Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 1) = c ciency

Open Access ffi Discussions Sciences Earth System Earth Hydrology and and Hydrology . Geometric total influence ( c ciency in order to provide guidelines ffi 1 ciency was explored. Eleven main classifica- 11902 11901 ffi ) on e c erent stages of the structures in a wide range of situa- ff , and J. A. Gómez 2 , R. Pérez 2 , 1 This discussion paper is/has beenSciences under (HESS). review Please for refer the to journal the Hydrology corresponding and final Earth paper System in HESS if available. Institute for Sustainable Agriculture, CSIC, ApartadoUniversity of 4084, Cordoba, 14080 Dept. Cordoba, of Spain Rural Engineering, Campus Rabanales, though there are examples of successfule.g. projects in Alcali gully Creek restoration using Project check dams, (Weinhold, 2007), on numerous occasions faults have been habitually recommended in technical manualsvalues for restoration, found but in was in spontaneous linereference and with for those stable man-made step-pools interventions. systems, which might serve as a 1 Introduction A check dam isment a deposition small in dam order designed to to control reduce soil flow erosion velocity within and a to stream, enhance such sedi- as a gully. Al- timations of HJand and HJ impact control lengths. defining Totalwas the influence a location valid of guaranteed criterion the maximumtions for optimal e provided the that di hydraulic roughnessthrough conditions revegetation. remained Our high total within the influence gully, criterion e.g. involved shorter spacing than that conditions as well asfor a optimal method design. of The estimatingfor e model assessing integrates the main severalvaried previous processes flows). involved mathematical Its (hydraulic performance approaches jump wasa compared HJ, with bi-dimensional impact the hydrodynamic flow, simulations model. gradually obtainedthe The from geometric IBER, impact factor of of check influence tions dam of spacing flow (defined regimes by wereThe identified model depending produced on similar the results element when and compared level of with influence. IBER, but led to higher es- There is little information incheck scientific dam literature systems regarding in thecial flow modifications issue regimes induced in for by restored themodel gully to design classify reaches, flow of despite regimes conservation in it straight measures. being rectangular a Here, channels for cru- we initial and develop dam-filling a conceptual Abstract A conceptual model of checkhydraulics dam for gully control C. Castillo Hydrol. Earth Syst. Sci. Discuss.,www.hydrol-earth-syst-sci-discuss.net/10/11901/2013/ 10, 11901–11941, 2013 doi:10.5194/hessd-10-11901-2013 © Author(s) 2013. CC Attribution 3.0 License. 1 2 Leonardo Da Vinci Building, 14071 Cordoba, Spain Received: 17 July 2013 – Accepted: 4Correspondence September to: 2013 C. – Castillo Published: ([email protected]) 30 SeptemberPublished 2013 by Copernicus Publications on behalf of the European Geosciences Union. 5 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | erent flow ff erences in these rec- ff erent criteria proposed ff 11904 11903 ciency of the interventions for a broad range of ffi ectiveness in erosion control. For this purpose, the follow- ff ectively so that their stability is guaranteed in the long-term. ciency of check dam interventions for initial and dam-filling condi- ff ffi Despite all this research, a detailed and systematic definition of the di The main aim of this paper is to develop a conceptual model of the hydraulics of The analogy between step-pool systems and check dam interventions has been Several approaches have contributed greatly to the understanding of some of the evaluating the e tions based on energymodel balance with considerations; (ii) an to acceptedcheck validate dam hydrodynamic the design model; performance to (iii) ofconditions. optimize this to the propose e general guidelines for check dam systems inbasis for straight estimating rectangular their gullies e ing specific in objectives order were considered: todescribing (i) establish to the develop a range a of hydraulic theoretical conceptual water model profile for types that might occur in restored gully reaches, than that recommended bydams soil (Heede, conservation 1976; handbooks Morgan, for 2005). gully control using check types that might occurby in the check authors dam in systems theon for scientific how gully literature. check restoration In dam has addition, design notditions, there should been is given take also found that into very account the littlevariable either filling information climatic the and period initial erosive is or conditions dam-filling highly (Boix-Fayos con- et variable al., within 2007). a specific location due to self-organized system of high stabilitystudies (Chin (Abrahams and et Phillips, al., 2007).2002) 1995; have Furthermore, shown Zimmermann several that and step-pool morphologies Church,ing tend 2001; to to Lee minimum maximize flow velocity and resistance,maximum and Ferguson, lead- flow shear resistance in stress, step-pool which series occurred is with the significantly shorter final spacing cause of its stability. The Yu, 2007; Chin et al., 2009). Step-pools represent an interesting case of spontaneous, check dam sequences in high-gradient streams stabilization (Lenzi, 2002; Wang and an equilibrium slope for incipient sedimentical motion observations (Porto of and Gessler, the 1999); sedimentIroume (c) deposit empir- and gradient Gayoso, in 1991). restored Itommendations, channels is despite (Heede, apparent the 1978; that there factand are that this great spacing leads di is to a an critical undesirable degree factor of for technical check uncertainty. recently dam recognized, design, to thethropogenic point equivalent that to check2004). step-pool dams Step-pool sequences have morphological in been features considered steep have inspired as mountain the the streams design an- (Milzow, criteria for artificial for determining the spacingof between water adjacent flow check inaccepted dams natural criterion. and derive The artificial three from criteria channels, observations head-to-toe most although criterion, commonly there namely, found the in is toe thethe no of literature top single are: the of (a) upstream universally the the dam downstream is dam at (Heede, the 1960); same (b) elevation the as ultimate slope criterion defining essential processes in drop(Rand, 1955; structures, Vischer and such Hager, as 1995;zation Chanson, of hydraulic dissipation 1999), phenomena. jump allowing Physically-based a hydraulic and precise modelsevaluate have characteri- waterfall flood been regimes used impact to and thein influence arid of regions channel (Merrit geometrythe and performance in Wohl, of ephemeral 2001) conceptual channels models andfiles which may in aim become to gullies a predict controlled useful the by free-surface tool hydraulic water for structures. pro- contrasting In fact, the di al., 2004), including channel degradation(Porto and scouring and downstream Gessler, of 2000; thequently, check Castillo for dams a et successful al., gullyhydraulic 2007; restoration, modifications Conesa-García it produced et would by al., bethese check necessary 2007). structures dams e to Conse- in describe the the water main flow in order to design reported in the performance of these structures (Heede, 1960; Iroume, 1996; Nyssen et 5 5 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ® erent ff 1). Since, in = F erent regimes on ff ciency. ffi 