1. Introduction

Forestry activities conducted in the snow-dominated, mountainous basins of the British Columbia (BC), Canada, interior can affect the hydrological processes generating streamflow. These activities can subsequently produce a shift in the streamflow regime and alter the frequency of geomorphically significant discharge events, which in mountainous terrain are typically associated with peak flows of recurrence intervals of anywhere from 1 to >100 yr [see Besehta et al. (2000) and Church (2002) for reviews]. Unfortunately, the available empirical evidence derived mainly from paired-basin studies is limited in its ability to quantify impacts for peak streamflow events with recurrence intervals larger than about 10 to 20 yr.

In order to fill knowledge gaps regarding the impacts of forest management activities upon peak streamflow, many investigators have espoused making greater use of long-term physically based hydrologic modeling (i.e., Thomas and Megahan 1998; Alila and Beckers 2001). This approach has been adopted in BC, and a project is currently underway to simulate the hydrologic impact of forest harvesting in basins spanning varied physiographic domains (Whitaker et al. 2002, 2003; Thyer et al. 2003; Schnorbus and Alila 2004). The goal of said project is to utilize continuous numerical simulation to generate large samples (i.e., N = 100) of pre- and postharvest peak flow events for various watersheds with which to assess forest harvesting impacts upon the peak flow regime. However, a major challenge for this simulation project is the collection of the required meteorological (met) forcing data. For instance, the hydrologic model used in this project, the Distributed Hydrology Soil Vegetation Model (DHSVM; Wigmosta et al. 1994), requires an extensive suite of nine met input variables provided as a time series at the temporal resolution of the model time step (1 h in this application). Met data of the necessary scope (number of variables) and resolution, let alone duration (100 yr), are nonexistent in the mountainous interior of BC.

There are, however, several experimental headwater basins in BC at which met data of the required scope have been collected at an hourly resolution over varying periods, with one significant drawback: the data records are of short duration, typically spanning no more than 5–10 yr. Nevertheless, it is feasible to extend these observed records and generate a proxy long-term met time series of an hourly resolution suitable for use in driving physically based hydrologic models. The purpose of such an extended record is not to recreate or forecast actual weather events, but to generate a proxy data series that resembles, statistically, the weather during the calibration period. It is expected that if such proxy met data were used to force a physically based hydrologic model, then the simulated output of that model (i.e., discharge) will statistically resemble the output generated had actual (i.e., measured) met data been available for input. One such attempt at generating a proxy met record was undertaken in order to support the long-term numerical simulation of forest harvesting effects upon the peak discharge regime of Redfish Creek, a mountainous, snowmelt-dominated basin located in southeastern BC (Schnorbus and Alila 2004).

This study addresses how well hourly met records can be extended from only a few years (<10) of observation and the effect of generated met data upon hydrologic simulation. Although the method is site specific to Redfish Creek, the authors believe that, with some modification, the technique can be applied in a wider variety of landscapes. Additionally, the requirement for extending and generating hourly resolution met data is not limited to hydrology but has utility in, for instance, agricultural, ecological, and climatic studies. The paper begins with a brief description of the study area and collected data in section 2. The met generation method is described in section 3. The performance of the proposed method is assessed in section 4 and discussed in section 5, and concluding remarks are provided in section 6.

2. Study area and data

The Redfish Creek watershed is located in the Selkirk Mountains of southeastern BC (Fig. 1, inset). The watershed has a drainage area of 26 km² and an elevation range of 700 to 2300 m, although 80% of the watershed lies above 1500-m elevation. Basin slopes are moderately steep, with a median gradient of 50%. Slopes are heavily forested, with the lower elevations falling within the Interior Cedar–Hemlock (ICH) and the upper elevations within Engelmann Spruce–Subalpine Fir (ESSF) biogeoclimatic zones. Above an approximate elevation of 1800 m, the ESSF zone transitions into subalpine parkland, which is a thinly wooded subzone that occupies roughly 40% of the basin.

The study region has a climate that is best described as humid continental, being subject to the influence of both maritime and continental airstreams (Demarchi 2004). Winter is by far the most variable season in southeastern BC; a nearly constant progression of eastward moving Pacific disturbances brings warm, moist air. However, influxes of cold, dry Arctic air occur with varying frequency from year to year, commonly during November to February (Hare and Thomas 1979). The influence of the Pacific is strongly felt with respect to precipitation, particularly at high altitude, and substantial frontal precipitation is deposited along the west slope of the Selkirk Mountains, making the region one of the wettest outside the coast (Meidinger and Pojar 1991). Local convective precipitation is also frequent during the summer, with June being one of the wettest months in the year. Mean annual precipitation is influenced by orographic effects and trends from 1100 to 1600 mm at Burn (1290-m elevation) and Cabin (1730-m elevation) stations, respectively. Because of the decrease in temperature with height, the proportion of precipitation that falls as snow increases with elevation such that the gradient of snow water equivalent (SWE) is quite pronounced; mean annual peak SWE is 220 and 1060 mm at Burn and Cabin stations, respectively, and 1500 mm at the highest elevations (as recorded at the Alpine climate station at 2045-m elevation; see Fig. 1). Air temperature displays a continental regime; however, altitudinal effects moderate annual variability, and monthly average temperature at Burn station ranges from −6°C in December to 15°C in July. Seasonal temperature variability decreases with elevation, and mean annual temperature observed over a 5-yr period decreases from 4°C at Burn station to 2°C at Cabin station.

