7. Establishment of a harmonized tool for calculating river discharge and nitrogen loads from unmonitored areas in Denmark
D.-I. Müller-Wohlfeil1, B. Kronvang1, S.E. Larsen1, N.B. Ovesen1 and F. Wendland2
1National Environmental Research Institute, Vejlsøvej 25, P.O. Box 314, DK-8600 Silkeborg
2Research Centre Jülich, Programme Group STE, D-52425 Jülich
Address: National Environmental Research Institute, Vejlsøvej 25, 8600 Silkeborg, Denmark
quire a large number of detailed data which are usually not available for large regions both with respect to temporal and spatial resolution the number of parameters. Secondly, the use of physi-cally based and conceptual models normally de-mands calibration. Beven and Binley (1992) have shown, that even for comparatively simple con-ceptual models, equally good modelling results can be achieved through calibration using various parameter combinations and a wide range of pa-rameter values. Accordingly, any objective or subjective parameter calibration procedure may lead to equivocal solutions. Moreover, even if the parameter sets would be incontestable, transfer to other regions requires a distinct relationship to be established between the parameters used and the regionally available data on which they have been based. To prove this, the models have to be cali-brated for many catchments varying in size and properties, though this does not guarantee that a high correlation between model parameters and catchment properties can be established (Uhlen-brook et al., 1999). Empirical hydrological models based on multiple regressions have previously often been used to estimate especially mean flow characteristics, such as mean annual streamflow (Vogel et al., 1999) and flood quantiles (Pandey and Ngyen, 1999, Tasker et al., 1996). The present paper focuses particularly on the current river discharge model concept and first application results.
2. Data and methods used
The development of the river discharge model is based on 1366 observations of annual river discharge for the period 1989-1997 from 159 hy-drometric gauging stations covering catchment
areas between 10 and 300 km2. We used annual total nitrogen load data from 71 catchments smaller than 30 km2 for the nitrogen load model.
Land use in these catchments is dominantly agri-culture with varying proportions of forests, and urban areas, etc. The nitrogen discharge from point sources was negligible within these catch-ments and there were no lakes. The reason for using 30 km2 as an upper limit was that nitrogen removal in watercourses and lakes should be con-sidered explicitly in larger areas.
2.1. The hydrological model
Our guideline for choosing the current version of the hydrological regression model from the large number of potential models available for the river discharge simulation was our aim to i) maximise the “coefficient of determination” (R2), ii) mini-mise the predicted variance of the model error (σ2), and iii.) keep the number of explanatory variables at a minimum. The variance of the error is estimated by the mean square error (MSE):
σ2 = MSE = [SSE/(n - p)] (1)
and SSE=
∑
n yi −yi1
)2
( ˆ (2)
where n is the number of observations, p is the number of explanatory variables, SSE is the sum of squares for error, yi is the ith observed response value (observed annual specific river discharge [mm]), and
y ˆ
iis the ith estimated response value (estimated annual river discharge [mm]). The coefficient of determination, R2, of the fitted re-gression is defined as the proportion of the total sample variability:SST
− SSE
1 (3a)
and SST =
∑
= n
−
i
i
y
y
1
)
2(
(3b)where SST is the total sum of squares and
y
is the sample mean of the response variable river dis-charge [mm].The final model equation (4), which consists of 5 variables, was established by including the most important explanatory variables from a list of 26 variables (Table 1) until the increase in fit became smaller than 1 %.
2 2
, 1 ,
,
ˆ )) 1074 . 1 ( )
* 34732 . 3 ( ) 1058 . 0 (
)) ln(
8663 . 5 ( )) ln(
1106 . 12 ( 995 . 105 (
σ +
⋅ + +
⋅
−
⋅ +
⋅ +
−
= −
aj aj j
j
j i j
i j
i
TC SL GWC
U
P P
Q (4)
where i indicates year, j is catchment, Q specific annual river discharge [mm], Pi annual precipita-tion ([mm], adjusted for among others, wind-induced errors, outsplashing and wetting effects (Danish Meteorological Institute, 1998), Pi-1 ad-justed precipitation of the previous year [mm], U urban areas [% of the total catchment area], SL Figure 2 The 49 catchment areas in Denmark used for
moni-toring river discharge and nutrient load.
mean slope along the main watercourses [degree], GWCa groundwater catchment area [m2], TCa the topographic catchment area [m2], and σˆ2 =6.3504.
