Statistical downscaling of historical monthly mean winds over a coastal region of complex terrain. I. Predicting wind speed

Surface wind speed is a key climatic variable of interest in many applications, including assessments of storm-related infrastructure damage and feasibility studies of wind power generation. In this work and a companion paper (van der Kamp et al. 2011), the relationship between local surface wind and large-scale climate variables was studied using multiple regression analysis. The analysis was performed using monthly mean station data from British Columbia, Canada and large-scale climate variables (predictors) from the NCEP-2 reanalysis over the period 1979–2006. Two regression-based methodologies were compared. The first relates the annual cycle of station wind speed to that of the large-scale predictors at the closest grid box to the station. It is shown that the relatively high correlation coefficients obtained with this method are attributable to the dominant influence of region-wide seasonality, and thus contain minimal information about local wind behaviour at the stations. The second method uses interannually varying data for individual months, aggregated into seasons, and is demonstrated to contain intrinsically local information about the surface winds. The dependence of local wind speed upon large-scale predictors over a much larger region surrounding the station was also explored, resulting in 2D maps of spatial correlations. The cross-validated explained variance using the interannual method was highest in autumn and winter, ranging from 30 to 70% at about a dozen stations in the region. Reasons for the limited predictive skill of the regressions and directions for future progress are reviewed.     

Impact of Megacity Shanghai on the Urban Heat-Island Effects over the Downstream City Kunshan

The impact of upstream urbanization on the enhanced urban heat-island (UHI) effects between Shanghai and Kunshan is investigated by analyzing seven years of surface observations and results from mesoscale model simulations. The observational analysis indicates that, under easterly and westerly winds, the temperature difference between Shanghai and Kunshan increases with wind speed when the wind speed \(<\) 5 m s \(^{-1}\) . The Weather Research and Forecasting (WRF) numerical model, coupled with a one-layer urban canopy model (UCM), is used to examine the UHI structure and upstream effects by replacing the urban surface of Shanghai and/or Kunshan with cropland. The WRF/UCM modelling system is capable of reproducing the surface temperature and wind field reasonably well. The simulated urban canopy wind speed is a better representation of the near-surface wind speed than is the 10-m wind speed at the centre of Shanghai. Without the urban landscape of Shanghai, the surface air temperature over downstream Kunshan would decrease by 0.2–0.4  \(^{\circ }\) C in the afternoon and 0.4–0.6  \(^{\circ }\) C in the evening. In the simulation with the urban landscape of Shanghai, a shallow cold layer is found above the UHI, with a minimum temperature of about \(-0.2\) to \(-\) 0.5  \(^{\circ }\) C during the afternoon hours. Strong horizontal divergence is found in this cold layer. The easterly breeze over Shanghai is strengthened at the surface by strong UHI effects, but weakened at upper levels. With the appearance of the urban landscape specific humidity decreases by 0.5–1 g kg \(^{-1}\) within the urban area because of the waterproof property of an urban surface. On the other hand, the upper-level specific humidity is increased because of water vapour transferred by the strong upward vertical motions.     

Numerical Simulations of Laminar Air–Water Flow of a Non-linear Progressive Wave at Low Wind Speed

A numerical simulation for two-dimensional laminar air–water flow of a non-linear progressive water wave with large steepness is performed when the background wind speed varies from zero to the wave phase speed. It is revealed that in the water the difference between the analytical solution of potential flow and numerical solution of viscous flow is very small, indicating that both solutions of the potential flow and viscous flow describe the water wave very accurately. In the air the solutions of potential and viscous flows are very different due to the effects of viscosity. The velocity distribution in the airflow is strongly influenced by the background wind speed and it is found that three wind speeds, $U=0$ , $U=u_m$ (the maximum orbital velocity of a water wave), and $U=c$ (the wave phase speed), are important in distinguishing different features of the flow patterns.     

