a final report on the further assessment of the …...2018/08/26 · statistical probabilities and...

NHDES-R-WD-18-13

A Final Report on the Further Assessment of the

QPPQ Transform Method for Estimating Daily Streamflow

at Ungaged Sites in New Hampshire

Prepared by

49 School Street

South Dartmouth, MA 02748

(508) 996-4505

For

New Hampshire Department of Environmental Services

PO Box 95, Concord, NH 03302-0095

www.des.nh.gov | (603) 271-3503

Robert R. Scott, Commissioner

Clark Freise, Assistant Commissioner

August 24, 2018

http://www.des.nh.gov/

1

HYSR / 49 School Street / South Dartmouth, MA 02748 USA

Table of Contents

Page

Table of Contents

Executive Summary 1

1. Introduction and Overview 3

2. QPPQ Method for Estimating Daily Flows at Ungaged Sites 4

3. HYSR Phase 1 Study Review 6

4. Generating QPPQ Transform Flows 10

5. QPPQ Transform Negative Run-length Analysis 17

6. QPPQ Transform Negative Run-length Analysis Test Results

6.1 Introduction

6.2 Seasonal Streamflow Duration Curve Evaluation

6.3 Negative Run-length Event Duration Frequency Histogram

Evaluation

6.4 Negative Run-length Probability Plot Duration Curve Evaluation

6.5 95% Confidence Interval of the Mean Negative Run-length

Duration Evaluation

6.6 Seasonal and POR Daily Time Series Coefficient of Variation

Evaluation

6.7 Final Evaluation of QPPQ Transform NN Index Daily Data versus

NN WA Index Daily Data

22

22

22

25

27

29

31

37

7. Summary and Conclusions 39

8. References 43

Appendix I. Seasonal Stream Flow Duration Curves: Test Sites 1-5;

Rearing & Growth Bioperiod

44

Appendix II. Number of Negative Run-length Events by Season: Test Site

1; All Bioperiods

50

Appendix III. Number of Negative Run-length Events by Season: Test

Sites 2-5; Rearing & Growth Bioperiod

57#


Table of Contents (cont’d)

Page

Appendix IVa. Qcritical and Qrare Negative Run-length Histograms: Test

Site 1, All Bioperiods.

66

Appendix IVb. Q85 and Q95 Negative Run-length Histograms: Test Site 1,

All Bioperiods

73

Appendix V. Q85 and Q95 Negative Run-length Histograms: Test Sites 2-5;


80

Appendix VIa. Qcritical and Qrare Negative Run-length Duration Curves:

Test Site 1; All Bioperiods

89

Appendix VIb. Q85 and Q95 Negative Run-length Duration Curves: Test

Site 1; All Bioperiods

96

Appendix VII. Q85 and Q95 Negative Run-length Duration Curves: Test

Sites 2-5; Rearing & Growth Bioperiod

103

Appendix VIII. 95% Confidence Intervals Mean Negative Run-length

Event Duration: Test Site 1; All Bioperiods

112

Appendix IX. 95% Confidence Intervals Mean Negative Run-length

Event Duration: Test Sites 2-5; Rearing & Growth

Bioperiod

119

1


Executive Summary

As part of its responsibilities under the New Hampshire River Management and Protection

Act, RSA 483, the New Hampshire Department of Environmental Services (NHDES) is tasked

with developing rules to determine protected instream flows on certain designated rivers and

river reaches. Because many of those waters lack streamgage data, NHDES needs a reliable

method of estimating daily streamflow at ungaged sites. HYSR’s QPPQ Transform is one such

method. It uses known flows from a USGS stream gage located elsewhere, together with

statistical probabilities and local soil, climate, and topographic data from the ungagged site’s

watershed to generate long periods of estimated daily flows at the ungagged site. NHDES asked

HYSR to conduct a two-phase proof-of-concept study to demonstrate the QPPQ method’s ability

to provide accurate daily streamflow data.

To evaluate the suitability of the QPPQ Transform method for New Hampshire’s needs,

HYSR completed the first-phase study (Fennessey, 2018). This involved evaluating new data

sources required by the method, updating the regional flow duration curve model that is a part of

the method, and then evaluating estimated daily streamflow time series against historic daily

flows at several sites in New Hampshire. For the present second-phase study NHDES and

HYSR developed the following tasks for the project:

Task 1. Graphically compare, using the QPPQ Transform Phase 1 study estimated daily

flows developed at the Souhegan River test site, the number and duration of sub-Critical flow

events and sub-Rare flow events for each of six bioperiods and compare those with the same

events observed at the Souhegan USGS streamgage;

Task 2. Graphically compare, using the QPPQ Transform estimated daily flows developed at

four other test sites under Phase 1, the number and duration of sub-Q85 events and sub-Q95 for

Bioperiod 5 Rearing & Growth and compare those with the same events observed at the four

USGS streamgages at these sites; and

Task 3. Graphically compare the QPPQ Transform estimated daily flows Bioperiod 5 Rearing

& Growth flow duration curves, with the same bioperiod’s curves observed at the five USGS

streamgages.

2


Following an assessment of preliminary results and consultation with NHDES, HYSR

undertook an additional task. This work focused on determining which would be the better

choice between two alternative types of historic record Index streamgage sites for driving the

QPPQ Transform method.

The QPPQ Transform Method is a way to generate accurate, daily stream flow records at

ungaged river locations. During the HYSR Phase 2 study, following extensive analysis, more

than 170 graphs were prepared that illustrate the closeness of fit between daily flow records

generated by the QPPQ Transform Method and records observed at USGS gages. The Phase 2

study also determined the best method for selecting the QPPQ Transform Index gage is to select

from the population of nearest neighbor HCDN Index gages, which confirms the findings of

Fennessey (1994) and Farmer et al. (2014). With both phases of the HYSR study complete,

NHDES will be able to make an informed decision about adopting the QPPQ Transform method

as the preferred way to estimate a long period time series of daily flows at ungaged sites in New

Hampshire.

3


1. Introduction and Overview

RSA 483, The New Hampshire Rivers Management and Protection Act, requires that instream

flow rules (IFR) be developed for rivers and river reaches designated by the state legislature.

These rules will describe how protected instream flows will be determined and implemented on

the designated rivers. NHDES is responsible for developing and applying the IFR. In the not-

too-distant future, NHDES will need long periods of estimated daily streamflow at one or more

sites on each designated river or river reach to quantify protected instream flows. Unfortunately,

many of the designated rivers and reaches lack daily streamflow gage records. Accordingly,

NHDES asked HYSR to propose a study to demonstrate HYSR’s QPPQ Transform method for

generating long records of daily streamflow at ungaged sites, a method that has been adopted by

the USGS and applied in a number of other states and studies (see Fennessey 2018)

HYSR proposed to demonstrate its QPPQ method by applying it to several New Hampshire

rivers of varying watershed areas with USGS stream gage sites. In a previous phase of this

work, a key aspect of the QPPQ Transform method was updated, namely a mathematical

regional streamflow duration model. The second phase included a special time-series analysis

designed to compare daily QPPQ Transform flows with USGS gaged flows at the same location

during summer and early fall, a period referred to as the Rearing & Growth bioperiod by fishery

biologists. This analysis will permit NHDES to better assess the effectiveness of applying

calculated streamflows to develop protected instream flows (PISF) on ungaged designated rivers

and reaches.

4


2. QPPQ Method for Estimating Daily Flows at Ungaged Sites

HYSR’s QPPQ Transform method for estimating daily streamflows at ungaged sites was

updated in 2018 under a contract with NHDES. The method uniquely extrapolates daily flows

from the gaged site to the ungaged site with greater accuracy than alternative methods, as

documented by Farmer et al. (2014). The QPPQ Transform process is summarized by the

following four steps and illustrated by Figure 2-1:

1. The upper left quadrant: Q. The analyst picks a suitable USGS index stream gage

site with a long period-of-record (POR) of observed daily flows, QI(t).

2. The upper right quadrant: P. The analyst estimates the probability of occurrence for

each observed daily flow and uses QI(t) to construct an “observed” period-of-record

(POR) Flow Duration Curve (FDC), QI(p).

3. The lower right quadrant: P. Using soil, climate, and topographic characteristics of

the ungaged watershed, the analyst uses a regional FDC model to construct a

“model” FDC, QO(p), at the ungaged site.

4. The lower left quadrant: Q. Knowing the probability of each daily flow during the

long sequence at the gaged site, and assuming those flows occur with equal

probability at the ungaged site, the analyst generates an equally long sequence of

daily flows at the ungaged site, QO(t).

5


Figure 2-1. The QPPQ Transform Method

6


3. HYSR Phase 1 Study Review

The result of the HYSR Phase 1 study (see Fennessey, 2018) was an update of the Fennessey

(1994) Generalized Pareto (GPA) regional flow duration model and a quantitative assessment of

its goodness-of-fit compared with observed streamflow data at eleven USGS streamgage

watershed sites in New Hampshire. The GPA regional flow duration curve model is based on

the Generalized Pareto probability distribution function as discussed by Fennessey (1994, 2018)

and others.

A streamflow duration curve (FDC) is constructed from the streamflow time series or

hydrograph. The FDC describes the probability that flows of some magnitude are equaled or

exceeded during the daily flows for the period-of-record analyzed. Very high flows have a small

probability of being exceeded (near 0%) and very low flows have a high probability of being

exceeded (near 100%) over a long period-of-record (POR). Figure 3-1 illustrates this

relationship. The observed daily flow data are shown as the solid black line that rises and falls

with the seasons, and the POR FDC is the solid green line. Q10 is a high flow, Q50 is the median

day flow, and Q90 is a low flow.

P[Q>q] x 100

0 10 20 30 40 50 60 70 80 90 100

QP

(cfs

)

10

100

1000

10000

10

100

1000

10000

Year

1950 1955 1960 1965 1970 1975

Observed FDC

Q10

Q50

Q90

Observed Daily Q

Fig. 3-1. Comparison between a River Hydrograph and its Flow Duration Curve

7


Through extensive analysis, Fennessey (1994) determined that the three-parameter GPA

probability function fits streamflow FDCs at sites in the northeast very well. The three-

parameter GPA quantile function is shown below as Eq. 3-1

p1κ

αξ Q k

p (3-1)

where ξ (lower bound), α (scale), and κ (shape) are the three probability function parameters and

p is the exceedance probability.

Fennessey (2018) revised a special USGS streamgage network that he originally constructed

(see Fennessey, 1994) which now consists of 133 gaged watersheds in the northeast U.S. that

were a part of the Hydro-Climatic Data Network described by Slack and Landwehr (1992). The

gaged watersheds in the updated Fennessey (2018) network range from 1.39 mi2 to 3,342 mi

2.

Figure 3-2. HYSR Stream Gage Network

The regional model update involved developing three multivariate regression equations, one

for each GPA parameter. The regional model’s regression equations use a mix of ten

independent soil, climate and topographic variables provided in the HCDN (Slack and

8


Landwehr, 1992) and the GAGES-II (2017) network (Falcone et al. 2010a, 2016) and estimated

for each of the 133 gages in the updated HYSR (Fennessey, 2018) gage network.

One test of goodness-of-fit between the daily POR observed FDC and the fitted FDC and the

regional model is to visually compare how well the fitted and the regional FDC model curves

match with the observed POR FDC. This is shown below in Figure 3-3 for the Souhegan River

at Merrimack, NH. The “Fitted FDC” is constructed using the GPA model with its three

parameters determined using observed data. The “Model FDC” is constructed using the

Fennessey (2018) regional FDC model with the three parameters determined using the regression

equations that apply the ten watershed variables of climate, soil, and topography but no observed

daily streamflow data.

