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        均質(zhì)土微潤(rùn)灌濕潤(rùn)體模型構(gòu)建及驗(yàn)證

        2020-08-12 15:01:58范嚴(yán)偉楊志偉胡五龍
        關(guān)鍵詞:微潤(rùn)濕潤(rùn)運(yùn)移

        范嚴(yán)偉,楊志偉,胡五龍

        均質(zhì)土微潤(rùn)灌濕潤(rùn)體模型構(gòu)建及驗(yàn)證

        范嚴(yán)偉1,楊志偉1,胡五龍2

        (1. 蘭州理工大學(xué)能源與動(dòng)力工程學(xué)院,蘭州 730050;2. 武漢理工大學(xué)理學(xué)院,武漢 430070)

        為探明微潤(rùn)灌土壤濕潤(rùn)體運(yùn)移的影響因素和變化規(guī)律,設(shè)置了56種微潤(rùn)灌情景(8種土壤質(zhì)地、3種土壤基質(zhì)勢(shì)和10種微潤(rùn)管比流量的不同組合),利用HYDRUS-2D軟件,模擬研究土壤飽和導(dǎo)水率、土壤基質(zhì)勢(shì)和微潤(rùn)管比流量對(duì)微潤(rùn)灌土壤濕潤(rùn)體的影響。綜合考慮單位長(zhǎng)度總滲水量、土壤飽和導(dǎo)水率、土壤基質(zhì)勢(shì)和微潤(rùn)管比流量等影響因素,基于量綱分析方法,建立了一種均質(zhì)土微潤(rùn)灌濕潤(rùn)體尺寸估算模型,并利用數(shù)值模擬結(jié)果,定量獲取了所建模型的待定參數(shù),最后,采用試驗(yàn)資料評(píng)價(jià)了估算模型的可靠性。結(jié)果表明,土壤飽和導(dǎo)水率、土壤基質(zhì)勢(shì)和微潤(rùn)管比流量對(duì)微潤(rùn)灌土壤濕潤(rùn)體形狀影響較小,且在濕潤(rùn)鋒未到達(dá)地表前,濕潤(rùn)體形狀均為以線源為軸線的近似“橢圓柱體”;相同土壤飽和導(dǎo)水率條件下,土壤濕潤(rùn)體水平、垂直向下和垂直向上方向上的濕潤(rùn)鋒運(yùn)移速率均隨土壤基質(zhì)勢(shì)和微潤(rùn)管比流量增大而增大;當(dāng)土壤基質(zhì)勢(shì)和微潤(rùn)管比流量恒定時(shí),隨土壤飽和導(dǎo)水率數(shù)值的增大,垂直向上和水平方向的濕潤(rùn)鋒運(yùn)移速率逐漸減小,而垂直向下的濕潤(rùn)鋒運(yùn)移速率存在先減小后增大的現(xiàn)象;所建模型的統(tǒng)計(jì)指標(biāo)平均絕對(duì)誤差、均方根誤差均趨近于0,納什效率接近1,說(shuō)明模型估算效果良好,可為微潤(rùn)灌工程的運(yùn)行及管理提供科學(xué)依據(jù)。

        模型;土壤;濕潤(rùn)體;量綱分析;微潤(rùn)灌

        0 引 言

        微潤(rùn)灌是一種地下線源灌溉技術(shù),其操作簡(jiǎn)單,工作水頭低,對(duì)大田及溫室作物具有較好的節(jié)水增產(chǎn)效果[1-2]。了解清楚不同影響因素下微潤(rùn)灌土壤濕潤(rùn)體的動(dòng)態(tài)變化特征,進(jìn)而構(gòu)建濕潤(rùn)體特征模型,對(duì)設(shè)計(jì)經(jīng)濟(jì)高效的微潤(rùn)灌溉系統(tǒng)至關(guān)重要。

