a. Correction of a CLWP bias in microwave retrieval products

Several sources of systematic error exist in passive microwave estimates of CLWP. Partitioning the emission signal between cloud and rainwater is most likely the largest source of error (Lebsock and Su 2014). This error derives from the cloud/rain mass partitioning, the assumptions of the precipitation drop size distribution, and the vertical structure of the cloud and precipitation water. Systematic errors are also associated with inhomogeneity within the sensor field of view (Bremen et al. 2002), cloud emission temperature (OWB08), instrument calibration, and uncertainty in the surface emissivity and spectroscopy (Meissner and Wentz 2012). These biases, particularly those associated with rain and cloud structure, are difficult to quantify and correct given the lack of an independent verification dataset for CLWP, but they may be as large as a factor of 2 in regions of shallow cumulus convection (Lebsock and Su 2014).

In this section we address one aspect of the bias that can be readily quantified that is most likely related to instrument calibration and/or bias in the radiative transfer: the CLWP clear-sky bias. Studies have found that RSS passive microwave CLWP tends to be (on average) nonzero in cases where coincident Moderate Resolution Imaging Spectroradiometer (MODIS;Platnick et al. 2003) observations show cloud-free scenes (e.g.,Greenwald et al. 2007;Greenwald 2009;Lebsock and Su 2014). It is possible that WVP or WIND or both are biased, with the residual microwave emission signal being artificially attributed to CLWP (i.e., a cross-talk issue). However, WVP and WIND have been found to be unbiased against in situ data (e.g.,Mears et al. 2001;Meissner et al. 2001;Trenberth et al. 2005;Wentz 2015). Such results argue against widespread cross-talk issues; although, in the less-commonly observed higher WVP or WIND scenes, where smaller magnitude WVP and WIND biases may be less apparent and studied, such issues may still be prevalent. Biases in the emissivity and/or atmospheric gaseous (oxygen, water vapor, etc.) absorption models used in the retrieval algorithm may be responsible for the CLWP biases. Either way, while one cannot definitively state the source of CLWP biases, bias correction is an important goal of the MAC-LWP product.

Using the MODIS Collection 6 Level 2 (i.e., 1 km) cloud mask and the version 7 Level 2B (i.e., pixel level) AMSR-E CLWP, we follow the approach ofGreenwald et al. (2007) andGreenwald (2009) to determine the extent to which clear-sky biases exist in the latest RSS passive microwave CLWP products. Cloud-free AMSR-E pixels are identified from the MYD35_L2 daytime cloud mask (thus, theoretically, CLWP = 0). Only AMSR-E pixels that are—in their entirety—determined to be probably or confidently clear are retained in the analysis. It is possible that nearby AMSR-E pixels containing precipitation could impact the clear-sky pixels; however, it was found these cases rarely occur. This clear-sky CLWP from the AMSR-E L2B product (2008 only) was composited as a function of AMSR-E WVP and WIND. Instead of finding that CLWP = 0 everywhere, it was found that CLWP systematically varied as a function of WVP and WIND. Because satellite sensors are intercalibrated (Wentz 2013), it is expected that this is not unique to AMSR-E and that the bias is characteristic of all microwave sensors used in the MAC-LWP product.

A WVP- and WIND-dependent bias correction was developed for the 0.25°-resolution RSS input based on the abovementioned empirical analysis. First, a cubic surface was fit to the observed clear-sky biases in order to extrapolate the observations to unobserved portions of the WVP/WIND space, given by the following equation:

