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MODerate Resolution Imaging Spectroradiometer (MODIS) aerosol retrievals over the North Atlantic spanning seven hurricane seasons are combined with the Statistical Hurricane Intensity Prediction Scheme (SHIPS) parameters. The difference between the current and future intensity changes were selected as response variables. For 24 major hurricanes (category 3, 4 and 5) between 2003 and 2009, eight lead time response variables were determined to be between 6 and 48 h. By combining MODIS and SHIPS data, 56 variables were compiled and selected as predictors for this study. Variable reduction from 56 to 31 was performed in two steps; the first step was via correlation coefficients (cc) followed by Principal Component Analysis (PCA) extraction techniques. The PCA reduced 31 variables to 20. Five categories were established based on the PCA group variables exhibiting similar physical phenomena. Average aerosol retrievals from MODIS Level 2 data in the vicinity of UTC 1,200 and 1,800 h were mapped to the SHIPS parameters to perform Multiple Linear Regression (MLR) between each response variable against six sets of predictors of 31, 30, 28, 27, 23 and 20 variables. The deviation among the predictors Root Mean Square Error (RMSE) varied between 0.01 through 0.05 and, therefore, implied that reducing the number of variables did not change the core physical information. Even when the parameters are reduced from 56 to 20, the correlation values exhibit a stronger relationship between the response and predictors. Therefore, the same phenomena can be explained by the reduction of variables.

Hurricane forces cause enormous natural disasters. Fortunately, the destruction capacity can be predicted ahead. Satellite measurements for hurricanes and the vast amount of data gathered by hurricane hunters; enable us to measure the force and to track hurricanes. National Oceanic and Atmospheric Administration (NOAA) hurricane hunter [

Satellite observations, hurricane hunters’ data collection and numerical weather predictions have advanced the forecasting of hurricane tracks over the last few decades. However, there have been limited improvements in forecasting hurricane intensity [

Rosenfield

The combination of SHIPS [

In December 1999, a new generation multi-spectral satellite (Terra, EOS AM-1) was launched carrying the first MODIS sensor. The second MODIS sensor was launched on the Aqua (EOS PM-1) platform on May 2002. Both MODIS sensors onboard Terra and Aqua platforms have been used to monitor the environment continuously in a wide range of spectral frequencies from the blue to the thermal infra-red range. MODIS is an exceptional source for monitoring the Earth’s water cycle and environment as both Terra and Aqua satellites have a sun-synchronous orbit at 705 km height. Aqua in ascending mode crosses the equator daily at 1:30 p.m. while Terra, in descending mode, crosses the equator at 10:30 a.m. daily [

The MODIS aerosol product measured over the ocean [

The reflectance is calculated from the geometry pertaining to the state of the ocean [

Aerosol measurements from MODIS over the oceans, such as aerosol optical thickness and aerosol size distribution can be retrieved from the daily Level 2 data at the spatial resolution of a 10 km × 10 km pixel array at nadir from MODIS Atmospheric Product website [

SHIPS data was collected based on DeMaria

The National Hurricane Center (NHC) of National Weather Service (NWS) issues public advisories for Atlantic tropical cyclones every six hours. Based on the NHC website [

Pixels close to the hurricane center are usually covered by clouds, making it impossible to retrieve AOT with MODIS measurements. Thus, for this study, a unique technique was developed to select spatial coordinates to investigate aerosol retrievals as shown in

The phenomena being investigated are three-dimensional in case of the variables such as Relative Humidity and Temperature where data is available between sea level and top of the atmosphere (between 100 to 1,000 mb). Vertical Shear and Wind are also three-dimensional phenomena. Although the MODIS sensor on both the Aqua and Terra satellites provides a measure of the vertically integrated dust concentration [

We investigated whether the 3 to 4 degrees of annulus size would be an appropriate spatial coordinate selection process because aerosol parameters were retrieved around each hurricane by following the direction of motion of a hurricane. Since linear motion of a hurricane is very slow, for example a hurricane’s forward speed averages around 15–20 mph [

MODIS aerosol data at 0.55 μm was averaged in the vicinity of 1,200 and 1,800 h and associated with the corresponding SHIPS data at 1,200 and 1,800 for each day. This technique was employed on a spatial area for studying all 24 hurricanes between the day they formed and the day they dissipated. The center of the concentric circle corresponds to the approximate location of the hurricane core. The angle within this region was spaced out into 36 segments of 10° each. Data for each 10° segment was retrieved and averaged resulting 36 data points at a particular time and date. The readings from these 36 segments were then further averaged to present a final average to demonstrate the values between 0° and 360°. For this analysis, this concentric circles center was programmed to move with the hurricane center for 1,200 and 1,800 h.

