Universal inverse power-law distribution for temperature and rainfall in the UK region

Meteorological parameters, such as temperature, rainfall, pressure, etc., exhibit selfsimilar space–time fractal fluctuations generic to dynamical systems in nature such as fluid flows, spread of forest fires, earthquakes, etc. The power spectra of fractal fluctuations display inverse power-law form signifying long-range correlations. A general systems theory model predicts universal inverse power-law form incorporating the golden mean for the fractal fluctuations. The model predicted distribution was compared with observed distribution of fractal fluctuations of all size scales (small, large and extreme values) in the historic month-wise temperature (maximum and minimum) and total rainfall for the four stations Oxford, Armagh, Durham and Stornoway in the UK region, for data periods ranging from 92 years to 160 years. For each parameter, the two cumulative probability distributions, namely c_max and c_min starting from respectively maximum and minimum data value were used. The results of the study show that (i) temperature distributions (maximum and minimum) follow model predicted distribution except for Stornowy, minimum temperature c_min. (ii) Rainfall distribution for c_min follow model predicted distribution for all the four stations. (iii) Rainfall distribution for c_max follows model predicted distribution for the two stations Armagh and Stornoway. The present study suggests that fractal fluctuations result from the superimposition of eddy continuum fluctuations.     

The role of wave energy accumulation in tropical cyclogenesis over the tropical North Atlantic

A hierarchical modeling approach is used to study the process by which interactions of easterly waves with the background flow can result in a reduction in the longitudinal and vertical scale of the waves. Theory suggests that in flows that possess a negative longitudinal gradient (U _x  < 0) there is a reduction of longitudinal and vertical group speeds and an increase in regional wave action density (or “wave energy”). Relative vorticity increases locally leading to an increase in the likelihood of tropical cyclogenesis near the wave axis. Opposite impacts on the structure of the waves is expected in a U _x  > 0 domain. In the simplified framework of a free-surface and divergent shallow water model, Rossby wave properties are tracked through a range of background flow scenarios to determine the important scales of interaction. The importance of wave energy accumulation for tropical cyclogenesis is then studied in a full physics and dynamics model using a nested regional climate model simulation, at 12 km horizontal grid spacing, over the tropical North Atlantic region for the entire 2005 hurricane season. The dynamical environment within which 70% of easterly waves formed tropical cyclones exhibits coherent regions in which easterly winds increase towards the east, consistent with the occurrence of wave energy accumulation.     

Impact of vegetation feedback on the temperature and its diurnal range over the Northern Hemisphere during summer in a 2 × CO2 climate

This study examines the potential impact of vegetation feedback on the changes in the diurnal temperature range (DTR) due to the doubling of atmospheric CO₂ concentrations during summer over the Northern Hemisphere using a global climate model equipped with a dynamic vegetation model. Results show that CO₂ doubling induces significant increases in the daily mean temperature and decreases in DTR regardless of the presence of the vegetation feedback effect. In the presence of vegetation feedback, increase in vegetation productivity related to warm and humid climate lead to (1) an increase in vegetation greenness in the mid-latitude and (2) a greening and the expansion of grasslands and boreal forests into the tundra region in the high latitudes. The greening via vegetation feedback induces contrasting effects on the temperature fields between the mid- and high-latitude regions. In the mid-latitudes, the greening further limits the increase in T _max more than T _min, resulting in further decreases in DTR because the greening amplifies evapotranspiration and thus cools daytime temperature. The greening in high-latitudes, however, it reinforces the warming by increasing T _max more than T _min to result in a further increase in DTR from the values obtained without vegetation feedback. This effect on T _max and DTR in the high latitude is mainly attributed to the reduction in surface albedo and the subsequent increase in the absorbed insolation. Present study indicates that vegetation feedback can alter the response of the temperature field to increases in CO₂ mainly by affecting the T _max and that its effect varies with the regional climate characteristics as a function of latitudes.     

