Ecological Modelling 114 (1999) 235 – 250
Nitrogen source apportionment—a comparison between a dynamic and a statistical model R. Lide´n a,*, A. Vasilyev b, P. Sta˚lnacke c, E. Loigu b, H.B. Wittgren a b
a Swedish Meteorological and Hydrological Institute, SE-601 76 Norrko¨ping, Sweden Department of En6ironmental Engineering, Tallinn Technical Uni6ersity, Jar6e6ana tee 5, EE-0001 Tallinn, Estonia c ˚ s, Norway Jordforsk–Centre for Soil and En6ironmental Research, N-1432 A
Accepted 29 July 1998
Abstract A dynamic model, HBV-N, and a statistical model, MESAW, for nitrogen source apportionment were compared regarding model performance, model uncertainty and user applicability. The HBV-N model simulates continuous series of nitrogen concentrations with meteorological data and sub-basin characteristics as input. Diffuse nitrogen emissions are defined as regional model parameters which are calibrated by comparison of observed and simulated nitrogen data. The MESAW model uses nitrogen loads for a fixed time interval at each monitoring site as response variable and sub-basin characteristics as explanatory variables to estimate diffuse nitrogen emissions through non-linear regression analysis. The two models were applied in the Matsalu Bay watershed (3640 km2) in Estonia and the same land use and point sources data were used as input. Both models gave similar levels of diffuse total nitrogen emissions and retention rates, which also fit well with previous estimates made in Estonia and Scandinavia. A sensitivity analysis of the model parameters also showed similar uncertainty levels, which indicated that the model uncertainty was more dependent on the availability of nitrogen data and land cover distribution than the choice of model. Furthermore, the sensitivity analysis showed a parameter interdependency in both models, which implied the risk of compensation between estimated diffuse emissions and retention. In conclusion, however, the study showed that both models were capable of estimating nitrogen leakage from the dominating land classes and giving reliable source apportionment from the available input data. The study indicated that the HBV-N model has its advantage in assessments where detailed outputs are needed and when run-off data are limited, while the statistical MESAW model has its advantage in extensive studies since it is easily applied to large watersheds that have dense monitoring networks. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Nitrogen source apportionment; Modelling; Water management
* Corresponding author. Tel.: +46-11-4958582; fax: + 46-11-4958001; e-mail:
[email protected] 0304-3800/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S0304-3800(98)00146-X
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1. Introduction Nitrogen source apportionment has normally been performed through inventories of point and diffuse sources (Fleischer and Hamrin, 1988; Lo¨fgren and Olsson, 1990; TTU and SEPA 1995). Areal nutrient leakage from soil is estimated from upscaling of plot experiments or through modelling of the upper soil layer (Johnsson et al., 1987; Jones et al., 1991). Geographical Information Systems (GIS) are often used to perform regional assessments (Jordan et al., 1994). An alternative approach is source apportionment based on statistical analysis of observed river nutrient transport. This methodology can be divided into two categories: regression analysis between observed concentration and water discharge (Behrendt, 1993; Tonderski et al., 1997), and regression analysis between observed load and watershed characteristics (Dillon et al., 1991; Grimvall and Sta˚lnacke, 1996). Recently another alternative of source apportionment has become available because dynamic process based models have been successfully applied in large watersheds (Lunn et al., 1996; Wittgren and Arheimer, 1996; Arheimer and Brandt, 1998). Dynamic models, which conceptually describe all physical, chemical and biological processes, aim to simulate time series of nutrient transport at the watershed outlet. Source apportionment is a parallel result even if the main purpose of these models is usually prediction or better understanding of processes. For large scale water management, all the above mentioned methods are potential tools that give results of different temporal and spatial scales. The different methods, however, also have a large variety of input demands in the form of data and work. For decision makers and scientists faced with a specific water management problem, it is therefore essential to choose a method which meets the often limited available input data, gives the wanted results, and is economically feasible. Unfortunately, comparable studies of different methods and models for nitrogen source apportionment are scarce. Model applications are often performed and described for specific watersheds,
where other models have not been applied. Continuous changes in land use and agricultural practices also prevent fair comparison, even if models are applied in the same watersheds but on different occasions. The main purpose of the present study was therefore to compare two structurally different models regarding model performance, model uncertainty and user applicability. A dynamic model (HBV-N) and a statistical model (MESAW) are presented and a comparison is made through a case study in Estonia, where both models were applied in the same watershed with essentially the same input data. The results of the two models are presented and the advantages and disadvantages of the two model approaches are discussed.
