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Systematic Errors in Simulated L-Band Brightness Temperature in the SMAP Level-4 Soil Moisture Analysis

The NASA Soil Moisture Active Passive (SMAP) mission has been providing L-band (1.4 GHz) brightness temperature (Tb) observations since April 2015. By assimilating the Tb observations into the NASA Catchment land surface model using a spatially distributed ensemble Kalman filter (EnKF), the SMAP Level-4 Soil Moisture (L4_SM) product provides global, 3-hourly, 9-km resolution estimates of surface (0-5 cm) and root-zone (0-100 cm) soil moisture with ~2.5-day latency for use in research and applications. The EnKF-based L4_SM analysis assumes unbiased forecast errors. Consequently, the seasonally varying bias between the model forecast Tb and the observed values is removed prior to the assimilation of the SMAP Tb observations. The L4_SM system is thus designed to only correct errors in synoptic-scale and interannual variations from the long-term mean seasonal cycle while maintaining the model’s (possibly wrong) climatology. In this paper, we examine the Tb observation-minus-forecast (O-F) residuals from the L4_SM Version 7 product (computed after rescaling the Tb observations to the mean seasonal cycle of the simulated Tb). The long-term average of the Tb O-F residuals has a global mean of only 0.13 K and locally small values, ranging from -1 to 3 K. The model forecast Tb, however, still exhibits undesirable systematic errors relative to the (rescaled) Tb observations. At some locations, the time-average Tb O-F values strongly depend on surface soil moisture (SM). At the Yanco SMAP core validation site, for example, the Tb O-F residuals typically range from 5 to 15 K under dry soil moisture conditions (SM < 0.15 m3 m-3) yet are predominantly negative under wet soil moisture conditions (SM > 0.25 m3 m-3), with values ranging from 0 to -40 K. This results in soil moisture analysis increments that persistently make the soil drier under dry SM conditions and persistently make the soil wetter under wet SM conditions, suggesting an error in the dynamic range of the simulated Tb, soil moisture or soil temperature. In this paper, we describe the higher-order systematic Tb forecast errors in more detail, examine their impact on the L4_SM product quality, and explore potential avenues to improve the L4_SM algorithm.

Rolf Reichle

Version 3 of the SMAP Level 4 Soil Moisture Product

The NASA Soil Moisture Active Passive (SMAP) Level 4 Soil Moisture (L4_SM) product provides 3-hourly, 9-km resolution, global estimates of surface (0-5 cm) and root zone (0-100 cm) soil moisture as well as related land surface states and fluxes from 31 March 2015 to present with a latency of 2.5 days. The ensemble-based L4_SM algorithm is a variant of the Goddard Earth Observing System version 5 (GEOS-5) land data assimilation system and ingests SMAP L-band (1.4 GHz) Level 1 brightness temperature observations into the Catchment land surface model. The soil moisture analysis is non-local (spatially distributed), performs downscaling from the 36-km resolution of the observations to that of the model, and respects the relative uncertainties of the modeled and observed brightness temperatures. Prior to assimilation, a climatological rescaling is applied to the assimilated brightness temperatures using a 6 year record of SMOS observations. A new feature in Version 3 of the L4_SM data product is the use of 2 years of SMAP observations for rescaling where SMOS observations are not available because of radio frequency interference, which expands the impact of SMAP observations on the L4_SM estimates into large regions of northern Africa and Asia. This presentation investigates the performance and data assimilation diagnostics of the Version 3 L4_SM data product. The L4_SM soil moisture estimates meet the 0.04 m3m3 (unbiased) RMSE requirement. We further demonstrate that there is little bias in the soil moisture analysis. Finally, we illustrate where the assimilation system overestimates or underestimates the actual errors in the system.

GEOS-

Soil Moisture Workshop

The Soil Moisture Workshop was held at the United States Department of Agriculture National Agricultural Library in Beltsville, Maryland on January 17-19, 1978. The objectives of the Workshop were to evaluate the state of the art of remote sensing of soil moisture; examine the needs of potential users; and make recommendations concerning the future of soil moisture research and development. To accomplish these objectives, small working groups were organized in advance of the Workshop to prepare position papers. These papers served as the basis for this report.

Heilman, J. L.

