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Great Falls of the Passaic River at Paterson, N.J

Great Falls of the Passaic River at Paterson, N.J.

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Ecological Relevant Hydrologic Indices for a Baseline Period of Record for Selected Stream Gages

 

Hydrologic Index Definitions

Source:  SRI 2007-5206:  Development of the Hydroecological Integrity Assessment Process for Determining Environmental Flows for

New Jersey Streams, Appendix 7.  Definitions of the 171 hydrologic indicies.

 

Explanation

The following information for the 171 hydrologic indices is from Olden and Poff, 2003 (see citation at end of this Help page). USGS revised a limited number of the formula and/or definitions when deemed appropriate. A USGS Scientific Investigation Report in preparation will document these changes. The Olden and Poff (2003) article contains twelve additional references from which the indices were derived. Two of these articles are referenced here because they provide examples and additional explanation for complex indices.

 
The alphanumeric code preceding each definition refers to the category of the flow regime (magnitude, frequency, duration, timing, and rate of change) the hydrologic index was developed to describe, and indices are numbered successively within each category. For example, MA1 is the first index describing magnitude of the average flow condition.

MA# - Magnitude, average flow event
ML# - Magnitude, low flow event
MH# - Magnitude, high flow event
FL# - Frequency, low flow event
FH# - Frequency, high flow event
DL# - Duration, low flow event
DH# - Duration, high flow event
TA# - Timing, average flow event
TL# - Timing, low flow event
TH# - Timing, high flow event
RA# - Rate of change, average event

Following each definition, in parentheses, are 1) the units of the index, and 2) the type of data, temporal or spatial data, from which the upper and lower percentiles limits (e.g., 75/25) are derived. Temporal data are from a multi-year daily flow record from a single stream gage. For example, index MA1 - mean for the entire flow record - uses 365 mean daily flow values for each year in the flow record to calculate the mean for the entire flow record. Consequently, there are 365 values for each year to calculate upper and lower percentile limits. However, formulas for 60 of the indices do not produce a range of values from which percentile limits can be calculated. MA5 (skewness), for example, - mean for the entire flow record divided by the median for the entire record - results in a single value, and thus, upper and lower percentile limits cannot be calculated. NJHAT uses spatial data, values for each stream gage for all the streams within a stream type, to compute limits. Upper and lower percentile limits are calculated from the 31 MA5 values from the 31 stream gages that were identified from the classification analysis as Stream Type A.

Exceedence and percentile are used in the calculation for a number of indices. Note the difference - a 90% exceedence means that 90% of the values are equal to or greater than the 90% exceedence value, while a 90th percentile means that 10% of the values are equal to or greater than the 90th percentile value.

Code Definition

MA1                Mean for the entire flow record (cubic feet per second - temporal).

MA2                Median for the entire flow record (cubic feet per second - temporal).

MA3                Mean (or median - Use Preference option) of the coefficients of variation (standard deviation/mean) for each year. Compute the coefficient of variation for each year of daily flows. Compute the mean of the annual coefficients of variation (percent - temporal).

MA4                Standard deviation of the percentiles of the logs of the entire flow record divided by the mean of percentiles of the logs. Compute the log10 of the daily flows for the entire record. Compute the 5th, 10th, 15th, 20th, 25th, 30th, 35th, 40th, 45th, 50th, 55th, 60th, 65th, 70th, 75th, 80th, 85th, 90th, and 95th percentiles for the logs of the entire flow record. Percentiles are computed by interpolating between the ordered (ascending) logs of the flow values. Compute the standard deviation and mean for the percentile values. Divide the standard deviation by the mean (percent - spatial)."

MA5                The skewness of the entire flow record is computed as the mean for the entire flow record (MA1) divided by the median (MA2) for the entire flow record (dimensionless - spatial).

MA6                Range in daily flows is the ratio of the 10% to 90% exceedence values for the entire flow record. Compute the 5% to 95% exceedence values for the entire flow record. Exceedence is computed by interpolating between the ordered (descending) flow values. Divide the 10% exceedence value by the 90% value (dimensionless - spatial).

MA7                Range in daily flows is computed like MA6 except using the 20% and 80% exceedence values. Divide the 20% exceedence value by the 80% value (dimensionless - spatial).

MA8                Range in daily flows is computed like MA6 except using the 25% and 75% exceedence values. Divide the 25% exceedence value by the 75% value (dimensionless - spatial).

