## Evaluating The Spatial Distribution Of Evaporation

WILLIAM P. KUSTAS, M. SUSAN MORAN, AND JOHN M. NORMAN

### 1 INTRODUCTION

Evaporation of water from soil and plant surfaces forms the connecting link between the energy balance and the water balance at Earth's surface. This phenomenon influences the large-scale circulation of the planetary atmosphere, affects soil moisture content that in turn affects hydrologie response, and regulates the microscale carbon dioxide uptake of stomata in individual plant leaves. The vast range of scales encompassed by the process of evaporation makes it of vital environmental interest.

Over the past century, theoretical, modeling, and experimental efforts have greatly expanded our ability to evaluate water loss due to evaporation at local scales using conventional instrumentation. In recent decades, a concerted effort has been made to develop techniques for evaluating the spatial distribution of evaporation at regional and global scales. This effort has been largely focused on the use of remotely sensed information available from sensors aboard orbiting satellite platforms. The result has been a variety of methods that vary in complexity from statistical approaches to physically based analytical approaches and ultimately to numerical process models that simulate the flow of heat and water through the soil, vegetation, and atmosphere.

This chapter will present a brief discussion of the physics of evaporation, highlight conventional methods for estimating evaporation rates, and then will focus on the use of remote sensing for evaluation of the spatial distribution of evaporation at the local, regional, and global scales. Emphasis will be placed on methods for estimating evaporation at an hourly to daily time frame, which is most appropriate for atmospheric, hydrological, and agricultural applications. This work will conclude

Handbook of Weather, Climate, and Water: Atmospheric Chemistry, Hydrology, and Societal Impacts, Edited by Thomas D. Potter and Bradley R. Colman. ISBN 0-471-21489-2 © 2003 John Wiley & Sons, Inc.

with a synthesis of the most important research and development issues related to the implementation of such approaches on an operational basis. Although much of the material in Sections 4 and 5 is from the work of Kustas and Norman ( 1996), new information and results from more recent studies are included.

### 2 SHORT HISTORY

Although the evaporation process has intrigued humankind for centuries, progress in understanding the physics of evaporation remained slow until the twentieth century when Bowen (1926) showed how the partitioning of available energy between the fluxes of sensible and latent heat could be determined from gradients of temperature and humidity:

where XE* is the latent heat flux (W/m2), R„ is the net radiation flux at the surface (W/m2), G is the sensible heat flux conducted to the soil (W/m2), and ß is the Bowen ratio (Table 1). The ratio of sensible heat (H) to latent heat flux density is

In Eq. (1), fluxes away from the surface are negative and those toward the surface are positive. The Bowen ratio can be derived from temperature and humidity measurements:

where y is referred to as the psychrometric constant (2.453 MJ/kg at 20° C), Kh and Kv are the eddy transfer coefficients for sensible and latent heat, respectively, and AT and Ae are the differences in temperature in degrees centigrade and vapor pressure in kilopascals over the same elevation difference, Az.

Following the work of Bowen (1926), Penman (1948) combined the thermal energy balance with certain aerodynamic aspects of evaporation and developed an

* Evaporation (E) is often represented in units of mm/day or mm/h but can also be expressed in energy units, where E is the evaporation rate (kg/sm2), A is the heat of evaporation (J/kg), and IE is the latent heat flux density (W/m2). Though expressed in different units, the terms E and XE are interchangeable. To avoid confusion herein, the term E* will represent evaporation rate in units of depth (mm/h or mm/d), E will represent mass flux density (kg/sm2 or kg/dm2), and XE will represent latent heat flux density (in units of W/m2 or MJ~2d~'). For further clarification on evaluation of Eqs. (1) to (9), readers are encouraged to review Table 1, and consult the treatise by Monteith (1981) and the books by Brutsaert (1982) and Jensen et al. (1989).

TABLE 1 Summary of Scientific and Technical Notation

IE XEc XEp N P

PNIR' PRed

Surface shortwave albedo

Priestley-Taylor coefficient, a — 1.26 for regions with no or low advective conditions Bowen ratio, where /? = H/aE Specific heat at constant pressure (kJ/kg'C) Displacement height (m)

Psychrometric constant (in units of MJ/kg or kPa/°C) ?(1 +rc/ra) (kPa/°C)

Difference in temperature (°C) over the elevation Az Difference in vapor pressure (kPa) over the elevation Az Elevation difference (m)

Slope of the saturation vapor pressure-temperature curve (kPa/°C) Saturation vapor pressure at the z level above the surface (kPa) Actual vapor pressure at the z level above the surface (kPa) Vapor pressure deficit (kPa)

Instantaneous deviation of the partial water vapor pressure from the mean at height z

Mass flux density (kg/s m2 or kg/d m2) Evaporation rate in units of depth (mm/h or mm/d) Evaporative fraction, where EF= —AE/(R„ + G) Surface emissivity

