Development of Pedotransfer Functions for Saturated Hydraulic Conductivity

Transcription

1 Open Journal of Modern Hydrology, 03, 3, Publhed Onlne July 03 ( Development of Pedotranfer Functon for Saturated Hydraulc Conductvty John P. O. Obero, Lawrence O. Gumbe, Chrtan T. Omuto, Mohammed A. Haan, Januaru O. Agullo Department of Envronmental and Boytem Engneerng, Unverty of arob, arob, Kenya; Department of Earth and Envronmental Scence and Technology, Techncal Unverty of Kenya, arob, Kenya. Emal: eceved March 4 th, 03; reved Aprl 4 th, 03; accepted May 3 rd, 03 Copyrght 03 John P. O. Obero et al. Th an open acce artcle dtrbuted under the Creatve Common Attrbuton Lcene, whch permt unretrcted ue, dtrbuton, and reproducton n any medum, provded the orgnal work properly cted. ABSTACT The purpoe of the tudy wa to develop pedotranfer functon for determnng aturated hydraulc conductvty (K ). Pedotranfer functon (PTF) for predctng ol phycal properte ued n determnng aturated hydraulc conductvty, baed on moturetenton charactertc, were developed. The van Genuchten moturetenton equaton wa ftted to meaured moturetenton properte obtaned from Internatonal Sol eference and Informaton Centre (ISIC) ol data bae n order to determne parameter n the equaton.e. aturated ol moture content (θ ), redual ol moture (θ r ), ar entry parameter (α) and the pore ze dtrbuton parameter (n). 457 ample drawn from the data bae were ued to be the maxmum poble ample ze that contaned the meaured ol charactertc data requred. Ung tattcal regreon, mathematcal relatonhp were developed between moturetenton parameter (repone varable) and approprately elected tranformed bac ol properte (predctor varable). The developed PTF were evaluated for accuracy and relablty. It wa found that pedotranfer functon developed for θ produced the bet performance n relablty compared to themanng parameter yeldng a correlaton coeffcent value of coeffcent of determnaton ( = 0.76), MSE =.09, SE = 0.75 and S = 0.5 ndcatng good performance. elatvely pooret performance wa obtaned from the pedotranfer functon developed for α whch yelded a correlaton coeffcent, = 0.06, MSE = 0.85 and a SE of 0.0 reflectng the bet poble equaton derved for the parameter for ue n predctng hydraulc conductvty. Out of the pedotranfer functon developed for each of the moturetenton parameter, the bet performng PTF wa dentfed for each parameter. The accuracy of the pedotranfer functon aeed baed on were for θ ( = 0.80), θ r ( = 0.4), α ( = 0.04) and for n ( = 0.30), when the varable were expreed drectly n term of the elected tranformaton of the bac ol properte. Keyword: Pedotranfer Functon; Development; Evaluaton. Introducton Hydraulc conductvty an mportant parameter that nfluence hydrologcal procee whch affect flow n rver. For ntance, ground water flow determned by aturated hydraulc conductvty (K ). A number of formulaton have been developed over the year to predct ol hydraulc conductvty from readly meaurable ol properte. The need for mathematcal modelng of K are from the fact that ntu or laboratory meaurement of hydraulc conductvty are tme conumng, labour ntenve and expenve a noted by [], makng t practcally unlkely n realty to collect permeablty data. Bede, drect meaurement are alo unrelable for te pecfc applcaton. The ue of pe- dotranfer functon an alternatve to determnng hydraulc conductvty and nvolvelatonhp that enable K to be predcted ung meaurable ol phycal and hydraulc properte. K erve a an nput parameter n many hydrologcal model. There no pecfc method condered mot accurate n determnng K a the method ued depend on ol and envronmental condton. Furthermore, data on K not readly avalable n mot local ol urvey data bae and even where they are avalable, thelablty not guaranteed. There uncertanty n the predcton of K ung extng pedotranfer functon. Method to develop PTF are alo unknown and not well undertood epecally n Afrca. Well known moture charactertc functon are baed Copyrght 03 Sce.

