6. Introduction to the specific studies performed
6.1 Modelling annual and monthly runoff
6.1.1 Annual river discharge and riverine nitrogen loadings
The first part of the thesis focuses on the estab-lishment of a frame for estimating annual runoff and nitrogen loading to coastal waters (Chapters 7/8 of the thesis) based on observations from the 9-year period 1989 to 1997. The NOVA programme committee suggested an extension of the existing empirical nitrogen load model (Larsen, 1996) by including rainfall components to facilitate a homogenised calculation of nutrient loads to the Danish coasts. The first approach, which was based on annual regression models for river discharge and nitrogen loads, is in compliance with this suggestion.
A prerequisite of this approach implicates i) the assessment of databases available at the national
scale to be used for catchment-based methods and ii) the establishment of a GIS-based database comprising all the necessary information for each catchment.
The second-order coastal catchments act as spatial reference units for NERI’s national reports on freshwater runoff and nutrient loads, and they are therefore chosen as the target units of the present study. The second-order coastal catchments can be further subdivided into third- and fourth-order coastal catchments. Initial assessments of mean annual runoff data revealed that the smallest catchments are often exposed to the greatest deviations from the mean river discharge. To remove the impacts of smallest scale specifics on the establishment of the river discharge model, the regression equation was based on discharge observations from catchments larger than 10 km2. To avoid overrepresentation of large catchments, basins larger than 300 km2 have also been omitted for this study. A problem in this context is that the unmonitored areas in many of these coastal second-order and third-order catchments are smaller than 10 km2 or larger than 300 km2. First, all islands smaller than 0.1 km2 were omitted, accounting for 0.023 % of the total land mass (total area 10 km2). Next, various digital catchment
Q =f (Precipitation, Land use, Relief- ..)
N =f(Runoff, Land use, Soils) Data extraction from
each catchment Statistical analysis
• Model application in ungauged areas
• Combination of model results in ungauged areas with measurement values in gauged areas
• Combination with information on point sources in ungauged areas
Climate Relief Water courses Runoff Land use Soils Geology Ground water Information from gauged areas
Figure 6.1. Establishment and application of the procedure used for estimating annual values of river discharge and riverine nitrogen loads.
databases were used to subdivide catchments larger than 300 km2 into smaller units. Likewise, catchments smaller than 10 km2 were aggregated taking into account their geographical location at the level of second-order coastal catchments.
However, many of the small catchment polygons could not be aggregated to units as large as 10 km2. The reason is that these polygons either represent islands or are located without any neighbours belonging to the same second-order catchment unit to which they could be aggregated.
Simultaneously, a GIS–database comprising information from all catchments considered for the derivation of the river discharge regression equation was established and data extracted for each catchment. After the derivation of the final regression model based on the analysis of the GIS-data and time series of climate and discharge GIS-data, annual river discharge was calculated for each of the spatial modelling units in the unmonitored areas. Subsequently, diffuse nitrogen loads from the areas were calculated based on calculated discharge and an empirical nitrogen loadings model (Larsen, 1996) and the calculation results for both river discharge and nitrogen loads were aggregated at the second-order coastal catchment level (Fig. 6.1).
While Chapter 7 gives an overview of the model-ling concept and test applications for the two-year period 1994/95, Chapter 8 includes a more detailed description of the parameterisation and a discussion of the model robustness in space and time.
Different tests were performed prior to the statistical analysis to identify the suitability of some hydrological features thought to be impor-tant as potential explanatory variables for the regression equation on annual river discharge.
With respect to catchment size, a small correlation can be found when considering all 224 catchments on which direct measurements of river discharge and digital information on catchment boundaries are available for the period 1989-1997. It suggests
slightly an increase in flow with catchment size (R2
= 0.006), meaning that area only explains less than 0.6 % of the annual flow variation found. When splitting the data sets according to geographical location, this very small correlation is maintained for watersheds located in Jutland (R2 = 0.008), while no correlation can be found for catchments located on the Danish islands. This confirms the findings of the previous work of Lyshede (1955) and the Danish Committee for Hydrology (1981), described in Chapter 4 of this thesis. However, the appropriateness of considering catchment size for annual runoff dynamics has been investigated additionally. To this end, precipitation of the current year and of the previous year, which have been identified as the most important variable to explain variation in annual river discharge, has been considered separately for two different datasets, the area threshold value chosen was 100 km2. It was found that while this year’s precipita-tion is, of course, generally more important than last year’s precipitation in all catchments, this importance is higher for smaller catchments than for larger ones. The opposite is true with respect to last year’s precipitation, which becomes increas-ingly important in larger catchments. However, both the increase in model fit (from 0.7 to 0.705) has been too small to consider a separate treatment of larger and smaller catchments for the establish-ment of the regression equation.
