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Wavelet regression model for short-term streamflow forecasting

Wavelet regression model for short-term stream?ow forecasting

Ozgur Kisi *

Erciyes University,Engineering Faculty,Civil Eng.Dept.,Hydraulics Division,38039Kayseri,Turkey

a r t i c l e i n f o Article history:

Received 21August 2009

Received in revised form 26May 2010Accepted 7June 2010

This manuscript was handled by

A.Bardossy,Editor-in-Chief,with the assistance of Alin Andrei Carsteanu,Associate Editor Keywords:Stream?ow

Wavelet regression Neural networks ARMA

Forecasting

s u m m a r y

Wavelet regression (WR)technique is proposed for short-term stream?ow forecasting in this study.The WR model is improved combining two methods,discrete wavelet transform and linear regression model.The proposed model is applied to the daily stream?ow data of two stations,Karabuk and Derecikviran,on the Filyos River in the Western Black Sea region of Turkey.Root mean square error (RMSE),mean absolute error (MAE)and correlation coef?cient (R )statistics are used for evaluating the accuracy of the WR mod-els.In the ?rst part of the study,the accuracy of the WR models is compared with the arti?cial neural network (ANN)and autoregressive moving average (ARMA)models in 1-day ahead stream?ow https://www.wendangku.net/doc/522290108.html,parison results reveal that the WR model performs better than the ANN and ARMA models.The ARMA model is also found to be slightly better than the ANN.For the Karabuk and Derecikviran stations,it was found that WR models with RMSE =8.48m 3/s,MAE =2.46m 3/s,R =0.978and RMSE =33.3m 3/s,MAE =10.2m 3/s,R =0.976in the validation stage are superior in forecasting 1-day ahead stream?ows than the most accurate ARMA models with RMSE =13.5m 3/s,MAE =3.44m 3/s,R =0.942and RMSE =46.5m 3/s,MAE =13.2m 3/s,R =0.953,respectively.In the second part of study,WR and ANN models are compared in 2-and 3-day ahead stream?ow forecasting.Based on the comparison results,WR models are found to be more accurate than the ANN models.

1.Introduction

Forecasts of future events are required for many of the activities associated with the planning and operation of the components of a water resource system.With regard to the hydrological compo-nent,both short-term and long term forecasts of stream?ow events are needed in order to optimize the system and to plan for future expansion or reduction.

The application of arti?cial neural network (ANN)method for stream?ow forecasting has received much attention in the last few decades (Karunanithi et al.,1994;Zealand et al.,1999;Chang and Chen,2001;Sivakumar et al.,2002;Sudheer and Jain,2003;Kisi,2004a,2007,2008;Cigizoglu and Kisi,2005;Sahoo and Ray,2006;Antar et al.,2006;Kisi and Cigizoglu,2007;Chokmani et al.,2008;Makkeasorn et al.,2008;Remesan et al.,2009;Wang et al.,2009).Karunanithi et al.(1994)used an ANN model to predict stream?ow.They compared the accuracy of the ANN model with an analytic nonlinear power model and found that the ANN model proved to be more accurate.Zealand et al.(1999)investigated the use of an ANN model for short-term stream?ow forecasting.Forecasting was conducted using quarter monthly time intervals.They explored the capabilities of ANN and compared the performance of this meth-od to conventional approaches used to forecast stream?ow.They

concluded that the ANN consistently outperformed a conventional model during the veri?cation (testing)phase.Chang and Chen (2001)used a fuzzy-neural network model for real-time stream?ow prediction.They compared the model’s results with those of an autoregressive moving average exogenous variables model (AR-MAX)and found that the fuzzy-neural network model could offer a higher degree of reliability and accuracy than the ARMAX in stream?ow forecasting.Sivakumar et al.(2002)used ANN models for 1-day and 7-day-ahead forecasts of daily stream?ow.Sudheer and Jain (2003)compared the feed-forward ANN (FFNN)and radial basis neural networks (RBNN)in daily stream?ow estimation.They found that the FFNN results were similar to those of the RBNN.Kisi (2004a)used ANN models in monthly stream?ow forecasting.He compared the ANN results with the autoregressive models (AR)and found that the ANN model performed better than the AR.MLP models were developed by Cigizoglu and Kisi (2005)which used dif-ferent training algorithms for 1-day ahead forecasting of daily stream?ows.They used k -fold partitioning,a statistical method,in the ANN training stage.Sahoo and Ray (2006)investigated the accu-racy of FFNN and RBNN models in forecasting the daily ?ows of a Hawaiian stream and found that the FFNN outperformed the RBNN.They used stream stage,width,cross-sectional area,and mean velocity as inputs to the FFNN and RBNN models to forecast stream-?ow.Antar et al.(2006)used an ANN model with a backpropagation algorithm in daily stream?ow estimation.Kisi and Cigizoglu (2007)used FFNN,RBNN and generalized regression neural network

*Tel.:+903524370080;fax:+903524375784.E-mail address:kisi@https://www.wendangku.net/doc/522290108.html,.tr

