A measure of watershed nonlinearity: interpreting a variable instantaneous unit hydrograph model on two vastly different sized – watersheds

Abstract. This paper reviews the use of an input-dependent kernel in a linear convolution integral as a quasi-nonlinear approach to unify nonlinear overland flow, channel routing and catchment runoff processes. The conceptual model of a variable kernel or instantaneous unit hydrograph (IUH) is characterized by a nonlinear storage-discharge relation, q=cNsN where the storage exponent N is an index or degree of watershed nonlinearity. When the causative rainfall excess intensity of a unit hydrograph is known, parameters N and c can be determined directly from its shape factor, the product of the unit peak ordinate and the time to peak. The model is calibrated by the shape factor and verified by convolution integral on two watersheds of vastly different sizes, each having a family of four or five unit hydrographs, data of which were published by Childs in 1958 for the Naugatuck River and by Minshall in 1960 for the Edwardsville catchment. For an 11-hectare catchment near Edwardsville in southern Illinois, the US, four moderate storms show an average N value of 1.79, which is 7% higher than the theoretical value of 1.67 by Manning friction law, while the heaviest storm, which is three to six times larger than the next two events in terms of the peak discharge and runoff volume, follows the Chezy law of 1.5. At the other end of scale, for the Naugatuck River at Thomaston in Connecticut, the US, having a drainage area of 186.2 km2, the average N value of 2.28 varies from 1.92 for a minor flood to 2.68 for a hurricane-induced flood, all of which lie between the theoretical value of 1.67 for turbulent overland flow and that of 3.0 for laminar overland flow. Short examples and a spreadsheet template are given to illustrate key steps in generating the direct runoff hydrograph by convolution integral with the 2-parameter variable IUH model.

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A measure of watershed nonlinearity: interpreting a variable instantaneous unit hydrograph model on two vastly different sized watersheds

Hydrology and Earth System Sciences ◽

10.5194/hess-15-405-2011 ◽

2011 ◽

Vol 15 (1) ◽

pp. 405-423 ◽

Cited By ~ 12

Author(s):

J. Y. Ding

Keyword(s):

Shape Factor ◽

Overland Flow ◽

Scale Parameter ◽

Computational Time ◽

Convolution Integral ◽

Unit Hydrograph ◽

Time Step ◽

N Value ◽

Instantaneous Unit Hydrograph ◽

The Impact

Abstract. The linear unit hydrograph used in hydrologic design analysis and flood forecasting is known as the transfer function and the kernel function in time series analysis and systems theory, respectively. This paper reviews the use of an input-dependent or variable kernel in a linear convolution integral as a quasi-nonlinear approach to unify nonlinear overland flow, channel routing and catchment runoff processes. The conceptual model of a variable instantaneous unit hydrograph (IUH) is characterized by a nonlinear storage-discharge relation, q = cNsN, where the storage exponent N is an index or degree of watershed nonlinearity, and the scale parameter c is a discharge coefficient. When the causative rainfall excess intensity of a unit hydrograph is known, parameters N and c can be determined directly from its shape factor, which is the product of the unit peak ordinate and the time to peak, an application of the statistical method of moments in its simplest form. The 2-parameter variable IUH model is calibrated by the shape factor method and verified by convolution integral using both the direct and inverse Bakhmeteff varied-flow functions on two watersheds of vastly different sizes, each having a family of four or five unit hydrographs as reported by the well-known Minshall (1960) paper and the seldom-quoted Childs (1958) one, both located in the US. For an 11-hectare catchment near Edwardsville in southern Illinois, calibration for four moderate storms shows an average N value of 1.79, which is 7% higher than the theoretical value of 1.67 by Manning friction law, while the heaviest storm, which is three to six times larger than the next two events in terms of the peak discharge and runoff volume, follows the Chezy law of 1.5. At the other end of scale, for the Naugatuck River at Thomaston in Connecticut having a drainage area of 186.2 km2, the average calibrated N value of 2.28 varies from 1.92 for a minor flood to 2.68 for a hurricane-induced flood, all of which lie between the theoretical value of 1.67 for turbulent overland flow and that of 3.0 for laminar overland flow. Based on analytical results from the small Edwardsville catchment, the 2-parameter variable IUH model is found to be defined by a quadruplet of parameters N, c, the storm duration or computational time step Δt, and the rainfall excess intensity i(0), and that it may be reduced to an 1-parameter one by defaulting the degree of nonlinearity N to 1.67 by Manning friction. For short, intense storms, the essence of the Childs – Minshall nonlinear unit hydrograph phenomenon is encapsulated in a peak flow equation having a single (scale) parameter c, and in which the impact of the rainfall excess intensity increases from the linear assumption by a power of 0.4. To illustrate key steps in generating the direct runoff hydrograph by convolution integral, short examples are given.

