5.1. Vegetation Optical Depth (VOD)
SCA retrievals of SMAP L2SM are reliant on climatological vegetation optical depth (VOD). However, VOD varies intra- and inter-annually in agricultural regions such as the South Fork due to both farm management decisions that determine planting date (e.g., antecedent meteorological conditions, tillage practices, and cultivar [
25]) and on temperature during crop development. This is due to corn and soybean development being governed by the accumulation of thermal time (e.g., [
26]), a measure of daily average temperatures within the range hospitable to crop growth. There may additionally be long-term differences between VOD and the current climatology as multi-decadal analyses of crop phenology in the Corn Belt indicate that planting is occurring earlier and growing seasons are longer than they were thirty years ago [
25,
27].
As shown in Equations (5) and (
7),
increases as VOD increases (assuming no other changes). If climatological VOD is too low, as was the case during spring 2012 when significantly warmer than normal temperatures accelerated planting and emergence [
28], then Equations (
6)–(
10) would retrieve a dry-biased soil moisture. Conversely, the use of a climatological VOD during a spring and early summer with delayed crop development would result in a wet bias during that period. This time corresponds with when SMAP L2SM SCA retrievals are noisiest in the South Fork.
The DCA attempts to bypass issues associated with climatological VOD by simultaneously retrieving L2SM and L2VOD. The sample timeseries of VOD previously given in
Figure 2 illustrates how the timing of SMAP DCA-retrieved L2VOD, which presumably represents the “actual” VOD, can differ from the SCA climatology during a single year. While retrieval of L2VOD by SMAP is theoretically possible, if
and
are not fully independent, then there may not be enough information available when only a single incidence angle is sampled [
29]. Furthermore, variations in soil surface roughness are interpreted by the DCA as L2VOD due to their producing the same changes to observed
at L-band [
30]. This is observed in the sample SMAP L2VOD timeseries in
Figure 2, where VOD increases during the spring and fall despite the lack of significant vegetation. Limitations aside, L2VOD provides useful information about the status of crop progress. SMOS L2VOD, similar to SMAP but retrieved using a large range of observed
, peaks after having accumulated a thermal time of approximately 1000 °C·day post-planting in the U. S. Corn Belt [
8]. This occurs between the second and third reproductive developmental stages of corn when
, defined as the mass of water in vegetation tissue per ground area, of the mixed corn and soybean canopy is at a maximum [
8].
5.2. Effective Surface Temperature
How realistic is the assumption that
at SMAP overpass times? This assumption is made so that
, dependent only on soil temperature, can be used to approximate the temperature of the entire surface viewed by SMAP. We compared flux tower observations of soil and vegetation temperatures at a central location in the South Fork for both corn (2015, 2018) and soybean (2015). Sampling was provided by Forrest Goodman (USDA, National Laboratory for Agriculture and the Environment) in 2015 and by Richard Cirone (Iowa State University, Department of Agronomy) in 2018.
Figure 3 illustrates relevant temperature observations. In addition to the more traditional infrared skin temperature,
, the air temperature within the canopy,
, was observed. Vertical temperature gradients in fully-grown corn are ≈1 K [
31]; this is accounted for in
sampling by vertically centering the observation within the canopy. As such, observations of
are limited to closed canopy periods (June–September). Soil temperature,
, was sampled at 6 cm in 2015 and 9 cm in 2018.
Table 3 presents the difference between
and
in corn and soybean for SMAP retrievals in June–September. For both crop types,
averages colder than
for morning overpasses and warmer for evening. This is consistent with previous investigation of vertical temperature gradients in a corn field that found the canopy was, on average, 2.5 K colder than the 4.5 cm soil temperature (shallower than
) at 6:00 a.m. solar time and 0.75 K warmer at 6:00 p.m. solar time [
31]. The 2015 comparison of
and
shows a slightly smaller difference (less negative) for morning overpasses and a larger (warmer) difference in the evening than observed in 2018; this is due to the discontinuity in installation depth. The deeper you observe soil temperature, the more diurnal variations are dampened from those of the soil surface [
32]. The 2015
, inserted at 6 cm, is therefore cooler for morning overpasses and warmer in the evening as compared to the deeper 9 cm sampling of 2018.
