This web page is called by a previous web page (MARS_Stratus Measurements) that describes a system used 20 years ago to monitor stratus cloud properties.  This web page describes calculations of "observables" that would be produced by an improved sensing system based upon the MARS and other experinces.  The hypothetical microwave remote sensing instrument system is optimized for meteorological conditions that are meant to resemble those of a stratus episode common on the U.S. West Coast.  The purpose in calculating such observables is to determine how well meteorological conditions, including fog density, can be measured by the instrument, with the hope that monitoring of such atmospheric properties can permit accurate predictions of fog formation and burn-off times.

The overall strategy is to first determine how well various hypothetical microwave instrument systems can monitor important stratus cloud properties.  Simulated atmospheric conditions intended to represent stages of stratus formation and dissipation will be subjected to simulated observations with the various microwave instrument systems.  The first stage will assume "perfect" instrumentation, that is, they will exhibit zero errors due to calibration errors and stochastic uncertainties.  If such systems cannot measure stratus properties adequately, then it will not be necessary to assess the impact of calibration and stochastic uncertainties.  However, if any of the systems do perform well enough to warrant further conisderation, then these error studies will be performed.

Hypothetical Stratus Microwave Radiometer Elements

I shall assume that the Stratus Radiometer System, SRS, will consist of subsets of the following 10 components:

    1)    20.7 GHz        Water vapor-sensitive channel
    2)    31.4 GHz        Liquid water-sensitive channel
    3)    51.0 GHz        Very low OXY absorption
    4)    54.0 GHz        Medium OXY absorption
    5)    56.0 GHz        Edge of OXY absorption
    6)    61.0 GHz        Peak OXY absorption
    7)    63.9 GHz        Edge of OXY absorption
    8)    68.9 GHz        Very low OXY absorption

I will assume that the microwave radiometers make brightness temperature measurements, TB, at the following elevation angles:

    Zenith            (air mass = 1.0)
    30 degrees     (air mass = 2.0)
    14.8 "            (air mass = 4.0)

    9)    IR radiometer brightness temperature (8-14 micron), at zenith

   10)    Surface temperature and absolute humidity.

An infrared radiometer is cheap, and would provide information crucial to the goal of estimating cloud base altitude.

Components 1) and 2) comprise a Water Vapor Radiometer, WVR.  They have been used for several decades to measure line-of-sight integrals of water vapor and liquid water.  I have led JPL deployments of WVRs in the field an at least 22 occasions.

Components 4) through 6) comprise a Microwave Temperature Profiler, MTP.  Such instruments, operating at slightly different frequencies, have also been used for decades to measure altitude profiles of air temperature.  Ground-based MTPs, and airborne MTPs (~3000 flight hours), have been deployed by JPL on approximately 27 field trip deployments.  Both the WVR and MTP technology are therefore "mature."

A "matched pairs" microwave radiometer hs been suggested (Mahoney, 1999) which attempts to incorporate the capabilities of both the WVR and MTP using only the so-called oxygen channels, such as components 3) and 8), plus 5) and 7).  It is thought that this matching may enable a determination to be made of liquid water concentration, LWC, within the cloud layer, without the need for a WVR.  For practical reasons it would be preferred to construct a microwave radiometer system using only the oxygen channel components, because they could share a single horn antenna and waveguide.  Such a system would be compact, light and cheap.  However, there is an unevaluated concern that it may be difficult to distinguish the contributions of water vapor from those of liquid water in the oxygen channel regime since these two water sources have an identical spectrum.  For the analysis reported on this web page I will not evaluate the "matched pairs" radiometer since the WVR/MTP combination is likely to be superior in terms of retrieval capability, and the objective of this analysis is only to evaluate the feasibility of using ANY subset of microwave channels for predicting fog/stratus formation and burn-off.

Approach

The first hypothetical system to be evaluated will be a WVR working alone.  It is anticipated that the simulations will show excellent performance in measuring water vapor and liquid water burdens, but it is not known whether a WVR working alone will be able to retrieve anything about Liquid Water Concentration, LWC, within the cloud.  This will be an objective of the present study.

The second hypothetical system will be a WVR working with a standard MTP consisting of three oxygen channels (that do NOT straddle the frequency of the oxygen absorption peak).  With MTP-generated T(z) information combined with the IT radiometer's brightness temperature, it should be possible to estimate cloud base altitude.  That information, combined with the cloud top altitude (assumed to correspond to the inversion base altitude determined from the MTP-generated T(z)), a determination should be possible of LWC properties.  Another objective of the present study is to assess the accuracy with which LWC can be determined at specified altitudes, such as 50 meters, 100 meters and 200 meters.

Model Atmosphere

In the model atmosphere under consideration the dew point temperature is a constant throughout the marine layer, and falls rapidly to low values in the overlying inversion layer.  During the formation phase, when the temperature at any level becomes colder than the dew point temperature, it is assumed that water changes phase from gaseous to liquid in a way that maintains water vapor denisty,VD, equal to the saturation vapor density, VDs, for that layer.  The difference in the layer's original VD and current VDs is assumed to represent a re-partitioned component of liquid water.  In this way it is possible to calculate profiles of Liquid Water Concentration, LWC [g/m³]. The following web page is devoted to this concept:  StartusFormationModel.