View Expanded

whereU = WIND (m s⁻¹), CLWP_clr (kg m⁻²) is the CLWP in clear skies (derived, again, using AMSR-E), and WVP has units of kg m⁻². The fitting coefficients for Eq.(1) are provided inTable 1. The extrapolation is only weakly constrained by observations and is likely unreliable at the edges of the WVP/WIND domain, so it is capped at ±30 g m⁻². We note that these regimes occur rarely in the data and that bias correction in these regimes contributes negligibly to the CLWP data record.Figure 2 shows the WVP/WIND-dependent CLWP bias. For all oceanic scenes, this CLWP bias is subtracted from each satellite record (at the native 0.25° RSS resolution) as a function of WVP and WIND prior to ingestion into the MAC-LWP merging algorithm. We make two assumptions in applying the clear-sky bias correction. First, we assume that the clear-sky bias does not systematically vary with the presence of clouds nor immediately delta drop to zero when cloud fraction becomes nonzero. The implication of this assumption is that the bias identified in clear sky can be corrected in all pixels (including cloudy-sky pixels). Evidence suggests this may be a reasonable assumption, since biases between AMSR-E and MODIS CLWP for warm clouds exhibit a similar behavior to the clear-sky biases for the same categories of WVP and WIND (Greenwald 2009). Second, we assume that the bias is constant for all utilized microwave sensors, which is likely realistic as a result of the similarity in microwave sensors used in RSS product creation (i.e., passive microwave imaging channels at similar frequencies), the intercalibration that has been applied to the observed brightness temperatures by RSS, and the use of an identical retrieval algorithm on each sensor.

Table 1.

Coefficients for the clear-sky bias correction [Eq.(1)].

View Table

View Full Size

(top) RSS) version 7 AMSR-E CLWP biases as a function of WVP and WIND for clear scenes identified from MODIS data. (center) Histogram of WVP and WIND computed by summing all RSS WVP and WIND counts for each sensor dataset used in the MAC-LWP product (each bin is normalized by the maximum count over all bins). (bottom) For DJF and JJA, MAC CLWP minus CLWP from a test product constructed (using the MAC algorithm) without the WVP- and WIND-dependent bias correction applied to each input sensor dataset.

Citation: Journal of Climate 30, 24;10.1175/JCLI-D-16-0902.1

• Download Figure
• Download figure as PowerPoint slide

The global mean bias correction is 1.14 g m⁻², although regional differences are larger. This global mean correction is a factor of ~6 smaller than that found inLebsock and Su (2014) for the version 6 RSS AMSR-E product (6.3 g m⁻²). The decrease in the bias is likely due to the inclusion of negative CLWPs in the RSS version 7 product, which were previously forced to zero (Hilburn et al. 2010). The bottom panels ofFig. 2 show the regional pattern of the mean bias correction for boreal winter and summer. The overall effect is to decrease CLWP in the western Pacific (WPAC) and ITCZ regions (consistent with the finding that the CLWP is positively biased in high-WVP regions), and to increase CLWP for higher-latitude regions (lower WVP and higher WIND speeds, where the CLWP is largely negatively biased in the top panel ofFig. 2). Smaller increases occur in stratocumulus decks. Additionally, we find that the impact on CLWP trends was minimal.

Since the empirical bias correction was derived during year 2008 at the AMSR-E pixel level, we evaluate the effect of the correction on 1°-gridded CLWP in clear-sky MODIS scenes during years 2009 and 2010. We use the daily Level 3 MODIS 1°-gridded product (MYD08_D3 collection;Platnick et al. 2015) and proceed by storing the grid center latitude, longitude, and time for all daytime- and ocean-only overpass segments where the 1° cloud fraction is zero. The total number of 1° clear-sky counts is shown in the top-right panel ofFig. 3. With respect to processing the microwave products, as we read the RSS daytime AMSR-E 0.25°CLWP estimates using the MAC algorithm and compute the 1° average, for grid centers collocated in space and time with the MODIS clear-sky box, we record the CLWP estimate and, at the end, average them over the entire 2009–10 period. We repeat this aggregation for two additional experiments: for the first, we apply our clear-sky bias correction equation to the input CLWP data prior to averaging (as discussed earlier); for the second, we apply both the clear-sky bias correction and the diurnal cycle correction (the latter correction being derived and discussed insection 2c). For all experiments, we do not tally AMSR-E/MODIS data for the first and last 3 h of each day because of how daily averages are computed (such that parts of orbits at the beginning/end of subsequent/prior days are overwritten, and thus the daily average may include data from a different day). These orbital seams are found over the Pacific Ocean. This is the reason that large portions of the Pacific Ocean are masked out for analysis, as evident inFig. 3.

View Full Size

(top left) Global map of 1° bias-corrected AMSR-E CLWP calculated as the average of all CLWP observed during times when the MODIS (MYD08_D3, 1° grids, daytime only) product indicates 100% clear sky. (top right) Corresponding MODIS 1° clear-sky counts. (bottom) Global histograms of the 1°-gridded AMSR-E CLWP without the clear-sky bias correction, with the bias correction, and with both the bias and diurnal cycle corrections applied.

