Surface soil moisture estimation over dense crop using Envisat ASAR and Landsat TM imagery: an approach

This study focuses on developing a new method of surface soil moisture estimation over wheat fields using Environmental Satellite Advanced Synthetic Aperture Radar (Envisat ASAR) and Landsat Thematic Mapper (TM) data. The Michigan Microwave Canopy Scattering (MIMICS) model was used to simulate wheat canopy backscattering coefficients from experiment plots at incidence angles of 23° (IS2) and 43.9° (IS7). Based on simulated data, the scattering characteristics of a wheat canopy were first investigated in order to derive an optimal configuration of polarization (HH) and incidence angle (IS2) for soil moisture estimation. Then a parametric model was developed to describe wheat canopy backscattering at the optimal configuration. In addition, direct backscattering and two-way transmissivity of wheat crowns were derived from the TM normalized difference vegetation index (NDVI); direct ground backscattering was derived from surface soil moisture and TM NDVI; and backscattering from double scattering was derived from total backscattering. A semi-empirical model for soil moisture estimation was derived from the parametric model. Coefficients in the semi-empirical model were obtained using a calibration approach based on measured soil moisture, ASAR, and TM data. A validation of the model was performed over the experimental area. In this study, the root mean square error (RMSE) for the estimated soil moisture was 0.041 m³ m^?3, and the correlation coefficient between the measured and estimated soil moisture was 0.84. The experimental results indicate that the semi-empirical model could improve soil moisture estimation compared to an empirical model.     

Estimation of soil and crop parameters for wheat from airborne radar backscattering data in C and X bands

The study of radar backscattering signatures of wheat fields was investigated, using data collected on the Orgeval agricultural watershed (France) by the airborne scatterometer ERASME in C and X bands, HH and VV polarizations, at incidence angles from 15° to 45°, during two years for different soil moisture conditions with simultaneous ground-based measurements. A simple parameterization as water-cloud model with two driving parameters (the surface soil moisture and the plant water content) gives satisfactory results to estimate radar cross sections of wheat for a wide range of frequencies (C and X bands) and incidence angles (20° and 40°) within 1 dB in CHH and XHH and 2 dB in CVV and XVV. At the lower frequency (C band) the attenuated soil backscattering by the vegetation is dominant. It is shown that simple linear relations in C band between radar cross section and soil moisture are insufficient. A correction term for the vegetation attenuation is needed and is determined. Low contrast between the backscattering of dry and wet soil (around 6 dB) for a given vegetation density leads to a relatively high error in the estimation of soil moisture by radar (0.06 cm³ / cm³). At the higher frequency (X band), the radar backscattering is negatively correlated to the vegetation water content with a saturation of the radar cross section as the plant grows (about 6 dB of dynamic range between low and fully grown canopy) with no dependence on the soil signal. The achievable accuracy in the estimation of crop water content is the same at 20° and 40° and higher in XHH (about 0.5 kg/m²) than in XVV.     

Assessing the influence of vegetation cover on soil-moisture signatures in fire-disturbed boreal forests in interior Alaska: Modelled results

A microwave backscattering model for shrub clumps was presented. The modelling approach was to treat the clumps as scatterers and attenuators. Three major model components were defined: surface backscattering, clump volume scattering, and multiple path interactions between clumps and ground. Total backscatter was computed by incoherent summation of the components. We then used the model to study the effects of variations in surface and willow properties (soil moisture content, and surface roughness rms height and correlation length, and willow ground coverage, clump height, and stem density) on backscatter from willows in Alaskan boreal forest region. We examined the sensitivity to variations of the six parameters combined and to variation of each parameter alone from willows of three clump sizes representing different stages of vegetation regrowth after fire. Modelled C-band backscatter was more sensitive to the variations of the surface and willow parameters than L-band backscatter at incidence angles between 20° and 60°. At incidence angles of 20-60°, C-HH and C-VV backscatter was sensitive to the variations of the three surface parameters. L-HV and L-VV backscatter were only sensitive to the moisture variation. Among the three willow parameters, change of willow ground coverage produced more sensitive cases than variations of clump height and stem density combined at C- and L-band.     