Assimilation of Passive and Active Microwave Soil Moisture Retrievals

Root-zone soil moisture is an important control over the partition of land surface energy and moisture, and the assimilation of remotely sensed near-surface soil moisture has been shown to improve model profile soil moisture [1]. To date, efforts to assimilate remotely sensed near-surface soil moisture at large scales have focused on soil moisture derived from the passive microwave Advanced Microwave Scanning Radiometer (AMSR-E) and the active Advanced Scatterometer (ASCAT; together with its predecessor on the European Remote Sensing satellites (ERS. The assimilation of passive and active microwave soil moisture observations has not yet been directly compared, and so this study compares the impact of assimilating ASCAT and AMSR-E soil moisture data, both separately and together. Since the soil moisture retrieval skill from active and passive microwave data is thought to differ according to surface characteristics [2], the impact of each assimilation on the model soil moisture skill is assessed according to land cover type, by comparison to in situ soil moisture observations.

Draper, C. S.

The critical role of soil moisture in compound hazards

Soil moisture regulates the exchange of energy, water, and carbon across land–vegetation–atmosphere interfaces. Extremes in soil moisture can amplify natural hazards through interactions with diverse Earth system processes. Despite its mechanistic importance, soil moisture remains underrepresented in hazard research and predictive frameworks. Here, in this study, we review our current understanding of the role of soil moisture in the evolution and onset of diverse compound hazards by synthesizing the latest findings from observational and modelling studies. We highlight key soil moisture mechanisms, including atmospheric feedbacks that amplify drought–heatwave–wildfire events, precipitation couplings that promote clustered storms, and threshold responses that drive vegetation die-offs, trigger landslides, and induce flooding. Persistent challenges in observational data, model representation and operational implementation have limited the integration of soil moisture into hazard early-warning systems. Addressing these gaps through advances in observations, data assimilation, and physics-based and data-driven modelling will enhance hazard prediction and preparedness in a rapidly changing world.

Li, Chuxuan [University of California, Los Angeles

Role of Subsurface Physics in the Assimilation of Surface Soil Moisture Observations

Root zone soil moisture controls the land-atmosphere exchange of water and energy and exhibits memory that may be useful for climate prediction at monthly scales. Assimilation of satellite-based surface soil moisture observations into a land surface model is an effective way to estimate large-scale root zone soil moisture. The propagation of surface information into deeper soil layers depends on the model-specific representation of subsurface physics that is used in the assimilation system. In a suite of experiments we assimilate synthetic surface soil moisture observations into four different models (Catchment, Mosaic, Noah and CLM) using the Ensemble Kalman Filter. We demonstrate that identical twin experiments significantly overestimate the information that can be obtained from the assimilation of surface soil moisture observations. The second key result indicates that the potential of surface soil moisture assimilation to improve root zone information is higher when the surface to root zone coupling is stronger. Our experiments also suggest that (faced with unknown true subsurface physics) overestimating surface to root zone coupling in the assimilation system provides more robust skill improvements in the root zone compared with underestimating the coupling. When CLM is excluded from the analysis, the skill improvements from using models with different vertical coupling strengths are comparable for different subsurface truths. Finally, the skill improvements through assimilation were found to be sensitive to the regional climate and soil types.

Reichle, R. H.

On Simulating the Impacts of Open Water Bodies on the SMAP Passive Soil Moisture Data Product

The Soil Moisture Active and Passive (SMAP) mission is a NASA earth science mission aiming at improving our understanding of the dynamics of the cycles of energy, water, and carbon at global scales. The mission features two complementary sensors on the same low-Earth orbiting platform: an L-band synthetic aperture radar (SAR) operating at 1.26 GHz and an L-band radiometer operating at 1.41 GHz. Together these instruments will provide global mapping of soil moisture and freeze/thaw states in 2-3 days, with a tentative launch date in 2014. The work reported in this study focuses primarily on the development of the SMAP radiometer-only soil moisture data product. For passive soil moisture retrieval at satellite footprint scales, one way to improve retrieval accuracy is to correct for the microwave emission from open water bodies prior to retrieval. The accuracy of this correction will depend on not only the locations of these water bodies, but also the geolocation accuracy of the instrument. As perfect knowledge is never attainable in practice, it is important to assess the impacts of these uncertainties on the SMAP radiometer observations and hence the passive soil moisture retrieval accuracy. In this presentation, we present the results of our preliminary assessment on the impacts of these uncertainties. Our study consists of two parts: (1) a sensitivity analysis on the SMAP radiometer observations due to uncertainties in water-body classification, and (2) realistic global simulations that take into account of additional uncertainties (e.g., geolocation and ancillary data) and SMAP-specific instrument characteristics (e.g., orbit sampling and antenna pattern). The results will provide valuable prelaunch guidance to the SMAP team in identifying different error sources and their relative impacts on the passive soil moisture data product.