2. Study area and data base The study was done in the Matsalu Bay watershed in SW Estonia (Fig. 1). The total drainage area, which can be characterised as a large flat lowland, is 3640 km2 (TTU and SEPA, 1995). The population density is relatively low, 11 inh/km2 and settlements only cover a small part of the watershed. Land use classification (Table 1) was based on remote sensing (Nisell et al., 1993). The dominating land cover classes are forests and transitional woodlands (58%), arable land (19%), pasture (11%) and bogs (9%). Lake area is close to zero but the river network is dense. Drainage systems are common and many river courses have been artificially changed (TTU and SEPA, 1995). Annual run-off and pollutant load are characterised by a pronounced peak during the time of snow melt in spring. Monthly water quality sampling data of total (Tot-N), inorganic (Inorg-N) and organic (Org-N) nitrogen from 11 sites (Fig. 1) were used in the present study. The chosen sites cover 3225 km2 or approximately 90% of the total Matsalu Bay watershed. During the period 1993–1994, monthly sampling was made at the 11 sites except during spring time when three samples per month were taken. Monthly sampling data for 1992 and 1995 were also available at four of the sites, Kasari,
392 12.2
1505 46.9
26 46 61 273 228 359 52 246 111 55 56
Forest (km2)
The annual Tot-N load was based on the year 1994.
614 19.1
Total %
Pasture (km2)
13 12 10 72 73 88 11 49 27 19 20
Arable (km2)
Rapla 22 Kodila 32 Valgu 18 Teenuse 86 Konuvere 124 Va¨ngla 143 Vanamo˜isa 18 Kasari 80 Liivi 47 Tuudi 20 Rannamo˜isa 25
Sub-basin
358 11.1
5 6 28 129 29 33 4 19 10 51 46
Trans. woodland (km2)
301 9.4
3 5 20 15 18 85 9 55 48 39 4
Bog (km2)
— —
73 111 74 373 600 578 77 1882 187 124 158
35388 —
10330 4110 380 4810 3090 7220 750 970 2500 1108 120
Tot-N load Urban point (103 kg year−1) sources (kg year−1)
24250 —
1050 1550 1300 4300 4250 4650 350 2500 1750 1500 1050
Rural inhabitants (Pers.)
30150 —
1050 1300 850 4750 5900 6950 850 3850 2200 1100 1350
Animal units (km−2)
Table 1 Land cover distribution (Nisell et al., 1993), urban point sources (Eesti veemajanduse, 1994), annual Tot-N load at outlet of sub-basin and estimated number of rural inhabitants and animal units in the Matsalu Bay watershed
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Tuudi, Liivi and Rannamo˜isa. Only one of the sites, Kasari, has a long series, 1985 – 1995, of water quality data. Sampling and chemical analyses were done by the Estonian Meteorological and Hydrological Institute (EMHI) up to 1992 and were then continued by the Tallinn Technical University (TTU).
Run-off data from five hydrological stations, precipitation data from five rainfall gauges and temperature data from four meteorological stations were available for the Matsalu Bay watershed. Daily hydrometeorological data for the period 1985–1995 were retrieved from the EMHI. Information about emissions of nutrients from
Fig. 1. The study area, Matsalu Bay watershed (3640 km2), in Estonia. The light grey area shows the sub-basins for the nitrogen sampling sites, which cover approximately 90% of the watershed.
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Fig. 2. The basic structure of the HBV-N model for Matsalu Bay watershed. Free model parameters are given in italics.
point sources was gathered from the Estonian Environmental Information Centre (Eesti veemajanduse, 1994).
3. The HBV-N model
3.1. Model structure Following the classification of ecological models (Jørgensen, 1994) the HBV-N model can be defined as a deterministic, holistic and dynamic model. Model inputs are causally related to the outputs through simple equations that conceptually describe the major processes in water and nitrogen transport. Free model parameters are empirically determined through calibration against observed data. The model is run with a daily time step in a distributed mode with subbasins as the basic unit. The base consists of the hydrological model HBV, (Bergstro¨m, 1976; Lindstro¨m et al., 1997), which produces hydrological input data to the nitrogen module. Daily input
data from the hydrological model are for each sub-basin; areal temperature, recharge from the unsaturated soil zone, local water volume and river run-off. The nitrogen module of the HBV-N model has been developed during several studies and is well described in previous literature (Brandt, 1990; Arheimer and Wittgren, 1994; Arheimer and Brandt, 1998). Nitrogen is routed from the root zone to the outlet of the watershed studied, including point sources contributions and biochemical transformation. Inorg-N and Org-N are modelled separately. The key equation, which is solved for local water (groundwater, small streams, ditches and ponds) and river water separately, is: d(cV) = cinVin + P+ D−R(c)− cVout(V) dt
(1)
where c is nitrogen concentration; V is water volumes; t is time; P is point sources; D is atmospheric deposition on open water bodies; R is retention of nitrogen due to biochemical transformation.
