本人發(fā)展了一個(gè)潮汐調(diào)和分析的新方法EHA，并以此開(kāi)發(fā)了工具包S_TIDE, S_TIDE功能要比T_TIDE工具包更為強(qiáng)大，T_TIDE只能用于分析平穩(wěn)潮，而S_TIDE既可以分析平穩(wěn)潮，也能分析非平穩(wěn)潮，還能用于分析非潮周期的時(shí)間序列。首先去https://www.researchgate.net/project/A-non-stationary-tidal-analysis-toolbox-S-TIDE下載工具包，并安裝到matlab當(dāng)前目錄下。

經(jīng)典調(diào)和分析方法及其開(kāi)發(fā)的工具包T_TIDE只能輸出調(diào)和常數(shù)（即不隨時(shí)間變化的振幅和遲角）。但是實(shí)際上由于潮汐與非潮過(guò)程（比如河流徑流）的非線性相互作用，會(huì)導(dǎo)致振幅和遲角在很短的時(shí)間內(nèi)有非常大的變化，這種情況下，T_TIDE就不適用了，而S_TIDE正是為這種情形開(kāi)發(fā)出來(lái)的。通過(guò)調(diào)整輸入?yún)?shù)獨(dú)立點(diǎn)個(gè)數(shù)，S_TIDE可以輸出振幅和遲角在不同時(shí)間尺度上的震蕩。獨(dú)立點(diǎn)越多，振幅和遲角的變化就包含更多高頻的震蕩。獨(dú)立點(diǎn)越少，振幅和遲角的變化就越簡(jiǎn)單。當(dāng)獨(dú)立點(diǎn)減少為1時(shí)，S_TIDE輸出結(jié)果和T_TIDE是一模一樣的，只能得到不隨時(shí)間變化的振幅和遲角。

S_TIDE 工具包主函數(shù)為s_tide.m（如下所示）,下面介紹一下輸入和輸出參數(shù)

[St,Ht,Gt,coef,xout,ju,Stint,Htint,Gtint]=s_tide(xin,IDP1,IDP2,tides,ntides,dt,interpolation,method)

輸入?yún)?shù)：xin待分析的水位時(shí)間序列?IDP1平均海平面使用的獨(dú)立點(diǎn)個(gè)數(shù)??IDP2分潮使用的獨(dú)立點(diǎn)個(gè)數(shù)

tides指定的分潮名稱 ntides輸入的分潮個(gè)數(shù) dt水位采樣間隔,一般為1小時(shí)

interpolation插值方法，一般為三次樣條插值?

method 擬合算法，可以選擇普通最小二乘（ols）或者魯棒擬合（robustfit)，魯棒擬合可以明顯減少數(shù)據(jù)中離群點(diǎn)對(duì)于擬合結(jié)果的影響，提高結(jié)果的可信度，但是它計(jì)算較慢

輸出參數(shù)：xout是調(diào)和分析回報(bào)水位，St是時(shí)間變化的平均海平面

Ht和Gt是時(shí)間變化的振幅和遲角，Stint,Htint和Gtint是St,Ht和Gt的95%置信區(qū)間

S_TIDE可以求解分潮時(shí)間變化的振幅和遲角，但是當(dāng)獨(dú)立點(diǎn)個(gè)數(shù)取1時(shí)，振幅和遲角都是常數(shù)，此時(shí)S_TIDE計(jì)算結(jié)果與T_TIDE是完全一樣的。下面的程序比較了獨(dú)立點(diǎn)個(gè)數(shù)取1時(shí)S_TIDE計(jì)算結(jié)果與T_TIDE計(jì)算結(jié)果。需要提前安裝T_TIDE工具包。本例子需要加載S_TIDE自帶的數(shù)據(jù)kushiro.mat，該數(shù)據(jù)是1993-01-01?到2012-12-31日本Kushiro驗(yàn)潮站的逐時(shí)水位（從PSMSL上下載的）

figure();load kushiro.mat

[St,Ht,Gt,coef,xout,ju,Stint,Htint,Gtint]=s_tide(kushiro(1:8760),1,1,{'M2';'S2';'K1';'O1';'N2';'Q1';'P1';'K2'},8,1,'spline','ols');

plot(xout-St,'r','linewidth',1.1);hold?on;

set(gca,'Fontsize',15,'linewidth',1.1);