MA9                Spread in daily flows is the ratio of the difference between the 90th and 10th percentile of the logs of the flow data to the log of the median of the entire flow record. Compute the log10 of the daily flows for the entire record. Compute the 5th, 10th, 15th, 20th, 25th, 30th, 35th, 40th, 45th, 50th, 55th, 60th, 65th, 70th, 75th, 80th, 85th, 90th, and 95th percentiles for the logs of the entire flow record. Percentiles are computed by interpolating between the ordered (ascending) logs of the flow values. Compute MA9 as (90th - 10th) /log10(MA2) (dimensionless - spatial)."

MA10                 Spread in daily flows is computed like MA9 except using the 20th and 80th percentiles (dimensionless - spatial).

MA11                Spread in daily flows is computed like MA9 except using the 25th and 75th percentiles (dimensionless - spatial).

MA12-MA23    Means (or medians - Use Preference option) of monthly flow values. Compute the means for each month over the entire flow record. For example, MA12 is the mean of all January flow values over the entire record (cubic feet per second - temporal)."

MA24-MA35     Variability (coefficient of variation) of monthly flow values. Compute the standard deviation for each month in each year over the entire flow record. Divide the standard deviation by the mean for each month. Average (or median - Use Preference option) these values for each month across all years (percent - temporal).

MA36              Variability across monthly flows. Compute the minimum, maximum, and mean flows for each month in the entire flow record. MA36 is the maximum monthly flow minus the minimum monthly flow divided by the median monthly flow (dimensionless - spatial)."

MA37              Variability across monthly flows. Compute the first (25th percentile) and the third (75th percentile) quartiles (every month in the flow record). MA37 is the third quartile minus the first quartile divided by the median of the monthly means (dimensionless - spatial).

MA38              Variability across monthly flows. Compute the 10th and 90th percentiles for the monthly means (every month in the flow record). MA38 is the 90th percentile minus the 10th percentile divided by the median of the monthly means (dimensionless - spatial).

MA39              Variability across monthly flows. Compute the standard deviation for the monthly means. MA39 is the standard deviation times 100 divided by the mean of the monthly means (percent - spatial).

MA40              Skewness in the monthly flows. MA40 is the mean of the monthly flow means minus the median of the monthly means divided by the median of the monthly means (dimensionless - spatial).

MA41              Annual runoff. Compute the annual mean daily flows. MA41 is the mean of the annual means divided by the drainage area (cubic feet per second/square mile - temporal).

MA42              Variability across annual flows. MA42 is the maximum annual flow minus the minimum annual flow divided by the median annual flow (dimensionless - spatial).

MA43              Variability across annual flows. Compute the first (25th percentile) and third (75th percentile) quartiles and the 10th and 90th percentiles for the annual means (every year in the flow record). MA43 is the third quartile minus the first quartile divided by the median of the annual means (dimensionless -spatial).

MA44              Variability across anual flows. Compute the first (25th percentile) and third (75th percentile) quartiles and the 10th and 90th percentiles for the annual means (every year in the flow record). MA44 is the 90th percentile minus the 10th percentile divided by the median of the annual means (dimensionless - spatial).

MA45              Skewness in the annual flows. MA45 is the mean of the annual flow means minus the median of the annual means divided by the median of the annual means (dimensionless - spatial).

ML1-ML12       Mean (or median - Use Preference option) minimum flows for each month across all years. Compute the minimums for each month over the entire flow record. For example, ML1 is the mean of the minimums of all January flow values over the entire record (cubic feet per second - temporal)."

ML13              Variability (coefficient of variation) across minimum monthly flow values. Compute the mean and standard deviation for the minimum monthly flows over the entire flow record. ML13 is the standard deviation times 100 divided by the mean minimum monthly flow for all years (percent - spatial).

ML14              Compute the minimum annual flow for each year. ML14 is the mean (or median - Use Preference option) of the ratios of minimum annual flows to the median flow for each year (dimensionless - temporal).

ML15              Low flow index. ML15 is the mean (or median - Use Preference option) of the ratios of minimum annual flows to the mean flow for each year (dimensionless - temporal).

ML16              Median of annual minimum flows. ML16 is the median of the ratios of minimum annual flows to the median flow for each year (dimensionless - temporal).

ML17              Base flow. Compute the mean annual flows. Compute the minimum of a 7-day moving average flow for each year and divide them by the mean annual flow for that year. ML17 is the mean (or median - Use Preference option) of those ratios (dimensionless - temporal).

