Introduction to Flood Routing Essays

Introduction to Flood Routing Essays Introduction to Flood Routing Paper Introduction to Flood Routing Paper The Muskingum flow routing method has been very well researched and established in the hydrological literature. Its modest data requirements make it attractive for practical use. The paper gives a general overview of the Flood routing concept and types, and then goes on to explain the Muskingum method in detail. Introduction to Flood Routing Flood routing is a technique which is used to determine the flow hydrograph characteristics like shape and movement along a water course, and how these are affected by various factors like system storage and system dynamics on the shape and movement of flow hydrographs along a watercourse. In other words Flood routing can be described as a process of calculating outflow rates, reservoir stage and storage volume from a stream channel once inflows and channel characteristics are known. The process of flood routing is used for the hydrologic analysis in flood forecasting, flood protection, reservoir design and spillway design etc. The principle of routing is used here for predicting the temporal and spatial distribution of hydrograph, during the course of its travel through the various sections of a stream (Subramanya 2002). Basic Principles of Routing All hydrologic routing methods use a common continuity equation as their common base. According to this equation, the difference between inflow and outflow rates is equal to the rate of change of storage. Mathematically the equation can be written as below: (Gosh 1997 p. 67) In the above equation, I is the rate of inflow, and at any time the corresponding outflow is O. dS is the storage that is accumulated during a very small duration of time dt. Figure below represents the pictorial relation between storage S and discharge Q: (Flood Routing) The above equation considers the losses due to seepage, evaporation and direct accretion to storage, as small enough to be ignored. The equation can be written in integral form as below: (Watson 1983 p. 490) Flood routing methods aim to solve the above one-dimensional mass continuity equation. Flood routing methods classification There are many flood routing methods available like using St. Venant equations, Level Pool Routing, Goodrich Method, Pul’s Method, Kinematic Routing, Muskingum equation, Muskingum-Cunge routing etc. These methods can be divided into the following two categories: Hydrological routing – These methods mainly use the continuity equation Hydraulic routing – These methods combine the equation of continuity with the equation of motion for unsteady flow. (Subramanya 2002 p. 271) Types of Flood Routing In all the hydrologic analysis applications mentioned above, two categories of routing can be clearly recognised: Reservoir routing – In this type of routing, the effect of a flood wave entering a reservoir is studied. This is done by determining the volume-elevation characteristic of a reservoir in addition to the outflow-elevation characteristic of the spillway and also other outlet structures present in the reservoirs (Chadwick Morfett 1986 p318). The results are used to predict the variation of reservoir elevation and outflow discharge with respect to time. This type of routing is necessary for: Designing the capacity of the spillway and other outlet structures Determining the correct location and size of capacity of the reservoir pertaining to a particular requirement condition. Channel routing – In this type of routing, a study is made of the change in shape of a hydrograph as it travels down a channel. This done by considering a channel reach i. e. the specific length of the stream channel, and an input hydrograph at the upstream end of the stream. The results are used to predict the flood hydrograph at various sections of the reach (Chadwick Morfett 1986 p. 322). The output data obtained using this method is, the information on the flood-peak attenuation and, the total duration of the high-water levels. This type of routing is considered very important for: Flood-forecasting operations Flood-protection related work Hydrologic Channel Routing In case of reservoir routing, the storage is a function of output discharge, whereas in case of channel routing, the storage is a function of both inflow and outflow discharges. This is the main reason why entirely different routing methods are needed for Channel routing. When a river is in flood, the flow can be characterized as gradually varied unsteady flow. In a particular channel reach the water surface as expected is not parallel to the channel both. Additionally it also varies with time. At the time of flood, the total volume in storage can be divided into two categories: Prism storage – This is defined as the volume that would exist in case there is uniform flow at the downstream depth. i. e. Prism storage = Wedge storage – This term represents the wedge-like volume which is formed between the actual water surface profile and the prism storage surface i. e. Wedge storage = In the downstream section of a river reach, the prism storage is observed to be constant, when the depth is fixed. However, the wedge storage changes from positive to negative depending on the type of flood. The wedge storage is positive at the time of advancing flood, while it is negative in case of a receding flood. (Subramanya 2002 p. 282-283) (Flow Routing 2) .Muskingum Method Introduction Flood routing in open channels can be determined using a variety of modeling procedures. These methods follow a wide range of methodologies, which can be categorized as: Simple like Muskingum-type approximations – Which have modest data requirements Complex like Muskingum–Cunge methods – Where the typically calibrated Muskingum routing parameters are related to physical and hydraulic characteristics such as reach length, flood wave celerity, unit width discharge and channel bed slope Highly complicated like the solution of the full dynamic flow i. e. St Venant equations – Which require surveyed cross-sectional channel profiles and flow resistance data Out of these the Muskingum and Muskingum–Cunge methods are well established in the hydrological literature, and the modest data requirements make these procedures attractive even though more rigorous hydraulic models are available for unsteady flow routing.