2 Development of Pedotranfer Functon for Saturated Hydraulc Conductvty 55 on parameter that can be determned ung moture retenton charactertc. Such data not readly avalable n mot ol data bae. It eental to etmate uch parameter ung bac and ealy avalable ol properte lke bulk denty, texture etc. Attempt to develop uch equaton rare. [] note that modern mulaton and analy of hydrologc proceele heavly on the accurate and relable decrpton of ol water holdng and tranmon charactertc. Predctng K from bac ol properte ung developed pedotranfer functon baed on analy of the extng data et, an approach appled n agrcultural hydrology and waterhed management. Th reearch demontrate how pedotranfer functon can be developed from a data bae, wth lmted ol data, n predctng van Genuchten moturetenton parameter, a tep n predctng K from readly avalable data on bac ol properte avalable from ol urvey data. K can be ndrectly predcted from ol properte ung moture retenton equaton lke van Genuchten, Brook Corey etc. where data on moturetenton curve avalable. Th technque wa ued n the tudy. eadly avalable data on meaured K rare and characterzed wth uncertanty on ther accuracy a dfferent method n dfferent envronment yeld vared reult a oberved by [3] therefore necetatng ue of the ndrect method. Three type of pedotranfer functon arecognzed [4]. One category predct ol moturetenton from bac ol properte. The other baed on pont predcton of water retenton charactertc a ued by [5] to predct pont along the moturetenton curve on Iranan ol. Another category nvolve predcton of parameter n model decrbng the θ-h-k relatonhp. Th latter approach ued n the tudy nvolved pedotranfer functon that relate the mple and eay to meaure ol properte to van Genutchen moturetenton parameter, a notable gap n the cence of development of pedotranfer functon. Mot etablhed pedotranfer functon for predctng ol hydraulc charactertc from contnuou ol properte are baed on tattcal regreon [6] n whch thepone varable, y, predcted from a number of n predctor varable, x yeld the tattcal multple lnear regreon tool expreed a y n a bx,,, n () where a the ntercept, b thegreon coeffcent and ε the error. The procedure to develop the pedotranfer functon nvolve tep whch nclude: The frt tep of tattcal analy ntended to tet f each repone varable dtrbuton may be condered a normal dtrbuton [7]. The normalty of a dtrbuton teted by certan tattc lke the Shapro-Wlk (Wvalue), Skewne coeffcent and Kurto. The hape of the dtrbuton determned by a meaure of t Skew- ne whch gven by the equaton, S n 3 n x x 3 nn () where S Skewne coeffcent, the tandard devaton, x the obervaton value, x the mean value and n the number of obervaton. For a normally dtrbuted data, the kewne = 0, hence the cloer the kewne coeffcent to zero (0), the better the normalty of the dtrbuton. The level of Kurto alo provde nformaton about the extent of the normalty of the dtrbuton and gven by, nn K nnn3 (3) 4 n x x 4 3n nn3 The meaure of Kurto zero (0) for a normally dtrbuted populaton. Graphcal ad ued to check normalty nclude the normal probablty plot. Mathematcal relatonhp between potental predctor varable and thepone varable are checked by detectng exponental, logarthmc, or quaroot tendence. Important to elmnate the problem of redundant nformaton n the predctor et brought about by lnear dependence between predctor varable [6]. Th problem of multcollnearty can be examned by mean of correlaton matrx. Common tattc ued n evaluatng pedotranfer functon nclude [4]: Multple determnaton coeffcent gven by oot mean quare error gven by y yˆ y y (4) MSE y ˆ y (5) Mean Error gven by y ˆ y ME (6) Mean Abolute Error gven by y ˆ y ME (7) where y denote the actual value, yˆ the predcted value, and y the average of the actual value and the total number of obervaton. [8] evaluated performance of dfferent pedotranfer functon for etmatng certan ol hydraulc properte that nclude Avalable Water Capacty (AWC) ung, MSE and ME. [9] Copyrght 03 Sce.