基于Sentinel-1和MODIS数据反演农田地表土壤水分—以REMEDHUS地区为例

土壤水分是陆地生态系统和水循环的重要状态变量,在植被生长监测、农作物产量评估等研究中均发挥着重要作用。为了消除植被散射的影响,进而实现农田地表土壤水分的高精度反演,以时间序列Sentinel-1影像及MODIS产品为实验数据,基于高级积分方程模型和比值植被模型的耦合模型,通过采用不同光学植被参数和VH交叉极化后向散射系数,分别对农田植被散射贡献进行表征,消除植被散射的影响,进而实现土壤水分的高精度反演。结果表明：当利用VH极化进行参数化植被散射贡献时,标定的耦合模型,虽然可消除对光学植被参数的依赖并较好地模拟Sentinel-1卫星观测,但土壤水分反演结果效果欠理想,相关系数R最大仅为0.54;与VH极化相比,利用光学植被参数表征植被散射贡献时,土壤水分整体反演效果较理想,R最大达到0.79,但光学植被参数反演结果在不同站点存在显著的空间差异性,R介于0.07~0.79之间。因此,在未来研究中可尝试将雷达数据与光学数据协同反演,以期在消除植被散射影响的基础上,实现植被覆盖区域土壤水分的高精度反演及动态变化监测。     

Ground-penetrating radar measurement of crop and surface water content dynamics

Ground-penetrating radar (GPR) with a suspended 1 GHz horn antenna was deployed for measurement of soil water contents and crop canopy properties over bare and electrically terminating surfaces. Surface reflection (SR) and signal propagation times (PT) were used to independently determine dielectric permittivity and water content of soil and canopy. Measured surface reflection coefficients progressively decreased with increasing canopy biomass according to Beer-Lambert type relationships. In contrast, PT measurements remained unaffected by canopy, and hence provided an accurate account of soil water content dynamics. Immediately after canopy removal, SR-based soil water content measurements were in close agreement with PT values. Canopy dielectric properties were inferred from canopy water contents (?_c-CWC) and canopy propagation times (?_c-CPT). Distinct canopy reflections were correlated with key canopy biophysical parameters. The study demonstrates the usefulness of a horn antenna GPR for characterization of vegetation canopy scattering, and for subcanopy water content measurements within a well-defined footprint, thereby offering a potential for calibration and verification of radar data collected from air- and spaceborne platforms.     

Radar response of periodic vegetation canopies

Vector radiative transfer theory is used to model the scattered intensity from a layer of randomly oriented particles over a periodic rough surface. To account for the periodic nature of row-structured vegetation, the number density of particles within the layer is assumed to be varying periodically in the horizontal direction. Using Fourier series expansions and orthogonality properties, the radiative transfer equation is solved for the transformation matrix relating the incident and scattered intensities, from which the backscattering coefficient of the layer can be computed for any incidence direction and polarization configuration. The experimental component of this investigation consisted of radar observations at 1–5,4–75, and 9–5 GHz made by a truck-mounted system for a field of corn under three conditions: (a) full, which means that the corn plants were in their natural state, (b) defoliated, which was accomplished by stripping off the leaves and removing them, thereby leaving behind only bare vertical stalks, and (c) bare soil, which corresponds to the soil surface after having removed the stalks. The soil surface is modelled as a composite consisting of a deterministic periodic component and a random roughness component. A two-scale polarimetric scattering model is formulated and used to compare with the experimental observations. Excellent agreement between theory and measurements is realized as a function of both incidence and azimuth angles at all three microwave frequencies. The canopy model was then applied to the corn canopy under the two other conditions: stalks alone and full canopy. The model results were compared with radar backscatter measurements made for each of three look directions, including perpendicular and parallel to the row direction and at 45° relative to the row direction. For the stalk canopy, it was observed that the quasi-periodic arrangement of the stalks within the row enhances the backscatter at L-band when looking perpendicular to the row direction, which is attributed to a coherent-scattering effect associated with the stalks. A heuristic approach is used to model the quasi-periodic structure of the stalks by deriving a coherency factor which multiplies the first-order radiative solution for randomly located stalks. A similar coherency factor was also introduced for the leaves of the full canopy. The modified model was found to provide good agreement with experimental observations at L-band for all polarizations and at all look directions.     

