noaa / NATIONAL OCEANIC AND

ATMOSPHERIC ADMINISTRATION

Office of Oceanic and

Atmospheric Research

NOAA Technical Memorandum OAR GSD-34

DEVISED SCHEME FOR GOES OPERATIONAL TOTAL PRECIPITABLE

WATER PRODUCT BIAS CORRECTION

D.L. Birkenheuer

S.I. Gutman

S.R. Sahm

K.L. Holub

Earth System Research Laboratory

Global Systems Division

Boulder, CO

July 2008

UNITED STATES

DEPARTMENT OF COMMERCE

Carlos M. Gutierrez

Secretary

NATIONAL OCEANIC AND

ATMOSPHERIC ADMINISTRATION

VADM Conrad C. Lautenbacher, Jr.

Under Secretary for Oceans

and Atmosphere/Administrator

Office of Oceanic and

Atmospheric Research

Dr. Richard Spinrad

Assistant Administrator

NOAA Technical Memorandum OAR GSD-34

DEVISED SCHEME FOR GOES OPERATIONAL TOTAL PRECIPITABLE

WATER PRODUCT BIAS CORRECTION

Daniel L. Birkenheuer

Seth I. Gutman

Susan R. Sahm

Kirk L. Holub

Earth System Research Laboratory

Global Systems Division

Boulder, CO

July 2008
NOTICE 

Mention of a commercial company or product does not constitute an endorsement by the 

NOAA Office of Oceanic and Atmospheric Research Laboratories. Use of information 

from this publication concerning proprietary products or the test of such products for 

publicity or advertising purposes is not authorized. 

For sale by the National Technical Information Service, 5285 Port Royal Road 

Springfield, VA 22061 
Contents 

Section Page 

Abstract. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv 

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 

2. GOES 12 and GPS Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 

3. GOES 10 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 

4. Real -Time Application of Correction Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 

5. Differences Observed Between GOES 10 and GOES 12 Correction Coefficients . . . . . .14 

6. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 

7. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18 

 

iii 
Abstract 

 The National Environmental Satellite Data and Information Service (NESDIS) 

Geostationary Observational Environmental Satellite (GOES)-derived, total precipitable 

water (TPW) vapor product is routinely produced at NESDIS for Advanced Weather 

Interactive Processing System (AWIPS) users, primarily for National Weather Service 

(NWS) forecast offices. Global Positioning System (GPS) signal delay due to 

atmospheric water vapor has been shown to provide accurate, real-time, measurement of 

TPW. Until GPS data came on the scene, there had been no way to validate GOES 

product data at asynoptic times (other than the occasional field experiment or limited 

regions such as the ARM CART sites), and therefore routine rawinsonde (RAOB) data 

have the largest influence on calibration, and these are constrained to fundamental 

synoptic times and frequency (every 12 hours). 

 This paper examines asynoptic satellite product performance and explores corrections 

to GOES product differences based on GPS measurements. The derived correction 

scheme is useful not only for applying to satellite data before use, but for studying error 

characterization as well. It becomes apparent that GOES 12 data error characteristics, 

measuring the eastern continental U.S. (CONUS) are also present in GOES 10, even 

though GOES 10 data are far drier (measuring the western CONUS) and from a 

completely different set of optics and satellite acquisition systems. This suggests that the 

observed product bias may be due to elements common to both satellite data products, 

e.g., model first guess, cloud clearing, tuning to only synoptic data, or some other 

unknown issue. 

 The development of the satellite product correction algorithm is detailed and 

coefficients for correction to GOES 12 and GOES 10 product data are presented. 

iv
1. Introduction 

 The investigation of the GOES 12 TPW product data and the coinciding GPS IPW 

record for the past year and a half have revealed that the moist bias in GOES 12 sounderderived products has remained virtually unchanged. This is in spite of a concerted effort 

during FY 2007 in which nearly 100 case study scenarios were gleaned and scrutinized 

by the product developers at the University of Wisconsin – Madison (UW) and NESDIS. 

