1、The importance of diverse data typesIn order to have confidence in a modelsJournal of Hydrology 321*Now with Barr Engineering, Minneapolis, MN, USA.model of the Trout Lake Basin, Northern Wisconsin, USARandall J. Hunta,*, Daniel T. Feinsteinb, Christine D. Pint1,c, Mary P. AndersoncaUS Geological Su
2、rvey, 8505 Research Way, Middleton, WI 53562, USAbUS Geological Survey, Milwaukee, WI, USAcUniversity of Wisconsin-Madison, Madison, WI, USAReceived 19 April 2005; revised 13 July 2005; accepted 1 August 2005AbstractAs part of the USGS Water, Energy, and Biogeochemical Budgets project and the NSF Lo
3、ng-Term Ecological Researchwork, a parameter estimation code was used to calibrate a deterministic groundwater flow model of the Trout Lake Basinin northern Wisconsin. Observations included traditional calibration targets (head, lake stage, and baseflow observations)as well as unconventional targets
4、 such as groundwater flows to and from lakes, depth of a lake water plume, and time oftravel. The unconventional data types were important for parameter estimation convergence and allowed the developmentof a more detailed parameterization capable of resolving model objectives with well-constrained p
5、arameter values.Independent estimates of groundwater inflow to lakes were most important for constraining lakebed leakance and thedepth of the lake water plume was important for determining hydraulic conductivity and conceptual aquifer layering. Themost important target overall, however, was a conve
6、ntional regional baseflow target that led to correct distribution of flowbetween sub-basins and the regional system during model calibration. The use of an automated parameter estimation code:(1) facilitated the calibration process by providing a quantitative assessment of the models ability to matc
7、h disparateobserved data types; and (2) allowed assessment of the influence of observed targets on the calibration process. The modelcalibration required the use of a universal parameter estimation code in order to include all types of observations in theobjective function. The methods described in
8、this paper help address issues of watershed complexity and non-uniquenesscommon to deterministic watershed models.q 2005 Elsevier B.V. All rights reserved.Keywords: Watershed; Numerical model; Parameter Estimation; Calibration; Lakes1. Introductionto calibrate a watershed(2006) simulates the natura
9、l system observed in thefield. This is typically done through calibration0022-1694/$ - see front matter q 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.jhydrol.2005.08.005gov (D.T. Feinstein), (C.D. Pint), andygeology.wisc.edu (M.P. Anderson).1interpretive or predictive capability, we need t
10、o assesshow well the simplified system represented in theCorrespondingauthor.Tel.:C1608 828 9901;fax:C1 608 8213817.E-mail addresses: rjhuntusgs.gov (R.J. Hunt), dtfeinstusgs.useful in calibrating a flow model. In the Trout Lakescale modeling (Krabbenhoft et al., 1990b; Hunt et al.,1998; Kim et al.,
11、 1999). Vertical anisotropy inhydraulic conductivity is relatively small, with theratio of horizontal to vertical conductivity rangingfrom 4:1 to 8:1 at a scale of a couple of meters(Kenoyer, 1988). The lakes occupy depressions in theglacial deposits that may penetrate more than 80% ofthe aquifer. T
12、rout Lake, the largest lake in the basinwith an area of 11 km2, is drained by the Trout River(Fig.1)andisfedbyfourstreams.Annualprecipitationaverages about 79 cm/yr (Cheng, 1994) and averageterrestrial groundwater recharge is estimated to be27 cm/yr (Hunt et al., 1998), with slightly higher ratesin
13、areas composed of a higher percentage of conifertrees(Drippsetal.,2006).Annualevaporationfromthelakes is about 54 cm/yr (Krabbenhoft et al., 1990;Wentz and Rose, 1991); thus, net precipitation on theFig. 1. Parameter zonation, model design, and target locations forthe Trout Lake watershed model. K,
14、hydraulic conductivity zones;R, recharge zones; and L, lakebed leakance zones.HydrologyBasin, a variety of data types have been collected thatare potentially useful in model calibration, includingcommonlycollectedheadandfluxdata.Lesscommonlycollected data available for this basin include waterisotop
15、es (Ackerman, 1992; Walker et al., 2003), andgroundwater age dating (Walker et al., in review).Travel times and groundwater and surface-waterinteraction have been previously simulated withthree-dimensional groundwater flow models. In thispaper, we describe how a combination of convention-al and unco
16、nventional information can improve thecalibration of a watershed-scale flow model.2. Site description and previous modelingThe Trout Lake Basin (Fig. 1) is home to the NorthTemperate Lakes Long Term Ecological Research(NTL-LTER) site and the US Geological SurveysNorthern Temperate Lakes Water, Energ
17、y, andBiogeochemical Budgets (WEBB) site. The system isgroundwater dominated, with groundwater derivedbaseflow accounting for over 90% of total streamflow(USGS,unpublisheddata). Theaquiferconsistsof4060 m of unconsolidated Pleistocene glacial deposits,mostly glacial outwashsands and gravel (Attig,19
