A Critique of the Triangle Method and a Version Suitable for Estimating Soil Moisture from Satellite Imagery

Toby N. Carlson *

Pennsylvania State University, University Park, PA 16802, United States of America.

*Author to whom correspondence should be addressed.


Abstract

A simple version of the triangle model is proposed, that of a right triangle, which allows one to estimate from remote thermal/optical measurements the evapotranspiration fraction and surface soil moisture availability without reference to external variables even in the absence of a full range of vegetation cover and soil dryness. To date however, the triangle method has yet to be applied widely in the field, partly because of the triangle’s limitations and partly due to its complexity whereby prospective users would be unequipped or unwilling to handle its technical aspects, including its mathematical requirements. After a brief description of the triangle geometry, the paper deals with current misconceptions in the use of the triangle/trapezoid method, including the way in which plants deal with water stress. The last part poses a scenario showing how the right triangle model could be applied easily and routinely at field level by the non-specialist.

Keywords: Triangle method, surface soil water content, evapotranspiration


How to Cite

Carlson , T. N. (2023). A Critique of the Triangle Method and a Version Suitable for Estimating Soil Moisture from Satellite Imagery. Journal of Geography, Environment and Earth Science International, 27(10), 1–16. https://doi.org/10.9734/jgeesi/2023/v27i10713

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References

Maltese A, Capodici F, Ciraolo G, LaLoggia G. Soil water content assessment: Critical issues concerning the operational application of the triangle method, Sensors.2015;15:6699-6718.

Price JC. Using special context in satellite data to infer regional scale evapotranspiration, IEEE Transactions Geoscience Remote Sensing.1990;28:940-948.

Zhao X, Liu Y, Peng J, Zhao D.: Evaluation of topography effect on evaporative fraction from MODIS data in Taihu Basin, China, 3rd International Conference on Biomedical Engineering and Informatics. Published by IEEE.; Accession Number 11662899, Yantai, China.2010. Available: https://doi.org/10.1109/BMEI.2010.5639357.

Zhang R, Tian J, Su H, Sun X, Chen S, Xia J. Two improvements of an operational two-layer model for terrestrial surface heat flux retrieval, Sensors.2008; 8:6663-6687.

Sun H, Wang Y, Liu W, Yuan S, Nie R, Comparison of three theoretical Methods for determining dry and wet edges of the LST/FVC space: Revisit of method physics, Remote Sensing. 2017;9,528.

Long D, V Singh, Scanlon B. Deriving theoretical boundaries to address scale dependencies of triangle models for evapotranspiration estimation, J. Geophysical Research. 2012;117.

Peng J, Liu Y, Zhao X , Loew A. Estimation of evapotranspiration from MODIS toa radiances in the Poyang Lake Basin, China, Hydrol. Earth Syst. Sci.2013;17:1431.

Jiang L, Islam, Estimation of surface evaporation map over southern Great Plains using remote sensing data, Water Resources Research. 2001;37:329-340.

de Tomas A, Nieto H, Guzinski R, Salas J, Sandholt I, Berliner P. Validation and scale dependencies of the triangle method for the evaporative fraction estimation over heterogeneous areas, Remote Sensing of Environment. 2014;152: 493-511.

Zhang H, Gorelick SM, Avisse N, Tilmant A, Rajsekhar D , Yoon J. A new temperature-vegetation triangle algorithm with variable edges (TAVE) for satellite-based actual evapotranspiration /estimation, Remote Sensing. 2016;8.

Silva-Fuzzo DF, Carlson TN, Kourgialas NN, Petropoulos GF, Coupling remote sensing with a water balance model for soybean yield predictions over large areas, Earth Science Informatics. 2019;13:345-359.

Kasim AA, Carlson TN, Lisman HS, Limitations in validating derived soil moisture content from thermal/optical measurements using the simplified triangle method, Remote Sensing. 2020;12: 1155.

