BIASES IN SURFACE REFERENCE ESTIMATESBY THE TRMM PR STANDARD ALGORITHM

P5R.3

Shinta Seto* and Toshio Iguchi
National Institute of Information and Communications Technology, Tokyo, Japan
1.

INTRODUCTION

Equation (2) can be rewritten into equation (6).

s0m (NR)= s0e (NR)

Attenuation correction is necessary for the ac­
curate rain rate estimation by TRMM/PR, which uses
relatively high frequency microwave (13.8GHz) com­pred with general precipitation radars.
The
traditional attenuation correction method developed
by Hitschfeld and Bordan (HB method) can analyti­cally solve this problem by assuming a k­Zm rela­tionship such as k=aZmb. However, this method can
not be applicable for heavy rainfall. Then, theTRMM/PR standard algorithm (Iguchi et al, 2000)
applies hybrid method with HB method and surface
reference technique (SRT) (Meneghini et al, 2000).
SRT makes use of the return echo by the land sur­face beyond the precipitation.
The return echo by the land surface is ex­pressed as the land surface backscattering cross
0section (denoted as s ). Due to the attenuation,00Measured s (denoted as s m) is smaller than actuals0 (denoted as s0e) if the observation error is ne­
glected. This difference is PIA (Path IntegratedAttenuation), the total attenuation along the pathfrom the radar to surface and its return path. This is0

written in equation (1). Please note that s is al­ways expressed in dB unit in this paper.
s0m= s0e ­PIA
(1)
Under no rain condition,s0m (NR)= s0e (NR) ­PIA (NR)

(2)
Under rain condition,s0m (R)=s0e (R) ­PIA (R)(3)PIA (NR) is attributed to the cloud water and thewater vapor, but it is smaller than precipitation at­0tenuation. Then, for simplicity, s e and PIA arere­defined as follows.
s0e =s0e ­PIA (NR)(4)
PIA=PIA ­PIA (NR)(6)
Equation (3) still holds. In this way, PIA (NR) isneglected except the case that the absolute value ofs0e and PIA is important.
0SRT assumes that s e does not change by theexistence of rainfall as described in equation (7).
s0e (NR)= s0e (R)(7)
From (6) and (7), equation (8) is given.

s0m (NR)= s0e (R)(8)
In the standard algorithm, SRT selects no­rain
pixels which may have similar characteristics withthe target pixel and calculates their sample averageand standard deviation. The average is used as the00estimates of s e (R) (denoted as s ref ). The stan­
dard deviation is also used as the reliability factor ofthe SRT estimates.
00

PIAref =s ref ­s m (R)(9)
PIAref is the estimates of PIA by the SRT. The final
PIA estimates after the hybrid method is denoted asPIAfin.
The assumption in equation (7) is suspecious.
Meneghini et al. (2004) acknowledged that this as­
0
sumption is sometimes inappropriate. s e is sensi­
tive to the land surface variables such as surface
wind speed over­ocean. The variables can changeby the rainfall, however, it is not considered in theSRT of standard algorithm.
0
Statistical analysis on the change of s e between
under rain condition and under no­rain condition isdone in this paper to point out some biases in theSRT of the current standard algorithm.
2.

DATA2.1. Standard Product(5)* Corresponding author address:
Shinta Seto,
National Institute of Information and Communica­
tions Technology, 4­2­1, Koganei, Tokyo, Japan,184­8795; e­mail: seto@nict.go.jp

The TRMM standard products (2A25, version 6)
for the entire year of 2000 are used in the data
analysis study in sections 3 to 5. The followings aremajor variables used in this study from the 2A25products.

000FIG. 1. Ds R (triangle, black), Ds ref (circle, blue), and Ds fin (square, red) for the rain rate categories. The left panel is forocean, and the right panel is for over land.

