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1.
Calibration of hydrologic models is very difficult because of measurement errors in input and response, errors in model structure, and the large number of non-identifiable parameters of distributed models. The difficulties even increase in arid regions with high seasonal variation of precipitation, where the modelled residuals often exhibit high heteroscedasticity and autocorrelation. On the other hand, support of water management by hydrologic models is important in arid regions, particularly if there is increasing water demand due to urbanization. The use and assessment of model results for this purpose require a careful calibration and uncertainty analysis. Extending earlier work in this field, we developed a procedure to overcome (i) the problem of non-identifiability of distributed parameters by introducing aggregate parameters and using Bayesian inference, (ii) the problem of heteroscedasticity of errors by combining a Box–Cox transformation of results and data with seasonally dependent error variances, (iii) the problems of autocorrelated errors, missing data and outlier omission with a continuous-time autoregressive error model, and (iv) the problem of the seasonal variation of error correlations with seasonally dependent characteristic correlation times. The technique was tested with the calibration of the hydrologic sub-model of the Soil and Water Assessment Tool (SWAT) in the Chaohe Basin in North China. The results demonstrated the good performance of this approach to uncertainty analysis, particularly with respect to the fulfilment of statistical assumptions of the error model. A comparison with an independent error model and with error models that only considered a subset of the suggested techniques clearly showed the superiority of the approach based on all the features (i)–(iv) mentioned above.  相似文献   

2.
Due to the nonlinear feature of a ozone process, regression based models such as the autoregressive models with an exogenous vector process (ARX) suffer from persistent diurnal behaviors in residuals that cause systematic over-predictions and under-predictions and fail to make accurate multi-step forecasts. In this article we present a simple class of the functional coefficient ARX (FARX) model which allows the regression coefficients to vary as a function of another variable. As a special case of the FARX model, we investigate the threshold ARX (TARX) model of Tong [Lecture notes in Statistics, Springer-Verlag, Berlin, 1983; Nonlinear time series: a dynamics system approach, Oxford University Press, Oxford, 1990] which separates the ARX model in terms of a variable called the threshold variable. In this study we use time of day as the threshold variable. The TARX model can be used directly for ozone forecasts; however, investigation of the estimated coefficients over the threshold regimes suggests polynomial coefficient functions in the FARX model. This provides a parsimonious model without deteriorating the forecast performance and successfully captures the diurnal nonstationarity in ozone data. A general linear F-test is used to test varying coefficients and the portmanteau tests, based on the autocorrelation and partial autocorrelation of fitted residuals, are used to test error autocorrelations. The proposed models were applied to a 2 year dataset of hourly ozone concentrations obtained in downtown Cincinnati, OH, USA. For the exogenous processes, outdoor temperature, wind speed, and wind direction were used. The results showed that both TARX and FARX models substantially improve one-day-ahead forecasts and remove the diurnal pattern in residuals for the cases considered.  相似文献   

3.
Application of the artificial neural network (ANN) to predict pseudospectral acceleration or peak ground acceleration is explored in the study. The training of ANN model is carried out using feed-forward backpropagation method and about 600 records from 39 California earthquakes. The statistics of the residuals or modeling error for the trained ANN-based models are almost the same as those for the parametric ground motion prediction equations, derived through regression analysis; the residual or modeling error can be modeled as a normal variate. The similarity and differences between the predictions by these two approaches are shown. The trained ANN-based models, however, are not robust because the models with almost identical mean square errors do not always lead to the same predictions. This undesirable behaviour for predicting the ground motion measures has not been shown or discussed in the literature; the presented results, at least, serve to raise questions and caution on this problem. A practical approach to ameliorate this problem, perhaps, is to consider several trained ANN models, and to take the average of the predicted values from the trained ANN models as the predicted ground motion measure.  相似文献   