Aerosol retrieval variables (_{future} = VMAX_{future} − VMAX_{current}, for example, FD_{06} = VMAX_{06} − VMAX_{current}, where VMAX is the maximum 1-min wind speed. Similarly, FD_{12}, FD_{18}, FD_{24}, FD_{30}, FD_{36}, FD_{42} and FD_{48} are calculated. We started our analysis by combining the 49 SHIPS parameters from DeMaria _{06} and FD_{48}). For each FD_{future} set, correlation analysis will be performed with each of the 56 variables to determine the correlation coefficient (cc) between each variable and the FD_{future}. Variables having small correlation (|cc| < 0.165) were filtered out. These correlation based filtering create the first set of predictor, Predictor_1 which comprised 31 variables.

As the second step of data reduction, PCA is carried out on selected variable groups. The reduction of variables for each group by PCA is described in

PCA is known as a variable reduction procedure and is useful when variables are significantly correlated. In each group, the variables describe the same physical mechanisms. The numbers of some group variables were shrunk to a reduced number of principal components. Although the details may be different among variables, their overall trends are the same based on their values. Therefore, using PCA to identify a reduced number of variables in the same group is a natural step. In this case, AOT, MCO, CCNO variables reduced to Aero-PC1 and Aero-PC2 for the Aerosol group and presented in the combination as Predictor_2. Similarly, for the Wind group, V20C U200 U20C TWAC TWXC are reduced to Wind-PC1 Wind-PC2 Wind-PC3 and presented as a combination of Predictor_3.

There will be some loss of information when a variable reduction was performed, therefore, when this technique was applied we made sure to select group of variables which exhibit similar physical phenomena to minimize loss of information. We have analyzed MODIS aerosol retrievals and SHIPS parameters for 24 hurricanes spanning 7 hurricane seasons. By combining MODIS and SHIPS data, 56 variables were compiled and selected as predictors. Variable reduction from 56 to 31 was performed via correlation coefficients. Among these 31 variables, some are highly correlated or “redundant” with one another. For example, Sea Surface Temperature, Air Temperature and Ocean depth of the (20 and 26 °C) isotherm for the Temperature group are usually very strongly correlated. Therefore, one or two of these variables or the combination of the variables (potentially for a newly defined, more representative variable) could be used as a substitution for all the others. For our study we selected the variable which is most likely to be the direct cause of categorical response and relevant to the hurricane intensity studies and of course highly correlated.

Identification and comparison of the impact of our approach on uncorrelated and correlated variables described in

When comparing the results we see for Predictor_2 and Predictor_6, R^{2}, Adjusted R^{2} and F Values had decreased for uncorrelated case while RMSE had creased increased. This illustrated that uncorrelated variables had lost more information than the correlated variables.

For the Relative Humidity group, RH-PC1 RH-PC2 principal components were extracted from the variables RHLO RHMD R000 and presented as Predictor_4. Predictor_5 and Predictor_6 were presented similarly for the Shear and Temperature groups. For each predictor the combination of variables along with the principal components are shown in

The average RMSE for the six Predictors for 06, 12, 18, 24, 30, 36, 42 and 48 h was found to be 8.33, 12.28, 14.76, 16.27, 17.96, 19.28, 19.69 and 20.38 respectively as illustrated in ^{2} value. The variation among the Predictors RMSE varied between 0.01 through 0.05. This small variation suggests that reducing the number of variables did not change the core physical information. Therefore, the same phenomena can be explained by the reduction of a variable.

As shown in

Dimensionality reduction infers loss of information; therefore, the goal is to preserve as much information as possible by minimizing difference between the higher (original) and lower dimensional variables representation. One of the commonly used methods to determine lower dimensional variables is the principal component analysis (PCA), in which the principal components, linear combination of the originals, ranked based on the contribution to the total variance, are chosen as new variables. The first few new variables are responsible for interpreting most of the physical phenomena described by the original variables that have been reduced.

Two Aerosol principal components explain 98.4% (loss = 1.6%) variability when variable reduction happened from three to two. For Wind, five variables were reduced to three principal components which resulted in a cumulative variability of 98.4% (loss = 1.6%). When PCA was performed on three Relative Humidity variables, it gave us cumulative variability for the two principal components as 95.20% (loss = 4.8%). PCA for eight Shear variables gives variability for the four reduced components as 88.8% (loss = 11.2%). Six Temperature variables were reduced to three components with 91.2% (loss = 8.8%) cumulative variability.