A universal spectrum for interannual variability of monsoon rainfall over India

Continuous periodogram analyses of 115 years (1871-1985) summer monsoon rainfall over the Indian region show that the power spectra follow the universal and unique inverse power law form of the statistical normal distribution with the percentage contribution to total variance representing the eddy probability corresponding to the normalized standard deviation equal to [(log L/log T50) – 1] where L is the period length in years and T50 the period up to which the cumulative percentage contribution to total variance is equal to 50. The above results are con-sistent with a recently developed non-deterministic cell dynamical model for atmospheric flows. The implications of the above result for prediction of interannual variability of rainfall is discussed.     

On the influence of frictional parameterization in wind-driven ocean circulation models

In a series of numerical experiments the wind-driven ocean circulation is studied in an idealized, rectangular model ocean, which is forced by steady zonal winds and damped by lateral and/or bottom friction. The problem as described by the barotropic vorticity equation is characterized by a Rossby number (R) and horizontal and/or vertical Ekman numbers (E_L, E_B) only.With free-slip conditions at the boundaries steady solutions for all chosen values of R are obtained, provided the diffusivity is sufficiently large. For both the forms of frictional parameterization a northern boundary current emerges with an eastward penetration scale depending on R. The recirculation pattern in the oceanically relevant ‘intermediate’ range of R is strongly affected by the type of friction. If lateral diffusion dominates bottom friction, a strong recirculating sub-gyre emerges in the northwestern corner of the basin. Its shape resembles the vertically integrated transport fields in recent eddy resolving model (EGCM) studies. The maximum transport is increased to values several times larger than the Sverdrup transport. The increase in transport is coupled with a development of closed contours of potential vorticity, enabling a nearly free inertial flow.This behaviour provides a sharp contrast to the bottom friction case (Veronis) where inertial recirculation only takes place with values of R so large that the eastward jet reaches the eastern boundary. It is shown that the linear friction law puts a strong constraint on the flow by preventing an intense recirculation in a small part of the basin.A reduction of the diffusivity (E_L) in the lateral friction case leads to quasi-steady solutions. The interaction with eddies becomes an integral part of the time mean energetics but does not influence the recirculation character of the flow.The main conclusion of the study is that the horizontal structure of the EGCM-transport fields can be explained in terms of a steady barotropic model where lateral friction represents the dominant dissipation mechanism.     

Dependence of NAO variability on coupling with sea ice

The variance of the North Atlantic Oscillation index (denoted N) is shown to depend on its coupling with area-averaged sea ice concentration anomalies in and around the Barents Sea (index denoted B). The observed form of this coupling is a negative feedback whereby positive N tends to produce negative B, which in turn forces negative N. The effects of this feedback in the system are examined by modifying the feedback in two modeling frameworks: a statistical vector autoregressive model (F _VAR) and an atmospheric global climate model (F _CAM) customized so that sea ice anomalies on the lower boundary are stochastic with adjustable sensitivity to the model??s evolving N. Experiments show that the variance of N decreases nearly linearly with the sensitivity of B to N, where the sensitivity is a measure of the negative feedback strength. Given that the sea ice concentration field has anomalies, the variance of N goes down as these anomalies become more sensitive to N. If the sea ice concentration anomalies are entirely absent, the variance of N is even smaller than the experiment with the most sensitive anomalies. Quantifying how the variance of N depends on the presence and sensitivity of sea ice anomalies to N has implications for the simulation of N in global climate models. In the physical system, projected changes in sea ice thickness or extent could alter the sensitivity of B to N, impacting the within-season variability and hence predictability of N.     