Annual water yield is dominated by snowmelt (60% of total yield), and the generally humid climate generates an annual runoff ratio (ratio of discharge to precipitation) of about 60%. A mixture of radiation melt and rain-on-melting-snow processes generate peak annual streamflow in Redfish Creek, although the peak flow regime is still fundamentally governed by the snowmelt process. On average, peak annual streamflow from Redfish Creek typically commences at the beginning of April and peaks between mid-May and mid-June. Hydrograph recession ceases around the first week of August, and base flow is maintained from late summer through to early spring.

DHSVM requires time series input of precipitation (P), air temperature (T_a), relative humidity (R), wind speed (U), solar beam irradiance (S_b), solar diffuse irradiance (S_d), downward longwave irradiance (L), temperature lapse rate (T_lapse), as well as a coefficient describing the increase in precipitation with elevation (P_grad), at one or more station locations within the study area. The original calibration and validation of Redfish Creek application of DHSVM was conducted using met time series data for Burn and Cabin climate stations spanning the period October 1992 to December 1997 (Whitaker et al. 2003). This initial dataset is referred to as the “observed” data and is used as the baseline for further discussion. During this period T_a, R, U, and P have been continuously recorded at both Burn and Cabin stations. Hourly values of global solar radiation (S_g) have only been recorded since July of 1994 and September 1995, for Burn and Cabin stations, respectively; therefore, prior to this period S_g was estimated using the method of Bristow and Campbell (1984) (Whitaker et al. 2003; see also section 3d). Hourly values of T_lapse were based on the observed hourly difference in T_a between Burn and Cabin climate stations whereas P_grad was based on the difference in monthly precipitation between Burn and Cabin stations. Values of L, S_b, and S_d are not collected in the study area and were estimated using the techniques described in section 3d. An additional three years of precipitation data (spanning 1998 to 2000) for Burn and Cabin stations, not used in the original observed dataset, were also available for this study. Hourly data from Alpine station was of too short a duration and contained too many gaps to be of use.

Streamflow has been gauged by the Water Survey of Canada since 1993 and is published as daily average discharge. Hourly discharge data have also been collected by the BC Ministry of Forests since April 1993, but some data gaps exist prior to November 1995.

3. Met generation

b. Stochastic precipitation generation and precipitation gradient

As indicated, the initial step in the met generation process is the direct generation of an hourly precipitation time series. It is desirable that not only should the generated hourly precipitation time series reproduce the stochastic structure of the observed hourly record, but that its associated daily time series also be statistically consistent. At the very least the generated daily time series had to adequately reproduce the daily precipitation occurrence structure of the observed data as the daily precipitation state is used to condition the generation of daily meteorological variables (see section 3c).

Stochastic precipitation models based on the clustered rectangular pulses point process are capable of generating an adequate representation of the precipitation process at a range of temporal scales. Conceptually, storms of random interarrival times and duration are generated, and each storm is composed of a cluster of precipitation cells, approximated by a random occurrence of rectangular “pulses,” each of random intensity and duration. The total storm intensity at a point in time is obtained by summing the intensities of each rain cell active at that time. In this study hourly precipitation data were generated directly using the modified version of the Bartlett–Lewis Rectangular Pulses Model (MBLRPM) as described by Rodriguez-Iturbe et al. (1988), which is based on a modification of the original work of Rodriguez-Iturbe et al. (1987).

In the original Bartlett–Lewis model storms are assumed to arrive randomly, following a Poisson process with rate parameter λ. Within each of these storms, a cell occurs at the storm origin and remaining cells arrive following a Poisson process with rate parameter β, and the duration of each cell is exponentially distributed with parameter η. The generation of cells within a storm terminates after a time that is exponentially distributed with parameter γ. The rainfall intensity of each cell follows an exponential distribution with mean value μ_x. Rodriguez-Iturbe et al. (1988) modified the original model by assuming that the parameter η varies randomly for each storm following a gamma distribution with shape parameter α and scale parameter ν. The mean cell interarrival time and duration, namely β⁻¹ and γ⁻¹, of each storm vary through the constant and dimensionless parameters κ = β/η and ϕ = γ/η. This allows for different storms to retain a similar structure but to occur on different time scales, where the number of cells per storm has a geometric distribution with mean μ_c = 1 + κ/ϕ. First- and second-order properties of the six-parameter (λ, κ, ϕ, α, ν, and μ_x) MBLRPM are given in Rodriguez-Iturbe et al. (1987, 1988).

Estimation of the six parameters of the MBLRPM is difficult and is typically accomplished by relating the analytical expressions for certain statistical moments to the corresponding observed values (Smithers et al. 2002). The resulting set of nonlinear equations is often solved simultaneously by minimizing a defined objective function, as unique roots rarely exist. Khaliq and Cunnane (1996) found that the MBLRPM most resembled historical data when more statistics than necessary were used to estimate model parameters and suggested using 16 statistics: mean, variance, lag 1 autocorrelation, and dry probability at 1-, 6-, 12-, and 24-h levels of temporal aggregation. This statistic set was adopted for the current study, and parameters were optimized by minimizing a least squares objective function (Khaliq and Cunnane 1996)

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where F_i(X) is the analytical expression for statistic i computed using the parameter vector X, F^o_i is the statistic i estimated from the data, and N is the number of statistics used in parameter optimization. The rainfall generation process was assumed seasonally variable but stationary by month (72 parameters in total).