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The retention of nitrogen is described through lumped estimates of all chemical and biological processes. Inorg-N retention is estimated to be linearly dependent on the mean temperature for the last ten days, while organic transformation is dominated by a biological production (Arheimer and Brandt, 1998). The retention of nitrogen is, for each time step, applied to a fixed volume, thus taking water retention time into account. In the local sub-basin water storage, which includes groundwater, the fixed volume represents open water in ponds, ditches and small streams where biochemical processes are assumed to occur. The nitrogen module of HBV-N used in the present study (Fig. 2) is similar to the model applied in Sweden by Arheimer and Brandt (1998). The main differences are: Root zone leakage concentrations were described through free parameters. In the Swedish model applications, root zone leakage data were available, estimated from plot experiments or from modelling of the upper soil layer (Johnsson and Hoffman, 1998). In the Matsalu Bay watershed these data were, however, not available, which forced the modifica-
Rinorg = k1,inorgTmean10cinorg
k2 + mQ 0.6 +
R2 (%)
Relative accumulated difference (%)
Rapla Kodila Konuvere Teenuse Valgu Vangla Vanamo˜isa Kasari Liivi Rannamo˜isa Tuudi
17 22 50 44 33 43 27 56 43 40 7
+20 +14 +5 +10 +43 +26 −5 0 −2 −6 −18
Mean
34
+8
Difference in Tot-N load was calculated as Qmod(cmod−cobs) during days with observed Tot-N concentrations.
(mQ 0.6)2 2
(2)
areariver
where k1,inorg is Inorg-N retention rate; Tmean10 is mean air temperature during the last 10 days; cinorg is concentration of Inorg-N; k2 is river pool depth; Q is total run-off from all upstream watersheds; w is mean river width; m is constant from approximate Manning formula, m= (MwS0.5) − 0.6 where M is the Manning coefficient and S is river slope.
Table 2 Explained variance (Nash and Sutcliffe, 1970) for Tot-N concentration and relative accumulated difference for load at the different monitoring stations in the Matsalu Bay watershed obtained by the HBV-N model Sub-basin
tion. Due to the risk of overparameterisation, the leakage parameters were limited to three for Inorg-N and Org-N respectively. The pasture areas and transitional woodlands were therefore lumped together with forests. Atmospheric deposition on open water bodies was omitted since there are no lakes in the Matsalu watershed. The retention of Inorg-N (Rinorg) in rivers was modified because of the absence of lakes, which play a dominating role in the Swedish applications. The river water volume was defined as a river channel volume plus a pool volume which enables retention even if run-off is zero. The river channel volume was estimated through an approximate Manning formula (river depth river width) for a channel with 45o, which yields the following expression for the Inorg-N retention:
Org-N production through decay of biological material, which is significant in Scandinavian forest streams, (Arheimer et al., 1996) could not be seen in the Org-N records from the Matsalu Bay watershed. It was therefore assumed that no transformation of Org-N occurred in the local sub-basin water, while retention (Rorg) in the rivers, through sedimentation of suspended organic material, was described by:
Rorg = k1,orgcorg k2 + mQ 0.6 +
(mQ 0.6)2 w
areariver (3)
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Fig. 3. HBV-N results for Kasari sampling site (2640 km2). Explained variance was 80% for run-off, −4% for Org-N, 63% for Inorg-N and 56% for Tot-N. Simulated run-off was overestimated by 12%, while simulated Tot-N gave good agreement in load.
where k1,org is Org-N retention rate; corg is concentration of Org-N. The HBV-N model for Matsalu Bay watershed thereby has six and five free parameters respectively for Inorg-N and Org-N (Fig. 2). The parameters were determined through regional calibration against observed Inorg-N and Org-N concentration records. The optimised criterion was the explained variance, (Nash and Sutcliffe, 1970): %(cmod −cobs)2 2
(4)
R =1− %(cobs − cobs)
2
which was calculated for all sub-basins having an observed record. A regional R 2-value was then computed through the geometric mean. Calibration was made through an iterative procedure (Harlin, 1991) where different model parameter sets were tested until the best regional R 2-value was derived.
