A flow and temperature model for the Vermillion River, Part I: Model development and baseflow conditions

Transcription

1 ST. ANTHONY FALLS LABORATORY Engneerng, Envronmental and Geophyscal Flud Dynamcs Project Report No. 57 A flow and temperature model for the Vermllon Rver, Part I: Model development and baseflow condtons by Wllam Herb and Henz Stefan Prepared for Mnnesota Polluton Control Agency St. Paul, Mnnesota September 08 Mnneapols, Mnnesota

2 The Unversty of Mnnesota s commtted to the polcy that all persons shall have equal access to ts programs, facltes, and employment wthout regard to race, relgon, color, sex, natonal orgn, handcap, age or veteran status. 2

3 Abstract Stream temperature and stream flow are mportant physcal parameters for aquatc habtat preservaton n rver and stream systems. Water temperature s partcularly mportant for coldwater stream systems that support trout. Summer base flow condtons wth low flows and hgh water temperatures can be crtcal for mantanng trout habtat. Surface runoff from ranfall events can lead to ncreases n stream temperature, partcularly n developed watersheds. To better understand the nteractons between stream temperature, land use, and clmate, an unsteady stream flow and temperature model has been developed for the Vermllon Rver. The model ncludes the man stem from Dodd Avenue to Goodwn Avenue and a number of trbutares, ncludng South Branch, South Creek, North Creek, and Mddle Creek. The EPDrv package was used to smulate stream flow, ncludng dstrbuted groundwater nputs. Smplfed stream channel geometry was requred to obtan converged flow solutons for unsteady low flows. A stream temperature model has been assembled based on prevous work at SAFL. The stream temperature model uses flow and flow area from the flow solver, along wth observed clmate data to calculate surface heat transfer. Groundwater nflows are an mportant component of both the flow and temperature model. For the Vermllon Rver, groundwater nflow rates were estmated from flow gagng stes, whle groundwater temperatures were estmated by calbratng the stream temperature model. The calbrated combnaton of groundwater flow and temperature results n a good match of smulated and observed stream temperature, wth RMSEs n the range of 0.75 to 2 ºC. The assembled flow and temperature model for the Vermllon Rver has been calbrated for baseflow condtons, and provdes a startng pont for future analyss of surface runoff nputs durng ranfall events. 3

4 Table of Contents. Introducton Stream flow model Man Stem of the Vermllon Rver Model development Baseflow scenaro for the Vermllon Rver man stem Flow models for Trbutares of the Vermllon Rver Stream Temperature Model Stream temperature model formulaton Temperature model for the man stem of the Vermllon Rver Temperature model for trbutares of the Vermllon Rver Summary and Conclusons Acknowledgments References Appendx I: Surface Heat Flux Formulaton Appendx II: Sedment Temperature Model Formulaton

5 . Introducton Stream temperature and stream flow are mportant parameters for aquatc habtat preservaton n rver and stream systems. Water temperature s partcularly mportant for coldwater streams that support trout. Summer base flow (low flow) condtons and hgh water temperatures can be crtcal for mantanng trout habtat. Surface runoff from ranfall events can lead to ncreases n stream temperature, partcularly n developed (urban) watersheds. To better understand the nteractons between stream temperature, land use, and clmate, an unsteady stream flow and temperature model has been developed for the Vermllon Rver. Ths rver s at the southern frnges of the Twn Ctes metropoltan area (Fgure.) and has a world-class brown trout fshery. Fgure.. The Vermllon Rver watershed n Scott and Dakota countes. The study area ncludes the Vermllon Rver man stem and major trbutares upstream of the VR803 staton, near the town of Vermllon, MN. The flow and temperature model s desgned to smulate the response of the rver to surface runoff and groundwater nputs. The model captures ndvdual ranfall events but can be run for contnuous analyss of several months. Stream flow s smulated at to 5 mnute tme steps, whle stream temperature s smulated at 5 mnute to hour tme steps, usng observed clmate data as the prmary nput. Groundwater nputs (flow per unt length and temperature) are also 5

6 ncluded, and are an mportant part of the flow and temperature smulatons. In addton to detaled temperature and flow tme seres, the model provdes broad scale characterzatons of heat transport n the Vermllon, ncludng the relatve mportance of groundwater temperature, atmospherc heat transfer, and surface water nputs n determnng stream temperature. The stream temperature model can therefore be used as a tool to determne what management practces (e.g. stormwater BMPs, bank shadng, groundwater conservaton) are best to mantan cold water temperatures for trout habtat. Ths report descrbes the model formulaton and calbraton for baseflow condtons. The response of the rver to surface runoff nputs wll be descrbed n a later report. Reach Length (km) Average Slope (m/m) Reach Length (km) Average Slope (m/m) Man Stem South Branch Trb Man Stem Trb South Creek Mddle Creek South Creek Trb North Creek South Creek Trb North Creek Trb South Creek Trb South Branch Fgure 2.. Extent of the flow and temperature model for the Vermllon Rver man stem (dark blue lne) and trbutares (pnk lnes). The upstream end (DOD) s Dodd Boulevard, and the downstream end (VR803) s Goodwn Avenue. Man stem Trb and Trb2 are specfed flow nput ponts to the man stem model, but these trbutares are not modeled separately. 6

