STUDY SITE

The Place Glacier (50°26′N, 122°36′W), located in the Coast Range of British Columbia, covers a small area of approximately 4 km². The glacier originates in an accumulation area that descends from ∼2610 m a.s.l. to an ablation zone, which terminates at ∼1850 m a.s.l. (Fig. 1). In contrast to many other glaciers that have been studied, the area of the accumulation zone is relatively small, taking up little more than a third of the glacier area. In fact, cold air drainage from the accumulation zone of the glacier would be expected to diverge in two directions: mostly toward the northwest, along the main tongue of the glacier, and southeastward, over the smaller tongue of the Joffre Glacier. As would be expected of a Coast Range glacier, winter accumulation can generate a deep snowpack (Østrem and Brugman, 1991), thus delaying the exposure of glacier ice well into the summer ablation period.

Figure 1

Map of the Place Glacier and adjacent ice areas (white line boundary), showing 1 km grid of UTM Zone 10 (lower left corner 526,000 m E., 5,584,000 m N., NAD83), likely directions for cold air drainage (broken line arrows), AWS sites (+ elevations) and 1991 micrometeorological site.

DATA

The off-glacier AWS was installed in July 2001 at 1840 m a.s.l., approximately 0.5 km northwest of the glacier terminus (Fig. 1). Data collected at this station throughout the year include hourly averages of air temperature, T_a, relative humidity fraction, rh, global radiation, K↓, wind speed, u, wind direction, u_dir, and total precipitation (P) for each hour (Table 1). The following year, the glacier AWS was installed in an open area (sky view factor 0.98) near the upper end of the ablation zone, at approximately 2044 m a.s.l. (Fig. 1). Hourly data obtained here include surface change, δh, due to ice and snow ablation (or accumulation) and averages of T_a, rh, u, K↓, and K↑, the reflected short-wave radiation (Table 1).

Table 1

Instruments deployed at AWS sites.

The glacier AWS functioned until the spring of 2003, when it was crushed by snow loading. In 2004, its air temperature and humidity sensor were relocated to a ridge above the base AWS, at 1901 m a.s.l. (Fig. 1). Also noted in Figure 1 is the site of a micrometeorological experiment conducted in 1991 from which wind speed and direction data were reviewed for the discussion section of this paper.

It is a straightforward matter to obtain vapor pressure, by applying the relative humidity fraction to the saturation vapor pressure at air temperature, using any one of a number of empirical relationships for that purpose (e.g., Oerlemans, 2000). However, inspection of the relative humidity records from the two stations showed that while data from the glacier station would maximize at ∼100%, those from the base station would achieve values no greater than ∼92%, thus casting suspicion on the results. Therefore, the sensors were brought together at the base AWS, for calibration against ventilated wet-bulb psychrometer vapor pressure values. In the case of the off-glacier AWS, it was found that a 1.23 multiplier and a −125 Pa offset were required to correct vapor pressures obtained from temperature and relative humidity data, while the equivalent corrections for the glacier AWS were 1.1 and −50 Pa. The corrections are likely to be specific to the sensors used in this study, so application elsewhere is not advised unless confirmed by other calibrations.

The water equivalent of snowfall at the glacier AWS site was estimated from the off-glacier AWS precipitation gauge record, setting the temperature threshold for snowfall at 1.5 °C (Klok and Oerlemans, 2002). Following Cheng (2001), noise in the gauge record was filtered by first taking differences between two moving 24-hour sums of the data, each one hour apart, to minimize diurnal variation. Then, expressing the results as hourly values, three passes of a moving 15-hour median filter were used to remove the remaining negative values. Gauge catch error was addressed by fitting second order polynomials to U.S. Army Core of Engineers corrections for the Alter shield (Anonymous, 1956), such that for wind speeds scaled to gauge height, of 4 and 8 m s⁻¹, respective multipliers of ∼1.6 and 2 applied to rain, ∼2.4 and 3.5 to snow. Using air temperature data from each AWS to separate snowfall from a total precipitation of ∼131 mm during the period of this experiment, total snowfall was estimated to be 4.83 mm at the off-glacier site, 30.7 mm at the glacier site.

