Kun-xia Yu

Estimation of the distribution of annual runoff from climatic variables using copulas

An approach of deriving the annual runoff distribution using copulas from an annual rainfall-runoff model is proposed to provide an alternative annual runoff frequency analysis method in case of changing climatic variables. The annual rainfall-runoff model is established on the basis of the Budyko formula to estimate annual runoff, with annual precipitation and potential evapotranspiration as input variables. The model contains one single parameter k that guarantees that annual water balance is satisfied. In the derivation of the annual runoff distribution, annual precipitation, annual potential evapotranspiration, and parameter k are treated as three random variables, while the annual runoff distribution is obtained by integrating the joint probability density function of the three random variables over the domain constrained by the annual rainfall-runoff model using the canonical vine copula. This copula-based derivation approach is tested for 40 watersheds in two large basins in China. The estimated annual runoff distribution performs well in most watersheds. The performance is mainly related to the accuracy of the marginal distribution of precipitation. The copula-based derivation approach can also be used in ungauged watersheds where the distribution of k at the local site is estimated from the regional information of the k variable, and it also has acceptable performance in most watersheds, while poor performance is observed in a few watersheds with low accuracy in the Budyko formula.

A framework of change‐point detection for multivariate hydrological series

Under changing environments, not only univariate but also multivariate hydrological series might become nonstationary. Nonstationarity, in forms of change-point or trend, has been widely studied for univariate hydrological series, while it attracts attention only recently for multivariate hydrological series. For multivariate series, two types of change-point need to be distinguished, i.e. change-point in marginal distributions and change-point in the dependence structure among individual variables. In this paper, a three-step framework is proposed to separately detect two types of change-point in multivariate hydrological series, i.e. change-point detection for individual univariate series, estimation of marginal distributions, and change-point detection for dependence structure. The last step is implemented using both the Cramer-von Mises statistic (CvM) method and the copula-based likelihood-ratio test (CLR) method. For CLR, three kinds of copula model (symmetric, asymmetric, and pair-copula) are employed to construct the dependence structure of multivariate series. Monte Carlo experiments indicate that CLR is far more powerful than CvM in detecting the change-point of dependence structure. This framework is applied to the trivariate flood series composed of annual maxima daily discharge (AMDD), annual maxima 3-day flood volume and annual maxima 15-day flood volume of the Upper Hanjiang River, China. It is found that each individual univariate flood series has a significant change-point; and the trivariate series presents a significant change-point in dependence structure due to the abrupt change in the dependence structure between AMDD and annual maxima 3-day flood volume. All these changes are caused by the construction of the Ankang Reservoir. This article is protected by copyright. All rights reserved.

Uncertainty Analysis of Multiple Hydrologic Models Using the Bayesian Model Averaging Method

Since Bayesian Model Averaging (BMA) method can combine the forecasts of different models together to generate a new one which is expected to be better than any individual model’s forecast, it has been widely used in hydrology for ensemble hydrologic prediction. Previous studies of the BMA mostly focused on the comparison of the BMA mean prediction with each individual model’s prediction. As BMA has the ability to provide a statistical distribution of the quantity to be forecasted, the research focus in this study is shifted onto the comparison of the prediction uncertainty interval generated by BMA with that of each individual model under two different BMA combination schemes. In the first BMA scheme, three models under the same Nash-Sutcliffe efficiency objective function are, respectively, calibrated, thus providing three-member predictions ensemble for the BMA combination. In the second BMA scheme, all three models are, respectively, calibrated under three different objective functions other than Nash-Sutcliffe efficiency to obtain nine-member predictions ensemble. Finally, the model efficiency and the uncertainty intervals of each individual model and two BMA combination schemes are assessed and compared.

