There are many techniques for evaluating the quality of atmospheric forecasts. The most commonly used tool is the surface observation network, which can be sufficient for low spatial resolution forecasts. However, the validations become more complicated for high-resolution simulations (25–0.5 km). The quality of the evaluation is directly related to the density of the observing stations. It is economically unfeasible to have an observation network with sufficient density to accurately evaluate and understand a high-resolution atmospheric forecast. The development of radar networks is an interesting alternative for this purpose. But the radar alone cannot solve all the observation problems, and it is for this reason that there are many field observation experiments.
A high-resolution simulation tries to represent physical events that are highly variable and sensitive, and the precipitation variable in particular can be very important in the validation of such simulations. This variable results from three-dimensional processes that can change rapidly and that could help us to diagnose the simulation problems. But it is also this high variability that renders the surface observations very difficult to use. The discrete nature of the precipitation observations, coupled with the high variability of the physical events and of the model errors, complicate the use of precipitation for model validation. It is for this reason that the use of the radar as a validation tool becomes interesting. The high density coverage of the precipitation field deduced from the radar observations permits great spatial and temporal improvements in the comparisons. But nothing is perfect and the radar observations have deficiencies too. It is at this point that a hydrological model becomes a very important complementary tool. The simultaneous use of the radar, the hydrological model, and the atmospheric model permits dependent and independent comparisons, thus greatly enhancing the impact of each tool. The new generation of hydrological models, which are physically based, provides a realisitic representation of the ground water cycle. The model Waterloo flood forecasting system (WATFLOOD) used here is sensitive enough to detect problems associated with the mesoscale atmospheric simulations and also with the radar observations. It will be shown that without the hydrologic model and the radar these later problems can be undetectable and even lead to a misevaluation of the atmospheric forecasts.
The southern Ontario watershed is a particularly good region to begin a detailed project of coupling between atmospheric and hydrological models. This basin is very well known by the hydrology research group of the University of Waterloo. The WATFLOOD model has been used and validated for many years with data from the King City radar. The main purpose of this project is to evaluate the utility of the hydrological model in validating and improving the atmospheric model. To know the capabilities and sensitivities of each tool, the two models have been joined by using a one-way coupling technique. In future work the hydrological model will become an integral part of the environmental modeling system that is being developed at Environment Canada. In this study we show that the hydrological model can play an important role in correctly evaluating and understanding a high-resolution atmospheric forecast. Although a demonstration of the skill of the atmospheric model was not one of the main purposes of this project, we have nevertheless been impressed by the quality of the simulations obtained.
The paper is organized as follows. Section 2 briefly describes the numerical models, the coupling strategy, and the tools used for the validations. The following section gives a short description of the case studied. Section 4 presents dependent and independent comparisons including the hydrological model, the atmospheric model, the radar, and the precipitation observations. Three resolutions of atmospheric simulations are used to provide input for the hydrological model, and the results are compared. Errors produced by the atmospheric model are described by using the radar and validated by using the hydrological model. The difficulties of using precipitation observations are also discussed. Conclusions are presented in section 5.
2. Modeling description
a. Atmospheric model
The use of an atmospheric model having the ability to solve the Euler equations at very high spatial resolution was essential for this study, given the use of radar observations and some model simulations at nonhydrostatic spatial resolutions. The MC2 research model is a fully compressible nonhydrostatic limited area model (Laprise et al. 1997; Benoit et al. 1997). The model employs a fully 3D semi-implicit semi-Lagrangian time discretisation scheme and a generalized terrain-following coordinate system. Lateral boundaries are specified as open with inflow–outflow determined by the normal components of velocity (Thomas et al. 1998).
The model uses the full unified Recherche en Prévision Numérique (RPN) physics package. This package consists of a multioptioned and comprehensive set of parameterizations of physical processes. A comprehensive description can be found in Mailhot (1998). The main components used for the experiments are summarized in Table 1. Advanced microphysical equations (Kong and Yau 1997) to simulate cloud scale processes were used for the high-resolution simulations (10 and 3 km). The prognostic microphysical variables are the water vapor, the cloud water, the rainwater, and the ice particles (two ice phases).
The model was run with horizontal resolutions of 35, 10, and 3 km. Figure 1 shows the simulation domains for the three resolutions. Grid A represents the limited area (7035 km × 7035 km) covered by a 201 × 201 uniform resolution grid at 35 km. Grids B and C represent, respectively, the domains for the 10-km (255 × 215 points) and 3-km (301 × 301 points) simulations. An important aspect of this study is the physical fields that are imposed at the initial time and also as boundary conditions. The 3D variational data assimilation scheme (Gauthier et al. 1996) using the Global Environmental Multiscale (GEM) model (Côté et al. 1998) was used to generate analyses at 35 and 15 km. These were used by the 35- and 10-km runs, respectively, as initial and boundary conditions (every 6 h). For each model resolution, the 3-day period of this storm case has been spanned by three different simulations with a duration of 36 h each. Each simulation (35 and 10 km) started 6 h before 0000 UTC of each day. The high-resolution simulations (3 km) were initiated (4 h after) and nested (every 2 h) directly with the outputs of the 10-km runs. Only the last 24 h of each of the three simulations at a particular resolution have been used for the assessment.
b. Hydrological model
1) Land surface model
The hydrological model (see Table 2) is a gridded grouped response unit (GRU) model called WATFLOOD (Tao and Kouwen 1989; Kouwen et al. 1993). The GRU technique models the land surface processes separately for each land cover within a computational grid element although all individual areas within that element are subject to the same meteorological conditions. The hydrological responses from all GRUs in a grid are summed to give its total response. The modeling parameters are tied to the land cover type and as such should apply to other watersheds where the land cover mix may be different, but where similarly vegetated areas can be expected to respond in the same way to meteorological conditions. This allows the model to be applied to regions composed of many watersheds with the same parameter set being applied throughout the region. Water is routed from grid point to grid point to give the total watershed outflow at the basin outlet.