7 2. Stream flow model The areal extent of the flow and temperature model ncludes the Vermllon Rver man stem from Dodd Avenue to Goodwn Avenue, along wth the lower reaches of major trbutares, ncludng North Creek, Mddle Creek, South Branch, and South Creek (Fgure 2.). 2. Man Stem of the Vermllon Rver 2.. Model development A stream flow model for the man stem of the Vermllon Rver was created for a channel length of approxmately 29 mles, between Dodd Boulevard (south of the Lakevlle arport) and Goodwn Avenue, just east of the town of Vermllon. The stream geometry for the man stem was suppled by Barr Engneerng, n HEC-RAS and HEC-2 format, wth about 240 channel and floodplan cross-sectons, and detaled descrptons of brdges and culverts. Man stem stream geometry was obtaned for statons between Dodd Blvd and Goodwn Avenue. The flow analyss for ths study dffers from prevous analyses of the Vermllon; prevous studes focused on flood flows, whle ths study s focused on md-summer baseflow condton and the response to moderate ranfall events. The flow analyss of the man stem was started by performng unsteady flow smulatons wth the HEC-RAS package (USACE 08). The flow model s requred to smulate the unsteady response of stream flow to surface runoff nputs. The ablty of HEC-RAS to handle unsteady flow startng from a low baseflow condton was therefore nvestgated. It was apparent that the HEC-RAS unsteady flow analyss had dffculty convergng for flows below about cfs, and some converged solutons had much hgher veloctes (5- ft/sec) than steady state flow solutons for the same flow rate. Snce the upper portons of the man stem often have baseflows of to 0 cfs, several modfcatons to the model were nvestgated to mprove ts ablty to handle low flows:. Addtonal cross sectons were added, nterpolatng between exstng cross-sectons. Ths appeared to gve lttle beneft. 2. The brdges and culverts were removed from the model to smplfy the channel geometry, reasonng that the flow restrctons of these structures are less mportant at low flows. Ths slghtly mproved the ablty to handle unsteady low flows. 3. The channel cross-sectons were smplfed. Smple parabolc shapes were ft to each of the surveyed channel cross-sectons (Fgure 2.), and a smooth varaton n the channel aspect rato from upstream to downstream was created to best ft the varaton n observed channel cross-sectons. The surveyed channel bottom elevatons were mantaned. Ths smplfed channel geometry enabled greatly mproved low flow solutons, wth reasonable smulatons for flows as low as -2 cfs. 4. In steady flow smulatons of some stream reaches, rregulartes n the surveyed channel bottom ponts caused predctons of overbank flows at baseflow condtons, of 2 0 cfs. These predcted flow condtons appeared to be unrealstc. As a correcton, the surveyed channel bottom elevatons were smoothed wth a second to thrd order polynomal n all stream reaches. 7

8 5. A second analyss package was evaluated, the EPD-Rv model, usng the smplfed channel geometry. The EPD-Rv model was found to have smlar capabltes as HEC- RAS for unsteady flow analyss at low flows. To evaluate the consequences of usng the smplfed geometry, smulatons were performed usng both the smplfed stream channel geometry and the orgnal geometry for a case where the full model converged. An nput pulse of to 40 cfs was specfed at the upstream end, and the responses of the models at the downstream end were compared (Fgure 2.3). The EPD-Rv model (USEPA 05) was also run wth the smplfed geometry for ths case. All three models (HEC-RAS full geometry, HEC-RAS smplfed geometry, EPD-Rv smplfed geometry) gave very smlar responses to the nput pulse, ndcatng that the smplfed geometry s a reasonable approach for ths study. The use of the smplfed geometry should be lmted to bankfull or lower dscharge, however, snce the stream geometry for overbank condtons wll not be represented, and flow restrctons due to brdges and culverts wll become more mportant for overbank flows. Surveyed cross-secton ManStemShort2 Plan: Plan 8 3/28/08 Ft Parabola to channel area: y=c*x 2 Test Plan: Plan 22 3/28/ Elevaton (ft) 924 Elevaton (ft) Staton (ft) Staton (ft) Fgure 2.. Example of a surveyed cross-secton and a smplfed (parabolc) cross-secton. The parabola was ft to the channel area for bank full flow,.e. between bank statons, and then extended upward. 8

