L Band salinity retrieval : SST & receiver effects

 

 

 

  1. Purpose

Retrieving sea surface salinity (SSS) from L band radiometric temperature TB measurements appears challenging becauses it implies removing, or accounting accurately for, phenomena which may have effects on the measured signal with magnitude vastly exceeding what corresponds to the accuracy aimed at for SSS.

These effects are many. This note adresses specifically :

The scope is restricted in this manner for the simple reason that the theoretical frame for combined (SST,SSS) dependance of the radiometric temperature is well established, considered as reliable, and readily available (see work by Klein and Swift), as well as orders of magnitude of the relevant quantities. It is not at all implied that other effects might not be more significant ; indeed this is probably the other way around, et more likely so for the very reason that the theroretical framework is less robust.

As for the receiver stability, it seems sensible to consider it here, since the approach is similar ; moreover, we shall have to discuss both the calibration procedures and requirements, and it is interesting to know that in this respect salinity measurements are very demanding, to say the least.

 

2 Method

Assessing the effect of SST imperfect knowledge on the accuracy of SSS measurements has already been done several times. The standard way of doing this consist of evaluating the sensitivity of the TB to SSS and SST separately, and then applying proportionality rules. Of course there is no point in criticizing this method ; however in this note an attempt is made to go somewhat nearer to the problem such as it is encountered in real life. That is :

The retrieval algorithm is the generalized least squares method elaborated by Marquart. This method offers the advantage that, inasmuch as the measurement errors are specified, it provides an estimate of the standard deviation s of the retrieved parameters.

This algorithm has been further completed in such a way that this estimate also accounts for the measurement error on fixed parameters. In other words, the predicted s(SSS) accounts for both the uncertainty on the TB values and the uncertainty on SSS.

Another specificity of this analysis is that it takes into account the capacity of a 2D interferometric device such as MIRAS to provide several independant views of the same area on the surface for various incidence angles. Therefore, s(SSS) will be estimated for several configurations in terms of this multi incidence angle capability.

 

3 Hypotheses ; range of tested cases

 

3.1 Configuration : characteristics assumed for the radiometer are close to the SMOS baseline options, such as they are known at the time of writing, and are expected not vary too much in the future.

Then, the radiometric sensitivity DTB is as follows :

DTB (K) # 0.43 + Tgeo x 4.7E-3

Where Tgeo corresponds to the power collected by the antenna. Since the range of TB is approximately between 60 and 160 K, it is seen that DTB will be in the vicinity of 1 K, and most of the time somewhat lower than that.

Since DTB is actually proportional to the total input temperature, it is also seen that, when talking of biases in relation with the receiver, one ought to adress two distinct cases :

It is safer to consider these two effects separately.

 

3.2 Considered cases

3.2.1 Surface salinity and temperature : since d(TB)/d(SSS) does not vary much with SSS for realistic open sea values, SSS is always taken equal to 35 PSU, in the middle of this range. As for SST, it takes several values (273, 283, 293, 303 K) ; this is necessary because, as is well known, the dependance of the TB upon SSS varies strongly with actual SST values over their physical variation range ;

3.2.2 As for incidence angle : 5 cases are tested :

Cases a c should help to assess the role of the actual incidence angle value, if any ; case e is closer to what should be possible with SMOS in the majority of cases. Case d is intermediary.

3.2.3 SST noise and bias : 1K amplitudes are selected. The noise and bias are applied separately ; when the bias is applied, the noise affecting TB is artificially brought close to zero, in order to assess accurately the magnitude of the resulaing bias on SSS.

3.2.4 Receiver biases : selected amplitudes are 1K for the additive bias, 1% for the multiplying bias. They are applied separately ; same as for the SST bias, the TB noise is then brought close to zero.

 

4 Results

On the whole, 100 cases are therefore considered : five incidence angle sets x four SST x five choices for noise and biases (none, SST noise, SST bias, additive reveiver bias, multiplying receiver bias). The results are shown accordingly on the table (see end of note), arranged in a sequence of 5 subsets

 

4.1 Neither noise nor bias (subset 1)

The major effect is the well known dependance of s(SSS) upon the SST value : as the SST increases from 0C to 30C, s decreases by a factor slightly above 3.

For a single view, the dependance of s upon the exact value of the incidence angle is quite weak ; there is on the whole a very slight deterioration as the incidence angle increases (possibly, this is due to the proportional part of the receiver noise).

For several views, then what really matters is their total number NI : s varies almost exactly as NI-1/2.

Observe that, if there was no other source of uncertainty, the situation would indeed look rather bright for warm seas : a single pixel would provide SSS values with a standard deviation of .23 to .30 PSU.

