The oxygen sag curve, formally described by the Streeter-Phelps model, is a fundamental concept in water quality science. It is a graphical representation illustrating the change in dissolved oxygen (DO) concentration in a river or stream downstream from a pollution source. The curve shows an initial, sharp decline in oxygen levels followed by a gradual, asymptotic recovery toward the stream’s natural saturation point. This characteristic “sag” shape maps the temporary imbalance between oxygen consumption by pollutants and the water body’s ability to replenish it. Environmental engineers use this model to predict and manage the impact of wastewater discharge on aquatic ecosystems.
Introducing the Organic Load and Oxygen Demand
The process begins with the introduction of an organic load into a waterway, typically from sources like municipal sewage, industrial effluents, or agricultural runoff. This organic load consists of biodegradable materials that serve as a food source for the aerobic microorganisms naturally present in the water. The immediate consequence of this discharge is a sudden, high demand for oxygen within the receiving water body.
This demand is quantified as Biochemical Oxygen Demand (BOD), which represents the amount of dissolved oxygen required by these aerobic microorganisms to chemically break down or oxidize the organic matter. A high concentration of organic waste translates directly into a high initial BOD, setting the stage for the subsequent drop in oxygen. This measurement helps gauge the short-term impact a waste discharge will have on the water’s oxygen levels.
Aerobic bacteria consume oxygen to metabolize the carbon-based compounds within the organic load, converting them into stable substances like carbon dioxide and water. The introduction of this high-BOD effluent creates an oxygen deficit. This deficit is the difference between the maximum amount of oxygen the water can hold at saturation and the actual measured DO concentration. This microbial action begins immediately at the point of discharge, initiating the deoxygenation phase of the curve.
The Mechanics of Dissolved Oxygen Depletion
The downward slope of the sag curve is governed by the rate of deoxygenation, driven by the respiration of the microbial population feeding on the organic load. This deoxygenation rate is directly proportional to the amount of organic material remaining in the water. As the bacteria consume the waste, they rapidly pull dissolved oxygen from the surrounding water, causing the concentration to plummet.
Working against this depletion is the rate of reaeration, which is the physical process of oxygen transferring from the atmosphere back into the water. This rate is dependent on the existing oxygen deficit; the lower the DO, the greater the driving force for oxygen to dissolve back in. Initially, the deoxygenation rate significantly exceeds the reaeration rate, resulting in a net loss of oxygen and the characteristic downward curve.
The depth of the sag is influenced by several environmental factors, including water temperature and flow characteristics. Higher water temperatures reduce the solubility of oxygen, meaning the stream can hold less oxygen at its saturation point, and simultaneously increase the metabolic rate of the microorganisms, accelerating oxygen consumption. Slower flow velocity and greater water depth also tend to decrease the reaeration rate, as they reduce the surface area and turbulence available for atmospheric gas exchange.
The lowest point on the curve is known as the critical point, where the rate of deoxygenation is balanced by the rate of reaeration. This is the location downstream where the dissolved oxygen concentration reaches its minimum value. Below this point, the aquatic ecosystem is under the greatest stress. DO levels may fall below the minimum threshold required for sensitive fish species, which typically need 4 to 7 milligrams per liter of oxygen to survive.
Natural Stream Recovery and Reaeration
The upward slope of the oxygen sag curve signifies the stream’s natural self-purification and recovery mechanism, dominated by the process of reaeration. As the stream flows downstream past the critical point, the concentration of the initial organic load has decreased through microbial decomposition or physical dispersion. This reduction in the food source causes the overall microbial activity and the oxygen demand to fall.
When the microbial oxygen consumption drops below the rate at which oxygen is naturally replenished from the atmosphere, the dissolved oxygen levels begin to rise again. Reaeration is a physical gas exchange process where oxygen molecules cross the air-water interface to achieve equilibrium with the atmosphere. The rate of this transfer is enhanced by turbulence, which constantly mixes the water column and exposes fresh water surfaces to the air.
Streams with high turbulence, such as those with rapids, riffles, or fast-moving sections, have a higher reaeration rate coefficient, allowing for quicker recovery from an oxygen deficit. As the water moves further downstream, the DO concentration increases asymptotically. This means it slowly approaches but may never fully reach its pre-discharge saturation level. This final portion of the curve completes the “sag” shape.