While
at SMAP overpass times in the South Fork, recall that
is meant to represent the combined effect of the two temperatures on
.
is defined by Equation (
13) via a modified Choudhury model [
33] as a function of the GEOS-5 0 to 10 cm and 10 to 30 cm layer temperatures (
and
, respectively), a coefficient,
C, that weights the relative contributions of
and
, and a bias correction factor,
K [
34].
is reported for each SMAP overpass in the SPL2SMP_E product:
In version 2 of the SPL2SMP_E (CRID: R16xxx),
for non-forest land classes,
for morning overpasses, and
for evening overpasses [
34]. At the beginning of the SMAP mission,
K was not a component of Equation (
13) (equivalently
) and
for all L2SM retrievals [
21].
, which warms
, was prompted by an observed cold bias in the GEOS-5 soil temperature at CVSs. It is also intended to address any potential mismatch between the GEOS-5 modeled soil layers and the layer of soil contributing to the temperature of the surface that SMAP views. Again, while calculated using modeled soil layer temperatures,
is not a physical soil temperature and is intended to represent both the vegetation canopy and the soil layer observed by the SMAP radiometer. The value of
for non-forest land classes was derived by minimizing the difference between the baseline
and that simulated via the SCA-V (personal communication, Steven Chan, NASA Jet Propulsion Laboratory).
The difference between SMAP
and “network
,” as well as the differences between SMAP
and observed in situ depths, are presented in
Table 4. Network
is calculated using Equation (
13) and South Fork in situ measurements, where
is the soil temperature at a depth of 5 cm,
is the temperature at 20 cm, and both
K and
C are parameterized as given in
Table 4. The correspondence between GEOS-5 temperatures (and thus
and
) and South Fork in situ soil temperatures is shown in
Figure 4. The period was limited to April 2015–November 2017 (excluding DJF) as 2017 is the last full year of SPL2SMP_E version 1 retrievals.
In version 1 of the SPL2SMP_E (CRID: R14xxx–R15xxx), when
K was not a part of
calculation, the difference between SMAP
(computed using GEOS-5 temperatures) and network
in
Table 4 is similar to the difference between SMAP
and the raw in situ measurements at 5, 10, 20, and 50 cm: all are within ±2 K. In version 2 of the SPL2SMP_E (CRID: R16xxx), SMAP
(computed using GEOS-5 temperatures)
is much warmer than the raw in situ measurements at 5, 10, 20, and 50 cm (by 4 to 9K). This could only be realistic for the combined soil-vegetation surface if
was significantly hotter (by at least 10 K) than
. This is contrary to our flux tower observations that show
for morning overpasses and
only 1 to 2 K warmer than
for evening overpasses. Evening overpasses were warmed more in version 2 as the use of
results in
being calculated entirely based on
rather than weighting towards
as with
.
We propose a modification to
that is more consistent with in situ network soil temperatures and would better approximate the differences between
and
at SMAP overpass times. This can be done by reverting to
(i.e., reversing the SPL2SMP_E adoption of
) but retaining the SPL2SMP_E version 2 change to
for evening overpasses. The cold bias in
that would return when
has a similar numerical effect of a colder morning canopy on surface temperature. While this would also make evening
colder, utilizing
in Equation (
13) weights
towards the warmer evening
. The difference between our proposed
and both the network
and observed in situ depths is shown in column three of
Table 4. As desired, SMAP
(which should account for the effect of both soil and vegetation temperatures) is about 1 K cooler than the network
(computed using only soil temperatures) at the AM overpass, and about 1 K warmer at the PM overpass. This method requires only the ancillary data already provided in the SPL2SMP_E. It is most applicable to overpasses that occur during vegetated periods. A truly representative approach may be to utilize separate
and
during L2SM retrieval, where
could be approximated by the GEOS-5
, which was a component of
calculation prior to launch [
21], and
.