9 45 40 Upstream nput Downstream response, HEC-RAS w/ brdges, surveyed XS's Downstream response, HEC-RAS, no brdges, smplfed XS's Downstream Response, EPA-Rv, no brdges, smplfed XS's 35 Flow (cfs) /2/05 0:00 8/3/05 0:00 8/4/05 0:00 8/5/05 0:00 8/6/05 0:00 Fgure 2.3. Smulated response of the man stem of the Vermllon to an nput pulse at Hamburg Ave. of to 40 cfs for the HEC-RAS and EPD-Rv models Baseflow scenaro for the Vermllon Rver man stem Usng the assembled geometry for the man stem, a md-summer baseflow scenaro was created based on observed 06 flow data to provde a calbraton flow condton for the temperature model. The baseflow scenaro was created for the perod August 9 to September 8, 06. Ths perod ncludes several ranfall events wth more than 0.5 n total precptaton, but no major precptaton and runoff events (Fgure 2.4). Stream flow data at Hamburg Ave. are not avalable for 06 and 07. The flow at Hamburg Ave. (Hamb) was estmated to be.2 cfs based on the flow at SC804 (3.3 cfs), and a relatonshp developed between SC804 and Hamb usng 05 data (Fgure 2.5). Man stem Trb and Trb2 flows were set based on 05 pont flow measurements by the Dakota County SWCD. Trbutary nflows were set to be a fracton of the flow at the USGS man stem staton at Empre, based on summer monthly-averaged flows at trbutary gagng statons (Herb and Stefan 08), as gven n Table 2.. Groundwater nflows were unformly dstrbuted over three reaches of the man stem (Table 2.2), based on monthlyaveraged flow dfferences between gagng statons (Herb and Stefan 08). The flow nputs to the man stem are summarzed n Table 2. and 2.2. A longtudnal dstrbuton of flow for ths perod s gven n Fgure 2.6, clearly showng step ncreases due to trbutares and upward trends due to dstrbuted groundwater nputs. 9

10 Table 2.. Specfed upstream flow and trbutary flow nputs to the man stem of the Vermllon Rver for the August /September 06 baseflow scenaro. Upstream and Trbutary Flow Inputs Trbutary Dod (upstream boundary) 0.25 Empre 3.3 Man Stem Trb.0 Man Stem Trb2 0.7 Man Stem Trb North Creek (ncludes Mddle Creek) 7.7 South Branch 6.7 South Creek 8. Flow Input (cfs) Table 2.2. Specfed groundwater flow nputs for the man stem of the Vermllon Rver for the August /September 06 baseflow scenaro. RS 32.4 s 0.7 mles downstream of Hamburg Avenue. Reach Length (km) Groundwater Input (cfs) DOD to VR VR809 to RS RS 32.4 tovr VR807 to USGS USGS to VR Groundwater Input Rate (cfs/km) Flow (cfs) SC804 USGS VR807 Precp.5 2 Daly Precp (n) //06 5/3/06 7//06 7/3/06 8/3/06 9/30/06 Date Fgure stream flow at three man stem statons (SC804, VR807, USGS) and daly precptaton at the Empre WWTP. 0

11 Flow, Hamburg (cfs) y = 0.04x x R 2 = Flow, SC804 (cfs) Fgure 2.5. Relatonshp between daly average flows at SC804 and Hamburg Avenue, based on 05 data Empre WWTP Goodwn Ave. Flow (cfs) South Creek North Creek South Branch 0 Dodd Ave Rver Mle Fgure 2.6. Smulated longtudnal dstrbuton of flow n the man stem of the Vermllon Rverfor the perod August 9 September 8, 06. rver mle =.6 km.

12 2.2 Flow models for Trbutares of the Vermllon Rver A seres of separate flow models were developed for trbutares of the Vermllon Rver, ncludng North Creek, Mddle Creek, South Creek, and South Branch (Fgure 2.). Channel geometry nformaton avalable for all major trbutares, and one flow gagng staton near the lower end of each trbutary was avalable. The excepton was South Creek, whch s gaged ndrectly va statons on the man stem upstream (SC804) and downstream (VR807) of the confluence wth South Creek. Based on the flow analyss of the man stem, the HEC-RAS channel geometry for the trbutares was substantally smplfed to enable unsteady, low flow solutons. Table 2.3 summarzes the specfed upstream nflows (baseflows) and dstrbuted groundwater nputs for each reach. In most cases, there was no flow gage at the upstream end of the trbutary. A mnmum value for the upstream nflow was assumed to be 0.25 cfs; ths value was ncreased f necessary to enable unsteady flow smulatons wth stormwater nputs. Groundwater nputs were adjusted to gve known downstream flow values, or to gve agreement n smulated and observed stream temperature at the downstream locaton. For the case of, e.g., South Creek Trb, groundwater nputs needed to be concentrated near the downstream end of the each to produce the low observed stream temperature. Table 2.3. Summary of specfed upstream nflows (baseflows) and dstrbuted groundwater nputs for each trbutary reach. The locaton of each trbutary s shown n Fgure 2.. Reach Length (km) Upstream Baseflow Groundwater Input (cfs) Input (cfs) Man Stem Trb Mddle Creek North Creek North Creek Trb South Branch South Branch Trb South Creek South Creek Trb South Creek Trb South Creek Trb Stream Temperature Model A -D model was developed to smulate stream temperature based on atmospherc heat transfer, sedment heat transfer, and groundwater nflows. It s based on prevous stream temperature models developed at SAFL, e.g. the MNSTEM model (Snokrot and Stefan 993). The model s based on a fnte dfference formulaton, solvng for the varaton of stream temperature as a functon of tme and streamwse dstance,.e. assumng that the stream channel s well mxed vertcally and laterally. Longtudnal transport of heat s by advecton only, neglectng dsperson. Ths lmts the applcablty of the present model to free-flowng rver systems wthout major pools or reservors, etc. Model nputs nclude clmate parameters (ar temperature, 2