A similar test was carried out to evaluate the advantages of a potential subdivision of the catchments according to the dominance of different flow-components, either “fast-flow”
(mainly comprising runoff from the soil surface, tile drainage networks and near-surface lateral flow) or “slow-flow” (mainly groundwater runoff) for annual discharge patterns. It was found that differences in soil properties can largely explain which of the two flow-components prevails, while other explanatory variables such as catchment slope or mean depths of the upper groundwater table are significantly less important. Despite the
10
0
-10
Ordered residuals Model residuals (mm)
Theoretical quantile Estimated values (mm)
-2 0 2
10
0
-10
10 15 20 25
Figure 6.2 Distribution of model residuals versus the theoretical quantile (a, left ) and model estimates (square root of annual river discharge) versus model residuals (b, right).
fact that neither soil type nor plant available water were identified as important variables when using the stepwise procedure applied for the selection of explanatory variables, soil type was tested for its suitability to be combined with the most important explanatory variables of the river discharge model, which are this year’s and last year’s precipitation.
For this purpose, the percentage area of loamy soils was used as a class variable introduced with 10 % intervals. Again, the importance of this years precipitation is higher for catchments covered by loamy soils than in catchments covered by sandy soils. However, despite these findings, which seem reasonable, area percentage of loamy soils was not considered for the final regression model, mainly for two reasons. First, the increase in model fit (expressed as R2) was slight (from 0.7 to 0.715).
Second, the introduction of additional variables increases the degree of freedom, which, in turn, by definition augments the root mean square error.
Moreover, when aggregating the model error (residuals) for areas dominated by sandy soils and comparing it with those dominated by loamy soils, no significant difference could be detected between the original river discharge model, for which soil was not been considered as an explanatory variable, and the other version, for which area percentage of loamy soils was introduced as class variable.
As pointed out earlier, an important condition to be checked when establishing a regression model is that the residuals, i.e. the model error, should follow a normal distribution. Figure 6.2a shows the distribution of the model residuals versus the theoretical quantile, both with respect to the runoff model. Apart from the final tails the distribution is normal. Observations deviating considerably from the slope of the distribution are ascribed to stations with a marked difference between the climatic water balance and the observed river discharge.
The normality of the distribution can also be tested using the “Kolmogorov-Smirnov-test”. The statistic variable D is defined as the maximum unsigned difference between two relative, cumulative frequency distributions (Sokal and Rohlf, 1981). The actual value (0.040, p-value 0.01) is slightly smaller than the critical D, which can be calculated as 1.628/ n= 0.44, with n being the number of observations. As required, the model residuals show a nearly constant variance and no trends of river discharge along the observed range (Fig. 6.2b).
The model-fit of the annual river discharge model expressed as the R2 was 0.7, which means that the current model is able to explain 70 % of the observed variation in river discharge. Testing the model for the independent validation period 1998/99 revealed that a nine-year period might be too short for establishment of the model, since the
model overestimated mean river discharge in 1999 when recent and previous precipitation was higher than in the previous years included. Consequently, model improvements are necessary before its operational use. The model error is higher in catchments where either the long-term difference between precipitation and potential evapotranspi-ration is (much) larger than the observed river discharge, or where river discharge is almost as high as the precipitation level. The fact that these catchments reveal extreme runoff behaviour may be ascribed to errors in the climatic or runoff data, special geomorphologic site conditions and/or water management measures.
The river discharge model was applied to all unmonitored areas in Denmark during the period 1989-1999 and the resulting runoff values were combined with the measurements recorded in the monitored areas to assess the total runoff from the whole Danish land mass. Generally, the resultant values for runoff at the national scale are slightly smaller than the values of the calculations previously reported, which can be explained by the fact that the new model-based method contrary to the previous method accounts for the observed gradients in precipitation from the inner parts of the country to the sea. Consequently, nitrogen loads are slightly lower compared to the results of the old model for most years when the combined river-discharge nitrogen-load model (1993-1997) was applied. In addition, lower nitrogen loads entail that many of the unmonitored areas along the coasts are not as highly exposed to intensive agricultural activities as the inner parts of the country.
6.1.2 Monthly runoff from Danish catchments The second part of the thesis aims to estimate monthly runoff from catchments located in various parts of Denmark, based on the application of a monthly water balance model (MWB-3 (Xu et al., 1996)) and regionalisation of the model parameters (Chapter 9). The data-modelling frame developed during the first step of the study could, however, be used as the basis for this second step. The total runoff computed consists of a fast-flow and a slow-flow component. The two slow-flow components and actual evapotranspiration are each associated with one parameter and all three parameters need to be calibrated according to local catchment conditions.