        田間灌溉時(shí),土壤濕潤(rùn)體的特性主要受土壤特性參數(shù)和灌水技術(shù)要素的影響。就土壤特性參數(shù)而言,土壤質(zhì)地對(duì)濕潤(rùn)模式影響顯著[3-4],然而,即使是同一土壤質(zhì)地,其容重不同,土壤內(nèi)部的孔隙分布不同,土壤濕潤(rùn)體的運(yùn)移速率也會(huì)有較大的差異,因此,灌溉參數(shù)不能僅視田間土壤質(zhì)地狀況而定;土壤飽和導(dǎo)水率受土壤質(zhì)地、孔隙分布特征和容重的影響較大,同時(shí)在灌溉、排水系統(tǒng)工程的設(shè)計(jì)和土壤剖面中水通量的計(jì)算中起重要作用,所以,在確定灌溉參數(shù)時(shí),可以考慮采用土壤飽和導(dǎo)水率來(lái)表征土壤質(zhì)地、容重以及孔隙分布的差異。土壤特性參數(shù)還包括土壤基質(zhì)勢(shì),根據(jù)土壤基質(zhì)勢(shì)制定灌溉方案是一種非常實(shí)用的方法[5-6],因?yàn)槠湟子谠诟鞣N田間條件下使用,無(wú)需對(duì)土壤類型或鹽分水平進(jìn)行校準(zhǔn),很多學(xué)者的研究表明,田間啟動(dòng)灌溉的土壤基質(zhì)勢(shì)適宜閾值大致在?50~?10 kPa之間[7-9]。從灌水技術(shù)要素考慮,微潤(rùn)管比流量與埋深是微灌系統(tǒng)較重要的2個(gè)參數(shù)。研究表明,相較于地下滴灌,微潤(rùn)管比流量更易受土壤質(zhì)地、土壤容重、微潤(rùn)管埋深、壓力水頭、土壤初始含水率等因素影響[10-13];埋深直接影響微潤(rùn)管周圍土壤濕潤(rùn)體的水分分布位置,但對(duì)土壤濕潤(rùn)體的運(yùn)移速率影響較小[11,14]。因此,在進(jìn)行土壤濕潤(rùn)體運(yùn)移距離的研究時(shí),重點(diǎn)應(yīng)考慮微潤(rùn)管比流量。

        土壤濕潤(rùn)體特征值是灌溉計(jì)劃制定和灌溉系統(tǒng)設(shè)計(jì)的重要依據(jù),但田間灌溉時(shí)土壤濕潤(rùn)體難以直接觀測(cè),導(dǎo)致問(wèn)題研究變得復(fù)雜。為此,國(guó)內(nèi)外學(xué)者開發(fā)了一些解析模型[15-18]、數(shù)值模型[19-20]和經(jīng)驗(yàn)?zāi)P蚚21-24]來(lái)描述濕潤(rùn)體運(yùn)移過(guò)程。Kandelous等[25-27]對(duì)上述3類模型進(jìn)行了分析與評(píng)價(jià):解析模型較復(fù)雜,求解較困難;數(shù)值模型在已知土壤水力特性參數(shù)的前提下對(duì)濕潤(rùn)體的動(dòng)態(tài)變化描述詳細(xì),但也存在模擬過(guò)程復(fù)雜和模擬參數(shù)難以獲得等問(wèn)題;經(jīng)驗(yàn)?zāi)P托问胶?jiǎn)單,但大多數(shù)針對(duì)具體灌溉技術(shù)而建,其在不同灌溉模式下的普適性不強(qiáng)。量綱分析法能夠合理恰當(dāng)?shù)剡x擇特征尺度,將有量綱量轉(zhuǎn)化為無(wú)量綱量,達(dá)到簡(jiǎn)化參數(shù)、量綱和諧的效果,為量化濕潤(rùn)體尺寸、解決濕潤(rùn)體不易觀測(cè)的問(wèn)題提供一種方便而實(shí)用的手段。

        為探明微潤(rùn)灌土壤濕潤(rùn)體運(yùn)移的影響因素及變化規(guī)律,采用HYDRUS-2 D軟件,模擬研究土壤飽和導(dǎo)水率、土壤基質(zhì)勢(shì)以及微潤(rùn)管比流量對(duì)微潤(rùn)灌濕潤(rùn)體的影響;通過(guò)量綱分析法得到微潤(rùn)灌土壤水平向、垂直向上和垂直向下的濕潤(rùn)體尺寸與土壤飽和導(dǎo)水率、土壤基質(zhì)勢(shì)、微潤(rùn)管比流量以及單位長(zhǎng)度總滲水量之間的關(guān)系,構(gòu)建土壤濕潤(rùn)體尺寸的估算模型;采用試驗(yàn)數(shù)據(jù)驗(yàn)證預(yù)測(cè)模型的可靠性,為微潤(rùn)灌溉工程的設(shè)計(jì)和運(yùn)行提供科學(xué)依據(jù)。

        1 基于數(shù)值模擬方法分析濕潤(rùn)體運(yùn)移影響因素

        1.1 數(shù)值模擬

        1.1.1 基本方程

        假定微潤(rùn)管的滲水速率沿微潤(rùn)管方向呈均勻分布且土壤均勻和各向同性,微潤(rùn)灌土壤水分運(yùn)動(dòng)可近似為點(diǎn)源在垂直面上的二維運(yùn)動(dòng),其土壤水流控制方程為二維Richards方程[28],即

        式中為垂向坐標(biāo),規(guī)定向下為正;為水平向坐標(biāo);為基質(zhì)勢(shì),cm;為土壤體積含水率,cm3/cm3;為時(shí)間,min;()為土壤非飽和導(dǎo)水率,cm/min。

