Flowing wells: history and role as a root of groundwater hydrology

10 The spewing of groundwater in flowing wells is a phenomenon of interest to the public, but little attention has been paid to the role of flowing wells on the science of groundwater. This study reviews that answering to problems related to flowing wells since the early 19 century led to the birth of many fundamental concepts and principles of groundwater hydrology. The concepts stemmed from flowing wells in confined aquifers include permeability and compressibility, while the principles include Darcy’s 15 law, role of aquitards on flowing well conditions and the piston flow pattern, steady-state well hydraulics in confined aquifers, and transient well hydraulics towards constant-head wells in confined or leaky aquifers, all of which are applicable even if flowing well conditions have disappeared. Due to the widespread occurrence of aquitards, there is a long-lasting misconception that flowing wells must be geologically-controlled. The occurrence of flowing wells in topographic lows of unconfined aquifers was 20 anticipated in 1940 and later verified in the 1960s, accompanying with the birth of the theory of topographically-driven groundwater flow, which has been considered as a paradigm shift in groundwater hydrology. Based on studies following this new paradigm, several preconditions of flowing wells given in the 19 century have been found to be not necessary at all. This historical perspective of the causes of flowing well conditions and the role of flowing wells on the science of groundwater could lead to a 25 deeper understanding of the evolution of groundwater hydrology. https://doi.org/10.5194/hess-2020-270 Preprint. Discussion started: 22 June 2020 c © Author(s) 2020. CC BY 4.0 License.


Introduction
The primary motivation for the study of groundwater is its role as a resource (Back and Herman, 1997;Freeze and Cherry, 1979). Water from springs was utilized by people in the Middle East about 10, 000 years ago (Beaumont, 1973), while from shallow flowing wells, which overflow at the surface, was 30 used in northern France as early as 1126 (Margat et al., 2013). Davis and De Weist (1966) pointed out that exploration of flowing wells in Europe in the 18 th century was responsible for stimulating the advancement of water well drilling technology. It was believed that the emergence of groundwater hydrology (hydrogeology) as a distinct science in the 19 th century was a result of the maturation of its mother sciences (geology and hydrology) in the 19 th century (Fetter, 2004;Meyer et al., 1988). Although

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it has been realized that flowing wells have always attracted considerable public interest (Chamberlin, 1885;Freeze and Cherry, 1979;Meiter, 2019), little attention has been paid to the role of flowing wells on the science of groundwater.
Due to the function of providing clean groundwater without pumping, flowing wells were a significant source of water supply for drinking and/or agriculture in Europe and the United States in the 40 19 th century and early 20 th century Konikow, 2013). During this period, in the process of exploring flowing wells and observing the flow rates in flowing wells, field observations of flowing wells led to some fundamental concepts and principles of groundwater hydrology in Europe and the United States. For example, based on field conditions in such regions as Paris, London, Wisconsin, and North and South Dakotas, the qualifying conditions of flowing wells were well recognized 45 (Chamberlin, 1885;Darton, 1905;Bond, 1865;Darton, 1897), which further led to the pattern of piston flow in confined aquifers; inspired by observations of flow rates of flowing wells in Paris, Darcy (1856) identified the controlling factors of flow in subsurface media and Dupuit (1863) established the principles of steady-state groundwater flow (Ritzi and Bobeck, 2008); based on the decreasing discharge in flowing wells with time and the excess of groundwater discharge compared to estimates of groundwater recharge, 50 Meinzer (1928) identified the compressibility of confined aquifers, which constitutes the basis of transient groundwater flow. Probably because these concepts and principles are applicable to nonflowing wells and most developments on well hydraulics since the 1930s were based on pumping in nonflowing wells, it seems that the role of flowing wells on the development of these concepts and principles in history was not realized in current textbooks. 55 https://doi.org/10.5194/hess-2020-270 Preprint. Discussion started: 22 June 2020 c Author(s) 2020. CC BY 4.0 License. 3 The widespread occurrence of confined aquifers and the accompanying phenomenon of flowing wells in the initial stage of groundwater development made the piston flow pattern and geologicallycontrolled flowing wells (Fig. 1a) a widely accepted conceptual model in groundwater hydrology. By analyzing the cross-sectional flow pattern from recharge to discharge areas in thick unconfined aquifers, Hubbert (1940) pointed out that a confined aquifer outcrops in the highlands and overlain by 60 impermeable strata in the lowlands as shown in Fig. 1a is by no means a necessary condition for flowing wells, and found that flowing wells could occur in topographic lows without an overlying confining bed (Fig. 1b). In the course of exploring groundwater in the Canadian Prairies, Tóth (Tóth, 1962(Tóth, , 1963(Tóth, , 1966 and Meyboom (1962; verified the occurrence of topographically-controlled flowing wells in the field and further developed Hubbert's model of topographically-driven groundwater flow from recharge 65 to discharge areas. In the Canadian Prairies, one of the topographically-controlled flowing wells has a well depth of only 9 m (Tóth, 1966). Kasenow (2010) reported a topographically-controlled flowing well in the discharge area of an unconfined aquifer, which was constructed at a depth of only 6.1 m below surface but has a head of around 1.4 m above surface. The principles of topographically-driven groundwater flow systems and the cause of topographically-controlled flowing wells constitute a 70 paradigm shift in groundwater hydrology (Bredehoeft, 2018;Madl-Szonyi, 2008). Unfortunately, topographically-controlled flowing wells, which is a natural consequence of topographically-driven groundwater flow, are described only in very few textbooks (Domenico and Schwartz, 1998;Freeze and Cherry, 1979;Heath, 1983;Kasenow, 2010), the number of which is very limited compared with the large number of groundwater textbooks. In other words, although the concept of flowing well is introduced in 75 almost every groundwater textbook, a complete understanding of the causes of flowing wells is still missing in most textbooks. This also undermines the role of topographically-controlled flowing wells on the paradigm shift from the conceptual model of piston flow to topographically-driven flow. https://doi.org/10.5194/hess-2020-270 Preprint. Discussion started: 22 June 2020 c Author(s) 2020. CC BY 4.0 License. Freeze and Back (1983) divided physical hydrogeology into three domains, i.e., physics of groundwater flow, well and aquifer hydraulics, and regional groundwater flow. Following this approach, studies directly related to flowing wells or bridge classical studies on flowing wells are divided into four threads (Fig. 2), which cover all of the three domains. The three threads shown in Fig. 2a-c are all 85 stemmed from geologically-controlled flowing wells, while the thread shown in Fig. 2d is from topographically-controlled flowing wells. Note that the seven classical studies which were selected by both Freeze and Back (1983) and Anderson (2008) as benchmark papers of groundwater hydrology (physical hydrogeology) have been included in the four threads, and four out of the seven papers are directly related to flowing wells, implying that flowing wells can be considered as, at least, one of the 90 roots of groundwater hydrology. The main aim of this review is to give a clear picture on the history of drilling flowing wells and the role of flowing wells on the evolution of the four threads of physical hydrogeology. ellipses are field phenomena of flowing wells, the purple boxes are papers directly related to flowing wells, and the white boxes are papers less or not directly related to flowing wells but have connections to previous or follow-up studies on flowing wells. The publications labeled with a "*" are included in both Freeze and Back (1983) and Anderson (2008).