3 56 Development of Pedotranfer Functon for Saturated Hydraulc Conductvty ued only MSE n aeng pedotranfer functon developed for predctng hydraulc conductvty and water retenton. The van Genuchten water retenton equaton whch relate moture content (θ) to the ol matrc ucton (h) and expreed a follow; where h S e S e n n (8) r (9) r To determne K, the hydraulc conductvty functon ued expreed a K h K h n h h n m n m (0) To determne K ung the above equaton, a relatonhp between hydraulc conductvty and matrc ucton, h ued and can be obtaned through equaton that relate hydraulc conductvty to permeablty [0].. Methodology.. Data Collecton and Analy [4] noted that data from extng nternatonal ol data bae havng meaured ol data can be analyzed to enable predcton of hydraulc charactertc from meaured ol data. Avalablty of meaured ol hydraulc charactertc for a wdange of ol and from a large and relable nternatonal data bae are condered prerequte for development of pedotranfer functon. The ISIC ol databae wa ued to obtan meaured data on ol hydraulc charactertc and bac ol properte. It wa poble to obtan all thequred meaured data on 457 ol ample from varou part of the world. The data contaned meaured moturetenton curve a well a data on texture (Sand%, Clay% and Slt%). The ISIC dataet [] wa ued for th tet. Th dataet contan Water etenton Curve (WC) for both topol (between 0 and 0 cm depth) and ubol (between 0 and 00 cm) from many countre n the world. It ha 8 level of meaured ucton potental (at 0, 0., 0.3,.0,.99, 5.0,.5, and 5.8 m) (Fgure ). The lowet ucton potental wa taken a 0.0 to avod error wth logarthmc tranformaton. The oberved moturetenton curve obtaned from meaured data on moturetenton charactertc wa ftted to the van Genuchten moture retenton Equaton () Fgure. Meaured water retenton charactertc from ISIC databae. h h n m r r () where (h) the ol moture content at h ucton potental, r thedual moture content, the aturated moture content, the nvere of ar-entry potental, and n and m are the hape parameter for the water retenton curvepreentng pore-ze dtrbuton ndex []. HydroMe computer programme wa ued to determne parameter of the van Genuchten equaton ( tml) and executable n programme The pedotranfer functon were then developed to etmate thee parameter from readly avalable meaured bac ol properte. elatng the moturetenton parameter to the bac ol properte then make t poble to predct the moturetenton charactertc from the bac properte and hence enablng predcton of the aturated hydraulc conductvty. It would therefore not be neceary to have meaured data on moturetenton charactertc to determne K but ntead, the bac ol properte would be ued n determnng the equaton for moturetenton whch can then be ued to etmate K. Meaurement of moturetenton charactertc qute elaborate, tedou, tme conumng and alo expenve epecally f a large number of te nvolved. From the ample data et of 457 ample, a ub dataet contng of 34 (75%) ample wa randomly elected for ue n calbraton of the pedotranfer functon to be developed whle themander porton of 5 ample (5%) of the data wa ued n the valdaton proce. In development of the pedotranfer functon, the followng procedure were undertaken.... Evaluaton of the Dtrbuton of the Moture etenton Parameter A requrement n developng pedotranfer functon that thepone (dependent) varable hould be normally Copyrght 03 Sce.

4 Development of Pedotranfer Functon for Saturated Hydraulc Conductvty 57 dtrbuted. A a reult, the moturetenton parameter of the van Genuchten equaton and ther poble tranformaton were evaluated to etablh whch would bet approxmate normal dtrbuton. To check the extent to whch thepone varable would be normally dtrbuted, tattcal meaure of Shapro Wlk (W-value), Skewne Coeffcent, and meaure of Kurto were ued n the aement.... Stattcal egreon Analy Stattcal regreon wa performed between each tranformed repone varable and each of the bac properte and ther tranformaton o a to etablh the goodne of ft n each cae baed on the meaure of the coeffcent of determnaton ( ). The purpoe of th wa to determne, for each repone varable, the predctor varable or t tranformaton that gve the bet qualty of ft between the two when a regreon performed. Th would gve an ndcaton of whch predctor varable or t tranformaton correlate bet wth thepone varable or t tranformaton...3. Analy of Cro Correlaton To etablh the level of dependence between the elected predctor varable for each repone varable bet correlated to them, a cro correlaton wa performed between the ndependent varable by determnng the correlaton coeffcent (r) between each par of the var able. Th knd of analy performed to determne f there any correlaton between two predctor varable among the et choen for determnng the multplegreon equaton. It preferable that the ndependent varable n a multple lnear regreon equaton be ndependent among themelve...4. Multple Lnear egreon and Valdaton of Developed Equaton Th wa carred out between each elected tranformed repone varable and elected combnaton of predctor varable/tranformaton contng of the ndependent varable for whch thepone varable bet correlated a determned by the meaure of coeffcent of determnaton. The multple coeffcent of determnaton wa determned for each equaton developed to ae the accuracy of the equaton. The multplegreon wa carred out between repone varable and the predctor varable or tranformaton contng of ndependent varable that are not themelve gnfcantly correlated (r < 0.5). After development of the pedotranfer functon ung the gven data et, ther relablty then teted by comparng the value of predcted parameter ung the developed equaton wth the oberved data ung an ndependent data et. An ndependent data et contng of 5 ample wa ued n the valdaton proce. The evaluaton tattc ued ncluded the correlaton coeffcent among other. 3. eult and Dcuon 3.. Evaluaton of the Dtrbuton of the Moture etenton Parameter Table how the value of tattcal parameter ued for evaluatng normalty of dtrbuton for thepone varable beng the van Genuchten moturetenton parameter and ther propoed tranformaton for the data et of 457 ample. The tranformaton of van Genuchten parameter (repone varable) that produced the bet approxmaton to normal dtrbuton are, e r, and n. Th wa baed on meaure of the Shapro- Wlk (W-value), Skewne coeffcent and Kurto. For llutraton, Fgure how the htogram and normalty plot n the normal dtrbuton check for the aturated ol moture content tranformaton (θ ).The tranformaton of van Genutchen parameter (repone varable) that produce the bet approxmaton to normal dtrbuton are, e r, and n. Th wa baed on meaure of the Shapro-Wlk (W-value), Skewne coeffcent and Kurto. 3.. Stattcal Lnear egreon Analy The qualty of ft for the lnear regreon between each Fgure. Check for normalty of dtrbuton of the aturated ol moture content (θ ) howng the htogram and normalty plot. Copyrght 03 Sce.

