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95-672: These numbers were first developed in hydrology , as a way of measuring the complexity of rivers and streams, by Robert E. Horton  ( 1945 ) and Arthur Newell Strahler  ( 1952 , 1957 ). In this application, they are referred to as the Strahler stream order and are used to define stream size based on a hierarchy of tributaries . The same numbers also arise in the analysis of L-systems and of hierarchical biological structures such as (biological) trees and animal respiratory and circulatory systems, in register allocation for compilation of high-level programming languages and in

190-468: A depth-first search and assigning each node's number in postorder . The same numbers may also be generated via a pruning process in which the tree is simplified in a sequence of stages, where in each stage one removes all leaf nodes and all of the paths of degree-one nodes leading to leaves: the Strahler number of a node is the stage at which it would be removed by this process, and the Strahler number of

285-402: A drainage basin are more likely to flood, comparatively, by looking at the separate ratios. Most British rivers have a bifurcation ratio of between 3 and 5. Gleyzer et al. (2004) describe how to compute Strahler stream order values in a GIS application. This algorithm is implemented by RivEX , an ESRI ArcGIS Pro 3.3.x tool. The input to their algorithm is a network of the centre lines of

380-422: A line source or area source , such as surface runoff . Since the 1960s rather complex mathematical models have been developed, facilitated by the availability of high-speed computers. The most common pollutant classes analyzed are nutrients , pesticides , total dissolved solids and sediment . Mississippi River The Mississippi River is the primary river of the largest drainage basin in

475-435: A piezometer . Aquifers are also described in terms of hydraulic conductivity, storativity and transmissivity. There are a number of geophysical methods for characterizing aquifers. There are also problems in characterizing the vadose zone (unsaturated zone). Infiltration is the process by which water enters the soil. Some of the water is absorbed, and the rest percolates down to the water table . The infiltration capacity,

570-542: A large mound of sand spanning the width of the river 55 feet below the surface, allowing fresh water and large cargo ships to pass over. Fresh river water flowing from the Mississippi into the Gulf of Mexico does not mix into the salt water immediately. The images from NASA 's MODIS show a large plume of fresh water, which appears as a dark ribbon against the lighter-blue surrounding waters. These images demonstrate that

665-734: A length of 3,710 miles (5,971 km), making it the fourth longest river in the world after the Nile , Amazon , and Yangtze . When measured by the largest stream source (by water volume), the Ohio River , by extension the Allegheny River , would be the source, and the Mississippi would begin in Pennsylvania . At its source at Lake Itasca , the Mississippi River is about 3 feet (0.91 m) deep. The average depth of

760-402: A more global approach to the understanding of the behavior of hydrologic systems to make better predictions and to face the major challenges in water resources management. Water movement is a significant means by which other materials, such as soil, gravel, boulders or pollutants, are transported from place to place. Initial input to receiving waters may arise from a point source discharge or

855-478: A natural process known as avulsion or delta switching, the lower Mississippi River has shifted its final course to the mouth of the Gulf of Mexico every thousand years or so. This occurs because the deposits of silt and sediment begin to clog its channel, raising the river's level and causing it to eventually find a steeper, more direct route to the Gulf of Mexico. The abandoned distributaries diminish in volume and form what are known as bayous . This process has, over

950-451: A prediction in practical applications. Ground water is water beneath Earth's surface, often pumped for drinking water. Groundwater hydrology ( hydrogeology ) considers quantifying groundwater flow and solute transport. Problems in describing the saturated zone include the characterization of aquifers in terms of flow direction, groundwater pressure and, by inference, groundwater depth (see: aquifer test ). Measurements here can be made using

1045-635: A tree is the number of stages required to remove all of its nodes. Another equivalent definition of the Strahler number of a tree is that it is the height of the largest complete binary tree that can be homeomorphically embedded into the given tree; the Strahler number of a node in a tree is similarly the height of the largest complete binary tree that can be embedded below that node. Any node with Strahler number i must have at least two descendants with Strahler number i  − 1, at least four descendants with Strahler number i  − 2, etc., and at least 2 leaf descendants. Therefore, in

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1140-475: A tree is. For each order i in a hierarchy, the i th bifurcation ratio is where n i denotes the number of nodes with order i . The bifurcation ratio of an overall hierarchy may be taken by averaging the bifurcation ratios at different orders. In a complete binary tree, the bifurcation ratio will be 2, while other trees will have larger bifurcation ratios. It is a dimensionless number. The pathwidth of an arbitrary undirected graph G may be defined as

