61 TFW-SHlO-93-001 Geomorphological Watershed Analysis Project Biennial Report For The Period From 10/l/91 to 6/30/93 BY

resulv, give insight into how erosion would vary with land use and climate We propose a grsphkal tsbnkqe to analyze the entirety dkmdckange as well as what erosion lam appear appropriate for modeling forms In s enrchmnt to d&e quantttatlvely the spatial vtitlon in long-tam Ian&ape evolution. the dombmnee of dIffereat emsicm pHigh-resolwbn dIgital elevation data of s 1.2 km2 billy tuw where the channel mark bad THRESHOLD THEORIES becnrm~inthcReldwneuredinUKdibiWterninmodel. We use three simple threshold equations to explore the relation TOPDG. to test threshold tbeorles for em&m. The land surface was between landform and currem erosion p-. Tha stations predict dtvidcd into -20 m* elemenLs whose shspes were then dwified ~1 a threshold condition for ground saturation, a threshold to landslide instaconvergent, pbuw. or dtvergeat. llte entire’landsqx plotted on a bility of the ground due to hii pore pr~6%ra. and a threshold of erc&a graph of M per unit cootour kngtk agafnst surface gmdknl shows due to mlumtion overland flow. All thrae theories have been propped in each planform plot&g us s6parste f&Id. A simple steady4te hydmvarious foormS hy others. Here we write them in s form w&l for analysis logtc model wss used to predii zones of ssbuntim and arw of high using a diiital temin model. Several simplifying aswnptions are made to porep-tomimictbeexkemtbydmk@ccveatsrrspondMe fo r mluce the pnmeten lo those that can be crudely estimated from @Id erosive &abtlity of the lnnd avhee. The field observntlon that ~nhldata and the proped graphical analysis. Thsc theories. however. are at ration overland llow Ir nre out&k c~~vergat zones provided a the same general level of simplicity IS those in most numerical models of signiit constraint on the hydmlogic parameter in the makl. This landsape evolution. Specifically. we use a steady-state runoff model tlut model wits used ia threslxdd thewies to prediit sreas of slope i&&lusames that runoff own 8s subsurface now prallel to the ground surhyandareassubjecttoerosionbysatu&on overland flow. both of face duriog signif~nt hydrologic events and that sdturated conductivity which call eonllibule to cbsmlel hdlkuon. The proportion of converssd tmnsmimitity of the scil maode me spatially contanL (Despite large gem1 ekmmts predicted to exceed the thresh& varies greatly with ditTerences in %il thickness between ridges and unchaoneled valleys, the relativ6ly 6msU changea in sur(see rrsidpncc demoastrsting a high slwated conductivity and, consequently. the tmosmissiviry are dominated semitivily to land use such as eattk graving. Overall, the lakeape by highly mnducdw near-smfaa soil [Wikoo. 198% Montgomery, canbedlvidul,llsklgeroslmthrrshddllnca,kuowrrpoaeto WI].) We propose that steady-state runoff for an extreme event will ckmmel tnst&llity due to runoff and stable m-eas wkere dftfudw mimic the spatial variation in sur&ce satumtion and overland flow that trsnqmi predombmta would occur in natural tmosicnt storm even& respoosibk for satwation ov~rkitd now erosion md land&ding. We ako issum+ that the vegetation INTRODUtXION and soil pmpcti fontrolling surface resistance to ucsion are spatially Although numerical m&k can create ralkd&xking landscapes awmnt. by generating ridge and valley topography (e.g.. Abner& 1976; Kirkby. For ruady-nru. shallow subsurface runoK paralkl to the ground 1987; Howard, 1990; Willgoose et al.. 1991X the thmedimemiciml form surface, the ground wii bc mlunted if the prsipiution (minus evaponof ml IanQclpes and the prshaping them are, swprisingly. not don and deeper drainage), 9, times the area of the upslope tatchment. a. well quantified. The ream development of digital terrain mad&, howequak or exe& the maximum llux the surface layer can mndua mmever, permiu quamitative analysis of actual Imd?capm and thw provides pmed from the prcdwt of tmnsmimivity, T, surf&x slope, hf. and unit an opportunity to examine