13 relatve humdty, wnd speed, and solar radaton), the channel geometry, streamflow values, lateral (trbutary) nflow rates and temperature, groundwater nflow rates and temperatures, and shadng/shelterng coeffcents (Fgure 3.). Upstream Flow Intal Condtons Trbutary Inflows Channel Geometry Shadng and Wnd Shelterng Observed Clmate Data EPA-Rv Streamflow Soluton Q(x,t) Stream Temperature Model Stream Temperature Soluton T(x,t) Groundwater Inflows Surface Inflows Trbutary Temperatures Groundwater Temperatures Surface Inflow Temperatures Fgure 3.. Flow chart summarzng the nput data and smulaton results for the flow and temperature solvers used n ths study. 3. Stream temperature model formulaton The stream temperature model s based on the unsteady, -D dfferental equaton for the advectve transport of a scalar (temperature), Equaton 3.. Longtudnal dsperson s neglected n ths formulaton. Lateral nflows and groundwater nflows are treated n the same way, as a specfed lateral flow (q l ) and temperature (T l ) for each control volume (Fgure 3.2). The parameter symbols are summarzed n Table 3.. t x 3. ( AT) + ( QT) = S 3.2 Bh S = ρc atm p + q T l l Wp h + ρc sed p 3

14 Table 3. Parameter Defntons Symbol Defnton and unts A flow cross-sectonal area (m 2 ) B stream wdth (m) h atm atmospherc heat transfer rate (W/m 2 ) h sed sedment heat transfer rate (W/m 2 ) cell number ndex (streamwse drecton) j tme step ndex q l lateral nflow (m 2 /s) n the stream temperature model q* l lateral nflow (m 2 /s) n the EPD-Rv flow solver Q flow rate (m 3 /s) S heat source term (ºC m 2 /s) t tme (s) T l lateral nflow temperature (ºC) T temperature (ºC) W p wetted permeter stream wdth (m) x streamwse dstance (m) ρcp densty specfc heat (J/m 3 ) t tme step (s) Control Volume: h atm q l, T l Q -,j Q,j T -,j A -,j, B,j T,j A,j, B,j h sed x Fgure 3.2. Schematc for mass and heat flows n and out of a stream channel control volume. Parameter defntons are gven n Table 3.. The fnte-dfference dscretzaton of Equatons 3. and 3.2 s gven n Equatons Stream flow values (Q,j ) from an unsteady flow soluton are suppled at the control volume faces, whle temperature (T,j ) s solved for at the center of each control volume (Fgure 3.2). The dscretzaton schemes used for the dervatve terms n Equaton 3. were chosen to match the dscretzaton used for the flow soluton n the EPD-Rv model, so that flow solutons obeyng contnuty n EPD-Rv would also obey contnuty n the temperature model. In the EPD-Rv model, each specfed lateral flow nput s splt between two cells, based on the relatve length of each cell. Equaton 3.5 was used to calculate an equvalent lateral flow nput 4

