Applying Multiscale Entropy to the Complexity Analysis of Rainfall-Runoff Relationships

This study compares the one-day-ahead stream flow forecasting performance of multiple-layer artificial neurons and a neuro-wavelet hybrid system at two sites. Morlet power spectra are used to identify the period-scale structure of the available rainfall and runoff time series. The time series are wavelet decomposed into three sub-series depicting the rainfall-runoff processes: short, intermediate, and long wavelet periods. Then, multiple-layer artificial neurons are trained for each wavelet sub-series. Results show that the short wavelet periods are responsible for most of the final neuro-wavelet hybrid forecasting error. Short period fluctuations are thus the key to any further improvements in artificial neural network (ANN) rainfall-runoff forecasting models. The final performance of the neuro-wavelet hybrid forecasting system and of the classic forecasting multiple-layer artificial neuron system is very similar. The slight advantage in performance of the neuro-wavelet system may be attributed to a better usage of the evapotranspiration time series. Key words: surface-water hydrology, rainfall-runoff, artificial neural networks, wavelet decomposition.

Hydrological response to an abrupt shift in surface air temperature over France in 1987/88

Post‐fire flooding and debris flows are often triggered by increased overland flow resulting from wildfire impacts on soil infiltration capacity and surface roughness. Increasing wildfire activity and intensification of precipitation with climate change make improving understanding of post‐fire overland flow a particularly pertinent task. Hydrologic signatures, which are metrics that summarize the hydrologic regime of watersheds using rainfall and runoff time series, can be calculated for large samples of watersheds relatively easily to understand post‐fire hydrologic processes. We demonstrate that signatures designed specifically for overland flow reflect changes to overland flow processes with wildfire that align with previous case studies on burned watersheds. For example, signatures suggest increases in infiltration‐excess overland flow and decrease in saturation‐excess overland flow in the first and second years after wildfire in the majority of watersheds examined. We show that climate, watershed and wildfire attributes can predict either post‐fire signatures of overland flow or changes in signature values with wildfire using machine learning. Normalized difference vegetation index (NDVI), air temperature, amount of developed/undeveloped land, soil thickness and clay content were the most used predictors by well‐performing machine learning models. Signatures of overland flow provide a streamlined approach for characterizing and understanding post‐fire overland flow, which is beneficial for watershed managers who must rapidly assess and mitigate the risk of post‐fire hydrologic hazards after wildfire occurs.

The Biliu River originates from the southern foot of Qinling Mountain in Gaizhou city, with an elevation of 1047 m, and is the largest river in Dalian. The hydrological elements mainly include rainfall, runoff, temperature, evaporation, and other time series associated with the hydrological cycle. Among them, runoff is the most visible output performance, and the direct source of runoff is during rainfall. This paper establishes a reservoir scheduling model that considers the influence of multiple uncertainty factors and analyzes the influence of mixed uncertainty on reservoir scheduling and Xingli’s objectives based on probability box theory. In terms of uncertainties, the uncertainty of hydrological model parameters and the randomness of precipitation processes are mainly considered, with the former having an impact on river runoff simulation and the latter having an impact on both river runoff simulation and crop irrigation water demand. In the case of the Jing River basin, for example, the results show that, compared to the stochasticity of the precipitation process, the variation in precipitation has a significant effect on irrigation water demand in maize, followed by the frequency of precipitation, and the interaction between the two is not significant.

