Convert a Pressure Reading to Depth of Water

i Introduction

For oceanic observations, the depth at which measurements are fabricated needs to exist determined. Usually oceanographers catechumen the measured pressure to musical instrument depth. The in situ pressure is the sum of the air pressure and the weight of water per unit area higher up the depth the measurement. The water weight can be found by integrating the production of the water density and gravitational acceleration through the water volume. Therefore, the conversion from force per unit area to water depth requires knowledge of the density of the local bounding main h2o and the gravitational acceleration. However, the density of sea water is a role of water temperature, salinity, and pressure level, which makes the conversion challenging.

One method currently used by the oceanography community was originally suggested about 40 years ago by Saunders and Fofonoff (1976). They developed an empirical formula to convert pressure to water depth using the hydrostatic equation and the Knudsen-Ekman Equation of Land (EoS) for sea water; all the same, they neglected the variation of density due to temperature and salinity and only considered the contribution from pressure (salinity is fix to 35 and the temperature to 0°C), while also taking into business relationship the variation in the gravitational acceleration which is a function of both latitude and water depth. Later, Saunders (1981) improved on Saunders and Fofonoff'due south (1976) method by adopting the EoS for seawater derived by Millero, Chen, Bradshaw, and Schleicher (1980). Saunders and Fofonoff 'due south (1976) method was further modified by Fofonoff and Millard (1983) using an improved EoS, which became the well-known United nations Educational, Scientific and Cultural Organization (UNESCO) algorithm.

To overcome the errors caused by neglecting the contributions of temperature and salinity in Saunders and Fofonoff's (1976) method, Leroy and Parthiot (1998) added a correction term. Based on the UNESCO algorithm, too temperature and salinity profiles, they provided 10 formulae for the correction term in different areas of the global bounding main. Assuming that the pressure sensor is accurate, this method can be used with an accuracy ameliorate than ±0.viii g in the open sea and better than ±0.2 m in most airtight basins. However, the method requires a lengthy adding.

The measurement of pressure is always influenced by the oceanic dynamic surround, such as waves, tide, and currents. Willumsen, Hagen, & Boge (2007) analyzed the effects of these factors on the measurement of water depth and suggested that the wave-induced pressure oscillations can be modelled as noise on the depth measurements fed into an aided inertial navigation system (AINS). By combining the superior AINS short-term estimates with the stable long-term estimates from the hydrostatic conversions, they filtered out the dynamic pressure level variations. Their results showed that there is an advantage in using AINS to obtain a smoothen and more correct depth estimate than the one given by a pressure level sensor.

In the present newspaper, a new method is introduced, which can be applied when a bottom-moored pressure sensor is available in add-on to the force per unit area measured by the musical instrument. Through fault analysis, the method provides a very simple formula for the calculation. The new method is introduced in Section two, and its fault assay is as well discussed in detail. In Department 3, the method is applied to observational information and compared with the results from Leroy and Parthiot's (1998) method. Section four contains a discussion and summary.

2 Methodology

Without because the accuracy of a pressure sensor, the pressure measured at the sea floor ( ; and the depth is , t is the measured time) is the sum of the atmospheric pressure at the sea surface ( ) and the weight of sea h2o per unit of measurement surface area in a higher place the bounding main floor, which tin can be expressed every bit (1)

where is the ocean surface elevation, z is the h2o depth, and and are sea h2o density and the acceleration due to gravity, respectively. The pressure at depth where an instrument (Audio-visual Doppler Current Profiler (ADCP), conductivity, temperature, depth (CTD) sensor, or any other musical instrument) is located can be expressed as (2)

Please annotation that is defined equally the depth relative to the mean ocean surface. Subtracting Eq. (2) from Eq. (one) yields (three)

The water depth can exist rewritten as (4)

where is the h2o depth of the musical instrument at , and is the vertical displacement of the musical instrument with respect to depth at . The ambient horizontal body of water current could exert an external force on the instrument and cause its horizontal motion that would consequence in a vertical displacement of the musical instrument when it is attached to a wire moored to the bottom.