3.2. Model application The HBV-N model was set up for the 11 subbasins with observed nitrogen concentration data (Fig. 1). Calibration of the hydrological model parameters was made against observed run-off,
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1985 –1990, at five stations. Local point sources were based on a Swedish study (Lo¨fgren and Olsson, 1990) and were estimated using data on the number of inhabitants together with standard potential production, 9.5 g N inh − 1 day − 1 and number of animal units (AU) together with estimated leakage from dunghills, 0.75 kg N AU − 1 year − 1. Diffuse leakage from urban areas was assumed to be 0.5 mg l − 1, which is 15% of the urban point sources (Lo¨fgren and Olsson, 1990). Concentration data from September 1991 to August 1995 were used for calibration of the nitrogen model parameters, since these years include concurrent nitrogen data series from the sampling sites. Further input data to the model were river density of natural flowing water, 0.39 km km − 2 and mean slope of Kasari river, 0.057% (TTU and SEPA, 1995). Mean river width was set at 10 m and the Manning co-efficient was set at 25 (winding natural channel with some pools and shoals).
major steps in the procedure are as follows: (i) estimation of riverine loads for the fixed time period at each monitoring site; (ii) sub-division of the entire drainage basin into sub-basins, defined by the monitoring sites for water quality and their upstream–downstream relationships; (iii) derivation of statistics on e.g. land use, soil type, lake area, point source emissions and other relevant data for each sub-basin; (iv) using a general non-linear regression expression with loads at each sub-basin as dependent/response variable (parametric models can be derived for both the riverine load at the mouth of each subbasin or the difference between output and input for each of the sub-basins) and sub-basin characteristics as explanatory variables. Load at the outlet of an arbitrary sub-basin can thus be estimated from the following general model: n
Li = % (1−Rj,i )Lj + (1− R1)Si + (1− R2)Pi j=1
+ (1− R3)Di + oi 4. The MESAW model
4.1. Model structure The MESAW model is a statistical model developed by Grimvall and Sta˚lnacke (1996) for source apportionment of riverine loads of pollutants. This model approach uses non-linear regression for simultaneous estimation of emission co-efficients for the different specified land use or soil categories and retention co-efficients for pollutants in a watershed. The basic principles and
(5)
where Li is load at outlet of sub-basin i; Lj is load at outlet of nearest upstream sub-basin j; Rj,i is retention on the way from outlet of subbasin j till outlet of sub-basin i; n is the number of sub-basins located nearest upstream (normally zero or one upstream sub-basin); Si is total losses from soil to water in sub-basin i; Pi is point source discharges to waters in sub-basin i; Di is atmospheric deposition on surface waters in subbasin i; R1-3 is retention for the source emissions S, P and D, respectively; oi is statistical error term.
Table 3 HBV-N estimated diffuse nitrogen emissions and river retention parameters for the Matsalu Bay watershed Parameter
Unit
Inorg-N
Org-N
Tot-N
Arable leakage Pasture, forest and woodland leakage Bog leakage Inorg. Retention rate (k1,inorg) Org. Retention rate (k1,org) River pool depth (k2)
103 kg km−2 103 kg km−2 103 kg km−2 o −1 C day−1 day−1 m
1.93 0.11 0.09 0.012 — 0
0.04 0.41 0.47 — 0.038 0
1.97 0.52 0.56 — — —
An obtained local Inorg-N retention of 3.4% between the root zone and the nearest stream has been applied to the values to make them comparable to the results of the MESAW model. See Eqs. (2) and (3) for explanation of river retention parameters.
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Table 4 MESAW estimates of emission co-efficients and retention index for the Matsalu Bay watershed Parameter/emission co-efficient
Unit
Point estimate
Standard error
t-ratio
u1 (Arable land) u2 (Pasture, forest and woodlands) u3 (Bog) l (Retention index)
103 kg km−2 103 kg km−2 103 kg km−2 —
2.22 0.38 0.65 0.00262
0.35 0.10 0.32 0.00072
6.34 3.80 2.03 3.64
See Eqs. (7) and (8) for explanation of co-efficients and retention index.
