Journal of Hydrology 505 (2013) 299–311
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Journal of Hydrology
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Dynamic analysis of stream flow and water chemistry to infer subsurface water and nitrate fluxes in a lowland dairying catchment ⇑ Simon J.R. Woodward a, , Roland Stenger a, Vincent J. Bidwell b,1 a Lincoln Agritech Limited, Private Bag 3062, Hamilton 3240, New Zealand b Lincoln Agritech Limited, PO Box 69133, Lincoln 7640, New Zealand article info summary
Article history: The use of process-based, dynamic and spatially-explicit models to describe water and nitrogen fluxes at Received 8 October 2012 the catchment-scale is often hampered by a shortage of detailed land use, hydrological and biogeochem- Received in revised form 30 April 2013 ical information. Accordingly, such complex models tend to be restricted to a small number of well inves- Accepted 28 July 2013 tigated catchments, often associated with research projects. On the other hand, stream flow and stream Available online 12 October 2013 water chemistry time series data are available for a much larger number of catchments, e.g. for many This manuscript was handled by Laurent Charlet, Editor-in-Chief, with the assistance catchments that are routinely monitored by government agencies for state-of-the-environment report- of M. Todd Walter, Associate Editor ing. It was the main aim of this study to provide a spatially lumped model that allows meaningful anal- ysis of catchment-scale water and nitrate fluxes based on such data sets. Keywords: Based on stream flow time series data, catchment hydrodynamics are often analysed using approaches Shallow groundwater derived from the linearised Boussinesq equation, which has analytical solutions for dynamic groundwa- Denitrification ter discharge expressed in terms of eigenvalues and eigenfunctions (eigenmodel approach). Calibrated Groundwater discharge Boussinesq models generally yield a good reproduction of stream flow dynamics, and stable estimates Lumped catchment model for aquifer parameters such as hydraulic conductivity and mean aquifer depth. By linking a soil water bal- Boussinesq equation ance model with two Boussinesq groundwater eigenmodels linked in series, and assuming constant sol- ute concentrations discharging from each source, a dynamic catchment model predicting stream flow and water chemistry at the catchment outlet (‘‘StreamGEM’’) was developed. Compared with previous approaches, inclusion of water chemistry in this model both aided hydrological understanding, and allowed assessment of catchmentscale nitrate fluxes. Simultaneous calibration of the model to stream flow and nitrate concentration data from a small lowland dairying catchment yielded good predictions to both variables (Nash–Sutcliffe Model Efficiency of 0.90 and 0.84), and the fitted parameters were able to be used to estimate annual flow and nitrate fluxes through near- surface, shallow groundwater, and deeper groundwater reservoirs conceptually present in the catchment. The calibration was cross-validated using an independent time series from the same catchment. The results support the hypothesis, based on groundwater observations, that stream flow in the catchment is the result of mixed discharge from a shallower, rapidly draining zone of oxidised groundwater carrying rel- atively high loads of agricultural nitrate, with a relatively deeper and slower draining zone of reduced groundwater that is essentially nitrate free. The proportions of stream flow discharging from the near-sur- face, shallow groundwater, and deeper groundwater reservoirs were estimated to be 5%, 80% and 15%, respectively. In spite of its small contribution to total stream flow, the deeper groundwater reservoir sus- tained stream flow during summer and dominated stream water chemistry 61% of the time. By combining the flow and nitrate concentration estimates derived from model calibration, it was esti- mated that discharge of shallow groundwater was responsible for 91% of the nitrate load entering the stream. However, the predicted nitrate concentration in this reservoir was significantly lower than the predicted nitrate concentration of near-surface flow and root zone leachate concentrations estimated using a nutrient budgeting model. This indicates that denitrification occurs within this reservoir. On the basis of the calibrated model, it was estimated that 36% of the nitrate recharged from the vadose zone gets denitrified within the shallow groundwater reservoir, and up to 9% in the deeper groundwater reservoir. Ó 2013 Elsevier B.V. All rights reserved.
⇑ Corresponding author. Tel.: +64 7 858 4840. E-mail addresses: [email protected] (S.J.R. Woodward), 1. Introduction [email protected] (R. Stenger), [email protected] (V.J. Bidwell). 1 Present address: Vincent Bidwell Consulting, 17 Brookside Road, Rolleston 7614, Diffuse nutrient losses from agriculture pose a globally recogni- New Zealand. sed threat to the quality of the world’s freshwater resources
0022-1694/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jhydrol.2013.07.044 300 S.J.R. Woodward et al. / Journal of Hydrology 505 (2013) 299–311
(Cherry et al., 2008; Heathwaite, 2010). Losses of nitrate ðNO3 Þ are dynamics and catchment baseflow (Pauwels et al., 2002). Numeri- particularly difficult to manage, as the anion is highly mobile and cal solutions of the full non-linear equation (Rupp and Selker, leaches rapidly to contaminate the underlying groundwater that 2006), and analytical solutions of the linearised equation (Pauwels subsequently discharges to surface waters (Pärn et al., 2012). This and Troch, 2010), can both be used to simulate water table and dis- means that nitrate losses cannot be effectively managed by ripar- charge dynamics, and by calibration to stream flow or groundwater ian exclusion zones or vegetation strips that are more effective in level time series, to estimate aquifer parameters such as saturated reducing the transfer of contaminants that are predominantly hydraulic conductivity and mean aquifer thickness. transported in surface runoff (e.g. sediment, phosphorus and mi- The Boussinesq model can be readily extended to include addi- crobes). Furthermore, the large volume and slow flow rate of many tional flow paths, such as overland/near-surface (NS) flow (Bidwell groundwater systems means that large quantities of leached ni- et al., 2008) or connection with regional groundwater systems trate can be stored and may continue to be discharged to surface (Broda et al., 2012). In an earlier study, Bidwell et al. (2008) cou- waters long after leaching losses have been reduced (Wriedt and pled an eigenvalue–eigenfunction solution of the linearised hori- Rode, 2006; Basu et al., 2010). zontal-aquifer Boussinesq equation (eigenmodel approach) with A mitigating factor is that in some situations nitrate leached a soil water balance and vadose zone model to estimate the rela- into groundwater may be denitrified, predominantly to harmless tive proportions contributed by near-surface drainage and ground- dinitrogen gas (N2). For denitrification to occur, oxygen-depleted water discharge to flow in the Pukemanga Stream, which drains a conditions, suitable electron donors (e.g. carbon, pyrite) and a small (3.0 ha), steep, farmed hill catchment in the southern Hakari- microbial community with the metabolic capacity for denitrifica- mata Range, west of Whatawhata in the Waikato region of New tion are required (Rivett et al., 2008). As nitrate is not necessarily Zealand. Results over 7 years indicated that 78–93% of stream flow conserved in the groundwater system, it is essential to understand was generated from groundwater discharge, the remainder coming not only the leaching losses, but also the flow paths and any atten- from surface runoff and interflow near the soil surface. uation processes possibly occurring between the bottom of the Temporal changes in the relative contributions of overland/ root zone and groundwater discharge into surface waters. The spa- near-surface flow and groundwater discharge may also be reflected tial and temporal variability of these conditions poses a significant in the chemistry of the stream water. Stewart et al. (2007), for challenge to identifying, measuring and quantifying denitrification example, showed how weekly samples from Pukemanga Stream, at a catchment scale (Wriedt and Rode, 2006; Groffman et al., analysed for oxygen-18, silica, tritium and sulphur hexafluoride, 2009; Hesser et al., 2010), and to establishing defensible cause–ef- provided additional evidence for the dominance of groundwater fect relationships, which are needed for improved resource flow. The longer transit times associated with water flowing along management. deeper flow paths was reflected in lower concentrations of tritium Most catchment scale nitrate modelling is done using spatially- and reactive ions, and higher concentrations of silica, relative to explicit forward models such as SWAT (Conan et al., 2003; Ekana- overland/near-surface flow water. This suggests that, by encapsu- yake and Davie, 2005; Glavan et al., 2011; Lam et al., 2012)or lating temporal changes in discharge from multiple flowpaths with MODFLOW-RT3D (Wriedt and Rode, 2006), which require detailed different biogeochemical characteristics, stream chemistry mea- land use and physical data that are often unavailable outside re- surements could provide