A Hamming filter (Hamming, 1989) was applied to the acoustic sounder record of the glacier AWS, choosing after some trial and error a 5-hour moving window for the task. Given the uncertainties associated with precipitation gauge corrections, it is interesting to take Σ(+δh) from the filtered acoustic sounder record during the summer snowfall period and to treat it as a snowfall thickness record. This period spanned one week, yielding Σ(+δh)  =  222 mm, which requires a multiplier of 0.138 to convert it to the 30.7 mm w.e. estimated from the gauge. This is a value that could reasonably apply to the specific density of fresh snow (Goodison et al., 1981), thus bolstering confidence in the precipitation estimates.

GLACIER AWS APPROACH

Glacier AWS data allow a combination of measurements and modeling to be used in estimating the net radiation terms:

The Q_H and Q_E transfers incorporate measurements of air and surface vapor pressures, e_a and e_s, as well as air and surface temperatures, T_a and T_s:

The bulk transfer coefficients depend upon the roughness scaling lengths for wind speed, z_o, temperature, z_H, and humidity, z_E:

OFF-GLACIER AWS APPROACH

Using the off-glacier AWS data, the net radiation components are calculated as

Turbulent transfers using off-glacier AWS data are modeled from the parameterization scheme developed by Oerlemans and Grisogono (2002):

The katabatic boundary-layer conductance follows from Oerlemans and Grisogono (2002), where the strength of turbulent transfer is parameterized according to the temperature difference between the air mass and the glacier surface for T_a > 0 °C, using the altitude adjusted off-glacier AWS data:

MODELING THE INCOMING RADIATION

Following Munro and Young (1982), K′↓ is comprised of a direct component, S, which depends upon hourly cloud cover fraction, n, and a diffuse component, D, which in addition to n depends upon a surface average reflectivity, α_S, cloud absorptivity, a_n  =  0.18, cloud base albedo, α_b  =  0.5, and an hourly cloud top albedo, α_n, the daily mean of which is close to α_b:

This is in contrast to the approach taken by Greuell et al. (1997) who, using a combination of their own cloud observations and data from Sauberer (1955), related cloud cover to atmospheric transmissivity (Fig. 2). A similar type of relationship, using n_* as the basis for cloud cover, indicated that although n_* estimates of n appeared to be reasonable in comparison to Greuell et al. near the extremes of the cloud cover range, they were comparatively low toward the middle. Divergence between their work and ours is consistent with Suckling and Hay (1977), who noted the tendency for observers to overestimate cloud cover fraction and for sunshine records to underestimate n.

Figure 2

Pyrometrically derived transmissivity and cloud cover scatter plot using values obtained from base (open symbols) and glacier (closed symbols) AWS data, with line plot showing the relationship of Greuell et al. (1997, their equation 4).

Therefore, to the extent that the pyranometer behaves like a sunshine recorder, as suggested by Equation 9b, an iteratively derived cloud cover fraction would be too low between the limits of its range. Munro and Young (1982) used a weighted combination of observer and sunshine record cloud estimates to develop Equation 9, giving the greater weight to observed cloud cover. The effect of their approach is represented by setting n  =  n_*^0.75 for long-wave radiation modeling. The result is overlapping sets of glacier and off-glacier AWS cloud fraction values that are well described by Greuell et al. (1997) throughout the range of values plotted (Fig. 2), so n  =  n_*^0.75 is used here.

Long-wave radiation depends upon hourly n from 0800 to 1600, but average n for this period is used to model L↓ from 1600 to 0800 of the following day. The L↓ model itself follows from Klok and Oerlemans (2002):

MODELING THE SURFACE ALBEDO

Surface albedo was modeled with reference to albedo measurements made at the glacier AWS site: α_S  =  K↓/K↑. They yield the hourly pattern plotted in Figure 3, wherein values toward sunrise and sunset rise above the mid-day minimum. Daily mean α_S were obtained by defining albedo according to the daily sums of the radiation terms. They occupy positions (not shown in Fig. 3) within the daytime range, closer to the minimum. It is toward the daily mean that modeling is directed.

Figure 3

Hourly α_S measurements (broken line plots) and modeled α_S using data from glacier (horizontal bars) and off-glacier (open circles) AWS sites. Also shown are water equivalent of old and new snow cover (heavy line plot), and model α_S for days 235 to 244 using d_*  =  32 mm (light line plot). Inset is the RMSE map, with ‘+’ at the minimum RMSE location.