1235-404: A tree with n nodes, the largest possible Strahler number is log 2   n  + 1. However, unless the tree forms a complete binary tree its Strahler number will be less than this bound. In an n -node binary tree , chosen uniformly at random among all possible binary trees , the expected index of the root is with high probability very close to log 4   n . In the application of

1330-861: Is 208,200 cu ft/s (5,900 m /s). Thus, by volume, the main branch of the Mississippi River system at Cairo can be considered to be the Ohio River (and the Allegheny River further upstream), rather than the Middle Mississippi. In addition to the Ohio River , the major tributaries of the Lower Mississippi River are the White River , flowing in at the White River National Wildlife Refuge in east-central Arkansas;

1425-575: Is a meandering river in a broad, flat area, only rarely flowing alongside a bluff (as at Vicksburg, Mississippi ). The Mississippi River is known as the Middle Mississippi from the Upper Mississippi River's confluence with the Missouri River at St. Louis, Missouri , for 190 miles (310 km) to its confluence with the Ohio River at Cairo, Illinois . The Middle Mississippi is relatively free-flowing. From St. Louis to

1520-402: Is affected by the interaction of dissolved oxygen with organic material and various chemical transformations that may take place. Measurements of water quality may involve either in-situ methods, in which analyses take place on-site, often automatically, and laboratory-based analyses and may include microbiological analysis . Observations of hydrologic processes are used to make predictions of

1615-769: Is an important part of the water cycle. It is partly affected by humidity, which can be measured by a sling psychrometer . It is also affected by the presence of snow, hail, and ice and can relate to dew, mist and fog. Hydrology considers evaporation of various forms: from water surfaces; as transpiration from plant surfaces in natural and agronomic ecosystems. Direct measurement of evaporation can be obtained using Simon's evaporation pan . Detailed studies of evaporation involve boundary layer considerations as well as momentum, heat flux, and energy budgets. Remote sensing of hydrologic processes can provide information on locations where in situ sensors may be unavailable or sparse. It also enables observations over large spatial extents. Many of

1710-498: Is called the Lower Mississippi River from its confluence with the Ohio River to its mouth at the Gulf of Mexico, a distance of about 1,000 miles (1,600 km). At the confluence of the Ohio and the Middle Mississippi, the long-term mean discharge of the Ohio at Cairo, Illinois is 281,500 cubic feet per second (7,970 cubic meters per second), while the long-term mean discharge of the Mississippi at Thebes, Illinois (just upriver from Cairo)

1805-912: Is controlled and managed as a series of pools created by 26 locks and dams. The Upper Mississippi River is joined by the Minnesota River at Fort Snelling in the Twin Cities ; the St. Croix River near Prescott, Wisconsin ; the Cannon River near Red Wing, Minnesota ; the Zumbro River at Wabasha, Minnesota ; the Black , La Crosse , and Root rivers in La Crosse, Wisconsin ; the Wisconsin River at Prairie du Chien, Wisconsin ;

1900-468: Is given by Smart. The Strahler numbering may be applied in the statistical analysis of any hierarchical system, not just to rivers. When translating a high-level programming language to assembly language the minimum number of registers required to evaluate an expression tree is exactly its Strahler number. In this context, the Strahler number may also be called the register number . For expression trees that require more registers than are available,

1995-520: Is largely a multi-thread stream with many bars and islands. From its confluence with the St. Croix River downstream to Dubuque, Iowa , the river is entrenched, with high bedrock bluffs lying on either side. The height of these bluffs decreases to the south of Dubuque, though they are still significant through Savanna, Illinois . This topography contrasts strongly with the Lower Mississippi, which

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2090-489: Is only one of many important aspects within those fields. Hydrological research can inform environmental engineering, policy , and planning . Hydrology has been subject to investigation and engineering for millennia. Ancient Egyptians were one of the first to employ hydrology in their engineering and agriculture, inventing a form of water management known as basin irrigation. Mesopotamian towns were protected from flooding with high earthen walls. Aqueducts were built by

2185-539: Is the only true waterfall on the entire Mississippi River. The water elevation continues to drop steeply as it passes through the gorge carved by the waterfall. After the completion of the St. Anthony Falls Lock and Dam in 1963, the river's head of navigation moved upstream, to the Coon Rapids Dam . However, the Locks were closed in 2015 to control the spread of invasive Asian carp , making Minneapolis once again