a useful adjunct to stream flow recording. search projects. At the same time, some of these models have Using stream chemistry time series data as the basis for calibration tended to focus on the more easily observed overland/near-surface for a groundwater model with multiple groundwater flow paths runoff and channel flow, with groundwater hydrology being with different dynamic response times and chemical signatures greatly simplified, despite groundwater being the main flow path could allow estimates of catchment scale water and solute fluxes transporting nitrate from the land surface to streams and lakes in (including attenuation) along each flow path. many lowland catchments (Ekanayake and Davie, 2005; Wriedt This paper therefore describes an extension of the eigenmodel and Rode, 2006; Hesser et al., 2010; Lam et al., 2012; Pärn et al., approach to estimate the relative contributions of near-surface 2012). drainage and groundwater discharge to nitrate load, as well as In catchments with limited available land and subsurface infor- stream flow, in catchments with limited spatial data. The model mation, detailed spatial modelling is not possible. However, stream is applied to analysis of stream flow and nitrate time series data ta- flow and chemistry time series data may be readily obtainable, and ken from the Toenepi Stream, which drains a lowland dairying may be interpreted as a signal representing integrative catchment catchment in the Waikato region of New Zealand’s North Island. function (Basu et al., 2010; Aubert et al., 2013). These data can pro- vide the basis for an alternative approach, inverse modelling using a spatially aggregated (‘‘lumped’’) catchment model. The calibrated 2. Methods model can be used to infer seasonal water and nutrient fluxes along surface and subsurface flowpaths, and to estimate attenua- 2.1. Site description tion at the catchment scale. This approach is potentially highly useful for understanding and quantifying nitrate fluxes and The Toenepi Stream drains a small catchment (15.1 km2, eleva- dynamics across a wide range of catchments where agricultural tion 40–130 m above sea level) north-west of Kiwitahi in the Wai- intensification is responsible for elevated groundwater and surface kato region of New Zealand (Fig. 1). The catchment is characterised water nitrate levels and resultant water quality degradation, but by lowland alluvial plains in the central portion of the catchment where detailed spatial data is not available. Development and test- and at the outlet, with the remainder of the catchment consisting ing of such an approach is the focus of this paper. mainly of rolling downlands and some hill country in the headwa- The simplest lumped catchment model comprises linked soil ter area. Most of the properties in the catchment are intensive pas- water balance and first order groundwater models (O’Brien et al., toral dairy farms (average 3.1 cows ha 1), complemented by a 2013). However, these models typically greatly underestimate small number of pastoral drystock farms. In 2003, the dairy land the baseflow contribution, as the more rapid groundwater re- received an average of 99 kg N ha 1 y 1 fertiliser (Stenger et al., sponses are not adequately represented by a first order model 2008). (Rupp et al., 2009). A more realistic approach uses the Boussinesq Intensive monitoring of the surface water (since 1995) and equation for a one-dimensional horizontal or sloping aquifer, a groundwater (since 2002) in this catchment has been motivated well-established physically-based model for aquifer water table by concerns about present and future effects of pastoral dairy S.J.R. Woodward et al. / Journal of Hydrology 505 (2013) 299–311 301
Fig. 1. Toenepi catchment boundary and stream network. The catchment is gauged at the Tahuroa Road bridge. Length of main channel is 6.66 km. Total stream length is 52.12 km. farming intensification on water quality (Wilcock et al., 1999; water table (uppermost sampling depth), but oxygen-depleted 1 Stenger et al., 2008). Stream flow exiting the catchment (at the and nearly nitrate-free (less than 0.5 mg L NO3–N) groundwater Tahuroa Road bridge) has been monitored continuously since June follows at slightly greater depth. 1995, with the exception of the periods April 1997–October 1998 This suggests the existence of two distinct groundwater reser- and November 2001–February 2002 (Wilcock et al., 1999, 2006). voirs at the catchment scale; one shallower, predominantly oxi- Instantaneous flow rate (L s-1) over a V-notch weir was recorded dised, nitrate–bearing and rapidly draining to the stream, and the at 15 min intervals using a stilling well and rating curve. Stream other slightly deeper, consistently reduced, denitrified, and drain- ammonium (including ammonia) and nitrate (including nitrite) ing more slowly. The shallower groundwater is thought to reside concentrations were measured weekly from March 1995–April in the young, friable volcanic ash beds and the deeper groundwater 1997, and then monthly from October 1998 until March 2011 (Wil- in the underlying substantially older and argillised ones (Stenger cock et al., 1999, 2006). Stream ammonium concentrations were et al., 2008). generally less that 0.1 mg L 1 after 1998, having declined as the Daily rainfall (midnight–midnight) was measured at a meteoro- practice of discharging dairy shed effluent directly to the stream logical station in the catchment headwaters, and potential has been phased out, so that nitrate was by far the dominant frac- evapotranspiration (PET) was calculated using the FAO Penman– tion (Wilcock et al., 2006). Furthermore, the vast majority of Monteith equation (Allen et al., 1998). Annual rainfall for the groundwater samples contained non-detectable or minute 2003–2010 period ranged from 1177 to 1383 mm with an average amounts of ammonium nitrogen (Stenger et al., 2008). Stream of 1291 mm. Annual PET ranged from 846 to 926 mm in the same chemistry at the catchment outlet shows a strong seasonal pattern, period, with an average of 892 mm. Water balance calculations with high nitrate concentrations in the winter, when high flow indicate that annual recharge closely matches annual stream flow rates are typical, contrasting with low nitrate concentrations in at the catchment outlet (304–584 mm, with an average of the summer, when low flow conditions prevail (Wilcock et al., 446 mm) (Stenger et al., 2009), suggesting that the catchment 1999, 2006; Morgenstern et al., 2010). approximates a closed hydrological system, with little if any ex- Despite the long history of intensive dairying, and documented change with deeper groundwater. Furthermore, the uniform land moderately high nitrate levels in the stream, observations of shal- use in the catchment means that there is little potential for dilution low groundwater (less than 3 m below ground surface) reported by of agricultural contaminants entering the groundwater system. Stenger et al. (2008) found generally low levels of nitrate—80% of the 843 samples taken between December 2002 and December 2.2. Model development 2004 were below the Australia and New Zealand Environment 1 and Conservation Council trigger value of 0.44 mg NO3–N L for These observations provided the conceptual basis for a lumped eutrophication of surface water. The observation that median con- catchment scale model, to use climatic and stream monitoring data 1 centrations below 0.44 mg NO3–N L were found at 28 of the 34 to characterise water and nitrate fluxes through surface runoff, monitoring wells demonstrates the spatially widespread occur- near-surface flow, and two groundwater reservoirs, and to esti- rence of low groundwater nitrate concentrations in this catchment. mate attenuation of nitrate prior to discharge into the stream. A Their relative stability over time is reflected by the fact that the similar enumeration of flow paths has been established in several measured nitrate concentration in 25 of the wells varied by less other catchment studies (Hesser et al., 2010; Broda et al., 2012; 1 than 1 mg NO3–N L between the 25 sampling dates. Subsequent O’Brien et al., 2013; Aubert et al., 2013), and the importance of research using multilevel well clusters with 0.5 m long well groundwater in determining stream nitrate loads has been ob- screens instead of the previously used monitoring wells (screen served in other lowland agricultural catchments (e.g. Conan length typically 2 m) revealed persistent vertical stratification et al., 2003; Ekanayake and Davie, 2005; Wriedt and Rode, 2006; within the groundwater underlying well-drained soils. This pattern Lam et al., 2012), suggesting that the approach could be widely is shown in Fig. 2 for two multilevel well sites that were sampled applicable. 16 times between May 2007 and September 2011. Oxidised and ni- The ‘‘streamflow generation eigenmodel’’ (StreamGEM) is based 1 trate-bearing (5–10 mg L NO3–N) groundwater occurs near the on the model of Bidwell et al. (2008), who linked soil water content 302 S.J.R. Woodward et al. / Journal of Hydrology 505 (2013) 299–311
-1 -1 (a) NO3-N (mg L ) (b) DO (mg L )
0246810 0246810 0 0
MLW1 MLW1 MLW2 -1 -1 MLW2
-2 -2
-3 -3 Depth (mbgl) Depth (mbgl)
-4 -4
-5 -5
Fig. 2. Profiles of (a) nitrate nitrogen (NO3–N) and (b) dissolved oxygen (DO) in shallow groundwater at multilevel well (MLW) sites 1 and 2. Average ± standard deviation of 16 sampling dates (May 2007–September 2011).
