What is Metric: Definition and 1000 Discussions

METRIC (Mapping EvapoTranspiration at high Resolution with Internalized Calibration) is a computer model developed by the University of Idaho, that uses Landsat satellite data to compute and map evapotranspiration (ET). METRIC calculates ET as a residual of the surface energy balance, where ET is estimated by keeping account of total net short wave and long wave radiation at the vegetation or soil surface, the amount of heat conducted into soil, and the amount of heat convected into the air above the surface. The difference in these three terms represents the amount of energy absorbed during the conversion of liquid water to vapor, which is ET. METRIC expresses near-surface temperature gradients used in heat convection as indexed functions of radiometric surface temperature, thereby eliminating the need for absolutely accurate surface temperature and the need for air-temperature measurements.

The surface energy balance is internally calibrated using ground-based reference ET that is based on local weather or gridded weather data sets to reduce computational biases inherent to remote sensing-based energy balance. Slope and aspect functions and temperature lapsing are used for application to mountainous terrain. METRIC algorithms are designed for relatively routine application by trained engineers and other technical professionals who possess a familiarity with energy balance and basic radiation physics. The primary inputs for the model are short-wave and long-wave thermal images from a satellite e.g., Landsat and MODIS, a digital elevation model, and ground-based weather data measured within or near the area of interest. ET “maps” i.e., images via METRIC provide the means to quantify ET on a field-by-field basis in terms of both the rate and spatial distribution. The use of surface energy balance can detect reduced ET caused by water shortage.
In the decade since Idaho introduced METRIC, it has been adopted for use in Montana, California, New Mexico, Utah, Wyoming, Texas, Nebraska, Colorado, Nevada, and Oregon. The mapping method has enabled these states to negotiate Native American water rights; assess agriculture to urban water transfers; manage aquifer depletion, monitor water right compliance; and protect endangered species.

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  1. Math Amateur

    MHB Countably Dense Subsets in a Metric Space .... Stromberg, Lemma 3.44 .... ....

    I am reading Karl R. Stromberg's book: "An Introduction to Classical Real Analysis". ... ... I am focused on Chapter 3: Limits and Continuity ... ... I need help in order to fully understand the proof of Lemma 3.44 on page 105 ... ... Lemma 3.44 and its proof read as follows: In the above...
  2. snoopies622

    I The vanishing of the covariant derivative of the metric tensor

    I brought up this subject here about a decade ago so this time I'll try to be more specific to avoid redundancy. In chapter five of Bernard F. Schutz's A First Course In General Relativity, he arrives at the conclusion that in flat space the covariant derivative of the metric tensor is zero...
  3. D

    I What is the Purpose of Calculating the Christoffel Symbols in Curved Spacetime?

    Calculating the christoffel symbols requires taking the derivatives of the metric tensor. What are you taking derivatives of exactly? Are you taking the derivatives of the inner product of the basis vectors with respect to coordinates? In curvilinear coordinates, for instance curved spacetime in...
  4. Math Amateur

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  5. K

    I Radius in Schwarzschild Metric: Definition Explained

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  6. DuckAmuck

    I Invariant Mass in Gravitational Fields: Special Relativity

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  7. Math Amateur

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  8. Math Amateur

    I Metric Spaces .... the Uniform Metric .... Garling, Proposition 11.1.11

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  9. D

    I Help Understanding Metric Tensor

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  10. olgerm

    I Invariant properties of metric tensor

    Which properties of metric tensor are invariant of basevectors transforms? I know that metric tensor depends of basevectors, but are there properties of metric tensor, that are basevector invariant and describe space itself?
  11. Zuhaa Naz

    Find the Tetrad for Kerr Metric: Step-by-Step Guide

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  12. A

    I How Does the Metric of a 4-D Spacetime Define Its Symmetry and Expansion?

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  13. A

    I Perturbation to Flat Space Metric: Geodesic Equation

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  14. V

    B Solving an Integral on a Spherical Surface - Tips

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  15. K

    I Schwarzschild metric not dependent on time

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  16. Z

    A Decoupling of SVT Metric Perturbations

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  17. A

    Liouville operator in Robertson Walker metric

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  18. A

    A Dark matter and spacetime metric

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  19. E

    B Solving the Kerr metric in the program Maxima

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  20. M

    A Orbit velocity in Schwarzschild metric?

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  21. Arman777

    I Metric of the Universe and dependence on Cosmological P

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  22. DaTario

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  23. jk22

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  24. E

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  25. George Keeling

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  26. saadhusayn

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  27. binbagsss

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  28. Chromatic_Universe

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  29. M

    I Convert Metric Tensor to Gravity in GR

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  30. Mr Davis 97

    I Hausdorff Metric: Definition 1 vs. Definition 2

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  31. Mr Davis 97

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  32. facenian

    I Metric Homeomorphism: Isometry Equivalence?

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  33. Safinaz

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  34. Mr Davis 97

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  35. K

    I Gradient vector without a metric

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  36. Ibix

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  37. F

    Complex numbers sequences/C is a metric space

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  38. C

    I Derivation of Rindler Metric and How It Resolves the Twin Paradox

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  39. E

    A Vec norm in polar coordinates differs from norm in Cartesian coordinates

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  40. M

    I Metric for knowing when numerical BC is "good"

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  41. J

    I Alcubierre Metric: Explaining Dark Matter Halo Speed

    So I have a question regarding the Alcubierre metric and the phenomena of stars on outer edges of galaxies moving at higher velocities than their orbital calculations state they should. When taking the accelerating expansion of space into account due to dark energy, could a sub-luminal...
  42. snoopies622

    I How to keep the components of a metric tensor constant?

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  43. K

    I Metric Compatibility: Is It Forbidden?

    My question is, is it forbidden to have a connection not compatible with the metric?
  44. T

    Metric space of continuous & bounded functions is complete?

    Homework Statement The book I'm using provided a proof, however I'd like to try my hand on it and I came up with a different argument. I feel that something might be wrong. Proposition: Let ##<X,d>## be a metric space, ##<Y,D>## a complete metric space. Then ##<C(X,Y), \sup D>## is a complete...
  45. T

    Is This Approach Valid for Proving the Discrete Metric in a Metric Space?

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  46. MathematicalPhysicist

    A Given a Metric, find the constants of motion

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  47. MathematicalPhysicist

    A The Metric Matrix: How Can I Invert a Non-Diagonal Matrix?

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  48. shahbaznihal

    A On metric and connection independence

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  49. redtree

    I Redshift and the Friedmann metric

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  50. Dale

    I Kruskal–Szekeres coordinates for Kerr metric

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