        通過(guò)van Genuchten-Mualem (VG-M)模型描述式(1)中、()和三者之間的關(guān)系[29]。即

        式中S為土壤相對(duì)飽和度,S=(?θ)/(θ?θ);K為土壤飽和導(dǎo)水率,cm/min;θθ分別為土壤殘余含水率和飽和含水率,cm3/cm3;和為經(jīng)驗(yàn)常數(shù),其中>1,=1?1/;為經(jīng)驗(yàn)參數(shù),cm-1;為經(jīng)驗(yàn)系數(shù),通常取0.5。

        1.1.2 定解條件

        圖1為微潤(rùn)灌土壤水分運(yùn)動(dòng)模擬示意圖??紤]田間微潤(rùn)管水平向鋪設(shè)的對(duì)稱性,模擬計(jì)算域的選取原則是,豎直向以微潤(rùn)管為起點(diǎn)的上至土壤表面、下至不受灌水影響的深度,水平向以微潤(rùn)管為起點(diǎn)向右至微潤(rùn)管間距的一半。

        注:D是微潤(rùn)管埋深,cm;W是微潤(rùn)管間距,cm;Dd為模擬計(jì)算域深度,cm;Ψ為土壤基質(zhì)勢(shì),cm;Ψ0為土壤初始基質(zhì)勢(shì),cm。

        模擬開始前,不同土壤類型的基質(zhì)勢(shì)均采用初始基質(zhì)勢(shì)。灌溉過(guò)程中,上邊界與大氣相接觸,按大氣邊界設(shè)置;下邊界在選取研究區(qū)域時(shí)不受灌水的影響,按自由邊界設(shè)置;左邊界為向下穿過(guò)微潤(rùn)管的中心線,右邊界為相鄰微潤(rùn)管中心線,均按零通量邊界設(shè)置;單位長(zhǎng)度微潤(rùn)管的出流量基本恒定[30-31],按定流量邊界設(shè)置。

        1.1.3 模擬方案

        為體現(xiàn)土壤類型的廣泛性和研究成果的普適性,選取田間常見的8種土壤質(zhì)地,其VG-M模型參數(shù)取自Carsel等[32]資料,土壤容重取自Pachepsky等[33]資料,具體見表1。

        表1 8種典型土壤的VG-M模型參數(shù)

        依據(jù)文獻(xiàn)[7-9],選取3種值(?100、?300和?500 cm)。參考文獻(xiàn)[1,10-12,30],壓力水頭取值范圍為0.6~2.4 m,取值大致在10~40 cm之間。通過(guò)給定的、和,采用文獻(xiàn)[34]中的比流量計(jì)算式確定模擬方案中的微潤(rùn)管比流量,模擬方案共計(jì)56種(8種土壤質(zhì)地、3種土壤基質(zhì)勢(shì)和10種微潤(rùn)管比流量的不同組合),具體模擬方案見表2。

        表2 模擬方案

        1.1.4 求解方法

        利用HYDRUS-2 D軟件[35]進(jìn)行數(shù)值求解時(shí),考慮到田間實(shí)際和計(jì)算精度的要求,模擬區(qū)域設(shè)為D=100 cm,/2=60 cm的矩形區(qū)域,空間步長(zhǎng)為1 cm,時(shí)間步長(zhǎng)為0.1 min。求解時(shí),對(duì)土壤剖面采用Galerkin有限元法進(jìn)行空間離散,對(duì)時(shí)間采用隱式差分格式進(jìn)行離散。

        1.2 模擬分析濕潤(rùn)體運(yùn)移影響因素

        1.2.1 濕潤(rùn)體運(yùn)移的影響因素

        從56組模擬方案中,選取不同K、和影響因素組合下的7組單因素對(duì)比方案,繪制土壤濕潤(rùn)體運(yùn)移變化圖,如圖2所示。

        由圖2可見,濕潤(rùn)鋒未到達(dá)地表前,土壤濕潤(rùn)體形狀差異較小,其輪廓線均為近似“橢圓柱體”;濕潤(rùn)鋒到達(dá)地表后,微潤(rùn)管上部濕潤(rùn)體形狀由“半橢圓”轉(zhuǎn)化為“梯形”,微潤(rùn)管下部濕潤(rùn)體形狀繼續(xù)保持“半橢圓”。隨灌水時(shí)間延長(zhǎng),濕潤(rùn)體向外逐漸擴(kuò)展增大,但擴(kuò)展速率逐漸減小。濕潤(rùn)體尺寸符合垂直向下>水平方向>垂直向上的規(guī)律。