15 (q l ) for each cell n the temperature model, based on the specfed lateral nflows used n the EPD-Rv model. Ths was a necessary step to ensure mass contnuty was mantaned n the temperature model. 3.3 ( AT) = ( A T + A T + A T A T ) t 2 t, j +, j +, j +, j ( QT) = ( Q T Q T ) 3.5 x q l, j+, j+ x x = q * l x + x, j+ + q * l, j+ x x + x +, j, j, j, j B ( h + h ) atm sed S = + B ρc p q T B, j + B, j + B, j+ + B = 4 l l, j+ The stream temperature model descrbed here s used n conjuncton wth flow data suppled by the EPD-Rv model. The lateral (q l ) and nstream (Q ) flows are transferred as text fles from the flow soluton to the stream temperature model. The need to addtonally transfer the flow areas (A ) for each node s elmnated by calculatng the flow areas n the stream temperature solver usng Equaton 3.8. Flow areas for the frst tme step are transferred from the flow solver as an ntal condton. Whle ths method elmnates the need to transfer flow area data for each tme step, t does requre that the flow data be transferred wth at least 5 to 6 sgnfcant dgts to avod cumulatve errors n the mass balance and the flow areas, partcularly for low flows. 2 t 3.8 = A + A A + ( Q + ql Q ) A, j+, j, j, j+, j+, j+, j+ x Insertng Equatons nto Equaton 3. gves the fnal equatons that are used to solve for the stream temperatures for each cell and each tme step: 3.9 C T, j+ = C2 T, j + C3 T, j+ + C 4T, j + C t Q, j+ 2 t B h atm h sed C = A, j+ + x ρc p T T 3. C 2 = A, j t Q, j+ C3 = A, j+ + x t B h atm h sed C 4 = A, j + ρc T T p 5

16 C 2 t B 5 = h + h + 2 t q T ρcp 3.4 ( atm sed ) l l Both h atm and h sed have a nonlnear dependence on stream temperature. The atmospherc heat transfer s calculated based on the current clmate condtons (ar temp, humdty, wnd, solar radaton, cloud cover) and the current stream temperature, as detaled n Appendx I. The vertcal profle of sedment temperature and the sedment heat flux (h sed ) s determned for each stream node at each tme step usng the formulatons gven n Appendx II. Ten to twelve nodes are typcally used n the sedment temperature model, wth closer node spacng near the sedment/water nterface. To mprove the numercal stablty of the soluton, both the atmospherc heat transfer and sedment heat transfer terms are lnearzed, by evaluatng both the heat flux and the dervatve of the heat flux at the current stream temperature T j : 3.5 h ( T,T ) h ( T ) atm j j+ 3.6 h ( T,T ) h ( T ) sed j j+ h ( Tj + δt) h atm ( Tj ) ( T T ) atm = atm j + j + h δt ( Tj + δt) h sed ( Tj ) ( T T ) sed = sed j + j + δt j j Table 3.2. Parameter symbols and values used n surface heat transfer model. Descrpton Nomnal Value C fc forced convecton transfer coeffcent C nc free convecton transfer coeffcent CS h wnd shelterng coeffcent for heat.5 transfer α surface albedo β fracton of solar radaton absorbed at 0.4 the water surface ε water emssvty Temperature model for the man stem of the Vermllon Rver A stream temperature model was assembled for the Vermllon Rver man stem from Dodd Blvd. to Goodwn Avenue. The model ncluded 469 statons over a reach length of 28.8 mles (46.3 km), gvng a staton spacng of about 00 m. The stream staton postons and trbutary nput locatons were determned from the orgnal HEC-RAS geometry. The stream temperature model for the man stem uses the same number of nodes as the flow model (Secton 2.), but the temperature nodes are offset from the flow soluton nodes, wth flows specfed at the boundares of the control volumes and temperatures calculated at the center of control volumes (Fgure 3.2). 6

17 Stream geometry s specfed by the flow area and the top wdth of the stream. The smplfed, parabolc cross-sectons used for the flow soluton (Secton 2.) were used to calculate the stream wdth (B) based on the calculated flow area (A) for each staton: (3.7) 3 B= C B A where C B s a constant based on the parabolc shape used to descrbe the stream cross-secton. C B was adjusted to gve an approxmate match of the smulated stream wdth (from the flow solver) to the observed stream wdth from aeral photographs. C B s used n both the flow and temperature solutons. Model Calbraton for Baseflow Condtons The man stem stream temperature model was calbrated wth data for the perod August 9, 08 to September 8, 08. Calbraton parameters ncluded the shadng and wnd shelterng coeffcents, and the flow rate and temperature of groundwater nputs. For the calbraton perod, ten observed 5 mnute stream temperatures were avalable for the man stem (Fgure 3.3). Clmate data used for the smulaton ncluded hour ar temperature, dew pont, and wnd speed from the Lakevlle (AIRLAKE) arport and 30 mnute solar radaton data from the UofM Rosemount Expermental Staton (Fgure 3.4). Fgure 3.3. Vermllon Rver stream temperature measurement statons. mle =.6 km. 7

18 35 30 Ar Temp Dew Pont Precp.5.25 Wnd Velocty (m/s) hour Precp (cm) /9 8/4 8/9 8/24 8/29 9/3 9/8 4 2 Wnd Solar Wnd Velocty (m/s) Solar (W/m 2 ) /9 8/4 8/9 8/24 8/29 9/3 9/8 Date Fgure 3.4. Observed clmate data from the Lakevlle Arport (ar temp, dew pont, wnd speed) and the UofM Expermental Ag Staton (solar radaton, precptaton) for the base flow perod August 9 to September 8, 06. 8