Reducing the variables does not always lead to a better result, but it is expected that the result should be comparable to that with original variables. Reduction of variables removes irrelevant features and dampens noise; it also leads to more comprehensible model because the model involves fewer variables [

For the aerosol category the first two components have the proportionality of 0.80 and 0.18 respectively. Most of the weight is on the Aero-PC1 component which is about four times larger than Aero-PC2. For the Wind category, the first component is less than two times the second component and over three times larger than the third component. The proportion for Humidity shows that the first component is twice as large as the second component. Shear has a proportion of about 51% for the first component. The first component of the temperature has about 59% weight. When comparing the first component of the Aerosol, Wind, Relative Humidity, Shear and Temperature we found that aerosol had the highest proportion followed by Humidity, Temperature, Wind and Shear. Therefore, aerosol might have some influence based on the first component comparison.

In

MLR technique was applied for the model forecast lead time of 06, 12, 18, 24, 30, 36, 42 and 48 h. For each FD_{future}, six predictor sets (Predictore_1 through Predictor_6) variables were analyzed. ^{2} varied between 15.0% and 18.8% which is about 25.3% variation. For FD12, R^{2} varied between 24.4% and 27.8% which is about 22.7% variation. The smallest variation for FD48 is 9.3% between the highest and lowest values.

Let us select FD48 as the response and explanatory variables as Original set of 56, Predictor_1 as 31 and Predictor_6 as 20. For the Original variables, 55 degrees of freedom (DF) provide us with RMSE = 19.47, R^{2}= 71.1%, R^{2} (adj) = 64.5%, F = 10.72 and P = 0.000. For Predictor_1, DF = 30, RMSE = 20.38 R^{2}= 65.1%, R^{2} (adj) = 61.1%, F = 16.46 and P = 0.000. For Predictor_6, DF = 19 RMSE = 20.36 R^{2} = 63.7% R^{2} (adj) = 61.2% F = 25.02 P = 0.000. One interesting finding is that the adjusted R^{2} with 20 variables is larger (or equal to) the corresponding value with 31 variables. At least in this special case, reducing the number of variables does not reduce the effectiveness of the MLR model but increases the efficiency.

^{2} = 71.1% indicating that about 71% of the variation in FD48 can be accounted for by the 56 predictors. Based on the results of the Sequential Sum of Squares we can see components such as zonal winds, estimated ocean heat content and sea surface components are the greatest contributors to the MLR. This is also true for the intensity changes at 06, 12, 18, 24, 30, 36 and 42 h.

In ^{2} = 65.1% indicating that about 65% of the variation in FD48 can be accounted for by the 31 explanatory variables. The contribution factor in this case is mainly governed by the same variables as shown in

The effect of the SHIPS and MODIS variables used on the FD48 as illustrated in ^{2} = 63.7% indicating that about 64% of the variation in FD48 can be accounted for by the 20 explanatory variables. The contribution factor in this case is governed by tangential and zonal wind in addition to AOT and RH.

^{2} and adjusted R^{2} values along with the RMSE and the Residual Errors for the MLR performed between the eight response variables and six predictor sets.

At 48 h forecast intervals as in ^{2}, adjusted R^{2} and RMSE are the largest and at 06 h, the smallest was recorded. The range of values of R^{2}, adjusted R^{2} and RMSE between 06 and 48 h for Predictor_6 were found to be (15.0% and 63.7%), (9.1% and 61.2%), (8.35 and 25.02) and (69.64 and 415.0) respectively. The RMSE and Residual errors found negligible for all six predictors. However, significant R^{2} values were found to be larger when considering the 42 and 48 h lead time for longer forecast intervals. This may be due to the results of discretization of the intensity of values as per DeMaria

In

In addition, for this study MODIS Aerosol Retrievals were averaged, therefore, it is important to articulate the statistical uncertainty for the three variables used in the Aerosol PCA. For example, the quoted uncertainties for Fabian 2003 found for AOT (0.23 ± 0.02), MCO (15.54 ± 1.89) and CCNO (3.98 ± 0.781) × 10^{8} when 95% confidence interval was considered.