5 58 Development of Pedotranfer Functon for Saturated Hydraulc Conductvty Table. ormalty of dtrbuton check for parameter n the van Genuchten water retenton charactertc and ther tranformaton. Kurto W-value Skewne θ r α n ln(θ ) n e ln(θ r ) r /θ r r 3 r ln(α) /α e α α Log(n) n n /n e n elected tranformed dependent varable (moturenton parameter) and the tranformed ndependent varable (bac ol properte) wa notably dfferent for each predctor varable tranformaton. For ntance, the lnear regreon performed between θ and and yelded a qualty of ft, meaured by the value of, to be 0.0 whle that between θ and e and yelded = 0.0 (Table ). The ame obervaton wa made n the cae of regreon performed wth lt, clay, bulk denty and organc carbon. Alo each elected tranformed varable (.e. ln(θ ), e r,, etc.) produced dfferent value of when a lnear regreon wa performed between each of thepone varable and a tranformed predctor varle for each of the varable and, lt, clay bulk denty and organc carbon. For example, a regreon performed between the ndependent varable and and yelded = 0.4 whle that between and and produced = 0.0, hence no partcular tranformed varable could be ad to generally gve the bet qualty of ft wth all the dependent varable whether t and, lt, clay, bulk denty or organc carbon. Alo, there no partcular repone varable that could be ad to yeld the bet qualty of ft compared to other for all the ndependent varable or tranformaton to whch regreon wa performed. The purpoe of regreon analy wa to dentfy the par of tranformed dependent and ndependent varable that yeld the bet qualty of ft between them a meaured by coeffcent of determnaton ( ) o that for each dependent varable, one able to dentfy whch tranformaton of each of the dependent varable would be ued n developng the pedotranfer functon durng multplegreon equaton to relate each repone varable and elected predctor varable and approprate tranformaton. Th would help etablh the bet poble mathematcal relatonhp between the moture retenton parameter (repone varable) and elected Table. Meaurement of the qualty of ft baed on coeffcent of determnaton ( ) between the moturetenton parameter (repone varable) and and wth t tranformaton (predctor varable) n the lnear regreon. Sand Sand Sand 3 Sand 5 Sand 0 Sand 5 Sand ln(and) and e Sand θ = 0.0 = 0.0 = 0.08 = 0.06 = 0.03 = 0.03 = 0.09 = 0.06 = 0.0 = 0.0 = 0.4 = 0.4 = 0. = 0.08 = 0.05 = 0.04 = 0. = 0.08 = 0.0 = 0.0 ln(θ ) = 0. = 0. = 0.0 = 0.0 = 0.07 = 0.04 = 0. = 0.08 = 0.0 = 0.0 θ = 0. = 0. = 0.9 = 0.5 = 0.04 = 0.03 = 0. = 0.07 = 0.0 = 0.0 = 0.0 = 0.0 = 0.8 = 0.3 = 0.07 = 0.05 = 0.8 = 0.3 = 0.0 = 0.03 = 0.0 = 0.0 = 0.0 = 0.0 = 0.0 = 0.0 = 0.00 = 0.00 = 0.00 = 0.0 ln(α) = 0.0 = 0.03 = 0.05 = 0.07 = 0.09 = 0.09 = 0.0 = 0.00 = 0.00 = 0.08 Log(n) = 0.0 = 0.3 = 0.5 = 0.5 = 0.6 = 0.5 = 0.5 = 0.08 = 0.0 = 0.08 n = 0. = 0.5 = 0.8 = 0. = 0.0 = 0. = 0.08 = 0.05 = 0.0 = 0.0 n = 0.07 = 0.08 = 0.09 = 0.08 = 0.09 = 0.06 = 0.06 = 0.04 = 0.0 = 0.03 Copyrght 03 Sce.