Surface type: ocean, land, and coast. Observations
over coast is not treated in this study.
Rain flag: no­rain, rain­possible, and rain­certain.
Rain­possible is regarded as no­rain.
Estimated surface rain rate:
A new variable“e_SurfRain” is used. Up to version 5, thestandard product gives “nearSurfRain”, which is
the rain rate at the lowest range bin free fromground clutter. In version 6, Zm is extraporated
into clutter region, then the rain rate is estimatedat real surface range bin.
PIA: Path integrated attenuation. Both PIAref andPIAfin are included in the 2A25 product. How­ever PIAfin is calculated only for the attenucation
caused by precipitation. Attenuation by cloudwater and water vapor are calculated and are
added to PIAfin for this analysis.
Observed surface cross section: s0m (NR) or s0m (R).
The incident angle q is approximately calculatedusing angle bin number a as q = 0.75 x | a­25 |.
(1<=a<=49, 0<=q<=18)
2.2. Definition
Using the data under rain conditions, three vari­ables are defined as below.
s0R=s0m (R)(10)
s0ref =s0m (R)+PIAref(11)00s fin =s m (R)+PIAfin(12)
They are analyzed in the following sections 3 to 5,
respectively.

s0R should be less than s0e (R) because s0R in­
volves the rainfall attenuation. s0ref and s0fin are
estimates of s0e (R). We would like to examine the00
anomaly of s e (R) from s e (NR), which is not known.
s0m (NR) are summarized for each surface type,
incident angle, 1 by 1 degree grid and 1month, andthe average is defined as s0NR. s0NR is used as the000
proxy of s e (NR). Ds indicates the anomaly of s0
from s NR as follows.
Ds0R =s0R ­s0NR(13)
Ds0ref =s0ref ­s0NR(14)
Ds0fin =s0fin ­s0NR
(15)

3.

s 0R

3.1. Results

Ds0R for different rain rate categories are shownin Fig. 1 (Ds0ref and Ds0fin in this figure are de­scribed later). For the weakest rain rate, Ds0R isalmost zero over ocean, but it is slightly positive overland. Over land, Ds0R keeps positive up to 4mm/h
rain. For these weak to moderate rainfall, Ds0e(R)= s0e (R) –s0NR is positive. In other words, s0e ishigher under rain condition than under no­rain condi­
tion. The map for Ds0R under weak rainfall (rainrate is less than 1mm/h) is shown in Fig. 2. Less
vegetated area such as the Sahel of Africa, India,Australia, and south­western America have positive
Ds0R. In the tropical rainforest such as Amazon,

00Fig. 2. Ds R (upper) and Ds ref (lower) under weak rain­
fall less than 1mm/h over land.

00Fig. 3. Ds R (triangle, black), Ds ref (circle, blue), andDs0fin (square, red) for different incident angles underweak rainfall less than 1mm/h over ocean.

Ds0R is almost zero.
The incident angle dependence of Ds0R forover­ocean under weak rainfall (rain rate is less than01mm/h) is shown in Fig. 3. Ds R is positively de­pendent on the incident angle. Ds0R is zero at ap­
proximately 10 degree. At larger than 10 degree,Ds0e (R) is higher under rain condition. At smaller
0incident angles, Ds e (R) may be lower under rain
condition.
3.2. Possible mechanism
The change of s0e under rain condition can beexplained as follows.
0Over land, s e increases because surface be­comes wet due to rainfall. It is known that the in­crease of soil moisture content increases the surface
backscattering cross section. The sensitivity of s0e
on the soil moisture content is limited if the surface iscovered by vegetation. This corresponds with thefact that Ds0R is almost zero in tropical rainforests.
Over ocean, the incident angle dependence ofs0e becomes weak due to stronger wind accompa­
nied with rainfall. Previous researches show thatthe dependence of s0e on the wind speed is almost
zero around 10 degree. This corresponds with theresult shown in Fig. 3.
These are mere hypotheses, as we do not haveany observational proof. However, we are sure that
this can partly explain the change of s0e. According
to the hypotheses, we called the phenomena that s0e
increases over land under rain condition as surface
wetness effect. Similarly, the phenomena that theincident angle dependence of s0e is weaken overocean is called as wind speed effect

4.

s0ref

s0ref is analyzed in this section. s0ref is esti­
0mates of s e (R) by SRT. It is focused on that the0s ref can explain the surface wetness effect and thewind speed effect.
4.1. General results

Ds0ref for different rain rate categories are shown
0in Fig. 1. Over land, Ds ref is positive for all thecategories. This indicates that the surface wetness
effects are in some degree explained. However,Ds0ref is smaller than Ds0R for weak rainfall. This
leads to negative PIAref because of the below equa­tion.
PIAref=s0ref ­s0R =Ds0ref ­Ds0R .
(16)
0s ref is underestimated at least for this case. The
map of Ds0ref under weak rainfall (rain rate is lessthan 1mm/h) is shown in Fig. 2. In the Sahel andIndia, where show large surface wetness effects,
Ds0ref is zero or slightly positive, and is much smaller
than Ds0R. On the other hand, in Australia, Ds0ref iscomparable to Ds0R.
The incident angle dependence of Ds0ref overocean under weak rainfall (rain rate is less than1mm/h) is shown in Fig. 3. Ds0ref is maximum at theincident angles around 12 to 15 degree. Ds0ref issmaller than Ds0R at 0 to 3 and near 18 degree.
SRT over ocean does not follow the wind speed
effect well.

