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... The best-known (Chow, 1962) found that the highway departments of five plains states, including Kansas, listed Dun's table as an acceptable design method. ...

... The 1911 AREMWA report on waterway sizing stated that the Talbot formula had "been very generally adopted, particularly in the West and in the southwestern portion of the country." The highway departments of 25 states, including Kansas, listed the Talbot formula as an acceptable design method in the University of Illinois's 1953 survey of design practices (Chow, 1962). ...

... The Burkli-Ziegler formula The Burkli-Ziegler formula was the most popular of the early formulas for design discharge. The highway department of eight states listed the Burkli-Ziegler formula as an acceptable design method in the University of Illinois's 1953 survey of design practices (Chow, 1962). However, there is no indication that it was ever widely used in Kansas. ...

... Following Bell (1969), National Weather Services (NWS, 1982) isohyetal maps of United States. Froehlich (1975) summarized the standard IDF equations following the work of Chow (1962). More recent IDF studies in Nigeria (Nwaogazie and Uba, 2001).These IDF model are inadequate for determination of a represent 1972). ...

... Oguarekpe (2014) developed and compared three IDF models, using exponential, logarithmic and power models. These models are not the standard forms of IDF models (Chow, 1962). The present study is based on a satisfactory data length (17-35yrs) and the models developed are suitable for computer modeling of rainfall-runoff processes. ...

... Map of Study Area, Southern Nigeria Source:Chow (1962) ...

Rainfall-Intensity-Duration-Frequency (IDF) models developed using standard statistical bivari applied to estimate 5-, 10-,15-,20 0.083 to 24hrs. Two-parameter model parameter (general) models (Type models per station. The coefficient and 1.0; three-parameter model models range between 0.645 and 1.0 developed are useful and programmable runoff and flooding.

... Therefore, for ungauged catchments, in order to estimate T c , equations relating T c to the physical characteristics of the catchment have been used. Since the 1920s many researchers have developed empirical equations for predicting T c for ungauged catchments of varying size and physiography including: Williams (1922), Kirpich (1940), Chow (1962), Kennedy and Watt (1967), Williams (1968), Watt and Chow (1985), NRCS velocity method (1986) and Haktanir and Sezen (1990). With the exception of the NRCS velocity method, these equations were developed using regression analysis, with input parameters as watershed and channel parameters, which include watershed drainage area, channel length, watershed or channel slope, and watershed shape parameters. ...

... The parameters within Williams' equation include the drainage area of the basin (A), the equivalent diameter (D) of a circular basin with the same drainage area, the main channel length (L c ) and the main channel slope (S c ). Williams' equation is typically applied to watersheds with drainage areas less than 129.5 km 2 (Fang et al., 2008). Watt and Chow (1985) developed an equation to estimate T c that was based on basin data derived from previous studies including Kirpich (1940), Chow (1962), Kennedy and Watt (1967) and basins from Quebec. The collected data cover a wide range of basin size, from 0.5 ha to 5840 km 2 , and the basins are located across North Haktanir and Sezen (1990) developed two-parameter gamma and three-parameter beta distributions as synthetic unit hydrographs for ten watersheds in Anatolia, Turkey. ...

... These correction factors are based on the inverse slope of the regression line between the predicted and referenced values; Table 3 lists the correction factors for each of the equations. Williams (1922) 0.642 Kirpich (1940) 0.389 Chow (1962) 5.613 Kennedy and Watt (1967) 4.155 Watt and Chow (1985) 2.918 NRCS Velocity Method (1986) Not Applicable Haktanir and Sezen (1990) 1.620 ...

Accurate modelling of flood flow hydrographs in ungauged catchments is a challenging task due to large errors in the estimation of its response time using existing empirical equations. The time of concentration (Tc) is a key catchment response time parameter needed for forecasting of the peak discharge rate and the timing of the flood event. At least eight different definitions have been presented in the literature for the time of concentration. In this study, a new definition of “Reference Tc” is presented along with a practical procedure for its estimation using readily available basin catchment characteristic parameters with the aim of standardizing this key parameter for practitioners. Nine different empirical models were calibrated and tested on nine catchments of the Credit River watershed, Ontario, Canada to determine which method would provide the most accurate prediction of the Reference Tc. The NRCS velocity method (1986) proved once again to be the most reliable and an accurate method. This study shows that the main reason for the higher accuracy of the NRCS velocity method predictions compared to the empirical equations is attributed to the inclusion of the Manning's roughness coefficient.

... Graphical intensity-duration curves have been prepared for some locations in the United States on the basis of recorded rainfall ("Rainfall" 1955). Equations of various forms giving rainfall intensity as a function of duration are also available for many locations (Chow 1962;Wenzel 1982). However, rainfall intensity-duration relations for a specific location will often not be available and, consequently, will need to be developed. ...

... = an interpolation factor applied to the t-minute, 100year depth. Interpolation factors for selected reCurrence intervals between two and 100 years are presented in HYDRO-35 and are given in Table 2. Chow (1962) summarizes a number of rainfall intensity-duration equations that have been prepared for various locations throughout the United States and elsewhere. The four basic forms of equations are given in Table 3, and are referred to as equation types I, II, III, and IV. ...

A procedure for developing rainfall intensity-duration equations for short durations (less than 1 hr) for any location in the United States is described. The procedure uses readily available isopluvial maps developed by the National Weather Service for four regions of the United States: (1) The 37 eastern and central states; (2) the 11 conterminous western states; (3) Alaska; and (4) Hawaii. Rainfall depths for five durations less than or equal to 1 hr obtained for each of the regions were used to determine optimal values of parameters for four empirical forms of rainfall intensity-duration equations. An intensive pattern search over the potential range of parameters was used to obtain the optimal values. For the central and eastern states, optimal equation parameters depend on the ratios of 5- and 15-min rainfall depths to the 60-min rainfall depth at a site. These relations are displayed graphically. For each of the three other regions of the United States, a single set of parameters provides the best equation fit to the available rainfall data. The procedure will be useful in designing minor drainage structures using the well-known rational formula, which requires an estimate of rainfall intensity for a duration equal to the time of concentration of a catchment.

... Determination of the volume of surface runoff and how it is routed through a subcatchment is one of the key features of modern day computer based hydrologic models. There are a plethora of methods available for performing these calculations ranging in complexity from something as simple as the Rational Method (Chow, 1962) to the more physically based Gridded Surface/Subsurface Hydrologic Analysis (GSSHA) model (Downer and Ogden, 2004). Each of the methods requires different subcatchment properties such as area, slope, length, land use, % imperviousness and connectedness. ...