1) at the impact zone. The spill- > erent output variables (flow depth, , the typical span of values for chan- ff 1 F ect by increasing the water depth im- − ff s 2 11906 11905 ranging from 0.1–1 m q of the check dam between 0.5–1.5 m. z ective height ff Rand Equations for the impact flow features in straight drop structures. Unitary discharge nels, gullies and step-poolChurch, reaches 2001; (Hager Merrit and and Wohl, Vischer, 2002; 1995; Castillo, 2012). Zimmerman and Channel roughness ranging fromwinding 0.03 channels to (Chow 0.06, et from al., clean 1994). and straight to weedy Classical hydraulic jump expressions (Vischer and Hager, 1995). Free-surface profiles, hereafter FSP, calculationscording to or Chanson backwater (1999). calculations, ac- Bed slopes ranging from 0.02 to 0.1. E 1). It also produces a water drop downstream of the check dam, which accelerates – – – c. b. The model was programmed in a standard spreadsheet implemented in a MS Excel The main input parameters of the model were: The model allowed the determination of the di The model features a combination of mathematical approximations to the di For dam-filling conditions, a hydraulic jump habitually occurs between the critical flow a. d. < the final FSP and, therefore, on dissipation patterns and overall e velocity, shear stress, Froude number, friction slope)intervals on as a well cross-sectional basis as at average 0.1 values m along the reach. file and was structured in fourFSP interrelated modules and (normal HJ flow conditions, features). impactHJ The flow, length) lengths were associated explicitly considered, to since rapidly their varied dimensions flows have a (i.e. relevant impact impact and on their classical form. subprocesses: present rectangular-shaped cross-sections; (b) the HJ characteristics correspond to calculations as simple as possible,The while still main keeping simplified track assumptions of the considered relevant were: phenomena. (a) gully reaches are straight and 2.2 Description of the conceptual model The conceptual model ofmodifications check induced dam by hydraulics checkreaches. was dam developed The to objectives construction simulate of inmain the the hydraulic the main processes model flow involved, were to regimethe assess to energy along the dissipation provide influence restored patterns a of and,at as the better the a di design understanding result, stage to of of gully inform the control the measures. decision-making One process of the main priorities was to keep the at the downstream spillway and theIn supercritical this regime at case, the impact weextending region from assumed upstream. the that spillway the ofcheck dam the top (Fig. downstream surface 1b). check of dam the to the sediment toe wedge of was the a upstream plane silting has taken place) itmediately creates upstream a of backwater e theF structure, leading tothe a flow subcritical leading regime toway (Froude supercritical performs number flow as conditions aa ( control restored section, reach, imposing subcritical criticalregime flow is flow conditions supercritical conditions exist in in ( theintermediate the upper cross part, downstream section a sections (Fig. hydraulic and jump 1a). the (hereafter HJ) develops in an 2.1 Introduction The construction of check damsand in downstream a of gully each reach causes structure. a In flow perturbation initial upstream conditions (after construction, when no 2 Methods 5 5 10 15 20 20 25 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (5) (6) (1) and Man- S n , q the impact i L equalling gully f , and are usually S S : d ∼ . Thus, the Froude number R d . (4) in a rectangular channel can be 0.45 d S which is dependent only on primary 0.5 0.9 · is significantly smaller than channel g n S n √ F 6 ciency of the conservation measures. d 0.1 / n ffi 1 n q d · = 11908 11907 ective height of the check dam,  can be estimated using Manning’s expression: ff in equilibrium with bed slope 0.319 n n 0.5 f F S · = S the bed slope of the gully. n g d , the flow depth 3 / the e q 2 S n p can be approximated by d g z 0.45  R √ S · ≈ 0.9 n 0.1 can be estimated directly from the input parameters  q n cient and . (2) n 0.5 u S ffi = · n 0.5 g d 3 / S 2 n p , we obtain: 0.5 and · R n n . (3) S n 3 1.275  d 5 / d 0.81  / 5 g 10 the supercritical flow depth at the impact. 3 , c  / = d i z n √ 1 c d  d z F n d  n q  is the critical depth, ≈ q · 0.5  · 0.5 c u at all sections), are not applicable. The value for each of the hydraulic variables , the hydraulic radius g d d n S S n d · w S  p 4.3 0.54  u ≈ = ≈ = = In rectangular channels in which flow depth For a given unitary discharge = i i n n , allowing the direct determination of the hydraulic regime for NC. n z z L d variables can be calculated: F Finally, using Eqs. (1) and (3), an expression for F a reference for comparisonMoreover, to once evaluate the the interventionNC) e has define the been situation carriedrium to of out, which the non-uniform normal flow flow with conditions regimes respect (hereafter, tend to since the bed itwidth slope. is an equilib- corresponding to normal conditions Uniform open channel flows arelocity characterized as by well a as constant byknown flow as a depth normal friction and flows slope (Chanson, mean 1999).ing ve- They straight represent uniform the starting channels) situation prior (assum- to check dam construction and thereby serve as 2.2.1 Assessment of normal flow conditions and waterfall impact. As a resultstress of vary these along transitions, flow the velocity, flowslope channel, depth and and normal shear conditionsin (friction a slope particular cross section can be calculated by solving iteratively the continuity and 2.2.3 Free-surface profile determination Check dam series simultaneously producesuper-critical gradually zones varied along flows the (GVF), gully i.e. (Fig. sub- 1), and and rapid varied flows (RVF), such as HJ where length and the flow characteristics at the impact: n 2.2.2 Flow regime at the impact Rand equations, in the form provided by Chanson (1999), were applied to determine Therefore, Solving this for d estimated using Manning’s equation and again assuming q where the subscript nning’s indicates roughness normal coe conditions for the hydraulic variables, 5 5 20 15 10 20 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | the L to refer (Heede, d S given by: erential energy of the HJ. c ff F ) (7) c regime of influence − (1 · S the bed slope and S =  S · z L 11910 11909 − 1  · S = set equal to the estimated HJ length. The cross-section at L z ff − : c S ective check dam height (to the bottom of the spillway), ff = z − L . (8) is the e S · 1 the deposition slope is zero, the surface of the sedimentation wedge S z · z L = (Chanson, 1999). Although the application of these equations on sloping L j c = H = d c For is horizontal and thethe bottom same spillway as elevation the of toe the elevation of downstream the check upstream dam check is dam (head-to-toe rule). For where check dam spacing in horizontal projection, Normal conditions (NC): For initial conditions, the HJ featurespercritical) are when controlled the by NC check (either damsallowing subcritical are the or at establishment su- enough of distance a normal toFor avoid flow. dam dam-filling influence, conditions, weslope can of assess the sediment the wedge modified or1976) deposition NC slope. can The corresponding deposition to be slope the expressedfactor of as influence a function of the originalS slope and the geometric Element exerting the influence: i. The regime of influence over the hydraulic