4.2. over land
The reason why SRT over land can follow thesurface wetness effect in some cases and the reason
why this technique can not quantitatively follow thesurface wetness effect are examined in more detail.
In the standard algorithm for over­land, two methods
are applied; along­track spatial reference method
and temporal reference method. The former takes
eight no­rain samples just prior to the current ob­
servation. TRMM always flies from west to east,
thus the sample are taken outside and west of rain
area. On the other hand, the latter takes no­rain
samples within the 1 by 1 degree grid box same as
the target pixel and in previous month. Of course,
the incident angle and surface type of sample pixels
should be the same as those of the target pixel.
Between two estimates, one with smaller standard
deviation of samples is chosen. Roughly speaking,along­track spatial reference method is chosen in
80 % cases.
In the along­track spatial reference method,
samples are taken from no­rain area neighboring
0rain system. The characteristics of s m (NR) in
such area are investigated. Figure 4 shows therelationship between Ds0m (NR)= s0m (NR) ­s0NR andthe distance (the number of pixels) to the neighbor­ing rain area.
The distance is calculated inalong­track direction. The west side and the eastside are discriminated. Within 10 pixels from therain area, Ds0m (NR) is positive and it becomes
higher by approaching to rain area. In the area
neighboring to rain system, it might rain temporally
just before with relatively high possibility. This canbe the cause of the positive Ds0m (NR) in theneighboring area. Although the along­track spatialreference method basically takes samples in theneighboring area, the temporal reference method
does not. Figure 5 is same as Fig. 1, but only incase of temporal reference method. Ds0ref is slightly
negative, thus surface wetness effect is not ex­plained at all in temporal reference method.
Asymmetry of Ds0m (NR) between the west sideand the east side is seen in some regions. If therain system moves from the west to the east, Ds0m(NR) can be higher in the west side, but not in theeast side. In mid latitudes, where the westerlies isdistinguished, Ds0m (NR) is higher in the west side.

0Fig. 4. Ds m (NR) for the distance to the neighboringrain system over land.

Fig. 5. The same as the right panel of Fig. 1, but for thecase of temporal reference method.

0Fig. 6. The difference between Ds m (NR) for the westside and that for the east side. Blue color indicates0
where Ds m (NR) of the west is higher and red color
0indicates Ds m (NR) of the east is higher.

On the other hand, in the Sahel, Ds0m (NR) is higher
in the east side. However, in the standard algorithm,
samples are taken in no­rain area outside and westof the rain system This may be the reason that thesurface wetness effect is not explained in the Saheleven if the along­track spatial reference method isapplied.

4.3. over ocean
Hybrid spatial reference method is applied if the0entire scan is over ocean. For each pixel, s e is00
prepared by using s m for no­rain pixel and s ref byalong­track spatial reference method for rain pixels.
0Then, s e is expressed by quadratic function of theincident angle q. This fitting procedure yields thebias in s0ref. If land or coast pixels exist in the scan,along­track or temporal reference method is appliedsame as over land. When the along­track spatial0reference method is applied, Ds ref is almost parallel0to Ds R (Fig. 7).
5.

Fig. 7. The same as the Fig. 3, but for the case of along
track spatial reference method.

s0fin

s0fin is another estimates of s0e (R). As con­trasted to s0ref, to estimate s0fin, observed Zm and s0m0of the target pixel can be used. Moreover, s fin isalways larger than s0R. Judging from these points,
s0fin should be more reliable than s0ref .
Over ocean, Ds0fin is always zero in Fig. 1. In0Fig. 3, the incident angle dependence of Ds fin for0
weak rainfall is parallel to that of Ds R. The incident
angle where Ds0fin is zero is around 8 degree. For
moderate to heavy rainfall, the incident angle de­
00pendence of s fin is deviated because biased s ref isrelied on in the hybrid method.
Over land, Ds0fin has positive dependence on
the rain rate (Figure 1). This is same in the case of
temporal reference method (Figure 4). Carefulanalysis is required to judge that this dependence isthe result of some physical phenomena.
6.