The load at each sub-basin can be broken down into contributions from sources located in subbasins further upstream (the first term in Eq. (5)) and contributions from sources located within the sub-basin being considered (the Si, Pi and Di terms in Eq. (5)). Two alternative dependent variables are available; the sub-basin specific loads, i.e. the difference between output and input, and loads at output. Retention from an arbitrary sub-basin m to the river mouth can be derived from: k
Rm,mouth =1− 5 (1− Rj )
(6)
j=1
where Rm,mouth is retention from the outlet of the sub-basin m on the way to the mouth of the whole river; k is number of sub-basins downstream of sub-basin m; Rj is the values of retention within the different sub-basins downstream of sub-basin m. The parameterisation of the model is flexible and study area specific. The model is fitted by minimising the sum of squares for the difference in observed and estimated load. The estimated emission co-efficients and retention parameters are finally used to calculate the contribution from each source and sub-basin to the riverine load at the mouth(s). Further details regarding the general matrix expression for emission co-efficients and retention can be found in Grimvall and Sta˚lnacke (1996).
4.2. Model application and parameterisation Time series of water quality and run-off from 1994 were used to estimate the annual Tot-N loads at each of the 11 monitoring sites located at the outlet of each sub-basin. The water run-off for
the year studied was 371 mm, which is higher than the long term average. Organic and inorganic fractions of nitrogen could be modelled separately but due to the limited number of input data were lumped together as Tot-N. The relatively homogenous precipitation and soil pattern over the whole study area did not force the use of different export co-efficients in different parts of the study area, which is possible to do in the general model. Therefore, the total loss of nitrogen from soil to water (Si ) in the ith sub-basin was in this study assumed to be a function of the land use: Si = (u1a1i + u2a2i + u3a3i )
(7)
where a1i, a2i and a3i respectively denote the area of arable land, combined area of transitional woodland, pasture and forests, and area of bogs in the sub-basins (Table 1), and u1, u2 and u3 are unknown emission co-efficients for the three land use categories. The point source emissions, Pi, were assumed to be known and were quantified in the same way as for the HBV-N model, and allocated to the respective sub-basin. Atmospheric deposition on surface waters, Di, was neglected and set at zero because of the insignificant lake area. Nitrogen is normally retained for a time and converted in watercourses and lakes before it reaches the sea. Retention in this model approach, as also in the HBV-N model, is used as a summarising expression for all hydrological and biogeochemical processes, e.g. denitrification, sedimentation and biological uptake, that may decrease or retard the transport of nitrogen. The parameterisation of the retention in the different sub-basins was done according to the following expression:
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244
Ri = 1−
1
i= 1, 2, …, N (8) 1+l areai where l denotes a regression index, while Ri and areai respectively denote the retention and the area in the ith sub-basin. The retention formula was derived from the concept that the removal of nitrogen takes place primarily in the river channels, due to the insignificant lake area in the Matsalu Bay watershed, and that the removal rate is proportional to the river network’s length, and subsequently is an indirect expression of the water residence time in the river channels. Local retention is consequently not expressed directly in the MESAW model, and estimated emission co-efficients for the three source categories are therefore the combined effects of root zone leakage, surface run-off and local retention. For simplicity and risk of overparameterisation, the retention of diffuse and point sources was assumed to be the same. By combining the parametric expressions for emission co-efficients and retention with empirical data regarding land use, sub-basin areas and point emissions, the contributions of the different
sources in a sub-basin to its own output can be expressed as a function of the parameters u1, u2, u3, and l and consequently estimated simultaneously by minimising the sum of squares for the difference in observed and estimated sub-basin loads.
5. Results The hydrological calibration of the HBV-N model yielded a mean explained variance (Nash and Sutcliffe, 1970) of 75% between simulated and observed water run-off for the validation period 1991–94. The annual runoff was 375 mm for arable land, pasture and transitional woodlands, 372 mm for forest areas, and 474 mm for bog areas. The calibration of the HBV-N nitrogen module gave a regional explained variance of 34% and a positive relative accumulated difference of 8% for Tot-N (Table 2). The results, however, varied greatly between the different sub-basins. The outlet of the Kasari sub-basin, which received the
Fig. 4. Scatterplot of observed and MESAW estimated loads for the various sub-basins in the Matsalu Bay watershed. Observed load is based on observed run-off and nitrogen concentrations calculated through linear interpolation of discrete N concentration observations.