 

4.2 Noise (s=1K) on SST (Subset 2 vs 1)

When using a noisy SST value, one expects the overall accuracy to deteriorate. For single incidence cases, there is no detectable variation. For the cases with 16 independant views, there is indeed an increase of s(SSS) with respect to subset 1 ; this increase is however moderate. For the SST values in the middle of the range ( 283 & 293 K), it is quite weak ; remember that in this region the influence of SST upon the radiometric temperature undergoes a minimum.

On the whole, keeping in mind that SST values available from other measurements are very likely to be known with a random uncertainty of less than 1K, it is seen that after all this should not be considered as a major problem when retrieving SSS from L-Band measurements.

 

4.3 Bias (1K) on SST (Subset 3)

The resulting bias on SSS does not depend upon the incidence range. It depends only on the actual SST value ; here, we simply find results that corroborate the well known variation of d(SSS) / d(TB ) from about +0.4 to about 0.2 when the SST varies from 0 to 30C.

The figures speak for themselves : while SST noise is of minor consequences, it is not so for SST biases. The requirement for SST provided from other sources is that it should be free of bias within better than at most 0.2 K for high latitudes.

 

4.4 Biases on the receiver noise and gain (subsets 4 & 5).

The resulting bias on SSS, same as before, is not reduced when the number of independant views increases ; this means that, unfortunately, the sensitivity of TB to the SSS does not vary much with incidence angle.

The bias on SSS due to poor knowledge of the receiver does diminish when the SST increases ; still, it remains very high, even for high SST values.

According to the figures, retrieving SSS to within 0.1 PSU depends upon keeping the additive receiver noise bias within 0.02-0.06 K (depending upon SST), and at the same time the gain bias within 0.02 0.06 % (depending upon SST).

Obviously, there is no hope of knowing neither a priori with this kind of accuracy. Rather, we should investigate the stability of the receiver and the possible sources for variation of characteristics (electric power, operating temperature). If the operating conditions are quite well controlled, then there are no reasons why the gain and noise should vary. As for calibrating the instrument, the table suggests that it will be difficult to obtain a measurement more sensitive thant the salinity itself, provided it is measured over a zone equipped with adequate sea level instrumentation.

It is worth stressing that time scales are very meaningful here. If the noise level and/or gain of the receive vary approximately in a random manner on a time scales, we have noise rather than bias ; while this noise broadens the radiometric sensitivity interval and thus deteriorates the accuracy of a single measurement, this accuracy may be improved by compounding independant measurements.

 

5 Concluding remark

At first sight, the main problem with radiometric SSS estimation appears to be the weak sensitivity of TB to SSS. On a second sight, the problem is further aggravated by this sensitivity d(TB)/d(SSS) having almost no dependancy upon either the polarisation state or the incidence angle. Therefore there is no hope of better discrimination of SSS with respect to other effects, by making use of the versatiliity of MIRAS with respect to these parameters ; all one can hope to do (and will do !) is to vastly improve the measurement accuracy due to the increased number of independant data.

This is worth mentioning ; by contrast, in several other cases (vegetation optical thickness over land, probably sea roughness over the sea..), the situation is expected to be quite different.

 

 

 

Table : SSS standard deviation /bias results

 

SST

 

(0.01K)

Nb incid. angles

Lowest value (0.1)

Angle step

(0.1)

noise on

SST (0.01K)

bias

on

SST (0.01K)

additive bias on TB (0.01K)

multiplying bias on

TB

(%%)

bias

on SSS (0.01psu)

s

(SSS)

(0.01psu)

27300

1

200

0

0

0

0

305

27300

1

350

0

0

0

0

295

27300

1

500

0

0

0

0

300

27300

4

200

80

0

0

0

0

144

27300

16

200

15

0

0

0

0

70

28300

1

200

0

0

0

0

175

28300

1

350

0

0

0

0

178

28300

1

500

0

0

0

0

181

28300

4

200

80

0

0

0

0

87

28300

16

200

15

0

0

0

0

43

29300

1

200

0

0

0

0

119

29300

1

350

0

0

0

0

120

29300

1

500

0

0

0

0

124

29300

4

200

80

0

0

0

0

60

29300

16

200

15

0

0

0

0

30

30300

1

200

0

0

0

0

91

30300

1

350

0

0

0

0

93

30300

1

500

0

0

0

0

94

30300

4

200

80

0

0

0

0

47

30300

16

200

15

0

0

0

0

23

 

 

SST

 

(0.01K)

Nb incid. angles

Lowest value (0.1)