(W), drainage-excess overland and near-surface flow entering the was considered by Kirchner (2009), who estimated that 0.3-1.6% of stream network directly (N) and the passage of drainage water precipitation might bypass catchment storage. Alternative mecha- through the vadose zone (V) to groundwater discharge. Groundwa- nisms considered were channel precipitation, and/or surface runoff ter discharge was modelled using an analytical eigenmodel solu- in dry conditions due to hydrophobicity, but these were unsuccess- tion to the linearised Boussinesq equation for a horizontal ful in explaining the observed stream flow and chemistry aquifer (Sloan, 2000). More general forms of the equation, which fluctuations. include time-varying transmissivity (Rupp and Selker, 2006)or The linkage between the reservoirs is illustrated in Fig. 3. The bedrock geometry (Troch et al., 2003) lead to non-linear differen- model is specified as a system of linear differential equations, tial equations. These can be solved by numerical methods, but which can be solved analytically for stress periods over which are much less convenient for computational purposes in compari- the model inputs remain constant. In the present study, the model son with the linear description. Furthermore, even the more gen- inputs are daily accumulated rainfall (R mm d 1) and daily poten- eral forms do not capture known dependencies of hillslope tial evapotranspiration (P mm d 1). The model (implemented in discharge on antecedent moisture conditions in the unsaturated Microsoft Excel 2003) was therefore solved with a daily time step. zone or bedrock flow (McGlynn et al., 2002; Lange and Haensler, Calculated stream flow (U mm d 1) (normalised over the catch- 2012). Shahedi (2008) examined simplifications to the Boussinesq ment area of 15.1 km2) and solute concentration time-series at model, and concluded that, for many purposes, representation of the catchment outlet were used as calibration and validation data. hillslope-stream interaction can be adequately represented by This kind of lumped catchment model has the virtue of requir- storage-discharge relationships. The eigenmodel used here yields ing relatively few input data (rainfall, PET and stream flow) and yet recession curves that improve on both linear (O’Brien et al., 2013) and non-linear storage-discharge curves by recognising that Rain ET the storage-discharge relationship is dynamic and depends on in- R E put history (Pauwels et al., 2002; Rupp et al., 2009). surface runoff On the basis of the groundwater observations described in the R previous section, in the present model groundwater was subdi- b W vided into two reservoirs with different hydraulic response times bypass Soil Water (W ) and chemical signatures. These were a relatively shallower, ‘‘fast’’ flow (bucket) reservoir (F), recharged from the vadose zone, and a slightly dee- per, ‘‘slow’’ reservoir (S), recharged from the fast reservoir. ‘‘Fast’’ DW near surface flow and ‘‘slow’’ here refer to the average hydrometric response times R drainage RV N of the two reservoirs. These two reservoirs were connected in ser- ies, with a portion (f ) of the discharge from F providing recharge to Vadose Zone (V ) Near Surface (N ) S (first order) S. (first order) D Several other changes were also made. First, the dry season DV N evapotranspiration was enhanced by using the model of Woodward et al. (2001), which gives more realistic (higher) evapo- Fast GW (F ) transpiration estimates following summer rainfall. Second, infiltra- (eigenmodel) (1 - f ) D tion-excess surface runoff was included by assuming that rainfall s F f D above a surface infiltration limit (RW,max) entered the stream via s F overland/near-surface flow (N). Third, a time delay was added to overland/near-surface flow (N), by modelling the flow as a first or- Slow GW (S ) der storage reservoir, rather than it being transmitted instanta- (eigenmodel) D S D neously to the stream. This allowed storm flow effects to extend U Discharge to the following days after the rain event. Lastly, dry season rainfall to Stream response was improved by allowing a small proportion (b) of sur- face infiltration to bypass the soil water storage reservoir (W) and Fig. 3. Catchment water reservoirs and flow paths simulated in the StreamGEM directly contribute to soil drainage. A similar bypass flow approach model. S.J.R. Woodward et al. / Journal of Hydrology 505 (2013) 299–311 303 can be used to estimate catchment scale water and nutrient fluxes The mean response times for these first order reservoirs are 1 1 for assessment purposes. Because StreamGEM was designed to (aV) and (aN) respectively. realistically characterise the time responses of the different flow paths, in order to allow decomposition of the stream flow in re- 2.2.3. Groundwater reservoirs sponse to rainfall, it provides a more accurate description of the The two groundwater reservoirs (F and S) are modelled as hydrodynamics compared with empirical recession curve, stor- eigenmodel reservoirs, i.e. as eigenvalue–eigenfunction solutions age-discharge or flow separation analyses that require fewer to a linearised Boussinesq equation. An eigenmodel reservoir is parameters (e.g. Kirchner, 2009; O’Brien et al., 2013). This offers characterised by a single response parameter, a (d 1), which com- a parsimonious approach to catchment analysis that is particularly bines the hydraulic conductivity K, storativity h, thickness B, and suitable for situations where time series data from a stream mon- length L parameters from the Boussinesq equation (Bidwell et al., itoring site exist, but little other information from the contributing 2008): catchment is available. KB The following sections describe the model equations in more a ¼ 2 : ð8Þ detail. hL In the solution, the spatially distributed groundwater reservoir 2.2.1. Soil water is represented by a parallel set of lumped reservoirs, each of which
Soil water content (W) is simulated using a tipping bucket mod- has a storage coefficient (ai) which is a multiple of a. These individ- el with storage capacity Wmax. Recharge to this storage (Rw ual storage coefficient values are provided by the analytical eigen- mm d 1) is equal to rainfall R less overland and bypass flow, value solution of the simple Boussinesq aquifer equation, as described in Bidwell et al. (2008). RW ¼ð1 bÞ minðR; RW; maxÞð1Þ The characteristic response parameter for the fast groundwa- 1 where RW,max is the maximum surface infiltration rate and b is the ter reservoir is aF (d ). This is decomposed to give the eigen- 1 ‘‘bypass’’ fraction that contributes to the soil drainage directly. Ac- values aFi (d ). Discharge from the reservoir (DF) is then tual evapotranspiration rate in a stress period (E mm d 1) is deter- calculated as: mined using the model of Woodward et al. (2001), as the minimum X of potential evapotranspiration (P mm d 1) and readily available DF ¼ aFiFi ð9Þ soil water (RAW mm): where Fi are the associated eigenmodel storage components. The first ten components are sufficient to give an accurate calculation E min P; RAW 1d 1 2 ¼ ð ÞðÞ (Bidwell et al., 2008). The hydrodynamic response time for each 1 where RAW = Ws +(W Ws) a P. That is, RAW is the water con- storage component is (aFi) , and the flow weighted average hydro- 1 tent in a rapidly recharged zone (Ws) plus a proportion (a P) of the dynamic response time for the whole reservoir is (3 aF) . remaining soil water (W Ws). Suitable values of Ws and a were Discharge from the fast groundwater reservoir is partitioned be- determined by Woodward et al. (2001) to be 25 mm and tween discharge to the slow groundwater reservoir, fS DF, and dis- 1 1 0.0073 d mm respectively. The factor 1 d in Eq. (2)is needed charge to the stream network, (1 fS) DF, as indicated in Fig. 3. to convert RAW from a quantity (mm) to a rate (mm d 1). The slow groundwater reservoir (S) is also modelled as an 1 Drainage from soil water (DW mm d ) during the stress period eigenmodel reservoir. The characteristic response parameter for 1 is then calculated as: this reservoir is aS (d ), which is decomposed to give the eigen- 1 values aSi (d ). Drainage from the slow groundwater reservoir DW ¼ maxðW þ RW E Wmax; 0Þþb minðR; RW; maxÞð3Þ (DS) discharges directly into the stream network, and is calculated where the first term is drainage of soil water in excess of saturation, as: X and the second term is bypass flow. Drainage from soil water (DW) DS ¼ aSiSi ð10Þ is partitioned between vadose zone (RV) and near-surface (RN) flow as follows: where Si are the associated eigenmodel storage components.