(GRNN)models for forecasting continuous and intermittent stream-?ow time series and found that the RBNN performed slightly better than the FFNN and that both outperformed the GRNN models.They used previous daily stream?ows as inputs to the FFNN,RBNN and GRNN models.Kisi(2007)compared the accuracy of different ANN training algorithms in daily stream?ow forecasting and found that the Levenberg–Marquardt algorithm was more powerful and faster than the conventional gradient descent,conjugate gradient and cas-cade correlation algorithms.Kisi(2008)also investigated the ability of three different ANN techniques for monthly stream?ow forecast-ing and estimation and found that the GRNN performed better than FFNN and RBNN in1-month ahead stream?ow forecasting.How-ever,using a nearby station’s data he found that the FFNN and RBNN outperformed the GRNN models in monthly stream?ow estimation. Chokmani et al.(2008)compared ANN and regression models for estimating river stream?ow when it is affected by icy conditions, and they showed that the ANN models performed better for winter stream?ow estimation.Makkeasorn et al.(2008)compared the accuracy of ANN and genetic programming techniques in short-term stream?ow forecasting.Remesan et al.(2009)used ANN and the Gamma Test in daily runoff prediction.Wang et al.(2009)com-pared the accuracy of ANN and several data-driven methods for forecasting monthly stream?ows and illustrated that arti?cial intel-ligence(AI)methods are powerful tools to model the monthly dis-charge time series and can give better prediction performance than traditional time series approaches(ARMA).ANN has the ability to learn complex and nonlinear relationships that are dif?cult to model with conventional techniques.This is the main reason ANN has become so popular.However,there are some disadvantages to the ANN method.The network structure is hard to determine,and it is usually determined using a trial and error approach,i.e.sensitiv-ity analysis(ASCE Task Committee,2000;Kisi,2004b).Its training algorithm has a tendency to get trapped in local minima,etc.In the present study,a wavelet regression(WR)model that is much easier to interpret is used as an alternative to ANN for short-term stream?ow forecasting.

In the past decade,wavelet transform has become a useful tech-nique for analysing variations,periodicities,and trends in time ser-ies(Smith et al.,1998;Labat et al.,2000,2005;Lu,2002;Chou and Wang,2002;Xingang et al.,2003;Coulibaly and Burn,2004;Labat, 2005;Partal and Kucuk,2006;Zhou et al.,2008).Smith et al. (1998)used a discrete wavelet transform(DWT)for quantifying stream?ow https://www.wendangku.net/doc/522290108.html,bat et al.(2000)applied wavelet methods to rainfall rates and runoffs measured at different sampling rates, from daily to half-hourly.Lu(2002)applied wavelet transform for the decomposition of interdecadal and interannual components of rainfall data during the rainy season.Chou and Wang(2002) used a DWT for the decomposition of the unit hydrograph.They employed on-line estimation of unit hydrograph using the DWT https://www.wendangku.net/doc/522290108.html,ing wavelet analysis Xingang et al.(2003)investi-gated the rainfall spectrum and its impact on North China during the rainy season with summer monsoon decaying in interdecadal time scales.Coulibaly and Burn(2004)used wavelet analysis to identify and describe variability in annual Canadian stream?ows and to gain insights into the dynamic link between the stream-?ows and the dominant modes of climate variability in the North-ern https://www.wendangku.net/doc/522290108.html,bat(2005)reviewed the most recent wavelet applications in the?eld of earth sciences and illustrated new wavelet analysis methods in the?eld of https://www.wendangku.net/doc/522290108.html,bat et al. (2005)demonstrated that the application of new wavelet indica-tors(combined continuous and multiresolution analysis,wavelet entropy,wavelet coherence,wavelet cross-correlation)leads to several improvements in the analysis of global hydrological signal (ENSO,SOI,NAO,SAO)?uctuations and of their mutual time vary-ing relationships.They concluded that wavelets should be used more systematically in preference to classical Fourier analysis,notably in hydrology.Partal and Kucuk(2006)used a DWT for determining possible trends in annual total precipitation series. They used the precipitation records from meteorological stations in Turkey and concluded that the trend analysis on DWT compo-nents of the precipitation time series clearly explained the trend structure of data.Zhou et al.(2008)proposed a wavelet predic-tor–corrector model for the simulation and prediction of monthly discharge time series.All these studies showed that wavelet trans-form is an effective tool for precisely locating irregularly distrib-uted multi-scale features of climate elements in space and time.

The aim of this paper is to investigate the performance of a wavelet regression model for short-term stream?ow forecasting and to compare it with the performance of arti?cial neural network and autoregressive moving average models.

2.Discrete wavelet transform(DWT)

Wavelet function w(t),called the mother wavelet,can be de-?ned as

Rt1

à1

wetTdt?0.w a,b(t)can be obtained through compress-ing and expanding w(t)

a;b

etT?j a jà1=2w

tàb

b2R;a2R;a–0e1T

where w a,b(t)=the successive wavelet,a=scale or frequency factor, b=a time factor;R=the domain of real numbers.

If w a,b(t)satis?es Eq.(1),for the time series f(t)e L2(R)or?nite energy signal,the successive wavelet transform of f(t)is de?ned as

W w fea;bT?j a jà1=2

fetT w

tàb

dte2T

where wetT=complex conjugate functions of w(t).It can be seen from Eq.(2)that the wavelet transform is the decomposition of f(t)at different resolution levels(scales).In other words,to?lter wave for f(t)with different?lters is the essence of wavelet transform.

The successive wavelet is often discrete in real applications.Let

a?a j

,b?kb0a j

,a0>1,b0e R,k,j are integer numbers.The dis-crete wavelet transform of f(t)can be written as

W w fej;kT?aàj=2

fetT weaàj

tàkb0Tdte3T

The most common(and simplest)choice for the parameters a0 and b0is2and1time steps,respectively.This power of two loga-rithmic scaling of time and scale is known as a dyadic grid arrange-ment and is the simplest and most ef?cient case for practical purposes(Mallat,1989).Eq.(3)becomes a binary wavelet trans-form when a0=2,b0=1

W w fej;kT?2àj=2

fetT we2àj tàkTdte4T

The characteristics of the original time series in frequency(a or j) and time domain(b or k)are re?ected at the same time by W w f(a,b) or W w f(j,k).When the frequency resolution of the wavelet trans-form is low,but the time domain resolution is high,a or j becomes small.When the frequency resolution of the wavelet transform is high,but the time domain resolution is low a or j becomes large (Wang and Ding,2003).