... Since the advent of computer technology, representation of urban catchments has fallen on computer models. Representation has evolved from simple back-of-theenvelope rational-method (Chow, 1962) and SewerGEMS (Haestad Methods, 2004). These simulation packages represent a stream of models that have been adapted to include state-of-the-art data management and GIS technologies. ...

What happens to the rain in highly urbanized catchments? That is the
question that urban hydrologists must ask themselves when trying to
integrate the hydrologic and hydraulic processes that affect the
hydrologic response of urban catchments. The Illinois Urban Hydrologic
Model (IUHM) has been developed to help answer this question and improve
understanding and prediction of hydrologic response in highly urbanized
catchments. Urban catchments are significantly different than natural
watersheds, but there are similarities that allow features of the
pioneering geomorphologic instantaneous unit hydrograph concept
developed for natural watersheds to be adapted to the urban setting.
This probabilistically based approach is a marked departure from the
traditional deterministic models used to design and simulate urban sewer
systems and does not have the burdensome input data requirements that
detailed deterministic models possess. Application of IUHM to the CDS-51
catchment located in the village of Dolton, Illinois, highlights the
model's ability to predict the hydrologic response of the catchment as
well as the widely accepted SWMM model and is in accordance with
observed data recorded by the United States Geological Survey. In
addition, the unique structure and organization of urban sewer networks
make it possible to characterize a set of ratios for urban catchments
that allow IUHM to be applied when detailed input data are not
available.

... The method used to calculate the mean slope is known as equivalent slope (S t ), proposed by Taylor & Schwarz (1952). Finally, the time of concentration (t c ) was calculated from the equations suggested by Kirpich (Kirpich 1940) and Ven Te Chow (Chow 1962) for ECW and the remaining watersheds, respectively. The choice of these t c equations was due to the compatibility between limitations for their applications and the watershed characteristics. ...

... t c ¹ -Chow (1962); t c² -Kirpich (1940). ...

Mathematical models have been widely used to quantify hydrological processes for various practical purposes. These models depend on geomorphological attributes which are derived from relief information represented by Digital Elevation Models (DEM). The objective of this study was to evaluate the influence of relief information sources (ASTER, SRTM-30, SRTM-90, and TOPO) over geomorphological characterization of five Brazilian watersheds. Geoprocessing tools were applied for extraction of the following geomorphological attributes for each DEM: drainage area, perimeter, and watershed slope; length and slope of the main stream; total length of streams; bifurcation, stream length and stream area ratios; and length of the highest order stream. The differences in the values of attributes were calculated in relation to the reference DEM (TOPO). It was found that: i) slope of main stream and bifurcation ratio were the most sensitive parameters regarding the relief information source; ii) flat watersheds were more susceptible to altimetric errors; iii) ASTER did not adequately represent drainage networks for flat watersheds, and iv) the differences in the geomorphological attributes increased as drainage area decreased. The results indicate that DEM may exert influence on the use of hydrological models that depend on geomorphological attributes.

... Dooge (1959) presented the general equations of the unit hydrographs by the assumption that the reservoir action in a catchment can be separated from translation. Chow (1962) evaluated three methods of determining a unit hydrograph: (1) a direct derivation from observed hydrographs; (2) hydrograph syntheses for a large number of observed hydrographs; and (3) a construction of hydrographs based on theory. ...

... In the classic models of hydrological engineering practice, unit hydrographs (UHs) are bell-shaped. In this paper, the theoretical construction model (Chow 1962) is applied to a simplified overland flow regime. Theoretical flow types are defined to support the flow conditions that determine the occurrence of the inflection point of the UH. ...

This study presents a conceptual model to obtain the shape of the unit hydrograph in a small rectangular basin with a collecting channel on one side of the flow plane. In classical hydrology, flows are classified as linear, convergent, and divergent. In the proposed model, a rainfall of constant intensity is assumed, with the duration equal to the time of concentration of the basin, as in the rational method. The shape of the plane is simplified in order to obtain an analytical solution. It is observed that in the plane of diffuse flow, the flow begins as a convergent of repletion, then passes to divergent of repletion, and finishes as a convergent of depletion. The applied theory allows the development of a classic bell-shaped unit hydrograph, a very common form of the theoretical hydrographs found in the literature. The proposed methodology was also applied to a practical flood damping problem in an urban watershed.

... Dooge (1959) presented the general equations of the unit hydrographs by the assumption that the reservoir action in a catchment can be separated from translation. Chow (1962) evaluated three methods of determining a unit hydrograph: (1) a direct derivation from observed hydrographs; (2) hydrograph syntheses for a large number of observed hydrographs; and (3) a construction of hydrographs based on theory. ...

... In the classic models of hydrological engineering practice, unit hydrographs (UHs) are bell-shaped. In this paper, the theoretical construction model (Chow 1962) is applied to a simplified overland flow regime. Theoretical flow types are defined to support the flow conditions that determine the occurrence of the inflection point of the UH. ...

This study presents a conceptual model to obtain the shape of the unit hydrograph in a small rectangular basin with a collecting channel on one side of the flow plane. In classical hydrology, flows are classified as linear, convergent, and divergent. In the proposed model, a rainfall of constant intensity is assumed, with the duration equal to the time of concentration of the basin, as in the rational method. The shape of the plane is simplified in order to obtain an analytical solution. It is observed that in the plane of diffuse flow, the flow begins as a convergent of repletion, then passes to divergent of repletion, and finishes as a convergent of depletion. The applied theory allows the development of a classic bell-shaped unit hydrograph, a very common form of the theoretical hydrographs found in the literature. The proposed methodology was also applied to a practical flood damping problem in an urban watershed.

... Por ejemplo, con un índice normal (n = 0,5), una lluvia de 60 mm en una hora se correspondería con una intensidad media máxima de unos 7,7 mm en un minuto, lo cual haciendo el cambio de unidades es 465 mm/h. Comparación entre diferentes acumulaciones, en función del índice de la precipitación, n, para el ejemplo de una lluvia de 60 mm en una hora El índice n ya ha sido empleado anteriormente para describir la distribución temporal de la precipitación extrema en Europa y América (Bernard, 1932;Chow, 1962;Ponce, 1989;Pizarro et al., 2003). Sin embargo el potencial de este índice es mucho mayor, ya que puede describir el comportamiento de cualquier precipitación, incluso de la precipitación moderada y débil. ...