6 Development of Pedotranfer Functon for Saturated Hydraulc Conductvty 59 bac ol properte (ndependent varable) n the pedotranfer functon. A number of obervaton on the regreon relatonhp can be made for each repone varable and how t relate wth each of the predctor varable and ther tranformaton. The tranformed re- pone varable yelded the bet qualty of ft ( = 0.4) wth the ndependent varable and or and compared to the other tranformaton when a regreon analy wa performed. In the cae of regreon wth lt, the bet poble qualty of ft wa obtaned wth the tranformaton lt ( = 0.04) and o wa wth bulk denty, BD 3 ( = 0.60), clay or clay ( = 0.), organc carbon, ln(orgc) ( = 0.7). In general, the ln- ear regreon performed between and the bulk denty tranformaton produced bet qualty of ft a compared to thoe of lt, and, organc carbon and clay, howng that the bet relatonhp wa obtaned wth bulk denty followed by organc carbon, and, clay and lt n that order. In the cae of redual moture content, θ r, the elected tranformaton varable related bet wth clay wth a qualty of ft = 0.3 obtaned when regreon wa performed between and clay. The pooret ft wa obtaned when thegreon wa performed wth tranformaton of organc carbon e.g. ln(orgc) wth = 0.0. α yelded the bet poble qualty of ft when a regreon wa performed wth clay or /clay. generally howed poor qualty of ft wth mot of the ndependent varable or tranformaton. The tranformaton n alo howed poor qualty ft wth mot of the elected repone varable when regreon analy wa performed. The bet qualty ft wa obtaned wth the tranformaton of and when the lnear regreon wa performed between n and and 3 ( = 0.09). Fgure 3(a)-(d) llutrate thegreon between elected tranformaton of repone varable and the predctor varable to whch they bet ft. (a) (b) (c) Fgure 3. epone veru predctor varable correlaton wth correpondng bet poble qualty ft. (d) Copyrght 03 Sce.

7 60 Development of Pedotranfer Functon for Saturated Hydraulc Conductvty After performng lnear regreon between two varable nvolvng the elected tranformed repone varable, aocated wth the moturetenton parameter, and the predctor varable aocated wth the bac ol properte, the followng concluon were arrved at. For the tranformed repone varable the predctor varable that yelded the bet poble qualty of ft wth t when lnear regreon wa performed were and, lt, BD 3, clay, and ln(orgc). Thee varable would then be ued n developng the multple lnear regreon between the ad repone varable and the predctor varable. In the cae of e r, the bet poble ft (meaured by the value of ) wa obtaned from lnear regreon wth and, lt 0, BD, clay, and ln(orgc), whle n the cae of the bet poble ft were obtaned wth e and, Slt, BD, Clay, and ln(orgc). In the cae of n, the bet poble qualty of ft wa obtaned wth the predctor varable Sand 5, lt, ln(clay), (orgc ) Multple egreon Analy and Accuracy of the Pedotranfer Functon Developed Table 3 how the qualty of ft obtaned when multple lnear regreon wa performed between each elected repone varable and the tranformed predctor varable to whch t relate bet e.g. a multple lnear regreon performed between thepone varable and and, lt, BD 3, clay, ln(orgc), yelded the qualty of ft mea ured by = 0.63 whch condered acceptable and therefore accurate. Theultng equaton llutrated below Equaton (). The predctor varable ndcated above that related bet n lnear regreon wth the elected repone varable were the one condered n developng the pedotranfer functon ung multple lnear regreon and 0.505lt 3 0.6BD 006clay ln orgc () where θ the aturated ol moture content (cm 3 /cm 3 ), lt the % lt, and the % and, BD the bulk denty (g/cm 3 ), clay the % clay, and orgc the Organc carbon content (g/kg). The qualte of ft for themanng tranformed repone varable are llutrated n Table 3 for each of e r, and n when