. Net ecosystem metabolism (NEM) indicates a heterotrophic or autotrophic situation in streams and other water bodies and is estimated by measuring diurnal variations of DO concentrations due to photosynthesis, respiration, and reaeration [16]. In this regard, high-frequency DO models for aquatic environments come into prominence. In the related literature, several DO and water quality process models were applied. Kisi, et al. [17] modeled DO in the South Platte River by using artificial Intelligence techniques. Haddam [18] applied two adaptive neuro-fuzzy inference systems-based neuro-fuzzy models for modeling hourly DO in the Klamath River. Zounemat-Kermani, et al. [19] proposed two standalone soft computing models, including a multilayer perceptron neural network and a cascade correlation neural network for estimating the DO concentration in the St. Johns River. Li, et al. [20] improved the hybrid evolutionary model to predict the water quality including DO in the Euphrates River. Ouma, et al. [21] presented an approach based on the feedforward neural network model for the simulation and prediction of DO in the Nyando River basin. Kisi et al. [22] proposed a new ensemble method, Bayesian model averaging, to estimate hourly DO in the Link and Klamath rivers. Lu and Ma [23] introduced two novel hybrid decision tree-based machine learning models to carry out short-term water quality (DO etc.) predictions of the Gales Creek, in the Tualatin River basin. Asadollah, et al. [24] developed a new ensemble machine learning model (Extra Tree Regression) for predicting monthly water quality (DO etc.) in the Lam Tsuen River. Dehghani, et al. [25] used hybrid machine learning techniques including metaheuristic algorithms to obtain DO predictions in the Cumberland River. But, the time resolution (frequency) of these models is commonly a one-hour, one-day interval or more (monthly) [26-29].

This paper is the first study performing the high-frequency modeling of DO and NEM with one-minute intervals for a stream. In this study, a high-frequency dynamic model was developed by using STELLA to estimate DO and NEM simultaneously at one-minute intervals in the stream throughout the day representing every month of the year. Although the predicted values did not agree very well (perfectly) with the observed values, the results demonstrated that the model could be a pioneer for future studies regarding high-frequency estimations of DO in streams.

Materials and methods

Study site

The Abant Creek is a forested stream, located in the province of Bolu in the western Black Sea region of Turkey, and rises from the Abant Lake at 1325 m elevation (Figure 1). According to the long-term meteorological data between 1927 and 2016, Bolu has a cool temperate climate with snowy winters and warm summers with cool nights. The mean annual temperature is 10.5 °C, the mean annual maximum and minimum temperature is 17.1 °C (max. 39.8 °C) and 4.5 °C (min. -34 °C), respectively, mean annual precipitation is 545.3 mm, the mean annual number of days with precipitation is 137.7, and mean annual sunshine hours are 65.6 h (total of the daily average of every month) [30]. Measurements of DO, water Temperature (Tw), and other environmental variables were carried out in a headwater (spring) reach of Abant Creek between August 2015 and December 2016. Upstream (US) and downstream (DS) coordinates (Lat., Long., in DD) of the reach are 40.612, 31.279, and 40.613, 31.280, reach slope and length are 0.0133 and 150 m, respectively (Figure 1).

Measurements of environmental variables

NEM was estimated by using a two-station method developed by Odum [16] for 17 months (between August 2015 and December 2016). DO and Tw measurements were performed at the upstream and downstream of the reach with one-minute intervals for at least 36 hours (2-3 days) by using oxygen data loggers (MiniDOT, PME, Vista, CA, USA). The reach length was selected as 150 m according to Bales and Nardi [31]. The data loggers were placed in protection cages throughout the measurements. While measuring DO and Tw, atmosphere pressure (Patm) was simultaneously measured by using data loggers (RHT50, Extech Instruments, USA). Water samples were collected at a 15-minute interval for two hours, while stream flow rate (Q), stream velocity (V), stream depth (D), and stream width (W) were measured by using an acoustic velocimeter (SonTek FlowTracker Handheld ADV, California, USA) at the time of both deployment and collection of the DO loggers in the reach. In water samples, pH and specific conductivity (SC) were measured by using a multi-parameter probe (Hach HQ40d portable meter, Hach Company, Loveland, CO, USA). Biochemical oxygen demand (BOD5) was measured by using a respirometric pressure system (WTW Oxitop IS6, Germany). Ortho-phosphate (orto-PO4-P), ammonium-nitrogen (NH4-N), and nitrate-nitrogen (NO3-N), chlorophyll a (chl-a) were measured by using a spectrophotometer (DR 5000 UV/VIS spectrophotometer, Hach Lange, Germany). Sampling days of the year (DOY) between August 2015 and December 2016 were 224-227, 244-246, 281-283, 316-318, 344-346 in 2015, and 13-15, 41-43, 77-79, 105-107, 140-142, 168-170, 195-197, 223-225, 265-267, 286-288, 314-316, 342-344 in 2016.

