The catchments used for this study are shown in Fig. 1, and some relevant hydrological characteristics in Table 1. More detail on each site is given in the papers quoted in this section. All the rivers are affected to some extent by groundwater abstractions and transfers, a common situation in southern England. The effects of these can be clearly seen in Table 1, with reduced specific flows in the Kennet and enhanced flows in The Cut due to water imports.

The upper River Kennet (Fig. 1a) was sampled at Mildenhall, some 2 km east of Marlborough (Palmer-Felgate et al., 2008). The catchment consists entirely of chalk of Cretaceous age. The river is predominantly groundwater-fed, with a baseflow index of 0.94 (Table 1), hence a damped hydrological response to rainfall. Land use is predominantly arable agriculture with some intensive livestock farming. The town of Marlborough (pop. ca. 8400) is the only significant urban settlement. Above Marlborough sewage treatment works (STW), the Water Framework Directive classification is “good”, deteriorating to “moderate” below (see http://maps.environment-agency.gov.uk/).

The River Enborne (Fig. 1b) was sampled near the catchment outlet at Brimpton (Halliday et al., 2014). Cretaceous chalk underlies the catchment and outcrops in the upper reaches, but much of the surface geology consists of impervious Tertiary clays. The Enborne is thus more hydrologically responsive than the Kennet. Land use is a mixture of grassland, arable and woodland. The WFD classification is a mixture of “good” and “moderate”, depending on the reach (Fig. 1b).

The Cut (Fig. 1c) was sampled near its confluence with the River Thames at Bray (Wade et al., 2012; Halliday et al., 2015). The catchment geology is predominantly London Clay and Reading Beds (Palaeocene clays and sands), giving an impermeable catchment with a baseflow index of 0.46. The catchment population is around 190 000, mostly in the large urban centres of Bracknell and Maidenhead. Improved grassland covers 30 % of the catchment and 26 % is classed as arable, mostly in the northern half, and woodland occupies 15 %, mostly in the south. River flows are substantially increased by abstraction from the Thames for drinking water (Halliday et al., 2015) and its subsequent release through the STWs, increasing the specific runoff (Table 1). The WFD classification is mostly “poor”, being “moderate” only in the upper reaches above the major conurbations. Note the river is called “The Cut”; hence “The” is capitalised throughout.

The River Frome (Fig. 1d) was sampled at East Stoke (Bowes et al., 2005, 2009, 2011). It has been studied for many years as an example of a chalk stream: the geology is mostly chalk, but there are other Cretaceous formations in the headwaters, principally the Gault and Upper Greensand formations in the headwaters, and sands, gravels and clays in the lower catchment. Dorchester (pop. 27 000) is the only significant urban centre. Land use is mainly agricultural, 47 % arable, 39 % grassland and 9 % woodland. There is some aquaculture, mainly watercress growing, affecting the river. The WFD classification is mostly “poor”, but “good” in some side streams.

Methods for collecting high-frequency water chemistry data varied somewhat between rivers: they are summarised here and are described in more detail in the papers cited below. Sampling of the River Enborne is described in Wade et al. (2012) and Halliday et al. (2014). Sampling began on 1 November 2009 and finished on 29 February 2012. Sampling frequency was hourly. A YSI 6600 multi-parameter sonde was used to measure a standard suite of parameters, including dissolved oxygen, pH and water temperature. A bankside mains-powered instrument, the Systea Micromac C, was used to make hourly measurements of total reactive phosphorus (TRP). The instrument uses the phosphomolybdenum blue complexation method on an unfiltered sample, hence TRP is an operationally defined measurement, predominantly comprised of orthophosphate (PO4) and readily hydrolysable P species.

The River Kennet at Mildenhall was sampled from January 2004 to November 2006 and used the same instrumental set-up as the Enborne, as described by Palmer-Felgate et al. (2008).

The Cut was sampled from April 2010 to February 2012 (Wade et al., 2012; Halliday et al., 2015). Sampling frequency was hourly and measurements of dissolved oxygen, pH and water temperature were made by a YSI multi-parameter sonde as above. Phosphorus species were measured using a Hach Lange Phosphax Sigma which uses phosphomolybdenum blue complexation to measure TRP as above, and also total phosphorus (TP) by acid persulfate digestion after heating to 140 ∘C, at a pressure of 2.5 bar (359 kPa), followed by phosphomolybdenum blue complexation. There was no filtration step in either analysis.

