Non-stationarity in long time series: some curious reversals in the ‘memory’ effect
✍ Scribed by Tim Burt; Fred Worrall
- Publisher
- John Wiley and Sons
- Year
- 2007
- Tongue
- English
- Weight
- 85 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0885-6087
- DOI
- 10.1002/hyp.6889
No coin nor oath required. For personal study only.
✦ Synopsis
Two decades ago in Hydrological Processes, one of us (Burt et al., 1988) reported stream nitrate levels in a small catchment of mixed land use (the Slapton Wood catchment) over a period of 15 years (1970)(1971)(1972)(1973)(1974)(1975)(1976)(1977)(1978)(1979)(1980)(1981)(1982)(1983)(1984)(1985). Multivariate analysis showed that variations in annual mean nitrate concentration were controlled by antecedent hydrological conditions, rather than by runoff conditions in the given year itself. This suggested that there was a strong lag or 'memory' effect in the hydrological system, with dry years being followed by higher concentrations than expected in subsequent years, while wet years exhausted the system so that subsequent years had lower than expected concentrations.
Two decades on, the Slapton nitrate record is still being maintained and it seems trite to note that the record is now, of course, much longer than the 15-year series we originally examined. The important point is that the much longer record includes unexpected changes in response, in addition to changes that we might have forecast 20 years ago. Here we look briefly at the 35-year record (October 1970-September 2005) and compare it to another long time series, dissolved organic carbon (DOC) records (using water colour as a surrogate) for the River Tees in northeast England (Worrall and Burt, 2004). We present correlations between annual mean concentration and annual rainfall totals, with the latter lagged by 1 (rf-1) and 2 years (rf-2) in addition to the current year (rf). Correlations for a 15-year period are repeated using a 'moving window' (Worrall et al., 2003) with the results being plotted against the final year of the series (Figure 1).
What is immediately apparent in both cases is that three out of four lagged variables show a complete reversal of sign over the period of analysis. For the Slapton nitrate record, both lagged variables have moved from negative to positive correlations with the dependent variable. For the Tees, the response is exactly the opposite for the rf-2 variable: positive correlations at the start of the series change to strongly negative by 1999, although with some move back towards zero correlation after that. These reversals were a complete surprise to us, but are they more common than we have realized? And what are the possible reasons behind the reversals-why might the 'memory' effect of a system change over time? One important word of caution: for n = 15, the 5% significant level is a correlation of ±0•51 and ±0•44 at 10%. This means that the trends plotted may have little meaning, although significant results are achieved in most cases at both ends of the analysis period.
Table I reminds us in general terms how sequences of wet and dry years might work out in terms of concentration, depending on whether the lag effects are positive or negative. The two catchments included here have very different characteristics so we might expect the process mechanisms to differ, although as we argue below, the general effect may have a similar basis. The Slapton Wood catchment (1 km 2 ) is an intensively farmed, lowland area; the Tees, a very much larger area (818 km 2 ), is dominated in its upland headwaters by blanket peat moorland, wetter and colder than the conditions at Slapton. We can, therefore, expect the soil nutrient cycles to be very different.
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