A scattering-based over-land rainfall retrieval algorithm for South Korea using GCOM-W1/AMSR-2 data

Heavy summer rainfall is a primary natural disaster affecting lives and properties in the Korean Peninsula. This study presents a satellite-based rainfall rate retrieval algorithm for the South Korea combining polarization-corrected temperature (PCT) and scattering index (SI) data from the 36.5 and 89.0 GHz channels of the Advanced microwave Scanning Radiometer 2 (AMSR-2) onboard the Global Change Observation Mission (GCOM)-W1 satellite. The coefficients for the algorithm were obtained from spatial and temporal collocation data from the AMSR-2 and groundbased automatic weather station rain gauges from 1 July - 30 August during the years, 2012-2015. There were time delays of about 25 minutes between the AMSR-2 observations and the ground raingauge measurements. A new linearly-combined rainfall retrieval algorithm focused on heavy rain for the PCT and SI was validated using ground-based rainfall observations for the South Korea from 1 July - 30 August, 2016. The validation presented PCT and SI methods showed slightly improved results for rainfall > 5 mm h^-1 compared to the current ASMR-2 level 2 data. The best bias and root mean square error (RMSE) for the PCT method at AMSR-2 36.5 GHz were 2.09 mm h^-1 and 7.29 mm h^-1, respectively, while the current official AMSR-2 rainfall rates show a larger bias and RMSE (4.80 mm h^-1 and 9.35 mm h^-1, respectively). This study provides a scatteringbased over-land rainfall retrieval algorithm for South Korea affected by stationary front rain and typhoons with the advantages of the previous PCT and SI methods to be applied to a variety of spaceborne passive microwave radiometers.     

Long-term variation of rainfall erosivity in Calabria (Southern Italy)

The changes in rainfall erosivity have been investigated using the rainfall erosivity factor (R) proposed for USLE by Wischmeier and Smith (R _W-S ) and some simplified indexes (the Fournier index modified by Arnoldus, F, a regional index spatial independent, R _Fr , and a regional index spatial dependent, R _Fs ) estimated by indirect approaches. The analysis has been carried out over 48 rainfall stations located in Calabria (Southern Italy) using data collected in the period 1936–2012 and divided in three sub-periods. The series of the erosivity indexes and of some precipitation variables have been analyzed for evidence of trends using standard methods. The simplified indexes suggested a general underestimation of the rainfall erosivity with respect to R _W-S . The mean underestimation ranged between 23 and 54 % for R _Fr and from 10 to 15 % for R _Fs . Both the sign and the magnitude of the trends were different for the different stations depending on the variable and sub-period considered. In general, the erosivity increased during the period 1936–1955 (1^st sub-period) and during the more recent sub-period (1992–2012, 3^rd sub-period), whereas it decreased during 1958–1977 (2^nd sub-period). The evidence of trends was generally higher for R _W-S than for R _Fr and R _Fs . Focusing on the most recent sub-period (3^rd sub-period), all the variables analyzed showed mainly increasing trends but with different magnitude. More particularly, R _W-S showed a mean increment of 29 %; F, R _Fr and R _Fs increased by 11, 15 and 18 %, respectively; the maximum intensity of 0.5-h precipitation increased by 5 %; and the annual precipitation increased by 22 %. Consequently, it remains difficult to define which precipitation variable plays the dominant role in the temporal variation of rainfall erosivity in the region. However, the overall results suggest that the indexes estimated by indirect procedures (F, R _Fr , and R _Fs ) should be used with caution for climate change analysis, despite they are used for practical purposes considering they are based on easily available information.     

Preparation of frost atlas using different interpolation methods in a semiarid region of south of Iran

In this research, suitability of different kriging and inverse distance weighted (IDW) methods in estimating occurrence date of frost was evaluated. Data included minimum daily air temperature values from 27 meteorological stations of Fars province in southern Iran from 18 to 45 years. Data ranges of 0 to ?1.5, ?1.5 to ?3 and below ?3°C were considered as mild, moderate and severe frost intensities, respectively. Starting with the first day of autumn, iso-occurrence days for the frost intensities and occurrence probabilities (25%, 50%, 75% and 90%) were estimated using ordinary kriging, cokriging, residual kriging type 1 (RK1), residual kriging type 2 (RK2), universal kriging and IDW methods. In these models, the errors of estimated frost intensities at different probabilities were lowest in the RK2 model, but lack of establishment of spatial structure due to long distance between stations caused the predictions not to be acceptable in some cases. In a proposed method (modified inverse distance weighted, MIDW), the trend between the first and last days of frost occurrence with earth elevation was removed, and the reminder values were estimated by (IDW) method. Although, the errors for estimated frost dates by MIDW and RK2 methods were the same, but the MIDW method did not have the spatial establishment shortcoming. Furthermore, the simplicity and practicality of the MIDW method makes it a reasonable selection.     

