- Soil Science Society of America
Precipitation is a key input variable to hydrological models, and the spatial variability of the input is expected to impact the hydrological response predicted by a distributed model. In this study, the effect of spatial resolution of precipitation on runoff, recharge and groundwater head was analyzed in the Alergaarde catchment in Denmark. Six different precipitation spatial resolutions were used as inputs to a physically based, distributed hydrological model, the MIKE SHE model. The results showed that the resolution of precipitation input had no apparent effect on annual water balance of the total catchment and runoff discharge hydrograph at watershed outlet. On the other hand, groundwater recharge and groundwater head were both affected. The impact of the spatial resolution of precipitation input is reduced with increasing catchment size. The effect on stream discharge is relatively low for a catchment size above 250 km2, and the effect is negligible when the entire catchment area of approximately 1000 km2 is considered. In the present case the highest resolution of 500 m was found to result in the best representation of the hydrological response at subcatchment scale. Stream discharge, groundwater recharge, and groundwater head were also affected by the method for correction of systematic errors in precipitation measurements. The results underscored the importance of using a spatial resolution of the precipitation input that captures the overall precipitation characteristics for the considered catchment or subcatchment. As long as the average precipitation of the considered catchment or subcatchment is accurately estimated, the spatial resolution seems less important when the integrated response in the form of stream flow is considered.
Precipitation is the most important input to hydrological models, and an accurate representation in space and time is critical for reliable predictions of the hydrological responses. However, a complicating factor is that precipitation often exhibits large spatial and temporal variations within a catchment. Particularly it is difficult to measure or infer the spatial structure from standard gauge measurements, and an improper spatial representation constitutes a significant source of uncertainty in hydrological modeling (Berne et al., 2004). Spatial variability of precipitation impacts the predictions of the hydrological processes such as seasonal flow in streams, floods, evapotranspiration, recharge, and groudwater heads. Moreover, it is of significant importance for the closure of the water balance of a watershed or a region (Vischel and Lebel, 2007).
Over the years considerable research into the effect of precipitation on runoff response has been performed (Obled et al., 1994; Sigh, 1997; Koren et al., 1999; Bell and Moore, 2000; Berne et al., 2004; Smith et al., 2004; Segond et al., 2007). Many studies have analyzed the impact of the spatial density of rain gauges on runoff mechanisms and found that generally the quality of the model simulations deteriorates when the density of the gauge network is reduced, see, for example, Bárdossy and Das (2008). However, studies have also shown that the significance of the impact varies widely with type of precipitation, type of model being used, general hydrological conditions of the catchment of interest, size of the catchment, and time span. Bell and Moore (2000) compared the sensitivity of basin runoff to two types of rainfall events. The authors found much greater runoff variability for convective in comparison to stratiform rainfall, noting significant dampening and reduced runoff variability during stratiform events. Koren et al. (1999) showed that the response of some rainfall–runoff models to spatial precipitation variability was scale dependent and that the level of dependency varied with different formulations of rainfall–runoff generating mechanism. Moreover, infiltration-excess type models have been shown to be more sensitive than saturation-excess type models (Milly and Eagleson, 1988; Winchell et al., 1998; Koren et al., 1999). Studies performed in the Walnut Gulch watershed in Arizona, across a range of sizes from 4 ha to 150 km2 (Faurès et al., 1995; Lopes, 1996), revealed that the spatial rainfall distribution is important for the runoff generating mechanisms at all scales, yet the importance decreased as the scale increased due to dampening effects. Effects also vary depending on antecedent conditions when storm runoff is considered. Based on results from a 10-km2 catchment in the UK, Shah et al. (1996) observed that under dry conditions, higher errors in runoff prediction (14 and 8% in peak flow and volume) were obtained to a spatially averaged rainfall input compared to the case with wet conditions (6 and 3%, respectively).