the mple lnear regreon wa done wth the elected predctor varable tranformaton Analy of Cro Correlaton and Correlaton Matrx Cro correlaton wa done for the ndependent varable (tranformaton) ued n developng multple lnear regreon for each of thepone varable, e r, and n. Table A-A4 (Appendx) how the relatonhp, baed on correlaton coeffcent, between the varou predctor varable ued for each of the repone varable tranformaton. In the cae of the predctor varable and and clay appear to be hghly negatvely correlated wth r = 0.7 whle BD 3 and ln(orgc) are alo farly correlated n a negatve ene (r = 0.59). For the dependent varable, thepone varable BD 3 and ln(orgc) are alo cloely correlated n the negatve ene wth r = 0.6. Other reaonable correlaton nclude that between e and and lt (r = 0.89), BD and ln(orgc) (r = 0.64) n the cae of predctor varable for. The other gnfcant correlaton oberved that between and 5 to (lt) (r = 0.74) and and 5 to ln(clay) (r = 0.69) n the predctor varable for n Multple Lnear egreon eult For each of the elected repone varable, Table 3 how the varou poble combnaton of the predctor varable that were ued n performng the multple lnear regreon and alo ndcate the qualte of ft obtaned baed on the coeffcent of determnaton. Table 3. Meaurement of Qualty of ft baed on coeffcent of determnaton ( ) between the moturetenton parameter (repone varable) and elected predctor varable tranformaton n the multple lnear regreon. and, lt, BD 3, clay, ln(orgc) and, e BD, and lt, BD 3 clay, BD, lt BD 3, ln(orgc) BD 3, clay and, BD 3 = 0.63 = 0.63 = 0.63 = 0.6 = 0.59 = 0.6 = 0.63 r and, lt 0, BD, clay, ln(orgc) and, clay clay, lt 0, BD clay, lt 0, BD clay, Slt 0, ln(orgc) clay, BD clay, ln(orgc) = 0.37 = 0.33 = 0.35 = 0.3 = 0.3 = 0.35 = 0.3 e and,lt, BD, clay, e and, BD, clay e and, clay, ln(orgc) clay, lt, ln(orgc) lt, BD, clay BD, clay lt, clay ln(orgc) and 5, /lt, ln(clay), orgc and 5, orgc lt, ln(clay) ln(clay), or GC orgc, BD 3 ln(clay), BD 3 and 5, BD 3 n = 0.4 = 0. = 0.3 = 0. = 0.04 = 0. = 0.0 Copyrght 03 Sce.

8 Development of Pedotranfer Functon for Saturated Hydraulc Conductvty 6 The varou poble multple lnear regreon equaton obtaned for the varou ndependent varable are underlted (Equaton (3)-(7)). The choce of the ndependent varable or ther tranformaton wa baed on combnaton that would yeld the hghet poble qualty of ft.e. the predctor varable combnaton choen nclude the varable that relate very well wth thepone varable, hence the equaton are the bet poble equaton that could be obtaned ung the varable ndcated. Equaton developed nvolvng are a follow wth the meaure of accuracy baed on coeffcent of determnaton ( ) ndcated: and (3) and BD e BD and 46BD lt and lt BD clay 0.045ln orgc 0.63 E (4) (5) (6) The et of poble multple lnear regreon equaton developed nvolvng are lted a follow: r e clay 5.090E (7) 0 0lt 0039BD 0.35 r e and clay 0.33 r e clay E 0lt ln orgc 0.3 r e clay BD (8) (9) (0) The et of poble multple lnear regreon equaton developed nvolvng are lted a follow: and E 043e BD lt clay gc ln or E 043exp and BD clay () () and E 043e ln orgc clay (3) The et of poble multple lnear regreon equaton developed nvolvng n are lted a follow: n E0and 0.63 lt ln Clay 0.4 orgc (4) n ln clay 0.4 lt (5) n E0and 5.59E orgc 5 (6) n ln clay 0. orgc (7) Baed on the above ndcated equaton that produced the bet qualty of ft, equaton relatng the moture retenton parameter that are not tranformed to the tran formed bac properte were alo compared to the meaured (ftted) parameter and yelded the value of ndcated (Equaton (8) to (3)) alongde the equaton and e BD (8) 3.6. Valdaton of the Developed Pedotranfer Functon to Evaluate elablty Table 4 how regreon equaton developed for each of lt r ln clay 5.09E0.0 BD 0.43 (9) and orgc 0.8 n E E (30) Copyrght 03 Sce.