Comprehensive modeling of monthly mean soil temperature using multivariate adaptive regression splines and support vector machine

Soil temperature (T _s) and its thermal regime are the most important factors in plant growth, biological activities, and water movement in soil. Due to scarcity of the T _s data, estimation of soil temperature is an important issue in different fields of sciences. The main objective of the present study is to investigate the accuracy of multivariate adaptive regression splines (MARS) and support vector machine (SVM) methods for estimating the T _s. For this aim, the monthly mean data of the T _s (at depths of 5, 10, 50, and 100 cm) and meteorological parameters of 30 synoptic stations in Iran were utilized. To develop the MARS and SVM models, various combinations of minimum, maximum, and mean air temperatures (T _min, T _max, T); actual and maximum possible sunshine duration; sunshine duration ratio (n, N, n/N); actual, net, and extraterrestrial solar radiation data (R _s, R _n, R _a); precipitation (P); relative humidity (RH); wind speed at 2 m height (u ₂); and water vapor pressure (V_p) were used as input variables. Three error statistics including root-mean-square-error (RMSE), mean absolute error (MAE), and determination coefficient (R ²) were used to check the performance of MARS and SVM models. The results indicated that the MARS was superior to the SVM at different depths. In the test and validation phases, the most accurate estimations for the MARS were obtained at the depth of 10 cm for T _max, T _min, T inputs (RMSE = 0.71 °C, MAE = 0.54 °C, and R ² = 0.995) and for RH, V _p, P, and u ₂ inputs (RMSE = 0.80 °C, MAE = 0.61 °C, and R ² = 0.996), respectively.     

Modeling monthly meteorological and agronomic frost days,based on minimum air temperature,in Center-Southern Brazil

Although Brazil is predominantly a tropical country, frosts are observed with relative high frequency in the Center-Southern states of the country, affecting mainly agriculture, forestry, and human activities. Therefore, information about the frost climatology is of high importance for planning of these activities. Based on that, the aims of the present study were to develop monthly meteorological (F _MET) and agronomic (F _AGR) frost day models, based on minimum shelter air temperature (T _MN), in order to characterize the temporal and spatial frost days variability in Center-Southern Brazil. Daily minimum air temperature data from 244 weather stations distributed across the study area were used, being 195 for developing the models and 49 for validating them. Multivariate regression models were obtained to estimate the monthly T _MN, once the frost day models were based on this variable. All T _MN regression models were statistically significant (p < 0.001), presenting adjusted R ² between 0.69 and 0.90. Center-Southern Brazil is mainly hit by frosts from mid-fall (April) to mid-spring (October). The period from November to March is considered as frost-free, being very rare a frost day within that period. Monthly F _MET and F _AGR presented significant sigmoidal relationships with T _MN (p < 0.0001), with adjusted R ² above of 0.82. The residuals of the frost day models were random, which means that the sigmoidal models performed quite well for interpreting the frost day variability throughout the study area. The highlands of Santa Catarina, Rio Grande do Sul, São Paulo, and Minas Gerais had in average more than 25 and 13 frosts per year, respectively, for F _MET and F _AGR. The F _MET and F _AGR maps developed in this study for Center-Southern Brazil is a useful tool for farmers, foresters, and researchers, since they contribute to reduce frost spatial and temporal uncertainty, helping in planning project for strategic purposes. Furthermore, the monthly F _MET and F _AGR maps for this Brazilian region are the first zoning of these variables for the country.     