VARIABLE Variable type
Annual precipitation at t-0
Annual precipitation at t-1
Annual precipitation at t-2 Annual evapotranspiration at t0 Precipitation January-March at t0
Mean annual precipitation during the normal period (1960-1990)
Mean annual evapotranspiration during the normal period (1960-1990)
Precipitation Maj-December at t0 Summer precipitation at t0 Winter precipitation at t0
Precipitation October-December at t-2
Precipitation October-December at t-1 Ratio gw-catchm/topogr. Catchment Mean slope
Mean topographic index (lna/tanβ) Slope along the main watercourses Mean elevation (m.a.s.l)
Max. depth of groundwater table Percentage of sandy geological unit Percentage of clayey geological unit Percentage of humic soils
Percentage of clayey soils Percentage of sandy soils Percentage of arable land Percentage of urban areas Region number
Table 1 Variables tested for the final model selection (where t0 denotes current year, t-1 last year and t-2 the year before last year).
The annual precipitation and the precipitation of the previous year explain 50.0 % and 9 %, respec-tively, of the total model variation, while the other variables are of minor importance. The correlation coefficient of this model is R2 0.70, P<0.0001%.
There are mainly two reasons for the fact that river discharge decreases with increasing urban coverage. Firstly, many of the larger cities and urban areas in Denmark are located along the coasts. Water used within these catchments is often directly transferred into the sea and there-fore not measured at the catchment gauging sta-tions. Secondly, in some of these catchments wa-ter abstraction causes a reduction in river dis-charge. As an example, in 1993 water abstraction in a catchment located north-west of Copenhagen (332 km2 in size, 50% urbanised areas) amounted to as much as 38 % of the net-precipitation. An-nual river discharge in one of the subcatchments
(110 km2 in size) was about 155 mm in 1993 and thus about 125 mm lower than the difference be-tween the adjusted precipitation and potential evapotranspiration on the one hand and observed river discharge on the other.
The least significant parameter included in the model is the ratio relating the ground-water catchment area to the topographic catchment area.
The ratio was based on the calculation of groundwater divides according to a digital map of groundwater potentials with a grid mesh size of 500 m (Friborg, county of Sønderjylland, pers.
communication, 1999) and includes some uncer-tainties.
Table 2 and figure 3 show the difference between measured annual river discharge and model pre-dicted river discharge. Note that the number of annual observations varies during the simulation period. The difference between annual modelled means and the observed annual means is small and varies from 24 mm overestimation in 1989 and 20 mm underestimation in 1994 (Table 2).
The Root Mean Squared Error (RMSE) is lowest under mean flow conditions (1992) and much smaller than the standard deviation of observed river discharge (STDDEV) during the 9-year period. Only a small difference exists between the RMSE of the year exhib-iting highest total river discharge (1994) and years with mean annual flow, such as 1991 and 1993. The model often underestimates the highest measured values (Fig.
3).
Year STDDEV RMSE q-measured q-estimated
1989 124.7 81.3 200.2 223.7
1990 131.7 76.6 273.6 285.3
1991 109.4 80.3 251.9 264.8
1992 121.6 68.6 241.7 247.4
1993 128.4 91.2 289.7 298.4
1994 140.1 92.3 406.6 386.2
1995 127.2 83.7 309.2 290.2
1996 113.4 79.4 153.7 141.8
1997 106.3 72.7 164.6 161.7
Table 2 Comparison between the estimated and meas-ured annual means of river discharge during the years 1989 and 1997, Root Mean Squared Error (RMSE) of the estimations and standard deviation of the observations. The root mean squared error is defined as the square root of the mean square error (MSE). All values are specified in [mm]
2.2. The total nitrogen load model
Based on monitoring of nitrogen fluxes in six small agricultural catchments, three of which are dominated by sandy soils and three by loamy soils.