ML18              Variability in base flow. Compute the standard deviation for the ratios of 7-day moving average flows to mean annual flows for each year. ML18 is the standard deviation times 100 divided by the mean of the ratios (percent - spatial).

ML19              Base flow. Compute the ratios of the minimum annual flow to mean annual flow for each year. ML19 is the mean (or median - Use Preference option) of these ratios times 100 (dimensionless - temporal).

ML20              Base flow. Divide the daily flow record into 5-day blocks. Find the minimum flow for each block. Assign the minimum flow as a base flow for that block if 90% of that minimum flow is less than the minimum flows for the blocks on either side. Otherwise, set it to zero. Fill in the zero values using linear interpolation. Compute the total flow for the entire record and the total base flow for the entire record. ML20 is the ratio of total flow to total base flow (dimensionless - spatial)."

ML21                 Variability across annual minimum flows. Compute the mean and standard deviation for the annual minimum flows. ML21 is the standard deviation times 100 divided by the mean (percent - spatial).

ML22                 Specific mean annual minimum flow. ML22 is the mean (or median - Use Preference option) of the annual minimum flows divided by the drainage area (cubic feet per second/square mile - temporal).

MH1-MH12      Mean (or median - Use Preference option) maximum flows for each month across all years. Compute the maximums for each month over the entire flow record. For example, MH1 is the mean of the maximums of all January flow values over the entire record (cubic feet per second - temporal)."

MH13              Variability (coefficient of variation) across maximum monthly flow values. Compute the mean and standard deviation for the maximum monthly flows over the entire flow record. MH13 is the standard deviation times 100 divided by the mean maximum monthly flow for all years (percent - spatial).

MH14              Median of annual maximum flows. Compute the annual maximum flows from monthly maximum flows. Compute the ratio of annual maximum flow to median annual flow for each year. MH14 is the median of these ratios (dimensionless - temporal).

MH15              High flow discharge index. Compute the 1% exceedence value for the entire data record. MH15 is the 1% exceedence value divided by the median flow for the entire record (dimensionless - spatial).

MH16                High flow discharge index. Compute the 10% exceedence value for the entire data record. MH16 is the 10% exceedence value divided by the median flow for the entire record (dimensionless - spatial).

MH17              High flow discharge index. Compute the 25% exceedence value for the entire data record. MH17 is the 25% exceedence value divided by the median flow for the entire record (dimensionless - spatial).

MH18              Variability across annual maximum flows. Compute the logs (log10) of the maximum annual flows. Find the standard deviation and mean for these values. MH18 is the standard deviation times 100 divided by the mean (percent - spatial).

MH19              MH19 = [N2 x sum(qm3)-3N x sum(qm) x sum(qm2) + 2 x (sum(qm))3]/[N x (N-1) x (N-2) x stddev3]

              where: N = Number of years
qm = Log10(annual maximum flows)
stddev = Standard deviation of the annual maximum flows
(dimensionless - spatial).

MH20              Specific mean annual maximum flow. MH20 is the mean (or median - Use Preference option) of the annual maximum flows divided by the drainage area (cubic feet per second/square mile - temporal).

MH21              High flow volume index. Compute the average volume for flow events above a threshold equal to the median flow for the entire record. MH21 is the average volume divided by the median flow for the entire record (days - temporal).

MH22              High flow volume. Compute the average volume for flow events above a threshold equal to three times the median flow for the entire record. MH22 is the average volume divided by the median flow for the entire record (days - temporal).

MH23              High flow volume. Compute the average volume for flow events above a threshold equal to seven times the median flow for the entire record. MH23 is the average volume divided by the median flow for the entire record (days - temporal).

MH24              High peak flow. Compute the average peak flow value for flow events above a threshold equal to the median flow for the entire record. MH24 is the average peak flow divided by the median flow for the entire record (dimensionless - temporal).

MH25              High peak flow. Compute the average peak flow value for flow events above a threshold equal to three times the median flow for the entire record. MH25 is the average peak flow divided by the median flow for the entire record (dimensionless - temporal).

MH26              High peak flow. Compute the average peak flow value for flow events above a threshold equal to seven times the median flow for the entire record. MH26 is the average peak flow divided by the median flow for the entire record (dimensionless - temporal).

MH27              High peak flow. Compute the average peak flow value for flow events above a threshold equal to 75th percentile value for the entire flow record. MH27 is the average peak flow divided by the median flow for the entire record (dimensionless - temporal).