The study was based upon the assumption that it is possible to estimate parameter values from catchment properties.
The main reason for not considering the use of a water balance model from the very start was that the model, like other simple conceptual hydrologi-cal models, requires a closed water balance, implying that total river discharge must be explained by the difference between precipitation
and actual evapotranspiration. According to the analysis performed when establishing the annual river discharge model, many Danish catchments do not reveal closed water balances. It is difficult to judge from the current material to which extent this phenomenon results from errors related to the measurement or processing of the water balance components. However, catchments without closed balances need to be excluded from the final calibration and validation of the water balance model. A reliable identification of all correspond-ing catchments is very difficult to perform due to the uncertainty related to all input and output flows across the boundaries of the hydrological system, including those below the soil surfaces.
One criterion chosen for catchment exclusion was therefore that the difference between corrected precipitation and potential evapotranspiration (the difference being denoted as the climatic water balance) was larger than the observed runoff, expressed as mean annual sums during the reference simulation period 1989–1997 (“positive water balance deviation”). No independent and reliable information exists at the catchment scale for the whole country about the difference between actual and potential evapotranspiration, rendering it difficult to determine the number to be excluded from the analysis of catchments where observed river discharge is only slightly larger than the climatic water balance. The calculation of potential evapotranspiration is typically related to a reference crop, here well-watered grass. More correctly, potential evapotranspiration should be estimated by multiplying the original or reference crop evapotranspiration representing the climatic forcing with a dynamic crop factor representing dynamically the effect of vegetation cover, depending on the actual land cover conditions.
Under perfect conditions, the resulting reference crop evapotranspiration and even the actual one can be higher than the original potential evapo-transpiration during some months of the year, if the crop factor values are higher than 1.0 (Henrik-sen, 1986; Allen et al., 1998). A more reliable estimation of the reference crop evapotranspiration for all catchments considered for the annual and monthly runoff studies requires crop type information from the agricultural databases and a detailed comparison of this with the CORINE or the AIS land use/land cover maps. The resulting crop factors would have to be dynamical depend-ing on growth conditions. The tight schedule of the thesis did not allow all these partial tasks to be performed. One might argue that catchments where river discharge is only slightly higher than the difference between corrected precipitation and potential evapotranspiration should be excluded.
However, the estimation of model parameters, which is necessary for application of the model in ungauged catchments, should be based on as
many catchments and observations as possible.
The exclusion from the study of several catchments for which the long-term difference between corrected precipitation and potential evapotranspi-ration is only slightly larger than the observed river discharge will therefore be problematic, in case the climatically defined potential evapotran-spiration is significantly underestimated (see discussion on the evapotranspiration in the final chapter 13 of this thesis), and/or the average crop factor applicable for the individual catchment is higher than 1.0.
Identification of catchments where discharge is
“too high” to be explained by processes exclu-sively restricted to areas within the corresponding watershed is even more difficult to make. Among all catchments potentially available for the analysis, none exists where mean annual observed river discharge is higher than mean annual precipitation during the reference period 1989-1997. To identify stations revealing extreme runoff response, another study was performed based on a hierarchical, average linkage cluster analysis (Müller-Wohlfeil et al., 2001; SAS, 2000). The variables included in the clustering were daily mean river discharge (mm), the ratio between the 95th and the 50th percentile of the flow duration curve, the frequency of flow events (per year) lower than one third of the 50th percentile, and the mean duration of flow events lower than one third of the 50th percentile. The reason for bringing slow-flow parameters into focus was the assumption that import or export of water, which may be attributed to either or both differences between the topographic catchment boundary and the ground watershed or water management measures, would primarily affect groundwater or slow-flow components. Three clusters and three outliers were identified (Fig. 6.3). The catchments belonging to Cluster 1 cover large parts of Jutland, while Cluster 2 comprises basically a smaller number of catchments located directly east of the border between the parts of Jutland that are predomi-nately covered by sediments of the Saalian period and those dominated by sediments of the Weichsel period, respectively. This border acts as a main water divide in Denmark. Areas located west of this borderline are known to export deep ground water to areas east of the water divide. Cluster 3 catchments are mainly located on the Danish islands. Please note that the cluster properties shown in figure 6.3 are normalised according to the highest values (based on values expressed in mm) found for each attribute. Clear differences exist between the three clusters in terms of runoff conditions and geographical properties.