Spatial patterns and trends of daily rainfall regime in Peninsular Malaysia during the southwest and northeast monsoons: 1975–2004

Model precipitation can be produced implicitly through convective parameterization schemes or explicitly through cloud microphysics schemes. These two precipitation production schemes control the spatial and temporal distribution of precipitation and consequently can yield distinct vertical profiles of heating and moistening in the atmosphere. The partition between implicit and explicit precipitation can be different as the model changes resolutions. Within the range of mesoscale resolutions (about 20 km) and cumulus scale, hybrid solutions are suggested, in which cumulus convection parameterization is acting together with the explicit form of representation. In this work, it is proposed that, as resolution increases, the convective scheme should convert less condensed water into precipitation. Part of the condensed water is made available to the cloud microphysics scheme and another part evaporates. At grid sizes smaller than 3 km, the convective scheme is still active in removing convective instability, but precipitation is produced by cloud microphysics. The Eta model version using KF cumulus parameterization was applied in this study. To evaluate the quantitative precipitation forecast, the Eta model with the KF scheme was used to simulate precipitation associated with the South Atlantic Convergence Zone (SACZ) and Cold Front (CF) events. Integrations with increasing horizontal resolutions were carried out for up to 5 days for the SACZ cases and up to 2 days for the CF cases. The precipitation partition showed that most of precipitation was generated by the implicit scheme. As the grid size decreased, the implicit precipitation increased and the explicit decreased. However, as model horizontal resolution increases, it is expected that precipitation be represented more explicitly. In the KF scheme, the fraction of liquid water or ice, generated by the scheme, which is converted into rain or snow is controlled by a parameter S ₁. An additional parameter was introduced into KF scheme and the parameter acts to evaporate a fraction of liquid water or ice left in the model grid by S ₁ and return moisture to the resolved scale. An F parameter was introduced to combine the effects of S ₁ and S ₂ parameters. The F parameter gives a measure of the conversion of cloud liquid water or ice to convective precipitation. A function dependent on the horizontal resolution was introduced into the KF scheme to influence the implicit and explicit precipitation partition. The explicit precipitation increased with model resolution. This function reduced the positive precipitation bias at all thresholds and for the studied weather systems. With increased horizontal resolution, the maximum precipitation area was better positioned and the total precipitation became closer to observations. Skill scores for all events at different forecast ranges showed precipitation forecast improvement with the inclusion of the function F.     

The Influence of Hilly Terrain on Aerosol-Sized Particle Deposition into Forested Canopies

Virtually all reviews dealing with aerosol-sized particle deposition onto forested ecosystems stress the significance of topographic variations, yet only a handful of studies considered the effects of these variations on the deposition velocity (V _d ). Here, the interplay between the foliage collection mechanisms within a dense canopy for different particle sizes and the flow dynamics for a neutrally stratified boundary layer on a gentle and repeating cosine hill are considered. In particular, how topography alters the spatial structure of V _d and its two constitutive components, particle fluxes and particle mean concentration within and immediately above the canopy, is examined in reference to a uniform flat-terrain case. A two-dimensional and particle-size resolving model based on first-order closure principles that explicitly accounts for (i) the flow dynamics, including the two advective terms, (ii) the spatial variation in turbulent viscosity, and (iii) the three foliage collection mechanisms that include Brownian diffusion, turbo-phoresis, and inertial impaction is developed and used. The model calculations suggest that, individually, the advective terms can be large just above the canopy and comparable to the canopy collection mechanisms in magnitude but tend to be opposite to each other in sign. Moreover, these two advective terms are not precisely out of phase with each other, and hence, do not readily cancel each other upon averaging across the hill wavelength. For the larger aerosol-sized particles, differences between flat-terrain and hill-averaged V _d can be significant, especially in the layers just above the canopy. We also found that the hill-induced variations in turbulent shear stress, which are out-of-phase with the topography in the canopy sublayer, play a significant role in explaining variations in V _d across the hill near the canopy top. Just after the hill summit, the model results suggest that V _d fell to 30% of its flat terrain value for particle sizes in the range of 1–10 μm. This reduction appears consistent with maximum reductions reported in wind-tunnel experiments for similar sized particle deposition on ridges with no canopies.     