Characteristics and Mechanisms of Low-Level Jets in the Yangtze River Delta of China

A dataset obtained using a wind-profile radar located at the Yangtze River Delta in China ( $31.14^{\circ }$ N, $121.81^{\circ }$ E) in 2009 was used to investigate the characteristics and evolution of low-level jets (LLJs) along the east China coast. The study investigated the daily and seasonal structures of LLJs as well as several possible causes. A total of 1,407 1-h LLJ periods were detected based on an adaptive definition that enabled determination of four LLJ categories. The majority (77 %) of LLJs were found to have speeds $<$ 14.0 m s $^{-1}$ (maximum of 34.6 m s $^{-1})$ and occur at an average altitude below 600 m (76 % of the observed LLJs). The dominant direction of the LLJs was from the south-south-west, which accounted for nearly 32 %, with the second most common wind direction ranging from $040^{\circ }$ to $100^{\circ }$ , albeit with a number of stronger LLJs from the west-south-west. A comparison of LLJs and South-west Jets revealed that the frequencies of occurrence in summer are totally different. Results also revealed that in spring and summer, most LLJs originate from the south-south-west, whereas in autumn and winter, north-east is the dominant direction of origin. The peak heights of LLJs tended to be higher in winter than in other seasons. The horizontal wind speed and peak height of the LLJs displayed pronounced diurnal cycles. The Hilbert–Huang transform technique was applied to demonstrate that the intrinsic mode functions with a cycle of nearly 23 h at levels below 800 m, and the instantaneous amplitudes of inertial events (0.0417–0.0476 h $^{-1}$ frequencies) have large values at 300–600 m. The variations in the occurrences of LLJs suggested connections between the formation mechanisms of LLJs and the South-west Jet stream, steady occupation of synoptic-scale pressure system, and land–sea temperature contrasts.     

Temporal Evolution of Low-Level Winds Induced by Two-dimensional Mesoscale Surface Heat-Flux Heterogeneity

Using large-eddy simulation (LES), the effects of mesoscale local surface heterogeneity on the temporal evolution of low-level flows in the convective boundary layer driven by two-dimensional surface heat-flux variations are investigated at a height of about 100 m over flat terrain. The surface variations are prescribed with sinusoids of wavelength 32 km and varying amplitudes of 0, 50, 100, and 200 W m $^{-2}$ . The Weather Research and Forecasting numerical model is used as a mesoscale-domain LES model that has a grid spacing fine enough to explicitly resolve energy-containing turbulent eddies and a model domain large enough to include mesoscale circulations. Mesoscale circulations induced by the two-dimensional surface heterogeneity may undergo a flow transition and an associated spectral energy cascade, which has been found previously but only with one-dimensional surface heat-flux variations. Over a strongly heterogeneous surface prescribed with a two-dimensional sinusoid of amplitude 200 W m $^{-2}$ , the domain-averaged variance of the horizontal wind component initially grows rapidly, then undergoes a flow transition and subsequently rapidly decays. With a background wind, the induced mesoscale circulations are inhibited in the streamwise direction. However in the spanwise direction, somewhat stronger mesoscale circulations are induced, compared with those with no background wind. The background wind attenuates the significant reduction of the low-level temperature gradient by the fully-developed mesoscale horizontal flow. Spectral decomposition reveals that this rapid transition also exists in the mesoscale horizontal flows induced by the intermediate surface heterogeneity prescribed with a sinusoid of amplitude 100 W m $^{-2}$ . However the transition is masked by continuously growing turbulence.     

Transfer Coefficients of Momentum, Heat and Water Vapour in the Atmospheric Surface Layer of a Large Freshwater Lake

In studies of lake–atmosphere interactions, the fluxes of momentum, water vapour and sensible heat are often parametrized as being proportional to the differences in wind, humidity and air temperature between the water surface and a reference height above the surface. Here, the proportionality via transfer coefficients in these relationships was investigated with the eddy-covariance method at three sites within an eddy-covariance mesonet across Lake Taihu, China. The results indicate that the transfer coefficients decreased with increasing wind speed for weak winds and approached constant values for strong winds. The presence of submerged macrophytes reduced the momentum transfer (drag) coefficient significantly. At the two sites free of submerged macrophytes, the 10-m drag coefficients under neutral stability were 1.8 $(\pm \,0.4) \times \,10^{-3}$ ( ± 0.4 ) × 10 ? 3 and $1.7\,(\pm \,0.3) \times \,10^{-3 }$ 1.7 ( ± 0.3 ) × 10 ? 3 at the wind speed of $9\,\text{ m } \text{ s }^{-1}$ 9 m s ? 1 , which are 38 and 34 % greater than the prediction by the Garratt model for the marine environment.     