4.
We summarize the main elements of a ground-motion model, as built in three-year effort within the Earthquake Model of the Middle East (EMME) project. Together with the earthquake source, the ground-motion models are used for a probabilistic seismic hazard assessment (PSHA) of a region covering eleven countries: Afghanistan, Armenia, Azerbaijan, Cyprus, Georgia, Iran, Jordan, Lebanon, Pakistan, Syria and Turkey. Given the wide variety of ground-motion predictive models, selecting the appropriate ones for modeling the intrinsic epistemic uncertainty can be challenging. In this respect, we provide a strategy for ground-motion model selection based on data-driven testing and sensitivity analysis. Our testing procedure highlights the models of good performance in terms of both data-driven and non-data-driven testing criteria. The former aims at measuring the match between the ground-motion data and the prediction of each model, whereas the latter aims at identification of discrepancies between the models. The selected set of ground models were directly used in the sensitivity analyses that eventually led to decisions on the final logic tree structure. The strategy described in great details hereafter was successfully applied to shallow active crustal regions, and the final logic tree consists of four models (Akkar and Ça?nan in Bull Seismol Soc Am 100:2978–2995, 2010; Akkar et al. in Bull Earthquake Eng 12(1):359–387, 2014; Chiou and Youngs in Earthq Spectra 24:173–215, 2008; Zhao et al. in Bull Seismol Soc Am 96:898–913, 2006). For other tectonic provinces in the considered region (i.e., subduction), we adopted the predictive models selected within the 2013 Euro-Mediterranean Seismic Hazard Model (Woessner et al. in Bull Earthq Eng 13(12):3553–3596, 2015). Finally, we believe that the framework of selecting and building a regional ground-motion model represents a step forward in ground-motion modeling, particularly for large-scale PSHA models.  相似文献   

5.
Correcting the effects of the sphericity of the Earth in the results of the interpretation of gravimetric data is a topical issue in modern gravimetry. Estimating the error of the gravity field calculations due to the replacement of the spherical Earth model by the plane model is an important part of this problem. In this paper, a method is proposed for transforming the plane density models into spherical ones and vice versa. Algorithms for calculating the vertical component of gravity field for both model types are presented. For two extensive plane models of the Earth’s density, their transformation into spherical models is carried out and the resulting gravity fields are compared. The relative root mean square residuals between the fields calculated with this replacement are at most 5%.  相似文献   

6.
Soil moisture is an integral quantity in hydrology that represents the average conditions in a finite volume of soil. In this paper, a novel regression technique called Support Vector Machine (SVM) is presented and applied to soil moisture estimation using remote sensing data. SVM is based on statistical learning theory that uses a hypothesis space of linear functions based on Kernel approach. SVM has been used to predict a quantity forward in time based on training from past data. The strength of SVM lies in minimizing the empirical classification error and maximizing the geometric margin by solving inverse problem. SVM model is applied to 10 sites for soil moisture estimation in the Lower Colorado River Basin (LCRB) in the western United States. The sites comprise low to dense vegetation. Remote sensing data that includes backscatter and incidence angle from Tropical Rainfall Measuring Mission (TRMM), and Normalized Difference Vegetation Index (NDVI) from Advanced Very High Resolution Radiometer (AVHRR) are used to estimate soil water content (SM). Simulated SM (%) time series for the study sites are available from the Variable Infiltration Capacity Three Layer (VIC) model for top 10 cm layer of soil for the years 1998–2005. SVM model is trained on 5 years of data, i.e. 1998–2002 and tested on 3 years of data, i.e. 2003–2005. Two models are developed to evaluate the strength of SVM modeling in estimating soil moisture. In model I, training and testing are done on six sites, this results in six separate SVM models – one for each site. Model II comprises of two subparts: (a) data from all six sites used in model I is combined and a single SVM model is developed and tested on same sites and (b) a single model is developed using data from six sites (same as model II-A) but this model is tested on four separate sites not used to train the model. Model I shows satisfactory results, and the SM estimates are in good agreement with the estimates from VIC model. The SM estimate correlation coefficients range from 0.34 to 0.77 with RMSE less than 2% at all the selected sites. A probabilistic absolute error between the VIC SM and modeled SM is computed for all models. For model I, the results indicate that 80% of the SM estimates have an absolute error of less than 5%, whereas for model II-A and II-B, 80% and 60% of the SM estimates have an error less than 10% and 15%, respectively. SVM model is also trained and tested for measured soil moisture in the LCRB. Results with RMSE, MAE and R of 2.01, 1.97, and 0.57, respectively show that the SVM model is able to capture the variability in measured soil moisture. Results from the SVM modeling are compared with the estimates obtained from feed forward-back propagation Artificial Neural Network model (ANN) and Multivariate Linear Regression model (MLR); and show that SVM model performs better for soil moisture estimation than ANN and MLR models.  相似文献   