The water balance deviation is defined as the long-term difference between corrected precipitation and the sum of potential evapotranspiration and
observed river discharge. Cluster 1 is characterised by a high ratio between the 95th percentile of the flow duration curve and the median daily flow, Q50. The percentage area covered by clay soils is significantly smaller in Cluster 1 than in Cluster 3, resulting also in smaller runoff variability (expressed by the coefficient of variation (CV), which is the ratio of the standard deviation of daily runoff divided by its mean). Cluster 2, which comprises the catchments with extreme runoff behaviour, is characterised by relatively high mean flow and an extremely high lowflow-index, Q95, indicating that these catchments might receive additional groundwater from adjacent areas.
The application of MWB-3 to the catchments used for calibration involved the use of an automatic calibration procedure. Conceptual and process-description based models typically require the adaptation of the model parameters to the hydrological conditions found in the respective catchments. The necessity for parameter calibra-tion results from the models’ imperfeccalibra-tion to represent the hydrological processes controlling water movement, owing to the fact that processes in nature are far more complex than in the idealised equations applied in a simulation model.
The same problem applies to the available databases. Distributed information is typically represented by spatially discrete, i.e. discontinuous and static units, despite the fact that these sharp borders, such as groundwater catchment bounda-ries, may be rather fuzzy in space and/or time.
MWB-3 supplies information, including local optima for each individual parameter, to the user.
As to parameters for which local minima could not be identified, the user is advised to change the starting values for the iterations.
To elaborate a procedure for the estimation of monthly runoff in unmonitored areas, the records for all 84 sub-catchments selected for the final analysis were split into a sub-set covering climate and river discharge observations from 62 sub-catchments used for calibration, and a sub-set encompassing 22 sub-catchments used for the model test. According to the experience derived from previous applications of the MWB-3 model, a
“running-in period” of three years was specified followed by a six-year calibration period.
The model fit (R2) achieved for the 62 catchments when applying the automatic calibration proce-dure varied between 0.94 and 0.45, with an average of 0.82 (table 6). Multiple regression equations were established between each of the three model parameters, A1, A2 and A3 on the one hand, and catchment properties on the other. Most of the explanatory variables found are related to soil conditions, potential evapotranspiration and mean catchment wetness (depths of groundwater tables, percentage of wetlands). When applying the model to the test catchments using the parameter values derived from the regression modelling, the resulting mean model fit expressed as R2 was nearly as large as for the calibration, but the average root mean square error (%) was higher (table 6.1).
Cluster 3
(water balance deviation: 63 mm ) Cluster 2
(water balance deviation: -162 mm )
0 20 40 60 80 100 MF
Frequency 1/3
Durance 1/3
Q95-index
CV Q5 July-fastflow
%Urban
%Clay
0 20 40 60 80 100 MF
Frequency 1/3
Durance 1/3
Q95-index
CV Q5 July-fastflow
%Urban
%Clay
0 20 40 60 80 100 MF
Frequency 1/3
Durance 1/3
Q95-index
CV Q5 July-fastflow
%Urban
%Clay
Cluster 1
(water balance deviation: 69 mm )
MF: Mean flow
Q5, Q50: The 5th and the 50th percentile of the daily flow duration curve, respectively Q95index: The 95th percentile of the flow duration
curve divided by Q50
Durance 1/3: Mean duration (in days) of flow events below one third of Q50
Frequency 1/3: Frequency of flow events (per year) below one third of Q50
July-fast-flow: Relative fast-flow contribution to runoff in July
CV: Coefficient of variation in daily flow
% Clay: Percentage of area covered by clay soils
% Urban: Percentage of area covered by urban or settlement areas
Figure 6.3 Characteristics of the three main clusters derived from an analysis of low-flow conditions.
Table 6.1 Modelling results based on automatic calibration of 62 catchments compared to results for 22 test catchments based on the application of parameters derived from the regression equations. RMSE: root mean square error. The average error (%) is defined as
å −
⋅ n Qobsi Qsimi n 1
,
, )
1 (
100 and avg. RMSE (%) is defined
as
2
1 ,
,
1 ,
100⋅
å
n ççèæ − ÷÷øöi obs
i sim i obs
Q Q Q n
, where Qobs and Qsim are
monitored and simulated river discharge and n is the number of observations
Data set Calibration Test data
n 62 22
Mean R2 0.82 0.79
Max R2 0.94 0.91
Min R2 0.45 0.64
Avg error (%) 3.77 -6.18
Avg RMSE (%) 5.24 10.72
Max RMSE (%) 22.02 20.88
Min RMSE (%) 0.02 3.24