FL1 L              ow flood pulse count. Compute the average number of flow events with flows below a threshold equal to the 25th percentile value for the entire flow record. FL1 is the average (or median - Use Preference option) number of events (number of events/year - temporal).

FL2                 Variability in low pulse count. Compute the standard deviation in the annual pulse counts for FL1. FL2 is 100 times the standard deviation divided by the mean pulse count (percent - spatial).

FL3                 Frequency of low pulse spells. Compute the average number of flow events with flows below a threshold equal to 5% of the mean flow value for the entire flow record. FL3 is the average (or median - Use Preference option) number of events (number of events/year - temporal).

FH1                High flood pulse count. Compute the average number of flow events with flows above a threshold equal to the 75th percentile value for the entire flow record. FH1 is the average (or median - Use Preference option) number of events (number of events/year - temporal).

FH2                Variability in high pulse count. Compute the standard deviation in the annual pulse counts for FH1. FH2 is 100 times the standard deviation divided by the mean pulse count (number of events/year - spatial).

FH3                High flood pulse count. Compute the average number of days per year that the flow is above a threshold equal to three times the median flow for the entire record. FH3 is the mean (or median - Use Preference option) of the annual number of days for all years (number of days/year - temporal).

FH4                median flow for the entire record. FH4 is the mean (or median - Use Preference option) of the annual number of days for all years (number of days/year - temporal).

FH5                Flood frequency. Compute the average number of flow events with flows above a threshold equal to the median flow value for the entire flow record. FH5 is the average (or median - Use Preference option) number of events (number of events/year - temporal).

FH6                F lood frequency. Compute the average number of flow events with flows above a threshold equal to three times the median flow value for the entire flow record. FH6 is the average (or median - Use Preference option) number of events (number of events/year - temporal).

FH7                Flood frequency. Compute the average number of flow events with flows above a threshold equal to seven times the median flow value for the entire flow record. FH6 is the average (or median - Use Preference option) number of events (number of events/year - temporal).

FH8                Flood frequency. Compute the average number of flow events with flows above a threshold equal to 25% exceedence value for the entire flow record. FH8 is the average (or median - Use Preference option) number of events (number of events/year - temporal).

FH9                Flood frequency. Compute the average number of flow events with flows above a threshold equal to 75% exceedence value for the entire flow record. FH9 is the average (or median - Use Preference option) number of events (number of events/year - temporal).

FH10               Flood frequency. Compute the average number of flow events with flows above a threshold equal to median of the annual minima for the entire flow record. FH10 is the average (or median - Use Preference option) number of events (number of events/year - temporal).        

FH11               Flood frequency. Compute the average number of flow events with flows above a threshold equal to flow corresponding to a 1.67 year recurrence interval. FH11 is the average (or median - Use Preference option) number of events (number of events/year - temporal).

                      Note - 1.67 year flood threshold (Poff, 1996) - For indices FH11, DH22, DH23, DH24, TA3, and TH3 compute the log10 of the peak annual flows. Compute the log10 of the daily flows for the peak annual flow days. Calculate the coefficients for a linear regression equation for logs of peak annual flow versus logs of average daily flow for peak days. Using the log peak flow for the 1.67 year recurrence interval (60th percentile) as input to the regression equation, predict the log10 of the average daily flow. The threshold is 10 to the log10 (average daily flow) power (cubic feet/second).

DL1                Annual minimum daily flow. Compute the minimum 1-day average flow for each year. DL1 is the mean (or median - Use Preference option) of these values (cubic feet per second - temporal).

DL2                Annual minimum of 3-day moving average flow. Compute the minimum of a 3-day moving average flow for each year. DL2 is the mean (or median - Use Preference option) of these values (cubic feet per second - temporal).

DL3                Annual minimum of 7-day moving average flow. Compute the minimum of a 7-day moving average flow for each year. DL3 is the mean (or median - Use Preference option) of these values (cubic feet per second - temporal).

DL4                Annual minimum of 30-day moving average flow. Compute the minimum of a 30-day moving average flow for each year. DL4 is the mean (or median - Use Preference option) of these values (cubic feet per second - temporal).

DL5                Annual minimum of 90-day moving average flow. Compute the minimum of a 90-day moving average flow for each year. DL5 is the mean (or median - Use Preference option) of these values (cubic feet per second - temporal).

