Upper Tropospheric Humidity from Microwave

CDR Case Study

By Martin Burgdorf and Theresa Lang

This is the account of generating the upper tropospheric humidity CDR from microwave sounders. For a more detailed description see Lang (2019).

Introduction

The microwave FCDR from FIDUCEO contains the brightness temperature measured by several microwave humidity sounders. This dataset can be further processed to determine essential climate variables, for example the upper tropospheric humidity. This is a vertical average of the relative humidity in the upper troposphere, roughly in a layer between 200 and 500hPa .However, the exact position of this layer depends on the amount of water vapor in the atmosphere, i.e. it is located in lower altitudes in a drier atmosphere and in higher altitudes in a moist atmosphere. Upper tropospheric humidity can be derived from the brightness temperatures measured at 183 GHz using a simple exponential relationship (Buehler and John, 2005):

\tag{Eq. 1} ln(UTH) = a + b BT

Where

  • UTH is the upper tropospheric humidity
  • BT is the brightness temperature measured by the sensor
  • a, b are constants derived from analyzing a set of typical humidity and temperature profiles

As the upper tropospheric humidity can be derived for example from observations of the n2 band at 1595 cm-1 as well, we introduced a new definition of UTH that is identical for the water vapor channels of an infrared sounder and the microwave instruments Special Sensor Microwave Water Vapor Profiler (SSMT-2), Advanced Microwave Sounding Unit-B (AMSU-B) and Microwave Humidity Sounder (MHS). Thus, it will allow to combine UTH CDRs based on infrared and microwave measurements at a later date. As there are no FIDUCEO FCDRs from infrared sounders yet, we calculated the UTH from microwave data only.   

For generating the CDRs we take full advantage of the information available in the FIDUCEO FCDRs. This means in particular propagating the uncertainties of the measured brightness temperature to the relative humidity in the upper troposphere. Hence the same classes of uncertainties, viz. independent, structured, and common effects, are present in FCDRs and CDRs. The CDRs benefit of course also from the improved calibration accuracy and consistency among different instruments in the FIDUCEO FCDRs.

A New Definition of Upper Tropospheric Humidity

The old definition of UTH, which is based on the water vapor Jacobian of a particular instrument channel, has two major shortcomings. Firstly, it is not equal and hence not readily comparable for IR and MW measurements, strictly speaking not even for MW measurements from instruments with different bandwidths. Secondly, to compare UTH derived from satellite measurements to UTH from climate model simulations a detour has to be made via radiative transfer simulations in order to obtain the Jacobians, introducing poorly known uncertainties.

Instead of weighting RH with the channel-specific Jacobian, an unweighted average of RH is performed over a certain atmospheric layer (Figure 1), hereafter referred to as UTH layer. The definition of this UTH layer is based on an idea from Wu et al. (1993). They showed that the atmospheric layer that contributes to the BT measured in the 6.7 μm channel is bound by two characteristic water vapor columns. One possibility to explain this in an intuitive way is Chapman’s Law. It says that the radiation escaping the atmosphere approximately originates from the altitude at which the optical thickness reaches one, seen from the top of atmosphere downwards. As the radiation originates from an extended atmospheric layer rather than from one distinct level, one can infer that this layer is bounded by two characteristic optical thicknesses that are close to one. Since the optical thickness in a UTH channel is closely linked to the water vapor column, a UTH layer that is bounded by two water vapor overburdens reflects the varying altitude of the emission layer, similar to the water vapor Jacobian in the traditional UTH definition.

Figure 1. Example of an atmospheric profile of relative humidity (RH, left panel) and the integrated water vapor (IWV) above every altitude level (right panel). The levels, at which the overlying IWV exceeds the two characteristic thresholds are indicated by dashed lines. UTH is calculated as vertical average of RH in the layer between these two levels (green shading, Lang, 2019).

Using this idea, the new UTH (UTHnew) is defined as the RH averaged over an atmospheric layer that is bounded by two altitude levels (Figure 1):

\tag{Eq. 2}

UTH_{new}(\theta) = \frac{1}{z(IWV_{1}(\theta)) – z(IWV_{2}(\theta))} \int_{z(IWV_{2}(\theta))}^{z(IWV_{1}(\theta))} \! RH(z)  \, \mathrm{d}z

\tag{Eq. 2} UTH_{new}(\theta) = \frac{1}{z(IWV_{1}(\theta)) – z(IWV_{2}(\theta))} \int_{z(IWV_{2}(\theta))}^{z(IWV_{1}(\theta))} \! RH(z) \, \mathrm{d}z

Where

  • RH is the relative humidity
  • z_{IWV_{n}} is the altitude level, at which the integrated water vapor above exceeds the threshold IWVn, n is one or two
  • \theta is the satellite viewing angle

Both IWV thresholds and UTHnew depend on the satellite viewing angle θ, because the altitude of the emission level changes with θ. The IWV thresholds are identically the same for all instruments. They are determined with a simple optimization procedure by performing the following steps for each of the three instruments AMSU-B, MHS, and HIRS:

1. Calculate UTHnew for a set of training atmospheres, starting with an arbitrary pair of IWV thresholds.

2. Use a radiative transfer model to simulate BTs measured in the UTH channel of the instrument for all training atmospheres.

3. Plot ln(UTHnew) against BT for all training atmospheres and perform a linear regression.

4. Repeat 1. and 3. for different pairs of IWV thresholds in the UTH definition to find the pair, for which the linear relationship is most pronounced.

