Generating high-resolution climate maps from sparse and irregular observations using a novel hybrid RBF network

ABSTRACT Sparse and irregular climate observations in many developing countries are not enough to satisfy the need of assessing climate change risks and planning suitable mitigation strategies. The wide-used statistical downscaling model (SDSM) software tools use multi-linear regression to extract linear relations between large-scale and local climate variables and then produce high-resolution climate maps from sparse climate observations. The latest machine learning techniques (e.g. SRCNN, SRGAN) can extract nonlinear links, but they are only suitable for downscaling low-resolution grid data and cannot utilize the link to other climate variables to improve the downscaling performance. In this study, we proposed a novel hybrid RBF (Radial Basis Function) network by embedding several RBF networks into new RBF networks. Our model can well incorporate climate and topographical variables with different resolutions and extract their nonlinear relations for spatial downscaling. To test the performance of our model, we generated high-resolution precipitation, air temperature and humidity maps from 34 meteorological stations in Bangladesh. In terms of three statistical indicators, the accuracy of high-resolution climate maps generated by our hybrid RBF network clearly outperformed those using a multi-linear regression (MLR), Kriging interpolation or a pure RBF network.


Introduction
Climate change is the biggest threat that life on our planet is facing.Compared with the global air temperature during the period of 1850-1900, the mean air temperature of 2001-2020 has risen by about 0.99℃, and that from 2011 to 2020 has risen by 1.1℃; and it is expected that the air temperature in the twenty-first century will continue to rise by 1℃ to 3℃ (IPCC, 2021).As the global air temperature rises, the global water cycle will continue to strengthen, and more regions will possibly face a significant increase in precipitation, especially in most of monsoon regions.Increased precipitation will cause sea levels in coastal areas to rise with more frequent and severe flooding in the low-lying area.Many developing countries have been considered the most severely affected countries in the world by climate change, due to their low sea level, flat terrain, high population density and/or high dependence on the natural environment (Carpenter et al., 2018;Ahmed et al., 2015).Continued rise in air temperatures will bring the risk of irregular monsoons, earlier rainfall seasons and increased flooding in these countries.Moreover, since global warming would lead to further melting of glaciers, surface runoffs would increase significantly and further cause flooding.At the same time, the sparse and irregular distribution of meteorological stations in these developing countries is not enough to satisfy the need of assessing climate change risks and planning suitable mitigation strategies.
The emergence of statistical downscaling techniques has increased the possibility of obtaining high-resolution spatial data from sparse climate observations or low-resolution climate modeling data (Ramirez et al., 2006;Hashmi et al., 2011;Yhang et al., 2017).The simplest approach to generate high-resolution climate maps is based on various interpolation algorithms.Main disadvantages of interpolation-based downscaling lie in that the resulting climate maps often contain obviously unrealistic parallel ripples or ring-like structures (Zhang, 2023).Moreover, the accuracy of downscaled data by interpolation is not high due to the ignorance of topographic effects.With the rapid development of GCMs, the widely used statistical downscaling model (SDSM) software is to use multilinear regressions to establish the relationship between massive large-scale atmospheric circulation variables from GCM outputs and several small-scale meteorological variables (Chen et al., 2012;Wilby & Dawson, 2013).These techniques are relatively simple and easy to implement (Saidi et al., 2020;Wilby & Dawson, 2013).However, large-scale atmospheric circulations always affect local climate through a complex nonlinear non-stationary process, and the SDSM makes the improvement of downscaling performance significantly limited (Huth et al., 2008), especially when these large-scale atmospheric circulation variables are not available (Zaytar & El Amrani, 2016;Yi et al., 2018).Compared with traditional downscaling methods, machine learning techniques (e.g.CNN, SVM, LSTM) and deep learning techniques (e.g.SRCNN, SRGAN) can extract complex nonlinear links (Tolika et al., 2007;LeCun et al., 2015;Harilal et al., 2021;Kumar et al., 2021;Serifi et al., 2021).These emerging techniques, arising in computer science, take low-resolution images as inputs and output high-resolution ones (Harilal et al., 2021).They are only suitable for downscaling grid data; for example, high-resolution rainfall maps were generated by inputting grid rainfall and topography data to SRCNN and ResDeepD (Kumar et al., 2021(Kumar et al., , 2023;;Mishra Sharma & Mitra, 2022).Although Harilal et al. (2021) used several gridded modeling variables in the input of LSTM to increase the accuracy of high-resolution climate projections, this method cannot utilize the link among observed climate variables with irregular distribution to improve the accuracy of high-resolution historical climate maps.
In this study, we developed a hybrid RBF network in downscaling processing which can generate climate maps with arbitrarily high resolution from sparse and irregular observation data.The main advantages include: (i) Its input is non-grid data while existing machine learning methods depends on grid data; (ii) It utilizes the link among sparse observed climate data to improve downscaling performance while existing methods only consider topographic effects; (iii) It has a very low computation cost.In downscaling experiments, inputting observed climate data from irregularly distributed 34 meteorological stations in Bangladesh to our hybrid RBF network, we generated high-resolution climate maps in Bangladesh.The average resolution of irregularly distributed 34 meteorological stations is about 0.5°×0.5°,and the resolution of the output high-resolution climate maps is 0.1°×0.1°.In terms of three error indicators, the accuracy of highresolution climate maps generated by our hybrid RBF network clearly outperformed those using a multiple linear regression (MLR), Kriging interpolation or a pure RBF network.