Chan, Steven

Microwave Soil Moisture Retrieval Under Trees

Soil moisture is recognized as an important component of the water, energy, and carbon cycles at the interface between the Earth's surface and atmosphere. Current baseline soil moisture retrieval algorithms for microwave space missions have been developed and validated only over grasslands, agricultural crops, and generally light to moderate vegetation. Tree areas have commonly been excluded from operational soil moisture retrieval plans due to the large expected impact of trees on masking the microwave response to the underlying soil moisture. Our understanding of the microwave properties of trees of various sizes and their effect on soil moisture retrieval algorithms at L band is presently limited, although research efforts are ongoing in Europe, the United States, and elsewhere to remedy this situation. As part of this research, a coordinated sequence of field measurements involving the ComRAD (for Combined Radar/Radiometer) active/passive microwave truck instrument system has been undertaken. Jointly developed and operated by NASA Goddard Space Flight Center and George Washington University, ComRAD consists of dual-polarized 1.4 GHz total-power radiometers (LH, LV) and a quad-polarized 1.25 GHz L band radar sharing a single parabolic dish antenna with a novel broadband stacked patch dual-polarized feed, a quad-polarized 4.75 GHz C band radar, and a single channel 10 GHz XHH radar. The instruments are deployed on a mobile truck with an 19-m hydraulic boom and share common control software; real-time calibrated signals, and the capability for automated data collection for unattended operation. Most microwave soil moisture retrieval algorithms developed for use at L band frequencies are based on the tau-omega model, a simplified zero-order radiative transfer approach where scattering is largely ignored and vegetation canopies are generally treated as a bulk attenuating layer. In this approach, vegetation effects are parameterized by tau and omega, the microwave vegetation opacity and single scattering albedo. One goal of our current research is to determine whether the tau-omega model can work for tree canopies given the increased scatter from trees compared to grasses and crops, and. if so, what are effective values for tau and omega for trees.

O'Neill, P.

Toward P-Band Passive Microwave Sensing of Soil Moisture

Currently, near-surface soil moisture at a global scale is being provided using National Aeronautics and Space Administration’s (NASA’s) Soil Moisture Active Passive (SMAP) and European Space Agency’s (ESA’s) Soil Moisture and Ocean Salinity (SMOS) satellites, both of which utilize L-band (1.4 GHz; 21 cm wavelength ) passive microwave remote sensing techniques. However, a fundamental limitation of this technology is that the water content can only be measured for approximately the top 5-cm layer of soil moisture, and only over low-to-moderate vegetation covered areas in order to meet the 0.04 m3/m3 target accuracy, limiting its applicability. Consequently, a longer wavelength radiometer is being explored as a potential solution for measuring soil moisture in a deeper surface layer of soil and under denser vegetation. It is expected that P-band ( wavelength of 40 cm and frequency of 750 MHz) could potentially provide soil moisture information for the top 10-cm layer of soil, being one-tenth to one-quarter of the wavelength. In addition, P-band is expected to have higher soil moisture retrieval accuracy due to its reduced sensitivity to vegetation water content and surface roughness. To demonstrate the potential of P-band passive microwave soil moisture remote sensing, a short-term airborne field experiment was conducted over a center pivot irrigated farm at Cressy in Tasmania, Australia, in January 2017. First results showing a comparison of airborne P-band brightness temperature observations against airborne L-band brightness temperature observations and ground soil moisture measurements are presented. The P-band brightness temperature was found to have a similar but stronger response to soil moisture compared to L-band.