Several albedo models can be considered, each of which has its strengths and weaknesses (Brock et al., 2000). We have chosen the α_S model of Oerlemans and Knap (1998):

As noted in Brock et al. (2000) there are disadvantages to the use of this model, such as higher than measured albedo values when old snow cover thins out to expose the ice (e.g., Fig. 3 of Klok and Oerlemans, 2002; Fig. 3 of this paper). Also, errors in α_S will be propagated in M_S(i), which is a problem for iterative modeling because this affects the calculation of M_S(i) through Q_M in Equation 1. Therefore Brock et al. (2000) recommended an air temperature–based parameterization of albedo that has since been applied to distributed modeling of Storglaciären (Hock and Holmgren, 2005). Nevertheless, we use Equation 11 here because the modeling proceeds sequentially, thus minimizing error propagation through M_S(i). Furthermore, it appeals to curiosity about whether higher than measured albedo values during snowpack thinning can be corrected by a suitable choice of optical depth, as discussed below.

Values for ρ_s and ρ_fs were not measured in the field, so optimal values were estimated according to a two-way minimization of the root-mean-square error (RMSE) between modeled and observed daily mean α_S (Fig. 3 inset), yielding ρ_s  =  0.568, ρ_fs  =  0.161. In so doing, Equation 11 was initialized with d_o  =  1115 mm, the snowpack thickness first measured in the field, and by setting i  =  31 to allow for aging of snow cover prior to when measurements began. The one modification to the model was to allow at least a fivefold increase in d_* for old snow, the better to capture the pattern of albedo decline before day 245, thus avoiding the higher than measured α_S that would otherwise be the result during the final 10 days of old snow cover (Fig. 3, days 235–244). Despite noticeable disagreement on some days the pattern of change throughout the experimental period is well captured by modeling with glacier AWS data, yielding a RMSE  =  0.034 to compare with the RMSE  =  0.050 that would be the outcome for an old snow d_*  =  32 mm. Also good is the α_S pattern modeled from non-glacier AWS data.

The snow densities seem to be reasonable relative to other findings. For example, mid-April old snow densities of ∼0.3–0.4 at Place Glacier are known to increase to 0.5 or more by mid-June due to settling and meltwater percolation (Østrem and Brugman, 1991), so a value of ∼0.57 by midsummer is plausible. The fresh snowfall density is close to the value of 0.138 suggested from the precipitation gauge and sonic sounder comparison stated above. In terms of work on other glaciers, ρ_fs  =  0.161 is not much different from the value of 0.18 used by Klok and Oerlemans (2002) to convert snow depths on the Morteratschgletscher to water equivalents.

More problematic is the better than fivefold increase in d_* for old snow, in this case to 170 mm. Tentatively, we suggest that this compensates for the effect of water building up in the base of the snow cover as melting proceeds, the effect being to increase the transmissivity of snow layers adjacent to the ice, thus enhancing the effect of α_ice as the snow cover thins. That said, there is no reason to suppose that d_*  =  170 mm is generally applicable, thus inviting further investigation.

RADIATIVE AND ATMOSPHERIC REGIMES

Incoming radiation comparisons for the two sites are shown in Figure 4. Despite the fact that the stations are less than 3 km apart there is noticeable scatter in the comparison of global radiation measurements (Fig. 4a), most likely as a result of spatial variation in partial cloud cover. At low solar elevations there could be scatter due to differing times of topographic shading as well as occasional scatter from snowfall accumulation on the glacier AWS pyranometer dome. In bulk statistical terms, however, both the comparison of mean values and the slope of the regression are consistent with the expectation that global radiation at the lower, less exposed off-glacier AWS site should be somewhat less than that measured at the glacier site. The effect of constraining the regression to pass through the origin has only a minor effect on the slope, raising it to 0.94 while maintaining the value of r².

Figure 4

Hourly off-glacier and glacier AWS incoming radiation values for (a) global radiation measurements and (b) long-wave radiation estimates. The intersection of the broken lines in (b) denotes long-wave radiation at 315 W m⁻².