2280-916: Is the scientific study of the movement, distribution, and management of water on Earth and other planets, including the water cycle , water resources , and drainage basin sustainability. A practitioner of hydrology is called a hydrologist . Hydrologists are scientists studying earth or environmental science , civil or environmental engineering , and physical geography . Using various analytical methods and scientific techniques, they collect and analyze data to help solve water related problems such as environmental preservation , natural disasters , and water management . Hydrology subdivides into surface water hydrology, groundwater hydrology ( hydrogeology ), and marine hydrology. Domains of hydrology include hydrometeorology , surface hydrology , hydrogeology , drainage-basin management, and water quality . Oceanography and meteorology are not included because water

2375-580: Is thought of as starting at the land-atmosphere boundary and so it is important to have adequate knowledge of both precipitation and evaporation. Precipitation can be measured in various ways: disdrometer for precipitation characteristics at a fine time scale; radar for cloud properties, rain rate estimation, hail and snow detection; rain gauge for routine accurate measurements of rain and snowfall; satellite for rainy area identification, rain rate estimation, land-cover/land-use, and soil moisture, snow cover or snow water equivalent for example. Evaporation

2470-513: Is utilized to formulate operating rules for large dams forming part of systems which include agricultural, industrial and residential demands. Hydrological models are simplified, conceptual representations of a part of the hydrologic cycle. They are primarily used for hydrological prediction and for understanding hydrological processes, within the general field of scientific modeling . Two major types of hydrological models can be distinguished: Recent research in hydrological modeling tries to have

2565-618: The American Civil War , the Mississippi's capture by Union forces marked a turning point towards victory , due to the river's strategic importance to the Confederate war effort. Because of the substantial growth of cities and the larger ships and barges that replaced steamboats, the first decades of the 20th century saw the construction of massive engineering works such as levees , locks and dams , often built in combination. A major focus of this work has been to prevent

2660-880: The Arkansas River , joining the Mississippi at Arkansas Post ; the Big Black River in Mississippi; and the Yazoo River , meeting the Mississippi at Vicksburg, Mississippi . Deliberate water diversion at the Old River Control Structure in Louisiana allows the Atchafalaya River in Louisiana to be a major distributary of the Mississippi River, with 30% of the combined flow of the Mississippi and Red Rivers flowing to

2755-637: The Greeks and Romans , while history shows that the Chinese built irrigation and flood control works. The ancient Sinhalese used hydrology to build complex irrigation works in Sri Lanka , also known for the invention of the Valve Pit which allowed construction of large reservoirs, anicuts and canals which still function. Marcus Vitruvius , in the first century BC, described a philosophical theory of

2850-640: The Gulf of Mexico , part of the Atlantic Ocean. The total catchment of the Mississippi River covers nearly 40% of the landmass of the continental United States. The highest point within the watershed is also the highest point of the Rocky Mountains , Mount Elbert at 14,440 feet (4,400 m). In the United States, the Mississippi River drains the majority of the area between the crest of

2945-603: The Minnesota River , James River , and Milk River valleys. When the ice sheet completely retreated, many of these "temporary" rivers found paths to Hudson Bay or the Arctic Ocean, leaving the Mississippi Basin with many features "over-sized" for the existing rivers to have carved in the same time period. Ice sheets during the Illinoian Stage , about 300,000 to 132,000 years before present, blocked

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3040-1320: The Rock River at the Quad Cities ; the Iowa River near Wapello, Iowa ; the Skunk River south of Burlington, Iowa ; and the Des Moines River at Keokuk, Iowa . Other major tributaries of the Upper Mississippi include the Crow River in Minnesota, the Chippewa River in Wisconsin, the Maquoketa River and the Wapsipinicon River in Iowa, and the Illinois River in Illinois. The Upper Mississippi

3135-887: The Rocky Mountains and the crest of the Appalachian Mountains , except for various regions drained to Hudson Bay by the Red River of the North ; to the Atlantic Ocean by the Great Lakes and the Saint Lawrence River ; and to the Gulf of Mexico by the Rio Grande , the Alabama and Tombigbee rivers, the Chattahoochee and Appalachicola rivers, and various smaller coastal waterways along

3230-496: The Sethi–Ullman algorithm may be used to translate an expression tree into a sequence of machine instructions that uses the registers as efficiently as possible, minimizing the number of times intermediate values are spilled from registers to main memory and the total number of instructions in the resulting compiled code. Associated with the Strahler numbers of a tree are bifurcation ratios , numbers describing how close to balanced

3325-618: The United States . From its traditional source of Lake Itasca in northern Minnesota , it flows generally south for 2,340 miles (3,766 km) to the Mississippi River Delta in the Gulf of Mexico . With its many tributaries , the Mississippi's watershed drains all or parts of 32 U.S. states and two Canadian provinces between the Rocky and Appalachian mountains. The river either borders or passes through