19 Each stream temperature observaton pont (Fgure 3.3) provded the opportunty to calbrate the shadng, shelterng, and groundwater parameters for a reach segment. The shadng and shelterng coeffcents were set to obtan the best match of smulated and observed daly durnal temperature excursons. The calbrated shadng and shelterng coeffcents, whch are defned n Appendx I, are gven n Table 3.3. The groundwater flow rate was set for each reach based on the baseflow scenaro developed for the perod, descrbed n Secton 2.2. For the man stem, the groundwater temperature for each reach was then set to obtan the best match of smulated and observed daly mean stream temperature. The calbrated groundwater flow rates and calbrated groundwater temperatures are summarzed n Table 3.4. Table 3.3. Calbrated shadng and wnd shelterng coeffcents for the man stem of the Vermllon Rver and the RMSE (root-mean-square error) of smulated stream temperature for the August 9 to September 8, 06 base flow scenaro. Both parameters vary from 0 to, wth representng complete shadng and wnd shelterng. Staton Shadng Shelterng RMSE (ºC) Coeffcent Coeffcent Hamburg SC VR CHP BSC AES AES AES VR Table 3.4. Specfed groundwater temperatures for the man stem of the Vermllon Rver for the August 9 to September 8, 06 base flow scenaro. RS 52. s approxmately. km downstream of Hamburg Avenue. Flow values are repeated from Table 2.2. Reach Groundwater Input (cfs) Groundwater Temperature (ºC) DOD to VR n/a VR809 to RS RS 52. tovr n/a VR807 to USGS USGS to VR Trbutary nput temperatures were ntally set equal to the observed temperature for the perod. The observed trbutary temperatures were then replaced wth smulated temperatures as the stream temperature models for the trbutares were completed and calbrated (see Secton 3.3.). Observed stream temperatures were not avalable for man stem Trb and Trb2, and models 9

20 were not constructed for these trbutares. Observed stream temperatures from the Hamburg Avenue locaton were used to represent the temperature of Trb and Trb2 n all cases. Plots of smulated and observed stream temperatures on the man stem of the Vermllon Rver are gven n Fgures 3.5 to 3.7. The RMSEs are gven n the last column of Table Temperature (C) 25 5 SC804 Smulated Observed 0 30 Temperature (C) 25 5 Hamburg Smulated Observed 0 8/7 8/2 8/7 8/22 8/27 9/ 9/6 Fgure 3.5. Smulated and observed stream temperature at the Hamburg Ave. and SC804 statons for the perod 8/9/06 to 9/8/06. The RMSEs at the Hamburg and SC804 statons are

21 2.0 and 0.7 ºC, respectvely. The observed temperature shfts upwards n September, lkely due to a very flow condton. Temperature (C) VR807 Smulated Observed Temperature (C) AES-58 Smulated Observed 0 8/9 8/4 8/9 8/24 8/29 9/3 9/8 Fgure 3.6. Smulated and observed stream temperature at the VR807 and AES-58 statons for the perod 8/9/06 to 9/8/06. The RMSEs at VR807 andaes-58 are. and.0 ºC, respectvely. 2

22 Temperature (C) AES-09 Smulated Observed 0 8/0 8/5 8/ 8/25 8/30 9/4 9/9 30 Temperature (C) 25 5 VR803 Smulated Observed 0 8/0 8/5 8/ 8/25 8/30 9/4 9/9 Fgure 3.7. Smulated and observed stream temperature at the AES-09 and VR803 statons for the perod 8/9/06 to 9/8/06. The RMSEs at VR803 andaes-09 are. and 0.7 ºC, respectvely. 3.3 Temperature model for trbutares of the Vermllon Rver Stream temperature models for trbutares of the Vermllon Rver were created n a smlar manner to the man stem model. The perod August 9 to September 8, 06 was used as the calbraton perod for the trbutary stream temperature models. Compared to the man stem, there are generally fewer stream flow and temperature observatons avalable for the trbutares. As a result, the upstream boundary condtons for the temperature model had to be assumed n many cases (Table 3.5). Groundwater temperature was adjusted to obtan the best ft of smulated and observed daly mean stream temperature, usng prevously establshed 22