By combining MODIS and SHIPS data, 56 variables were compiled and selected as predictors for this study. Variable reduction from 56 to 31 was performed via correlation coefficients (cc) followed by Principal Component Analysis (PCA) extraction techniques to further reduce these 31 variables to 20. Among the 31 variables, PCA candidates were selected for the variables describing the same physical mechanism and the PCA procedure reduces the numbers from 3–8 to 1–4 for each group of variables. Five categories: wind, aerosols, shear, relative humidity, and temperature components were established by reducing 56 variables to 20. Aerosol, wind, humidity, shear and temperature are all contributing factors in the regression equation with the ranking for the contribution found to be (1) Wind, (2) Aerosols, (3) Shear, (4) Relative Humidity, and (5) Temperature components. Indicating that aerosols predictor surpass the other predictors especially shear. However, from a dynamics point of view, it is impossible for aerosol to be more important than shear and temperature. The aerosol rank preceded the shear, which could be because our sample size was too small (306 data points) when compared to the original SHIPS dataset (over 6,000 data points) and inadvertently the value ranges of shear and temperature are not large. As a result, the limited variance in those parameters makes it is difficult to demonstrate the importance of those parameters. This is practically similar to a study with other parameter values being controlled. When the coefficient of variations (cv) was calculated we found cv for AOT 40.29%, Wind 37.61%, Shear 35.50%, SST 3.65% and Relative Humidity (RH) 6.8%. SST and RH cv values are so low that we can consider the experiment to be controlled at a specific value. In the same sense, it is not surprising to that AOT was the second dominated factor in this study because AOT are of the largest variability. When MLR is performed on all 56 variables (without any variable reduction) as illustrated in

There are plenty of benefits for overcoming the curse of dimensionality. Original variables may demonstrate better results but the reduced variables gave similar results with much lower dimensionality and improved efficiency. For computational purposes, improved efficiency is much more important than highly precise results.

One interesting finding is that the adjusted R^{2} with Predictor_6, 20 variables is larger than (or equal to) the corresponding value with Predictor_1 of 31 variables. At least in this special case, reducing the number of variables does not reduce the effectiveness of the MLR model but increases the efficiency.

The variation among the Predictors RMSE varied between 0.01 through 0.05. This implies that reducing the number of variables did not change the core physical information because variation is from the mean for all sets of predictors and very small. Therefore, the same phenomena can be explained by the reduction of the variable. R^{2} values were found to be larger when considering the 42 and 48 h lead time. R^{2}, adjusted R^{2}, RMSE and residual error among Predictor 1 through 6 was negligible. The RMSE and residual errors difference among the six predictor groups were found to be negligible.

We acknowledge the MODIS mission scientists and associated NASA personnel for the production of the data used in this research effort. The HDF Group,

Selected SHIPS parameters based on the website at [

SST | Climatological SST (deg C × 10) |

RHLO | 850–700 mb relative humidity (%) |

RHMD | 700–500 mb relative humidity (%) |

RHHI | 500–300 mb relative humidity (%) |

SHRS | 850–500 mb shear magnitude (kt × 10) |

VMAX | The current maximum wind intensity in kt |

MSLP | Mean sea level pressure (hPa) |

INCV | Intensity change (kt) −18 to −12, −12 to −6, ... 114 to 120 hr. |

SST | SST (deg C × 10) |

DTL | Distance to nearest major land mass (km) |

PHCN | Estimated ocean heat content (kJ/cm^{2}) from climo OHC and current SST anomaly. Designed to fill in for RHCN when that is missing. |

U200 | 200 mb zonal wind (kt × 10) |

U20C | Same as U200 but for r = 0–500 km) |

V20C | Same as U20C, but for the v component of the wind |

E000 | 1,000 mb theta_e (r = 200–800 km) |

EPOS | The average theta_e difference between a parcel lifted from the surface and its environment (200–800 km average) |

ENEG | Same as EPOS, but only negative differences are included. The minus sign is not included. |

EPSS | Same as EPOS, but the parcel theta_e is compared with the saturated theta_e of the environment |

ENSS | Same as ENEG, but the parcel theta_e is compared with the saturated theta_e of the environment |

PSLV | Pressure of the center of mass (mb) of the layer where storm motion best matches environmental flow (t = 0 only) |

Z850 | 850 mb vorticity (sec^{−1} × 10^{7}) |

D200 | Same as above for 200 mb divergence |

REFC | Relative eddy momentum flux convergence (m/sec/day, 100–600 km avg) |

PEFC | Planetary eddy momentum flux convergence (m/sec/day, 100–600 km avg) |

T000 | 1,000 mb temperature (dec C × 10) (200–800 km average) |

R000 | 1,000 mb relative humidity (200–800 km average) |

Z000 | 1,000 mb height deviation (m) from the US standard atmosphere |

TWAC | 0–600 km average symmetric tangential wind at 850 mb from NCEP analysis (m/sec × 10) |