RV ¼ minðDW; RV; maxÞð4Þ 2.2.4. Flow equations
RN ¼ maxðR RW; max; 0ÞþmaxðDW RV; max; 0Þð5Þ The system of model equations is then, where RV,max is the maximum infiltration rate to the vadose zone. dW ¼ R E RN RV Eq. (5) (RN) therefore has terms for infiltration-excess surface runoff dt and drainage-excess saturated near-surface flow respectively. Both dN ¼ RN DN of these processes are only active during major storm events; dt stream flow at other times is dominated by groundwater discharge dV ¼ R D ð11Þ (McGlynn et al., 2002). dt V V dF i ¼ b D a F 2.2.2. Vadose zone and near-surface drainage dt Fi V Fi i The vadose zone and near-surface water reservoirs (V and N) dSi are modelled as first order reservoirs with relative discharge ¼ bSifSDF aSiSi 1 1 dt rates aV (d ) and aN (d ) respectively. The vadose zone dis- charges/drains into the fast groundwater reservoir, and the where the bFi and bSi are the gain coefficients that partition ground- near-surface water discharges directly into the stream network, water recharge to the fast and slow groundwater reservoir compo- with rates, nents respectively, as described in Bidwell et al. (2008). The first ten eigenvalues of the fast and slow groundwater reservoirs were used. DV ¼ aVV ð6Þ and 2.2.5. Stream discharge and water quality Discharge to the stream (D ) is the sum of discharges from the D ¼ a N: ð7Þ U N N near-surface, fast groundwater and slow groundwater reservoirs: 304 S.J.R. Woodward et al. / Journal of Hydrology 505 (2013) 299–311
DU ¼ DN þð1 fSÞDF þ DS: ð12Þ 2013 ), which is beyond the scope of this study, weighting of objec- tive criteria is necessarily subjective. The strong hydrological basis It is assumed that water discharged to the stream network trav- of our model, with its many physically-based parameters, is well els rapidly to the catchment outlet. Discharge to the stream, D , U matched to the relatively dense stream flow data. By comparison, can then be compared directly with measured stream flow at the while the model chemistry is simplistic, the infrequency of the catchment outlet, U. stream chemistry data may not support calibration of a more de- While some temporal variation is evident in the field data tailed model. In addition, the focus of our study is not on catchment (Fig. 2), as a first approximation the nitrate concentrations (C , C N F hydrology per se, but on hydrology as the basis for nitrate move- and C ) associated with the near-surface, fast and slow groundwa- S ment and transformations. This provides an additional justification ter discharge in the model were assumed to be constant with time. for giving greater weight to nitrate calibration than might be war- These concentrations were estimated by model calibration to ranted by the nitrate model and nitrate data. stream chemistry data. Daily rainfall and PET data were entered into the model for the Attenuation of discharged nitrate due to hyporheic or in-stream period 1 January 2007–31 March 2011, and the model parameters uptake was not modelled. Several authors have highlighted the dif- listed in Table 2 were adjusted using PIKAIA to maximise the com- ficulties in quantifying the impacts of in-stream processes at the posite objective function, with 100 randomly generated initial catchment scale (Migliaccio et al., 2007; Hesser et al., 2010; Glavan parameters sets, then 100 PIKAIA generations, each producing a et al., 2011), and Wilcock et al. (1999) found stream nitrate concen- further 100 parameter sets. Calibration took 5 min on a desktop trations to be similar between three widely spaced sampling sites PC. Estimated parameters were constrained as indicated in Table 2. at Toenepi, suggesting that in-stream attenuation is relatively The constraints were chosen primarily to limit the search space for small in this catchment. the PIKAIA genetic algorithm, not to predefine the expected values In-stream concentrations of nitrate (C ) at the catchment outlet, U of the parameters, and in most cases the calibrated parameters therefore, were calculated by dividing the total loads (i.e. the sum were not limited by the constraints. A 3 month run-in period of discharge concentration multiplied by discharge rate) by stream meant that the initial conditions (on 1 January 2007) did not signif- flow (D ): U icantly affect the calibration period (which started on 1 April
CNDN þ CFð1 fSÞDF þ CSDS 2007). CU ¼ ð13Þ DU The model variables are summarised in Table 1, and the model 2.4. Model evaluation parameters are summarised in Table 2. The aim of model evaluation is to ascertain whether, given the 2.3. Model calibration highly abstracted model structure, the estimated parameters rep- resent the dynamic response of the physical system, or merely re- A Visual Basic implementation of the PIKAIA 1.2 genetic algo- flect the idiosyncrasies of the particular calibration data set rithm optimiser (Charbonneau, 2002; Pelletier, 2002) was used to (Doherty, 2011). Such a demonstration may be obtained by using calibrate the model to stream flow and chemistry data collected the calibrated model to make predictions for another data set at the Toenepi catchment outlet during the 4-year period 1 April drawn from the same underlying system, or ‘‘cross-validation’’. A 2007–31 March 2011, and to estimate the model parameters listed suitable data series was available for the period 1 April 1995–31 in Table 2. The statistics of the calibration data are given in Table 3. March 1997, during which stream nitrate was measured weekly The composite objective function to be maximised was the sum (Wilcock et al., 1999). Stream flow was also recorded during this of the Nash–Sutcliffe Model Efficiencies (Nash and Sutcliffe, 1970; period, although the flow data from 30 October 1996 onwards
Wöhling et al., 2013), NSEj, for the two datasets: were excluded, as drought conditions at this time resulted in extre- P mely low stream flows which were not able to be accurately mea- nj model data 2 i¼1ðxj;i xj;i Þ sured. The cross-validation data are summarised in Table 4. Using NSEj ¼ 1 P ð14Þ nj data 2 rainfall and evapotranspiration data from the new time period, and ðxj x Þ i¼1 j;i the parameter values previously obtained (Table 2), model outputs data model and model efficiencies were calculated for the new time period. where xj;i is observation i of dataset j, xj;i is the corresponding model value, and xj is the mean of the observations. Despite the much greater availability and accuracy of the flow data (j = 1), equal 2.5. Uncertainty analysis weight was given to the concentration data (j = 2) in the calibration. In the absence of a formal trade-off analysis (e.g. Wöhling et al., One by-product of the genetic algorithm calibration method is that it generates a large number of parameter sets during the search for the best fit. Analysis of near-optimal parameter sets gen- Table 1 erated during model calibration provides an estimate of how much Model variables. each parameter might be able to vary while still giving a good fit. Symbol Range Units These are called ‘‘behavioural solutions’’ by Beven (2006), because their outputs behave in a similar way to the field data. Analysis of Input data –a Rainfall R 0.0–103.2 mm d 1 the behavioural parameter sets and behavioural solutions allows Potential evapotranspiration P 0.2–7.0 mm d 1 an informal uncertainty analysis to be carried out. Model variables –b Behavioural parameter sets were defined as those that gave 1 Actual evapotranspiration E 0.1–5.9 mm d objective values greater than or equal to 0.95 of the optimum Soil water storage W 12.6–204.5 mm Near-surface storage N 0.0–20.8 mm objective value (this value was chosen by analogy with the com- Vadose zone storage V 0.0–6.3 mm monly use 95% confidence intervals in statistics). There were Fast groundwater storage F 0.0–46.9 mm 9366 parameter sets that met this criterion, out of the 10,100 Slow groundwater storage S 6.6–87.1 mm parameter sets generated during calibration. Because the parame- a Range of input data. ter sets were generated during the optimisation search process, b Range of values of model variables during best fit simulation. they are not fully random or independent, but tend to be S.J.R. Woodward et al. / Journal of Hydrology 505 (2013) 299–311 305
Table 2 Model parameters.