MODIFICATION OF SRT OVER LAND

The reasons for the lack of explanation of sur­face wetness effect over land are that temporal ref­erence method is used and that sampling is always
taken outside and west of the rain system. In orderto overcome this weakness, modified SRTs aretested. In this section, the data in July 2001 areused.
Five modified SRTs are tested with the original
SRT. All of them always apply along­track spatialreference method. WT takes eight samples prior tothe observation (the west side) same as the standard
algorithm, but ET takes eight samples posterior to0Fig. 8. The incident angle dependence of Ds fin forvarious rain rate categories.

the observation (the east side). Other three meth­ods choose WT or ET each time. S1 applies WT if
the target pixel is in the west half of rain area andapplies ET if the target is in the east half of rain area.
S2 chooses the method where the total distancesfrom the target to the samples are shorter. S3chooses the method that has smaller standard de­viation of samples.
s0ref from the five modified methods and theoriginal method are compared in Fig. 9. By replac­
ing the temporal reference method with the spatialreference method, the surface wetness effect can bepartly explained. For the entire region, WT canfollow the surface wetness effect compared with ET.
S3 is similar to ET. This suggests that choosing
smaller standard deviation contradicts with the ex­planation of the surface wetness effects. In theSahel, ET is better than WT, as is expected from theresult of Section 4.

0Fig. 9. Ds ref for five modified SRT and the original SRT
0and the original Ds fin for different rain rate categories.
The left panel is for all the pixels where the temporalreference method is applied in the original. The rightpanel is for all the pixels in the Sahel (10­15N, 10­15E).

The final rain rate estimates are significantly
changed by the replacing SRT methods (Fig. 10).
Applying the along­track spatial reference method
instead of the temporal reference method, rain rateestimates tend to increase. In the Sahel, the rain
rate estimates from the SRT of ET are generally
higher than that from the SRT of WT. The effect islarger for heavy rainfall than for weak rainfall.
7.

SUMMARY

Comparing the observed backscattering coeffi­
cients between under rain and no­rain conditions, it
0is found that over less vegetated land, s m under
weak rainfall is statistically higher than s0m underno­rain condition. This suggests that s0e is higher
under rain conditions than under no­rain condition.
0This increase of s e can be partly explained by theincrease of surface wetness as a result of rainfall(surface wetness effect). Over ocean the incidentangle dependence of s0e is weaken under rainfall
probably due to the increase of wind speed (windspeed effect).
Surface reference estimates s0ref by the stan­
dard algorithm can follow the surface wetness effectand the wind speed effect in some degree particu­
larly by the along­track spatial reference method.
Temporal reference method does not explain thesurface wetness effect at all, and hybrid spatial ref­erence method yields the bias in the incident angle
dependence of s0e. Along­track spatial reference
method does not work well in the Sahel comparedwith in the mid latitude. It can be because thesamples are always taken outside and west of rain

Fig. 10. Comparison of rain rate estimates from differ­ent SRTs. Left panel is for the pixels where the tempo­
ral reference method is originally applied. The ordinate
is for the original case and the abscissa is for the cases
applying spatial reference method (WT). Right panel isfor the pixels in the Sahel (10­15N, 10­15E). The ordi­
nate is for the cases applying spatial reference method(WT) and the abscissa is for the cases applying spatialreference method (ET).

area.
Modified SRTs are applied. By replacing tem­poral reference method with spatial reference
method, the surface wetness effect becomes partlyexplained. In the Sahel, by taking samples not westof but east of rain system, the estimated s0e seems
to be improved. The change of SRT also affects on
the final rain rate estimates especially for heavy
rainfall.
Acknowledgements. This study is part of a larger
study,“Productionofa
high­precision,high­resolution global precipitation map using satel­
lite data (GSMaP)” led by Prof. Ken’ichi Okamoto(Osaka Prefecture University, Japan) under the pro­gram, “Core Research for Evolutional Science andTechnology (CREST)” of the Japan Science andTechnology Agency (JST).
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