Análisis del Rendimiento por Regiones Faciales

Suspended sediment transport from subglacial drainage systems is commonly presented as either suspended sediment concentration or load. Studies that have investigated the mechanisms o f subglacial sediment evacuation by fluvioglacial processes have generally employed records o f suspended sediment concentration, since the concentration of sediment is suggestive o f the efficiency o f the drainage system at accessing and entraining basal sediments irrespective o f discharge. For geomorphological purposes, such as the calculation o f catchment sediment yields or denudation rates (cf. Hallet et al., 1996), suspended sediment transport is commonly presented as suspended sediment load (i.e. the weight o f sediment transported by the proglacial stream per unit of time).

Analysis o f suspended sediment transport in the context of the investigation o f the mechanisms o f suspended sediment evacuation by subglacial drainage is discussed below.

4.1.2.1 S u sp en d ed sed im en t concentration

Variation in suspended sediment concentration has typically been related to variation in proglacial discharge, since the latter provides a crude indicator o f subglacial hydrological conditions (e.g. flow capacity). The development o f ‘ordinary’ linear rating curves is by far the most common means o f investigating such relationships, due to the simplicity o f their construction and interpretation (Hodgkins, 1999). Analysis commonly involves the logarithmic transformation o f both variables in order to linearize the relationship and stabilise variance in the individual series (Gumell et al., 1994; Willis et al., 1996). r2 values for log-transformed data are often high, suggesting that flow capacity is a key control on suspended sediment entrainment and transport. However, it is important to note that: 1) high r 2 values should not be unexpected where n (the number o f observations) is large; and 2) rating curves developed for one season’s data are rarely found to be applicable outside that season (Fenn, 1989). Furthermore, the relationship

between suspended sediment concentration and discharge during individual melt seasons has been found to evolve (Gumell et al., 1992a, 1994; 0strem , 1975).

The method o f subdividing individual melt seasons based on the systematic evolution of meltwater sources and pathways, demonstrated in Chapter 3, has also been applied to the analysis o f relationships between suspended sediment concentration and discharge.

Changing relationships between suspended sediment concentration and discharge are reflected in the changing form o f the linear rating curve. Changes in r2 may also occur, suggesting changing dependence o f suspended sediment concentration on discharge as the melt season progresses. Albeit erroneously, Gumell et al. (1992a, 1994) used the changing slope o f rating curves developed for various subperiods o f the 1989 and 1990 melt seasons to make inferences about the changing availability o f basal sediment at Haut Glacier d ’Arolla (see Section 2.1.4). Hodson et al. (1998) used the technique more reliably at Austre Broggerbreen, Svalbard by plotting the regression relationships over the range o f discharges recorded during individual subperiods o f the melt season. By identifying statistically significant changes in the form o f the rating curves, temporal trends in the relationship between suspended sediment concentration and discharge were reflected in changes in both regression intercept and slope.

Relationships between suspended sediment concentration and discharge for an individual melt season generally exhibit low r2 values indicative o f high scatter, suggesting that

‘seasonal’ ordinary rating curves are inappropriate. Fenn et al. (1985) considered such scatter to be the result o f 5 separate effects: 1) seasonal variations in sediment availability, as represented by early season flushing and late season exhaustion effects; 2) diumal variations in sediment availability, especially the hysteresis effect related to diumal flow cycles (but also exhaustion over a number o f days following recent high flows, e.g. Clifford et al., 1995b); 3) transient flushes o f sediment that are independent of discharge and therefore generated by some other means; 4) sediment sources and sinks in the proglacial region; and 5) sediment supplied by rainfall-induced events. It may be possible to isolate seasonal variations in sediment availability by developing relationships for subperiods o f the melt season, such that ordinary rating curves for individual subperiods should demonstrate improved r2 values with respect to the seasonal rating curve. However, diumal hysteresis effects are more difficult to account

for, since in effect there are two values of suspended sediment concentration for each value o f discharge in a given diumal flow cycle.