2) Channel flow routing model
A two-stage flow routing procedure is used in WATFLOOD. For overland flow, an explicit, noniterative method is used that is based on continuity and Manning’s formula and incorporates the average surface slope and roughness for each grid. River flows are similarly based on continuity and Manning’s formula but separate parameters are used for channel and floodplain roughness and an iterative approach is employed. A geomorphologic relationship is used to relate channel cross-sectional area to the drainage area of the basin. The grid size provides the overland flow distance in each grid. The channel reach lengths and riverbed elevations, obtained from topographic maps, provide channel slope. Up to five separate classes of channel may be used, such as steep mountain creeks or flat meandering rivers.
c. Coupling strategy
One of the purposes of this experiment is to study the impact of the atmospheric model on the hydrological model, where there is no feedback into the atmospheric model. The sensitivity of each model is the main point treated here and is considered as a baseline for our future studies with more complex couplings. Thus a one-way coupling is used to connect the two models. The atmospheric model (1-h precipitation accumulation and temperature) influences the hydrological model at each hour of simulation (Fig. 2). Both models use their own simplified land surface physical processes. For the moment the hydrological model uses a water balance calculation as opposed to a water and energy balance calculation. In future studies, the atmospheric and hydrological model will share the same detailed land surface processes (e.g., Canadian Land Surface Scheme, Interactions Soils–Biosphere–Atmosphere) in a two-way interaction (Fig. 2). The hydrological model (routing model) will become an integral part of the environmental modeling system.
The two-dimensional fields required for the one-way coupling and generated by the atmospheric model at 35 and 10 km on a polar stereographic projection are interpolated to the 10-km universal transverse mercator (UTM) grid of the WATFLOOD hydrological model. The 3-km resolution results are averaged onto the WATFLOOD grid. The hydrological simulations are started 49 days before our period of interest and are driven each hour with radar data and ground surface observations. This warming-up period allows a good initialization of the physical variables (soil moisture content). The data produced by the atmospheric simulations (3 × 24 h) are embedded in this warming-up period.
d. Watershed and tools used for the validation
The precipitation patterns observed by the radar are compared directly with those simulated by the model. The radar and model data are also used in the hydrological model to compare the simulated flow with the flow observed at 23 stream gauges. The amount of precipitation produced by the atmospheric model is also compared with 72 rain gauges. With these different types of comparisons (independent and dependent), it is possible to establish the quality level of each component. Figure 3 presents the topography of the southern Ontario watershed, with the main rivers and the political borders superimposed. The labels mark the 23 stream gauges used for the verification. The circles represent the distances from the King City radar at 50, 100, 150, and 200 km.
3. Case studied
On 20 April 1993 at 0000 UTC (Fig. 4), a surface low was located over the Missouri–Iowa border. The system moved eastward toward the study area and was centered over Michigan at 1200 UTC. The low moved directly over the watershed between 1200 UTC on 20 April and 0600 UTC on 21 April. The dates 19, 20, and 21 April 1993 have been modeled (3 × 24 h). Many small waves successively passed over the domain, generating precipitation.
The weather during the 3 days was quite varied in type and in scale (Joe et al. 1994). During the day on 20 April one area to the northeast of the radar reported strong winds and a variety of precipitation types: snow, freezing rain, thunderstorms, and hail. However, the surface precipitation type in the study area overwhelmingly consisted of rain, the temperatures varied from just above freezing to nearly 20°C and the radar-measured precipitation aloft could have been quite varied. During the study period the precipitation was mainly stratiform, associated with the warm front ahead of the low, but there were several convective periods. Table 3 is a brief log of observations based on the radar data. No compensation for storm type was made in the radar analysis. Richards and Crozier (1983) studied the relationship between Z and R under different meteorological conditions in southern Ontario and found that stratifying the data by precipitation type or weather type did not reduce the variance in the Z–R relationship. The important conclusion was that a single Z–R was appropriate for this weather regime. [Even in the Tropics, where the diffferences between the stratiform and convective precipitation regimes are very large, work such as Steiner and Houze (1997) indicates the difficulty of improving rainfall accumulations by varying Z–R between regimes.] Joss and Waldvogel (1990) indicated that the Z–R dependency on drop size distribution is only one factor in the ability to use radar for precipitation estimation; it is not the limiting factor in this study.