the relation between sediment tmosport pmckngth of the contour aaom which Ihe catchmeet is draining, b (O’Loughegeg and landscape form (e.g., Mcare ti al., 19884 1988b; Vemy et al, lie, 1986). Becaure of the steep slopa in the study area, M is calculated m 1990. Tuboton et al., 1991). the more physically correct sine d the grwndauface inclination, 6, rather Herein we propox a graphical tedmique for cbanuerkiog real than tan g, as med by O’Laghlin (1986). The threshold ofground mtumlandscapes wing digit.31 elevation dam to examine the appliotion of emtion can lx expressed S rion theories. We focus on a landwpc where previous afudis (Mont(I T gomery and Dietrich, 1988, 1989. 1992; Montgomery, 1991) have ib 3 M . (1) diated that thue k good evidence that threshold-based erosion models b 9 are appropriate. Field monitoring and mapping suggest that surface cm. This simple hydrologic model has been wed with good succor to predict sion leading to channel initiation wxs where a resistant to saturation saturatexl fana and runotT response in the computer model TOPOG by overland now (see Dunn~ 1980). seepage erosion (see Dtmne, 1990). or O’Loughlin (1936) and by Moore et al. (19884 1988b). It is ewmklly shallow landsliding is exceeded. Thea ppredominate in valleys, the same model dmt underlies the widely used TOPMODEL by Beven whereas on ridges the shallow soil k currently transported primarily by and Kirkby (1979). biogenic activity such m burrowing by gophers (Black and Montgomery, All parts of the landscape where the area per unit eootour length, 1991). a pthat perhaps can be treated OS largely slope dependent a/b, equals or exceeds the term on the right-hand side of equation I will Although our analysk focmes on cument runoff awl erosion pmcemes, our be saturated. Note that if measured values from a landxape of a/b are GEOWCY. Y. 20. p 615-679. Augw ,992 675 plotkd agdns~ M, then equation 1 will be a straight line with a slope given by the hydrologic prametcn ‘f/9, ad all points above this line will k satumlcd, Thii olxewation suggest that a useful rnalysir of digital elev~. tion data is to divide the land surface into diie small catchmcnts for which the physical attriiute~ a/b and Mean be determined and plotted on such a graph. Other threshold aiterir can be expressed u functions of these two physical chamcteristita A coupled hydrolc@c and slopestability model proposed by Dietrich et II. (1986) and subsequently moditied 4 tested by Montgomery and DiiIridl(l989) El” be written a.$ Slope instability oc~uls wbete o/b equals 01 txccedrc the tetm ~1 the right-hand side, which varies with the ratio of ground surface, tan B, to angle of internal friction. tan 6. Note that the bydrolcgic componat of equation 2 is the same model a~ that which luds to equation I and that equation 2 uses a fern, of the infbdtc slope model that ignorea strength contribution due to mhaion; i.e., at Lure aan 0 = [(p, p@)lpJ @, where p, and pv are the soil and water bulk densities and m is the proportion d the soil that is saturated. Fiild data suggM that (p,-p,#p, is -0.5 The hydr&gic model is hydmstati$ hence, excessive pore prcv surcs are not predicted and all s&s Im than 0.5 tan 4 are stable even if satumkd. Several authors have suggested that channd initiation by overland flow can be estimated by assuming tbat incision owus where some critical boundary shear stress, TV. or some other measure of resistance is cueded (c-z%., Honon, 1945; Schaefer, 1979; Moore et d, 1988b; Vertcaey et aI., 1990, Montgomery. 1991). In the gudy*te model used bm, sltuntion overland tlow dis%tgc is simply qud to qa Z%4b; i.e. water that cannot be camid as shallow subsurfiae flow mw travel ovedand. This qu.tion can be solved for the discharge that attains sulfiit depth for a given dope lo produoc * boundary shed1 swc5 qud to the critical value for the sutfrce. Lating qrr TM = I& rr = p&M, ” = (Z.