TWXC | Maximum 850 mb symmetric tangential wind at 850 mb from NCEP analysis (m/sec × 10) |

PENC | Azimuthally averaged surface pressure at outer edge of vortex ( (mb − 1,000) × 10) |

SHDC | Same as SHRD but with vortex removed and averaged from 0–500 km relative to 850 mb vortex center |

SDDC | Heading (deg) of above shear vector |

SHGC | Same as SHRG but with vortex removed and averaged from 0–500 km relative to 850 mb vortex center |

DIVC | Same as D200, but centered at 850 mb vortex location |

T150 | 200 to 800 km area average 150 mb temperature (deg C × 10) vs. time |

T200 | Same as above for 200 mb temperature (deg C × 10) |

T250 | Same as above for 250 mb temperature (deg C × 10) |

SHRD | 850–200 mb shear magnitude (kt × 10) |

SHTD | Heading (deg) of above shear vector |

SHTS | Heading of above shear vector |

SHRG | Generalized 850–200 mb shear magnitude (kt × 10) |

PENV | 200 to 800 km average surface pressure ((mb − 1,000) × 10) |

VMPI | Maximum potential intensity from Kerry Emanuel equation (kt) |

VVAV | Average (0 to 15 km) vertical velocity (m/s × 100) of a parcel lifted from the surface where entrainment, the ice phase and the condensate weight are accounted for. Note: Moisture and temperature biases between the operational and reanalysis files make this variable inconsistent in the 2001–2007 sample, compared 2,000 and before. |

VMFX | Same as VVAV, but a density weighted vertical average. |

VVAC | Same as VVAV but with soundings from 0–500 km with GFS vortex removed |

IRXX | Same as IR00 below, but generated from other predictors (not satellite data). These should only be used to fill in for IR00 as needed. |

IR00 | Predictors from GOES data (not time dependent). The 17 values in this record are as follows:
Time (hr × 10) of the GOES image, relative to this case Average GOES ch 4 brightness temp (deg C × 10), r = 0–200 km Stan. Dev. of GOES BT (deg C × 10), r = 0–200 km Same as (2) for r = 100–300 km Same as (3) for r = 100–300 km Percent area r = 50–200 km of GOES ch 4 BT < −10 C Same as (6) for BT < −20 C Same as (6) for BT < −30 C Same as (6) for BT < −40 C Same as (6) for BT < −50 C Same as (6) for BT < −60 C max BT from 0 to 30 km radius (deg C × 10) avg BT from 0 to 30 km radius (deg C × 10) radius of max BT (km) min BT from 20 to 120 km radius (deg C × 10) avg BT from 20 to 120 km radius (deg C × 10) radius of min BT (km) |

IRM3 | Same as IR00 but at three hours before initial time |

RD20 | Ocean depth of the 20 deg C isotherm (m), from satellite altimetry data |

RD26 | Ocean depth of the 26 deg C isotherm (m) from satellite altimetry data |

RHCN | Ocean heat content (kJ/cm^{2}) from satellite altimetry data |

(

Average root mean square error (RMSE) for each future difference (FD).

Contribution Factors on the MLR between the FD48 and Original set of 55 variables. MSLP was removed from the analysis.

Contribution Factors on the MLR between the FD48 and Predictor_1 which has 31 variables.

Contribution Factors on the MLR between the FD48 and Predictor_6 which has 20 variables.

R^{2} values and RMSE at eight lead time positions 06, 12, 18, 24, 30, 36, 42 and 48 h.

Residual plots for FD06 and FD48.

Twenty four hurricanes selected between 2003 and 2009 based on the category 3, 4 and 5 and their lifespan.

2003 | 4 | Fabian | 27 Aug–8 Sep | 125 | 939 | 14.60–31.50 | 49.80–39.20 |

2003 | 5 | Isabel | 6–19 Sep | 140 | 920 | 14.00–34.00 | 42.00–80.70 |

2003 | 3 | Kate | 25 Sep–7 Oct | 110 | 952 | 11.70–38.30 | 49.30–45.80 |

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2004 | 3 | Alex | 31 Jul–6 Aug | 105 | 957 | 30.60–78.60 | 47.50–34.60 |