The highly nonlinear analytical expressions for the first- and second-order moments of the MBLRPM renders them sensitive to any inconsistencies in the data, a situation that would become more acute in a short data record. As a result, it was found that the unconstrained optimization of all six parameters often resulted in physically unrealistic storm properties. Consequently, optimization for 11 months was conducted using a reduced parameter space by fixing the value of υ (Smithers et al. 2002). As storm and cell properties cannot be separated out from gauge data, no information on precipitation structure was available with which to constrain υ. Values in the range of 0.2 to 2.1 (which are within the range of values reported in the literature) were found to produce what the authors felt were qualitatively reasonable storm and cell properties, the final value being selected on the basis of the greatest minimization of the objective function. Generally, the value of υ was found to vary proportionally with average monthly precipitation. Optimized model parameters are given in Table 1, and derived precipitation properties, are shown in Fig. 3.

Given that the horizontal separation between the Burn and Cabin climate stations is only 3000 m, it is likely that both locations are generally subject to the same storm events, such that temporal storm structure is roughly identical at both locations. The observed data do not refute this assumption, although the data do indicate that precipitation depth must be scaled for elevation between the two stations. Based on this assumption, the hourly precipitation time series for Cabin station was generated by scaling the Burn station precipitation time series using P_grad (see below). This alleviated the need to employ a more complicated multisite stochastic technique (i.e., Cox and Isham 1994).

At a subseasonal time scale the change of precipitation depth with elevation is highly variable, changes from storm to storm, and cannot be realistically calculated for each hourly time step. On a seasonal or monthly basis, however, precipitation in Redfish Creek shows a strong orographic influence with a clear trend of increasing accumulation with increasing elevation (Whitaker et al. 2003). Within DHSVM, precipitation depth at a location of higher elevation than a reference location is estimated by

P₂P_gradz₂z₁P₁(2)

where P₂ is the precipitation depth at elevation z₂, P₁ is the precipitation depth at elevation z₁(z₂ > z₁), and P_grad is a coefficient representing the relative increase of precipitation (relative to P₁) per unit increase in elevation (with units of m⁻¹). The actual precipitation gradient (in units of m m⁻¹) is represented by the quantity P₁P_grad. The value in square brackets in (2) (the ratio P₂/P₁) was estimated on a monthly basis from the slope of the double mass curve of Burn and Cabin precipitation depth for the period 1992 to 2000, an example of which is given for January and June in Fig. 4. Given this empirical evidence, the assumed linear relationship advocated by (2) is considered reasonable. The difference in slopes is attributed to a shift from a predominance of cyclonic activity during the winter to a predominance of convective activity, which displays a smaller altitudinal effect, during the summer (Barry 1992). The monthly precipitation gradient calculated between Burn and Cabin stations was assumed to apply uniformly across the basin, and the hourly P_grad for each station was set equal to the derived interstation monthly value (Fig. 2). This assumption, in conjunction with the IDW extrapolation employed by DHSVM, effectively means that basinwide precipitation is extrapolated solely from the generated Burn station precipitation time series. Current estimates of P_grad are higher than those of Whitaker et al. (2003) because of the inclusion of the additional three years of precipitation data. The partitioning of precipitation into rain or snow is based on temperature thresholds and executed from within DHSVM.

d. Empirical disaggregation

At the current stage of the met generation algorithm we are left with an hourly precipitation time series and a daily time series for both Burn and Cabin climate stations (Fig. 2). The next stage involves the disaggregation of the daily time series into the final hourly time series of the appropriate met variables.

1) Air temperature and lapse rate

Hourly temperature (T_a) was extrapolated from T_m and T_n independently at each station by assuming a periodic, quasi-sinusoidal diurnal variation that can be approximated by a Fourier series of the form (McCutchan 1979)

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where T_a(t) is the hourly air temperature (°C) at time t (hours from midnight); A₀ is the annual mean of the Fourier series; a₁, b₁, b₂, c₁, and c₂ are regression coefficients; T is the daily mean temperature [=(T_m + T_n)/2]; and ΔT is the daily range of temperature (=T_m − T_n). Assessment of bias and root-mean-square error suggested that using monthly parameters in (4) produced negligible improvement in model accuracy versus the use of annual parameters, as such annual parameters were used in the met generation model. Hourly temperature lapse rate (T_lapse) was estimated using the extrapolated Burn and Cabin hourly air temperatures as follows:

T_lapsetT_a2tT_a1tz₂z₁(5)

where superscripts 1 and 2 denote Burn and Cabin stations, respectively.

2) Relative humidity

Although water vapor pressure (e) varies diurnally, the magnitude of e fluctuations are considerably less than those for temperature; therefore, it is assumed that e, and therefore T_d, is constant throughout the day (Campbell and Norman 1998). Estimates of R at time t can then be calculated as the ratio of daily average e to hourly saturation vapor pressure (e_s),

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where e_s (daily average e) is calculated from T_a(T_d) using the common Magnus formulation (Abbott and Tabony 1985)

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with T_a(T_d) expressed in degrees Celsius, and vapor pressure expressed in millibars. The values of the coefficients a and b in (7) are a = 17.38, b = 239.0 and a = 22.4, b = 272.4 for evaporation over water and sublimation over ice, respectively.

3) Wind speed

The spatial and temporal complexity of the wind field in mountainous topography renders its disaggregation to and quantification at a subdaily time scale problematic and complex (Barry 1992). In order to limit model complexity it is assumed that hourly wind speed is equal to the daily average wind speed [i.e., U(t) = U_d].