3420-429: The headwaters region and serve multiple purposes, including power generation and recreation. The remaining 29 dams, beginning in downtown Minneapolis, all contain locks and were constructed to improve commercial navigation of the upper river. Taken as a whole, these 43 dams significantly shape the geography and influence the ecology of the upper river. Beginning just below Saint Paul, Minnesota , and continuing throughout

3515-491: The most recent Ice Age . The southernmost extent of this enormous glaciation extended well into the present-day United States and Mississippi basin. When the ice sheet began to recede, hundreds of feet of rich sediment were deposited, creating the flat and fertile landscape of the Mississippi Valley. During the melt, giant glacial rivers found drainage paths into the Mississippi watershed, creating such features as

3610-399: The return period of such events. Other quantities of interest include the average flow in a river, in a year or by season. These estimates are important for engineers and economists so that proper risk analysis can be performed to influence investment decisions in future infrastructure and to determine the yield reliability characteristics of water supply systems. Statistical information

3705-455: The 20th century, while governmental agencies began their own hydrological research programs. Of particular importance were Leroy Sherman's unit hydrograph , the infiltration theory of Robert E. Horton , and C.V. Theis' aquifer test/equation describing well hydraulics. Since the 1950s, hydrology has been approached with a more theoretical basis than in the past, facilitated by advances in the physical understanding of hydrological processes and by

3800-579: The Earth's mantle (specifically, the Bermuda hotspot ) that was undergoing a period of intense activity. The upwelling of magma from the hotspot forced the further uplift to a height of perhaps 2–3 km of part of the Appalachian-Ouachita range, forming an arch that blocked southbound water flows. The uplifted land quickly eroded and, as North America moved away from the hot spot and as

3895-632: The French rendering of the Anishinaabe ( Ojibwe or Algonquin ) name for the river, Misi-ziibi (Great River). In the 18th century, the river was set by the Treaty of Paris as, for the most part, the western border of the new United States. With the Louisiana Purchase and the country's westward expansion, it became a convenient boundary line between the western and eastern halves of

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3990-656: The Gulf of Mexico by this route, rather than continuing down the Mississippi's current channel past Baton Rouge and New Orleans on a longer route to the Gulf. Although the Red River was once an additional tributary, its water now flows separately into the Gulf of Mexico through the Atchafalaya River. The Mississippi River has the world's fourth-largest drainage basin ("watershed" or "catchment"). The basin covers more than 1,245,000 square miles (3,220,000 km ), including all or parts of 32 U.S. states and two Canadian provinces. The drainage basin empties into

4085-495: The Gulf. The Mississippi River empties into the Gulf of Mexico about 100 miles (160 km) downstream from New Orleans. Measurements of the length of the Mississippi from Lake Itasca to the Gulf of Mexico vary somewhat, but the United States Geological Survey 's number is 2,340 miles (3,766 km). The retention time from Lake Itasca to the Gulf is typically about 90 days; while speed varies along

4180-469: The Illinoian Stage. Timeline of outflow course changes In March 1876, the Mississippi suddenly changed course near the settlement of Reverie, Tennessee , leaving a small part of Tipton County, Tennessee , attached to Arkansas and separated from the rest of Tennessee by the new river channel. Since this event was an avulsion , rather than the effect of incremental erosion and deposition,

4275-578: The Midwestern and eastern U.S. These earthquakes created Reelfoot Lake in Tennessee from the altered landscape near the river. When measured from its traditional source at Lake Itasca , the Mississippi has a length of 2,340 miles (3,766 km). When measured from its longest stream source (most distant source from the sea), Brower's Spring in Montana , the source of the Missouri River , it has

4370-480: The Mississippi River between Saint Paul and Saint Louis is between 9 and 12 feet (2.7–3.7 m) deep, the deepest part being Lake Pepin , which averages 20–32 feet (6–10 m) deep and has a maximum depth of 60 feet (18 m). Between where the Missouri River joins the Mississippi at Saint Louis, Missouri, and Cairo, Illinois, the depth averages 30 feet (9 m). Below Cairo, where the Ohio River joins,

4465-411: The Mississippi River has experienced numerous large and small changes to its main course, as well as additions, deletions, and other changes among its numerous tributaries, and the lower Mississippi River has used different pathways as its main channel to the Gulf of Mexico across the delta region. As Pangaea began to break up about 95 million years ago, North America passed over a volcanic " hotspot " in