Symbol Fit constraint Units Best fit value Mean (±s.d.)a Model parameters 1 Maximum infiltration to soil water RW,max 10–110 mm d 86 85 (±3) Rainfall bypass fraction b 0-0.1 – 0.0068 0.0090 (±0.0016)
Soil water holding capacity Wmax 100-300 mm 204 202 (±5) 1 Maximum infiltration to vadose zone RV,max 10–70 mm d 35 39 (±5) 1 Near-surface discharge rate aN 0.1-10.0 d 0.93 1.11 (±0.22) 1 Vadose zone discharge rate aV 0.1-10.0 d 5.5 5.4 (±1.1) 1 Fast groundwater parameter aF 0-0.2 d 0.085 0.084 (±0.002) 1 Slow groundwater parameter aS 0-0.01 d 0.0015 0.0018 (±0.0004)
Fraction recharge to slow groundwater fs 0-0.2 – 0.18 0.17 (±0.01) 1 Near-surface nitrate-N CN 0.0–10.0 mg L 7.25 7.4 (±0.4) 1 Fast groundwater nitrate-N CF 0.0–10.0 mg L 4.76 4.6 (±0.1) 1 Slow groundwater nitrate-N CS 0.0–10.0 mg L 0.05 0.06 (±0.03)
a Mean and standard deviation (s.d.) of parameter values in near-optimal parameter sets.
Table 3 The uncertainty of these fluxes was assessed using the method Number (n), mean and standard deviation (s.d.) of the two time series datasets used described in the previous section. in model calibration (1 April 2007–31 March 2011). NSEj is the calibrated Nash– Sutcliffe Model Efficiency for each variable.
Observation dataset (j) n Mean s.d. Range NSEj 3. Results and discussion Stream flow (mm d 1) 1461 1.37 2.61 0.008–33.76 0.90 1 Nitrate-N concentration (mg L ) 47 1.94 2.01 0.001–6.96 0.84 3.1. Model structure
Early simulations using the model found that the exact routing correlated. Nevertheless, they do provide the basis for a simple of the water reservoirs (in particular, using one or two groundwa- uncertainty calculation. ter reservoirs) made little difference to its ability to predict stream Parameter uncertainty was therefore estimated by calculating flow alone. Some improvement in low flow prediction was the mean and standard deviation of the parameter values in the achieved by including ‘‘bypass’’ flow, which allowed the model to behavioural parameter sets. Parameters with a low standard devi- reproduce the small transients observed in summer flow rates in ation were interpreted as being more reliably estimated (because response to even small rainfall events. However, as found by Kirch- they converged to a narrow value range), while the values of those ner (2009), overall model fit was only marginally improved. Mod- with high standard deviation were interpreted as being more elling of precipitation falling directly into the stream channel, uncertain (because they did not converge towards a narrow range). which has been found by other authors to be a significant driver The same analysis was carried out on the model outputs (e.g. of stream response (Weiler and McDonnell, 2007), was also tested, annual fluxes), to yield a mean and standard deviation value for but resulted in unrealistically variable stream flow response. each. Inclusion of a second ‘‘slow’’ groundwater reservoir was moti- vated by a desire to simulate the observed seasonal patterns of stream nitrate concentration, which was not possible when a sin- 2.6. Annual flux calculations gle groundwater reservoir with constant nitrate concentration was used. In this two reservoir model, the fast groundwater pro- As well as simulating daily stream flow and concentration, the vides the dynamics of short term stream flow responses, while model can be used to calculate catchment scale fluxes on an annual the slow groundwater provides the underlying base flow. In this basis. By accumulating the discharge and solute loads in Eqs. (12) way, seasonal changes in the balance between fast flow and base and (13) through time, average annual water discharge and nitrate flow explain the annual cycle of wet season and dry season nitrate load to the stream were calculated for each reservoir. The number concentrations in the stream. Conversely, the stream nitrate con- of days for which the near-surface, fast groundwater and slow centration data are necessary to determine the different hydraulic groundwater, respectively, provided the majority of the discharge parameters of the fast and slow groundwater reservoirs. was also recorded. In reality, there exists a continuum of flow paths with different Along with annual nitrate loads, estimates were made of nitrate characteristic response times and chemical signatures. Dating of attenuation along the various flow paths. It was assumed that CN Toenepi Stream water revealed a continuous variation of mean res- represented the nitrate concentration in water leached below the idence time with stream flow rate. Mean transit times were 2– root zone, CN–CF the nitrate reduction in the fast groundwater 5 years during high baseflow conditions in winter, increasing to zone, and CF–CS further reduction in the slow groundwater zone. 30–40 years as baseflow decreases in summer, and then to more Multiplying the reduction in nitrate concentration by the annual than 100 years during drought conditions (Morgenstern et al., water flux through each groundwater reservoir allowed annual ni- 2010). Despite this evidence for a continuum, our hypothesis trate reduction in each reservoir to be estimated. was that the simplified two reservoir model may be adequate to
Table 4
Data used in model evaluation (1 April 1995–31 March 1997). NSEX,j is the cross-validation efficiency, NSEj is the fitted efficiency.
Cross-validation data set (j) n Mean s.d. Range NSEX,j NSEj Stream flow (mm d-1) 474 2.16 3.50 0.03–28.28 0.68 0.70 Nitrate-N concentration (mg L-1) 101 2.30 1.71 0.00–5.95 0.54 0.74 306 S.J.R. Woodward et al. / Journal of Hydrology 505 (2013) 299–311 represent the overall physical structure of the catchment’s ground- 100 water system.