RBF network model
The radial basis function (RBF) is usually a function with a local sensing domain; that is, only when the input falls on a small designated area in the input space, the hidden neuron will make a meaningful non-zero response (Fritzke, 1994).The three commonly used RBFs are a Gaussian function, a Reflected Sigmoidal (RS) function and an Inverse Multiquadrics (IM) function as follows: where σ is called the expansion constant of the RBF.
The RBF network is a three-layer static feedforward neural network.The first layer is the input layer, which is composed of signal nodes, the second layer is the hidden layer, which is composed of multiple neurons, and the third layer is the output layer.An RBF network uses a radial basis function as the activation function in the hidden layer.The relation between the input x ¼ x 1 ; x 2 . . .x n ½ � and the output Y ¼ y 1 ; y 2 . . .y s ½ � in an RBF network with m nodes can be represented as: where w j is the weight of connecting the hidden layer to the output layer; f j is the radial basis function (i.e.Gaussian, RS or IM), c j is the center vector.The RBF network has strong nonlinear mapping ability and strong self-learning ability.When there are enough hidden layer nodes, the learning process of RBF networks can approximate any nonlinear process with arbitrary accuracy; even with sparse samples, RBF neural networks can still maintain good simulation performance.

Hybrid RBF network for generating high-resolution climate maps
Developing countries are sensitive to global and regional climate change.Unfortunately, the distribution of meteorological stations in these countries is often sparse.Therefore, it is crucial to produce high spatial resolution climate maps to satisfy the need of assessing climate change risks and adopting suitable mitigation measures.As various climate variables are closely linked, we need to establish a new model to make full use of both sparse observed climate (e.g.temperature, precipitation, humidity) and continuous topographical (e.g.longitude, latitude, elevation) data to produce high-resolution climate maps.Since the resolution of irregularly distributed observed climate data is much lower than that of topographical data, it is impossible to directly input climate and geographical data to a regular neural network.In order to solve this issue, we propose the hybrid RBF network and use it to generate high-resolution climate maps through two steps (Figure 1): Step 1.We consider all climate variables separately at first and roughly view each climate variable as a function of longitude, latitude and altitude.We establish an RBF network whose input and output are three topographical variables (longitude, latitude and altitude) and one climate variable, respectively.We used longitude, latitude, elevation and observed climate data from sparse meteorological stations to train the RBF network and then determined the parameters of the RBF network, i.e. searched the optimal parameters w j and c j in Formula (1).Finally, based on this RBF, by inputting different topographical data (longitude, latitude and altitude), we can roughly downscale each climate variable.Although the accuracy of these downscaled climate data is not enough, their resolution can be made the same as that of topographical data.
Step 2. In order to make full use of strong nonlinear relationship between climate variables, we viewed each climate variable as a function of longitude, latitude and altitude and the remaining climate variables.Then, we can establish a new RBF network whose input is three topographical variables (longitude, latitude and altitude) and the remaining climate variables.Since we have downscaled roughly each climate variable in Step 1, all input topographical and climate data have the same spatial resolution.Finally, based on this new RBF, we can downscale each climate variable by making full use of nonlinear/ non-stationary relation among climate and topographical variables and generated highresolution climate maps.In the above downscaling process, since several RBF networks are embedded into a new RBF network, we call the whole process a hybrid RBF network.
In the evaluation of the downscaling performance of our hybrid RBF networks, we adopt a wide-used approach in machine learning models (i.e.5-fold cross test method).It randomly divides the input data from irregularly distributed meteorological stations into two groups: the training data and the test data.The ratio of the training dataset to the test data is 4:1.The training data is used to establish a machine learning model and the test data is used to evaluate the performance of the model.This process will be repeated five times until all stations are selected once.The performance of our downscaling model is measured by three criterions: Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), and Coefficient Determination (R 2 ), i.e.
where fy s g are the observed values at meteorological stations and fy � s g are the downscaling values.