7.
Much research has been devoted to the development of numerical models of river incision. In settings where bedrock channel erosion prevails, numerous studies have used field data to calibrate the widely acknowledged stream power model of incision and to discuss the impact of variables that do not appear explicitly in the model's simplest form. However, most studies have been conducted in areas of active tectonics, displaying a clear geomorphic response to the tectonic signal. Here, we analyze the traces left in the drainage network 0.7 My after the Ardennes region (western Europe) underwent a moderate 100–150 m uplift. We identify a set of knickpoints that have traveled far upstream in the Ourthe catchment, following this tectonic perturbation. Using a misfit function based on time residuals, our best fit of the stream power model parameters yields m = 0.75 and K = 4.63 × 10‐8 m‐0.5y‐1. Linear regression of the model time residuals against quantitative expressions of bedrock resistance to erosion shows that this variable does not correlate significantly with the residuals. By contrast, proxies for position in the drainage system prove to be able to explain 76% of the residual variance. High time residuals correlate with knickpoint position in small tributaries located in the downstream part of the Ourthe catchment, where some threshold was reached very early in the catchment's incision history. Removing the knickpoints stopped at such thresholds from the data set, we calculate an improved m = 0.68 and derive a scaling exponent of channel width against drainage area of 0.32, consistent with the average value compiled by Lague for steady state incising bedrock rivers. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

8.
Two analyses, one based on multiple regression and the other using the Holt–Winters algorithm, for investigating non‐stationarity in environmental time series are presented. They are applied to monthly rainfall and average maximum temperature time series of lengths between 38 and 108 years, from six stations in the Murray Darling Basin and four cities in eastern Australia. The first analysis focuses on the residuals after fitting regression models which allow for seasonal variation, the Pacific Decadal Oscillation (PDO) and the Southern Oscillation Index (SOI). The models provided evidence that rainfall is reduced during periods of negative SOI, and that the interaction between PDO and SOI pronounces this effect during periods of negative PDO. Following this, there was no evidence of any trend in either the PDO or SOI time series. The residuals from this regression were analysed with a cumulative sum (CUSUM) technique, and the statistical significance was assessed using a Monte Carlo method. The residuals were also analysed for volatility, autocorrelation, long‐range dependence and spatial correlation. For all ten rainfall and temperature time series, CUSUM plots of the residuals provided evidence of non‐stationarity for both temperature and rainfall, after removing seasonal effects and the effects of PDO and SOI. Rainfall was generally lower in the first half of the twentieth century and higher during the second half. However, it decreased again over the last 10 years. This pattern was highlighted with 5‐year moving average plots. The residuals for temperature showed a complementary pattern with increases in temperature corresponding to decreased rainfall. The second analysis decomposed the rainfall and temperature time series into random variation about an underlying level, trend and additive seasonal effects and changes in the level; trend and seasonal effects were tracked using a Holt–Winters algorithm. The results of this analysis were qualitatively similar to those of the regression analysis. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

9.
Gerd Bürger 《水文研究》2017,31(22):4039-4042
A main obstacle to trend detection in time series occurs when they are autocorrelated. By reducing the effective sample size of a series, autocorrelation leads to decreased trend significance. Numerous recipes attempt to mitigate the effect of autocorrelation, either by adjusting for the reduced effective sample size or by removing the autocorrelated components of a series. This short note deals with the latter, also called prewhitening (PW). It is known that removal of autocorrelation also removes part of the trend, which may affect the signal‐to‐noise ratio. Two popular methods have dealt with this problem, the trend‐free prewhitening (TFPW) and the iterative prewhitening. Although it is generally accepted that both methods reduce the adverse effects of PW on the trend magnitude, corresponding effects on statistical significance have not been clearly stated for TFPW. Using a Monte Carlo approach, it is demonstrated that both methods entail quite different Type‐I error rates. The iterative prewhitening produces rates that are generally close to the nominal significance level. The TFPW, however, shows very high Type‐I error rates with increasing autocorrelation. The corresponding rate of false trend detections is unacceptable for applications, so that published trends based on TFPW need to be reassessed.  相似文献   

