A cluster-optimizing regression-based approach for precipitation spatial downscaling in mountainous terrain

Precipitation temporal and spatial variability often controls terrestrial hydrological processes and states. Common remote-sensing and modeling precipitation products have a spatial resolution that is often too coarse to reveal hydrologically important spatial variability. A statistical algorithm was developed for downscaling low-resolution spatial precipitation fields. This algorithm auto-searches precipitation spatial structures (rain-pixel clusters), and orographic effects on precipitation distribution without prior knowledge of atmospheric setting. It is composed of three components: rain-pixel clustering, multivariate regression, and random cascade. The only required input data for the downscaling algorithm are coarse-pixel precipitation map and a topographic map. The algorithm was demonstrated with 4 km × 4 km Next Generation Radar (NEXRAD) precipitation fields, and tested by downscaling NEXRAD-aggregated 16 km × 16 km precipitation fields to 4 km × 4 km pixel precipitation, which was then compared to the original NEXRAD data. The demonstration and testing were performed at both daily and hourly temporal resolutions for the northern New Mexico mountainous terrain and the central Texas Hill Country. The algorithm downscaled daily precipitation fields are in good agreement with the original 4 km × 4 km NEXRAD precipitation, as measured by precipitation spatial structures and the statistics between the downscaling and the original NEXRAD precipitation maps. For three daily precipitation events, downscaled precipitation map reproduces precipitation variance of the disaggregation field, and with Pearson correlation coefficients between the downscaled map and the NEXRAD map of 0.65, 0.71, and 0.80. The algorithm does not perform as well on downscaling hourly precipitation fields at the examined scale range (from 16 km to 4 km), which underestimates precipitation variance of the disaggregation field. For a scale range from 4 km to 1 km, the algorithm has potential to perform well at both daily and hourly precipitation fields, indicated from good regression performance.     

Simulated precipitation fields with variance-consistent interpolation

Abstract

Gridded meteorological data are available for all of Norway as time series dating from 1961. A new way of interpolating precipitation in space from observed values is proposed. Based on the criteria that interpolated precipitation fields in space should be consistent with observed spatial statistics, such as spatial mean, variance and intermittency, spatial fields of precipitation are simulated from a gamma distribution with parameters determined from observed data, adjusted for intermittency. The simulated data are distributed in space, using the spatial pattern derived from kriging. The proposed method is compared to indicator kriging and to the current methodology used for producing gridded precipitation data. Cross-validation gave similar results for the three methods with respect to RMSE, temporal mean and standard deviation, whereas a comparison on estimated spatial variance showed that the new method has a near perfect agreement with observations. Indicator kriging underestimated the spatial variance by 60–80% and the current method produced a significant scatter in its estimates.

Citation Skaugen, T. & Andersen, J. (2010) Simulated precipitation fields with variance-consistent interpolation. Hydrol. Sci. J. 55(5), 676–686.     

Assessing the impact of land use change on hydrology by ensemble modelling (LUCHEM) IV: Model sensitivity to data aggregation and spatial (re-)distribution

This paper analyses the effect of spatial resolution and distribution of model input data on the results of regional-scale land use scenarios using three different hydrological catchment models. A 25 m resolution data set of a mesoscale catchment and three land use scenarios are used. Data are systematically aggregated to resolutions up to 2 km. Land use scenarios are spatially redistributed, both randomly and topography based. Using these data, water fluxes are calculated on a daily time step for a 16 year time period without further calibration. Simulation results are used to identify grid size, distribution and model dependent scenario effects. In the case of data aggregation, all applied models react sensitively to grid size. WASIM and TOPLATS simulate constant water balances for grid sizes from 50 m to 300–500 m, SWAT is more sensitive to input data aggregation, simulating constant water balances between 50 m and 200 m grid size. The calculation of scenario effects is less robust to data aggregation. The maximum acceptable grid size reduces to 200–300 m for TOPLATS and WASIM. In case of spatial distribution, SWAT and TOPLATS are slightly sensitive to a redistribution of land use (below 1.5% for water balance terms), whereas WASIM shows almost no reaction. Because the aggregation effects were stronger than the redistribution effects, it is concluded that spatial discretisation is more important than spatial distribution. As the aggregation effect was mainly associated with a change in land use fraction, it is concluded that accuracy of data sets is much more important than a high spatial resolution.     