Large-Eddy Simulation of Mesoscale Circulations Forced by Inhomogeneous Urban Heat Island

The large-eddy simulation mode of the Weather Research and Forecasting model is employed to simulate the planetary boundary-layer characteristics and mesoscale circulations forced by an ideal urban heat island (UHI). In our simulations, the horizontal heterogeneity of the UHI intensity distribution in urban areas is considered and idealized as a cosine function. Results indicate that the UHI heating rate and the UHI intensity heterogeneity affect directly the spatial distribution of the wind field; a stronger UHI intensity produces a maximum horizontal wind speed closer to the urban centre. The strong advection of warm air from the urban area to the rural area in the upper part of the planetary boundary-layer causes a more stable atmospheric stratification over both the urban and rural areas. The mesoscale sensible heat flux caused by the UHI circulation increases with UHI intensity but vanishes when the background wind speed is sufficiently high $(>$ 3.0  $\mathrm{{m\,s}}^{-1})$ .     

Statistical Downscaling of Pattern Projection Using Multi-Model Output Variables as Predictors

A pattern projection downscaling method is employed to predict monthly station precipitation. The predictand is the monthly precipitation at 1 station in China, 60 stations in Korea, and 8 stations in Thailand. The predictors are multiple variables from the output of operational dynamical models. The hindcast datasets span a period of 21 yr from 1983 to 2003. A downscaled prediction is made for each model separately within a leave-one-out cross-validation framework. The pattern projection method uses a moving window, which scans globally, in order to seek the most optimal predictor for each station. The final forecast is the average of the model downscaled precipitation forecasts using the best predictors and is referred to as DMME. It is found that DMME significantly improves the prediction skill by correcting the erroneous signs of the rainfall anomalies in coarse resolution predictions of general circulation models. The correlation coefficient between the prediction of DMME and the observation in Beijing of China reaches 0.71; the skill is improved to 0.75 for Korea and 0.61 for Thailand. The improvement of the prediction skills for the first two cases is attributed to three steps: coupled pattern selection, optimal predictor selection, and multi-model downscaled precipitation ensemble. For Thailand, we use the single-predictor prediction, which results in a lower prediction skill than the other two cases. This study indicates that the large-scale circulation variables, which are predicted by the current operational dynamical models, if selected well, can be used to make skillful predictions of local precipitation by means of appropriate statistical downscaling.     

The Effect of Wind-Turbine Wakes on Summertime US Midwest Atmospheric Wind Profiles as Observed with Ground-Based Doppler Lidar

We examine the influence of a modern multi-megawatt wind turbine on wind and turbulence profiles three rotor diameters ( $D$ D ) downwind of the turbine. Light detection and ranging (lidar) wind-profile observations were collected during summer 2011 in an operating wind farm in central Iowa at 20-m vertical intervals from 40 to 220 m above the surface. After a calibration period during which two lidars were operated next to each other, one lidar was located approximately $2D$ 2 D directly south of a wind turbine; the other lidar was moved approximately $3D$ 3 D north of the same wind turbine. Data from the two lidars during southerly flow conditions enabled the simultaneous capture of inflow and wake conditions. The inflow wind and turbulence profiles exhibit strong variability with atmospheric stability: daytime profiles are well-mixed with little shear and strong turbulence, while nighttime profiles exhibit minimal turbulence and considerable shear across the rotor disk region and above. Consistent with the observations available from other studies and with wind-tunnel and large-eddy simulation studies, measurable reductions in wake wind-speeds occur at heights spanning the wind turbine rotor (43–117 m), and turbulent quantities increase in the wake. In generalizing these results as a function of inflow wind speed, we find the wind-speed deficit in the wake is largest at hub height or just above, and the maximum deficit occurs when wind speeds are below the rated speed for the turbine. Similarly, the maximum enhancement of turbulence kinetic energy and turbulence intensity occurs at hub height, although observations at the top of the rotor disk do not allow assessment of turbulence in that region. The wind shear below turbine hub height (quantified here with the power-law coefficient) is found to be a useful parameter to identify whether a downwind lidar observes turbine wake or free-flow conditions. These field observations provide data for validating turbine-wake models and wind-tunnel observations, and for guiding assessments of the impacts of wakes on surface turbulent fluxes or surface temperatures downwind of turbines.     