Nguyen HH, Cho S, Choi M. Synergy of SAR and optical-thrmal infrared remote sensing for soil moisture estimation in agro-pastoral transitional zone, Ag. and Forest Meteorology. 2022;312, 108719.

Nishida K, Nemani RR, Glassy JM, Running SW. Development of an evapotranspiration index from Aqua/MODIS for monitoring surface moisture status, Trans on Geoscience and Remote Sensing. 2003;41:493- 501.

Wang S, Garcia M, Ibrom A, Jakobsen J, Koppl CJ, Mallick K, Loomis MC, Bauer-Gottwein P. Mapping root-zone soil moisture using a temperature-vegetation-triangle approach with an Unmanned Aerial System: Incorporating surface roughness from structure and motion, Remote Sensing. 2018:10.

Batra N, Islam S, Venturini V, Bisht G, Jiang L. Estimation and comparison of evapotranspiration from MODIS and AVHRR sensors for clear sky days over the Southern Great Plains, Remote Sensing Environ. 2006;103:1-15.

Sandholt I, Rasmussen K, Andersen J. A simple interpretation of the surface temperature/vegetation index space for assessment of surface moisture status, Remote Sensing Environ. 2002;79: 213-224.

Long D, Singh VP. Assessing the impact of end-member selection on the accuracy of satellite-based spatial variability models for actual evaporation estimation, Water Resources Research. 2013;49: 2601-2618.

Yang Y, Sheng S.A hybrid dual-source scheme and trapezoid framework-based evapotranspiration model (HTEM) using satellite images: Algorithm and model test, J. Geosphys. Res. 2013;228: 2284-2300.

Carlson TN, A brief analysis of the triangle method and a proposal for its operational implementation, Remote Sensing, 2020;12. Available:https://doi.org/10.3390/rs2223832.

Gillies RR, Carlson TN, Cui J, Kustas WP, Humes KS. A Verification of the ‘Triangle’ Method’ for obtaining surface soil water content and energy fluxes from remote measurements of the normalized difference vegetation index (NDVI) and surface radiometric temperature. International Journal of Remote Sensing.1997;18: 3145–3166.

Li ZL, Tang R, Wan Z, Bi Y, Zhou C, Tang B, Yan G, Zhang X. A review of current methodologies for regional evapotranspiration estimation from remotely sensed data, Sensors. 2009; 9:3901-3853.

Stisen S, Sandholt I, Norgaard A, Fensholt R, Jensen KH. Combining the triangle method with thermal inertia to estimate regional evapotranspiration -- Applied to MSG-SEVIRI data in the Senegal River basin, Remote Sensing of Environment. 2008;112:1242-1255.

Shu Y, Stisen S, Jensen KH, Sandholt I. Estimation of regional evapotranspiration over North China Plain using geostationary satellite data, Int. J. Appl. Earth Observation and Geoinformation. 2011;13:192-206.

Liu M, Tang R, Li Z-L, DuanS, Gao M, Ziwei X. Separating soil evaporation from vegetation transpiration by remotely sensed one phase and two-phase trapezoids, Ag. and Forest Meteor. 2022;327:109215.

Long D, Singh VP, A modified surface energy balance for land (in SEBAL) based on a trapezoidal framework, Water Resources Research, 2012a;48:W02528.

Long D, Singh VP. A two-source trapezoid for evapotranspiration (TTIME) from satellite imagery, Remote Sensing of Environment. 2012b;121:370-388.

Sun H. A two-source model for estimating evaporative fraction (TMEF) coupling Priestly Taylor formula and two-stage trapezoid, Remote Sensing. 2016a;8: 248.

Sun H. Two-stage trapezoid: A new interpretation of the land surface temperature and fractional coverage space, IEEE J. Sel. Top. Appl. Earth Obs. Remote Sensing. 2016b:9:336- 346.

Tang R. Li ZL An end-member-based two-source approach for estimating land surface evapotranspiration from remote sensing data. IEEE Transactions on Geoscience and Remote Sensing, 2017;55(10):5818-5832.