For a discrete time series f(t),where occurs at different time t (i.e.here integer time steps are used),the DWT can be de?ned as

W w fej;kT?2àj=2

X Nà1

t?0

fetT we2àj tàkTe5T

where W w fej;kTis the wavelet coef?cient for the discrete wavelet at scale a=2j,b=2j k.

O.Kisi/Journal of Hydrology389(2010)344–353345

DWT operates two sets of functions viewed as high-pass and low-pass?lters.The original time series are passed through high-pass and low-pass?lters and separated at different scales.The time series is decomposed into two:one comprising its trend(the approximation)and the other comprising high frequencies and the fast events(the detail).In the present study,the detail coef?-cients and approximation(A)sub-time series are obtained using Eq.(5).

3.Description of data

The time series of daily stream?ow data from two stations, Karabuk(station no:1314)and Derecikviran(station no:1335) on the Filyos River in the Western Black Sea Region of Turkey were used in this study(Fig.1).The drainage areas at these sites are 5087km2and13,300km2for the Karabuk and Derecikviran sta-tions,respectively.The data used spans a period of16years (5840days)with an observation period between1986and2001 for both stations.The observed data is for hydrological years,i.e. the?rst month of the year is October and the last month of the year is September.

After examining the data and noting the periods in which there were gaps in the?ow variable,the periods for training,testing and validation were chosen.The?rst8years of?ow data(2920days, 50%of the whole data set)was used for training,the second4years of?ow data(1460days,25%of the whole data set)was used for testing and the remaining4years data(1460days,25%of the whole data set)was used for validation.For the Karabuk and Dere-cikviran Station,the daily?ow statistics of training,test,validation and entire data set are presented in Table1.In this table x mean,S x, C sx,x min,x max,r1,r2,r3and r4denote the overall mean,standard deviation,skewness,lag-1,lag-2,lag-3and lag-4auto-correlation coef?cients,respectively.The observed daily stream?ows show high positive skewness(C sx=4.65and4.63).The auto-correlations are quite high showing high persistence(e.g.,r1=0.942,r2=0.847, r3=0.770and r4=0.712).In the training?ow data of the Karabuk Station,minimum and maximum values fall in the ranges1.98–413m3/s.However,the maximum validation?ow data of the Kara-buk Station is595m3/s which is higher than the corresponding training set’s value and the minimum testing?ow data for the Karabuk Station is1.68m3/s which is lower than the correspond-ing training set’s value.The results for the other station are the same.This may cause some extrapolation dif?culties in the predic-tion of extreme?ow values(Kisi,2007).

4.Application and results

WR models were obtained by combining two methods,DWT and linear regression(LR).The WR model is an LR model which uses sub-time series components obtained using DWT on original data.For the WR model inputs,the original time series were decomposed into a certain number of sub-time series components (Ds)by the Mallat DWT algorithm(Mallat,1989).Each component plays a different role in the original time series,and the behavior of each sub-time series is distinct(Wang and Ding,2003).Thus a WR was constructed in which the Ds.of the original input time series are the input of the LR and the original output time series are the output of the LR.

In the present study,the previous stream?ow time series were decomposed into various Ds.at different resolution levels by using DWT to estimate current?ow value.Three resolution levels(2-4-8) were employed in this study.The original stream?ow input time series of the Karabuk and Derecikviran stations and their Ds,that is,the time series of2-day mode(D1),4-day mode(D2),8-day mode(D3)and approximate mode are shown in Figs.2and3. The approximate mode indicates the trend(low frequency)of the original stream?ow time series.The sum of effective details(D2, D3)and approximation components are also given in Figs.2and 3for the Karabuk and Derecikviran stations,respectively.It is clear that the sum of the series is very similar to the original stream?ow time series.

The correlation coef?cients between each D sub-time series and original daily stream?ow time series are given in Table2for the Karabuk and Derecikviran stations,respectively.In this table,the D tà1and Q t denotes the D sub-time series at time tà1and mea-sured stream?ow at time t,respectively.As an example,the à0.029shows the correlation value between D1sub-time series at time tà1(D1tà1)and measured stream?ow at time t,Q t.Thus,

BLACK SEA

Filyos River

Karabuk Station

Derecikviran Station 346O.Kisi/Journal of Hydrology389(2010)344–353

the D1tà1,D2tà1,...denote the sub-time series of the Q tà1and vice versa.The correlation values given in Table2provide information for the determination of effective wavelet components on stream-?ow.It can be seen from Table2that the D1component shows low correlations for both stations.The D3components have the highest correlations.According to these correlation analyses between Ds. and original current stream?ow data(output),the effective com-ponents(D2and D3)were selected.For the WR model,the new series obtained by adding the effective Ds.and approximation component were used as inputs to the LR model.The structure of the WR model is shown in Fig.4.

Root mean square error(RMSE),mean absolute error(MAE)and correlation coef?cient(R)statistics were used to evaluate the accu-racy of the WR model.The RMSE and MAE are de?ned as

RMSE?

???????????????????????????????????????????????????????????

X N

i?1

eYi obser v edàY i estimateT2

v u

u t

e6T

MAE?1

X N

i?1

j Y i obser v edàY i estimate je7T

in which N is the number of data set,and Y i is the daily stream?ow.

