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AND ..JUt.. ANALYSIS OP DATA TO DETERMINE LOCATION ,Qf. __ •• Jll!t 19 l DSS File PP962-9-0092/0l-OSC Prepared for Tidal Division Department of Fisheries and Oceans Bedford Institute of Oceanography P.O. Box 1006 Dartmouth, N.S. B2Y 4A2 July 1989 DISCOVERY CONSULTANTS LIMITED P.O. Box 599 Wolfville, N.S. BOP !XO DISCOVERY CONSULlT-lNTS LTD. P.O. Box 599, Ublfvtlle, N.S. OOP lXD (902) 542-7988 13 July 1989 Mr. S.T. Grant Head, Tidal Division Canadian Hydrographic Service Bedford institute of Oceanography P.O. Box 1006 Dartmouth, N.S. B2Y 4A2 Dear Mr. Grant, We are pleased to submit our Final Report on the determination of the upstream limit of tidal influence in the Little Southwest Miramichi River. We have enjoyed working on this assignment. Yours truly, DISCOVERY CONSULTANTS LIMITED D.L. Dewolfe President ------Ocean Science • Tides • Applied Aeseorth • Planning • Project M:inagement • ~Assessment ------Table of Contents EXECUTIVE SUMMARY 1.0 INTRODUCTION 1 1.1 Project Objectives 1 1.2 Format of the Report 1 2.0 FIELD PROGRAM 2 2.1 Overview 2 2.2 Site Selection and Installation . 2 2.2 Recovery 3 2.3 Summary 3 3.0 DATA PROCESSING AND ANALYSIS 5 3.1 Introduction 5 3.2 Data Reduction. 5 3.3 Time Series Plots and Remarks • • • • • 6 3.4 Analysis 7 3.4.1 Harmonic Analysis ...... • 13 3.4.2 Spectral Analysis . . . . • 13 3.5 Results ...... • 13 3.5.1 Basic Statistics . 13 3.5.2 Harmonic Tidal Constituents . . . . • . 14 3.5.3 Variance at Tidal Frequencies • 15 3.5.5 Spectral Plots ...... • 16 3.5.4 Highest Monthly Tides . 18 3.6 Discussion 18 4.0 SUMMARY and CONCLUSIONS ...... •...•..•.. 20 5.0 Appendix A. Harmonic Analyses . . • • • . • . . . . • • • 21 EXECUTIVE SUMMARY This report provides the results of a study to determine the location of the upstream influence of the tide in the Little Southwest Miramichi River, New Brunswick. The study was conducted by Discovery Consultants Limited for Fisheries and Oceans Canada, Atlantic Region. Six bottom mounted tide gauges were deployed for a period of one month in the vicinity of the confluence of the Little Southwest Miramichi River and the Northwest Miramichi River. The data sets obtained from the instruments were analyzed to determine the presence of a tidal signal. It was found that there was a tide at the two locations furthest downstream, no tide at the three locations furthest up stream and a very small tide at the location between the two. The tide is virtually cut off by Mitchell's Rapids, about 1 km upstream from the mouth of the Little Southwest Miramichi River. The head of the tide was determined to lie within a 0.5 km section of the Little Southwest Miramichi River known as the Oxbow. 1.0 INTRODUCTION 1.1 Project Objectives The primary objectives of this investigation are to: o conduct a field measurement program to measure the tide 1n the Little Southwest Miramichi River in the vicinity of the upstream limit of tidal influence for a one month period; o analyze the results of the measurement program to determine the location in the river beyond which no tidal influence occurs. 1.2 Format of the Report The work conducted to address the the study objectives is suumarized 1n the present report. The report is organized as follows: o the introduction sets out the objectives; o section 2 describes the field program to deploy and recover the instruments; o section 3 presents a detailed analysis of the data and presents the results of the data interpretation; o the final section provides a number of conclusions. 1 2.0 PIBLD PROGRAM 2.1 Overview The project commenced in May of 1989 to determine the upstream limit of tidal influence on the Miramichi River in New Brunswick. The focus of the project was along the Little Southwest Miramichi River in the vi cinity of Red Bank Indian Reserves 7 & 4. A one month tidal record was collected at six sites along the river in order to measure spring tides and maximum spring run-off. Submersible tide gauges were placed in the river in the vicinity of the suspected head of tide and above and below the suspected head of tide on 13 and 14 May 1989. They were subsequent ly collected about one month later on 10 June 1989. 2.2 Site Selection and Installation Unmarked submersible tide gauges ~ere installed along the river on 13 and 14 May 1989 using a SCUBA diver. The six sites were chosen for easy concealment and retrieval, as most of the area is populated. The chan nels between the islands at the juncture of the Little SW Miramichi and the NW Miramichi were too shallow to safely place an instrument. Where it was possible gauges were installed directly from the shore; the re mainder were installed by boat. The gauges were placed upright on the bottom of the river and were supported by rocks. Shoreline references were used to locate the position of each gauge for easy retrieval. Depth, bearing, and distance from shore was measured for each site at the time of installation. The water levels in the Little Southwest Miramichi River in the area above the estimated head of tide were about a metre above SWilller level, and there was a substantial current, estimated to be about 2 metres/sec ond. This strong flow presented problems with diving, so the instru ments were placed in locations along the shore with less current (back waters). Location IF 1 Installed from shore in a small sheltered cove on the south side of the Miramichi River between South Bsk and Cassilis. 