2004 | 4 | Charley | 9–15 Aug | 124 | 941 | 11.70–61.10 | 43.00–69.00 |

2004 | 4 | Frances | 25 Aug–9 Sep | 125 | 935 | 11.20–36.00 | 41.40–79.40 |

2004 | 5 | Ivan | 2–24 Sep | 145 | 910 | 9.70–29.10 | 31.00–94.90 |

2004 | 3 | Jeanne | 13–28 Sep | 110 | 985 | 16.00–60.40 | 37.00–80.30 |

2004 | 4 | Karl | 16–24 Sep | 120 | 938 | 11.40–32.80 | 47.30–40.40 |

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2005 | 4 | Dennis | 5–13 Jul | 130 | 930 | 12.50–63.10 | 38.60–86.80 |

2005 | 4 | Emily | 11–21 Jul | 135 | 929 | 10.80–42.90 | 25.00–101.20 |

2005 | 5 | Katrina | 23–31 Aug | 150 | 902 | 23.20–75.50 | 41.10–81.60 |

2005 | 3 | Maria | 1–10 Sep | 100 | 960 | 19.00–46.10 | 43.60–38.60 |

2005 | 5 | Rita | 18–26 Sep | 150 | 897 | 22.00–69.70 | 40.80–86.80 |

2005 | 5 | Wilma | 15–25 Oct | 150 | 882 | 17.60–78.80 | 41.70–62.80 |

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2006 | 3 | Gordon | 11–20 Sep | 105 | 955 | 20.20–54.50 | 39.20–16.60 |

2006 | 3 | Helene | 12–24 Sep | 105 | 954 | 12.50–23.00 | 40.90–37.50 |

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2007 | 5 | Dean | 13–23 Aug | 145 | 918 | 12.00–31.60 | 20.50–100.00 |

2007 | 5 | Felix | 31 Aug–5 Sep | 145 | 929 | 11.80–58.60 | 14.00–87.00 |

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2008 | 3 | Bertha | 3–20 Jul | 105 | 948 | 12.60–22.70 | 51.30–35.70 |

2008 | 4 | Gustav | 25 AUG–04 Sep | 130 | 941 | 15.50–70.10 | 35.60–93.20 |

2008 | 4 | Ike | 1–14 Sep | 125 | 935 | 17.60–39.50 | 36.40–92.50 |

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2009 | 4 | Bill | 15–24 Aug | 115 | 945 | 11.50–34.00 | 48.60–50.20 |

2009 | 3 | Fred | 7–12 Sep | 105 | 958 | 12.50–24.50 | 17.70–33.70 |

MODerate Resolution Imaging Spectroradiometer (MODIS) Aerosol retrievals.

Effective Optical Depth Best Ocean | AOT |

Mass Concentration for Best and Average Solutions | MCO |

Effective Radius of Both Solutions at 0.55 μm | ERO |

Column Number of Cloud Condensation Nuclei (CCN) of Both Solutions at 0.55 μm | CCNO |

Asymmetry Factor for Best Solution ^{1} |
AFBO |

Backscattering Ratio of Best Solution ^{1} |
BRBO |

Mean Reflectances ^{1} |
MRO |

at 7 bands 0.47, 0.55, 0.66, 0.86, 1.24, 1.63, and 2.13 μm.

Reduction of Variables by Principal Component Analysis (PCA).

Aerosol | AOT MCO CCNO | Aero-PC1 Aero-PC2 |

Wind | V20C U200 U20C TWAC TWXC | Wind-PC1 Wind-PC2 Wind-PC3 |

Relative Humidity | RHLO RHMD R000 | RH-PC1 RH-PC2 |

Shear | SDDC SHDC SHGC SHRD SHRG SHRS SHTD SHTS | Shear-PC1 Shear-PC2 Shear-PC3 Shear-PC4 |

Temperature | SST T250 T200 RD20 ENEG ENSS | Temp-PC1 Temp_PC2 Temp-PC3 |

Multiple Linear Regression (MLR) results for uncorrelated aerosol and temperature variables.

^{2} |
^{2} |
|||||
---|---|---|---|---|---|---|

Uncorr_Predictor_2 | 64.80% | 60.90% | 16.85 | 20.43 | 417.30 | |

Corr_Predictor_2 | 65.00% | 61.10% | 17.00 | 20.37 | 414.90 | |

Uncorr_Predictor_6 | 63.40% | 60.80% | 24.69 | 20.45 | 418.00 | |

Corr_Predictor_6 | 63.70% | 61.20% | 25.02 | 20.36 | 415.00 |

Reduction of variables.

