Applying multi-resolution analysis to differential hydrological grey models with dual series

Abstract:This study aims to investigate trends in streamflow and precipitation in the period 1954-2010 in a semiarid region of the Yellow River watershed, Huangfuchuan basin, China. The combination of the wavelet transform and different Mann-Kendall (MK) tests were employed to figure out the basic trends structure in streamflow and precipitation and what time scales are affecting the observed trends. The comparative analysis with five MK test methods showed that the modified MK tests with full serial correlation structure performed better when significant autocorrelations exhibited for more than one lag. Three criteria were used to determine the optimal smooth mother wavelet, the decomposition level and the extension mode used in the discrete wavelet transform (DWT) procedure. The first criteria referred to the relative error of the wavelet approximated component and the original series. The second one was the relative error of MK Z-values of approximation component and the original series. Additionally, a new criterion (Er), based on the relative error of energy between the approximate component and the original series, was proposed in this study, with better performance than the previous two criteria. Further, a new powerful index, the energy of the hydrological time series, was proposed to verify the dominant periodic components for the observed trends. The analysis indicated that all monthly, seasonal and annual streamflow showed significant decreasing trends, while no significant trends were found in precipitation. Results from the DWT and MK tests revealed that the main factors influencing the trends in the monthly and seasonal series in Huangfuchuan watershed are intra-annual cycles, while the leading factors affecting the trends in the annual series are decadal events. Different driving factors (e.g., seasonal cycles, solar activities, etc.) related to the periodicities identified in these data types resulted in this discrepancy.

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“…The DWT is normally based on the dyadic calculation of position and scale of a signal [55] and the form of DWT can be written as…”

Section: Discrete Wavelet Transform (Dwt)mentioning

confidence: 99%

Investigating Trends in Streamflow and Precipitation in Huangfuchuan Basin with Wavelet Analysis and the Mann-Kendall Test

Chen

Guan

Guang-hua

et al. 2016

Water

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“…On the other hand, DWT decomposes signals on discrete number of scales. In DWT the dyadic scale for dilation and the corresponding value of transformation are usually used (integer power of two) (Chou 2007). In this study only DWT was used for trend analysis.…”

Section: Wavelet Analysismentioning

confidence: 99%

“…It may be more acceptable to apply DWT over CWT in rainfall data analysis because CWT does not generate information in terms of time series (Percival 2008). In addition, process of transformation by DWT is simplified because it is based on the dyadic calculation of position and scale of a signal (Chou 2007). In DWT, the signal is decomposed into approximation and detail series (Misiti and Misiti 1996).…”

Section: Wavelet Analysismentioning

confidence: 99%

Precipitation trend analysis using discrete wavelet transform at the Langat River Basin, Selangor, Malaysia

Palizdan

Falamarzi

Huang

et al. 2016

Stoch Environ Res Risk Assess

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The main purpose of this study was to determine the most dominant periodic components that affect the annual and seasonal precipitation trends in each homogenous rainfall region in the Langat River Basin, Malaysia for the period 1982-2011. Performing this research could be essential because in the previous studies on detection of trend in Malaysia, the details of variations of different time scales and the periodic responsible for the observed trends were not investigated. Using discrete wavelet transform (DWT) coupled with Mann-Kendall at the regional scale for the first time particularly in the context of Malaysia is the contribution of this study. In order to form the homogenous rainfall regions, first the total annual and seasonal precipitation in each year was spatialized into 5 km 9 5 km grids using the inverse distance weighting method. The obtained precipitation series for the grids were then grouped applying the Ward's clustering method based on the similarity of precipitation time series. After allocating a cluster number to each grid, the boundary of the regions was formed in ArcGIS software. Following which, in each homogenous region the areal precipitation series were computed by the Thiessen polygon method. The Mann-Kendall (MK) test was used to detect trend and the DWT coupled with the MK test and the sequential MK analysis were then utilized in order to find out the time scale which affected the observed trend in each homogenous region. On annual scale, it was found that D 1 (plus approximation) component in regions Annual Cluster1 (AC1) and AC2 was the periodic mode responsible for trends. On seasonal scale, in regions Northeast monsoon Cluster 1 (NC1), NC3, SC1 and Southwest monsoon Cluster 2 (SC2), D 1 (with approximation), in regions NC4, Inter monsoon 1 Cluster 1 (I1C1), I1C2, Inter monsoon 2 Cluster 1 I2C1 and I2C2, Detail 2 (D 2 ) (plus approximation) and in region NC2, Detail 3 (D 3 ) (with approximation added) component were the most influential periodicity for trends.