Despite these efforts, essentially no progress was achieved at improving asynoptic bias 

error; in effect, the data from the operational GOES 12 shared almost identical error 

characteristics with the data sets garnered during the 2002 International H2O Project 

(IHOP) from GOES 8 and GOES 11. So the compelling question for us at the Earth 

System Research Laboratory (ESRL) was just how we can best use the GPS asynoptic 

data to improve the satellite operational products. The result is work summarized by this 

paper in which we established a means to characterize the GOES error based on past data 

and applied the correction in real time to new product data. Furthermore, we examined 

the characteristics of the correction algorithm for clues as to the cause of the error. 

 Another concern is how the error from other GOES platforms compares with the 

highly studied GOES 12. We compared archived data for GOES 10 between the two 

satellites to ascertain whether there were any similarities in error structure. We viewed 

this information as useful in determining the source of the error. If the nature of the error 

from the two instruments was different, one could speculate that the errors were 

instrument related. On the other hand, error similarities might well indicate some kind of 

common thread between the systems; perhaps in the retrieval algorithm, model first guess 

moisture processes, or types of data assimilated and used for first-guess model 

initialization. 

2. The GOES 12 and GPS Datasets 

 GOES 12 data were acquired from the NESDIS Center for Satellite Applications and 

Research (STAR) and the development and testing group that prepared the product prior 

to releasing it to NESDIS operations in support of National Weather Service activities. 

Typically, the data were garnered in the second step of a three-step process designed to 

get the data products to the field. The first step was the algorithm development at the 

University of Wisconsin, the second was initial product testing on a routine basis at 

NESDIS (the data used in this study), and the third was the actual data production. We 

chose to assess the data in the second level of development since it was one step ahead of 

operational status (somewhat improved) and perhaps not as volatile in change of 

attributes that would be produced by developers. It could potentially be modified if we 

discovered some kind of issue that could be corrected. The data used here were fairly 

close to what was operationally produced by NESDIS. GOES sounder data were used to 

1 
solve a retrieval of thermal and moisture profiles. The moisture profile was integrated to 

compute total precipitable water fundamentally equivalent to that measured by GPS. 

 GPS TPW data were produced at ESRL using techniques for production that are now 

routine after about a decade of development. The system is planned to be transferred to 

the National Weather Service for operational management. The acquisition of water 

vapor from GPS satellites is tantamount to discerning the change in the speed of light 

through the atmosphere due to the presence of water vapor (Wolf and Gutman 2000). 

The determination of water vapor-induced “signal delay” is used to derive a value for the 

zenith “equivalent” integrated water. Unlike satellite sounder retrievals, the distribution 

or profile of the water vapor in the vertical is not measured; only the sum total can be 

computed, however there is a good match in the asynoptic measuring abilities of both 

GPS and GOES systems. 

 Even though the satellite and GPS are totally different systems, and use different 

techniques to compute TPW, the end result should be the same. The GPS system is 

known to be more accurate, comparable to ground-based, passive microwave 

measurements and much better than traditional radiosonde data. In fact, GPS 

measurements have been used to identify bad “batches” of radiosonde instruments. The 

typical precision of GPS water measurements is on the order of 0.2 to 0.3 mm liquid 

water equivalent. What GPS lacks is the ability to reveal the vertical distribution of 

moisture. Also GPS measurements are essentially point data where there are working 

ground stations. GPS data therefore overlap GOES data in geographic location and 

measurement time, enabling a fair comparison of the two systems. 

 The GOES 12 data used in this statistical assessment were archived coinciding with 

GPS IPW data (Birkenheuer and Gutman, 2005) over the course of about two years. 

Pairs of data were identified satisfying the criteria that the distance between the GPS and 

satellite locations were within 10km and both data samples were collected within 20 

minutes of each other. We did not discriminate whether the GPS or GOES data were 

obtained first or second. This was similar to the criteria used in the IHOP data 

comparison effort. 