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COMPARISON OF DIMENSIONLESS UNIT HYDROGRAPHS IN THAILAND AND TAIWAN

Hydrology Research ◽

10.2166/nh.1971.0002 ◽

1971 ◽

Vol 2 (1) ◽

pp. 23-46 ◽

Cited By ~ 2

Author(s):

EDMUND F. SCHULZ ◽

SUBIN PINKAYAN ◽

CHUMPORN KOMSARTRA

Keyword(s):

Base Length ◽

Unit Hydrograph ◽

Time To Peak ◽

Dimensionless Unit ◽

Instantaneous Unit Hydrograph ◽

Subsurface Runoff ◽

Tropical Watersheds ◽

Unit Hydrographs ◽

Similar Unit ◽

Two Parameter

The characteristics of dimensionless unit hydrographs were derived from floods from watersheds smaller than 1000 square kilometers located in Thailand. The dimensionless unit hydrographs were expressed as ratios of q/qq as a function of t/tp. These dimensionless unit hydrographs were compared with similar unit hydrographs derived from floods on Taiwan and with the unit hydrographs derived from a mathematical model developed from the two parameter gamma function developed from the theory of the instantaneous unit hydrograph. It was found that the unit hydrographs derived from the Thai watersheds had much longer base length and much longer time to peak than similar unit hydrographs derived from floods on Taiwan. This increase in length of response time is attributed to a larger component of subsurface runoff believed to be present in the floods from tropical watersheds.

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A Comparison of Some Methods of Deriving the Instantaneous Unit Hydrograph

Hydrology Research ◽

10.2166/nh.1985.0001 ◽

1985 ◽

Vol 16 (1) ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

V. P. Singh ◽

C. Corradini ◽

F. Melone

Keyword(s):

Peak Flow ◽

Central Italy ◽

Effective Rainfall ◽

Unit Hydrograph ◽

Time To Peak ◽

Wide Range ◽

Instantaneous Unit Hydrograph ◽

Similar Accuracy ◽

Two Parameters ◽

Range Of Values

The geomorphological instantaneous unit hydrograph (IUH) proposed by Gupta et al. (1980) was compared with the IUH derived by commonly used time-area and Nash methods. This comparison was performed by analyzing the effective rainfall-direct runoff relationship for four large basins in Central Italy ranging in area from 934 to 4,147 km2. The Nash method was found to be the most accurate of the three methods. The geomorphological method, with only one parameter estimated in advance from the observed data, was found to be little less accurate than the Nash method which has two parameters determined from observations. Furthermore, if the geomorphological and Nash methods employed the same information represented by basin lag, then they produced similar accuracy provided the other Nash parameter, expressed by the product of peak flow and time to peak, was empirically assessed within a wide range of values. It was concluded that it was more appropriate to use the geomorphological method for ungaged basins and the Nash method for gaged basins.