Citation: Journal of Climate 30, 24;10.1175/JCLI-D-16-0902.1

• Download Figure
• Download figure as PowerPoint slide

Histograms of the 1°-gridded CLWP estimates for these three experiments are shown inFig. 3. In theory, CLWP is 0 g m⁻². Without the bias correction (“No Corrections”), the histogram is skewed to the left with a mean (median) CLWP bias of −2.37 (−1.88) g m⁻². With the clear-sky bias correction (“Bias Corrected”), the histogram becomes less skewed and centered closer to zero, and the calculated global mean (median) bias improves to −0.95 (−0.42) g m⁻². When we include both the diurnal cycle and clear-sky corrections, the histogram broadens but remains comparably biased relative to the case with the clear-sky correction only (mean/median is −0.65/−0.68 g m⁻²). We include the latter experiment because the diurnal cycle correction is included, and thus it represents the closest approximation to the MAC-LWP methodology. Importantly, the overall global bias is not degraded in this case. A spatial map of the AMSR-E CLWP (after the clear-sky correction) is provided in the top-left panel ofFig. 3. Most striking is the residual systematic negative bias off the west coasts of major continents, consistent with the remaining longer tails of the histograms inFig. 3 extending to negative CLWPs. A number of these locations are close to major deserts, and large dust particles blown off the continents may provide enough scattering to reduce the 37-GHz brightness temperature used in CLWP retrieval [e.g.,Ge et al. (2008) discuss such issues for this microwave frequency where depressions of up to 5 K can occur]. A systematically reduced brightness temperature would lead to a consistently smaller retrieved CLWP. Overall, while clear-sky CLWP is in better agreement with MODIS in the global-average sense, future investigations of regional parameters impacting the retrievals will have to be performed.

b. Computation of individual sensor TLWP fields

As mentioned, algorithms relying upon passive microwave radiation for cloud water retrieval often have difficulty distinguishing the radiative signal arriving from precipitation-sized hydrometeors (i.e., rainwater) from that of cloud water (Bennartz et al. 2010). Microwave attenuation is strongly related to the TLWP, with some variability arising as a result of dependence on drop size distributions (DSDs) that likely vary with environment. To separate CLWP from TLWP, assumptions must be made about the ratio of cloud to precipitating liquid, the precipitation DSD, droplet fall speeds, and the vertical distribution of the condensate. Reliable observations of such variables are lacking, and thus most retrieval algorithms have historically treated the separation more simply (e.g.,Petty 1994;Wentz and Spencer 1998). Below a threshold of 180 g m⁻², in the RSS retrieval algorithm, all TLWP is assumed to be CLWP (Hilburn and Wentz 2008). Above this threshold, RSS computes CLWP through the use of the following equation (Wentz and Spencer 1998;Hilburn and Wentz 2008):

View Expanded

whereH is the height of the rain column (km), andR is the surface rainfall rate (mm h⁻¹). VariableH is assumed to be the height of the freezing level and is parameterized as a function of sea surface temperature (SST). The formulations forH, provided inHilburn and Wentz (2008), are based on regressions of freezing-level heights on SSTs from the National Centers for Environmental Prediction (NCEP) reanalysis product.

The form of Eq.(2) itself is likely to not capture the complete physical relationship betweenR,H, and CLWP. But form aside, it is also expected that there will be variability in the threshold for nonzero rainwater content [e.g., Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) retrievals discussed inBerg et al. (2006) andElsaesser and Kummerow (2008)]. Cloud–rain processes are complicated, and thus large uncertainty may be introduced into the CLWP climatology for regions where TLWP approaches 180 g m⁻² (and again, even below this threshold, since conversion of cloud to rainwater is environment dependent). Evidence that some aspect of the RSS cloud–rain partitioning is biased is revealed by the correlation ofCloudSat rainwater path with the bias of MODIS and AMSR-E CLWP for low-lying liquid clouds (Lebsock and Su 2014). Given the inherent uncertainty in the cloud–rain partitioning methods, one way to mitigate using biased CLWP in the MAC-LWP climatology is to screen oceanic regions for which TLWP is substantially larger than CLWP. Here, we outline the mathematical steps taken to reproduce the TLWP field to facilitate such filtering of the data.