 No attempt was made to “clean up data.” Both GOES and GPS TPW were essentially 

in their rawest operational form. It became evident after assessment (refer to the points in 

the upper portion of Fig. 1) that some comparisons were indeed outliers. However, these 

are relatively few in number, and given the enormous size of the overall dataset (nearly 

1.8 million pairs) were deemed insignificant and any affect they may have is ignored. 

 Of course, one motivation for this work was to not only characterize the GOES bias 

(differences between GOES and GPS), but also to see if applying a correction based on 

this characterization would be useful on real-time data acquired after this sample was 

2 
evaluated. Furthermore, another point of interest was a comparison of this evaluation to 

that of GOES 10 data with GPS. GOES 10 data were acquired at roughly the same time 

as the GOES 12 data set, but the GOES 10 acquisition was begun at a later date, so that 

the sample was not as large. Also, there were not as many matches between GPS sites 

and GOES 10 because there are fewer GPS sites in the western CONUS. 

Figure 1 above shows the scatter plot of roughly 1.8 million GPS-GOES 12-derived 

total moisture comparisons for approximately 1.5 years, ending January 2007. A 

1:1 line is plotted from 0.0 to 8.0 cm. This exhibits a GOES moist bias similar to 

what we observed during IHOP 2002; as the moisture amount increases, the GOES 

bias increases. We refer to this as the “rooster tail” effect since the moist bias 

appears to curve toward a greater bias at higher moisture levels. The above plot 

represents data pairs from all times of the day and represents all observations. 

3 
 We decided to further examine the hourly bias at asynoptic times in a similar fashion 

to the one we used during the IHOP data analysis, Birkenheuer and Gutman 2005. That 

study revealed a strikingly similar pattern (Fig. 2) in which minima are seen near 00 UTC 

and 12 UTC while intervening times show the bias figures climbing. The overall moist 

GOES bias is computed to be near 0.19 cm for the entire data set. The hourly values lay 

on either side of this value. 

Figure 2 shows the hourly bias observed in the data set acquired for GOES 12 and 

GPS-paired comparisons from June 2005 to January 2007. The essence of the bias 

characteristics for this data set emulates the observations made during IHOP 2002. 

Again the lowest bias is seen at 00 UTC and a secondary minimum is seen at 11 

UTC, identical to the IHOP results. 

4 
 Our next obvious question is just how we can affect operations in a positive way with 

the above information. Clearly, the case studies generated in 2006 focused on major 

discrepancies between GOES and GPS TPW, and were not effective in finding solutions 

to correct problems. It was apparent that these cases could not reveal a systematic 

asynoptic bias as shown by long-term statistics; rather they were effective for examining 

outliers. 

 To better utilize the archived data as a whole, we decided to provide UW and NESDIS 

with bias correction algorithms for each hour. Not only could we produce these 

correction algorithms from the data we have archived, we could both test the 

effectiveness on past data and offer them as 24-bias correction algorithms unique to each 

hour; making them easy to incorporate on the operational product computation for GOES 

12. 

 The basic formulation of the bias correction was decided to be a power law 

relationship that would guarantee zero change for zero moisture (no imposed linear bias). 

It can be seen in Fig. 1 that bias does tend to 1:1 as we near the zero point on the plot. 

Therefore, the overall correction strategy is: 

= 

b G aG c (1) 

where Gc is the corrected GOES moisture values, G is the initial product values as 

received from NESDIS, a is a scaling term and b is a power term, both dimensionless. 

The b term removes curvature from the paired measurements, while the scaling term 

helps to move the linear agreement to the 1:1 line. The selection of this fitting equation 

was made such that no absolute bias offset was defined. 