Substituting Eq. (iv) into Eq. (iii) yields, (v)

When , Eq. (v) becomes (vi)

Subtracting Eq. (vi) from Eq. (5) yields, (seven) Considering the ho-hum flow near the body of water floor, the depth of the bottom-moored pressure sensor (which is a few metres from the bottom) can be considered to maintain a fixed depth (i.east., is constant). Assuming «T (i.e., the fourth dimension length of the measurement is much smaller than the time calibration (T) of the density variation in the subsurface), the showtime term on the right-hand side of Eq. (seven) can exist neglected. The body of water water density and the gravitational dispatch can be written as (eight) (9)

where and are the sea water density and the acceleration due to gravity, respectively, at depth . The second term on the right-hand side of Eq. (7) can exist approximated as, (10)

At a fixed location, is only a function of depth and increases at approximately i.092 × 10⁻⁶ 1000 s⁻² m⁻¹ (Fofonoff & Millard, 1983). According to the EoS of seawater, is a function of temperature, salinity, and depth (Millero et al., 1980). Within the vertical deportation of the musical instrument, which is generally of the club of 10 m or less, varies in a range from −10 to x kg m⁻ⁱⁱⁱ and varies in a range from −x^−four to ten⁻⁴ m s⁻². Compared with the first term on the right-hand side of Eq. (10), the last three terms can be estimated as (11) (12)

and (13)

Therefore, neglecting the last iii terms leads to a relative fault of less than one%, which comes mainly from Eq. (12); then, the accented error is of the guild of 0.one m given that the vertical displacement of an instrument is of the order of 10 thou. Equation (ten) can be rewritten equally (xiv)

Substituting Eq. (14) into Eq. (vii) yields (xv)

Therefore, (16)

In Eq. (16), and can be written equally (17)

and (18)

where = 1020 kg chiliad⁻ⁱⁱⁱ and = 9.8 one thousand southward⁻² are the sea h2o density and gravitational dispatch, respectively. Substituting Eqs (17) and (18) into the second term on the correct-hand side of Eq. (16) and using the first-order Taylor expansion yields (19)

In the ocean, varies in a range from −xx to 20 kg thou⁻³ and varies in a range from −0.ane to 0.1 m s⁻² (Gill, 1982). In Eq. (19), the estimates of the first-club terms can be expressed equally (20) (21)

and (22)

Therefore, again neglecting both the variations in density and the acceleration due to gravity leads to a relative mistake less than three%, which is mainly contributed past Eq. (twenty). And then the absolute fault is of the order of 0.three m given that the vertical displacement of an musical instrument is of the order of x k. Equation (16) can be rewritten as (23)

The initial depth ( ) tin can be obtained from Leroy and Parthiot's (1998) method or adamant at the start of the instrument deployment. Thus, from Eq. (23), the depth ( ) of the instrument at time t can be calculated given the pressures at that depth from the musical instrument and the bottom-moored sensor at time t and the initial time t₀ . It is also noted that whatever mistake with the force per unit area measurement is not amplified but linearly presented in the formula.

3 An application to a field experiment

A field experiment was conducted on the Myanmar coast (92°37′11″E, 19°03′20″N) in December 2012. A mooring organization was set up with an acoustic release, a tidal approximate with a built-in high accuracy pressure sensor (XR420-PARO), and a downwards-looking ADCP (WHS 75 KHz with a built-in pressure sensor) were mounted to the nylon cablevision at 5, 10, and 1833 m, respectively, from the bottom end of the cable where a ii-ton metal weight was attached. The acoustic release is used for advice with the system. The organisation was released into the ocean water at a location where the h2o depth is approximately 1900 thou, which was measured using an echo sounder. The ii-ton metallic weight is sufficiently heavy to keep the line moored to the bounding main floor. A total of twelve deep-sea drinking glass spheres were mounted forth the cable to provide buoyancy in the water (come across Fig. ane for the schematic diagram of the mooring organization). Yet, equally discussed in Section ii, a stiff horizontal oceanic current could tilt the cable with respect to the vertical, which might result in the vertical displacement of the instruments relative to their original positions. Therefore, the mark on the cable for the ADCP location can only be used as a reference for the depth where the measurement was taken. An authentic depth of the ADCP must be calculated from the pressure level measured by the force per unit area sensor.

Fig. 1 Schematic diagram of the mooring organization.

The time series of the pressures obtained at the ADCP depth (-h) ( ) and the tidal gauge depth (about the bottom) ( ) are shown in Fig. two.

