SR50 programming notes for CR1000

description of sensor

The SR50 emits an audible pulse of sound and measures the interval of time until an echo of the pulse is detected. Directed down from a height above the ground, the SR50 is used here to measure the distance between the sensor and the surface of the bare ground or the accumulated snow pack.

The SR50 is a ``smart sensor with onboard processing, and interfaces to the datalogger using the serial SDI12 protocol. Various commands are supported, but for our purposes the ``M or ``M1 commands are key. Both commands cause the sensor to take several readings and return the average distance to the target; the latter command additionally returns a ``quality value.

The SR50 directly measures time, but returns distance; its onboard time-to-distance calculation assumes nominal air conditions, including a temperature of 0C (273.15K). A correction should be made to the sensor's output distance to account for the actual ambient air temperature. (Other factors which might affect the speed-of-sound in air are not corrected for, e.g., atmospheric pressure or relative humidity, but are presumably negligible...)

existing CR1000 programming for Bullen and Foothills projects

The sensor is read once per minute using the ``M command, and including a multiplier of 100 to convert output from m to cm:

     SDI12Recorder(DT,SR50_CNTRL,0,"M!",100.0,0)

The distance corrected for ambient air temperature:

     TCDT = DT*SQR((AT+273.15)/273.15)

The presumed snow depth is calculated by subtracting the measured and temperature-corrected distance from the fixed sensor height, which is measured during site visits and entered into the program:

     SD = SD_Ht-TCDT

The SD snow depth value is logged as an average of the 1-minute measurements every hour in the HrlyAtms output table, and once per day in the Daily table. In addition, the DT raw distance (not temperature-corrected) is output as an average in the DailyRaw table.

proposed CR1000 programming changes

The sensor is read once per minute using the ``M1 command:

     SDI12Recorder(SR50,SR50_CNTRL,0,"M1!",100.0,0)

This instruction outputs two values into the ``SR50 array variable, which is further expanded into ``SR50_cm for distance and ``SR50_Q for quality. (In addition, an alias is provided for ``DT for output in the DailyRaw table.)

The temperature-corrected distance is also converted to a negative value, reflecting the fact that it is directed *down*:

     SR50_tc = -SR50_cm*SQR((AT+273.15)/273.15)

The previous snow depth calculation and data output tables are not changed, with the ``SD value averaged in the HrlyAtms and Daily tables:

     SD = SD_Ht+SR50_tc

New programming is added, first skipping further processing if either the raw distance or quality value is zero:

     if (SR50_cm <> 0) AND (SR50_Q <> 0) then

The sensor quality value is used to derive a quality weighting factor using an ad hoc and arbitrary function, with the goal of placing higher confidence in the data when the quality is between 162 and 210, and lower confidence for greater values:

         qf = 162 ^ 2 / SR50_Q ^ 2

A wind weighting factor is defined for accounting for sensor problems in high winds, but is not yet used:

         wf = 1

The above weighting factors are applied to a filter time constant which is used to implement a simple digital low-pass filter. Three different time constants are used, 1 hour, 4 hours, and 12 hours, to smooth the temperature-corrected data over those intervals.

The time constants are hard-coded in the program to go along with the named filter variables, SR50_f1h, SR50_f4h, and SR50_f12h, which are output in the new ``SR50 data table.

The weighted 1-hour time constant is factored by the 1-minute measurement scan to derive a working fraction x:

         x = qf * wf * 60 / 3600  1 hour time constant

The filter operation consists of taking 1/x'th of the current measurement and 1/(1-x) of the previous filtered value and storing it as the new filtered value:

         SR50_f1h = SR50_tc * x + SR50_f1h * (1 - x)

The fraction x is adjusted to represent the additional 4- and 12-hour time constants, and the corresponding filtered values are updated:

         x = x / 4  4 hour time constant
         SR50_f4h = SR50_tc * x + SR50_f4h * (1 - x)

         x = x / 3  12 hour time constant
         SR50_f12h = SR50_tc * x + SR50_f12h * (1 - x)

     endif

APPENDIX: information on quality numbers from the SR50 manual

The SR50 quality numbers seem like they should be useful, but it is not clear how they are derived (i.e., in the sensor's processor) nor exactly what they represent.