23 groundwater nflow rates. A parabolc functon (Equaton 3.7) was agan used to calculate the stream wdth based on the specfed flow area from the flow soluton. Shadng and shelterng coeffcents (defned n Appendx I) were adjusted to match smulated and observed durnal temperature change. The resultng smulated temperature RMSEs are summarzed n Table 3.6, rangng from 0.8 ºC for South Branch to.4 ºC for North Creek. A dfferent calbraton perod was used for Mddle Creek (July to July 30, 07), South Branch trb (Sept. to Sept. 30, 06), and South Creek trb2 (Sept. to Sept. 30, 06) because of the avalablty of stream temperature data for that perod. Relable temperature calbraton data were not avalable for North Creek trb and South Creek trb3. For these cases, the calbraton parameters were set equal to those for smlar, calbrated trbutares. Smulated and measured stream temperatures for trbutares are shown n Fgures 3.8 to 3.. RMSE values are gven n Table 3.6. Table 3.5. Summary of specfed upstream nput temperatures and dstrbuted groundwater temperatures for each trbutary reach. Flow values are repeated from Table 2.3 for reference, and the locaton of each trbutary s shown n Fgure 2.. Reach Upstream Input Groundwater Input Flow (cfs) Temp. (ºC) Flow (cfs) Man Stem Trb Mddle Creek North Creek North Creek Trb South Branch South Branch Trb South Creek South Creek Trb South Creek Trb South Creek Trb Temp. (ºC) Table 3.6. Calbrated shadng and wnd shelterng coeffcents for trbutares of the Vermllon Rver, and the RMSE of smulated stream temperature for the perod August 9 to September 8, 06. Staton C B (m /3 ) Shadng Coeffcent Shelterng Coeffcent Man Stem Trb Mddle Creek North Creek North Creek Trb South Branch South Branch Trb South Creek South Creek Trb South Creek Trb South Creek Trb RMSE (ºC) 23

24 25 AES2 Temperature (C) Smulated Observed 0 8/8 8/3 8/8 8/23 8/28 9/2 9/7 Fgure 3.8. Smulated and observed stream temperature n South Branch at the AES-2 (SB802) staton for the perod 8/9/06 to 9/8/06. The RMSE s 0.8 ºC. Temperature (C) AES63 0 8/8 8/3 8/8 8/23 8/28 9/2 9/7 Fgure 3.9. Smulated and observed stream temperature n North Creek at the AES-63 (MC80) staton, downstream of the confluence wth Mddle Creek, for the perod 8/9/06 to 9/8/06. The RMSE s.4 ºC. 24

25 25 AES80 (lower South Creek) Temperature (C) Smulated Observed 0 8/8 8/3 8/8 8/23 8/28 9/2 9/7 Fgure 3.0. Smulated and observed stream temperature n South Creek at the AES-80 (SC-) staton for the perod 8/9/06 to 9/8/06. The RMSE s.2 ºC. Temperature (C) Smulated Observed AES85 0 8/8 8/3 8/8 8/23 8/28 9/2 9/7 Fgure 3.. Smulated and observed stream temperature n South Creek Trb at the AES-85 (SC-) staton for the perod 8/9/06 to 9/8/06. The RMSE s 0.8 ºC. The peaks n observed temperature on August 25 and September 3 are lkely due to surface runoff nputs. 25

26 4. Summary and Conclusons An unsteady (tme-varable) stream flow and temperature model has been assembled for the Vermllon Rver n Dakota/Scott County, Mnnesota. The model covers the man stem from Dodd Avenue to Goodwn Avenue and a number of trbutares, ncludng the South Branch, South Creek, North Creek, and Mddle Creek. The EPD-Rv package was used to smulate stream flow, ncludng dstrbuted groundwater nputs. Smplfed stream channel geometry was requred to obtan solutons for unsteady low flows. A stream temperature model has been assembled based on the MNSTREM model (Snokrot and Stefan 993). The stream temperature model uses flow velocty and flow area from the flow solver, along wth observed clmate data to calculate surface heat transfer. Groundwater nflows are an mportant component of both the flow and temperature models. For the Vermllon Rver, groundwater nflow rates were estmated from flow gagng stes, whle groundwater temperatures were estmated by calbratng the stream temperature model. The calbrated groundwater flow and temperatures the smulated and observed stream temperatures match well, wth RMSE-values n the range of 0.75 to 2 ºC. However, uncertanty n the groundwater nflow rates lead to a correspondng uncertanty n the calbrated groundwater nflow temperature. Several smaller trbutares ncluded n the flow and temperature model could not be calbrated due to lack of feld data. In these cases, the calbraton parameters were set equal to smlar, calbrated trbutares. The assembled flow and temperature model for the Vermllon Rver has been calbrated for baseflow condtons, and provdes a startng pont for the analyss of surface runoff effects durng ranfall events for present and future land use scenaros. Acknowledgments Ths study was conducted wth support from the Mnnesota Polluton Control Agency, St. Paul, Mnnesota, wth Bruce Wlson as the project offcer. Stream flow and temperature data were suppled by Travs Bstodeau of the Dakota County SWCD and the USGS. Precptaton data were obtaned from Karen Jensen at the Met Councl, and the Unversty of Mnnesota Rosemount Research and Outreach Center. Stream channel geometry was suppled by Barr Engneerng Company. The authors are grateful to these ndvduals and organzatons for ther cooperaton. 26

