Spatial interpolation schemes of daily precipitation for hydrologic modeling

Distributed hydrologic models typically require spatial estimates of precipitation interpolated from sparsely located observational points to the specific grid points. We compare and contrast the performance of regression-based statistical methods for the spatial estimation of precipitation in two hydrologically different basins and confirmed that widely used regression-based estimation schemes fail to describe the realistic spatial variability of daily precipitation field. The methods assessed are: (1) inverse distance weighted average; (2) multiple linear regression (MLR); (3) climatological MLR; and (4) locally weighted polynomial regression (LWP). In order to improve the performance of the interpolations, the authors propose a two-step regression technique for effective daily precipitation estimation. In this simple two-step estimation process, precipitation occurrence is first generated via a logistic regression model before estimate the amount of precipitation separately on wet days. This process generated the precipitation occurrence, amount, and spatial correlation effectively. A distributed hydrologic model (PRMS) was used for the impact analysis in daily time step simulation. Multiple simulations suggested noticeable differences between the input alternatives generated by three different interpolation schemes. Differences are shown in overall simulation error against the observations, degree of explained variability, and seasonal volumes. Simulated streamflows also showed different characteristics in mean, maximum, minimum, and peak flows. Given the same parameter optimization technique, LWP input showed least streamflow error in Alapaha basin and CMLR input showed least error (still very close to LWP) in Animas basin. All of the two-step interpolation inputs resulted in lower streamflow error compared to the directly interpolated inputs.     

Comparison of transfer functions in statistical downscaling models for daily temperature and precipitation over Canada

This study compares three linear models and one non-linear model, specifically multiple linear regression (MLR) with ordinary least squares (OLS) estimates, robust regression, ridge regression, and artificial neural networks (ANNs), to identify an appropriate transfer function in statistical downscaling (SD) models for the daily maximum and minimum temperatures (T_max and T_min) and daily precipitation occurrence and amounts (P_occ and P_amount). This comparison was made over twenty-five observation sites located in five different Canadian provinces (British Columbia, Saskatchewan, Manitoba, Ontario, and Québec). Reanalysis data were employed as atmospheric predictor variables of SD models. Predictors of linear transfer functions and ANN were selected by linear correlations coefficient and mutual information, respectively. For each downscaled case, annual and monthly models were developed and analysed. The monthly MLR, annual ANN, annual ANN, and annual MLR yielded the best performance for T_max, T_min, P_occ and P_amont according to the modified Akaike information criterion (AICu). A monthly MLR is recommended for the transfer functions of the four predictands because it can provide a better performance for the T_max and as good performance as the annual MLR for the T_min, P_occ, and P_amount. Furthermore, a monthly MLR can provide a slightly better performance than an annual MLR for extreme events. An annual MLR approach is also equivalently recommended for the transfer functions of the four predictands because it showed as good a performance as monthly MLR in spite of its mathematical simplicity. Robust and ridge regressions are not recommended because the data used in this study are not greatly affected by outlier data and multicollinearity problems. An annual ANN is recommended only for the T_min, based on the best performance among the models in terms of both the RMSE and AICu.     

Univariate streamflow forecasting using commonly used data-driven models: literature review and case study

Eight data-driven models and five data pre-processing methods were summarized; the multiple linear regression (MLR), artificial neural network (ANN) and wavelet decomposition (WD) models were then used in short-term streamflow forecasting at four stations in the East River basin, China. The wavelet–artificial neural network (W-ANN) method was used to predict 1-month-ahead monthly streamflow at Longchuan station (LS). The results indicate better performance of MLR and wavelet–multiple linear regression (W-MLR) in analysing the stationary trained dataset. Four models showed similar performance in 1-day-ahead streamflow forecasting, while W-MLR and W-ANN performed better in 5-day-ahead forecasting. Three reservoirs were shown to have more influence on downstream than upstream streamflow and models had the worst performance at Boluo station. Furthermore, the W-ANN model performed well for 1-month-ahead streamflow forecasting at LS with consideration of a deterministic component.     

