Dynamique et modélisation de l’oxygène dissous en rivière Dynamics and modelling of dissolved oxygen in rivers

Résumé

La concentration en oxygène dissous en milieu fluvial varie selon un cycle diurne (24 h) qu’il est essentiel de considérer dans l’évaluation de l’état d’oxygénation d’un cours d’eau. En principe, seules des mesures en continu recueillies au cours de cycles de 24 h permettent d’évaluer correctement l’état d’oxygénation d’une rivière, ce que, en pratique, les contraintes logistiques et budgétaires ne permettent pas de réaliser. Le présent article vise à faire la synthèse des connaissances sur les facteurs de contrôle et la modélisation des variations diurnes de la concentration en oxygène dissous en rivière. Parmi les facteurs biologiques et physico-chimiques, les activités autotrophe et hétérotrophe sont les facteurs dominants responsables des variations diurnes de l’oxygène dissous. Certains modèles de qualité de l’eau permettent de modéliser la teneur en oxygène et, dans certains cas, la variation diurne. Toutefois, ces modèles sont souvent complexes, d’utilisation ardue et impliquent la mesure directe sur des cycles de 24 h des variables qui régissent la concentration en oxygène dans le milieu. Une démarche est proposée pour l’élaboration d’un modèle et a été appliquée dans une étude de cas réalisée dans la rivière Saint-Charles (Québec, Canada). Un modèle simple (une fonction sinusoïdale) dont les paramètres ont été corrélés à la température et à la concentration moyenne en nitrate a permis de générer des valeurs simulées d’oxygène dissous très proches des valeurs observées in situ. Un modèle alternatif utilisant des valeurs ponctuelles de température et de concentration de nitrate a donné des résultats équivalents. L’approche proposée constitue donc une alternative simple et pratique à la mesure en continu de l’oxygène et permet une évaluation plus réaliste de l’état réel d’oxygénation d’une rivière que la prise de mesures ponctuelles.

Mots clés:

• oxygène,
• dynamique,
• modélisation,
• cycle diurne,
• qualité de l’eau,
• rivière,
• photosynthèse,
• respiration

Summary

In rivers, dissolved oxygen concentrations typically show diel variations with maximum values during daytime and minimum values at night. The diel cycle must be taken into account when assessing the state of oxygenation of a watercourse. However, in water quality monitoring programs, dissolved oxygen concentrations are usually obtained from single measurements taken during daytime. The resulting data do not represent the real overall oxygen levels of a watercourse and thus can lead to erroneous conclusions regarding the oxygen status of a river. Continuous data collected over 24‑hour cycles are required for an accurate oxygen status assessment, but in practice, logistic and budget constraints do not allow such samplings. Modelling can be a convenient alternative to direct measurements. However, the water quality models that take into account the diel cycle of oxygen are generally complex to run. The purpose of this study was to review the information relating to the dynamics and the modelling of the diel variations in dissolved oxygen in rivers and to apply a simple model in a case study involving dissolved oxygen, nutrients, temperature and chlorophyll a data collected over 24‑hour cycles in the St. Charles River near Quebec City (Canada).

Photosynthesis by algae, both benthic and planktonic, as well as by macrophytes, is an important and sometimes dominant factor in the oxygen budget of a river. Sediments and heterotrophic activity by bacteria, particularly in rivers receiving important loads of wastewaters, can be important sinks for oxygen. Temperature determines the solubility of oxygen, thereby directly influencing oxygen concentrations. Diel variations in oxygen thus reflect diel variations in temperature. Temperature also has an effect on biological processes such as respiration and photosynthesis. Reaeration varies not only with temperature, but also with the type of flow (laminar vs. turbulent) and current velocity. In rivers with important slopes and current velocities, reaeration can be sufficient to make up for oxygen losses due to high heterotrophic activity. Nevertheless, light is the first causative factor for the diel variations in oxygen, determining both autotrophic activity and water temperature. However, suspended matter in the water column reduces light penetration. Higher levels of suspended matter result in lower levels of photosynthesis and oxygen production. The sudden or large influx of runoff waters after heavy rain or snowmelt can also have an important impact on the oxygen budget of a river. Finally, chemical factors can have an influence on the diel variations in oxygen: nutrient inputs, in particular, can stimulate the rate of photosynthesis and oxygen production. Overall, oxygen dynamics are determined by the relative importance of biological, physical and chemical factors, which vary in time and space. However, biological processes often dominate over the other causative factors affecting diel variations in oxygen. In temperate climates, biological processes have a controlling function only during warmer months, with temperature and flow being the dominant controlling factors during colder months.

Water quality models that take into account diel variations in oxygen are often designed to assess primary production and respiration. These models are based on either ODUM’s (1956) concept of oxygen curves or on direct and continuous measurements of dissolved oxygen. Periodic functions or Fourier series are also used to simulate diel variations in oxygen. The widely used USEPA QUAL2e model predicts diel variations in oxygen from different measurements including light intensity and from computation of the rates of photosynthesis and respiration. Several other modelling approaches use various combinations of indirect methods to predict the variations in oxygen, based on light intensity, algal biomass, primary production, and reaeration. Specific models are sometimes necessary due to particular regional characteristics or environmental issues.

In general, water quality models designed for water management purposes are complex and require the measurement of a large number of parameters, which necessitates elaborate and costly logistics. Estimating the parameters controlling the oxygen budget in a river thus ends up being more time and labour consuming than the direct measurement of diel variations in oxygen. A simpler model leading to the estimation of the concentrations and the amplitude of the variations of dissolved oxygen was developed and applied to the St. Charles River.

The St. Charles River flows from the Laurentians north of Quebec City to the St. Lawrence River. The vast upper watershed is mostly forested, but the lower part is heavily urbanized. Two stations were located in the upper watershed and one in the section of the river within Quebec City. Water quality was excellent at the upstream stations and poor at the downstream station, due to wastewater inputs and low flow rates. Sampling was carried out in the months of July and August of 1996 and 1997. Physico-chemical and light measurements were made every two hours for periods of 24 hours. Nutrient and chlorophyll a samples were collected every four hours. Small diel variations in oxygen (amplitude: 1.48 mg/L) were observed at the upstream station, while much larger ones (amplitude: 4.23 mg/L) were measured at the downstream station. Modelling of the diel variations in oxygen was carried out using a sine function. Oxygen concentrations over 24 hours were successfully predicted from average concentration of dissolved oxygen, amplitude, and phase of the cycle. Average oxygen concentrations and amplitude can be derived from physico-chemical and/or biological variables easily measured in standard water quality monitoring programs. Average oxygen concentrations showed a very strong correlation with temperature (r² = 0.91) and amplitude of oxygen level variations was strongly correlated with average nitrate concentration (r² = 0.58). These relations were used in the sine function and resulted in significantly correlated modelled and measured oxygen concentrations for six of the seven cycles. Overall correlation between modelled and observed values was high (r² = 0.77). Modelled values obtained with single measurements of temperature (taken at 2:30 P.M.) and nitrate concentration (which shows no diel variation) were also highly correlated with observed data (r² = 0.75). Absolute and relative bias as well as root-mean-square error also showed the validity and the equivalence of the two approaches.

This study shows that simple models based on available water quality data may generate realistic oxygen values over 24‑hour cycles. These models would be a valuable diagnostic and decision making tool for the management of water quality in rivers.

Key words:

• oxygen dynamics,
• modelling,
• diel cycle,
• water quality,
• river,
• photosynthesis,
• respiration