极化分解技术在估算植被覆盖地区土壤水分变化中的应用

地表植被覆盖是影响雷达遥感估算土壤水分的主要因素之一。本文探讨了将极化分解技术与植被覆盖地区的一阶散射模型结合估算土壤水分变化的方法。雷达数据经极化目标分解技术分解后得到的双次散射项和一阶植被散射模型的植被-地表的双次散射项一一对应，再利用多时相雷达数据消除植被层后向散射的影响，从而估算出地表土壤水分变化量。最后应用全极化机载雷达数据（AirSAR）对该方法进行了检验，结果表明该方法能够较好的估算植被覆盖地表的土壤水分变化。     

A combined passive/active microwave remote sensing approach for surface variable retrieval using Tropical Rainfall Measuring Mission observations

The backscattering and emission measured simultaneously by radar and radiometer show promise for the estimation of surface variables such as near-surface soil moisture and vegetation characteristics. In this paper, the 10.7 GHz Tropical Rainfall Measuring Mission (TRMM) microwave imager (TMI) channel and 13.8 GHz precipitation radar (PR) observations are simultaneously used for the estimation of the near-surface soil moisture and vegetation properties. The Fresnel model for soil and a simple model for vegetation are used to simulate the passive microwave emission at 10.7 GHz. To determine the PR backscatter signal from a land surface, a theoretical approach is used based on the Geometric Optics Model for simulating bare soil and a semi-empirical water-cloud model for vegetation. The model parameters required in specifying the nature of the soil and vegetation are calibrated on the basis of in situ soil moisture data combined with remotely sensed observations. The calibrated model is subsequently used to retrieve near-surface soil moisture and leaf area index for assumed values of surface roughness and temperature. Algorithm assessment using synthetic passive and active microwave data shows a nonlinearity effect in the system inversion, which results in a varying degree of error statistics in soil wetness and vegetation characteristics retrieval. The technique was applied on TRMM radar/radiometer observations from three consecutive years and evaluated against in situ near-surface (5 cm) soil moisture measurements from the Oklahoma Mesonet showing a consistent performance.     

Microwave electromagnetic modelling of Sahelian grassland

In this paper radar scattering models based on coherent and incoherent formulations for an African grassland (Sahelian) are examined. The coherent model is used to account for the structure of the grass plants and the results are compared with the same model assuming random placement and orientation of scatters, and the radiative transfer model. The validity of the three models applied to grass vegetation is determined by comparing the model predictions with Envisat Advanced Synthetic Aperture Radar (ASAR) data gathered in 2005 over Sahelian grassland. The Agoufou site, as defined in the African Monsoon Multidisciplinary Analysis (AMMA) project, is selected as the test target and a set of ground data was collected during 2004 and 2005. Through a comprehensive data comparison, it is shown that the coherent scattering model with a generator considering botanical information is the best model to predict the backscattering data that matches Envisat measurements well (correlation?=?0.92). At low incidence angles (<30°), the radar backscatter shows a strong dependence on soil moisture variations. The analysis of the different contributions leads to a study of the main scattering mechanisms. For high incidence angles, the backscattering coefficient at HH polarization shows a marked seasonal variation associated with grass presence.     

Characterization of the coherent scattering induced by ridging patterns in agriculture by the use of polarimetric SAR imagery

This article investigates the scattering characteristics of ridging patterns in agriculture by the use of C-band polarimetric synthetic aperture radar (PolSAR) images. The polarimetric signatures of periodic potato fields and row wheat in different directions are highlighted using a set of polarimetric parameters. Enhanced coherent scattering is observed when the alignment direction of the ridging patterns is perpendicular to the radar’s line of sight (LOS). The dominant backscattering mechanism of the ridging patterns is deduced by evaluating different polarimetric parameters. The increased copolarized backscattering coefficients and copolarized correlation coefficient, and the reduced entropy and polarimetric alpha angle, indicate a strong contribution of odd scattering to ridging patterns aligned perpendicular to the LOS. We also compare the dominant contributions to the backscattering of ridging patterns in different phenological stages. Although the canopy changes of potato and wheat with time are significant, the underlying periodic surface changes the dominant scattering mechanism of potato fields over all the phenological stages, and the wheat aligned parallel with the flight direction of radar still has relatively high coherent scattering in the different vegetation development stages. The variability analyses undertake in this study allow a more detailed documentation of the physical scattering process of the ridging patterns in agriculture, and will improve the applicability of synthetic aperture radar images in agriculture.     