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The paper is organized as follows. We first introduce the terms used to represent flowing wells, and the evolution of the ambiguous term "artesian well", which was initially used to represent flowing wells in confined aquifers but was later widely used to denote flowing well in both confined and unconfined aquifer, or any well penetrating a confined aquifer (Sect. 2). After introducing the history of drilling https://doi.org/10.5194/hess-2020-270 Preprint. Discussion started: 22 June 2020 c Author(s) 2020. CC BY 4.0 License. 5 flowing wells in selected regions that had inspired groundwater hydrologists in Sect. 3, the four threads 105 of evolution of groundwater hydrology rooted from flowing wells are briefly summarized in Sect. 4 through 7, which are sequenced based on the order of earliest publications about each thread. Finally, some concluding remarks are given in Sect. 8.
2 Terms related to flowing wells and definitions of "artesian"

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Photos of flowing wells were used as the cover image or frontispiece of some professional publications (Chamberlin, 1885;Freeze and Back, 1983;Hudak, 2005;Deming, 2002;Younger, 2007), which indicates the interest of groundwater professionals in flowing wells. In groundwater hydrology, hydrogeology or hydrology textbooks available to the authors, we found the phenomenon of a well which overflows at the surface is defined or mentioned in 34 textbooks. The widely used terms include "flowing 115 well", "artesian well" and "flowing artesian well", which appear in 17, 15 and 13 textbooks, respectively (sometimes more than one term is used in a book). Other less frequently used terms include "artesian flowing well", "overflowing well", and "free flowing well". For convenience of discussion, we divide the six terms into two categories based on whether "artesian" is shown.
The terms "flowing well", "overflowing well" and "free flowing well" stem purely from the 120 phenomenon of water overflow at the well outlet. The term "overflowing well" has been used in Britain since at least 1820s (Anonymous, 1822), and currently is still widely used in Britain, as found in several textbooks (Hiscock and Bense, 2014;Price, 1996;Rushton, 2003). To the authors' knowledge, the term "flowing well" was first used in the USGS hydrogeologic report Requsite and Qualifying Conditions of Artesian Wells (Chamberlin, 1885) and is currently the most widely used one. The term "free flowing 125 well" can be found in three textbooks (Fitts, 2013;Kruseman and de Ridder, 1990;Nonner, 2003). By including the adjectives "flowing", "overflowing" or "free flowing", these terms have clear meaning to represent wells that do not need pumping.
The number of textbooks that use one or two of the terms "artesian well", "flowing artesian well" and "artesian flowing well" is as high as 28, indicating the popularity of the adjective "artesian".

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"Artesian well" derived its name from the place Artois ("Artesia" is the historical Latin name of Artois) where the first flowing wells were obtained in the 12 th century, and gives birth to the terms "flowing artesian well" and "artesian flowing well" by adding the adjective "flowing". Currently, in the majority https://doi.org/10.5194/hess-2020-270 Preprint. Discussion started: 22 June 2020 c Author(s) 2020. CC BY 4.0 License. of textbooks in Europe (Hendriks, 2010;Kruseman and de Ridder, 1990;Price, 1996;Rushton, 2003;Brassington, 2017;Davie, 2008;de Marsily, 1986;Hölting and Coldewey, 2019) and in at least eight 135 textbooks in North America (Deming, 2002;Domenico and Schwartz, 1998;Driscoll, 1986;Pinder and Celia, 2006;Yeh et al., 2015;Hornberger et al., 2014;Fitts, 2013;Alley and Alley, 2017) , the term "artesian well" is synonymous with flowing well. Note that in ten textbooks in North America (Fetter, 2001;Freeze and Cherry, 1979;Batu, 1998;Kasenow, 2010;LaMoreaux et al., 2009;Mays, 2012;McWhorter and Sunada, 1977;Heath, 1983;Schwartz and Zhang, 2003;Todd and Mays, 2004), an 140 artesian well means a well that derives its water from a confined aquifer, the details of which are discussed in Subsect. 2.2 and 2.3. Before 1940s, it was believed that only a confined aquifer has the possibility to have hydraulic head higher than the ground surface elevation, i.e., flowing wells could occur only in confined aquifers. Hubbert (1940) first noted that flowing wells could occur in the discharge area of a homogeneous basin 145 (Fig. 1b, the details can be found in Subsect.7.1). This explanation of the cause of flowing wells was accepted by the USGS (Heath, 1983;Lohman, 1972a;Lohman, 1972b). In Heath (1983) andLohman (1972b), the term "flowing artesian well" was restricted to flowing wells in confined aquifers, and in Heath (1983), it was explicitly pointed out that "a flowing well does not necessarily indicate artesian conditions". To differentiate the two types of flowing wells due to different causes, Freeze and Cherry

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(1979) defined geologically-controlled flowing wells and topographically-controlled flowing wells. As shown in Fig. 1, the former develop in confined aquifers and receive recharge at upland outcrops, while the latter occur in the topographic lows of unconfined aquifers.