jump has been classified following two In the model, the HJ characteristics were estimated by comparing graphically the The determination of free-surface profiles (FSP) in a reach controlled by a series of 1. criteria: (i) the element that exerts the influence; (ii) the level of influence. The hydraulic jump is thecheck most relevant dam process systems produced on byto the water the hydraulic flow. influence control Here of exerted we overgully the use or HJ the the characteristics term check either dam by downstream. the normal conditions in the 2.3 Analysis of the regimes of influence in the hydraulic jump which both curves intersectedand defined the the value location of of the the common Froude subcritical number, section that of is, the the subcritical HJ channels (either positive or negative)energy produces errors calculations, in they the provide estimationsessment a of of the valid the flow FSP approximation regimes, and for while keeping the the overall simplicity of conceptual the as- modelFSP implementation. calculated in both directionsthe in downstream order subcritical to find andFroude the upstream point numbers supercritical of at regimes. correspondence For between theconsidering this a supercritical purpose, longitudinal zone o the were transformed to their sequent values 2.2.4 Hydraulic jump equations Classical hydraulic jump expressionsmine (flat the main rectangular HJ channel), characteristics,energy were i.e. length used of to the roller deter- and the amount of dissipated wards (subcritical regime imposed bydam the forward water (supercritical surface regime elevation)method-depth after and calculated from the the drop). from upper Withincomprised distance the the was FSP following steps: applied approach, (i)spillway, the (Chanson, where definition step 1999). of critical the This conditions controlistics are method sections can reached) downstream be (at and the estimated upstreamequation at at (where 0.1 m the flow intervals impact character- inand both zone); derivative directions variables (ii) in (velocity, order friction application to slope, of determine shear the the stress) FSP at di (flow each depth) cross-section. approach can be applied totrolled the by hydraulic backwater conditions) calculations as both wellcontrols). in as subcritical in regimes supercritical (con- flows (governed by upstream check dams requires hydraulic calculation in both directions, from the lower dam back- energy equations following backwater calculation methodology (Chanson, 1999). This 5 5 20 15 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | d S can i 1 and, E , since . How- . Thus, i i c ≤ E F c 1 and total and n  E c is below ciency of the HJ oc- n ciency lower than TI 1. In both cases, the E ffi ffi ≥ c ciency of the HJ is below the must be positive to define any ffi 1. While the geometric influence d S > c 11912 11911 1 or even ∼ ciently low to achieve subcritical conditions. If values in the proximity of 0.6 (typical of slow-flow is negative. As c . (9) ffi n z d F S + c . Thus, the dissipation e . d ers from the geometric influence determined by i 1 ff F F ) downstream of the check dam is smaller than the Froude 1.5 1 = F i = F z must remain su + is small or the flow discharge high, similar values for d c S z E = i E cient. It corresponds with very slow regimes, high discharges and/or small 1, the deposition slope = ffi > n We named partial hydrauliccertain influence distance (PI) from that the situationnumber check in of dam which the toe HJ HJ and,number ( occurs therefore, at the at supercritical the a Froude impact maximum. Total hydraulic influence (TI): The influence willimpact, be where total all the (TI) energyperformance when provided and by the the drop HJ is takes employed to place enhanceSubmerged the immediately jump: HJ after the The subcritical Froude numberupstream defined check by dam thethe is hydraulic tail-water smaller jump level is than submerged, atconditions the producing (Vischer the a sequent and toe dissipation Hager, Froude e 1995). of number the of E Submergence is not awould limiting require factor negligible for checkquired check dam for dam heights gully design whencases restoration in compared and and practice, around with 0.1 since practical the mconditions it for considerations: scale such as less re- weedy than downstream reaches 0.4 close m toPartial in the hydraulic gully influence all mouth). (PI): Downstream check dam: dam-filling conditions, this influencecheck is dam influence only dominates exerted over the for enough NC not when adjacent to check allow dams the are development close ofLevel a of normal influence: flow. This classification takes into considerationcurring the dissipation in e atail-water controlled level. reach Several cases as canon a be the considered consequence HJ: regarding of the the level of controlSubmergence: influence imposed by the This phenomenon is characterized by the absence of HJ. In this case, due to the ine check dam heights. Normally,ever, when the specific energybe for obtained. NC At theevolve to limit, NC if without those thethe values development submergence of were threshold: a equal, hydraulic jump. the This water condition free-surface defines will c normal flow regime, modified NC conditionsin only addition, can be determined for did not fulfill thisalong latter the requirement, reach no will hydraulic remain supercritical. jump will occur and the regime As for the initialditions conditions, imposed the by the HJelevation downstream location of check is dam the controlled as free-surface by a over the consequence the subcritical of spillway the con- (downstream rise control). in As for the negligible check dam dimensionsify for the a flow givenproduce regime flow, any corresponding the impact structure to on does NC. the not The hydraulic mod- regime check and dam the construction control will measure not would be ii. The hydraulic influence di 3. 4. 2. 1. 2. merely a geometric relationship. Partial hydraulicinfluence conditions occur is when usually produced when the former refers to the dissipation performance of the HJ, whereas the latter expresses 5 5 25 20 15 10 15 10 25 20 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | S · are (14) (10) (11) (12) L i ) and u z + ciency in the mean c and due to the ffi i E i m d L R , i was estimated j E H ). The e + the hydraulic radius i S n H = R = t fm H S ciency of check dam ffi . Therefore, all the energy needs 3 − . (13) m j · H at the corrected reach when compared N ! m m were estimated assuming a classical HJ. L separately for such a complex hydraulic + 2 fm τ g j i R i j · u · S 2 H H H L is the mean shear stress and γ + 11914 11913 − ), reducing the dissipation through bed friction i m j = ) at all the cross-sections. τ d S and H S i

fm = ) are reduced in the post-intervention scenario at the = H S at the corrected reach was calculated according to − f m ·
100. (15) j ) S τ fm · L z H j S can be directly calculated using Eq. (15): = + + dis H n and n S s i c