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Table 5 Estimated annual nitrogen load (103 kg km−2) and retention in the Matsalu Bay watershed based on calculations for 90% (3225 km2) of the total drainage area HBV-N model
Load to main rivers River retention Net load to sea
MESAW model
Inorg-N
Org-N
Tot-N
Tot-N
0.49 12% 0.43
0.36 14% 0.31
0.84 13% 0.74
0.80 9% 0.72
most run-off and load gave the best results (Fig. 3), while the Tuudi sub-basin gave the lowest explained variance. Fig. 3 shows that the HBV-N model generally described the seasonal dynamics of Inorg-N well, but failed to capture individual concentration values during the winter season. Org-N concentrations showed very low seasonal variation and therefore became important for the total nitrogen concentration during the summertime, when Inorg-N concentrations were close to zero. The HBV-N model’s estimated diffuse leakage from the dominating land classes (Table 3) showed that the most important sources of riverine nitrogen in the Matsalu Bay watershed were arable land for Inorg-N and bogs, forests, pasture land and transitional woodlands for Org-N. Table 4 summarises the final parameter estimates of the MESAW model when the difference between output and input for the different subbasins was used as a dependent variable. All estimated parameters were statistically significant at 10% significance level. The emission co-efficient for arable land had the highest confidence level whereas the co-efficients for bogs and retention were more uncertain. The sub-basin loads observed were relatively well predicted by the model (Fig. 4). The largest residual was found for the Tuudi sub-basin. Tests of other MESAW model runs with other combinations of land use categories gave similar results (not shown); e.g. the classification with arable land and pasture combined showed slightly lower point estimates than for arable land alone. All MESAW runs that produced a good fit to observed data had two features in common; the values for the retention parameter were all comparatively low and the emission co-efficients for
arable land were much larger than the co-efficients for other land use categories. The HBV-N and MESAW models estimated the riverine export of Tot-N from the Matsalu Bay watershed to 0.74 and 0.72 103 kg km − 2 yr − 1 respectively (Table 5). The total retention of TotN was estimated to be 13 and 9% respectively. For the most upstream sub-basins (i.e. Rapla, Kodila and Valgu), about 20% of the gross load was estimated by the HBV-N model to be retained, while MESAW gave 10% retention during the transport to the most downstream sampling site. The average nitrogen river retention for each sub-basin was estimated to be 7 and 3.5% respectively by the two models. The differences in diffuse emissions obtained by the HBV-N and the MESAW models are summarised in the resulting source apportionment for the Matsalu Bay watershed (Fig. 5). Both models indicated that the contribution from arable land was the largest nitrogen source in the watershed, followed by contributions from pastureland, forest and transitional woodlands. The HBV-N model showed that 75% of Inorg-N could be traced to the arable land area, while 54% of Org-N comes from pastureland, forest and transitional woodlands. The estimated point sources contributed only by 5% as calculated in both models. The relative uncertainty of the estimated diffuse emissions and retention was illustrated through calculation of the intervals for each parameter that gives an acceptable model performance (Table 6). Calculation of standard errors is not possible for the HBV-N model parameters since the number of degrees of freedom for each model parameter is not known, (Nash and Sutcliffe,
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Fig. 5. Nitrogen source apportionment for Matsalu Bay watershed according to the two model approaches. The source apportionment was based on the same land cover distribution and point sources but on different diffuse emissions as obtained by the two models.
1970). The intervals for both the HBV-N and MESAW models were therefore defined as the parameter range, which gives less than 10% increase of the sum of squared errors (SSE). According to Table 6, the intervals for the MESAW model are slightly smaller than for the HBV-N model. The two models show, however, similar patterns in uncertainty. As a percentage the smallest interval is retrieved for arable land, while the bog leakage was the most uncertain figure among the three leakage parameters. Both the HBV-N and the MESAW model produced larger intervals, if the other model parameters were allowed to vary.