 The method of solution for (1) was variational analysis. This was chosen because it 

has an advantage over traditional linear least squares determination of coefficients a and 

b. In traditional least squares fitting of (1), the corrected GOES measurement Gc would 

be replaced with the corresponding set of GPS measurements. The log of the equation 

would be first taken rendering a linear form. The log of the GOES moisture and log of 

GPS data would be terms used in computation of coefficients. The absolute values of 

very small (near zero) numbers would be very large, as well as numbers that were 

naturally large; however, the upper limit to the moisture values would typically be near 7 

to 8 cm. For example, the log of 8 is 0.9 while the log of 0.003 is -2.522. Thus, very 

small and very large values drive the solution for the least squares since the absolute 

value of the log terms is largest at both extremes. If one only focuses on very tiny and 

very large numbers, the resulting correction becomes potentially highly unrepresentative. 

5 
Instead, the variational method was used as the following simple functional: 

2

1

( )

N

ci i

i

J G GPS == − ∑ (2) 

where J was minimized via iteration using the Powell (1962) method by modifying 

coefficients a and b from (1) and summed over all of the data (N points) consisting of 

paired (i) GOES and GPS data. The “best fit” (and lowest J value) therefore forced all of 

the corrected GOES measurements to be as close as possible in magnitude to GPS. The 

variational method puts direct linear weight on the water amount differences. Thus, 

small differences (less than one, even if they described large amounts of water) would 

likely carry almost insignificant weight in determining the result, while ever increasing 

values of moisture discrepancies would proportionally influence the correction terms. 

 Table 1 enumerates the tabulated statistical data for each hour and summarizes the 

plotted data in Fig 1. 

6 
Table 1. Overall Statistics of the GOES 12 Compared with GPS TPW 

Sample Size Difference mean (cm) Difference sigma (cm) 

1846382 0.189954087(~0.2) 0.340749055 

Hourly statistics: 

 Hour 

 77149 0.1451841 0.326997399 0 

 79163 0.167799324 0.333233804 1 

 79677 0.187112406 0.340882629 2 

 79633 0.199308515 0.34721899 3 

 64712 0.188389182 0.354360223 4 

 55388 0.215271473 0.366844922 5 

 63340 0.203290358 0.363681376 6 

 78400 0.193654135 0.354441524 7 

 78478 0.185493708 0.355892688 8 

 79518 0.177166924 0.354920417 9 

 78712 0.169746995 0.360813648 10 

 78860 0.168546513 0.351962864 11 

 80721 0.183212727 0.349612921 12 

 83206 0.186258167 0.332360089 13 

 84387 0.183728412 0.319724947 14 

 81874 0.18580541 0.323772699 15 

 78148 0.21556583 0.324803203 16 

 74347 0.228538767 0.327521175 17 

 76359 0.230120406 0.33018446 18 

 76794 0.223517194 0.336179137 19 

 78273 0.210550457 0.330599844 20 

 80293 0.197571233 0.332213998 21 

 81052 0.175653189 0.325276226 22 

 77922 0.151863873 0.329036385 23 

 Referring to Table 1, we see that the hourly sigma in many cases is less than the 

overall sigma for the entire population. It was not surprising to discover that the bias 

corrected sigma as a whole population is reduced. 

 Table 2 summarizes the terms a and b for each hour followed and Table 3 enumerates 

GOES-GPS differences and standard deviation (sigma) on an hourly basis. There are 

many interesting highlights that can be gleaned from this information. The simple 

algorithm appears to work well providing a robust correction algorithm that is a function 

of hour. The hourly corrections after 16 UTC are interesting in that the b term, or power 

7 
term, is near unity, which indicates that at these times there was minimal curvature in the 

bias, and the bias correction was more of a simple linear scaling function. On the other 

hand, hours 0 and 11 had the lowest initial bias requiring more curvature correction. 