4) Beam and diffuse solar irradiance

Hourly global irradiance (S_g) at the ground surface was estimated by calculating above-atmosphere potential irradiance (S^o_g), using standard solar geometry (i.e., Gates 1980), attenuated for atmospheric transmissivity (H), which is assumed to be constant throughout the day. The topography in the immediate vicinity of Cabin station (Fig. 1) produces observations of S_g that are confounded due to shading effects. For this reason, H was derived for Burn station only and, assuming uniform atmospheric properties across the basin (i.e., Tarboton et al. 2000), applied directly to Cabin station (Fig. 2). Daily atmospheric transmissivity was estimated from the relationship (Bristow and Campbell 1984)

HH_maxBT^c(8)

where ΔT is the diurnal range in air temperature {T_m(j) − [T_n(j) + T_n(j + 1)]/2, where j is the day identifier}, H_max is the maximum observed clear-sky atmospheric transmissivity, and B and C are empirical coefficients, optimized using S_g data from the period July 1994 to December 1997. The use of a constant B in (8) represents a slight simplification over the method originally used by Whitaker et al. (2003) to derive S_g estimates for the period October 1992 to July 1994. Inspection of the hourly radiation data for Burn station reveals that hourly H is, in fact, nonuniform throughout the daylight hours. Transmissivity is a function of solar angle and is minimum at dawn and dusk and maximum during midday, with the daytime H_max at times reaching 10 times the minimum value. As a result, the relationship in (8) was optimized using an observed H estimated from radiation data for the midday period between 1000 to 1400 LST. Final parameter estimates for (8) are 0.89 for H_max, the maximum observed midday average H, 0.0039 for B, locally optimized, and 2.4 for C, the value derived by Bristow and Campbell (1984) using data from western Washington.

Hourly values of S_b and S_d were partitioned from S_g using the following empirical formula (Black et al. 1991):

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As only global solar irradiance was observed at Burn station, the selected technique of partitioning S_g into S_b and S_d is quite arbitrary, and its performance can not be evaluated. The relationship proposed in (9) was selected based on its use in deriving S_b and S_d for the met time series used in the original calibration of DHSVM for Redfish Creek (Whitaker et al. 2003). Values of S_b and S_d were calculated assuming a horizontal surface, the influence of topography being accounted for explicitly within DHSVM.

5) Longwave sky irradiance

Hourly longwave irradiance, L, was calculated based on the Stefan–Boltzmann law (Gates 1980), an effective clear-sky atmospheric emmissivity, and a cloud modification factor. The effective clear-sky atmospheric emmissivity was calculated separately for each station from ɛ_c = 0.70 + [5.95 × 10⁻⁵e exp(1500/T_a)], where e is calculated from (7) and T_a is given as an absolute temperature (K) (Idso 1981). The cloud modification factor was given as K = 1 + 0.17 [(1 − H/H_max)/0.65]. The cloud modification factor was calculated for Burn station and extrapolated to Cabin station assuming uniform cloud cover over the basin. The adequacy of the proposed approach can not be assessed, as observations of L were not collected at either Burn or Cabin stations. Again, the given approach was selected as it was used to derive the original L time series used in model calibration (Whitaker et al. 2003).

4. Results

a. Met generator performance

1) Precipitation

The stochastic generation of daily meteorology is based on the conditioning of the generated variables on the precipitation status of the day, either wet or dry. As such, it is informative to compare the generated marginal probability of the occurrence of a dry day for the observed and generated daily precipitation time series. As this statistic was used directly in model parameterization it is expected that it will be accurately reproduced, and this is for the most part verified by Fig. 5. Generated dry-day probabilities are within 10% of observed, with the exception of May, which has a 20% overconditioning error in dry-day probabilities (i.e., less frequent dry days). It is expected that errors due to under- or overconditioning for dry-day occurrence in the generation of daily met will be minimal.

Seasonal precipitation, given as monthly averages, of the observed (1993–2000) and generated time series (based on 15-yr run) is given in Fig. 6. Empirical P_grad values are also included in Fig. 6 for comparison purposes. The seasonal precipitation pattern is well represented, including the two seasonal maxima during May–June and October–November, and this despite the overconditioning of precipitation occurrence in May. Relative errors in monthly precipitation are less than 10% for all months, with the exception of August, which has a relative error of 21%. On an annual basis, observed (1010 mm) and generated (1022 mm) precipitation differ by only 1%, and total generated winter precipitation [October–February (ONDJF)] of 505 mm is only 2% lower than the observed value of 515 mm.

MBLRPM accuracy was further assessed by comparing the observed and generated distributions of dry spell (P = 0) durations, wet spell (P > 0) durations, and conditional (wet spell) precipitation depth. The use of very large sample sizes in the current study makes it difficult to test hypotheses of statistical equality between two empirical distribution functions as any model departure, no matter how small, will be detected as significant. In such cases it is almost impossible to generate a statistically equivalent model of an observed distribution function (Martin-Löf 1974). Therefore, model fit is only assessed graphically by comparing plots of the empirical cumulative density function (ECDF). The comparisons for the month of July and December, which are representative of good and poor model performance, respectively, are shown in Fig. 7. In July the distribution of dry spell durations is accurately reproduced, although wet spell durations tend to be underestimated, and conditional precipitation depth is slightly overestimated. In December both dry and wet spells are overestimated— dry spells substantially more so than wet spells—and conditional precipitation depth is overestimated. However, regardless of discrepancies, the generated distributions of wet and dry spell durations and conditional precipitation depth for each month are structured in such a way that mean seasonal precipitation accumulation is accurately maintained (Fig. 6). Additionally, seasonal changes in precipitation structure are also captured by the generated series: wet spells occur more frequently and are of shorter duration and low intensity in December, whereas wet spells occur much less frequently and are of slightly shorter duration and higher intensity in July. Average precipitation for both months is roughly identical. No seasonal pattern is apparent in model performance when examined over all months. In general, generated dry spell durations show the highest discrepancy, and wet spell durations show the lowest.

