Calibrations: Static and Dynamic Sensor response: As stated above, the sensor is the ocean scientist and engineer's interface with the real world. Any sensor acts as a filter on the data it processes. The observer must understand these filter effects in order to be able to remove them and truly estimate the statistics of the environment. We will discuss these effects in the following sections on calibrations, the frequency response of the sensors and how to correct the spectra and series for their effects, and finally the limit imposed on measurements by the sensor noise itself. Static Calibrations: Everyone is aware that sensors must be calibrated against some standard in order that the results can be relied upon. However, some of the details as to how this is done are a bit vague. For example let us take the case of the temperature sensor on the CTD system used for vertically profiling the water column. It is calibrated in a temperature controlled water bath. The temperature of this bath is cooled by a water-cooling heat exchanger that constantly removed heat from the tank. A temperature controller measures the temperature of the bath with a thermistor, and puts heat into the water by an immersion heater to maintain the desired temperature. The water in the tank is will mixed by a stirring motor. This whole procedure is illustrated below for a calibration setup at Univ. New Hampshire. 55The temperature sensor or sensors to be calibrated are placed in this well mixed tank, and allowed to come to thermal equilibrium. A reference thermometer is placed with the sensors under calibration, and the readings from the reference thermometer and sensors being calibrated are recorded. The reference thermometer is regularly sent back to a national calibration facility that calibrates it with standards traceable to the National Institute of Standards and Technology. This reference thermometer is generally a platinum resistance thermometer, and with repeated calibrations accumulates a history on how it changes with time. In order to check its operation before each calibration, the reference thermometer is generally “standardized” in a triple-point-of-water cell to check one point in absolute temperature and a Gallium melt cell to check a second point. The triple point is defined in terms of the temperature where gas, water and ice phase all exist as 0.010,00 °C ±0.000,01 °C. The Gallium melt cell (29.7646°C) provides an upper point for oceanographic range of temperatures. The PRT is used to interpolate between these two points based on its calibration. We will discuss the temperature standard, currently the IPT90, when we discuss water properties, and temperature measurement. The actual temperature of the water is then calculated and plotted versus the output from each sensor. When a number of points at different temperatures have been taken, plotted, and appear consistent, the results are then fit to the functional form of the sensor. If the sensor were linear, then a least squares linear fit is done on the actual temperature and the sensor output, and the derived coefficients can then be used to normalize any data collected with the sensor. The least squares fitting removes some of the random statistical error associated with a single calibration point, and gives a smoothed, consistent summary of the calibration results. It is obvious that other functional forms can be used to fit the data. It is best to study the sensor's physical behavior, and choose a functional form that best represents the type of sensor being used, rather than just expand the calibration in a power series. As an example, the Vibrotron pressure sensor (used in early bottom pressure measurements) is best fit by the frequency output squared is a linear function of pressure P = A + B f². and not f. The Sea Bird temperature sensors used on moorings in the Gulf of Maine and on Georges Bank (which we will discuss in more detail below) was fit by the following relationship T[°C] = (A + B ln(F) + C ln2(F) + D ln3(F))-1 - 273.15 where F = f0/f, f is the sensor frequency, f0, A, B, C, and D are the calibration constants. The natural logarithms in this case take into account the kind of sensitivity of the thermistor used in the sensor. (See Sea Bird Electronics temperature sensor calibration on following page.) Calibration history: Calibration history is an important part of knowing data quality. Normally sensors are calibrated before and after each cruise. If a calibration record is maintained, and the sensors are not adjusted at calibration time, then the long-term drift of the sensors can be observed, and any sudden changes in behavior used to determine sensor problems before failure. Some of the Sea Bird temperature sensors have a 30-year calibration history that shows a smooth drift that decreases with time to less than 1 m° C per year at present. This means that I can believe the temperatures that the sensor sees to better than 1 m° C in absolute value. And the calibration history on the sensor gives me the information to make such a statement. This 56information is required to justify observations made in the field, and is generally summarized in a data quality or quality assurance document that we will examine in more detail later. 57Dynamic Calibrations or Frequency Response: A sensor is a filter that affects the frequency content of the data that passes through it. It is up to the experimentalist to make sure that these filtering effects are understood and do not effect the results that he is trying to obtain. To measure the frequency response of a sensor, one could input an impulse, measure the response, transform it and obtain the frequency response function. An impulse is a good input since it contains all frequencies. To see this, consider our gate function again δ(t) ≈ 1/τ Π(t/τ) ⊃ Sinc(fτ) = Sin(πfτ)/πfτ as τ -> 0, the gate function goes to an impulse. The first zero crossing of the SINC function occurs at f = 1/τ, where the Sin goes to zero. This is also observed to be the inverse of the length of the gate function, τ. So as τ goes to zero, the zero crossing moves to higher and higher frequency and the Sinc function broadens. See graph below for three different width gate functions and associated Sinc function. In the limit of a delta function, the Sinc function goes to constant function of