P[Q>q] x 100

0 10 20 30 40 50 60 70 80 90 100

QP

(cfs

)

1

10

100

1000

10000

1

10

100

1000

10000

Fitted FDC

Model FDC

Observed FDC

Fig. 3-3. Period-of-Record Flow Duration Curve for the Souhegan River, Merrimack, NH

A quantitative goodness-of-fit measure FDC called the bias is shown below as Figure 3-4. The

bias describes the average error between the two FDC pairs for the HYSR Phase 1 study that

focused on eleven New Hampshire USGS streamgage sites.

9


P[Q>q] x 100

1 2 5 10 20 30 50 70 80 90 95 98 99

BIA

SP (

%)

-100

-50

0

50

100

-100

-50

0

50

100

Fitted FDC

Model FDC

Figure 3-4. Fitted and Regional FDC Model Bias for New Hampshire Stream Gage Sites

10


4. Generating QPPQ Transform Flows

During the Phase 1 study for NHDES, HYSR used the QPPQ Transform to generate a long

period of record of estimated daily flows for eleven rivers at the site of each river’s USGS stream

gage. For the Phase 2 study, five of those sites were chosen for a second evaluation test called a

negative run-length analysis. These sites, their watershed areas, and PORs are listed in Table 4-

1.

Table 4-1

QPPQ Transform Test Sites

GAGE_ID NAME SQ.MI POR

01094000 SOUHEGAN RIVER AT MERRIMACK, NH 170.2 1950-1976

01052500 DIAMOND RIVER NEAR WENTWORTH LOCATION, NH 148.3 1950-1990

01064500 SACO RIVER NEAR CONWAY, NH 383.8 1950-1990

01073000 OYSTER RIVER NEAR DURHAM, NH 12.1 1950-1990

01076500 PEMIGEWASSET RIVER AT PLYMOUTH, NH 621.5 1950-1990

For the Phase 2 study HYSR conducted negative run-length event duration analyses of the

observed USGS daily stream gage data from these five sites and the QPPQ Transform’s

estimated daily data generated at each test site’s streamgage. HYSR constructed negative run-

length duration histograms and probability plots for both the Critical and Rare flows for each of

the six Souhegan River bioperiods. Negative run-length frequency histograms and probability

plots were constructed for the other four sites during only the Rearing & Growth bioperiod.

A University of New Hampshire et al. study (2007) identified six bioperiods within a calendar

year for the lower Souhegan River watershed. The six bioperiods are shown below in Table 4-2.

The study identified two protected instream flow (PIF) rates for each Souhegan River bioperiod:

the Critical and the Rare protected instream flow rates. The Critical and Rare protected

instream flow rates are shown in Table 4-3.

Negative run-length event duration analyses were also conducted for the remaining four gage

sites listed in Table 4-1. PIF studies similar to that conducted by University of New Hampshire

(2007) necessary to determine the watershed’s bioperiod calendar and each bioperiod’s Critical

flow and Rare flow have yet to be done. Instead, in consultation with NHDES, estimates of Q85

and Q95 for each of these sites were determined during the earlier HYSR Phase 1 study

11


(Fennessey, 2018). Q85 and Q95 determined for each of these four evaluation sites are used as the

negative run-length thresholds and applied during the Souhegan River summertime Rearing &

Growth PISF bioperiod (Table 4-2.). The flow quantile rates for the four evaluation watersheds

are listed below in Table 4-4.

Table 4-2

Protected Instream Flow Bioperiods for the Souhegan River near Merrimack, NH

Bioperiod

Number Start End Bioperiod

1 15-Nov 28-Feb Over-Wintering

2 1-Mar 30-Apr Spring Flood

3 1-May 14-Jun Shad Spawning

4 15-Jun 14-Jul GRAF Spawning

5 15-Jul 30-Sep Rearing & Growth

6 1-Oct 14-Nov Salmon Spawning

Table 4-3

Protected Instream Flow Rates for the Lower Souhegan River Watershed at the Souhegan

River at Merrimack, NH USGS Stream Gage Site

Critical flow Rare Flow

Bioperiod

Number Bioperiod

Critical

flow (cfs)

Critical

flow

(cfsm)

Rare flow

(cfs)

Rare flow

(cfsm)

1 Over-Wintering 86 0.50 51 0.30

2 Spring Flood 188 1.1 137 0.80

3 Shad Spawning 96 0.56 88 0.51

4 GRAF Spawning 26 0.15 17 0.10

5 Rearing & Growth 26 0.15 17 0.10

6 Salmon Spawning 96 0.56 39 0.23

12


Table 4-4

Observed Rearing & Growth Bioperiod Q85 and Q95 Flow Rates at USGS Gaged Test Sites

Q85 Q95

USGS Gage Site (cfs) (cfsm) (cfs) (cfsm)

DIAMOND RIVER NEAR

WENTWORTH

LOCATION, NH

33 0.22 21 0.14

SACO RIVER NEAR

CONWAY, NH 148 0.39 116 0.3

OYSTER RIVER NEAR

DURHAM, NH 0.8 0.07 0.6 0.05

PEMIGEWASSET RIVER

AT PLYMOUTH, NH 184 0.3 144 0.23

HYSR’s original study plan was to determine daily flows using each of two index gages. The

plan was to use the Phase 1 HYSR study gage network derived from the HCDN network

developed by Slack and Landwher (1992) and the GAGES II network developed and described

by Falcone et al. (2010a and 2016) to assign Index gages to each evaluation site as alternative

pairs. The motivation for the experiment was to determine how to select the best Index gage to

be used. A choice was available between an HCDN gage from among the 133 gages of the

Fennessey (2018) network or a GAGES II gage that was not necessarily among the original

HCDN (Slack and Landwher, 1992) network as the Index gage.

The experiment was to compare the evaluation gage’s flows to each of the daily data time

series of the two proposed Index gages. Both Index gages’ daily data were constructed using the

QPPQ Transform method. The idea was to use the nearest neighbor HCDN (HCDN NN) gage

as one test index gage and the nearest GAGES II network gage having a watershed area within

+/- 10% of the evaluation site’s watershed area (GAGES II NN WA) as the second test index

gage.

Each of the GAGES II Index gages paired with the five evaluation sites also has a Disturbance

Index of 13 or less. The Falcone et al. (2010b) developed a Disturbance Index based on six

statistically significant variables by analyzing the available GIS data for nearly 1000 watersheds

located in the western US. The Disturbance Factor (Falcone, 2016) now consists of seven

13


variables: major dam density (number per 100 km2; freshwater withdrawal (1000 m

3 per year

per km2); change in dam storage 1950-1990 (1000 m

3 per km

2); percent of stream km coded as

“canal’; raw straightline distance (km) of gage location to nearest "major" NPDES (municipal

or industrial wastewater discharge) point in watershed; roads (km per km2) and Fragmentation

Index of "undeveloped" land in the watershed.

GAGES II Sites with a Disturbance Index approaching 1 are judged by the USGS (see

Falcone, 2016) as having little anthropomorphic and those with a Disturbance Index approaching

40 as having been highly impacted by human activity. HYSR’s choice of maximum Disturbance

Index of 13 or less was rather subjective, although a Disturbance Index of 10 or less was the

initial goal and would have been preferred. Table 4-5 lists the five test sites and each site’s

nearest neighbor HCDN index gage and GAGES II index gage. Also shown is the distance

between the centroid of the index gage watershed and the centroid of the companion test

watershed. Because all five of the evaluation sites are listed in GAGES II, each site’s

Disturbance Index is shown too. Despite being a part of the original HCDN, note that the

Disturbance Index for the Souhegan River is 24.

14


Table 4-5

Evaluation Sites and their HCDN NN and GAGES II QPPQ Transform Index Sites

Role GAGE_ID NAME Mi

2

Dist (miles)

Disturb.Index

Test Site 1 01094000 SOUHEGAN RIVER AT MERRIMACK, NH 170.2 - 24

HCDN NN 01165000 EAST BR. OF TULLY RIVER NEAR ATHOL, MA 129.5 24.6 15

GAGES II 01329000 BATTEN KILL RIVER AT ARLINGTON, VT 150.4 114.9 6

Test Site 2 01052500 DIAMOND R. NEAR WENTWORTH LOCATION, NH

148.3 - 8

HCDN NN 01055000 SWIFT RIVER NEAR ROXBURY,MA 98.6 32.4 3

GAGES II 04296500 CLYDE RIVER AT NEWPORT, VT 144.9 78.2 10

Test Site 3 01064500 SACO RIVER NEAR CONWAY, NH 383.8 - 7

HCDN NN 01054200 WILD RIVER AT GILEAD,ME 69.9 18.5 4

GAGES II 01065000 OSSIPEE RIVER AT EFFINGHAM FALLS, NH 330.4 14.5 12

Test Site 4 01073000 OYSTER RIVER NEAR DURHAM, NH 12.1 - 14

HCDN NN 01094000 SOUHEGAN RIVER AT MERRIMACK, NH 170.2 45.8 24

GAGES II 01097300 NASHOBA BROOK NEAR ACTON, MA 11.9 61.0 13

Test Site 5 01076500 PEMIGEWASSET R. AT PLYMOUTH, NH 621.5 - 16

HCDN NN 01075000 PEMIGEWASETT R. AT WOODSTOCK, NH 194.8 11.2 8

GAGES II 01144000 WHITE RIVER AT WEST HARTFORD, VT 691.5 50.6 8

Five sets of daily time series consisting of the evaluation site POR daily flows, the HCDN NN

QPPQ flows and the GAGES II NN WA daily flows were prepared and forwarded to NHDES

for evaluation. NHDES staff determined that, upon close inspection of the set of flows for the

Diamond River evaluation site, the Clyde River GAGES II QPPQ Transform-generated daily

flows appeared to be highly regulated despite having a Falcone (2016) Disturbance Index of 10.

Close review of Falcone’s spreadsheet (Falcone, 2016) revealed that the Clyde River watershed

is highly regulated because of three hydroelectric power plants located on the river. One plant

diverts flows from the river upstream of the gage and returns the discharge below the gage

making it unsuitable for the present study.

As a consequence of this finding, HYSR and NHDES agreed that it would be appropriate to

abandon using GAGES II network Index gages solely based upon a Disturbance Index of

approximately 10 or less and having a watershed area within +/- 10 percent of the evaluation site

15


watershed. Instead, the Phase 2 study was conducted using the nearest-neighbor HCDN gage

(HCDN NN) and the nearest-neighbor HCDN gage having a watershed area that was within +/-

20 percent of the evaluation site’s watershed area (HCDN NN WA) as alternative index gages.

These sets are listed below in Table 4-6.

Table 4-6

Evaluation Sites and their HCDN NN and HCDN NN WA QPPQ Transform Index Sites

Role GAGE_ID NAME SQ.MI

Dist. (miles)

Impact Factor

Test Site 1 01094000 SOUHEGAN RIVER AT MERRIMACK, NH 170.2 - 24

HCDN NN 01165000 EAST BR. OF TULLY RIVER NEAR ATHOL, MA 129.5 24.6 15

HCDN NN WA 01086000 WARNER RIVER AT DAVISVILLE, NH 147.4 33.2 13

Test Site 2 01052500 DIAMOND R. NEAR WENTWORTH LOCAT., NH 148.3 - 8

HCDN NN 01055000 SWIFT RIVER NEAR ROXBURY,MA 98.6 32.4 3

HCDN NN WA 01055500 NEZINSCOTT RIVER NEAR N. HANSON, ME 135.0 60.9 13

Test Site 3 01064500 SACO RIVER NEAR CONWAY, NH 383.8 - 7

HCDN NN 01054200 WILD RIVER AT GILEAD,ME 69.9 18.5 4

HCDN NN WA 01047000 CARABASETT RIVER AT NORTH HANSON, ME 351.2 84.9 7

Test Site 4 01073000 OYSTER RIVER NEAR DURHAM, NH 12.1 - 14

HCDN NN 01094000 SOUHEGAN RIVER AT MERRIMACK, NH 170.2 45.8 24

HCDN NN WA 01165500 MOSS BROOK AT WENDELL DEPOT, MA 12.7 79.9 7

Test Site 5 01076500 PEMIGEWASSET R. AT PLYMOUTH, NH 621.5 - 16

HCDN NN 01075000 PEMIGEWASETT R. AT WOODSTOCK, NH 194.8 11.2 8

HCDN NN WA 01144000 WHITE RIVER AT WEST HARTFORD, VT 691.5 50.8 8

To ensure a fair evaluation, the test site gage POR and the QPPQ Transform’s Index gage

POR needed to be concurrent. Although four out of the five evaluation sites have a 41-year POR

of 1950-1990 water years1--the exception being the Souhegan River (1950-1967)--some of the

QPPQ Transform index sites have shorter PORs as well. Table 4-7 lists the concurrent POR of

the test site and QPPQ Transform test pairs.

