Modeling Soil Moisture Profiles in Irrigated Fields by the Principle of Maximum Entropy

Mishra, Vikalp; Ellenburg, W. L.; Al‐Hamdan, Osama Z.; Bruce, Josh; Cruise, J. F.

doi:10.3390/e17064454

Cited by 19 publications

(19 citation statements)

References 48 publications

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“…As a first test case, SCAN site number 2078 in Madison, Alabama, which was also used in Mishra et al [43] was considered. Mishra et al [43] found the SCAN data to provide ideal test cases for evaluating fitting capabilities of their proposed SMP model. They indicated that two general shapes of soil moisture profiles are commonly observed in course of the drying process: (i) the "dynamic case", which is analogous to earlier times of drying shown in Figure 1; and (ii) the "dry case", which is similar to the late drying times in Figure 1.…”

Section: Measured Datamentioning

confidence: 99%

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Advancing NASA’s AirMOSS P-Band Radar Root Zone Soil Moisture Retrieval Algorithm via Incorporation of Richards’ Equation

et al. 2016

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P-band radar remote sensing applied during the Airborne Microwave Observatory of Subcanopy and Subsurface (AirMOSS) mission has shown great potential for estimation of root zone soil moisture. When retrieving the soil moisture profile (SMP) from P-band radar observations, a mathematical function describing the vertical moisture distribution is required. Because only a limited number of observations are available, the number of free parameters of the mathematical model must not exceed the number of observed data. For this reason, an empirical quadratic function (second order polynomial) is currently applied in the AirMOSS inversion algorithm to retrieve the SMP. The three free parameters of the polynomial are retrieved for each AirMOSS pixel using three backscatter observations (i.e., one frequency at three polarizations of Horizontal-Horizontal, Vertical-Vertical and Horizontal-Vertical). In this paper, a more realistic, physically-based SMP model containing three free parameters is derived, based on a solution to Richards' equation for unsaturated flow in soils. Evaluation of the new SMP model based on both numerical simulations and measured data revealed that it exhibits greater flexibility for fitting measured and simulated SMPs than the currently applied polynomial. It is also demonstrated that the new SMP model can be reduced to a second order polynomial at the expense of fitting accuracy.

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Section: Measured Datamentioning

confidence: 99%

Section: Measured Datamentioning

confidence: 99%

Advancing NASA’s AirMOSS P-Band Radar Root Zone Soil Moisture Retrieval Algorithm via Incorporation of Richards’ Equation

et al. 2016

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“…Some infiltration equations were derived based on the principle of maximum entropy (PME) with the Shannon entropy or information entropy [9] as well as soil moisture movement on the basis of PME with Tsallis entropy [10]. The soil moisture distribution was also estimated in an irrigated field in North Central Alabama, USA, based on the PME [11]. These studies assumed that the vertical soil moisture distribution curve is a scaled probability density function (PDF) that follows PME.…”

Section: Introductionmentioning

confidence: 99%

Entropy Base Estimation of Moisture Content of the Top 10-m Unsaturated Soil for the Badain Jaran Desert in Northwestern China

Zhou

Lei

2016

Entropy

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Estimation of soil moisture distribution in desert regions is challenged by the deep unsaturated zone and the extreme natural environment. In this study, an entropy-based method, consisting of information entropy, principle of maximum entropy (PME), solutions to PME with constraints, and the determination of parameters, is used to estimate the soil moisture distribution in the 10 m deep vadose zone of a desert region. Firstly, the soil moisture distribution is described as a scaled probability density function (PDF), which is solved by PME with the constraints of normalization, known arithmetic mean and geometric mean, and the solution is the general form of gamma distribution. A constant arithmetic mean is determined by considering the stable average recharge rate at thousand year scale, and an approximate constant geometric mean is determined by the low flow rate (about 1 cm a year). Followed, the parameters of the scaled PDF of gamma distribution are determined by local environmental factors like terrain and vegetation: the multivariate linear equations are established to qualify the relationship between the parameters and the environmental factors on the basis of nineteen random soil moisture profiles about depth through the application of fuzzy mathematics. Finally, the accuracy is tested using correlation coefficient (CC) and relative error. This method performs with CC larger than 0.9 in more than a half profiles and most larger than 0.8, the relative errors are less than 30% in most of soil moisture profiles and can be as low as less than 15% when parameters fitted appropriately. Therefore, this study provides an alternative method to estimate soil moisture distribution in top 0-10 m layers of the Badain Jaran Desert based on local terrain and vegetation factors instead of drilling sand samples, this method would be useful in desert regions with extreme natural conditions since these environmental factors can be obtained by remote sensing data. Meanwhile, we should bear in mind that this method is challenged in humid regions since more intensive and frequent precipitation, and more vegetation cover make the system much more complex.

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“…(4). In fact, it is clear that some profiles can be parabolic in shape (i.e., demonstrate an inflection point), especially immediately subsequent to rain events (dynamic case), or due to sharp changes in soil characteristics (Al-Hamdan and Cruise, 2010;Mishra et al, 2015). These cases are identified when mass balance cannot be kept by the monotonic assumption and thus Eq.…”

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confidence: 99%

“…(4) has no solution. In these cases, it is 290 assumed that the inflection point is located in the soil layer with the greatest field capacity (Mishra et al, 2015). The POME model is then applied twice; from the surface to the inflection point, and then from the inflection point to the bottom boundary.…”

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confidence: 99%

Development of Soil Moisture Profiles Through Coupled Microwave-Thermal Infrared Observations in the Southeastern United States

Mishra¹,

Cruise²,

Hain³

et al. 2017

Preprint

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Abstract. The principle of maximum entropy (POME) can be used to develop vertical soil moisture profiles. The minimal inputs required by the POME model make it an excellent choice for remote sensing applications. Two of the major input requirements of the POME model are the surface boundary condition and profile-mean moisture content. Microwave-based soil moisture estimates from Advanced Microwave Scanning Radiometer (AMSR-E) can supply the surface boundary 5 condition whereas thermal infrared-based moisture estimated from the Atmosphere Land Exchange Inverse (AELXI) surface energy balance model can provide the mean moisture condition. A disaggregation approach was followed to downscale coarse resolution (∼25 km) microwave soil moisture estimates to match the finer resolution (∼5 km) thermal data. The study was conducted over multiple years (2006)(2007)(2008)(2009)(2010)

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Modeling Soil Moisture Profiles in Irrigated Fields by the Principle of Maximum Entropy

Cited by 19 publications

References 48 publications

Advancing NASA’s AirMOSS P-Band Radar Root Zone Soil Moisture Retrieval Algorithm via Incorporation of Richards’ Equation

Advancing NASA’s AirMOSS P-Band Radar Root Zone Soil Moisture Retrieval Algorithm via Incorporation of Richards’ Equation

Entropy Base Estimation of Moisture Content of the Top 10-m Unsaturated Soil for the Badain Jaran Desert in Northwestern China

Development of Soil Moisture Profiles Through Coupled Microwave-Thermal Infrared Observations in the Southeastern United States

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