### Abstract

Step-pool mountain streams contain a rhythmic structure that can be characterized by the periodicity, commonly determined using spectral analysis. However, this analysis often requires data series recorded at equal intervals and exhibiting stationary patterns. Previous methods of transforming the original step-pool sequence into this required format have not been rigorously tested and consequently may generate misleading periodicity results. To this end, we apply both spectral analysis and autoregressive integrated moving average (ARIMA) modeling, a parsimonious stochastic approach to 11 alluvial mountain step-pool streams for identifying their periodicities. We interpolate the original sequences into those with four different equal-space intervals, 0.1m, 0.2m, 0.3m, and 0.4m, and demonstrate that the differencing detrending method is statistically more effective to transform the sequences into stationary ones than the commonly used linear detrending method. Subsequently, we identify periodicities of these sequences using the two approaches and determine the degree of stability for these periodicities for each original step-pool sequence using R ^{2} values obtained by least squares linear regression between the log-transformed identified periods and the associated equal-space intervals. Eight out of 11 step-pool sequences have relatively stable periodicities (R ^{2} ≥ 0.79) when the spectral analysis approach is used, while those identified using the ARIMA modeling approach are much less stable. Further comparison of periodicities identified using both approaches suggests that periodicities of step-pool sequences are inherently unstable and hence cannot be appropriately determined based on a single equal-space interval. A general procedure for identifying the periodicity of a step-pool sequence using spectral analysis with the differencing detrending method and multiple equal-space intervals is proposed. The identified periodicities might serve as an independent morphologic index to infer hydraulic processes controlling the formation of the alluvial step-pools.

Original language | English (US) |
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Pages (from-to) | 258-277 |

Number of pages | 20 |

Journal | Geographical Analysis |

Volume | 44 |

Issue number | 3 |

DOIs | |

State | Published - Jul 1 2012 |

### ASJC Scopus subject areas

- Geography, Planning and Development
- Earth-Surface Processes

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## Cite this

*Geographical Analysis*,

*44*(3), 258-277. https://doi.org/10.1111/j.1538-4632.2012.00850.x