On the Arctic Ocean ice thickness response to changes in the external forcing

Submarine and satellite observations show that the Arctic Ocean ice cover has undergone a large thickness reduction and a decrease in the areal extent during the last decades. Here the response of the Arctic Ocean ice cover to changes in the poleward atmospheric energy transport, F _wall, is investigated using coupled atmosphere-ice-ocean column models. Two models with highly different complexity are used in order to illustrate the importance of different internal processes and the results highlight the dramatic effects of the negative ice thickness—ice volume export feedback and the positive surface albedo feedback. The steady state ice thickness as a function of F _wall is determined for various model setups and defines what we call ice thickness response curves. When a variable surface albedo and snow precipitation is included, a complex response curve appears with two distinct regimes: a perennial ice cover regime with a fairly linear response and a less responsive seasonal ice cover regime. The two regimes are separated by a steep transition associated with surface albedo feedback. The associated hysteresis is however small, indicating that the Arctic climate system does not have an irreversible tipping point behaviour related to the surface albedo feedback. The results are discussed in the context of the recent reduction of the Arctic sea ice cover. A new mechanism related to regional and temporal variations of the ice divergence within the Arctic Ocean is presented as an explanation for the observed regional variation of the ice thickness reduction. Our results further suggest that the recent reduction in areal ice extent and loss of multiyear ice is related to the albedo dependent transition between seasonal and perennial ice i.e. large areas of the Arctic Ocean that has previously been dominated by multiyear ice might have been pushed below a critical mean ice thickness, corresponding to the above mentioned transition, and into a state dominated by seasonal ice.     

An Analytical Model for the Distribution of CO2 Sources and Sinks, Fluxes, and Mean Concentration Within the Roughness Sub-Layer

A one-dimensional analytical model that predicts foliage CO₂ uptake rates, turbulent fluxes, and mean concentration throughout the roughness sub-layer (RSL), a layer that extends from the ground surface up to 5h, where h is canopy height, is proposed. The model combines the mean continuity equation for CO₂ with first-order closure principles for turbulent fluxes and simplified physiological and radiative transfer schemes for foliage uptake. This combination results in a second-order ordinary differential equation in which soil respiration (R) and CO₂ concentration well above the RSL are imposed as lower and upper boundary conditions, respectively. An inverse version of the model was tested against datasets from two contrasting ecosystems: a tropical forest (h = 40m) and a managed irrigated rice canopy (h = 0.7m), with good agreement noted between modelled and measured mean CO₂ concentration profiles within the entire RSL. Sensitivity analysis on the model parameters revealed a plausible scaling regime between them and a dimensionless parameter defined by the ratio between external (R) and internal (stomatal conductance) characteristics controlling the CO₂ exchange process. The model can be used to infer the thickness of the RSL for CO₂ exchange, the inequality in zero-plane displacement between CO₂ and momentum, and its consequences on modelled CO₂ fluxes. A simplified version of the solution is well suited for being incorporated into large-scale climate models. Furthermore, the model framework here can be used to a priori estimate relative contributions from the soil surface and the atmosphere to canopy-air CO₂ concentration, thereby making it synergetic to stable isotopes studies.     

Markov chain simulations of vertical dispersion from elevated sources into the neutral planetary boundary layer