DL6                Variability of annual minimum daily average flow. Compute the standard deviation for the minimum daily average flow. DL6 is 100 times the standard deviation divided by the mean (percent - spatial).

DL7                Variability of annual minimum of 3-day moving average flow. Compute the standard deviation for the minimum 3-day moving averages. DL7 is 100 times the standard deviation divided by the mean (percent - spatial).

DL8                Variability of annual minimum of 7-day moving average flow. Compute the standard deviation for the minimum 7-day moving averages. DL8 is 100 times the standard deviation divided by the mean (percent - spatial).

DL9                Variability of annual minimum of 30-day moving average flow. Compute the standard deviation for the minimum 30-day moving averages. DL9 is 100 times the standard deviation divided by the mean (percent - spatial).

DL10               Variability of annual minimum of 90-day moving average flow. Compute the standard deviation for the minimum 90-day moving averages. DL10 is 100 times the standard deviation divided by the mean (percent - spatial).

DL11               Annual minimum daily flow divided by the median for the entire record. Compute the minimum daily flow for each year. DL11 is the mean of these values divided by the median for the entire record (dimensionless - temporal).

DL12               Annual minimum of 7-day moving average flow divided by the median for the entire record. Compute the minimum of a 7-day moving average flow for each year. DL12 is the mean of these values divided by the median for the entire record. (dimensionless - temporal).

DL13               Annual minimum of 30-day moving average flow divided by the median for the entire record. Compute the minimum of a 30-day moving average flow for each year. DL13 is the mean of these values divided by the median for the entire record. (dimensionless - temporal).

DL14               Low exceedence flows. Compute the 75% exceedence value for the entire flow record. DL14 is the exceedence value divided by the median for the entire record. (dimensionless - spatial).

DL15               Low exceedence flows. Compute the 90% exceedence value for the entire flow record. DL15 is the exceedence value divided by the median for the entire record (dimensionless - spatial).

DL16               Low flow pulse duration. Compute the average pulse duration for each year for flow events below a threshold equal to the 25th percentile value for the entire flow record. DL16 is the median of the yearly average durations (number of days - temporal).

DL17               Variability in low pulse duration. Compute the standard deviation for the yearly average low pulse durations. DL17 is 100 times the standard deviation divided by the mean of the yearly average low pulse durations (percent - spatial).

DL18               Number of zero-flow days. Count the number of zero-flow days for the entire flow record. DL18 is the mean (or median - Use Preference option) annual number of zero flow days (number of days/year - temporal).

DL19               Variability in the number of zero-flow days. Compute the standard deviation for the annual number of zero-flow days. DL19 is 100 times the standard deviation divided by the mean annual number of zero-flow days (percent - spatial).

DL20               Number of zero-flow months. While computing the mean monthly flow values, count the number of months in which there was no flow over the entire flow record (percent - spatial)."

DH1                Annual maximum daily flow. Compute the maximum of a 1-day moving average flow for each year. DH1 is the mean (or median - Use Preference option) of these values (cubic feet per second - temporal).

DH2                Annual maximum of 3-day moving average flows. Compute the maximum of a 3-day moving average flow for each year. DH2 is the mean (or median - Use Preference option) of these values (cubic feet per second - temporal).

DH3                Annual maximum of 7-day moving average flows. Compute the maximum of a 7-day moving average flow for each year. DH3 is the mean (or median - Use Preference option) of these values (cubic feet per second - temporal).

DH4                Annual maximum of 30-day moving average flows. Compute the maximum of a 30-day moving average flow for each year. DH4 is the mean (or median - Use Preference option) of these values (cubic feet per second - temporal).

DH5                Annual maximum of 90-day moving average flows. Compute the maximum of a 90-day moving average flow for each year. DH5 is the mean (or median - Use Preference option) of these values (cubic feet per second - temporal).

DH6                Variability of annual maximum daily flows. Compute the standard deviation for the maximum 1-day moving averages. DH6 is 100 times the standard deviation divided by the mean (percent - spatial).

DH7                Variability of annual maximum of 3-day moving average flows. Compute the standard deviation for the maximum 3-day moving averages. DH7 is 100 times the standard deviation divided by the mean (percent - spatial).

DH8                Variability of annual maximum of 7-day moving average flows. Compute the standard deviation for the maximum 7-day moving averages. DH8 is 100 times the standard deviation divided by the mean (percent - spatial).