Cloud cover cannot be used to interpret the differences between means in Figure 4b; in fact, they differ by only ∼3 W m⁻². The implications of the regression parameters are only important well outside the data range plotted here; in fact, a constrained regression results in a slope that is very close to one. The scatter is substantial over this range, as one would expect from using two different sets of n estimates obtained from the pyranometer record of each AWS, as well as the temperature records specific to each station. The interesting point about Figure 4b, however, is that many L↓ values exceed 315 W m⁻², which is the approximate value of blackbody radiation from melting ice. This indicates that L* can contribute to melting at times when cloud cover and air temperature are sufficiently high. At this well exposed site, where a view factor ∼0.98 applies, the effect of topography is to increase L↓ by ∼1 W m⁻².

Comparisons of hourly temperature and humidity at the sites (Fig. 5) show that there is close agreement between the two sets of humidity data. In fact the contrast between means over the study period, 709 Pa off-glacier compared to 695 Pa on the glacier, is consistent with the expected atmospheric pressure change as elevation rises from 1840 to 2044 m. Contrasts between the temperature data sets are manifest in the diurnal temperature range, where the smaller range for the glacier AWS is consistent with its location over a melting surface. Both air temperature and vapor pressure tend to be above their respective ice point values of 0 °C and 6.11 hPa, except during summer snowfall events, though drops in vapor pressure below ice point value do occur briefly elsewhere in the record.

Figure 5

Hourly temperature and humidity series for the AWS sites, with glacier AWS values shown as dots, off-glacier AWS values as light line plots and precipitation as bars. Inset shows estimated and measured glacier temperature comparisons.

Peyto Glacier estimates of glacier air temperature from off-glacier AWS temperatures, adjusted according to the normal lapse rate, yielded values that were approximately 20% higher above ice point than those measured at a glacier AWS (Munro, 2004). The same procedure for the Place Glacier yields glacier T_a estimates that are only slightly more, even potentially less than measured according to the slope of the regression between them (Fig. 5, inset). This could mean that the glacier cooling effect is being felt at the off-glacier site, a thought supported by subsequent comparison of air temperatures measured at 1901 and 1840 m. The comparison indicates that if T_a at 1901 m, adjusted according to the normal lapse rate were used to estimate T_a at 1840 m, the result would be ∼0.7 °C warmer than T_a recorded at the off-glacier AWS. Therefore, it may be that the off-glacier AWS record is influenced by the glacier wind, thus making it less representative of the regional air mass than initially thought.

Also worthy to note are the contrasting summer wind speed regimes at the two AWS sites and the predominance of glacier wind directions in the off-glacier AWS record (Fig. 6). At first, the summer wind speed pattern of the glacier AWS was thought to reflect sensor malfunction because much of the record indicated wind speeds less than the anemometer stall speed. But AWS comparisons during the winter, when air temperatures are below 0 °C and regional winds dominate, show vigorous wind speeds for both data sets. This suggests that although air temperatures above 0 °C needed for glacier wind development prevail during the summer at Place Glacier, they do not necessarily lead to persistent katabatic flow. Instead, the summer pattern appears to reflect an intermittent glacier wind regime, one that is not easily amenable to current modeling approaches. Furthermore, it offers another interpretation of the small contrast between off-glacier and glacier mean air temperatures: that the cooling effect of this glacier could be rather weak.

Figure 6

Summer and winter hourly wind speeds for off-glacier (lines) and glacier (dots lines) AWS sites. Also plotted (broken lines) are the off-glacier wind directions, the 120° to 180° range encompassing glacier wind direction.

Bearing these considerations in mind, off-glacier AWS data were prepared for modeling ablation at the glacier site, first by adjusting T_a to 2044 m, using a normal lapse rate of −0.0065 °C m⁻¹, then by adjusting vapor pressure according to the expected ratio (0.98) of air pressure at the two sites. No elevation adjustment was made to off-glacier global radiation data, its sole purpose being to generate cloud estimates for radiation modeling. Also, for modeling purposes, the 1.5 °C temperature threshold for glacier snowfall was determined by the adjusted off-glacier T_a, the effect of which was to raise the total snowfall estimate at the glacier site to 31.7 mm.

