Estimation of the transfer function by autoregressive deconvolution techniques—An application to time series analysis

The transfer function of time-dependent models is classically inferred by the ordinary least squares (OLS) techniques. This OLS technique assumes independence of the residuals with time. However, in practical cases, this hypothesis is often not justified producing inefficient estimation of the transfer function. When the residuals constitute an autoregressive process, we propose to apply the Box-Jenkins' method to model the residuals, and to modify in a simple manner the primary convolution equation. Then, a multivariate regression technique is used to infer the transfer function of the new equation producing time-independent residuals. This three-step autoregressive deconvolution technique is particularly efficient for time series analysis. The reconstitution and the forecasting of real data are improved efficiently. Theoretically, the proposed method can be extended to the convolution equations for which the residuals follow a moving average or an autoregressive-moving average process, but the mathematical formulation is no longer direct and explicit. For this general case, we propose to approximate the moving average or the autoregressive-moving average process by an autoregressive process of sufficient order, and then the transfer function. Two case studies in hydrogeology will be used to illustrate the procedure.     

川滇强震的回归—马尔可夫链联合预测

本文应用回归—马尔可夫链联合预测地震的方法,结合川、滇强震的特点,对川、滇强震进行了计算,并作了预测验证。结果表明,该方法对川、滇强震的预测效果较好。     

集成奇异谱分析和自回归滑动平均预测日本近海海平面变化

本文从日本沿岸选取了28个验潮站及联测的GPS站,利用奇异谱分析（Singular Spectrum Analysis,SSA）和SSA+自回归滑动平均（Auto Regression Moving Average,ARMA）方法预测了2014—2018年的近海海平面变化和地壳垂直变化.并用同时段的验潮及GPS的实际测量值进行验证,结果显示,SSA+ARMA预测的相对海平面精度为0.0357~0.0607 m,地壳垂直运动的精度为0.0049~0.0077 m,绝对海平面的精度为0.0433~0.0683 m,且三者SSA+ARMA的预测结果均优于只用SSA预测的结果.在此基础上本文利用SSA+ARMA预测了日本沿岸2019—2023年的近海绝对海平面变化,结果显示,2019—2023年的平均海面高较往年（2014—2018）升高0.0353 m,2003—2023年绝对海平面的变化率为0.0039 m·a^-1,预测结果较为理想.     

A minimalistic approach for evapotranspiration estimation using the Prophet model

ABSTRACT

This study aimed to evaluate the potential of the recently introduced Prophet model for estimating reference evapotranspiration (ETo). A comparative study was conducted for benchmarking the model results with support vector regression (SVR) and temperature-based empirical models (Thornthwaite and Hargreaves) in southern Japan. The performance of the Prophet, SVR and temperature-based empirical models was evaluated by Nash–Sutcliffe efficiency (NSE) and coefficient of determination (R²). The results indicate that temperature-based Prophet and SVR models have greater accuracy than the empirical models. The Prophet model with sole input of relative humidity, sunshine hours or windspeed showed acceptable accuracy (NSE > 0.80; R² > 0.80), while SVR models with similar inputs showed greater errors. Accuracy improved with increasing number of input parameters, giving excellent performance (NSE > 0.95; R² > 0.95) with all input parameters. Hence, the Prophet model is a new promising approach for modelling ETo with limited input variables.     

Improvement of spatial interpolation accuracy of daily maximum air temperature in urban areas using a stacking ensemble technique

ABSTRACT

The reliable and robust monitoring of air temperature distribution is essential for urban thermal environmental analysis. In this study, a stacking ensemble model consisting of multi-linear regression (MLR), support vector regression (SVR), and random forest (RF) optimized by the SVR is proposed to interpolate the daily maximum air temperature (T_max) during summertime in a mega urban area. A total of 10 geographic variables, including the clear-sky averaged land surface temperature and the normalized difference vegetation index, were used as input variables. The stacking model was compared to Cokriging, three individual data-driven methods, and a simple average ensemble model, all through leave-one-station-out cross validation. The stacking model showed the best performance by improving the generalizability of the individual models and mitigating the sensitivity to the extreme daily T_max. This study demonstrates that the stacking ensemble method can improve the accuracy of spatial interpolation of environmental variables in various research fields.     