2 Location IF 2 Installed by boat on the east side of the Northwest Mira michi River across from Indian Island near Tozers Is. Location # 3 Installed by boat on the western side of the Northwest Miramichi River across from McHughs Island, near the northern boundary of I.R IF 7. Location 4F 4 Installed from the northern shore immediately downstream of the Oxbow in the Little Southwest Miramichi River. Location IF 5 Installed from shore approximately 0. 6 km downstream from Johnsons Park on the Little Southwest Miramichi River, on the north side of the river. Location IF 6 Installed from shore immediately below the footbridge approximately 0.6 km upstream from Johnsons Park, on the north side of the Little Southwest River. 2.2 Recovery The tide gauges were retrieved on 10 June 1989. All gauges were re trieved routinely except for the instrument in location # 1. This in strument had been located by a 11 year old boy and eventually was turned in to the Newcastle RCMP, from whom it was recovered. It had a much shortened record, and had been opened and turned off. 2.3 Summary A swmnary table showing location and time information for the gauges is shown below. Inst. Gauge Serial 4> A depth start time end time # (N) (W) (m) 1 336 46 51'. SN 65 43' .3W 2.5 14/13/05/89 12/20/05/89 2 998 46 56' .9N 65 49'.3W 2.5 8/14/05/89 9/10/06/89 3 995 46 57' .4N 65 49' .aw 3.5 10/14/05/89 10/10/06/89 4 996 46 57' .3N 65 50' .9W 1.5 12/14/05/89 7/10/06/89 5 335 46 57' .4N 65 51'. 6W 2.0 16/13/05/89 8/10/06/89 6 997 46 57'. lN 65 52' .4W 2.0 17/13/05/89 9/10/06/89 3 ';-.. Indian Point ••• ••• Indian Reserve I ~> _.. ---· ' .·· -_... _...... -· '/ .-· --- .... -- ------..... ------_,,._ ... --- Locat;on map showing the locat;on of the s;x stations observed for the Head of Tide Project --· in the Little Southwest Miremichi River _:.- --· -·· .... --- Head of Tide 0 I 2 I<"" - 4 3.0 DATA PROCESSING AND ANALYSIS 3.1 Introduction This section describes briefly the data reduction, analysis and inter pretation of the water level data from the six instruments. The data sets from the six water level gauges were augmented by the surface atmospheric pressure record from CPB Chatham. 3.2 Data Reduction The data tapes were translated by the tidal section at the Bedford In stitute of Oceanography and the raw translated data was placed on the BIO mainframe computer. It was then converted to a human readable for mat and transferred to to a PC for further processing and analysis. The atmospheric pressure during the period of observation is required because it must be subtracted from the total pressure record recorded by the water level gauges to obtain water level. It was converted to the standard hourly heights format in units of millibars •. As previously mentioned, the pressure recorder at location # 1 was re moved early. The data record from this instrument was not only short ened, but also appears to have had changes in the characteristics of the pressure sensor that resulted in what appears to be a shift of the ' ze- ro' value of about 2 metres. The water level data was converted to units of pressure and checked for bad data values. None of the records needed correction. The barometric pressure signal was then removed from the gauge total pressure, yielding a water level, in centimetres, for each station location. Adjustment was then made to the datum by adjusting the lowest reading in each data set to be equal to zero. 5 3.3 Time Series Plots and Remarks Time series plots of the data are shown on the next three pages. Some general remarks about them follow. Plot # 1 shows the tide at location # 1. Although short, it clearly shows that there is a tide at this location. Plots It 2 and It 3 show the tide at locations It 2 and It 3. The data is clean, and is clearly tidal. The magnitude of the tidal signal at lo cation It 3 is somewhat diminished when compared to the data in plot It 2. Plots It 4, 5 and 6 show the tide at locations It 4,5 and 6 in the Little Southwest Miramichi. A striking characteristic of these plots is the absence of a visual tidal signal, except for a very brief period in the record at location # 4. This exception will be discussed in § 3.5. The plots clearly show the diminishing elevation of the spring run-off over the month, as well as a temporary increase in the level due to a 10 mn rainfall on June 1-2. The slight 'wiggliness' in the data is the result of instrument 'noise' and is caused by the 1 cm recording accuracy and by pressure fluctuations caused by the current over the pressure samp ling port. Plot It 7 shows the tide at location # 2 (dotted curve) superimposed on the data for station # 4. This plot shows that the bottom of the tidal curve at location It 2 follows the level in location it 4. This is be cause # 2 has been truncated because of the high level of the river due to the spring run-off. Plot # 8 shows a 'close-up' of the water level at both stations 2 and 4 during the period of the highest tides of the month. The tidal signal at station 4 is evident on June 5 and 6, the 2 highest tides of the month. The purpose of this plot is to show 2 small tidal 'bumps' on the station# 4 record. It is further discussed in§ 3.5.5. Plot it 9 shows the predicted tide at Newcastle for the same period of 6 time. Visual comparison of this plot with the plots for locations 1, 2, and 3 show that the observed tide has the bottom truncated by the spring run-off and by the slope of the river. Plot # 10 shows the barometric pressure at CPB Chatham, about 40 km from the area of investigation. 