Calculations of NEM

NEM was calculated by using the following equations [28]:

F r (t) =  Deficit avg ×  K 2 ( T w ) × Q ×  T t ×  C f      (1) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@6BC5@

Where Fr (t) is the reaeration flux (mg O2 reach-1 min-1) at time t, Deficitavg is the reach-averaged DO deficit (mg L-1) as DOsat (t) (DO saturation concentration) minus DO(t), K2(Tw) is the reaeration rate coefficient (min-1) at water temperature (Tw), Q is the stream flow rate (L s-1), Tt is travel time (min), and Cf is the unit conversion factor (one min = 60 s). K2 at Tw = 20°C was estimated using the equation by Owens, et al. [32] due to its suitability to the characteristics of the reaches sampled in this study.

K 2 =5.35× V 0.67 × D 1.85 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaGaae4samaaBaaaleaacaqGYaaabeaakiabg2da9iaaiwdacaGGUaGaaG4maiaaiwdacqGHxdaTcaWGwbWaaWbaaSqabeaacaaIWaGaaiOlaiaaiAdacaaI3aaaaOGaey41aqRaamiramaaCaaaleqabaGaeyOeI0IaaGymaiaac6cacaaI4aGaaGynaaaaaaa@4898@ Tw = 20 °C (0.12 ≤ D ≤ 3.35 m ve 0.03 ≤ V ≤ 1.52 m s-1) (2)

K2 at any Tw was calculated by using the following equation by Elmore and West [33]:

K 2 ( T w )= K 2 ( T w =20 °C)×1.02 4 ( T w -20)      (3) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaqcLbsacaWGlbqcfa4aaSbaaSqaaKqzGeGaaGOmaaWcbeaajugibiaacIcacaWGubqcfa4aaSbaaSqaaKqzGeGaam4DaaWcbeaajugibiaacMcacqGH9aqpcaWGlbqcfa4aaSbaaSqaaKqzGeGaaGOmaaWcbeaajugibiaacIcacaWGubqcfa4aaSbaaSqaaKqzGeGaam4DaaWcbeaajugibiabg2da9iaaikdacaaIWaacbaGaa8hiaiaa=blacaWFdbGaa8xkaiabgEna0kaa=fdacaWFUaGaa8hmaiaa=jdacaWF0aqcfa4aaWbaaSqabeaajugibiaa=HcacaWFubqcfa4aaSbaaWqaaKqzGeGaa83Daaadbeaajugibiaa=1cacaWFYaGaa8hmaiaa=LcaaaqcfaOaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGOaGaae4maiaabMcaaaa@6157@

NEM(t)=( [ DO d (t) DO u (t T t ) ]×Q ) F r (t)      (4) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@6567@

Where NEM (t) is the net metabolism flux (mg O2 reach-1 min-1) at time t, DOd(t) is downstream DO concentration (mg L-1) at time t, DOu(t-Tt) is upstream DO concentration (mg L-1) at time t-Tt.

High-frequency process model

The model was developed by using the software STELLA to predict DO concentrations at one-minute intervals downstream of a 150-m headwater reach of Abant Creek. NEM was also estimated at each interval by using the two-station method in the model. The model was run for a day (including two nighttime and one daytime period) representing every month of the year. Measured data from January 2016 to December 2016, and from August 2015 to December 2015 were used for model calibration and validation, respectively. Model parameters were calibrated and validated according to mean absolute error (MAE) between measured and simulated (predicted) values of DO and NEM. The structure of the model was illustrated in Figure 2.