Spatial interpolation schemes of daily precipitation for hydrologic modeling

Distributed hydrologic models typically require spatial estimates of precipitation interpolated from sparsely located observational points to the specific grid points. We compare and contrast the performance of regression-based statistical methods for the spatial estimation of precipitation in two hydrologically different basins and confirmed that widely used regression-based estimation schemes fail to describe the realistic spatial variability of daily precipitation field. The methods assessed are: (1) inverse distance weighted average; (2) multiple linear regression (MLR); (3) climatological MLR; and (4) locally weighted polynomial regression (LWP). In order to improve the performance of the interpolations, the authors propose a two-step regression technique for effective daily precipitation estimation. In this simple two-step estimation process, precipitation occurrence is first generated via a logistic regression model before estimate the amount of precipitation separately on wet days. This process generated the precipitation occurrence, amount, and spatial correlation effectively. A distributed hydrologic model (PRMS) was used for the impact analysis in daily time step simulation. Multiple simulations suggested noticeable differences between the input alternatives generated by three different interpolation schemes. Differences are shown in overall simulation error against the observations, degree of explained variability, and seasonal volumes. Simulated streamflows also showed different characteristics in mean, maximum, minimum, and peak flows. Given the same parameter optimization technique, LWP input showed least streamflow error in Alapaha basin and CMLR input showed least error (still very close to LWP) in Animas basin. All of the two-step interpolation inputs resulted in lower streamflow error compared to the directly interpolated inputs.     

Crustal geomagnetic field: two-dimensional intermediate-wavelength spatial power spectra

Two-dimensional Fourier spatial power spectra of equivalent magnetization values are presented for a region that includes a large portion of the western United States. The magnetization values were determined by inversion of POGO satellite data, assuming a magnetic crust 40 km thick, and were located on an 11 × 10 array with 300 km grid spacing. The spectra appear to be in good agreement with values of the crustal geomagnetic field spatial power spectra given by McLeod and Coleman (1980) and with the crustal field model given by Serson and Hannaford (1957). The spectra show evidence of noise at low frequencies in the direction along the satellite orbital track (N-S), indicating that for this particular data set additional filtering would probably be desirable. These findings illustrate the value of two-dimensional spatial power spectra both for describing the geomagnetic field statistically and as a guide for diagnosing possible noise sources.     

Estimation and spatial interpolation of rainfall intensity distribution from the effective rate of precipitation

Great emphasis is being placed on the use of rainfall intensity data at short time intervals to accurately model the dynamics of modern cropping systems, runoff, erosion and pollutant transport. However, rainfall data are often readily available at more aggregated level of time scale and measurements of rainfall intensity at higher resolution are available only at limited stations. A distribution approach is a good compromise between fine-scale (e.g. sub-daily) models and coarse-scale (e.g. daily) rainfall data, because the use of rainfall intensity distribution could substantially improve hydrological models. In the distribution approach, the cumulative distribution function of rainfall intensity is employed to represent the effect of the within-day temporal variability of rainfall and a disaggregation model (i.e. a model disaggregates time series into sets of higher solution) is used to estimate distribution parameters from the daily average effective precipitation. Scaling problems in hydrologic applications often occur at both space and time dimensions and temporal scaling effects on hydrologic responses may exhibit great spatial variability. Transferring disaggregation model parameter values from one station to an arbitrary position is prone to error, thus a satisfactory alternative is to employ spatial interpolation between stations. This study investigates the spatial interpolation of the probability-based disaggregation model. Rainfall intensity observations are represented as a two-parameter lognormal distribution and methods are developed to estimate distribution parameters from either high-resolution rainfall data or coarse-scale precipitation information such as effective intensity rates. Model parameters are spatially interpolated by kriging to obtain the rainfall intensity distribution when only daily totals are available. The method was applied to 56 pluviometer stations in Western Australia. Two goodness-of-fit statistics were used to evaluate the skill—daily and quantile coefficient of efficiency between simulations and observations. Simulations based on cross-validation show that kriging performed better than other two spatial interpolation approaches (B-splines and thin-plate splines).     