DH9                Variability of annual maximum of 30-day moving average flows. Compute the standard deviation for the maximum 30-day moving averages. DH9 is 100 times the standard deviation divided by the mean (percent - spatial).

DH10              Variability of annual maximum of 90-day moving average flows. Compute the standard deviation for the maximum 90-day moving averages. DH10 is 100 times the standard deviation divided by the mean (percent - spatial).

DH11              Annual maximum of 1-day moving average flows divided by the median for the entire record. Compute the maximum of a 1-day moving average flow for each year. DH11 is the mean of these values divided by the median for the entire record (dimensionless - temporal).

DH12              Annual maximum of 7-day moving average flows divided by the median for the entire record. Compute the maximum daily average flow for each year. DH12 is the mean of these values divided by the median for the entire record (dimensionless - temporal).

DH13              Annual maximum of 30-day moving average flows divided by the median for the entire record. Compute the maximum of a 30-day moving average flow for each year. DH13 is the mean of these values divided by the median for the entire record. (dimensionless - temporal).

DH14              Flood duration. Compute the mean of the mean monthly flow values. Find the 95th percentile for the mean monthly flows. DH14 is the 95th percentile value divided by the mean of the monthly means (dimensionless - spatial).

DH15              High flow pulse duration. Compute the average duration for flow events with flows above a threshold equal to the 75th percentile value for each year in the flow record. DH15 is the median of the yearly average durations (days/year - temporal).

DH16              Variability in high flow pulse duration. Compute the standard deviation for the yearly average high pulse durations. DH16 is 100 times the standard deviation divided by the mean of the yearly average high pulse durations (percent - spatial).

DH17              High flow duration. Compute the average duration of flow events with flows above a threshold equal to the median flow value for the entire flow record. DH17 is the average (or median - Use Preference option) duration of the events (days - temporal).

DH18              High flow duration. Compute the average duration of flow events with flows above a threshold equal to three times the median flow value for the entire flow record. DH18 is the average (or median - Use Preference option) duration of the events (days - temporal).

DH19              High flow duration. Compute the average duration of flow events with flows above a threshold equal to seven times the median flow value for the entire flow record. DH19 is the average (or median - Use Preference option) duration of the events (days - temporal).

DH20              High flow duration. Compute the 75th percentile value for the entire flow record. Compute the average duration of flow events with flows above a threshold equal to the 75th percentile value for the median annual flows. DH20 is the average (or median - Use Preference option) duration of the events (days - temporal).

DH21              High flow duration. Compute the 25th percentile value for the entire flow record. Compute the average duration of flow events with flows above a threshold equal to the 25th percentile value for the entire set of flows. DH21 is the average (or median - Use Preference option) duration of the events (days - temporal).

DH22              Flood interval. Compute the flood threshold as the flow equivalent for a flood recurrence of 1.67 years. Determine the median number of days between flood events for each year. DH22 is the mean (or median - Use Preference option) of the yearly median number of days between flood events (days - temporal).

                      Note - 1.67 year flood threshold (Poff, 1996) - For indices FH11, DH22, DH23, DH24, TA3, and TH3 compute the log10 of the peak annual flows. Compute the log10 of the daily flows for the peak annual flow days. Calculate the coefficients for a linear regression equation for logs of peak annual flow versus logs of average daily flow for peak days. Using the log peak flow for the 1.67 year recurrence interval (60th percentile) as input to the regression equation, predict the log10 of the average daily flow. The threshold is 10 to the log10 (average daily flow) power (cubic feet/second).

DH23              Flood duration. Compute the flood threshold as the flow equivalent for a flood recurrence of 1.67 years. Determine the number of days each year that the flow remains above the flood threshold. DH23 is the mean (or median - Use Preference option) of the number of flood days for years in which floods occur (days - temporal).

                      Note - 1.67 year flood threshold (Poff, 1996) - For indices FH11, DH22, DH23, DH24, TA3, and TH3 compute the log10 of the peak annual flows. Compute the log10 of the daily flows for the peak annual flow days. Calculate the coefficients for a linear regression equation for logs of peak annual flow versus logs of average daily flow for peak days. Using the log peak flow for the 1.67 year recurrence interval (60th percentile) as input to the regression equation, predict the log10 of the average daily flow. The threshold is 10 to the log10 (average daily flow) power (cubic feet/second).

DH24              Flood free days. Compute the flood threshold as the flow equivalent for a flood recurrence of 1.67 years. Compute the maximum number of days that the flow is below the threshold for each year. DH24 is the mean (or median - Use Preference option) of the maximum yearly no flood days (days - temporal).        