Table 2: Hourly Correction Coefficients for GOES 12 

 a b Hour 

 0.979470611 0.952045858 0 

 0.96386236 0.958807886 1 

 0.951016307 0.962379932 2 

 0.932851493 0.974993765 3 

 0.938412488 0.973992229 4 

 0.928518832 0.971161544 5 

 0.932472348 0.975237787 6 

 0.936737478 0.97503674 7 

 0.943030536 0.971995413 8 

 0.945574582 0.972088754 9 

 0.953864217 0.967487574 10 

 0.952823639 0.967738211 11 

 0.944226384 0.970142543 12 

 0.934683204 0.977410853 13 

 0.928368866 0.98369354 14 

 0.923411667 0.988313854 15 

 0.90421778 0.997356713 16 

 0.896550059 1.00138319 17 

 0.896099865 1.00216639 18 

 0.900296807 1.00008261 19 

 0.905209124 1.00010216 20 

 0.923843801 0.986412048 21 

 0.942986071 0.975428104 22 

 0.970267594 0.958948851 23 

 The following shows a summary similar to the first table after applying the GOES 

correction algorithms. Bias results are near zero at all hours and we see a reduction in the 

GOES variance overall. 

8 
Table 3: Statistics after Applying Bias Corrections 

Num Bias (cm) Sigma (cm) Hour 

 77149 0.00177616451 0.292245328 0 

 79163 0.00261056516 0.297694743 1 

 79677 0.00169990247 0.302271068 2 

 79633 -0.000553681341 0.310711473 3 

 64712 0.000401427213 0.319695294 4 

 55388 -0.000414054375 0.322597355 5 

 63340 -0.00131554063 0.325285763 6 

 78400 -1.90824721E-05 0.319985747 7 

 78478 9.41948019E-05 0.321559876 8 

 79518 -0.000290779368 0.322418272 9 

 78712 0.000494285661 0.329654783 10 

 78860 -0.000135583352 0.31978035 11 

 80721 -0.000470061059 0.31356591 12 

 83206 -0.00125479081 0.29614839 13 

 84387 -0.00253195036 0.284297198 14 

 81874 -0.00316451443 0.289983094 15 

 78148 -0.00477298256 0.285934418 16 

 74347 -0.00472133886 0.289746225 17 

 76359 -0.00413449015 0.293306589 18 

 76794 -0.00375525164 0.300256968 19 

 78273 -0.00458336901 0.297615409 20 

 80293 -0.0032954677 0.298026621 21 

 81052 -0.0024598802 0.291823328 22 

 77922 0.00016256237 0.296616346 23 

------------------------------------------------------------------------------------ 

 Overall Bias (cm) Overall Sigma (cm) 

-0.00129276153 0.30450815 

------------------------------------------------------------------------------------ 

 The hourly corrections were applied to all data and then the overall statistics were 

recomputed at the end of Table 3. The results show very little bias and an overall 

reduction in sigma by 0.0362 cm. 

9 
 Figure 3 shows the GOES corrected data when broken down by hour, similar to Fig. 2. 

Figure 3. Hourly bias (GOES-GPS differences) modified by one of 24 unique 

algorithms. Bias values are all near zero cm. 

 Figure 4 is the recomputed scatter plot similar to Fig. 1 that shows the comparison of 

GPS and GOES TPW data after the correction has been applied to each data point. 

10 
Figure 4. Scatter plot of corrected GOES data compared with GPS values. 

 Noteworthy is that the data now line up with the diagonal 1:1 line and the spread in 

the data appears to be improved near 2 cm and at the high moist end of the plot. 

11 
3. GOES 10 Evaluation 

 GOES 10 was paired with GPS TPW data in a similar fashion as just described for 

GOES 12 data, but fewer data pairs were studied since roughly a half year (June 2006-

January 2007) were archived. GOES 10 was scanning the drier western CONUS and 

generally measured differences were less than what was seen for GOES 12. The lower 

differences did not surprise us given that GOES 12 scatterplots showed better agreement 

at low vapor totals. Somewhat more surprising was that the bias-corrected technique 

applied to GOES 10 data using the same correction relationship (1) performed just about 

as well as GOES 12. Applying the same variational scheme as used for GOES 12, the 

correction coefficients were worked out for GOES 10 and shown in Table 4. 