Fig. 2 Fourth dimension series of pressures at the bottom from a tidal gauge (a pressure sensor) (upper panel) and at the depth where the ADCP is attached (lower panel).

In Eq. (23), t ₀ was fix to 0000 UTC 6 December 2012 and obtain , which is the initial h2o depth of the ADCP, past employing Leroy and Parthiot'south (1998) method. It should exist pointed out that unlike Leroy and Parthiot's method that uses data from a unmarried force per unit area meter, the present method involves the difference between information from two pressure meters; therefore, information technology removes the variation in the sea surface. Since Leroy and Parthiot'southward (1998) method is used for the initial depth, the time series of the ADCP depth, , obtained from Eq. (23) (shown as a red line in the top panel of Fig. iii) includes the ocean surface peak at the initial time, especially tidal signals; therefore, it is fourth dimension dependent. For comparison, the time serial of the ADCP depth from Leroy and Parthiot's method is also presented (the blue line in the top panel of Fig. 3). The results from the two methods are very like. The difference between the two results is plotted in the middle panel of Fig. 3 and is seemingly explained by the sea surface variation, dominated by the barotropic tidal oscillation. Using a twoscore h low pass filter, it can be seen that the difference betwixt the two methods is approximately 0.05 k (lesser panel of Fig. 3). Notwithstanding, the divergence can vary with the initial time chosen. In general, the batropic tidal signals can exist extracted from the information recorded by the lesser force per unit area sensor and can be easily removed.

Fig. 3 Time series of (tiptop panel) the ADCP depths using Leroy and Pathiot's (LP; 1998) method and the present method and their differences (middle console) before and (lower panel) after applying a xl h low pass filter.

four Discussion and summary

In this study, a new method is proposed to convert measured force per unit area to h2o depth when a bottom-moored pressure sensor is available. The conversion equation is based on a perturbation analysis. Based on the theoretical derivation, when an additional data source is available (a lesser force per unit area sensor), the conversion of pressure level to depth becomes very simple and practical. The present method needs the initial depth of the instrument, which can usually exist obtained when the in situ experiment is initially gear up up by marking the location on the cablevision/wire/rope where the instrument is placed. In the preceding section, for comparing purposes, the Leroy and Parthiot (1998) method was used to gauge initial depth. Therefore, a one-fourth dimension error associated with this method is carried into the adding. Equally demonstrated past the theoretical assay, the fault associated with the method itself comes from two sources: temporal variation in deep water (deeper than the instrument) and variation in gravitational acceleration with instrument displacement. These two sources contribute almost four% of the error relative to the vertical displacement of the instrument. When the vertical displacement of an instrument is on the order of 10 g, the absolute fault is on the order of 0.4 m. The method is simple and easy to implement. In this written report, this method was applied to data from a field experiment on the Myanmar coast in December 2012.

Information technology should be noted that when Leroy and Parthiot's (1998) method is used to approximate the initial depth of the musical instrument, the ocean surface elevation acquired by the barotropic tides is included. The tidal signals can exist removed through a tidal point extraction.

Indeed, the applicability of the electric current method is dependent on the availability of the bottom pressure. Although such dependence limits the wide application of the method, bottom pressure gauges are being deployed more oftentimes in deep-ocean observational systems.

It should be pointed out that any instrument carries its ain error. The apply of ane additional musical instrument could add together additional instrumental error in the conversion calculation. The instrumental fault is categorized as a different type in error analysis in any measurement arrangement, which is parallel to the error introduced past a method. From Eq. (23), it can exist seen that the musical instrument mistake has a simple linear relationship with the method error; in other words, if the fault of the pressure judge (instrumental error) is available, the total error in the measurement organization is simply the sum of the method error and the instrumental fault.

humesmanch1937.blogspot.com

Source: https://www.tandfonline.com/doi/full/10.1080/07055900.2015.1074883

Convert a Pressure Reading to Depth of Water

i Introduction

2 Methodology

3 An application to a field experiment

Published online:

Published online:

Published online:

four Discussion and summary

0 Response to "Convert a Pressure Reading to Depth of Water"

Post a Comment

Iklan Atas Artikel

Iklan Tengah Artikel 1

Iklan Tengah Artikel 2

Iklan Bawah Artikel