3.4 Analvsis The purpose of the analysis of this data is to determine whether or not there is a tidal signal present in each of .the records. In searching for a tidal signal in a water level record, emphasis has been placed on determining where the tidal motion was 'perceptible' • This definition lends itself to discussion as to what is meant by per ceptible. The Heritage Illustrated Dictionary defines perceptible as being Capable of being perceived; discernible by the senses of the mind. In our case, we must use analytical tools and some definitions to make an assessment as to what constitutes no tidal motion. Two common tools can be used to make this assessment. The first is the standard tidal (or harmonic) analysis which is in world-wide use to determine the values of the amplitudes and phases of the numerous tidal components that can exist in a tidal record. The second is spectral analysis, which calculates the variance, or average magnitude of the fluctuations, of the water level data and estimates the amount present at various frequencies, e.g. tidal frequencies. These were both used, and are discussed in the following sub-sections. 7 PLOTS 1 & 2 "J:RAttlCHl 2 4 e e 11 12 "lRAttlCHl 13 1115 l'T 19 21 23 31 2 4 8 e 11 12 MAY ~UNE 8 PLOTS 3 & 4 "IRAl1ICHI CHEAD OF TJ:DE> • 3 13 115 17 18 21 23 27 .. 31 2 e e 11 12 "IRN'IICHI CHl!AD OF TIDE> • 4 13 115 17 18 21 e 11 12 MAY JUNE 9 PLOTS 5 & 6 "IRAt'IICHI 211.11 181.111 12•···· E u ee.eee 41.111 •••• 13 17 18 21 23 - 12 t'IIRMICHJ:
MAY ~UNE
10 PLOTS 7 & 8
KlfMHlCHl <~ OF TlDI!> STNS 4 & 2
13 12 MAY ~UNE
KlRMlCHl OEAD OF TlDI!> 2 & 4 cot1PAR1SOH
2 3 e JUNE
11 PLOTS 9 & 10
13 us 17 18 21 23 31 2 • e 1• 12
13 115 17 18 21 23 31 2 • 9 11 12 MAY JUNE
12 3.4.1 Harmonic Analysis
All of the records were analyzed with the standard tidal analysis soft ware, used by various agencies around the world such as the Canadian Hydrographic Service. The results are listed in Appendix A, two pages per station. The first page shows the basic information resulting from the analysis and the second shows the summary of the results, together with the calculation of the lunitidal intervals and ratios. Section 3.5 discusses the results of the harmonic analyses.
3.4.2 Spectral Analysis
Spectral analysis can be used to make an assessment of the variability of the data record and how this variability is divided among the various frequencies that are present in the data. Slow changes in water level induced by changes in meteorological conditions would show up as vari ability at a low frequency of about 1 cycle per 3 or 4 days, while the tides would show up as variability at a frequency of 1 and 2 cycles per day. The same form of analysis is also used to make an assessment of the relationship between two data records at specific frequencies. These analyses were both performed and Section 3. 5 discusses the re sults.
3.5 Results
3.5.1 Basic Statistics
The following table swmnarizes the basic statistics of the data sets.
Location f~ obs min. max. mean (cm) (cm) (cm)
1 167 0 153 55.0 2 649 0 199 84. 7 3 648 0 169 57.1 4 643 0 82 24.1 5 665 0 110 35.2 6 666 0 85 29.1
13 3.5.2 Harmonic Tidal Constituents
The principal results obtained from the harmonic tidal analysis, and shown in their entirety in Appendix A, are sumnarized below in Table 1. The values for P , 0 , K and S for station 1 are not shown, due to the t t t 2 shortness of the record.
Table 1. The amplitude and phase of the principal tidal con- stituents. The amplitude is rounded to the nearest centi- meter, the phases are in degrees. Where the amplitudes are less than 1 cm, the phase is meaningless and is not shown.
diurnal semi-diurnal
p 0 K N M s t t t 2 2 2
Loe. amp ph amp ph amp ph amp ph amp ph amp ph
1 ------12 180 49 195 - - 2 7 276 21 250 21 282 10 186 40 200 9 277 3 6 282 19 253 19 288 8 186 34 201 9 277 4 0 - < 1 268 0 - 0 - 0 - 0 - 5 0 - < 1 267 0 - 0 - 0 - 0 - 6 0 - < 1 266 0 - 0 - 0 - 0 -
A number of features of the tide are evident from the table. At locat ions I~ 1, 2 and 3 all the constituents have a tidal signal. The ampli - tudes of all of the constituents diminish as the tide progresses from location 1 to 3. The only evidence of a tidal signal at locations 4 to 6 is an amplitude of < 1 cm for the 0 constituent. This amplitude is t small enough that that the amplitude 1s close to the recording threshold of the instrument. The phases show a progression up the river for lo cations 1 to 3, as would be expected.
The analysis results shown in Appendix A consist of 2 pages per station. For locations 2 to 6, the bottom of the second of the two pages lists the tidal ranges. For stations 4, 5 and 6, these figures indicate the attempt by the analysis program to fit the fort-nightly tide to the
14 changes in river elevation due to run-off. These values are meaningless in the context of a periodic tide at these locations. Their inclusion 1s for the sake of completeness.
3.5.3 Variance at Tidal Frequencies
The percentage of the total variance which occurs at tidal frequencies for the record observed at each station is shown in Table 2. The re sults, computed by spectral analysis of the data, are shown for three frequency bands - low (> 3 days; river run off), diurnal (daily tide) and semi-diurnal (lunar tide). Por locations 1 to 3, the tidal frequen cies account for over 85% of the variance in the record, and the low frequency 6% or less. The data is clearly tidal • For locations 4, 5 .and 6 the variance due to the tidal signal is less than 0.5%.
Table 2. The variance of the records expressed as a per- centage of the total record variance at the low frequency (>3 days) and the diurnal and semi-diurnal frequencies.
