Water vapor is one of the most important gases in the Earth's atmosphere. Its relevance has led to the development of several techniques for measuring its vertical distribution as well as the vertically integrated atmospheric water vapor content, which is often referred to as precipitable water, total water vapor, integrated water vapor, integrated precipitable water vapor, or total column water vapor. The Global Climate Observing System has highlighted the utility of total column water vapor observations, declaring it as an essential climate variable , which the World Meteorological Organization defines as a physical, chemical, or biological variable that critically contributes to the characterization of Earth's climate.

Passive satellite total column water vapor retrievals typically use instruments that measure in the visible e.g.,, near-infrared e.g.,, infrared e.g.,, and microwave spectral regions e.g.,. However, each spectral region has its limitations: visible and near-infrared measurements are limited to cloud-free daytime regions and to land areas where the relatively bright surface reflection increases the signal compared to the dark ocean surfaces; infrared and microwave measurements can operate only over ice-free oceans, where the surface emissivity is well characterized. Additionally, infrared measurements are not possible in the presence of clouds or rain.

This study explores the feasibility of using a differential absorption radar (DAR) to remotely measure total column water vapor under all sky conditions, for all surface types and during day and night. The DAR technique is analogous to the differential absorption lidar (DIAL) technique e.g., but operates in the microwave or millimeter-wave regime. In essence, the difference between the radar reflectivity at two nearby frequencies, “on” and “off” an absorption line, can be related to the amount of absorbing gas between the radar and the scattering target, which in this case is the Earth's surface.

Prior studies have shown that the DAR technique can be used to derive water vapor profiles using three frequencies around 22 GHz and two frequencies at around 10 and 94 GHz or at 2.8 and 35 GHz . However, these studies require distinct radar transmitters for each frequency, which complicates the DAR measurement due to independent system calibration and beam overlap issues. , , and explored the feasibility of water vapor profiling with a narrow-band transmitter on the wings of the 183 GHz water vapor line, in which case the DAR measurement can be made with a single transceiver, greatly simplifying the measurement interpretation.

With respect to remotely measuring total column water vapor, and assessed the feasibility of using two frequencies near the 183 GHz water absorption line and using large eddy simulations and global cloud observations from CloudSat , respectively. These studies concluded that the DAR technique could provide nearly spatially continuous observations of total column water vapor, even under rainy conditions. However, both studies assumed a constant instrument error model, with a 0.16 dBZ radar precision and around a -30 dBZ minimum detectable signal. Here we use a more realistic uncertainty model (described in Sect. ) that includes speckle noise, that is, that depends on the magnitude of the return power, which in turn depends on the water vapor burden. Furthermore, their simulations explored frequencies prohibited by the Federal Communications Commission for spaceborne transmission.

Here, we assume a frequency-chirp, pulsed radar system, similar to the proof-of-concept instrument described by and by . Currently, a similar airborne radar operating near 170 GHz is being developed and has recently been validated during a ground-based deployment . The motivation of this study is to investigate the transmit power necessary to achieve close to global total column water vapor measurements from a space platform given realistic instrument and orbital parameters and using frequencies that could be available for space transmission.

It has been shown that the ratio of two surface returns can be used to estimate the total column water vapor. Nevertheless, for completeness, a description of the radar theory is summarized here. Neglecting multiple scattering, the surface return power measured by a monostatic radar which transmits a power PT at a given frequency ν is given by 1PR(ν)=PT(ν)G(ν)2λ2Ω(ν)(4π)3r2Υ2(ν)σ0(ν), where G(ν) is the antenna gain, r is the distance to the surface, Ω(ν) is the integral of the normalized two-way antenna pattern, and σ0(ν) is the normalized surface cross section. Υ2(ν) is the two-way transmission given by 2Υ2(ν)=exp⁡-2∫0rσgas(ν,r′)+σPext(ν,r′)dr′, where σgas(ν,r) represents the gaseous absorption coefficient and σPext(ν,r) the particulate extinction (the sum of absorption and scattering) coefficient along the radar path.