        注:縱坐標(biāo)20 cm處為微潤(rùn)管所在位置。

        1)土壤飽和導(dǎo)水率對(duì)濕潤(rùn)體運(yùn)移的影響

        圖2a、2b和2c顯示了不同K條件下濕潤(rùn)體隨時(shí)間的變化規(guī)律。對(duì)比圖2a、2b和2c,發(fā)現(xiàn)相同和條件下,隨K的增大,同一時(shí)刻垂直向上和水平方向上的濕潤(rùn)鋒運(yùn)移距離逐漸減小。如持續(xù)微潤(rùn)灌24 h,K=0.007 5 cm/min土壤的垂直向上和水平濕潤(rùn)尺寸分別為12.0和12.3 cm,K=0.017 3 cm/min的土壤則減小為11.1和11.6 cm,而K=0.073 7 cm/min的土壤則再縮減為10.2和11.0 cm。相同和條件下,隨K的增大,同一時(shí)刻垂直向下方向上的濕潤(rùn)鋒運(yùn)移距離表現(xiàn)出先減小后增大的現(xiàn)象。如持續(xù)微潤(rùn)灌48 h,3種K(0.007 5、0.017 3和0.073 7 cm/min)下的垂直向下濕潤(rùn)尺寸分別為12.7、12.0和13.2 cm。灌水結(jié)束時(shí)(132 h),3種K(0.007 5、0.017 3和0.073 7 cm/min)下的垂直向上的運(yùn)移距離比垂直向下的運(yùn)移距離分別下降35.5%,31.8%和38.1%;而水平方向的運(yùn)移距離比垂直向下的運(yùn)移距離分別下降6.5%,8.5%和28.9%。

        2)土壤基質(zhì)勢(shì)對(duì)濕潤(rùn)體運(yùn)移的影響

        圖2d、2f和2g給出了壤土在不同條件下濕潤(rùn)體的運(yùn)移特性。對(duì)比圖2d、2f和2g,發(fā)現(xiàn)相同K和條件下,3個(gè)方向上值越高,同一時(shí)刻濕潤(rùn)體運(yùn)移距離越大,而且垂直向下方向上對(duì)濕潤(rùn)鋒運(yùn)移的影響更顯著。如持續(xù)微潤(rùn)灌24 h,=?500 cm的3個(gè)方向(垂直向上、水平方向和垂直向下)濕潤(rùn)尺寸分別為11.5、12.0和12.5 cm,=?300 cm的增長(zhǎng)為12.3、12.9和13.5 cm,而=?100 cm的再提升為13.3、15.0和17.0 cm。灌水結(jié)束時(shí)(132 h),3種值下垂直向上方向的濕潤(rùn)體運(yùn)移距離均到達(dá)地表,水平方向,=?100和?300 cm的濕潤(rùn)體運(yùn)移距離分別比=?500 cm的運(yùn)移距離大31.0%,34.6%;而垂直向下方向,=?100和?300 cm的濕潤(rùn)體運(yùn)移距離分別比=?500 cm的運(yùn)移距離大7.5%,9.3%。

        3)微潤(rùn)管比流量對(duì)濕潤(rùn)體運(yùn)移的影響

        對(duì)比分析3種條件下壤土濕潤(rùn)體運(yùn)移過(guò)程(圖2b、2d和2e)??梢钥闯?,相同K和條件下,值越大,濕潤(rùn)體運(yùn)移速度越快,同一時(shí)刻濕潤(rùn)體尺寸越大。如持續(xù)微潤(rùn)灌48 h,3種(0.010 7,0.014 5和0.018 2 mL/(cm·min))下3個(gè)方向濕潤(rùn)尺寸分別為15.5、16.3、17.1 cm(垂直向上),17.1、18.1、19.2 cm(水平方向)和18.7、19.6、21.0 cm(垂直向下)。灌水結(jié)束時(shí)(132 h),3種下垂直向上方向的濕潤(rùn)體運(yùn)移距離均到達(dá)地表,水平方向,微潤(rùn)管比流量為0.014 5和0.018 2 mL/(cm·min)的濕潤(rùn)體運(yùn)移距離分別比0.010 7 mL/(cm·min)的運(yùn)移距離增大11.2%和20.5%;而垂直向下方向,微潤(rùn)管比流量為0.014 5和0.018 2 mL/(cm·min)的濕潤(rùn)體運(yùn)移距離分別比0.010 7 mL/(cm·min)的運(yùn)移距離增大13.1%和23.7%。

        1.2.2 濕潤(rùn)體運(yùn)移輪廓

        對(duì)圖2進(jìn)行分析,發(fā)現(xiàn)均質(zhì)土條件下微潤(rùn)灌濕潤(rùn)體輪廓可分上下兩部分,當(dāng)上半部分在濕潤(rùn)邊界未到達(dá)地表前,可用半橢圓形方程表示,如式(4)所示。

        式中為水平向的最大濕潤(rùn)體尺寸,cm;為垂直向上或垂直向下的最大濕潤(rùn)體尺寸,cm;為濕潤(rùn)體輪廓上任意點(diǎn)的坐標(biāo)。

