Seasonal Kendall Test Research Articles

SELECTING TREND TESTS FOR WATER QUALITY SERIES WITH SERIAL CORRELATION AND MISSING VALUES1

ABSTRACT: The use of nonparametric tests for monotonic trend has flourished in recent years to support routine water quality data analyses. The validity of an assumption of independent, identically distributed error terms is an important concern in selecting the appropriate nonparametric test, as is the presence of missing values. Decision rules are needed for choosing between alternative tests and for deciding whether and how to pre‐process data before trend testing. Several data pre‐processing procedures in conjunction with the Mann‐Kendall tau and the Seasonal Kendall test (with and without serial correlation correction) are evaluated using synthetic time series with generated serial correlation and missing data. A composite test (pre‐testing for serial correlation followed by one of two trend tests) is evaluated and was found to perform satisfactorily.

Trend detection in water quality time series of LRTAP-Quebec network lakes

After 5 yr of monitoring the LRTAP-Quebec network lakes, time series having 25 to 30 values each for 5 water quality parameters or combinations of parameters, for 12 temporal lakes, were investigated in terms of trend detection capability. Their persistence and seasonality were determined, then the appropriate trend detection test was applied. Lakes of regions 2 and 3 in the eastern part of the network show patterns that indicate acidification from 1982 to 1985 followed by a slight recovery from 1985 to 1988 with a return to higher lakewater sulphate concentrations in 1988. In region 1 (eastern part of the network), there is evidence of acidification from 1982 to 1985 followed by a leveling off of sulphate and alkalinity values from 1985 to 1988. Lakes situated in regions 4 and 5 (western part of the network) show signs of recovery from acidification. For the series with neither persistence nor periodicity (as were most of the alkalinity series), trends were detected close to the original assumptions (i.e. one standard deviation) using the Kendall test. Series with seasonality only (such as most of the nitrate series) allow trend detection below one standard deviation, using the Seasonal Kendall test. Series with persistence only (sulphates for example), tested with the Spearman/Lettenmaier test, or both persistence and seasonality (some of the nitrate series), tested with the Hirsch and Slack test, allow trend detection above 1.5 and 2.5 standard deviations respectively. Work on a calibrated watershed weekly time series shows that even if the sampling frequency is doubled, the information content increases by 10 to 25% only. The trend to standard deviation ratio decreases much the same way. Thus, the network design seems to be appropriate for detecting trends with a trend to standard deviation ratio of 1 after 7 to 10 yr of operation with a confidence level (1-α) and a power of the test (1-Β) of 90%, respectively.

Trends in stream quality in the continental United States, 1978–1987

The nonparametric seasonal Kendall's test, and a related multivariate test were used to analyze 403 National Stream Quality Accounting Network (NASQAN) stations for trend for the period 1978–1987. Nominal sampling frequencies were quarterly or bimonthly. For all groups and individual constituents, trends were detected for only a minority of stations at the relatively liberal 10% significance level. The groups with the greatest percentage of trends were common ions (mostly upward) and nutrients and suspended sediment (mostly upward for total nitrogen and mostly downward for total phosphorus). In the pH and alkalinity group, the trends were dominantly upward; while this might be the result of reductions in atmospheric deposition, this hypothesis is clouded by the existence of uptrends in sulfate at many of the same stations. The trace metal analyses showed that the constituents with the greatest number of trends (dominantly downward) were arsenic and cadmium; most of the stations with downtrends were in the major population areas of the east and midwest. Additional exploratory analyses of possible relationships between trends and land use and population did not give strong evidence of possible causation.

WATER QUALITY TRENDS AT INFLOWS TO EVERGLADES NATIONAL PARK1

ABSTRACT: Water quality data collected at inflows to Everglades National Park (ENP) are analyzed for trends using the seasonal Kendall test (Hirsch et al., 1982; Hirsch and Slack, 1984). The period of record is 1977–1989 for inflows to Shark River Slough and 1983–1989 for inflows to Taylor Slough and ENP's Coastal Basin. The analysis considers 20 water quality components, including nutrients, field measurements, inorganic species, and optical properties.Significant (p<0.10) increasing trends in total phosphorus concentration are indicated at eight out of nine stations examined. When the data are adjusted to account for variations in antecedent rainfall and water surface elevation, increasing trends are indicated at seven out of nine stations. Phosphorus trend magnitudes range from 4 percent/year to 21 percent/year Decreasing trends in the Total N/P ratio are detected at seven out of nine stations. N/P trend magnitudes range from ‐7 percent/year to ‐15 percent/year. Trends in water quality components other than nutrients are observed less frequently and are of less importance from a water‐quality‐management perspective. The apparent nutrient trends are not explained by variations in marsh water elevation, antecedent rainfall, flow, or season.

Short-term trends in sulfate deposition at selected bulk precipitation stations in New York

Trends in rainfall-adjusted sulfate concentration were assessed for 5-yr subrecords of the 14.5–17 yr of monthly bulk-deposition data from five stations in New York by using the seasonal Kendall test. For the 5-yr subrecord from 1978 to 1982, the trends for the bulk deposition were similar to those for weekly wet-only deposition for adjacent stations of the National Atmospheric Deposition Program (NADP). The long-term trend at each of the bulk-precipitation sites was downward and statistically significant at P < 0.02, whereas 26% of the 69 subrecords had trends that were statistically significant only at P < 0.2. Of these statistically significant subrecord trends, 10% were positive (opposite to the long-term trend). Furthermore, the slopes of the subrecord trends tended to be much steeper than those of the whole record. These 5-yr trends, consequently, are poor indicators of the trends that occur over much longer periods in the same record.

Techniques of trend analysis for monthly water quality data

Some of the characteristics that complicate the analysis of water quality time series are non‐normal distributions, seasonality, flow relatedness, missing values, values below the limit of detection, and serial correlation. Presented here are techniques that are suitable in the face of the complications listed above for the exploratory analysis of monthly water quality data for monotonie trends. The first procedure described is a nonparametric test for trend applicable to data sets with seasonality, missing values, or values reported as ‘less than’: the seasonal Kendall test. Under realistic stochastic processes (exhibiting seasonality, skewness, and serial correlation), it is robust in comparison to parametric alternatives, although neither the seasonal Kendall test nor the alternatives can be considered an exact test in the presence of serial correlation. The second procedure, the seasonal Kendall slope estimator, is an estimator of trend magnitude. It is an unbiased estimator of the slope of a linear trend and has considerably higher precision than a regression estimator where data are highly skewed but somewhat lower precision where the data are normal. The third procedure provides a means for testing for change over time in the relationship between constituent concentration and flow, thus avoiding the problem of identifying trends in water quality that are artifacts of the particular sequence of discharges observed (e.g., drought effects). In this method a flow‐adjusted concentration is defined as the residual (actual minus conditional expectation) based on a regression of concentration on some function of discharge. These flow‐adjusted concentrations, which may also be seasonal and non‐normal, can then be tested for trend by using the seasonal Kendall test.