RESUMEN A menudo se habla de precipitación intensa refiriéndose a la acumulación en una hora o en pocos segundos, incluso realizando comparaciones lineales entre ambas. Sin embargo el comportamiento natural de la precipitación hace que sea necesario hablar de una relación no lineal para referirse a cómo cambia la intensidad de la precipitación con el intervalo de tiempo medido. En ese sentido, este artículo intenta aproximarse a la descripción del índice n, que caracteriza la intensidad media máxima (IMM), según su comportamiento convectivo (acumulando un máximo de precipitación en poco tiempo, n cercano a 1) o advectivo (acumulando la precipitación regularmente, n cercano a 0). El estudio se realiza desde tres perspectivas diferentes: conjunto del planeta, Península Ibérica y Sur de Valencia – Norte de Alicante. El análisis matemático de las precipitaciones máximas mundiales desprende que éstas presentan una máxima eficiencia entre el origen convectivo y advectivo (n igual a 0,5). A partir del análisis climático del índice n en la Península Ibérica se pueden distinguir grandes zonas caracterizadas por máximos de lluvia de origen más tormentoso (interior peninsular) y áreas caracterizadas por máximos de lluvia de origen más frontal (suroeste, litoral atlántico y litoral mediterráneo), aunque con gran influencia aún de las tormentas (n generalmente superior a 0,5). Por último, para el Sur de Valencia – Norte de Alicante, se obtiene que el índice n es en general cercano a 0,35, exceptuando el caso de Sueca en 2008, con un índice n inferior a 0,2. Palabras clave: récord de precipitación, distribución de precipitación, clasificación de la precipitación, torrencial.

... 1964). Ven Te Chow (1962), who examined a large number of similar flood formulas, states that because of the personal judgement involved in using empirical formulas a solution should be sought by means of correlation analysis on a large number of data. The requirement lies in the operation of a sufficient number of catchments to carry out a satisfactory correlation analysis with a data collection programme that includes all major variables affecting flood discharges. ...

New Zealand has an extreme range of topography, geology and rainfall over a relatively small area, and with the explosive settlement of the European in the 19th century major erosion and flood problems arose. The classic investigation to find the effect of a changing land surface on some aspects of the hydrological cycle by the establishment of small Experimental Basins has so far not given a general prediction equation. Most Experimental Basins are operated merely to solve specific problems and no means are available for applying the results obtained from such basins to large areas. A method of research is outlined that aims at obtaining the data required to generate eventually such a prediction equation. This requires the operation of basic networks of Experimental and Representative Basins and the setting up of such networks in New Zealand is described. New Zealand comprises two elongated islands with a total area of 260,000 sq. km. It exhibits an extreme topographical and geological diversity and an extraordinari ly wide range of regional and local climates with a consequent marked variation in vegetation over very short distances. Some 16 % of the area has an elevation of >1 000 m; 57 % of the area lies between 200 and 1 000 m and only 27 % has an altitude of

... When surface runoff records are unavailable, as in the case of ungauged catchments, or if records are missing for various reasons from gauged catchments, surface runoff can be estimated by derived relationships. The most common techniques are correlation of runoff record with various catchment characteristics known as rainfall-runoff models [2]. ...

... Method 2 refers to the numerous procedures that are in common use for estimating peak discharges: Those of the Soil Conservation Service, Chow (1962), the Bureau of Public Roads (Potter, 1961), and the Rational method are a few examples. Shortcomings of these methods are significant. ...

... S and Q are very sensitive to precipitation inputs, with a reaction time within a 30 min period. This reaction time is consistent with the watershed 10-20 min concentration time calculated using classical empirical formulations (Kirpich 1940;Chow 1962;Watt and Chow 1985). ...

Peatlands occupy around 13% of the land cover of Canada, and thus play a key role in the water balance at high latitudes. They are well known for having substantial water loss due to evapotranspiration. Since measurements of evapotranspiration are scarce over these environments, hydrologists generally rely on models of varying complexity to evaluate these water exchanges in the global watershed balance. This study quantifies the water budget of a small boreal peatland-dominated watershed. We assess the performance of three evapotranspiration models in comparison with in situ observations and the impact of using these models in the hydrological modeling of the watershed. The study site (~1-km2) is located in the Eastern James Bay lowlands, Québec, Canada. During summer 2012, an eddy flux tower measured evapotranspiration continuously, while a trapezoidal flume monitored streamflow at the watershed outlet. We estimated evapotranspiration with a combinational model (Penman), a radiation-based model (Priestley-Taylor), and a temperature-based model (Hydro-Québec), and performed the hydrological modeling of the watershed with HYDROTEL, a physically-based semi-distributed model. Our results show that the Penman and Priestley-Taylor models reproduce the observations with the highest precision, while a substantial drop in performance occurs with the Hydro-Québec model. However, these discrepancies did not appear to reduce the hydrological model efficiency, at least from what can be concluded from a 3-month modeling period. HYDROTEL appears sensitive to evapotranspiration inputs, but calibration of model parameters can compensate for the differences. These findings still need to be confirmed with longer modeling periods.

... where P (t) is the maximum accumulation in a time t, and I(t) is the maximum average intensity in a time t. According to Chow (1962), he maximum average intensity can be adjusted as a triparametric function: ...

The Potential Distribution model can describe at once the probability distribution and temporal distribution of rainfall. It also allows the incorporation of the dependence of the probability with the number of independent stations. This paper analyzes the probability distribution and temporal distribution of extreme rainfall in the Autonomous Community of the Basque Country using daily data from 43 stations, with an average of 31 active stations between 1961 and 2000. It was found that this model provided a good adjustment (NMAE = 1.4%) for rainfall over 115 mm in 24 h, and is consistent with other analyses of extremes. Finally, the article proposes a mathematical relationship to estimate the maximum expected rainfall for a return period equal to or more than 10 years, with a duration longer than 1 minute, and for a given set of independent stations. This relationship depends on two exponents, one for the return period (m = 0.23 ± 0.02) and another for the duration (n = 0.63 ± 0.06). In addition, it also depends on a scale factor, which takes values between P o = 42 ± 2 mm to the south of the region and P o = 71 ± 5 mm to the north, with an average value for the Basque Country equal to 58 ± 2 mm.

... Intensity-Duration DD DD , 1948;Chow, 1962Bernard, 1932, 1961;Chen, 1975 DD DD Suda 1991 Sherman 2 Menabde et al. 1999 DD Sherman Sherman 1 Nguyen et al., 1998;Borga et al., 2005;Bougadis andAdamowski, 2006, Nhat et al., 2008a García- Bartual Table 1 Correlation coefficients between constants in the 10-year probable rainfall depth-duration equation. ...