        由式(4)可知,濕潤(rùn)體的大小由水平向、垂直向上以及垂直向下的濕潤(rùn)體尺寸的最大值確定,基于此,建立3個(gè)方向上濕潤(rùn)體尺寸的估算模型則為確定濕潤(rùn)體大小的關(guān)鍵。

        2 模型建立與評(píng)價(jià)

        2.1 量綱分析

        通過(guò)定性分析微潤(rùn)灌濕潤(rùn)體運(yùn)移的影響因素,可知:K、和對(duì)微潤(rùn)灌土壤濕潤(rùn)體尺寸均有影響,另外,濕潤(rùn)體尺寸還受灌水時(shí)間的影響,故依據(jù)文獻(xiàn)[21]將灌水時(shí)間對(duì)濕潤(rùn)體尺寸的影響用單位長(zhǎng)度總滲水量(,mL/cm)代替。基于此,最終確定微潤(rùn)灌溉系統(tǒng)的水平向()、垂直向上(1)以及垂直向下(2)的濕潤(rùn)尺寸取決于K、、以及。假設(shè)這些參數(shù)之間的關(guān)系為

        式中表示參數(shù)之間存在某種關(guān)系。

        式(5)中的7個(gè)參數(shù)根據(jù)量綱分析法及定理可得到5個(gè)獨(dú)立的項(xiàng),其之間的關(guān)系表示如下:

        式中表示5個(gè)獨(dú)立的項(xiàng)之間存在某種關(guān)系;1、2、3、4和5為由定理得到的無(wú)量綱量。

        根據(jù)量綱和諧原理得到5個(gè)獨(dú)立項(xiàng)的具體表達(dá)式,即

        無(wú)量綱體積*、無(wú)量綱水平向濕潤(rùn)尺寸*、無(wú)量綱垂直向上濕潤(rùn)尺寸1*以及無(wú)量綱垂直向下濕潤(rùn)尺寸2*可由5個(gè)獨(dú)立項(xiàng)的組合產(chǎn)生:

        1)4與5的乘積得到無(wú)量綱體積*,表示如下:

        2)1的平方與4的乘積得到無(wú)量綱水平向濕潤(rùn)尺寸*,表示如下:

        3)2的平方與4的乘積得到無(wú)量綱垂直向上濕潤(rùn)尺寸1*,表示如下:

        4)3的平方與4的乘積得到無(wú)量綱垂直向上濕潤(rùn)尺寸2*,表示如下:

        式(12)~式(15)所表示的無(wú)量綱參數(shù)之間的關(guān)系由文獻(xiàn)[21]可得,即

        在式(16)~式(18)中,1、2和3是指數(shù),1、2和3是系數(shù)。將WV的值代入式(16)中獲得式(19):

        同樣地,將1*2*和*的值放在式(17)與式(18)中獲得式(20)與式(21):

        2.2 參數(shù)確定及模型構(gòu)建

        利用HYDRUS-2D軟件的模擬結(jié)果及式(12)~式(15)計(jì)算無(wú)量綱項(xiàng)*1*2*和*,并借助Origin 9.0,采用式(16)~式(18)擬合獲得參數(shù)1、2、3和1、2、3,如圖3所示。其中,式(12)~式(15)與式(19)~式(21)中的微潤(rùn)管比流量()為單位長(zhǎng)度微潤(rùn)管的總出流量。

        由圖3可見,利用式(16)~式(18)擬合得到無(wú)量綱水平向濕潤(rùn)尺寸W、無(wú)量綱垂直向上濕潤(rùn)尺寸1以及無(wú)量綱垂直向下濕潤(rùn)尺寸2與無(wú)量綱體積*之間的關(guān)系,其指數(shù)1、2、3分別為0.53、0.53、0.56,常數(shù)1、2、3分別為2.91、2.65、4.88,擬合回歸線的決定系數(shù)2分別為0.96、0.97、0.97,均接近1,說(shuō)明擬合效果良好。將擬合獲得的結(jié)果代入式(19)~式(21),得到不同K、、以及下的濕潤(rùn)體尺寸預(yù)測(cè)模型。即:

        注:W*、Z1*、Z2*分別代表無(wú)量綱條件下水平方向、垂直向上和垂直向下濕潤(rùn)尺寸。

        2.3 土箱試驗(yàn)

        土箱試驗(yàn)用于模型的驗(yàn)證,供試土樣分別取自甘肅省蘭州市七里河區(qū)的粉壤土和武威市民勤縣的砂黏壤土,且取土深度均為0~40 cm。土樣經(jīng)風(fēng)干、碾壓、過(guò)2 mm篩后待用。為獲得均勻土壤剖面,試驗(yàn)前,土樣按設(shè)定基質(zhì)勢(shì)加水并均勻混合,然后用塑料薄膜將土樣密封,靜置1 d,之后按設(shè)定好的容重分層(每層5 cm)裝入土箱。裝土完畢靜置1 d開始試驗(yàn),灌水時(shí)間設(shè)為3 d。土壤特性參數(shù)和灌水技術(shù)參數(shù)見表3。