                      Note - 1.67 year flood threshold (Poff, 1996) - For indices FH11, DH22, DH23, DH24, TA3, and TH3 compute the log10 of the peak annual flows. Compute the log10 of the daily flows for the peak annual flow days. Calculate the coefficients for a linear regression equation for logs of peak annual flow versus logs of average daily flow for peak days. Using the log peak flow for the 1.67 year recurrence interval (60th percentile) as input to the regression equation, predict the log10 of the average daily flow. The threshold is 10 to the log10 (average daily flow) power (cubic feet/second).

TA1                Constancy. Constancy is computed via the formulation of Colwell (see example in Colwell, 1974). A matrix of values is compiled where the rows are 11 flow categories and the columns are 365 (no Feb 29th) days of the year. The cell values are the number of times that a flow falls into a category on each day. The categories are:

              log(flow) < .1 x log(mean flow),
log(flow) < .1 x log(mean flow), .1 x log(mean flow) <= log(flow) < .25 x log(mean flow)
.1 x log(mean flow) <= log(flow) < .25 x log(mean flow).25 x log(mean flow) <= log(flow) < .5 x log(mean flow)
.25 x log(mean flow) <= log(flow) < .5 x log(mean flow).5 x log(mean flow) <= log(flow) < .75 x log(mean flow)
.5 x log(mean flow) <= log(flow) < .75 x log(mean flow).75 x log(mean flow) <= log(flow) < 1.0 x log(mean flow)
.75 x log(mean flow) <= log(flow) < 1.0 x log(mean flow)1.0 x log(mean flow) <= log(flow) < 1.25 x log(mean flow)
1.0 x log(mean flow) <= log(flow) < 1.25 x log(mean flow)1.25 x log(mean flow) <= log(flow) < 1.5 x log(mean flow)
1.25 x log(mean flow) <= log(flow) < 1.5 x log(mean flow)1.5 x log(mean flow) <= log(flow) < 1.75 x log(mean flow)
1.5 x log(mean flow) <= log(flow) < 1.75 x log(mean flow)1.75 x log(mean flow) <= log(flow) < 2.0 x log(mean flow)
1.75 x log(mean flow) <= log(flow) < 2.0 x log(mean flow)2.0 x log(mean flow) <= log(flow) < 2.25 x log(mean flow)
2.0 x log(mean flow) <= log(flow) < 2.25 x log(mean flow)log(flow) >= 2.25 x log(mean flow)
log(flow) >= 2.25 x log(mean flow)log(flow) >= 2.25 x log(mean flow)

The row totals, column totals, and grand total are computed. Using the equations for Shannon information theory parameters, constancy is computed as:

              1 - (uncertainty with respect to state)/log(number of states)

              (dimensionless - spatial).

TA2                   Predictability. Predictability is computed from the same matrix as constancy (see example in Colwell, 1974). It is computed as:

              1 - (uncertainty with respect to interaction of time and state - uncertainty with respect to time)/ log (number of states)

              (dimensionless - spatial).

TA3                Seasonal predictability of flooding. Divide years up into 2-month periods(i.e. Oct-Nov, Dec-Jan, etc.). Count the number of flood days (flow events with flows > 1.67 year flood) in each period over the entire flow record. TA3 is the maximum number of flood days in any one period divided by the total number of flood days (dimensionless - spatial)."

TL1                 Julian date of annual minimum. Determine the Julian date that the minimum flow occurs for each water year. Transform the dates to relative values on a circular scale (radians or degrees). Compute the x and y components for each year and average them across all years. Compute the mean angle as the arc tangent of y-mean divided by x-mean. Transform the resultant angle back to Julian date (Julian day - spatial).

TL2                 Variability in Julian date of annual minima. Compute the coefficient of variation for the mean x and y components and convert to a date (Julian day - spatial).

TL3                 Seasonal predictability of low flow. Divide years up into 2-month periods (i.e. Oct-Nov, Dec-Jan, etc.). Count the number of low events (flow events with flows <= 5 year flood threshold) in each period over the entire flow record. TL3 is the maximum number of low flow events in any one period divided by the total number of low flow events (dimensionless - spatial).