) 10
3.2. Model calibration -1
A good calibration was obtained to both stream flow and nitrate 1 concentration. The calibrated model efficiency values (NSEj, Table 3) indicate that the model was simultaneously able to reproduce 90% and 84% of the variation in each of the data sets 0.1 respectively. The ranges of values of the model variables are given in Table 1, and the calibrated values of the model parameter in Table 2. Stream flow model (mm d 0.01
3.2.1. Calibration to stream flow Fig. 4 shows the observed and modelled stream flow on linear 0.001 and log scales. On the linear scale, the model hydrograph matches 0.001 0.01 0.1 1 10 100 the observed flow very well, and without obvious bias. On the log Stream flow data (mm d -1) scale, however, it is apparent that the model was less able to accu- rately reproduce low flow patterns. Fig. 5 demonstrates that the Fig. 5. Calibration of the model to Toenepi Stream flow and nitrate data (log–log calibrated model fits well for flows above 1.0 mm d 1, underpre- scale) collected at the Tahuroa Road bridge. Only stream flow shown. dicts flows in the range 0.1–1.0 mm d 1, and overpredicts flow less than 0.1 mm d 1 (see also Fig. 4b). Poor low flow predictions are often observed in flow calibrations (Wöhling et al., 2013), partly still occasionally discharged in summer (Fig. 7), slow groundwater because calibration to untransformed stream flow gives relatively discharge is simulated at an unrealistically high level (Fig. 4b) in less weight to low flow periods. However, the main cause of low order to maintain low stream nitrate concentrations. This artefact flow overprediction in our study was inclusion of the nitrate data may be a result of our assumptions of constant groundwater ni- in the calibration. The results of calibration to log transformed trate concentrations and/or negligible in-stream nitrate attenua- stream flow data alone do not exhibit these biases (Fig. 6). tion. A closer consideration of the shallow groundwater data The poor simulation of very low flows in the combined calibra- (Fig. 2) raises the possibility that while the nitrate gradient may tion originate in the need for the model to simulate the very low remain relatively stable with time at a given depth below ground stream nitrate concentrations observed in summer (Fig. 8). Since level, the average nitrate concentration of the shallowest ground- fast groundwater, with relatively higher nitrate concentration, is water might vary seasonally as the water table rises and falls
30 100 (a) Observed streamflow 25 Predicted total discharge (a) )
-1 10 20 ) -1
15 1
10 0.1 5 Stream flow (mm d
0 Stream flow (mm d 0.01 Observed streamflow -5 Predicted total discharge 0.001 Jul-11 Jul-10 Jul-09 Jul-08 Jul-07 Oct-10 Oct-09 Oct-08 Oct-07 Apr-11 Apr-10 Apr-09 Apr-08 Apr-07 Jan-11 Jan-10 Jan-09 Jan-08 Jan-07 Jul-07 Jul-08 Jul-09 Jul-10 Oct-07 Oct-08 Oct-09 Oct-10 Apr-07 Apr-08 Apr-09 Apr-10 Apr-11 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11
100 (b) 100
) (b) )
10 -1
-1 10
1 1
0.1 0.1
Stream flow (mm d 0.01 Observed streamflow 0.01 Predicted total discharge 0.001 Stream flow model (mm d 0.001 0.001 0.01 0.1 1 10 100 Jul-10 Jul-09 Jul-08 Jul-07 Oct-10 Oct-09 Oct-08 Oct-07 Apr-11 Apr-10 Apr-09 Apr-08 Apr-07 Jan-11 Jan-10 Jan-09 Jan-08 Jan-07 Stream flow data (mm d-1) Fig. 4. Comparison of measured and modelled stream flow at the Tahuroa Road bridge, on (a) linear, and (b) log scales. Model simultaneously calibrated for stream Fig. 6. Calibration of the model to log transformed Toenepi Stream flow data only, flow and nitrate concentrations. showing (a) hydrograph on log scale, and (b) model-data scatter on log–log scale. S.J.R. Woodward et al. / Journal of Hydrology 505 (2013) 299–311 307
2.0 10 NS flow (a) Nitrate Data ) 1.8 Fast GW 9 -1 Slow GW Nitrate Model 1.6 8 1.4 7 1.2 6 1.0 5 0.8 4 0.6 3 0.4 Stream nitrate (ppm) 2
Stream flow model (mm d 0.2 1 0.0 0 Jul-07 Jul-08 Jul-09 Jul-10 Oct-07 Oct-08 Oct-09 Oct-10 Apr-07 Apr-08 Apr-09 Apr-10 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 Jul-07 Jul-08 Jul-09 Jul-10 Oct-07 Oct-08 Oct-09 Oct-10 Apr-07 Apr-08 Apr-09 Apr-10 Apr-11 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11
(b) 100% Fig. 8. Comparison of the calibrated model to Toenepi Stream nitrate data collected at the Tahuroa Road bridge.
80%
60% flow conditions. Ideally, much more frequent stream concentration data should be available to robustly calibrate this highly dynamic 40% system. Data presented by other authors show that in-stream nutrient concentrations can change rapidly on a daily scale (Heath- 20% NS flow waite, 2010; Hesser et al., 2010; Aubert et al., 2013), whereas less
Stream flow model (%) Fast GW Slow GW frequent data may give the impression that changes only occur on
0% a seasonal basis (Wilcock et al., 2006; Glavan et al., 2011; Lam et al., 2012). As this model is designed to be applied to catchments pr-07 pr-08 pr-09 pr-10
Jul-07 Jul-08 Jul-09 Jul-10 which are relatively data poor, reliable calibration of storm flow Oct-07 Oct-08 Oct-09 Oct-10 A A A A Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 events will frequently not be achievable with available data sets. Fig. 7. Modelled stream flow contributions from near-surface (NS), fast ground- Development of cost-effective, in-stream nitrate sensors for high- water and slow groundwater reservoirs, (a) truncated at 2 mm d 1, to illustrate the resolution measurements would help overcome this challenge. seasonality of slow groundwater discharge, and (b) displayed as percentages of total flow. The above results illustrate the ability of this simple, lumped catchment model to reproduce the complex patterns of stream flow and chemistry observed in the catchment. Assigning constant (above the well screen), rising in winter as increasing amounts of nitrate concentrations to the three reservoirs discharging into the oxidised, nitrate bearing water are recharged, and falling in summer stream (Fig. 3) is a simplification, particularly in the more dynamic as this oxidised water is depleted, resulting in the discharge of a NS and fast groundwater reservoirs. As evident in the vertical pro- greater proportion of reduced, low nitrate groundwater. Addition- files shown in Fig. 2, measured groundwater nitrate concentrations ally, the extremely low stream nitrate concentrations observed in are highest near the water table and decrease drastically with summer may be a consequence of reduced flow and increased biotic increasing depth. These strong gradients at shallow depth, as well uptake in summer, as the stream typically becomes very sluggish, as the nitrate load calculations reported in Section 3.6, indicate warm and choked with weeds at this time of year. These possibilities that nitrate concentrations are reduced by denitrification occurring will need to be considered in future applications of the model. within the depth range of the fast (shallow) groundwater reservoir. Under the highest water table conditions in winter, this reservoir is 3.2.2. Relative contributions of different flow paths at its maximum and considered to be dominated by well-oxidised Model analysis allows separation of stream flow into its fresh recharge with high nitrate concentrations. As this reservoir is constituent sources. Fig. 7a shows the contributions of stream flow gradually depleted due to ongoing discharge into the stream, its generated by the different water reservoirs, and Fig. 7b expresses average nitrate concentration is thought to decrease, as denitrifica- this on a percentage basis. Notably, summer flow is dominated tion in the deeper part of the fast groundwater reservoir has a by discharge from the slow groundwater reservoir, even though stronger effect on the average nitrate concentration when the its flow contribution is only 15% on an annual basis. In contrast, water table drops in spring and summer. We consider this mecha- the 5% contribution of overland/near-surface (NS) flow is barely nism the reason for the model’s tendency to underestimate the discernable on an annual basis, as it only contributes to total stream nitrate concentrations under high flow conditions in winter stream flow during a few major storm events (these can be identi- and overestimate them during the lowest flows in summer (cf. fied as spikes descending from the top of Fig. 7b). Fig. 8). While the simplified assumption of constant concentrations 3.2.3. Calibration to stream chemistry does not allow us to describe this fine detail, the quite respectable The seasonal change between fast groundwater and slow Nash–Sutcliffe Model Efficiency (NSE) values demonstrate that the groundwater discharge dominance in Fig. 7 is the basis for the seasonal pattern of stream nitrate concentrations can largely be stream chemistry dynamics of the model. This simple approach as- explained by the changing dominance of discharge from the fast sumes constant solute concentrations in the discharge from each versus slow groundwater reservoirs (Table 3; Figs. 7 and 8), with- reservoir, yet generates complex seasonal patterns of stream out the need to consider the temporal dynamics of nitrate leaching, chemistry that broadly match the sample data (Fig. 8). denitrification or in-stream attenuation. Good reproduction of Stream nitrate concentrations under storm flow conditions, stream flow and nitrate concentrations also provides a sound basis indicated by spikes in Fig. 8, could not be reliably estimated, due for the calculation of annual water and nitrate fluxes, which are the to the scarcity of available stream concentration data under storm key results of this study, and are described in more detail below. 308 S.J.R. Woodward et al. / Journal of Hydrology 505 (2013) 299–311