Spatial downscaling of TRMM precipitation data based on the orographical effect and meteorological conditions in a mountainous area

The lack of high resolution precipitation data has posed great challenges to the study and management of extreme rainfall events. Satellite-based rainfall products with large areal coverage provide a potential alternative source of data where in situ measurements are not available. However, the mismatch in scale between these products and model requirements has limited their application and demonstrates that satellite data must be downscaled before being used. This study developed a statistical spatial downscaling scheme based on the relationships between precipitation and related environmental factors such as local topography and pre-storm meteorological conditions. The method was applied to disaggregate the Tropical Rainfall Measuring Mission (TRMM) 3B42 products, which have a resolution of 0.25° × 0.25°, to 1 × 1 km gridded rainfall fields. The TRMM datasets in accord with six rainstorm events in the Xiao River basin were used to validate the effectiveness of this approach. The downscaled precipitation data were compared with ground observations and exhibited good agreement with r² values ranging from 0.612 to 0.838. In addition, the proposed approach provided better results than the conventional spline and kriging interpolation methods, indicating its promise in the management of extreme rainfall events. The uncertainties in the final results and the implications for further study were discussed, and the needs for additional rigorous investigations of the rainfall physical process prior to institutionalizing the use of satellite data were highlighted.     

Seasonal evaluation of rainfall estimation by four cumulus parameterization schemes and their sensitivity analysis

Sustainable water resources management require scientifically sound information on precipitation, as it plays a key role in hydrological responses in a catchment. In recent years, mesoscale weather models in conjunction with hydrological models have gained great attention as they can provide high‐resolution downscaled weather variables. Many cumulus parameterization schemes (CPSs) have been developed and incorporated into three‐dimensional Pennsylvania State University/National Center for Atmospheric Research (PSU/NCAR) mesoscale model 5 (MM5). This study has performed a comprehensive evaluation of four CPSs (the Anthes–Kuo, Grell, Betts–Miller and Kain–Fritsch93 schemes) to identify how their inclusion influences the mesoscale model's precipitation estimation capabilities. The study has also compared these four CPSs in terms of variability in rainfall estimation at various horizontal and vertical levels. For this purpose, the MM5 was nested down to resolution of 81 km for Domain 1 (domain span 21 × 81 km) and 3 km for Domain 4 (domain span 16 × 3 km), respectively, with vertical resolutions at 23, 40 and 53 vertical levels. The study was carried out at the Brue catchment in Southwest England using both the ERA‐40 reanalysis data and the land‐based observation data. The performances of four CPs were evaluated in terms of their ability to simulate the amount of cumulative rainfall in 4 months in 1995 representing the four seasonal months, namely, January (winter), March (spring), July (summer) and October (autumn). It is observed that the Anthes–Kuo scheme has produced inferior precipitation values during spring and autumn seasons while simulations during winter and summer were consistently good. The Betts–Miller scheme has produced some reasonable results, particularly at the small‐scale domain (3 km grid size) during winter and summer. The KF2 scheme was the best scheme for the larger‐scale (81 km grid size) domain during winter season at both 23 and 53 vertical levels. This scheme tended to underestimate rainfall for other seasons including the small‐scale domain (3 km grid size) in the mesoscale. The Grell scheme was the best scheme in simulating rainfall rates, and was found to be superior to other three schemes with consistently better results in all four seasons and in different domain scales. Copyright © 2011 John Wiley & Sons, Ltd.     

Ocean response to strong precipitation events in the Gulf of Lions (northwestern Mediterranean Sea): a sensitivity study