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“…Many hybrid models have been proposed as predictors to improve the accuracy of hydrological time-series forecasts, such as the wavelet artificial neural network (ANN) model (Anctil and Tape, 2004;Krishna et al, 2011;Nayak et al, 2013), the periodic ANN (PANN) model (Wang et al, 2006), the chaotic ANN model (Karunasinghe and Liong, 2006), the hybrid fuzzy-ANN model (Nayak et al, 2007), the wavelet-based grey model (Chou, 2007), the wavelet-based NF (neuro-fuzzy) model (Partal and Kisi, 2007;Engin et al, 2007;El-Shafie et al, 2007), the non-supervised ANN-EA (evolutionary algorithms) model (Cao and Park, 2007;Chang et al, 2007), the fuzzy-SVM model (Hua et al, 2008), the wavelet-based multi-layer perceptron model (Kisi, 2008), the wavelet-regression (WR) model (Kisi, 2011), and the wavelet-based fuzzy logic model (Ozger et al, 2012). These hybrid models have shown different advantages for accurate predictions due to their capabilities of utilising present information effectively.…”

Section: J-s Yang Et Al: Multi-step-ahead Predictor Design For Effmentioning

confidence: 99%

Multi-step-ahead predictor design for effective long-term forecast of hydrological signals using a novel wavelet neural network hybrid model

Yang

Liu

2013

Hydrol. Earth Syst. Sci.

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Abstract. In order to increase the accuracy of serialpropagated long-range multi-step-ahead (MSA) prediction, which has high practical value but also great implementary difficulty because of huge error accumulation, a novel wavelet neural network hybrid model -CDW-NN -combining continuous and discrete wavelet transforms (CWT and DWT) and neural networks (NNs), is designed as the MSA predictor for the effective long-term forecast of hydrological signals. By the application of 12 types of hybrid and pure models in estuarine 1096-day river stages forecasting, the different forecast performances and the superiorities of CDW-NN model with corresponding driving mechanisms are discussed. One type of CDW-NN model, CDW-NF, which uses neuro-fuzzy as the forecast submodel, has been proven to be the most effective MSA predictor for the prominent accuracy enhancement during the overall 1096-day long-term forecasts. The special superiority of CDW-NF model lies in the CWT-based methodology, which determines the 15-day and 28-day prior data series as model inputs by revealing the significant short-time periodicities involved in estuarine river stage signals. Comparing the conventional single-stepahead-based long-term forecast models, the CWT-based hybrid models broaden the prediction range in each forecast step from 1 day to 15 days, and thus reduce the overall forecasting iteration steps from 1096 steps to 74 steps and finally create significant decrease of error accumulations. In addition, combination of the advantages of DWT method and neuro-fuzzy system also benefits filtering the noisy dynamics in model inputs and enhancing the simulation and forecast ability for the complex hydro-system.

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Applying multi-resolution analysis to differential hydrological grey models with dual series

Cited by 32 publications

References 19 publications

Investigating Trends in Streamflow and Precipitation in Huangfuchuan Basin with Wavelet Analysis and the Mann-Kendall Test

Investigating Trends in Streamflow and Precipitation in Huangfuchuan Basin with Wavelet Analysis and the Mann-Kendall Test

Precipitation trend analysis using discrete wavelet transform at the Langat River Basin, Selangor, Malaysia

Multi-step-ahead predictor design for effective long-term forecast of hydrological signals using a novel wavelet neural network hybrid model

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