Liang et al. (2004) tested the impact of spatial precipitation resolution on the quality of model calibration based on the runoff of the 1233-km2 Blue river watershed. They found that for finer spatial resolution of precipitation input, a better calibration was obtained. A critical scale was 1/8 degree (∼14 km). The errors started to be significant when resolutions lower than 1/8 degree were used. Vischel and Lebel (2007) found that a threshold resolution of 20 km as a characteristic spatial scale over which the performance of the model rapidly decreased. Segond et al. (2007) compared effects of different spatial precipitation resolutions on runoff response and found that higher resolutions resulted in better predictions of peak discharge and runoff volume. The results provided by Bárdossy and Das (2008) showed that using too coarse of a rain-gauge network for estimating the rainfall input can result in poor simulation results and the hydrological model needed recalibration when different raingauge networks were used. Other studies have shown, however, that fine spatial resolution was not so important for the dynamics (Winchell et al., 1998; Booij, 2002) but important for the estimation of basin-average incoming volume (Obled et al., 1994).
The above review has shown that the effect of spatial precipitation variability on runoff response is complex, as it depends not only on the degree of spatial variability but also on catchment properties such as soils, geology, and river morphology and results from one region are not directly transferable to another.
The purpose of this study is to assess the effect of spatial resolution of precipitation on streamflow and recharge for a catchment in Denmark using an integrated and distributed hydrological model. In the analysis, degradation of the gauge network is not considered, but the same number of rain gauging stations is used for defining different spatial schemes. The effect of precipitation variability and its spatial representation is analyzed for different scales of the catchment. Further, different bias correction methods for wind effects are also included as part of the analysis.
Studied Area and Hydrological Model
The Study Area
The study area, the Alergaarde catchment in the Skjern watershed, is located at the central part of the peninsula Jutland, with an area of 1055 km2 (Fig. 1 ). The area is relatively flat, with altitudes from 10 to about 130 m above sea level. The topography slopes gently from east to west (Fig. 2 ). Ninety-five percent of the soil is sandy, and the rest is characterized as clayey soil types. Land use is 60.5% agriculture, 17.4% grass, 14.0% forest, 6.3% heather, and 1.8% urban area (Fig. 3 ).
The weather in the area is highly dependent on the wind direction because of the proximity to both the ocean and the European continent. The dominant westerly wind results in mild winters and cool summers with variable weather and often with rain and showers. Winds from the south and east are influenced by continental weather systems characterized by low temperatures in winter and high temperatures in summer (van Roosmalen et al., 2007). During winter the dominant precipitation system is extratropical storms from directions between southwest and northwest. The frontal precipitation mechanism is enhanced by orographical effects caused by the moderate increase in surface elevation from west to east. In summer convective rain events dominate the precipitation pattern, and the most intensive rainfall events are observed from June to August with maximum daily rainfall of up to 50 to 60 mm. On average (1961–1990, Frich et al., 1997) the number of days per year with precipitation in the area with intensities larger than 0.1, 1.0, and 10 mm d−1 are approximately 180, 130, and 25, respectively. The number of days with snowfall averages 33 (Laursen et al., 1999), which is almost equally distributed in the period from January through March. Mean annual precipitation is 1056 mm according to rainfall data from 1990 to 1995. Maximum precipitation is observed in autumn, and the minimum is found in spring.
The soils in the area are generally highly permeable (Fig. 3), and surface runoff (Hortonian) is normally not produced. Exceptions occur for rainfall events in situations where the soil is frozen; however, this mechanism is observed relatively seldom. In wetlands and areas near streams, surface runoff may be generated by saturation excess mechanisms. However, about 90% of the precipitation infiltrates into the soil and only a small fraction results in overland flow. The rest is evaporated to the atmosphere by interception loss. The infiltrated water is either returned to the atmosphere by evapotranspiration or recharged to groundwater. Some of the recharge is captured by the drainage system composed of tile drains, ditches, and small creeks and is transferred relatively rapidly to the streams. The remaining part of the recharge enters the aquifers and discharges to the streams downstream of the infiltration areas as base flow. The main river in the catchment is the Skjern River. The river water flows from north and east to west determined by the slopes of land surface elevation. Average discharge at Alergaarde discharge station at the outlet of the catchment is 16 m3 s−1 corresponding to 480 mm yr−1 (1990–1995). Hence, approximately 45% of the precipitation leaves the catchment as stream flow. Evapotranspiration and groundwater discharge out of the catchment are responsible for the remaining components in the water balance.