Evolution of "artesian well" and the birth of "flowing artesian well"
Literally, "artesian well" stands for "well of Artois". It is unquestionable that it was the phenomenon 155 of water overflow at the surface which attracted people's attention to wells of Artois (Fuller, 1906;Norton, 1897). As early as 1805, the name "artesian fountain" was applied in French scientific literature to represent flowing wells (Lionnais, 1805). In later publications, "artesian well" was widely used to represent flowing wells in France and Britain (Arago, 1835;de Thury, 1830;Garnier, 1822;Buckland, 1836). The term "artesian well" was introduced in the United States in 1835 (Storrow, 1835). In

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Probably because most artesian wells were much deeper than traditional dug wells, and a driller could not assure a deep well could overflow at the surface before finishing drilling, the term "artesian well" was frequently used to denote a deep well that did not overflow. Chamberlin (1885) condemned 165 such a use, however, in less than 20 years, Chamberlin and Salisbury (1904) pointed out that "at present time any notably deep well is called artesian, especially if it descends to considerable depths". Moreover, because deep wells or artesian wells were drilled instead of being dug, artesian wells were also widely used to denote drilled/bored well in the 19 th century. Fortunately, such usages were seldom adopted in subsequent years, probably due to the contribution of definitions given in Meinzer (1923b).

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As the geologic conditions governing flowing wells became known, the term "artesian well" was suggested to represent any well in which hydraulic head is higher than the elevation of water table in the 1890s (Carpenter, 1891;Norton, 1897;Slichter, 1899). Norton (1897) insisted that if there are two wells in the same town derived from the same aquifer and rising to the same height, one could overflow at the surface but the other could not just because of slightly higher ground surface, it was preferable to term 175 both wells artesian wells. Such a usage was accepted and popularized by the USGS (Lohman, 1972b;Meinzer, 1923b). In some later publications by authors of the USGS, the term "artesian well" was used equivalently to a well in a confined aquifer (Jacob, 1940(Jacob, , 1946(Jacob, , 1947Meinzer, 1928;Theis, 1935).
Since the 19 th century, artesian wells were not restricted to a flowing wells and can be divided into flowing artesian wells and non-flowing artesian wells. Although the term "non-flowing artesian well" 180 (or "negative artesian well") was used in the 19 th century and early 20 th century (Arago, 1835;Norton, 1897;Slichter, 1899;Meinzer, 1928), the adjective "non-flowing" is used only in very limited textbooks (Heath, 1983;Schwartz and Zhang, 2003;Singhal and Gupta, 2010). In the textbooks that define an artesian well to be any well tapping a confined aquifer, an artesian well is by default a non-flowing artesian well (Fetter, 2001;Todd and Mays, 2004;Abdrashitova, 2015;Kasenow, 2010).

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Many basins throughout the world were called artesian basins. The Great Artesian Basin in Australia is one of the largest artesian basins in the world and is well known for its numerous flowing wells in confined aquifers. In the United States, many basins were termed artesian basins, for example, the artesian basin of the Dakotas (Darton, 1905;Swenson, 1968), the great Paleozoic artesian basin of the Mississippi Valley region (Meinzer, 1923a), the Rowsell artesian basin in New Mexico (Fiedler and Nye, 210 1933), and the Grand Junction artesian basin (Jacob and Lohman, 1952). According to Meinzer (1923b), an artesian basin is a geologic structural feature or combination of such features in which water is confined under artesian pressure, implying that the hydraulic head being greater than the elevation of ground surface is not a necessary condition of an artesian basin . In fact, all of these well-known artesian basins have many flowing wells in the initial stage of groundwater development. Therefore, it is difficult 215 to interpret the meaning of the adjective "artesian" in the term "artesian basin".
The different meanings of "artesian" caused confusion not only to beginners of groundwater hydrology, but also to professional groundwater hydrologists. The confusion caused by "artesian " has been realized by some textbook authors. Deming (2002) and Younger (2007) both chose photos of a flowing well for their cover image, but they have quite opposite viewpoints on "artesian". Deming (2002) 220 from the United States held the opinion that "artesian" implies that the hydraulic head is greater than the https://doi.org/10.5194/hess-2020-270 Preprint. Discussion started: 22 June 2020 c Author(s) 2020. CC BY 4.0 License. elevation of ground surface, and defining "artesian aquifer" to be identical to confined aquifer would make the definition not only conceptually useless, but also etymologically incorrect because wells drilled in Artois in 1126 could flow spontaneously. On the contrary, Younger (2007) from the United Kindom believed that "artesian" is a synonym of "confined", and pointed out that "artesian" is also widely 225 misused to refer to any well from which water flows without pumping, a phenomenon which is not restricted to confined aquifers. Younger also discouraged further use of "artesian" because it lacks intuitive meaning in modern English.
To sum up, hydrogeologists are keenly interested in flowing wells, but are also confused by the term "artesian". This confusion leads to underestimation of the role of flowing wells on the development 230 of groundwater hydrology. In the following discussion, we avoid using the confusing adjective term "artesian well". Instead, following Freeze and Cherry's (1979) classification of flowing wells, we use geologically-controlled flowing wells to represent flowing wells in confined aquifers or leaky aquifers, and topographically-controlled flowing wells for wells in aquifers without a confining bed.

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Many aquifers had hydraulic heads above the land surface when the first deep wells were drilled (Fetter, 2001). A thorough review on the history of flowing well drilling is beyond the scope the current discussion. Here, we briefly review the history of flowing well in regions that directly inspired hydrogeologists.

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As early as 1126, the first shallow flowing well tapping the confined fringe of the chalk aquifer was obtained in Artois in northern France (Margat et al., 2013). The technique of cable-tool drilling (also called percussion drilling) resulted in drilling of deeper flowing wells in France in the early 19th century. Garnier (1822) published the first technical guidebook on drilling artesian wells. It was stated that with the exception of some provinces, there are few parts of France where artesian wells might not be procured.