6. Discussion
6.1. Comparison with pre6ious estimates Results of reported emission co-efficients in this paper were compared with the results of three other studies performed in the Matsalu Bay watershed (Krysanova et al., 1989; TTU and SEPA, 1995; Vasilyev et al., 1996). Krysanova et al. (1989) used a dynamic modelling approach and received emission co-efficients for arable land similar to those obtained in this study. Vasilyev et al. (1996) was in fact using the MESAW-model. The land use classification and studied time period
were, however, different and the number of subbasins were larger (n= 16). The estimated emission co-efficients were despite this to a large extent in line with the MESAW-model results here, with the exception that the standard errors were lower than those obtained in this study. TTU and SEPA (1995) made a source apportionment in the Matsalu watershed through inventories of point and diffuse sources. The results showed that agricultural land contributed the Table 6 Sensitivity analyses of the model parameters HBV-N model
MESAW model
If the other parameters are fixed Arable land 1.70–2.28 1.93–2.34 emissions Pasture, forest and 0.42–0.66 0.29–0.41 woodlands emissions Bog emissions 0.35–1.07 0.17–0.86 River retention 8–19% 7–12% If the other parameters are allowed to vary Arable landffl 1.29–2.80 1.80–2.64 emissions Pasture, forest and 0.32–0.80 0.25–0.49 woodlands emissions Bog emissions 0.32–1.21 0.23–1.03 River retention 7–21% 6–12% The intervals give the diffuse emission of Tot-N (103 kg km−2) and river retention that gave less than 10% increase in sum of squared errors (SSE).
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most, followed by background load from forests and natural grasslands. Point sources differed, however, much from the present study since TTU and SEPA (1995) estimated the contribution from point sources, including husbandry, to be 22% of the total nitrogen load. Mainly different data sources and different methods used to estimate point sources explain the differences. Considering different use of nitrogen fertilisers, the obtained annual diffuse emission from arable land also fits well with estimates in Scandinavia (Kronvang et al., 1993; Rekolainen et al., 1995; Arheimer and Brandt, 1998). Emissions from forests were, however, generally higher compared to corresponding Scandinavian estimates, which probably was a result of lumping forests together with pastureland in the present study. Riverine export of nitrogen from watersheds in the Gulf of Riga has been estimated to be 0.77 – 0.92 103 kg km − 2, based on the years 1977 – 95 (Laznik et al., 1998). The present study, therefore, indicated that the Matsalu Bay watershed contributes less than average to the nitrogen load of the Gulf of Riga (Table 5).
6.2. Model performance and uncertainty Both models gave similar levels for Tot-N emissions and retention and the results also fit well with previous estimates. The differences between the two model results were mainly higher diffuse emission from pastureland, forest and transitional woodlands, as well as higher river retention rates by the HBV-N model. Diffuse emissions from arable land were slightly lower in the HBV-N results. All differences, however, compensate each other and the estimated net load to the Gulf of Riga therefore agrees between the two models. The difference in diffuse Tot-N emission from pastureland, forests and woodlands can probably be traced to the simulation of Org-N in the HBVN model, which by itself gives higher emissions than the Tot-N emissions estimated by MESAW (Tables 3 and 4). The Org-N point sources are distributed equally over the year in the HBV-N model, which may give very large concentration
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peaks during extremely low run-off. These high concentration peaks were not seen in observed concentrations (Fig. 3) and the dynamic HBV-N model therefore reduced these simulated peaks by a relatively high Org-N retention (Table 5) through sedimentation, which is most effective during low run-off. This high Org-N retention may, however, have led to a compensation of high diffuse emissions during the wintertime. A possible explanation for both the higher HBV-N emissions and retention rates for Tot-N may therefore be an overestimation of Org-N diffuse emissions and Org-N retention in the dynamic model. The two model results show very similar patterns for model accuracy. Both models produced the poorest results for the Tuudi sub-basin, and the uncertainty intervals (Table 6) were similar. This indicates that the uncertainty is more dependent on which input data are available and on the distribution of land cover in the monitored watersheds, than on which model that is chosen. The number of nitrogen sampling sites used in the present study, however, appeared to be sufficient. The optimisation procedure in the HBV-N model gave distinct optima in the response surfaces of the objective function. MESAW also showed a statistical significance of less than 10%, which must be regarded as acceptable. The better statistical significance when 16 monitoring sites were used (Vasilyev et al., 1996), however, shows the sensitivity to the monitoring network density. Both the HBV-N and the MESAW model give larger intervals if the other model parameters are allowed to vary, which shows that there exists interdependency between the parameters or coefficients. The possibility of compensation in the diffuse emissions and retention rates, which seriously affect the source apportionment, must therefore be considered.
6.3. Model comparison One of the main differences between the two model applications (Table 7) was that the HBVN model optimised the emission co-efficients and retention parameters through maximising the ex-
The table presents the model application in the present study, and the description may therefore differ somewhat from the general structure and applications of the two models. a Calculated through linear interpolation of discrete N concentration observations. b Calculated by the hydrological model HBV (Lindstro¨m et al., 1997) with daily point precipitation, air temperature and monthly potential evapotranspiration as input data.