If two radar tones are measured simultaneously, the ratio of two surface returns can be expressed as 3PR(ν2)PR(ν1)=C(ν2)C(ν1)Υ2(ν2)Υ2(ν1)σ0(ν2)σ0(ν1), where C(ν) is the radar system parameter given by the first term of Eq. (), that is, PT(ν)G(ν)2λ2Ω(ν)(4π)3r2.

Assuming that the frequency dependence of σPext(ν,r) and σ0(ν) is small relative to that of σgas(ν,r), this equation becomes PR(ν2)PR(ν1)4=C(ν2)C(ν1)exp⁡(-2∫0rσgas(ν2,r′)-σgas(ν1,r′)dr′), which can be rewritten as PR(ν2)PR(ν1)=C(ν2)C(ν1)exp⁡(-2∫0rρ(r′)∑ivi(r′)[κi(ν2,r′)5-κi(ν1,r′)]dr′), where ρ(r) is the air density and the sum is over all the absorbers with mass extinction cross section κi(ν,r) and volume mixing ratio vi(r). If the radar tones are close to a strong absorption line, the associated gas dominates the absorption. For example, absorption due to water vapor dominates the atmospheric attenuation near 183 GHz. In that scenario, the only unknowns remaining are pressure, temperature, and water vapor mixing ratio. It follows that, assuming a temperature and pressure profile (for example, from reanalysis fields or a climatology) and a water vapor profile shape, it should be possible to retrieve total column water vapor from the ratio of two surface returns. The uncertainties associated with these assumed profiles will be discussed in Sect. .

To explore the capabilities of this technique, the radar reflectivity uncertainty needs to be properly simulated. Here we assume a moving satellite platform with velocity V and antenna diameter D. Following and , the uncertainty in the received power (see Eq. ), assuming decorrelated pulses, is given by 6ΔPR(ν)2=PR(ν)2Np+2PNPR(ν)Np+2PN2Np, where Np is the number of pulses used in each measurement of PR(ν). The first term is due to speckle noise, the second term is known as Townes noise i.e.,, and the last term is due to the instrument thermal noise PN. Speckle noise can be understood as the variation in backscatter from randomly distributed scatterers causing interference effects in the coherent measurement of the total returned electric field. In simple terms, Townes noise is due to the cross term of the sum of the signal and noise voltages. The instrument thermal noise is determined by 7PN=kbTsysτ, where kb is the Boltzmann constant, Tsys is the system noise temperature, and τ is the chirp time which we fix according to the relation given by 8τ=D2V, which ensures that sequential pulses are decorrelated.

The number of pulses is then determined by 9Np=ςTτ, where ς is the duty cycle, assumed to be 0.25 using a chirped pulse, and T is the total integration time available for each radar tone, estimated using 10T=ΔLVNT, where ΔL is the desired along-track horizontal resolution and NT is the number of radar tones (e.g., at least two, for the online and offline tones).

In this study we assume a 405 km orbit, a 1 m antenna diameter, radar tones at 167 and 174.8 GHz, a system temperature of 1800 K, a desired horizontal integration of 500 m, and transmit powers varying from 0.1 to 100 W. These assumptions result in a footprint diameter of ∼850 m, a chirp time of 66 µs, a total incoherent integration time per tone of 33 ms, and 125 number of pulses. These radar characteristics are listed in Table  (which also includes the symbols used throughout this study). Further, we define the minimum detectable signal to be PR(ν)=PN (i.e., where a single-pulse signal-to-noise ratio (SNR) is equal to 1). This determines the sensitivity of the DAR measurement system. Despite the relatively long chirp time, we do not simulate any side lobes because, as demonstrated by RainCube (a Ka-band 6U cubesat radar with a 166 µs pulse length) through an optimal selection of pulse shape and digital processing, side lobes can be suppressed to accurately measure the most relevant precipitation processes near the surface .