3.3. Model evaluation 10 9 Nitrate Data Nitrate Model Following calibration, the model was cross-validated to data for 8 the period 1 April 1995–31 March 1997 (Table 4), as described 7 above. The predictions of stream flow are shown in Fig. 9, and of 6 stream nitrate in Fig. 10. 5 The resulting cross-validation model efficiency values (0.68 and 0.54 respectively, Table 4) were somewhat lower than the equiva- 4 lent calibration values (0.90 and 0.84 respectively, Table 3). These 3 poorer fits may be partly explained by differences in the climate Stream nitrate (ppm) 2 and land use practices between the two data sets. 1 The stream nitrate data (Fig. 10) followed a similar pattern to 0 that in the calibration period (Fig. 8). Stream nitrate again varied pr-96 pr-95 Jul-96 seasonally through the year, and the measurements were statisti- Jul-95 Oct-96 Oct-95 A A Jan-97 Jan-96 Jan-95 cally well matched by the model at most times (Table 4). There was no rainfall event large enough to generate overland/near-sur- Fig. 10. Cross-validation of the model to Toenepi Stream nitrate data. face flow during this period, which explains the absence of the near-surface spikes observed in Fig. 8. The more frequent sampling rithm. Examination of the parameter sets generated during an during this period (weekly, as opposed to monthly in Fig. 8) draws extended calibration (300 search generations) indicated that attention to several periods where the model consistently under- near-optimal parameter values (as defined above) did not change or over-predicted stream nitrate concentration, and winter con- significantly, and the standard deviations of parameter values in centrations seem somewhat higher during this period than they near-optimal parameter sets declined only slowly, after the first were in 2007–2011. This can probably be explained by the sharp 100 search generations. This indicated that, for this model, 100 decline in dairy effluent discharge to the stream between 1995 search generations was sufficient to give reliable parameter values and 2003, as noted by Wilcock et al. (2006), and the concomitant and uncertainty estimates. increase in effluent treatment by irrigation to pasture. In broad terms, parameters which did not converge to a well de- Following cross-validation analysis, the model was calibrated to fined value had standard deviations that were greater than 20% of the 1995–1997 data series to determine whether the goodness of their means (i.e. coefficient of variation (CV) greater than 20%), fit could be greatly improved. Compared with the cross-validation indicating that the calibration target was insensitive to their value. statistics (NSEX,j in Table 4), calibration gave a slightly better fit to Four parameters were uncertain in this respect: rainfall bypass stream flow, but a much better fit to nitrate (0.70 and 0.74 respec- fraction (b), maximum infiltration to the vadose zone (RV,max), tively, Table 4). The more significant improvement in stream ni- near-surface discharge rate (aN) and vadose zone discharge rate trate calibration can be attributed to changes in effluent (aV). The insensitivity of these parameters is easily explained. First, management, and thus direct stream contamination, between the rainfall bypass fraction (b) improves the model predictions of low two periods. flow rates, as shown in Fig. 6a. Since the calibration was to untransformed stream flow only, this had little effect on the flow objective function. Inclusion of a log-transformed flow objective 3.4. Uncertainty analysis function would help identify this parameter, as indeed is recom- mended (Wöhling et al., 2013). Second, maximum infiltration to The mean and standard deviations of parameter values that the vadose zone (RV,max) influences surface runoff under high rain- gave near-optimal calibration (i.e. that were ‘‘behavioural’’ param- fall intensity events. As there are relatively few high intensity eter sets) are listed in the right hand column of Table 2. These re- events in the calibration period, the precise value of this parameter flect how identifiable the different parameters are. In general the therefore has relatively little impact on the overall flow calibration. standard deviations are relatively small. Caution must be exer- Third, the calibrated values of near-surface discharge rate (aN) and cised, however, as the parameter values are not sampled entirely vadose zone discharge rate (aV) are both fast relative to the model at random, but are generated during a genetic algorithm search. time step of one day. It is to be expected that sub-daily processes As the genetic algorithm narrows down its search, the sampled val- would be relatively poorly identified by the calibration process. ues of well identified parameters become increasingly narrow, Two other parameters had CV greater than 20%; these were the leading to low standard deviations as a result of the search algo- slow groundwater response rate (aS) and the slow groundwater ni- trate concentration (CS). However, in the case of these two param- 1000 eters the high CV was primarily due to their low absolute values, which tends to exaggerate their perceived uncertainty. In fact the 100 absolute values of these parameters were well identified. This )
-1 highlights that the CV should not be used alone to evaluate the 10 uncertainty of parameter values. By contrast, even though only a single storm event nitrate sam- 1 ple (on 16 April 2008, Fig. 7) was available to estimate near-surface
nitrate concentration (CN), the value of this parameter in Table 2 0.1 appears relatively well defined. The calibration process assumes
Stream flow (mm d that the data is accurate and representative, which may not be 0.01 Observed streamflow the case in reality. This highlights the importance of understanding Predicted total discharge data quality (and treatment of their uncertainty), and of careful 0.001 interpretation of computational results. Accurate estimation of parameters in a dynamic model requires that the calibration data Jul-95 Jul-96 Oct-95 Oct-96 Apr-95 Apr-96 Jan-95 Jan-96 Jan-97 provide a good representation of the system across its range of re- Fig. 9. Cross-validation of the model to Toenepi Stream flow data (log scale). sponse, e.g. flow and chemistry data are required in both storm and S.J.R. Woodward et al. / Journal of Hydrology 505 (2013) 299–311 309 drought conditions. The lack of stream chemistry data during the balance between inflow and outflow, with no preset upper lim- storm events in the Toenepi data consequently precluded accurate it. Therefore, the peak storage over the four-year simulation is re- estimates of near-surface nitrate concentration. This highlights the ported as an estimate of the maximum dynamic storage in each need for development of cost-effective, in-stream chemistry sen- reservoir. sors for high-resolution measurements. The total dynamic storage in the two groundwater reservoirs In terms of hydrological characteristics, the response parame- was estimated to be 126.1 (±12.7) mm (Table 5). This compares ters for the four main water reservoirs; near-surface (aN), vadose with 1020 mm groundwater storage estimated by Morgenstern zone (aV), fast groundwater (aF) and slow groundwater (aS); were et al. (2010) in the same catchment, using tracer analysis. The dis- of particular interest (Table 2). When these were converted to re- crepancy between hydrological- and tracer-based estimates is not sponse times, the mean and standard deviation of the hydrody- uncommon, and may be explained by the existence of a large pas- namic responses of the water reservoirs were TN = 0.92 ± 0.14 d, sive storage component, typically an order of magnitude