Study area and data
Bangladesh is bordered on the west, north and east by India, on the southeast by Myanmar, and on the south by the Bay of Bengal.It is a nation of rivers, mainly located on river delta plains in the South Asian subcontinent.As a low-lying country, flood-prone areas account for 80% of the country.The average elevation of tidal floodplains is <1 m, and the average elevation of major river and estuary floodplains is 1-3 m.Only the northeast and southeast portions of Bangladesh are hilly, with some tertiary hills over 1000 meters above sea level (Ahammed et al., 2019).
Bangladesh's climate is affected significantly by south Asia monsoon.Since the monsoon generally starts in June and ends in October, Bangladesh can be divided into four seasons: namely winter (December to February), pre-monsoon (March to May), monsoon (June to early October), and post-monsoon (late October to November) (Alamgir et al., 2019).The winter is relatively cold and dry, with an average minimum temperature of 10.1°C and a maximum of 27°C.In winter, the temperature in the southern region is 5°C higher than that in the northern region.Before the onset of the monsoon, the average temperature can climb as high as 36.7°C, and the temperature peaks in April.In the whole country, the average temperature before the monsoon shows a decreasing trend from the southwest to the northeast.The southwest is warmer and the northeast is colder Hoque et al. (2020).Since the monsoon can bring a lot of precipitation, the climate during the monsoon season is generally hot and humid.Three-quarters of the precipitation in a year occurs during the monsoon season.After the monsoon season, the precipitation decreases and the air temperature gradually decreases.
Due to topographical and environmental factors, the distribution of 34 meteorological stations in Bangladesh is sparse and their average resolution is about 0.5°×0.5°(Figure 2, Table 1).The daily temperature, precipitation and humidity data during the period of 1999-2018 were collected from all meteorological stations of Bangladesh Meteorological Department.Topographical data (longitude, latitude and altitude) was extracted from GoogleEarth.In order to demonstrate the downscaling performance of our hybrid RBF networks, by applying 5-fold cross test method, we randomly chose the observed climate data from 27 meteorological stations (i.e.training datasets) to train the hybrid RBF model and then generate climate maps with resolution 0.1°×0.1°,and then used the observation data from the remaining 7 meteorological stations (test datasets) to evaluate the performance.This process will be repeated five times by using different training datasets and test datasets.