2) Daily met data

The observed and generated frequency distributions of T_m, T_n, T_d, and U_d are compared for Burn station for January and June in Figs. 8 and 9, respectively. The generation of the daily met time series is generally poor in January (Fig. 8), mostly attributable to the nonnormal distribution of all four met residuals (Table 2), although slight errors in the generated daily precipitation occurrence (Fig. 5) are also a factor. The observed distributions of T_m, T_n, and T_d for January display distinct bimodal behavior (also present in February) that cannot be accounted for with a normal distribution; the observed distribution of U_d is also more skewed than the generated distribution. In June (Fig. 9) the daily model performs quite well in reproducing the frequency structure of the daily met variables for Burn station, despite the nonnormal distribution of the observed residuals for T_d and U^T_d (Table 2). The fact that the daily distributions are unimodal in June (and most months) likely contributes to the improved agreement between modeled and observed values. The stochastic generator performance generally correlates with the results of Table 2 in that poorer performance occurs for those months for which most of the residuals can not be adequately described by the standard normal distribution, specifically December, January, and February. Performance of the daily stochastic model at Burn station for the remaining months is similar to that of June, and results for Cabin station mirror those of Burn.

3) Hourly nonprecipitation met data

An assessment of the overall accuracy of generated T_a, T_lapse, U, R, and S_g was done by comparing ECDFs of the 5-yr observed and a 15-yr generated time series. The empirical frequency distributions are only compared graphically [owing to the very large sample sizes; see earlier discussion in section 4a(1)], yet they provide an efficient and effective means of showing the magnitude and nature of any model discrepancies. Agreement between the observed and generated met time series was assessed using the monthly bias statistic, B! = G/O, where G and O are the monthly mean of the generated and observed hourly data, respectively, in which greater accuracy (lower bias) is represented by values closer to unity. The ability of the met generator to capture the correct diurnal structure of the nonprecipitation met variables was assessed using the mean hourly value for each month of the observed and generated time series (Waichler and Wigmosta 2003). The efficiency statistic of Nash and Sutcliffe (1970)

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is used to assess model fit on the basis of the mean hourly value, where O_t and G_t are, respectively, the observed and generated monthly average value at time t. The E! statistic has a possible range of −∞ to 1, where greater accuracy is represented by values closer to unity; a value of E! less than zero indicates that the error variance is greater than the observation variance. The E! and B! statistics for hourly nonprecipitation variables are summarized in Table 3. The time series of S_b, S_d, and L were not compared owing to a lack of observed data.

For most months, generated T_a is generally in good agreement with observations (Figs. 10 and 11), E! is greater than 0.85, and B! is close to 1.0 (Table 3). The months of November through February are exceptions, in which either E! is negative and/or B! is >1.0. The large B! between average generated and observed temperature in March (5.18) is due to the very low observed mean temperature (−0.2°C), as by all other indications generated T_a for this month shows good agreement with observations. Generated T_lapse exhibits greater discrepancy with the observed data than does air temperature (Fig. 12). Lapse rates are generally underestimated (less negative) from November through January and overestimated from May through September. Inversions also occur more frequently in the generated time series during September through January. The generated mean hourly T_lapse is greatly simplified compared to the observed profile; the minimum lapse rate consistently occurs at midday whereas the strongest lapse rates occur in late evening, entirely failing, for the most part, to capture observed mean hourly T_lapse, which is highly variable between months (Fig. 13).

As one would expect, the generated U data fail to accurately reproduce the ECDF and mean hourly averages of the observed data for most months (Figs. 14 and 15), the exceptions being October through December, in which observed U shows little variability throughout the day. As expected, however, mean wind speed is accurately captured in all months (as indicated by B! close to unity; Table 3), generating E! values near or equal to zero. Although some accuracy in the generation of U is due to inaccuracy in the generation of U_d (Figs. 8 and 9), the major source of error is the assumption that U is constant throughout the day (Fig. 15).

Generated monthly R distributions show slightly less variability than the corresponding observed data (Fig. 16). For April through September both the observed and generated mean hourly R show very close correlation with air temperature (Fig. 17), and corresponding E! is high (Table 3). Very large errors between the generated and observed data are apparent for October through March, as shown by large negative E! in Table 3. During the months of November through January R remains, on average, uniform throughout the day, suggesting that the absolute vapor content of the air varies diurnally. In all months B! is close to unity, indicating the monthly R mean is accurately reproduced throughout the year.

Given that errors in reproducing the correct day length are negligible and, when discrepancies exists, they involve S_g values that are relatively small compared to midday values, assessment of model by ECDF for S_g is restricted to daytime (S_g > 0) values only. The generated monthly frequency distributions of conditional solar irradiance (S_g) show a poor model fit during October through April, consistently underestimating observed S_g (Fig. 18). Model fit is substantially improved for the period of May through September, although S_g is still underestimated. Hourly average S_g reveals a similar story: in all months midday S_g is underestimated, with the largest relative errors occurring in the winter months (Fig. 19). The B! between the observed and generated time series indicates that average S_g is underestimated by as much as 50% in November (worst month) and 6% in August (best month). Model E! for average hourly S_g is positive in all months and tends to be slightly higher in summer than in winter (Table 3).