% Variance in Location low freq diurnal semi-diurnal total tidal (%) (%) (%) (%) 1 4.6 22.2 67.2 89.4 2 3.5 40.7 51.1 91.8 3 6.2 40.5 48.0 88.5 4 99.2 0.4 0.0 0.4 5 99.4 0.3 0.0 0.3 6 99.1 0.4 o.o 0.4
The relationship between location # 2 and each of the upstream stations can be expressed by 2 parameters for each frequency band; the gain and the phase. The gain is the fraction of the signal at the output (3, 4,5, 6) divided by the signal at the input (2). The phase is represent ative of the time lag between the input and the output. In Table 3, it can be seen, for example, that at the diurnal tidal frequency ( 1 cycle /day) the signal at location 3 1s 88% that at location 2.
15 Table 3. The relationship between location 2 (input) and each of the upstream stations (output), at the tidal frequencies.
diurnal semi-diurnal input output gain phase gain phase
2 3 0.88 5 .86 0.3 2 4 < .01 - .00 - 2 5 < .00 - .oo - 2 6 < .01 - .oo -
The reduction in the gain at location 4, 5 and 6 to a value of less than 0.01 of the signal to that of location 2 is significant. If location 2 has a tide of 2 metres, then the up-stream locations 4, 5, and 6 would have a tidal variation of < 2 cm. Over the short distances involved, it shows that the tide is effectively choked in the 2.5 km or so that se parates them.
3.5.4 Spectral Plots
Standard plots of the spectrum (plots 11 - 15) in units of the log of the variance vs. frequency are shown below. In the plots for records 2 and 3 the tide is represented by the two peaks at 0.4 and 0.8 cycles per hour. It should be noted that the Y axis scale is logarithmic; a peak at -3 has 100 times as much variance or energy as a peak at -5. Plots 13, 14 and 15 show no significant variability at the tidal frequencies.
16 PLOT 11 PLOT 12
Spectrum of Kiramichi Station # 2 Spectrum of Miramichi Station # 3 -1 -1 ~--3 ~~ ! _., I -e i -u .! -13
-15-1-...... -.-~..-.~-.-.,L-,~-T--~---''-r--...:-._.;...~ 0.0 OJ. OA
PLOT 13 PLOT 14
Spectrum al Miramichi Station # .to Spectrum of Miramichi station # 5
-1 -1 -3 ~ --3 ~ t' ~ ~ ~_., _., I l I -9 I -9 i -11 ~ -11 .! -13 .! -13 -15-l--...-:.1¢:~;:::::::::~ocr=:;:::....-.-.....-...... -.-.....-..-.~~ -15.l.-~:::(.!::;=~--..,...... ~.-~~.-~~ 0.0 0.1 o.o 0.1 DA
PLOT 15
Spectrum of Miramichi station # 6
17 3.5.5 Highest Monthly Tides
Plot 8 on page 11 shows a close-up of the water levels at stations 2 and 4 during the period 3 to 8 June. The record for location # 4 has been offset by 200 cm for clarity. Note that the 2 highest tides of the month occur on June 5 and 6, and at those times there is a small 'spike' in the record for II 4. The general wiggliness in the II 4 record has a magnitude of 1 cm (due to instrument resolution), but the 2 peaks in question have an amplitude of 2 cm. A spectral analysis was performed on this section of the record. It showed the following:
Frequency: diurnal Input: location 2 Output: location 4 Gain: (2 to 4) 0.012 Phase (2 to 4) 6.2 degrees Coherence 0.99
The coherence (a measure of the linear. correlation between the 2 com ponents at a given frequency; analogous to the square of the usual cor relation coefficient) was significantly high. This implies that the unexplained variation between the two data sets is in the order of 1%. The phase difference is equivalent to about 25 minutes in time.
3.6 Discussion
The analysis of the data clearly shows a number of features of the tide in the area.
As expected, the range of the tide diminishes between stations 2 and 3. The magnitude of this reduction is principally due to the slope of the river between the two points.
The spring run-off is very evident in all the records. Plot 7 illus trates this very well by superimposing the data for locations 2 and 4. It can be seen that the low waters of record # 2 follows the river ele-
18 vation of record # 4.
There is a dramatic reduction in the tide between station 2 and station 4. For all of the month with the exception of 2 days at the time of two of the highest tides of the year, there was no tide recorded at station 41 4.
It would be useful to take a more detailed look at the relationship between the high tides at location 2 and the tide at location 4. The tide for location 2 was predicted at hourly intervals for a period of a year, and the number of hours and percentage of time that the tide was above a specified elevation was calculated. For elevations of 185 cm and greater, the results are:
elevation (cm) 41 hours % of the year
185 84 1.0 190 57 0.7 . ··-·--·-·-·-· 19 5 ·-·-·-·-·-·· ··-·-· 29 ·-·-·· ··-·-·-·-· 0.3 ·-·-·-·-·-·· 200 12 0.1
Noting that the tide appeared at location 41 4 only when the level at location # 2 was greater than 195 cm, it can be concluded that the tide will appear at location II 4 about 29 hours of the year, or about 0 .1% of the time.
If it is assumed that the spring run off is not quite finished, but has (say) 10 cm yet to drop, then the above table shows that the tide will appear at # 4 about 1.0% of the time.
Given the slope of the river in the vicinity of II 4, it 1s very unlikely that the tide will progress much more than several hundred metres above # 4, at any stage of the tide or run-off.
19 4.0 SUMMARY and CONCLUSIONS
A tidal signal is present at locations 1, 2 and 3 at all times.
There is no tide at the upstream locations 5 and 6.