Original Set | MSLP INCV SST DTL PHCN U200 U20C V20C E000 EPOS ENEG EPSS ENSS RHLO RHMD RHHI PSLV Z850 D200 REFC PEFC T000 R000 Z000 TWAC TWXC PENC SHDC SDDC SHGC DIVC T150 T200 T250 SHRD SHTD SHRS SHTS SHRG PENV VMPI VVAV VMFX VVAC IR00 IRM3 RD20 RD26 RHCN AOT AFBO BRBO MRO MCO ERO CCNO | From the 56 variables, less correlated predictors (|cc|<=0.165) were filtered out to present Predictor_1 (31 variables) |

Predictor_1 | AOT MCO CCNO PENC V20C MSLP PEFC PSLV U200 U20C Z850 REFC RHLO RHMD R000 SDDC SHDC SHGC SHRD SHRG SHRS SHTD SHTS SST T250 TWAC TWXC T200 RD20 ENEG ENSS | PCA on AOT MCO CCNO to reduce them into Aero-PC1 Aero-PC2 make Predictor_2 (30 variables) |

Predictor_2 | Aero-PC1 Aero-PC2 PENC V20C MSLP PEFC PSLV U200 U20C Z850 REFC RHLO RHMD R000 SDDC SHDC SHGC SHRD SHRG SHRS SHTD SHTS SST T250 TWAC TWXC T200 RD20 ENEG ENSS | PCA on V20C U200 U20C TWAC TWXC to reduce them into Wind-PC1 Wind-PC2 Wind-PC3 make Predictor_3 (28 variables) |

Predictor_3 | Aero-PC1 Aero-PC2 Wind-PC1 Wind-PC2 Wind-PC3 PENC MSLP PEFC PSLV Z850 REFC RHLO RHMD R000 SDDC SHDC SHGC SHRD SHRG SHRS SHTD SHTS SST T250 T200 RD20 ENEG ENSS | PCA on RHLO RHMD R000 to reduce them into RH-PC1 RH-PC2 Predictor_4 (27 variables) |

Predictor_4 | Aero-PC1 Aero-PC2 Wind-PC1 Wind-PC2 Wind-PC3 PENC MSLP PEFC PSLV Z850 REFC RH-PC1 RH-PC2 SDDC SHDC SHGC SHRD SHRG SHRS SHTD SHTS SST T250 T200 RD20 ENEG ENSS | PCA on SDDC SHDC SHGC SHRD SHRG SHRS SHTD SHTS to reduce them into Shear-PC1 Shear-PC2 Shear-PC3 Shear-PC4, Predictor_5 (23 variables) |

Predictor_5 | Aero-PC1 Aero-PC2 Wind-PC1 Wind-PC2 Wind-PC3 PENC MSLP PEFC PSLV Z850 REFC RH-PC1 RH-PC2 Shear-PC1 Shear-PC2 Shear-PC3 Shear-PC4 SST T250 T200 RD20 ENEG ENSS | SST T250 T200 RD20 ENEG ENSS reduce to Temp-PC1 Temp_PC2 Temp-PC3 make Predictor_6 (20 variables). |

Predictor_6 | Aero-PC1 Aero-PC2 Wind-PC1 Wind-PC2 Wind-PC3 PENC MSLP PEFC PSLV Z850 REFC RH-PC1 RH-PC2 Shear-PC1 Shear-PC2 Shear-PC3 Shear-PC4 Temp-PC1 Temp_PC2 Temp-PC3 |

Each parameter used in this

Principal components for Aerosol, Wind, Relative Humidity, Vertical Shear and Temperature.

Aerosol | Aero-PC1 | 80.40% |

Aero-PC2 | 98.40% | |

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Wind | Wind-PC1 | 52.80% |

Wind-PC2 | 82.80% | |

Wind-PC3 | 98.40% | |

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Relative Humidity | RH-PC1 | 66.67% |

RH-PC2 | 95.20% | |

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Vertical Shear | Shear-PC1 | 50.70% |

Shear-PC2 | 72.00% | |

Shear-PC3 | 81.40% | |

Shear-PC4 | 88.80% | |

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Temperature | Temp-PC1 | 58.50% |

Temp-PC2 | 76.10% | |

Temp-PC3 | 91.20% |

Response and Predictor Variables.