Table 4: Bias Correction Coefficients for GOES 10 

 a b Hour (UTC) 

 n/a* n/a 0 

 0.996533394 0.95236516 1 

 0.996538579 0.946112096 2 

 0.989015937 0.951574981 3 

 0.983487904 0.952166796 4 

 0.988218307 0.950105309 5 

 0.986881852 0.944489419 6 

 0.987462819 0.942130029 7 

 0.982085943 0.954229712 8 

 0.977829933 0.967253745 9 

 0.977529407 0.956604183 10 

 0.982349575 0.9490183 11 

 0.981856227 0.955889702 12 

 0.975823998 0.963789642 13 

 0.982822776 0.962480724 14 

 0.988664567 0.972649038 15 

 0.985295117 0.980493426 16 

 0.975872576 0.987788618 17 

 0.964276195 0.994780362 18 

 0.963219404 0.993331313 19 

 0.959865749 1.00000048 20 

 0.952994823 0.996276438 21 

 0.970916569 0.983162522 22 

 0.973964751 0.969606757 23 

*Coefficients are not available at 00 UTC in the western US due to the lack 

of continuous surface data for GPS computations. As the stations in the 

12 
western CONUS mature, 00 UTC data will eventually become routine as 

they are with the eastern CONUS. 

 As can be seen in Table 4, the nature of the correction terms is similar to GOES 12. 

This was surprising since the initial bias values did not appear to be that significant, but 

as mentioned, the water vapor levels out west are typically lower than those measured by 

GOES 12. However, these results indicate that the nature of the bias for GOES 10 is 

strikingly similar to GOES 12. We note the very similar “b” term result near 20 UTC 

when it is very near unity. This indicates, as in the case of GOES 12, that in the local 

afternoon time frame the bias lacks curvature and needs simple scaling to remove the 

bias. At other times, however, especially near synoptic times, the bias correction requires 

more of a curvature correction. Though the magnitude of the coefficients for GOES 12 

and GOES 10 are not identical, they are similar enough to suggest a fundamental 

commonality. 

4. Real-Time Application of Correction Coefficients 

 During the summer months of 2007, the coefficients derived from earlier GOES 12 

and GPS measurements were used to correct GOES 12 real-time data, and compare these 

corrected results to simultaneous GPS measurements. The object was to discern whether 

the correction algorithm based on earlier data would effectively improve subsequent data. 

Various comparisons were made. Initially, single stations were examined and found to 

be vastly improved by the correction algorithm. We then examined specific geographic 

regions to see if there were any latitudinal differences in correction or possibly optical 

path preferences (i.e., would we see better results in the south where there were higher 

water vapor amounts?). 

(a) 

13 
(b) 

Figures 5(a) and 5(b). Two scatter plots showing the improvement to 2007 GOES 12 

data before and after applying the correction algorithm based on earlier data. Fig. 

5(a) shows the uncorrected data identified by region, indicating the southeast 

CONUS (triangles) contained the greatest moist bias; Fig. 5(b) shows the same data 

after application of the bias correction algorithm. Data are clustered closer to the 

zero bias line with the most improvement seen in the southeast. 

5. Differences Observed Between GOES 10 and GOES 12 Correction Coefficients 

 Near the end of this study we explored the tabulated correction coefficients (Tables 2 

and 4) and decided to plot the coefficients as a function of hour. This was initially done 

to better visualize how they compared; as noted in the text they appeared similar. When 

plotted, a potentially much more important feature becomes apparent. Figure 6 shows the 

a and b correction terms for each satellite. As we anticipated, they are similar, but what 

was not apparent until plotted was that they appear to be phase shifted. 

