Richard Crago

Analytical Land–Atmosphere Radiometer Model

Abstract Conversion of radiometric land surface temperature (θr) to an equivalent isothermal (aerodynamic) surface temperature (θi) is important in balancing the land surface energy budget with satellite-based θr measurements. An analytical land–atmosphere radiometer model (ALARM) has been developed to convert θr taken at any zenith view angle to θi at a specified scalar roughness length z0h,i. Field data from 1987 and 1989 at the First International Satellite Land Surface Climatology Project (ISLSCP) Field Experiment (FIFE) were used to evaluate the performance of ALARM. It was possible to find an optimal foliage temperature profile such that ALARM is consistent with these radiometric and atmospheric field data. The errors were significantly less when radiometer zenith angles were less than 40°. The foliage temperature at the canopy top θfh and the foliage temperature profile curvature parameter b were parameterized as functions of air temperature and leaf area index, respectively. Using these parameteri...

A calibration‐free formulation of the complementary relationship of evaporation for continental‐scale hydrology

An important scaling consideration is introduced into the formulation of the complementary relationship (CR) of land surface evapotranspiration (ET) by specifying the maximum possible evaporation rate (Epmax) of a small water body (or wet patch) as a result of adiabatic drying from the prevailing near-neutral atmospheric conditions. In dimensionless form the CR therefore becomes yB = f( Epmax−EpEpmax−EwxB) = f(X) = 2X2 − X3, where yB = ET/Ep, xB = Ew/Ep. Ew is the wet-environment evaporation rate as given by the Priestley-Taylor equation, Ep is the evaporation rate of the same small wet surface for which Epmax is specified and estimated by the Penman equation. With the help of North American Regional Reanalysis data, the CR this way yields better continental-scale performance than earlier, calibrated versions of it and is on par with current land surface model results, the latter requiring vegetation, soil information and soil moisture bookkeeping. Validation has been performed by Parameter-Elevation Regressions on Independent Slopes Model precipitation and United States Geological Survey runoff data. A novel approach is also introduced to calculate the value of the Priestley-Taylor parameter to be used with continental-scale data, making the new formulation of the CR completely calibration free.

Rescaling the complementary relationship for land surface evaporation

Recent research into the complementary relationship (CR) between actual and apparent potential evaporation has resulted in numerous alternative forms for the CR. Inspired by Brutsaert [2015], who derived a general CR in the form y=function(x), where x is the ratio of potential evaporation to apparent potential evaporation and y is the ratio of actual to apparent potential evaporation, an equation is proposed to calculate the value of x at which y goes to zero, denoted xmin. The value of xmin varies even at an individual observation site, but can be calculated using only the data required for the Penman (1948) equation as expressed here, so no calibration of xmin is required. It is shown that the scatter in x-y plots using experimental data is reduced when x is replaced by X=(x-xmin)/(1-xmin). This rescaling results in data falling along the line y=X, which is proposed as a new version of the CR. While a reinterpretation of the fundamental boundary conditions proposed by Brutsaert [2015] is required, the physical constraints behind them are still met. An alternative formulation relating y to X is also discussed. This article is protected by copyright. All rights reserved.

Satellite‐derived surface temperatures with boundary layer temperatures and geostrophic winds to estimate surface energy fluxes

The surface sensible heat flux, H, and the latent heat flux, LE, were determined under unstable conditions for the First ISLSCP (International Satellite Land Surface Climatology Project) Field Experiment (FIFE) site in eastern Kansas. NOAA 9 and 11 AVHRR radiative surface temperatures, corrected for atmospheric effects using the split window technique, were used for the surface temperature in a bulk atmospheric boundary layer similarity formulation for H. Mean vertically integrated mixed layer temperatures, determined from radiosonde data, were also required in this technique. However, unlike previous applications, the present approach avoids the need for direct wind speed measurements by using instead the geostrophic wind speed, VG, as derived from the routine measurements of the surface pressure field. LE was then determined as the residual term of the surface energy balance, using H from the bulk similarity formulation. Under the unstable conditions considered, results for both H and LE were comparable to those found in previous work by means of measured wind speeds with the same FIFE data. It is shown that for slight to moderate instabilities a 1% error in the friction velocity generally produces less than 1% error in H.

Equations for the Drag Force and Aerodynamic Roughness Length of Urban Areas with Random Building Heights

We use a conceptual model to investigate how randomly varying building heights within a city affect the atmospheric drag forces and the aerodynamic roughness length of the city. The model is based on the assumptions regarding wake spreading and mutual sheltering effects proposed by Raupach (Boundary-Layer Meteorol 60:375–395, 1992). It is applied both to canopies having uniform building heights and to those having the same building density and mean height, but with variability about the mean. For each simulated urban area, a correction is determined, due to height variability, to the shear stress predicted for the uniform building height case. It is found that u*/u*R, where u* is the friction velocity and u*R is the friction velocity from the uniform building height case, is expressed well as an algebraic function of λ and σh/hm, where λ is the frontal area index, σh is the standard deviation of the building height, and hm is the mean building height. The simulations also resulted in a simple algebraic relation for z0/z0R as a function of λ and σh/hm, where z0 is the aerodynamic roughness length and z0R is z0 found from the original Raupach formulation for a uniform canopy. Model results are in keeping with those of several previous studies.

Use of land surface temperature to estimate surface energy fluxes: Contributions of Wilfried Brutsaert and collaborators

Land surface temperature (LST) plays a key role in governing the land surface energy budget, and measurements or estimates of LST are an integral part of many land surface models and methods to estimate land surface sensible heat (H) and latent heat fluxes. In particular, the LST “anchors” the potential temperature profile in Monin-Obukhov similarity theory, from which H can be derived. Brutsaert has made important contributions to our understanding the nature of surface temperature measurements as well as the practical but theoretically sound use of LST in this framework. His work has coincided with the wide-spread availability of remotely sensed LST measurements. Use of remotely sensed LST estimates inevitably involves complicating factors, such as: varying spatial and temporal scales in measurements, theory, and models; spatial variability of LST and H; the relationship between measurements of LST and the temperature “felt” by the atmosphere; and the need to correct satellite-based radiometric LST measurements for the radiative effects of the atmosphere. This paper reviews the progress made in research in these areas by tracing and commenting on Brutsaerts contributions.

Reply to comment by Ma and Zhang on “Rescaling the complementary relationship for land surface evaporation”

Ma and Zhang [2017] note a concern they have with our rescaled Complementary Relationship (CR) for land surface evaporation [Crago et al., 2016] when daily wind speeds are very low. We discuss conditions and specific formulations that lead to this concern, but ultimately argue that under these conditions, a key assumption behind the CR itself may not be satisfied at the daily time scale. Thus, careful consideration of the reliability of the CR is needed when wind speeds are very low.