The Earth's surface is a bright target, meaning that the SNR should be large. In this scenario, PR(ν) is generally much larger than PN, and the last two terms of Eq. () (the contributions from the Townes noise and the instrument noise) are small. Thus, in high-SNR regimes the fractional uncertainty in the received power simply becomes 1/Np.

Radar returns are simulated using the radiometric model described in . In short, radar reflectivities are estimated using the time-dependent two-stream approximation , gaseous absorption is evaluated using the clear-sky forward model for the EOS Microwave Limb Sounder , hydrometeor scattering properties are evaluated using Mie scattering theory (assuming spherical solid hydrometeors), and the surface cross section is calculated using a quasi-specular scattering model for the ocean surface. More details, such as the dielectric constants and the particle size distributions used, can be found in Table .

The hydrometeor fields used in this study are supplied by cloud/rain profiles observed by CloudSat. CloudSat is a NASA satellite carrying a 94 GHz profiling radar sensitive to both cloud and precipitation particles . CloudSat retrievals provide the hydrometeor information, while spatially and temporally interpolated weather analysis provides the meteorological conditions. In particular, rain and snow profiles are taken from the 2C-RAINPROFILE products and liquid water content (LWC) and ice water content (IWC) from the 2B-CWCRO R04 . Temperature, pressure, and water vapor are taken from the European Centre for Medium-Range Weather Forecasts auxiliary (ECMWF-aux) products . Note that to decrease the number of calculations, we subsample these fields; we only used 1 out of every 50 CloudSat measurements. In other words, we under-sample CloudSat to save computational time. It is noted that non-uniformities within the beam at scales smaller than the CloudSat horizontal resolution are not included in these simulations. They will be better addressed using either high-resolution ground-based data or high-resolution atmospheric models in subsequent studies.

Figure  shows an example simulation at 167 and 174.8 GHz, which are the two frequencies used throughout this study. These frequencies are the extreme frequency values achievable due to international transmission restrictions . The observed scene is heavily overcast with snow aloft and rain beneath the freezing level. The simulation is repeated for two distinct water vapor burdens; a wet atmosphere as estimated from the weather analysis and a hypothetical dry atmosphere (with 44 and 4 mm of total column water vapor burden and 298 and 257 K surface temperature, respectively). As expected, the dry atmosphere simulations show considerably less attenuation, but nevertheless, the impact of the water vapor burden is clearly visible in the extra attenuation experienced by the 174.8 GHz radar tone compared to 167 GHz. As examples of this burden, Fig.  shows the spectral variation of the surface return for different total column water vapor burdens under clear-sky conditions. The spectral contrast between 174.8 and 167 GHz varies from 0.1 dB for no water vapor to 31 dB for 60 mm of total column water vapor.

We use a quasi-specular surface backscatter model over the oceans assuming monthly climatological values derived from the ERA-Interim reanalysis for near-surface wind speed and sea surface temperature . Over land surfaces there are no empirical models for the radar cross section at these frequencies. Therefore we use the observed cross sections from CloudSat to scale the ocean frequency dependence of the model as follows: 11σ0(ν)′=σ0c(ν94)ψ, where σ0(ν)′ is the modified surface cross section at a given frequency, σ0c(ν94) is the measured CloudSat cross section, and ψ is the ratio between the cross section simulated by the ocean backscatter model at the desired frequency and the cross section simulated by the ocean backscatter model at 94 GHz (CloudSat's frequency). Under most wind, temperature, and salinity conditions, ψ is ∼0.78 at 167 GHz and ∼0.76 at 174.8 GHz. We emphasize that this method is ad hoc and does not properly account for the differences in the spectral dependence of the reflectance properties of land surfaces vs. water surfaces. Nonetheless it allows us to examine the feasibility of the remote sensing method. As an example, Fig.  shows maps of the measured CloudSat cross section as well as the modeled surface cross section at 167 GHz for the simulations used in this study. As explained by , σ0c(ν94) displays large spatial variability over land, where σ0(ν) depends on vegetation, soil moisture, surface slope, snow cover, etc., as opposed to over the oceans, where it mostly depends upon the wind speed through its effect on the surface slope distribution. Although Eq. () approximates the frequency dependence of land surface backscatter using an ocean model, the land-specific frequency dependence is minimal and should have only a minor effect on results. The impact of uncertainties on σ0(ν) will be discussed in Sect. .