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Spatial Patterns in Baseflow Mean Response Time across a Watershed in the Loess Plateau: Linkage with Land-Use Types

Forest Science ◽

10.1093/forsci/fxz084 ◽

2020 ◽

Vol 66 (3) ◽

pp. 382-391 ◽

Cited By ~ 5

Author(s):

Xu-dong Huang ◽

Dong Wang ◽

Pei-pei Han ◽

Wen-chuan Wang ◽

Qing-jie Li ◽

...

Keyword(s):

Land Use ◽

Response Time ◽

Overland Flow ◽

Agricultural Land ◽

Least Squares Regression ◽

Unit Hydrograph ◽

Mean Response Time ◽

Impervious Area ◽

Land Use Types ◽

Instantaneous Unit Hydrograph

Abstract Understanding the relation between land-use types and baseflow mean response time (BMRT) is important to explore the response mechanism of baseflow processes in watersheds. BMRT was determined using an instantaneous unit hydrograph. The instantaneous unit hydrograph parameters were estimated by autocorrelation functions. The relative importance of land-use types in determining BMRT dynamics was assessed by hydrological model and partial least-squares regression. Our study suggests greater effects of urban area on BMRT than the effects of forest and agricultural land. This may be because the urban interception impervious area may impede baseflow generation over a short timescale. The effects of agricultural land are greater than those of forest in areas with steeper hillslopes, but lower than those of the forest in areas with more plains, reflecting the varied ability of forest and agricultural lands with different topography to hinder overland flow. Variations of BMRT are strongly linked to land use in the watershed. Overall, our study provides insight into the BMRT and dominant factors of land-use types in watersheds, planning of sustainable water resource use, and ecological protection in watersheds.

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The Role of Topography on the Shape of Unit Hydrographs in Small and Medium Sized Watersheds through a Physical Model

Water ◽

10.3390/w12082270 ◽

2020 ◽

Vol 12 (8) ◽

pp. 2270

Author(s):

Alicia A. Del Rio ◽

Aldo I. Ramirez ◽

Mauricio A. Sanchez

Keyword(s):

Fuzzy Logic ◽

Polynomial Regression ◽

Synthetic Methods ◽

Main Stream ◽

Unit Hydrograph ◽

Watershed Area ◽

Time To Peak ◽

Logic Models ◽

Empirical Relations ◽

Unit Hydrographs

This study intends to establish the main relations between topographic characteristics of the watershed and the main parameters of the unit hydrograph measured at the outlet. It looks to remove the subjectivity found in traditional synthetic methods and the trial and error setting of the main parameters of the hydrograph. The work was developed through physical experimentation of the rainfall-runoff process using the observed information of different watersheds of Chiapas, Mexico, as the reference. The experiments were carried out on a state-of-the-art semi-automatic runoff simulator, which was designed and built specifically for this study. Polynomial regression and fuzzy logic models were obtained to confirm the hypothesis of hydrological parameters being obtained from topographic data only by assuming uniform precipitation. Empirical relations were found for the peak flow, time to peak, base time and volume of the unit hydrograph and the watershed area, the main stream average slope, and the length of the stream of highest order. The main finding is that a unit hydrograph can be described based only on the watershed area when fuzzy logic models are applied.

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Regionalization of rainfall–runoff processes in rice agriculture dominated watersheds

Water Science & Technology ◽

10.2166/wst.2006.306 ◽

2006 ◽

Vol 53 (10) ◽

pp. 131-139 ◽

Cited By ~ 4

Author(s):

N.V. Rajyalakshmi ◽

S. Dutta

Keyword(s):

Rice Field ◽

Storm Event ◽

Rainfall Runoff ◽

Unit Hydrograph ◽

Stream Network ◽

Rice Agriculture ◽

Watershed Response ◽

Instantaneous Unit Hydrograph ◽

Daily Water ◽

Unit Hydrographs

An approach for computing the instantaneous unit hydrograph of rice agriculture dominated watesheds is proposed using the topology and hydraulic charcterstics of its stream network and the hydrologic behaviour of the rice agriculture area. The effect of rice agriculture on the watershed response is considered as partial sink areas. The sink factor, a time-variant weight factor for a particular storm event, is computed from the daily water balanace equation of the rice field. The critcal features of the simulated instantaneous unit hydrographs in three gauged watersheds located in the river Mahanadi, India were then compared with that of the observed 24-hr unit hydrograph. The comparison shows a significant correlation between the two results.