27 References Ednger, J., D.K. Brady and J.C. Geyer (974). Heat exchange and transport n the envronment. Report No. 4, Electrc Power Research Insttute, Coolng Water Dscharge Research Project (RP-49), Palo Alto, CA, 25 pp. Herb, W.R. and H.G. Stefan (08). Analyss of Vermllon Rver Stream Flow Data (Dakota and Scott Countes, Mnnesota). Project Report No. 54, St. Anthony Falls Laboratory, Unversty of Mnnesota, 28 pp. Snokrot, B.A. and Stefan, H.G. (993). Stream Temperature Dynamcs: Measurements and Modelng, Water Resources Research 29(7): US ACE (08). HEC-RAS Rver Analyss System, verson 4.0, U.S. Army Corps of Engneers, US EPA (05). One Dmensonal Rverne Hydrodynamc and Water Qualty Model, U.S. Envronmental Protecton Agency, 27

28 Appendx I: Surface Heat Flux Formulaton The net vertcal heat transfer at the ar-water nterface ncludes components due to long wave radaton, short wave (solar) radaton, evaporaton, and convecton. The surface heat transfer formulatons used n ths study are based on those gven by Ednger et al. (968, 974) for lake and reservor surfaces. The evaporatve heat transfer formulaton (Equaton A.3) uses the aerodynamc method to enable smulatons at hourly tme steps or less. The evaporaton and convecton heat transfer components consder both forced convecton, proportonal to wnd speed, and natural convecton, related to the dfference n temperature (densty) of the ar between the ground surface and the atmosphere. Ths dffers from the formulatons gven n Ednger (968, 974), whch do not take nto account natural convecton. The wnd velocty (u 0 ) measured at 0 m heght at a weather staton s downscaled by a wnd shelterng coeffcent (C Shel ) as shown by Equaton A.8, to take nto account the effect of stream banks, trees, buldngs, and topographcal features on surface wnd velocty (u s ) over the water surface. Incomng atmospherc long wave radaton (h l, Equaton A.6) s calculated based on ar temperature (T a ) and cloud cover (CR). h h h h h h atm rad evap conv s = h h h h (A.) rad s evap conv l lo 0.33 v ( Cfc u s + Cnc θ v )( esat ea ) ro = h + h h (A.2) = ρ L (A.3) a 0.33 a p ( Cfc u s + Cnc θ v )( Ts Ta ) ( α s ) R s 0.08 εσ CR ( CR) e T = ρ c (A.4) = (A.5) ( ) 4 = (A.6) l 4 lo εσt sk a h = (A.7) u s = (-C Shel ) u 0 (A.8) R s = (-C Shad ) R (A.9) ak where h atm s the total net surface heat transfer, h rad s net radaton, h s s the ncomng short wave (solar) radaton, h evap and h conv are the evaporatve and convectve heat fluxes, respectvely, ε and σ are the surface emssvty and the Stefan-Boltzmann constant, respectvely, ρ a s ar densty, c p s the specfc heat of water, L v s the latent heat of vaporzaton, C fc anf C nc are coeffcents for forced and natural convecton, respectvely, T ak and T sk are the absolute ar and surface temperature ( K), respectvely, e sat and e a are the saturated and ambent vapor pressure, respectvely, θ v s the dfferent n vrtual temperature between the surface and atmosphere, and α s s the surface albedo. θ v s set to zero for cases where the surface temperature s lower than ar temperature. To account for partal or complete shadng of the stream (water surface), the solar radaton R measured at an unsheltered weather staton s reduced by a shadng coeffcent C Shad. 28

29 Appendx II: Sedment Temperature Model Formulaton The vertcal dstrbuton of temperature n the stream sedment s determned usng a -D heat dffuson model. Snce there are no nternal heat sources n the sedment, the governng dfferental equaton s: T T (A2.) + D = 0 t z z where T s temperature, t s tme, z s vertcal dstance below the streambed and D s the thermal dffusvty. The dfferental equaton A2. s dscretzed based on a control volume (Fgure A2.) as follows: (A2.2) T, j+ T t, j = D z T z L T z U = D z ( T T ) ( T T ) + δz δz The resultng equaton for each nodal temperature s: (A2.3) A T, j+ = A T, j+ + A + T +, j+ z (A2.4) A = A A + t z (A2.5) S= T, j t D (A2.6) A = δz D (A2.7) A + = δz + S z u δz - δz T - T T + δ z T u, dt u /dz T L, dt L /dz Fgure A2.. The fnte dfference control volume. Boundary condtons are set at the sedment/water nterface (sedment temperature = stream temperature) and at the bottom of the sedment column (adabatc, A + =0). The heat flux between the sedment and stream channel (h sed ) s calculated for each tme step by ntegratng the change n temperature over the sedment column: n (A2.8) h sed = ρc p ( T, j T, j ) = z where j denotes the tme step and n s the number of sedment layers. 29