The description of the geology in the region is mainly based on the lithological information from water supply and oil exploration boreholes combined with seismic data. The well log information was obtained from the well database Jupiter of the Geological Survey of Denmark and Greenland (GEUS). The study area is dominated by glacial outwash sand and gravel of Quaternary age, with isolated islands of Saalian sandy till. Alternating layers of marine, lacustrine, and fluvial deposits of Miocene age underlie the Quaternary deposits. The sequence is formed by layers of mica clay, silt, and sand, together with quartz sand and gravel. Thick clay layers from Paleogene underlie the Miocene deposits, and these act as an impermeable flow boundary (van Roosmalen et al., 2007).
In this study, the hydrological modeling system MIKE SHE is selected as the model code. MIKE SHE is a spatially distributed, physically based hydrologic modeling system (Abbott et al., 1986a,b; Refsgaard and Storm, 1995). It simulates all major flow processes occurring in the land phase of the hydrological cycle. It solves the process relations for six components, each representing important physical processes in individual parts of the hydrological cycle: (i) interception and evapotranspiration, (ii) overland and channel flow, (iii) unsaturated flow, (iv) groundwater flow, (v) snowmelt, and (vi) exchange between aquifers and rivers. In this study a two-layer water balance method is used to describe flow in the root zone. Flow in the aquifer systems is based on a three-dimensional representation of the geological stratification over which the three-dimensional governing equation for groundwater flow is solved. Flow in rivers is simulated based on river geometry, slope, and the Manning roughness factor using the Muskingum–Cunge routing method implemented in the MIKE 11 model that is used to represent river flow. Further details on MIKE SHE can be found in the model user manual (DHI, 2007).
Model Set Up
The model setup is based on the National Water Resources Model (Henriksen et al., 2003) with the modifications introduced by van Roosmalen et al. (2007). The model covers a total area of 1055 km2 and is simulated on a 500 by 500 m computational grid. Ground surface elevation for grid cells is calculated from digital elevation maps on the scale of 1:25,000. The geological settings are interpreted in layers of 10-m depths based on lithological data from boreholes. A total of 38 geological layers are classified in terms of the horizontal distribution in geological units and associated hydraulic parameters. In the vertical, 16 computational layers with nonuniform thickness are used. Averaging of the hydraulic parameters within the computational layers is performed when the computation model layers are not aligned with the geological layers. The boundary conditions for the model domain are defined from surface topography and groundwater head configuration. At a given location the same conditions are specified for all computational layers over the vertical. No-flow boundary conditions are specified along the natural groundwater divide at the upstream periphery of the catchment, while a gradient of −0.0005 is specified along a 14-km segment near the outlet of the catchment.
The stream system is digitized and bank elevations assigned to specific points along the river course. Cross-sections are assessed based on measurements at specific locations in the stream system. In the model drains represent both artificial tile drains and ditches. Additionally, the drainage description captures flow through creeks and small streams not explicitly described by the river setup. The information on the drainage system in the area is limited; therefore, the model setup is simplified using drains in the entire model area and parameterized with a constant drain level of 0.5 m below soil surface. Since the topography in the study area is very flat, drain codes that specifies to which stream the generated drain flow should be routed are specified. Based on satellite data, land use is classified as grain/maize, grass, forest, heather, and urban areas (Fig. 3). The root zone is defined using two soil types, sand and sandy till. The distribution of soil type is shown in Fig. 3.