The Mediterranean Sea is a region of intense air–sea interactions, with in particular strong evaporation over sea which drives the thermohaline circulation. The Mediterranean region is also prone to strong precipitation events characterized by low spatial extent, short duration, and high temporal variability. The impacts of intense offshore precipitation over sea, in the Gulf of Lions which is a spot for winter deep convection, are investigated using four sensitivity simulations performed at mesoscale resolution with the eddy-resolving regional ocean model NEMO-MED12. We use various atmospheric fields to force NEMO-MED12, downscaled from reanalyses with the non-hydrostatic mesoscale Weather Research and Forecasting model but differing in space resolutions (20 and 6.7 km) or in time frequencies (daily and three-hourly). This numerical study evidences that immediate, intense, and rapid freshening occurs under strong precipitation events. The strong salinity anomaly induced extends horizontally (≃50 km) as vertically (down to 50 m) and persists several days after strong precipitation events. The change in the space resolution of the atmospheric forcing modifies the precipitating patterns and intensity, as well as the shape and the dynamics of the low-salinity layer formed are changed. With higher forcing frequency, shorter and heavier precipitation falls in the ocean in the center of the Gulf of Lions, and due to a stronger vertical shear and mixing, the low-salinity anomaly propagates deeper.     

Reconstructing the gravity gradient anomaly field from surveys with wide line spacing using equivalent source processing: an error analysis

When anomalous gravity gradient signals provide a large signal‐to‐noise ratio, airborne and marine surveys can be considered with wide line spacing. In these cases, spatial resolution and sampling requirements become the limiting factors for specifying the line spacing, rather than anomaly detectability. This situation is analysed by generating known signals from a geological model and then sub‐sampling them using a simulated airborne gravity gradient survey with a line spacing much wider than the characteristic anomaly size. The data are processed using an equivalent source inversion, which is used subsequently to predict and grid the field in‐between the survey lines by means of forward calculations. Spatial and spectral error analysis is used to quantify the accuracy and resolution of the processed data and the advantages of acquiring multiple gravity gradient components are demonstrated. With measurements of the full tensor along survey lines spaced at 4 × 4 km, it is shown that the vertical gravity gradient can be reconstructed accurately over a bandwidth of 2 km with spatial root‐mean square errors less than 30%. A real airborne full‐tensor gravity gradient survey is presented to confirm the synthetic analysis in a practical situation.     

基于随机森林模型的GRACE数据3种空间降尺度对比

陆地水储量是赋存在陆地上各种形式水的综合体现,研究其时空变化对认识区域水循环过程和水资源调控等具有重要意义。然而现有陆地水储量变化数据实际分辨率较低,限制了其在中小流域或地区中的应用。针对这一问题,本文基于GRACE重力卫星和其后续卫星GRACE-FO反演的陆地水储量变化数据,首先采用随机森林模型,分别基于格点、区域(流域)和区域(全国)3种空间降尺度思路将GRACE数据降尺度至0.25°×0.25°,后结合GLDAS模型数据,基于水量平衡原理计算得到地下水储量变化数据,最后基于降尺度模型模拟效果和实测地下水位数据评估3种降尺度思路在全国的适用性。结果表明:随机森林模型能够较好地模拟驱动数据(降水、气温、植被条件指数和土壤水储量)与GRACE数据的统计关系,验证期格点降尺度思路的平均相关系数总体在0.6左右,区域降尺度思路的平均纳什效率系数、相关系数和均方根误差分别>0.5、>0.75和<6.6 cm,3种空间降尺度思路的模拟精度均满足基本要求;2003—2021年间,GRACE数据、格点降尺度、区域降尺度(流域)和区域降尺度(全国)得到的我国陆地水储量亏缺量分别约为...     