Fraction of green or actively transpiring vegetation Fraction of green vegetation viewed by the radiometer Soil heat flux density (W/m2) Sensible heat flux density to the air (W/m2) Turbulent fluxes (W/m2)

Sensible heat flux density from the canopy (W/m2) Sensible heat flux density from the soil (W/m2) von Karman's constant (~0.4)

Eddy transfer coefficients for sensible and latent heat, respectively

Latent heat flux density (W/m2 or MJ"2 d ')

Latent heat flux density from the canopy (W/m2)

Potential latent heat flux density (W/m2)

Day length (h)

Air density (kg/m3)

Surface reflectance factor for the spectral range AX

Surface reflectance factors in the near-infrared (NIR) and red spectrum, respectively Atmospheric pressure (kPa) Aerodynamic resistance (s/m) Canopy resistance to vapor transport (s/m)

Resistance to heat flow in the boundary layer immediately above the soil surface (s/m)

Net radiant flux density at the surface (W/m) Available energy (W/m2)

Absorbed net radiant flux density by the plant canopy (W/m2)

TABLE 1 |
(continued) |

Rs |
Incoming shortwave solar radiant flux density (W/m2) |

Ru |
Incoming longwave radiant flux density (W/m2) |

R\u |
Upwelling longwave radiant flux density, represented by esaT*h |

a |
Stefan-Boltzman constant (5.67 x 10"8 W/m2 K4) |

t |
Time starting at sunrise (h) |

Ta |
Air temperature (°C) |

aero |
Surface aerodynamic temperature (°C) |

A c |
Canopy temperature (°C) |

Trad |
Radiometric temperature measured by an infrared radiometer from a space-borne |

platform | |

Ts |
Soil surface temperature (°C) |

Hemispherical radiometric temperature (C or K) | |

u |
Horizontal wind speed (m/s) |

us |
Horizontal wind speed (m/s) about 5 cm above the soil surface |

w |
Mean vertical wind at height z (m/s) |

w' |
Instantaneous deviation of vertical wind speed from w (m/s) |

wf |
Wind function [generally, a + b(u), where u is the wind speed in m/s] |

Stability corrections for heat and momentum, respectively | |

z |
Height above the surface at which u is measured (m) |

^iini ■ -^oh |
Roughness lengths for momentum and heat (m), respectively |

subscript i |
Instantaneous values |

subscript d |
Daily values |

subscript m |
Midday values |

equation for estimating evaporation that was soon adopted by hydrologists and irrigation specialists. The general form of the Penman combination equation is

XE = -[(A/(A + y))(R„ + G) + (y/(A + y))6AlWf{e° - ez)] (4)

where A is the slope of the saturation vapor pressure-temperature curve (kPa/°C), y is the psychrometic constant (kPa/°C), it', is a wind function [generally, ct 4-where u is the wind speed in m/s)], e°z and ez are the saturation and actual vapor pressures at the z level above the surface (kPa), and — ez) is vapor pressure deficit (kPa).

The Penman formula was recast in terms of an aerodynamic resistance and a surface resistance for application to single leaves (Penman, 1953) and vegetation canopies (Rijtema, 1965; Monteith, 1965). This result, now referred to as the Penman-Monteith equation, is probably the most universally used equation for calculating evaporation:

XE = -[A(*„ + G) + PCp(e° - ez)/ra]/[A + y*] (5)

where p is air density (kg/m3), Cp is specific heat at constant pressure (kJ/kg°C). and the aerodynamic resistance, ra (s/m) is ra = {Pn((* - d0)/z0m) + Hz0m/z0h) - <5A][ln((z - d0)/z0m) - OJ\¡k2u (6)

and z is the height above the surface at which u is measured (m), d0 is the displacement height (m), z0m and z0h are the roughness lengths for momentum and heat (m), respectively, <!>/, and <l>m are the stability corrections for heat and momentum, respectively, and k is von Karman's constant (^0.4). The integral stability functions were summarized by Beljaars and Holtslag (1991) for the stable and unstable conditions. The value of y* (kPa/°C) in Eq. (5) is a function of ra and the canopy resistance to vapor transport [rc (s/m)], where

Priestley and Taylor (1972) proposed a simplified version of the Penman combination equation for computation of potential evaporation heat flux density (/.Ep) for a surface that has minimal resistance to evaporation. Under these conditions, the aerodynamic component was ignored and the energy component was multiplied by a coefficient, where a = 1.26 for regions with no or low advective conditions.

Regional-scale estimates of evaporation have been made using properties of the atmospheric boundary layer (ABL). One approach applies similarity theory to humidity, temperature, and wind in the ABL (Brutsaert and Mawdsley, 1976). Another approach involves the development of simplified conservation equations for the ABL (McNaughton and Spriggs, 1986). This links the surface fluxes to temporal changes in temperature and humidity in the mixed layer. There are problems in employing either approach. The former has difficulties related to the specification of appropriate roughness parameters, especially in heterogeneous terrain, while the latter must develop parameterizations for advection and entrain-ment processes that commonly exist in the ABL.

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