The Talbot formula R=at/(t+b) and the Sherman formula R=ctⁿ were fitted as a rainfall depth-duration formula to the relation between probable rainfall depth and duration (DD relation), where R and t respectively represent the probable rainfall depth and the duration: a, b, c and n are constants.
Both value a/b in the Talbot formula and value c in the Sherman formula represent characteristics of short-duration heavy rainfall. The geographical distributions of the two values show large latitudinal differences. Both value b in the Talbot formula and value n in the Sherman formula represent the continuity of heavy rainfall. The geographical distributions of the two values are closely related to topography.
The DD relation is convex upward on a log-log plot. Therefore, the relation has a characteristic duration. This duration is definable as the duration for which the curvature of the logarithmically transformed Talbot equation is at its maximum [(1+√5)b/2] and can thereby be regarded as a continuous duration of heavy rainfall.
One-to-one correspondence between values b and n and between values b and a/c is provable analytically. Value a/c, as well as values b and n, represents the continuity of heavy rainfall.

... (2) Chow [1962], based on areas from 0.012 to 18.5 km 2 using data from 20 catchments in the United States; (3) the National Environmental Research Council [1975] for the United Kingdom; and (4) Watt and Chow [1985], based on data from 44 catchments across the USA. This formulation was developed for catchments with areas from 0.01 to 5840 km 2 , and for slopes of the main channel ranging from 0.00121 to 0.0978. ...

Evidence that extreme rainfall intensity is increasing at the global scale has strengthened considerably in recent years. Research now indicates that the greatest increases are likely to occur in short-duration storms lasting less than a day, potentially leading to an increase in the magnitude and frequency of flash floods. This review examines the evidence for sub-daily extreme rainfall intensification due to anthropogenic climate change, and describes our current physical understanding of the association between sub-daily extreme rainfall intensity and atmospheric temperature. We also examine the nature, quality and quantity of information needed to allow society to adapt successfully to predicted future changes, and discuss the roles of observational and modelling studies in helping us to better understand the physical processes that can influence sub-daily extreme rainfall characteristics. We conclude by describing the types of research required to produce a more thorough understanding of the relationships between local scale thermodynamic effects, large-scale atmospheric circulation and sub-daily extreme rainfall intensity.

... Bunun için 1938 yılında ilk defa Snyder [6] isimli araştırmacı tarafından havzanın yüzey şekilleri fiziki yapısına bakılarak sentetik BH üretilmiş ve günümüzde de yoğun bir şekilde kullanılmaktadır. Yukarıda bahsedilen yöntemlerin uygulamalarına dair daha ayrıntılı bilgileri Chow [7]'un eserinden edinmek mümkündür. ...

Bu çalışma Yavuz Sultan Selim Köprüsü’ne bağlantıyı sağlayan Kuzey Marmara Otoyolu’nun Ümraniye Alemdağ dere köprüsüne ait hidrolojik, hidrolik ve boyutlandırma hesaplarını içermektedir. Bu çalışmada kullanılan veriler Meteoroloji Genel Müdürlüğü (MGM)’nden alınmıştır. İstanbul’un 33 m rakımlı Göztepe yağış istasyonunda yapılmış ölçümler 1942-2007 arasında 66 yılın en yüksek yağışları olarak seçilmiştir. Üç ana adımdan müteşekkil bu uygulama çalışması için ilk aşamada yağış verilerinin trend (eğilim) analizleri gerçekleştirilmiştir. Bunun için Şen yöntemi ve Mann-Kendall sınaması ile trend analizi çalışması ortaya koyulmuştur. Elde edilen analiz sonuçlarına göre ikinci ana adımda olasılık ve yığışımlı (kümülatif) dağılım fonksiyonları kullanılarak ilgili grafikler ve sayısal sonuçlar hesaplanmıştır. Üçüncü ana adımda tasarım debisi hesaplama kısmına geçilerek ilgili havzada belli tekerrür aralığında düşecek yağış değerine göre toplanacak debi belirlenmiştir. Tasarım debisi hesaplama yöntemleri Snyder yapay birim hidrograf yaklaşımı ve DSİ yöntemi kendisinde barındırdıkları tepe (pik) debi ile bu çalışma için yeterli olmuştur. Kanalın debi kapasitesinin hesaplaması ise klasik Manning denklemi ile yapılmıştır.

... Equation (1) was initially proposed by Sherman [33] when studying precipitation in the Boston area. Equation (2) was studied by Chow et al. [34]. Note that these two equations do not have a return period as the input and thus can be used for a specific return period only. ...

Climate change is one of the prominent factors that causes an increased severity of extreme precipitation which, in turn, has a huge impact on drainage systems by means of flooding. Intensity–duration–frequency (IDF) curves play an essential role in designing robust drainage systems against extreme precipitation. It is important to incorporate the potential threat from climate change into the computation of IDF curves. Most existing works that have achieved this goal were based on Generalized Extreme Value (GEV) analysis combined with various circulation model simulations. Inspired by recent works that used machine learning algorithms for spatial downscaling, this paper proposes an alternative method to perform projections of precipitation intensity over short durations using machine learning. The method is based on temporal downscaling, a downscaling procedure performed over the time scale instead of the spatial scale. The method is trained and validated using data from around two thousand stations in the US. Future projection of IDF curves is calculated and discussed.

... If the base flow at the time of the peak runoff is Qb, then the design peak runoff is Q d = Q + Qb Chow (1962) stated that "Although the procedure illustrated in this report was prepared for design conditions in Illinois, the concept of the method is universally applicable to other states provided adequate data in these states are available for similar analysis and development". ...

... However, depending on the climatic and hydro-geomorphic differences the coefficient and the exponent varies significantly. For example, Kirpich [43] derived α as 0.00032 and β as 0.77, Chow [44] derived α as 0.0012 and β as 0.64, Kennedy and Watt [45] derived α as 0.00018 and β as 0.75, Natural Environment Research Council [46] derived α as 0.0215 and β as 0.47. For the present case, the algorithm of Dickens as mentioned by Alexander [47] has been embraced as it was developed to compute the peak discharge (Q) of the then Bengal province of India. ...

The Mayurakshi River Basin (MRB), one of the most flood-prone areas of India, registers flood almost every year. The present work intends to identify the relative capacity of the tributary basins of the Mayurakshi system (three sub-basins of Dwaraka, two of Kuye and eight of Mayurakshi) to induce flood in its lower stretch. Based on basic morphometric parameters (basin length, area, perimeter, relief, stream number, and length) computed from Survey of India topographical maps (1:50,000) and SRTM DEM (30 m) using ArcGIS 10.4 software, we have derived 15 morphometric indices (linear-2, areal-7
and relief-6). The principal component analysis (PCA) depicts that there are three clusters of indices on the varimaxrotated component plot with the centroid of the distribution in positive–positive (++) quadrant which signifies a peak flow. Besides, the bi-variate relations between basin lag time and different morphometric indices signal that all the variables except compactness coefficient, hypsometric integral, dissection index, and bifurcation ratio portray negative relations implying peak flow instead of sustained one. In this paper, we have developed a technique called the flood-inducing capacity index (FCI) to measure the contribution of a tributary river to its master based on the morphometric coefficient and basin area coefficient. The FCI depicts that sub-basin Mayurakshi-6 has topped the list with ~ 21% contribution to MRB flood while Mayurakshi-8 having less than 2% contribution lies at the bottom. Besides, Dwaraka-3,Dwaraka-1 and
Mayurakshi-3 basins each having more than 8% contribution control flood in the lower stretch of the Mayurakshi system. A statistically significant positive correlation (R2 = 0.75) between the maximum discharge measured for the nine sub-basins and the FCI and the area under curve (0.889) on ROC plot ground the validation of the proposed method.