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Garnier obtained a prize from the Society for the Encouragement of Industry due to the publication of this book, which reflects the interest of the French government in such wells.

Great Britain
In Great Britain, James Ryan obtained a patent on boring for minerals and water in 1805, while John Goode obtained a patent on boring for the purpose of obtaining and raising water in 1823 (Macintosh, 1827). The grant of these patents indicates that Great Britain was active in drilling wells in the early 19 th century. In 1807, it was reported that there were flowing wells in the Thames Basin, London (Farey,  The publication of Garnier (1822) in France aroused further interest in Great Britain (Farey, 1823). By 1840, many "artesian wells" had been drilled in the London Basin (Mylne, 1840), although 275 many boreholes failed because of lack of geological information. The experience gained from the costly failures improved understanding of conditions necessary for the success of a flowing well, the details of which are to be discussed in Subsect. 4.1.

The United States
To meet the water supply in some cities as well as irrigation demands in farms, numerous flowing 280 wells were drilled in the United States beginning in the 19 th century as a direct result of the increased drilling technology. Here, we list some regions where flowing wells were drilled, causing significant advances in groundwater hydrology.
Development of the Cambrian-Ordovician aquifer system in the northern Midwest can be traced to 1864 when a flowing well with a depth of 217 m was drilled in Chicago (Konikow, 2013). By the end of 285 the 19 th century, flowing wells were common in topographically low areas in the Mississippi, Missouri, and Illinois River valleys, near Lake Michigan, and around Lake Winnebago in northeastern Wisconsin (Young, 1992). At the beginning of the 21st century, there were still many flowing wells newly drilled in Michigan (Gaber, 2005). Chamberlin's (1885) classic report was based on the hydrogeologic conditions in Wisconsin, and is considered as one of the roots of groundwater hydrology in Wisconsin 290 (Anderson, 2005). In 1876, a flowing well with a depth of 293 m and an initial flow rate of 3270 m 3 /d, which was named The Greatest Artesian Fountain in America, was drilled in Prairie du Chien, Wisconsin (Meiter, 2019). The photo of this flowing well was used as the frontispiece of Chamberlin (1885) and Freeze and Back (1983), the cover image of Deming (2002), and was also cited in Anderson (2005).
In the Great Plains, interest in groundwater emerged due to the irrigation demands beginning in the 295 1880s, due to the widespread drought. In early 20 th century, flowing wells were common in topographic lows near rivers, for example, in the Arkansas River valley of southeastern Colorado, much of South Dakota, and parts of southeastern North Dakota and northeastern Nebraska in the Missouri River valley (Darton, 1905). In South and North Dakota within the Great Plains, there were about 400 deep wells https://doi.org/10.5194/hess-2020-270 Preprint. Discussion started: 22 June 2020 c Author(s) 2020. CC BY 4.0 License. drilled to the Dakota sandstone by 1896, of which over 350 were flowing wells (Darton, 1897). Due to 300 the introduction of the jetting method of drilling in around 1900, thousands of small-diameter wells were drilled to the Dakota sandstone during the following two decades. There were about 10,000 deep wells in South Dakota in 1915, and between 6,000 and 8,000 deep wells in North Dakota in 1923 (Meinzer and Hard, 1925). Due to the increased withdrawal of deep groundwater, many flowing wells became nonflowing wells, accompanied by decreasing flow rates in the flowing wells that still flowed. The condition 305 of flowing wells led to improved understanding of the pattern of groundwater circulation in confined aquifers (Darton, 1905), while the imbalance between groundwater discharge and recharge led to the birth of the concept of compressibility of confined aquifers (Meinzer and Hard, 1925;Meinzer, 1928).
In flowing wells of the Dakota aquifer, it was noted that "the pressure increases for several hours or even days after the flow is shut off, and when opened the flow decreases in the same way until the 310 normal flow is reached" (Meinzer, 1928). Several decades later, based on field observations of decreasing flow rate with time in flowing wells in the Grand Junction artesian basin and in the Rowsell artesian basin in New Mexico, constant-drawdown aquifer tests were proposed to obtain hydraulic parameters (Jacob and Lohman, 1952;Hantush, 1959).

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The Great Artesian Basin, which covers 1/5 of the total area of Australia, is one of the largest and well-known groundwater basins in the world (Ordens et al., 2020). The first shallow flowing well with a depth of 43 m was dug by using an auger near a spring in New South Wales in 1878, while the first drilled flowing well with a depth of 393 m was completed near Cunnamulla, Queensland in 1887 (Williamson, 2013). By the end of the 19 th century, there were already around 1000 flowing wells (van 320 der Gun, 2019). The discovery of flowing wells and "artesian water" triggered the emergence of hydrogeology as a discipline in Australia (Williamson, 2013), and the development of "artesian water" have played a vital role on the pastoral industry in the arid and semi-arid regions of Australia (Habermehl, 2020).
Due to the occurrence of intervening aquifers and aquitards, the Great Artesian Basin is a multi-325 layered confined aquifer system. Although head drawdowns of up to 100 m have been recorded in highly developed areas, hydraulic heads in the Jurassic and Lower Cretaceous aquifers are still above ground surface throughout most of the basin (Habermehl, 2020). In Australia, currently the term "artesian" still https://doi.org/10.5194/hess-2020-270 Preprint. Discussion started: 22 June 2020 c Author(s) 2020. CC BY 4.0 License. 13 implies that a bore will flow naturally (Williamson, 2013). A comprehensive review of the history and recent research status of the basin can be found in Ordens et al. (2020).