1 A USGS water year begins October 1 and ends September 31 of the following year. For

example, the 1970 water year began October 1, 1969, and ended September 30, 1970.

16


Table 4-7

Paired Test Site and QPPQ Transform Index Site Period-of-Record

Test Pair

Role GAGE_ID NAME POR

Site 1 Pair 1

Test Site 1 1094000 SOUHEGAN RIVER AT MERRIMACK, NH 1950-1976

HCDN NN 1165000 EAST BR. OF TULLY RIVER NR. ATHOL, MA

Site 1 Pair 2

Test Site 1 1094000 SOUHEGAN RIVER AT MERRIMACK, NH 1950-1976

HCDN NN WA 1086000 WARNER RIVER AT DAVISVILLE, NH

Site 2 Pair 1

Test Site 2 1052500 DIAMOND R. NR. WENTWORTH LOCAT., NH 1950-1990

HCDN NN 1055000 SWIFT RIVER NEAR ROXBURY,MA

Site 2 Pair 2

Test Site 2 1052500 DIAMOND R. NR. WENTWORTH LOCAT., NH 1950-1990

HCDN NN WA 1055500 NEZINSCOTT RIVER NEAR N. HANSON, ME

Site 3 Pair 1

Test Site 3 1064500 SACO RIVER NEAR CONWAY, NH 1965-1990

HCDN NN 1054200 WILD RIVER AT GILEAD, ME

Site 3 Pair 2

Test Site 3 1064500 SACO RIVER NEAR CONWAY, NH 1950-1990

HCDN NN WA 1047000 CARABASETT RIVER AT N. HANSON, ME

Site 4 Pair 1

Test Site 4 1073000 OYSTER RIVER NEAR DURHAM, NH 1950-1976

HCDN NN 1094000 SOUHEGAN RIVER AT MERRIMACK, NH

Site 4 Pair 2

Test Site 4 1073000 OYSTER RIVER NEAR DURHAM, NH 1950-1982

HCDN NN WA 1165500 MOSS BROOK AT WENDELL DEPOT, MA

Site 5 Pair 1

Test Site 5 1076500 PEMIGEWASSET R. AT PLYMOUTH, NH 1950-1977

HCDN NN 1075000 PEMIGEWASETT R. AT WOODSTOCK, NH

Site 5 Pair 2

Test Site 5 1076500 PEMIGEWASSET R. AT PLYMOUTH, NH 1950-1990

HCDN NN WA 1144000 WHITE RIVER AT WEST HARTFORD, VT

17


5. QPPQ Transform Method Negative Run-Length Analysis

In a previous study, Fennessey (1997) conducted a negative run-length analysis of the Saco

River using preliminary criteria developed by NHDES. That study used seasonal flow rates and a

duration of seven consecutive days of flows below a prescribed threshold that would then trigger

management. For the purposes of that study, Fennessey defined a negative run-length event as a

period of one or more days during which streamflow fell below a threshold of QP. QP is the

streamflow rate that is equaled or exceeded “P” percent of the time. Figure 5-1 illustrates three

such events with a hypothetical river. The first event, lasting T1 days, began when Q(t) fell

below QP and ended when flows rose above QP; the second event lasted T2 days. The third time

Q(t) fell below Qp, the event lasted T3 days.

Fig. 5-1. Negative Run-Length Events

Figure 5-2 illustrates how flows rose and fell during six years of 77-day-long Rearing &

Growth bioperiods for the Souhegan River relative to Qcritical and Qrare. Six seasonal bioperiods,

each having Qcritical (yellow dashed line) and Qrare (red dashed line), are streamflow rates

determined by specialists, as mentioned earlier and discussed by University of New Hampshire

(2007). During the four Rearing & Growth Bioperiods of the 1963-1966 drought years, using

Figure 5-2, it is difficult to discern more than that the flows fell below Qcritical and Qrare each

summertime season. If one looks carefully, it appears that during the Rearing & Growth

bioperiods of 1963 through 1966, the Souhegan River flowed less than Qcritical for long runs of

time. During the height of the 1960s drought, in 1965 and 1966, flows were less than Qrare a

18


significant portion of time, but it is not possible to “see” the individual events. For this reason,

negative run-length event behavior is best summarized with statistics.

Q (

cfs

)

1

10

100

1

10

100

Year

1964 1966 1968

Fig. 5-2. 1963-68 Rearing & Growth Bioperiod Flows in the Souhegan River Relative to

Qcritical (yellow dashed line) and Qrare (red dashed line)

Figure 5-3 shows the 77 day-long Rearing & Growth bioperiod FDC for the Souhegan River

during the 1950-1976 water years POR. Flows exceeded Qcritical approximately 75 percent of the

time and Qrare about 90 percent of the time during this season over the POR.

19


P[Q>q] x 100

0 10 20 30 40 50 60 70 80 90 100

QP

(cfs

)

1

10

100

1000

1

10

100

1000

Obs

Qcritical

Qrare

Fig. 5-3. Rearing & Growth Bioperiod Flow Duration Curve Relative to Qcritical and Qrare

Several aspects of the negative run length analysis can be presented. A run-length histogram

summarizes the events that occurred during the POR. Of course that exact timing of the

streamflow pattern will not repeat itself during the future. To determine which year(s) an event

of some particular duration occurred, one would have to inspect the streamgage daily records.

Figures 5-4a and 5-4b respectively show the POR Rearing & Growth bioperiod negative run-

length histograms with Qcritica+ and Qrare as threshold flows. In Figure 5-4a, there were only two

one-day sub-Qcritical events, six two-day events, and so on, up to one event that lasted fifty-five

consecutive days during one particular water year’s Rearing & Growth season. Similarly, as

shown in Figure 5-4b, there were only two three-day sub-Qrare events, one fifteen-day event, and

so on, up to one thirty-five-day-long sub-Qrare event.

The probability plot, or run-length duration curve (RDC), provides an estimate of how likely

and for how long a sub-threshold event occurred over the POR and might occur in the future.

Figure 5-5a shows that during the POR’s 77-day-long Rearing & Growth bioperiod, given that a

sub-threshold event has occurred, i.e. “| Q<q”, there is about a 20 percent chance (0.2

probability) that a sub-Qcritical Souhegan River event will last fourteen or more days. Figure 5-5b

shows that there is about a 10 percent chance that a sub-Qrare event will last fifty or more days.

20


Number of Consecutive Days Q<Qcritical

0 5 10 15 20 25 30 35 40 45 50 55 60

Fre

que

ncy

0

2

4

6

0

2

4

6Obs

Fig. 5-4a. Rearing & Growth Qcritical Negative Run-Length Histogram, Souhegan River

Number of Consecutive Days Q<Qrare

0 5 10 15 20 25 30 35 40

Fre

que

ncy

0

1

2

3

4

0

1

2

3

4

Obs

Fig. 5-4b. Rearing & Growth Qrare Negative Run-Length Histogram, Souhegan River

21


P[N>nday | Q<q] x 100

1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

50

60

0

10

20

30

40

50

60

Obs

Fig. 5-5a. Rearing & Growth Qcritical Negative Run-Length Duration Curve, Souhegan R.


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

0

10

20

30

40

Obs

Fig. 5-4b. Rearing & Growth Qrare Negative Run-Length Duration Curve, Souhegan River

22


6. QPPQ Transform Method Negative Run-Length Analysis Results

6.1 Introduction

The primary product of this Phase 2 study is the construction of a series of graphs to visually

assess how accurately the QPPQ Transform estimates daily flow data as compared with the site’s

observed historic stream flow data. Accompanying this qualitative graphic/visual comparison

assessment is a quantitative assessment that compares the evaluation site daily data with the daily

data constructed using the QPPQ Transform method with alternative Index gage sites.

As discussed above, the alternative Index gage sites are the HCDN NN (nearest neighbor) and

the HCDN NN WA (nearest neighbor with a watershed area equal to +/- 20 percent of the

evaluation site gage watershed). HYSR reasoned that the HCDN NN watershed would likely

share the climate of the evaluation site watershed. HSYR also reasoned that the HCDN NN WA

might also share the same climate and being of similar size, experience a more similar response

to precipitation events. The HCDN NN WA recognizes that the runoff from a smaller watershed

will rise and fall in response to a precipitation event more quickly than a larger watershed. By

testing two Index gage types for each test site, NHDES will know which would be the better

choice to apply during future analysis.

6.2 Seasonal Streamflow Duration Curve Evaluation

A good place to start this evaluation is to compare seasonal streamflow duration curves

(FDCs) of each type of Index gage to that of the test site. Figure 6-1a compares USGS

streamgage data for the Rearing & Growth bioperiod FDC for the Souhegan River with that

generated using the QPPQ Transform HCDN NN Index gage. Similarly, Figure 6-1b compares

the same USGS gage data Rearing & Growth bioperiod FDC, but now against QPPQ Transform

HCDN NN WA Index gage data FDC. Each figure also shows both the Qcritical (yellow line) and

Qrare (red line) PIFs for this bioperiod.

A visual comparison suggests that the FDC constructed with the NN WA Index gage data

better matches the observed Souhegan River seasonal FDC than does the analysis using the NN

Index gage QPPQ Transform. Similar pairs of graphs for the Rearing & Growth bioperiod for

the Diamond River, Saco River, Oyster River, and Pemigewasset River are found in Appendix I.

23


P[Q>q] x 100

0 10 20 30 40 50 60 70 80 90 100

QP

(cfs

)

1

10

100

1000

1

10

100

1000

Obs

QPPQ NN

Qcritical

Qrare

Fig. 6-1a. Rearing & Growth Bioperiod FDCs of the Souhegan River and QPPQ NN

P[Q>q] x 100

0 10 20 30 40 50 60 70 80 90 100

QP

(cfs

)

1

10

100

1000

1

10

100

1000

Obs

QPPQ NN WA

Qcritical

Qrare

Fig. 6-1b. Rearing & Growth Bioperiod FDCs of the Souhegan River and QPPQ NN WA6.2

Number of Negative Run-length Events Evaluation

24


The second evaluation test conducted during the Phase 2 study compared the number of

negative run-length events between NN and NN WA pairs. This test was run for the six

Souhegan River bioperiods and for the Rearing & Growth bioperiod for the other four evaluation

sites.

Figure 6-2a below illustrates the difference between the number of sub-Qcritical and sub-Qrare

run-lengths events that took place over the POR during the Rearing & Growth bioperiod for the

lower Souhegan River from the USGS streamgage data (white bar) and the QPPQ Transform

HCDN NN daily data (green bar). There were 42 sub-Qcritical observed events compared with 58

QPPQ Transform sub-Qcritical events for the NN pair. There were 21 sub-Qrare observed events

compared with 28 QPPQ Transform sub-Qrare events for the NN pair.