This section presents traditional and nontraditional tools for the validation of precipitation fields produced by atmospheric models. Radar data and precipitation observations are two tools allowing us to do a direct comparison of precipitation field characteristics. These tools are compared with the new indirect tool that is being tested here—the hydrological model. These experiments show the uncertainties of each tool independently, but also their interesting complementary nature when they are used together. The predicted precipitation patterns are compared directly with rain gauge observations and with radar data, another particularly powerful tool. This comparison allows us to diagnose errors generated by the model. But the available radar coverage does not permit a comprehensive verification over the entire domain. It is demonstrated that the hydrological model is sufficiently sensitive and accurate to diagnose model and radar errors. Note that the several figures (Figs. 5, 6, 7, 9) are on a UTM projection corresponding to the WATFLOOD model while others (Figs. 1, 3, 4) are on a polar-stereographic projection with a different orientation of the meridians.
a. Observed and simulated precipitation patterns
1) Radar observations
The radar rainfall accumulations presented here are based on the 2 km × 2 km Cartesian 1.5-km constant-altitude plan-position indicator (CAPPI) radar product that is built from a 24-elevation-angle volume scan with a 1-km range bin and 1° in azimuth resolution. The radar is a C-band (5 cm) radar with a 0.65° beamwidth (Crozier et al. 1991). The radar data have been compared with rain gauge data in the past and appropriate corrections for bias have been applied. Note that the lowest angle, at 0.3°, lies above 1.5 km beyond about 140 km, so that the CAPPI level rises higher beyond that range. Previous studies show that a single Z–R relationship (a = 295 and b = 1.43) is appropriate for this locale (C. L. Crozier 1998, personal communications; Richards and Crozier 1983). No adjustments are made for vertical profile effects.
Figure 5a presents the 72-h precipitation accumulation observed by the radar. The data are averaged to a resolution of 4 km. The domain of 190 km × 210 km corresponds to the grid used by the hydrological model. A maximum of accumulation is located in the northern part of the domain, a second one is in the center, and a third one is in the southeast corner. These maxima correspond to the trajectories of the storms contributing most to the precipitation. The circle located near the radar represents an area of particularly high ground clutter. The hydrological basins affected by this area are not modeled in this study. Figure 3 shows that these latter basins flow toward Lake Ontario.
Figure 5a shows a decreasing amount of accumulated precipitation with increasing range from the radar. The decrease is due mostly to vertical profile effects, beam averaging, and beam filling. The slanting radar beam increases in size and in height with range. The profile of reflectivity decreases with height due to a phase change from rain to snow as well as due to particle size evolution. The radar averages more lower reflectivity targets and eventually no targets as the beam scans higher in the atmosphere and farther from the radar. During the study period there were some times when the radar appeared to be contaminated by brightband effects, but these times do not seem to have contributed significantly to the total accumulations. Attenuation also plays a small role (Joss and Waldvogel 1990). The effective range for quantitative precipitation estimation by the King City radar without sophisticated vertical profile correction has been estimated to be 130 km (C. L. Crozier 1998, personal communication).
2) Rain gauge observations
The analysis presented in Fig. 5b is based on observations from the 72 rain gauges. The spacing between the stations varies from approximately 5 to 60 km. The approximate average spacing of the rain gauges is about 20 km. Given the lack of resolution, particularly in the upper part of the domain, it is difficult to do a detailed comparison with the radar data (Fig. 5a); for example, the third maximum of precipitation seen in the southeast corner of the radar is not observed with the rain gauges. However, the two main storm paths are still visible. Two 40-mm maxima located on the top center and near the bottom center of the analysis are not visible in the radar picture. The southern maximum seems to be primarily due to the low topped convective lines early on 20 April, while the northern maximum is due to a combination of persistent stratiform precipitation and thunderstorms on 20 April.
3) Atmospheric simulations at grid resolutions of 35 and 10 km
Figure 6 presents the 72-h precipitation accumulation simulated by the atmospheric model at 35 and 10 km. The low-resolution patterns produced by the 35-km run do not compare well with the radar picture (Fig. 5a). Given the lack of resolution, the model has only generated a big maximum centered on the watershed. The simulation at 10 km has a significant increase in the details. These improvements are the result of the physical events being better resolved by the model, as well as the use of better precipitation schemes at the higher resolution. The 10-km simulation develops the two main trajectories (dashed lines) seen by the radar (Fig. 5a). Clearly the simulated patterns converge to those seen by the radar. We also see a good correlation with the patterns, as well as the amounts, of the analysis (Fig. 5b). However, in comparing Fig. 6b with Fig. 5b, it seems that trajectory 2 (V shape) produced by the atmospheric model is shifted in the westward direction. Section 4b will discuss this simulation error in more detail. Clearly we still need to increase the grid resolution to really be able to compare with radar patterns.
4) High-resolution atmospheric simulations (3 km)
The simulations at 10-km resolution have been used to directly nest simulations at 3-km resolution. These high-resolution simulations do not use a convective parameterization scheme for the precipitation. All the precipitation processes are solved directly at the model scale by using advanced microphysical equations (Kong and Yau 1997). The prognostic microphysical variables are the water vapor, the cloud water, the rainwater, and the ice particles. This scheme has been used in parallel with the Kain–Fritsch scheme (Kain and Fritsch 1993) for the 10-km simulations. To assume that all the precipitation events are resolved by the model at 3-km resolution is probably unrealistic given that the effective resolution is somewhat coarser. But parameterization schemes such as Kain–Fritsch have not been developed for use at these high resolutions, and even 10 km is approximately the limit to which the scheme has been tested to date. It is not one of the objectives of this paper to test the use of convective parameterization schemes at high resolutions (10–5 km), although this could be considered in future studies.