基于下一代三向车轮双星编队改善地球重力场空间分辨率研究

由于当前GRACE(Gravity Recovery and Climate Experiment)串行式编队存在"南北向条带误差"等缺陷,因此本文基于星间速度插值法开展了利用下一代三向车轮双星编队ACR(Along-Cross-Radial)-Cartwheel提高地球重力场空间分辨率的可行性研究论证.第一,采用GRACE卫星轨道参数和关键载荷精度,利用三向车轮双星编队ACR-Cartwheel-A/B反演了120阶地球重力场.结果表明:基于ACR-Cartwheel-A/B双星编队反演地球重力场的模拟精度较德国波茨坦地学研究中心(GFZ)公布的EIGEN-GRACE02S地球重力场模型的实测精度平均提高2.6倍,从而检验了基于下一代三向车轮双星编队ACR-Cartwheel-A/B反演地球重力场精度优于当前GRACE串行式双星编队的可行性.第二,通过星间速度插值法,采用卫星轨道参数(初始轨道高度350km、平均星间距离100km、初始轨道倾角89°、初始轨道离心率0.0046)、卫星关键载荷精度指标(星间速度10-7 m·s-1、轨道位置10-3 m、轨道速度10-6 m·s-1、非保守力10-11 m·s-2)、观测时间30天和采样间隔10s,基于经向车轮双星编队Lo-AR(Longitudinal-Along-Radial)-Cartwheel-A/B、纬向车轮双星编队La-AR(Latitudinal-Along-Radial)-Cartwheel-A/B和三向车轮双星编队ACR-Cartwheel-A/B,分别反演了120阶地球重力场;在120阶处,累计大地水准面精度分别为5.115×10-4 m、4.923×10-4 m和3.488×10-4 m.结果表明:(1)由于La-AR-Cartwheel-A/B编队的轨道稳定性优于Lo-AR-Cartwheel-A/B编队,因此基于La-AR-Cartwheel-A/B编队反演重力场精度高于Lo-AR-CartwheelA/B编队;(2)由于ACR-Cartwheel-A/B编队可以同时获得轨向、垂向和径向的重力场信息,卫星观测数据具有各向同性优点,因此ACR-Cartwheel-A/B编队是建立下一代高精度和高空间分辨地球重力场模型的优化选择.     

Hydrodynamic modelling of mesoscale eddies in the Black Sea

A three dimensional structure of mesoscale circulation in the Black Sea is simulated using the Proudman Oceanographic Laboratory Coastal Ocean Modelling System. A number of sensitivity tests reveal the response of the model to changes in the horizontal resolution, time steps, and diffusion coefficients. Three numerical grids are examined with x-fine (3.2 km), fine (6.7 km) and coarse (25 km) resolution. It is found that the coarse grid significantly overestimates the energy of the currents and is not adequate even for the study of basin-scale circulation. The x-fine grid, on the other hand, does not give significant advantages compared to the fine grid, and the latter is used for the bulk of simulations. The most adequate parameters are chosen from the sensitivity study and used to model both the basin-scale circulation and day-to-day variability of mesoscale currents for the months of May and June of 2000. The model is forced with actual wind data every 6 h and monthly climatic data for evaporation, precipitation, heat fluxes and river run-off. The results of the fine grid model are compared favourably against the satellite imagery. The model adequately reproduces the general circulation and many mesoscale features including cyclonic and anticyclonic eddies, jets and filaments in different parts of the Black Sea. The model gives a realistic geographical distribution and parameters of mesoscale currents, such as size, shape and evolution of the eddies.     

Assessing the Sensitivity of a Model of Runoff Formation in the Ussuri River Basin

A physically based model of runoff formation with daily resolution has been developed for the upper part of the Ussuri basin with an area of 24400 km² based on ECOMAG hydrological modeling platform. Two versions of the hydrological model have been studied: (1) a crude version with the spatial schematization of the drainage area and river network based on DEM 1 × 1 km with the use of soil and landscape maps at a scale of 1: 2500000 and (2) a detailed version with DEM 80 × 80 m and soil and landscape maps of the scale of 1: 100000. Each version of the model has been tested for two variants of meteorological inputs: (1) meteorological forcing data (temperature, air humidity, precipitation) at eight weather stations and (2) with the involvement of additional data on precipitation collected at 15 gages in the basin. The model has been calibrated and validated over a 34-year period (1979–2012) with the use of runoff data for the Ussuri R. and its tributaries. The results of numerical experiments for assessing the sensitivity of model hydrological response to the spatial resolution of land surface characteristics and the density of precipitation gaging stations are discussed.     