The River Frome at East Stoke was sampled as described by Bowes et al. (2009) between 1 February 2005 and 31 January 2006, as part of a much longer, lower-frequency study (Bowes et al., 2011). Samples of river water (500 mL) were taken from approximately the mid depth of the river using an automatic water sampler (Montec Epic, model 1011). Sampling frequency varied from two to four times per day during dry periods and up to eight samples per day during periods of rainfall. A total of 1358 samples were taken over the 1 year monitoring period. Total phosphorus was determined in the laboratory by digesting the sample with acidic potassium persulfate in an autoclave at 121 ∘C, then reacting with acidic ammonium molybdate reagent to produce phosphomolybdenum blue complex (Murphy and Riley, 1962). Soluble reactive phosphorus (SRP) was determined by filtering river water samples through a 0.45 µm cellulose nitrate membrane, and analysing for phosphate as above.

As the determination of the WFD status of a water is based on annual means, the data sets were divided into annual subsets: 2010 and 2011 for the Enborne; 2004 and 2005 for the Kennet; 2011 for The Cut; and 2005 for the Frome. A standard set of descriptive statistics was then calculated for all the data sets, including those required for WFD determinations in the UK, which are the mean for P and pH; the 10th percentile for dissolved oxygen; and the 98th percentile for water temperature. The analysis in this paper is restricted to these four variables. Each of the high-frequency annual data sets was then resampled using two different sampling frequencies and five different sampling strategies, to create a series of ten sampling scenarios. Sampling frequency was either monthly or weekly. Within each of these, the strategies were (with abbreviations in brackets) the following:

sampling at any time (ANY);

Though it is clear a priori that weekly sampling will give a more precise estimate than monthly sampling, Figs. 2 to 5 show that the magnitude of the effect varies between determinands and sites, and even between different years at the same site. The improvement in precision between monthly and weekly sampling is however generally considerable. For instance, the mean TRP in the River Kennet in 2004 for the MF9-18 sampling strategy (Fig. 2) was 103 µg P L-1, with a 95 % confidence interval (CI) of 38–251 µg P L-1. For weekly sampling the corresponding CI was 74–138 µg P L-1; mean, 102 µg P L-1. As can be seen in Fig. 2, the monthly TRP CI covers three WFD classes (poor, moderate and good, just missing high), whereas the weekly sampling CI is contained entirely within the moderate class. Similarly, the 95 % CI for MF9-18 sampling of TRP on The Cut covers 247 µg P L-1 (480–727), whereas the corresponding 95 % CI for weekly sampling is only 70 µg P L-1 (546–616), though all samples are in the “poor” WFD class. The width of the weekly sampled confidence intervals was about 33 % that of the monthly for P species and pH (Figs. 2 and 4), about 50 % for dissolved oxygen (Fig. 3) and about 67 % for temperature (Fig. 5). Whether the improvement of precision of weekly sampling makes any difference to the possible range of WFD classes depends on the closeness of the range of concentrations to the class boundaries. For instance, monthly sampling of temperature is less precise than weekly (Fig. 5), but this makes no difference to the WFD classification except on The Cut, whereas for P species (Fig. 2) the difference is considerable.

Another way to evaluate the effect of sampling frequency on WFD classification is to calculate the probability that a water body will be allocated to a given class in any one year. This is shown for dissolved oxygen (DO) on The Cut in Fig. 6, and TRP on the Kennet in Fig. 7. Monthly sampling at any time could result in The Cut being allocated to any of the five WFD classes in any one year due to random sampling effects (with a 0.3 % chance of “high” just visible on the diagram). The probability of any one year being allocated to the correct class for this sampling strategy, which was “poor” according to the high-frequency data, was just 47 %. In contrast, weekly sampling under the same conditions allocated The Cut to three classes, with a 78 % chance of “poor”. These results have implications for detecting trends in the data. For instance, using the most common sampling strategy (MF9-18), the probability of the WFD class being correctly assigned to “good” is 52 % for monthly sampling and 89 % for weekly sampling (Fig. 6). Assuming DO concentrations stayed the same for 5 years, the probability of the classification being correct in every year is only 4 % (0.525) with monthly sampling, whereas it is 54 % (0.895) with weekly sampling. The potential for generating spurious “trends” in the WFD classification due to purely random sampling effects is obvious, if the sampling frequency is not great enough. For TRP on the Kennet (Fig. 7), weekly sampling always produces the correct classification of “good”, whereas with monthly sampling the classification is correct only 65–75 % of the time. Proportions of other classifications are “moderate”, 16–20 %; “poor”, 5–11 %; and “high”, 0–2 %, indicating the considerable uncertainty and wide range of possible classifications if the sampling frequency is not high enough. These considerations apply when the confidence intervals of the mean re-sampled concentrations crosses one or more WFD class boundaries – inspection of Figs. 2–5 shows where this occurs. For some cases, e.g. pH (Fig. 4), class boundaries are not crossed and any sampling strategy always gives the same classification.