The accuracy of observation and data reduction is estimated to be about ± 1 cm. The data is rounded to the nearest cm.
At location # 4, there is a diurnal tidal signal with a 2 cm. range during the two highest tides of the month. The presence of this tidal signal will be a function of both the height of the tide in the down stream section of the river and the stage of the river due to the river discharge. For a tide of 195 cm at the mouth of the Little Southwest Miramichi and a river level equivalent to that present on June 5 and 6, the tide in the river would progress to no more than 100 JDetres past location # 4. Under the lowest river level and the highest tides of the year, it is estimated that the tide would progress to less than 0.5 km above station # 4, given the slope of the river.
There is a rapids known as Mitchells Rapids (see location map} about mid-way between the entrance to the Little SW Miramichi and location # 4. Given the dramatic reduction in the tidal signal in traversing this portion of the river, it is clear that the rapids choke off the tidal signal and let only the highest tides pass further up river.
It is considered that the head of tide lies within a 0.5 km section of the river, in the Oxbow, and indicated on the location map by the hat ched area.
20 Appendix A Tidal Analysis Ver 2.20 Date: 21/06/89
Stn. Miramichi Head Tide # 1 Start = 14h 13/ 5/89 I~ obs. = 167 End = 12h 20/ 5/89 # Analyzed = 167 Midpoint = lh 17/ 5/89 Separation = 1.00 Number of valid data = 167 Mean = 0.55 RMS error = 0.21 Units = CM S.D. = 0.34 Matrix Con. = 0.98 Nodal = y Inference data for 2000 Lower Escuminac
Inf erred Prom Ratio Phase diff, Pl Kl 0.316 6.3 2N2 MU2 0.500 22.4 NU2 N2 0.219 13.2 N2 M2 0.249 14.7 K2 S2 0.266 1.1
No Name Frequency ampl. ph. al gl
1 zo 0.0000000 0.5501 0.00 0.5501 o.oo 2 Pl 0.0415526 0.0301 228.06 Inf fr Kl 0.0298 357.52 3 Kl 0.0417807 0.0952 234.36 0.1049 70.85 4 N2 0.0789993 0.1218 180.15 Inf fr M2 0.1179 252 .57 5 M2 0.0805114 0.4894 194.85 0.4742 83.85 6 M3 0.1207671 0.0290 236.39 0.0276 69.61 7 M4 0.1610228 0.0511 347.01 0.0480 125.02 8 2MK5 0.2028036 0.0094 120.90 0.0097 95.39 9 M6 0.2415342 0.0091 330.74 0.0083 357.76 10 3MK7 0.2833149 0.0081 19.59 0.0081 243.09 11 MB 0.3220456 0.0028 192.05 0.0025 108.08 12 MlO 0.4025570 0.0061 103.92 0.0052 268.95
21 Tidal Analysis Ver. 2.20 Date: 21/06/89
Zone Lat Long Length C.T. Miramichi Head Tide # 1 AST 4657 6543 6 589 North West Days MOYR Units = CM Reference Station - 2000 Lower Escuminac Name Amp! Phase Name Amp! Phase Name Amp! Phase zo 0.550 0.0
Pl 0.030 228.1 Kl 0.095 234.4
N2 0.122 180.1 M2 0.489 194.8
M3 0.029 236.4
M4 0.051 347.0
2MK5 0.009 120.9
M6 0.009 330.7
22 Tidal Analysis Ver 2.20 Date: 21/06/89
Stn. Miramichi Head Tide # 2 Start = 13h 14/ 5/89 I~ obs. = 643 End = 7h 10/ 6/89 I~ Analyzed = 643 Midpoint = 22h 27/ 5/89 Separation = 1.00 Number of valid data = 643 Mean = 0.85 RMS error = 0.17 Units = CM S.D. = 0.42 Matrix Con. = 0.91 Nodal = y Inference data for 2000 Lower Bscuminac
Inf erred Prom Ratio Phase diff. Pl Kl 0.316 6.3 2N2 MU2 0.500 22.4 NU2 N2 0.219 13.2 N2 M2 0.249 14.7 K2 S2 0.266 1.1
No Name Frequency amp!. ph. al gl