9 6 Development of Pedotranfer Functon for Saturated Hydraulc Conductvty Table 4. Summary of equaton for tranformaton of van Genuchten parameter and ther performance n relablty. epone varable Equaton MSE S SE ME PBIAS = and e (BD) = and BD = SAD 0.505/lt + 0.6BD E 006clay ln(orgC) = and 0.433lt BD = clay 5.090E 0lt BD = and clay = clay E 0lt ln(orgC) = clay BD = clay ln(orgC) = E 043exp(and) lt BD /clay ln(orgC) = E 043e and BD clay = E 043e and /clay ln(orgC). n n = E 0and lt ln(Clay) /orgC n n = /lt 0.078ln(Clay) n n = E 0and E 005/orgC n n = ln(Clay) /orgC and E043e Ln orgc clay 0.04 (3) the elected tranformaton of the moturetenton parameter of the van Genutchen moturetenton equaton and meaure of ther performance n valdaton baed on the tattcal meaure ndcated. The tranformed model parameter that yelded the bet relablty the aturated ol moture content (conderng the meaure of coeffcent of determnaton ( = 0.76). Th ndcate that θ reaonably well predcted by the pedotranfer functon developed. Predcton of tranformed varable yelded the lowet poble value for the elected meaure for the qualty of ft (r = 0.5) reflectng the lowet level of relablty compared to the other pedotranfer functon developed for moture retenton parameter under conderaton.the tranformed varable for redual moture content yelded modet performance wth the bet poble value of = 0.4. [4] note that contnuou pedotranfer functon can be appled n the cae of more te pecfc applcaton, where meaured data avalable, nce they do not provde te pecfc nformaton. The pedotranfer functon predct ol hydraulc charactertc for broadly defned textural clae. Fgure 4-7 llutrate the performance of the developed pedotranfer functon for the tranformed repone varable baed on analy by lnear regreon. 4. Concluon and ecommendaton The performance of developed pedotranfer functon for etmatng moturetenton parameter n the van Genuchten moturetenton equaton vared for the ndvdual moturetenton parameter. Equaton deve- Copyrght 03 Sce.

10 Development of Pedotranfer Functon for Saturated Hydraulc Conductvty 63 Fgure 4. Predcted value of tranformed varable veru meaured by correlaton for a developed equaton that yelded the bet poble qualty of ft. r Fgure 5. Predcted value of tranformed varable e veru meaured by correlaton for a developed equaton that yelded the bet poble qualty of ft. Fgure 7. Predcted value of tranformed varable n veru meaured by correlaton for a developed equaton that yelded the bet poble qualty of ft. loped for predctng aturated ol moture content (θ ) yelded the bet performance n model valdaton wth the hghet poble value of coeffcent of determnaton = 0.76, MSE =.09 and a SE of Thelatvely pooret performance wa oberved wth the parameter α wth the bet poble value of beng 0.06 ndcatng unatfactory performance and a MSE value of Themanng parameter (θ r and n ) regtered performance ntermedate between the aforementoned two extreme. It therefore evdently not poble to obtan excellent performance n pedotranfer functon for all the parameter. The equaton derved from thee parameter would be the bet poble obtanable for etmatng hydraulc conductvty. Contnued effort hould be made n developng more pedotranfer functon to provde uer wth more alternatve equaton and epecally thoe PTF that ue the very bac ol properte avalable n many local ol data bae. 5. Acknowledgement I wh to acknowledge the upport provded by the Dean Commttee eearch Grant, Unverty of arob (Uo) who funded theearch project, The Prncpal offce College of Archtecture and Engneerng (Uo) who funded journal publcaton fee. I alo wh to acknowledge upport gven by taff of the department of Envronmental and Boytem Engneerng (Uo) who contrbuted ueful academc dea that enrched th document. Fgure 6. Predcted value of tranformed varable veru meaured by correlaton for a developed equaton that yelded the bet poble qualty of ft. EFEECES [] H.. Fooladmad, Pedotranfer Functon for Pont Etmaton of Sol Moture Charactertc Curve n Some Iranan Sol, Afrcan Journal of Agrcultural eearch, Copyrght 03 Sce.