The equations used in the model are as follows (Brown & Barnwell, 1987):

dDO dt = K 2 ( D O sat DO ) + ( α 3 ×μ - α 4 ×ρ )A K 1 L BOD K 4 D                     Reaeration       Photosynthesis-Respiration    BOD        SOD  α 5 × β 1 N H 4 -N α 6 × β 2 N O 2 -N +D O input D O output                                        (5)                         Nitrification                                                                                             MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGceaqabeaajuaGdaWcaaGcbaqcLbsacaWGKbGaamiraiaad+eaaOqaaKqzGeGaamizaiaadshaaaGaeyypa0tcfa4aaGbaaOqaaKqzGeGaam4saKqbaoaaBaaaleaajugibiaaikdaaSqabaqcfaOaeyyXICTcdaqadaqaaiaadseacaWGpbWaaSbaaSqaaiaadohacaWGHbGaamiDaaqabaGccqGHsislcaWGebGaam4taaGaayjkaiaawMcaaaWcbaaakiaawIJ=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aKqzGeGaa8hiaiaa=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@73A4@

Reaeration DO input= K 2 ×Mean DO Deficit      (6) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaqcLbsacaqGsbGaaeyzaiaabggacaqGLbGaaeOCaiaabggacaqG0bGaaeyAaiaab+gacaqGUbGaaeiiaiaabseacaqGpbGaaeiiaiaabMgacaqGUbGaaeiCaiaabwhacaqG0bGaeyypa0Jaam4saKqbaoaaBaaaleaajugibiaaikdaaSqabaqcLbsacqGHxdaTcaWGnbGaamyzaiaadggacaWGUbGaaeiiaiaabseacaWGpbGaaeiiaiaabseacaqGLbGaaeOzaiaabMgacaqGJbGaaeyAaiaabshacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGOaGaaeOnaiaabMcaaaa@6074@

Reaeration DO output= K 2 ×| Mean DO Deficit |     (7) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaqcLbsacaqGsbGaaeyzaiaabggacaqGLbGaaeOCaiaabggacaqG0bGaaeyAaiaab+gacaqGUbGaaeiiaiaabseacaqGpbGaaeiiaiaab+gacaqG1bGaaeiDaiaabchacaqG1bGaaeiDaiabg2da9iaadUeajuaGdaWgaaWcbaqcLbsacaaIYaaaleqaaKqzGeGaey41aqBcfa4aaqWaaOqaaKqzGeGaamytaiaadwgacaWGHbGaamOBaiaabccacaqGebGaam4taiaabccacaqGebGaaeyzaiaabAgacaqGPbGaae4yaiaabMgacaqG0baakiaawEa7caGLiWoajuaGcaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabIcacaqG3aGaaeykaaaa@65B7@

K 2 = K 2 (20 °C)× 1.024 (Mean  T w 20) × T t      (8) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaqcLbsacaWGlbqcfa4aaSbaaSqaaKqzGeGaaGOmaaWcbeaajugibiabg2da9iaadUeajuaGdaWgaaWcbaqcLbsacaaIYaaaleqaaKqzGeGaaiikaiaaikdacaaIWaacbaGaa8hiaiabgclaWkaadoeacaGGPaGaey41aqRaaGymaiaac6cacaaIWaGaaGOmaiaaisdajuaGdaahaaWcbeqaaKqzGeGaaiikaiaad2eacaWGLbGaamyyaiaad6gacaqGGaGaaeivaKqbaoaaBaaameaajugibiaabEhaaWqabaqcLbsacqGHsislcaaIYaGaaGimaiaacMcaaaGaey41aqRaamivaKqbaoaaBaaaleaajugibiaadshaaSqabaqcfaOaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGOaGaaeioaiaabMcaaaa@6246@

K 2 (20°C)=(5.35× V 0.67 × D 1.85 )/1440     (9) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaqcLbsacaWGlbqcfa4aaSbaaSqaaKqzGeGaaGOmaaWcbeaajugibiaacIcacaaIYaGaaGimaGqaaiaa=blacaWGdbGaaiykaiabg2da9iaacIcacaaI1aGaaiOlaiaaiodacaaI1aGaey41aqRaamOvaKqbaoaaCaaaleqabaqcLbsacaaIWaGaaiOlaiaaiAdacaaI3aaaaiabgEna0kaadseajuaGdaahaaWcbeqaaKqzGeGaeyOeI0IaaGymaiaac6cacaaI4aGaaGynaaaacaGGPaGaai4laiaaigdacaaI0aGaaGinaiaaicdacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabIcacaqG5aGaaeykaaaa@5C1D@

