anomalies: Anomalies

In USGS-R/smwrBase: Functions to import and manipulate hydrologic data

Anomalies

Description

Decompose a series of observations into deviations (anomalies) from the mean for selected periods and the remainder (HFV or high frequency variation) using the method described in Appendix A of Vecchia (2000).

Usage

anomalies(x, ...)

Arguments

x	a time series (ts) or a vector of observations that represents a daily series. Missing values (NAs) are allowed only at the beginning and end of the series.
...	named anomalies and the length of the selected periods, generally in days. The anomalies must be specified in order of decreasing length.

Details

The intent of computing anomalies is to give flexibility in fitting the relation between flux, or concentration, and flow for time periods longer than a couple of years. Taking a very simple regression model:

C = B0 + B1 * Q + e,

where C is the concentration, B0 and B1 are the regression coefficients, Q is the flow, and e is the error. This can be re-expressed in terms of flow anomalies (for this example, 5- and 1-year anomalies are used, many others are possible):

C = B0 + B1 * Qbar + B1 * A5 + B1 * A1 + B1 * HFV + e,

where C, B0, B1, and e are the same as the simple regression, and Qbar is the mean flow, A5 is the 5-year anomaly, A1 is the 1-year anomaly, and HFV is the high-frequency variation. The simple regression model assumes that the regression coefficient (B1) is constant for all anomalies. Computing anomalies removes that constraint and is represented by this model:

C = B0 + B1 * A5 + B2 * A1 + B3 * HFV + e,

where C, A5, A1, HFV, and e are the same as the re-expressed model, and B0, B1, B2, and B3 are regression coefficients (numerically different from the simple coefficients). Qbar is a constant and is not needed for the regression.

Anomalies are computed sequentially. First, the mean of x is computed and subtracted from the data. Then for each anomaly, the running mean of the specified period is computed (the anomaly) and is subtracted from the data. The remainder is the HFV. This procedure ensures that the sum of the anomalies plus the mean is equal to the original data.

Value

A matrix of the specified anomalies and HFV. The mean of x is included as an attribute.

Note

The output matrix contains missing values in the beginning, corresponding to the length of the longest anomaly.

A long time-frame anomaly that is often of interest, is the 5-year anomaly, which is 1,826 days.

References

Vecchia, A.V., 2000, Water-quality trend analysis and sampling design for the Souris River, Saskatchewan, North Dakota, and Manitoba: U.S. Geological Survey Water-Resources Investigations Report 00-4019, 77 p.

Examples

## Not run: 
library(smwrData)
data(Q05078770)
anomalies(log(Q05078770$FLOW), A3mo=90)

## End(Not run)

USGS-R/smwrBase documentation built on Oct. 18, 2022, 9:55 a.m.