Figure  shows maps of the DAR simulations used in this study. Panel a is an 8 d average (1–8 January 2007) of the CloudSat ECMWF-aux total column water vapor to show the context of the simulations. Panels b and c show the average effective surface cross section, that is, σ0(ν)Υ(ν)2, at 167 and 174.8 GHz. Lastly, the bottom panel shows the difference between the 174.8 and 167 GHz simulations. Note that the simulations also include the hydrometeor burden, that is, the IWC, LWC, rain, and snow found on each CloudSat profile, which in principle is frequency-dependent. In these maps there are around 80 000 simulations (we only used every 50 CloudSat measurements). These simulations include, according to the CloudSat classification algorithm , more than 10 000 clouds identified as cirrus and stratocumulus, around 500 as cumulus, 7000 as nimbostratus, and 800 as deep convection. Further, these simulations include around 400 precipitating scenes with rain rates of up to 4.5 mmh-1 according to the rain profile product .

As shown, the impact of the water vapor burden can be seen at both radar tones; however, at 174.8 GHz the radar signal has been considerably more attenuated than at 167 GHz (which is further from the absorption line). Furthermore, the effective cross-sectional difference (174.8–167 GHz), equivalent to the surface radar power ratios, is clearly strongly correlated with the total column water vapor field.

The aims of this study are (1) to quantify the uncertainties in DAR retrievals of total column water vapor and (2) to explore the trade-offs between radar transmit power and sampling of the Earth's real-world meteorological variability. To accomplish this goal we performed end-to-end retrieval simulations. The retrieval algorithm used is 12wi+1=wi+∂y^(w,b)∂wy-y^(wi,b), where the total column water vapor, wi, is computed by suitably integrating the vertical water vapor profile xi, and y is determined by the ratios between surface radar returns at different frequencies, that is to say 13y=PR(ν2)PR(ν1), and the simulated measurements, y^(wi,b), are given by 14y^(wi,b)=Fν2(wi,b)Fν1(wi,b), where F is the radar forward model described in Sect.  and b is comprised of forward model parameters that influence the simulated radar observations but are not retrieved. For example, these include spectroscopic parameters, profiles of temperature, pressure, ice water content, liquid water content, rain or snow. The assumptions made in b contribute to the systematic errors in the estimates of the total column water vapor. In each iteration, ∂y^(w,b)/∂w is evaluated by finite differences by perturbing the entire water vapor profile, xi, by 1 %. Lastly, after each iteration xi+1 is computed following 15xi+1=wi+1wixi. That is, the shape of the assumed water vapor profile does not change during the retrieval: it is simply scaled according to the total column water vapor retrieved.

The estimated precision (the error due to random noise affecting the instrument) in the retrieved total column water vapor, w, is given by 16σw2=∂y^(w,b)∂wσy2, where σy is given by 17σy2=PR(ν2)PR(ν1)ΔPR(ν2)PR(ν2)2+ΔPR(ν1)PR(ν1)22, which is simply the propagation of combining the individual errors of PR(ν2) and PR(ν1).