In calculating VD(z) it will be necessary to calculate VDs, which only depends upon temperature (to first order).  A temperature dependence for VDs will be determined that is valid for the range of temperatures in the model atmosphere of this study (-50 to +13 C).

I will calculate microwave TB in a spreadsheet using absorption coefficients, Kv, for oxygen, water vapor and liquid water that pertain to each frequency.  Pressure and temperature dependencies of Kv for oxygen and water vapor will be determined using quadratic fits to exact calculations of Kv at a wide range of conditions.  A multiple regression 2nd-order fit will be used, as necessary, to represent the temperature and pressure dependencies of Kv for water vapor and oxygen.

Liquid water absorption is calculated from the following equation:

    KvLIQ = 0.075 * LWC * (280/T)^6.87 * (F/22.2)^1.9
        where LWC is liquid water concentration [g/m³],
        T = temperature [K],
        F = frequency [GHz]

Brightness temperatures will be calculated in the spreadsheet using 10-meter intervals from surface to 24 km.  Each frequency/elevation combination corresponding to a microwave TB observable will be assigned to a group of columns in the spreadsheet for each frequency.  Columns will be used to calculate the absorption coefficients KvOXY, KvVAP and KvLIQ.  The next column in the group is "optical depth" for the altitude region "surface to the altitude layer assoicated with the row."  This is just the sum of all lower-altitude rows of "absorption coefficients times layer thickenss."  The third column in a group is "transparency" (from ground level to the layer in question.  The last column for a frequency is the product of transparency and air temperature.  Sums of the last two columns are used to derive TB, taking transparency into account (using a cosmic background value of 2.73 K).

IR brightness temperature will be set equal to air temperature at the cloud base altitude when cloud is present, and will be assigned a low value when the sky is clear.

Fit Results

Saturation vapor density is calculated from temperature using the following equation:
    VDs = 4.896 +0.35232 * T[C] +9.651e-3 * T[C]^2 +9.11321e-5 * T[C]^3

At 20.7 GHz,
    KvVAP = (0.00390 -8.31e-6 * (T[C] - 5) -1.428e-6 * (P[mb] - 900)) * VD[g/m³]
    KvOXY = (P[mb]/1000) * (4.062e-4 -1.409e-5 * T[C] +3.655e-3 * (P[mb]/1000))

At 31.4 GHz,
    KvVAP = (0.00227 - 2.57e-5 * (T[C] - 5) +1.70e-6 * (P[mb] - 900)) * VD[g/m³]
    KvOXY = (P[mb]/1000) * (-8.014e-4 -2.7714e-5 * T[C] +7.0805e-3 * (P[mb]/1000))

At 54.0 GHz,
    KvVAP =  VD[g/m³] * (-9.986e-4 +5.393e-3 * (P[mb]/1000) -1.3573e-5 * T[C])
    KvOXY = (4.062e-4 -1.409e-5 * (T[C] - 5) +3.655e-3 * (P[mb]/1000)) * (P[mb]/1000)

At 56.0 GHz,
    KvVAP =  VD[g/m³] * (-1.3446e-3 +6.193e-3 * (P[mb]/1000) -2.2843e-5 * T[C])
    KvOXY =  (P[mb]/1000) * (1.2155 +0.66049*(P[mb]/1000) -7.60692* T[C])

At 61.0 GHz,
    KvVAP =  VD[g/m³] * (-1.706e-3 +7.4895e-3 * (P[mb]/1000) -3.2274e-5 * T[C])
    KvOXY =  (P[mb]/1000) * (3.3378 +0.97466*(P[mb]/1000) -0.0412517* T[C])

In order to derive meaningful performance statistics (for any remote sensor system) it is necessary to simulate a variety of atmospheric conditions, some cloudy and some clear, for example.  The next figure shows the same 9 T(z) profiles in the previous web page (MARSVan, Fig.'s 10 and 11) plus three dew point temperature, DPT, profiles.  There are 27 ways to combine the T(z) and DPT(z) profiles, and all 27 combinations of them were used to calculate WVR TBs.  These 27 atmospheric conditions can be thought of as representing 3 different stratus/fog formation and dissipation episodes.

Figure 1.  All T(z) and Dew Point Temperature profiles used in all possible combinations for constructing 27 simulation conditions.

 Of the 27 conditions 19 produce clouds (with liquid burdens, Lz, that range from 4 to 732 microns) and 8 are clear.

WVR-Only Results

A simulation was run using only the WVR channels, 20.1 and 31.4 GHz.  This is a sensible first step since WVR instruments have been in use for several decades, and they represent a mature technology at this time.

The first atmospheric property to be studied is cloud liquid burden, Lz.  A multiple regression analysis was performed for the 6 independent WVR variables, the 3 pairs of TBs, and the one independent variable, Lz.  All observables had statistically significant correlations with Lz.  The correlation coefficients were then used to calculate retrieved Lz for the 27 cases, and these are shown in the next figure.