The performance of the WR models was then tested and

validated for two different applications.In the?rst application,

1-day-ahead stream?ow was predicted using the preceding

stream?ow values,and WR models were compared with the ANN

and ARMA models.In the second application,2-and3-day-ahead

stream?ow forecasting were employed,and WR models were com-

pared with ANN models.The test and validation results of the

models are presented and discussed below.

4.1.One-day-ahead stream?ow forecasting

In this part of the study,the focus is given to the performance

comparison of the WR and ANN models in1-day ahead prediction

of stream?ows.For the Karabuk and Derecikviran stations,the cor-

relation analyses of the data were employed for selecting appropri-

ate input vectors to the WR and ANN models.The auto-correlation

statistics and the corresponding95%con?dence bands from lag-0

to lag-10were estimated for the stream?ow time series(Fig.5).

It is obvious from Fig.5that the stream?ow data have signi?cant

Table1

The daily statistical parameters of the data set for Karabuk and Derecikviran station(x mean,S x,C sx,x min,x max,r1,r2,r3and r4denote the overall mean,standard deviation,skewness, lag-1,lag-2,lag-3and lag-4auto-correlation coef?cients,respectively).

Station Data set x mean(m3/s)S x(m3/s)C sx(m3/s)x min(m3/s)x max(m3/s)r1r2r3r4

Karabuk(1314)Training24.333.8 3.60 1.984130.9430.8550.7900.741 Test19.231.4 4.550.903410.9660.9050.8450.794

Validation25.240.0 5.79 1.685950.9250.7970.6920.617

Entire23.234.9 4.650.905950.9420.8470.7700.712

Derecikviran(1335)Training98.2103 3.098.513730.9250.8210.7430.692 Test86.2108 3.2559120.9680.9200.8790.841

Validation112153 5.549.822040.9380.8200.7190.651

Entire98.2119 4.63522040.9390.8420.7630.708

O.Kisi/Journal of Hydrology389(2010)344–353347

auto-correlations for both stations.The estimated partial auto-cor-relation statistics and corresponding 95%con?dence limits be-tween lag-0and lag-10are also presented in Fig.5.For the Karabuk station,the partial auto-correlation function (PACF)indi-cated signi?cant correlation up to lag-3for the Karabuk station and up to lag-4for the Derecikviran station and,thereafter,fell

Table 2

The correlation coef?cients between each of sub-time series and original stream?ow data.Discrete wavelet components

Correlations Mean absolute correlation

D t ài /Q t

D t à2/Q t D t à3/Q t D t à4/Q t Karabuk (1314)station D1à0.029à0.0510.0230.0180.030D20.078à0.062à0.106à0.0290.069D3

0.2690.128à0.046à0.1750.155Approximate

0.9200.9040.8790.8490.888Derecikviran (1335)station D1à0.079à0.0370.0470.0130.044D20.114à0.105à0.174à0.0500.111D3

0.2810.147à0.033à0.1790.160Approximate

0.902

0.885

0.858

0.826

0.868

348O.Kisi /Journal of Hydrology 389(2010)344–353

within the con?dence limits,respectively.The rapid decaying pat-tern of the PACF con?rmed the dominance of the autoregressive process relative to the moving average process.The partial auto-correlation coef?cients suggested incorporating daily stream?ow values up to4day-lag in input vector to the WR and ANN models.

Considering the correlation analyses,four input combinations based on previous daily stream?ows were evaluated to estimate current?ow value.The input combinations evaluated in the study were;(i)Q tà1,(ii)Q tà1and Q tà2,(iii)Q tà1,Q tà2and Q tà3and(iv) Q tà1,Q tà2,Q tà3and Q tà4.In all cases,the output was the stream?ow Q t for the current day.A program code including wavelet toolbox was written in MATLAB language for the development of WR mod-els.The RMSE,MAE and R statistics of WR models in training and test periods are given in Table3.By studying this table,it is obvi-ous that the WR model used at the Karabuk station whose inputs were the?ows of four previous days(input combination iv),has the smallest RMSE,MAE and the highest R.For the Derecikviran station,however,the WR model comprising three previous?ow values was the most accurate.The WR equations obtained for the Karabuk and Derecikviran station are respectively

Qt?2:34TD tà1à2:52TD tà2t1:66TD tà3à0:50TD tà4e8TQt?1:85TD tà1à1:46TD tà2t0:59TD tà3e9T

where Q t denotes the stream?ow value of the current day,TD tà1is obtained by adding the effective details(D2tà1and D3tà1)and approximation components(A tà1)of the Q tà1values.