Canada
Since the beginning of the 20th century, the hydrogeology of the Canadian Prairies has been studied.
Groundwater in this region is obtained from surficial Pleistocene glacial drift and from the underlying bedrock of Tertiary or Cretaceous age. Quaternary glacial deposits and the underlying Tertiary Paskapoo sandstone constitute a thick unconfined aquifer. A similarity between the potentiometric surface and the 335 local topography were widely observed in many parts of the Canadian Prairies (Jones, 1962;Meyboom, 1962;Tóth, 1962;Farvolden, 1961). Due to the occurrence of a large number of flowing wells, either in the glacial drift or in the bedrock, great attention was paid to the relation between topography, geology and areas with flowing wells during basin-scale groundwater surveys (Meyboom, 1966).
The Trochu area in central Alberta, which covers an area of 67 km 2 , is representative of the 340 hydrogeology of Canadian Prairies. There were 10 shallow flowing wells ranging in depth from 9 m to 27 m in topographic lows (Tóth, 1966). Because the glacial deposits have low contents of clay, they are efficient for infiltration of rainfall and evaporation of soil water. Therefore, the Quaternary glacial deposits and the underlying Tertiary Paskapoo sandstone constitute a thick unconfined aquifer.
Combined with previous theoretical findings on topographically-driven flow systems (Hubbert, 345 1940;Tóth, 1962Tóth, , 1963, these flowing wells in unconfined aquifers were considered to be controlled by topography and are typical manifestations of groundwater discharge (Tóth, 1966). The details are discussed in Sect. 7.

Conditions of geologically-controlled flowing wells
Due to the progress of hydrology and geology in the 18 th century, it was accepted in the early 19 th century that the water of flowing wells came from rainfall, which found its way through the pores or fractures of a permeable stratum enclosed between two water-tight strata (Garnier, 1822). de Thury (1830) summarized three conditions of flowing wells in confined aquifers. The first is to reach a flow of deep 355 water coming from higher basins and passing along the bosom of the earth between compact and https://doi.org/10.5194/hess-2020-270 Preprint. Discussion started: 22 June 2020 c Author(s) 2020. CC BY 4.0 License. impermeable rocks; the second is to afford this deep water the possibility of rising to the surface by using an artificially bored well; and the third is to prevent the spreading of the ascending water into the surrounding sand or rock by inserting tubes into the bored well.
Following the successful drilling of flowing wells in France, the theory behind the occurrence of "(1) A pervious stratum to permit the entrance and the passage of the water; (2) A water-tight bed below to prevent the escape of the water downward; (3) A like impervious bed above to prevent 375 escape upward, for the water, being under pressure from the fountain-head, would otherwise find relief in that direction; (4) An inclination of these beds, so that the edge at which the waters enter will be higher than the surface at the well; (5) A suitable exposure of the edge of the porous stratum, so that it may take in a sufficient supply of water; (6) An adequate rain-fall to furnish this supply; (7) An absence of any escape for the water at a lower level than the surface at the well."

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In fact, the seven prerequisites given by Chamberlain (1885) (1830), therefore, we assume their findings were obtained independently. Chamberlin (1885) also pointed out that confining layers are not totally impermeable, which foreshadowed later studies on well hydraulics 385 of leaky aquifers (Hantush, 1959;Hantush and Jacob, 1955;Jacob, 1946) (Swenson, 1968). Chamberlin's report was recognized as the first classic paper on regional groundwater flow in the United States (Bredehoeft et al., 1982).

Piston flow in confined aquifers
In the late 1890s, Darton (1897) investigated the occurrence of flowing wells in the Dakotas and 390 plotted the cross-section of the Dakota aquifer (Fig. 4). By constructing the hydraulic head contours of the Dakota aquifer in South Dakota, which shows the head loss through the confined aquifer, Darton (1905) concluded that groundwater discharged by the flowing wells in the east had flowed hundreds of kilometers through the confined aquifer from the outcrops in the west. This study popularized the pattern of groundwater flow in a confined aquifer which outcrops in topographic highs as shown in Fig. 1a. In

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the Great Artesian Basin of Australia, there was also a long-lasting conceptual model that each aquifer can be considered to be laterally continuous across the extent of the basin (Habermehl, 2020). In the Dakota confined aquifer, vertical leakage into the aquifer from adjacent strata was identified in the 1960s (Swenson, 1968). In Australia, several recent studies also identified vertical connections between aquifers (Pandey et al., 2020;Smerdon and Turnadge, 2015). However, vertical leakage seldom change 400 the direction of groundwater flow within the confined aquifer.

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As shown in Fig. 4, the flow pattern in a confined aquifer is similar to flow through a pipe, and is commonly referred to as piston flow (Bethke and Johnson, 2008;Hinkle et al., 2010). Because many hydrogeochemical processes are dependent on travel time through the aquifer, hydrochemical facies 410 (Back, 1960; usually evolve along the flow path within the piston flow. Therefore, the piston flow model, which stemmed from analyzing geologically-controlled flowing wells, is the cornerstone of sampling and analyzing groundwater geochemistry and isotopes in confined or leaky aquifers. https://doi.org/10.5194/hess-2020-270 Preprint. Discussion started: 22 June 2020 c Author(s) 2020. CC BY 4.0 License.

The birth of Darcy's law evoked by flowing wells
It is widely known that Darcy's law, which represents the beginning of groundwater hydrology as a quantitative science (Freeze and Back, 1983), was established based on sand column experiments. In fact, the sand column experiments were designed to confirm a linear correlation between flow rate and head loss in sands which was discovered in flowing wells (Brown, 2002;Ritzi and Bobeck, 2008).