The model was calibrated in two steps (van Roosmalen et al., 2007). First, a steady-state version of the model was optimized using the automatic parameter estimation procedure UCODE (Poeter and Hill, 1999). Here the hydraulic conductivities of the groundwater zone and the leakage coefficient (conductance) controlling the magnitude of base flow were estimated. Subsequently, a transient version of the model was calibrated by trial and error against observations of hydraulic head and stream discharge from station 25.05 (Fig. 2) for the period 1991 through 1995. The parameters found in the steady-state automatic optimization were transferred to the transient model (Sonnenborg et al., 2003), while the parameters controlling the dynamics of the model response, such as storage coefficients of the saturated zone and drainage coefficients, were estimated. The calibration procedure was followed by a split-sample validation test against measurements of hydraulic head and stream discharge from the subsequent validation period. The model was calibrated using climate data from a 40-km grid network provided by the Danish Meteorological Institute (Scharling, 1999b). As will be shown below, the resolution of precipitation only has a negligible effect for the discharge simulation at the downstream station 25.05. Hence, the results presented later are expected to be unaffected by the fact that the resolution of the precipitation input used for calibration was different from the resolution of the various precipitation schemes used in the current study.
To test the effect of different spatial resolutions of precipitation on the hydrological response, daily records from 21 rain gauge stations (14 stations inside and 7 stations outside the catchment, Fig. 2) for the period from 1985 to 1995 are used. The data are split into two periods. Data from 1985 to 1989 were used as a warm-up period to reach a dynamic equilibrium, and the remaining period were used for analysis of the effects of spatial variability in precipitation.
Aerodynamic effects are the most significant source of error of point measurements of precipitation in Denmark. To correct for the undercatch caused by turbulence effects, Allerup et al. (1998) have developed correction factors that vary with the month of the year. Each rain gauge location is categorized by a shelter class according to the angle between horizontal and the surrounding obstacles, see Table 1 . Shelter classes A, B, and C are assumed to result in variable degrees of measurement error due to aerodynamic effects. The most frequent shelter condition at the field site is B, followed by A and C (Table 1). The correction factors corresponding to the different classes are listed in Table 2 . Shelter class A has the best shelter resulting in the lowest catch correction factors, whereas shelter class C is most unprotected and therefore has the highest correction factors.
In the study, the effect of precipitation spatial resolution and correction method on hydrological response is investigated. The six precipitation inputs presented in Table 3
P1: For each rain gauge a Thiessen polygon based on 21 rain gauge stations was defined, resulting in 21 areas of various sizes within which precipitation is assumed uniform. The precipitation amount for each rain gauge was corrected using actual gauge catch corrections.
P2: Kriging interpolation based on 21 rain gauge stations to a square 500-m grid was conducted. The precipitation amount for each rain gauge was corrected using actual gauge catch corrections.
P3: Inverse distance interpolation to a 10-km grid was conducted. The precipitation amount for each rain gauge was corrected using only shelter class B corrections.
P4: Kriging interpolation of available rainfall stations to a square 10-km grid. The Alergaarde catchment is covered by 22 10-km grids. The precipitation amount for each rain gauge was corrected using actual gauge catch corrections.
P5: Kriging interpolation of available rainfall stations to a square 10-km grid. The Alergaarde catchment is covered by 22 10-km grids. The precipitation amount for each rain gauge was corrected using only shelter class B corrections.
P6: Daily rainfall calculated as the average of data from the 21 rainfall stations. The precipitation amount for each rain gauge was corrected using actual gauge catch corrections.