Angle step

(0.1)

noise on

SST (0.01K)

bias

on

SST (0.01K)

additive bias on TB (0.01K)

multiplying bias on

TB

(%%)

bias

on SSS (0.01psu)

s

(SSS)

(0.01psu)

27188

1

200

100

0

0

0

284

27202

1

350

100

0

0

0

305

27411

1

500

100

0

0

0

318

27236

4

200

80

100

0

0

0

158

27327

16

200

15

100

0

0

0

85

28288

1

200

100

0

0

0

171

28374

1

350

100

0

0

0

178

28365

1

500

100

0

0

0

179

28358

4

200

80

100

0

0

0

88

28114

16

200

15

100

0

0

0

47

29323

1

200

100

0

0

0

119

29243

1

350

100

0

0

0

120

29174

1

500

100

0

0

0

125

29211

4

200

80

100

0

0

0

61

29184

16

200

15

100

0

0

0

31

30299

1

200

100

0

0

0

94

30308

1

200

100

0

0

0

95

30281

1

500

100

0

0

0

99

30075

4

200

80

100

0

0

0

51

30262

16

200

15

100

0

0

0

32

27300

1

200

0

100

0

0

44

0

27300

1

350

0

100

0

0

46

0

27300

1

500

0

100

0

0

53

0

27300

4

200

80

0

100

0

0

46

0

27300

16

200

15

0

100

0

0

45

0

28300

1

200

0

100

0

0

13

0

28300

1

350

0

100

0

0

14

0

28300

1

500

0

100

0

0

18

0

28300

4

200

80

0

100

0

0

14

0

28300

16

200

15

0

100

0

0

14

0

29300

1

200

0

100

0

0

-9

0

29300

1

350

0

100

0

0

-8

0

29300

1

500

0

100

0

0

-6

0

29300

4

200

80

0

100

0

0

-8

0

29300

16

200

15

0

100

0

0

-9

0

30300

1

200

0

100

0

0

-21

0

30300

1

350

0

100

0

0

-21

0

30300

1

500

0

100

0

0

-19

0

30300

4

200

80

0

100

0

0

-21

0

30300

16

200

15

0

100

0

0

-21

0

 

 

SST

 

(0.01K)

Nb incid. angles

Lowest value (0.1)

Angle step

(0.1)

noise on

SST (0.01K)

bias

on

SST (0.01K)

additive bias on TB (0.01K)

multiplying bias on

TB

(%%)

bias

on SSS (0.01psu)

s

(SSS)

(0.01psu)

27300

1

200

0

0

100

0

-433

0

27300

1

350

0

0

100

0

-430

0

27300

1

500

0

0

100

0

-416

0

27300

4

200

80

0

0

100

0

-430

0

27300

16

200

15

0

0

100

0

-431

0

28300

1

200

0

0

100

0

-261

0

28300

1

350

0

0

100

0

-259

0

28300

1

500

0

0

100

0

-250

0

28300

4

200

80

0

0

100

0

-259

0

28300

16

200

15

0

0

100

0

-260

0

29300

1

200

0

0

100

0

-180

0

29300

1

350

0

0

100

0

-178

0

29300

1

500

0

0

100

0

-171

0

29300

4

200

80

0

0

100

0

-178

0

29300

16

200

15

0

0

100

0

-179

0

30300

1

200

0

0

100

0

-141

0

30300

1

350

0

0

100

0

-139

0

30300

1

500

0

0

100

0

-133

0

30300

4

200

80

0

0

100

0

-139

0

30300

16

200

15

0

0

100

0

-140

0

27300

1

200

0

0

0

10

-418

0

27300

1

350

0

0

0

10

-425

0

27300

1

500

0

0

0

10

-449

0

27300

4

200

80

0

0

0

10

-425

0

27300

16

200

15

0

0

0

10

-424

0

28300

1

200

0

0

0

10

-255

0

28300

1

350

0

0

0

10

-259

0

28300

1

500

0

0

0

10

-273

0

28300

4

200

80

0

0

0

10

-259

0

28300

16

200

15

0

0

0

10

-258

0

29300

1

200

0

0

0

10

-175

0

29300

1

350

0

0

0

10

-178

0

29300

1

500

0

0

0

10

-188

0

29300

4

200

80

0

0

0

10

-178

0

29300

16

200

15

0

0

0

10

-178

0

30300

1

200

0

0

0

10

-136

0

30300

1

350

0

0

0

10

-138

0

30300

1

500

0

0

0

10

-145

0

30300

4

200

80

0

0

0

10

-138

0

30300

16

200

15

0

0

0

10

-138

0