1 zo 0.0000000 0.8447 360.00 0.8447 360.00 2 MSP 0.0028219 0.0351 342.97 0.0351 157.89 3 01 0.0387307 0.2124 249.74 0.2458 264.76 4 Pl 0.0415526 0.0675 275.75 Inf fr Kl 0.0668 100.92 5 Kl 0.0417807 0.2136 282.05 0.2353 152.74 6 N2 0.0789993 0.0998 185.78 Inf fr M2 0.0966 35.40 7 M2 0.0805114 0.4009 200.48 0.3885 84.61 8 S2 0.0833333 0.0926 276.57 0.0928 336.64 9 K2 0.0835615 0.0246 275.47 Inf fr S2 0.0314 196.56 10 M3 0.1207671 0.0194 77 .60 0.0185 83.50 11 SK3 0.1251141 0.0280 95.27 0.0309 26.04 12 M4 0.1610228 0.0505 348.83 0.0475 117 .08 13 MS4 0.1638447 0.0131 84.57 0.0127 28.77 14 S4 0.1666667 0.0041 292.39 0.0042 52.53 15 2MK5 0.2028036 0.0066 184.68 0.0068 183.63 16 2SK5 0.2084474 0.0034 265.12 0.0037 255.96 17 M6 0.2415342 0.0038 114.96 0.0034 127.35 18 2MS6 0.2443561 0.0081 213.49 0.0076 41.82 19 2SM6 0.2471781 0.0049 343.93 0.0047 348.20 20 3MK7 0.2833149 0.0026 122.27 0.0026 5.35 21 MB 0.3220456 0.0027 306.08 0.0024 202.59 22 MlO 0.4025570 0.0014 1.40 0.0012 142.03
23 Tidal Analysis Ver. 2.20 Date: 21/06/89
Zone Lat Long Length C.T. Miramichi Head Tide II 2 AST 4656 65.49 26 589 North West Days MOYR
Units = CM Reference Station - 2000 Lower Escuminac
Name Ampl Phase Name Amp! Phase Name Ampl Phase
zo 0.845 360.0
MSP 0.035 343.0
01 0.212 249.7 Pl 0.067 275.7 Kl 0.214 282.0
N2 0.100 185.8 M2 0.401 200.5 S2 0.093 276.6 K2 0.025 275.5
M3 0.019 77.6 SK3 0.028 95.3
M4 0.051 348.8 MS4 0.013 84.6 S4 0.004 292.4
2MK5 0.007 "184.7 2SK5 0.003 265.1
M6 0 .004 115 .o 2MS6 0.008 213.5 2SM6 0.005 343.9
AGE M2/S2 AGE Kl/01 DL-SL DL SD DL/SD DL+SD 76 4.31 32 1.01 162 0.31 0.42 0.73 0.73
Mean Tide Times and Heights 1910 1.59 708 1.01 1300 0.57 208 0.28 HHW LHW HLW LLW
Large Tides Ranges 2.00 0.20 1.31 1.80 HHW LLW MT LT
24 Tidal Analysis Ver 2.20 Date: 21/06/89
Stn. Miramichi Head Tide ti 3 Start = 13h 14/ 5/89 ti obs. = 643 End = 7h 10/ 6/89 ti Analyzed = 643 Midpoint = 22h 27/ 5/89 Separation = 1.00 Number of valid data = 643 Mean = 0.57 RMS error = 0.16 Units = CM S.D. = 0.37 Matrix Con. = 0.91 Nodal = y
Inference data for 2000 Lower Escuminac
Inf erred From Ratio Phase diff. Pl Kl 0.316 6.3 2N2 MU2 0.500 22.4 NU2 N2 0.219 13.2 N2 M2 0.249 14.7 K2 S2 0.266 1.1
No Name Frequency ampl. ph. al gl
1 zo 0.0000000 0.5676 0.00 0.5676 0.00 2 MSF 0.0028219 0.0682 51.59 0.0682 226.52 3 01 0.0387307 0.1909 253.33 0.2209 268.35 4 Pl 0.0415526 0.0590 281. 74 Inf fr Kl 0.0584 106.92 5 Kl 0.0417807 0.1868 288.04 0.2058 158.74 6 N2 0.0789993 0.0851 186.04 Inf fr M2 0.0824 35.67 7 M2 0.0805114 0.3419 200.74 0.3314 84.87 8 S2 0.0833333 0.0874 277.12 0.0876 337.19 9 K2 0.0835615 0.0233 276.02 Inf fr S2 0.0297 197.11 10 M3 0.1207671 0.0158 108.29 0.0150 114.19 11 SK3 0.1251141 0.0257 114.07 0.0284 44.84 12 M4 0.1610228 0.0418 358.81 0.0393 127.07 13 MS4 0.1638447 0.0078 71.13 0.0076 15.33 14 S4 0.1666667 0.0028 318.80 0.0028 78.94 15 2MK5 0.2028036 0.0152 205.27 0.0158 204.23 16 2SK5 0.2084474 0.0028 264.25 0.0031 255.09 17 M6 0.2415342 0.0034 118.63 0.0031 131.01 18 2MS6 0.2443561 0.0035 250.78 0.0033 79.11 19 2SM6 0.2471781 0.0029 51.68 0.0028 55.95 20 3MK7 0.2833149 0.0001 40.41 0.0001 283.49 21 MB 0.3220456 0.0011 336. 60 0.0009 233.11 22 MlO 0.4025570 0.0009 289.97 0.0008 70.61
25 Tidal Analysis Ver. 2.20 Date: 21/06/89
Zone Lat Long Length C.T. Miramichi Head Tide 4~ 3 AST 4657 6550 26 589 North West Days MOYR Units = CM Reference Station - 2000 Lower Escuminac Name Ampl Phase Name Ampl Phase Name Ampl Phase zo 0.568 0.0
MSF 0.068 51.6
01 0.191 253.3 Pl 0.059 281. 7 Kl 0.187 288.0
N2 0.085 186.0 M2 0.342 200.7 S2 0.087 277 .1 K2 0.023 276.0
M3 0.016 108.3 SK3 0.026 114.1
M4 0.042 358.8 MS4 0.008 71.1 S4 0.003 318.8
2MK5 0.015 205.3 2SK5 0.003 264.3