H τ · j R + E d H · fm · i L H L , the mean values of the hydraulic variables responsible for the S L H γ X + − 1.5 ( i + = = S ) at the wetted perimeter of the cross section at a rate given by H j = dis-NC · the water specific-weight in i H H L γ E − 100 + < · dis-NC dis-CN i = − S H · H H dis ) fm z dis H L is the mean friction slope, = = S is the specific energy for critical depth over the spillway and ciency of a check dam intervention was defined as the percentage of reduc- erence in total head between adjacent check dams corresponds to the erence of total heads between the critical regime at the spillway ( is the shear stress for normal conditions (NC) in Pa, H L + S ff = ff fm P ) and at the hydraulic jump ( c − ffi i S S n c S · · τ P E H E S dis interventions ( L L ): = H culties inherent in calculating = = = = dis The e The energy losses at the hydraulic jump Since The average slope friction In contrast, after the check dam construction, energy losses appear at the impact The di ffi i s fm H X Eq. (13): S erosion processes (e.g. expense of creating local energy lossesunder at non-protected particular conditions, locations. an If this intensificationplace. dissipation of occurs the erosive processes might take where for NC in m and to be dissipated by exertingslope a is drag equal tension to over the the bed gully slope bed. ( Inzone this ( case, the friction ( H H In this study, a new methodologydam is construction proposed to when estimate compared theconsiderations with performance (Fig. of 2). a the non-intervention check scenario based on energy product. In a gullybed without friction intervention, ( thisthe energy NC regime. is Assuming dissipated uniformhydraulic completely and flow, this geometric through energy variables: can be expressed as a function of FSP using a hydraulic model. 2.4 An energy-based approach to assessing the e is straightforward to determine, the hydraulic influence requires the solution of RVF and to the friction slopereduction value of friction for slope NC prior to the interventionE ( the subcritical conditions imposed bydi tail-water level at theregime. impact length tion of the mean value of the friction slope where the specific energy, flow depthcharacteristics and at the velocity impact at zone the were impact estimated zone, using respectively. Eq. The (6). For HJ flow submergence conditions, the totalas energy the dissipation di H The energy losses at the impact zone were estimated using Eq. (14): where hydraulic radius in the controlled reach. 5 5 20 15 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , a z ciency ciency scripts ffi ffi ® between f S coordinate system were ciency (unitary discharge, S ffi , , i.e. value of the geometric q c over a ective height of the check dam in order to characterize the e ff c c 4.5 was fixed, the threshold value to achieve ciency, was obtained through several trial runs 11916 11915 = ffi i erent types of regime described in Sect. 2.5.2. ff F ciency ffi erent flow regimes that might occur in a restored reach using ff ). In order to design the e n Inc., Natick, MA, USA) specifically designed by the authors for this , z TM , S cient HJ (Chanson, 1999). , ffi q Additionally, the regions of validity for optimal The procedure for obtaining the IBER simulation was as follows: (i) definition of the low slopes (usually below 5 %).induce In lower addition, regimes high and hydraulic roughness thereby or promote low subcritical discharges flows. stable and e 3 Results 3.1 Normal conditions and Froude regime Figure 3 shows thetions. region Supercritical flow where is sub- the predominant and regime, supercritical while subcritical flows flow occur only in occurs on normal condi- for the design offactor check of influence dam defining interventions. maximum e Theof optimal the model untilconditions total ( influence conditionsFroude were number at achieved the for impact each region particular set of check dam height, bedducted by slope executing and the model roughness)for with was a increasing carried representative sample out.The of This mean the study friction di slope wasall along con- cross-sections the (0.1 m reach apart) was and,was also, calculated estimated by applying by using Eq. averaging Eq. (13) the (15). and, finally, the e determined for medium to high roughness conditions to provide practical guidelines (The MathWorks purpose. 2.5.4 Evaluating check dam e An analysis of the main factors of influence on check dam e applications featuring a hydrodynamicand module a based finite-volume on methoddraulic jump 2D-Saint-Venant used formations. equations for the characterization of unsteadygeometry flows as and a hy- triangulatedand irregular boundary network conditions; of (iii)lations; 0.1 creation m (iv) of cells; definition the (ii) model ofas definition mesh channel graphics of for roughness; (e.g. the the Froude (v) mathematical initial number calculationsducing calcu- longitudinal the and profiles). initial extraction The and of 3-D dam-filling input channel results geometry geometry was repro- obtained using Matlab 2.5.3 Contrasting the model To validate the conceptual model,the we compared results the provided performance by ofInstituto the the Flumen model hydrodynamic and against bi-dimensional CIMNE, IBER Spain). model IBER v1.9 is (GEAMA, free-to-use software for flow simulation evaluate the conditions in which they appear in gully2.5.2 networks (Eq. 4). Classifying free-surface profiles We have classified the di four indices: (a) siltingregime of for the NC: check subcritical dams:influence. or initial supercritical; or (c) dam-filling element conditions; controlling (b) the Froude HJ; (d) level of 2.5.1 Determining the hydraulic regime forThe normal areas conditions of occurrenceassessed for sub- as and a supercritical function regimes of in the normal unitary conditions discharge, were bed slope and roughness in order to 2.5 Methodology for analyzing check dam systems 5 5 20 15 10 20 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , a c values. erences ff c ciency curves corresponding ffi is the key factor F d cient to guarantee S ciency ffi ffi , varying one key factor c erent FSP types that may develop in ff at the impact zone and the location of the i F 11918 11917 ciently low to create subcritical conditions (F-SUB- are input factors) and the design of the intervention of the flow along the restored reach as predicted by ffi ) for an HJ to occur may require horizontal or even n d F ciency curves as a function of S at the HJ in the supercritical region. On the other hand, ffi and F S , ). As for initial conditions (Fig. 6a to d), the e q n to remain su d and S ciency occur when the conceptual model overestimates the Froude S ffi , z (F-D-PI and F-D-TI) to be established. , d q mainly, which define ciency by the conceptual model (22.3 % instead of 36.6 % and 28.2 % against S ffi c sets between both curves at the supercritical region. The biggest di ective transition to subcritical flow, since, in terms of energy, the flow requires ff ff and Overall, the model performed well, producing comparable results with IBER. The As for the dam-filling situation, the value of the deposition slope Supercritical NC lead to an undesirable uncertainty in the location of the HJ, since z parabolic segment in the middle and an asymptotic maximum at the highest tion of e 44.1 %). 