In addition,daily stream?ow prediction was carried out by feed-forward arti?cial neural networks and autoregressive moving average models.Arti?cial neural networks(ANNs)are based on the present understanding of the biological nervous system.ANNs are massive parallel systems consisting of many processing elements connected by links of weights.Of the many ANN paradigms,the feed-forward backpropagation network(FFBP)is by far the most popular(Haykin,1994).The network is composed of layers of par-allel processing elements,called neurons,with each layer being fully connected to the proceeding layer by interconnection strengths,or weights.Initial estimated weight values are progres-sively corrected during a training process(at each iteration)that compares predicted outputs with known outputs,and backpropa-gates any errors to determine the appropriate weight adjustments which are necessary to minimize the errors.In this study,different FFBP-based ANN models were established for each input combina-tion.The methodology used for adjusting the weights of the ANN model was Levenberg–Marquardt because this technique is more powerful than conventional gradient descent techniques(Hagan and Menhaj,1994;Kisi,2007).Sigmoid and linear activation func-tions were used for the hidden and output node(s),respectively. The hidden layer node numbers of each model were determined after trying various network structures.The ANN networks training was stopped after100iterations.For the Karabuk and Derecikviran stations,the performance statistics of ANN models in training and test periods are given in Table4.The optimum ANN structures are also provided in this table.Here,the ANN(1,2,1)denotes an ANN model comprising1input,2hidden and1output nodes.The num-ber of hidden nodes giving the minimum RMSE in the test period was selected for each ANN model.The optimal number of hidden nodes for the ANN models was found to vary between1and3. For the Karabuk station,the ANN(3,2,1)model,whose inputs were the stream?ows of the three previous days(input combination iii) had the smallest RMSE,MAE and the highest R in the test period. For the Derecikviran station,the ANN(1,1,1)model(input combi-nation i)performed slightly better than the others.By studying Ta-bles3and4,we can see that the WR models seem to be more accurate than the ANN models in training and test periods.The Akaike information criterion(AIC)was used for selecting the best ARMA(p,q)models for each station.Akaike(1974)proposed the information criterion,known as the AIC.We selected the informa-tion criterion proposed by Akaike(1974)as the best ARMA model. The AIC is:

AICekT?N lneMSETt2ke10T

O.Kisi/Journal of Hydrology389(2010)344–353349

where N is the number of data points(for calibration),and k is the number of free parameters used in the ARMA model.The mean square error(MSE)and AIC values of the ARMA(p,q)models are provided for the Karabuk and Derecikviran stations in Table5.It can be seen from this table that the ARMA(2,3)and ARMA(2,2) models perform better than the others for the Karabuk and Dere-cikviran stations,respectively.

The optimal WR,ANN and ARMA models obtained in the test period were validated using the corresponding data set.The perfor-mance statistics of each model for the Karabuk and Derecikviran stations are given in Table6.It is obvious from this table that the WR models perform much better than the ANN and ARMA models. The ARMA models seem to be slightly better than the ANN models. For the Karabuk and Derecikviran stations,the relative RMSE and MAE differences between the WR and ARMA models in the valida-tion period were37–28%and28–23%,respectively.Fig.6demon-strates the stream?ow forecasts of the WR and ANN models in the validation period for the Karabuk station.The forecasts of the WR model are closer to the exact line than those of the ANN and ARMA models.This con?rms the RMSE and MAE statistics,which were evaluated in Table6.There,the WR and ARMA models predict the maximum peak as649m3/s and605m3/s instead of measured 595m3/s,with overestimations of9%and2%,while the ANN re-sults in378m3/s,as the maximum peak with an underestimation of36%.However,the ANN and ARMA prediction of the second maximum peak521m3/s are225m3/s and218m3/s,respectively with underestimations of57%and58%,while the WR predicts it as385m3/s,with an underestimation of26%,respectively.The ANN seems to be the worst at forecasting peak?ows.The compar-ison of the WR,ANN and ARMA models for the Derecikviran station is made in Fig.7.Here,also,the superiority of the WR model can be clearly seen.While the WR and ARMA models predict the maxi-mum peak as2362m3/s and2296m3/s respectively instead of measured2204m3/s,with overestimations of7%and4%,the ANN computes it as1810m3/s,with an underestimation of18%.

Table3

The RMSE,MAE and R statistics of WR models–1-day ahead stream?ow forecasting.

Model inputs Training period Test period

RMSE MAE R RMSE MAE R

(m3/s)(m3/s)(m3/s)(m3/s)

Karabuk station

(i)Q tà110.2 3.360.9537.48 2.530.971

(ii)Q tà1and Q tà28.27 2.930.970 5.46 2.000.985 (iii)Q tà1,Q tà2and Q tà3 6.24 2.400.983 4.23 1.530.991 (iv)Q tà1,Q tà2,Q tà3and Q tà4 5.62 2.070.986 3.97 1.340.992

Derecikviran station

(i)Q tà133.512.70.94624.110.70.975

(ii)Q tà1and Q tà227.311.10.96520.19.280.983 (iii)Q tà1,Q tà2and Q tà322.89.020.97517.17.410.987 (iv)Q tà1,Q tà2,Q tà3and Q tà433.716.50.94526.013.70.971

Table4

The RMSE,MAE and R statistics of ANN models–1-day ahead stream?ow forecasting.

Model inputs ANN structures Training period Test period

RMSE MAE R RMSE MAE R

(m3/s)(m3/s)(m3/s)(m3/s)

Karabuk station

(i)Q t ANN(1,2,1)10.9 3.640.9468.19 2.760.965

(ii)Q tà1and Q tà2ANN(2,3,1)9.97 3.340.9567.49 2.370.972 (iii)Q tà1,Q tà2,and Q tà3ANN(3,2,1)9.73 3.310.9587.26 2.420.973 (iv)Q tà1,Q tà2,Q tà3,and Q tà4ANN(4,2,1)9.75 3.230.9587.39 2.350.972

Derecikviran station

(i)Q t ANN(1,1,1)38.714.70.92627.513.10.968

(ii)Q tà1and Q tà2ANN(2,1,1)33.612.50.94527.811.70.967 (iii)Q tà1,Q tà2,and Q tà3ANN(3,1,1)33.612.50.94527.711.60.967 (iv)Q tà1,Q tà2,Q tà3,and Q tà4ANN(4,3,1)30.212.00.95628.011.40.966

Table5

The MSE and AIC values of the ARMA(p,q)models in test period.