4560-469: The Mississippi River near New Madrid, Missouri , between Memphis and St. Louis, is related to an aulacogen (failed rift) that formed at the same time as the Gulf of Mexico. This area is still quite active seismically. Four great earthquakes in 1811 and 1812 , estimated at 8 on the Richter magnitude scale , had tremendous local effects in the then sparsely settled area, and were felt in many other places in

4655-456: The Mississippi near Rock Island, Illinois, diverting it to its present channel farther to the west, the current western border of Illinois. The Hennepin Canal roughly follows the ancient channel of the Mississippi downstream from Rock Island to Hennepin, Illinois . South of Hennepin, to Alton, Illinois , the current Illinois River follows the ancient channel used by the Mississippi River before

4750-786: The Missouri River; the Middle Mississippi, which is downriver from the Missouri to the Ohio River; and the Lower Mississippi , which flows from the Ohio to the Gulf of Mexico. The Upper Mississippi runs from its headwaters to its confluence with the Missouri River at St. Louis, Missouri. It is divided into two sections: The source of the Upper Mississippi branch is traditionally accepted as Lake Itasca , 1,475 feet (450 m) above sea level in Itasca State Park in Clearwater County, Minnesota . The name Itasca

4845-584: The Ohio River confluence, the Middle Mississippi falls 220 feet (67 m) over 180 miles (290 km) for an average rate of 1.2 feet per mile (23 cm/km). At its confluence with the Ohio River, the Middle Mississippi is 315 feet (96 m) above sea level. Apart from the Missouri and Meramec rivers of Missouri and the Kaskaskia River of Illinois, no major tributaries enter the Middle Mississippi River. The Mississippi River

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4940-405: The Strahler stream order to hydrology, each segment of a stream or river within a river network is treated as a node in a tree, with the next segment downstream as its parent. When two first-order streams come together, they form a second-order stream. When two second-order streams come together, they form a third-order stream. Streams of lower order joining a higher order stream do not change

5035-430: The Upper Mississippi River is the Upper St. Anthony Falls Lock and Dam in Minneapolis. Above the dam, the river's elevation is 799 feet (244 m). Below the dam, the river's elevation is 750 feet (230 m). This 49-foot (15 m) drop is the largest of all the Mississippi River locks and dams. The origin of the dramatic drop is a waterfall preserved adjacent to the lock under an apron of concrete. Saint Anthony Falls

5130-426: The Upper Mississippi is a simple steel culvert, through which the river (locally named "Nicolet Creek") flows north from Lake Nicolet under "Wilderness Road" to the West Arm of Lake Itasca, within Itasca State Park . The earliest bridge across the Mississippi River was built in 1855. It spanned the river in Minneapolis where the current Hennepin Avenue Bridge is located. No highway or railroad tunnels cross under

5225-513: The advent of computers and especially geographic information systems (GIS). (See also GIS and hydrology ) The central theme of hydrology is that water circulates throughout the Earth through different pathways and at different rates. The most vivid image of this is in the evaporation of water from the ocean, which forms clouds. These clouds drift over the land and produce rain. The rainwater flows into lakes, rivers, or aquifers. The water in lakes, rivers, and aquifers then either evaporates back to

5320-453: The analysis of social networks . All trees in this context are directed graphs , oriented from the root towards the leaves; in other words, they are arborescences . The degree of a node in a tree is just its number of children. One may assign a Strahler number to all nodes of a tree, in bottom-up order, as follows: The Strahler number of a tree is the number of its root node. Algorithmically , these numbers may be assigned by performing

5415-555: The areas drained by them. Denser salt water from the Gulf of Mexico forms a salt wedge along the river bottom near the mouth of the river, while fresh water flows near the surface. In drought years, with less fresh water to push it out, salt water can travel many miles upstream—64 miles (103 km) in 2022—contaminating drinking water supplies and requiring the use of desalination . The United States Army Corps of Engineers constructed "saltwater sills" or "underwater levees" to contain this in 1988, 1999, 2012, and 2022. This consists of

5510-530: The atmosphere or eventually flows back to the ocean, completing a cycle. Water changes its state of being several times throughout this cycle. The areas of research within hydrology concern the movement of water between its various states, or within a given state, or simply quantifying the amounts in these states in a given region. Parts of hydrology concern developing methods for directly measuring these flows or amounts of water, while others concern modeling these processes either for scientific knowledge or for making

5605-415: The basin in increasing numbers. The river served sometimes as a barrier, forming borders for New Spain , New France , and the early United States, and throughout as a vital transportation artery and communications link. In the 19th century, during the height of the ideology of manifest destiny , the Mississippi and several tributaries, most notably its largest, the Ohio and Missouri , formed pathways for