We use optimally interpolated SSTs (Reynolds et al. 2002) and Eqs. (22a)–(22c) fromHilburn and Wentz (2008) to inferH. By using the RSSR and assuming it is constant with height overH [Hilburn and Wentz 2008, Eq. (21)], we can reverse engineer the 0.25°CLWP retrieval to compute TLWP for each satellite record. Consistent with the RSS algorithm, we assume a Marshall–Palmer exponential DSD and the following general formulations [also provided and discussed inBennartz and Petty (2001)]:

View Expanded

View Expanded

View Expanded

whereN(D) is the number of drops per volume and size interval;N₀ = 8 × 10⁶ m⁻⁴, λ varies with rainfall rate; andA,B,C, andE are constants. With a Marshall–Palmer DSD,A =N₀ andB = 0. We can integrate Eq.(3) multiplied by the mass of a drop of diameterD (assuming a liquid water densityρ_w = 1000 kg m⁻³) to arrive at the following formulation for rainwater content (RWC):

View Expanded

The RSS algorithm, followingWilheit et al. (1977), assumesC to be 81.6 mm h⁻¹. Note that when all parameters are converted to SI units,C becomes 171.3 m s⁻¹, which is comparable to the 172.1 m s⁻¹ value provided in Table 1 ofBennartz and Petty (2001), andE is fixed at −0.21. Substituting all constants into (and algebraically rearranging) Eq.(6), recalling the assumed constant RWC with height overH, and adding the result to CLWP, we arrive at the following expression for TLWP:

View Expanded

where for clarity TLWP and CLWP are in kg m⁻³,H is in km, andR in mm h⁻¹. We then proceed with computing TLWP for each sensor product.

c. Multisensor data record construction and available output fields

The satellite data merging process largely follows the UWisc approach, and we refer the reader to section 3 ofOWB08 for an in-depth discussion. We summarize important points here and note any differences in the methodology used. We also refer the reader to the MAC-LWP algorithm theoretical basis document (Elsaesser et al. 2015) for additional technical details on combining satellite swaths. All 0.25°CLWP, TLWP, and observation times [local solar times (LSTs)] are binned to a 1° resolution. Thus, the 1° grids are gridbox average estimates of all scenes, since all 0.25° estimates, whether clear sky (theoretically, CLWP = 0 and TLWP = 0) or not, are included. For the non-sun-synchronous TMI product,OWB08 previously neglected data over the 30°–40° latitude belts because of concerns in how multiple ascending (or descending) overpasses—sensing at different LSTs—were averaged. However, we have determined that the reported LST and CLWP are still the most recent data at the higher TRMM latitudes, and not an average over previous ascending (or descending) swaths. Therefore, diurnal cycle information is retained, and we use these data now in our 1° averages. The use of the precessing Global Precipitation Measurement (GPM) Microwave Imager (GMI) also allows for greater resolving of the diurnal cycle for latitudes between 40° and 60°. While the amplitude and phases of the diurnal cycles over midlatitude open ocean are likely more random and noncyclical (i.e., variation is more influenced by synoptic-scale weather systems), distinct CLWP diurnal cycles near higher-latitude coasts may be present during some seasons; at this point though, with less than 3 years of GMI data available, we are as yet unable to determine any notable differences in CLWP near coasts compared to the product derived without GMI. For each 1° grid box and month, we also store the standard deviation of CLWP (σ_CLWP), TLWP (σ_TLWP), and the number of 0.25° RSS pixels going into each grid box.

Figure 1 shows the suite of satellites (used in the MAC-LWP product) observing Earth at varying equatorial overpass times. On any given day, for sun-synchronous satellites and a diurnal cycle of clouds well approximated by a first harmonic sinusoid, varying observation times have no impact on the computation of the daily average. However, varying overpass times (either from combining different satellites or the same satellite with temporally drifting overpass times) superposed upon a diurnal cycle characterized by higher harmonics implies a potentially spurious variation in retrieved CLWP. This is especially the case for periods where the availability of orbiting sensors is limited (e.g., prior to 1993). The removal of such a diurnal cycle effect prevents artificial trends and variability from being introduced into the CDR arising from a variation in the LST of the observations over time (i.e.,Fig. 1), and thus this is one important component of our merging technique. Fortunately, the diurnal cycle problem for orbiting microwave sensors is, overall, less of an issue relative to sensors observing in the VIS/IR spectrum (Waliser and Zhou 1997).