Mean T w =(Downstream T w +(Upstream T w (t T t )))/2     (10) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaacbaqcLbsacaWFnbGaa8xzaiaa=fgacaWFUbGaa8hiaiaa=rfajuaGdaWgaaWcbaqcLbsacaWF3baaleqaaKqzGeGaa8hiaiaa=1dacaGGOaGaamiraiaad+gacaWG3bGaamOBaiaadohacaWG0bGaamOCaiaadwgacaWGHbGaamyBaiaa=bcacaWFubqcfa4aaSbaaSqaaKqzGeGaa83DaaWcbeaajugibiabgUcaRiaacIcacaWGvbGaamiCaiaadohacaWG0bGaamOCaiaadwgacaWGHbGaamyBaiaa=bcacaWFubqcfa4aaSbaaSqaaKqzGeGaa83DaaWcbeaajugibiaa=bcacaGGOaGaamiDaiabgkHiTiaadsfajuaGdaWgaaWcbaqcLbsacaWG0baaleqaaKqzGeGaaiykaiaacMcacaGGPaGaai4laiaaikdacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabIcacaqGXaGaaeimaiaabMcaaaa@6BB1@

Mean DO Deficit =(Downstream DO Decifit+Upstream DO Deficit(t T t ))/2     (11) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaacbaqcLbsacaWFnbGaa8xzaiaa=fgacaWFUbGaa8hiaiaa=reacaWGpbGaaeiiaiaabseacaqGLbGaaeOzaiaabMgacaqGJbGaaeyAaiaabshacaWFGaGaa8hiaiabg2da9iaacIcacaWGebGaam4BaiaadEhacaWGUbGaam4CaiaadshacaWGYbGaamyzaiaadggacaWGTbGaa8hiaiaa=reacaWGpbGaaeiiaiaabseacaqGLbGaae4yaiaabMgacaqGMbGaaeyAaiaabshacaqGRaGaaeyvaiaabchacaqGZbGaaeiDaiaabkhacaqGLbGaaeyyaiaab2gacaWFGaGaa8hraiaad+eacaqGGaGaaeiraiaabwgacaqGMbGaaeyAaiaabogacaqGPbGaaeiDaiaacIcacaWG0bGaeyOeI0IaamivaKqbaoaaBaaaleaajugibiaadshaaSqabaqcLbsacaGGPaGaaiykaiaac+cacaaIYaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGOaGaaeymaiaabgdacaqGPaaaaa@78E8@

Photosynthesis= α 3 ×μ×A     (12) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaqcLbsacaWGqbGaamiAaiaad+gacaWG0bGaam4BaiaadohacaWG5bGaamOBaiaadshacaWGObGaamyzaiaadohacaWGPbGaam4Caiabg2da9iabeg7aHLqbaoaaBaaaleaajugibiaaiodaaSqabaqcLbsacqGHxdaTcqaH8oqBcqGHxdaTcaWGbbGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGOaGaaeymaiaabkdacaqGPaaaaa@5595@

μ=μ (20 °C)× 1.066 (Mean  T w 20) ×min(G(OrthoP O 4 P),G(N H 4 N),G(N O 3 N))× T t      (13) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@84F4@

