Correction of Vaisala RS92 Radiosonde Humidity Measurements
Larry Miloshevich (May 2011)
This is a summary of my method of correcting RS92 radiosonde RH measurements for sensor time-lag error, mean calibration bias, and solar radiation error. Details can be found in Miloshevich et al. [2004, 2009].
Overview of RS92 RH Measurement Errors and Corrections
1. Sensor Time-lag Error is caused by slow sensor response at temperatures below about -40°C, which "smooths" and distorts features in the RH profile in the UT/LS. Vaisala laboratory measurements of the sensor time-constant tau (τ) as a function of temperature (T), as shown in Fig. 1, allow the ambient (or "corrected") humidity (Uc) to be calculated from the measured humidity (U), assuming exponential sensor response. Correction algorithms based on either Eq. (2) or Eq. (4) in Miloshevich et al.  produce nearly identical results for short time steps, such as 2 s or 6 s data:
(2) Uc = U + τ(T)∗dU/dtwhere dU/dt is the local humidity gradient, OR
(4) Uc = (U − [U(t0)∗X]) / (1−X) where X = exp(−Δt/τ) and Δt = t−t0 (t0 is the previous time)
Figure 1. RS90 and RS92 RH sensor time-constant (63% response time) as a function of temperature from Vaisala laboratory measurements. The black data points are the same as in Fig. 2 of Miloshevich et al. , but the simple exponential fit shown here is more sensible and justifiable than the elaborate procedure described in the paper. The scale factor α=0.8 (dashed) corresponds to about 2 standard deviations below the mean, meaning that 95% of sensors will be slightly undercorrected and 5% will be overcorrected (i.e., a conservative approach).
2. Mean Calibration Bias reflects inaccuracy in the factory calibration (apart from sensor-to-sensor "random production variability"). The mean calibration bias is inherently a function of RH and T, and it can change with time due to drift in the factory calibration references, periodic re-calibration of the references, or tweaks in the calibration function or manufacturing process. The mean calibration bias was determined by comparing RS92 RH measurements with simultaneous measurements from 3 reference sensors of known accuracy, namely the cryogenic frostpoint hygrometer (CFH) above the 700 mb level, 6 calibrated RH probes from the ARM THref system at the surface, and ARM microwave radiometer (MWR) measurements representing the lower troposphere. The RS92 mean calibration bias is shown in Fig. 2a (Nighttime) as a function of P and RH. The correction for mean calibration bias consists of interpolating between the curve fits to find the bias for given (P,RH) conditions and then subtracting it from the measurements.
3. Solar Radiation Error is a dry bias caused by solar heating of the RH sensor, such that the temperature of the humidity sensor (Tu) is warmer than the measured air temperature (T) that is used in the sensor calibration function. The sensor heating is inherently a function of pressure (or air density) and the solar elevation angle (α). The total RS92 mean bias relative to the reference sensors for Daytime soundings (Fig. 2b) contains both solar radiation error and mean calibration bias. The solar radiation error is given by subtracting the Nighttime bias from the Daytime bias. This represents the solar radiation error for the high solar elevation angles and clear-sky conditions represented by the data. The fraction of this solar radiation error to apply for a given solar elevation angle was derived from ARM RS92 and MWR comparisons (Fig. 2c). Correction of the total bias error for daytime soundings consists of subtracting both the calibration bias and the solar radiation error from the measurements.
Figure 2. The RS92 mean bias relative to the consensus of the reference sensors (CFH, MWR, and SurTHref) is shown for (a) nighttime soundings, and (b) daytime clear-sky soundings with α=62-70°. Polynomials are fit to the CFH comparisons, and the fit extrapolations (dashed) are constrained by the MWR and SurTHref comparisons. The RS92 mean bias for any data point is given by interpolating between the curve fits, which are valid from the surface to 75 mb (night) or 100 mb (day) (vertical black lines). Lower curves give the standard deviation of the bias, offset to the bottom of the panel for clarity. Right: Dependence of RS92 solar radiation error (SRE) on solar elevation angle, expressed as a fraction of the SRE at α=66°, which is the mean for the daytime WAVES CFH/RS92 soundings. (Figs. 9 and 10 from Miloshevich et al. ).
Example Corrected RH Profiles
The RS92 and CFH RH profiles below illustrate the magnitude and characteristics of the corrections, where the CFH measurements (purple) are taken as "truth", but keeping in mind that the CFH uncertainty is ±4% at the surface to ±9% at the tropopause (that's %, not %RH). Relative to CFH, the measured RS92 profile (black) contains a dry bias that increases with decreasing temperature, and is larger in the daytime due to solar radiation error in addition to the mean calibration bias seen in the nighttime profile. Time-lag error smooths the vertical structure and poorly resolves the tropopause, moreso in the nighttime profile due to the lower temperatures. The RS92 data after correcting for time-lag error, mean calibration bias and solar radiation error (red) agrees well with the CFH and recovers the detailed vertical structure in the UT/LS.
The accuracy of corrected RS92 RH measurements is discussed by Miloshevich et al. , and is summarized here.
Figure 3. Example (a) nighttime and (b) daytime RS92 soundings from the NASA WAVES campaign before and after applying corrections, and comparison to CFH on the same balloon. Shown are: the measured RS92 profile (black); the RS92 profile after applying the time-lag and bias corrections (red); the RS92 profile if only the bias corrections are applied (i.e., it still contains time-lag error) (yellow); the reference CFH profile (purple); and ice-saturation (dashed). (Fig. 15 from Miloshevich et al. ).