18、85).Horizontalhydraulicconductivitiesareestimatedtobeabout10 m/d(Okwueze,1983;Huntetal.,1998),withlocalized zones of higher conductivity in the near-surface sedimentsaroundSparkling and Crystal Lakeswhereby simulated heads and fluxes are compared tofield measurements. Inclusion of flux targets, inad
19、dition to heads, is important because it overcomesparameter correlation between hydraulic conductivity(K) and recharge, and facilitates unique calibrations(Poeter and Hill, 1997). Head and flux targets may notbe sufficient, however, for constraining some modelparameters such as streambed conductance
20、 (Hunt,2002). Hence, other insight (e.g. Seibert andMcDonnell, 2002), or field data in addition to headsand fluxes, can be important for improved calibrationand system understanding. Previous work has demon-strated that solute distributions (Christensen et al.,1995; Anderman et al., 1996), isotopes
21、(Krabbenhoftet al., 1990a; Poeter and Gaylord, 1990), andtemperature distributions (Bravo et al., 2002) areR.J. Hunt et al. / Journal of(K4,K5inFig.1)basedonfieldevidence andsmaller-321 (2006) 286296 287lakes is about 25 cm/yr. Lakes are well connected toThe MODFLOW grid was extended beyond theHydro
22、logygroundwatershed boundaries; groundwater fluxes cal-culatedattheboundariesoftheMODFLOWgridbytheAE model were distributed to the upper three layers ofthe finite difference model proportional to layertransmissivityandinputtoMODFLOWswellpackage.Crystallinebedrockunderliestheglacialdepositsandisassum
23、edtoactasanimperviousbottomboundaryofthemodel. Recharge flux was specified across the watertable, which formed the upper boundary.Thirty lakes within the Trout Lake basin or near itsthe groundwater system and many lakes are flow-through lakes with respect to groundwater.The Trout Lake basin has been
24、 the focus of severalmodeling studies (Cheng, 1994; Hunt et al., 1998;Champion, 1998; Pint, 2002) that represent stages inthe development and refinement of a regionalgroundwater model, which will be used in futurestudies to address a variety of research problemsincluding the effects of climate chang
25、e.3. Methods3.1. Model designA steady-state model was constructed using MOD-FLOW2000 (Harbaugh et al., 2000) and MODPATH(Pollock, 1994). The three-dimensional model applieda uniform horizontal nodal spacing of 75 m and fourlayers (Fig. 1). The bottom three layers ranged inthickness from 5 to 15 m wh
26、ile the upper layer wasrelatively thick, with a saturated thickness between 8and 35 m, to minimize the possibility of nodes dryingduring calibration and during transient simulations. Atwo-dimensional analytic element (AE) model usingGFLOW (Haitjema, 1995a) was modified from anexisting regional model
27、 of the Trout Lake area (Huntet al., 1998) and was used to derive boundaryconditions for the finite difference model accordingto the methodology of Hunt et al. (1998). The modelincluded areas outside the Trout Lake basin to allowgroundwater divides to move as the model wascalibrated. This is importa
28、nt in this study because thegroundwatershedandsurfacewatershedarenotaligned(Huntetal.,1998)andthegroundwatershedisestimatedto be more than 40% larger than the surface watershed.R.J. Hunt et al. / Journal of288boundary were simulated using the LAK3 LakePackage (Merritt and Konikow, 2000), which calcu
29、-lates lake stages based on volumetric water budgets.Simulating lakesstageswithinthe modelissuperior tospecifying lake stages using constant head nodesbecause it helps ensure that heads are not overlyspecified in the immediate area of interest. Similarly,streams located within the Trout Lake basin w
30、eresimulated using the Streamflow Routing Package(Prudic et al., 2004), thereby allowing calculation ofstream stage and flow. For convenience, other lakesand streams distant from the area of interest wererepresented as head dependent flux boundaries usingthe River Package (McDonald and Harbaugh, 198
31、8).The streambed sediments were assumed to have auniform thickness of 1 m and a vertical hydraulicconductivity of 8.63 m/day; though it should be notedthis parameter was relatively insensitive over therange of reasonable values in this watershed (Hunt,2002). All aquifer hydraulic conductivity zones
32、wereassumed to have a vertical anisotropy ratio (Kx/Kz)equal to four (Kenoyer, 1988) within a given modellayer. Effective porosity,usedinparticletracking,wasset equal to 0.29 (Krabbenhoft and Babiarz, 1992).3.2. Calibration approachCalibration was automated using the non-linearregression parameter e
33、stimation codeUCODE (Poeterand Hill, 1998). Eleven model parameters (tworecharge zones, five hydraulic conductivity zones,and four lakebed leakance zonesFig. 1)wereallowed to vary during model calibrations. UCODEadjusts the squared model residual by a weight(variance of the measurementK1), resulting