Figure 5,
Figure 6 and
Figure 7 present the effect of adopting the more realistic modified
in the South Fork as quantified by the bias, ubRMSE, and R
2, respectively. Decreasing
dries monthly biases for both SCA and the DCA: mean SCA retrievals are at least 0.03 and as much as 0.12 m
3 m
−3 too low as compared to in situ South Fork measurements, and DCA retrievals vary from about zero bias in the fall and early spring to 0.10 m
3 m
−3 too low in the middle of the summer. This occurs because the retrieval algorithms now calculate a higher
for the same observed
. While this is worse performance in terms of bias, the monthly ubRMSE decreases, particularly for both SCA in May/June when they previously far exceeded the SMAP mission accuracy goal. This is likely due to
amplifying any noisiness in GEOS-5 temperatures by an additional 2%. The coefficient of determination significantly improves for the DCA (its mean value is higher in
every month) when the modified
is used; however, large inter-annual variations remain for all three algorithms. R
2 does decrease slightly for the SCA when the modified
is used during retrieval; however, this is not surprising when you consider that the
depth correction scheme was intended to optimize
.
The significant difference between and observed temperatures at all in situ depths leads to the conclusion that does not produce a physically realistic surface temperature. Flux tower observations of soil temperature and indicate that using to calculate , in conjunction with using for evening overpasses and the slight cold bias of GEOS-5 soil temperature in the South Fork, reproduces the effect of having a cooler canopy in the morning but a warmer canopy in the evening. While retrieving L2SM with the modified does degrade the bias in the South Fork, the combination of improved ubRMSE for both SCA and DCA and the significantly increased coefficient of determination for DCA can be interpreted as an overall improvement in retrieval quality if we consider that the bias may be caused by some other ancillary factor.
An additional consideration of modifying
is how it affects retrieved L2VOD. The VOD produced during our DCA retrievals using the proposed
will hereafter be referred to as “reprocessed L2VOD.”
Figure 8 presents a comparison of L2VOD in the South Fork during 2017 as retrieved by both versions 1 and 2 of the SPL2SMP_E product, the reprocessed L2VOD, and VOD from SMOS. When
was warmed dramatically in version 2 of the the SPL2SMP_E, the DCA-retrieved L2VOD increased with it. This was problematic for those utilizing the vegetation product as the operational L2VOD is now unrealistically large. L2VOD retrieved using our
decreases back to values similar to those of the version 1 SPL2SMP_E and is in-line with the SMOS L2VOD in the South Fork. The L2SM and L2VOD reprocessed with our modified
are publicly available for EASE09 pixels in the state of Iowa as
Supplementary Material.
5.3. Single Scattering Albedo
Scatter darkening, where
is reduced by radiation scattering within the canopy, occurs when the size of plant components (e.g., stems, leaves, ears) is similar to the wavelength (SMAP:
21 cm). This effect must be considered in corn [
35,
36]. The components of soybean plants are much smaller and as such there is relatively little scattering [
36]. The
model, which assumes that the canopy is a weakly scattering media, accounts for this via the
parameter [
37]. Non-zero values of
inform Equations (
6)–(
10) that
, and hence
, has been reduced by scattering.
The South Fork CVS is classified as entirely croplands by the MODIS-IGBP [
3] and consequently
is parameterized as 0.05 [
21]. While
for SMAP, there have been several values of
used for L-band soil moisture retrieval in croplands. For example, while noting that certain crop types, such as corn, can approach
, the SMOS L2 algorithm treats all “low vegetation” such as croplands to be non-scattering (
) [
38]. The SMOS-IC algorithm parameterizes stronger scattering (
) [
39]. The MT-DCA utilizes an
retrieved from SMAP
timeseries; 0.04 ± 0.04 for croplands pixels [
40]. We simulated L2SM using
0, 0.05 and 0.12 for the South Fork CVS to determine the effect changing
has on retrieval performance.
was calculated via our more physically realistic proposed method (
Section 5.2). The resulting metrics are given in
Table 5 for a crop development subset of June–September, 2015–2018.