... In the Rational Method, ta is assumed to be a constant. However, Chow (14,15) and , Reich and Hiemstra (16) runoff analysis in which ta is allowed to vary to produce a maximum peak discharge for a rainfall of a given frequency. While these methods have an interesting basis, the writer is unable to determine any advantage to a statistical extension of these methods over a statistical extension of the Rational Method. ...

... However, models based on plot data have been used to estimate the effect of agriculture on flood regime. For example, using empirical relationships developed by Chow [1962], Knox [1977] estimated that the magnitude of floods that recur more frequently than once in ten years in the Platte River of southwestern Wisconsin increased by a factor of three to five as a result of agricultural development. The timing of large flow events also changed. ...

This book concentrates on the development and evolution of fluvial
systems by natural and human processes, highlighting new insights and
knowledge about the concept of magnitude and frequency, effects of
land-use, and effects of human regulation of streamflow. The papers
describe new research developments and approaches to understanding the
origins of channels, water and sediment movement on slopes and in
streams, the magnitude and frequency of physical processes that affect
water and sediment movement, and the implications of these processes for
policy decisions such as stream restoration. This is an appropriate time
to pause and evaluate what is known about the hydrologic interactions of
natural processes, changing land-use, and forced physical constraints on
hillslope and fluvial systems. The recent emphasis on ecosystems by the
federal government, and the inseparable connection to hydrology, make
these prime subjects to ponder in this volume. Included are papers that
directly address some of the most difficult and pressing issues related
to the role of geomorphology in strategic science.

... As one can see in Figure 3b, the resulting formula is better adapted to large basins than previous ones [Kiprich, 1940; Figure 3. Time-to-peak (t p ) calculation : (a) example of the automated method to define observed t p from hydrographs and (b) comparison of estimated and observed time-to-peak values derived from different equations. Chow, 1962;Natural Environment Research Council, 1975;Watt and Chow, 1985] when t p estimates are compared against observations at gauging stations located within the Amazon Basin. This is explained by the fact that previous equations were derived for small catchments. ...

[1] Research on actual requirements for a numerically consistent representation of flow dynamics in large-scale river-flood models are needed to improve both modeling performance and computational efficiency. Still, regional- and global-scale characterizations of river hydrodynamics are absent. A first attempt to map river hydrodynamics in the Amazon Basin is presented. Flood wave type maps at 0.25° spatial resolution are derived from a classification method based on the analysis of Saint-Venant equation terms. Global river geometry data sets derived from both digital elevation models and empirical equations supported by stream gauge observations are used as input variables. Errors of input variables are estimated, and a sensitivity analysis is performed. Results show that 64.5% of rivers (headwaters and high-slope rivers) can be represented by the kinematic wave (KI), 34.5% (main Amazon tributaries, low slope, and wetland regions) by the diffusive wave (DF), and 1% (lower Amazon) by the full Saint-Venant equations (SV). In a rigorous scenario, i.e., a case where the most restricted classification of each grid cell is considered, ∼33% is classified as KI, ∼62% as DF, and ∼5% as SV. Most of the basin presents subcritical flow with very low Froude number (Fr), while the Andean region is dominated by larger Fr values and supercritical flow can be found. According to our evaluation mostly based on in situ data, the map has a percentage of detection of 83.4%.

... However, models based on plot data have been used to estimate the effect of agriculture on flood regime. For example, using empirical relationships developed by Chow [1962], Knox [1977] estimated that the magnitude of floods that recur more frequently than once in ten years in the Platte River of southwestern Wisconsin increased by a factor of three to five as a result of agricultural development. The timing of large flow events also changed. ...

Agricultural development of the United States profoundly altered
hydrologic processes, resulting in severe degradation of aquatic
ecosystems. The conversion of natural landscapes to agricultural lands
increased the peak and volume of surface runoff, causing massive soil
erosion, stream channel enlargement, and introduction of enormous
quantities of fine-grained sediment to lakes, streams, floodplains, and
wetlands. During the years following the creation of the U.S. Soil
Conservation Service in 1935, the gradual adoption of conservation
practices resulted in significant reductions in surface runoff, soil
erosion and sediment transport, as well as increases in baseflow. This
amelioration of agricultural impacts is not well documented in most
areas. More recently, increasing yield pressures, loss of soil
fertility, and poor nutrient management have resulted in excess
agricultural fertilizer use. Today, by adopting appropriate agricultural
practices, it is possible to greatly reduce, and in some cases
eliminate, adverse impacts of agriculture. However, the historical use
of damaging agricultural practices has left a lasting legacy in many
regions. Some of these legacies, such as channel straightening, can and
have been reversed by restoration. Others, such as fine-grained sediment
in streams, channels disconnected from their floodplains, and
eutrophication due to excess nutrients, are much more difficult to
reverse and represent a fundamental change in riparian habitat.
Restoration of this habitat is infeasible in many situations.

... Permeability, evaporation velocity, drainage rate and the retention property of pervious pavements are largely dependent on the size of surface voids and the particle size distribution of the sub-base layer (Andersen et al., 1999;James & Shahin, 1998). The runoff coefficients estimated in this study ranged from 0, 15 to 0, 30, versus a runoff coefficient of 0, 95 for standard asphalt (Chow et al., 1962). Brattebo and Booth (2003) examined the long-term efficiency of pavement permeability in Renton, Washington. ...

Permeable pavements are among the most effective alternative solutions for sustainable stormwater management. They decrease impervious surfaces in urban areas, reduce the risk of flooding under high rainfall conditions and protect the natural environment against stormwater pollution. In a view to ensuring sustainable stormwater management, a new eco-material has been designed for producing permeable pavements. This material is a mixture of construction wastes (crushed concrete) and organic matter (compost). The crushed concrete is the structural support and the compost is used for retention and the biological treatment of stormwater pollution. The purpose of the research work presented in this paper was to evaluate the hydrodynamic behaviour of a new permeable pavement material under high rainfall conditions. The experimental approach adopted for this research study is a temporal moment analysis. Therefore, for the experimental study, we simulated high rainfall with a return period of 10 years (Torreilles in 2001, France). The rainfall data were provided by Meteo France. The rainfall was maintained at an intensity of 126 mm/h, corresponding to a flow rate of 16 l/h at laboratory apparatus scale. Then, the flow rate was increased three times, to 25 l/h, 50 l/h and finally 100 l/h to subject the material to extreme conditions.