As inOWB08, a harmonic regression method is used to simultaneously compute the fit for both the mean monthly diurnal and semidiurnal (i.e., second harmonic) cycles, and the monthly mean CLWP. The predictor variables are trigonometric functions of LST, and the approach produces monthly means that are automatically corrected for diurnal cycle effects. For each grid box and month, the LWP is modeled using the following sinusoidal function:

View Expanded

where CLWP(Y_i, LST_i) is the CLWP of sensor measurementi at yearY and time LST. The top panels ofFig. 4 show CLWP(Y_i, LST_i) for three grid boxes. The is the best-fit average of CLWP for a given year (e.g., the weighted average of all the same-colored CLWP measurements, taking into account the intramonthly variability in CLWP and sample counts).TermA₁ (T₁) is the amplitude (phase) of the first-harmonic fit,A₂ (T₂) is the amplitude (phase) of the second-harmonic fit, ω is the radial frequency corresponding to a 24-h period, and ε is an error term that is considered independent of all mentioned variables. This error term is discussed at length inOWB08 as well. The inclusion of this term allows us to compute statistical errors on the monthly CLWP estimates and the diurnal cycle fit parameters (all of which we make available, as shown inTable 2). The covariance matrix corresponding to the fit parameters can be used in standard error propagation packages to compute the envelope of uncertainty on the diurnal cycle for any grid box and month; example uncertainty envelopes are shown inFig. 4.

View Full Size

(top) For different grid boxes and years, the satellite-sensor CLWP as a function of LST. Vertical errors bars for each CLWP observation are shown (see text for explanation). The best-fit diurnal cycle is overlain on each panel (dashed black line), with the 1-, 2- and 3-sigma errors (shades of gray) on the calculated best fits. (bottom) The corresponding numbers of samples going into the gridbox CLWP estimates.

Citation: Journal of Climate 30, 24;10.1175/JCLI-D-16-0902.1

• Download Figure
• Download figure as PowerPoint slide

Table 2.

MAC-LWP data fields provided in netCDF4 format. CLWP and TLWP fits are derived month by month for the 1988–2016 period for all oceanic grid boxes. The “order of fit” variable for every grid box is an integer that varies from 0 to 2 with the following meanings: 0 = (fit for CLWP mean only), 1 = (fit for CLWP mean and first harmonic), and 2 = (fit for CLWP mean and two harmonics). TermM (in the covariance matrix) is the monthly mean fitted gridbox CLWP. Variances and covariances are monthly climatologies (i.e., currently 29-yr averages; thus, 12 values—January–December—for each grid box). Only boldface entries of the covariance matrix are made available (symmetric matrix). In the output files, off-diagonal elements of the covariance matrix are converted to correlations, and diagonal elements are converted to standard deviations.

View Table

Overall, for any grid box, year, and month, in order for a fit to be derived (whether a weighted-mean or sinusoid fit), the following criteria must be met: 1) a minimum of 10 years of data; 2) for any year, at least 10 (or 3) days had to be sampled by sun- (or nonsun-) synchronous sensors; and 3) the range of days had to exceed 25 (4) for the sun (or nonsun-) synchronous sensors. Such requirements ensure that a given month is well sampled over time (as opposed to days clustered toward the beginning, middle, or end of a given month during any year). No sinusoid fit is performed if a temporal gap of greater than 12 h occurs without a CLWP(Y_i, LST_i) measurement. Additionally, if there is a gap of greater than 5 h in a given month for which no CLWP(Y_i, LST_i) measurements are available, then a fit is performed for only the first harmonic of the diurnal cycle. These gap thresholds follow the general Nyquist sampling frequency thresholds necessary for fitting cycles with periods of 12 and 24 h.