Estimating the characteristics of vegetation canopies with airborne radar measurements

Abstract

Possible use of synthetic aperture radars (SAR) for monitoring agricultural canopies is investigated in this paper. Data have been acquired on the Orgcval watershed during the AGRISCATT'88 campaign. Four radar experiments were carried out with the airborne scattcrometer ERASME (C and X bands, HH and VV polarizations, multi-incidence angles). Simultaneous ground measurements (soil moisture, leaf area index, water content of the canopy) were conducted on 11 wheat fields. Backscattering coefficients of the canopies arc interpreted in the framework of semi-empirical ‘water-cloud’ models. A simple paramctrization of the angular effect of soil roughness is introduced, allowing the simultaneous use of multi-incidence angle radar data. With a unique set of parameters for each radar configuration ‘ frequency and polarization’ the water-cloud model appears to describe adequately the backscattering of all the fields, over the range of incidence angles. It is shown that in this case, attenuation is the dominant effect of the vegetation and an inversion algorithm is proposed for estimating the water content of vegetation. This algorithm requires measurements at two different incidence angles and various combinations of radar configurations are then tested.     

Potential of ASAR/ENVISAT for the characterization of soil surface parameters over bare agricultural fields

The objective of this investigation is to analyze the sensitivity of ASAR (Advanced Synthetic Aperture Radar) data to soil surface parameters (surface roughness and soil moisture) over bare fields, at various polarizations (HH, HV, and VV) and incidence angles (20°-43°). The relationships between backscattering coefficients and soil parameters were examined by means of 16 ASAR images and several field campaigns. We have found that HH and HV polarizations are more sensitive than VV polarization to surface roughness. The results also show that the radar signal is more sensitive to surface roughness at high incidence angle (43°). However, the dynamics of the radar signal as a function of soil roughness are weak for root mean square (rms) surface heights between 0.5 cm and 3.56 cm (only 3 dB for HH polarization and 43° incidence angle). The estimation of soil moisture is optimal at low and medium incidence angles (20°-37°). The backscattering coefficient is more sensitive to volumetric soil moisture in HH polarization than in HV polarization. In fact, the results show that the depolarization ratio σ_HH⁰/σ_HV⁰ is weakly dependent on the roughness condition, whatever the radar incidence. On the other hand, we observe a linear relationship between the ratio σ_HH⁰/σ_HV⁰ and the soil moisture. The backscattering coefficient ratio between a low and a high incidence angle decreases with the rms surface height, and minimizes the effect of the soil moisture.     

土壤湿度微波遥感中的植被散射模型进展

植被是影响土壤湿度微波遥感的主要因子之一,土壤湿度微波遥感的主要任务是建立含有地表土壤信息的植被散射模型。植被散射模型的建立可以加深我们对植被和土壤散射机理的理解,定量分析微波后向散射系数对于各散射因子的敏感性,进一步达到从微波信息中反演土壤湿度的目的。植被散射模型可以分为经验模型、理论模型和半经验模型,各种模型都具有自身的优势和局限性。经验模型的建立比较简单,但一般只适用于特定的研究条件;理论模型是建立在一定的理论基础之上,对于散射因子的考虑相对详尽,但一般模型比较复杂,反演相对困难;半经验模型是前两者的折中,它以植被的宏观物理参量为模型参数,模型的建立和反演比理论模型要简单,但同时也具有一定的理论依据,适用性也较经验模型广。     

Simple modelling of radar backscattering coefficient over a bare soil: variation with incidence angle,frequency and polarization

As a basis for inversion algorithms, there is a need for the development of simple backscattering soil models which can account for the variations of incidence angle observed in the same picture or in multiangle systems. A correction factor for the variations of incidence angle is therefore coupled with a classical linear model of the variation of backscattering coefficient with surface soil moisture in a four-parameter model. The correction factor is based on the cosine-type behaviour of the backscattering coefficient as a function of incidence angle, which is observed for rough agricultural surfaces. This simple model is tested on radar measurements performed over a large range of radar configurations. The model is shown to reproduce correctly the observed variations of the radar signal with incidence angle and soil moisture. Its parameters have a physical sense and vary as expected, from literature, with frequency and polarization. When tested on data simulated by the analytical Integral Equation Model, the results of the cosine model are confirmed, as well as the variation of its calculated parameters with frequency and polarization. The inversion of the model with the angular correction factor shows that the cosine model allows the retrieval of soil moisture with a precision of about 20 per cent of the value at C band and at HV and HH polarization.     