Figure 7 compares the 3-km simulations with the radar picture. The orientations and shapes of the northern and southern simulated lines (dashed and dotted) compare well with the radar. However, the northern line seems shifted by approximately 30 km in the westward direction. The comparison of the V shape (solid line) is more difficult to do. This shape is the result of a subset of many small events having different trajectories, which can be more or less missed by the atmospheric simulations. The next section shows that the line forming the northwest part of the V shape (Fig. 7b: V1) is effectively shifted in the westward direction. This could explain the minimum located in the center of the simulated pattern (V shape). Nevertheless, the simulated pattern has approximately the correct V shape compared with the radar pattern. The same shift was also observed at 10 km (Fig. 6b). A small maximum located to the north of the Walkerton and Hanover stations (station numbers 200 and 210, cf. Fig. 3) is clearly overestimated by the model compared to the radar. In this case, the use of the hydrological model as a complementary tool will be very useful. In general, the events produced by the model seem to agree with the radar observations. But it also seems evident that the simulated patterns can have a shifting problem. The next sections will describe these errors in more detail and will demonstrate the utility of the hydrological model as a diagnostic tool.
b. Errors produced by the atmospheric model
The previous section has shown errors and uncertainties related with the atmospheric simulations and radar observations. This section will briefly describe this problem and will allow a better understanding of the type of errors produced by the atmospheric model. It will be easier to interpret the hydrological results consequently, in the subsequent sections.
1) Large-scale patterns
Figure 8 presents the large-scale pattern of the 850-hPa geopotential height valid at 1200 UTC April 20. The dashed contours represent the 15-km analysis whereas the solid contours represent a 24-h simulation by the 10-km model. This figure clearly shows the time discrepancies of the atmospheric simulation. On that day (20 April), the simulation has a lead over the analysis.
2) Small-scale time frames
Figures 9 show a comparison of several time frames between the high-resolution atmospheric simulation (3 km) and the radar observations. The contours represent 1 h of precipitation accumulation (mm). Pattern recognition serves as the basic criterion for the comparison. The frames produced by the model are not synchronized with the observations: the first simulation (Fig. 9b) is 3 h slow (19 April), whereas the second simulation (Figs. 9a and 9b) is 1 h ahead of the radar (20 April).
The physical events of Fig. 9a came before the convective period (1700–2100 UTC 20 April). The scales of the events in that period are large enough to be well represented by the grid of the atmospheric model (3 km). The first comparison (Fig. 9a, row I) shows that the model reproduces patterns with approximately the same shape (dashed lines) as those observed by the radar. The simulated patterns are more extensive, however, and the amounts are also a bit greater. This problem could probably be an effect of the spatial resolution that is not yet quite sufficient for the atmospheric simulation. The decrease in radar signal beyond about 140 km is evident. The radar underestimates the major precipitation event coming in from the western border (Fig. 9a, row I.m) of the domain. For the second and third comparisons (Fig. 9a, rows II and III) the radar is able to detect the precipitation event. The patterns produced by the model are very similar to those observed by the radar. The arrows in Fig. 9a, row III represent the trajectories of the main simulated and observed events (between rows II and III). The model has produced a trajectory toward the northeast (row III.m) while the radar observed a trajectory more eastward than northward (row III.r). These possible errors in the trajectories of the simulated physical events could explain the spatial shift of precipitation patterns (72 h; Fig. 7) seen in the last section (4b). Yu et al. (1998) have already compared 6-km simulated precipitation events with Doppler radar and found similar errors relative to an in situ network.
The second part of this comparison (Fig. 9b) presents physical events of smaller scale than those observed in the previous figure. The first comparison (Fig. 9b, row I) shows an event affecting the northern part of the domain. The model overestimates the precipitation amount by a factor 2. The same conclusion is found for the event simulated 8 h later (Fig. 9b, row II). This second event overestimates by a factor 3 the water amount for the Grand River Basin. The last event compared (Fig. 9b, row III) arises just after the event presented in Fig. 9a and right in the convective period (1900 UTC April 20). The arrows represent the respective trajectories. It is clear that the trajectory followed by the simulated events is shifted in the northwest direction. This can explain the minimum located in the center of the V-shaped pattern in Fig. 7b (section 4a).
This sequence of time frames more directly illustrates the errors produced by the atmospheric model. When the physical events are large enough to be correctly seen by the numerical grid (3 km), it seems that the model produces a very good representation of the observed events (position and amount) with limited time and space shifts. However, the smaller events are not correctly resolved by the simulation. The precipitation amounts produced by the smaller scales are systematically overestimated. A resolution of 3 km is not sufficient to accurately represent all the convective events, and too high to use the available convective parametrization scheme. The energy that is not dissipated by the missing convection scheme can contribute to produce unrealistic physical events. Clearly this process is only one of many factors that could prevent the smaller events from being correctly modeled.
In general, the character of the simulated events agrees with the observations. The same conclusions were reached in the previous section.
c. The use of rain gauge observation
It is often a difficult task to use precipitation observations to validate the precipitation predicted by atmospheric models. Many different independent factors can influence the comparison. Probably the most important factor is the fact that we try to compare a discrete point observation with a grid point representing the average of an area of 10 squared kilometers or more in the forecast of an event that can have a high spatial variability. Frequently the models do not have enough degrees of freedom to correctly represent the precipitation events seen by point observations. For this reason, the density of observation stations has an important impact on the quality of the comparison. As it is not always possible to produce a good analysis (Fig. 5b), particularly in mountainous regions, a scatterplot comparison is often used as an evaluation tool. Figure 10 presents a comparison between the precipitation amounts predicted and the precipitation observed at 72 stations. We can see that the best curve fits improve with increasing model resolution. But this is almost all the pertinent information that we can extract for the type of forecast that we want to assess.