Num

be

r o

f E

ve

nts

0

10

20

30

40

50

60

0

10

20

30

40

50

60

Obs NN Qcrit

QPPQ NN Qcrit

Obs NN Qrare

QPPQ NN Qrare

Fig. 6-2a. Rearing and Growth Bioperiod Number of Negative Run-length Events

Test Site & HCDN gage NN Pair

Figure 6-2b below illustrates the number of sub-Qcritical and sub-Qrare run-lengths events that

took place over the POR during the Rearing & Growth bioperiod for the lower Souhegan River

according to the USGS streamgage data (white bar) and the QPPQ Transform HCDN NN WA

daily data (green bar). There were 42 sub-Qcritical observed events and 45 QPPQ Transform sub-

Qcritical events for the NN pair. There were 21 sub-Qrare observed events versus 31 QPPQ

25


Transform sub-Qrare events for the NN WA pair. From these results, one might conclude that the

NN WA QPPQ Transform daily performed better than the NN when it comes to Qcritical in the

Souhegan but the NN did better when matching the number of Rearing & Growth bioperiod sub-

Qrare events. N

um

be

r o

f E

ve

nts

0

10

20

30

40

50

60

0

10

20

30

40

50

60

Obs NN WA Qcrit

QPPQ NN WA Qcrit

QPPQ NN WA Qrare

QPPQ NN WA Qrare

Fig. 6-2b. Rearing and Growth Bioperiod Number of Negative Run-length Events

Test Site & HCDN gage NN WA Pair

Similar pairs of graphs for all six bioperiods in the Souhegan River are provided in Appendix

II. Graph results for the Rearing & Growth bioperiod with NN and NNWA pairs using Q85 and

Q95 as test thresholds for the Diamond River, Saco River, Oyster River, and Pemigewasset River

are found in Appendix III.

6.3 Negative Run-length Event Duration Frequency Histogram Evaluation

The next test of NN versus NN WA index gages compared the negative run-length event,

duration-frequency histogram. As discussed earlier, the negative run-length histogram

graphically shows the frequency of the duration of negative run-length events. Figures 6-3a

through 6-3d below illustrate the respective distributions of sub-Qcritical and sub-Qrare run-lengths

events that took place over the POR during the Rearing & Growth bioperiod for the lower

Souhegan River from the USGS streamgage data (black bars) and the QPPQ Transform daily

26


data (green bars). As shown in the histograms in Fig. 6-3a and 6-3b, the NN WA histogram

appears to better match the observed data histogram than does the NN histogram during sub-

Qcritical events. The NN index site had many more one-, two- and three-consecutive-day duration

events than were observed. As shown in the histograms of Figures 6-3c and 6-3d, the NN

appears to have an edge over the NN WA histograms for sub-Qrare events. In this case, the NN

WA index site had many more one-, two-, and three-consecutive-day duration events than were

observed using the NN index gage results.


0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Fre

que

ncy

0

2

4

6

8

10

0

2

4

6

8

10

Obs

QPPQ NN

Fig. 6-3a. Test Site and NN HCDN gage


0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Fre

que

ncy

0

2

4

6

8

10

0

2

4

6

8

10

Obs

QPPQ NN WA

Fig 6-3b Test Site and NN WA HCDN gage

Souhegan Rearing and Growth Bioperiod Frequency Histogram of Negative Run-length

Events


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Fre

que

ncy

0

2

4

6

8

0

2

4

6

8

Obs

QPPQ NN

Fig. 6-3c. Test Site and NN HCDN gage


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Fre

que

ncy

0

2

4

6

8

0

2

4

6

8

Obs

QPPQ NN WA

Fig 6-3d. Test Site and NN WA HCDN gage

27


Souhegan Rearing and Growth Bioperiod Frequency Histogram of Negative Run-length

Events

Similar pairs of histograms for all six bioperiods in the Souhegan River are provided in

Appendix IV and Appendix IVb. Graph results for the Rearing & Growth bioperiod with NN

and NNWA pairs for the Diamond River, Saco River, Oyster River, and Pemigewasset River are

found in Appendix V.

6.4 Negative Run-length Probability Plot Duration Curve Evaluation

The third evaluation test to compare the NN and NN WA index pairs focused on the negative

run-length duration probability plot, or run-length duration curve (RDC). Similar to a FDC, an

RDC is an empirical cumulative probability plot of the negative run-length frequency data

discussed in the previous section. This test compares how well the NN index RDC and NN WA

RDC overlie the observed RDC. The Weibull plotting position method was used (see Vogel and

Fennessey, 1994) to construct the RDCs. Because few events are involved, it was not possible to

use the Parzen (1978) quantile estimator that was used to construct the FDCs shown in Appendix

I and discussed by Vogel and Fennessey (1994) and Fennessey (2018) in the HYSR Phase 1

report.

Figures 6-4a through 6-4d below illustrate the difference between the run-length RDCs of

sub-Qcritical and sub-Qrare run-lengths events on the Lower Souhegan River during the Rearing &

Growth bioperiod using USGS streamgage data (black bars) and QPPQ Transform daily data

(green bars). As shown in the RDCs in Fig. 6-4a and 6-4b, the NN WA probability plot appears

to more closely match the observed data histogram better than does the NN probability plot

during sub-Qcritical events. For the RDCs shown in Figures 6-4c and 6-4d, the NN probability

plot seems to be better than the NN WA RDC for sub-Qrare events.

28



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

20

40

60

80

0

20

40

60

80

Obs

QPPQ NN

Fig. 6-4a. Test Site and NN HCDN gage


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

20

40

60

80

0

20

40

60

80

Obs

QPPQ NN WA

Fig 6-4b Test Site and NN WA HCDN gage

Rearing and Growth Bioperiod Probability Plot of Qcritical Negative Run-length Events


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

20

40

60

80

0

20

40

60

80

Obs

QPPQ NN

Fig. 6-4c. Test Site and NN HCDN gage


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

20

40

60

80

0

20

40

60

80

Obs

QPPQ NN WA

Fig 6-4d Test Site and NN WA HCDN gage

Rearing and Growth Bioperiod Probability Plot Qrare of Negative Run-length Events

Pairs of graphs for all six bioperiods in the Souhegan River are provided in Appendix VIa and

Appendix VIb. Probability plots of only the Rearing & Growth bioperiod with NN and NNWA

pairs for the Diamond River, Saco River, Oyster River, and Pemigewasset River are found in

Appendix VII.

29


6.5 95% Confidence Interval of the Mean Negative Run-length Duration Evaluation

The next evaluation assessment compared the 95% confidence intervals for the mean or

average negative run-length event duration estimated for the daily gage data and the QPPQ

Transform daily data NN and NN WA pair partner. As shown by histograms of Figures 6-2a

through 6-2d, the frequency distribution of the negative run-length event durations are not

normally distributed (bell-shaped); instead the data are exponentially distributed. For this

reason, the 95% confidence interval of the mean event duration is estimated using the two-sided

t-test, as described by Fennessey (2000), among others.

Equation 6-1 was used to estimate the mean event duration, E[durat] using the Method of

Moments. Let durati equal the duration in days of the ith

of the nseas negative run-length event

that occurred during a particular bioperiod over the entire period-of-record. Using negative run-

length events of sub-Qthreshold flow rates (Qcritical, Qrare, Q85, or Q95), the sample population of

durati, i=1,nseas is developed.

nseas

1=i

idurat

nseas

1= E[durat] (6-1)

Given nseas negative run-length events during the period-of-record, the standard deviation of the

duration of an event, SD[durat], is estimated using the Method of Moments as shown by

Equation (6-2).

nseas

1=i

2

iduratEdurat

1nseas

1 =]durat[SD (6-2)

The 95% confidence interval of the true mean duration of a sub-threshold event, durat, could

be estimated by assuming that the mean of the mean event duration, E[durat], are approximately

normally distributed, with the standard deviation of the mean event duration, SD[durat]),

unknown. One could then assume that the (1-)100% confidence interval for durat is described

by Equation (6-3) and shown below

n

St+x

n

St-x /2

durat

/2 (6-3)

where x equals E[durat]; S equals SD[durat]; t/2 equals the value of the Student’s t distribution

with =n-1 degrees of freedom. For this study, HYSR assumes that the 95% confidence interval

30


for the mean duration of a sub-threshold event with nseas > 30 is adequately described by letting

t0.025=2.0.

The distributions of the 95% confidence interval for the mean durations that compare the NN

and the NN WA to the observed and are shown in the figures below. Figures 6-5a and 6-5b are

box plots for the Rearing & Growth bioperiod of the Souhegan River that show the 95% CI of

the mean event duration with the value E[durat], determined using Equation (6-1), shown as the

horizontal black line in the middle of each box. Because all four box-plots vertically overlap,

there is no statistically significant difference among them, and therefore there is no statistically

significant difference between the QPPQ Transform NN or QPPQ Transform NN WA pairs.

Qualitatively speaking, the range of the NN Qcritical 95% CI box plot is about the same as the Obs

NN 95% CI, as shown in Fig 6-5a whereas the NN WA Qcritical 95% CI box plot is smaller than

the Obs NN 95% CI, as shown in Fig. 6-5b,. The same could be said about the NN WA Qrare and

the Obs NN WA box plots of Fig 6-5b as compared to the NN Qrare pairing in Fig. 5-5a.

Obs Qcrit QPPQ Qcrit Obs Qrare QPPQ Qrare

Eve

nt D

ura

tio

n (

days)

0

5

10

15

20

Fig. 6-5a. Test Site & NN HCDN gage

Rearing and Growth Bioperiod 95% C.I. of E [Sub-threshold Event Duration]

31



Eve

nt D

ura

tio

n (

days)

0

5

10

15

20

Fig 6-5b Test Site & NN WA HCDN gage

Rearing and Growth Bioperiod 95% C.I. of E [Sub-threshold Event Duration]

Pairs of graphs for all six bioperiods in the Souhegan River are provided in Appendix VIII.

The 95% C.I. of the mean event duration for the Rearing & Growth bioperiod with NN and

NNWA pairs for the Diamond River, Saco River, Oyster River, and Pemigewasset River are

found in Appendix IX.

6.6 Seasonal and POR Daily Time Series Coefficient of Variation Evaluation

The final evaluation test considered the coefficient of variation, R2, between the paired test

site daily data and the QPPQ Transform data for the entire POR and by bioperiod season. Let Q1

equal the daily flows observed at the test site stream gage and Q2 be the daily flows generated

using the QPPQ Transform for either the NN or the NN WA pair partner. The means of Q1 and

Q2 are estimated using the Method of Moments approach, as described by Equation 6-1. The

coefficient of determination, R2, is given by Equation 6- 4, where nday is the number of days

within the pair’s entire period-of record or for the POR of a particular bioperiod. .

32


nday

1i

2

2i,2

nday

1i

2

1i,1

2

2i,2

nday

1i

1i,1

2

QEQQEQ

QEQQEQ

=R (6-4)

Results for the POR and each of the six bioperiods for all five test sites are shown below as

Tables 6-1 through 6-5. Each table also lists the watershed areas of the test site, the NN Index

gage and the NN WAS Index gage, taken from Table 4-6. Also shown are the watershed-

centroid-to-watershed-centroid distances between the test site and the NN Index gage and the

NN WA Index gage.