M6 0.003 118.6 2MS6 0.004 250.8 2SM6 0.003 51. 7
AGE M2/S2 AGE Kl/01 DL-SL DL SD DL/SD DL+SD 76 3.93 35 0.98 166 0.27 0.36 0.75 0.64
Mean Tide Times and Heights 1916 1.22 710 0.70 1254 0.32 213 0 .10 HHW LHW HLW LLW
Large Tides Ranges 1.57 -0.03 1.12 1.60 HHW LLW MT LT
26 Tidal Analysis Ver 2.20 Date: 21/06/89
Stn. Miramichi Head Tide It 4 Start = 13h 14/ 5/89 It obs. = 643 End = 7h 10/ 6/89 It Analyzed = 643 Midpoint = 22h 27/ 5/89 Separation = 1.00 Number of valid data = 643 Mean = 0.24 RMS error = 0.21 Units = CM S.D. = 0.22 Matrix Con. = 0.91 Nodal = y Inference data for 2000 Lower Escuminac
Inf erred Prom Ratio Phase diff. Pl Kl 0.316 6.3 2N2 MU2 0.500 22.4 NU2 N2 0.219 13.2 N2 M2 0.249 14.7 K2 S2 0.266 1.1
No Name Frequency ampl. ph. al gl 1 zo 0.0000000 0.2368 360.00 0.2368 360.00 2 MSF 0.0028219 0.1304 289.48 0.1304 104.40 3 01 0.0387307 0.0084 268.21 0.0097 283.23 4 Pl 0.0415526 0.0013 47.70 Inf fr Kl 0.0012 232.88 5 Kl 0.0417807 0.0040 54.00 0.0044 284.70 6 N2 0.0789993 0.0008 222.81 Inf fr M2 0.0008 72.43 7 M2 0.0805114 0.0032 237.51 0.0031 121.63 8 S2 0.0833333 0.0033 118.07 0.0033 178.14 9 K2 0.0835615 0.0009 116.97 Inf fr S2 0.0011 38.06 10 M3 0.1207671 0.0027 149.20 0.0025 155.11 11 SK3 0.1251141 0.0025 89.58 0.0027 20.35 12 M4 0.1610228 0.0020 47.52 0.0018 175.78 13 MS4 0.1638447 0.0016 306.58 0.0015 250.77 14 S4 0.1666667 0.0021 122.69 0.0021 242.82 15 2MK5 0.2028036 0.0013 11.87 0.0014 10.82 16 2SK5 0.2084474 0.0013 81. 71 0.0015 72.61 17 M6 0.2415342 0.0024 221.34 0.0022 233.73 18 2MS6 0.2443561 0.0022 66.11 0.0021 254.44 19 2SM6 0.2471781 0.0018 257.81 0.0018 262.08 20 3MK7 0.2833149 0.0014 174.18 0.0014 57.26 21 MS 0.3220456 0.0015 357.60 0.0013 254.12 22 MlO 0.4025570 0.0009 176.77 0.0008 317.41
27 Tidal Analysis Ver. 2.20 Date: 21/06/89
Zone Lat Long Length C.T. Miramichi Head Tide II 4 AST 4657 6551 26 589 North West Days MOYR
Units = CM Reference Station - 2000 Lower Escuminac
Name Ampl Phase Name Ampl Phase Name Ampl Phase
zo 0.237 360.0
MSF 0.130 289.5
01 0.008 268.2 Pl 0.001 47.7 Kl 0.004 54.0
N2 0.001 222.8 M2 0.003 237.5 S2 0.003 118.1 K2 0.001 117 .o
M3 0.003 149.2 SK3 0.002 89.6
M4 0.002 47.5 MS4 0.002 306.6 S4 0.002 122.7
2MK5 0.001 11.9 2SK5 0.001 81.8
M6 0.002 221.3 2MS6 0.002 66.1 2SM6 0.002 257.8
AGE M2/S2 AGE Kl/01 DL-SL DL SD DL/SD DL+SD 241 1.00 146 0.50 217 0.01 o.oo 2.01 0.01
Mean Tide Times and Heights 1845 0.25 945 0.22 HHW LHW HLW LLW
Large Tides Ranges 0.26 0.22 0.03 0.04 HHW LLW MT LT
28 Tidal Analysis Ver 2.20 Date: 21/06/89
Stn. Miramichi Head Tide II 5 Start = 13h 14/ 5/89 II obs. = 643 End = 7h 10/ 6/89 II Analyzed = 643 Midpoint = 22h 27/ 5/89 Separation = 1.00 Number of valid data = 643 Mean = 0.33 RMS error = 0.22 Units = CM S.D. = 0.25 Matrix Con. = 0.91 Nodal = y Inference data for 2000 Lower Escuminac
Inferred From Ratio Phase diff. Pl Kl 0.316 6.3 2N2 MU2 0.500 22.4 NU2 N2 0.219 13.2 N2 M2 0.249 14.7 K2 S2 0.266 1.1
No Name Frequency ampl. ph. al gl