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Rainfall Runoff Hydrograph Prediction Using Dynamic Wave Based Instantaneous Unit Hydrograph

10.5194/egusphere-egu2020-4376 ◽

2020 ◽

Author(s):

Minyeob Jeong ◽

Jongho Kim ◽

Dae-Hong Kim

Keyword(s):

Rainfall Intensity ◽

Wave Model ◽

Test Results ◽

Rainfall Runoff ◽

Unit Hydrograph ◽

Time To Peak ◽

Instantaneous Unit Hydrograph ◽

Runoff Hydrographs ◽

Dynamic Wave ◽

Peak Value

<p>A method to predict runoff based on the instantaneous unit hydrograph and dynamic wave approximation is proposed. The method is capable of generating IUH of a watershed without the need of observed rainfall and runoff data, and only topography and surface roughness of a watershed are needed. IUHs were generated using a dynamic wave model and S-hydrograph method, and IUH generated was a function of both watershed and rainfall properties. The ordinate of IUH depends on the rainfall intensities, and the peak value of IUH was proportional to the rainfall intensity while the time to peak of the IUH was inversely proportional to the rainfall intensity.&#160; Corresponding IUHs for different rainfall intensities were used to generate runoff hydrographs. Since the IUH is generated using a dynamic wave model, it can be a tool to physically simulate the rainfall-runoff processes. Also, nonlinear rainfall-runoff relationship can be taken into account by expressing IUH as a function of rainfall excess intensity. Several test results in ideal basins and in a real watershed show that the proposed method has a good capability in predicting runoff, while several limitations remain.</p><p>Keywords: rainfall-runoff, instantaneous unit hydrograph, dynamic wave model</p>

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Development of geomorphological instantaneous unit hydrograph (GIUH) model for a new un-gauged watershed

International Journal of Agricultural Invention ◽

10.46492/ijai/2017.2.1.13 ◽

2017 ◽

Vol 2 (01) ◽

pp. 54-59

Author(s):

Jeetendra Kumar ◽

R. Suresh ◽

Safi Hassan

Keyword(s):

Peak Discharge ◽

Prediction Errors ◽

Effective Rainfall ◽

Storm Events ◽

Unit Hydrograph ◽

Time To Peak ◽

Initial Stage ◽

Damodar Valley ◽

Geomorphological Instantaneous Unit Hydrograph ◽

Instantaneous Unit Hydrograph

A geomorphological instantaneous unit hydrograph (GIUH) model was developed for a watershed of Damodar valley corporation, Hazaribagh, using Nash (1959) and Itrube (1982) methods to compute peak discharge (qpeak) and time to peak (tpeak). The model was calibrated and validated for five storm events, i.e. June 24-25 (1992), October 12-13 (1993), November 2-3 (1993), June 28 (1994) and August 6 (1996) by comparing their ordinates with the ordinates of instantaneous unit hydrograph (IUH). The GIUH was tested with absolute prediction errors (APE) of the ordinate of peak discharge. On comparison, it was found that, most of the GIUH models overestimated the runoff at initial stage, while underestimated at the latter stage in comparison to the IUHs, which was mainly due to consideration of const ant value of Ф-index, for computation of effective rainfall. The absolute prediction errors (APE) were computed to be 5.97, 18.09, 23.32, 9.64 and 7.52% of the ordinates of peak discharge for the storm events of June 24-25 (1992), October 12-13 (1993), November 2-3 (1993), June 28 (1994) and August 6 (1996) respectively.

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