Battle of Pea Ridge in the Civil War

Battle of Pea Ridge in the Civil War Battle of Pea Ridge - Conflict and Dates: The Battle of Pea Ridge was fought March 7-8, 1862, and was an early engagement of the American Civil War (1861-1865). Armies Commanders: Union Brigadier General Samuel R. Curtis10,500 men Confederate Major General Earl Van Dorn16,000 men Battle of Pea Ridge - Background: In the wake of the disaster at Wilsons Creek in August 1861, Union forces in Missouri were reorganized into the Army of the Southwest. Numbering around 10,500, this command was given to Brigadier General Samuel R. Curtis with orders to push the Confederates out of the state. Despite their victory, the Confederates also altered their command structure as Major General Sterling Price and Brigadier General Benjamin McCulloch had shown an unwillingness to cooperate. To keep the peace, Major General Earl Van Dorn was given command of the Military District of the Trans-Mississippi and oversight of the Army of the West. Pressing south into northwest Arkansas in early 1862, Curtis established his army in a strong position facing south along Little Sugar Creek. Expecting a Confederate attack from that direction, his men began emplacing artillery and fortifying their position. Moving north with 16,000 men, Van Dorn hoped to destroy Curtis force and open the way to capture St. Louis. Eager to destroy outlying Union garrisons near Curtis base at Little Sugar Creek, Van Dorn led his men on a three-day forced march through severe winter weather. Battle of Pea Ridge - Moving to Attack: Reaching Bentonville, they failed to capture a Union force under Brigadier General Franz Sigel on March 6. Though his men were exhausted and he had outrun his supply train, Van Dorn began formulating an ambitious plan to assault Curtis army. Dividing his army in two, Van Dorn intended to march north of the Union position and strike Curtis from the rear on March 7. Van Dorn planned to lead one column east along a road known as the Bentonville Detour which ran along the north edge of Pea Ridge. After clearing the ridge they would turn south along the Telegraph Road and occupy the area around Elkhorn Tavern. Battle of Pea Ridge - McCullochs Defeat: The other column, led by McCulloch, was to skirt the western edge of Pea Ridge then turn east to join with Van Dorn and Price at the tavern. Reunited, the combined Confederate force would attack south to strike at the rear of the Union lines along Little Sugar Creek. While Curtis did not anticipate this type of envelopment, he did take the precaution of having trees felled across the Bentonville Detour. Delays slowed both Confederate columns and by dawn, Union scouts had detected both threats. Though still believing that Van Dorns main body was to the south, Curtis began shifting troops to block the threats. Due to the delays, Van Dorn issued instructions for McCulloch to reach Elkhorn by taking the Ford Road from Twelve Corner Church. As McCullochs men marched along the road, they encountered Union troops near the village of Leetown. Dispatched by Curtis, this was a mixed infantry-cavalry force led by Colonel Peter J. Osterhaus. Though badly outnumbered, the Union troops immediately attacked around 11:30 AM. Wheeling his men south, McCulloch counterattacked and pushed Osterhaus men back through a belt of timber. Reconnoitering the enemy lines, McCulloch encountered a group of Union skirmishers and was killed. As confusion began to reign in the Confederate lines, McCullochs second-in-command, Brigadier General James McIntosh, led a charge forward and was also killed. Unaware that he was now the senior officer on the field, Colonel Louis HÃ ©bert attacked on the Confederate left, while the regiments on the right remained in place awaiting orders. This assault was halted by the timely arrival of a Union division under Colonel Jefferson C. Davis. Though outnumbered, they turned the tables on the Southerners and captured HÃ ©bert later in the afternoon. With confusion in the ranks, Brigadier General Albert Pike assumed command around 3:00 (shortly before HÃ ©berts capture) and led those troops near him in a retreat north. Several hours later, with Colonel Elkanah Greer in command, many of these troops joined rest of the army at Cross Timber Hollow near Elkhorn Tavern. On the other side of the battlefield, fighting began around 9:30 when the lead elements of Van Dorns column encountered Union infantry in Cross Timber Hollow. Sent north by Curtis, Colonel Grenville Dodges brigade of Colonel Eugene Carrs 4th Division soon moved into a blocking position. Battle of Pea Ridge - Van Dorn Held: Rather than pressing forward and overwhelming Dodges small command, Van Dorn and Price paused to fully deploy their troops. Over the next several hours, Dodge was able to hold his position and was reinforced at 12:30 by a Colonel William Vandevers brigade. Ordered forward by Carr, Vandevers men attacked the Confederate lines but were forced back. As the afternoon wore on, Curtis continued to funnel units into the battle near Elkhorn, but Union troops were slowly pushed back. At 4:30, the Union position began to collapse and Carrs men retreated back past the tavern to Ruddicks Field about a quarter mile to the south. Reinforcing this line, Curtis ordered a counterattack but it was halted due to darkness. As both sides endured a cold night, Curtis busily shifted the bulk of his army to the Elkhorn line and had his men resupplied. Reinforced by the remnants of McCullochs division, Van Dorn prepared to renew the assault in the morning. Early in the morning, Brigadier Franz Sigel, Curtis second-in-command, instructed Osterhaus to survey the farmland to the west of Elkhorn. In doing do, the colonel located a knoll from which Union artillery could strike the Confederate lines. Quickly moving 21 guns to the hill, Union gunners opened fire after 8:00 AM and drove back their Confederate counterparts before shifting their fire to the Southern infantry. As Union troops moved into attack positions around 9:30, Van Dorn was horrified to learn that his supply train and reserve artillery was six hours away due to a mistaken order. Realizing he could not win, Van Dorn began retreating east along the Huntsville Road. At 10:30, with the Confederates beginning to leave the field, Sigel led the Union left forward. Driving the Confederates back, they retook the area near the tavern around noon. With the last of the enemy retreating, the battle came to an end. Battle of Pea Ridge - Aftermath: The Battle of Pea Ridge cost the Confederates approximately 2,000 casualties, while the Union suffered 203 killed, 980 wounded, and 201 missing. The victory effectively secured Missouri for the Union cause and ended the Confederate threat to the state. Pressing on, Curtis succeeded in taking Helena, AR in July. The Battle of Pea Ridge was one of the few battles where Confederate troops possessed a significant numerical advantage over the Union. Selected Sources CWSAC Battle Summaries: Battle of Pea RidgePea Ridge National Military ParkBattle of Pea Ridge Maps