Table 6-1

R2 for Souhegan River Gage (170.2 mi

2) and QPPQ Transform Pairs

for all Calendar Days and all Bioperiod-Specific Days for the POR

Obs and QPPQ

NN

Obs and QPPQ

NN WA

NN & NN WA

Watershed areas: 129.5 mi

2 147.4 mi

2

Centroid-to-

Centroid Distances: 24.6 miles 33.2 miles

R2 (%) R

2 (%)

POR 34.2 68.5

Bioperiod

Over-Wintering 30.7 74.5

Spring Flood 13.4 61.2

Shad Spawning 34.6 79.5

GRAF Spawning 57.0 63.4

Rearing & Growth 26.8 57.1

Salmon Spawning 27.1 57.1

33


Table 6-2

R2 for Diamond River Gage (148.3 mi



Obs and QPPQ

NN

Obs and QPPQ

NN WA

NN & NN WA


2 135.0 mi

2

Centroid-to-


R2 (%) R

2 (%)

POR 65.8 30.4

Bioperiod







34


Table 6-3

R2 for Saco River Gage (383.8 mi



Obs and QPPQ

NN

Obs and QPPQ

NN WA

NN & NN WA


2 351.2 mi

2

Centroid-to-


R2 (%) R

2 (%)

POR 79.9 73.5

Bioperiod







35


Table 6-4

R2 for Oyster River Gage(12.1 mi



Obs and QPPQ

NN

Obs and QPPQ

NN WA

NN & NN WA


2 12.7 mi

2

Centroid-to-


R2 (%) R

2 (%)

POR 70.0 54.9

Bioperiod







36


Table 6-5

R2 for Pemigewasset River Gage (621.5 mi



Obs and QPPQ

NN

Obs and QPPQ

NN WA

NN & NN WA


2 691.5 mi

2

Centroid-to-


R2 (%) R

2 (%)

POR 81.6 70.2

Bioperiod







6.7 Final Evaluation of QPPQ Transform NN Index Daily Data versus NN WA Index Daily

Data

With the exception of the coefficient of variation evaluation discussed in the prior section, the

comparative assessment of the graphic results discussed above and presented as Appendices I

through IX are qualitative and somewhat subjective at best and therefore, perhaps like beauty, in

the eye of the beholder. HYSR evaluated the better fit with the observed data for each test pair,

NN or NN WA Index gage, evaluated. HYSR’s selection of best fit, applied to the Qcritical and

Qrare flow thresholds for the Souhegan, and to the four test sites’ individual Q85, and Q95 flows,

and evaluation test are summarized in Tables 6-6 through 6-11. For those evaluation tests that

involved all six bioperiods for the Souhegan but only the Rearing & Growth bioperiod for the

Diamond River, Saco River, Oyster River, and Pemigewasset River test sites, only the Rearing &

Growth Souhegan River graphs are used for this final evaluation.

37


Table 6-6


Streamflow Duration Curves

QPPQ

Transform

NN

Index gage

QPPQ

Transform

NN WA

Index gage

Sub-total 2 2

Ties: 1

Table 6-7


Number of Run-Length Events

QPPQ

Transform

NN

Index gage

QPPQ

Transform

NN WA

Index gage

Sub-total 6 4

Ties: 0

Table 6-8


Run-length Frequency Histograms

QPPQ

Transform

NN

Index gage

QPPQ

Transform

NN WA

Index gage

Sub-total 7 5

Ties: 0

Table 6-9


Run-length Duration Curves

QPPQ

Transform

NN

Index gage

QPPQ

Transform

NN WA

Index gage

Sub-total 8 4

Ties: 0

Table 6-10


95% CI of the Mean Event Duration

QPPQ

Transform

NN

Index gage

QPPQ

Transform

NN WA

Index gage

Sub-total 3 4

Ties: 3

Table 6-11

All Bioperiod

R2 of Daily Data Time Series

QPPQ

Transform

NN

Index gage

QPPQ

Transform

NN WA

Index gage

Sub-total 27 8

Ties: 0

Table 6-12 counts HYSR’s selection of best fit for the QPPQ Transform NN Index gage and

the NN WA Index gage. By a margin of nearly two to one in New Hampshire, the nearest-

neighbor HCDN Index gage (NN) from the Fennessey (2018) streamgage network is

38


recommended over the nearest-neighbor HCDN gage having a watershed area within +/- 20

percent of that of the ungaged site (NN WA).

Table 6-12

Grand Total

QPPQ

Transform

NN

Index gage

QPPQ

Transform

NN WA

Index gage

T 53 27

Ties: 4

39


7. Summary and Conclusions

This study is the second of a two-part study by HYSR to support NHDES in its efforts to

determine, evaluate, and protect streamflows on certain rivers and river reaches designated by

the Legislature. Because some of those designated rivers have not had gages measuring actual

flows, NHDES requires a practical and accurate alternative method of estimating historical daily

streamflows at ungaged sites. This two-part study considers in depth one such method, the

QPPQ Transform, which has been adopted by the USGS and several states as a method for

generating estimated daily streamflows, and applies it to New Hampshire waterways.

A key component of Fennessey’s 1994 QPPQ Transform method was the application of a

regional streamflow duration curve (FDC) model at the ungaged site. The regional FDC model

was developed using historical daily streamflow data from USGS gage sites located in the

northeast U.S. The model is based on a probability distribution function that has three

parameters.

During the Phase 1 study, HYSR updated the original Fennessey (1994) regional equations,

which describe each parameter, using new soil, climate and topographic variables from the

extensive EXCEL spreadsheet data files of Geospatial Attributes of Gages for Evaluating

Streamflow, version II (GAGES-II, 2017)as developed by Falcone et al. (2010a). In addition to

the updated Regional parameter equations, various goodness-of-fit tests were conducted at

eleven USGS gage sites in New Hampshire to compare how the updated model did as compared

to the USGS gage data using streamflow duration curves (FDCs). The final product of the Phase

1 study was the construction of daily time series data for five USGS streamgage sites using the

QPPQ Transform. The QPPQ method requires daily data from a second USGS streamgage,

called the Index gage, to generate the desired daily data time series at the ungaged site.

The focus of this HYSR Phase 2 study is the continued evaluation of the QPPQ Transform

method. With the ultimate goal being to confidently estimate daily flows to develop protected

instream flow (PIF) criteria for ungaged segments of presently and future designated rivers in the

state, it is important to extensively test the method. While the Phase 1 study focused on an

evaluation that compared streamflow duration curves, as other researchers have done, HYSR

also undertook as a new approach an extensive negative run-length analysis.

40


A negative run-length event is the period of time during which streamflow falls below a

management threshold for some duration of days and then rises above the threshold flow rate,

which occurs in the natural state following a precipitation event. An event might be only one

day, or during an extended drought, an event might last for weeks, even months. PIFs

assessments applied on the Lamprey and Souhegan Rivers used negative run-length analyses to

define the PIF criteria. HYSR and NHDES decided that comparing the negative run-length

analyses of the QPPQ-calculated flow to the observed flows would be very useful for evaluating

the use of the QPPQ-calculated flows for defining PIFs.

Using streamflow thresholds described in the Phase 1 study, the negative run-length duration

characteristics for both evaluation site streamgage data and the QPPQ Transform method

generated data are graphically compared side-by-side. Additionally, HYSR took this opportunity

to compare the results from using two selected Index gages to develop alternate sets of QPPQ

Transform method daily flow time series. The goal of the experiment being to determine which

alternative was better.

Two time series were constructed for each of the five evaluation sites. One Index gage is

from a special streamgage network described by Fennessey (2018) whose watershed is closest to

the evaluation site’s watershed. This Index gage is called the HCDN NN where “HCDN” refers

to the original source gage network (Slack and Land, 1992) and “NN” stands for “nearest

neighbor.” The second Index gage is called the HCDN NN WA. It too comes from the Slack

and Landwehr (1992) HCDN gage network but it is the nearest neighbor (NN) with a watershed

area that is within +/- 20 of the watershed area (WA) of the evaluation site’s watershed.

Task 1 of the Phase 2 study involved constructing a series of graphs to compare the results of

a negative run-length analysis study as a different way to evaluate how well the QPPQ

Transform method does in New Hampshire. For the Souhegan River evaluation site, run-length

frequency histograms were constructed for two different management thresholds, Qcritical and

Qrare for the six bioperiods defined for the calendar year during the University of New Hampshire

(2007) study. Two sets of twelve graphs show these results to compare the evaluation site’s

historic run-length duration frequency plots with those with those of the two different QPPQ

Transform Index gage site frequency histogram graphs, respectively the HCDN NN and HCDN

NN WA.

41


Task 2 of the Phase 2 study involved constructing a series of graphs to compare negative run-

length probability plots as a way to evaluate how well the QPPQ Transform method does. The

probability plot, also referred herein as a run-length duration curve (RDC) is constructed from

the Task 1 frequency histogram plots. For the Souhegan River evaluation site, RDCs were

constructed for the two management thresholds, Qcritical and Qrare for the six calendar year

bioperiods. Two sets of twelve graphs show these results to compare the evaluation site’s

historic RDCs with those of HCDN NN and HCDN NN WA QPPQ Transform Index gage site

RDCs.

Task 3 of the Phase 2 study involved constructing, run-length frequency histograms for the

July 15 through September 30 Rearing & Growth bioperiod for two different test thresholds, Q85

and Q95 for an evaluation using the Diamond River, Saco River, Oyster and Pemigewasset River

streamgage sites as test locations. Two sets of eight graphs show these results to compare the

four evaluation site’s historic run-length duration frequency plots with those with the two HCDN

NN and HCDN NN WA frequency histogram graphs.

Task 4 of the Phase 2 study involved constructing, RDCs for the Rearing & Growth

bioperiod for two different test thresholds, Q85 and Q95 for an evaluation at the Diamond River,

Saco River, Oyster and Pemigewasset River test sites. Two sets of eight graphs show these

results to compare the four evaluation site’s historic run-length RDC probability plots with those

with those of the two different QPPQ Transform Index gage site RDC graphs.

Task 5 of the Phase 2 study involved constructing streamflow duration curves for only the

Rearing & Growth bioperiod. This evaluation used all five test sites: the Souhegan, Diamond,

Saco, Oyster and Pemigewasset River test sites. Two sets of five graphs show these results to

compare the five evaluation site’s historic Rearing & Growth bioperiod FDCs with those of the

HCDN NN and HCDN NN WA FDC graphs.

In addition to these five assigned tasks, HYSR on its own initiative, conducted additional

evaluation tests at the five evaluation sites. Volunteer Task 1consisted of constructing graphs

that show the number of negative run-length events that occurred in a bioperiod for the period-

of-record. Two sets of six graphs were prepared for the Souhegan River to compare the number

of events for all six bioperiods and for both the Qcritical and Qrare PIF thresholds. Two sets of

eight graphs were prepared to compare the number of events for the Rearing & Growth

42


bioperiod over the POR for the Diamond, Saco, Oyster and Pemigewasset River test sites but

using the Q85 and Q95 test thresholds.

Volunteer Task 2 consisted of constructing 95% confidence intervals of the mean negative

run-length event duration. Box plot graphs were made that show the 95% CI occurred in a

bioperiod for the period-of-record. Two sets of six boxplot graphs were prepared for the

Souhegan River to compare the 95% CIs for all six bioperiods and for both the Qcritical and Qrare

PIF thresholds. Two sets of four boxplot graphs were prepared to compare the 95% CI of the

mean number of events for the Rearing & Growth bioperiod over the POR for the Diamond,

Saco, Oyster and Pemigewasset River test sites using the Q85 and Q95 test thresholds.

Volunteer Task 3 consisted of determining the coefficient of variation statistics, R2, for the

POR and each of the six bioperiods for all five evaluation test site. Six tables compare the R2

estimated between the evaluation site gage data and each of the HCDN NN and HCDN NN WA

QPPQ Transform method Index data time series.

HYSR visually assessed each graph and table to determine whether the QPPQ NN Index gage

or the QPPQ NN WA Index gage graph results better matched the graphs of the evaluation site

gage data graphs results. HYSR counted the best-fit occurrences between the two Index gage

types and determined, by two to one, that the HCDN NN Index gages performed better than the

HCDN NN WA Index gages.

In summary, the results of the HYSR Phase 2 study indicate that over a very broad range of

tests, both qualitative and quantitative, the QPPQ Transform data compares well with the historic

observed data. Following its own review of the Phase 2 HYSR study, NHDES will be able to

make an informed decision about adopting the QPPQ Transform method as the preferred way to

estimate a long period time series of daily flows at ungaged sites in New Hampshire.

43


8. References

Falcone, J.A., (2016) GAGES-II: Geospatial Attributes of Gages for Evaluating Streamflow.

https://water.usgs.gov/GIS/metadata/usgswrd/XML/gagesII_March11_2015_conterm.xml

Falcone, J.A., D. M. Carlisle, D. M. Wolock and M. R. Meador, (2010a), GAGES: A stream

gage database for evaluating natural and altered flow conditions in the conterminous United

States. Ecology 91:621.