^{2} |
^{2} |
|||||
---|---|---|---|---|---|---|

Predictor_1 | 18.80% | 9.60% | 2.05 | 8.32 | 69.23 | |

Predictor_2 | 18.80% | 9.90% | 2.12 | 8.31 | 68.98 | |

Predictor_3 | 17.70% | 9.40% | 2.13 | 8.33 | 69.38 | |

Predictor_4 | 17.60% | 9.60% | 2.20 | 8.32 | 69.26 | |

Predictor_5 | 16.40% | 9.60% | 2.41 | 8.32 | 69.22 | |

Predictor_6 | 15.00% | 9.10% | 2.52 | 8.35 | 69.64 | |

| ||||||

Predictor_1 | 27.80% | 19.60% | 3.40 | 12.27 | 150.50 | |

Predictor_2 | 27.80% | 19.90% | 3.52 | 12.25 | 150.10 | |

Predictor_3 | 26.90% | 19.50% | 3.63 | 12.28 | 150.90 | |

Predictor_4 | 26.80% | 19.70% | 3.77 | 12.27 | 153.40 | |

Predictor_5 | 25.40% | 19.30% | 4.17 | 12.30 | 151.20 | |

Predictor_6 | 24.40% | 19.10% | 4.60 | 12.31 | 151.60 | |

| ||||||

Predictor_1 | 37.90% | 30.80% | 5.39 | 14.76 | 217.70 | |

Predictor_2 | 37.90% | 31.10% | 5.59 | 14.73 | 217.00 | |

Predictor_3 | 37.10% | 30.80% | 5.84 | 14.77 | 218.00 | |

Predictor_4 | 37.10% | 31.00% | 6.08 | 14.74 | 217.20 | |

Predictor_5 | 36.10% | 30.80% | 6.91 | 14.76 | 217.80 | |

Predictor_6 | 34.90% | 30.30% | 7.63 | 14.81 | 219.40 | |

| ||||||

Predictor_1 | 45.40% | 39.30% | 7.36 | 16.27 | 264.60 | |

Predictor_2 | 45.40% | 39.40% | 7.62 | 16.24 | 263.80 | |

Predictor_3 | 44.70% | 39.10% | 7.99 | 16.29 | 265.30 | |

Predictor_4 | 44.60% | 39.20% | 8.29 | 16.27 | 264.80 | |

Predictor_5 | 43.80% | 39.30% | 9.57 | 16.27 | 264.60 | |

Predictor_6 | 43.10% | 39.10% | 10.78 | 16.29 | 265.40 | |

| ||||||

Predictor_1 | 50.90% | 45.40% | 9.18 | 17.92 | 321.10 | |

Predictor_2 | 50.90% | 45.50% | 9.50 | 17.90 | 320.30 | |

Predictor_3 | 50.20% | 45.10% | 9.96 | 17.97 | 322.70 | |

Predictor_4 | 49.70% | 44.90% | 10.19 | 18.01 | 324.20 | |

Predictor_5 | 49.40% | 45.20% | 11.96 | 17.94 | 322.00 | |

Predictor_6 | 48.30% | 44.70% | 13.31 | 18.04 | 325.40 | |

| ||||||

Predictor_1 | 54.90% | 49.80% | 10.76 | 19.25 | 370.40 | |

Predictor_2 | 54.60% | 49.90% | 11.14 | 19.22 | 369.50 | |

Predictor_3 | 54.10% | 49.40% | 11.64 | 19.32 | 373.40 | |

Predictor_4 | 53.70% | 49.20% | 11.95 | 19.36 | 374.80 | |

Predictor_5 | 53.40% | 49.60% | 14.07 | 19.27 | 371.70 | |

Predictor_6 | 53.00% | 49.70% | 16.04 | 19.28 | 371.60 | |

| ||||||

Predictor_1 | 61.80% | 57.50% | 14.31 | 19.64 | 385.80 | |

Predictor_2 | 61.70% | 57.50% | 14.75 | 19.64 | 385.80 | |

Predictor_3 | 61.20% | 57.20% | 15.59 | 19.70 | 388.10 | |

Predictor_4 | 60.70% | 56.90% | 15.92 | 19.78 | 391.10 | |

Predictor_5 | 60.60% | 57.30% | 18.82 | 19.68 | 387.30 | |

Predictor_6 | 60.20% | 57.40% | 21.51 | 19.67 | 387.10 | |

| ||||||

Predictor_1 | 65.10% | 61.10% | 16.46 | 20.38 | 415.30 | |

Predictor_2 | 65.00% | 61.10% | 17.00 | 20.37 | 414.90 | |

Predictor_3 | 64.80% | 61.20% | 18.20 | 20.35 | 414.00 | |

Predictor_4 | 64.30% | 60.80% | 18.55 | 20.45 | 418.20 | |

Predictor_5 | 64.00% | 61.10% | 21.84 | 20.38 | 415.30 | |

Predictor_6 | 63.70% | 61.20% | 25.02 | 20.36 | 415.00 |