Polarimetric rainfall retrieval from a C-Band weather radar in a tropical environment (The Philippines)

We evaluated the potential of polarimetric rainfall retrieval methods for the Tagaytay C-Band weather radar in the Philippines. For this purpose, we combined a method for fuzzy echo classification, an approach to extract and reconstruct the differential propagation phase, Φ _DP , and a polarimetric self-consistency approach to calibrate horizontal and differential reflectivity. The reconstructed Φ _DP was used to estimate path-integrated attenuation and to retrieve the specific differential phase, K _DP . All related algorithms were transparently implemented in the Open Source radar processing software wradlib. Rainfall was then estimated from different variables: from re-calibrated reflectivity, from re-calibrated reflectivity that has been corrected for path-integrated attenuation, from the specific differential phase, and from a combination of reflectivity and specific differential phase. As an additional benchmark, rainfall was estimated by interpolating the rainfall observed by rain gauges. We evaluated the rainfall products for daily and hourly accumulations. For this purpose, we used observations of 16 rain gauges from a five-month period in the 2012 wet season. It turned out that the retrieval of rainfall from K _DP substantially improved the rainfall estimation at both daily and hourly time scales. The measurement of reflectivity apparently was impaired by severe miscalibration while K _DP was immune to such effects. Daily accumulations of rainfall retrieved from K _DP showed a very low estimation bias and small random errors. Random scatter was, though, strongly present in hourly accumulations.     

Statistics of the <Emphasis Type="Italic">Z</Emphasis>–<Emphasis Type="Italic">R</Emphasis> Relationship for Strong Convective Weather over the Yangtze–Huaihe River Basin and Its Application to Radar Reflectivity Data Assimilation for a Heavy Rain Event

The relationship between the radar reflectivity factor (Z) and the rainfall rate (R) is recalculated based on radar observations from 10 Doppler radars and hourly rainfall measurements at 6529 automatic weather stations over the Yangtze–Huaihe River basin. The data were collected by the National 973 Project from June to July 2013 for severe convective weather events. The Z–R relationship is combined with an empirical q_r–R relationship to obtain a new Z–q_r relationship, which is then used to correct the observational operator for radar reflectivity in the three-dimensional variational (3DVar) data assimilation system of the Weather Research and Forecasting (WRF) model to improve the analysis and prediction of severe convective weather over the Yangtze–Huaihe River basin. The performance of the corrected reflectivity operator used in the WRF 3DVar data assimilation system is tested with a heavy rain event that occurred over Jiangsu and Anhui provinces and the surrounding regions on 23 June 2013. It is noted that the observations for this event are not included in the calculation of the Z–R relationship. Three experiments are conducted with the WRF model and its 3DVar system, including a control run without the assimilation of reflectivity data and two assimilation experiments with the original and corrected reflectivity operators. The experimental results show that the assimilation of radar reflectivity data has a positive impact on the rainfall forecast within a few hours with either the original or corrected reflectivity operators, but the corrected reflectivity operator achieves a better performance on the rainfall forecast than the original operator. The corrected reflectivity operator extends the effective time of radar data assimilation for the prediction of strong reflectivity. The physical variables analyzed with the corrected reflectivity operator present more reasonable mesoscale structures than those obtained with the original reflectivity operator. This suggests that the new statistical Z–R relationship is more suitable for predicting severe convective weather over the Yangtze–Huaihe River basin than the Z–R relationships currently in use.     

Spatiotemporal variations in rainfall erosivity during the period of 1960–2011 in Guangdong Province,southern China

Rainfall erosivity, which shows a potential risk of soil loss caused by water erosion, is an important factor in soil erosion process. In consideration of the critical condition of soil erosion induced by rainfall in Guangdong Province of southern China, this study analyzed the spatial and temporal variations in rainfall erosivity based on daily rainfall data observed at 25 meteorological stations during the period of 1960–2011. The methods of global spatial autocorrelation, kriging interpolation, Mann–Kendall test, and continuous wavelet transform were used. Results revealed that the annual rainfall erosivity in Guangdong Province, which spatially varied with the maximum level observed in June, was classified as high erosivity with two peaks that occur in spring and summer. In the direction of south–north, mean annual rainfall erosivity, which showed significant relationships with mean annual rainfall and latitude, gradually decreased with the high values mainly distributed in the coastal area and the low values mainly occurring in the lowlands of northwestern Guangdong. Meanwhile, a significant positive spatial autocorrelation which implied a clustered pattern was observed for annual rainfall erosivity. The spatial distribution of seasonal rainfall erosivity exhibited clustering tendencies, except spring erosivity with Moran’s I and Z values of 0.1 and 1.04, respectively. The spatial distribution of monthly rainfall erosivity presented clustered patterns in January–March and July–October as well as random patterns in the remaining months. The temporal trend of mean rainfall erosivity in Guangdong Province showed no statistically significant trend at the annual, seasonal, and monthly scales. However, at each station, 1 out of 25 stations exhibited a statistically significant trend at the annual scale; 4 stations located around the Pearl River Delta presented significant trends in summer at the seasonal scale; significant trends were observed in March (increasing trends at 3 stations), June (increasing trends at 4 stations located in the Beijiang River Basin), and October (decreasing trends at 4 stations) at the monthly scale. In accordance with the mean annual rainfall over Guangdong Province, the mean annual rainfall erosivity showed two significant periodicities of 3–6 and 10–12 years at a confidence level of 95 %. In conclusion, the results of this study provide insights into the spatiotemporal variation in rainfall erosivity in Guangdong Province and support for agrolandscape planning and water and soil conservation efforts in this region.     