Falcone, J.A., D. M. Carlisle, L. C. Weber, (2010b), Quantifying human disturbances in

watersheds: Variable selection and performance of a GIS-based disturbance index for predicting

the biological condition of perennial streams.. Ecological Indicators Vol 10, pp. 264-273.

Farmer, W.H, S.A. Archfield, T. Over and J.E. Kiang, (2014), A comparison of methods to

predict historical daily streamflow time series in the southeastern United States, U.S. Geological

Survey Scientific Investigations Report 2014-5231, DOI: 10.3133/sir2014-5231.

Fennessey, N.M., (1994), A hydro-climatological model of daily streamflow in the northeast

United States, Ph.D. Dissertation, Tufts University, August.

Fennessey, N.M., (1997), An Event Duration Analysis of New Hampshire's Proposed Instream

Flow Rules, J. New England Water Works Association, , Vol. 111, No. 2, pp. 107-126.

Fennessey, N.M., (2000), A frequency and event duration analysis of the State of New

Hampshire’s proposed instream flow rules, prepared by Hydrologic Services, Inc. for the New

Hampshire Dept. of Environmental Services.

https://www.des.nh.gov/organization/divisions/water/wmb/rivers/instream/documents/hysr.pdf

Fennessey, N.M., (2018), A Final Report on the Update of a Regional Streamflow Duration

Curve Model for the Northeast United States and the Generation of Estimated Daily Flows

Using the QPPQ Transform Method at Ungaged Sites in New Hampshire, prepared by HYSR for

the New Hampshire Dept. of Environmental Services, . NHDES-R-WD-18-03, 67 pages.

https://www4.des.state.nh.us/blogs/rmac/wp-content/uploads/HYSR-Final-Report-3-26-

2018.pdf

GAGES-II, (2017), GAGES-II: Geospatial Attributes of Gages for Evaluating Streamflow,

updated December 11, https://catalog.data.gov/dataset/gages-ii-geospatial-attributes-of-gages-

for-evaluating-streamflow

Parzen, E., (1979), Nonparametric Statistical Data Modeling , Journal of the American

Statistical Association, Vol. 74, No. 365, pp. 105-121

Slack, W.J. and J.M. Landwehr, (1992), Hydro-Climatic Data Network (HCDN): A U.S.

Geological Survey streamflow data set for the United States for the study of climate variations,

1878-1988, U.S. Geological Survey Open-file Report 92-129, Reston, VA.

University of New Hampshire, the University of Massachusetts and Normandeau Assoc., (2007),

Final Souhegan River Protected Instream Flow Report, NHDES-R-WD-06-50, prepared for the

New Hampshire Dept. of Environmental Services.

http://mesohabsim.org/projects/finalreports/souhegan/Souhegan%20River%20PISF%20-

%20Executive%20Summary%20-%201%20October%202007.pdf

https://www.des.nh.gov/organization/divisions/water/wmb/rivers/instream/documents/hysr.pdf

http://mesohabsim.org/projects/finalreports/souhegan/Souhegan%20River%20PISF%20-%20Executive%20Summary%20-%201%20October%202007.pdf

http://mesohabsim.org/projects/finalreports/souhegan/Souhegan%20River%20PISF%20-%20Executive%20Summary%20-%201%20October%202007.pdf

44


Appendix I

New Hampshire QPPQ Transform Assessment

Seasonal Stream Flow Duration Curves

Season 5

Test Sites 1 - 5:

Test Site 1

01094000 Souhegan River at Merrimack, NH

Test Site 2

01052500 Diamond River at Wentworth Location, NH

Test Site 3

01064500 Saco River near Conway, NH

Test Site 4

01073000 Oyster River near Durham, NH

Test Site 5

01076500 Pemigewasset River at Plymouth, NH

45


P[Q>q] x 100

0 10 20 30 40 50 60 70 80 90 100

QP

(cfs

)

1

10

100

1000

1

10

100

1000

Obs

QPPQ NN

Qcritical

Qrare

Fig. AI-1a. FDCs of the Souhegan River and QPPQ NN

P[Q>q] x 100

0 10 20 30 40 50 60 70 80 90 100

QP

(cfs

)

1

10

100

1000

1

10

100

1000

Obs

QPPQ NN WA

Qcritical

Qrare

Fig. AI-1b. FDCs of the Souhegan River and QPPQ NN WA

46


P[Q>q] x 100

0 10 20 30 40 50 60 70 80 90 100

QP

(cfs

)

10

100

1000

10000

10

100

1000

10000

Obs

QPPQ NN

Q85

Q95

Fig. AI-2a. FDCs of the Diamond River and QPPQ NN

P[Q>q] x 100

0 10 20 30 40 50 60 70 80 90 100

QP

(cfs

)

10

100

1000

10000

10

100

1000

10000

Obs

QPPQ NN WA

Q85

Q95

Fig. AI-2b. FDCs of the Diamond River and QPPQ NN WA

47


P[Q>q] x 100

0 10 20 30 40 50 60 70 80 90 100

QP

(cfs

)

10

100

1000

10000

10

100

1000

10000

Obs

QPPQ NN

Q85

Q95

Fig. AI-3a. FDCs of the Saco River and QPPQ NN

P[Q>q] x 100

0 10 20 30 40 50 60 70 80 90 100

QP

(cfs

)

10

100

1000

10000

10

100

1000

10000

Obs

QPPQ NN WA

Q85

Q95

Fig. AI-3b. FDCs of the Saco River and QPPQ NN WA

48


P[Q>q] x 100

0 10 20 30 40 50 60 70 80 90 100

QP

(cfs

)

0.1

1

10

100

0.1

1

10

100

Obs

QPPQ NN

Q85

Q96

Fig. AI-4a. FDCs of the Oyster River and QPPQ NN

P[Q>q] x 100

0 10 20 30 40 50 60 70 80 90 100

QP

(cfs

)

0.1

1

10

100

0.1

1

10

100

Obs

QPPQ NN WA

Q85

Q95

Fig. AI-4b. FDCs of the Oyster River and QPPQ NN WA

49


P[Q>q] x 100

0 10 20 30 40 50 60 70 80 90 100

QP

(cfs

)

10

100

1000

10000

10

100

1000

10000

Obs

QPPQ NN

Q85

Q95

Fig. AI-5a. FDCs of the Pemigewasset River and QPPQ NN

P[Q>q] x 100

0 10 20 30 40 50 60 70 80 90 100

QP

(cfs

)

10

100

1000

10000

10

100

1000

10000

Obs

QPPQ NN WA

Q85

Q95

Fig. AI-5b. FDCs of the Pemigewasset River and QPPQ NN WA

50


Appendix II


Number of Negative Run-length Events by Season

Seasons 1-6

Test Site 1:


Nearest neighbor HCDN index gage:

01165000 East Br. of the Tully River near Athol, MA

1950-1976

Nearest neighbor HCDN index gage with watershed area +/- 20% test site:

01086000 Warner River at Davisville, NH

1950-1976

51


Bioperiod 1 Over-Wintering POR Number of Negative Run-length Events

Num

be

r o

f E

ve

nts

0

10

20

30

40

50

0

10

20

30

40

50

Obs NN Qcrit

QPPQ NN Qcrit

Obs NN Qrare

QPPQ NN Qrare

Fig. AII-1a. Test Site & NN HCDN gage

Num

be

r o

f E

ve

nts

0

10

20

30

40

50

0

10

20

30

40

50

Obs NN WA Qcrit

QPPQ NN WA Qcrit

Obs NN WA Qrare

QPPQ NN WA Qrare

Fig. AII-1b. Test Site & NN WA HCDN gage

52


Bioperiod 2 Spring Flood POR Number of Negative Run-length Events

Num

be

r o

f E

ve

nts

0

10

20

30

40

0

10

20

30

40

Obs NN Qcrit

QPPQ NN Qcrit

Obs NN Qrare

QPPQ NN Qrare


Num

be

r o

f E

ve

nts

0

10

20

30

40

0

10

20

30

40

Obs NN WA Qcrit

QPPQ NN WA Qcrit

QPPQ NN WA Qrare

QPPQ NN WA Qrare


53


Bioperiod 3 Shad Spawning POR Number of Negative Run-length Events

Num

be

r o

f E

ve

nts

0

5

10

15

20

25

30

0

5

10

15

20

25

30

Obs NN Qcrit

QPPQ NN Qcrit

Obs NN Qrare

QPPQ NN Qrare


Num

be

r o

f E

ve

nts

0

5

10

15

20

25

30

0

5

10

15

20

25

30

Obs NN WA Qcrit

QPPQ NN WA Qcrit

QPPQ NN WA Qrare

QPPQ NN WA Qrare


54


Bioperiod 4 GRAF Spawning POR Number of Negative Run-length Events

Num

be

r o

f E

ve

nts

0

2

4

6

8

10

12

0

2

4

6

8

10

12

Obs NN Qcrit

QPPQ NN Qcrit

Obs NN Qrare

QPPQ NN Qrare


Num

be

r o

f E

ve

nts

0

2

4

6

8

10

12

0

2

4

6

8

10

12

Obs NN WA Qcrit

QPPQ NN WA Qcrit

QPPQ NN WA Qrare

QPPQ NN WA Qrare


55


Bioperiod 5 Rearing and Growth POR Number of Negative Run-length Events

Num

be

r o

f E

ve

nts

0

10

20

30

40

50

60

0

10

20

30

40

50

60

Obs NN Qcrit

QPPQ NN Qcrit

Obs NN Qrare

QPPQ NN Qrare


Num

be

r o

f E

ve

nts

0

10

20

30

40

50

60

0

10

20

30

40

50

60

Obs NN WA Qcrit

QPPQ NN WA Qcrit

QPPQ NN WA Qrare

QPPQ NN WA Qrare


56


Bioperiod 6 Salmon Spawning POR Number of Negative Run-length Events

Num

be

r o

f E

ve

nts

0

10

20

30

40

50

60

0

10

20

30

40

50

60

Obs NN Qcrit

QPPQ NN Qcrit

Obs NN Qrare

QPPQ NN Qrare


Num

be

r o

f E

ve

nts

0

10

20

30

40

50

60

0

10

20

30

40

50

60

Obs NN WA Qcrit

QPPQ NN WA Qcrit

QPPQ NN WA Qrare

QPPQ NN WA Qrare


57


Appendix III


Number of Negative Run-length Events

Season 5

Test Sites 2 - 5

58


Test Site 2:



0105500 Swift River Near Roxbury, ME

1950-1990


01055500 Nuzinscott River at Turner Center, ME

1950-1990

59


Bioperiod 5 Rearing and Growth

POR Number of Negative Run-length Events

Num

be

r o

f E

ve

nts

0

20

40

60

80

100

120

140

160

0

20

40

60

80

100

120

140

160

Obs NN Q85

QPPQ NN Q85

Obs NN Q95

QPPQ NN Q95

Fig. AIII-1a. Test Site and NN HCDN gage

Num

be

r o

f E

ve

nts

0

20

40

60

80

100

120

140

160

0

20

40

60

80

100

120

140

160

Obs NN WA Q95

QPPQ NN WA Q95

QPPQ NN WA Q95

QPPQ NN WA Q95

Fig AIII-1b Test Site and NN WA HCDN gage

60


Test Site 3:



01054200 Swift River near Gilead, ME

1965-1990


01047000 Carabasset River near North Hanson, ME

1950-1990

61




Num

be

r o

f E

ve

nts

0

20

40

60

80

100

120

0

20

40

60

80

100

120

Obs NN Q85

QPPQ NN Q85

Obs NN Q95

QPPQ NN Q95


Num

be

r o

f E

ve

nts

0

20

40

60

80

100

120

140

0

20

40

60

80

100

120

140

Obs NN WA Q85

QPPQ NN WA Q85

QPPQ NN WA Q95

QPPQ NN WA Q95


62


Test Site 4:




1950-1976


01165500 Moss Brook at Wendell Depot, MA

1950-1982

63




Num

be

r o

f E

ve

nts

0

20

40

60

80

100

0

20

40

60

80

100

Obs NN Q85

QPPQ NN Q85

Obs NN Q95

QPPQ NN Q95


Num

be

r o

f E

ve

nts

0

20

40

60

80

100

0

20

40

60

80

100

Obs NN WA Q85

QPPQ NN WA Q85

QPPQ NN WA Q95

QPPQ NN WA Q95

Fig. AIII-3b Test Site and NN WA HCDN gage

64


Test Site 5:

01076500 Pemigewasset River at Plymouth NH


01075000 Pemigewasset River at Woodstock, NH

1950-1977


01144000 White River at W. Hartford, VT

1950-1990

65




Num

be

r o

f E

ve

nts

0

20

40

60

80

100

120

140

160

0

20

40

60

80

100

120

140

160

Obs NN Q85

QPPQ NN Q85

Obs NN Q95

QPPQ NN Q95


Num

be

r o

f E

ve

nts

0

20

40

60

80

100

120

140

160

0

20

40

60

80

100

120

140

160

Obs NN WA Q85

QPPQ NN WA Q85

QPPQ NN WA Q95

QPPQ NN WA Q95


66


Appendix IVa


Site 1 Negative Run-length Histograms

Test Thresholds: Qcritical and Qrare

Seasons 1-6

Test Site 1:




1950-1976



1950-1976

67


Bioperiod 1 Over-Wintering Negative Run-length Frequency Histograms

Critical Flow Threshold


0 5 10 15 20 25

Fre

que

ncy

0

2

4

6

8

0

2

4

6

8

Obds

QPPQ NN

Fig. AIVa-1a. Test Site & NN HCDN gage


0 10 20

Fre

que

ncy

0

2

4

6

8

0

2

4

6

8

Obs

QPPQ NN WA

Fig. AIVa-1b Test Site & NN WA HCDN gage

Rare Flow Threshold


0 5 10 15 20

Fre

que

ncy

0

2

4

6

0

2

4

6Obs

QPPQ NN

Fig. AIVa-1c. Test Site & NN HCDN gage


0 5 10 15 20

Fre

que

ncy

0

2

4

6

8

0

2

4

6

8

Obs

QPPQ NN WA

Fig. AIVa-1d Test Site & NN WA HCDN gage

68


Bioperiod 2 Spring Flood Negative Run-length Frequency Histograms



0 1 2 3 4 5 6 7 8 9 10

Fre

que

ncy

0

2

4

6

8

10

12

0

2

4

6

8

10

12

Obds

QPPQ NN



0 1 2 3 4 5 6 7 8 9 10

Fre

que

ncy

0

2

4

6

8

10

12

0

2

4

6

8

10

12

Obs

QPPQ NN WA


Rare Flow Threshold


0 10

Fre

que

ncy

0

1

2

3

4

5

0

1

2

3

4

5

Obs

QPPQ NN



0 10

Fre

que

ncy

0

1

2

3

4

5

0

1

2

3

4

5

Obs

QPPQ NN WA


69


Bioperiod 3 Shad Spawning Negative Run-length Frequency Histograms



0 1 2 3 4 5 6 7 8 9 10

Fre

que

ncy

0

2

4

6

8

10

12

14

0

2

4

6

8

10

12

14

Obds

QPPQ NN



0 1 2 3 4 5 6 7 8 9 10

Fre

que

ncy

0

2

4

6

8

10

12

14

0

2

4

6

8

10

12

14

Obs

QPPQ NN WA


Rare Flow Threshold


0 1 2 3 4 5 6 7 8 9 10

Fre

que

ncy

0

1

2

3

4

5

0

1

2

3

4

5

Obs

QPPQ NN



0 1 2 3 4 5 6 7 8 9 10

Fre

que

ncy

0

1

2

3

4

5

0

1

2

3

4

5

Obs

QPPQ NN WA


70


Bioperiod 4 GRAF Spawning Negative Run-length Frequency Histograms



0 1 2 3 4 5 6 7 8 9 10

Fre

que

ncy

0

1

2

3

4

0

1

2

3

4

Obs

QPPQ NN



0 1 2 3 4 5 6 7 8 9 10

Fre

que

ncy

0

1

2

3

4

0

1

2

3

4

Obs

QPPQ NN WA


Rare Flow Threshold


0 1 2 3 4 5

Fre

que

ncy

0

1

2

3

4

0

1

2

3

4

Obs

QPPQ NN



0 1 2 3 4 5

Fre

que

ncy

0

1

2

3

4

0

1

2

3

4

Obs

QPPQ NN WA


71


Bioperiod 5 Rearing and Growth Negative Run-length Frequency Histograms



0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Fre

que

ncy

0

2

4

6

8

10

0

2

4

6

8

10

Obs

QPPQ NN



0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Fre

que

ncy

0

2

4

6

8

10

0

2

4

6

8

10

Obs

QPPQ NN WA


Rare Flow Threshold


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Fre

que

ncy

0

2

4

6

8

0

2

4

6

8

Obs

QPPQ NN



0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Fre

que

ncy

0

2

4

6

8

0

2

4

6

8

Obs

QPPQ NN WA


72


Bioperiod 6 Salmon Spawning Negative Run-length Frequency Histograms



0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Fre

que

ncy

0

2

4

6

8

0

2

4

6

8

Obs

QPPQ NN



0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Fre

que

ncy

0

2

4

6

8

0

2

4

6

8

Obs

QPPQ NN WA


Rare Flow Threshold


0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Fre

que

ncy

0

2

4

6

8

10

12

0

2

4

6

8

10

12

Obs

QPPQ NN



0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Fre

que

ncy

0

2

4

6

8

10

12

0

2

4

6

8

10

12

Obs

QPPQ NN WA


73


Appendix IVb


Site 1 Negative Run-length Histograms

Test Thresholds: Q85 and Q95

Seasons 1-6

Test Site 1:




1950-1976



1950-1976

74


Bioperiod 1 Over-Wintering Negative Run-length Frequency Histograms

Q85 Threshold

Number of Consecutive Days Q<Q85

0 5 10 15 20 25 30 35 40

Fre

que

ncy

0

2

4

6

8

10

0

2

4

6

8

10

Obds

QPPQ NN

Fig. AIVb-1a. Test Site & NN HCDN gage


0 10 20 30 40

Fre

que

ncy

0

2

4

6

8

10

0

2

4

6

8

10

Obs

QPPQ NN WA

Fig. AIVb-1b Test Site & NN WA HCDN gage

Q95 Threshold


0 5 10 15 20 25 30

Fre

que

ncy

0

1

2

3

4

5

6

0

1

2

3

4

5

6

Obs

QPPQ NN

Fig. AIVb-1c. Test Site & NN HCDN gage


0 5 10 15 20 25 30

Fre

que

ncy

0

1

2

3

4

5

6

0

1

2

3

4

5

6

Obs

QPPQ NN WA

Fig. AIVb-1d Test Site & NN WA HCDN gage

75


Bioperiod 2 Spring Flood Negative Run-length Frequency Histograms

Q85 Threshold


0 5 10 15 20 25 30 35

Fre

que

ncy

0

2

4

6

8

10

12

14

0

2

4

6

8

10

12

14

Obds

QPPQ NN



0 10 20 30

Fre

que

ncy

0

2

4

6

8

10

12

14

0

2

4

6

8

10

12

14

Obs

QPPQ NN WA


Q95 Threshold


0 5 10 15 20

Fre

que

ncy

0

1

2

3

4

5

6

0

1

2

3

4

5

6

Obs

QPPQ NN



0 5 10 15 20

Fre

que

ncy

0

1

2

3

4

5

6

0

1

2

3

4

5

6

Obs

QPPQ NN WA


76


Bioperiod 3 Shad Spawning Negative Run-length Frequency Histograms

Q85 Threshold


0 5 10 15 20 25

Fre

que

ncy

0

2

4

6

8

0

2

4

6

8

Obds

QPPQ NN



0 10 20

Fre

que

ncy

0

2

4

6

8

0

2

4

6

8

Obs

QPPQ NN WA


Q95 Threshold


0 5 10 15

Fre

que

ncy

0

1

2

3

4

0

1

2

3

4

Obs

QPPQ NN



0 5 10 15

Fre

que

ncy

0

1

2

3

4

0

1

2

3

4

Obs

QPPQ NN WA


77


Bioperiod 4 GRAF Spawning Negative Run-length Frequency Histograms

Q85 Threshold


0 5 10 15 20 25

Fre

que

ncy

0

2

4

6

8

0

2

4

6

8

Obds

QPPQ NN



0 10 20

Fre

que

ncy

0

2

4

6

8

0

2

4

6

8

Obs

QPPQ NN WA


Q95 Threshold


0 5 10 15 20

Fre

que

ncy

0

1

2

3

4

5

0

1

2

3

4

5

Obs

QPPQ NN



0 5 10 15 20

Fre

que

ncy

0

1

2

3

4

5

0

1

2

3

4

5

Obs

QPPQ NN WA


78



Q85 Flow Threshold


0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Fre

que

ncy

0

2

4

6

8

10

12

0

2

4

6

8

10

12

Obds

QPPQ NN



0 10 20 30 40 50 60 70

Fre

que

ncy

0

2

4

6

8

10

12

0

2

4

6

8

10

12

Obs

QPPQ NN WA


Q95 Threshold


0 5 10 15 20 25 30 35 40 45 50 55 60

Fre

que

ncy

0

2

4

6

8

0

2

4

6

8

Obs

QPPQ NN



0 5 10 15 20 25 30 35 40 45 50

Fre

que

ncy

0

2

4

6

8

0

2

4

6

8

Obs

QPPQ NN WA


79


Bioperiod 6 Salmon Spawning Negative Run-length Frequency Histograms

Q85 Threshold


0 5 10 15 20 25 30 35 40

Fre

que

ncy

0

2

4

6

8

10

0

2

4

6

8

10

Obds

QPPQ NN



0 5 10 15 20 25 30 35 40

Fre

que

ncy

0

2

4

6

8

10

0

2

4

6

8

10

Obs

QPPQ NN WA


Q95 Threshold


0 5 10 15 20 25 30 35 40

Fre

que

ncy

0

1

2

3

4

5

6

0

1

2

3

4

5

6

Obs

QPPQ NN



0 5 10 15 20 25 30 35 40

Fre

que

ncy

0

1

2

3

4

5

6

0

1

2

3

4

5

6

Obs

QPPQ NN WA


80


Appendix V


Negative Run-length Histograms

and Run-length Duration Curves

Season 5

Test Site 2 - 5

81


Test Site 2:




1950-1990



1950-1990

82



Q85 Threshold


0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Fre

que

ncy

0

5

10

15

20

25

30

0

5

10

15

20

25

30

Obds

QPPQ NN

Fig. AV-1a. Test Site and NN HCDN gage


0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Fre

que

ncy

0

5

10

15

20

25

30

0

5

10

15

20

25

30

Obs

QPPQ NN WA

Fig. AV-1b Test Site and NN WA HCDN gage

Q95 Threshold


0 5 10 15 20 25 30 35 40 45

Fre

que

ncy

0

5

10

15

20

25

0

5

10

15

20

25

Obs

QPPQ NN

Fig. AV-1c. Test Site and NN HCDN gage


0 5 10 15 20 25 30 35 40 45

Fre

que

ncy

0

5

10

15

20

25

0

5

10

15

20

25

Obs

QPPQ NN WA

Fig. AV-1d Test Site and NN WA HCDN gage

83


Test Site 3:




1965-1990



1950-1990

84



Q85 Threshold


0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Fre

que

ncy

0

2

4

6

8

10

12

14

16

18

0

2

4

6

8

10

12

14

16

18

Obds

QPPQ NN



0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Fre

que

ncy

0

2

4

6

8

10

12

14

16

18

0

2

4

6

8

10

12

14

16

18

Obs

QPPQ NN WA


Q95 Threshold


0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34

Fre

que

ncy

0

5

10

15

20

25

30

0

5

10

15

20

25

30

Obs

QPPQ NN


Saco River near Conway, NH


0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34

Fre

que

ncy

0

5

10

15

20

25

30

0

5

10

15

20

25

30

Obs

QPPQ NN WA


85


Test Site 4:




1950-1976



1950-1982

86



Q85 Threshold


0 5 10 15 20 25 30 35 40 45 50

Fre

que

ncy

0

5

10

15

20

25

0

5

10

15

20

25

Obs

QPPQ NN



0 5 10 15 20 25 30 35 40 45 50

Fre

que

ncy

0

5

10

15

20

25

0

5

10

15

20

25

Obs

QPPQ NN WA


Q95 Threshold


0 5 10 15 20 25 30 35 40 45

Fre

que

ncy

0

2

4

6

8

10

12

14

16

0

2

4

6

8

10

12

14

16

Obs

QPPQ NN



0 5 10 15 20 25 30 35 40 45

Fre

que

ncy

0

2

4

6

8

10

12

14

16

0

2

4

6

8

10

12

14

16

Obs

QPPQ NN WA


87


Test Site 5:




1950-1977



1950-1990

88



Q85 Threshold


0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

Fre

que

ncy

0

5

10

15

20

0

5

10

15

20

Obs

QPPQ NN



0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

Fre

que

ncy

0

5

10

15

20

0

5

10

15

20

Obs

QPPQ NN WA


Q95 Threshold


0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

Fre

que

ncy

0

5

10

15

20

25

0

5

10

15

20

25

Obs

QPPQ NN



0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

Fre

que

ncy

0

5

10

15

20

25

0

5

10

15

20

25

Obs

QPPQ NN WA


89


Appendix VIa


Negative Run-length Duration Curves

Test Thresholds: Qcritical and Qrare

Seasons 1-6

Test Site 1:




1950-1976



1950-1976

90


Bioperiod 1 Over-Wintering Negative Run-length Duration Curves



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

50

0

10

20

30

40

50

Obs

QPPQ NN

Fig. AVIa-1a. Test Site & NN HCDN gage


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

50

0

10

20

30

40

50

Obs

QPPQ NN WA

Fig. AVIa-1b Test Site & NN WA HCDN gage

Rare Flow Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

0

10

20

30

40

Obs

QPPQ NN

Fig. AVIa-1c. Test Site & NN HCDN gage


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

0

10

20

30

40

Obs

QPPQ NN WA

Fig. AVIa-1d Test Site & NN WA HCDN gage

91


Bioperiod 2 Spring Flood Negative Run-length Duration Curves



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

50

0

10

20

30

40

50

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

50

0

10

20

30

40

50

Obs

QPPQ NN WA


Rare Flow Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

0

10

20

30

40

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

0

10

20

30

40

Obs

QPPQ NN WA


92


Bioperiod 3 Shad Spawning Negative Run-length Duration Curves



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

50

0

10

20

30

40

50

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

50

0

10

20

30

40

50

Obs

QPPQ NN WA


Rare Flow Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

0

10

20

30

40

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

0

10

20

30

40

Obs

QPPQ NN WA

Fig. AVIa-3d Test Site& NN WA HCDN gage

93


Bioperiod 4 GRAF Spawning Negative Run-length Duration Curves



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

2

4

6

8

10

12

14

0

2

4

6

8

10

12

14

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

2

4

6

8

10

12

14

0

2

4

6

8

10

12

14

Obs

QPPQ NN WA


Rare Flow Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

2

4

6

8

0

2

4

6

8

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

2

4

6

8

0

2

4

6

8

Obs

QPPQ NN WA


94


Bioperiod 5 Rearing and Growth Negative Run-length Duration Curves



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

20

40

60

80

0

20

40

60

80

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

20

40

60

80

0

20

40

60

80

Obs

QPPQ NN WA


Rare Flow Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

20

40

60

80

0

20

40

60

80

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

20

40

60

80

0

20

40

60

80

Obs

QPPQ NN WA


95


Bioperiod 6 Salmon Spawning Negative Run-length Duration Curves



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

0

10

20

30

40

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

0

10

20

30

40

Obs

QPPQ NN WA


Rare Flow Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

0

10

20

30

40

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

0

10

20

30

40

Obs

QPPQ NN WA


96


Appendix VIb


Negative Run-length Duration Curves

Test Thresholds: Q85 and Q95

Seasons 1-6

Test Site 1:




1950-1976



1950-1976

97


Bioperiod 1 Over-Wintering Negative Run-length Duration Curves

Q85 Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

50

0

10

20

30

40

50

Obs

QPPQ NN

Fig. AVIb-1a. Test Site & NN HCDN gage


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

50

0

10

20

30

40

50

Obs

QPPQ NN WA

Fig. AVIb-1b Test Site & NN WA HCDN gage

Q95 Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

5

10

15

20

25

30

0

5

10

15

20

25

30

Obs

QPPQ NN

Fig. AVIb-1c. Test Site & NN HCDN gage


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

5

10

15

20

25

30

0

5

10

15

20

25

30

Obs

QPPQ NN WA

Fig. AVIb-1d Test Site & NN WA HCDN gage

98


Bioperiod 2 Spring Flood Negative Run-length Duration Curves

Q85 Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

0

10

20

30

40

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

0

10

20

30

40

Obs

QPPQ NN WA


Q85 Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

5

10

15

20

0

5

10

15

20

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

5

10

15

20

0

5

10

15

20

Obs

QPPQ NN WA


99


Bioperiod 3 Shad Spawning Negative Run-length Duration Curves

Q85 Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

5

10

15

20

25

0

5

10

15

20

25

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

5

10

15

20

25

0

5

10

15

20

25

Obs

QPPQ NN WA


Q95 Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

2

4

6

8

10

12

14

0

2

4

6

8

10

12

14

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

2

4

6

8

10

12

14

0

2

4

6

8

10

12

14

Obs

QPPQ NN WA


100


Bioperiod 4 GRAF Spawning Negative Run-length Duration Curves

Q85 Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

5

10

15

20

25

0

5

10

15

20

25

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

5

10

15

20

25

0

5

10

15

20

25

Obs

QPPQ NN WA


Q95 Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

5

10

15

20

0

5

10

15

20

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

5

10

15

20

0

5

10

15

20

Obs

QPPQ NN WA


101



Q85 Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

20

40

60

80

0

20

40

60

80

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

20

40

60

80

0

20

40

60

80

Obs

QPPQ NN WA


Q95 Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

20

40

60

80

0

20

40

60

80

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

20

40

60

80

0

20

40

60

80

Obs

QPPQ NN WA


102


Bioperiod 6 Salmon Spawning Negative Run-length Duration Curves

Q85 Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

0

10

20

30

40

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

0

10

20

30

40

Obs

QPPQ NN WA


Q95 Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

0

10

20

30

40

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

0

10

20

30

40

Obs

QPPQ NN WA


103


Appendix VII


Negative Run-length Duration Curve Probability Plots

Season 5

Test Sites 2 - 5

104


Test Site 2:




1950-1990



1950-1990

105



Q85 Threshold


2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

20

40

60

80

0

20

40

60

80

Obs

QPPQ NN

Fig. AVII-1a. Test Site and NN HCDN gage


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

20

40

60

80

0

20

40

60

80

Obs

QPPQ NN WA

Fig. AVII-1b Test Site and NN WA HCDN gage

Q95 Threshold


2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

50

0

10

20

30

40

50

Obs

QPPQ NN

Fig. AVII-1c. Test Site and NN HCDN gage


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

50

0

10

20

30

40

50

Obs

QPPQ NN WA

Fig. AVII-1d Test Site and NN WA HCDN gage

106


Test Site 3:




1965-1990



1950-1990

107



Q85 Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

5

10

15

20

25

0

5

10

15

20

25

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

5

10

15

20

25

0

5

10

15

20

25

Obs

QPPQ NN WA


Q95 Threshold


2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

0

10

20

30

40

Obs

QPPQ NN



2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

0

10

20

30

40

Obs

QPPQ NN WA

Fig AVII-2d Test Site and NN WA HCDN gage

108


Test Site 4:




1950-1976



1950-1982

109



Q85 Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

50

0

10

20

30

40

50

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

50

0

10

20

30

40

50

Obs

QPPQ NN WA


Q95 Threshold


1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

50

0

10

20

30

40

50

Obs

QPPQ NN



1 2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

10

20

30

40

50

0

10

20

30

40

50

Obs

QPPQ NN WA


110


Test Site 5:




1950-1977



1950-1990

111



Q85 Threshold


2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

20

40

60

80

0

20

40

60

80

Obs

QPPQ NN



2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

20

40

60

80

0

20

40

60

80

Obs

QPPQ NN WA


Q95 Threshold


2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

20

40

60

80

0

20

40

60

80

Obs

QPPQ NN



2 5 10 20 30 50 70 80 90 95 98 99

nd

ay

0

20

40

60

80

0

20

40

60

80

Obs

QPPQ NN WA


112


Appendix VIII


95% Confidence Intervals Mean Negative Run-length Event Duration

Seasons 1-6

Test Site 1:




1950-1976



1950-1976

113


Bioperiod 1 Over-Wintering

95% C.I. of the Mean Number of Negative Run-length Event Duration


Eve

nt D

ura

tio

n (

days)

-4

-2

0

2

4

6

8

10

12

14

Fig. AVIII-1a. Test Site & NN HCDN gage


Eve

nt D

ura

tio

n (

days)

-4

-2

0

2

4

6

8

10

12

14

Fig AVIII-1b Test Site & NN WA HCDN gage

114


Bioperiod 2 Spring Flood



Eve

nt D

ura

tio

n (

days)

-5

0

5

10

15

20



Eve

nt D

ura

tio

n (

days)

-5

0

5

10

15

20


115


Bioperiod 3 Shad Spawning



Eve

nt D

ura

tio

n (

days)

0

2

4

6

8

10



Eve

nt D

ura

tio

n (

days)

0

2

4

6

8

10


116


Bioperiod 4 GRAF Spawning



Eve

nt D

ura

tio

n (

days)

-2

0

2

4

6

8

10

12



Eve

nt D

ura

tio

n (

days)

-2

0

2

4

6

8


117





Eve

nt D

ura

tio

n (

days)

0

5

10

15

20



Eve

nt D

ura

tio

n (

days)

0

5

10

15

20


118


Bioperiod 6 Salmon Spawning



Eve

nt D

ura

tio

n (

days)

0

5

10

15

20

25

30



Eve

nt D

ura

tio

n (

days)

0

5

10

15

20

25

30

35


119


Appendix IX


95% Confidence Intervals of the Mean Negative Run-length Duration

Season 5

Test Sites 2- 5

120


Test Site 2:




1950-1990



1950-1990

121



95% CI Interval of the Mean Run-length Duration


Eve

nt D

ura

tio

n (

days)

0

5

10

15

20

Fig. AIX-1a. Test Site and NN HCDN gage


Eve

nt D

ura

tio

n (

days)

0

5

10

15

20

Fig. AIX-1b Test Site and NN WA HCDN gage

Test Site 3:

122





1965-1990



1950-1990

123





Eve

nt D

ura

tio

n (

days)

0

2

4

6

8

10

12



Eve

nt D

ura

tio

n (

days)

0

2

4

6

8

10

12

14


124


Test Site 4:




1950-1976



1950-1982

125





Eve

nt D

ura

tio

n (

days)

0

5

10

15

20



Eve

nt D

ura

tio

n (

days)

0

5

10

15

20


126


Test Site 5:




1950-1977



1950-1990

127





Eve

nt D

ura

tio

n (

days)

0

5

10

15

20

25



Eve

nt D

ura

tio

n (

days)

0

5

10

15

20

25


a final report on the further assessment of the …...2018/08/26 · statistical probabilities and...

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