G(OrthoP O 4 P)= OrthoP O 4 P Concentration K P +OrthoP O 4 P Concentration       (14) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaqcLbsacaWGhbGaaiikaiaad+eacaWGYbGaamiDaiaadIgacaWGVbGaamiuaiaad+eajuaGdaWgaaWcbaqcLbsacaaI0aaaleqaaKqzGeGaeyOeI0IaamiuaiaacMcacqGH9aqpjuaGdaWcaaGcbaacbaqcLbsacaWFpbGaa8NCaiaa=rhacaWFObGaa83Baiaa=bfacaWFpbqcfa4aaSbaaSqaaKqzGeGaa8hnaaWcbeaajugibiabgkHiTiaadcfacaqGGaGaae4qaiaab+gacaqGUbGaae4yaiaabwgacaqGUbGaaeiDaiaabkhacaqGHbGaaeiDaiaabMgacaqGVbGaaeOBaaGcbaqcLbsacaWGlbqcfa4aaSbaaSqaaKqzGeGaamiuaaWcbeaajugibiabgUcaRiaa=9eacaWFYbGaa8hDaiaa=HgacaWFVbGaa8huaiaa=9eajuaGdaWgaaWcbaqcLbsacaWF0aaaleqaaKqzGeGaeyOeI0IaamiuaiaabccacaqGdbGaae4Baiaab6gacaqGJbGaaeyzaiaab6gacaqG0bGaaeOCaiaabggacaqG0bGaaeyAaiaab+gacaqGUbaaaKqbakaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabIcacaqGXaGaaeinaiaabMcaaaa@8018@

G(N H 4 N)= N H 4 N Concentration K N +N H 4 N Concentration      (15) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@724F@

G(N O 3 N)= N O 3 N Concentration K N +N O 3 N Concentration       (16) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@7305@

BOD= K 1 × L BOD       (17) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaqcLbsacaWGcbGaam4taiaadseacqGH9aqpcaWGlbqcfa4aaSbaaSqaaKqzGeGaaGymaaWcbeaajugibiabgEna0kaadYeajuaGdaWgaaWcbaqcLbsacaWGcbGaam4taiaadseaaSqabaqcfaOaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeikaiaabgdacaqG3aGaaeykaaaa@4B1A@

K 1 =  K 1 (20°C)× 1.047 (Mean  T w 20) × T t       (18) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaqcLbsacaWGlbqcfa4aaSbaaSqaaKqzGeGaaGymaaWcbeaajugibiabg2da9iaabccacaWGlbqcfa4aaSbaaSqaaKqzGeGaaGymaaWcbeaajugibiaacIcacaaIYaGaaGimaiabgclaWkaadoeacaGGPaGaey41aqRaaGymaiaac6cacaaIWaGaaGinaiaaiEdajuaGdaahaaWcbeqaaKqzGeGaaiikaiaad2eacaWGLbGaamyyaiaad6gacaqGGaGaaeivaKqbaoaaBaaameaajugibiaabEhaaWqabaqcLbsacqGHsislcaaIYaGaaGimaiaacMcaaaGaey41aqRaamivaKqbaoaaBaaaleaajugibiaadshaaSqabaqcfaOaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeikaiaabgdacaqG4aGaaeykaaaa@6399@

Respiration= α 4 ×ρ×A      (19) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaqcLbsacaqGsbGaaeyzaiaabohacaqGWbGaaeyAaiaabkhacaqGHbGaaeiDaiaabMgacaqGVbGaaeOBaiabg2da9iabeg7aHLqbaoaaBaaaleaajugibiaaisdaaSqabaqcLbsacqGHxdaTcqaHbpGCcqGHxdaTcaWGbbGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeikaiaabgdacaqG5aGaaeykaaaa@5341@

ρ=ρ (20°C)× 1.047 (Mean  T w 20) × T t       (20) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaqcLbsacqaHbpGCcqGH9aqpcqaHbpGCcaqGGaGaaiikaiaaikdacaaIWaGaeyiSaaRaam4qaiaacMcacqGHxdaTcaaIXaGaaiOlaiaaicdacaaI0aGaaG4naKqbaoaaCaaaleqabaqcLbsacaGGOaGaamytaiaadwgacaWGHbGaamOBaiaabccacaqGubqcfa4aaSbaaWqaaKqzGeGaae4DaaadbeaajugibiabgkHiTiaaikdacaaIWaGaaiykaaaacqGHxdaTcaWGubqcfa4aaSbaaSqaaKqzGeGaamiDaaWcbeaajuaGcaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGOaGaaeOmaiaabcdacaqGPaaaaa@6036@