The June–September, 2015–2018 bias is smallest when
. The SCA-V additionally has the least amount of noise and is more correlated when
is small. The SMAP default for croplands,
, results in drier soil moisture retrievals; however, this is more physically realistic than parameterizing the annual crops as non-scattering. DCA performance in terms of ubRMSE and R
2 significantly improves with the increase to
. Retrieving SMAP L2SM utilizing
for croplands, as is done in the SMOS-IC algorithm, worsens the dry bias and significantly degrades ubRMSE and R
2. In addition, using a larger value of
reduces the number of soil moisture retrievals. Only 42% (201 of 479 overpasses) of attempted SCA-V retrievals with
are successful during June–September, 2015–2018, while 91% (435 of 479) of attempted SCA-V retrievals are successful when
. The SCA-H and DCA were both better able to optimize
at
with 83% (361 of 479) of attempted retrievals being successful. Our attempted retrievals fail when the difference between simulated and observed
in the cost functions given by Equation (
11) and Equation (
12) is >1.5 K.
The difference between SCA-V and SCA-H behavior suggests that scattering effects in the South Fork are lesser for v-pol than h-pol. While
is often assumed to be unpolarized [
41], several tower-based experiments have found that
in agriculture. This would occur if scattering plant structures appeared different when observed at
h– and
v–pol; for example,
for the REBEX-8x experiment in corn [
35].
Table 5 indicates that lower values of
result in the best soil moisture retrievals as quantified by ubRMSE and R
2.
5.4. Soil Texture
In soil, water molecules can either be mobile (free water) or tightly bound to the surface area of particles (bound water) [
42]. Bound water exhibits distinctly different dielectric properties than free water at L-band [
43]. The amount of bound water is determined by soil texture as characterized by particle size distribution: the largest particles are sand (2 to 0.05 mm), the smallest are clay (<0.002 mm), and those in between are silt. A predominantly clay soil has a much larger particle surface area, and consequently more bound water, than a sandy soil. Inaccuracies in parameterized clay fraction therefore result in errors in retrieved soil moisture as the bound water component is miscalculated. Overestimation of clay theoretically results in wet-biased retrievals as the algorithms add more bound water when calculating
for high clay soils.
Dielectric mixing models simulate
, the component of Equations (
6)–(
10) that allows for soil moisture retrieval, as a function of soil moisture, texture, and temperature. SMAP L2SM is currently retrieved using the Mironov model [
44], although functionality exists for both the Dobson [
45] and Wang and Schmugge [
46] models to be implemented if desired [
34]. Utilizing the Mironov model, which requires ancillary soil temperature and clay fraction, results in wetter global soil moisture retrievals than the Dobson model [
47]. The Dobson and Wang and Schmugge models additionally require sand fraction and bulk density.
Figure 9 presents the sensitivity of L2SM retrieval to errors in the SMAP ancillary clay fraction for a bare soil scenario (VOD = 0) with clay fractions within ±0.10 of the SMAP L1-L3 Ancillary Static Data value of 0.31 in the South Fork. Moderately moist to saturated soils (tested: 0.25 and 0.40 m
3 m
−3) have similar sensitivities while dry soils (tested: 0.10 m
3 m
−3) are less sensitive. This is due to there being two distinct regions in
sensitivity to soil moisture that are separated by a “transition soil moisture” related to the wilting point [
46]. The Dobson and Wang and Schmugge models are included in
Figure 9 to illustrate how changing the dielectric model used during L2SM retrieval would affect the sensitivity to clay for a soil whose sand fraction and bulk density are similar to that of the South Fork. While both the Mironov and Wang and Schmugge models both behave as expected, with overestimation of clay content resulting in wet-biased retrievals as theorized, the Dobson model exhibits an inverse relationship. This was previously noted for South Fork soil textures and is likely due to the empirical nature of dielectric mixing models [
12]. We tested soil temperatures of 280, 290 and 300 K (
Figure 9 was produced for 300 K); temperature was not found to have a significant impact on the L2SM sensitivity to clay fraction within this range.