ABLATION MODELED FROM GLACIER AWS DATA

The surface energy balance components of Q_M (Fig. 7) show that the turbulent transfer contributions are small relative to the net radiation terms on most days. Values plotted in Figure 7, averaged over the whole study period, are 93.1 W m⁻² for K_*, −22.6 W m⁻² for L_*, 14.4 W m⁻² for Q_H, and 3.91 W m⁻² for Q_E. The value for Q_H is no more than half what has been reported elsewhere from bulk transfer estimates over melting ice and snow (e.g., Munro, 1990; Oerlemans, 2000; Pohl et al., 2006). Together, the turbulent transfers amount to less than the estimated long-wave radiation loss from the site. Also, they depend on wind speed data, so hourly Q_H and Q_E show the same discontinuous behavior noted in the wind speed record (Fig. 5). The expected consequence of this is extreme stability, such that the effect of applying the stability correction scheme described in Munro (2004) is minimal. The impression gained from these results is one of summer melt that is dominated by radiative transfer. Nevertheless, the turbulent transfers are included in modeling cumulative δh from Equation 1 because they still account for approximately 15% of the ablation.

Figure 7

Surface energy exchange components computed from hourly glacier AWS data.

The ability to capture the cumulative sonic sensor δh with Equation 1, using glacier AWS data to model Q_M, appears to be good near the beginning and end of the old snow decay period, less so in the middle of this period, where failure to account for density variation within the snowpack may explain the result (Fig. 8). Substantial disagreement is seen after the old snow is gone, when the step change expected from the first fresh snow events of days 245 and 246 does not stand out in the sensor record, resulting in a modeled offset to cumulative δh after day 246 of approximately 0.1 m. Nevertheless, modeled change after that time is broadly similar to measured change, even to the extent that the change expected from snowfall on days 251 and 252 appears to be the same for both. A comparison between simulation and measurements yields a RMSE  =  87 mm, 57% of which is systematic, according to the statistical measures of Willmott et al. (1985). Better agreement can be forced by injecting a 0.1 m step into the measurement record, beginning with day 246, in which case the RMSE  =  38 mm, 31% of which is systematic (Table 1).

Figure 8

Measured (dots) and modeled cumulative δh, using data from glacier AWS (heavy line) and off-glacier AWS (light line), with snowfall (bar graph). Upward displacement of measurements, δh ∼0.1 m, compensates for initial lack of sonic sounder response to snowfall.

The question remains as to why the sonic sensor record should initially be so unresponsive to fresh snow accumulation. There was no observer on site to witness events. But one may speculate from the low albedo recording on day 244 that the events entailed melting out of the old snowpack, followed by fresh snowfall that accounts for albedo rise through days 245 and 246 (Fig. 3). In such circumstances there could have been water on the surface which initially absorbed or melted snow on contact, thus compromising snow layer thickening. After day 246, when absorption and freezing had firmed the surface, snow accumulation was fully effective in thickening the snow cover.

Some support for this speculation can be gained by looking at daily P_s/Σ(+δh) values which are 0.395 and 0.302 for the first two days, when P_s was estimated to total 12.1 mm w.e., but 0.147, 0.020, and 0.117 on the last three days, when the total P_s w.e. estimate was 17.6 mm. The smallest P_s/Σ(+δh) values, 0.026 and 0.018, apply to days 247 and 248, when less than 1 mm w.e. snowfall was estimated for each day. The fact that P_s/Σ(+δh) for the first two days stands well above the rest is consistent with the idea of initial loss from accumulation due to melt and absorption on contact, a process which is not included in the model.

ABLATION MODELED FROM OFF-GLACIER AWS DATA

Off-glacier data were introduced into the ablation model in a series of steps, each step constituting a replacement of a glacier-based model element with one from the off-glacier approach. Because the sonic sensor appears to have missed the early new snow events, δh  =  0.1 m at the start of day 246 was applied to the measurement record, as stated above. Thus the experiment is to see if off-glacier data and procedures can do as well as glacier data and procedures. This is done with distinction between the systematic (RMSE_S) and unsystematic (RMSE_U) parts of the RMSE (Table 2), as outlined in Willmott et al. (1985), stating the statistics in mm. Included are the slope and intercept of the best fit line to modeled and observed Σ(δh).

Table 2

Glacier and off-glacier AWS ablation model outcomes.