Precipitation
We used our hybrid RBF network to downscale sparse daily-observed precipitation data and generated high-resolution precipitation maps, where Gaussian, Reflected Sigmoidal (RS) and Inverse Multiquadrics (IM) functions were chosen as the radial basis function in our hybrid RBF network.In order to make full use of nonlinear relation among precipitation, humidity and air temperature, we first performed a coarse downscaling for humidity    and air temperature as in Figure 1.Then we performed a fine downscaling for precipitation using obtained downscaled humidity and air temperature data and continuous topographical data (longitude, latitude and altitude).
The accuracy performance of high-resolution monthly precipitation maps by our hybrid RBF network, multi-linear regression (MLR), Kriging interpolation and pure RBF network was demonstrated in Table 2.
Our hybrid RBF network model significantly outperformed the MLR model and Kriging interpolation.The MAPE and MAE (mm/month) 2 values of the hybrid RBF network were 6. 69%-12.23% and 17.76-20.26lower than that of MLR model, respectively, and the R 2 values of the hybrid RBF neural network was 0.11-0.15higher than that of the MLR model.The MAPE and MAE (mm/month) 2 values of the hybrid RBF network were 12.4-17.94%and 13.03-15.53lower than that of the Kriging model, respectively; and the R 2 value of the hybrid RBF neural network was 0.28-0.32higher than that of the Kriging model.
Our hybrid RBF neural network also outperformed a pure RBF model.On average, the R 2 value of the hybrid RBF neural network increased by 0.09 on average, and the MAPE and MAE (mm/month) 2 of hybrid RBF network decreased by 4.36% and 8.79, respectively.This improvement is due to our making full use of a nonlinear relationship between air temperature, humidity and precipitation.Since coarse downscaling of air temperature and humidity was used as the input to strengthen the learning ability of the model, our hybrid RBF model achieved more accurate downscaling results of precipitation.Among three kinds of hybrid RBF networks, choosing Gaussian functions as RBFs always produced the best accuracy in generating high-resolution climate maps.
The accuracy performance of high-resolution weekly precipitation maps by four models was demonstrated in Table 3.Our hybrid RBF network significantly outperformed MLR and Kriging interpolation.The MAPE values of the hybrid RBF network were 5.46%-10.39%and 8.67%-13.6%lower than that of MLR and Kriging interpolation, respectively.The MAE (mm/week) 2 values of the hybrid RBF network were 4.75-7.17and 8.27-10.69lower than that of MLR and Kriging interpolation, respectively; and the R 2 values of the hybrid RBF network were 0.12-0.15and 0.15-0.18higher than that of MLR and Kriging interpolation.Our hybrid RBF neural network also outperformed a pure RBF model.On average, the R 2 value of the hybrid RBF neural network increased by 0.09 on average, and the MAPE and MAE (mm/week) 2 of hybrid RBF network decreased by 2.21% and 8.05, respectively.
The Kolmogorov-Smirnov (K-S) test is a nonparametric goodness-of-fit test and we used it to test whether two distributions are same or not.The higher the P-value is, the more similar two distributions are.We carried out the K-S Test to compare observed monthly precipitation distribution at different meteorological stations and downscaled precipitation distribution by MLR, Kriging interpolation, pure RBF network and Hybrid RBF network.Table 4 demonstrates the average P-value of the K-S test on different meteorological stations from test datasets of model.The p-value of the hybrid RBF network was much higher than that of the pure RBF network, MLR and Kriging interpolation. Figure 3 demonstrates the corresponding probability distribution function of mean observed and downscaled monthly precipitation at all meteorological stations from test datasets of model.The precipitation maps generated by hybrid RBF network matched the observed precipitation better.The high-resolution map of mean annual precipitation in Bangladesh during the period of 1999-2018 generated by hybrid RBF networks with Gaussian/RS/IM functions and the MLR model are shown in Figure 4. Patterns and spatial trends in precipitation maps generated by the three kinds of hybrid RBF networks were similar, and were different from that by the MLR and the Kriging interpolation.Even in high altitude areas, the precipitation distribution has been well reproduced by hybrid RBF networks.The spatial distribution of precipitation shows an increasing trend from the north (south) to the center.The north and southeast regions of Bangladesh (i.e.Chittagong and Sylhet regions) have the most annual precipitation.
Figures 5-7 demonstrate high-resolution mean monthly precipitation maps in Bangladesh generated by the hybrid RBF network with a Gaussian function, MLR and Kriging interpolation.Many of the high-resolution precipitation maps generated by MLR and Kriging interpolation contained obviously unrealistic parallel ripples.By Tables 2-4, high-resolution mean monthly precipitation in Figure 5 had the highest accuracy.It demonstrated that monthly precipitation concentrated mainly in northern and southeastern regions of Bangladesh.Affected by south Asia monsoon, monthly precipitation begins to increase significantly since March, and it reaches the maximum from June to August.When the monsoon season ends, monthly precipitation decreases significantly after September.