For P species, DO, and pH, the means of the monthly and weekly sampled average values are essentially the same (Figs. 2–5). They are also close to the true means calculated from all the high-frequency observed data – normally within 1 % of the true mean value, with weekly sampling a little more precise. This shows that sampling introduces no systematic bias, and the means shown in Figs. 2 to 5 represent the observed means. It does not follow from this that monthly and weekly sampling would generally give the same mean in a given year – only that the mean would be the same if it was possible to continue the sampling for long enough, effectively 1000 years in this case. For the 98th percentile water temperatures, however, the yearly means of monthly samples are clearly lower than the weekly means (Fig. 5), and sampling frequency does introduce a systematic bias. Table 2 shows the true and sampled temperatures for each river and sampling strategy, “true” being defined as the temperature calculated from all the measured data for the particular frequency, strategy and river. Table 2 shows that monthly sampling is underestimating water temperatures by about 1 ∘C, sometimes more, whereas weekly sampling overestimates less consistently, by about 0.1 ∘C. These differences arise from the methods used to interpolate the 98th percentile temperature. When there are not many measurements (as in the monthly samples here), a systematic bias is likely as well as wide confidence intervals. The problems involved in the estimation of percentiles used as water quality standards are extensively discussed by Ellis and Lacey (1980), who note that the confidence limits are likely to be very wide for high (or low) percentiles and depend markedly on the underlying distributions of the measured values. The adoption of a 98th percentile as a standard was probably intended to apply to continuously measured temperature data where the large number of data points reduces both random error and systematic bias in estimation of the percentile. Use of a high percentile as a standard with spot measurements, which are typically fewer in number, needs to be more critically evaluated.

One aim of this paper is to investigate whether restricting the times at which samples are taken would improve the precision of the estimates for the chemical variables. This can be measured by comparing the height of each bar in Figs. 2–5 with the bar corresponding to unrestricted sampling (“ANY”). Table 3 shows a quantitative measure of this, i.e. 95 % CI(s)/95 % CI(Any) expressed as a percentage, where 95 % CI(s) is the 95 % confidence interval for a particular strategy and 95 % CI(Any) is the 95 % CI for sampling at any time. Overall, restricting the sampling time improves the precision of the estimates in 71 % of cases – those where it does not do so are highlighted in the table. The most consistent improvements in precision are obtained using the 3 h sampling strategies (AW9-12 and MF9-12) for TRP, DO and pH with weekly sampling. Monthly sampling shows a similar pattern but is less consistent. In general, the 3 h strategies improve the precision more than the full working hours strategies (AW9-18 and MF9-18) – the average CI is 88 % of unrestricted for the 9–12 strategies versus 95 % for the 9–18 strategies. There is no overall difference between the precision of sampling on the AW versus the MF strategies (both 91 % of unrestricted). There are differences in response between the rivers, and between the same river in different years, and between weekly and monthly sampling. In spite of these inconsistencies, however, it seems that restricting the sampling time to a 3 h window would in general give a worthwhile improvement in precision of the estimates of the four chemical variables, and thus a more accurate estimate of the WFD class.