Nitrification= α 5 × β 1 ×N H 4 N+ α 6 × β 2 ×N O 2 N     (21) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaqcLbsacaWGobGaamyAaiaadshacaWGYbGaamyAaiaadAgacaWGPbGaam4yaiaadggacaWG0bGaamyAaiaad+gacaWGUbGaeyypa0JaeqySdewcfa4aaSbaaSqaaKqzGeGaaGynaaWcbeaajugibiabgEna0kabek7aILqbaoaaBaaaleaajugibiaaigdaaSqabaqcLbsacqGHxdaTcaWGobGaamisaKqbaoaaBaaaleaajugibiaaisdaaSqabaqcLbsacqGHsislcaWGobGaey4kaSIaeqySdewcfa4aaSbaaSqaaKqzGeGaaGOnaaWcbeaajugibiabgEna0kabek7aILqbaoaaBaaaleaajugibiaaikdaaSqabaqcLbsacqGHxdaTcaWGobGaam4taKqbaoaaBaaaleaajugibiaaikdaaSqabaqcLbsacqGHsislcaWGobGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGOaGaaeOmaiaabgdacaqGPaaaaa@6FCD@

β 1 = β 1 (20°C)× 1.065 (Mean  T w 20) × T t      (22) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaqcLbsacqaHYoGyjuaGdaWgaaWcbaqcLbsacaaIXaaaleqaaKqzGeGaeyypa0JaeqOSdiwcfa4aaSbaaSqaaKqzGeGaaGymaaWcbeaajugibiaacIcacaaIYaGaaGimaiabgclaWkaadoeacaGGPaGaey41aqRaaGymaiaac6cacaaIWaGaaGOnaiaaiwdajuaGdaahaaWcbeqaaKqzGeGaaiikaiaad2eacaWGLbGaamyyaiaad6gacaqGGaGaaeivaKqbaoaaBaaameaajugibiaabEhaaWqabaqcLbsacqGHsislcaaIYaGaaGimaiaacMcaaaGaey41aqRaamivaKqbaoaaBaaaleaajugibiaadshaaSqabaqcfaOaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGOaGaaeOmaiaabkdacaqGPaaaaa@63F0@

SOD= K 4 /D     (23) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaqcLbsacaWGtbGaam4taiaadseacqGH9aqpcaWGlbqcfa4aaSbaaSqaaKqzGeGaaGinaaWcbeaajugibiaac+cacaWGebGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGOaGaaeOmaiaabodacaqGPaaaaa@44D6@

K 4 = K 4 (20°C)× 1.06 (Mean  T w 20) × T t      (24) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaqcLbsacaWGlbqcfa4aaSbaaSqaaKqzGeGaaGinaaWcbeaajugibiabg2da9iaadUeajuaGdaWgaaWcbaqcLbsacaaI0aaaleqaaKqzGeGaaiikaiaaikdacaaIWaGaeyiSaaRaam4qaiaacMcacqGHxdaTcaaIXaGaaiOlaiaaicdacaaI2aqcfa4aaWbaaSqabeaajugibiaacIcacaWGnbGaamyzaiaadggacaWGUbGaaeiiaiaabsfajuaGdaWgaaadbaqcLbsacaqG3baameqaaKqzGeGaeyOeI0IaaGOmaiaaicdacaGGPaaaaiabgEna0kaadsfajuaGdaWgaaWcbaqcLbsacaWG0baaleqaaKqbakaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeikaiaabkdacaqG0aGaaeykaaaa@6197@

Where α3 is the rate of DO production per unit of algal photosynthesis (mg O2 mg A-1), µ is the algal growth rate (min-1), α4 is the rate of DO uptake per unit of algae respired (mg O2 mg A-1), ρ is algal respiration rate (min-1), A is algal biomass concentration (mg L-1), K1 is carbonaceous deoxygenation (BOD) rate (min-1), LBOD is a concentration of carbonaceous BOD (mg L-1), K4 is sediment oxygen demand (SOD) rate (mg O2 m-2 min-1), D is a depth of stream (m), G(Ortho-PO4-P), G(NH4-N) and G(NO3-N) are monod expressions for phosphorus and nitrogen, respectively, KP and KN are half-saturation constants, α5 is the rate of DO uptake per unit of NH4-N oxidation (mg O2 mg N-1), α6 is the rate of DO uptake per unit of NO2-N oxidation (mg O2 mg N-1), β1 and β2 are nitrification rate coefficients (min-1) of NH4-N and NO2-N. NO2-N was neglected while the oxidation of NH4-N to NO3-N was in the nitrification process. So, α5 included α6 while β1 was including β2 in the model. The ratio of chl-a to algal biomass was assigned as 50 µg CHL-a/mg A [27].