The previous section showed that the character of the atmospheric simulations seems to agree with the observations, but it also seems that the models produced errors in the specific timing and location of events. Considering that the models have problems producing the correct events at the right place and the right moment, combined with the fact that these events can be undetected or wrongly measured by the observation network, it is clear that this tool is not entirely appropriate to use to accurately evaluate and understand the forecast. Therefore, the use of radar data and hydrological models becomes crucial in the evaluation of high-resolution simulations. Figure 11 presents precipitation accumulation (72 h) along a narrow east–west band for the three model resolutions and the rain gauge observations available in that band. The graph shows increasing spatial variability with finer simulation resolution. In general, the line representing the high-resolution runs (solid) has the best synchronization with the observed interpolated line (dashed line). The values can be over- or underestimated but the horizontal gradients have approximately a comparable slope. One exception is seen for the interval between 15 and 35 km. The interval of highest density of observations (between 60 and 80 km) shows a higher variability for the observed curve than the 3-km curve. This shows that, effectively, the 3-km atmospheric simulations still seem to lack resolution (Fig. 11: circle). This type of problem could be poorly assessed using only station observations. The major precipitation event produced by the model at 105 km (Fig. 11:square) is difficult to assess given the lack of observing stations in that region.
As we have seen, both the radar data and the station observations can be inadequate as validation tools for the numerical simulations. It is important to be very careful with the conclusions found from this type of comparison. This is particularly true if the physical field is highly variable in space and/or time. It can be very difficult to do an evaluation based on an imperfect model that moreover has been designed to represent areal (grid box) averages rather than discrete point values corresponding to the observation sites. The next section will present the possibilities that the hydrological simulations can offer to complement the radar and the raingauges.
d. Observed and simulated streamflows
The purpose of this section is to present the interesting opportunities offered by the hydrological model as a new tool to validate and interpret results produced by atmospheric models. The advantages offered by the flow observations are different from those offered by precipitation observations. The dependency between basins and their subbasins can be very useful to understand the possible problems of spatial shifting in the modeled atmosphere. The spatial integrating effect of precipitation also permits a better estimate of the amount of water that has fallen over a region.
Hydrological simulations have been performed by using data from the radar and the atmospheric simulations (35, 10, and 3 km). This physically based model does not need to be adjusted depending of the watershed modeled (as opposed of a model based on statistic relations). Coupling has been done between WATFLOOD and radar data (King City) over many years, with very good results. This suggests that this tool is probably precise enough to be used in the evaluation of atmospheric simulations. The main uncertainties related to the hydrological model can be attributed to three factors:the quality of the initial conditions (initial soil moisture content), the dynamical formulation (channel routing and roughness), and the physical processes (evaporation, number of soil layers, depth of saturated zone, . . . ). The initial conditions have been generated by running the hydrological model during the 49 days before the storm, using radar data (precipitation) and ground surface observations (temperature). The initial soil moisture affects the initial rise of the hydrograph. The dynamical formulation is the factor having the most important impact for our experimentation. The channel routing component of the water’s path is the dominant factor in timing the flow. There are separate slopes for overland (very small channels) and stream or river channels. After the model has been applied to many watersheds, the river roughness parameters can be fairly well estimated and they do not change much over time (although there are exceptions due to weeds and ice). As for the physical processes, they have a less important impact given that our period of interest is only three days long. Clearly there are uncertainties related to the hydrological model and it is for this reason that the experimentation includes the use of two independent sources of meteorological fields (radar and atmospheric model). Nevertheless, we emphasize that the purpose is not to validate the hydrological model, but rather to show that it can be useful to improve the different techniques used to generate numerical atmospheric fields. We are still trying to assess if the precipitation fields from weather models and radar are reasonable.
The first part of this section presents the sensitivity of the hydrological model to different horizontal resolutions used in the atmospheric simulations. The second part demonstrates the sensitivity of the hydrological model in detecting the strengths and weaknesses related to the atmospheric models and radar data.
The hydrological network is composed of five principal basins covering 20 630 km2 (Fig. 12). These are subdivided into 23 subbasins. The Grand River Basin (3543 km2) located near Kitchener–Waterloo is particularly interesting for this study. Its location near the radar (<100 km) makes it a particularly well observed basin in terms of radar estimates of precipitation. The Nottawasaga River Basin, located in the northern part, is also near the radar (<50 km). The Saugeen River Basin, located in the western part, stretches from 75 to 150 km from the radar. The fourth basin (Maitland River), located near Wingham, is at approximately 140 km from the radar. The last basin (Thames River) is located in the south, near London. It is far from the radar (between 125 and 170 km).
1) Impact of different resolutions of atmospheric simulations
Figure 13 presents a comparison between synthetic (model results) and real hydrographs for the five major basins. The calculated flows have been produced by WATFLOOD using atmospheric data from simulations at 35, 10, and 3 km. The water amount generated by the model at 35-km resolution is systematically overestimated. It is also clear that there is a significant improvement between the 35- and 10-km simulations. The increased resolution better resolves the precipitation events. Galt and Baxter stations (Fig. 13) show that effectively the first major event generated in the 35-km simulations has been resolved into several smaller events in the 10-km simulations. The same conclusions are found between the 10- and the 3-km simulations. For Galt, Baxter, Belgrave, and Thorndale the higher-resolution simulations have systematically improved the water amounts. It is only for Walkerton that we cannot clearly see an improvement. For this station, the atmospheric model overestimates the intensity of the physical events. The improvement of accuracy in the hydrological results seems to indicate that increasing the resolution allows the atmospheric model to better resolve the observed physical events. However, the intensities of these events can be underestimated or overestimated. The variability in the quality of the results obtained over different basins suggests that the atmospheric model effectively resolves mesoscale events. It is important to note that all the conclusions found in the previous sections (comparisons with radar and ground stations) have also been observed and in part validated with the hydrological results. It is difficult and even impossible to draw these conclusions when only using the rain gauge observations (Fig. 10). The next section will show that the hydrological model can be still more effective.