Air temperature
We used our hybrid RBF network to generate high-resolution air temperature maps from sparsely observed air temperature data in Bangladesh.The performance of various models was demonstrated in Table 5.Our hybrid RBF network significantly outperformed the MLR and Kriging interpolation.The MAPE values of hybrid RBF network were 0.78%-0.8%and 2.62%-2.73%lower than that of MLR and Kriging interpolation, respectively.The MAE (℃/month) 2 values of hybrid RBF network were 0.26-0.34and 0.31-0.39lower than that of MLR and Kriging interpolation, respectively, and the R 2 values of hybrid RBF network were 0.14-0.18and 0.29-0.33higher than that of MLR and Kriging interpolation, respectively.Our hybrid RBF network also outperformed the pure RBF network.This improvement is due to the fact that coarse downscaling of precipitation and humidity was used as the input to strengthen the learning ability of the model.The accuracy performance of high-resolution weekly air temperature maps generated by the four models is demonstrated in Table 6.The performance of our hybrid RBF network was significantly superior to MLR and Kriging interpolation.The MAPE values of the hybrid RBF network were 0.2%-2.28%and 1.47%-1.55%lower than that of MLR and Kriging interpolation, respectively.The MAE (℃/week) 2 values of the hybrid RBF network were 0.22-0.29 and 0.33-0.4lower than that of MLR and Kriging interpolation, respectively; and the R 2 values of the hybrid RBF network were 0.11-0.13and 0.2-0.22 higher than that of the MLR and Kriging interpolation.Our hybrid RBF network also   outperformed a pure RBF network.On average, the R 2 value of the hybrid RBF network increased by 0.08 on average, and the MAPE and MAE (mm/week) 2 of hybrid RBF network decreased by 0.13% and 0.04, respectively.Similar to downscaled precipitation distribution, we also conducted a K-S test to compare observed and downscaled air temperature distribution generated by the four models.Table 7 demonstrates the average P-value of the K-S test on different stations.The P-value of the hybrid RBF network was much higher than those of the remaining three methods, and it indicates that downscaled air temperature maps generated by the hybrid RBF network matched the observed air temperature best.To compare probability distribution function of mean downscaled monthly air temperature at meteorological stations of test datasets of model (Figure 8), the distribution air temperature distribution by the hybrid RBF network is the closest to the distribution of the observed data.
In aspect of spatial distribution (Figure 9), high-resolution annual precipitation maps generated by three hybrid RBF networks were similar, and different from those by MLR and Kriging interpolation.The mean annual air temperature can reach 33°C in regions such as the north of Chittagong, the west of Rangpur and Rajshahi.However, in the southeast and north of Bangladesh, the mean annual air temperature is as low as about 21°C in regions, such as Chittagong, Dhaka and Sylhet.This is mainly because these regions have relatively high altitudes and more precipitation.obviously unrealistic parallel ripples.By Tables 5-7, high-resolution mean monthly air temperature in Figure 10 had the highest accuracy.The air temperature in Bangladesh rises rapidly from March due to the influence of the monsoon.The monsoon period (June to August) not only ushered in the rainy season, but also ushered in the hottest period of the year; notably the highest air temperature in the northeast reaches 38°C.From October to next February, the mean monthly air temperature in the northeast and southwest regions was relatively low.This difference is caused by the influence of topography.

Humidity
Similar to precipitation and air temperature, we used the hybrid RBF network to generate high-resolution humidity maps, where air temperature and precipitation data obtained after coarse downscaling were also used as inputs into the model.The performance of hybrid RBF networks was still better than MLR and Kriging interpolation (Table 8).Its R 2 values were 0.12-0.16and 0.1-0.14 higher than that of MLR and Kriging interpolation, respectively.The MAPE values were 0.84%-1.04%and 0.52%-0.72%lower than those of  MLR and Kriging interpolation, respectively; and the MAE (%rh/month) 2 values were 0.46-0.6 and 0.4-0.54lower than those of MLR and Kriging interpolation, respectively.The accuracy of the hybrid RBF network model was significantly improved compared with a pure RBF neural network (Table 8): the R 2 value increased from 0.81-0.86 to 0.90-0.94,and the MAPE and MAE (%rh/month) 2 values decreased by 0.34% and 0.27 on average, respectively.
To generate downscaled weekly humidity maps, the hybrid RBF network was also significantly superior to MLR model and Kriging interpolation (Table 9).The MAPE values of the hybrid RBF network were 1.24-1.26%and 0.74-0.76%lower than that of MLR and Kriging interpolation, respectively.The MAE (%rh/week) 2 values of the hybrid RBF network were 0.32-0.38 and 0.36-0.42lower than that of MLR and Kriging interpolation, respectively; and the R 2 values of the hybrid RBF network were 0.1-0.13 and 0.1-0.13higher than that of the MLR model and Kriging interpolation.The accuracy performance of the hybrid RBF network was significantly improved compared with a pure RBF network (Table 9): the R 2 value increased from 0.85-0.92 on average, and the MAPE and MAE (%rh/ week) 2 values decreased by 0.64% and 0.2 on average, respectively.The K-S test results showed that the downscaled monthly humidity maps by the hybrid   RBF network attained the highest P-value (Table 10); and the associated probability distribution function is the closest to that of observed data (Figure 13).
The spatial distribution maps of high-resolution mean annual humidity generated by the four models are demonstrated in Figure 14.By Table 9, the hybrid RBF network with a Gaussian function can generate the best high-resolution humidity maps, and different from those by MLR and Kriging interpolation.The spatial distribution of annual humidity is high in the South and Southeast, and low in the middle.Such humidity change mainly depends on their distance from the ocean.