Figure 2.  WVR-Only performance in retrieving liquid water burden.

It should be noted that all observables are "perfect" - that is, they do not contain calibration errors or stochastic measurement uncertainties.  Based on this figure, a WVR working by itself is capable of producing good solutions for stratus cloud liquid content.  This is unsurprising since real WVRs have been used for this purpose on thousands of occasions during the past several decades.

The same procedure was used to evaluate the WVR's ability to determine the maximum Liquid Water Concentration, LWC, and the results of retrieved LWCmax are shown in the next figure.

Figure 3.  WVR-Only performance in retrieving the maximum value for liquid water concentration within the stratus cloud.

The performance in Fig. 3 for retrieving LWCmax should be described as a "best possible" performance, since TB observables were not assigned stochastic and calibration errors.  Nevertheless, with a properly calibrated WCR, working alone, it should be possible to retrieve useful values for LWCmax, which will apply to the top of the stratus layer.

Finally, vapor burden performance is shown in the next figure.

Figure 4.  WVR-Only performance in retrieving water vapor burden throughout the entire atmosphere.

Unsurprisingly, the WVR observables do a good job of retrieving water vapor burden, Vz.  This atmospheric parameter is the "reason for being" of the WVR instrument type.  Even though there are only three Vz values in the simulation we have every reason to believe, based on abundant experience in the past, that Vz will be retrieved with very good accuracy, even in the presence of cloud liquid.

There is no point in evaluating the WVR-only system's ability to retrieve certain other atmospheric properties, such as the altitude of the cloud base and top, or the lapse rate at various altitudes, since the WVR's observables are insensitive to them.  For these properties we require a microwave radiometer operating at frequencies where oxygen is the principal absorber.  The balance of this web page is devoted to evaluating the addition of oxygen channels to the proposed remote sensing system.

WVR Plus Microwave Temperature Profiler Radiometer System

The strategy for this section will be to add "oxygen channel observables" to the WVR observables, and evaluate the performance of retrievals of various stratus cloud properties.  A Microwave Temperature Profiler, or MTP, can be used in a ground-based or airborne mode for the retrieval of T(z).  For the ground-based setting, when stratus clouds may be present, it is important to rely upon some sort of WVR for the "correction" of oxygen channel observables due to cloud liquid water effects.  A traditional 21/31 GHz WVR can be used, which should provide the best possible measurement of water vapor and liquid water properties.  This section reports on performance using a simple 2-channel WVR and a simple 3-channel MTP.  The MTP operates at 54.0, 56.0 and 61.0 GHz, and it scans through the same 3 elevation angles as the WVR (corresponding to air masses of 1, 2 and 4).  The WVR produces 6 observables, the MTP produces 9 observables, the IR radiometer produces one observable, and the surface temperature and absolute humidity constitute two more observables.  Altogether, there are 18 observables in this analysis.  As before, all observables are assumed to be perfect, having zero calibration error and zero stochastic noise.

The retrievables of interest using such a sensing system are:  LWC at 50 meters, LWC at 100 meters, LWC at 200 meters, cloud base altitude, lapse rate from surface to 100 meters, and lapse rate from 100 meters to 300 meters.

The next figure shows retrieved LWC at 50 meters versus the "true" (i.e., model) value for LWC at 50 meters.

Figure 5.  Retrieved and true LWC at 50 meters altitude.

From this figure it is apparent that the WVR/MTP/IR/surface sensing system is able to monitor LWC at an altitude of 50 meters with good accuracy, provided the observables are well calibrated and have small stochastic noise.  I believe it is legitimate to accept this analysis because the analysis is for a wide range of LWC50 values, and they span the entire formation and dissiapation phases of 3 hypothetical events.

Figure 6.  Retrieved and true LWC at 100 meters altitude.

An equally impressive performace is achieved for LWC at 100 meters altitude.

Figure 7.  Retrieved and true LWC at 200 meters altitude.

LWC can even be retrieved at 200 meters altitude.

The following figure shows performance for retrieved stratus cloud base altitude.

Figure 8.  Retrieved and true cloud base altitude.

Cloud base altitude can be determined with impressive accuracy, thanks to the combination of the IR radiometer and T(z) from the MTP.

The following two figures show retrieval performacne for lapse rate (defined as the vertical gradient of temperature) for two altitude regions.

Figure 9.  Retrieved and true lapse rate (defined as dT/dZ) for the altitude region surface to 100 meters.

Figure 10.  Retrieved and true lapse rate (defined as dT/dZ) for the altitude region 100 meters to 300 meters.

Lapse rate is easily measured for both the lowest 100 meters and the altitude region from 100 meters to 300 meters, thanks mostly to the MTP.

Degraded Performance Using Realistic Observable Errors

Go to the following web page for a description of the analysis of stratus/fog properties retrieval performance using realistic observable uncertainties:

    RealisticPerformance web page.

This site opened:  January 24, 2001.  Last Update: May 23, 2003