Once we remove the diurnal cycle fit from the CLWP measurements for each grid box and month, the actual intramonthly variability estimates are calculated through use of the standard pooled variance equation that computes the standard deviation of a dataset using only the averages and standard deviations of the subcomponents. Here, the diurnal cycle adjusted CLWP(Y_i, LST_i) estimates are the averages, and the associated σ_CLWP estimates are the subcomponent standard deviations. Each error bar on CLWP(Y_i, LST_i) inFig. 4 is actually the σ_CLWP/, wheren is the sample count. While the diurnal cycle fitting methodology has been tailored to CLWP, we perform the exact same technique on the TLWP fields. We make available all CLWP parameter fields and error estimates, and all TLWP monthly mean estimates and statistical errors. The complete list of MAC-LWP data fields is shown inTable 2.

a. Mean state and diurnal cycle climatologies

The CLWP and TLWP climatologies for the boreal winter and summer seasons are shown inFig. 5. For the overlapping period terminating in December 2008, MAC CLWP systematically decreases by 10%–20% relative to the UWisc climatology over most low-cloud regimes; in fact, this decrease extends to nearly all locations where CLWP is less than 80 g m⁻². The UWisc climatology was constructed using the version 6 RSS products. The currently used version 7 products were processed using a retrieval algorithm that included an improved water vapor continuum absorption model and beamfilling correction for rainfall retrieval (Wentz 2013). Such changes would impact CLWP via cross-talk issues that inevitably arise during the retrieval of multiple parameters. Perhaps more relevant for CLWP was the aforementioned removal of a clear-sky positive bias in cloud water that partly resulted from forcing negative CLWP retrievals to zero in the version 6 RSS products (Hilburn et al. 2010). Negative cloud water retrievals are a consequence of random errors in brightness temperatures producing negative cloud retrievals, and while unphysical, the forcing to zero led to a high-CLWP bias, especially in regions characterized by low-LWP clouds (e.g., stratocumulus, trade cumulus). This partly explains the pattern of differences found between MAC and UWisc inFig. 5. Larger remaining MAC and UWisc differences are the result of the bias correction detailed insection 2a (andFig. 2). Specifically, decreases of 5%–10% over the western Pacific, Indian Ocean, and intertropical convergence zone (ITCZ) regions and increases of 5%–20% over portions of the southern oceans and poleward of 40°N (including the midlatitude storm tracks) were found in the MAC climatology relative to a test product constructed without the empirical bias correction.

View Full Size

(top to bottom) For the 29-yr record, the (left) DJF/(right) JJA average of CLWP, MAC CLWP minus the UWisc (OWB08) record for the overlapping 1988–2008 period, the TLWP, and the ratio of CLWP:TLWP.

Citation: Journal of Climate 30, 24;10.1175/JCLI-D-16-0902.1

• Download Figure
• Download figure as PowerPoint slide

Figure 5 also shows the seasonal TLWP maps. As discussed, while low-frequency microwave attenuation is mostly proportional by liquid water mass, the dependence on DSD is not negligible. The assumption of a Marshall–Palmer DSD is most reasonable for portions of the midlatitudes and most of the tropical oceans. Thus, the TLWP product is most reliable there. While uncertainty in TLWP still exists, the CLWP:TLWP ratio map (Fig. 5) allows the product user to determine where rainwater contribution to LWP is minimal. There is subjectivity in the ratio to use for filtering areas of lower confidence in the CLWP climatology. If we consider a ratio of 0.8² as the metric for expressing our greatest confidence in the CLWP estimate, then most of the southern oceans, polar latitudes of the Northern Hemisphere, and nearly all of the trade cumulus and stratocumulus decks are included. The importance of these cloud regimes in determining cloud–climate feedbacks was discussed, and the availability of the TLWP field for use in establishing confidence in CLWP in such regions is a unique feature of the MAC-LWP product.

Global maps of CLWP statistical (i.e., random) errors and reduced chi-square are shown inFig. 6. For presentation purposes, statistical errors are normalized by the monthly mean CLWP [averaged over all years and December–January (DFJ) or June–August (JJA), as indicated] and converted to percentage errors. As discussed inOWB08, these errors integrate down over longer periods, whereas systematic errors (e.g., cloud–rain partitioning), which are likely larger to begin with, would become more dominant. The map can be used for assessing the goodness of fit. The reduced is the standard chi-square estimate divided by the degrees of freedom (N₁ −N₂), whereN₁ is the total number of CLWP(Y_i, LST_i) measurements spanning 29 years (for any given grid box/month) andN₂ is the number of fit parameters (i.e., 33, or the number of years for which the monthly means are estimated plus the four diurnal cycle fit parameters). The reduced normalizes for the number of data points, which varies by geographic location, and thus we expect that the reduced should beO(1).