1 zo 0.0000000 0.3260 360.00 0.3260 360.00 2 MSF 0.0028219 0.1567 286.78 0 .1567 101. 71 3 01 0.0387307 0.0092 266.58 0.0107 281.60 4 Pl 0.0415526 0.0019 52.70 Inf fr Kl 0.0018 237.87 5 Kl 0 .0417807 0.0059 59.00 0.0065 289.70 6 N2 0.0789993 0.0009 232.57 Inf fr M2 0.0009 82.20 7 M2 0.0805114 0.0036 247.27 0.0035 131.40 8 S2 0.0833333 0.0041 96.78 0.0041 156.85 9 K2 0.0835615 0.0011 95.68 Inf fr S2 0.0014 16.77 10 M3 0.1207671 0.0024 141.22 0.0023 147.13 11 SK3 0.1251141 0.0020 82.09 0.0022 12.86 12 M4 0.1610228 0.0017 54.73 0.0016 182.98 13 MS4 0.1638447 0.0023 284.26 0.0022 228.45 14 S4 0.1666667 0.0022 131.91 0.0022 252.05 15 2MK5 0.2028036 0.0013 42.47 0.0014 41.43 16 2SK5 0.2084474 0.0016 86.56 0.0018 77 .40 17 M6 0.2415342 0.0025 218.23 0.0023 230.62 18 2MS6 0.2443561 0.0031 78.32 0.0029 266.65 19 2SM6 0.2471781 0.0022 259.20 0.0021 263.47 20 3MK7 0.2833149 0.0018 186.80 0.0018 69.88 21 MB 0.3220456 0.0014 357.06 0.0012 253.57 22 MlO 0.4025570 0.0015 159.73 0.0013 300.37
29 Tidal Analysis Ver. 2.20 Date: 21/06/89
Zone Lat Long Length C.T. Miramichi Head Tide # 5 AST 4657 6552 26 589 North West Days MOYR Units = CM Reference Station - 2000 Lower Escuminac Name Ampl Phase Name Ampl Phase Name Ampl_ Phase zo 0.326 360.0
MSF 0.157 286.8
01 0.009 266.6 Pl 0.002 52.7 Kl 0.006 59.0
N2 0.001 232.6 M2 0.004 247.3 S2 0.004 96.8 K2 0.001 95.7
M3 0.002 141.2 SK3 0.002 82.1
M4 0.002 54.7 MS4 0.002 284.3 S4 0.002 131.9
2MK5 0.001 42.5 2SK5 0.002 86.6
M6 0.002 218.2 2MS6 0.003 78.3 2SM6 0.002 259.2
AGE M2/S2 AGE Kl/01 DL-SL DL SD DL/SD DL+SD 210 1.00 152 0.67 244 0.01 0.01 1.89 0.02
Mean Tide Times and Heights 1849 0.34 949 0.31 HHW LHW HLW LLW
Large Tides Ranges 0.34 0.30 0.03 0.05 HHW LLW MT LT
30 Tidal Analysis Ver 2.20 Date: 21/06/89
Stn. Miramichi Head Tide ti 6 Start = 13h 14/ 5/89 ti obs. = 643 End = 7h 10/ 6/89 ti Analyzed = 643 Midpoint = 22h 27/ 5/89 Separation = 1.00 Number of valid data = 643 Mean = 0.27 RMS error = 0.18 Units = CM S.D. = 0.20 Matrix Con. = 0.91 Nodal = y Inference data for 2000 Lower Bscuminac
Inferred Prom Ratio Phase diff. Pl Kl 0.316 6.3 2N2 MU2 0.500 22.4 NU2 N2 0.219 13.2 N2 M2 0.249 14.7 K2 S2 0.266 1.1
No Name Frequency ampl. ph. al gl
1 zo 0.0000000 0.2702 360.00 0.2702 360.00 2 MSF 0.0028219 0.1232 290.57 0.1232.105.50 3 01 0.0387307 0.0072 266.29 0.0084 281.31 4 Pl 0.0415526 0.0012 56.70 Inf fr Kl 0.0012 241.87 5 Kl 0.0417807 0.0038 63.00 0.0042 293.70 6 N2 0.0789993 0.0005 232.15 Inf fr M2 0.0005 81.77 7 M2 0.0805114 0.0022 246.85 0.0021 130.98 8 S2 0.0833333 0.0023 102.91 0.0023 162.98 9 K2 0.0835615 0.0006 101.81 Inf fr S2 0.0008 22.90 10 M3 0.1207671 0.0018 146.10 0.0018 152.00 11 SK3 0.1251141 0.0019 87.49 0.0020 18.26 12 M4 0.1610228 0.0013 30.03 0.0012 158.29 13 MS4 0.1638447 0.0018 283.20 0 .0017 227 .40 14 S4 0.1666667 0.0020 132.52 0.0020 252.66 15 2MK5 0.2028036 0.0009 36.82 0.0009 35. 77 16 2SK5 0.2084474 0.0014 90.10 0.0015 80.94 17 M6 0.2415342 0.0017 214.34 0.0016 226.72 18 2MS6 0.2443561 0.0025 75.26 0.0023 263.59 19 2SM6 0.2471781 0.0020 250.17 0.0019 254.44 20 3MK7 0.2833149 0.0014 195.93 0.0014 79.01 21 MS 0.3220456 0.0009 340.04 0.0008 236.55 22 MlO 0.4025570 0.0012 158.04 0.0010 298.68
31 Tidal Analysis Ver. 2.20 Date: 21/06/89
Zone Lat Long Length C.T. Miramichi Head Tide # 6 AST 4657 6553 26 589 North West Days MOYR
Units = CM Reference Station - 2000 Lower Escuminac
Name Ampl Phase Name Ampl Phase Name Ampl Phase
zo 0.270 360.0
MSP 0.123 290.6
01 0.007 266.3 Pl 0.001 56.7 Kl 0.004 63.0
N2 0.001 232.2 M2 0.002 246.9 S2 0.002 102.9 K2 0.001 101.8
M3 0.002 146.1 SK3 0.002 87.5
M4 0.001 30.0 MS4 0.002 283.2 S4 0.002 132.5
2MK5 0.001 36.8 2SK5 0.001 90.1
M6 0.002 214.3 2MS6 0.002 75.3 2SM6 0.002 250.2
AGE M2/S2 AGE Kl/01 DL-SL DL SD DL/SD DL+SD 216 1.00 157 0.57 221 0.01 o.oo 2.57 0.01
Mean Tide Times and Heights 1800 0.28 900 0.26 HHW LHW HLW LLW
Large Tides Ranges 0.29 0.25 0.02 0.03 HHW LLW MT LT
32