Model Karabuk station Derecikviran station

MSE AIC MSE AIC

AR166.361267459658 AR255.258666939554 AR353.558176779521 AR453.158176809531 ARMA(1,1)53.258146709505 ARMA(2,1)53.158126829532 ARMA(1,2)53.058126859538 ARMA(2,2)52.758096659498 ARMA(3,2)52.858026719514 ARMA(2,3)52.458026739518 ARMA(3,3)52.658086739520Table6

The comparison of WR,ANN and ARMA models–1day aheadtream?ow forecasting.

Model Test period Validation period

RMSE MAE R RMSE MAE R

(m3/s)(m3/s)(m3/s)(m3/s)

Karabuk station

WR(4,1) 3.97 1.340.9928.48 2.460.978 ANN(3,2,1)7.26 2.420.97314.0 3.680.938 ARMA(2,3)7.27 2.230.97313.5 3.440.942

Derecikviran station

WR(3,1)17.17.410.98733.310.20.976 ANN(1,1,1)27.513.10.96852.616.30.940 ARMA(2,2)25.810.10.97146.513.20.953

350O.Kisi/Journal of Hydrology389(2010)344–353

However,the WR prediction of the second maximum peak 2142m 3/s is 1577m 3/s,with an underestimation error of 26%,while the ANN and ARMA models yield as 991m 3/s and 1200m 3/s respectively,with underestimations of 54%and 44%.When compared with the WR and ARMA models,the ANN model is found to be worst.

4.2.Two-and 3-day ahead stream?ow forecasting

The future prediction ability of WR and ANN techniques was tested and validated for 2-and 3-day ahead stream?ow forecast-ing.All of the simulations were conducted for the optimal WR and ANN model con?gurations selected in previous applications.The same data sets were used for the training,testing and valida-tion of the models.Two-day ahead stream?ow forecasting perfor-mances of the WR and ANN models in the test and validation period are presented in Table 7.For the ANN(3,2,1)model,three input nodes represent the daily stream?ows at times ‘t à1’,‘t à2’,and ‘t à3’,whereas the ?ow in the output layer corresponds to time ‘t +1’for the 2-day ahead prediction work.Table 7indi-cates that the WR model performs better than the ANN model according to various performance criteria.Two-day ahead stream-?ow estimates of the WR and ANN models for the Karabuk and Derecikviran stations in the validation period are illustrated in Figs.8and 9.It is clear from the scatterplots that the forecasts of the WR model are less scattered and closer to the exact line than those of the ANN.

The accuracy of the WR and ANN models in 3-day ahead stream?ow forecasting is given in Table 8.According to Table 8,the WR models seem to perform better than the ANN model.The WR and ANN models’3-day ahead stream?ows estimated for the Karabuk and Derecikviran stations in the validation period are illustrated in Figs.10and 11.According to the R coef?cient,the WR model performs better than the ANN model.Tables 6–8and Figs.6–11indicate that both models (WR and ANN)are the most accurate in 1-day ahead stream?ow forecasting.Increasing the time horizon signi?cantly affects the models’performances.

Increasing prediction intervals from 1-day to 3-day leads to deteri-oration in the model’s accuracy.This can be seen from the values of the lag-1,lag-2and lag-3auto-correlation coef?cients given in Table 1which decrease with increasing time intervals.By increas-ing lead times,the WR and ANN models generally underestimate the corresponding stream?ows.Negative biases are clearly seen for the ANN in cases of 2-and 3-day lead times.This indicates that the WR models are superior to the ANN models not only for 1-day ahead stream?ow forecasting but also for 2-and 3-day ahead forecasting.

Table 7

The comparison of WR and ANN models –2-day ahead stream?ow forecasting.Model

Test period Validation period RMSE MAE

RMSE MAE R

(m 3/s)

(m 3/s)(m 3/s)(m 3/s)Karabuk station WR(4,1)9.63

3.300.95216.9 5.200.908ANN(3,2,1)12.7

4.520.91522.5 6.470.828Derecikviran station WR(3,1)34.41

5.90.94960.220.40.920ANN(1,1,1)44.1

24.5

0.920

88.5

30.6

0.815

O.Kisi /Journal of Hydrology 389(2010)344–353351

Overall,improved wavelet regression models which combine two methods,discrete wavelet transform(DWT)and linear regression(LR),seem to be better than ANN and ARMA models for forecasting short-term stream?ows.The original signal(daily stream?ow time series in the present study)is represented at different resolution intervals by DWT.In other words,complex hydrological time series are decomposed into several simple time series using the DWT.Thus,some features of the sub-series,such as its daily periodicity can be seen more clearly than the original signal.To set up a WR model,LR model is constructed with appro-priate sub-series which belong to different scales.Forecasts are more accurate than those obtained directly by original signals be-cause features of the sub-series(such as periodically)are obvious (Ning and Yunping,1998).This is why the WR model performs bet-ter than the ANN.In practice,studying stream?ow time series is dif?cult because it is affected by complex factors.Each time series contains different frequency https://www.wendangku.net/doc/522290108.html,ing only one resolu-tion component to model the stream?ow time series does not eas-ily clarify the internal mechanism of the phenomenon(Chou and Wang,2004).Therefore a WR model that uses several resolution components could be applied to model short-term stream?ow time series.