The SMAP ancillary clay fraction is derived from STATSGO, the State Soil Geographic dataset [
48], over CONUS and posted to the EASE03 [
49].
Figure 10 provides a subset of this map for the South Fork. The 33 km radiometric domain for EASE09 cell [row:264, col:928] and the in situ stations presented in
Figure 1 are overlaid for reference. While SMAP L2SM is posted to the EASE09 grid, the clay fraction utilized during retrieval is that of the radiometric domain (personal communication, Narendra Das, NASA JPL). The SMAP clay fraction for the 33 km domain over the South Fork is 0.31. The Soil Survey Geographic Database (SSURGO), which has a finer scale than STATSGO (100 to 500 m vs 2.5 km), indicates a clay fraction of 0.27 for the South Fork (
personal communication, Alex White, USDA ARS Hydrology and Remote Sensing Laboratory). The SSURGO value of 0.27 has been used in previous modeling of the South Fork CVS [
17]. If the “true” clay fraction in the South Fork is similar to the SSURGO value, then
Figure 9 suggests that SMAP L2SM retrievals for bare soil may currently be 0.004 to 0.007 m
3 m
−3 wetter than they should be. The impact would be lesser for vegetated periods. Interestingly, while the SMOS mission utilizes the same ancillary dataset as SMAP, albeit posted to different grid with ≈4 km resolution [
50], the clay fraction of its map is 0.25 for the South Fork domain [
12], which is closer to that derived from SSURGO.
5.5. Soil Surface Roughness
Soil surface roughness, defined as mm-scale variations in soil surface height, is rarely smooth in agricultural fields and is dependent on field management activities such as tillage [
51]. This is particularly important when modelling
as a rough soil is less reflective, and thus has a higher emissivity, than a smooth soil with the same characteristics [
52,
53]. Roughness additionally effects the L-band sampling depth as smooth soils have a shallower sampling depth than equivalent rough soils during dry conditions [
54]. SMAP L2SM retrievals account for roughness in Equation (
8) as an exponential decay of the specular reflectivity,
, characterized by non-dimensional coefficients HR and NR
; for croplands, HR = 0.108 [
21] and
2 for both
h- and
v-pol [
34].
Tillage, prevalent in the South Fork [
55], increases soil surface roughness as residue (dead plant material) from the prior crop is churned into the upper layer of soil. If the South Fork soils are, on average, rougher than the relatively smooth soil parameterized, then SMAP L2SM would be biased dry, particularly during periods of bare soil. This correlates with observed dry biases for both the SCA-H and SCA-V; however, the DCA does not exhibit a dry bias during the bare soil period (March–May and October–November). That said, the DCA-retrieved SMAP L2VOD is likely masking the effect of a too-smooth soil parameterization. Changes in soil surface roughness appear the same at L-band as changes in L2VOD [
30]. Therefore, when HR is assumed to be static, as is the case in SMAP L2SM retrieval, any increase to surface roughness is interpreted by the DCA as increasing vegetation. This is visible in the sample L2VOD timeseries, previously given in
Figure 2 and
Figure 8, where L2VOD is unrealistically large during the non-vegetative spring and late-fall months and subsequently wets L2SM retrievals similar to how assuming a rougher soil would.
L-band retrievals of soil moisture are especially sensitive to parameterization of roughness [
41]. There are several methods to convert physical observations (e.g., standard deviation of soil surface height) to the non-dimensional HR [
41,
52,
56]. Attempts to retrieve HR directly, either from tower-based or satellite observations of
, have produced variable results with HR ranging from near 0 to <2 for bare soil and cultivated croplands ([
56,
57,
58,
59] and others). SMAP documentation does not recommend a particular method for calculating HR.