11 64 Development of Pedotranfer Functon for Saturated Hydraulc Conductvty Vol. 6, o. 6, 0, pp [8]. T. Walczack, F. Moreno, C. Slawnk, E. Fernandez [] J. P. O. Obero, Evaluaton of Infltraton Ung Green and J. L. Arrue, Modellng of Sol Water etenton Curve Ampt Model and anfall unoff Data for Lagan and Ung Sol Sold Phae Parameter, Journal of Hydrol- Sambret Catchment, Kercho, Kenya, M.Sc. The, De- ogy, Vol. 39, o. 3-4, 006, pp partment of Agrcultural Engneerng, Unverty of a- do:0.06/j.jhydrol rob, arob, 996. [9] T. Well, S. Ftyu, D. W. Smth and H. Moe, The Ind- [3] A. aoulzadeh, Etmatng Hydraulc Conductvty Urect Etmaton of Saturated Hydraulc Conductvty of ng Pedotranfer Functon, In: L. Elango, Ed., Hydrau- Sol, Ung Meaurement of Ga Permeablty. I. Labolc Conductvty Iue, Determnaton, and Applcaton, ratory Tetng wth Dry Granular Sol, Autralan Jour- Intech, 0, pp do:0.577/753 nal of Sol eearch, CSIO Publhng, [4] K. E. Saxton and W. J. awl, Sol Water Charactertc Etmate by Texture and Organc Matter for Hydrologc Soluton, Sol Scence Socety of Amerca Journal, Vol. 70, o. 5, 006, pp [5] M. G. Schaap and F. J. Lej, Ung eural etwork to Predct Sol Water etenton and Sol Hydraulc Conductvty, Sol and Tllage eearch, Vol. 47, o. -, 998, pp do:0.06/s (98) [6] J. Tomaella and M. Hodnett, Pedotranfer Functon n Tropcal Sol, In: Y. Pachepky and W. J. awl, Ed., Development of Pedotranfer Functon n Sol Hydrology. Development n Sol Scence, Vol. 30, Elever B. V., Amterdam, 004, pp [7] H. Vereecken and M. Herbt, Stattcal egreon, In: Y. Pachepky and W. J. awl, Ed., Development of Pedotranfer Functon n Sol Hydrology. Development n Sol Scence, Vol. 30, Elever B. V., Amterdam, 004, pp [0] J. H. Woten, M. Y. A. Pachepky and W. J. awl, Pedotranfer Functon: Brdgng the Gap between Avalable Bac Sol Data and Mng Sol Hydraulc Charactertc, Journal of Hydrology, Vol. 5, o. 3-4, 00, pp do:0.06/s00-694(0) []. H. Batje, Ed., A Homogenzed Sol Data Fle for Global Envronmental eearch: A Subet of FAO, IS- IC, and CS Profle (Veron.0), Workng Paper and Preprnt 95/0b, Internatonal Sol eference and Informaton Centre, Wagenngen, A-DBF57E9FA67F.htm [] M. van Genutchen, A Cloed Form Equaton for Predctng the Hydraulc Conductvty of Unaturated Sol, Sol Scence Socety of Amerca Journal, Vol. 44, o. 5, 980, pp do:0.36/aj x Appendx Analy of Cro Correlaton Table A. Cro correlaton tet for tranformed predctor varable for. Sand Slt BD 3 clay ln(orgc) Sand r = r = 0.4 r = 0.6 r = 0.7 r = 0.0 Slt r = 0.4 r = r = 0.9 r = 0.3 r = 0.5 BD 3 r = 0.6 r = 0.9 r = r = 0.8 r = 0.59 clay r = 0.7 r = 0.3 r = 0.8 r = r = 0.08 ln(orgc) r = 0.0 r = 0.5 r = 0.59 r = 0.08 r = Table A. Cro correlaton tet for tranformed predctor r varable n e. Sand Slt 0 BD clay ln(orgc) Sand r = r = 0.5 r = 0.3 r = 0.7 r = 0.0 Slt 0 r = 0.5 r = r = 0.06 r = 0. r = 0.09 BD r = 0.3 r = 0.06 r = r = 0.4 r = 0.09 clay r = 0.7 r = 0. r = 0.4 r = r = 0.08 ln(orgc) r = 0.0 r = 0.09 r = 0.6 r = 0.08 r = Table A3. Cro correlaton tet for tranformed predctor varable n. e and lt BD clay ln(orgc) e and r = r = 0.89 r = 0.3 r = 0.3 r = 0. lt r = 0.89 r = r = 0.4 r = 0.3 r = 0.4 BD r = 0.3 r = 0.4 r = r = 0. r = 0.64 clay r = 0.30 r = 0.3 r = 0. r = r = 0.08 ln(orgc) r = 0. r = 0.4 r = 0.64 r = 0.08 r = Table A4. Cro correlaton tet for tranformed predctor varable n n. and 5 Slt ln(clay) orgc and 5 r = r = 0.74 r = 0.69 r = 0.34 Slt r = 0.74 r = r = 0.5 r = 0.5 ln(clay) r = 0.69 r = 0.5 r = r = 0. orgc r = 0.34 r = 0.5 r = 0. r = Copyrght 03 Sce.