It is clear from Figs. 2 to 5 that different sampling strategies give different estimates for the variables being considered. Apart from the differences in water temperature between monthly and weekly sampling referred to in Sect. 3.1, these are largely due to diel variations in processes affecting the variables. It is well known that DO has a strong diel variation due to the balance between photosynthesis and respiration, with low DO concentrations at night when there is no photosynthesis and high concentrations during the day when photosynthesis is active. This explains the patterns seen in Fig. 3, when the AW/MF9-18 strategies have higher DO concentrations than the average for the entire 24 h (ANY), and the AW/MF9-12 strategies are intermediate (as DO concentrations are generally higher in the afternoon). The patterns are most pronounced on The Cut, which has a very strong diel DO cycle (Wade et al., 2012; Halliday et al., 2015), and least on the Enborne, where heavy riparian shading due to deciduous trees restricts a strong diel DO cycle to the early spring (Halliday et al., 2014). The same cycle can be seen in the pH values (Fig. 4), where higher pH in the AW/MF9-18 samples is due to lower carbonic acid concentrations during the day because of photosynthetic uptake of carbon. Likewise, the prevalence of high water temperatures is lower in the morning than for the whole day, or even the full 24 h (Fig. 5). Phosphorus species have a less obvious pattern (Fig. 2), though there is a suggestion that MF values are slightly higher than AW values, reflecting a different outflow pattern from sewage treatment works between weekday and weekend (see Halliday et al., 2014).

These results raise the question of which sampling strategy generates the best concentration estimates for use in WFD classifications. The differences between strategies are greatest with dissolved oxygen, and can substantially affect the WFD classification. To take the most extreme example, The Cut has a classification of “poor” if sampled at any time of day (ANY), “good” if sampled at any time during working hours, and “good” but with less certainty if sampled from 09:00 to 11:59. It could be argued that “poor” is the correct classification, since organisms are exposed to conditions throughout the 24 h period, including low DO concentrations during the night. Conversely it could be argued that since the boundaries between the WFD classes are derived in the UK from statistical associations between chemical parameters and biological quality based on sampling at conventional times, i.e. during working hours, then the correct classification is “good”. Whether “good” is a reasonable representation may depend on the diel dynamics of DO at the particular site. The Cut is a productive stream with both high photosynthesis and respiration rates – DO concentrations can fall to as little as 27 % at night (Wade et al., 2012; Halliday et al., 2015). The Enborne in 2011 would also have been classified as “good”, but the magnitude of diel fluctuations is much smaller, with night-time DO concentrations no lower than 60 % (Halliday et al., 2014). Clearly The Cut is much more at risk of deleterious effects due to anoxia than the Enborne, but the daytime sampling regime does not register this difference very strongly (Fig. 3). If the issue is low night-time DO concentrations, and the measurements are available because the site is being continuously monitored, then it would seem more logical to use measurements made at night as the standard. The Cut might however be seen as an extreme case given its high STW load, and comparing the working day and anytime means and CIs in Fig. 3 shows that working day sampling is a better representation of the full range of DO concentrations on the Enborne than The Cut, with the Kennet intermediate. Based on this sample of three rivers, it may be that daytime sampling for DO is not a good measure of risk for rivers with high respiration rates due to organic loading and/or high rates of primary production. This would need further investigation on more sites. What is not satisfactory, however, is that it is possible to obtain such widely differing WFD classifications because the sampling time is not defined. Defining a sampling time as part of the assessment procedure would be a straightforward process and reduce some of the uncertainty being discussed here, as previously suggested for The Cut by Halliday et al. (2015).

The Kennet and Enborne were both assessed for 2 consecutive years, and it is therefore possible to obtain an indication of the extent to which chemical concentrations and WFD class assignments are stable with time. River pH was essentially the same between years (Fig. 4), but the other determinands show differences. TRP concentrations fell between 2010 and 2011 on the Enborne (Fig. 2), increasing the WFD class from “poor” to “moderate”. If non-overlapping confidence intervals are taken as a measure of a significant difference, this is a significant improvement detectable with weekly sampling, but not with monthly sampling. This is the only significant difference between years evident in the data. DO, in contrast, declined on the Enborne between the same years, and the mean WFD class fell from “high” to “good”. On the Kennet, the mean TRP stayed much the same between years, but TRP had much wider confidence intervals in 2004 than in 2005, due to some especially high values. DO was lower on the Kennet in 2005 than in 2004, though the WFD classification did not change. The differences between years are likely to be due to hydrological differences rather than any change in management. On the Kennet, flows in 2004 were close to the long-term average, whereas 2005 was a dry year, with flows only 62 % of the average (UKNRFA, 2014), leading to a higher volume-specific rate of oxygen consumption, which depresses the 10th percentile value. On the Enborne, 2010 was a wetter year than 2011, with high and variable flows at the beginning of the period, explaining the greater variation in most concentrations in 2010 observable in Figs. 2–5. In general, the range in concentrations is determined by individual flow events which are not apparent in annually aggregated statistics, but this study illustrates that such differences do occur and will add to the variation observed.