&4)“.s m-s, and/n Kvhd. the fotloting thnsboki ofemsion quation an be derived in the de&d form: a ~1 T ->-+-At . . b q@ q Henu=Z~lO~r~K-‘~r,istheai~boun~~~su~Kir the mughnss intercept for the inverse relation betwaD friction fact0r.f. and Reynolds number (velocity, P, times depth, d, diviti by cbe kii mtic vircosity, Y that typkies faminar-like tlow in gruslandr (Duane and DiIrich. 19SOi Wilson, 1988; see review in Reid, 1989). Gnvitaticmd aa~lemti~n is g. and the ownedcal mnstant k for 10 T w.ter and hm units of (cm&g? DIGITAL TERRAIN MODEL ANALYSIS Weselstedmutaiathcbilly~udcbapsrr~Lndsnonhof San Fnncixo where extensive mapping and hydrologicst~ have been condudcd (Wiban and Diccrich. 1987; Montgomery and Diaridr, 1988, 1989; Black and Moatgo~, 1991; Montgomety, 1991). ‘T&e stud& have shown that Pnuation ovedud tlow is canlmm in the lawcf~ valleys, and most of the targc~ det&tlow scam originate .I cbanad he& Diild ekvetion dam were obtlincd at a dmdty of 1bout every IO m for the 1.21 km2 cat&mat from stereo digitiratiw of low-level black and 616 GEOUXY. Au.@ 1992 while aerial pbotogmpb% several map@ ground fealwcr were used to mntrd the registration of digital mordirates. Taking edvantage of the clur ground visibility. we sckcted data p&a to capture topogmphic change rather than (0 fdlow a regukr grid. Thr: digital elevation m&l component of TOPOG (O’Lwghlin, 1986) was tben.wd to castma digital surfaca. A sarond pragrom in TOF’OG divides the surface by drwing the equivaknl of flow lines acrc~ the cantours from valley hoctom6 to divides at a w-spedtied interval (UC O’Loughlin, 1986. la examples). The program draws flaw lines starting II low elevations and projects upslope. so contour length sepamting flow lines tend to lunow on t~mpbiilly divergent slops. Individual ekmen~ ddined by I pair of conlow lines on tbe upslope and downdope sides of tbe element and a pair of sBe.amlines 0” the Interal boundariY (Fig. I) are tbrrr created. For each &men& tbe total contributing area, 0. an be cakukted and the ratio a/b determined from the bottom contow length of UK element The loul slope between the two catour lines ma!+ up the demmt is also detemCned. Exb element shape was d&M IS convergent, planar. OI divergent, tamding to the differena in length of the updope, bi. and &wn.dope cmtwr length. bI, o f fbc ekmee$ i.c whnhn the ratio (b*-b,)/(b2+b,)rrmdedaplperapaafhangc76LpaMugeirsoms what arbitrary. We chose the rmalkst values atimated to be rektively free of artifaac of the model (<-O.lO is cmvergmt, >O.lO is divergent, otherwise planar). These values dearly delineated the mevergeet vIlky axes in the kndsupe (vi. I). ln addition. we wed ddld field mapping of the cment CXM~ ol the channel network to dassify those elemme (always mnve~en~) chat mntained a channel. Figure 2 SLOWS the daa tield for each element type IIS a function of spezilic utchmen~ (u/b) and local slope (tan g) for B 5 III contour interval and 20 m interval between llow linea For I given slop. the dunnd elements drain the krgest Jpsirc catchmml. Wbemas tbe divergent ekmenu drain tbe smdka There is wry little owkp between diwgent and movergent ekment data fidds andwsentially non+ between divergent and channel ekments. These diffewe much larger than that which might be created bv the ddinition of element 1~s. Ccmparigm of the data fk!ds for diffemt~co&u intervals and floV;-iine spa&g shows that there are some mirkis in Figure 2. The rpperen! log-linear date in the divergem ckment~ are a port& of the uiangukr-shaped ekments created at divides by diverging flow lines. Tbey have cm physical nktion to each other, and although they are purely en artilact of the analysis, they slill descrii r~peus of the divergent topqnphy and so were retained. For planar dunmu. tbe minimum size oftbe elements v&s with slope as mntrdkd by the mntour spacing (5 m in tbis use). hence a/b (minimum) = 5/tan 8. md no point0 plot below this valve in Figure 2. Reducing tbe contour spacing and the flow-line spacing. however. had negligible effect on the lo” .,’ . nn.*t?dd*of 7 ‘; ’ \ Lmdrliing p b 10-l . Divergent ’ / . Thresholds --,I I 10-2 10-l 1 0 0 10.2 10-1 1 0 0 l&Id data.