To investigate the effect o f diumal hysteresis, Collins (1979b) estimated separate relationships for periods o f rising and falling discharge during diumal flow cycles at Gomergletscher, Switzerland. Different relationships were found for rising and falling limbs; however, there appears to have been little consistency in the form o f relationships for rising and falling limbs respectively, and r2 values were rarely better than a single relationship estimated for the whole season. More commonly, hysteresis effects have been accounted for by lagging the suspended sediment series in order to maximise r2 (e.g. Gumell and Fenn, 1984a; Fenn et al., 1985; Gumell et al., 1994). Such methods have indicated that for temperate alpine glaciers, suspended sediment concentration precedes discharge by ~ 1-2 hours. However, coefficients o f determination may increase only marginally (e.g. Gumell and Fenn, 1984a; Fenn et al., 1985), suggesting that lagging poorly accounts for the hysteresis effect or that a large proportion o f the scatter is from other sources.

A different approach has been to eliminate temporal variations in sediment availability by fitting rating curves to suspended sediment concentration and discharge after first differencing the series; i.e. by replacing variable x, by Ax,, where Ax, = x, - x,_i (e.g.

Gumell and Fenn, 1984a; Gumell et al., 1992; Willis et al., 1996). First differencing generates a stationary time series where rate o f change o f suspended sediment concentration is related directly to rate o f change o f discharge. However, r2 values for such relationships are generally very poor (r2 < 0.1; Gumell and Fenn, 1984a; Willis et al., 1996). Lagging the suspended sediment concentration series only marginally improves r2; however, it demonstrates that rates o f change o f suspended sediment concentration still precede rates o f change o f discharge and therefore some form o f hysteresis remains.

Despite eliminating temporal changes in sediment availability, it is not unusual for a large proportion o f the variance in the suspended sediment concentration series to remain unexplained (e.g. Gumell et al., 1992a). However, it is inappropriate to assume a priori that suspended sediment concentrations are controlled solely by flow capacity, and

instead multivariate rating curves that include variables other than discharge may account for some o f the scatter (e.g. Willis et al., 1996; Hodson and Ferguson, 1999).

These additional variables are intended to represent seasonal and diumal trends in suspended sediment availability, and variations in sediment supply due to rainfall, to which a suggestion o f some process significance may be ascribed. Diumal hysteresis is commonly represented using the variable Tate o f change o f discharge’, which is obtained by first differencing the raw (Richards, 1984; Willis et al., 1996) or log- transformed (Hodson and Ferguson, 1999) discharge series. Using stepwise or best subsets regression, an appropriate multivariate rating curve is identified using only the variables that are statistically significant, typically at p < 0.05 (Hodson and Ferguson,

1999). Such techniques have mostly been applied to high-arctic glaciers without subdivision o f the melt season into hydrologically ‘stable’ periods. These models have had mixed success, achieving only modest r 2 values (~ 0.5) whilst the residual series remain highly autocorrelated (e.g. Willis et al., 1996; Hodson and Ferguson, 1999;

Hodgkins, 1999).

Analysis o f the residual series is a common method o f evaluating the performance of ordinary and multivariate rating curves, r 2 values indicate the proportion o f the variance in the dependent series explained by the independent variables; however, some o f the variance in the output series may be due to random processes, such as sampling error or bank collapse within subglacial channels, and therefore r2 values o f 1 may be impossible to achieve. The presence o f autocorrelation in the residual series indicates pattern in the dependent series that the rating curve has failed to account for. Two forms of autocorrelation can be identified depending on its source (Fenn et al., 1985). ‘Quasi­

autocorrelation’ results from: 1) the inappropriate specification o f the regression model, for example applying a linear rating curve to non-linear data; 2) omitting relevant explanatory variables; or 3) failing to identify lags or changes in response between the dependant and independant variables. ‘True-autocorrelation’ is due to an inherent dependence in the dependent series such that values in the series are not independent o f each other but instead depend upon both previous values and upon present and previous random disturbances. True-autocorrelation is likely to exist in suspended sediment time series if basal sediment sources are accessed discretely and quasi-randomly, increasing sediment availability over several successive measurements (Willis et al., 1996; Hodson

and Ferguson, 1999). However, true-autocorrelation should also be expected due to the settling velocity o f fine particles being lower than their entrainment velocity, meaning that sediment is likely to remain in transport even if discharge falls (Richards, 1982;

Willis et al., 1996).