b. Hydrologic simulation

An initial analysis of the coupling of full synthetic met time series with DHSVM is conducted by comparing the simulated average annual water balance using both observed (control; 5 yr) and entirely generated met data (15 yr), as shown in Table 4. The comparison is restricted to simulated water balance components, as insufficient data exists with which to derive an accurate determination of the actual water balance components for the 1992–97 period. The water balance results indicate that none of the individual components shows substantial change (<10%) when simulated using the full synthetic met time series. Average annual accumulated streamflow, SWE, melt, and evapotranspiration (ET) simulated using both generated and observed met input time series are given in Fig. 20. In general, the simulated temporal distribution of major water balance components is little affected by the use of generated as opposed to observed met data; however, some discrepancies are apparent. The basinwide ET rate tends to be underestimated when using generated met data during winter and spring, such that cumulative ET differs by 31% as of 1 May. Conversely, the ET rate tends to be slightly overestimated during summer and fall such that by the end of the water year (30 October) cumulative ET differs by less than 2%. Simulated snow accumulation is overestimated when using the generated met data, and average 1 April SWE differs by 9% between the two series. This discrepancy is due to increased precipitation and reduced winter ET when using the generated met input. Basinwide melt and streamflow show little sensitivity to the use of generated met data.

The spatial distribution of simulated peak SWE, assumed equivalent to 1 April SWE, was used to further evaluate the coupled models. The study basin was divided into 10 elevation bands based on equal elevation intervals of 167 m, and area-average simulated peak SWE was calculated for each band for each simulation year. The median SWE simulated using observed (control; 5 yr) and synthetic met data (generated; based on 15-yr time series) are plotted for each elevation band in Fig. 21. The SWE values simulated with the synthetic met data are shown with the 50% interquartile range. The area of each elevation band, as a proportion of total basin area, is plotted as a separate series in Fig. 21. The use of the synthetic met data overestimates 1 April SWE below 1366- and above 2034-m elevation, respectively. The largest discrepancy between generated and control SWE occurs in the elevation range of 1032–1365 m, within which generated SWE is roughly 3 times that of the control value. Surprisingly, this is also the elevation range containing the Burn climate station (1290 m), from which basinwide precipitation is estimated. Regardless, within the elevation range of 1366–2034 m, within which lies 85% of basin area, peak SWE simulated with the observed and synthetic met data compares to within 2%.

The flow duration curves (FDC) developed from simulated streamflow using both observed (5 yr) and synthetic (15 yr) met data, and from observed streamflow (5 yr) are compared in Fig. 22. Because of gaps in the observed hourly streamflow record prior to 1995, data are presented for daily discharge. The FDCs are constructed using the annual-based FDC technique and are plotted as a median FDC with the 5% to 95% confidence intervals indicated for the observed FDC [using the method of Vogel and Fennessey (1994)]. The simulated FDCs are in close agreement for the full range of exceedance probabilities. Of greater note is that differences between the simulated FDCs and the observed FDC; the two simulated median FDCs fall within the 90% confidence region of the observed FDC curve only for exceedance probabilities <0.20. Both simulated FDCs underestimate observed discharge for exceedance probabilities >0.20. Overall, the difference between the two simulated FDCs is substantially less than the differences between each simulated FDC and the observed FDC.

The average hourly discharge hydrographs for simulated (using observed and synthetic met data) and observed discharge are shown in Fig. 23. The average hydrographs indicate that little difference exists between all three streamflow series during the annual freshet peak (1 May to 1 August) and that the two simulated streamflow series are in close agreement for the entire hydrograph. However, the underestimation of observed fall and winter base flow by the two simulated streamflow series is again evident. The three average streamflow series were further compared using three statistics. The first statistic calculates the volume error δV between control and test flows, where

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and the flow volume V (control or test) for a given period is calculated as the summation of flow rates Q over the period of simulation N as

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The coefficient of determination, D!, relates how well the test hydrographs compares in shape to the control hydrograph and depends only on timing, not on volume (Whitaker et al. 2002):

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The third statistic is the efficiency statistic given by (10). All statistics are based on hourly discharge. Greater accuracy is represented by values of δV close to zero and D! close to unity. Results are presented in Table 5. The δV statistic shows that the volume error between the two simulated hydrographs is an order of magnitude less than that between each simulated hydrograph and the observed hydrograph. The D! statistic shows that all three hydrographs compare equally well (all have the same shape), whereas the E! statistic reveals that the two simulated hydrographs compare better to each other than to the observed hydrograph. It is clear that model error in replicating the observed average hydrograph is greater than any differences that exists between the two simulated hydrographs because of the use of synthetic input met data.

5. Discussion

With regard to precipitation the authors had anticipated that storm structure would be an important mechanism for controlling evapotranspiration. However, within the climate of Redfish Creek, ET forms a very small component of annual water balance (Table 4) and has a negligible impact on peak flow (Fig. 20). As such, modeled streamflow results appear relatively insensitive to discrepancies between the generated and observed temporal structure of precipitation (although this is not conclusive, as ET is also sensitive to errors in U, R, and S_g). Given that ET is small, seasonal precipitation depth is more important than subdaily storm structure, and the MBLRPM is satisfactory in this respect. Hydrologic simulation of a coastal watershed dominated by frontal precipitation of long duration and low intensity was also found to be relatively insensitive to the subdaily time structure of precipitation input (Waichler and Wigmosta 2003). However, the ability to correctly model subdaily precipitation structure may prove sensitive for modeling the water balance over smaller time scales, in areas that experience more frequent convective precipitation (short duration, high intensity), in less humid climates, or in other applications (i.e., agricultural modeling). As such, performance of the model in reproducing the temporal structure of hourly precipitation could be improved by explicitly accounting for the structure of wet and dry spells during parameter optimization. Onof et al. (1994) describe an optimization procedure for the MPLRPM whereby the parameter υ is initially optimized by using observed and simulated values for mean dry spell duration and mean number of wet spells per month. With υ fixed, the remaining five parameters are then optimized in the usual manner.