On the influence of canopy structure on the radar backscattering of mangrove forests

This paper is the third of a series which aims to evaluate the effects of canopy structure on the polarimetric radar response of mangrove forests. It complements the experimental and theoretical study of closed canopies presented in the previous papers by analysing two different mangrove stands of equal biomass but which greatly differ in their structure. For the three considered frequencies (C-, L- and P-band), experimental observations show that the back-scattering from the open declining stand is higher than that of the closed forest. The corresponding enhancement factor increases with wavelength and shows maximum values for the HH polarization. The identification of the scattering mechanisms occurring between the incident radar wave and the forest components was performed with the assistance of a polarimetric scattering model based on a radiative transfer approach. For the co-polarizations, results of the simulation study confirm that the backscatter enhancement is mainly due to an increase of either the surface scattering or the interaction component. For the cross-polarization HV at L- and P-bands, the increase of the volume component, originating from a stronger interaction with bigger branches, is found to be responsible for the observed enhancement. These findings confirm the large effect of the canopy structure on the forest backscatter and give rise to two important applications. First, the mapping of open declining mangrove stands appears feasible by using either the backscattering coefficient values, especially at P-HH and P-HV, or the HH-VV phase difference at P-band. Second, the use of the σ °-biomass statistical relationships must be restricted to homogeneous closed canopies.     

C-band radar backscatter of Baltic sea ice: theoretical predictions compared with calibrated SAR measurements

Abstract

Airborne Synthetic Aperture Radar (SAR) data have been analysed together with in situ measurements of sea ice during the Bothnian Experiment in Preparation for ERS-1 (BEPERS) in March 1988. Based on the physical properties of the snow-covered level ice, a scattering model is used to predict the C-band like-polarization backscattering coefficient in an experiment area. Both the average backscattering coefficient and the SAR image texture were found to be in good agreement with the scattering model predictions. The backscatter signature of the level ice was found to be dominated by the ice surface r.m.s. height and autocorrelation function. These parameters were determined from profiles of the ice surface height, which were measured using a laser profiler device with sub-mm accuracy. The present model is expected to be accurate when the backscattering is dominated by scattering from the cm-scale snow or ice surface roughness.     

Temporal and spatial soil moisture change pattern detection in an agricultural area using multi‐temporal Radarsat ScanSAR data

Monitoring the characteristics of spatially and temporally distributed soil moisture is important to the study of hydrology and climatology for understanding and calculating the surface water balance. The major difficulties in retrieving soil moisture with Synthetic Aperture Radar (SAR) measurements are due to the effects of surface roughness and vegetation cover. In this study we demonstrate a technique to estimate the relative soil moisture change by using multi‐temporal C band HH polarized Radarsat ScanSAR data. This technique includes two components. The first is to minimize the effects of surface roughness by using two microwave radar measurements with different incidence angles for estimation of the relative soil moisture change defined as the ratio between two soil volumetric moistures. This was done by the development of a semi‐empirical backscattering model using a database that simulated the Advanced Integral Equation Model for a wide range of soil moisture and surface roughness conditions to characterize the surface roughness effects at different incidence angles. The second is to reduce the effects of vegetation cover on radar measurements by using a semi‐empirical vegetation model and the measurements obtained from the optical sensors (Landsat TM and AVHRR). The vegetation correction was performed based on a first‐order semi‐empirical backscattering vegetation model with the vegetation water content information obtained from the optical sensors as the input. For the validation of this newly developed technique, we compared experimental data obtained from the Southern Great Plain Soil Moisture Experiment in 1997 (SGP97) with our estimations. Comparison with the ground soil moisture measurements showed a good agreement for predication of the relative soil moisture change, in terms of ratio, with a Root Mean Square Error (RMSE) of 1.14. The spatially distributed maps of the relative soil moisture change derived from Radarsat data were also compared with those derived from the airborne passive microwave radiometer ESTAR. The maps of the spatial characteristics of the relative soil moisture change showed comparable results.     