larger TV = 0.19 ± 0.03 d, TF = 4.0 ± 0.1 d, and TS = 195.9 ± 44.1 d (Table 5). than the active water component. Passive storage plays little part As expected, rainfall entering the stream from surface runoff pro- in hydrodynamics, but makes a significant contribution to ground- duces a response within a day (TN), and rainfall recharge to ground- water chemistry via mixing exchange (Birkel et al., 2011; Soulsby water produces a response within a few days (TV + TF). On the other et al., 2011). hand, the slow groundwater reservoir produces a much more damped response, in the order of a year (T ), which essentially pro- S 3.6. Annual nitrate–nitrogen fluxes vides a ‘‘base flow’’ effect that is not simulated in single reservoir models. Note that these are not transit times of water or solute, The estimated near-surface nitrate-nitrogen concentration of but hydrodynamic response times (i.e. times required for pressure 7.42 (±0.41) mg L 1 (Table 6) lies within the range of 7–11 mg L 1 responses to travel through the reservoir). The present model does calculated for leachate from dairy farms in the catchment using not explicitly model solute transport processes or allow transit the OVERSEER nutrient budgeting model (Wheeler et al., 2006; times to be calculated (as mentioned above, these are many times Stenger et al., 2008). Assuming that this represents the nitrate- larger than hydrodynamic response times). nitrogen concentration in leachate draining from the root zone, A more robust formal uncertainty analysis using Markov Chain an average nitrate-nitrogen yield across the catchment of 40.19 Monte Carlo (MCMC) methods (e.g. Wöhling and Vrugt, 2011; (±2.15) kg ha 1 y 1 can be calculated (by multiplication by the Wöhling et al., 2012) could be adopted to support our findings. annual discharge, 541.4 (±6.0) mm y 1, Table 5). If no attenuation These methods can also treat measurement uncertainty, but come occurred along the water flow paths between the bottom of the at a higher computational burden, and are thus beyond the scope root zone and the groundwater discharge into the stream, the of this study. resulting total catchment load would therefore amount to 60.69 1 (±3.25) t NO3–N y . 3.5. Annual water fluxes However, the lower nitrate–nitrogen concentrations estimated for the groundwater reservoirs (Table 6) relative to the near-surface The average annual discharges from each reservoir were calcu- and OVERSEER estimates, and in line with the earlier groundwater lated for the calibrated model, and are summarised in Table 5. The investigations (described in Section 2.1), demonstrate that attenua- variation in these figures was calculated using the same method as tion is taking place within the groundwater reservoirs. The effective the uncertainty analysis; calculations were done for each of the average nitrate-nitrogen yield across the catchment derived from near-optimal/behavioural parameter sets (as defined above), and the fitted model is only 22.06 (±0.65) kg ha 1 y 1 and the total 1 the mean and standard deviation of the results was reported. catchment load 33.31 (±0.98) t NO3–N y , which equates to an Over the period 1 January 2007–31 March 2011, overland/near- overall nitrate attenuation of 44.9% (±3.4%) (Table 6) (this value is surface, fast groundwater and slow groundwater were estimated to slightly different from that which would be obtained by comparing contribute 4.9%, 80.5% and 14.5% of annual flow respectively the mean fluxes directly, because it is the average percentage atten- (Fig. 7a). On a time-basis, overland/near-surface flow was the dom- uation calculated from a large number of model runs). inant contributor to stream flow on only 0.8% of days, compared In spite of accounting for 90.8% (±2.5%) of the nitrate-nitrogen with 38.6% for fast groundwater and 60.6% for slow groundwater discharge into the stream (Table 6), the fast groundwater reservoir (Fig. 7b). Despite its low discharge rate, therefore, the slow ground- also accounts for 80.0% (±3.3%) of total attenuation, equating to water reservoir plays a very significant role in determining stream 36.0% (±4.0%) of the potential load. This finding indicates that condi- water quality during the summer season. tions conducive to denitrification not only occur in the slow ground- Table 5 also reports the estimated dynamic storage in each res- water reservoir deemed to reside in the older argillised volcanic ash ervoir. This is the fraction of the reservoir that fills and empties as beds, but also in the overlying much more friable younger ones. part of the hydrodynamics of the catchment (which may be only a Since low nitrate–nitrogen concentrations in the slow ground- small fraction of the water physically present). Apart from soil water reservoir may be attributable to groundwater recharged water (W), which has a maximum storage limit of Wmax, dynamic prior to agricultural land use rather than denitrification, denitrifi- storage in the other model reservoirs (V, N, F, S) is determined as cation estimates in this reservoir can be considered as upper
Table 5 Estimated hydrodynamic response time, discharge, and dynamic storage of water reservoirs from 1 April 2007–31 March 2011. Mean and standard deviations are calculated as described in the uncertainty analysis section.
Characteristic response time (d) Annual discharge (mm y 1) Annual discharge (%) Dominant days (%) Dynamic storage (mm) Soil water 202.0 (±4.6) Near-surface flow 0.92 (±0.14) 26.7 (±7.3) 4.9 (±1.4) 0.8 (±0.1) 16.7 (±3.8) Vadose zone 0.19 (±0.03) 7.4 (±1.4) Fast groundwater 4.0 (±0.1) 436.0 (±10.6) 80.5 (±1.9) 38.6 (±1.0) 50.1 (±3.2) Slow groundwater 195.9 (±44.1) 78.7 (±7.1) 14.5 (±1.3) 60.6 (±0.9) 76.0 (±12.2) Total 541.4 (±6.0) 100.0 100.0 310 S.J.R. Woodward et al. / Journal of Hydrology 505 (2013) 299–311
Table 6 Estimated nitrate yield and estimated attenuation of water reservoirs from 1 April 2007–31 March 2011. Mean and standard deviations are calculated as described in the uncertainty analysis section.
Nitrate-N concentration Nitrate-N yield Nitrate-N yield Nitrate-N attenuation Nitrate-N attenuation (mg L 1) (kg ha 1 y 1) (%) (kg ha 1 y 1) (%)b Near-surface 7.42 (±0.41) 1.99 (±0.57) 9.0 (±2.5) –a –a flow Fast groundwater 4.66 (±0.12) 20.02 (±0.70) 90.8 (±2.5) 14.56 (±2.41) 36.0 (±4.0) Slow 0.06 (±0.03) 0.05 (±0.02) 0.2 (±0.1) 3.57 (±0.37) 8.9 (±1.1) groundwater Total 22.06 (±0.65) 100.0 18.13 (±2.34) 44.9 (±3.4)
a Nitrate attenuation in near-surface flow is assumed to be zero. b Percentage of total catchment input yield (estimated to be 40.19 (±2.15) kg ha 1 y 1). bounds only. Due to its low contribution to stream flow, nitrate taining the minimum period and frequency of catchment data re- attenuation in the slow groundwater reservoir accounts for a max- quired for meaningful analysis. imum of 8.9% (±1.1%) of the potential load, notwithstanding the very low nitrate–nitrogen concentrations estimated for this reservoir. Acknowledgements The identification of fast, shallow groundwater as the main source of both nitrate discharge and nitrate attenuation has been This work was funded under the New Zealand Foundation for previously made by several other authors, applying more complex, Research, Science and Technology ‘‘Groundwater Quality’’ distributed models, mainly in Europe. Lam et al. (2012), for exam- (LVLX0302) and ‘‘Groundwater Assimilative Capacity’’ ple, using the SWAT model in a lowland agricultural catchment in (C03X1001) contracts. Aaron Wall, Juliet Clague and Brian Moor- Northern Germany, estimated that shallow groundwater discharge head are thanked for their excellent technical support. Thanks to contributed 93% of stream nitrate-nitrogen load, compared with 7% Bob Wilcock (NIWA) for making flow and in-stream nitrate con- from near-surface or overland flow, values which are similar to our centration data available. Helpful feedback by Thomas Wöhling, results. As in our study, stream nitrate load was high in winter, low Lee Burbery (ESR) and two anonymous reviewers substantially im- in summer, and dominated by shallow groundwater discharge at proved this manuscript. all times. Regarding denitrification, Conan et al. (2003), modelling a small References catchment in Brittany using SWAT-MODFLOW-MT3D and assum- ing first order reaction rates, estimated 65% removal of nitrate in Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration– the subsurface. Wriedt and Rode (2006), using a more detailed guidelines for computing crop water requirements–FAO irrigation and reaction model in MODFLOW-RT3D to simulate nitrate transport drainage paper 56. FAO: Food and Agriculture Organization of the United Nations, Rome.
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