5.Conclusions

The accuracy of the wavelet regression(WR)technique in fore-casting short-term(1-,2-and3-day ahead)stream?ows has been investigated in this study.The sum of effective details and the approximation component were used as inputs to the WR model. The WR models were tested and validated by applying different in-put combinations of daily stream?ow data of two stations on the Filyos River in the Western Black Sea Region of Turkey.In the?rst part of the study,the test and validation results of the WR models were compared with ANN and ARMA models in1-day ahead stream?ow https://www.wendangku.net/doc/522290108.html,parison results indicated that the WR model performed better than ANN and ARMA models.The ARMA model showed slightly better accuracy than the https://www.wendangku.net/doc/522290108.html,-pared with the ARMA model,the WR model reduced root mean square error and mean absolute error by37–28%and28–23%for the Karabuk and Derecikviran stations,respectively.In the second part of the study,WR forecasts were compared with those of the ANN models in2-and3-day ahead stream?ow forecasting.Results showed that the WR model performed better than the ANN.It can be said that,in general,the simple WR model provides a superior alternative to ANN and ARMA models for developing input–output simulations and for forecasting short-term stream?ows.

The wavelet regression model presented in this study is a sim-ple explicit mathematical formulation.In contrast,the ANN model is a black-box model,that is,the inputs and outputs are known but the box(i.e.model formulation)is closed.Input data is usually fed into the black-box model and output is obtained without under-standing what happens inside the box.The WR model is much sim-pler in contrast to ANN model and can be successfully used in modelling short-term stream?ows.

In the present study,three resolution levels were employed for decomposing stream?ow time series.If more resolution levels were used,the results from the wavelet regression models may turn out to be better.This may be a subject of another study. References

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The comparison of WR and ANN models–3-day ahead stream?ow forecasting.

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Karabuk station

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商务英语词汇与翻译

Unit 1 外资企业foreign enterprise 合资企业joint venture 合作企业cooperative enterprise 龙头企业 a locomotive 国有企业state-owned enterprise 私营企业privately-owned enterprise 荣誉企业honorable enterprise 优质企业qualified enterprise 一级企业class A enterprise 跨国公司multinational company 母公司parent company 子公司subsidiary company 总公司head office 分公司branch office 代表处representative offices 上市公司listed company 私人股份有限公司private limited company 拳头产品core product 环保产品environment-friendly product 专业生产经营specialize in, engage in, handle a range of business including… 占地面积cover an area of… 年产量with an annual output 具有自营进出口权being entitled to self-import and self-export rights 奉行坚持..原则；以..宗旨,在…方针指导下 abide by the principles of …, adhere to the aims of…, based on the motto of the company 产品销往products have been distributed to 获得奖项rank the titles 通过ISO9000 质量认证 be granted the Certificate of ISO9000 International Quality System unit 2 ?维持升幅to an increase sustain) ?到达最高点to reach a peak ?保持不变to remain constant/ stable ?降到最低点to bottom out ?正值…之际on the occasion of ?代表on the behalf of ?承蒙盛情邀请at the gracious invitation of ?年会annual meeting ?商界的朋友们friends from the business community ?marketing presentation营销报告会 ?sales representative 销售代表 ?sales record 销售记录 ?customers’satisfaction顾客满意度 ?manufacturer 生产商 ?retailer 零售商 ?merchant wholesaler 批发商 ?commission agent 佣金代理商 ?facilitating agent 服务代理商 ?经销渠道distribution channel ?营销目标marketing objective ?战略营销strategic marketing ?目标市场target market ?潜在的风险和potential threats and opportunities ?可控因素controllable components ?销售业绩sales performance Unit 3 1、Business relations and cooperation business connections business cooperation technological cooperation scope of cooperation mutually beneficial relations close relationship to cement / continue / enlarge / promote / improve / maintain / interrupt / restore / speed up / reactivate business relationship to reach an agreement to make a deal 2、Investment a heavy /a long-term/ a profitable/ a safe and sure investment foreign direct investment (FDI) portfolio investment investment environment investment intent/ partner exclusively foreign-owne enterprise joint venture cooperative enterprise equity joint venture contractual joint venture 3、Form of Trade merchandise exports and imports service exports and imports bilateral trade leasing trade processing with supplied material processing with imported materials processing with supplied sample assembling with supplied parts 4、Describing products genuine article imitation low-priced goods low quality goods inferior goods superior quality unfinished products top grade goods showy goods high-tech products durable consumer goods modern and elegant in fashion complete in specifications sophisticated technology attractive and durable skillful manufacture 5、Credit commercial credit trade reputation