关中盆地近地面风场和大气输送特征分析

利用2017年151个地面气象站的逐时观测数据和相关高空资料分析关中盆地近地面风场与输送特征。首先分析盆地内代表性站点的风速和风向观测事实,然后用CALMET风场诊断模式和轨迹计算模式获取当地逐小时风场和每日逐小时传输轨迹,分析风场类型。结果表明:关中盆地内日平均风速约1～3 m s?1,夏季风速高、秋冬季低;盆地中央的主导风向以沿地形走向的东北风和西南风为主,盆地四周测站的主导风向表现出顺着地形向盆地中央汇流的趋势。各站主导风向的季节变化不大。盆地内风场分为系统控制型、弱天气背景型和局地环流型3类,全年出现日数比例分别占8%、17.3%和74.7%。以山谷风日夜循环为特征的局地环流型风场最多。以西安城区为源点的大气输送轨迹显示,系统控制型风场以偏东北方向的输送为主,弱天气背景型和局地环流型风场的轨迹输送都大致以偏东北和偏西（以及偏西南）沿盆地走向以及偏东南朝向秦岭山地这三个方向为主。局地环流型的轨迹影响范围小,集中于盆地中央和南侧山地之间,表明这是一种不利于污染扩散的风场类型。     

Storm Surges in New York During Hurricane Sandy in 2012: A Verification of the Wind-Stress Tide Relation

In October 2012 Hurricane Sandy devastated New York City and its vicinity caused mainly by the storm surge, which is the water height above normal astronomical tide level. The meteorological conditions were as follows: minimum central pressure, 962 hPa, highest sustained wind speed 27.1 m s $^{-1}$ ? 1 and maximum gust 37.8 m s $^{-1}$ ? 1 . The peak storm surge was at 3.9 m and the peak storm tide at 4.4 m (which is referenced above mean lower low water). The wind-stress tide relation shows that $S=K\,V^{2}$ S = K V 2 , where $S$ S is the storm surge, $V$ V is the wind speed and $K$ K is the coefficient. It is found that with $S$ S in units of m, and $V$ V in  m s $^{-1}$ ? 1 , $K = 0.0051$ K = 0.0051 with $R^{2}= 0.91$ R 2 = 0.91 ( $R$ R is the correlation coefficient) indicating that 91 % of the total variation of the storm surge can be explained by variations in the wind stress, which is proportional to $V^{2}$ V 2 . Similar results were obtained during Hurricane Irene in 2011, which also affected the New York area. Therefore, this simple wind stress-tide relation should be useful in coastal engineering, urban planning, and emergency management.     

Streamwise Versus Spanwise Spacing of Obstacle Arrays: Parametrization of the Effects on Drag and Turbulence

A Reynolds-averaged Navier–Stokes model is used to investigate the evolution of the sectional drag coefficient and turbulent length scales with the layouts of aligned arrays of cubes. Results show that the sectional drag coefficient is determined by the non-dimensional streamwise distance (sheltering parameter), and the non-dimensional spanwise distance (channelling parameter) between obstacles. This is different than previous approaches that consider only plan area density $(\lambda _\mathrm{p})$ . On the other hand, turbulent length scales behave similarly to the staggered case (e. g. they are function of $\lambda _\mathrm{p}$ only). Analytical formulae are proposed for the length scales and for the sectional drag coefficient as a function of sheltering and channelling parameters, and implemented in a column model. This approach demonstrates good skill in the prediction of vertical profiles of the spatially-averaged horizontal wind speed.     