Due to the impact of changing climate and human activities on hydrology, non-stationary research is becoming more popular. In the Wei River Basin, which is the largest tributary of the Yellow River, non-stationary has been studied for decades and has found non-stationary signals in discharge and precipitation records. However, these studies have mainly focused on the annual time series and ignored the seasonal signal.In this study, to investigate the non-stationarity more comprehensively, two non-stationary tests have been applied including the Mann-Kendall test and the Heuristic segmentation algorithm. These tests were applied to runoff time series from 12 catchments and catchment averaged precipitation and temperature time series derived from 114 meteorological stations. Like other studies, our results, show that on the annual timescale, non-stationary signals (multiple change points and decreasing trends) are found in the runoff time series on most catchments along the mainstem, while the runoff time series of the Beiluo catchment does not show any non-stationarity signal. However, our results show that there is clearly a seasonal difference with change points occurring at contrasting times. Among all time series, about 40% show only single nonstationary signals (trend or change point), while the remainder exhibit multiple signals indicating the importance of using multiple tests. While the results show that non-stationary signals exist in all time series, further work is needed to quantify if or to what level are meteorological variables the driver of non-stationary signals in the runoff time series.  

Persistence and multifractality are two fundamental properties of hydrological time series. This study aims at understanding the origin of the Hurst exponent of streamflow time series. Thus, we have obtained streamflow, rainfall, and potential evapotranspiration (PET) time series data pertaining to 101 stations in 17 river basins in India. The persistence and multifractal properties of the time series were estimated using multifractal detrended fluctuation analysis (MFDFA). Results suggest that most of the rainfall time series (85%) exhibit short-term persistence while all the PET time series and 59% of the streamflow time series exhibit long-term persistence. The Hurst exponent exhibited by the river flow series simulated by the dynamic Budyko (DB) model that considers only rainfall and PET as inputs displayed a good agreement with the Hurst exponent of observed streamflow, supporting our hypothesis that climatic factors typically shape the value of the Hurst exponent.

Abstract. There is increasing concern in southern Africa about the possible decline of rainfall as a result of global warming. Some studies concluded that average rainfall in Zimbabwe had declined by 10% or 100 mm during the last 100 years. This paper investigates the validity of the assumption that rainfall is declining in Zimbabwe. Time series of annual rainfall, and total rainfall for (a) the early part of the rainy season, October-November-December (OND), and (b) the mid to end of the rainy season, January-February-March (JFM) are analysed for the presence of trends using the Mann-Kendall test, and for the decline or increase during years with either high or low rainfall using quantile regression analysis. The Pettitt test has also been utilized to examine the possible existence of change or break-points in the rainfall time series. The analysis has been done for 40 rainfall stations with records starting during the 1892–1940 period and ending in 2000, and representative of all the rainfall regions. The Mann-Kendal test did not identify a significant trend at all the 40 stations, and therefore there is no proof that the average rainfall at each of these stations has changed. Quantile regression analysis revealed a decline in annual rainfall less than the tenth percentile at only one station, and increasing of rainfall greater than the ninetieth percentile at another station. All the other stations had no changes over time in both the low and high rainfall at the annual interval. Climate change effects are therefore not yet statistically significant within time series of total seasonal and annual rainfall in Zimbabwe. The general perception about declining rainfall is likely due to the presence of multidecadal variability characterized by bunching of years with above (e.g. 1951–1958, 1973–1980) and below (e.g. 1959–1972, 1982–1994 ) average rainfall.

Maximum Entropy Spectral Analysis (MESA) Method is a powerful alternative to the traditionally used Blackman Tukey (BT) and Fast Fourier Transform (FFT) Methods in hydrologic and climatologic time series analysis. Maximum entropy spectra of annual rainfall time series measured at Mangalore and Waltair and monthly flow time series of Godavari and Krishna Rivers in India are presented and compared with the spectra obtained by using BT and FFT methods. A recently developed Bayesian decision rule is applied to determine the length of filters in MESA. Sensitivity of the maximum entropy spectra to the length of filter used is also discussed.