The grid-based precipitation data set (P3) is produced by the Danish Meteorological Institute using inverse distance interpolation (Scharling, 1999a). First, interpolation of uncorrected gauge data to a 5-km grid is performed where the weights used at a particular grid are calculated as the inverse of the squared distance to the precipitation station. The interpolation routine searches for stations in four sectors and selects the nearest station in each sector. Each sector is defined according to compass directions E-N, N-W, W-S, and S-E. Hence, the interpolation may not be based on the four nearest stations. Second, the 5-km grid values are averaged to obtain 10-km grid values. Subsequently, according to the recommendations of Scharling and Kern-Larsen (2002), the grid precipitation data are corrected using correction factors of shelter class B. The Kriging data sets (P2, P4, and P5) are based on ordinary kriging of daily rainfall data where the variogram is estimated on a daily basis assuming an exponential variogram model. In Table 4 the mean annual precipitation for each of the six precipitation products are listed. Note that the differences between the precipitation sums are small.
Evaluation of Hydrological Response
Daily stream-flow data from three river discharge stations (25.05, 25.08, and 25.24; Fig. 2) for the period 1990 through 1995 are used for comparing the responses of the hydrological model to different precipitation schemes. In addition, river discharge from 13 points representing different catchment areas is extracted from the MIKE 11 model. Groundwater head elevation data from two wells in the catchment (Fig. 2) are also used in the analysis. The daily head elevation data of the two wells are extracted from the simulation results of MIKE SHE model. Further, the mean daily head elevation at a shallow (layer 2) and a deep (layer 14) layer are also extracted for the whole watershed to show the effect of precipitation input on groundwater elevation.
The Nash–Sutcliffe model efficiency coefficient (E1) (Nash and Sutcliffe, 1970) is used as an objective performance criterion when evaluating the ability of the model to simulate streamflow at multiple sites. The model efficiency index is computed aswhere and are the observed and simulated river discharges at time t, respectively, and is the average observed discharge.
To compare the effect of different spatial precipitation resolutions on river discharges, the simulated river discharge for P1 is considered as a reference, and a modified Nash–Sutcliffe coefficient (E2) is defined for the comparison analysiswhere is simulated river discharges for precipitation input P1 and represents simulated discharges for one of the alternative precipitation models, respectively. is the average discharge for simulation P1.
Precipitation Spatial Variability
Based on station data corrected using site specific correction factors, the coefficient of variation of daily rainfall has been computed (Fig. 4 ). The CV varies from 0.05 to 4.59 with an exponential decrease for larger daily rainfall amounts. If only rainfall events larger than 1 mm d−1 are considered, 62% has a CV less than 0.5, and if only rainfall events above 10 mm d−1 are considered 95% has a CV less than 0.5. This shows that high-intensity precipitation events apply more uniformly over the catchment, whereas low-intensity events are associated with higher spatial variability.
The spatial distribution of average annual precipitation based on measurements from the 21 stations for the period 1990 to 1995 is depicted in Fig. 5 . The Thiessen polygon method, P1, using site specific gauge catch correction factors yields mean annual precipitation between 900 and 1100 mm, with a relatively homogeneous distribution in the southern part of the study area, whereas more spatial variability is found in the northern and eastern parts. Minimum annual rainfall is found in the northeast corner of the catchment, while maximum is observed in the center and in the northwest part. The ratio of maximum to minimum mean annual precipitation is 1.23, and the CV of annual values is 0.05.
Figure 5 also depicts the spatial configuration of the other precipitation schemes as represented by the annual means for the period 1990 through 1995. The largest variation in precipitation is found for P1 with up to 200 mm in difference between subregions of highest and lowest rainfall. It is interesting to see that the different resolutions used for deriving the data sets P2, P4, and P6 result in considerable differences in spatial patterns. P2, with a grid size of 500 m, has a higher spatial variation of precipitation with differences up to 160 mm, while the larger grid size used for P4 results in smaller spatial variation in precipitation, with a difference in precipitation of only 80 mm.