Kronvang et al. (1995) showed that nitrogen leaching on sandy soils was more than twice as high than on loamy soils due to higher fertiliser application rates as well as net mineralization loss from the soil. However, since loamy catchments are typically tile-drained, a smaller percentage of the nitrogen leaching from the root zone reaches surface water directly. Accordingly, nitrogen stream-water concentration was twice as high in catchments on loamy soils than in catchments on sandy soils. Larsen et al. (1996) showed that the annual diffuse loss of total nitrogen (N, [kgNha-1]) can be estimated by the following empirical mul-tiple regression model (5)
( )
( )
(
0.50.1686)
exp
0243 . 0 0032 . 0 log 6707 . 0 exp
⋅
⋅
⋅ +
⋅
−
⋅ +
= i ij j j
ij R S A
N α (5)
where R is annual river discharge [mm], S are areas with sandy soils [% of the total catchment area] in the catchment and A arable areas [% of the total catchment area]. The annual parameter α includes variations in both climatic factors not explained by the variation in annual river dis-charge and in agricultural practices affecting catchment nitrogen loss such as, for instance, variations in harvested yield and trends in N-consumption in fertilizer. The values of this di-mensionless annual parameter vary between -2.80 and -2.31 during the period 1989-1996. The model is based on 437 observations and R2=0.82 (P<0.01%).
The explanatory variable represented by annual river discharge explained 29 % of the annual total nitrogen loss, while sandy soil explained 5% and arable land 31% of the total variation. The re-maining 17% is explained by the parameterα, which needs to be calibrated for each year.
We would anticipate that not only the proportion of agricultural land within the catchments but also the amount of nitrogen in chemical fertilizer and animal manure applied to agricultural land and the harvested nitrogen with the crops would be important for the total nitrogen loss. This is also the case as described in Andersen et al.
(1999). We have unfortunately not yet admission to obtain such data for catchments all over Den-mark. However, in the near future such data will be recoverable from Danish national agricultural databases linked to GIS and hence we will be able to apply more advanced empirical models (cf.
Müller-Wohlfeil et al., 2000).
3. Application of the river discharge and the nitrogen load model to coastal areas at the national scale
Prior to the model application, we have to distin-guish between the gauged and unmonitored ar-eas, which can be divided further regionally ac-cording to the location of the 49 topographic catchments that have hitherto been used to calcu-late river discharge and nitrogen transport to the Danish coastal waters. These second-order coastal catchments can be further subdivided into a total of 185 fourth-order coastal catchments with an average catchment size of 130 km2. Accordingly, the following steps were used for the model ap-plications:
• Extraction of all parameters necessary to de-rive the statistical model from digital geo-graphical databases for all monitored catch-ments included in the study (162 catchcatch-ments for the river discharge model, 71 catchments for the nitrogen load model).
Predicted river discharge (mm/ yr)
0 100 200 300 400 500 600 700 800
0 100 200 300 400 500 600 700 800 Measured river discharge (mm/ yr)
Figure 3 Plot of measured versus predicted river discharge for the simulation period 1989 to 1997
5 5 0 - 60 0 6 0 0 - 65 0 6 5 0 - 70 0 7 0 0 - 75 0 7 5 0 - 80 0 8 0 0 - 85 0 8 5 0 - 90 0 9 0 0 - 95 0 9 5 0 - 10 0 0 1 0 0 0 - 1 0 50 1 0 5 0 - 1 1 00 1 1 0 0 - 1 1 50
Figure 4 Mean annual precipitation (mm) in Denmark during 1971-1998
• Calculation of annual river discharge for the unmonitored areas according to equation (4)
• Calculation of the annual diffuse load from unmonitored areas according to the combined application of the river discharge model (equation (4)) and the equation (5) for the ni-trogen load model (Larsen et al., 1996).
• Addition of nitrogen discharge from point sources within unmonitored areas at the sec-ond-order coastal catchment level.
• Aggregation of measured river discharge and total nitrogen load at monitoring stations within the monitored areas of the second-order coastal catchments.
• Aggregation of both river discharge and ni-trogen load at the second-order coastal catchment level based on the model simula-tion results and point source discharges of nitrogen in the unmonitored areas, and the measured river discharge and nitrogen load from the monitored areas.
4. Modelling results
4.1. River discharge
In our study we chose two subsequent test years (1994 and 1995), the former being a very wet year (880 mm precipitation on the national scale) and the latter a dry year (652 mm precipitation on the national scale). The mean area weighted river discharge from Denmark was about 8.4 % lower in 1994 and 8.9% lower in 1995 when applying the new river discharge model (4) as compared to the nationally applied method (area/runoff-relationship procedure for unmonitored areas).