A Lagrangian statistical-trajectory model based on a Markov chain relation is used to investigate vertical dispersion from elevated sources into the neutral planetary boundary layer. The model is fully two-dimensional, in that both vertical and longitudinal velocity fluctuations, and their correlation, are simulated explicitly. The best observational information currently available is used to characterize the mean and turbulent structure of the neutral boundary layer. In particular, a realistic vertical profile of the Lagrangian integral time scale is proposed, based partly on a review of direct measurements and partly on a comparison of the model predictions with published diffusion data. The model predictions are shown to agree well with a variety of dispersion observations. The model is used to study vertical diffusion as a function of release height H, friction velocity u* and surface roughness z ₀ for downwind distances up to 10 km from the source. The equivalent Gaussian dispersion parameter Σ _z is shown to decrease slightly with an increase in H, and to increase with increases in z ₀ or u*. It is demonstrated that relationships valid in a field of homogeneous turbulence can be applied to vertical dispersion in the atmosphere if the release occurs above the region of strongest gradients in the mean and turbulent parameters. Scaling in terms of the standard deviation in elevation angle of the wind at the release point leads to a universal curve which provides accurate estimates of Σ _z over a wide range of values of H, z ₀ and the meteorological parameters.     

The Parameterisation of Scalar Transfer over Rough Ice

We test a surface renewal model that is widely used over snow and ice surfaces to calculate the scalar roughness length (z _s ), one of the key parameters in the bulk aerodynamic method. For the first time, the model is tested against observations that cover a wide range of aerodynamic roughness lengths (z ₀). During the experiments, performed in the ablation areas of the Greenland ice sheet and the Vatnajökull ice cap in Iceland, the surface varied from smooth snow to very rough hummocky ice. Over relatively smooth snow and ice with z ₀ below a threshold value of approximately 10^?3 m, the model performs well and in accord with earlier studies. However, with growing hummock size, z ₀ increases well above the threshold and the bulk aerodynamic flux becomes significantly smaller than the eddy-correlation flux (e.g. for z ₀ = 0.01 m, the bulk aerodynamic flux is about 50% smaller). Apparently, the model severely underpredicts z _s over hummocky ice. We argue that the surface renewal model does not account for the deep inhomogeneous roughness sublayer (RSL) that is generated by the hummocks. As a consequence, the homogeneous substrate ice grain cover becomes more efficiently ‘ventilated’. Calculations with an alternative model that includes the RSL and was adapted for use over hummocky ice, qualitatively confirms our observations. We suggest that, whenever exceedance of the threshold occurs (z ₀  >  10^?3 m, i.e., an ice surface covered with at least 0.3-m high hummocks), the following relation should be used to calculate scalar roughness lengths, ln (z _s /z ₀)  =  1.5  ? 0.2 ln (Re _*)  ? 0.11(ln (Re _*))².     

Modeling the photosynthetically active radiation in South West Amazonia under all sky conditions

Accurate estimates of photosynthetically active radiation (PAR) are critical for the development of realistic models of plant productivity. However, in many areas such as the vast Amazon region of South America, there have been few empirical studies of PAR. Here, we analyzed the relationship between PAR and broadband solar irradiance (R _s) and formulated models to estimate PAR in two experimental sites (pasture and forest) in the Brazilian Amazon. Three different models of increasing complexity were developed based on information from R _s (model 1), R _s and clearness index (k _t; model 2), and R _s, k _t, and water vapor pressure (model 3). Estimates of PAR were generated for each season and for the entire year. All models had very high determination coefficients and indices of agreement for both pasture and forest sites. This strongly supports the use of R _s and k _t to produce robust estimates of PAR. The results obtained by annual models were close than that found by seasonal models, demonstrating that a single annual model is able to estimate PAR, albeit with lower accuracy.     

On the solution of the stationary,baroclinic Ekman-layer equations with a finite boundary-layer height

The stationary, Ekman-layer equations have been solved in closed form for two expressions of the eddy viscosity as a function of height, z: v _τ=cu*z(1?z/h)and v _τ=cu*z(1?z/h) ², where u* is the friction velocity, h the boundary-layer height and c a constant. The main difference between both solutions is that the quadratic K-profile leads to a velocity discontinuity at the top of the boundary layer, while the solution for the cubic profile approaches the geostrophic wind at z=h smoothly. We discuss the characteristics of the solutions in terms of a dimensionless parameter C=fh/cu*, where f is the Coriolis parameter. The dependence on C can be interpreted in terms of a varying boundary-layer height or in terms of stability. The results for C ~ 1 are related to a neutral boundary layer. They agree well with results of a second-order model. The limit C → 0 is investigated in detail. We find that the stress profile becomes linear. The velocity profile shows different characteristics depending on whether we consider a shallow or a very unstable boundary layer. The results agree with observations. Finally we consider the influence of baroclinicity on the wind and stress profiles.     