10.
The CE-Qual-ICM model computes phytoplankton biomass and production as a function of temperature, light, and nutrients. Biomass is computed as carbon while inorganic nitrogen, phosphorus, and silica are considered as nutrients. Model formulations for production, metabolism, predation, nutrient limitation, and light limitation are detailed. Methods of parameter determination and parameter values are presented. Results of model application to a ten-year period in Chesapeake Bay indicate the model provides reasonable representations of observed biomass, nutrient concentrations, and limiting factors. Computed primary production agrees with observed under light-limited conditions. Under strongly nutrient-limited conditions, computed product is less than observed. The production characteristics of the model are similar to behavior reported for several similar models. Process omitted from the model that may account for production shortfalls include variable algal stoichiometry, use of urea as nutrient, and vertical migration by phytoplankton.  相似文献   

11.
In the present study, a seasonal and non-seasonal prediction of the Standardized Precipitation Index (SPI) time series is addressed by means of linear stochastic models. The methodology presented here is to develop adequate linear stochastic models known as autoregressive integrated moving average (ARIMA) and multiplicative seasonal autoregressive integrated moving average (SARIMA) to predict drought in the Büyük Menderes river basin using SPI as drought index. Temporal characteristics of droughts based on SPI as an indicator of drought severity indicate that the basin is affected by severe and more or less prolonged periods of drought from 1975 to 2006. Therefore, drought prediction plays an important role for water resources management. ARIMA modeling approach involves the following three steps: model identification, parameter estimation, diagnostic checking. In model identification step, considering the autocorrelation function (ACF) and partial autocorrelation function (PACF) results of the SPI series, different ARIMA models are identified. The model gives the minimum Akaike Information Criterion (AIC) and Schwarz Bayesian Criterion (SBC) is selected as the best fit model. Parameter estimation step indicates that the estimated model parameters are significantly different from zero. Diagnostic check step is applied to the residuals of the selected ARIMA models and the results indicated that the residuals are independent, normally distributed and homoscedastic. For the model validation purposes, the predicted results using the best ARIMA models are compared to the observed data. The predicted data show reasonably good agreement with the actual data. The ARIMA models developed to predict drought found to give acceptable results up to 2 months ahead. The stochastic models developed for the Büyük Menderes river basin can be employed to predict droughts up to 2 months of lead time with reasonably accuracy.  相似文献   

12.
Spatial (two-dimensional) distributions in ecology are often influenced by spatial autocorrelation. In standard regression models, however, observations are assumed to be statistically independent. In this paper we present an alternative to other methods that allow for autocorrelation. We show that the theory of wavelets provides an efficient method to remove autocorrelations in regression models using data sampled on a regular grid. Wavelets are particularly suitable for data analysis without any prior knowledge of the underlying correlation structure. We illustrate our new method, called wavelet-revised model, by applying it to multiple regression for both normal linear models and logistic regression. Results are presented for computationally simulated data and real ecological data (distribution of species richness and distribution of the plant species Dianthus carthusianorum throughout Germany). These results are compared to those of generalized linear models and models based on generalized estimating equations. We recommend wavelet-revised models, in particular, as a method for logistic regression using large datasets.  相似文献   

13.
We describe an objective method for evaluating the spatial distribution of water equivalents of the snow cover within a small catchment. Regression analysis is used to quantify the relationship between elevation, presence or absence of forest, and potential direct solar radiation as independent variables and water equivalent as measured at a number of sites. First, this regression relationship is used to interpolate water equivalent data all over the basin area. Then we interpolate the residuals of the regression using a geostatistical approach. Superimposing the results obtained by interpolating the regression relationship and the interpolated residuals eventually yields the water equivalent distribution over the test area. The advantages of the interpolation method used lie in the optimal (effective, unbiased) estimation of the interpolated values as well as in the possibility to quantify the associated estimation variances.  相似文献   