        表3 供試土樣特性參數(shù)和灌水技術(shù)參數(shù)

        試驗(yàn)裝置由土箱、高度可調(diào)節(jié)支架、橡膠管、馬氏瓶和微潤(rùn)管組成(圖4)。土箱由10 mm厚的有機(jī)玻璃制成,尺寸為60 cm(長(zhǎng))×60 cm(寬)×100 cm(高)。為防止土體內(nèi)部氣阻的發(fā)生,土箱底部留有多個(gè)通氣孔(直徑2 mm)。為便于觀測(cè)濕潤(rùn)體形狀與尺寸,裝土?xí)r將微潤(rùn)管緊靠土箱壁,水平放置于設(shè)定的埋深處。試驗(yàn)中,馬氏瓶在恒定水頭下提供水量,馬克筆繪制不同時(shí)刻濕潤(rùn)體輪廓。

        2.4 誤差分析

        用平均絕對(duì)誤差、均方根誤差和納什效率系數(shù)對(duì)模型的性能進(jìn)行評(píng)價(jià)。如果比較結(jié)果顯示平均絕對(duì)誤差和均方根誤差接近0,納什效率系數(shù)接近1,則表明模型具有良好的模擬性能。統(tǒng)計(jì)參數(shù)使用以下方程計(jì)算[36]:

        式中MAE、RMSE和NSE分別為平均絕對(duì)誤差、均方根誤差和納什效率系數(shù);OC分別為第個(gè)實(shí)測(cè)值和第個(gè)計(jì)算值;為所有實(shí)測(cè)值的平均值;表示數(shù)據(jù)總個(gè)數(shù)。

        注:H為供水面至土壤表面的壓力水頭,cm。

        3 結(jié)果與分析

        為進(jìn)一步評(píng)價(jià)預(yù)測(cè)模型的準(zhǔn)確性,利用室內(nèi)土箱試驗(yàn)和已發(fā)表的有關(guān)微潤(rùn)灌濕潤(rùn)體運(yùn)移的文獻(xiàn)資料[12,30,37]中的實(shí)測(cè)數(shù)據(jù)對(duì)預(yù)測(cè)模型進(jìn)行驗(yàn)證,并繪制實(shí)測(cè)值與預(yù)測(cè)模型計(jì)算值對(duì)比圖(圖5),且已發(fā)表文獻(xiàn)資料中的土壤的相關(guān)基本性質(zhì)見表4。采用式(25)~式(27)對(duì)計(jì)算值與實(shí)測(cè)值進(jìn)行統(tǒng)計(jì)學(xué)分析(表4)。

        注:*表示取自文獻(xiàn)[30]; **表示取自文獻(xiàn)[12];***表示取自文獻(xiàn)[37]。

        表4 濕潤(rùn)體運(yùn)移距離實(shí)測(cè)值與模型計(jì)算值

        由圖5可見,以各土壤的水平、垂直向上以及垂直向下方向的濕潤(rùn)體運(yùn)移距離的實(shí)測(cè)值與模型計(jì)算值為坐標(biāo)的點(diǎn)均分布在1:1線附近,且利用檢驗(yàn)計(jì)算得到各土壤在水平、垂直向上以及垂直向下方向的值均大于0.05,說(shuō)明3個(gè)方向上各土壤的實(shí)測(cè)值與模型計(jì)算值均無(wú)顯著性差異,一致性較好。借助指標(biāo)MAE、RMSE和NSE對(duì)模型誤差進(jìn)行統(tǒng)計(jì)分析,如表4所示。由表4可知,MAE介于1.16~2.10 cm之間,RMSE介于1.20~2.46 cm之間,NSE介于0.83~0.95之間,模型預(yù)測(cè)效果良好。

        4 討 論

        相同和條件下,水平和垂直向上的濕潤(rùn)鋒運(yùn)移距離隨K的增大而減小,而垂直向下的濕潤(rùn)鋒運(yùn)移距離隨K的增加存在先減小后增大的現(xiàn)象。分析原因可能是:1)相同和條件下,土壤飽和度隨K的增大而減小,而飽和度越低,土壤的儲(chǔ)水能力越強(qiáng),濕潤(rùn)鋒運(yùn)移越慢[38-39];2)相同和條件下,微潤(rùn)管處土壤基質(zhì)勢(shì)隨K的增大而增大,而此處基質(zhì)勢(shì)越高,土壤水勢(shì)梯度越大,濕潤(rùn)鋒運(yùn)移越快;3)相同和條件下,K越大,越有利于土壤水分運(yùn)動(dòng)。文中模擬情景融合了上述3種原因的影響,使K對(duì)土壤水分運(yùn)動(dòng)規(guī)律的影響變得較為復(fù)雜,后期仍需進(jìn)一步定量研究其影響機(jī)理。