3.4 Assessing the influence of keyFigure factors 6 on shows check a dam sample e at of a e time ( present an irregular sigmoid shape typically featuring a linear segment at low importantly, in the values of there are deviations withHJ. respect Higher to HJ the andible impact o lengths were predictedin with check our dam model, e number explaining at the the vis- impact (IN-SUP-CN-PI and IN-SUP-D-PI), leading to an underestima- The results of the comparison betweenof the model contrasting and IBER types for a ofevolution representative sample of FSP the are Froude shown number the in conceptual Fig. model 5. and These byto IBER. curves NC In represent (for the the the sameshown, spatial figure, in initial order the situation) to constant understand and FSP also evolution better. modified NCcurves (for are a mostly coincident dam-filling especially scenario) with are regard to the subcritical region, but also, ( negative 3.3 Contrasting the model channel characteristics ( a certain length to evolve from the supercritical flow at the impact. Depending on the the spillway to the bedsequent depth slope. of The supercritical HJ NC. occurs when the subcriticaldetermining regime reaches the the type ofassociated regime with which the develops, modifiedtake since place NC. since it If there controls theit is the is modified no necessary Froude downstream NC for regime control arePI). to supercritical, Nevertheless, cause in a it some (F-SUP-NHJ). HJthe cases, Therefore, will e this not condition might not be su IN-SUB-D-TI). this occurs at thatcontrol (IN-SUP-NC-PI). point The where length the ofapproximation, the downstream without subcritical check doing zone dam can the be produces FSP estimated, calculations, the as by a subcritical first drawing a horizontal line from HJ is dependent on thea element HJ will exerting occur the close influence. toenergy Thus, the and if impact has the region as NC reached soon are theical as subcritical, supercritical depth the associated sequent flow has with depth dissipated that correspondingto the NC to excess reach (IN-SUB-NC-PI). the the If subcrit- sequent thethe NC depth check were dam of subcritical (IN-SUB-NC-TI). the enough Thus,performance impact total influence of flow, is the the achieved, HJ HJ. leadingwhen to would Finally, the maximum downstream take adjacent control dams place are by at close dam the enough influence to toe dominate can of over only the NC begin (IN-SUB-D-PI and Figure 4 includes aa graphical gully depiction restoration. of For the initialquence di conditions, of the the HJ elevation occurrencevided is of that guaranteed the submergence as conditions water a are profile conse- not behind verified (IN-SUB-SUM). the The downstream location check of the dam, pro- 3.2 Classifying free-surface water profiles 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | c 72. and = using z ciency n 1. This f ffi ciencies S ≤ ffi c was calcu- 80 %) than , presented > 1 when com- z S > 0.99 for was to increase c = 1. to reach the max- z 2 = c R c ciency for (Fig. 6b). High slopes ffi 1.4 producing poor HJ and c = n ciencies will result in a sig- ). In this case (dotted lines F or high slopes ffi q = s-0.1m z 1 ciency at the expense of higher E · , from a five- to ten-fold reduction ciency value (Fig 6e and 6f). An as input variables ( F for initial conditions. As the check ffi ffi fm and smaller maximum e c S S c 1.01 ciency) valid for both initial and dam- = ffi and cient required smaller q 0.8, are presented. Here, it was apparent ffi at 0.1 m intervals and calculating > s-Eq.13 f c 11920 11919 ciency took place around E S below 2 %. In most situations, this large drop in ffi erence between the hydraulic roughness results represents a floor-type threshold, i.e. the points ff fm . t were easily known, as in the case of total influence. c S j were calculated for initial conditions using the model H H (Fig. 6a). The main impact of higher c are constant, as calculated using Eq. (14). The dissipa- i ciencies and a displacement of the maximum e c H ffi and c i H erence in total head between adjacent dams (LS) decreases. and, therefore, the total energy losses at dissipation phenom- ff j H ) i ciency and displace it towards increasing F 0.7, the NC flow supercritical and ciency was slightly lower (Fig. 6h). ffi 4.5 criterion which is only dependent on , that is, at a larger spacing. Those high e conditions above this line verify an optimum e ffi = 90 %), although for initial conditions, the location of the maximum took c = c ciencies were achieved, slightly lower in the former case ( i S > ciency performance, with no clear maximums (Fig. 6f and g). Higher ffi F , q ffi led to the displacement of the curve maximum in the direction of decreasing ciency obtained by averaging , are maximum. At shorter spacings, the HJ becomes submerged and loses t q ffi H 1 and ciency, causing a decrease in ciency and the location of the turning points. Thus, increasing unitary discharges Firstly, the curves of optimal To provide a better understanding of the processes involved, Fig. 7 shows the evolu- Considering all the cases included in the above analysis, the relationship between Overall, it was clear that in both situations (initial and dam-filling conditions) high For dam-filling conditions (Fig. 6e–h), only cases where HJ occurred were consid- The influence of the key factors was noticeable mainly on the maximum level of (Fig. 6g). Finally, a higher roughness coe = ffi ffi , but in most cases they had little impact on the e floor-type threshold behaviour is alength consequence on of the the influence optimal of spacing. the HJ If and their impact length is negligible, total influence is typically (i.e. total influence conditionfilling and conditions. maximum e and considering a rangelated of using situations with in Fig. 8a),above the the curve line verify of thec optimal condition. For instance, the upper dotted line corresponds to ena e 3.5 Regions of optimal Figure 8 illustrates the procedure employed to determine the regions of optimal dams get closer, the di Energy losses at the impact tion of energy at the(in hydraulic this jump is case minimumperformance) throughout and the starts NC-influence segment tothe grow dam as influence, the the damperformance. lower When influence the total begins subcritical influence to flow issequent operate. achieved at value The (subcritical of tail-water higher tail-water level, level enhancing reaches the the HJ of the original slope,the leading friction to slope a is likelyerosive to processes. be enough to reduce shear stresses below the thresholdtion of of the main energy parameters with increasing nificant decrease in the final average friction slope in the latter ( place at lower imum and the e the e Eq. (13) rendered the linear regression Thus, the combination of Eqs.mate (13) the and performance (15) if represented a straightforward way to esti- maximum e a poorer e lower c intermediate slope produced the highestc maximum e (Fig. 6c), whereas there(Fig. was 6d). little In di all cases, the maximum e ered. Therefore, relatively highthat, values, although a general sigmoidworth shape noting was that found, the in curves mostpared were cases, more the with irregular. curve the It maximums is initial movedbetween towards conditions adjacent curves. check Those dams, cases either low corresponding dam to heights short spacing e produced lower maximum e in the direction of decreasing the maximum e produced a displacement of the curve to lower 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | q ect de- − dis- ff c S 1 below, − s F 2 above the F points below it S , . The length of the q c as long as the slope c got closer to 1.2 since were obtained for dam- c c 1 was not valid to create op- 1 and the for initial and dam-filling situ- = c = c c 0.04 (clean, winding channels) and 1. Only for high unitary discharge or = = n c 0.04), since its region of validity was negli- = n 11922 11921 cients: to achieve total influence, but also enough dis- is low, a large part of the gully remains under ), the larger the region of validity of the design. ffi c d c S 1. In this case, the way in which the flow is controlled ciencies for < ffi c values above 1 be required. c 1.2. However, since both processes need space to develop, they ∼ erent roughness coe c ff . c ciencies along clean channels ( ffi 0.06, Fig. 9b), there is a significant area (up to 9 % of slope and 0.5 m 0.06 (winding channels with weeds and pools). ciencies delimited a ceiling-type threshold, i.e. the points below the line verify the = If this happens, the new situation is more erosive than that prior to the intervention Figure 9a shows that the total geometric influence The optimal curves were much more sensitive to roughness in the dam-filling sce- Finally, the area enclosed between two of these optimal curves for the same Secondly, similarly to the former analysis, curves of optimal = ffi n structures might in fact be more harmful than non-intervention (Heede, 1978). since the waterfall at thethe former check situation dam until produces itNC an line evolves accelerated to indicates flow NC. more more erosive Thisless intense power fact erosive than than is conditions. the illustrated In non-intervention in addition, scenarioof Fig. HJ and the 5: occurs reach at an favouringscouring intermediate, further processes unprotected degradation reported section processes. in Boththe many reasons complete check contribute dam destruction works, to of which the the may ultimately structure. lead Consequently, to badly designed check dam rapid supercritical flows are associated withwhich high are shear stress the and final frictiongrowth cause slope of values, of gully networks. the Their erosionof spatial processes the extent that is downstream only lead dam,supercritical controlled to conditions. by so the the that, development backwater and if e steep slopes would 4 Discussion 4.1 Erosion implications of the typologiesThe of study flow of regimes the Froude regimein for gullies NC defined showed that by supercritical erosion flows surfaces are with predominant scarce vegetation and steep slopes. These timal e gible (small black triangle). Valuesslope up and to unitary 1.2 discharge would be( defined. necessary However, if to a cover channel thecharge) is range that of covered reaches with optimal vegetation e from Fig. 8a andunchanged. b), whereas in the initial conditions, the thresholdsfined remained a almost region of optimalintensive control the valid throughout control the exerted lifetimeThese (higher of the results structure. are The more shownplane verifying in simultaneously Figure the condition 9,ations of for representing optimal two the di regionsn obtained on a the impact. Consequently, low slopes (largecontrol distances) since and their small Froude discharges number (easier andto to energy smaller evolves faster for the same distance) led nario (see the movement upwards of the optimal curves when the roughness increases filling conditions (solid linese in Fig. 8b). Conversely, thecondition. geometric For example, places the for upper optimum linesverify correspond the to optimal condition for is through the deposition slopeditions and commonly the spacing require between negative checktance dams. to Dam-filling develop con- the required subcritical flow corresponding to the Froude number at push adjacent check dams furtherRVF away (typically leading around to one smaller or optimal tworemained meters) high. had Figure a 8 strong shows impactthe how, on as RVF the lengths slopes were decreased, their comparatively influence small was compared barely to noticeable. the check dam spacing, and achieved when 5 5 20 25 15 10 25 20 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | c to be q ciency were ciency (maxi- ffi between 0.3– to the ffi q z ect of moving the ff ciency. This suggests that ffi ciency in the reduction of ero- is fixed with respect to HJ sta- since the reduction in LS com- ffi i c F can be estimated using a function remains constant but LS decreases. z value around 1m, which are suitable t H z ect, allowing an increase of the spacing be- 4.5 criterion is recommended, which is the ff = 11924 11923 F ciency results from the ratio of dissipated energy , the check dam spacing must be reduced, while z ffi . t H but lower losses. The total influence defines maximum e ect is achieved if a minimum j ff S H will remain lower than 2 m. However, values of , provided that the gully bed is at least the same width to avoid z q , and 1 . (16) − q s 2 are recommended, resulting in a 0.67 4.5). The vegetation of the gully sides, a common practice used to increase q ective height definition, the 1 and low LS) which is maintained for higher · ff = 1 m − t i s = F H 2 1.9 q : q Although the model proved to be successful in providing insight into the key pro- The contrast with the simulations performed by the IBER model was satisfactory Achieving total influence is recommended both for e For higher The response in check dam e = attain the target scouring the banks. cause scouring. When thisof criterion is applied, z For 0.5 m dimensions for constructing simple, inexpensive checkthe dams in farmer’s agricultural own areas means. using In this respect, the width of the spillway can be selected to ifications produced by check dam measures in complex channel4.3 morphologies. Practical guidelines for check damAs design for e threshold for stable HJ without creating an excessively powerful waterfall prone to cesses involved in gully control,more it realistic does situations not account suchpresence for as of many pools, those phenomena stones and occurring derived weeds, in erosionmay from and have local sedimentation a dynamics, slope all strong of changes, impact which reported on meanders, partial flow burying characteristics. For atfrom instance, the the Polyakov assumed downstream et spillway-to-toe hypothesis part al. for (2013) ies a of should plane check undertake sediment more wedge. dams, sophisticated Further a hydraulic stud- of analysis, fact check combined dam which with systems observation departs under field conditions, to improve our understanding of the mod- profiles. The discrepancies found inexpected, the due estimation of to RVF theFSP lengths and complexity to e the of length modelling ofin these the the proximity impact processes of and and 1. HJ the with the sensitivity short of spacing derived from keeping our model can be applied with confidence for a general assessment of free-surface both in the longitudinal hydraulic profiles and in overall e system into a moredam-filling stable conditions. stage since it increases hydraulic roughness,4.2 especially in Validity of the model Although the hypothesis underlying itslar definition gullies, led to classical major HJ), simplificationsconcepts the (rectangu- and simplicity an of overall thepossible using understanding calculations more enabled of sophisticated us tools. the to hydraulics, focus which on may the not have been increasing roughness has the oppositetween e check dams.controlled, A and suitable this choice e bility is ( to adaptslope the stability against dam bank height failure, has the additional positive side e pensates for the decrease in sive power, as well asmaximum for dissipation protection losses of located thetotal at check head), the dam where toe system. a of Totalwith protective the influence low apron check implies erosive must dam power be (around willof set. 90 develop new % As along stages of the a of the rest degradation. result, of a the slow gully, subcritical hindering flow the activation and decreasing totalinfluence available segment, energy the growth LS,The is as parabolic linear shape illustrated since (dam-influence inand conditions) the Fig. stems increase from 10. of bothmum Along the reduction the of NC- LS 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , but for c (Lenzi and c 0.72 for