... Rainfall intensity-duration equations of various forms have been developed for many cities throughout the United States [see, for example, Chow (1962) and Wenzel (1986)1. One of the most widely used forms is ...

Design of a stormwater pump station is a complicated procedure because of the large number of parameters that are involved. Even the most basic pump station serving a small catchment requires a computationally intensive iterative evaluation. However, the design problem consists primarily of finding the combination of temporary storage and pump capacity that accommodates runoff of the selected recurrence interval for the least cost. A procedure is developed for rapidly obtaining the needed relation between storage volume and discharge for small pump stations where a constant outflow can be assumed and the inflow hydrograph can be represented using the modified rational method with rainfall given by a widely-used intensity-duration equation. Accepting the limitations of the modified rational method and the simplifications applied to pump station operation, the procedure provides an uncomplicated way of rapidly finding the stormwater runoff volume that needs to be temporarily stored for given values of pump discharge and activation water level (or, equivalently, activation storage volume). Ultimate determination of temporary runoff storage will depend on an economic analysis of the trade-off between storage volume and pump capacity.

... The simplest type of these models is a relationship between i (rainfall intensity) and t (rainfall duration) for a given frequency. Chow [3] ...

Rainfall intensity at different durations and frequencies (IDF curves) are widely needed in nearly all water projects, e.g., culverts, urban drainage, etc. However, IDF curves are reported at discrete durations and frequencies. To avoid subjective decisions, however, IDF models have been developed and are used universally. In this article, the performance of five commonly used IDF models is analyzed for three synoptic stations in Iran. The results show that there is an overall acceptable performance for all models, as far as the prediction of rainfall intensity from duration and frequency is concerned. However, from a probabilistic point of view, the non-negativity of a cumulative distribution function is not satisfied. Therefore, the non-negativity concept was added as a constraint. Consequently for this case, the performance of the models decreased considerably. It seems that all IDF models currently in use are not efficient, yet more efficient models must be developed to take into account all characteristics of the phenomena.

In any urban area it is necessary to provide a collection system for the efficient and effective collection of the sewage generated from that locality and convey it to a point where treatment will be given to this collected wastewater to facilitate reuse of it or safe disposal of it either in water body or on land.

In the 19th and early 20th centuries, American civil engineers sized bridges and culverts by empirical methods based on the observed performance of existing structures during floods. Most of these early methods provided a direct estimate of the required waterway area rather than a design discharge. No particular recurrence intervals were associated with the designs. The shortcomings of these early design methods stemmed more from a shortage of useful hydrologic data than from an inadequate understanding of the relevant factors. The first reliable rainfall frequency maps for durations shorter than 24 hours were published in 1935. Advances in frequency analysis in the 1940s led to the development of regional flood-frequency methods for ungaged streams. The 1950s marked the transition to modern frequency-based hydrologic methods in design practice.

Über den Amplitudengang eines Verzögerungsglieds 2. Ordnung wird ein einfaches Modell für den Scheitelabfluss eines Hochwassers, ausgelöst von einem isolierten, zeitbegrenzten Starkniederschlag, hergeleitet. Die Überlegungen führen zum Amplitudengang eines Verzögerungsglied 1. Ordnung (PT1, Tiefpass 1. Ordnung) dessen Argument, bestehend aus dem Produkt aus der Kreisfrequenz ω und der Zeitkonstante des Systems T, lediglich durch der den Quotient to/d = Δ aus Verzögerungszeit to und Regendauer d, zu ersetzen ist.

Understanding the effects of land use change on the hydrological cycle is very important for development of sustainable water resource in an upland field catchment. In this study, soil and hydrological properties in an upland field catchment, which was reclaimed partially from a forest catchment, were compared with another forest catchment. The soil properties of surface and subsurface layers were investigated in the two catchments. The soil was compacted and waterholding capacity of soil in the upland field catchment became smaller after the reclamation from forest to upland field, which decreased infiltration rate and water storage in the soil layers.We found that peak discharge and direct runoff in the upland field catchment increased compared with the forest catchment. Annual evapotranspiration from the upland field catchment tended to be lower due to the change in vegetation type and soil properties. Furthermore, a semi-distributed hydrological model was applied in the upland field catchment to understand the integrated effects of reclamation on the hydrological cycle. The model parameters, which were determined using a nonlinear optimization technique-the Shuffled Complex Evolution method (SCE), were compared between the two catchments. The Nash and Sutcliffe coefficient was used to evaluate the model performance. The simulated results indicated that evapotranspiration was decreased and change in discharge was more obvious in the surface layer. We considered that declined infiltration and water storage and increased peak discharge and direct runoff have a negative impact on water resources in the upland field catchment. This study will provide information for forest managers in planning and making decisions for land and water resource management.

Hydrology is the science that describes the occurrence of water on earth, its areal and temporal distribution, and its quantitative and qualitative aspects. It is estimated that approximately 97% of all the water in the world -1.2 × 1018 m3—is in the oceans. The remaining 3%, or about 4 × 1016 m3, is fresh water that may be usable for irrigating lands. More than 3/4 of the fresh water cannot be developed and utilized with the current technology: 3 × 1016 m3 is frozen into polar ice caps and mountain glaciers, and more than 4 × 1015 m3 is estimated to lie in aquifers at depths exceeding 800 m below the ground surface, leaving only about 4.4 × 1015 m3 that could be used each year for the benefit of mankind. The available amount is divided between surface water (rivers, streams, freshwater lakes), groundwater (to a depth of 800 m below the ground surface), and atmospheric water (atmospheric moisture, clouds, etc.) as follows:
Surface water
0.13 × 1015 m3
Groundwater
4.27 × 1015 m3
Atmospheric water
0.01 × 1015 m3
Total
4.41 × 1015 m3

The time of concentration is a fundamental parameter in many hydrological models. Nowadays there is no universally accepted definition for such parameter. However, many definitions and estimation procedures can be found in the technical literature. After an extensive bibliographic review, the current study brings up the variability of empiric methodologies used in its estimations. Thirty empiric methodologies were listed and estimations of time of concentration were performed by applying such methodologies using data from a rural watershed. The hierarchical cluster analysis (Cluster) was applied in order to assess the similarity degree among the selected methodologies. Among all methodologies, Pasini’s and Ventura’s are the ones that present higher similarity to each other, whereas Pasini and Arizona DOT show stronger dissimilarities to each other.