        濕潤(rùn)鋒運(yùn)移距離隨的增大而增大。究其原因?yàn)椋?)相同K和條件下,越大,土壤初始越高,而初始越高,入滲開始前土壤孔隙所含水分越多,則土壤達(dá)到飽和狀態(tài)時(shí)所需水分越少,所需時(shí)間越短[38];2)土壤初始越大,()越大,水分在土壤中的運(yùn)移速率越快[40]。濕潤(rùn)鋒運(yùn)移距離隨的增大而增大。主要是越大,相同時(shí)間內(nèi)進(jìn)入土壤的水量越多,濕潤(rùn)鋒運(yùn)移越快。

        灌水過(guò)程中,微潤(rùn)管內(nèi)外水勢(shì)梯度會(huì)影響微潤(rùn)管比流量,但作用時(shí)間較短,一般48 h后會(huì)保持穩(wěn)定,這在牛文全等[13,41]的研究中得到驗(yàn)證。需要說(shuō)明的是,微潤(rùn)灌作為一種地下續(xù)灌技術(shù),可能會(huì)在植物整個(gè)生育期持續(xù)灌溉,土壤水分消耗問(wèn)題是不可避免的,土壤水分消耗主要包括根系吸水消耗與土壤水分蒸發(fā)損失。因此,后期將結(jié)合根系吸水和土壤水分蒸發(fā)等對(duì)水分消耗開展研究,以期將濕潤(rùn)體大小保持在有效根區(qū)。

        濕潤(rùn)體模型包含的土壤物理參數(shù)(土壤飽和導(dǎo)水率和土壤基質(zhì)勢(shì))和灌溉技術(shù)參數(shù)(微潤(rùn)管比流量)容易測(cè)定,便于設(shè)計(jì)者針對(duì)不同土壤特性確定合理的灌水參數(shù)。需要說(shuō)明的是,灌水推進(jìn)過(guò)程中,濕潤(rùn)邊界會(huì)達(dá)到地表,垂直向上的式(20)不再適用,但估算值大于微潤(rùn)管埋深時(shí)可取埋深值。濕潤(rùn)邊界到達(dá)地表對(duì)水平向與垂直向下的濕潤(rùn)體運(yùn)移影響不大,式(19)與式(21)依舊適用。

        5 結(jié) 論

        1)土壤飽和導(dǎo)水率、土壤基質(zhì)勢(shì)和微潤(rùn)管比流量對(duì)微潤(rùn)灌濕潤(rùn)體運(yùn)移影響顯著。3個(gè)方向(水平、垂直向上和垂直向下)濕潤(rùn)鋒運(yùn)移速率隨基質(zhì)勢(shì)和比流量增大而增大;隨飽和導(dǎo)水率的增大,水平和垂直向上的濕潤(rùn)鋒運(yùn)移速率逐漸減小,而垂直向下的濕潤(rùn)鋒運(yùn)移速率先減小后增大。

        2)基于量綱分析法建立了一種均質(zhì)土微潤(rùn)灌濕潤(rùn)體模型。采用試驗(yàn)數(shù)據(jù)進(jìn)行驗(yàn)證,平均絕對(duì)誤差介于1.16~2.10 cm之間,均方根誤差介于1.20~2.46 cm之間,納什效率系數(shù)介于0.83~0.95之間,所建模型估算效果良好,能夠解決微潤(rùn)灌地下土壤濕潤(rùn)體難以觀測(cè)的問(wèn)題,為微潤(rùn)灌的工程設(shè)計(jì)和田間運(yùn)行提供科學(xué)依據(jù)。

        [1] 張明智,牛文全,路振廣,等. 微潤(rùn)灌對(duì)作物產(chǎn)量及水分利用效率的影響[J]. 中國(guó)生態(tài)農(nóng)業(yè)學(xué)報(bào),2017,25(11):1671-1683.

        Zhang Mingzhi, Niu Wenquan, Lu Zhenguang, et al. Effect of moistube-irrigation on crop yield and water use efficiency[J]. Chinese Journal of Eco-Agriculture, 2017, 25(11): 1671-1683. (in Chinese with English abstract)

        [2] Sun Q, Wang Y, Chen G, et al. Water use efficiency was improved at leaf and yield levels of tomato plants by continuous irrigation using semipermeable membrane[J]. Agricultural Water Management, 2018, 203: 430-437.

        [3] 余小弟,劉小剛,朱益飛,等. 土壤質(zhì)地和供水壓力對(duì)豎插式微潤(rùn)管入滲的影響[J]. 排灌機(jī)械工程學(xué)報(bào),2017,35(1):71-79.