Alcali Creek = values typically ranged c H LS has remarkable similarities ectiveness requirement) and c ff erent previous approaches related ff erences in the hydraulic jump and im- ff 1 criterion can also be valid in this case. = c 11926 11925 ected by the deposition or, more frequently, the index was defined as the key variable controlling ff ciencies at an optimal H ciency is maximised (e LS ffi values obtained in this study for dam-filling situations ffi c 1 criterion) to operate with a wider safety margin, taking into cient. = ffi c ective control. Thus, it would be preferable to increase the cost 1 criterion is recommended, since it provides the interventions ff 1) turned out to be a suitable criterion to reach optimal control at = = c c , which could be a ciency in most gully conditions, while representing a straightforward H ffi . In fact, c erent filling stages of the structures as well as a convenient rule for dam location ff If this hypothetical analogy is valid, it will provide an interesting parallel between One main drawback of the ultimate slope criterion is its assumption of the devel- The occurrence of maximum e Despite the fact that authors such as Heede (1978) have proposed using empirical Furthermore, the combination of a check dam construction along with vegetation is in the field. The maximisationities of with energy the dissipation maximum by total resistance influence principle presents formulated similar- by Abrahams et al. (1995) for cations that check damsproduced produce. comparable Its results, comparison although with somepact di the lengths hydrodynamic were IBER found. model Amonguation all in the which possible the regimes, total dissipationthe influence e HJ is is the only also sit- forcedhigh to roughness occur conditions at the (eithermetric toe natural influence of ( or the induced structurethe (security by di requirement). revegetation), Under the total geo- 5 Conclusions The model has combined into a hydraulic processes single occurring framework in di restored channels to explain the basic flow modifi- heights were considereddams (Fig. were 6f considered. and Thesethey g), assumptions are i.e. steep might streams when be with short applicable step heights to spacing limited step-pools, between by since theman-made adjacent interventions available boulder and size. natural self-organized streams,of pointing imitating out nature the to necessity ensurereinforce the our stability conclusions of regarding the intervention thethe in geometric need the total to long-term. influence design It criterion. check will dam also locations following Comiti, 2003). Its definition isthe almost numerator identical to geometricalscouring influence beneath factor thebetween step. 1 In and natural 2. The step-poolfell optimal streams, within this interval, with values around 1.5 or above when high slopes or small resistance and, later, this parameter was named as steepness factor pool streams. In their study, the opment of a uniforma regime situation when which the isuniform ultimate regimes. not slope Furthermore, is applicable the relatively achieved insediments small in restored diameter in filling of agricultural reaches conditions, soil areas characterised particlebles (in size and by of boulders contrast highly gully might with be non- predominant)slopes steep will to mountain probably keep lead reaches the to bed where gentle,sideration shear almost cob- regarding stresses horizontal the below suitability the of critical the value. Thus, the previous con- with the maximum resistance principle formulated by Abrahams et al. (1995) for step- constructions by 30 % ( account the real risk of undercuttingdischarges, and which reactivation of is gully bound erosion(usually with 25 to eventual yr). high happen during the expected lifetime of the structures level). If steeper reaches are consideredthe (20 % excess or energy more), of alternativemight the ways of be flow dissipating costly should and be ine explored, since restoration ofrules the to check determine dam the ultimatebed slope slope of (e.g. sediment deposits awatershed) as in ratio a order of function to of avoid 0.28 overdesign,required the between our original to findings slopes suggest provide and that e shorter thereby spacings are highly recommendable, not only becausevides the the additional banks, protection but that also plant becauseoptimal cover it pro- increases the hydraulic roughnesswith leading to optimal lower e rule for check dam spacing in the field (head-to-toe rule applicable with a simple water 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ects of check-dams, ff ect of check dams on http://www.iberaula.es/ ff 11928 11927 airs) and FEDER funds. This support is gratefully ff This study was supported by Projects P08-AGR-03925 (Andalusian Gov- ectiveness and geomorphological impacts of check dams for soil erosion ff , last access: 5 June 2012. ectiveness of loose rock check dams for gully control in Tigray, northern Ethiopia, ff , sediment yield and retention on small semi-arid watersheds, in review, 2013. ff runo G.: The e Soil Use Manage., 20, 55–64, 2004. dgenössische Technische Hochschule Zürich, InstitutZürich, 2004. für Hydrologie und Wasserwirtschaft, 2005. flood along an ephemeral, arid-region drainage, Geomorphology, 52, 165–180, 2003. ogy features in Northern Italy, Geomorphology, 45, 243–260, 2002. with check-dam sequences, Geomorphology, 55, 97–109, 2003. ogy, 46, 59–71, 2002. cana S.A., Santafé de Bogotá, Colombia, 1994. 81, 1996. Divisadero, Coyhaique, Chile, Bosque, 12, 27–35, 1991. M., O’Hirok, L. S.,restoration Purcell, of A. step-pool H., streams, Environ. Riley, Manage., A. 43, L., 645–661, and 2009. Wohl, E.: Linking theory and practice for 509–522, 1978. Oxford, UK, 512 pp., 1999. phology, 83, 346–358, 2007. Forest Service, USDA, Fort Collins, Colorado, 1960. RM 169, Forest Service, USDA, Fort Collins, Colorado, 1976. Bermúdez, F.: E control in a416–427, semiarid 2007. Mediterranean catchment: El Cárcavo (Murcia, Spain), Catena, 70, check dam construction in32, torrential 2165–2184, channels 2007. (South-East Spain), Earth Surf. Proc.web/index.php Land., reforestation and land use changescatchment on river (Murcia, channel Spain), morphology: Geomorphology, study 91, case 103–123, of 2007. the Rogativa diante diques de retención, PhD Thesis, University of Córdoba, 2012. resistance, Water Resour. Res., 31, 2593–2602, 1995. systems and man-made interventions. step-pool streams, which suggests there is a close bond between naturally developed Polyakov, V. O., Nichols, M. H., McClaran, M. P., and Nearing, M. A.: E Nyssen, J., Veyret-Picot, M., Poesen, J., Moeyersons, J., Haile, M., Deckers, J., and Govers, Morgan, R. P. C.: Soil Erosion and Conservation, 3rd Edn., Blackwell Publishing, Cornwall, UK, Milzow, C.: The step-pool morphology of a steep mountain stream, Diploma thesis. ETH, Ei- Merritt, D. M. and Wohl, E.: Downstream hydraulic geometry and channel adjustment during a Lenzi, M. A. and Comiti, F.: Local scouring and morphological adjustments in steep channels Lenzi, M. A.: Stream bed stabilization using boulder check dams that mimic step-pool morphol- Lee, A. J. and Ferguson, R. I.: Velocity and flow resistance in step-pool streams, Geomorphol- Chow, V. T., Maidment, D. R., and Mays, L. W.: Hidrología Aplicada, McGraw-Hill Interameri- Iroume, A. and Gayoso, J.: Evaluación de obras y sistemas de corrección de torrentes del cerro Iroume, A.: Corrección de los cauces torrenciales del Cerro Divisadero, Chile, Bosque, 17, 65– Heede, B. H.: Designing gully control