View Full Size

(top to bottom) For (left) DJF/(right) JJA 1988–2016, the average monthly statistical error on fitted CLWP, and the chi-square metric for assessing the goodness of fit between the observed CLWP and the assumed harmonic fits.

Citation: Journal of Climate 30, 24;10.1175/JCLI-D-16-0902.1

• Download Figure
• Download figure as PowerPoint slide

Overall, for areas where the metric far exceeds unity, we can expect a poor fit—for example, Eq.(8) would not be a suitable choice for modeling the diurnal cycle—or an inappropriate estimation of intramonthly variability. In fact, there is some indication of reduced quality of fit in the subtropical stratocumulus regions that are characterized by high-amplitude diurnal cycles. However, the deviation from unity is small and the two-mode harmonic fit is sufficient for modeling CLWP across most oceanic regions. While within the expected bounds, the slight increase in across the 40°S–40°N domain reflects the use of TRMM data. For any given LST bin, TRMM samples any grid box a limited number of times per month. Thus, the TRMM diurnal cycle depiction is characterized by additional noise (also evident inFig. 4) and the elevated reflects this. Portions of the Mediterranean Sea, during boreal summer, exhibit the highest values (2–4) found in the dataset. These regions and times of year are among the least cloudy locations in the MAC-LWP dataset; in terms of monthly CLWP, magnitudes are often less than 10 g m⁻². An investigation of the input RSS satellite datasets for grid boxes in this region show that for nearly all LSTs, CLWP is often negligible; therefore, intramonthly variability is negligible too. However, there are small systematic biases between the datasets (~1–5 g m⁻²), and therefore because the intramonthly variability is nearly zero, there is a large penalty for any departure of the fit from any individual sensor CLWP estimate. This leads to a larger estimate in these regions.

Figure 7 shows MAC CLWP diurnal cycle information, which is useful for process-level studies and particularly useful for assessing model-simulated diurnal cycles. Consistent with what was shown inOWB08, the normalized amplitude of the diurnal cycle first harmonic is greatest near coastal regions, and across the South American and Namibian stratocumulus decks. The amplitude is larger than the semidiurnal (second) harmonic amplitude. While the second harmonic amplitude is greatest near coastal regions, it is commonly nonzero over the open oceans. We discussed that sensors observing a grid box at varying times of the day may be expected to disagree with each other if the cloud diurnal cycle is best described with the inclusion of a nonzero second harmonic sinusoid. In the following section, we assess some of the impacts of the second harmonic on the multisensor record construction.

View Full Size

(top to bottom) For the 29-yr record, the (left) DJF/(right) JJA average first harmonic phase (i.e., LST of the maximum first harmonic fitted CLWP), average first harmonic normalized amplitude (actual amplitude divided by the average CLWP), average phase of the second harmonic, and average second harmonic normalized amplitude.

Citation: Journal of Climate 30, 24;10.1175/JCLI-D-16-0902.1

• Download Figure
• Download figure as PowerPoint slide

b. Diurnal cycle correction impacts on individual sensor CLWP and trend computations

Consider two sensors [Special Sensor Microwave Imager (SSM/I)F13 andF14] whose LST records trend relative to each other over their common shared-time period (Fig. 1, and bottom panels ofFig. 8). The tropical-average and two regional-averaged CLWP records associated with each sensor are shown in the top-left three panels ofFig. 8. Note that a product creation technique that would entail a straight (or sample count weighted) average of these two records would give an artificial upward trend in CLWP over the period, since the two records approach each other toward the end of the period due to the positive trend of SSM/IF14. The diurnal cycle corrected CLWP records are shown in the top-right three panels ofFig. 8. Note that a diurnal cycle correction [which, on a sensor-by-sensor basis, is performed through subtraction of the Eq.(8) fit at every month/year/grid box] yields two sensor CLWP records that barely exhibit any intersensor trends. Therefore, an average of the two records would yield a CLWP record that does not trend with time. These results demonstrate the value of the framework utilized for creating the multidecadal, multisensor CDR.