14 
Figure 6. Correction coefficients for both satellites plotted as a function of hour 

(UTC). Apparent is the temporal phase shift in the sunny part of the day (between 

12 and 00 UTC). 

 Figure 6 clearly shows a phase shift relationship between both the a and b terms from 

the correction equation with about a 3-hr offset. One can see that the b power term for 

GOES 10 is shifted to the right about 3 hours later especially between 12-18 UTC. 

Furthermore, the shift in the minima of both a terms occurs at 17 UTC for GOES 12 and 

about 21 UTC for GOES 10 is roughly a 3-hr difference, similar to the b term. Could this 

have something to do with the apparent solar or “time zone” difference between the two 

satellites? GOES 12 is stationed at a subpoint near 75 west longitude and GOES 10 was 

positioned at 135 west longitude, a difference of 60 degrees or 4 time zones. This would 

15 
translate to an approximate solar time of day shift between each satellite of about 4 hours, 

on the order of what we observe in Fig. 6. So what is responsible for what appears to be 

a “solar effect” in the correction coefficients between the two moisture products from 

GOES? The algorithms for both spacecraft and channels are the same, all in the infrared 

and presumably at wavelengths deemed far enough away from the solar spectrum to be 

effectively insensitive to sunlight. Though they use the same a-priori guess model profile 

in the retrieval algorithm, there appears to be a solar component to the bias correction. At 

this time we can only present the observation here and have no established explanation, 

only speculation that the phase shift appears to be solar related (it does not appear during 

dark hours and the phase shift is seemingly well correlated to the spacecraft’s 

longitudinal separation or possibly the CONUS solar separation of the ground locations 

used in this study). 

6. Summary 

 The primary outcome of this study is a technique to correct satellite TPW product 

bias. Even more important, the study shows that the correction technique is valuable for 

real-time correction when based on prior data. The correction algorithm was devised 

using variational methods and has shown similar correction coefficients for both GOES 

10 and 12. Individual station data have been assessed both as a long-term and real-time 

trend (not shown here). It was also shown that the previously derived coefficients were 

useful in different geographic regions. These tests were only performed for GOES 12 for 

which there was the largest database for coefficient computation, but also consisted of the 

data set with the greatest variations in total water amount (the western CONUS being 

climatologically drier). 

 The fact that correction coefficients for both satellites studied are so similar suggests 

that the nature of the observed bias is not specific to hardware, i.e., the particular satellite, 

but instead is related to some aspect common to both data sets – namely the retrieval 

system or design of the instruments. The algorithms used in the retrieval system, 

including the model first guess (model initialization or influence by synoptic data) the 

forward radiance model, or some other aspect in deriving water profiles from radiometric 

data common to both GOES 12 and 10 has a non-random behavior that can be 

characterized. One would never have surmised this relationship by looking at the raw 

data (scatterplots), since the data for GOES 10 is far drier and the synoptic curvature 

effect is not that noticeable when plotted. It was shown (Fig. 3) that overall bias can be 

reduced to very close to zero with the algorithm. It is probably more useful to take from 

this study not so much that we now have an algorithm to correct GOES water vapor 

values, but instead to draw our attention to improving the product generation from 

GOES, since there seems to be something germane to the nature of the bias in both 

satellites. 

16 
 Finally, the fact that we have a clear solar-related signal in the correction terms 

suggests that either sunlight is playing a role in the satellite measurement, or the retrieval 

algorithm is somehow sensitive to solar effects. Given that the satellite channels used for 

moisture and thermal retrievals are theoretically not influenced by solar effects, one can 

only rationalize that this phase difference is coming into play in the retrieval system by 

way of the raw measurement in a way we don’t understand, or some other means that is 

not fully accounted for such as the model first guess. Certainly the results illustrated in 

Fig. 6 deserve attention, and future study should focus on solar dependence in the 

forecast model and any aspect of the GOES TPW generation that might relate to observed 

solar influence. 

17 
18 

References 

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