A combined rotated general regression neural network method for river flow forecasting

ABSTRACT

This study focused on the performance of the rotated general regression neural network (RGRNN), as an enhancement of the general regression neural network (GRNN), in monthly-mean river flow forecasting. The study of forecasting of monthly mean river flows in Heihe River, China, was divided into two steps: first, the performance of the RGRNN model was compared with the GRNN model, the feed-forward error back-propagation (FFBP) model and the soil moisture accounting and routing (SMAR) model in their initial model forms; then, by incorporating the corresponding outputs of the SMAR model as an extra input, the combined RGRNN model was compared with the combined FFBP and combined GRNN models. In terms of model efficiency index, R², and normalized root mean squared error, NRMSE, the performances of all three combined models were generally better than those of the four initial models, and the RGRNN model performed better than the GRNN model in both steps, while the FFBP and the SMAR were consistently the worst two models. The results indicate that the combined RGRNN model could be a useful river flow forecasting tool for the chosen arid and semi-arid region in China.

Editor D. Koutsoyiannis; Associate editor not assigned     

A non-linear and non-stationary perspective for downscaling mean monthly temperature: a wavelet coupled second order Volterra model

This study presents a multiscale framework for downscaling of the General Circulation Model (GCM) outputs to the mean monthly temperature at regional scale using a wavelet based Second order Voltera (SoV) model. The models are developed using the reanalysis climatic data from the National Centers for Environmental Prediction (NCEP) and are validated using the simulated climatic dataset from the Can CM4 GCM for five locations in the Krishna river basin, India. K-means clustering, based on the multiscale wavelet entropy of the predictors, is used for obtaining the clusters of the input climatic variables. Principal component analysis (PCA) is used to obtain the representative variables from each cluster. These input variables are then used to develop a wavelet based multiscale model using Second order Volterra approach to simulate observed mean monthly temperature for the selected locations in the basin. These models are called W-P-SoV models in this paper. For the purpose of comparison, linear multi-resolution models are developed using Multiple Linear regression (MLR) and are called W-P MLR models. The performance of the models is further compared with other Wavelet-PCA based models coupled with Multiple linear regression models (P-MLR) and Artificial Neural Networks (P-ANN), and, stand-alone MLR and ANN to establish the superiority of the proposed approach. The results indicate that the performance of the wavelet based models is superior in terms of downscaling accuracy when compared with the other models used.     

Long-range forecasting of suspended sediment

This study examines the employment of two methods, multiple linear regression (MLR) and an artificial neural network (ANN), for multistep ahead forecasting of suspended sediment. The autoregressive integrated moving average (ARIMA) model is considered for one-step ahead forecasting of sediment series in order to provide a comparison with the MLR and ANN methods. For one- and two-step ahead forecasting, the ANN model performance is superior to that of the MLR model. For longer ranges, MLR models provide better accuracy, but there is an important assumption violation. The Durbin-Watson statistics of the MLR models show a noticeable decrease from 1.3 to 0.5, indicating that the residuals are not dependent over time. The scatterplots of the three methods (MLR, ARIMA and ANN) for one-step ahead forecasting for the validation period illustrate close fits with the regression line, with the ANN configuration having a slightly higher R² value.     

Modelling long-term groundwater fluctuations by extreme learning machine using hydro-climatic data

The ability of the extreme learning machine (ELM) is investigated in modelling groundwater level (GWL) fluctuations using hydro-climatic data obtained for Hormozgan Province, southern Iran. Monthly precipitation, evaporation and previous GWL data were used as model inputs. Developed ELM models were compared with the artificial neural networks (ANN) and radial basis function (RBF) models. The models were also compared with the autoregressive moving average (ARMA), and evaluated using mean square errors, mean absolute error, Nash-Sutcliffe efficiency and determination coefficient statistics. All the data-driven models had better accuracy than the ARMA, and the ELM model’s performance was superior to that of the ANN and RBF models in modelling 1-, 2- and 3-month-ahead GWL. The RMSE accuracy of the ANN model was increased by 37, 34 and 52% using ELM for the 1-, 2- and 3-month-ahead forecasts, respectively. The accuracy of the ELM models was found to be less sensitive to increasing lead time.     

Hyperspectral estimation model of soil Pb content and its applicability in different soil types

In order to obtain Pb content in soil quickly and efficiently,a multivariate linear regression(MLR) and a principal component regression(PCR) Pb content estimation model were established on the basis of hyperspectral techniques,and their applicability in different soil types was evaluated.Results indicated that Pb exhibited strong spatial heterogeneity in the study area,and more than 82% of the samples exceeded the background value.In addition,the pollution range was large.Pb was sensitive in the nearinfrared band,and the correlation of absorbance(AB) was most significant of all the transformed forms.Both models achieved optimal stability and reliability when AB was used as an independent variable.Compared with the PCR model,the stability,fitting accuracy,and predictive power of the MLR model were superior with a coefficient of determination,root mean square error,and mean relative error of 0.724%,24.92%,and 28.22%,respectively.Both models could be applied to different soil types;however,MLR had better applicability compared with PCR.The PCR model that distinguished different soil types had better reliability than one that did not.Thus,the model established via hyperspectral techniques can achieve largearea,rapid,and efficient soil Pb content monitoring,which can provide technical support for the treatment of heavy metal pollution in soil.     