The Talbot formula R = at /(t + b) and the Sherman formula R = ctⁿ were fitted to the relation between probable rainfall depth and duration, where R and t respectively represent the probable rainfall depth and the duration, and a, b, c, and n are constants.
On the whole, value n in the Sherman equation and value b in the Talbot equation, both of which represent the continuity of heavy rainfall, respectively decreases and increases as the durations in a duration range increase. However, the variations of the values with the duration range are markedly different among stations.
When the magnitude of the variation of a constant in a rainfall depth-duration formula with the duration range is expressed by the coefficient of variation, a strong negative correlation can be found between the coefficients of variation of the constants in the Talbot and the Sherman formulas.
For durations in a duration range that are short (e.g., 1-24 h) or long (e.g., 10-72 h), the number of stations at which the Sherman formula provides the better fit is greater. For durations in a duration range that are medium (e.g., 3-40 h), the number of stations at which the Talbot formula provides the better fit is greater. The constants in a rainfall depth-duration formula that provides the better fit vary little with the duration range. In southern and northern Japan, respectively, the Sherman and the Talbot formulas provide the better fit.

Empirical cross-hazard analysis and prediction of disaster vulnerability, resilience, and risk requires a common metric of hazard strengths across hazard types. In this paper, the authors propose an equivalent intensity scale for cross-hazard evaluation of hazard strengths of events for entire durations at locations. The proposed scale is called the Murphy Scale, after Professor Colleen Murphy. A systematic review and typology of hazard strength metrics is presented to facilitate the delineation of the defining dimensions of the proposed scale. An empirical methodology is introduced to derive equivalent intensities of hazard events on a Murphy Scale. Using historical data on impacts and hazard strength indicators of events from 2013 to 2017, the authors demonstrate the utility of the proposed methodology for computing the equivalent intensities for earthquakes and tropical cyclones. As part of a new area of research called hazard equivalency, the proposed Murphy Scale paves the way toward creating multi-hazard hazard maps. The proposed scale can also be leveraged to facilitate hazard communication regarding past and future local experiences of hazard events for enhancing multi-hazard preparedness, mitigation, and emergency response.

Genome editing, or genome engineering, or gene editing, is a type of genetic engineering in which DNA is inserted, deleted, modified, or replaced in the genome of a living organism. Unlike early genetic engineering techniques that randomly insert genetic material into a host genome, genome editing targets the insertions to site-specific locations.
In 2018, the common methods for such editing used engineered nucleases, or "molecular
scissors". These nucleases create site-specific double-strand breaks (DSBs) at desired locations in the genome. The induced double-strand breaks are repaired through nonhomologous end-joining (NHEJ) or homologous recombination (HR), resulting in targeted mutations ('edits').
As of 2015 four families of engineered nucleases were used: meganucleases, zinc finger nucleases (ZFNs), transcription activator-like effector-based nucleases (TALEN), and the
clustered regularly interspaced short palindromic repeats (CRISPR/Cas9) system. Nine
genome editors were available as of 2017.

The time of concentration (Tc) is the main hydrological parameter used to characterize the response of a given Hydrological Response Unit (HRU) to a precipitation event. Because of its importance, the determining Tc is an integral step in several studies involving runoff. Thus, this work presents an unprecedented review of the application of Tc in different lines of research involving water resources around the world. In this article, 1252 publications were listed, obtained from seven different databases, published by 2020, that presented the expressions “time of concentration,” “runoff,” and “watershed.” The articles and conference papers obtained in this research were classified into 12 topics. The number of publications per topic and per country was measured and a cluster analysis was developed to verify the similarity of the distribution of topics per country. In addition, 125 equations applied in related publications for the estimation of Tc are also listed.
Graphical abstract

O semiárido brasileiro é acometido por condições climáticas extremas, em que o baixo índice e a irregularidade das chuvas são fatores que intervêm negativamente no seu desenvolvimento. Logo, encontra-se na captação de água das chuvas uma alternativa importante para a região, sendo possível aumentar o volume de água disponível mediante o aproveitamento do regime pluvial. O objetivo principal desse trabalho foi estimar os Volumes Potenciais de Captação de Água da Chuva (VPC) para a área urbana do município de São João do Cariri. Estes volumes foram aferidos com base na proposta de utilização das superfícies impermeáveis da cidade como áreas de captação de água das chuvas, para fins não potáveis. A estimativa é de suma importância para o dimensionamento adequado de cisternas, de modo a garantir o suprimento das demandas não potáveis de água da cidade, durante o período de estiagem.

The performance and durability of wall assemblies are greatly affected by the moisture load to which they may be subjected, in particular those arising from Wind-Driven Rain (WDR). Standard approaches for estimating such moisture loads assume 1% of the WDR load, whereas these loads have also been assessed from watertightness tests, although these assumed loads have been determined based on limited climate information. To more accurately estimate the moisture loads to which wall assemblies may be subjected over their service life, an analysis of historical WDR loads was completed for 11 cities across Canada. The magnitude, probability of occurrence of WDR loads in different cities and correlations between WDR related climate parameters, are discussed in this paper. Also, a novel WDR severity index is introduced, referred to as the Wind-Driven Rain Pressure Index, to permit quantifying the real-time and simultaneously occurring effects of WDR intensity and Driving Rain Wind Pressure (DRWP). To estimate the WDR intensity and DRWP with a specific probability of occurrence, an Extreme Value Analysis (EVA) was completed for a climate dataset of 31 years (1986–2016) using the Generalized Extreme Value and Gumbel distributions.

During a period of nearly three decades from the 1950s to the 1970s at University of Illinois, Urbana-Champagne, Professor Ven Te Chow made many major technical contributions that changed the landscape of hydrology, hydraulics, and water resources engineering. These contributions encompass a broad spectrum of areas, including (1) deterministic hydrology, (2) stochastic hydrology, (3) open-channel hydraulics, and (4) water resources. In addition, he greatly contributed to the advancement of the entire water resources area through education, supervision of outstanding graduate students, mentoring of junior colleagues, technology transfer by consulting and lecturing, editorships of journals and book series, organization and direction of conferences, professional service, and founding of International Association of Water Resources. This paper reflects on Chow's contributions and concludes that our profession is better off today because Chow graced the profession for three decades. He was an outstanding scholar, an extraordinary researcher, a renowned educator, and a water resources engineer par excellence. His accomplishments have inspired generations of water resources professionals. The paper concludes with a personal note.