Changes in temporal concentration property of summer precipitation in China during 1961–2010 based on a new index

Based on the property of entropy, a new index Q was defined to measure the temporal concentration property of summertime daily rainfall in China, based on daily precipitation data collected at 553 observation stations in China during 1961–2010. Furthermore, changes in the temporal concentration property of summer precipitation in China were investigated. The results indicate that the regions with larger Q values were located in most parts of Northwest China and the north of the Yellow River, where daily precipitation tended to become temporally concentrated during the study period. On the contrary, smaller Q values were found in eastern Tibetan Plateau, southeastern Northwest China, and most parts of Southwest and South China. The most obvious increasing trend of Q index was found in South China and most parts of Southwest China, where precipitation showed a temporal concentration trend. However, a decreasing trend of Q index was found in Northwest China, the Tibetan Plateau, and the north of the Huaihe River. Variations of the Q index and the summer rainfall total during 1961–2010 in China both exhibited an increasing trend, implying larger temporal variability in rainfall attributes. It is illustrated that the summer precipitation in general became more temporally concentrated with more intense rainfall events and wetter days.     

Estimation of ground heat flux from soil temperature over a bare soil

Ground soil heat flux, G ₀, is a difficult-to-measure but important component of the surface energy budget. Over the past years, many methods were proposed to estimate G ₀; however, the application of these methods was seldom validated and assessed under different weather conditions. In this study, three popular models (force-restore, conduction-convection, and harmonic) and one widely used method (plate calorimetric), which had well performance in publications, were investigated using field data to estimate daily G ₀ on clear, cloudy, and rainy days, while the gradient calorimetric method was regarded as the reference for assessing the accuracy. The results showed that harmonic model was well reproducing the G ₀ curve for clear days, but it yielded large errors on cloudy and rainy days. The force-restore model worked well only under rainfall condition, but it was poor to estimate G ₀ under rain-free conditions. On the contrary, the conduction-convection model was acceptable to determine G ₀ under rain-free conditions, but it generated large errors on rainfall days. More importantly, the plate calorimetric method was the best to estimate G ₀ under different weather conditions compared with the three models, but the performance of this method is affected by the placement depth of the heat flux plate. As a result, the heat flux plate was recommended to be buried as close as possible to the surface under clear condition. But under cloudy and rainy conditions, the plate placed at depth of around 0.075 m yielded G ₀ well. Overall, the findings of this paper provide guidelines to acquire more accurate estimation of G ₀ under different weather conditions, which could improve the surface energy balance in field.     

Statistical characteristics of environmental parameters for warm season short-duration heavy rainfall over central and eastern China