Drought, a normal recurrent event in arid and semiarid lands such as Iran, is typically of a temporary nature usually leaving little permanent aftermath. In the current study, the rainfall and drought severity time series were analyzed at 10 stations in the eastern half of Iran for the period 1966–2005. The drought severity was computed using the Standardized Precipitation Index (SPI) for a 12‐month timescale. The trend analyses of the data were also performed using the Kendall and Spearman tests. The results of this study showed that the rainfall and drought severity data had high variations to average values in the study period, and these variations increased with increasing aridity towards the south of the study area. The negative serial correlations found in the seasonal and annual rainfall time series were mostly insignificant. The trend tests detected a significant decreasing trend in the spring rainfall series of Birjand station at the rate of 8.56 mm per season per decade and a significant increasing trend in the summer rainfall series of Torbateheydarieh station at the rate of 0.14 mm per season per decade, whereas the rest of the trends were insignificant. Furthermore, the 12‐month values of the standardized precipitation index decreased at all the stations except Zabol during the past four decades. During the study period, all of the stations experienced at least one extreme drought which mainly occurred in the winter season. Copyright © 2011 John Wiley & Sons, Ltd.

This study aimed at characterization of rainfall dynamics in a hot arid region of Gujarat, India by employing time-series modeling techniques and sustainability approach. Five characteristics, i.e., normality, stationarity, homogeneity, presence/absence of trend, and persistence of 34-year (1980–2013) period annual rainfall time series of ten stations were identified/detected by applying multiple parametric and non-parametric statistical tests. Furthermore, the study involves novelty of proposing sustainability concept for evaluating rainfall time series and demonstrated the concept, for the first time, by identifying the most sustainable rainfall series following reliability (R y), resilience (R e), and vulnerability (V y) approach. Box–whisker plots, normal probability plots, and histograms indicated that the annual rainfall of Mandvi and Dayapar stations is relatively more positively skewed and non-normal compared with that of other stations, which is due to the presence of severe outlier and extreme. Results of Shapiro–Wilk test and Lilliefors test revealed that annual rainfall series of all stations significantly deviated from normal distribution. Two parametric t tests and the non-parametric Mann–Whitney test indicated significant non-stationarity in annual rainfall of Rapar station, where the rainfall was also found to be non-homogeneous based on the results of four parametric homogeneity tests. Four trend tests indicated significantly increasing rainfall trends at Rapar and Gandhidham stations. The autocorrelation analysis suggested the presence of persistence of statistically significant nature in rainfall series of Bhachau (3-year time lag), Mundra (1- and 9-year time lag), Nakhatrana (9-year time lag), and Rapar (3- and 4-year time lag). Results of sustainability approach indicated that annual rainfall of Mundra and Naliya stations (R y = 0.50 and 0.44; R e = 0.47 and 0.47; V y = 0.49 and 0.46, respectively) are the most sustainable and dependable compared with that of other stations. The highest values of sustainability index at Mundra (0.120) and Naliya (0.112) stations confirmed the earlier findings of R y–R e–V y approach. In general, annual rainfall of the study area is less reliable, less resilient, and moderately vulnerable, which emphasizes the need of developing suitable strategies for managing water resources of the area on sustainable basis. Finally, it is recommended that multiple statistical tests (at least two) should be used in time-series modeling for making reliable decisions. Moreover, methodology and findings of the sustainability concept in rainfall time series can easily be adopted in other arid regions of the world.