5700-403: The bodies of water, represented as arcs (or edges) joined at nodes. Lake boundaries and river banks should not be used as arcs, as these will generally form a non-tree network with an incorrect topology. Alternative stream ordering systems have been developed by Shreve and Hodgkinson et al. A statistical comparison of Strahler and Shreve systems, together with an analysis of stream/link lengths,

5795-411: The country. This is reflected in the Gateway Arch in St. Louis, which was designed to symbolize the opening of the West, and the focus on the " Trans-Mississippi " region in the Trans-Mississippi Exposition . Regional landmarks are often classified in relation to the river, such as "the highest peak east of the Mississippi " or "the oldest city west of the Mississippi". The FCC also uses it as

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5890-427: The course of the river, this gives an overall average of around 26 mi (42 km) per day, or 1 mi (1.6 km) per hour. The stream gradient of the entire river is 0.01%, a drop of 450 m over 3,766 km. The Mississippi River discharges at an annual average rate of between 200 and 700 thousand cubic feet per second (6,000 and 20,000 m /s). The Mississippi is the fourteenth largest river in

5985-403: The delta of the Chippewa River of Wisconsin as it enters the Upper Mississippi, is more than 2 miles (3.2 km) wide. By the time the Upper Mississippi reaches Saint Paul , Minnesota, below Lock and Dam No. 1, it has dropped more than half its original elevation and is 687 feet (209 m) above sea level. From St. Paul to St. Louis, Missouri, the river elevation falls much more slowly and

6080-532: The depth averages 50–100 feet (15–30 m) deep. The deepest part of the river is in New Orleans, where it reaches 200 feet (61 m) deep. The Mississippi River runs through or along 10 states, from Minnesota to Louisiana , and is used to define portions of these states' borders, with Wisconsin , Illinois , Kentucky , Tennessee , and Mississippi along the east side of the river, and Iowa , Missouri , and Arkansas along its west side. Substantial parts of both Minnesota and Louisiana are on either side of

6175-405: The dividing line for broadcast call-signs , which begin with W to the east and K to the west, overlapping in media markets along the river. Due to its size and importance, it has been nicknamed The Mighty Mississippi River or simply The Mighty Mississippi . The Mississippi River can be divided into three sections: the Upper Mississippi , the river from its headwaters to the confluence with

6270-627: The future behavior of hydrologic systems (water flow, water quality). One of the major current concerns in hydrologic research is "Prediction in Ungauged Basins" (PUB), i.e. in basins where no or only very few data exist. The aims of Statistical hydrology is to provide appropriate statistical methods for analyzing and modeling various parts of the hydrological cycle. By analyzing the statistical properties of hydrologic records, such as rainfall or river flow, hydrologists can estimate future hydrologic phenomena. When making assessments of how often relatively rare events will occur, analyses are made in terms of

6365-441: The hotspot's activity declined, the crust beneath the embayment region cooled, contracted and subsided to a depth of 2.6 km, and around 80 million years ago the Reelfoot Rift formed a trough that was flooded by the Gulf of Mexico . As sea levels dropped, the Mississippi and other rivers extended their courses into the embayment , which gradually became filled with sediment with the Mississippi River at its center. Through

6460-413: The hydrologic cycle, in which precipitation falling in the mountains infiltrated the Earth's surface and led to streams and springs in the lowlands. With the adoption of a more scientific approach, Leonardo da Vinci and Bernard Palissy independently reached an accurate representation of the hydrologic cycle. It was not until the 17th century that hydrologic variables began to be quantified. Pioneers of

6555-430: The important areas of hydrology is the interchange between rivers and aquifers. Groundwater/surface water interactions in streams and aquifers can be complex and the direction of net water flux (into surface water or into the aquifer) may vary spatially along a stream channel and over time at any particular location, depending on the relationship between stream stage and groundwater levels. In some considerations, hydrology

6650-446: The inequalities The ability to handle graphs with cycles and not just trees gives pathwidth extra versatility compared to the Strahler number. However, unlike the Strahler number, the pathwidth is defined only for the whole graph, and not separately for each node in the graph. Hydrology Hydrology (from Ancient Greek ὕδωρ ( húdōr )  'water' and -λογία ( -logía )  'study of')

6745-416: The largest in North America. Native Americans have lived along the Mississippi River and its tributaries for thousands of years. Many were hunter-gatherers , but some, such as the Mound Builders , formed prolific agricultural and urban civilizations, and some practiced aquaculture . The arrival of Europeans in the 16th century changed the native way of life as first explorers, then settlers, ventured into