View Full Size

(top to bottom) Original SSM/I sensor (from RSS) CLWP as a function of year for the tropical ocean belt (40°S–40°N), the Southern Oceans (60°–45°S), the South America stratocumulus deck (20°–12°S, 271°–281°E), and the corresponding morning equatorial overpass times (LSTs) for the two sensors. (right) As in (left), except that the satellite records have been corrected for diurnal cycle effects using the MAC-LWP diurnal cycle amplitude/phase information. The equatorial overpass time panel has been repeated to aid in visual interpretation.

Citation: Journal of Climate 30, 24;10.1175/JCLI-D-16-0902.1

• Download Figure
• Download figure as PowerPoint slide

These results further suggest that the observed CLWP record—including trend computations—may be different depending on whether the diurnal cycle correction was taken into account. But, to what extent is a diurnal cycle correction affecting trends? InFig. 9, we show the CLWP trend maps for MAC-LWP and the trend map for a record created by simply averaging all sensor products together (where each is weighted by the number of samples). Our focus is only on trends and time series in regions for which we have high confidence in the CLWP estimates (i.e., CLWP:TLWP ratio is >0.8) and where trends were identified as statistically significant at the 95% level (using the methodology ofSanter et al. 2000). Note that we are not arguing the physical causes of trends or the significance of trends; instead, we are investigating only the effect of the diurnal cycle correction to infer to what extent our correction impacts the overall record. Instead of large changes in CLWP time series and trends, we find that our accounting of the diurnal cycle mostly impacts the CLWP record prior to 1993 (e.g., highlighted boxes inFig. 9), which is the period when only two SSM/I sensors were observing Earth (Fig. 1). This period is analogous to our discussion of the two SSM/I sensors inFig. 8, which we can consider to be a limiting case where few orbiting satellites implies greater discrepancy in CLWP before and after a diurnal cycle correction. For the box 1 region ofFig. 9, which comprises two negative trend bull’s-eyes in the Pacific Ocean off the immediate west coast of South America, the amplitude of the second harmonic of the diurnal cycle was among the highest found (Fig. 7). After the diurnal cycle correction was applied, the negative trends were no longer statistically significant. As for the physical cause of a bimodal diurnal cycle, the increased second harmonic amplitude may be attributed to the superposition of diurnal cycles in solar heating and vertical velocity (Garreaud and Muñoz 2004). For a detailed discussion on the impact of solar heating on CLWP in this region, seeWood et al. (2009, and in particular their Fig. 6).

View Full Size

(top) The 29-yr CLWP trends from MAC-LWP and a proof-of-concept dataset (i.e., “uncorrected”) that assumes no diurnal cycle when the satellite products are merged. The boundary is drawn where the CLWP:TLWP ratio falls below 0.8 (light gray line; wide swaths of white). Inside the boundary, only regions for which trends are significant at the 95% level are shaded. (bottom) CLWP time series from the MAC-LWP and uncorrected datasets: comprising two <0 g m⁻² y⁻¹ trend bull’s-eyes in the strip off the west coast of South America (where the second harmonic normalized amplitude exceeds 12% inFig. 7; box 1); comprising the southeast Pacific stratocumulus deck (box 2), and covering the southern oceans (60°–45°S; box 3). For all panels, the seasonal cycle in CLWP has been removed. Computed trends for each box (color coded by dataset) are listed at the top of each time series panel. CLWP trends for MAC are not statistically significant in box 1 and are masked out with asterisks.

Citation: Journal of Climate 30, 24;10.1175/JCLI-D-16-0902.1

• Download Figure
• Download figure as PowerPoint slide

Fortuitously perhaps, it appears that for the remainder of the 29-yr record, enough satellites were observing Earth at various LSTs to effectively “resolve” the diurnal cycle in a manner that the average is nearly unbiased, and trend computations are minimally affected (mostly, a slight decrease in magnitudes for all regions characterized by positive trends).Figure 4 supports this claim as well, where we find that rarely does 3 h pass without a passive microwave observation (especially over the 40°S–40°N domain).