Nan Ye

Passive microwave sensing of soil moisture content - The effects of soil bulk density and surface roughness

Microwave radiometric measurements over bare fields of different surface roughness were made at frequencies of 1.4 GHz, 5 GHz, and 10.7 GHz to study the frequency dependence, as well as the possible time variation, of surface roughness. An increase in surface roughness was found to increase the brightness temperature of soils and reduce the slope of regression between brightness temperature and soil moisture content. The frequency dependence of the surface roughness effect was relatively weak when compared with that of the vegetation effect. Radiometric time-series observations over a given field indicate that field surface roughness might gradually diminish with time, especially after a rainfall or irrigation. The variation of surface roughness increases the uncertainty of remote soil moisture estimates by microwave radiometry. Three years of radiometric measurements over a test site revealed a possible inconsistency in the soil bulk density determination, which is an important factor in the interpretation of radiometric data.

Wang, J. R.

The SMAP Level 4 Surface and Root-zone Soil Moisture (L4_SM) Product

The Soil Moisture Active and Passive (SMAP) mission is being developed by NASA for launch in 2013 as one of four first-tier missions recommended by the U.S. National Research Council Committee on Earth Science and Applications from Space in 2007. The primary science objectives of SMAP are to enhance understanding of land surface controls on the water, energy and carbon cycles, and to determine their linkages. Moreover, the high resolution soil moisture mapping provided by SMAP has practical applications in weather and seasonal climate prediction, agriculture, human health, drought and flood decision support. In this paper we describe the assimilation of SMAP observations for the generation of the planned SMAP Level 4 Surface and Root-zone Soil Moisture (L4_SM) product. The SMAP mission makes simultaneous active (radar) and passive (radiometer) measurements in the 1.26-1.43 GHz range (L-band) from a sun-synchronous low-earth orbit. Measurements will be obtained across a 1000 km wide swath using conical scanning at a constant incidence angle (40 deg). The radar resolution varies from 1-3 km over the outer 70% of the swath to about 30 km near the center of the swath. The radiometer resolution is 40 km across the entire swath. The radiometer measurements will allow high-accuracy but coarse resolution (40 km) measurements. The radar measurements will add significantly higher resolution information. The radar is however very sensitive to surface roughness and vegetation structure. The combination of the two measurements allows optimal blending of the advantages of each instrument. SMAP directly observes only surface soil moisture (in the top 5 cm of the soil column). Several of the key applications targeted by SMAP, however, require knowledge of root zone soil moisture (approximately top 1 m of the soil column), which is not directly measured by SMAP. The foremost objective of the SMAP L4_SM product is to fill this gap and provide estimates of root zone soil moisture that are informed by and consistent with SMAP observations. Such estimates are obtained by merging SMAP observations with estimates from a land surface model in a soil moisture data assimilation system. The land surface model component of the assimilation system is driven with observations-based surface meteorological forcing data, including precipitation, which is the most important driver for soil moisture. The model also encapsulates knowledge of key land surface processes, including the vertical transfer of soil moisture between the surface and root zone reservoirs. Finally, the model interpolates and extrapolates SMAP observations in time and in space. The L4_SM product thus provides a comprehensive and consistent picture of land surface hydrological conditions based on SMAP observations and complementary information from a variety of sources. The assimilation algorithm considers the respective uncertainties of each component and yields a product that is superior to satellite or model data alone. Error estimates for the L4_SM product are generated as a by-product of the data assimilation system.

Reichle, Rolf

Ultrasound Algorithm Derivation for Soil Moisture Content Estimation

Soil moisture content can be estimated by evaluating the velocity at which sound waves travel through a known volume of solid material. This research involved the development of three soil algorithms relating the moisture content to the velocity at which sound waves moved through dry and moist media. Pressure and shear wave propagation equations were used in conjunction with soil property descriptions to derive algorithms appropriate for describing the effects of moisture content variation on the velocity of sound waves in soils with and without complete soil pore water volumes, An elementary algorithm was used to estimate soil moisture contents ranging from 0.08 g/g to 0.5 g/g from sound wave velocities ranging from 526 m/s to 664 m/s. Secondary algorithms were also used to estimate soil moisture content from sound wave velocities through soils with pores that were filled predominantly with air or water.

Belisle, W.R.