The spatial difference in precipitation found for P3 and P5 is the effect of different interpolation methods. The kriging interpolation, P5, yields higher precipitation than P3 using inverse distance interpolation. This is partly explained by the truncation performed in the kriging method where negative precipitation estimates are set equal to zero. As a result the average precipitation found using the kriging method is higher, which is also seen from Table 4. However, the spatial distribution in precipitation of P3 and P5 is similar. The resulting spatial variation of P3 and P5 is notably smaller (<100 mm) than P1, even though the three products have similar resolution. Reasons for this difference are that (i) correction of grid precipitation for P3 and P5 is performed using only shelter class B and the variation in correction factors is therefore not considered and (ii) grid values are found from interpolation (both kriging and inverse distance) averaging out spatial heterogeneity.
Effects on the Integrated Catchment Response
Table 4 shows the simulated annual water balance for the whole catchment. Evapotranspiration and base flow to rivers vary only marginally among the six simulation scenarios, while the drain to river components of P3, P4 and P5 are slightly higher than those of P1, P2, and P6 because of higher precipitation. However, the effect of precipitation input on the overall hydrological responses and on the integrated water balance is relatively small.
The simulated discharge hydrographs at station 25.05 at the outlet of the catchment (Fig. 6 ) show no apparent differences for the six different precipitation resolutions. Recall that we adopted a calibration from another study and we made no attempt to improve simulations of, for example, low-flow situations.
The simulated peak flows of P5 are slightly higher than the others while for lower flows the simulated discharges are almost the same. These results are also reflected by the Nash–Sutcliffe coefficients (E1) for P1, P2, P3, P4, P5, and P6, which are found to 0.89, 0.88, 0.90, 0.90, 0.92, and 0.88, respectively. Overall, almost the same integrated response is obtained irrespectively of the spatial resolution of the precipitation input.
Effects on Subcatchment Scale
Observed and simulated river discharges for station 25.24, with a watershed area of 117 km2, are compared in Fig. 7a , and it shows that at subcatchment scale the choice of precipitation model affects the hydrograph simulation. Nash–Sutcliffe coefficients (E1) for the six scenarios P1, P2, P3, P4, P5, and P6 are found to 0.27, 0.25, −0.24, −0.21, −0.78, and −0.60, respectively. The largest impact is seen in the relatively wet period from December to May, where the largest differences between correction factors of the different shelter conditions are found (Table 2).
The difference in stream discharge between P2, P4, and P6 shows the effect of spatial precipitation resolution. The discharge of P2, with a spatial resolution of 500 m yields a result that is very different from P4 and P6. For the current discharge station the average precipitation increases with grid size, resulting in higher peak flow rate. The effect of resolution is also recognized in the Nash–Sutcliffe coefficients of 0.25, −0.21, and −0.60, respectively, for P2, P4, and P6.
When comparing the results of P4 to P1, both describing the precipitation at approximately the same resolution, it is seen that resolution is not the only factor that affects the results. The interpolation and averaging performed in the 10-km kriging product smears out local precipitation heterogeneity patterns and impacts the discharge simulations by the hydrological model.
The E2 values for station 25.24 presented in Fig. 8 shows that resolution (compare P2, P4, and P6), the procedure for correction of measured precipitation (compare P4 to P5), and the interpolation method (compare P3 to P5) are important for the simulation of discharge response. The three precipitation stations located in northeastern part of the catchment upstream of station 25.24 are classified as shelter condition A, corresponding to relatively small correction factors (Fig. 2). When deriving the grid precipitation schemes P3 and P5, shelter class B is a standard routine used for all stations without consideration of the local shelter classes. The shelter class issue also explains why the largest differences between precipitation models are observed in the winter period since the correction factors of the different shelter classes vary mostly in this period. Based on the simulation results of stream discharge for station 25.24 it seems that the true precipitation is described most accurately by methods using relatively high resolution and site-specific catch correction factors.
For station 25.08 with a watershed area of 82 km2 (Fig. 7b), similar results are obtained with relatively large and small effects for the winter and summer seasons, respectively. As for discharge station 25.08, P5 produces the highest discharges due to catch correction and interpolation methods. Comparison of the discharges using P2, P4, and P6 shows that apparently the resolution does not affect the results at this station, and the same are found from the E2 values of the three results (Fig. 8).