Weibull-k Revisited: “Tall” Profiles and Height Variation of Wind Statistics

The Weibull distribution is commonly used to describe climatological wind-speed distributions in the atmospheric boundary layer. While vertical profiles of mean wind speed in the atmospheric boundary layer have received significant attention, the variation of the shape of the wind distribution with height is less understood. Previously we derived a probabilistic model based on similarity theory for calculating the effects of stability and planetary boundary-layer depth upon long-term mean wind profiles. However, some applications (e.g. wind energy estimation) require the Weibull shape parameter (k), as well as mean wind speed. Towards the aim of improving predictions of the Weibull- \(k\) profile, we develop expressions for the profile of long-term variance of wind speed, including a method extending our probabilistic wind-profile theory; together these two profiles lead to a profile of Weibull-shape parameter. Further, an alternate model for the vertical profile of Weibull shape parameter is made, improving upon a basis set forth by Wieringa (Boundary-Layer Meteorol, 1989, Vol. 47, 85–110), and connecting with a newly-corrected corollary of the perturbed geostrophic-drag theory of Troen and Petersen (European Wind Atlas, 1989, Risø National Laboratory, Roskilde). Comparing the models for Weibull-k profiles, a new interpretation and explanation is given for the vertical variation of the shape of wind-speed distributions. Results of the modelling are shown for a number of sites, with a discussion of the models’ efficacy and applicability. The latter includes a comparative evaluation of Wieringa-type empirical models and perturbed-geostrophic forms with regard to surface-layer behaviour, as well as for heights where climatological wind-speed variability is not dominated by surface effects.     

Statistical-dynamical downscaling of wind roses over the Czech Republic

The present study describes a new method for statistical-dynamical downscaling that combines two different approaches, namely, a set of patterns simulated with a numerical flow model and a transformation function used to process both calculated data and measurements at a reference station. The combined method produces wind roses and wind speed histograms at an arbitrary location in the model domain. The inflow wind direction represented the key parameter to define a set of wind field simulations. The other two inflow parameters, namely, thermal stratification and geostrophic wind speed, were derived from corresponding averaged soundings. The results showed that in the Czech Republic, there are areas where wind roses are deformed by the surrounding terrain. The deformations occur in relatively shallow and wide valleys, and they are more sensitive to the inflow wind direction. Calculated wind roses are compared to corresponding observations at 22 synoptic stations. The most frequent wind direction sector in simulations agreed with measurements at 17 stations. The resulting error in frequency in that sector was under 5 % at 10 stations. In general, the main features of the wind roses are modelled well, even at a relatively large distance from the reference station. However, better performance was achieved for smaller distances between reference station and the site. In further studies, a more extensive set of flow patterns with reduced intervals of thermal stratification and wind speed will likely improve calculated wind roses.     

Characteristics of the sea breeze in Attica,Greece

The characteristics of the sea breeze in the Attica region of Greece, in which Athens is located, have been studied for occasions of weak synoptic-scale pressure gradient. The analysis is based on synoptic observations from six meteorological stations, three on the coast and three inland. The three inland stations and one of the coastal stations lie almost in a straight line at different distances from the coast. For each meteorological station, the basic characteristics of the sea breeze were determined, i.e.,

1. The mean number of sea-breeze days for each calendar month.
2. The monthly mean wind speed for each synoptic hour.
3. The times of onset and cessation of the sea breeze.
4. The monthly vector mean wind, and its constancy ‘Constancy’ is defined as 100{itV{inr}/V{ins}}, where {itV{inr}} is the magnitude of the vector mean wind, and {itV{ins}} is the scalar mean wind speed. See Brooks and Carruthers (1953). (In this paper, the factor 100 is not used.) for each synoptic hour.
5. For days on which there was a sea breeze at Helliniko (the coastal reference station), the percentage number of days on which there was also a sea breeze at the given station.

An attempt was also made to determine further characteristics, such as the inland penetration of the sea breeze, its depth, the spatial and temporal variation of wind speed and direction, and the existence of the return flow. Finally, the properties of the land breeze are briefly outlined.     

