The featured image is a representation of an electrical field. It is from the Smith-Root, Inc. GPP manual and is used with permission from SRI.

Prior blogs have mentioned and discussed electrical fields including their measurement and how to visualize them. Let this be the first in a series of blogs which delve deeper into the topic of electrical fields and provide useful equations for describing and predicting field intensity and field size. The primary purpose of this blog is to explain the rationale for using applied current – instead of voltage or power – for standardization across water conductivity.

Electrofishing is the use of electricity to capture fish. This is accomplished by generating an electrical field in water to produce in fish a capture-prone response such as forced swimming (including taxis or attraction to the anode), inhibited swimming or immobilization. According to the power transfer theory of electrofishing, a threshold level of electrical power must be transferred from the water to the fish to produce such a response in the fish (Kolz 1989). The power measure in the water and in fish is termed power density in μW/cc (= μW/cm^{3}) or microwatts per cubic centimeter.

To adjust for changes in water conductivity requires standardizing by power according to the power transfer theory of electrofishing (Kolz 1989). The term standardizing by power has led to some confusion among fisheries biologists who use electrofishing. What is being standardized for any water conductivity is the size of the electrical field, i.e. the effective fishing zone around the anodes so that capture efficiency is the same for any water conductivity value. For a given electrode arrangement and electrode immersion depth, the distribution (shape) of the electrical field around the electrodes will remain constant. The magnitude or intensity of the field will depend upon some measure of the electricity applied from the electrofisher and upon the water conductivity. The logical inference is that the preferred electrical measure from the pulsator to standardize by power is power in watts, i.e. μW/cc in the water should most closely relate to watts from the electrofisher. This may not be the case. To understand the distribution of power density in water requires knowledge of electrical fields.

The electric field is a vector field with both magnitude and direction (Halliday et al. 1997). Further, fields are considered a form of matter with energy and momentum (Ohanian 1994). The field intensity, or voltage gradient, in volts per centimeter (V/cm), *E*, is a function of electrical charge divided by the surface area of the medium, air or water, at some distance from an electrode. This dispersion of a field from an electrode is most easily described and quantified for an isolated sphere. Thus, for an isolated sphere:

*E* = q’/(4πr^{2}εₒ) where q’ is electrical charge, 4πr^{2 }is the surface area of a sphere and of the medium at some distance from the sphere, and εₒ is the permittivity constant. This equation is for a static charge situation. How does it apply to electrofishing? Electrical current, I, is a measure of electrical charges moving past a surface per time; it is measured in amperes or amps, A. The notation I is from a French term for current intensity. A field measure of current is current density, J, in amperes per centimeter squared.

From Novotny and Priegel (1974), the current distribution of an isolated sphere has a spherical symmetry; the current density at any point is radial and has a value J = I/(4πr^{2}) in A/cm^{2}. Thus, the current density at the sphere surface or of the water surface at some radius r from the sphere is equal to the applied current I divided by the surface area as defined by the radius r and by the formula for the surface area of a sphere of radius r. Field intensity *E* = J/σ where σ is ambient water conductivity in Siemens per centimeter, S/cm. Thus, E = I/(4πr^{2}σ) in V/cm. In electrofishing, ambient water conductivity generally is so low that σ is multiplied by one million and reported in μS/cm, Ca.

A few more terms are needed to explain electrical fields more fully. System resistance, Rs, in ohms equals voltage in volts divided by current in amperes when the electrodes are deployed as for typical fishing. Rs is determined at an ambient water conductivity for a given body of water at that temperature; ambient conductivity is a function of water temperature. The R_{100} value is the resistance of the electrodes if they were in water of 100 μS/cm ambient conductivity. R_{100} = (Rs x Ca)/100. SAr is the Surface Area in cm^{2} at some distance, or radius, r from the electrode center, or from the electrode array center in the case of multiple droppers from a Wisconsin ring or spider array. *E*r is the field intensity or voltage gradient in V/cm at some distance r from the anode or array center. From the above measures and their relationships, it can be shown that the field intensity,

*E*r = (I x 1,000,000)/(SAr x Ca) or (V x 10,000)/(SAr x R_{100}). Electrode changes most likely will cause changes in both SAr and R_{100} values.

Field intensity is a function of either current, surface area and ambient conductivity or of voltage, surface area and the R_{100} value. If the electrodes for a given electrofishing unit – boat, backpack, barge, etc. – are constant in all cases, then one should be able to standardize by power using either voltage, current or their product, power. However, if there are changes made to electrodes, or if electrodes differ among a fleet of boats, for example, then there should be less variation in the field intensity if one standardizes the electrical field using electrical current. That is the inference. Two examples are given below to test that hypothesis. One is a carefully controlled measurement of electrical fields in an experimental tank; the other is an estimate of fishing thresholds from four boats at a lake. Both involve electrofishing electrode arrays for which the fields are more complex than for a single sphere.