Monthly total sediment forecasting using adaptive neuro fuzzy inference system

Accurate forecasting of sediment is an important issue for reservoir design and water pollution control in rivers and reservoirs. In this study, an adaptive neuro-fuzzy inference system (ANFIS) approach is used to construct monthly sediment forecasting system. To illustrate the applicability of ANFIS method the Great Menderes basin is chosen as the study area. The models with various input structures are constructed for the purpose of identification of the best structure. The performance of the ANFIS models in training and testing sets are compared with the observed data. To get more accurate evaluation of the results ANFIS models, the best fit model structures are also tested by artificial neural networks (ANN) and multiple linear regression (MLR) methods. The results of three methods are compared, and it is observed that the ANFIS is preferable and can be applied successfully because it provides high accuracy and reliability for forecasting of monthly total sediment.     

西藏地区复杂地形下的降水空间分布估算模型

本文提供了一个描述西藏地区年、季降水量空间分布的估算模型.利用卫星遥测数字化地形高程资料和西藏地区仅有的27个常规气象站的多年平均降水整编资料,根据地形坡向站点分为三类.再采用多元逐步回归方法,建立西藏地区的年、季降水量和经度、纬度、海拔高度、坡度、坡向、遮蔽度等6个地理、地形因子之间的关系模型,估算西藏地区降水量的空间分布.结果表明,此方法建立的关于西藏地区降水量与诸因子之间方程的相关性显著,平均绝对误差、相对误差分别为093mm和116%,对估算模型进行F检验,均通过置信度为095的相关检验,回归效果较显著.分析表明估算降水能够定量、定性地再现西藏地区的实际降水分布.     

Non-linear fuzzy-set based uncertainty propagation for improved DO prediction using multiple-linear regression

In this paper, a new non-linear fuzzy-set based methodology is proposed to characterize and propagate uncertainty through a multiple linear regression (MLR) model to predict DO using flow and water temperature as the regressors. The output is depicted as probabilistic rather than deterministic and is used to calculate the risk of low DO concentration. To demonstrate the new method, data from the Bow River in Calgary, Alberta from 2006 to 2008 are used. Low DO concentration has been occasionally observed in the river and correctly predicting, and quantifying the associated uncertainty and variability of DO is of interest to the City of Calgary. Flow, temperature and DO data were used to construct five MLR models, using different combinations of linear and non-linear fuzzy membership functions. The results show that non-linear representation of variance is superior to the linear approach based on model performance. Normal and Gumbel based membership functions produced the best results. The outputs from two non-linear fuzzy membership models were used to calculate risk of low DO. The predicted risk was between 3.9 and 4.9 %. This is an improvement over the traditional method, which can not indicate a risk of low DO for the same time period. This study demonstrates that water resource managers can adequately use MLR models to predict the risk of low DO using abiotic factors.     

Multi-layer perceptrons with Levenberg-Marquardt training algorithm for suspended sediment concentration prediction and estimation / Prévision et estimation de la concentration en matières en suspension avec des perceptrons multi-couches et l’algorithme d’apprentissage de Levenberg-Marquardt

Abstract

Abstract The prediction and estimation of suspended sediment concentration are investigated by using multi-layer perceptrons (MLP). The fastest MLP training algorithm, that is the Levenberg-Marquardt algorithm, is used for optimization of the network weights for data from two stations on the Tongue River in Montana, USA. The first part of the study deals with prediction and estimation of upstream and down-stream station sediment data, separately, and the second part focuses on the estimation of downstream suspended sediment data by using data from both stations. In each case, the MLP test results are compared to those of generalized regression neural networks (GRNN), radial basis function (RBF) and multi-linear regression (MLR) for the best-input combinations. Based on the comparisons, it was found that the MLP generally gives better suspended sediment concentration estimates than the other neural network techniques and the conventional statistical method (MLR). However, for the estimation of maximum sediment peak, the RBF was mostly found to be better than the MLP and the other techniques. The results also indicate that the RBF and GRNN may provide better performance than the MLP in the estimation of the total sediment load.     