Singular spectrum analysis and forecasting of hydrological time series

A variety of different methods have been suggested to classify catchment runoff or groundwater dynamics, to relate these to catchment or aquifer properties and thus to utilize inherent information of data. To that end, the correlation dimension method, a powerful nonlinear time series analysis method based on the chaos theory, has been suggested to assess the intrinsic dimensionality of time series according to Takens (1981). It can provide an assessment of the minimum number of processes that is required to map the observed dynamics. In the first study, the correlation dimension method was applied to the observed hydrographs of 35 catchments in the Federal State of Brandenburg, Germany. The intrinsic dimensionality of these catchments ranged from 2.2 to 5.8. It was uncorrelated with the results of standard time series analysis methods, such as autocorrelation, the slope of the power spectrum and the Hurst coefficient, revealing that the correlation dimension method captured information independent from these measures. The correlation dimension values did not exhibit any clear spatial patterns, but showed significant correlations with the spatial heterogeneity within the catchments. In addition, the correlation dimension method was applied to groundwater head and lake level data in the biosphere reserve Schorfheide-Chorin region. The intrinsic dimensionality of groundwater level ranged from 0.9 to 5, while lake level exhibited small variations, around 1.57 to 2. The correlation dimension values of groundwater level exhibited no correlation with the screening depth of groundwater wells, but displayed spatial patterns due to the different aquifer conditions (confined or unconfined). It seems that high correlation dimension values indicate partly confined conditions. Most of the available hydrological models are highly over-parameterized concerning available data and encounter the equifinality problem: different model parameterizations and even different models yield the same best results, which has severe consequences with respect to model uncertainty. However, if these models are used for process identification or as a basis for the modeling of reactive solute transport, they exhibit substantial variety. The same problem exists for model applications to different boundary conditions. Thus, model validation by comparing measured with simulated time series only is not sufficient. In the second study, we proposed a different approach based on the correlation dimension method. Simulated hydrographs from three hydrological models with increasing complexities were investigated using the correlation dimension method and the relationship between correlation dimension values and Nash-Sutcliffe efficiency values was explored. The correlation dimension method imposes additional constraints to the models and is more powerful to reduce the equifinality problem compared with the traditional Nash-Sutcliffe efficiency criteria. Therefore, the combination of the Nash-Sutcliffe efficiency criterion and the correlation dimension method detects the intrinsic property underlying the system dynamics, but also improves the prediction accuracy, serving as a promising approach for model performance evaluation. In addition, the correlation dimension analyses of model rainfall, evapotranspiration and discharge time series suggested that the hydrological models likely acted as intrinsic dimensionality reducing filters for the high- dimensional model inputs to outputs. The model reduced more intrinsic dimensionalities of simulations, if the higher model complexity was.

Abstract. A better understanding the effects of rainfall and evapotranspiration statistics on groundwater recharge (GR) requires long time series of these variables. However, long records of the relevant variables are scarce. To overcome this limitation, time series of rainfall and evapotranspiration are often synthesized using different methods. Here, we attempt to study the dependence of estimated GR on the synthesis methods used. We focus on regions with semi-arid climate conditions and soil types. For this purpose, we used longer than 40 year records of the daily rain and climate variables that are required to calculate the potential evapotranspiration (ETref), which were measured in two semi-arid locations.These locations, Beit Dagan and Shenmu, have aridity indices of 0.39 and 0.41, respectively, and similar seasonal and annual ETref rates (1370 and 1030 mm yr−1, respectively) but different seasonal rain distributions. Stochastic daily rain and ETref time series were synthesized according to the monthly empirical distributions. This synthesis method does not preserve the monthly and annual rain and ETref distributions. Therefore, we propose different correction methods to match the synthesized and measured time series' annual or monthly statistics. GR fluxes were calculated using the 1D Richards equation for four typical semi-arid soil types, and by prescribing the synthesized rain and ETref as atmospheric conditions. The estimated GR fluxes are sensitive to the synthesis method. However, the ratio between the GR and the total rain does not show the same sensitivity. The effects of the synthesis methods are shown to be the same for both locations, and correction of the monthly mean and SD of the synthesized time series results in the best agreement with independent estimates of the GR. These findings suggest that the assessment of GR under current and future climate conditions depends on the synthesis method used for rain and ETref.