2) Impact/synergy of two sources of hydrological forcing: Radar and atmospheric model
Figure 14 compares simulated flows obtained by forcing WATFLOOD with radar data and with the high-resolution atmospheric data (3 km) versus the observed flows. Figure 14a presents results for Grand River. Its location near the radar (<100 km) makes it a particularly well-observed basin. Furthermore the main precipitation events occur here (Fig. 7: V shape). The arrows joining two graphs in Fig. 14a indicate that the first basin is a tributary of the other one. The Marsville Basin (694 km2) is located very near the radar (<70 km). A very good fit is obtained between the radar (long-dashed line) and the observations (solid line). The radar curve is slightly underestimated for the secondary Montrose Basin (1170 km2) and slightly overestimated for Guelph (518 km2). But the biggest basin (Galt, 3543 km2), which includes all the subbasins, indicates that the average precipitation estimated by the radar for this region is very good.
Section 4a has shown that the precipitation accumulation patterns produced by the high-resolution atmospheric simulations seemed shifted by approximately 30 km in the westward direction compared with the radar data. The same conclusions have been found in the following section (4b) in comparing more directly some important time frames of the simulation. The possible spatial shifting, in the westward direction, of the trajectory of an important simulated event has been used as a hypothesis to explain the minimum in the V shape in Fig. 7b. Using the hydrological model to evaluate this possible error is particularly interesting, given that it occurred directly over the main hydrological basin (Grand River). In order to evaluate/confirm this finding, all the precipitation events produced by the model have been systematically shifted by approximately 30 km in the eastward direction. However, it is not certain that the model has produced the same shifting error for all the events. The precipitation accumulation patterns (Fig. 7) have been used to find an average of the errors that developed during the simulations. The main purpose of this test is to evaluate the ability of the hydrological simulations to detect/confirm small-scale errors produced by a mesoscale atmospheric model. The short-dashed line (Fig. 14a) represents the flow simulated by the hydrological model using the shifted events. In comparing with the original events (dashed–dotted–dashed line) it is clear that the shifting had a positive impact for all the subbasins. The flows have been increased for the Montrose Basin and reduced for the tributary Marsville Basin. The improvement is most evident for the Drayton Basin (a very small basin). The shifting has reduced the flow at the Guelph station during the first period of the storm. In summary, the flows have been increased for the eastern part and reduced for the western part of the Grand River Basin resulting in a positive impact on the main stream gauge located at the Galt station. As this last measurement represents the precipitation that has fallen over all the basin, and given that the results have been greatly improved by the shifting, this supports the hypothesis stated in the last section. The overestimation (a factor of 3) obtained in using the model data, between 1800 UTC on April 19 and 1200 UTC on April 20 at the Galt station (T1 and T2 in Fig. 14a: Galt) could be explained by the overestimation of precipitation produced by the small physical events. Figure 9b, row II effectively shows an overestimation of flow (also by a factor 3) that directly affects the Galt station.
The Nottawasaga River Basin (Fig. 14b), located in the northern part, is also near the radar (<50 km). The radar gives a small overestimation and the atmospheric model gives a small underestimation. The shifted pattern has improved both station comparisons. As we have seen in Fig. 9a, row III, which presents a comparison between the radar and the model, it was evident that the model produced a northward shift for an important event that occurred directly over this basin. This error could explain the underestimation at the Hockley station and also the fact that a minimum is found on the simulated curve at Baxter.
The Saugeen River (Fig. 14b), located in the western part, stretches from 75 to 150 km from the radar. This river is particularly interesting for seeing the effect of underestimation of precipitation by radar with range over a single basin. Hanover and Walkerton (basins) are located between 75 and 125 km from the radar. A very good correlation is obtained between the radar and the observations for both. However, the location of Port Elgin farther from the radar (150 km) clearly gives an underestimation of the simulated flow. This underestimation is shown in Fig. 9a, row I and Fig. 7a.
The extension of the Port Elgin Basin over a distance of 75 km allows us to see the time lag for the flow in the river. The Port Elgin flow stays high for a longer time than for Walkerton and Hanover. The radar does not see the events near the station, explaining the low flow until 21 April. The water flow after 21 April comes from the tributary basins located nearer to the radar (Hanover and Walkerton), which are correctly observed. It is clear that the atmospheric model overestimates the precipitation amount for this basin. The curves for the three stations have approximately the correct shape, suggesting that the model has generated the correct events but not with the right strength. The observed ascending slope at the Port Elgin station is greater than the slope simulated by the atmospheric model, suggesting that the precipitation events simulated near the station were not intense enough. And the inverse is observed for the Walkerton station located more to the south. The large overestimation obtained 22 April at Port Elgin when using the model data comes from the overestimation obtained over the tributary basins (Hanover and Walkerton: 200 and 210). This can be explained in part by Figs. 7 and 9b (row I), which show an overestimation of the precipitation events affecting the Saugeen Basin.
The fourth basin (Fig. 14c: Maitland River) located near Wingham is approximately 140 km from the radar. The good correlation between the radar curves and the observed curves (Fig. 14c) suggests that the radar sees the correct events but underestimates their strength. The atmospheric model has produced very good simulations for the Wingham Basin, but slightly overestimates the Belgrave Basin observations.