Notes on the Mean Bias Corrections (Calibration and Solar Radiation)
Notes on Implementing a Time-lag Correction
There are several possible approaches to implementing a time-lag correction based on either Eq. (2) or Eq. (4) above. The challenge is that the time-lag correction is a physically-based correction that is sensitive to the local humidity gradient (point-to-point slope of the RH profile). The correction amplifies the humidity gradient in proportion to the factor τ(T)/Δt, where Δt is the time interval of the data (e.g., 2 s), so any non-physical contribution to the measurements (random noise, data processing artifacts) is also amplified. Since the noise is generally constant, one could use averaging to operate over a longer timestep, or one could use my method of applying a fancy smoothing algorithm to the data to produce a "smooth" (physically realistic) profile that retains the detailed vertical structure as much as possible. Details of my method depend on whether it is EDT or FLEDT data, whether it is "Normal mode" or "Research mode" data processing, and whether it is noisy on account of RF interference or something else.
Algorithm Changes Since the Published Version of the Bias Corrections in 2009
Not counting the experimental daytime cloud adjustment factor, the other items above are rigorously tied to the published bias curves, but they are "patches" that produce better results but not the best possible results. The best results would come from re-deriving the corrections from scratch using lessons learned and a better approach that is now apparent (isn't everything this way?). So, if anyone knows of a good potential funding source for such work, please let me know!
Figure 4. This corrected RS92 RH profile from TCSP illustrates the experimental cloud extinction model (right) that is used to reduce the full clear-sky solar radiation correction (left) for cloudy daytime conditions. The yellow curve is the percentage of the clear-sky solar radiation correction that was applied, which is equal to the calculated fractional solar transmission. The full clear-sky solar radiation correction was applied in the left panel, resulting in obvious overcorrection in the lower troposphere, and less obvious overcorrection in the mid troposphere. Shown are the original EDT data (blue), the smoothed profile (black), after correcting for time-lag error (red), after also correcting for mean calibration bias and solar radiation error (purple), and ice-saturation (dashed). Extinction per meter increases with increasing temperature and is very strong for liquid water layers (RH≥100%) due to the small particle sizes. Fortunately, extinction is less in the UT due to low IWC (even though particle sizes are small), which minimizes uncertainty resulting from the inability to distinguish cirrus clouds from clear-sky ice-supersaturation. Note that the smooth profile and minimal vertical structure at low temperatures results from the loss of information when the RH data in EDT files were irretrievably rounded to integers.
Sources of Measurement Error Not Considered
Sensor Icing. RS90 and RS92 radiosondes use dual RH sensors that are alternately heated to minimize the effect of sensor icing by supercooled liquid water, and the heating cycle is currently turned off below about -40°C or -60°C depending on the radiosonde model. However, deposition of a thin frost layer on the sensor ("light" sensor icing) can occur in prolonged ice-supersaturated conditions in the UT, and measurements are affected by this "microclimate" until the frost sublimates in drier conditions above the ice-supersaturated layer. Therefore the magnitude of measured ice-supersaturation in the UT is questionable, and TCSP CFH/RS92 comparisons show that sometimes it is a km or more above cloudtop before the frost layer sublimates (Fig. 5, left). For RS80 radiosondes, sensor icing is more substantial and can occur at warmer temperatures.
Ground Check (GC) Correction. The GC procedure involves checking the sensor calibration at 0% RH during the launch preparation by placing the sensor in a container with desiccant that is assumed to produce an environment of 0.0% RH. The offset is optionally subtracted from the RH measurements to account for drift in the calibration during shipping and storage. It is apparent from scrutiny of many different datasets that too much GC correction is often applied, moreso for field campaign datasets than operational datasets such as at ARM, presumably because operators are less experienced. There is inherent uncertainty in the GC assumptions because there is evidence that desiccant can at best produce an environment of 0.5% RH. More troubling is that inattention to the freshness of the desiccant and the reasonableness of the GC values can result in a true environment of several %RH, resulting in excessive GC correction and a constant dry bias throughout the profile, and also reduced accuracy of bias corrections because they are RH-dependent (Fig. 5, right). Analysis of ARM data suggests that a GC correction of 0, −1, or maybe −2% RH is reasonable and indicates fresh desiccant and good procedures. Unless great care is taken with the GC procedure, it is advisable to apply zero GC correction and possibly accept a small moist bias rather than risk a potentially larger dry bias. An excessive GC correction can be identified by negative stratospheric RH values in the RAW data (EDT and FLEDT files limit the values to RH≥1%). Another sign of excessive GC correction is negative RH values produced by the time-lag correction. Note that it is possible to reprocess the data with zero GC correction using the Vaisala database file (".dc3db") produced by Digicora III systems.
Figure 5. Examples of RS92 sensor icing (left) and excessive GC correction (right). Note that colors have different meanings in these two figures. Left: Measured RS92 profile (black), corrected RS92 profile (red), CFH profile (purple), and ice-saturation (dashed), from a dual sounding during TCSP. The corrected RS92 does not see the decrease to ice-subsaturated conditions above the tropopause (asterisk), indicating that the measured RS92 data are affected by sensor icing until the frost layer sublimates at about 18 km altitude. Right: Ticosonde RS92 sounding affected by severe error in the GC correction, showing: original EDT data (blue), smoothed profile (black), time-lag-corrected profile (red), fully-corrected profile (purple), and the cloud adjustment factor for the solar radiation correction (yellow). The applied GC correction for this sounding was −7% RH, leading to original measurements that were set to the minimum value of 1% RH at altitudes 15.7-16.3 km and >19 km (rather than the negative RH values that were actually measured). The odd results of the time-lag correction (red) reveal that there is a problem, and in fact the entire profile should be moister by 5-7% RH.