Results and discussions

The mean monthly environmental variables measured and metabolism rates calculated between August 2015 and December 2016 were given in Table 1. The model coefficients were calibrated according to the ranges of Brown and Barnwell [27]. The calibrated coefficients, calibration, and validation results were given in Tables 2-4, respectively. MAEs between measured and simulated values of NEM ranged from 0.58 to 7.92 gr O2 m-2 day-1 and 1.3 – 7.78 gr O2 m-2 day-1 for calibration and validation, respectively. Figure 3-7 illustrated comparisons of one-minute measured and predicted DO concentrations during a day representing each month from August 2015 to December 2015 for validation. In the model, photosynthesis and respiration processes depend on only algal biomass. Aquatic plants and heterotrophs such as insects, and heterotrophic microorganisms living in the water were not included in these processes. Therefore, these deficiencies affected the DO predictions of the model.

According to calibration and validation results, differences (MAE and R2) between measured and predicted DO concentrations increased in July, August, September, October, November 2016, and August, September, and October 2015, respectively (Tables 3,4). In these months, the flow rate and velocity of the stream were very low (Table 1). Thus, high hydraulic retention durations might have enhanced photosynthesis and respiration processes by algae, aquatic plants, and heterotrophs in the water. Consequently, unavailable aquatic plant inputs in the model explain high differences between measured and predicted DO concentrations in these months. As is seen in Figures 3,4, the model was not able to simulate DO trends increasing in the daytime due to the causes/reasons mentioned above. In Figure 5, the measured DO concentration decreased suddenly. This might have been because of organic matters arising from rare leakages of the hotel sewage system around the study reached in a day (Figure 1). The model was not able to catch this fall in DO concentration since BOD input was constant for each interval (not temporal in a day) in the model. However, according to the rest of the months, the results showed that the model was successful and appeared to be promising in terms of high-frequency estimations of DO.

High-frequency values of NEM (as gr O2 m-2 min-1) were sensitive to DO differences with high flow rates even if there was a low difference (such as 0.1 mg L-1) between measured and predicted DO concentrations. Therefore, R2 between calculated and simulated NEMs was low (Tables 3,4).

Conclusion

The results demonstrated that algal biomass was inadequate for high-frequency modeling of DO oscillations in a daytime. Thus, aquatic plant inputs were also significant and should be considered for high-frequency DO modeling. BOD and nutrients (NH4-N, NO3-N, and orto-PO4-P) were measured in the two composite water samples taken at the time of deployment and collection of the DO loggers in the reach for 17 months. The means of two measurements of BOD and nutrients were assigned as constant inputs for each interval (dt = 1 min) in each month. Instead, all these inputs should be temporal (not constant) throughout the day for more accuracy.

Consequently, it can be said that aquatic plants in addition to the algal biomass, BOD, and nutrients are the main effective inputs. The model is modular and improvable to integrate more inputs (aquatic plants, etc.) so that much better predictions in high-frequency DO modeling can be obtained. Because it was very hard to estimate/predict DO concentrations and NEM values simultaneously within every minute during the day, the model was not able to predict observed values accurately (perfectly). However, acceptable predictions were obtained in this hard task. In future studies, the model can be modified and tested by using more inputs and data. Also, it can be applied under different conditions (instantaneous wastewater discharges, etc.) to predict DO and NEM variations.

Highlights
  • The paper is the first study to include high-frequency modeling of both DO and NEM with one-minute intervals for the stream.
  • The model was built in STELLA for the headwater reach of the Abant Creek in Bolu, Turkey.
  • The model is simple and modular for high-frequency estimations of DO and NEM in the streams.

The authors thank Bolu Abant Izzet Baysal University for supporting the study. Also, the authors thank H. Fidan and E. Özalp for their help with field campaigns.

Funding information

This study was financially supported by the Scientific Research Projects Unit of Bolu Abant Izzet Baysal University (Grant No: BAP–2015.09.02.851).

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