14.
Improving Regional Seismic Event Location in China   总被引：1，自引：0，他引：1  
—?In an effort to improve our ability to locate seismic events in China using only regional data, we have developed empirical propagation path corrections and applied such corrections using traditional location routines. Thus far, we have concentrated on corrections to observed P arrival times for crustal events using travel-time observations available from the USGS Earthquake Data Reports, the International Seismic Centre Bulletin, the preliminary International Data Center Reviewed Event Bulletin, and our own travel-time picks from regional data. Location ground truth for events used in this study ranges from 25?km for well-located teleseimic events, down to 2?km for nuclear explosions located using satellite imagery. We also use eight events for which depth is constrained using several waveform methods. We relocate events using the EvLoc algorithm from a region encompassing much of China (latitude 20°–55°N; longitude 65°–115°E). We observe that travel-time residuals exhibit a distance-dependent bias using IASPEI91 as our base model. To remedy this bias, we have developed a new 1-D model for China, which removes a significant portion of the distance bias. For individual stations having sufficient P-wave residual data, we produce a map of the regional travel-time residuals from all well-located teleseismic events. Residuals are used only if they are smaller than 10?s in absolute value and if the seismic event is located with accuracy better than 25?km. From the residual data, correction surfaces are constructed using modified Bayesian kriging. Modified Bayesian kriging offers us the advantage of providing well-behaved interpolants and their errors, but requires that we have adequate error estimates associated with the travel-time residuals from which they are constructed. For our P-wave residual error estimate, we use the sum of measurement and modeling errors, where measurement error is based on signal-to-noise ratios when available, and on the published catalog estimate otherwise. Our modeling error originates from the variance of travel-time residuals for our 1-D China model. We calculate propagation path correction surfaces for 74 stations in and around China, including six stations from the International Monitoring System. The statistical significance of each correction surface is evaluated using a cross-validation technique. We show relocation results for nuclear tests from the Balapan and Lop Nor test sites, and for earthquakes located using interferometric synthetic aperture radar. These examples show that the use of propagation path correction surfaces in regional relocations eliminates distance bias in the residual curves and significantly improves the accuracy and precision of seismic event locations.  相似文献   

15.
This paper proposes a simple class of threshold autoregressive model for purpose of forecasting daily maximum ozone concentrations in Southern California. Linear time series model has been widely considered in environmental modeling. However, this class of models fails to capture the nonlinearity in ozone process and the complexity of meteorological interactions with ozone. In this article, we used the threshold autoregressive models with two classes of regimes; periodic and meteorological regimes. Days in week were used for the periodic regimes and the regression tree method was used to define the regimes as a function of meteorological variables. As the reference model we used the autoregressive model with lagged ozone and various lagged meteorological variables as the covariates. The proposed models were applied to a 3-year dataset of daily maximum ozone concentrations obtained from five monitoring stations in San Bernardino County, CA and their forecast performances were evaluated using an independent year-long dataset from the same stations. The results showed that the threshold models well capture the nonlinearity in ozone process and remove the nonstationarity in model residuals. The threshold models outperformed the non-threshold autoregressive models in day-ahead forecasts. The tree-based model showed slightly better performance than the periodic threshold model.  相似文献   

16.
高精度GRACE卫星时变重力场反演一直是卫星重力测量中的难题.为了恢复高精度的时变地球重力场模型,本文联合GRACE卫星的星载GPS和KBR星间测速观测数据,在对GRACE卫星进行精密定轨的同时,解算出60阶月平均地球重力场模型.通过对GRACE卫星的定轨精度、星载GPS相位和KBR星间测速数据的拟合残差以及时变地球重力场模型解算精度等分析,表明:(1)与美国宇航局喷气推进实验室(JPL)发布的约化动力学精密轨道相比,本文确定GRACE卫星轨道三维位置误差小于5 cm.(2)星载GPS相位数据拟合残差为5~8 mm,KBR星间测速数据拟合残差为0.18~0.30μm·s~(-1).(3)解算的月平均重力场模型与美国德克萨斯大学空间研究中心(CSR)、德国地学研究中心(GFZ)和JPL发布的RL05模型精度接近,时变信号在全球范围内具有很好的空间分布一致性.通过计算亚马逊流域和长江流域的水储量变化,本文与上述三个机构的计算结果无明显差异,且相关系数均达0.9以上.可见,本文建立的卫星轨道与重力场同解算法具有反演高精度GRACE时变重力场能力,为我国卫星重力场反演提供了重要的技术支持.  相似文献   