High autocorrelation in the residual series from bivariate rating curves was successfully removed by Gumell and Fenn (1984a) using first differencing; however, they argued that such methods produce rating curves that are remote from the original data and, as a result, are difficult to interpret. As noted above, introducing additional explanatory variables to create multivariate rating curves can also fail to remove all o f the autocorrelation. As a result, auto-regressive moving average (ARIMA) models have been applied that aim to characterise the internal dependence in the residual series (e.g.

Gurnell et al., 1992a; Willis et al., 1996). However, Hodson and Ferguson (1999) have argued that ARIMA parameters are difficult to interpret physically when the models are applied to residual series. As shown in Section 2.1.4, Gumell et al. (1992) inferred seasonal exhaustion o f suspended sediment at Haut Glacier d ’Arolla during 1989 from the moving average component o f their ARIMA models, whilst sediment load data (Gumell et al., 1995b; see also Table 2.4) and the form o f bivariate rating curves (Gumell et al., 1994; see also Figure 2.3) do not support this conclusion. Instead, Hodson and Ferguson (1999) found that simply including the previous value of suspended sediment concentration in the original multivariate rating curve satisfactorily removed almost all the residual autocorrelation.

An assumption o f all regression and time series (e.g. ARIMA) techniques is that a successful model will remove all residual autocorrelation: in effect, the autocorrelation pattern will resemble ‘white noise’ (e.g. Willis et al., 1996). It could be argued that, in pursuit of this aim, many studies have resorted to complex rating curve/time series models in which the physical meaning o f many o f the explanatory variables is of secondary importance. Moreover, the variance in the residual series, which is held to be truly random and somehow, therefore, unimportant, is rarely subject to scrutiny.

However, using a simple and physically comprehensible ordinary rating curve for the entire melt season at Haut Glacier d ’Arolla, Clifford et al. (1995b) demonstrated that the residual series from a very simple model can be very revealing o f important systematic

trends and processes. Clearly, there is value in some o f the more complicated regression techniques, enabling the isolation o f sediment availability factors, changing relationships between variables over time and additional important explanatory variables. However, care must be taken such that models do not become over-specified and explanatory variables are introduced only with a sound physical basis for doing so. Confidence limits (cf. Hodson and Ferguson, 1999) should be applied to autocorrelation patterns to test for significance in the remaining pattern before further investigation is undertaken. Attention should also be paid to time series plots o f the residuals, even when remaining autocorrelation has been eliminated, as this may still be revealing o f very important processes. For example, Willis et al. (1996) linked large positive residuals, which represent short-term sediment flushes, to glacier dynamics at Midtdalsbreen, Norway. A degree of correlation was found between sediment flushes and glacier motion peaks, suggesting sudden reorganisation o f subglacial drainage associated with enhanced forward glacier motion. Such detailed information, however, is rarely available, and, when the remaining variance is small (i.e. r2 is large), sampling errors are likely to obscure any meaningful pattern.

4.1.2.2 S u sp en d ed sed im en t load

Rating curves have also been used to investigate the relationship between suspended sediment load and discharge, although such relationships are somewhat spurious since discharge is incorporated into both variables. More usefully, annual suspended sediment loads have been used to estimate subglacial erosion rates (e.g. Hallet et al., 1996). By converting loads into spatially-averaged rates o f sediment evacuation (or yields) and assuming a homogeneous bedrock density, a rough estimate o f the rate o f mechanical catchment denudation can be made.

Emphasis is generally placed on annual yields that are commonly found to be very variable even for glaciers o f similar type, bedrock lithology and location (see Section 1.1). A more profitable approach might be to examine how yields vary at seasonal or sub-seasonal scales, and how this may be related to glacial or glacier-hydrological processes. An understanding of variation in sediment load at sub-seasonal scales may explain why annual yields are highly variable and hence little progress has been made in

understanding the efficiency o f glacier erosion. An enhanced understanding of this problem is likely to have significant geomorphological implications.