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Because flowing wells were important sources of water supply in the Paris Basin, flow rates at different elevations of discharge orifices were measured in several flowing wells in the 1840s (Fig. 5), which were called experiments of head loss versus riser pipe height (Ritzi and Bobeck, 2008). In fact, such experiments can be regarded as constant-head (drawdown) tests in single wells. As shown in Fig. 5a, the flow rates measured in September and November increased linearly as the elevation of discharge orifice 425 decreased. The higher flow rate in November can be a result of higher hydraulic head surrounding the flowing well, probably due to the contribution of groundwater recharge. Darcy was interested by this linear correlation (Brown, 2002;Ritzi and Bobeck, 2008). and at high water velocity, the head loss was found to be linear to the square of discharge rate, which can be written as where L is length, r is pipe radius, q is the volume discharge rate, and a and b are empirical coefficients of proportionality. Eq. (1) verified Poiseuille (1841)  By assuming that head loss from the recharge area to the discharge orifice occurs in both the aquifer and the well pipe, equations similar to the following forms were obtained: where L' is flow distance in the aquifer from the recharge area, r' is radius representative of pores in the aquifer, H1 and H2 are the lengths of well pipes from the bottom to the discharge orifice, and C is an unnamed constant. The linear relationship between h1-h2 and q1-q2 shown in Fig. 5a indicates that the second term on the left side of Eq. (3b) is negligible, and C can be interpreted as the slope shown in Fig.   5a. To further confirm that head loss in aquifers is linear to the velocity, in 1855, Darcy conducted the where s is the total cross-sectional area perpendicular to flow, and k is a coefficient unnamed by Darcy, today call k the hydraulic conductivity. Hubbert (1940) rigorously interpreted hydraulic conductivity and examined Darcy's law in the light of the microscopic Navier-Stokes flow theory, which raised the understanding of Darcy's law to a higher level of sophistication.

Steady-state well hydraulics in confined aquifers: Dupuit equation
where B is the thickness of the confined aquifer, x is the radius within the cone of depression, and y is the corresponding head with reference to the elevation of the discharge orifice. Dupuit (1863) obtained 485 the following equation by integrating equation (5) from the radius of the well, rw, to the radius of influence, R: where hw is the elevation of the discharge orifice, and h0 is the hydraulic head at the radius of influence, which equals the initial hydraulic head of the flowing well when the well has been closed for a duration 490 of time. By comparing Eq. (4) and (6), it can be interpreted that (1863) explicitly stated that Eq. (6) is supported by the measurements of flow rate versus elevation of discharge orifice of flowing wells reported in Darcy (1856).
Although Eq. (6) was derived based on the hydrogeologic condition of a flowing well in a confined aquifer, it is applicable to non-flowing wells in a confined aquifer. A limitation of the equation is the 495 difficulty of determining the radius of influence in the field. Thiem (1906) improved Eq. (6) by integrating Eq. (5) between two wells within the cone of depression and obtained an equation to determine hydraulic conductivity, which is known as the Thiem equilibrium method. Although the Thiem equation (Thiem, 1906) was introduced in almost all textbooks, Dupuit's pioneering study on steadystate radial flow to a flowing well in confined aquifers (Dupuit, 1863) was seldom mentioned in textbooks.

500
Dupuit (1863) also derived similar equations for a well in unconfined aquifers by neglecting the vertical hydraulic gradient, which is currently known as Dupuit-Forchheimer approximation. Although the vertical hydraulic gradient is neglected, the Dupuit-Forchheimer approximation is still useful in interpreting regional scale groundwater flow problems (Haitjema and Mitchell-Bruker, 2005). resources were already undergoing development, therefore, much of the effort of the USGS turned toward inventory (Domenico and Schwartz, 1998). The inventory of groundwater resources in the Dakota aquifer,

510
where the number of flowing wells was decreasing in the 1920s, led to the theoretical finding of aquifer compressibility (Meinzer, 1928;Meinzer and Hard, 1925 (Meinzer and Hard, 1925). Although these estimates could be very inaccurate, they were sufficient to 520 demonstrate the excess of discharge through flowing wells over recharge. Meinzer and Hard (1925) concluded that most of the water discharged through the flowing wells was taken out of storage in the sandstone aquifer, indicating that the sandstone aquifer was compressible. It was also observed that the artesian head would increase gradually for some time after a flowing well was shut off, which is a manifestation of elasticity of the aquifer medium (Meinzer and Hard, 1925).

525
By summarizing these observations of flowing wells, as well as the evidences of compressibility and elasticity of compacted sand, land subsidence in an oil field, water level fluctuations produced by ocean tides, and water level fluctuations produced by railroad trains, Meinzer (1928) concluded that confined aquifers are compressible and elastic. Although geochemical and numerical studies several decades later showed that leakage also contributed to well discharge in the Dakota aquifer (Bredehoeft 530 et al., 1983;Leonard et al., 1983;Swenson, 1968), this did not undermine the role of flowing wells that had intrigued the interest of hydrogeologists.
Several years later, by assuming that discharge of groundwater from storage as head falls is similar to release of heat as temperature decreases, Theis (1935)

Transient well hydraulics in flowing wells and non-flowing wells in confined aquifers
In the early 1930s, the high demand for groundwater led to evaluation of groundwater in different parts of the United States and pumping tests using the Thiem equilibrium method were conducted to obtain hydraulic conductivity in several regions (Lohman, 1936;Theis, 1932;Wenzel, 1936).
Unfortunately, it was found difficult to consistently obtain aquifer parameters because of the increasing 545 drawdown with time (Wenzel, 1936).
To interpret the time-varying drawdown, Charles Vernon Theis assumed that groundwater flow disturbed by a sink withdrawing water was analogous to heat conduction disturbed by a sink withdrawing heat and resorted to Clarence Isador Lubin, a mathematician at the University of Cincinnati, for the solution of temperature distribution of a uniform plate under two different conditions (White and Clebsch, 550 1993). The first condition is the introduction of a sink kept at 0 temperature, which corresponds to the constant-drawdown aquifer test problem and is applicable to flowing wells, and the second condition is the introduction of a sink with a uniform heat flow rate, which corresponds to the constant-rate pumping test problem. It was fortunate that the solution of the second problem was readily available in the field of heat conduction (Carslaw, 1921). In this way, Theis (1935) obtained the analytical solution of time- When a flowing well has been shut off for a duration of time, upon reopening, the discharge rate decrease with time, which can be considered as a constant-drawdown aquifer test. Based on Smith (1937) solution to the analogous problem in heat conduction (the first problem raised by Theis), Jacob and 560 Lohman (1952) derived a solution to the constant-drawdown well test problem in a confined aquifer and verified the results based on flowing wells in the Grand Junction artesian basin, Colorado. Several years later, after the classical work on constant-rate pumping problem in leaky aquifers (Hantush and Jacob, 1955), Hantush (1959) derived a solution to the constant-drawdown well hydraulics to a flowing well in leaky aquifers. In fact, constant-drawdown tests can also be carried out in non-flowing wells 565 either by using a specially designed pump or by connecting the well to a pressurized water container at the surface (Mishra and Guyonnet, 1992). Such constant-drawdown tests have been found to be https://doi.org/10.5194/hess-2020-270 Preprint. Discussion started: 22 June 2020 c Author(s) 2020. CC BY 4.0 License.
In summary, although the door of transient well hydraulics was directly opened by Theis (1935) based on constant-rate pumping tests, constant-drawdown well tests triggered by flowing wells belong 570 to an indispensable component of transient well hydraulics and are still receiving active attention in the current century (Chang and Chen, 2002;Wen et al., 2011;Tsai and Yeh, 2012;Feng and Zhan, 2019). It is worth noting that current models on transient well hydraulics did not fully account for the relationship between groundwater recharge from precipitation and groundwater discharge in wells, for example, the higher flow rate in November than that in September shown in Fig. 5a can not be explained by current 575 theories.