6840-402: The last two decades, this number was only 160 million short tons (145 million metric tons) per year. The reduction in sediment transported down the Mississippi River is the result of engineering modification of the Mississippi, Missouri, and Ohio rivers and their tributaries by dams, meander cutoffs , river-training structures, and bank revetments and soil erosion control programs in

6935-502: The lower 10 miles (16 km) of the Kaskaskia River, forming a new Mississippi channel and cutting off the town from the rest of the state. Later flooding destroyed most of the remaining town, including the original State House. Today, the remaining 2,300 acres (930 ha) island and community of 14 residents is known as an enclave of Illinois and is accessible only from the Missouri side. The New Madrid Seismic Zone , along

7030-415: The lower Mississippi from shifting into the channel of the Atchafalaya River and bypassing New Orleans . Since the 20th century, the Mississippi River has also experienced major pollution and environmental problems — most notably elevated nutrient and chemical levels from agricultural runoff, the primary contributor to the Gulf of Mexico dead zone . The word Mississippi itself comes from Misi zipi ,

7125-403: The maximum rate at which the soil can absorb water, depends on several factors. The layer that is already saturated provides a resistance that is proportional to its thickness, while that plus the depth of water above the soil provides the driving force ( hydraulic head ). Dry soil can allow rapid infiltration by capillary action ; this force diminishes as the soil becomes wet. Compaction reduces

7220-523: The modern science of hydrology include Pierre Perrault , Edme Mariotte and Edmund Halley . By measuring rainfall, runoff, and drainage area, Perrault showed that rainfall was sufficient to account for the flow of the Seine. Mariotte combined velocity and river cross-section measurements to obtain a discharge value, again in the Seine. Halley showed that the evaporation from the Mediterranean Sea

7315-484: The most powerful river, the Amazon , at its mouth). The Ohio River is of order eight and the Mississippi River is of order 10. Estimates are that 80% of the streams on the planet are first to third order headwater streams . If the bifurcation ratio of a river network is high, then there is a higher chance of flooding. There would also be a lower time of concentration. The bifurcation ratio can also show which parts of

7410-449: The new river channel, contiguous with the adjacent state. Also, due to a meander in the river, a small part of western Kentucky is contiguous with Tennessee but isolated from the rest of its state. Many of the communities along the Mississippi River are listed below; most have either historic significance or cultural lore connecting them to the river. They are sequenced from the source of the river to its end. The road crossing highest on

7505-484: The order of the higher stream. Thus, if a first-order stream joins a second-order stream, it remains a second-order stream. It is not until a second-order stream combines with another second-order stream that it becomes a third-order stream. As with mathematical trees, a segment with index i must be fed by at least 2 different tributaries of index 1. Shreve noted that Horton's and Strahler's Laws should be expected from any topologically random distribution. A later review of

7600-620: The past 5,000 years, caused the coastline of south Louisiana to advance toward the Gulf from 15 to 50 miles (24 to 80 km). The currently active delta lobe is called the Birdfoot Delta, after its shape, or the Balize Delta , after La Balize, Louisiana , the first French settlement at the mouth of the Mississippi. The current form of the Mississippi River basin was largely shaped by the Laurentide Ice Sheet of

7695-549: The plume did not mix with the surrounding sea water immediately. Instead, it stayed intact as it flowed through the Gulf of Mexico, into the Straits of Florida , and entered the Gulf Stream . The Mississippi River water rounded the tip of Florida and traveled up the southeast coast to the latitude of Georgia before finally mixing in so thoroughly with the ocean that it could no longer be detected by MODIS. Over geologic time,

7790-461: The porosity and the pore sizes. Surface cover increases capacity by retarding runoff, reducing compaction and other processes. Higher temperatures reduce viscosity , increasing infiltration. Soil moisture can be measured in various ways; by capacitance probe , time domain reflectometer or tensiometer . Other methods include solute sampling and geophysical methods. Hydrology considers quantifying surface water flow and solute transport, although

7885-465: The relationships confirmed this argument, establishing that, from the properties the laws describe, no conclusion can be drawn to explain the structure or origin of the stream network. To qualify as a stream a hydrological feature must be either recurring or perennial . Recurring (or "intermittent") streams have water in the channel for at least part of the year. The index of a stream or river may range from 1 (a stream with no tributaries) to 12 (globally