Variations in runoff and sediment in watersheds in loess regions with different geomorphologies and their response to landscape patterns

In this study, two typical watersheds, i.e., the Dalihe watershed in the loess hilly–gully region of, and the Hailiutuhe watershed in the windy–sandy region of the Wudinghe Basin, were selected as study objects to evaluate the relationship between landscape indices and runoff and sediment, with the long-series data of runoff, sediment, and land use, using the GIS and Fragstats platforms. The results showed that between two watersheds showed that all of the contagion index, Shannon’s diversity index, and patch cohesion index exhibited an ascending trend in the Dalihe watershed, and a descending trend in the Hailiutuhe watershed. In the Dalihe watershed, only Shannon’s diversity index had a very significantly negative correlation with the runoff, whereas in the Hailiutuhe watershed, the contagion index had a significantly negative correlation with the runoff, and all of the Shannon’s diversity index, the Shannon’s evenness index, and the Simpson’s evenness index had a significantly positive correlation with the runoff. In respect of correlation of sediment with landscape pattern, the sediment had a very significantly negative correlation only with Shannon’s diversity index in the Dalihe watershed, whereas in the Hailiutuhe watershed, the sediment had a significantly negative correlation with all of the number of patches, the patch density, and the landscape shape index, and a very significantly positive correlation with the aggregation index. The importance of each landscape index in the regression equation and the positive or negative correlations indicated that erosion in watersheds could be reduced by strengthening the control function of the dominant patch, thoroughly improving the evenness of the landscape patch types, enriching the landscape types, reducing the physical connectivity between patches, and enhancing the degree of aggregation in landscape patches.

Distribution of soil organic carbon impacted by land-use changes in a hilly watershed of the Loess Plateau, China

Vegetation restoration, terrace and check dam construction are the major measures for soil and water conservation on the Loess Plateau. These effective measures of stabilizing soils have significant impacts on soil organic carbon (SOC) distribution. However, following ecological construction, whether the hilly watershed acts as a source or a sink of soil carbon is still unknown. To understand the impact of land-use changes combined with check dam construction on SOC distribution, 1060 soil samples were collected from a 100 cm soil profile across a watershed on the Loess Plateau. The soils in the 0-20 cm layer had a higher SOC concentration than those of the 20-40, 40-60, 60-80 and 80-100 cm layers. Forestland, shrubland and terrace had significant higher SOC concentrations in the 0-20 cm soil layer than that of sloping cropland and dammed farmland (p < 0.05). SOC densities (0-100 cm) in terrace, forestland, shrubland, grassland, sloping cropland and dammed farmland were 12.09, 11.99, 11.89, 11.77, 11.41 and 10.11 kg m-2, respectively. These estimations suggested that SOC was redistributed in the watershed through land-use changes. Topographical factors, including altitude, aspect and slope had impacts on SOC concentrations. The application of hydrological controls to hillslopes and along river channels should be considered when assessing carbon sequestration within the soil erosion subsystem.

Analyzing the Impacts of Climatic and Physiographic Factors on Low Flow Distributions

Low flow distributions are derived using the derived distribution function approach while considering the variabilities in the dry spell and recession response time to explore the impacts of climatic and physiographic factors on low flow distributions. The low flow distributions are separately derived from the distributions of the dry spell and the recession ratio, i.e., the ratio of the dry spell to the recession response time, on the basis of the linear recession equation, and the dry spell and recession ratio are both assumed to follow normal, gamma, and lognormal distributions. The parameters of these low flow distributions are estimated from the moments of the dry spell and recession ratio series. Applications of these low flow distributions are exemplified in three basins with different hydrological and climatic conditions in China. The gamma distribution outperforms the other two distributions while describing the distributions of the dry spell and the recession ratio. The derived low flow distributions with parameters estimated from the moments of the recession ratio show good consistency with the low flow empirical distributions, and the derived distributions can be applied to estimate the flow quantiles when continuous records of the streamflow are not available. The relationships between the quantiles of the low flow distributions and the moments of climatic factors and watershed characteristic variables show that the recession ratio has the largest influence on the low flow quantiles regardless of the hydrological regime and that the second-largest influencing factor is the dry spell distribution. Meanwhile, the recession response time has a prominent influence on the low flow distributions in erratic hydrological regimes.