[NAME,FREQ,TIDECON,XOUT]=t_tide(kushiro(1:8760),'interval',1,?'rayleigh',{'M2';'S2';'K1';'O1';'N2';'Q1';'P1';'K2'});

plot(XOUT,'k*');xlim([1 300])

xlabel('Time(hour)');ylabel('Water level(mm)')

運(yùn)行結(jié)果如下圖所示，回報(bào)水位完全一樣：

?

如果未指定具體分潮，s_tide會(huì)根據(jù)數(shù)據(jù)長(zhǎng)度和瑞利準(zhǔn)則自動(dòng)選取分潮。

[St,Ht,Gt,coef,xout,ju,Stint,Htint,Gtint]=s_tide(kushiro(1:8767),1,1,'autoselected','autoselected',1,'spline','ols');

[nameu,fu,tidecon,xout]=t_tide(kushiro(1:8767));?

以下是S_TIDE部分輸出結(jié)果，與T_TIDE輸出結(jié)果幾乎完全一樣

tidal amplitude and phase with 95% CI estimates

tide??freq??????amp????amp_err???pha???pha_err????snr

?SA??0.0001141??14.5843??20.802??-23.71???77.16????0.49

?SSA?0.0002282??24.8904??20.828??152.41???46.20?????1.4

?MSM?0.0013098??15.0585??20.402??226.16????77.42 ????0.54

?MM??0.0015122??25.2273??18.874??138.08???42.92?????1.8

?MSF?0.0028219???7.5535??18.409??221.90??140.95????0.17

?MF??0.0030501??18.3465??19.661???14.29???61.96????0.87

?ALP1 0.0343966???0.8332???2.600??-36.45??178.07?????0.1

*2Q1?0.0357064???3.7988???2.633??152.00???39.17?????2.1

*SIG1 0.0359087???6.1160???2.604??232.25???24.48?????5.5

*Q1??0.0372185??33.7891???2.576????0.92????4.65??1.7e+02

*RHO1 0.0374209???6.9896???2.622??159.79???21.52?????7.1

*O1??0.0387307?184.5366???2.612??-69.90????0.81???5e+03

需要注意的是上面求得的分潮振幅和遲角都沒(méi)有進(jìn)行18.61年矯正，下面的程序T_TIDE和S-TIDE都做了18.61年矯正，二者結(jié)果仍然一樣。

[nameu,fu,tidecon,xout]=t_tide(kushiro(1:8767),'latitude',42.5,'start time',[1993,01,01,00]);%with nodal corrections

[St,Ht,Gt,coef,xout,ju,Stint,Htint,Gtint]=s_tide(kushiro(1:8767),1,1,'autoselected','autoselected',1,'spline','ols');

nobs=length(kushiro(1:8767));nobsu=nobs-rem(nobs-1,2);% makes series odd to give a center point

ctime=datenum(1993,1,1)+(ceil(nobsu/2)-1)/24.0;?% 使用中間時(shí)刻做矯正

[v,u,f]=t_vuf('nodal',ctime,ju,42.5);

u=360*u;%convert to degree

v=360*v;

Hc=Ht(:,1)./f;?%nodal corrected amplitudes 矯正后的振幅

?