34、 in dimen-sionless residuals. This formulation allows differenttarget types to be evaluated in the same objectivefunction. Taking advantage of this capability, fivetypes of targets were used. The first two types aretypicallyusedingroundwatermodelsandreferredtoastraditional targets; these included wa
35、ter levels fromlakes and wells (head targets) and the groundwatercomponent of streamflow (baseflow targets). FiveLong-Term Ecological Research (LTER) lakes hadmeasured stages; 20 additional lake stages wereestimated from topographic maps. The LTER laketargets were given a relatively high importance,
36、 thus arelativelysmallstandarddeviationinUCODE0.5 m321 (2006) 286296for lakes without surface water outflows (seepagetermination zone specified at P7. It should beHydrologylakes) and 0.25 m for drainage lakes based on the 17year (19842001) measured range. A range of G2standard deviations represents
37、the approximate 95%confidence interval around the observed value. Lakestagesobtainedfromtopographicmapsweregivenlessimportance by using a standard deviation equal to 1 mto reflect the increased uncertainty of their verticalelevationanduncertaintyassociatedwithhowwellthestage reported on the topograp
38、hic map represents along-term average. Groundwater level measurementsfrom 58 wells measured during July 2001a nearaverage period(Pint,2002)wereusedasheadtargets.The UCODE weight assigned to all head targets(standard deviation equal to 0.3 m) corresponds to arepresentative variation determined using
39、wells withlong-term data sets. The 10-year (19912000) meanbaseflows at the four stream gaging stations werecalculated using the methods of White and Sloto(1990) and used as baseflow targets. These dischargerecords are of relatively high quality and were given acoefficientofvariation(CV)rangingfrom0.
40、02to0.05.A CV of 0.02 represents an approximate 95%confidence interval of G4% around the observedmean baseflow at a given station.In addition to traditional head and baseflow targets,three types of unconventional data were also used inthe parameter-estimation objective function (the sumof squares of
41、 weighted residuals) as discussed below. Groundwater fluxes (m3/d) to and from 11 selectedlakes in the basinThese targets were obtainedusing a stable-isotope mass balance (Ackerman,1992) and water budget analysis. Groundwaterinflow rates are considered to have less uncertaintythan the groundwater ou
42、tflow rates for the lakes;thus, inflow rates were given a CV of 0.3 and theoutflow rates were given a CV of 0.7. Thesimulated values were obtained from the LAK3package (Merritt and Konikow, 2000) output. Elevation of the top of the Big Muskellunge lakewater plumeElevation targets also wereincluded i
43、n the objective function at two piezo-meter nest locations (labeled P7 and P14 in Fig. 1).Using stable isotopes of water, the interfacebetween terrestrial-derived and lake-derivedwater sources was found to be approximately 11and 16 m below the water table at P7 and P14,R.J. Hunt et al. / Journal ofr
44、espectively. These targets were given a standardnoted that this data class would have limited utilitywithout adequate control on lateral and verticalflowpaths. Moreover, the use of groundwatersamples for measuring groundwater age hasrecently been questioned (e.g. Bethke and John-son, 2002; Pint et a
45、l., 2003).3.3. Statistical analysis of target influenceOnewaytoassesstheinfluenceofagivenobservation target on the parameter estimationregression is to compare the results using allobservations with the results when the observationin question is omitted (Hadi, 1992). This methodassigns increased inf
46、luence to observations whosedeletion from the parameter-estimation process has arelatively large effect on the overall measure of modelerror (the residual sum of squares) and whosesimulated values are relatively sensitive to smallchanges in parameter values. However, influence isgreatest for paramet
47、er-sensitive observations that arespatially isolated, that is, not clustered with otherobservations within a property zone of the model.Fig. 2 shows a simple linear regression model withtwo observations that are difficult to match and whosesimulated values are sensitive to small parameterdeviation o
48、f 0.5 m to account for the uncertaintythat the plume may lie between two verticallyspaced sampling points. The simulated lake plumeelevations were obtained from MODPATH flow-paths that traveled from Big Muskellunge Lake tothe piezometers; two MODPATH automatictermination zones were used to obtain el
49、evationresults at the piezometer nest locations. Time of travel to one well nestTravel time fromBig Muskellunge Lake to P7 (Fig. 1)wasestimated using CFC and tritium sampling(Walker et al., in review). The approximateflowpath and sampling depth were identifiedusing the analytic element model of Hunt et al.(1998). A standard deviation of 1 year wasassigned to the target value (8 years), reflectingthe expected uncertainty in aquifer porosity. Thesimulated result was obtained from the MOD-PATH travel time output