Kolz (1993) carefully measured voltage profiles (volts at distance from electrodes) for a variety of electrode types and sizes. His voltage at distance data were carefully estimated from digital images of his graphs using a digital measurement program and then each data set was fitted to a shifted power regression with an offset using Excel Solver.

Figure 1. Example of volts by distance data (open circles) re-created from graphs in Kolz (1993). The line is the shifted power regression with offset fit to the data.

The first derivatives of those regressions were used to calculate the field intensity (V/cm) at 90 cm from each electrode array center. These were radial field intensities in the horizontal plane. For this exercise, the electrodes were a 58-cm Wisconsin ring with 4 rod droppers of 2.54 cm diameter stock, a 58-cm ring with 6 rods of 2.54 cm diameter, and a 30.5-cm ring with 4 rods of 0.64 cm diameter; all rods were 60 cm long. The field intensities at 90 cm were calculated based on 300 volts for each array, again at 5 amps for each array, and again at 1500 watts for each array. Coefficients of variation were 26.0, 3.6 and 12.0 percent for the constant voltage, constant current and constant power groups, respectively.

Figure 2. Field intensity (V/cm) by distance calculated by using the first derivative of the volts by distance regression equation. Dropper number, four vs six, had little effect on the field intensity profile whereas Wisconsin ring diameter had a much larger effect. The field intensity at 90 cm varied substantially when the same voltage was applied to each array.

Figure 3. Similar graph to above except the field intensity at 90 cm was similar when applied current was constant. Thus, the electrode configuration had little effect on field intensity, especially beyond about 70 cm from the array center.

Figure 4. Similar to two preceding graphs except field intensity at 90 cm varied somewhat when applied power was constant. Power is the product of voltage and current. Field intensity varied little when current was held constant, so the variation in this graph likely originated primarily from the variation associated with voltage.

Fishing thresholds were determined for four boats at a boat electrofishing course in Redding, California. The boats varied in length (4.3 to 5.5 m) and width, whether hulls were painted, and if they had an auxiliary set of cathode droppers at the bow; three of the four had a cathode skirt. All pulsators were SRI GPP units (three GPP 5.0, one GPP 7.5), and all used the boat hulls as cathodes and SRI spider arrays as anodes. Thus, the differences in electrodes primarily were in the cathodes, though the distance of the anodes from the cathodes differed, as well as the distance between the anodes. Fishing threshold voltage and current were measured with an oscilloscope and a current probe. Thresholds were calculated in terms of voltage, current and power. Coefficients of variation were 18.8, 8.0 and 26.0 percent, respectively. More information about this comparison of boat thresholds is at: electrofishing.net/2016/05/21/boat-fleet-fishing-thresholds/.

For the lab study and the fishing results, using applied current produced less variation in field intensity and in fishing thresholds. There are other practical reasons for using current not only for typical electrofishers but especially for the Paupier boat. The above discussion has considered either a single sphere or more typical anode arrays used for electrofishing. For a typical two-boom electrofishing boat, the wiring circuit can be classified as series-parallel in which the two boom arrays are wired in parallel. Actually, each dropper is in parallel with the others, but we typically consider just the two boom arrays in parallel with each other. Their resistances can be combined mathematically into one equivalent resistance and that is in series with the cathode. In a parallel circuit, each branch has the same applied voltage, but the current is divided among or between the branches (the two boom anode arrays in this case) depending upon their relative resistances. For electrofishing boats, the two anode array resistances ideally are similar, and therefore the current to each array should be similar. The above equation for field intensity in relation to current is most appropriate for each array, and current to each array can be easily measured with a current probe connected to an oscilloscope or with a current clamp. Conversely, the voltage applied to each array is the same, but the voltage drop for each array is a function of its resistance and applied current. The resistance of each array can be calculated for a typical electrofishing boat with two anode arrays from the applied voltage and from the current to each array plus a measure of the boat hull resistance; estimation of the latter requires an extra set of measurements and a calculation. The calculation is more accurate if the current to the two anode arrays is the same or nearly so. It is easier and more accurate to measure current to each anode array than it is to estimate the voltage drop across an array. And current to an electrode array relates directly to the resultant electrical field for that array.

Based upon physics and upon measurements of fields from electrodes and upon fishing thresholds from electrofishing boats, using current as the measure to standardize effective fishing zones is preferred over voltage or power if electrodes are changed or if they vary among a fleet of boats…and they will vary among a fleet of boats. Future blogs will further explain the concept of electrical fields and how to estimate their sizes.

Halliday, D., R. Resnick and J. Walker. 1997. Fundamentals of physics, 5th ed. John Wiley & Sons, NY, 984pp.

Kolz, A. L. 1989. A power transfer theory for electrofishing. U. S. Fish and Wildlife Service Technical Report 22:1-11.

Kolz, A. L. 1993. In-water electrical measurements for evaluating electrofishing systems. U. S. Fish and Wildlife Service Biological Report 11.

Ohanian, H. C. 1994. Principles of physics. W. W. Norton & Company, NY, 915 pp.