At discharge station Q1 (Fig. 2), representing a catchment area of 431 km2, the effect of precipitation model is relatively low (Fig. 7c). P5 deviates slightly from the other precipitation models; however, the impact of precipitation input is not significant. The effect is almost eliminated at station 25.05, with a catchment area of 1055 km2, as shown in Fig. 6 and 7d. This station effectively integrates rainfall heterogeneity within the catchment, and no effect is manifested of either resolution or correction method.
The interrelation between precipitation resolution and catchment size is also demonstrated in Fig. 9 , which plots the changes in the Nash–Sutcliffe coefficients (E2) for 13 discharge points randomly distributed in the river system. E2 was calculated using the results from P1 as reference. E2 is independent of precipitation resolution for catchment areas larger than 250 km2, while for sizes below this value the E2 coefficient shows sensitivity to the spatial resolution and the correction–interpolation method. The discharge stations with most variability in E2 are all located in the northern area characterized by relatively large differences between the precipitation models.
Effects on Groundwater
In Fig. 10 the spatial distribution of recharge for the various precipitation schemes is illustrated. Since virtually no overland flow is present in the catchment, spatially averaged annual groundwater recharge corresponds to the sum of drain flow, base flow, and the export of groundwater out of the catchment presented in Table 4. From the simulation based on P6, representing spatially averaged precipitation, it is evident that recharge is affected by parameters other than precipitation. Recharge varies due to variations in soil type and land use, with the latter factor having the highest impact. Areas with relatively low recharge are found where the land cover is forest. The dominating forest type in the area is conifer, which is assumed to have higher evapotranspiration than the other land use types, mainly because of higher interception loss, and thus a resulting lower recharge. However, the P1 simulation in particular also demonstrates that variability in precipitation is reflected in the recharge as the polygon shapes are clearly distinguishable on the recharge patterns. The annual recharge in this scheme varies from less than 450 mm to approximately 800 mm.
The relative effect of precipitation product and associated recharge on the shallow mean daily groundwater heads is shown in Fig. 11 . The results are illustrated as changes in mean daily heads for scenario P1, P2, P3, P4, and P5 relative to the simulation results based on P6. Spatial heterogeneity in precipitation is seen to have an impact on groundwater head distribution, and as expected, the spatial pattern of changes in hydraulic heads is consistent with the spatial pattern in precipitation. However, it is interesting to see that the impact on heads spreads outside the area of influence from precipitation. For example, the Thiessen polygon product, P1, with lower precipitation in the eastern part of the catchment (Fig. 5) affects the groundwater heads in a much larger area surrounding the polygon. The effects are most pronounced for P1 and P2, where the differences compared to P6 ranges from −1.5 and up to 0.6 m.
The effect on the deep groundwater (not shown) is comparable to the results for shallow groundwater, yet the distribution of the differences is smoother. The results show that the precipitation model is important for both shallow and deep groundwater.
Figure 12 shows the effect of precipitation model on the temporal response on groundwater head at location 87.57 (Fig. 2) representing shallow and deep groundwater, respectively. The differences between the six models are generally within 2 m, with a tendency for increasing differences during winter. The impact of recharge events is clearly seen for all the models, and the responses of the different models are similar. In Fig. 12b the response of the deep groundwater at the same location is shown. Here there are differences of up to 2 m between the P1 and the P6 models due to significantly different precipitation inputs. Contrary to the shallow groundwater, the effect of the individual recharge events is not seen at depth, resulting in a much smoother and delayed response over the season. In Fig. 13 the model response from well 105.374 is shown together with monthly measurements from shallow groundwater. At this location the difference between the models is relatively small. Only P5 produces a significantly higher groundwater level because of the relatively high precipitation and recharge in this area. All models underestimate the measured hydraulic heads; however, the bias is within a few meters, which is considered satisfactory. Although the groundwater dynamics are not captured well by the monthly data, they indicate that the fluctuations of models are slightly overestimated.