The modeling steps were as follows, the first three involving straightforward change of data or procedure, the last two minimization of RMSE error between modeled and observed Σ(δh):

The only effect of changing to off-glacier T_a is to increase the glacier P_S estimate by 1 mm, the effect upon Σ(δh) being too small to generate more than a 0.002 m change from the glacier AWS result. Fortuitously, the RMSE measures are noticeably smaller (Table 2, step 1). On average, the replacement of the incoming radiation terms lowers K↓ by 1 W m⁻², raises L↓ by 3 W m⁻², and the RMSE, now at its highest value of 41 mm, has equal parts of RMSE_S and RMSE_U (Table 2, step 2). Despite the 1.2 W m⁻² decrease in K_* and 2.7 W m⁻² increase in L_* that follows from this, the change in Σ(δh) from the glacier AWS result is still well within 0.01 m.

Incorporation of the albedo model raises K_* to 95.8 W m⁻² and Σ(δh) to −1.228 m, the most extreme of the ablation simulations, but with a reduced RMSE (Table 2, step 3). A comparison of the off-glacier modeled albedo pattern to that modeled from glacier AWS data shows that the rise in average K_* does not always signify reduction in off-glacier modeled albedo (Fig. 3). Off-glacier albedo outcomes are lower than those from the glacier AWS near the end of the old snow cover period and on some days of new snow cover, but they are higher on other days of new snow, as would accord with the increased snowfall outcome of step 1. Nevertheless, most of the change from Figure 3 is toward lower albedo, so it appears that the effect on M_S of the rise in L↓ outweighed the relatively small reduction in K↓.

Following Klok and Oerlemans (2002), the Q_H and Q_E parameterization entailed adjusting K_b in Equation 7 to obtain agreement between measured and modeled ablation, using the criterion of minimal RMSE (Table 2, step 4). The parameterized fluxes are clearly smaller than the glacier AWS values that they have replaced and, because this affects M_S in the albedo model, K_* has changed slightly. Error measures have changed slightly as well, but the outcome was achieved by setting K_b  =  −0.0051 m s⁻¹ and constraining Q_H + Q_E to 0 for K_kat + K_b < 0.

To use a negative K_b to achieve a fit is to adopt the physically untenable position that the geostrophic momentum flux is upward from the ground. Therefore, optimization was done again, this time setting K_kat  =  0 and K_b  =  0.0026 m s⁻¹ to minimize the RMSE (Table 2, step 5). Now Q_H and Q_E are closer to the glacier AWS values than they were before and the RMSE measures are reduced to the levels that apply to step 1. Furthermore, the hourly Q_H pattern is closer to that of the bulk transfer estimates but well short of agreement (Fig. 9), as further discussed below. The key point, however, is that K_b is now positive and its order of magnitude is similar to that of values used elsewhere (Klok and Oerlemans, 2002; Munro, 2004).

Figure 9

A 10-day sample of sensible heat flux model results from Equation 4a, using glacier AWS data (dots) compared to Equation 7a results for steps 4 (light line) and 5 (heavy line), using off-glacier AWS data. Inset shows a sample of wind directions at the 1991 site.

DISCUSSION

One should not place undue emphasis upon the relative sizes of the RMSE measures for glacier and non-glacier AWS model outcomes, or the size of RMSE_S relative to RMSE_U. Although the RMSE for the final off-glacier model result is slightly smaller than that of the glacier model result, the former benefits from optimization of the turbulent transfer terms according to the RMSE but the latter does not. This has the effect of allowing the choice of Q_H and Q_E to absorb the effects of errors in other aspects of the model. Had the results of the first three steps in changing to the off-glacier model not turned out as well as they did, departure of the turbulent transfer values from those of the glacier AWS could have been greater than indicated in Table 2.

The RMSE_S can be reduced by constrained regression, the effect upon the outcome in Table 2, step 5 being a slope of ∼1.01 and a RMSE_S  =  4 mm. In fact, constraining the intercept to zero for each outcome listed in Table 2 resulted in a slope close to one. The fact that each of the outcomes has a substantial intercept stems from the obvious divergence between measured and modeled ablation that is seen in the middle of the old snow decay period (Fig. 8). Perhaps this reflects the density variation within the snowpack alluded to above because such variation is commonly observed in mass balance work on the Place Glacier and elsewhere (Østrem and Brugman, 1991), but it is beyond the scope and information base of this study to include it in the modeling approach.