BOOK REVIEWS

Abstract

A distributed eco-hydrological model based on soil—vegetation—atmosphere transfer processes is applied to estimate actual evapotranspiration (ET) and gross primary production (GPP) over the Wuding River basin, Loess Plateau, China, based on digital elevation model, vegetation and soil information between 2000 and 2003 over three grid sizes: 250 m, 1 km and 8 km. The spatial patterns of annual ET and GPP are related to precipitation variability and land-use/cover conditions. The grid size is shown to affect the spatial patterns of annual ET and GPP, the effect on GPP being more significant than that on ET. Geostatistical and regression analyses demonstrate that precipitation and vegetation influence the scaling effect of ET and GPP in a complex way. When precipitation is high, the scaling effect of ET is more dependent on precipitation. The scaling effect of ET and GPP from 1-km to 8-km grid size is much larger than that from 250-m to 1-km grid size, showing the 1-km grid size to be a feasible choice for simulation of their spatial patterns. Although the annual GPP is more sensitive to the grid size than annual ET, both daily ET and daily GPP averaged over the whole basin seem to be insensitive to the grid size, illustrating that the coarse grid size can be used to simulate spatially-averaged variables without losing much accuracy.     

区域气候模式RegCM3对华北地区未来气候变化的数值模拟

采用高水平分辨率区域气候模式进行区域未来气候变化预估,对理解全球增暖对区域气候的潜在影响和科学评估区域气候变化有很好的参考价值.这里对国家气候中心使用25 km高水平分辨率区域气候模式RegCM3单向嵌套全球模式MIROC3.2_hires在观测温室气体(1951—2000)和IPCC A1B温室气体排放情景下(2001—2100)进行的共计150年长时间模拟结果,进行华北地区未来气温、降水和极端气候事件变化的分析.模式检验结果表明:模式对当代(1981—2000)气温以及和气温有关的极端气候事件(霜冻日数、生长季长度)的空间分布和数值模拟较好;对降水及和降水有关的极端气候事件(强降水日期、降水强度、五日最大降水量)能够模拟出它们各自的主要空间分布特征,但在模拟数值上存在偏大、偏强的误差.和全球模式驱动场相比,区域模式模拟的气温、降水和极端气候事件有明显的改进.2010—2100年华北地区随时间区域平均气温升高幅度逐渐增大,随之霜冻日数逐渐减少,生长季长度逐渐增多;同时随温室效应的不断加剧,未来降水呈增加的趋势,强降水日期和五日最大降水量逐渐增多、降水强度逐渐增大.从空间分布看,21世纪末期(2081—2100)气温、降水以及有关的极端气候事件变化比21世纪中期(2041—2060)更加明显.     

Complexity‐reduction modelling for assessing the macro‐scale patterns of historical soil moisture in the Euro‐Mediterranean region

Complexity‐reduction modelling can be useful for increasing the understanding of how the climate affects basin soil moisture response upon historical times not covered by detailed hydrological data. For this purpose, here is presented and assessed an empirical regression‐based model, the European Soil Moisture Empirical Downscaling (ESMED), in which different climatic variables, easily available on the web, are addressed for simplifying the inherent complexity in the long‐time studies. To accommodate this simplification, the Palmer Drought Severity Index, the precipitation, the elevation and the geographical location were used as input data in the ESMED model for predicting annual soil moisture budget. The test area was a large region including central Europe and Mediterranean countries, and the spatial resolution was initially set at 50 km. ESMED model calibration was made according to the soil moisture values retrieved from the Terrestrial Water Budget Data archive by selecting randomly 285 grid points (out of 2606). Once parameterized, ESMED model was performed at validation stage both spatially and temporally. The spatial validation was made for the grid points not selected in the calibration stage while the comparison with the soil moisture outputs of the Global Land Data Assimilation System–NOAH10 simulations upon the period 1950–2010 was carried out for the temporal validation. Moreover, ESMED results were found to be in good agreement with a root‐zone soil moisture product obtained from active and passive microwave sensors from various satellite missions. ESMED model was thus found to be reliable for both the temporal and spatial validations and, hence, it might represent a useful tool to characterize the long‐term dynamics of soil moisture–weather interaction. Copyright © 2013 John Wiley & Sons, Ltd.     