Water vapor content,instability,and convergence conditions are the key to short-duration heavy rainfall forecasting.It is necessary to understand the large-scale atmospheric environment characteristics of shortduration heavy rainfall by investigating the distribution of physical parameters for different hourly rainfall intensities.The observed hourly rainfall data in China and the NCEP final analysis（FNL）data during 1May and 30 September from 2002 to 2009 are used.NCEP FNL data are 6-hourly,resulting in sample sizes of 1573370,355346,and 11401 for three categories of hourly rainfall（P）of no precipitation(P<0.1 mm h^-1),ordinary precipitation(0.1≤P<20 mm h^-1),and short-duration heavy rainfall(P≥20.0 mm h^-1),respectively,by adopting a temporal matching method.The results show that the total precipitable water（PWAT）is the best parameter indicating the hourly rainfall intensity.A PWAT of 28 mm is necessary for any short-duration heavy rainfall.The possibility of short-duration heavy rainfall occurrence increases with PWAT,and a PWAT of 59 mm is nearly sufficient.The specific humidity is a better indicator than relative humidity.Both 700-and 850-hPa relative humidity greater than 80%could be used to determine whether or not it is going to rain,but could not be used to estimate the rainfall intensity.Temperature and potential pseudo-equivalent temperature are also reasonable indicators of short-duration heavy rainfall.Among the atmospheric instability parameters,the best lifted index（BLI）performs best on the shortduration rainfall discrimination;the next best is the K index（KI）.The three rainfall categories are not well recognized by total totals（TT）or the temperature difference between 850 and 500 hPa（DT85）.Threequarters of short-duration heavy rainfall occurred with BLI less than-0.9,while no short-duration heavy rainfall occurred when BLI was greater than 2.6.The minimum threshold of KI was 28.1 for short-duration heavy rainfall.The importance of dynamic conditions was well demonstrated by the 925-and 850-hPa divergence.The representativeness of 925-hPa divergence is stronger than that of 850 hPa.Three-quarters of short-duration heavy rainfall occurred under a negative divergence environment.However,both the best convective potential energy（BCAPE）and vertical wind shear were unable to discriminate the hourly rainfall intensities.     

Utilization of PSO algorithm in estimation of water level change of Lake Beysehir

In this study, unlike backpropagation algorithm which gets local best solutions, the usefulness of particle swarm optimization (PSO) algorithm, a population-based optimization technique with a global search feature, inspired by the behavior of bird flocks, in determination of parameters of support vector machines (SVM) and adaptive network-based fuzzy inference system (ANFIS) methods was investigated. For this purpose, the performances of hybrid PSO-ε support vector regression (PSO-εSVR) and PSO-ANFIS models were studied to estimate water level change of Lake Beysehir in Turkey. The change in water level was also estimated using generalized regression neural network (GRNN) method, an iterative training procedure. Root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R ²) were used to compare the obtained results. Efforts were made to estimate water level change (L) using different input combinations of monthly inflow-lost flow (I), precipitation (P), evaporation (E), and outflow (O). According to the obtained results, the other methods except PSO-ANN generally showed significantly similar performances to each other. PSO-εSVR method with the values of minMAE = 0.0052 m, maxMAE = 0.04 m, and medianMAE = 0.0198 m; minRMSE = 0.0070 m, maxRMSE = 0.0518 m, and medianRMSE = 0.0241 m; minR ² = 0.9169, maxR ² = 0.9995, medianR ² = 0.9909 for the I-P-E-O combination in testing period became superior in forecasting water level change of Lake Beysehir than the other methods. PSO-ANN models were the least successful models in all combinations.     

Analysis of photosynthetically active radiation and applied parameterization model for estimating of PAR in the North China Plain

As photosynthetically active radiation (PAR) variability and PAR estimating methods play an important role in climate change and ecological process research, PAR variation trends and broadband global solar radiation (R _s ) ratios (PAR/R _s ) in the North China Plain (NCP) are examined using in situ PAR and R _s observed data for 2005 to 2011. The annual average PAR value found in the NCP is 22.9 mol m^?2 d^?1. The highest and lowest values were recorded at Changwu and Luancheng sites, respectively. The highest PAR/R _s value was found in Jiaozhouwan due to large water vapor volumes present in this area. PAR/R _s levels have increased in the NCP due to a decrease in fine aerosols and increase in water vapor concentration. From these analysis results, a parameterization model that can be applied to all sky conditions was checked. Empirical estimation model comparisons for obtaining PAR values indicate that model was least accurate when R _s was used independently. When the model included R _s, the clearness index (K _s) and the solar zenith angle, the model estimated PAR values with acceptable accuracy. A parameterization model was constructed by considering K _s and attenuation factors of PAR under clear weather conditions (ρ _clear). The improved parameterization model more accurately predicts values for local sites and for various observation sites.     