Causal (dynamic) Diffuse emissions were defined as regional model parameters calibrated by comparison of observed and simulated Org-N and Inorg-N for a 4-year long concentration series
MESAW
Statistical (static) Diffuse emissions were defined as regional co-efficients obtained through non-linear regression analysis between Tot-N loada for the fixed period of one year (response) and sub-basin characteristics (explanatory) Inorg-N retention Dependent on Dependent on the mean air temperature for the last ten days sub-basin area river water residence time regional retention parameter found by a regional co-efficient, which is determined through non-linear recalibration gression analysis Optimisation Maximising the mean explained variance calculated from observed and Minimising the sum of squared residuals between estimated and obmethod simulated N concentration at each sub-basin outlet served annual N-loada at each sub-basin outlet Input data Observed daily Q Calculatedb daily areal temperature, recharge from unsaturated zone, water run-off and volume Observed Org-N and Inorg-N concentration Observed Tot-N concentration Land use distribution Land use distribution Urban and rural point sources Total point sources Output data Specific leakage from different land uses Specific leakage from different land uses Estimated local and river retention of Org-N and Inorg-N Estimated river retention of Tot-N Daily series of Org-N and Inorg-N concentration Gross and net nitrogen load Gross and net nitrogen load Nitrogen source apportionment Nitrogen source apportionment
Definition Methodology
HBV-N
Table 7 Comparison of the two models used for nitrogen source apportionment in the Matsalu Bay watershed
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plained variance of simulated and observed concentration values, while the MESAW model minimised SSE for nitrogen load, where the observed load was calculated through linear interpolation. The HBV-N thereby removed possible errors in the estimation of nitrogen concentration between the sampling occasions, but instead introduced errors through simulating hydrometeorological variables such as areal temperature, groundwater volume and run-off. The hydrological part of HBV-N model has, however, been scientifically validated and shown to work very well in several studies (Bergstro¨m, 1992). The use of nitrogen load for the optimisation procedure in MESAW also restricts the time step, which must be longer than the time of residence of the water in the river system. It should, however, be noted that the MESAW model in general might use any method to calculate the nitrogen load. Another major difference in the two model applications was that the HBV-N model treated Org-N and Inorg-N separately, which gave source apportionment also for these fractions. Even if the aim had been only Tot-N source apportionment, the HBV-N model still needed both fractions as input data. The present study showed that the HBV-N model in general demanded more data input as well as considerably more input of work and experience than the MESAW model. The MESAW model was easily applied in the watershed studied and model runs with alternative data inputs were easily performed. An uncertainty measure, the standard error, for the estimated emission and retention was also retrieved directly in the MESAW, while the uncertainty analysis of the HBV-N estimates demanded further work. The higher demands of the HBV-N were, however, accompanied by a larger variety of output data and a platform for further and more extensive assessment.
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reliable source apportionment with the available input data from 11 sampling sites in the Matsalu Bay watershed. Estimated nitrogen emissions from the different land classes, as well as the nitrogen retention and source apportionment for the Matsalu Bay watershed agreed well with previous estimates made in Estonia and Scandinavia. The two model applications indicated that both models are sensitive to the density and location of nitrogen sampling sites. Model uncertainty seems to be more dependent on the availability of nitrogen data and land cover distribution of the monitored watersheds than of the choice of model. The interdependency between model parameters or coefficients in both models, however, indicates a risk for compensation between estimated diffuse emissions and retention, which may affect the source apportionment result. The study has also shown that the HBV-N model demands considerably more input of data, work and user experience than the MESAW model, which is easily applied in large watersheds with dense monitoring networks. The HBV-N model, however, can be used with scarce run-off data and gives larger variety in data output as well as possibilities for further assessments.
Acknowledgements This study was a part of the Gulf of Riga Project within the Nordic Environmental Research Programme and has been financed by the Nordic Council of Ministers and the Swedish Meteorological and Hydrological Institute (SMHI). Alvina Reihan at the Estonian Meteorological and Hydrological Institute (EMHI) and Andrus Meiner at the Environmental Information Centre in Estonia are greatly acknowledged for compilation of data and valuable information. Thanks also to Berit Arheimer, SMHI, for valuable advice and discussion.
7. Conclusion Both the HBV-N and the MESAW model were capable of estimating the diffuse nitrogen emissions and river retention rates and thus perform a
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