Evaluation of the Weather Research and Forecasting Mesoscale Model for GABLS3: Impact of Boundary-Layer Schemes,Boundary Conditions and Spin-Up

We evaluated the performance of the three-dimensional Weather Research and Forecasting (WRF) mesoscale model, specifically the performance of the planetary boundary-layer (PBL) parametrizations. For this purpose, Cabauw tower observations were used, with the study extending beyond the third GEWEX Atmospheric Boundary-Layer Study (GABLS3) one-dimensional model intercomparison. The WRF model (version 3.4.1) contains 12 different PBL parametrizations, most of which have been only partially evaluated. The GABLS3 case offers a clear opportunity to evaluate model performance, focusing on time series of near-surface weather variables, radiation and surface flux budgets, vertical structure and the nighttime inertial oscillation. The model results revealed substantial differences between the PBL schemes. Generally, non-local schemes tend to produce higher temperatures and higher wind speeds than local schemes, in particular, for nighttime. The WRF model underestimates the 2-m temperature during daytime (about \(2\) K) and substantially underestimates it at night (about \(4\) K), in contrast to the previous studies where modelled 2-m temperature was overestimated. Considering the 10-m wind speed, during the night turbulent kinetic energy based schemes tend to produce lower wind speeds than other schemes. In all simulations the sensible and latent heat fluxes were well reproduced. For the net radiation and the soil heat flux we found good agreement with daytime observations but underestimations at night. Concerning the vertical profiles, the selected non-local PBL schemes underestimate the PBL depth and the low-level jet altitude at night by about 50 m, although with the correct wind speed. The latter contradicts most previous studies and can be attributed to the revised stability function in the Yonsei University PBL scheme. The local, turbulent kinetic energy based PBL schemes estimated the low-level jet altitude and strength more accurately. Compared to the observations, all model simulations show a similar structure for the potential temperature, with a consistent cold bias ( \(\approx \) 2 K) in the upper PBL. In addition to the sensitivity to the PBL schemes, we studied the sensitivity to technical features such as horizontal resolution and domain size. We found a substantial difference in the model performance for a range of 12, 18 and 24 h spin-up times, longer spin-up time decreased the modelled wind speed bias, but it strengthened the negative temperature bias. The sensitivity of the model to the vertical resolution of the input and boundary conditions on the model performance is confirmed, and its influence appeared most significant for the non-local PBL parametrizations.     

Air–Sea \mathrm{CO}_{2} Gas Transfer Velocity in a Shallow Estuary

The air–sea transfer velocity of $\mathrm{CO}_{2}\, (k_{\mathrm{CO}_{2}})$ was investigated in a shallow estuary in March to July 2012, using eddy-covariance measurements of $\mathrm{CO}_{2}$ fluxes and measured air–sea $\mathrm{CO}_{2}$ partial-pressure differences. A data evaluation method that eliminates data by nine rejection criteria in order to heighten parametrization certainty is proposed. We tested the data evaluation method by comparing two datasets: one derived using quality criteria related solely to the eddy-covariance method, and the other derived using quality criteria based on both eddy-covariance and cospectral peak methods. The best parametrization of transfer velocity normalized to a Schmidt number of 600 $(k_{600})$ was determined to be: $k_{600} = 0.3\,{U_{10}}^{2.5}$ where $U_{10}$ is the wind speed in m $\mathrm{s}^{-1}$ at 10 m; $k_{600}$ is based on $\mathrm{CO}_{2}$ fluxes calculated by the eddy-covariance method and including the cospectral peak method criteria. At low wind speeds, the transfer velocity in the shallow water estuary was lower than in other coastal waters, possibly a symptom of low tidal amplitude leading to low intensity water turbulence. High transfer velocities were recorded above wind speeds of 5 m $\mathrm{s}^{-1}$ , believed to be caused by early-breaking waves and the large fetch (6.5 km) of the estuary. These findings indicate that turbulence in both air and water influences the transfer velocity.     