The last basin (Fig. 14d: Thames) is located in the south near London. It is the farthest from the radar (between 150 and 175 km). The underestimation effects are also clearly evident and are largely caused by overshooting the low-level precipitation and beam averaging. All the subbasins are underestimated or even completely missed (Ealing) by the radar. The hydrographs simulated for the major basins Thorndale and Ealing have reacted positively to the shifted model patterns. However, the eastern part has been underestimated by the atmospheric model. The results obtained at the Thamesford station suggest that the model has completely missed or underestimated some small events [see the 40-mm blob appearing at the tail of trajectory 2 in the subjective analysis (Fig. 5b), which would affect more the eastern branch of the Thames watershed]. In this region far from the radar the hydrological simulations indicate clearly that the model data are of better quality than the radar data. The relatively good correspondence between the curve shapes generated using the atmospheric model and the curve shapes of the observed flow strongly suggest that the model produces physical events that are very realistic. It is also evident that the model can overestimate or underestimate these events. Figure 15 shows the rms errors between the calculated (3 km without shift) and observed flow for each station. The stations are arranged from the closest to the farthest distance from the radar. The graph shows that up to a distance of 125 km (station 300: Wingham) the quality of the radar data (solid line) is better than or equal to the atmospheric model result (dashed line). Beyond Walkerton, from 125 to 170 km, we find the inverse: now it is the model result that is better than or equal to the result using radar data. Note that this comparison uses the original data (without shift) of the atmospheric simulations. It is clear that the use of the corrected atmospheric data would improve the dashed line. The significant overestimation produced by the model for the Saugeen River Basin is clearly visible.
3) Accuracy of the hydrological simulations
Up to this point, the hydrological simulations have been used to evaluate the accuracy of the radar observations and the atmospheric simulations. However, we have not really questioned the accuracy of the hydrological simulations. The quality of comparisons obtained between the observed and simulated flows (Fig. 15) suggests an interesting insight produced by the hydrological model. As described at the beginning of this section, the main uncertainties related with the hydrological model and which could be visible in our simulations are the quality of the initial conditions (soil moisture content) and the accuracy of the dynamical formulation (channel routing).
It is possible to estimate the quality of the initial soil moisture content by comparing the initial rise of the simulated hydrograph with the observation. If the soil is too wet, the simulated hydrograph will rise sooner. For each basin of our experiment, at least one of the simulated hydrographs (with radar or atmospheric model) give a good timing of the initial rise. This analysis suggests that the initial soil moisture was relatively well estimated by the warming-up period (section 4c). The accuracy of the channel routing component of the water’s path can be estimated in comparing the timing of many simulated flows with observations. Undoubtedly the timing is also dependent on the uncertainties related with the atmospheric model and the radar. But in general for each basin always one maximum of the simulated flow corresponds relatively well with the observed values.
Figure 16 shows the rms errors between calculated and observed flows versus the watershed areas. The errors have been normalized as a function of the area of the biggest watershed (Galt). Given that the purpose is to estimate the quality of the hydrological simulations, only the watersheds near the radar have been used for the comparison. We make the hypothesis that the Grand River and the Nottawasaga River are close enough to the radar to neglect the effects of radar underestimation of precipitation in these regions. The radar line (solid) is considered as the observation line, the limit of accuracy for the hydrological simulation. Ten hydrological stations have been used and two stations (Eramosa and Pine) have been eliminated given a lack of data. Lines with markers join the individual stations, and the darker lines represent the best fits (power). The dotted lines present the results for the (unshifted) atmospheric simulation at 3-km resolution, and the dashed lines represent the shifted atmospheric simulation at 3-km resolution. The similarity in shape of the best fits obtained for the three cases indicates that the sensitivity of the hydrological simulation is being effectively measured. The error levels are approximately constant for the large areas. Significantly increased error levels are seen for the areas smaller than 500 km2 (for the radar). This could be explained by many factors, such as problems with the observations, but the most plausible explanation is the lack of spatial resolution of the hydrological model. With the horizontal resolution of 10 km used here, it can be difficult to accurately represent the smaller basins. For example, the watershed of Drayton on the Grand River (293 km2) is represented by only three grid points in the hydrological model. It is probably for this reason that any of the simulated hydrographs perfectly correlates with the observed curve.
It is also interesting to compare the curves (best fit) produced by the atmospheric simulations versus the radar curve. The difference between the dotted and solid lines indicates that the atmospheric model produces more errors than the radar-deduced precipitation. However, the biggest basins (3000 and 4000 km2) show approximately the same error level for the atmospheric model. The increasing difference between the atmospheric curves and the radar curves, for the smaller basins, is the result of the atmospheric model’s problem in correctly positioning the physical events.
The small basins are more sensitive to the spatial shifting problems. The improvement with the spatial shifting (Fig. 14) is visible in the dashed curve. All the basins have a better spatial distribution of the precipitation. The difference between the dashed and solid lines could indicate that the correction applied to the atmospheric simulations does not compensate for all the deficiencies (water amount). The difference is negligible for the large basins (1000–4000 km2) indicating that the simulated atmospheric events are very realistic. This conclusion is in agreement with the comparisons versus the radar images presented in section 4b (Figs. 9 and 7). The atmospheric model seems to create physical events reflecting the observed events, but not necessarily with the exact position and the right strength.
This graph also supports the comment made in section 4c regarding the difficulties in using precipitation observations to accurately evaluate a high-resolution atmospheric simulation. In Fig. 16, a rain gauge could be seen as a watershed of ∼0 km2. The gap between the dotted and solid lines increases with the decreasing of the area, suggesting the possibility of very large errors for a very small area. This type of graph gives very interesting insight into the accuracy of the hydrological and atmospheric simulations.