Topographically-controlled flowing wells
Based on the principle of the conservation of mass and the laws of thermodynamics, Hubbert (1940) 580 proposed the fundamental rules to obtain graphical solutions of regional groundwater flow. In a homogeneous and isotropic aquifer with a symmetrical topography between two streams, a crosssectional flow net was drawn by assuming that groundwater recharge is distributed over the whole airwater interface except for the streams at the valleys. Fig. 7 shows that flow lines diverge from recharge areas and converge toward discharge area at the bottoms of valleys. Fetter (1994) superposed some 585 piezometers onto the equipotential lines, which clearly shows that hydraulic head decreases with well depth in topographic highs near the divide, and increases with well depth in topographic lows near the valley. Moreover, below the streams, hydraulic head in the aquifer is higher than the elevation of ground surface, which constitutes a necessary and sufficient condition of vertical flowing wells. Such flowing wells in homogeneous unconfined aquifers were termed topographically-controlled flowing wells 590 (Freeze and Cherry, 1979 Fig. 7 The flow net of groundwater flow between two river and the head in selected piezometers (Modified from Fetter, 1994).

595
Although the concept of topographically-controlled flowing wells has been included in some textbooks (Domenico and Schwartz, 1998;Freeze and Cherry, 1979;Heath, 1983;Kasenow, 2010;Lohman, 1972a), and basin width/depth ratios (L/|D|, where L is the basin length and |D| is the basin depth). By fixing |D|, increases in α and decreases in L both lead to increased hydraulic gradient between recharge and discharge areas. Based on the distribution of head exceeding surface (termed artesian head in their paper), it was found that the zone with flowing wells is always within the discharge area and the ratio of its size 605 to the whole basin is proportional to the hydraulic gradient (Fig. 8). Therefore, in homogeneous basins, the hydraulic gradient is the main control factor of flowing wells.

Topographically-driven groundwater flow systems
In the 1950s and 1960s, the high demand for water on the Canadian Prairies led to institutional programs of ground water exploration and research. The phenomena anticipated by Hubbert (1940), like the mean water table closely follows the topography, hydraulic head decreases with well depth in 615 topographic highs (corresponding to recharge areas) and increases with well depth in topographic lows (corresponding to discharge areas), and flowing wells occur in topographic lows, were quite common in the Canadian Prairies (Meyboom, 1962(Meyboom, , 1966Tóth, 1962Tóth, , 1966. Based on the field observations, two similar but slightly different conceptual models of topographically-induced groundwater flow were developed by Tóth (1962) and Meyboom (1962), both of which believed that flowing wells could occur 620 in the discharge area (Fig. 9).   (Fig. 9a) slightly different from Hubbert's. It was found that groundwater discharge could cover the entire lower half of the unit basin, and the whole discharge area has higher hydraulic head than the 630 corresponding elevation of water table (the cases shown in Fig. 8h,i,j), which fulfills Meinzer's (1923) definition of "artesian water". In a composite basin whose water table configuration is the superposition of a sinusoidal curve and a linear regional slope, Tóth (1963) (Back, 1960;Back, 1966) to support his finding. Because Back (1960) andToth (1963) are not directly related to flowing wells, plots of nested flow systems are not shown here. Meyboom (1962) qualitatively plotted the flow net called the "Prairie Profile" (Fig. 9b), which considered the higher permeability of the sandstone than glacial deposits. The profile has large zones of 640 shallow or deep flowing wells as well as large zones of evapotranspiration in the discharge area. Although Toth and Meyboom had disagreement on some specific details, they agreed that the combination of the two models "gives a good description of the unconfined region of groundwater flow in the western Canadian Prairies" (Tóth, 2005). Several years later, as a PhD student, R. Alan Freeze decided to bring the ideas of Meyboom and Toth together by numerically simulating steady-state regional groundwater 645 flow in heterogeneous basins with any desired water table configuration (Freeze, 2012). Freeze and Witherspoon (1967) demonstrated that heterogeneity does not affect the topographically-induced flow pattern from recharge to discharge areas (Fig. 10). In fact, Fig. 10 b and 10c indicate that a higher permeability in the lower aquifer could lead to a larger area of flowing wells. Moreover, they found that confined aquifers like those shown in Fig. 10b and 10c need not outcrop to produce flowing well  shallow part corresponding to the Quartnary deposits. It is interesting that groundwater collected at the flowing wells has a hydrochemical facies of Na-HCO3, does not contain NO3 -, and is depleted in δ 2 H and δ 18 O, all of which are quite different from groundwater in recharge areas (Wang et al., 2015a). Moreover, Mg in groundwater collected from flowing wells has been greatly removed by the process of clay formation, leading to much lower δ 26 Mg than samples in recharge areas (Zhang et al., 2018a). These 670 hydrochemical and isotopic evidences show that groundwater collected at the outlets of flowing well could represent deep groundwater and is seldom mixed with shallow groundwater (Zhang et al., 2019).
To examine the hydraulics of topographically-controlled flowing wells, the water exchange between the aquifer and the flowing well has been simulated using the revised multi-node well (MNW2) package (Konikow et al., 2009) of MODFLOW by considering a flowing well in a three-dimensional 675 unit basin (Zhang et al., 2018b). The hydraulic head of the flowing well, Hw, is set equal to the elevation of the ground surface. The trend of increasing hydraulic head with depth in the discharge area results in hydraulic head in the aquifer smaller than Hw in the shallow part and larger than Hw in the deep part.
Therefore, there is groundwater inflow from the aquifer to the flowing well (Qin) in the deep part, and groundwater outflow from the flowing well to the aquifer (Qout) in the shallow part. If Qin=Qout, then flow 680 rate at the well outlet equals 0 (Fig. 11a), which is the same as a non-flowing well in the discharge area as reported in Zinn and Konikow (2007). However, if Qin>Qout, flow rate at the well outlet is above 0 ( Fig. 11b), which results in water overflow at the surface. In some extreme cases, for example, if the water table coincide with the ground surface, or the shallow part is cased, Qout equals 0 and flow rate at the well outlet is determined by Qin (Fig. 11c). It has also been found that the simultaneous occurrence 685 of inflow and outflow could occur in a thick confined aquifer (Zhang et al., 2018b). Therefore, the 3 rd condition proposed by both de Thury (1830) and Bond (1865), and the 7 th condition given by Chamberlin (1885), is not a necessary condition for flowing wells.  (Bredehoeft, 2018;Tóth, 2005). The spatial distribution of groundwater age in thick 700 unconfined aquifers (Jiang et al., 2010;Jiang et al., 2012) is also more complicated than that in a confined aquifer. Although the transient behavior of groundwater flow to geologically-controlled flowing wells has been studied in the 1950s (Hantush, 1959;Jacob and Lohman, 1952), there is no research on the transient groundwater flow to topographically-controlled flowing wells. Moreover, research coupling groundwater recharge from precipitation and groundwater discharge through flowing wells, which is 705 critical to interpret the increased flow rate from September to November as shown in Fig. 5a, is also missing.