From a hydrologic perspective the spatial variation of precipitation in Redfish Creek is important only so far as it affects snow accumulation, which is well described using elevation as an explanatory variable. This may not be a defensible assumption in situations where basin scale is increased and/or the streamflow is derived mainly from rainfall. Such situations will likely require a more complicated multisite precipitation model to account for spatial variability in both precipitation occurrence and intensity. Additionally, the generation of precipitation that derives from complex (highly variable) precipitation fields will likely require a higher density of station inputs, particularly for mountainous topography.

The use of a Fourier series to disaggregate hourly air temperature proves accurate for reproducing the monthly temperature statistics at each individual station for March through October, even when using annual (as opposed to monthly) parameters. However, this approach breaks down during the remaining months. The use of monthly parameters may improve accuracy by accounting for the seasonal shift in the occurrence of T_m and T_n, which on average occur several hours after noon and just before sunrise, respectively (Fig. 11). The use of a Fourier series also oversimplifies the hourly average temperature profile during the winter, suggesting that a more complex profile, such as the combined truncated sine wave and exponential function of Parton and Logan (1981), may be a more appropriate model. Problems also occur when attempting to reproduce the temperature lapse rate between Burn and Cabin stations. The observed hourly lapse rates inherently incorporate the cross-correlation structure between the hourly temperature series at the two stations. When modeling temperature, hourly disaggregation occurs individually at each station, and this cross correlation is not explicitly maintained and subsequently weakens in the generated record. Additionally, generated air temperatures at Cabin station show a slight upward bias during the winter months (not shown), which accounts as well for the downward bias (less negative) in generated winter lapse rates.

The generation of solar radiation is based on the simplification that diurnal temperature fluctuations are closely correlated to fluctuations in the local heat balance (i.e., solar radiation converted to sensible heat). This assumption breaks down in the presence of local- or large-scale advection, which manifests more frequently in winter when air temperature is strongly influenced by both arctic and maritime air masses. In fact, initial attempts to derive monthly or seasonal parameters for the Bristow and Campbell model [Eq. (5)] failed to produce physically reasonable values (i.e., H_max > 1.0) for November, December, and January. As a result, parameters were optimized by pooling the data on an annual basis. This tends to reduce model accuracy in all months, but biases the model toward more accurate generation of summer values and less accurate generation of winter values (a consequence also attributed to the higher number of observations available for the summer months). Finally, using H values based on 4-h midday averages, although still based on S_g measurements at the midday peak in solar irradiance, will always underestimate the peak daily S_g value. A general underprediction of H also implies a that a higher proportion of S_d versus S_b will be generated than occurs in the observed record. The two components of solar radiation are subject to different topographic influences: S_d is affected by sky view (proportion of hemisphere visible from a point, which is affected by basin-scale topography on a scale of 10³ m), whereas S_b is influenced by local topography (slope and aspect variations on a scale of 10¹ m). Topography tends to exert stronger control on S_b, which displays much more spatial variability, whereas S_d is less attenuated by topography and is more spatially uniform. Therefore, a greater proportion of S_d versus S_b could offset somewhat the overall reduction in S_g. Regardless, hydrologic simulations show that the effect of the downward bias in generated S_g has a marginal effect on the simulation of snowmelt and streamflow (Table 4 and Fig. 20).

The use of the daily average value clearly fails to capture the cumulative distribution and diurnal structure of hourly wind speed for most months. This time, however, more accurate generation occurs in the winter months when wind speed is generally uniform throughout the day and well described by the daily mean value (Fig. 15). The diurnal pattern that exists in most months could be exploited in order to improve the accuracy of the disaggregation step at the measurement site. However, wind speed is highly sensitive to topography (Barry 1992), and the use of simple IDW spatial extrapolation will most likely introduce large discrepancies in the generated wind field. Therefore, any gains in accuracy made at the point scale may well be overshadowed by discrepancies introduced during spatial extrapolation of the point input, which has an uncertain impact on hydrologic simulation.

The use of a daily average dewpoint temperature for estimating relative humidity is a valid assumption only for the April through September half of the year. As the temperature drops and the day length shortens during the winter, R becomes progressively more uniform throughout the day (Fig. 17). During the winter months air temperature more frequently reaches the dewpoint level and R more frequently reaches 100% (Fig. 16). Under these conditions condensation occurs and the dewpoint temperature no longer remains constant but decreases as air temperature continues to decrease (but remains fixed if air temperature increases). During the actual implementation of the met generator model, when T_a drops below the dewpoint level, R is truncated to 100%, but the dewpoint, T_d, is not adjusted (until the next day when a new T_d value is generated). Further difficulties arise from discrepancies in generated T_a, which is generally underestimated and fails to capture the average diurnal structure of observed air temperature during the winter months. Relative humidity is very sensitive to even small variations in air and dewpoint temperature: for a 1°C change in T_a or T_d, R changes by 6% to 10% for −20°C ≤ T_a, T_d ≤ 20°C, with sensitivity increasing with decreasing temperature. Accuracy can be improved by explicitly accounting for the diurnal variability of T_d. This issue also reinforces the requirement to use monthly parameters for the temperature disaggregation step, which would more accurately account for seasonal shifts in the time of occurrence of T_m and T_n.

Although the accuracy of the generated meteorological data does leave opportunity for improvements and added complexity, the comparison of hydrologic simulation results for Redfish Creek question whether such added complexity is necessary. Any discrepancy between simulated hydrology that occurs due to alternating between observed and generated meteorological data is far outweighed by the discrepancy that exists between simulated and observed hydrologic fluxes and discharge. In other words, model skill shows negligible sensitivity to changes in the driving meteorology.