<p>Dam breaks can be driven by a flood that exceeds the design spillway capacity, causing important economic and human losses. Dam spillways are designed for a flood that is usually estimated through either hydrometeorological or statistical analyses with observed data. However, time series of observations are usually short, incomplete and recorded at a daily time step. Moreover, design floods have to be estimated for high return periods greater than 500 years, leading to high uncertainties. In addition, climate change is expected to increase the frequency and magnitude of floods in the future. Therefore, new methodologies are required to assess hydrological dam safety considering both short time series of observations and climate change.</p><p>A stochastic methodology is presented here to assess hydrological dam safety considering the impact of climate change on floods, by integrating a stochastic rainfall generator and a rainfall-runoff model. The methodology is applied to the Eugui Dam on the Arga River in the north of Spain. The Eugui Dam has a draining catchment area of 69 km<sup>2</sup>, a reservoir volume of 22 hm<sup>3</sup>, and a gated spillway.</p><p>First, the stochastic rainfall generator STORAGE (De Luca and Petroselli, 2021) based on the Neymann-Scott Rectangular Pulse Model has been used to simulate long time series of 500 years of precipitation with a time step of 15 minutes. The generator has been calibrated with rainfall observations. In addition, the STORAGE model has been used to generate synthetic time series of precipitation considering climate change. Delta changes extracted from precipitation projections of 12 climate models, three periods (2011-2040, 2041-2070, 2071-2100) and two emission scenarios (RCP 4.5 and RCP 8.5) are considered (Garijo and Mediero, 2019).</p><p>Second, the stochastic precipitation time series are transformed into runoff time series by using the COSMO4SUB model (Grimaldi et al., 2021). COSMO4SUB is a continuous model that uses a high-resolution digital terrain model, land cover / soil type data, and precipitation supplied by the STORAGE model as input data, providing continuous runoff time series as output. The COSMO4SUB parameters have been calibrated with runoff observations by minimizing a set of objective functions.</p><p>Third, annual maximum hydrographs, peak flows and hydrograph volumes are extracted from the runoff time series generated by COSMO4SUB. The Volume Evaluation Method (MEV) (Girón, 1988) is used to simulate the operation of spillway gates in flood events, obtaining maximum water levels in the reservoir and outflow hydrographs. The MEV method specifies when the spillway gates are opened and closed to reach the target reservoir water level at the end of the flood event. Hydrological dam safety at the Eugui Dam is assessed by analysing the frequency curve of maximum water levels in the reservoir for the 12 climate models, three return periods and two emission scenarios mentioned above. Therefore, the methodology proposed allows practitioners and dam owners to check the hydrological dam safety requirements detailed in the regulations, accounting for climate change.</p><p>Acknowledgments: This research has been supported by the project SAFERDAMS (PID2019-107027RB-I00) funded by the Spanish Ministry of Science and Innovation.</p>

Flood events can be highly localized in both time and space. Many of the most severe events observed in recent years have occurred in small catchments, where high flow velocities and the rapid development of floods substantially limit the effectiveness of monitoring and hydrometeorological forecasting. When reconstructing the characteristics of such events, together with the analysis of catchment response times, attention is commonly given to soil infiltration and retention processes. In engineering applications, the runoff coefficient is often used to describe the proportion of rainfall that becomes runoff during an event.For a given watershed, the runoff coefficient is not a fixed parameter; it varies considerably with event intensity and the physical and hydrological characteristics of the catchment. This study proposes a practical methodology for estimating a representative catchment runoff coefficient where high-resolution rainfall and streamflow time series are lacking. Leveraging more than 1,000 historical events from 60 small to medium-sized catchments in diverse climatic regions of Italy, sourced from national Hydrological Yearbooks, we reconstruct annual runoff coefficients from historical hydrological extremes and compare two estimation methods: an event-based and a frequency-based approach.A key element of the event-based method is the development of a procedure to associate discharge maxima with their corresponding rainfall maxima in time, which was necessary because, in many cases, the dates of occurrence of extremes (day/month) were not recorded. On the other hand, a frequency-based pairing of rainfall and discharge extremes was shown to provide runoff coefficient estimates that are comparably robust to those obtained with the event-based approach.Further investigation of case studies characterized by unusually low (below 0.1) or high (above 1) runoff coefficients highlighted several sources of data inconsistency that can compromise estimate reliability. The most common issues include spatial mismatches between rain gauge locations and catchment boundaries, transcription errors in historical datasets, and additional runoff contributions, such as snowmelt in Alpine regions. Recognizing and accounting for these factors allowed for a more consistent and reliable estimation of runoff coefficients.