                      Note - 5 year flood threshold (Poff, 1996) - For TL3 and TH3 compute the log10 of the peak annual flows. Compute the log10 of the daily flows for the peak annual flow days. Calculate the coefficients for a linear regression equation for logs of peak annual flow versus logs of average daily flow for peak days. Using the log peak flow for the 5 year recurrence interval (20th percentile) as input to the regression equation, predict the log10 of the average daily flow. The threshold is 10 to the log10 (average daily flow) power (cubic feet per second).

TL4                 Seasonal predictability of non-low flow. Compute the number of days that flow is above the 5-year flood threshold as the ratio of number of days to 365 or 366 (leap year) for each year. TL4 is the maximum of the yearly ratios (dimensionless - spatial).

                      Note - 5 year flood threshold (Poff, 1996) - For TL3 and TH3 compute the log10 of the peak annual flows. Compute the log10 of the daily flows for the peak annual flow days. Calculate the coefficients for a linear regression equation for logs of peak annual flow versus logs of average daily flow for peak days. Using the log peak flow for the 5 year recurrence interval (20th percentile) as input to the regression equation, predict the log10 of the average daily flow. The threshold is 10 to the log10 (average daily flow) power (cubic feet per second).

TH1                Julian date of annual maximum. Determine the Julian date that the maximum flow occurs for each year. Transform the dates to relative values on a circular scale (radians or degrees). Compute the x and y components for each year and average them across all years. Compute the mean angle as the arc tangent of y-mean divided by x-mean. Transform the resultant angle back to Julian date (Julian day - spatial).

TH2                Variability in Julian date of annual maxima. Compute the coefficient of variation for the mean x and y components and convert to a date (Julian days - spatial).

TH3                Seasonal predictability of non-flooding. Computed as the maximum proportion of a 365-day year that the flow is less than the 1.67 year flood threshold and also occurs in all years. Accumulate non-flood days that span all years. TH3 is maximum length of those flood free periods divided by 365 (dimensionless - spatial).

                      Note - 1.67 year flood threshold (Poff, 1996) - For indices FH11, DH22, DH23, DH24, TA3, and TH3 compute the log10 of the peak annual flows. Compute the log10 of the daily flows for the peak annual flow days. Calculate the coefficients for a linear regression equation for logs of peak annual flow versus logs of average daily flow for peak days. Using the log peak flow for the 1.67 year recurrence interval (60th percentile) as input to the regression equation, predict the log10 of the average daily flow. The threshold is 10 to the log10 (average daily flow) power (cubic feet/second).

RA1                Rise rate. Compute the change in flow for days in which the change is positive for the entire flow record. RA1 is the mean (or median - Use Preference option) of these values (cubic feet per second/day - temporal).

RA2                Variability in rise rate. Compute the standard deviation for the positive flow changes. RA2 is 100 times the standard deviation divided by the mean (percent - spatial).

RA3                Fall rate. Compute the change in flow for days in which the change is negative for the entire flow record. RA3 is the mean (or median - Use Preference option) of these values (cubic feet per second/day - temporal).

RA4                Variability in fall rate. Compute the standard deviation for the negative flow changes. RA4 is 100 times the standard deviation divided by the mean (percent - spatial).

RA5                Number of day rises. Compute the number of days in which the flow is greater than the previous day. RA5 is the number of positive gain days divided by the total number of days in the flow record (dimensionless - spatial).

RA6                Change of flow. Compute the log10 of the flows for the entire flow record. Compute the change in log of flow for days in which the change is positive for the entire flow record. RA6 is the median of these values (cubic feet per second - temporal).

RA7                Change of flow. Compute the log10 of the flows for the entire flow record. Compute the change in log of flow for days in which the change is negative for the entire flow record. RA7 is the median of these log values (cubic feet per second/day - temporal).

RA8                Number of reversals. Compute the number of days in each year when the change in flow from one day to the next changes direction. RA8 is the average (or median - Use Preference option) of the early values (days - temporal).

RA9                Variability in reversals. Compute the standard deviation for the yearly reversal values.RA9 is 100 times the standard deviation divided by the mean (percent - spatial).

 
References

Colwell R.K. 1974. Predictability, constancy, and contingency of periodic phenomena. Ecology 55: 1148-1153.

Olden, J.D. and N.L. Poff. 2003. Redundancy and the choice of hydrologic indices for characterizing streamflow regimes. River Research and Applications 19:101-121.

Poff NL. 1996. A hydrogeography of unregulated streams in the United States and an examination of scale-dependence in some hydrological descriptors. Freshwater Biology 36: 71-91.

 

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