A perfect prognosis approach for daily precipitation series in consideration of space–time correlation structure

Downscaling techniques are the required tools to link the global climate model outputs provided at a coarse grid resolution to finer scale surface variables appropriate for climate change impact studies. Besides the at-site temporal persistence, the downscaled variables have to satisfy the spatial dependence naturally observed between the climate variables at different locations. Furthermore, the precipitation spatial intermittency should be fulfilled. Because of the complexity in describing these properties, they are often ignored, which can affect the effectiveness of the hydrologic process modeling. This study is a continuation of the work by Khalili and Nguyen (Clim Dyn 49(7–8):2261–2278.  https://doi.org/10.1007/s00382-016-3443-6, 2017) regarding the multi-site statistical downscaling of daily precipitation series. Different approach of multi-site statistical downscaling based on the concept of the spatial autocorrelation is presented in this paper. This approach has proven to give effective results for multi-site multivariate statistical downscaling of daily extreme temperature time series (Khalili et al. in Int J Climatol 33:15–32.  https://doi.org/10.1002/joc.3402, 2013). However, more challenges are presented by the precipitation variable because of the high spatio-temporal variability and intermittency. The proposed approach consists of logistic and multiple regression models, linking the global climate predictors to the precipitation occurrences and amounts respectively, and using the spatial autocorrelation concept to reproduce the spatial dependence observed between the precipitation series at different sites. An empirical technique has also been involved in this approach in order to fulfill the precipitation intermittency property. The proposed approach was performed using observed daily precipitation data from ten weather stations located in the southwest region of Quebec and southeast region of Ontario in Canada, and climate predictors from the NCEP/NCAR (National Centers for Environmental Prediction/National Centre for Atmospheric Research) reanalysis dataset. The results have proven the ability of the proposed approach to adequately reproduce the observed precipitation occurrence and amount characteristics, temporal and spatial dependence, spatial intermittency and temporal variability.     

THE FRACTAL DIMENSION OF GRAVITY DATA SETS AND ITS IMPLICATION FOR GRIDDING1

Gravity survey station locations are, in general, inhomogeneously distributed. This inevitably results in interpolation errors in the computation of a regular grid from the gravity data. The fractal dimension of the station distribution can be used to determine if an interpolated map is aliased at a specific wave-length and, moreover, it is often possible to determine an optimum gridding interval. Synthetic distributions of gravity station locations have been used for theoretical studies and it is found that for randomly distributed data there is a range of sizes for which the spatial data distribution has a fractal dimension of 2; that is, Euclidean. The minimum length scale at which the distribution ceases to be Euclidean is the optimum interpolation interval obeying Shannon's sampling theorem. For dimensions less than 2, the optimum interpolation interval is the shortest length at which the scaling regime is constant. In this case the gravity field cannot be interpolated without introducing some aliasing. As the fractal dimension characterizes the data distribution globally over the whole study area, the actual gridding interval, in some cases, will be smaller in order to represent short-wavelength features properly in the more densely sampled sub-areas, but this may generate spurious anomalies elsewhere. The proposed technique is applied to the station distribution of the Canadian national gravity data base and a series of sub-areas. A fractal dimension of 1.87 is maintained over a range of sizes from 15 km to over 1600 km. Although aliasing occurs, since the gravity field certainly contains much shorter wavelength anomalies, aliasing errors may be minimized by selecting the proper interpolation interval from the fractal analysis.     

Toward very high horizontal resolution NWP over the alps: Influence of increasing model resolution on the flow pattern

The increasing resolution of contemporary regional numerical weather prediction (NWP) models, reaching horizontal grid sizes of O(1 km), requires robust and reliable dynamical cores, working well beyond the approximation of quasi-horizontal flows. That stimulates an interest in an application for NWP purposes of dynamical cores based on the anelastic, or — more generally — sound-proof flow equations, and characterized by appropriate robustness and reliability. The paper presents results from testing the dynamical core of EULAG, the anelastic research model for multi-scale flows, as a prospective NWP dynamical core. The model simulates the semi-realistic frictionless and adiabatic flow over realistic steep Alpine topographies, employing horizontal grid sizes of 2.2, 1.1, and 0.55 km. The paper demonstrates not only the numerical robustness of EULAG, but also studies the influence of the varying horizontal resolution on the simulated flow. Results show that the increased horizontal resolution increases orographic drag on the flow. While the general flow pattern remains the same, increased resolution influences the flow on scales from hundreds of kilometers to meso-gamma scales. The differences are especially apparent in the near-surface layer of 1.5 to 3 km deep, and in the distribution and amplitudes of the orographically-induced gravity waves.