Discussion and Conclusions
In this study the effects of resolution and measurement error correction method of precipitation have been analyzed. The results presented show that precipitation input may have major impact on the response of a distributed hydrological model. Stream discharge, groundwater recharge, and groundwater heads may be affected by both the resolution of the precipitation input and the method used for measurement error correction. For stream discharge Nash–Sutcliffe coefficients between 0.27 and −0.78 are found for the different models for station 25.24, and for groundwater heads differences ranging from −1.5 to 0.6 m are found. The results underline the importance of using a spatial resolution of precipitation that is representative for the scale of interest. The appropriate spatial resolution will depend on the characteristic scale of the precipitation structure in relation to the problem scale.
In the present case the impact of resolution of precipitation input is reduced with increasing catchment size. This result is supported by studies of Obled et al. (1994), Winchell et al. (1998), and Booij (2002). The effect on stream discharge is relatively low for catchment sizes above 250 km2, and the effect is negligible for catchments larger than 1000 km2, which indicates that high resolution of precipitation input cannot improve the simulation results of streamflow for large-scale models. Generally, the catchment area required for averaging out the effects of precipitation variability and differences in shelter classes depends on the degree of heterogeneity of the precipitation distribution. The area studied is characterized by a relatively homogeneous distribution in precipitation. Ground surface elevation is relatively flat, with moderate increases towards the east, resulting in small orographical effects. The precipitation mechanism in the area is dominated by frontal rain that results in relatively homogeneously precipitation distribution (Fig. 4). However, in areas characterized by larger heterogeneity in precipitation distribution, it is expected that the area required to integrate out the impact may be larger.
The study also shows that it is important to use the local shelter conditions of the precipitation stations when correcting measurement errors. From a practical point of view it is attractive to generate grid precipitation without consideration of the local shelter conditions. The produced grid product can subsequently be corrected using the correction methods preferred by the user, which makes it robust both for different applications and for changes in correction factors. The correction factors are determined based on experimental data that are hard to generate and associated with substantial uncertainty. During the last 30 years the correction factors used in Denmark have been modified twice (Allerup and Madsen, 1979; Allerup et al., 1998), illustrating the difficulties of assessing such factors. Additionally, the shelter conditions at a precipitation station are likely to change with time as vegetation and other obstacles surrounding the station may change. Hence, the correction factors may change with time, and this adds to the problem of estimating grid precipitation without consideration of the shelter conditions at the individual station used in the interpolation scheme.
The study also shows that spatial heterogeneity in precipitation impacts the local recharge and thus the local groundwater head dynamics. While the impact of precipitation variability on streamflow is dampened due to the smoothing effect of the catchment, this effect is less dominant for recharge and groundwater heads.
The effects of precipitation input are so dominant that it could potentially impact the estimates of model parameters when the hydrological model is calibrated. To compensate for errors using a low resolution precipitation input or a precipitation input with inaccurate corrections for measurement errors, the model parameters controlling, for example, evapotranspiration or groundwater flow will be biased. This results in a hydrological model that is likely to lose predictive capability, especially in situations with significant changes in meteorological input, such as when used for climate change impact studies.
On the basis of this study, we recommend using station specific catch correction of measured precipitation. Further, it is important to avoid spatial heterogeneity being averaged out by inappropriate use of interpolation schemes. If the Thiessen polygon method is used, averaging effects are avoided, but at the expense of unrealistic jumps in rainfall when crossing the boundaries between the polygons. These unphysical structures are propagated through the hydrological model to groundwater recharge and to some extend also to groundwater levels. Therefore, interpolation is necessary, but to a scale that hinders too much averaging of the spatial heterogeneity. In the present case kriging interpolation to a 500-m grid has allowed us to meet these requirements.
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- Received December 11, 2009.
Freely available online through the author-supported open access option.