The Water Residence Time distribution is the equivalent of the impulse response of a linear system allowing the propagation of water through a medium, e.g. the propagation of rain water from the top of the mountain towards the aquifers. We consider the output aquifer levels as the convolution between the input rain levels and the Water Residence Time, starting with an initial aquifer base level. The estimation of Water Residence Time is important for a better understanding of hydro-bio-geochemical processes and mixing properties of wetlands used as filters in ecological applications, as well as protecting fresh water sources for wells from pollutants. Common methods of estimating the Water Residence Time focus on cross-correlation, parameter fitting and non-parametric deconvolution methods. Here we propose a 1D full-deconvolution, regularized, non-parametric inverse problem algorithm that enforces smoothness and uses constraints of causality and positivity to estimate the Water Residence Time curve. Compared to Bayesian non-parametric deconvolution approaches, it has a fast runtime per test case; compared to the popular and fast cross-correlation method, it produces a more precise Water Residence Time curve even in the case of noisy measurements. The algorithm needs only one regularization parameter to balance between smoothness of the Water Residence Time and accuracy of the reconstruction. We propose an approach on how to automatically find a suitable value of the regularization parameter from the input data only. Tests on real data illustrate the potential of this method to analyze hydrological datasets.
The cross-correlation implicitly assumes that the input rainfall is white noise. In this case, the auto-correlation of each rain fall time series would be a Dirac at the center. Since real rainfall time series have actually long-tailed statistics, the cross-correlation method is inexact. Here we use multifractals to simulate realistic rainfall @cite_30 . Therefore, we expect the cross-correlation method to have a limited performance in real life tests.
@cite_30
2895618990 2097102810 2407858842 2282974639
The primary accomplishment of this research has been demonstrating the power of the deconvolution technique developed by Neuman and de Marsily (1976) in dealing with noisy rainfallrunoff records of short duration. Such records are encountered in arid environments where rainfall often occurs in short isolated bursts and the data are measured with a considerable margin of error. Our research work consisted of superimposing known noise on synthetic rainfallrunoff data and examining the ability of the Neuman -de Marsily deconvolution method to estimate the correct impulse response of the system when the data include only a single storm event. Approximately 50 Monte Carlo simulation runs were performed for each of three different noise models considered in our work. The results clearly demonstrated that the deconvolution model leads to reliable estimates and can be used with confidence in the presence of realistic noise levels. In addition to the Monte Carlo simulation tests and their analysis, certain improvements were introduced into the original deconvolution technique. In particular, the original version of the technique required that the hydrologist exercise subjective judgement in choosing the "best" solution for the deconvolution problem from a large number of admissible solutions. Our new method of selecting the "best" result is based on a comparative analysis of residuals and is more reliable than the earlier subjective approach. The improved method has been applied to real as well as synthetic rainfall runoff data. Summary We study the temporal variability of water transfer through the infiltration zone of a karst aquifer by estimating the impulse response of the system using cross-correlogram analyses between rainfall and piezometric level time series. We apply a sliding-window cross-correlation method, which calculates cross-correlograms on partially superposed short time series windows. We apply this method for rainfall and piezometric level time series at six boreholes in a fractured karstic aquifer located in Burgundy, France. Based on cross-correlogram functions, we obtain a time series of response time. At most of the boreholes, the cross-correlation functions change over time, and the response times vary seasonally, being shorter during the summer. This unusual structure can be partly explained by the seasonal variability in rainfall intensity, which is higher during the summer (May–September), inducing the seasonal behaviour of the epikarst. During the summer, when rainfall intensity is higher, the epikarst is more easily and quickly saturated. This induces an increase in lateral water transfer within the epikarst and an increase in concentrated fast flows. We also show that the response time seems to tend towards a limit which represents the maximum saturation of the epikarst. Heavy precipitation for several days and weeks always leads to some extreme nature disasters. Long-lead term precipitation forecasting plays an important role on the prevision of such calamities. Most works focus on the generation of training labels with allocation of the proper corresponding spatio-temporal information. In this paper, we will provide a different path by performing regression analysis using the precipitation amounts at particular locations. This method is called Hierarchical Clustering based Bayesian Structural Vector Autoregression (HC-BSVAR). The approach for HC-BSVAR is divided into two steps. First, we apply a hierarchical clustering algorithm to identify the Elite locations and then transfer the 3-dimensional data space into a new traditional 2-dimensional data space. Every column of the new data frame is a hydro-meteorological feature of the original data and each row represents a time point (day) in the original space. Secondly, an economic-based multivariate time series model called Bayesian-based Structural Vector Autoregression (BSVAR) is exploited to perform the final prediction result. The prediction quality will be vary for different cut of tree structure which generated by hierarchical clustering. The coefficient for determination of each location by each level of cut is applied to quantize the quality of prediction. The relationship between the cut level of clustering geographic locations and the regression model performance are also discussed, based on the result of prediction quality. Long-lead prediction of heavy precipitation events has a significant impact since it can provide an early warning of disasters, like a flood. However, the performance of existed prediction models has been constrained by the high dimensional space and non-linear relationship among variables. In this study, we study the prediction problem from the prospective of machine learning. In our machine-learning framework for forecasting heavy precipitation events, we use global hydro-meteorological variables with spatial and temporal influences as features, and the target weather events that last several days have been formulated as weather clusters. Our study has three phases: 1) identify weather clusters in different sizes, 2) handle the imbalance problem within the data, 3) select the most-relevant features through the large feature space. We plan to evaluate our methods with several real world data sets for predicting the heavy precipitation events.