The off-glacier modeled α results also warrant discussion because, in addition to these being smaller than the glacier modeled α values near the end of the old snow cover period, the difference between them increases from ∼0.01 on day 239 to ∼0.03 on day 243, the last full day of old snow (Fig. 3). This invoked the caution stated in Brock et al. (2000) that the structure of Equation 11 allows errors in α to propagate through M_S. Therefore, each of steps 4 and 5 in Table 2 was initiated with the α pattern of Figure 3, continued with optimization of K_b according to the RMSE, and completed with inclusion of the off-glacier α model.

Error propagation in the albedo model could, in distributed modeling terms, translate to errors in snowline migration. So the question was explored further, by reiterating the α values obtained at the conclusion of step 5. The α reduction of ∼0.03 for day 239 changed to ∼0.04 after the first iteration, where it remained through nine more iterations. The changes to new snow were greater, with α for day 247 rising to its limit of 0.9 by the fourth iteration, α for day 251 falling from ∼0.8 to ∼0.5. Given the small mass of the fresh snow cover, the effect on Σ(δh) was small, changing its value from −1.196 to −1.225 m. Therefore, with the caveat of greater error sensitivity for thin, fresh snow cover, it seems that Equation 11 is a good choice for distributed modeling, as exemplified in the latest version of the Storglaciären model (Reijmer and Hock, 2008).

More problematical for distributed modeling are the outcomes of steps 4 and 5 because they stem from attempting to fit a continuous modeling structure to what is essentially an intermittent flow regime. Parameterization of K_kat according to air temperature invokes the assumption of turbulent mixing even if the wind has nearly ceased, as is the case for all of day 232 and many hours on other days of the sample displayed in Figure 9. If the assumption is wrong, the error is compounded in K_kat as well as in the air temperature and humidity differences in Equation 7, the result being Q_H and Q_E outcomes that are at least double the values listed in Table 2, even with K_b  =  0. The results look more realistic with optimization according to a fixed value for K_b, with K_kat  =  0 (Fig. 9), but even so there is the inherent assumption of continuous flow and therefore little agreement with bulk transfer results. It is possible that the model could be improved by incorporating an “on/off flow switch,” but glacier-based wind speed data would be required, thus defeating the goal of reliance upon off-glacier data.

Furthermore, it may not be the case that the wind regime at one glacier site typifies the whole glacier. The data suggest that Place Glacier may be too small to sustain a katabatic flow regime, but a different picture emerges from wind direction data retrieved from the micrometeorological study conducted further toward the glacier terminus in 1991 (Fig. 9, inset). The data show marked deviations of wind direction from the expected direction of glacier winds, extremely so on days 230 and 236 of that summer. The deviations were often associated with notable reductions in wind speed (not shown), but with none that were below 0.75 m s⁻¹. This observation, and the seemingly glacier-like winds recorded at the off-glacier AWS, which also show extreme directional deviation (Fig. 6), suggest that there is more to consider for the wind regime at the glacier AWS than the failure of a small glacier to maintain a katabatic flow regime.

If the off-glacier AWS is recording katabatic winds, the glacier AWS wind record could be interpreted in terms of insufficient fetch down-glacier for katabatic flow to be established. The contrasting summer wind regimes of the two sites would then be interpreted in terms of insufficient fetch at 2044 m but sufficient fetch at 1840 m, notwithstanding the 500 m of separation between the glacier tongue and the off-glacier AWS. The 1991 results would fit well into such a picture. However, without wind direction data at 2044 m and concordant timing of measurements further down the glacier, the picture is inconclusive.

Also to consider is the unusual shape of the glacier: a small upper glacier area that feeds a larger lower glacier area comprised of two tongues. The glacier AWS appears to be sufficiently close to where airflow streams might diverge to each tongue to suggest that conflicting flow directions could also be a factor to suppress wind speed. It is also possible that the small size of the glacier makes it particularly susceptible to topographic steering of entrained regional airflow, such as to conflict with the establishment of the glacier wind. In this regard, it is noteworthy that the summer and winter wind direction regimes at the off-glacier site appear to be much the same (Fig. 6).