Equilibrium Atmospheric Boundary-Layer Flow: Computational Fluid Dynamics Simulation with Balanced Forces

Forcing relationships in steady, neutrally stratified atmospheric boundary-layer (ABL) flow are thoroughly analyzed. The ABL flow can be viewed as balanced between a forcing and a drag term. The drag term results from turbulent stress divergence, and above the ABL, both the drag and the forcing terms vanish. In computational wind engineering applications, the ABL flow is simulated not by directly specifying a forcing term in the ABL but by specifying boundary conditions for the simulation domain. Usually, these include the inflow boundary and the top boundary conditions. This ‘boundary-driven’ ABL flow is dynamically different from its real counterpart, and this is the major reason that the simulated boundary-driven ABL flow does not maintain horizontal homogeneity. Here, first a dynamical approach is proposed to develop a neutrally stratified equilibrium ABL flow. Computational fluid dynamics (CFD) software (Fluent 6.3) with the standard \(k\) – \(\varepsilon \) turbulence model is employed, and by applying a driving force profile, steady equilibrium ABL flows are simulated by the model. Profiles of wind speed and turbulent kinetic energy (TKE) derived using this approach are reasonable in comparison with the conventional logarithmic law and with observational data respectively. Secondly, the equilibrium ABL profiles apply as inflow conditions to simulate the boundary-driven ABL flow. Simulated properties between the inlet and the outlet sections across a fetch of 10 km are compared. Although profiles of wind speed, TKE, and its dissipation rate are consistently satisfactory under higher wind conditions, a deviation of TKE and its dissipation rate between the inlet and outlet are apparent (7–8 %) under lower wind-speed conditions (2 m s \(^{-1}\) at 10 m). Furthermore, the simulated surface stress systematically decreases in the downwind direction. A redistribution of the pressure field is also found in the simulation domain, which provides a different driving pattern from the realistic case in the ABL.     

Wind erosion climatic erosivity

A physically based wind-erosion climatic factor has been derived: $$CE = \rho \int {[u^2 } - (u_T^2 + \gamma ^l /\rho a^2 )]^{3/2} f(u)du$$ where ? is the air density, a is a constant made up of other constants (von Karman, height of wind speed observation, roughness parameter), u is the horizontal wind speed, u _T is threshold wind speed, f(u) u) is a wind speed probability density function, and γ is the cohesive resistance caused by water on the soil particles. Cohesive resistance is proportional to the square of water content relative to water content at ?1500 J kg^?1. Relative water content is approximated from the Budyko dryness ratio and the Thornthwaite PE index with similar results. CE is calculable from wind speed and other generally available meteorological data, and is usable in the wind erosion equation without some of the limitations of a previously used wind erosion climatic factor.     

Decadal predictability and forecast skill

The “potential predictability” of the climate system is the upper limit of available forecast skill and can be characterized by the ratio p of the predictable variance to the total variance. While the potential predictability of the actual climate system is unknown its analog q may be obtained for a model of the climate system. The usual correlation skill score r and the mean square skill score M are functions of p in the case of actual forecasts and potential correlation ρ and potential mean square skill score $\mathcal{M}$ are the same functions of q in the idealized model context. In the large ensemble limit the connection between model-based potential predictability and skill scores is particularly straightforward with $q=\rho^{2}=\mathcal{M}.$ Decadal predictions of annual mean temperature produced with the Canadian Centre for Climate Modelling and Analysis coupled climate model are analyzed for information on decadal climate predictability and actual forecast skill. Initialized forecast results are compared with the results of uninitialized climate simulations. Model-based values of potential predictability q and potential correlation skill ρ are obtained and ρ is compared with the actual forecast correlation skill r. The skill of externally forced and internally generated components of the variability are separately estimated. As expected, ρ > r and both decline with forecast range τ, at least for the first five years. The decline of skill is associated mainly with the decline of the skill of the internally generated component. The potential and actual skill of a forecast of time-averaged temperature depends on the averaging period. The skill of uninitialized simulations is low for short averaging times and increases as averaging time increases. By contrast, skill is high at short averaging times for forecasts initialized from observations and declines as averaging times increase to about three years, then increases somewhat at longer averaging times. The skills of the initialized forecasts and uninitialized simulations begin to converge for longer averaging times. The potential correlation skill ρ of the externally forced component of temperature is largest at tropical latitudes and the skill of the internally generated component is largest over the North Atlantic, parts of the Southern Ocean and to some extent the North Pacific. Potential skill over extratropical land is somewhat weaker than over oceans. The distribution of actual correlation skill r is broadly similar to that of potential skill for the externally forced component but less so for the internally generated component. Differences in potential and actual skill suggest where improvements in the forecast system might be found.