Steps 1 to 3 are performed separately for every viewing angle of the instrument. The corresponding nadir regression coefficients are listed in Table 1.

Table 1. Scaling coefficients a and b for the nadir view of the instruments HIRS, AMSU-B, and MHS for the new and the traditional definition of UTH.

Definition of UTH Instrument a (intercept) b (slope)
New AMSU-B       
MHS
HIRS  		 22.4942
22.5022
29.604		 -0.095
-0.0951
-0.126
Old AMSU-B
MHS
HIRS		 18.382
18.3889
25.681		 -0.0778
-0.0779
-0.1093

To give an impression of the performance of the UTH retrieval with the new UTH definition, Figure 2 shows UTHfitted, i. e. the UTH that is retrieved from BT with the coefficients from Table 1, versus UTHtrue, i. e. the UTH that is calculated directly from the humidity profile, for the nadir views of AMSU-B and HIRS.

Figure 2. Fitted nadir UTH for HIRS (left panel) and AMSU-B (right panel) versus true nadir UTH for the Eresmaa data set. UTH is calculated according to the new definition based on the water vapor overburden (Lang, 2019).

CDR Processing Chain

The UTH CDR processing chain is shown schematically in Figure 3. It starts with the FCDRs and involves a pre-screening of pixels, the transformation of BT to UTH, and the aggregation and averaging of the pixels to get a monthly gridded field. Moreover, uncertainties of the FCDR BTs are propagated to the CDR quantities. Finally, the FIDUCEO CDR format is implemented to provide easily accessible NetCDF-4 files.

The final CDR consists of three core variables: UTH, cloud-cleared BTs, which is the BT used to derive UTH, and unfiltered brightness temperatures (BTfull), which are not cloud-cleared. Consequently, the processing chain consists of three branches leading to these three variables (Figure 3).

Figure 3. Schematic illustration of the UTH CDR processing chain, which is subdivided into pre-screening of pixels (blue), transformation of BT to UTH (green) and gridding and temporal averaging (red). Ellipses denote input data, the rounded rectangle denotes auxiliary input, other rectangles denote processing steps, parallelograms with solid borders denote input or output data sets and parallelograms with dashed borders denote intermediate products that are not available to the user (Lang, 2019).

Description of the FIDUCEO UTH CDR

The CDR generator is run over all available Microwave FCDR data of SSMT-2, AMSU-B, and MHS instruments (see Table 1 in the FCDR Case Study). The final CDR does not cover exactly the same time periods as the FCDR, since only measurements from the 183.31±1 GHz channel are used to derive UTH. Data gaps in this channel in the FCDR lead to data gaps in the CDR. All satellite missions and time periods covered by the UTH CDR are illustrated as a bar chart in Figure 4. The only differences to FCDRs concern the end dates of AMSU-B.

Figure 4. Time periods covered by the satellite missions contained in the UTH CDR (Lang, 2019).

Example Content

The core quantities of the CDR are the monthly averages of 183.31±1GHz BT and UTH, together with their uncertainties. They are shown in Figures 5 and 6 for the example of July 2012, using data from the ascending overpasses of MHS on NOAA18. In the uncertainties of UTH (Figure 6) the same structures as in the uncertainties of BT (Figure 5) are generally visible. However, there is another pattern superimposed, which resembles the UTH itself. It is a consequence of the exponential relationship between BT and UTH. In the non-systematic uncertainties striped and chessboard-like patterns are visible. This is because the grid cells are observed with varying frequencies as a result of the way the satellite samples the Earth. The more observations are available, the smaller are the random uncertainties of each pixel.

Figure 5. Example CDR content: Monthly mean brightness temperature (first panel) for July 2012 from ascending passes of MHS on NOAA18 as well as standard deviation of daily brightness temperature averages (second panel) and uncertainties of brightness temperature split into three classes: independent, structured and common uncertainties (third to fifth panel) (Lang, 2019).

Figure 6. Example CDR content: Monthly mean UTH (first panel) for July ascending passes of MHS on NOAA18 as well as standard deviation of daily temperature averages (second panel) and uncertainties of UTH split into three classes: independent, structured and common uncertainties (third to fifth panel) (Lang, 2019).

Validation of the CDR

Figure 7 is a comparison of the FIDUCEO UTH CDR und CM-SAF UTH CDR for AMSU-B and MHS. The overall agreement between the two data sets is very good, confirming the validity of our method to derive the upper tropospheric humidity. As a consequence of the improved calibration of the FCDR, also the FIDUCEO CDR is more consistent among the different instruments. Its total uncertainty is depicted as a shaded area around the time series of each satellite mission. Common uncertainties represent the largest part of the total uncertainties, because they are not reduced by the averaging that is part of the processing. In most cases, the time series of different satellite missions agree within their uncertainties and are more consistent than CDRs based on operational data. Generally, it is important to note that the uncertainty shown here is only the uncertainty associated with the measurement of BT that was propagated from the FCDR. There are additional sources of uncertainty that emerge during the CDR processing.  

Figure 7: Top:Tropical area-weighted mean of cloud filtered BT for all available satellite missions, except for DMSP, of the FIDUCEO UTH CDR. The range of ± one measurement uncertainty is indicated as shaded area around the monthly means. Bottom: UTH from CM-SAF for comparison

Overall, the new UTH definition introduced by FIDUCEO will allow a synergistic view on infrared and microwave UTH in the future. With the creation of the FIDUCEO microwave UTH CDR, the way to go towards a combined infrared and microwave UTH data record has been successfully demonstrated.