7980-479: The river, although the Mississippi defines part of the boundary of each of these states. In all of these cases, the middle of the riverbed at the time the borders were established was used as the line to define the borders between adjacent states. In various areas, the river has since shifted, but the state borders have not changed, still following the former bed of the Mississippi River as of their establishment, leaving several small isolated areas of one state across

8075-400: The site of the head of navigation of the river. The Upper Mississippi has a number of natural and artificial lakes, with its widest point being Lake Winnibigoshish , near Grand Rapids, Minnesota , over 11 miles (18 km) across. Lake Onalaska , created by Lock and Dam No. 7 , near La Crosse, Wisconsin , is more than 4 miles (6.4 km) wide. Lake Pepin , a natural lake formed behind

8170-414: The smallest number w such that there exists an interval graph H containing G as a subgraph, with the largest clique in H having w  + 1 vertices. For trees (viewed as undirected graphs by forgetting their orientation and root) the pathwidth differs from the Strahler number, but is closely related to it: in a tree with pathwidth w and Strahler number s , these two numbers are related by

8265-532: The state line still follows the old channel. The town of Kaskaskia, Illinois once stood on a peninsula at the confluence of the Mississippi and Kaskaskia (Okaw) Rivers . Founded as a French colonial community, it later became the capital of the Illinois Territory and was the first state capital of Illinois until 1819. Beginning in 1844, successive flooding caused the Mississippi River to slowly encroach east. A major flood in 1881 caused it to overtake

8360-460: The states of Minnesota , Wisconsin , Iowa , Illinois , Missouri , Kentucky , Tennessee , Arkansas , Mississippi , and Louisiana . The main stem is entirely within the United States; the total drainage basin is 1,151,000 sq mi (2,980,000 km ), of which only about one percent is in Canada. The Mississippi ranks as the world's tenth-largest river by discharge flow, and

8455-440: The treatment of flows in large rivers is sometimes considered as a distinct topic of hydraulics or hydrodynamics. Surface water flow can include flow both in recognizable river channels and otherwise. Methods for measuring flow once the water has reached a river include the stream gauge (see: discharge ), and tracer techniques. Other topics include chemical transport as part of surface water, sediment transport and erosion. One of

8550-573: The upper and lower river, the Mississippi is further controlled by thousands of wing dikes that moderate the river's flow in order to maintain an open navigation channel and prevent the river from eroding its banks. The head of navigation on the Mississippi is the St. Anthony Falls Lock. Before the Coon Rapids Dam in Coon Rapids, Minnesota , was built in 1913, steamboats could occasionally go upstream as far as Saint Cloud, Minnesota , depending on river conditions. The uppermost lock and dam on

8645-604: The variables constituting the terrestrial water balance, for example surface water storage, soil moisture , precipitation , evapotranspiration , and snow and ice , are measurable using remote sensing at various spatial-temporal resolutions and accuracies. Sources of remote sensing include land-based sensors, airborne sensors and satellite sensors which can capture microwave , thermal and near-infrared data or use lidar , for example. In hydrology, studies of water quality concern organic and inorganic compounds, and both dissolved and sediment material. In addition, water quality

8740-469: The western expansion of the United States. The river also became the subject of American literature , particularly in the writings of Mark Twain . Formed from thick layers of the river's silt deposits, the Mississippi embayment is one of the most fertile regions of the United States; steamboats were widely used in the 19th and early 20th centuries to ship agricultural and industrial goods. During

8835-479: The world by volume. On average, the Mississippi has 8% the flow of the Amazon River , which moves nearly 7 million cubic feet per second (200,000 m /s) during wet seasons. Before 1900, the Mississippi River transported an estimated 440 million short tons (400 million metric tons) of sediment per year from the interior of the United States to coastal Louisiana and the Gulf of Mexico. During

8930-500: Was chosen to designate the "true head" of the Mississippi River as a combination of the last four letters of the Latin word for truth ( ver itas ) and the first two letters of the Latin word for head ( ca put ). However, the lake is in turn fed by a number of smaller streams. From its origin at Lake Itasca to St. Louis, Missouri , the waterway's flow is moderated by 43 dams. Fourteen of these dams are located above Minneapolis in

9025-618: Was sufficient to account for the outflow of rivers flowing into the sea. Advances in the 18th century included the Bernoulli piezometer and Bernoulli's equation , by Daniel Bernoulli , and the Pitot tube , by Henri Pitot . The 19th century saw development in groundwater hydrology, including Darcy's law , the Dupuit-Thiem well formula, and Hagen- Poiseuille 's capillary flow equation. Rational analyses began to replace empiricism in

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