From section 5.0 (source paragraph expanded):

   Target quality numbers can also be recorded when using the SDI-12
   or ASCII output option.

   The quality numbers provide the user with an indication of the
   measurement certainty.

   The quality numbers can vary from 162 to 600.

   A quality number between 162 and 210 indicates that the SR50 detected
   a solid target.

   A number between 210 and 300 is an indication that the target is
   not definitive ...

   ... and a number between 300 and 600 is an indication that the target
   is of poor quality (see section 3.0 for possible causes).

   Though quality numbers of 210 to 600 indicate that the target was
   not clearly definitive, it does not mean that the measurement was
   inaccurate.

   It is only an indication that the SR50 detected a target of poor
   quality.

   Consideration should be given when interpreting data with high
   quality numbers.

From section 3.0:

   Numbers lower than 210 are considered to be measurements of good
   quality.  A value of zero however, indicates a reading was not
   obtained. Numbers greater than 300 indicate that there is a degree
   of uncertainty in the measurement. Causes of high numbers include:
   ·     the sensor is not perpendicular to the target surface
   ·     the target is small and reflects little sound
   ·     the target surface is rough or uneven
   ·     the target surface is a poor reflector of sound (low density snow)
   It is not necessary to make use of the quality numbers but they
   can provide additional information such as an indication of surface
   density in snow monitoring applications.

APPENDIX: digital filter

The digital filter implemented above is the simplest type of infinite impulse response filter, and is equivalant to an analog low-pass filter consisting of a single resistor and a capacitor.

The ``infinite part of the name reflects the fact that each measurement (or ``impulse) going into the filtered value remains there, albeit with diminished influence over time.

This simple filter has exponential response, so that the impact of any individual measurement decays exponentially over time. Since only a small portion of the noisy input data is ``accumulated in the stored filtered value, even large diversions have little impact. Conversely, if the noisy input data roughly approximates the ``actual or ideal input value, that ideal value will be reinforced continously and will dominate the stored value.

A consequence of the filter operation is that a step change in the input value, e.g., perhaps caused by a physical adjustment to the sensor height, will appear gradually in the stored filter value. After one time constant period, 1-e^-1 or about 63% of the step change will be reflected in the filter value, and it will approach the new value asymptotically over time.

APPENDIX: weighted time constants

It is observed that the SR50 can produce ``noisy output, rather than the ideal clean data that would be preferred. To a large extent the noise signal should be filtered away by the digital filter implemented in the program, but we're also attempting to make use of the SR50 `quality number to influence the data processing and interpretation.

The SR50 quality value as defined is somewhat fuzzy, consisting of some arbitrary number ranges with different meanings. In the above program, we've attempted to use the quality to derive a weighting factor which should be close to 1 when in the ``good range, smaller in the ``not so good range, and much smaller in the ``poor range. The relation used is just one that seems to work well enough

We've also allowed for using a similar relation to try to account for degradation of sensor performance in high wind conditions, perhaps accompanied by blowing snow. This effect is not well studied, and for now we've left the wind weighting factor at 1, so that it has no effect, but it is there to allow for future use and also just to demonstrate what these weighting factors do and how they are used.

Specifically, the quality (qf) and wind (wf) weighting factors are divisors to the filter algorithm time constant. A weighting factor of 1 has no effect, and the time constant is not changed. A weighting factor of 0.5 causes the effective time constant to be twice the nominal value; a factor of 0.01 would increase the effective time constant 100 times; and so on.

Note that the weighting factors are applied to the filter time constant, and not to the data values themselves. With an increased time constant, each measurement is still used, but with a lesser impact than with the nominal time constant. Effectively, we're giving more confidence to data values with good quality (or perhaps when winds are calm) than to those with lower quality (or when winds are high).

NOTE: In the process of describing the algorithm and processing, it now seems better to perhaps drop this whole weighting business and let the digital filter stand on its own. So long as the noise in the SR50 data output is ``random, varying around the desired, ideal value, the filter alone should be sufficient to produce good results. So we'll probably be rethinking some of the above...