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        Establishment and validation of wetting pattern model of moistube irrigation in homogeneous soil

        Fan Yanwei1, Yang Zhiwei1, Hu Wulong2

        (1.730050;2.430070)

        Moistube irrigation is a kind of underground line source infiltration irrigation technology developed by using the principle of polymer semi permeable membrane. The growth and yield of crops are affected by the shape and size of soil wetting pattern but the wetting pattern is not easy to observe. Therefore, it is very important to understand the shape and size of wetting pattern for the design of economic and efficient moistube irrigation system. In order to facilitate users to quickly evaluate the moistube irrigation wetting pattern, a total of 56 moistube irrigation scenarios (different combinations of eight soil textures, three soil matrix potentials and ten specific discharges of moistube) were set up. By using HYDRUS-2D software, the dynamic changes of wetting pattern under different combinations of soil saturated hydraulic conductivity, soil matrix potential and specific discharge of moistube were simulated and analyzed. The results showed that before the soil wetting front reached the surface, there was little difference in the shape of the soil wetting pattern, and its contour was almost "elliptical cylinder"; after the wetting front reached the surface, the shape of the wetting pattern at the upper part of the moistube changed from "semi ellipse" to "trapezoid", and the shape of the wetting pattern at the lower part of the moistube kept "semi ellipse". In general, soil saturated hydraulic conductivity, soil matrix potential and specific discharge of moistube had little influence on the shape of the moistube irrigation soil wetting pattern; The size of moistube irrigation soil wetting pattern at the vertical downward was larger than that at the horizontal direction and vertical upward, and with the extension of irrigation time, the wetting pattern expanded outward gradually, but the expansion rate decreased gradually. Under the condition of homogeneous soil, the contour of moistube irrigation wetting pattern was divided into two parts: the upper part and the lower part. When the upper part of the wetting boundary did not reach the surface, it could be expressed by semi elliptic equation. Under the same soil matrix potential and specific discharge of moistube conditions, with the increase of soil saturated hydraulic conductivity, at the same time, the vertical upward and horizontal migration distance of the wet front gradually decreased, while the vertical downward migration distance of the wet front first decreased and then increased; Under the same soil saturated hydraulic conductivityand specific discharge of moistube conditions, there was a positive correlation between the migration distance of the wetting front and soil matrix potential in three directions. The higher the soil matrix potential value resulted in the greater the migration distance of the wetting pattern at the same time; Under the same soil saturated hydraulic conductivity and soil matrix potential conditions, the migration distance of wetting pattern was positively correlated with specific discharge of moistube. The larger the specific discharge of moistube value could result in the faster the migration speed of wetting pattern and the larger the size of wetting pattern at the same time. Generally speaking, soil saturated hydraulic conductivity, soil matrix potential and specific discharge of moistube had significant influence on the migration of wetting pattern in moistube irrigation. On this basis, taking into the influence factors such as the total water seepage per unit length, soil saturated hydraulic conductivity, soil matrix potential and specific discharge of moistube, and based on the dimensional analysis method, the estimation model for the wetting pattern of moistube irrigation of homogeneous soil was established, and the undetermined parameters of the model were obtained quantitatively by using the numerical simulation results. Finally, the reliability of the estimation model was evaluated by the test data. The mean absolute error was not more than 2.10 cm, the root mean square error was not more than 2.46 cm, and the Nash efficiency coefficient was not less than 0.83 of statistical index of the model. It showed that the measured value was consistent with the estimated value of the model, and the model estimation effect was well. It provides a scientific basis for the operation and management of moistube irrigation engineering.

        models; soils; wetting pattern; dimensional analysis; moistube irrigation

        范嚴(yán)偉,楊志偉,胡五龍. 均質(zhì)土微潤(rùn)灌濕潤(rùn)體模型構(gòu)建及驗(yàn)證[J]. 農(nóng)業(yè)工程學(xué)報(bào),2020,36(13):83-91.doi:10.11975/j.issn.1002-6819.2020.13.010 http://www.tcsae.org

        Fan Yanwei, Yang Zhiwei, Hu Wulong. Establishment and validation of wetting pattern model of moistube irrigation in homogeneous soil[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2020, 36(13): 83-91. (in Chinese with English abstract) doi:10.11975/j.issn.1002-6819.2020.13.010 http://www.tcsae.org

        2020-03-25

        2020-06-10

        國(guó)家自然科學(xué)基金項(xiàng)目(51409137、51969013);甘肅省科學(xué)基金項(xiàng)目(18JR3RA144)

        范嚴(yán)偉,博士,副教授,主要從事水土資源利用和節(jié)水灌溉技術(shù)方面的研究。Email:fanyanwei24@163.com

        10.11975/j.issn.1002-6819.2020.13.010

        S274.3; S155.4+4

        A

        1002-6819(2020)-13-0083-09

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