4.1. Combining Observed and Simulated Precipitation
 The absence of observed precipitation data from mountainous regions as well as biases in the amount of precipitation simulated by HIRHAM4 were expected to cause incorrect estimates of runoff when these data sets were used separately as input in the hydrological model. To overcome these problems, a combined data set was generated, in which the spatial distribution of the precipitation calculated by the climate model was adjusted with a mean field bias correction using the absolute values of the observed precipitation data. This way, the simulated precipitation was bias-adjusted with observations. The combined data set (HIRHAM4 adjusted with observed precipitation) was generated for 1981–1986. In Figure 5, a schematic representation of the method used is shown.
 The spatial distribution of the precipitation simulated by HIRHAM4 is consistent with the distribution of observed precipitation at the resolution of the model. The climatology at the monthly scale as simulated with HIRHAM4 was thoroughly evaluated by Christensen and Kuhry . They found that the model was depicting the areal distribution quite realistically when compared to the limited amount of station data available in the vicinity of the Usa river catchment. Basically the same systematic errors were found for all stations, namely a tendency for too much precipitation during summer and quite agreeable amounts in the (very long) winter season. A particularly important feature of RCMs is that they take into account orographic effects (at the model resolution). In a set of simulations over Scandinavia, Christensen et al.  assessed the hydrological cycle as simulated by a GCM and HIRHAM4 at two different resolutions including one at 19 km, comparable to the 16 km adopted in this work. One major conclusion from that work was that at the highest resolution (19 km) it was found that in mountainous regions the high-resolution RCM simulation shows an improved performance in simulating the various components of the hydrological cycle, compared to the GCM simulation. Moreover, when compared with observed data from Sweden, the simulated runoff indicated that a precipitation analysis based on observations is underestimating true precipitation severely, which accordingly should be almost doubled on an annual basis in the most mountainous regions of Sweden. These conclusions referred specifically to regions where the rain gauge network is particularly sparse. Due to the absence of rain gauges at high elevation in the Ural Mountains, it is not possible in the present case to assess the accuracy of the simulated precipitation amount (but see also the study by Christensen and Kuhry ). The only way to assess it, therefore, is via indirect methods. One possibility is to follow Christensen et al.  and try to validate the other components of the hydrological cycle and this way get at least a qualitative feeling for the accuracy. Here we used the HIRHAM4 precipitation to drive the calibrated USAFLOW hydrological model and by analyzing the resulting runoff for various subcatchments of the Usa basin we obtained such a qualitative assessment of the modeled precipitation at least in a climatological sense.
 A mean annual HIRHAM4 precipitation distribution was obtained by averaging the precipitation distribution over all available model years, which are 1979 to 1993. The resulting spatial distribution is represented as a GIS-layer, with high precipitation values in front of and within the Ural Mountains and low values in the lowlands. As it is not obvious how the precipitation should be distributed within the 16 km grid, the grid point values representing an area mean were used also at the 1 km grid (Figure 6).
 Annual observed precipitation was calculated for each station and averaged for each year between 1981 and 1986. The average HIRHAM4 precipitation at the same locations was derived from the HIRHAM4 precipitation distribution calculated above. For each year, the mean-field bias was calculated, i.e., the difference between the average annual observed precipitation at the location of the stations and the corresponding average HIRHAM4 precipitation for those locations:
where: ΔP(t) is the mean-field bias for year t (mm/year); Pa(xs,ys,t) is annual observed precipitation averaged over all stations s in year t (mm/year); Pa,m(xs,ys) is average annual HIRHAM4 precipitation averaged over all stations s (mm/year).
 As a first step we chose to use the long-term annual mean HIRHAM4 precipitation pattern, mainly because this is a robust pattern in the sense that the annual precipitation does not vary substantially between the years. At the monthly scale, systematic biases between simulated and observed precipitation are known to vary during the year, with a relative overestimation during summer and more realistic values during winter [Christensen and Kuhry, 2000]. Sources of bias are the relative proportion of convective and stratiform precipitation during warm seasons and the gauge undercatch of snow. Evidently, gauge undercatch of snow is partly responsible for the wet bias of simulated precipitation by HIRHAM4 during the winter months [Christensen and Kuhry, 2000]. Consequently, negative rain gauge corrections in these months may be excessive, since they are based on biased observations. The biases in the warm season and in winter would suggest the use of a variable bias during the year. However, the interannual variation of monthly—and even seasonal—precipitation is much larger than for the annual mean. Therefore, the monthly HIRHAM4 precipitation bias is likely to be more variable than at the annual scale, which will require use of a different bias for each month in the entire model period. This will not only significantly increase the degree of freedom, but also prevents the application of the method to periods outside the range of HIRHAM4 simulation, while the method can be applied to other time periods when a long-term mean precipitation pattern is used. Given the desire to apply this technique outside the HIRHAM4 simulation period, the negative effect of using a long-term annual precipitation bias instead of a monthly bias on the accuracy of the results is accepted, especially when compared to using only raingauge data. The use of an annual average HIRHAM4 precipitation field instead of a HIRHAM4 precipitation field for each individual year is acceptable in relatively small geographic regions where spatial patterns of precipitation do not vary significantly from year to year, or in regions orographic modulation of precipitation is significantly greater in magnitude than interannual variations in the spatial distribution.
 For each year, the grid cells with the average HIRHAM4 precipitation were altered with ΔP to create combined annual precipitation for each cell:
where: Pout(x, y, t) is combined precipitation at grid cell x, y, in year t (mm/year); Pm(x,y) is average annual HIRHAM4 precipitation at grid cell x, y (mm/year).
 The combined precipitation was not allowed to be less than zero, because the total amount of precipitation is always larger than the overestimation of precipitation by the HIRHAM4 model. The biases in HIRHAM4 precipitation were nearly constant over the whole area where comparison with observations is possible [e.g., Christensen and Kuhry, 2000, Figure 5]. While, it seems likely that the bias should be different in the mountains than in the lowlands, it was not possible to assess how much in a quantitative sense. In a recent study, Dethloff et al.  assessed the ability of HIRHAM4 to simulate net accumulation over Greenland. It was demonstrated that HIRHAM4 depicts the general patterns well, particularly the areas with very low accumulation rates over the interior parts of the Ice Sheet (annual accumulation of below 150 mm/yr). But there is also considerable evidence for a good representation of the precipitation/accumulation in the complex coastal mountain ranges, particularly in the southern part of Greenland (annual values exceed 2500 mm/yr). Given the caveat that the observations within the coastal ranges are heavily biased due to the undercatch of solid precipitation in winter and that the gauge stations are located near the sea surface and thus not representative for the complex terrain, this study suggests that even with this large dynamical range of precipitation values, there is no reason to assume that there is a simple multiplicative relation between the HIRHAM4 precipitation bias in regions with low precipitation when compared to regions with high precipitation. Therefore, the correction for the Usa basin was made in an additive way instead of using a ratio, which was done by Fulton et al. . The use of a ratio would in fact imply that biases are always higher (or lower) in the mountains. This would not depict any geographical skewness, which could easily be introduced from systematic regional errors in the mean flow conditions.
 The combined precipitation was converted to monthly values by using the distribution of the annual observed precipitation over the months:
where: Pm(x, y, t) is monthly combined precipitation at grid cell x, y, in month t (mm/month); d is the percentage of the annual observed precipitation that falls in month t (%).
 This procedure was repeated for the entire model period to create time series of monthly precipitation.