Stream flow forecasting using neuro‐wavelet technique

This paper proposes the application of a neuro‐wavelet technique for modelling monthly stream flows. The neuro‐wavelet model is improved by combining two methods, discrete wavelet transform and multi‐layer perceptron, for one‐month‐ahead stream flow forecasting and results are compared with those of the single multi‐layer perceptron (MLP), multi‐linear regression (MLR) and auto‐regressive (AR) models. Monthly flow data from two stations, Gerdelli Station on Canakdere River and Isakoy Station on Goksudere River, in the Eastern Black Sea region of Turkey are used in the study. The comparison results revealed that the suggested model could increase the forecast accuracy and perform better than the MLP, MLR and AR models. Copyright © 2008 John Wiley & Sons, Ltd.     

Estimation of the Budyko model parameter for small basins in China

At the mean annual scale, water availability of a basin is substantially determined by how much precipitation will be partitioned into evapotranspiration and run-off. The Budyko framework provides a simple but efficient tool to estimate precipitation partitioning at the basin scale. As one form of the Budyko framework, Fu's equation has been widely used to model long-term basin-scale water balance. The major difficulty in applications of Fu's equation is determining how to estimate the curve shape parameter ω efficiently. Previous studies have suggested that the parameter ω is closely related to the long-term vegetation coverage on large river basins globally. However, on small basins, the parameter ω is difficult to estimate due to the diversity of controlling factors. Here, we focused on the estimation of ω for small basins in China. We identified the major factors controlling the basin-specific (calibrated) ω from nine catchment attributes based on a dataset from 206 small basins (≤50,000 km²) across China. Next, we related the calibrated ω to the major factors controlling ω using two statistical models, that is, the multiple linear regression (MLR) model and artificial neural network (ANN) model. We compared and validated the two statistical models using an independent dataset of 80 small basins. The results indicated that in addition to vegetation, other landscape factors (e.g., topography and human activity) need to be considered to capture the variability of ω on small basins better. Contrary to previous findings reached on large basins worldwide, the basin-specific ω and remote sensing-based vegetation greenness index exhibit a significant negative correlation. Compared with the default ω value of 2.6 used in the Budyko curve method, the two statistical models significantly improved the mean annual ET simulations on validation basins by reducing the root mean square error from 114 mm/year to 74.5 mm/year for the MLR model and 70 mm/year for the ANN model. In comparison, the ANN model can provide a better ω estimation than the MLR model.     

Evaluation of multiple stochastic rainfall generators in diverse climatic regions

Long term synthetic precipitation data are useful for water resources planning and management. Commonly stochastic weather generator (SWG) models are useful to produce synthetic time series of unlimited length of weather data based on the statistical characteristics of observed weather at a given location. However, it is difficult to find a single model which works best for all weather (climate) patterns. The objective of this study is to evaluate five different SWG models namely CLIGEN, ClimGen, LARS-WG, RainSim and WeatherMan to generate precipitation at three diverse climatic regions: a Mediterranean climate of western USA, temperate climate of eastern Australia and tropical monsoon region in northern Vietnam. The performance of SWG models to generate precipitation characteristics (i.e., precipitation occurrence; wet and dry spell; and precipitation intensity on wet days) varies between three selected climatic regimes. It was observed that the second order Markov chain (ClimGen and WeatherMan) performed well for all three selected regions in generating precipitation occurrence statistics. All models are able to simulate the ratio of wet/dry spell lengths with respect to observed precipitation. The RainSim performed well in reproducing wet/dry spell lengths in comparison to other models for wetter regions in Australia and Vietnam. ClimGen and WeatherMan are the two best models in simulating precipitation in the western USA, followed by CLIGEN and LARS. Similarly, ClimGen and WMAN are the two best models for synthetic precipitation generation for eastern Australian and northern Vietnam stations, but CLIGEN performs poorly over these regions. All SWG model performed differently with respect to climatic regimes, therefore careful validation is required depending on the weather pattern as well as its application in different water resources sectors. Although our findings are preliminary in nature, however, in order to generalize the performance of SWG’s in a given climate type, it is recommended that more number of stations needs to be evaluated in future studies.     