The main purpose of this project was to estimate the utility of hydrological models for the evaluation of atmospheric simulations. It has been demonstrated that the hydrological model is sufficiently sensitive to help us to improve atmospheric models. The hydrological results have shown that increasing the spatial resolution improved the atmospheric simulations (at least for the case studied here). This improvement is not so evident when using only the precipitation observations as a validation tool.
The validation of high-resolution simulations is not an easy task. The discrete nature of the precipitation observations, coupled with the high variability of the physical events and of the model errors, complicate the use of precipitation observations for model atmospheric validation. The hydrological basins can be seen as macro–rain gauges with variable interception areas. This areal variability allows us to diagnose different problems associated with the atmospheric simulations. The largest basins allow us to estimate the quality of the larger scales simulated, whereas the smaller basins give information on the smaller precipitation events. It is important to note that the accuracy obtained for a big watershed does not certify the same accuracy for its smaller subbasins.
Prediction errors detected with the radar data have also been correctly seen by the hydrological model. A spatial shifting of the precipitation events by the atmospheric model has been identified with the radar observations, and was also observed and in part validated with the hydrological simulations. Shifting the atmospheric model patterns to compensate for this error greatly improved the streamflow results. It is evident that applying this shift systematically to each event is only an approximate compensation for the atmospheric problems that occurred during these simulations. A better technique recently developed by Grassotti et al. (1999) could be used for future study. Nonetheless, examining this problem has allowed us to see the sensitivity of the hydrological simulations.
The good correlation in shapes of the simulated hydrographs obtained for the majority of the southern Ontario watersheds indicates, first, that the dynamic part of the hydrological model seems to have represented a good approximation of the truth and, second, that the atmospheric model produced physical events that seem to also approximate the relevant process. However, the position, the timing, and/or the strength of these events were missed in some instances. For these cases, the position and time errors are approximately 30 km and 1–3 h. The over-underestimation of the streamflows (using radar and atmospheric model data) produced by the hydrological model (section 4d) has been correlated with other tools traditionally used for validation (sections 4a–c).
The radar is also an important tool for validation. The hydrological model correctly estimates the underestimation of precipitation with range by radar. Even if the radar has deficiencies, this tool remains very important for the validation and the comprehension, particularly in the region of low risk of attenuation effects (<125 km). The correctly estimated amounts of water observed in the regions of good radar coverage are also very important in the validation (atmospheric and hydrologic).
The hydrological simulations, combined with hydrological observations, give indispensable information on the amount of precipitation. Although a demonstration of the skill in the atmospheric simulations was not a main objective of this project, we have nevertheless seen impressive quality in the simulations obtained. For distances up to 125 km from the radar, the quality of the radar data (Fig. 15) is better than or equal to that of the atmospheric model result. And the inverse is found beyond 125 km where it is the model result that is better than or equal to that produced using the radar data. It should be noted that accumulated 1.5-km CAPPIs were used to estimate the precipitation on the ground. Specific radar-derived precipitation products that account for vertical profile effects, beam filling, beam broadening, attenuation, bright band, precipitation type and others are still being developed (Joss and Waldvogel 1990; Fulton et al. 1998). The estimate of an effective range of 130 km is quite good. Other estimates of the effective range of radar estimates of precipitation have ranged from 75 to 120 km. The simultaneous use of the radar, the hydrological model, and the atmospheric model allows dependent and independent comparisons. The complementary nature of these tools leads to a great enhancement in the efficiency and the understanding of each.
The one-way coupling between the hydrological model and the atmospheric model permits a first determination of the sensitivity of each. It has been shown that the quality of the hydrological simulations decreased for basins smaller than 500 km2. This problem is related to the inadequate representation of a small basin by a low-resolution hydrological grid (10 km). The spatial resolution of the hydrological model will be increased in future studies. Also in the future, the hydrological model will become an integral part of the environmental modeling system being developed at Environment Canada. The southern Ontario watershed that has been examined in this study has the advantage of relatively simple topography. It remains to be seen whether the coupled atmospheric–hydrologic model will perform equally well in regions with more complex topography. This aspect is to be examined in future work.
The authors are most grateful to the anonymous referees for their detailed comments and reviews. We would also like to thank the following: M. Desgagné, S. Thomas, and C. Girard for the support to the MC2 model (AES/RPN); S. Laroche and S. Pellerin for their precious help for the use of 3D variational analysis system (AES/RPN); A. Méthot and M. Roch for the support with the GEM model (AES/CMC, RPN);C. Beaudoin for the support with the SEF spectral model (AES/RPN); and J. St.-James for the surface fields used at very high resolution (AES/CMC). This work also benefited from precious discussions with S. Bélair and B. Bilodeau concerning the precipitation schemes used (AES/RPN). The help and advice of M. Valin and V. Lee have been very appreciated (AES/RPN). We are also grateful for the exceptional collaboration of the team of hydrological researchers of the University of Waterloo (F. Seglenieks, A. Graham); the efficient and excellent collaboration of the Water Survey of Canada with S. Saunders; and the advice of R. Hale and W. Brimley (Environment Canada, hydrology). Finally we would like to especially thank the B.C. Hydro Company (B. Chin and D. Cattanach) for the strong link created between hydrologists and atmospheric researchers.
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Summary of the RPN physics options used.
Summary of hydrological abstractions in WATFLOOD.
Description of precipitation on radar images 18–20 Apr 1993 (all times UTC).