Time of Concentration is the period required for the water that have precipitated at the farthest point of the river basin to move to its main section, which is a key parameter for urban drainage. However, it is difficult to obtain this variable from observations, thus there are several empirical equations that can be used to calculate this period. One of the most used methods in Brazil is Kirpich (1940) that was originally adjusted to seven small mountainous basins of the USA and is therefore not recommended for other circumstances. In this work, the difference between the tc observed and the one calculated by Kirpich was verified in the Gregório (SP) and Prado Velho (PR) basins, observing variations of 227% and 59%, respectively. Subsequently, a sensitivity analysis of the method was performed and the most sensitive parameter was calibrated, taking the data from the two basins together, obtaining a reduction of the error to 70% and 26%, while an individual calibration for each location provided errors of 19% in the Gregório basin and 12% in the Prado Velho. The peak flows with calculated tc showed a maximum error of 49%.

There are different flood discharge calculation methodologies that have started more than 100 years ago, and most of the first ones are based on logical and rational thinking. The very early ones do not include any information because there were no rain gauges established at that time. As already mentioned in the previous section, they were all related to drainage area nonlinearly without any further consideration of the surface features as soil type, land use, etc., or rainfall characteristics. Reliability of these early methodologies is discussed with comparison to the present most advanced techniques. For flood discharge estimations and preliminary appreciation of the magnitude, flood envelop curves are presented, and their usage procedures are given for different parts of the world again in comparative manner. For the application of rational methods (RMs) in arid regions, empirical runoff coefficient formulation is presented with applications to some of the drainage basins in the southwestern corner of the Arabian Peninsula. Irrationality of the RM is explained, and instead, a new and innovative modification of it is presented with application example. Practical surface water discharge calculation methods are presented on the basis of different ration based on the drainage area, mean flow, and standard deviation of the flow records.

Protection against floods is possible by construction of some engineering structure, but their dimensioning needs to scientific calculations, where flood design discharge plays the major role. The definition of flood design discharge is given with different choices including probable maximum flood (PMF) as explained in Chap. 2, standard project flood, flood of a specific return period, and the use of intensity-duration-frequency curves. The causes of floods are explained in terms of landslides, rock falls, debris flow, and sediment yieldwith suitable calculation methodologies and design methodologies.

Hydrological modeling is an important tool to manage water resources, allowing a better
understanding of a water system, complementing existing observations and a response
simulation of this system under different conditions. Due to the complexity and
heterogeneity of a natural system like a watershed, the importance and relevance of the
integration of hydrological models with geographic information systems (GIS) is well
known. Among the integration strategies the complete integration presents more
advantages, and besides making the hydrological simulations more sophisticated, it also
optimizes the processes due to the logical and physical proximity between the
subsystems. Since the late 1990s, the possibilities of this type of integration have been
widened due to the increase in the availability of free and open source geospatial software
with possibilities of functionalities customization through scripts in several programming
languages. Among the available software, QGIS stands out as one of the most promising
desktop GIS in the open source environment, and has the largest FOSS4G.user
community. Thus, considering that traditionally the concepts of spatial analysis optimize
the hydrological simulations, the benefits of the use of free GIS, the resources limitations
and the lack of data availability in projects related to water resources management and
urban drainage in Brazil, this work developed a computational tool (plugin) with an intuitive
interface that integrated a hydrological model with the QGIS, focused on the Brazilian
reality. The full coupling strategy used for integration enabled the hydrological model to
directly rely on the GIS functionality, allowing the rapid and automatic realization of a large
volume of simulations, from which it was possible to analyze the behavior of selected
urban basins for different hydrological scenarios.

The present study showed the influence of lithology-controlled hydraulics on pothole evolution. For this study, using tools of geometry, mathematics, and statistics, the morphology (depth and diameter of aperture) of a sample of 135 potholes has been analyzed from Ghagra waterfall of Tarafeni River, Belpahari, West Bengal, India. It was found that the depths of potholes are proportional to their diameter (\(h = 0.97{{D}}^{0.97}\)). Equal percentile distribution of depth and average diameter indicate the consistent rate of evolution of diameter along with depth. Out of total potholes, only 1.5% are circular and 41.48% are near circular while ~ 57% of potholes are either oval or elongated. Variability in diameter (CV = 0.79) of potholes is lesser than variability in the depth (CV = 1.12). The orientation of joints significantly determines the orientation of the major axis of potholes’ diameter. Flow duration and distance from the active channel have a role in determining the size of potholes. Potholes are very common in dyke-controlled hydraulics environments. Initial seminal depression is essential for the origin of potholes. The evolution of potholes passes through sequential phases of distinct characteristics of aperture diameter/depth ratio, rates of deepening and widening, and coalescence. This study will widen the avenue for further research on the model of pothole formation and will enable replicating this evolutionary model in like situation.

In the last few years, as research attention in the earth and atmospheric sciences has been turned toward the flows and storages of energy and matter in the shells of our planet, much basic knowledge has been obtained that can be organized into three frameworks, whose locus is the earth's surface, in its variegated small-scale mosaics, its continental patterns and global distributions, its solar rhythms, episodic interruptions, and modifications by man. These three frameworks are the budget of radiant energy exchange, its higher echelon neighbor the balance of energy or heat, and the balance of water as a particular form of matter. The frameworks share a common accounting procedure that expresses their continuity as special cases of the laws of conservation of mass and energy, and that provides an efficient means of organizing a large volume of information about the individual fluxes and storages at the surface, and about the surface itself in its areal differentiation over the globe. These frameworks serve earth scientists well, first, as a unifying center for physical geography, second, as a means of comparing regions, and third, as a means of evaluating the modifications on the earth's surface brought about by man. The surface of the land, augmented by the biosphere, variegated by its geology, dissected by streams, mantled with a medium that stores heat and water, plays an important role in the balances of energy and matter. The role of the surface also varies, in response to changes in its own character, which affect the reception of the incoming fluxes, the access to storage, and the release of stored energy or water. The value of the heat and water budget in presenting a coherent scheme of physical phenomena to university classes has been demonstrated in this chapter; its value in research has been shown in specific regions.

A practical numerical method has been developed for storm hydrograph
analysis that allows variation of unit response functions during
multiple periods of runoff producing rainfall. Previous methods of
analytical derivation of unit responses from multiple period storms
require superpositional linearity. This requirement is eliminated by
substituting two stages of convolution for the conventional single stage
process of storm hydrograph generation. The first stage convolves a
fixed area-characteristic function with a variable state function. The
state function is determined by streamflow and differs for each
increment of effective rainfall. First stage convolution thus produces a
different unit response for each increment. The second stage convolves
the variable unit responses and the effective rain increments. Validity
of the technique is demonstrated by applying the analytical model to 10
complex storms. The conceptual components of area-characteristic,
area-state, and variable response functions resulting from the analyses
are seen to be hydrologically rational.

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