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?C395, 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 ?? and ?? _h /h _m , where ?? is the frontal area index, ?? _h is the standard deviation of the building height, and h _m is the mean building height. The simulations also resulted in a simple algebraic relation for z ₀/z _0R as a function of ?? and ?? _h /h _m , where z ₀ is the aerodynamic roughness length and z _0R is z ₀ found from the original Raupach formulation for a uniform canopy. Model results are in keeping with those of several previous studies.     

Comparison of artificial neural network and multivariate linear regression methods for estimation of daily soil temperature in an arid region

Soil temperature (T _S) strongly influences a wide range of biotic and abiotic processes. As an alternative to direct measurement, indirect determination of T _S from meteorological parameters has been the focus of attention of environmental researchers. The main purpose of this study was to estimate daily T _S at six depths (5, 10, 20, 30, 50 and 100?cm) by using a multilayer perceptron (MLP) artificial neural network (ANN) model and a multivariate linear regression (MLR) method in an arid region of Iran. Mean daily meteorological parameters including air temperature (T _a), solar radiation (R _S), relative humidity (RH) and precipitation (P) were used as input data to the ANN and MLR models. The model results of the MLR model were compared to those of ANN. The accuracy of the predictions was evaluated by the correlation coefficient (r), the root mean-square error (RMSE) and the mean absolute error (MAE) between the measured and predicted T _S values. The results showed that the ANN method forecasts were superior to the corresponding values obtained by the MLR model. The regression analysis indicated that T _a, RH, R _S and P were reasonably correlated with T _S at various depths, but the most effective parameters influencing T _S at different depths were T _a and RH.     

Evaluation of turbulent Prandtl (Schmidt) number parameterizations for stably stratified environmental flows

In this study, we evaluate four different parameterizations of the turbulent Prandtl (Schmidt) number Pr_t = ν_t/Γ_t where ν_t is the eddy viscosity and Γ_t is the scalar eddy diffusivity, for stably stratified flows. All four formulations of Pr_t are strictly functions of the gradient Richardson number Ri, which provides a measure of the strength of the stratification. A zero-equation (i.e. no extra transport equations are required) turbulence model for ν_t in a one-dimensional, turbulent channel flow is considered to evaluate the behavior of the different formulations of Pr_t. Both uni-directional and oscillatory flows are considered to simulate conditions representative of practical flow problems such as atmospheric boundary layer flows and tidally driven estuarine flows, to quantify the behavior of each of the four formulations of Pr_t. We perform model-to-model comparisons to highlight which of the models of Pr_t allow for a higher rate of turbulent mixing and which models significantly inhibit turbulent mixing in the presence of buoyancy forces resulting from linear (continuous) stratification as well as two-layer stratification. The basis underlying the formulation of each model in conjunction with the simulation results are used to emphasize the considerable variability in the different formulations and the importance of choosing an appropriate parameterization of Pr_t given a model for ν_t in stably stratified flows.     