英语词汇学课本与译文

Introduction 绪论 0.1 The nature and Domain of English lexicology 英语词汇学的定义及研究范围 Lexicology is a branch of linguistics, inquiring into the origins and meanings of words. 词汇学是语言学的一个分支，研究词汇的起源和意义。 English lexicology aims at investigating and studying the morphological structures of English words and word equivalents, their semantic structures, relations, historical development, formation and usages. 英语词汇学研究英语词汇的形态结构、词的对应及其语义结构、词义关系、词的历史演变、词的构成及词的用法等。 English lexicology is a theoretically-oriented course. 英语词汇学是一门理论性课程。 It is chiefly concerned with the basic theories of words in general and of English words in particular. 该课程主要论述词汇学的基本理论，特别是英语词汇的理论知识。 However, it is a practical course as well, for in the discussion, we shall inevitably deal with copious stocks of words and idioms, and study a great many usage examples. 但是，英语词汇学也是一门实践性课程，在该书的论述中，我们将遇到大量的词汇和习语，学习大量词汇用法实例。 Naturally, there will be a large quantity of practice involved. 当然，同时还要接触到大量的词汇练习。 0.2 Its Relation to Other Disciplines 英语词汇学与其它学科的关系 English lexicology itself is a subbranch of linguistics. 英语词汇学是语言学的一个分支。 But it embraces other academic disciplines, such as morphology, semantics, etymology, stylistics, lexicography. 但它却与其他学科相关，如形态学、语义学、词源学、文体学和词典学等。 Each of them has been established as a discipline in its own right. 而这些学科都各成一门学科。 Morphology is the branch of grammar which studies the structure or forms of words, primarily through the use of morpheme construct. 形态学是语法学的一个分支，主要通过运用词素（形位）结构研究词的结构或形式。 This is one of the major concerns of lexicology, for we shall discuss the inflections of words and word-formation and examine how morphemes are combined to form words and words to form sentences. 这是词汇学研究的主要内容之一，因为研究词汇就必需讨论的屈折变化和构词法，考察词素如何构成词、词如何构成句子。 Etymology is traditionally used for the study of the origins and history of the form and meaning of words. 词源学研究词的形式和意义的起源及其历史变化。 Modern English is derived from the languages of early Germanic tribes with a fairly small vocabulary. 现代英语源于词汇量颇小的古日尔曼语。 We shall study how this small vocabulary has grown into a huge modern English vocabulary and explain the changes that have taken place in the forms and meanings of words. 我们将研究这门词汇量很小的语言是如何发展成为词汇量庞大的现代英语，并解释英语词汇的形式和意义是如何变化的。 Stylistics is the study of style. 文体学研究文体。 It is concerned with the user’s choices of linguistic elements in a particular context for special effects. 主要对语用者在特定语境中如何选择语言要素（即如何选择用词、句型等）以达到特定的表达效果进行观察研究。 Among the areas of study: lexis, phonology, syntax, graphology, we shall concentrate on lexis, exploring the stylistic values of words. 在文体学所研究的词汇、音系学、句法学和书写法范围中，我们主要研究词汇，探讨词汇的文体价值。Lexicography shares with lexicology the same problems: the form, meaning, origins and usages of words, but they have a pragmatic difference. 词典学和词汇学探讨同样的问题：词汇的形式、意义、词汇的起源及用法，但两者在语用上还有差异。 A lexicographer’s task is to record the language as it is used so as to present the genuine picture of words to the reader, providing authoritative reference, whereas the student of lexicology is to acquire the knowledge and information of lexis so as to increase their lexical awareness and capacity of language use. 词典学家的任务是实录词汇的用法并把词汇用法的真实情形呈现给读者，为其提供权威性的参考；而词汇学家则是研究词汇的知识和信息，以增强读者对词汇的了解和语言的使用能力。 Though English lexicology has a wide coverage of academic areas, our task is definite and consistent. 英语词汇学的研究范围很大，但我们的任务是明确而系统的。 That is to study English words in different aspects and from different angles. 即从不同角度研究英语词汇的各个方面。0.3 Method of Study 英语词汇学的研究方法 There are generally two approaches to the study of words, namely synchronic and diachronic. 一般来说，词汇研究有两种

自考英语词汇学翻译精华整理

English Lexicology(英语词汇学) 1.English lexicology aims at investigating and studying the morphological structures of English words and word equivalents, their semantic structures, relations, historical development, formation and usages.英语词汇学旨在调查和研究英语单词和单词的等价物的形态结构,其语义结构、关系、历史发展、形成和用法。 2.English Lexicology is correlated with such linguistic disciplines as morphology(形态学), semantics(语义学), etymology(词源学),stylistics （文体论）and lexicography(词典学) Chapter 1--Basic concepts of words and vocabulary 1.Word（词的定义）: A word is a minimal free form of a language that has a given sound and meaning and syntactic function. (1)a minimal free form of a language (2)a sound unity (3)a unit of meaning (4)a form that can function alone in a sentence 词语是语言最小的自由形式，拥有固定的声音和意义以及句法作用。 2.Sound and meaning（声音与意义）: almost arbitrary, “no logical relationship between the sound which stands for a thing or an idea and the actual thing and idea itself”词语是一个符号，代表着世界上其他的事物。每种世界文化已经赞成一定的读音将代表一定的人，事，地方，特性，过程，行动，当然是在语言系统之外。这种象征性的联系几乎总是主观的，并且“在代表事物和思想的声音和实际的事物和思想之间没有法定关系” 3.Sound and form（读音和形式）:不统一的四个原因（1）the English alphabet was adopted from the Romans,which does not have a separate letter to represent each other内因是因为英语字母表采用罗马字母，罗马字母没有独立的字母代表每个读音，因此一些字母代表两个读音或者组合在一起发音。

英语词汇学术语翻译

Terminology Translations on lexicology 英语词汇学术语翻译 A acronym首字母拼音词acronymy首字母拼音法 addition增词 adjective compound复合形容词 affective meaning感情意义 affix词缀 affixation词缀法 Albanian阿尔巴尼亚语（族）aliens非同化词alliteration头韵（法）allomorph词素（形位）变体ambiguity歧义 amelioration of meamng词义的升华analogy类推 analytic language分析性语言antithsis对偶 antonym反义词 antonymy反义关系 appreciative term褒义词 archaic word古词 archaism古词语

argot隐语（黑话）Armenian亚美尼亚语（族）Associated transfer联想转移association联想 associative meanings关联意义 B back－formation逆生法 back clipping词尾截短 Balto－Slavic波罗斯拉夫语（族）bilinguall双语的 basic word stock基本词汇 blend拼缀词 blending拼缀法 borrowed word借词 bound form粘着形式 bound morpheme粘着语素（形位）bound root粘着词根 C casual style随便文体 catchPhrase时髦语 Celtic凯尔特语（族）central meaning中心意义 Clipping截短法 collocability搭配能力

0.高一英语牛津：上海教材牛津版高一年级英语词汇、短语、翻译(按照单元顺序排列)

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