Soil Moisture Data Assimilation

Accurate knowledge of soil moisture at the continental scale is important for improving predictions of weather, agricultural productivity and natural hazards, but observations of soil moisture at such scales are limited to indirect measurements, either obtained through satellite remote sensing or from meteorological networks. Land surface models simulate soil moisture processes, using observation-based meteorological forcing data, and auxiliary information about soil, terrain and vegetation characteristics. Enhanced estimates of soil moisture and other land surface variables, along with their uncertainty, can be obtained by assimilating observations of soil moisture into land surface models. These assimilation results are of direct relevance for the initialization of hydro-meteorological ensemble forecasting systems. The success of the assimilation depends on the choice of the assimilation technique, the nature of the model and the assimilated observations, and, most importantly, the characterization of model and observation error. Systematic differences between satellite-based microwave observations or satellite-retrieved soil moisture and their simulated counterparts require special attention. Other challenges include inferring root-zone soil moisture information from observations that pertain to a shallow surface soil layer, propagating information to unobserved areas and downscaling of coarse information to finer-scale soil moisture estimates. This chapter summarizes state-of-the-art solutions to these issues with conceptual data assimilation examples, using techniques ranging from simplified optimal interpolation to spatial ensemble Kalman filtering. In addition, operational soil moisture assimilation systems are discussed that support numerical weather prediction at ECMWF and provide value-added soil moisture products for the NASA Soil Moisture Active Passive mission.

radar backscatter

Assimilation of Satellite Soil Moisture for Improved Atmospheric Reanalyses

Satellite soil moisture observations are assimilated into NASA's Global Earth Observing System using a weakly coupled land/atmosphere data assimilation system. Specifically, Advanced Scatterometer and Soil Moisture Ocean Salinity soil moisture retrievals are assimilated with an Ensemble Kalman Filter into a system that uses the same model, atmospheric assimilation system (3DVar), and atmospheric observations as the Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2). The first set of experiments investigate the impact of the soil moisture assimilation on the model states and fluxes within the cycling DA system. Comparison to independent ground-based observations from global networks of soil moisture, latent and sensible heating, and 2m temperature and specific humidity showed small, but positive, improvements in the global mean statistics. Additionally, in some regions, the soil moisture assimilation induced more substantial improvements. For all variables evaluated, the soil moisture assimilation improved the model at monthly to seasonal, rather than daily, time scales. Based on the above experiments, it is recommended that satellite soil moisture be assimilated into future reanalyses, including the follow-on to MERRA-2.

Draper, Clara

Assimilation of SMOS Retrieved Soil Moisture into the Land Information System

Soil moisture retrievals from the Soil Moisture and Ocean Salinity (SMOS) instrument are assimilated into the Noah land surface model (LSM) within the NASA Land Information System (LIS). Before assimilation, SMOS retrievals are bias-corrected to match the model climatological distribution using a Cumulative Distribution Function (CDF) matching approach. Data assimilation is done via the Ensemble Kalman Filter. The goal is to improve the representation of soil moisture within the LSM, and ultimately to improve numerical weather forecasts through better land surface initialization. We present a case study showing a large area of irrigation in the lower Mississippi River Valley, in an area with extensive rice agriculture. High soil moisture value in this region are observed by SMOS, but not captured in the forcing data. After assimilation, the model fields reflect the observed geographic patterns of soil moisture. Plans for a modeling experiment and operational use of the data are given. This work helps prepare for the assimilation of Soil Moisture Active/Passive (SMAP) retrievals in the near future.

Data Assimilation

Validation of Remotely Sensed and Modeled Soil Moisture at Forested and Unforested Sites