Conclusions and suggestions
The first recorded recognition of flowing wells was as early as 1126 in northern France, but it was the advent of modern cable-tool drilling equipment in Europe in the early 19 th century that made flowing 710 wells common. In the textbook by Davis and De Weist (1966), it was pointed out that exploration of flowing wells in Europe in the 18 th century was responsible for stimulating the advancement of water well drilling technology. In fact, flowing wells, which represent a spectacular natural phenomenon of deep groundwater, also instigated the science of groundwater. The pursuit of answers to fundamental questions generated by flowing wells in confined aquifers moved the science forward for more than a 715 century since the early 19 th century. Moreover, it is interesting that since the 1940s, flowing wells in unconfined aquifers played a significant role on the new paradigm, i.e., a paradigm shift from piston flow in confined aquifers to topographically-driven flow in either homogeneous or heterogeneous basins.
The spectacular flowing wells in Paris and London in the early 19 th century drew widespread attention to this most noticeable feature of groundwater, which was the early impetus behind the start of 720 groundwater science in the mid 19 th century. It was not a coincidence that Darcy (1856) did his monumental laboratory experiments soon after he did pipe flow experiments prompted by flowing wells.
He was followed by his colleague Dupuit (1863) to develop the hydraulics of steady flow to wells. The term "flowing well" was introduced by Chamberlain (1885)  investigations of the Cambrian-Ordovician aquifer system in Wisconsin, he recognized the role of confining beds in creating flowing well conditions and also that these confining beds are leaky. This was followed soon after by the classic work by Darton (1897Darton ( , 1905 who studied the regional Dakota aquifer. Meinzer and Hard (1925) and Meinzer (1928) deduced from declining discharge of flowing wells and excess of discharge over recharge that confined aquifers are elastic and have storage capability related to 730 compressibility. This prompted Theis (1935) of the USGS to initiate unsteady state well hydraulics for non-leaky aquifers, although leakage recognized decades earlier set the stage for Hantush to pioneer the hydraulics of pumping wells and flowing wells in aquifers with leaky confining beds in the 1950s (Hantush and Jacob, 1955;Hantush, 1959).
The wide occurrence of regional scale confined aquifers showing ubiquitous flowing wells in 735 sedimentary rocks in France, England and the United States resulted in confined-aquifer piston flow being a broadly useful conceptualization. However, this resulted in the common misconception that flowing wells must be geologically-controlled, and the confusion of the term "artesian". In his monumental treatise on the theory of groundwater motion, Hubbert (1940) realized flowing wells can occur in entirely unconfined and homogeneous conditions based only on topographic control. Hubbert's 740 concepts of topographically-driven groundwater flow and topographically-controlled flowing wells were further developed by Toth (1962Toth ( , 1963Toth ( , 1966 and Meyboom (1962Meyboom ( , 1966 in the Canadian Prairies. Subsequent studies by Freeze and Witherspoon (1967) and Zhang et al. (2018b) found that several qualifying conditions of flowing wells proposed by Chamberlain (1885) are not necessary at all.
Although the theory of topographically-driven groundwater flow systems has been considered to be a 745 paradigm shift of modern hydrogeology (Bredehoeft, 2018;Madl-Szonyi, 2008;Tóth, 2005), the misconception that flowing wells must be geologically-controlled is still impeding the acceptance of the new paradigm. Moreover, many modern textbooks still have not fully clarified the differences and implications of the two types of flowing wells, geologically versus topographically controlled. Therefore, consistent terminology and a complete description of both types of flowing wells are expected in future 750 groundwater textbooks.
Based on the summary of the role of flowing wells on the evolution of many concepts and principles of groundwater hydrology, it is desirable that integrating the root of flowing wells into textbooks and courses of groundwater hydrology would inspire the interest of beginners, and also lead to a deeper understanding of the science of groundwater (Deming, 2016). Although the number of flowing wells has