To perform end-to-end retrievals, we first need to define a set of conditions regarded as truth as well as the radar characteristics. As detailed in Sect. , these conditions were taken from CloudSat measurements (IWC, LWC, rain, snow, temperature and pressure), while the radar characteristics are listed in Table . With these atmospheric conditions and radar parameters, we compute synthetic radar returns to be used as measurements; that is, the synthetic radar returns are given by 18PR=F(wT,bT), where wT is the true water vapor state as provided by the CloudSat-ECMWF product and where bT represents the rest of the atmospheric state (temperature, pressure, and hydrometeor profiles) also provided by the CloudSat-ECMWF product.

These synthetic radar returns are then run through the retrieval algorithm. For the retrieved profile shape, x0, a water vapor profile taken from a ERA-Interim monthly climatology was used. The iterative procedure stops when |1-wi+1wi| is lower than 0.05, which is normally achieved within two iterations.

During these retrievals we assume perfect knowledge of the forward model parameters; that is, the simulated radar returns used during the retrieval are given by 19PR^=F(wi,bT), or in other words, the only variable changing between y and y^ is the water vapor burden.

Sensitivity to assumed parameters is estimated using a perturbed set of synthetic radar returns following 20PR′=F(wT,b′), where b′ represents the perturbed forward model parameter. Only one of the parameters is perturbed at a time; for instance, when computing the systematic uncertainty related to temperature, only the temperature values are perturbed, while the rest (IWC, LWC, rain, snow, particle size distributions, etc.) are left unperturbed. Then, the retrieved total column water vapors using the perturbed measurements are compared to the retrieved values from an unperturbed run, i.e., using the measurements given by Eq. (). The difference between the two retrieved total column water vapors is used a measure of the impact of a given systematic error source. Instrument noise is not added to any of these simulations because its impacts are studied through Eq. ().

First we will explore the precision, that is, the expected random error associated with the radar uncertainty described in Sect. . Then we will explore potential systematic errors, such as the impact of not knowing the hydrometeor burden by assuming clear-sky conditions throughout the forward model simulations, the impact of not knowing precisely the temperature and pressure by using climatological values, the impact of changing the initial assumed water vapor profile, the impact of the spectroscopy errors, and surface roughness uncertainties by using a constant value.

We have evaluated the precision, yield, and systematic uncertainties of a differential absorption radar to measure total column water vapor from space. This technique requires at least two radar tones near the 183 GHz water vapor absorption line (“on” and “off” the line) to infer the humidity burden between the radar and the surface. In this work, we used 167 and 174.8 GHz, the extremes of the frequency range of VIPR . Further, we assume an antenna diameter of 1 m, a horizontal integration of 500 m, an integration time of 33 ms, a system temperature of 1800 K, an orbit of 405 km, and transmit powers varying from 0.1 to 100 W.

We apply a radar instrument simulator to weather analysis fields colocated with CloudSat near-global measurements to simulate surface radar returns to be used as measurements in end-to-end retrievals. We use an iterative least-squares fit retrieval algorithm that allows us to quantify both the expected precision and the impact of potential systematic uncertainties upon the retrieved total column water vapor.

Systematic uncertainties related to the pressure and temperature, the hydrometeor burden, the initial guess, the water vapor line strength, the water vapor, O2 and N2 continuum, multiple scattering effects, and the magnitude of the surface winds could result in potential biases lower than 0.5 mm. Systematic uncertainties associated with the water vapor line width could be up to 1.4 mm. This approximately corresponds to 4 % of the total column water vapor because a H2O line width perturbation mostly equates to perturbing the ratio of the surface radar returns by the same amount.

Precision and yield results can be summarized as follows.

Outside the tropics, regardless of transmit power, random errors are generally below 1.2 mm with fractional yields better than 0.7. With a transmit power of at least 10 W the random errors are below 1 mm and the fractional yield improves to better than 0.9.

These results suggest that at least 20 W of transmit power are needed to be able to measure total column water vapor globally with a reasonable yield. Output powers in the 10–100 W range would require additional research and development. DAR holds considerable potential as a technique to study the distribution of total column water vapor globally, that is, under most terrains and under most meteorological conditions, with considerably high horizontal resolution.