17.
Abstract: Linear continuous time stochastic Nash cascade conceptual models for runoff are developed. The runoff is modeled as a simple system of linear stochastic differential equations driven by white Gaussian and marked point process noises. In the case of d reservoirs, the outputs of these reservoirs form a d dimensional vector Markov process, of which only the dth coordinate process is observed, usually at a discrete sample of time points. The dth coordinate process is not Markovian. Thus runoff is a partially observed Markov process if it is modeled using the stochastic Nash cascade model. We consider how to estimate the parameters in such models. In principle, maximum likelihood estimation for the complete process parameters can be carried out directly or through some form of the EM (estimation and maximization) algorithm or variation thereof, applied to the observed process data. In this research we consider a direct approximate likelihood approach and a filtering approach to an algorithm of EM type, as developed in Thompson and Kaseke (1994). These two methods are applied to some real life runoff data from a catchment in Wales, England. We also consider a special case of the martingale estimating function approach on the runoff model in the presence of rainfall. Finally, some simulations of the runoff process are given based on the estimated parameters.  相似文献   

18.
Abstract

Application of the concept of combining the estimated forecast output of different rainfall-runoff models to yield an overall combined estimated output in the context of real-time river flow forecasting is explored. A Real-Time Model Output Combination Method (RTMOCM) is developed, based on the structure of the Linear Transfer Function Model (LTFM) and utilizing the concept of the Weighted Average Method (WAM) for model output combination. A multiple-input single-output form of the LTFM is utilized in the RTMOCM. This form of the LTFM model uses synchronously the daily simulation-mode model-estimated discharge time series of the rainfall-runoff models selected for combination, its inherent updating structure being used for providing updated combined discharge forecasts. The RTMOCM is applied to the daily data of five catchments, using the simulation-mode estimated discharges of three selected rainfall-runoff models, comprising one conceptual model (Soil Moisture Accounting and Routing Procedure—SMAR) and two black-box models (Linear Perturbation Model—LPM and Linearly-Varying Variable Gain Factor Model—LVGFM). In order to get an indication of the accuracy of the updated combined discharge forecasts relative to the updated discharge forecasts of the individual models, the LTFM is also used for updating the simulation-mode discharge time series of each of the three individual models. The results reveal that the updated combined discharge forecasts provided by the RTMOCM, with parameters obtained by linear regression, can improve on the updated discharge forecasts of the individual rainfall-runoff models.  相似文献   

19.
通过福建及台湾海峡地区的新一维速度模型与现有华南速度模型的对比,讨论了新一维速度模型在福建地震观测台网的适用性。理论走时分析结果表明,尽管两个速度模型差异明显,但震中距在0—100 km范围内的震相理论走时相差较小,一定程度上说明两速度模型所给出的本区域地壳平均速度差异较小。对利用18次人工定点爆破记录的地震定位结果的分析表明:当震源深度不受约束时,应用华南速度模型的定位结果精度稍优于新一维速度模型;将震源深度固定为0 km后,应用新一维速度模型的定位结果精度则明显优于华南模型。对19个仙游震群序列事件进行定位的结果显示,由于华南地区速度结构的横向变化较小,应用两模型的地震定位精度结果基本相当,但新一维速度模型定位的发震时刻较华南速度模型普遍早0.61 s左右,因此使得事件定位残差显著增大。   相似文献   

20.
Stochastic Environmental Research and Risk Assessment - Regression modelling where explanatory variables are measured with error is a common problem in applied sciences. However, if inappropriate...  相似文献   

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