Non-stationary frequency analysis of extreme precipitation in South Korea using peaks-over-threshold and annual maxima

The conventional approach to the frequency analysis of extreme precipitation is complicated by non-stationarity resulting from climate variability and change. This study utilized a non-stationary frequency analysis to better understand the time-varying behavior of short-duration (1-, 6-, 12-, and 24-h) precipitation extremes at 65 weather stations scattered across South Korea. Trends in precipitation extremes were diagnosed with respect to both annual maximum precipitation (AMP) and peaks-over-threshold (POT) extremes. Non-stationary generalized extreme value (GEV) and generalized Pareto distribution (GPD) models with model parameters made a linear function of time were applied to AMP and POT respectively. Trends detected using the Mann–Kendall test revealed that the stations showing an increasing trend in AMP extremes were concentrated in the mountainous areas (the northeast and southwest regions) of South Korea. Trend tests on POT extremes provided fairly different results, with a significantly reduced number of stations showing an increasing trend and with some stations showing a decreasing trend. For most of stations showing a statistically significant trend, non-stationary GEV and GPD models significantly outperformed their stationary counterparts, particularly for precipitation extremes with shorter durations. Due to a significant-increasing trend in the POT frequency found at a considerable number of stations (about 10 stations for each rainfall duration), the performance of modeling POT extremes was further improved with a non-homogeneous Poisson model. The large differences in design storm estimates between stationary and non-stationary models (design storm estimates from stationary models were significantly lower than the estimates of non-stationary models) demonstrated the challenges in relying on the stationary assumption when planning the design and management of water facilities. This study also highlighted the need of caution when quantifying design storms from POT and AMP extremes by showing a large discrepancy between the estimates from those two approaches.     

中国区域地理、地形因子对降水分布影响的估算和分析

不同与以往基于最小二乘的多元线性回归方法，本文首次尝试将新型的第二代回归分析方法——偏最小二乘回归分析方法应用到中国区域的降水建模中．利用区域内394个气象观测站建站到2000年45年(及以上)的降水资料，建立了一个简单的年、季降水量和地理、地形因子(包括纬度、经度、地形高程、坡度、坡向和遮蔽度)的关系模型，估算了区域降水量中地理、地形的影响部分，并分析了这种影响的特征．结果表明，用此方法建立的模型能够解释70%以上的因变量的变异，相关系数基本都在0.84以上，经交叉有效性检验，模型的回归效果较显著．分析表明，在多元线性回归不适用的情况下，本文基于偏最小二乘法的简单模型能够比较准确地定性、定量地再现实际降水分布．     

Multiple linear regression,multi-layer perceptron network and adaptive neuro-fuzzy inference system for forecasting precipitation based on large-scale climate signals

ABSTRACT

Nowadays, mathematical models are widely used to predict climate processes, but little has been done to compare the models. In this study, multiple linear regression (MLR), multi-layer perceptron (MLP) network and adaptive neuro-fuzzy inference system (ANFIS) models were compared for precipitation forecasting. The large-scale climate signals were considered as inputs to the applied models. After selecting the most effective climate indices, the effects of large-scale climate signals on the seasonal standardized precipitation index (SPI) of the Maharlu-Bakhtaran catchment, Iran, simultaneously and with a delay, was analysed using a cross-correlation function. Hence, the SPI time series was forecasted up to four time intervals using MLR, MLP and ANFIS. The results showed that most of the indices were significant with SPI of different lag times. Comparison of the SPI forecast results by MLR, MLP and ANFIS models showed better performance for the MLP network than the other two models (RMSE = 0.86, MAE = 0.74 for the first step ahead of SPI forecasting).

Editor D. Koutsoyiannis; Associate editor F. Pappenberger     

Anomalies in the US precipitation extremes and their association with different modes of climate variability

ABSTRACT

In this study, we investigate the temporal oscillations of precipitation extremes in different climate regions of the United States. We apply quantile perturbation analysis to average daily precipitation and, to 1041 weather stations with high-quality data from 1900 to 2016. Moreover, we explore the relationship between the extreme precipitation and different well-known cyclical climate modes. Overall, the analysis of average daily precipitation identifies a drier condition in the middle decades of the twentieth century and, a wetter climate in the early century and recent decades. Moreover, the in situ analysis reveals a significant anomaly, mainly prevalent in the Central and Southern regions of the United States. We applied a finite set of linear regression models with different combinations of cyclical climate modes to inform the variability of anomalies with best performing models. Our results highlight the dominant effect of ENSO and NAO in the wide area of the United States.