Gc=Gt(:,1)+u+v;?%nodal corrected phases 矯正后的遲角

這個(gè)博客只是初步介紹一下S_TIDE工具包的使用，關(guān)于S_TIDE更多的例子（比如用stide工具包里的函數(shù)s_tide_m3來(lái)處理衛(wèi)星高度計(jì)數(shù)據(jù)，s_tide_m6可以處理非均勻采樣衛(wèi)星數(shù)據(jù)）請(qǐng)參考S_TIDE工具包里自帶的s_demo.m里的算例和中英文教程以及發(fā)表的相關(guān)論文

本人開(kāi)發(fā)的S_TIDE工具包最新版本1.19里s_calculate_tidal_ellipse.m 函數(shù)可以計(jì)算最大流速，最大流速時(shí)刻，最大流速方向，以及最小流速，最小流速時(shí)刻，最小流速方向六個(gè)潮流橢圓參數(shù)，s_plot_tidal_ellipse.m可以繪制潮流橢圓。

關(guān)于S_TIDE你如果有什么想法或者困惑，歡迎聯(lián)系我和我交流（panhaidong_phd@qq.com）

如果你使用了S_TIDE工具包，請(qǐng)?jiān)谡撐睦镆梦业恼撐模?/strong>

1. Pan, H., X. Lv, Y. Wang, P. Matte, H. Chen, and G. Jin (2018), Exploration of Tidal-Fluvial Interaction in the Columbia River Estuary Using S_TIDE, J. Geophys. Res. Ocean., 123(9), 6598–6619, doi:10.1029/2018JC014146.

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2. Jin, G., H. Pan, Q. Zhang, X. Lv, W. Zhao, and Y. Gao (2018), Determination of Harmonic Parameters with Temporal Variations: An Enhanced Harmonic Analysis Algorithm and Application to Internal Tidal Currents in the South China Sea, J. Atmos. Ocean. Technol., 35(7), 1375-1398

下面是引用了S_TIDE論文的匯總：

2019年

1.?Olga Bjelotomi Or?uli, Matej Varga, Danko Markovinovi, Tomislav Ba?i, LTide - Matlab/Octave software tool for temporal and spatial analysis of tidal gravity acceleration effects according to Longman formulas, Earth Science Informatics, 10.1007/s12145-019-00379-y, (2019).

2. Min Gan, Yongping Chen, Shunqi Pan, Jiangxia Li, Zijun Zhou, A Modified Nonstationary Tidal Harmonic Analysis Model for the Yangtze Estuarine Tides, Journal of Atmospheric and Oceanic Technology, 10.1175/JTECH-D-18-0199.1, 36, 4, (513-525), (2019).

3. Yuzhe Wang, haidong Pan, Daosheng Wang, Xianqing Lv, A Methodology for Fitting the Time Series of Snow Depth on the Arctic Sea Ice, Journal of Atmospheric and Oceanic Technology, 10.1175/JTECH-D-18-0093.1, 36, 8, (1449-1462), (2019).

4. haidong Pan, Xianqing Lv, Reconstruction of spatially continuous water levels in the Columbia River Estuary: The method of Empirical Orthogonal Function revisited, Estuarine, Coastal and Shelf Science, 10.1016/j.ecss.2019.04.011, 222, (81-90), (2019).

5. haidong Pan, Quanxin Zheng, Xianqing Lv, Temporal changes in the response of the nodal modulation of the M2 tide in the Gulf of Maine, Continental Shelf Research, 10.1016/j.csr.2019.07.007, (2019).

6. Min Gan et al. Application of Modified Nonstationary Tidal Harmonic Analysis Approach to Data Recovery of Missing Water Level Measurements of Yangtze Estuary,??The 29th International Ocean and Polar Engineering Conference(ISOPE-2019).

2020年

7. Yu Ying et al. Temporal Variations in the Amplitude of the M2 Nodal Cycle at San Francisco,?The 30th International Ocean and Polar Engineering Conference (ISOPE-2020)

8. Daosheng Wang, haidong Pan, Guangzhen Jin, Xianqing Lv, Seasonal variation of the principal tidal constituents in the Bohai Sea, Ocean Science, 10.5194/os-16-1-2020, 16, 1, (1-14), (2020).

9. Weiwei Li, Data Adaptive Analysis on Vertical Surface Deformation Derived from Daily ITSG-Grace2018 Model, Sensors, 10.3390/s20164477, 20, 16, (4477), (2020).

10. Min Zhang et al. Impacts of secondary and quarter-diurnal tidal species on backwater hydrodynamics in tidal rivers, Advances in Water Resources, (2020).

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