The hydrology of Redfish Creek, particularly the generation of peak annual discharge, is fundamentally snowmelt driven. In this regard the important issues from a met input perspective are the accurate (in the statistical sense) accumulation of a snowpack during the winter and the accurate delivery of solar and longwave radiation, which are the primary source of melt energy during the spring and summer period (Adams et al. 1998). As it turns out, these rather simple requirements ensure that hydrologic simulation of Redfish Creek is rather forgiving of errors in the met generator. Under these circumstances the most critical met inputs are P, T_a, and S_g; P provides the moisture source for snow accumulation; T_a determines the precipitation phase (rain or snow) and directly influences estimates of longwave radiation; and S_g (partitioned into S_b and S_d) provides a direct source of melt energy.

The precipitation phase (either rain or snow) in DHSVM is determined using a temperature threshold; therefore, the accumulation of snow is sensitive to the frequency distribution the generated hourly air temperature. The slight bias toward lower generated air temperatures during the winter months at Burn station, particularly November, December, and January (Figs. 10 and 11), causes a greater proportion of simulated precipitation to occur as snowfall, thus explaining the overprediction of SWE in the vicinity of the Burn climate station (Fig. 21). A slight upward bias in the generation of Cabin station winter air temperatures is expected to be the cause of the underestimation of winter snow accumulation between 1700- and 2034-m elevation; however, the overall lower temperatures at Cabin station mitigate the impact of this shift in generated air temperature. The overestimation of peak SWE above 2034-m elevation is attributed to the higher P_grad values assumed for the current study.

The turbulent heat fluxes generally provide a negligible contribution to the snowpack energy balance during the spring/summer snowmelt period. Therefore, any energy balance discrepancies in the sensible and latent heat fluxes resulting from discrepancies in the generated U (which shows large discrepancy during the summer) and R time series has a negligible effect on simulated snowmelt rates and streamflow. No longwave observations were available for comparison, but prior work suggests that satisfactory estimation of L can be achieved with several common empirical models (Saunders et al. 1997). Regardless, the strong dependence of L on temperature would suggest that as long as T_a is accurate, values of L should be reasonably accurate as well.

During the winter ET is predominantly a function of evaporation and sublimation from snow-covered surfaces (50% of which occurs from precipitation intercepted by the overstory), which is generally an energy-limited process. As such, errors in generating U, R, and S_g (as well as the temporal structure of precipitation) will have a noticeable effect, manifested as an underestimation of ET during the snow accumulation period (up to 1 April; Fig. 20); however, the effect upon simulated hydrology is marginal. Despite substantial melt during the freshet period, the steep slopes and shallow soils of Redfish Creek favor runoff over storage such that ET is limited by water availability (Whitaker et al. 2002); summer soil water depletion also limits ET. Under these circumstances, errors in generating U, RH, and S_g are expected to be largely insignificant, and the slightly increased rate of ET simulated with the generated met data is attributed to slightly increased moisture availability during the spring and summer (Fig. 20).

Hydrologic simulation driven with both the observed and generated meteorology captures the annual water balance, the spatial distribution of peak snow water equivalent and freshet runoff, and both simulations consistently underestimate low flow during the late summer and winter periods. Considering that accurate simulation of peak discharge is of primary concern to the authors, the generated meteorology is considered accurate enough for the purpose of driving hydrologic simulations of Redfish Creek.

6. Conclusions

A relatively simple method has been presented for extending short-duration meteorological records by using a combined stochastic–empirical technique, and application has been demonstrated for the Redfish Creek basin in southeastern British Columbia. The synthetic meteorology was generated in three major steps. Hourly precipitation was stochastically generated using a random pulse model, daily meteorology was stochastically generated using a multivariate first-order autoregressive model, and hourly meteorology was disaggregated from daily meteorology and precipitation.

Despite discrepancies in all three steps of the met generation algorithm, synthetic hourly meteorology was generated with enough accuracy to reproduce the simulated annual water balance, spatial distribution of winter snow accumulation, flow duration, and average annual hydrographs derived when using observed meteorology. In fact, model skill is fairly consistent between simulations, particularly in light of the disparity that exists between simulated output and observation. Regardless, both meteorology datasets, when used to force DHSVM, render accurate simulations of discharge during the freshet period, which is of most concern to the authors. As such, the proxy input data provided by the met generation model will be useful in generating large samples of peak annual discharge for use in investigating the peak flow regime of Redfish Creek. The reader is reminded that several aspects of the generation algorithm, specifically the partitioning of solar radiation into beam and diffuse components and the estimation of longwave radiation, could not be assessed as these variables were estimated in both the synthetic and “observed” datasets.

Several additional issues remain to be addressed. The short-duration record available for calibration implies that the generated meteorology is only a stationary representation of a very short climate period. As such, the simulated hydrologic processes at Redfish Creek may not be representative of those that would occur when subject to low-frequency climatic variability. This issue can only be investigated with the use of longer datasets. Although the proposed model is considered generally applicable to mountainous topography, its specific application to Redfish Creek is sensitive to the regional climate and the (short) calibration record and could not be applied to other study areas without recalibration. In fact, the model will benefit from periodic updating for use in Redfish Creek as more calibration data become available. Investigation of regional parameters will likely prove fruitless given the very low density of meteorological observations in the mountainous topography of British Columbia. The present study clearly illustrates the value of maintaining, and even expanding, the current hydrometeorological collection program in the British Columbia interior.