### Abstract

A challenging problem in basin-scale hydrology is the ability to represent and quantify the nonlinearity of the output hydrograph or response. An important aspect of this challenge is to clearly distinguish among different sources of nonlinearity. To address the previous, a scale-dependent network instantaneous response function (IRF) is obtained by using the theory of transport by travel times, relationships of basin geomorphology, hydraulic geometry, and the inverse Gaussian (IG) distribution. Inverse Gaussian is used to represent the network response because of its connection with diffusion processes. It is shown that both geometric and hydraulic regularity in the stream network, together with the scaling property of IG, can result in the network response being approximately scaling, implying in turn that the peak flow and time to peak of the response are scaling as well. The derived IRF has the advantage over previous formulations of explicitly distinguishing between nonlinearity and scaling. In addition, it provides an explanation for the scaling in terms of well-known hydrogeomorphic relationships. The scaling is found to arise from the dependence of the network length (i.e., the mean path length) and hydraulic geometry, specifically the mean velocity and the cross-sectional area, on the basin size. Moreover, after dividing the network travel times by the mean travel time, a response that is independent of scale is obtained. This response can be seen as analogous to the instantaneous unit hydrograph but representing instead the output associated with a unit travel time. Furthermore, the derived IRF may be useful in design applications as it provides a way for estimating the response across basin sizes by using readily available data sets. For the latter, additional comparison against observed data is necessary to better understand the applicability of the proposed scaling under a variety of climatic and terrain scenarios.

Original language | English (US) |
---|---|

Pages (from-to) | 1786-1789 |

Number of pages | 4 |

Journal | Journal of Hydrologic Engineering |

Volume | 18 |

Issue number | 12 |

DOIs | |

State | Published - Nov 26 2013 |

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### All Science Journal Classification (ASJC) codes

- Environmental Science(all)
- Environmental Chemistry
- Water Science and Technology
- Civil and Structural Engineering

### Cite this

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**Scaling of the network instantaneous response function from basin geomorphology and hydraulic geometry.** / Mejia, Alfonso Ignacio.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Scaling of the network instantaneous response function from basin geomorphology and hydraulic geometry

AU - Mejia, Alfonso Ignacio

PY - 2013/11/26

Y1 - 2013/11/26

N2 - A challenging problem in basin-scale hydrology is the ability to represent and quantify the nonlinearity of the output hydrograph or response. An important aspect of this challenge is to clearly distinguish among different sources of nonlinearity. To address the previous, a scale-dependent network instantaneous response function (IRF) is obtained by using the theory of transport by travel times, relationships of basin geomorphology, hydraulic geometry, and the inverse Gaussian (IG) distribution. Inverse Gaussian is used to represent the network response because of its connection with diffusion processes. It is shown that both geometric and hydraulic regularity in the stream network, together with the scaling property of IG, can result in the network response being approximately scaling, implying in turn that the peak flow and time to peak of the response are scaling as well. The derived IRF has the advantage over previous formulations of explicitly distinguishing between nonlinearity and scaling. In addition, it provides an explanation for the scaling in terms of well-known hydrogeomorphic relationships. The scaling is found to arise from the dependence of the network length (i.e., the mean path length) and hydraulic geometry, specifically the mean velocity and the cross-sectional area, on the basin size. Moreover, after dividing the network travel times by the mean travel time, a response that is independent of scale is obtained. This response can be seen as analogous to the instantaneous unit hydrograph but representing instead the output associated with a unit travel time. Furthermore, the derived IRF may be useful in design applications as it provides a way for estimating the response across basin sizes by using readily available data sets. For the latter, additional comparison against observed data is necessary to better understand the applicability of the proposed scaling under a variety of climatic and terrain scenarios.

AB - A challenging problem in basin-scale hydrology is the ability to represent and quantify the nonlinearity of the output hydrograph or response. An important aspect of this challenge is to clearly distinguish among different sources of nonlinearity. To address the previous, a scale-dependent network instantaneous response function (IRF) is obtained by using the theory of transport by travel times, relationships of basin geomorphology, hydraulic geometry, and the inverse Gaussian (IG) distribution. Inverse Gaussian is used to represent the network response because of its connection with diffusion processes. It is shown that both geometric and hydraulic regularity in the stream network, together with the scaling property of IG, can result in the network response being approximately scaling, implying in turn that the peak flow and time to peak of the response are scaling as well. The derived IRF has the advantage over previous formulations of explicitly distinguishing between nonlinearity and scaling. In addition, it provides an explanation for the scaling in terms of well-known hydrogeomorphic relationships. The scaling is found to arise from the dependence of the network length (i.e., the mean path length) and hydraulic geometry, specifically the mean velocity and the cross-sectional area, on the basin size. Moreover, after dividing the network travel times by the mean travel time, a response that is independent of scale is obtained. This response can be seen as analogous to the instantaneous unit hydrograph but representing instead the output associated with a unit travel time. Furthermore, the derived IRF may be useful in design applications as it provides a way for estimating the response across basin sizes by using readily available data sets. For the latter, additional comparison against observed data is necessary to better understand the applicability of the proposed scaling under a variety of climatic and terrain scenarios.

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U2 - 10.1061/(ASCE)HE.1943-5584.0000760

DO - 10.1061/(ASCE)HE.1943-5584.0000760

M3 - Article

VL - 18

SP - 1786

EP - 1789

JO - Journal of Hydrologic Engineering - ASCE

JF - Journal of Hydrologic Engineering - ASCE

SN - 1084-0699

IS - 12

ER -