Transient hysteresis of near-surface permafrost response to external forcing

Estimates of changes in near-surface permafrost (NSP) area S _p relative to change in globally averaged surface air temperature T _g are made by using the global climate model developed at the A.M. Obukhov Institute of Atmospheric Physics RAS (IAP RAS CM). For ensemble of runs forced by scenarios constructed as return-to-preindustrial continuations of the RCP (Representative Concentration Pathways) scenarios family, a possibility of transient hysteresis in dependence of S _p versus T _g is exhibited: in some temperature range which depends on imposed scenario of external forcing, NSP area is larger, at the same global mean surface air temperature, in a warming climate than in a cooling climate. This hysteresis is visible more clearly for scenarios with higher concentration of greenhouse gases in the atmosphere in comparison to those in which this concentration is lower. Hysteresis details are not sensitive to the type of the prescribed continuation path which is used to return the climate to the preindustrial state. The multiple-valued dependence of S _p on T _g arises due to dependence of soil state in the regions of extra-tropical wetlands and near the contemporary NSP boundaries on sign of external climatic forcing. To study the dependence of permafrost hysteresis on amplitude and temporal scale of external forcing, additional model runs are performed. These runs are forced by idealised scenarios of atmospheric CO₂ content varying, depending on run, with periods from 100 to 1,000 year and with different amplitudes. It is shown that the above-mentioned hysteresis is related to the impact of phase transitions of soil water on apparent inertia of the system as well as to the impact of soil state on atmospheric hydrological cycle and radiation transfer in the atmosphere.     

Comparison of mean radiant temperature from field experiment and modelling: a case study in Freiburg,Germany

Mean radiant temperature (T _mrt) based on two measurement methods and outputs from three models are compared in this study. They are the six direction radiation method, globe thermometer method, RayMan model, ENVI-met model and SOLWEIG model. The comparison shows that globe thermometer method may overestimate the T _mrt since wind velocity is a key variable in the estimation based on this method. For better estimation, T _mrt measured by the globe-thermometer method be corrected by the imported wind speed (stable, low and assuming wind speed) and validated by the six-direction radiation method. The comparison of models shows that the RayMan model’s evaluation of T _mrt involving global radiation with fine time resolution was better than the corresponding evaluations under the other two models (ENVI-met and SOLWEIG) in this case. However, the RayMan model can only assess T _mrt for a one-point one-time context, whereas the other two models can evaluate two-dimensional T _mrt. For two-dimensional evaluations of T _mrt, SOLWEIG have a better prediction of T _mrt than ENVI-met, and ENVI-met can simulate several different variables, which are wind field, particle distribution, CO₂ distribution and the other thermal parameters (T _a, surface temperature and radiation fluxes), that SOLWEIG cannot.     

A new nonlinear analytical model for canopy flow over a forested hill

A new nonlinear analytical model for canopy flow over gentle hills is presented. This model is established based on the assumption that three major forces (pressure gradient, Reynolds stress gradient, and nonlinear canopy drag) within canopy are in balance for gentle hills under neutral conditions. The momentum governing equation is closed by the velocity-squared law. This new model has many advantages over the model developed by Finnigan and Belcher (Quart J Roy Meteorol Soc 130: 1–29 2004, hereafter referred to as FB04) in predicting canopy wind velocity profiles in forested hills in that: (1) predictions from the new model are more realistic because surface drag effects can be taken into account by boundary conditions, while surface drag effects cannot be accounted for in the algebraic equation used in the lower canopy layer in the FB04 model; (2) the mixing length theory is not necessarily used because it leads to a theoretical inconsistency that a constant mixing length assumption leads to a nonconstant mixing length prediction as in the FB04 model; and (3) the effects of height-dependent leaf area density (a(z)) and drag coefficient (C _d ) on wind velocity can be predicted, while both a(z) and C _d must be treated as constants in FB04 model. The nonlinear algebraic equation for momentum transfer in the lower part of canopy used in FB04 model is height independent, actually serving as a bottom boundary condition for the linear differential momentum equation in the upper canopy layer. The predicting ability of the FB04 model is largely restricted by using the height-independent algebraic equation in the bottom canopy layer. This study has demonstrated the success of using the velocity-squared law as a closure scheme for momentum transfer in forested hills in comparison with the mixing length theory used in FB04 model thus enhancing the predicting ability of canopy flows, keeping the theory consistent and simple, and shining a new light into land-surface parameterization schemes in numerical weather and climate models.