On solution of the inverse problem for confined aquifer flow via maximum likelihood

Joint estimation of transmissivity (T) and storativity (S) in a confined aquifer is done via maximum likelihood (ML). The differential equation of groundwater flow is discretized by the finite-element method, leading to equation _t+x _t=u _t. Elements of matrices and , as well as estimated covariance matrix of noise termu _t, are functions of T and S. By minimizing the negative loglikelihood function corresponding to discretized groundwater flow equation with respect to T and S, ML estimators are obtained. The ML approach is found to yield accurate estimates of T and S (within 9 and 10% of their actual values, respectively) and showed quadratic convergence in Newton's search technique. Prediction of aquifer response, using ML estimators, results in estimated piezometric heads accurate to ±0.5 m from their actual, exact values. Statistical properties of ML estimators are derived and some basic results for statistical inference are given.     

Statistical Downscaling Based on Dynamically DownscaledPredictors： Application to Monthly Precipitation in Sweden

A prerequisite of a successful statistical downscaling is that large-scale predictors simulated by the General Circulation Model (GCM) must be realistic. It is assumed here that features smaller than the GCM resolution are important in determining the realism of the large-scale predictors. It is tested whether a three-step method can improve conventional one-step statistical downscaling. The method uses predictors that are upscaled from a dynamical downscaling instead of predictors taken directly from a GCM simulation. The method is applied to downscaling of monthly precipitation in Sweden. The statistical model used is a multiple regression model that uses indices of large-scale atmospheric circulation and 850-hPa specific humidity as predictors. Data from two GCMs (HadCM2 and ECHAM4) and two RCM experiments of the Rossby Centre model (RCA1) driven by the GCMs are used. It is found that upscaled RCA1 predictors capture the seasonal cycle better than those from the GCMs, and hence increase the reliability of the downscaled precipitation. However, there are only slight improvements in the simulation of the seasonal cycle of downscaled precipitation. Due to the cost of the method and the limited improvements in the downscaling results, the three-step method is not justified to replace the one-step method for downscaling of Swedish precipitation.     

Glacier development and topographic context

This paper analyses the topographic context of the remaining glaciated areas in the Maladeta Massif (Central Spanish Pyrenees). These ice‐covered surfaces have been incorporated into a geographic information system (GIS) in an attempt at correlating the presence of ice with a range of topographic variables obtained from a digital elevation model. The use of generalized additive models and binary regression tree models enabled us (i) to quantify the spatial variability in the distribution of glaciers attributable to characteristics of the local terrain, (ii) to investigate the interaction between the variables that account for the ice cover distribution and (iii) to map the probability of glacier development. Our results show that although the development of glaciers depends on regional climate conditions, the topographic context is of paramount importance in determining the location, extent, shape and recent evolution of each glacial body. Thus, the joint effect of altitude, exposure to incoming solar radiation, slope and mean curvature is able to explain more than 70 per cent of the observed variance. Copyright © 2006 John Wiley & Sons, Ltd.     

基于改进的Elman神经网络的中长期径流预报

径流中长期预报长期以来一直都是人们关注的热点研究问题。现行的径流预报方法很多,传统的有时间序列法,多元回归分析法等,这些方法虽然简单易用,但是如果预报对象提供的样本容量偏小或者因子选择不够合理,都会造成预报精度偏差过大,难于有效的指导工程应用。鉴于此,本文提出一种改进的采用局部回归的Elman神经网络方法。并应用到凤滩水库优化调度的径流预报中。结果表明,与回归分析法、BP网络相比较,该方法不仅提高了算法的效率,而且提高了预报的精度,在径流预报中具有有效性和优越性。     

近50年汾河上中游流域径流对气候变化的响应分析

以汾河上中游干流水文站近50年的气象水文资料为基础,采用多元回归及敏感性分析方法,对径流、降水和气温三者之间变化规律以及区域水文对气候变化的响应进行了定量分析,结果表明气候变暖导致了蒸发的加剧,并一定程度上造成了汾河干流径流量的减少。预估暖干气候条件下引发干旱灾害的可能性将增强。