Forest canopy height and carbon estimation at Monks Wood National Nature Reserve, UK, using dual-wavelength SAR interferometry

Forest canopy height is a critical parameter in better quantifying the terrestrial carbon cycle. It can be used to estimate aboveground biomass and carbon pools stored in the vegetation, and predict timber yield for forest management. Polarimetric SAR interferometry (PolInSAR) uses polarimetric separation of scattering phase centers derived from interferometry to estimate canopy height. A limitation of PolInSAR is that it relies on sufficient scattering phase center separation at each pixel to be able to derive accurate forest canopy height estimates. The effect of wavelength-dependent penetration depth into the canopy is known to be strong, and could potentially lead to a better height separation than relying on polarization combinations at one wavelength alone. Here we present a new method for canopy height mapping using dual-wavelength SAR interferometry (InSAR) at X- and L-band. The method is based on the scattering phase center separation at different wavelengths. It involves the generation of a smoothed interpolated terrain elevation model underneath the forest canopy from repeat-pass L-band InSAR data. The terrain model is then used to remove the terrain component from the single-pass X-band interferometric surface height to estimate forest canopy height. The ability of L-band to map terrain height under vegetation relies on sufficient spatial heterogeneity of the density of scattering elements that scatter L-band electromagnetic waves within each resolution cell. The method is demonstrated with airborne X-band VV polarized single-pass and L-band HH polarized repeat-pass SAR interferometry using data acquired by the E-SAR sensor over Monks Wood National Nature Reserve, UK. This is one of the first radar studies of a semi-natural deciduous woodland that exhibits considerable spatial heterogeneity of vegetation type and density. The canopy height model is validated using airborne imaging LIDAR data acquired by the Environment Agency. The rmse of the LIDAR canopy height estimates compared to theodolite data is 2.15 m (relative error 17.6%). The rmse of the dual-wavelength InSAR-derived canopy height model compared to LIDAR is 3.49 m (relative error 28.5%). From the canopy height maps carbon pools are estimated using allometric equations. The results are compared to a field survey of carbon pools and rmse values are presented. The dual-wavelength InSAR method could potentially be delivered from a spaceborne constellation similar to the TerraSAR system.     

Potential of SAR sensors TerraSAR-X, ASAR/ENVISAT and PALSAR/ALOS for monitoring sugarcane crops on Reunion Island

Multi-temporal TerraSAR-X, ASAR/ENVISAT and PALSAR SAR data acquired at various incidence angles and polarizations were analyzed to study the potential of these new spaceborne SAR systems for monitoring sugarcane crops. The sensitivity of different radar parameters (wavelength, incidence angles, and polarization) to sugarcane growth stages was analyzed to determine the most suitable radar configuration for better characterisation of sugarcane fields and in particular the monitoring of sugarcane harvest.Correlation between backscattered signals and crop height was also carried out. Radar signal increased quickly with sugarcane height until a threshold height, which depended on radar wavelength and incidence angle. Beyond this threshold, the signal increased only slightly, remained constant, or even decreased. The threshold height is higher with longer wavelengths (L-band in comparison with C- and X-bands) and higher incidence angles (~ 40° in comparison with ~ 20°).The radar backscattering coefficients (σ°) were also compared to the Normalized Difference Vegetation Index (NDVI) calculated from SPOT-4/5 images. Results showed a high correlation between the behaviors of σ° and NDVI as a function of sugarcane crop parameters. A decrease in NDVI for fully mature sugarcane fields due to drying of the sugarcane (water stress) was also observed in the radar signal. This decrease in radar signal was of the same order as the decrease in radar signal after the sugarcane harvest. In general, it is more suitable to monitor the sugarcane harvest using high incidence angles regardless of the radar wavelength. SAR data in L- and C-bands showed an ambiguity between the signals of ploughed fields and those of fields in vegetation because of the high sensitivity of the radar signal at these wavelengths to surface roughness of bare soils. Indeed, sometimes the radar signal of ploughed fields was of the same order as that of harvested or mature sugarcane fields. Results showed better discrimination between ploughed fields and sugarcane fields in vegetation (sugarcane canopy) when using TerraSAR-X data (X-band).Concerning the influence of radar polarization, results showed that the co-polarizations channels (HH and VV) were well correlated, but had slightly less potential than cross-polarization channels (HV and VH) for the detection of the sugarcane harvest. Finally, SAR data at high spatial resolution were shown to be useful and necessary for better analysis of SAR images when the fields were of small size.