Geo-spatial analysis of temporal trends of temperature and its extremes over India using daily gridded (1°×1°) temperature data of 1969–2005

Daily gridded (1°×1°) temperature data (1969–2005) were used to detect spatial patterns of temporal trends of maximum and minimum temperature (monthly and seasonal), growing degree days (GDDs) over the crop-growing season (kharif, rabi, and zaid) and annual frequencies of temperature extremes over India. The direction and magnitude of trends, at each grid level, were estimated using the Mann–Kendall statistics (α = 0.05) and further assessed at the homogeneous temperature regions using a field significance test (α=0.05). General warming trends were observed over India with considerable variations in direction and magnitude over space and time. The spatial extent and the magnitude of the increasing trends of minimum temperature (0.02–0.04 °C year^?1) were found to be higher than that of maximum temperature (0.01–0.02 °C year^?1) during winter and pre-monsoon seasons. Significant negative trends of minimum temperature were found over eastern India during the monsoon months. Such trends were also observed for the maximum temperature over northern and eastern parts, particularly in the winter month of January. The general warming patterns also changed the thermal environment of the crop-growing season causing significant increase in GDDs during kharif and rabi seasons across India. The warming climate has also caused significant increase in occurrences of hot extremes such as hot days and hot nights, and significant decrease in cold extremes such as cold days and cold nights.     

Recent trends in annual snowline variations in the northern wet outer tropics: case studies from southern Cordillera Blanca,Peru

TL-moments approach has been used in an analysis to identify the best-fitting distributions to represent the annual series of maximum streamflow data over seven stations in Johor, Malaysia. The TL-moments with different trimming values are used to estimate the parameter of the selected distributions namely: Three-parameter lognormal (LN3) and Pearson Type III (P3) distribution. The main objective of this study is to derive the TL-moments (t ₁,0), t ₁?=?1,2,3,4 methods for LN3 and P3 distributions. The performance of TL-moments (t ₁,0), t ₁?=?1,2,3,4 was compared with L-moments through Monte Carlo simulation and streamflow data over a station in Johor, Malaysia. The absolute error is used to test the influence of TL-moments methods on estimated probability distribution functions. From the cases in this study, the results show that TL-moments with four trimmed smallest values from the conceptual sample (TL-moments [4, 0]) of LN3 distribution was the most appropriate in most of the stations of the annual maximum streamflow series in Johor, Malaysia.     

A compact form for the analytic description of temperature dependence of saturation vapor pressure over plane surfaces of water and ice

A possibility is studied of extending the range of action of the simple three-parameter formula (ITS-90 scale) proposed in the previous work of the author [2] for the dependence of saturation vapor pressure E on temperature T within the range of 250 to 490 K. The results demonstrated that the dependence ln[E(T)/E(T _bas)] = (T - T _bas)[A - B(T - T _bas) + C(T - T _bas)²]/T with four sets of coefficients A, B, and C obtained using one base temperature Tbas equal to the temperature of triple point of water T _t = 273.16 K and two additional base values T _bas2 = 473.16 K and T _bas3 = 623.16 K makes it possible to approximate rather accurately the initial experimental and computed data in the temperature range from the point of homogeneous freezing of 235 K to the critical temperature of 647 K for liquid water and from 193 K to T _t for ice. A procedure used for obtaining the inverse function T(E) by solving the third-degree algebraic equation is validated. A hypothesis is proposed for the physical substantiation of additional base points in the form of “a noticeable appearance of dimers at the point T _bas2 and their 100% concentration at the temperature T _bas3.”     

Investigation of dominant modes of monsoon ISO in the northwest and eastern Himalayan region

This study investigates the altitudinal variation of dominant modes of summer monsoon intra-seasonal oscillation (ISO) over the Northwest (NWH) and Eastern Himalayan (EH) region using (i) spatially scattered 133 number of station rainfall observations and (ii) latitudinal transect-wise (LT) rainfall variation, obtained from an observed interpolated gridded rainfall data for the period 1995–2004. The altitudinal variation of dominant modes of monsoon ISO were investigated by exploring the strong and weak phases of the principal components of 10–90 days bandpass rainfall data of June to September with respect to location specific station height. Investigation of frequency of days for light and moderate rainfall along with the occurrence of total seasonal rainy days has revealed existence of a rainfall maximum around 2100 m height for the NWH region. Similarly, the total seasonal rainy days of EH region was found to have maxima between 1100 and 1400 m height. Analyses of the spatially scattered station rainfall observation for the NWH region showed that the strong periods of ISO modes exist around 747.9 (±131.7) m and 2227.2 (±100.2) m heights. Over the EH region, the dominant modes of the monsoon ISO were found to be centred around 1200 m. Significant alterations of strong and weak phases of monsoon ISO as a response to altitudinal variation in the mountain surface were observed when latitudinal transect-wise variation of monsoon ISO modes were investigated.     