Carlson TN, Ripley DA. On the relationship between NDVI, fractional vegetation cover and leaf area Index, Remote Sensing of Environment. 1997;62: 241–252.

Lynn BH, Carlson TN. Stomatal resistance model illustrating plant vs external control of transpiration, Ag. and Forest Meteor. 1990;52:5-43.

Olioso A, Carlson TN, Bresson N. Simulations of a diurnal transpiration and photosynthesis of a water stressed soybean crop, Ag. and Forest Meteor.1996;81: 41-59.

Piles M, Vali-Ilossera M, Corbella I, Panciera R, Rudiger C, Corbella YI, Panciera R, Rudiger C, Kerr Y, Walker J. Downscaling SMOS-derived soil moisture using MODIS visible/infrared data, IEEE Trans.on geosc. and remote sensing. 2011;49:3156-3166.

Amani M, Parsian S, MirMazloumi SM, Aieneh O. Two new soil moisture indices based on the NIR-red triangle space of Landsat 8 data, Int. J. Appl. Earth Obs. Geoinform. 2016;50:176-186.

Chandrasekar K, Srikanth P, Chakraborty A, Choudhary K, Ramana KV. Response of crop water indices to soil wetness and vegetation water content, Advances in Space Research. Available: https//doi.org/10.1016/j.asr.2022.11.019.

Mallick K, Bhattacharya BK,Patel NK. Estimating volumetric surface moisture content for cropped soils using a soil wetness index based on surface temperature and NDVI, Ag. And Forest Meteorology. 2009;149:1327-1342.

Sadeghi M, Babaeian E, Tuller M, Jones SB. The optical trapezoid model: A novel approach to remote sensing of soi moisture applied to Sentinel-2 and Landsat-8 observations, Remote Sensing of Environment. 2017;198:52-63.

Tang R, Z-L Li, Tang B. An application of the T-VI triangle method with enhanced edges determination for evapotranspiration estimation from MODIS data in arid and semi-arid regions. Remote Sensing of Environment. 2010;114:540-551.

Rahimimzadeh-Bajgiran P, Berg AA, Champagne C, Omasa K, Estimation of soil moisture using optical/thermal infrared remote sensing in the Canadian Prairies, ISPRS J. of Photogrammetry and Remote Sensing. 2013;83:94-103.

Capehart WJ, Carlson TN, Estimating near-surface soil moisture availability using a meteorologically driven soil water profile model, J. Hydro. 1994;160: 1-20.

Capehart WJ, Carlson TN, Decoupling of surface and near-surface soil water content: A remote sensing perspective, Water Resources Research, 1997;33: 1383-1395.

Wang W, Huang D, Wang XG, Liu YR, Zhou E. Estimation of soil moisture using trapezoidal relationship between remotely sensed land surface temperature and vegetation index, Hydrology and Earth System Sciences. 2011;15:1699-1712.

Carlson TN, Sanchez-Azofeifa GA. Satellite remote sensing of land use changes in and around San Jose’ Costa Rica, Remote Sensing Environ. 1999; 70:247-256.

Minacapilli M, Consoli S, D. Vanella, G. Ciraolo, and A. Motisi, 2016: A time domain triangle method approach to estimate evapotranspiration: Application in a Mediterranean region using MODIS and MSG SEVIRI products, Remote Sensing Environ. 174 10-23.

Tang R, Li ZL, Liu M, Jiang Y, Peng Z. A moisture-based triangle approach for estimating surface evaporative fraction with time series of remotely sensed data, Remote Sensing of Environ. 2022;280:113-212.

Jiang L, Islam, A methodology for estimation of surface evapotranspiration over large areas using remote sensing observations, Geophys. Research Letters. 1999;26: 2773-2776.

Singh R, Srivastava PK, Petropoulos G, Shukla S, Prasad R. Improvement of the triangle method for soil moisture retrieval using ECOSTRESS and Sentinel-2: Results over a heterogeneous agricultural field in northern India, Water. 2022;14:31-79.