Soil moisture is an important driver for forest ecosystems, influencing fire occurrence and extent, insect and pathogen impacts, and tree growth, which creates a need for regular, globally extensive soil moisture information that only satellite-based sensors or models can achieve. However, the reliability of soil moisture measurements in forests is not well understood due to a lack of suitable validation sites (especially relative to unforested ecosystems) and interference caused by high vegetation water content on remotely sensed measurements; although recent studies have started to address this gap [1], [2], [3], [4]. Here we validate the performance of multiyear remotely sensed (SMAP/Sentinel), remotely sensed data assimilation modelled (SMAP-L4), and modelled (NLDAS) surface and root zone (0-1 m) soil moisture datasets with data from in-situ sensors at 39 National Ecological Observatory Network (NEON) sites throughout the contiguous US. Due to differences in spatial resolution, NEON soil moisture (~0.2 km measurement zone) correlations were expected to be stronger with the SMAP/Sentinel product (3 km resolution) than with coarser resolution SMAP-L4 (9 km resolution) or NLDAS products (13 km resolution). However, given the sensitivity of satellite measurements to vegetation water content we expected a deterioration in the correlations based on remotely sensed measurements (SMAP/Sentinel and SMAP-L4) as aboveground biomass increased, whereas the model-based data (NLDAS) was expected to be largely insensitive to vegetation type. We recognize that the SMAP/Sentinel product was developed for unforested regions, therefore our application is outside its primary use case. Soil moisture is measured at up to 8 depths in five soil plots spaced up to 40 m apart at each NEON terrestrial site. Correlation parameters were calculated for the three remotely sensed and modelled data products relative to in-situ measurement following Entekhabi et al. [5]. The datasets comprised 94 (SMAP-L4), 28 (SMAP/Sentinel), and 106 (NLDAS) sites-years for surface soils and 13 (SMAP-L4) and 14 (NLDAS) site-years for the root zone. At unforested sites, the performance of the three remotely sensed and modelled data products was similar for surface soils (Table 1). For example, unbiased RMSD (ubRMSD), which SMAP uses as its primary performance metric [6], ranged from 0.05 to 0.06 m3 m-3 (Table 1), indicating the ability of all three products to track changes in soil moisture over time. The performance of the three products deteriorated at forested sites, however, while the difference in performance was modest for SMAP-L4 and NLDAS, the deterioration in SMAP/Sentinel performance was substantial. For instance, SMAP/Sentinel ubRMSD increased from 0.06 to 0.11 m3 m-3 and absolute mean difference (Abs MD; which includes measurement bias and spatial representativeness errors) increased from 0.06 to 0.16 m3 m-3, indicating both a reduction in ability to track temporal changes and absolute amounts of soil moisture in forest ecosystems. SMAP-L4 and NLDAS had lower unbiased RMSD for root zone (0-1 m) than surface soils at both forested and unforested sites (Tables 1 and 2; SMAP/Sentinel does not produce a root zone measurement). However, in most cases the correlation coefficient (r) was lower for the root zone than surface soils, suggesting the lower unbiased RMSD may be attributed to greater temporal stability of soil moisture in the root zone rather than improved data product performance. Mean difference and absolute mean difference, which encompass measurement bias and spatial representativeness errors, were greater for root zone than surface soils at unforested sites for both data products, but the opposite was generally true at forested sites. As with surface soils, there was relatively little change in the performance of SMAP-L4 and NLDAS between the unforested and forested sites. In summary, all three data products were able to adequately represent soil moisture at unforested sites, at least when aggregating across sites. However, while the performance of all three products deteriorated at forested sites, SMAP-L4 and NLDAS maintained sufficient performance to remain suitable for some use cases (ubRMSD <0.06 m3 m-3 and RMSD <0.13 m3 m-3). In contrast, the relatively poorer performance of the SMAP/Sentinel product at forested sites seems insufficient for most use cases (ubRMSD >0.1 m3 m-3 and RMSD >0.2 m3 m-3). We attribute the large reduction in the performance of the SMAP/Sentinel product in forests to its use of C-band wavelengths, which are particularly sensitive to vegetation interference, and apparently outweighed any gains provided by its higher spatial resolution. A combined SMAP/NISAR soil moisture product may provide improved performance relative to SMAP/Sentinel due to NISAR’s use of L-band wavelengths, which are less sensitive to vegetation (NISAR is scheduled for launch in early 2024).

Edward Ayres

Evaluation of HCMM data for assessing soil moisture and water table depth

Soil moisture in the 0-cm to 4-cm layer could be estimated with 1-mm soil temperatures throughout the growing season of a rainfed barley crop in eastern South Dakota. Empirical equations were developed to reduce the effect of canopy cover when radiometrically estimating the soil temperature. Corrective equations were applied to an aircraft simulation of HCMM data for a diversity of crop types and land cover conditions to estimate the soil moisture. The average difference between observed and measured soil moisture was 1.6% of field capacity. Shallow alluvial aquifers were located with HCMM predawn data. After correcting the data for vegetation differences, equations were developed for predicting water table depths within the aquifer. A finite difference code simulating soil moisture and soil temperature shows that soils with different moisture profiles differed in soil temperatures in a well defined functional manner. A significant surface thermal anomaly was found to be associated with shallow water tables.

Moore, D. G.