Projection methods for error suppression in the meteorological fields before calculation of derivatives

In finite-difference approximation of derivatives on a grid with step of h, the error decreases with decreasing h. However, if the original function is given on a grid with an error of order of ?, then the approximate differentiation error grows like C?h ^k , where k is the derivative order and C is a constant depending on a chosen finite-difference approximation. Projection methods are discussed that are designed to decrease the errors of this kind. On the latitude-longitude grids, the step near the poles along the latitude circles is very small. Methods are proposed for projecting scalar and vector meteorological fields on the subspaces of smooth fields. The projected fields obtained take into account asymptotics of the smooth fields in the vicinity of the pole in the spherical coordinates, separately for each Fourier harmonic in longitude. Results are presented of such smoothing in the polar regions on the fields of objective analysis by Hydrometeorological Center of Russia and on the first-guess fields at standard isobaric heights.     

Relationship Between Fine-Particle Pollution and the Urban Heat Island in Beijing,China: Observational Evidence

Urbanization has led to a significant urban heat island (UHI) effect in Beijing in recent years. At the same time, air pollution caused by a large number of fine particles significantly influences the atmospheric environment, urban climate, and human health. The distribution of fine particulate matter (PM_2.5) concentration and its relationship with the UHI effect in the Beijing area are analyzed based on station-observed hourly data from 2012 to 2016. We conclude that, (1) in the last five years, the surface concentrations of PM_2.5 averaged for urban and rural sites in and around Beijing are 63.2 and 40.7 µg m^?3, respectively, with significant differences between urban and rural sites (ΔPM_2.5) at the seasonal, monthly and daily scales observed; (2) there is a large correlation between ΔPM_2.5 and the UHI intensity defined as the differences in the mean (ΔT_ave), minimum (ΔT_min), and maximum (ΔT_max) temperatures between urban and rural sites. The correlation between ΔPM_2.5 and ΔT_min (ΔT_max) is the highest (lowest); (3) a Granger causality analysis further shows that ΔPM_2.5 and ΔT_min are most correlated for a lag of 1–2 days, while the correlation between ΔPM_2.5 and ΔT_ave is lower; there is no causal relationship between ΔPM_2.5 and ΔT_max; (4) a case analysis shows that downwards shortwave radiation at the surface decreases with an increase in PM_2.5 concentration, leading to a weaker UHI intensity during the daytime. During the night, the outgoing longwave radiation from the surface decreases due to the presence of daytime pollutants, the net effect of which is a slower cooling rate during the night in cities than in the suburbs, leading to a larger ΔT_min.     

Retrieving air humidity,global solar radiation,and reference evapotranspiration from daily temperatures: development and validation of new methods for Mexico. Part III: reference evapotranspiration

We evaluated two methods to estimate evapotranspiration (ETo) from minimal weather records (daily maximum and minimum temperatures) in Mexico: a modified reduced set FAO-Penman-Monteith method (Allen et al. 1998, Rome, Italy) and the Hargreaves and Samani (Appl Eng Agric 1(2): 96–99, 1985) method. In the reduced set method, the FAO-Penman-Monteith equation was applied with vapor pressure and radiation estimated from temperature data using two new models (see first and second articles in this series): mean temperature as the average of maximum and minimum temperature corrected for a constant bias and constant wind speed. The Hargreaves-Samani method combines two empirical relationships: one between diurnal temperature range ΔT and shortwave radiation Rs, and another one between average temperature and the ratio ETo/Rs: both relationships were evaluated and calibrated for Mexico. After performing a sensitivity analysis to evaluate the impact of different approximations on the estimation of Rs and ETo, several model combinations were tested to predict ETo from daily maximum and minimum temperature alone. The quality of fit of these models was evaluated on 786 weather stations covering most of the territory of Mexico. The best method was found to be a combination of the FAO-Penman-Monteith reduced set equation with the new radiation estimation and vapor pressure model. As an alternative, a recalibration of the Hargreaves-Samani equation is proposed.