This was, however, to be expected as the mean model simulation results of annual river dis-charge were lower than the measured annual river discharge in the 162 model catchments dur-ing both years (Table 2). Moreover, our new river discharge model includes precipitation as the most important driving parameter, and precipita-tion is generally lower in Danish coastal near ar-eas than in the monitored region (Fig. 4). At the first-order coastal catchment level, the difference between the total river discharge to coastal waters (mm) according to previous reports and the new model was between –14.4% and 3.3 % in 1994 and between –19.6% and 8.5% in 1995 (Table 3). It is, however, important to keep in mind that the new approach is based on river discharge data. There are indications that some of the runoff from the Danish land-mass occurs through deeper groundwater and thereby passes gauging stations (Henriksen et al., 1997).
1994 First-order
Catch-ment region
Simulated Q [mm]
NERI-Report
Difference (%) report – simulated
1 541 569 -4,9
2 397 424 -6,4
3 376 423 -11,2
4 378 439 -13,7
5 505 489 3,3
6 339 398 -14,9
7 264 287 -8,0
8 259 283 -8,7
9 309 356 -13,2
Mean 454 416 -8,4
1995 First-order
Catchm.
region
Simu-lated Q
[mm]
NERI-Report
Difference (%) report –
simu-lated
1 461 494 -6,6
2 322 331 -2,7
3 307 349 -12,0
4 272 307 -11,5
5 399 368 8,5
6 217 270 -19,6
7 186 214 -12,9
8 172 188 -8,3
9 199 211 -5,6
Mean 363 331 -8,9
Table 3 Comparison between simulated and modelled total river discharge in 1994 and 1995, first-order coastal catchments.
4.2. Nitrogen loads
The previously reported values are typically higher than the new model based estimations in those areas along the coast that are dominated by non-agricultural land use and/or sandy soils, which in combination or alone will give rise to lower nitrogen loads.
Area Previously reported (kg Nha-1)
New estima-tions (kg Nha-1)
Absolute difference
(kgNha-1)
1 19.40 18.70 0.70
2 20.90 14.70 6.20
3 20.00 15.47 4.53
4 19.40 14.77 4.63
5 23.60 23.35 0.25
6 19.60 15.73 3.87
7 10.60 10.30 0.30
8 16.70 11.74 4.96
9 18.70 16.35 2.35
Table 4 Riverine nitrogen loads in 1995 at the level of first order catchments according to previous and new estimations.
As the method hitherto applied in the Danish counties for estimating nitrogen loads from un-monitored areas does not incorporate information on land use and soil type, the resulting nitrogen loads will inevitably be an overestimate. Moreo-ver, in most cases river discharge is significantly lower when applying the new empirical model.
The difference between the modelled and the previously reported nitrogen loads at the second highest level of aggregation (nine first-order coastal catchment areas) varies in 1995 between approximately 0.3 and 6.2 kg N ha-1 yr-1 (average approx. 3 kg N ha-1 yr -1 (Table 4)).
5. Conclusions and future outlook
The empirical river discharge and nitrogen mod-els presented together with monitored river dis-charge and nitrogen loads provide a basis for a comprehensive and harmonized tool for the cal-culation of annual river discharge and nitrogen loads from 49 second-order coastal catchments to Danish coastal waters. The model was capable of simulating both high and low runoff conditions.
Further development of the existing model re-quires additional inclusion of quantitative subsur-face features that cannot be extracted directly from the available nation-wide Danish data sets.
The derivation of storage properties is also re-quired for the establishment of a water balance concept that we are aiming at as a next step. Fu-ture tasks involve:
• Clustering of gauging stations according to their general runoff behaviour using indices such as the base flow or the seasonal index (c.f. Burn and Borman, 1993; Sefton et al., 1995). These indices provide additional in-formation that may be related to regional geographic properties.
• Identification of regions with discharge sur-plus opposed to areas with loss of discharge, based on a newly derived improved edition of a map of ground water catchments, as well improved information on drinking water ab-straction.
• Separate treatment of base-flow and fast run-off.
• Improvement of the model’s temporal resolu-tion towards monthly water balances follow-ing the examples of Xu (1999).
• Substitution of the annual calibration factor of the nitrogen load model by parameters that represent annual changes in land use patterns and agricultural practises.
• Inclusion of a model to estimate nitrogen re-tention lakes, located in ungauged areas
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