systems for eroding watersheds, Environ. Manage., 6, Chin, A., Anderson, S., Collison, A., Ellis-Sugai, B., Haltiner, J., Hogervorst, J., Kondolf, G. Chin, A. and Phillips, J. D.: The self-organization of step-pools in mountain streams, Geomor- Heede, B. H.: Early gully-control structures in the ColoradoHeede, Front Range, B. Station H.: Paper no. Gully 55, development and control: the status of our knowledge, Research paper GEAMA: Instituto Flumen and CIMNE: IBER model v.1.9, available at Castillo, V. M., Mosch, W., Conesa García, C., Barberá, G. G., Navarro Cano, J. A., and López- Chanson, H.: The Hydraulics of Open Channel Flow: An Introduction, Butterworth-Heinemann, Conesa-García, C., López Bermúdez, F., and García-Lorenzo, R.: Bed stability variations after Castillo, C.: Metodología de medida de la erosión por cárcavas y modelado de su control me- Boix-Fayos, C., Barberá, G. G., López-Bermúdez, F., and Castillo, V. M.: E Abrahams, A. D., Li, G., and Atkinson, J. F.: Step–pool streams: adjustment to maximum flow References for Environment and Ruralacknowledged. and Marine A Acknowledgements. ernment), AGL2009-12936-C03-01 (Spanish Ministry40128-C03-01 (Spanish of Ministry Science of Economy and and Innovation), Competitiveness), RESEL AGL2012- (Spanish Ministry 5 5 30 25 20 15 10 25 20 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 11930 11929 ) j H + cient i ffi H ciency predicted in IBER ciency predicted by the model ffi ffi ciency in the reduction of friction slope erence in total head between adjacent dams ective check dam height ff ffi ff e check dam e check dam e dam-filling conditions Froude number in normal conditions energy dissipated due to bedenergy friction dissipated in due the to supercritical bedenergy region, friction dissipated varied in due flow the to conditions supercritical bedenergy region, friction dissipated normal in at conditions the the subcritical impactenergy region zone dissipated at the hydraulictotal jump energy dissipated ( critical depth normal depth supercritical depth at the hydraulicsubcritical jump depth at the hydrauliccheck jump dam influence Manning roughness coe unitary discharge bed slope average friction slope flow velocity in normal conditions e Abbreviations. so sp dis1 dis2 dis3 i j t fs fm n c n 1 2 : check dam spacing n Ef Ef F F FSPH free-surface water profiles H H H H H d d d d D E HJIN hydraulic jump L initialLS conditions n di NCNHJ normal conditions PI no hydraulic jump q partialS influence S SUBSUP subcritical normal conditions TI supercritical normal conditions u Totalz influence during flood in a step-pool channel, Geomorphology, 40, 311–327, 2001. lands, 1995. Keynote Paper, in: Proc. ofFactor International in Sustainable Conference River on Basin Erosion Management, and Belgrade, Torrential Serbia, Control 1–17, as 2007. vice a National Earth Sciences689, Conference, 18–22 Department October of 2004, San Agriculture,land, Diego, USA, Forest CA, 2007. Service, PNWGTR- Pacific Northwest Research Station, Port- Field Study, J. Hydraul. Eng., 125, 1231–1242, 1999. Table A1. Zimmermann, A. and Church, M.: Channel morphology, gradient profiles and bed stresses Wang, Z. Y. and Yu, G. A.: Step-pool system forWeinhold, erosion M.: The control Alkali Creek and Story: ecological 40 Years restoration, of Gully Control, Proceedings of the Forest Ser- Vischer, D. L. and Hager, W. H.: Energy dissipators, IAHR, AA Balkema, Rotterdam, the Nether- Porto, P. and Gessler, J.: Ultimate Bed Slope in Calabrian Streams Upstream of Check Dams: 5 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | deposition slope; = d : check dam spacing; S L ective check dam height. ff e = z spacing between adjacent check gully slope; : bed slope; = S = L S energy dissipated due to bed friction at the energy dissipated due to bed friction at the = = energy dissipated due to bed friction at the sub- dis2 dis1 = H 11932 11931 H dis3 H dam-filling situation. (b) energy dissipated at the hydraulic jump; = j erence in elevation between check dams; H initial conditions; ff di (a) = erence of total head between adjacent check dams; Energy balance in a controlled gully reach with supercritical normal conditions. ff Sketch of the main hydraulic features and geometric variables after check dam con- di ective height of the check dam. ff = energy dissipated at the impact zone; e = S = · i z critical region; L supercritical region, normal conditions; Fig. 2. H supercritical region, varied flow conditions; struction, dams; LS Fig. 1. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | erent ff , bed slope q no hydraulic critical depth; = = c d supercritical normal dam-filling conditions; = = F supercritical depth at the hydraulic jump; = 1 d check dam influence; = normal conditions influence; NHJ 11934 11933 D = subcritical normal conditions; SUP cient. Grey lines and associated text correspond to di = ffi depth over the spillway; = s d total influence. = partial influence; SUB = Manning roughness coe Classifications of free-surface water profiles in restored gullies. Froude regime for normal conditions as a function of the unitary discharge n initial conditions (no deposition); NC normal depth; subcritical depth at the hydraulic jump; = = = and n 2 Fig. 4. d d IN jump; PI conditions; TI Fig. 3. S roughness conditions. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | dam-filling erent free- check dam ff = = F so no hydraulic jump; = supercritical normal condi- = check dam influence; Ef = D ciency predicted by the model; ffi 11936 11935 curves between the model and IBER for di normal conditions influence; NHJ F = check dam e = sp subcritical normal conditions; SUP = initial conditions; NC = total influence. = Comparison of Froude number partial influence; SUB ciency predicted in IBER; Ef = ffi e PI tions; TI Fig. 5. surface water profiles types as ablack function lines of the correspond distance to from theconceptual predicted downstream model, results check dam. the by Solid IBER, greyified solid dashed normal grey line line conditions to to for normal predicted a conditions results dam-filling and by scenario. dashed-dotted the conditions; line IN to mod- Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | unitary dis- = q ciency in the reduc- cient; ffi e ffi energy dissipated at the = fs = j E H erence in total head between ad- ff 1.19). di = = z ); LS j 0.04; H = + n Manning roughness coe i = H 11938 11937 n 5 %; = S ; 1 − s 2 ective check dam height. ff e 0.5 m energy dissipated at the impact zone; = = = z i q H total energy dissipated ( = t for a range of conditions. H c bed slope; ciency in the reduction of average friction slope as a function of the geometric in- = ffi S E Profiles of the main energetic parameters as a function of the geometric influence factor for initial conditions ( jacent dams. Fig. 7. c hydraulic jump; Fig. 6. tion of friction slope; charge; fluence factor Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | cients ffi 0.06. = for initial (grey n c valid throughout c (b) 0.04; = n erent roughness coe ff (a) cients ffi 11940 11939 for a particular geometric influence factor c erent roughness coe ff ciency for a particular geometric influence factor ffi 0.06. = n (b) 0.04; Threshold curves of optimal Regions of optimal e = n Fig. 9. the lifetime of the structure for di Fig. 8. dotted line) and(a) dam-filling (solid black line) conditions with di Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ciency as a function of the geometric influence ffi 11941 Conceptual diagram of check dam e for initial conditions. c Fig. 10. factor