Conclusion
Many developing countries are always extremely vulnerable to climate change due to their rain-fed agriculture and weak industry basis.These countries need urgently to measure evolution patterns and resulting disastrous effects of climate change.At the same time, the distribution of meteorological stations in these countries are always very sparse and irregular.Therefore, the obtained climate data is not enough to satisfy their needs of mitigating climate change risks.The widely-used statistical downscaling model (SDSM) software uses multi-linear regression to extract linear relations between largescale and local climate variables and then produces high-resolution climate maps from sparse climate observations.However, large-scale atmospheric circulations always affect local climate through a complex nonlinear non-stationary process.The latest deep learning techniques (e.g.SRCNN, SRGAN), whose principles are to take low-resolution images as inputs and output high-resolution ones, can well extract nonlinear links, but they are only suitable for downscaling low-resolution grid data.In this study, by embedded several RBF networks into new RBF networks, we proposed a novel hybrid RBF network structure to generate climate maps with arbitrarily high resolution from sparse and irregular observation data.The main advantages include: (i) Its input is non-grid data while existing machine learning methods depends on grid data; (ii) It utilizes the link among sparse observed climate data to improve downscaling performance while existing methods only consider topographic effects; (iii) It has a very low computation cost.The high-accuracy and high-resolution climate maps generated by our hybrid RBF network model will become a necessary tool for these developing countries to build data-driven climate disaster monitoring system and make suitable decisions in mitigating climate risks.

Figure 1 .
Figure 1.Generation of high-resolution climate maps by the hybrid RBF network.

Figure 2 .
Figure 2. Distribution of meteorological stations in Bangladesh.

Figure 3 .
Figure 3. Probability distribution function of observed and downscaled monthly precipitation generated by the four models.

Figure 5 .
Figure 5. High-resolution maps of mean monthly precipitation in Bangladesh during the period of 1999-2018 generated by the Hybrid RBF network with a Gaussian function.

Figure 4 .
Figure 4. High-resolution maps of mean annual precipitation in Bangladesh during the period of 1999-2018 generated by hybrid RBF networks with a Gaussian/RS/IM function, an MLR model and a Kriging interpolation.

Figure 7 .
Figure 7. High-resolution maps of mean monthly precipitation in Bangladesh during the period of 1999-2018 generated by the Kriging interpolation.

Figure 6 .
Figure 6.High-resolution maps of mean monthly precipitation in Bangladesh during the period of 1999-2018 generated by the MLR model.
Figures 10-12 demonstrate high-resolution mean monthly air temperature maps in Bangladesh generated by the hybrid RBF network with a Gaussian function, MLR model and Kriging interpolation.Similar to precipitation maps, many of high-resolution air temperature maps generated by MLR model and Kriging interpolation contained

Figure 8 .
Figure 8. Probability distribution function of observed and downscaled monthly air temperature by Hybrid RBF network, Pure RBF networks, MLR and Kriging interpolation.

Figure 9 .
Figure 9. High-resolution mean annual temperature maps by hybrid RBF networks with Gaussian/RS/ IM function, MLR and Kriging interpolation.

Figure 10 .
Figure 10.High-resolution mean monthly air temperature maps generated by the hybrid RBF network with a Gaussian function.

Figure 12 .
Figure 12.High-resolution mean monthly air temperature maps generated by the Kriging interpolation.

Figure 11 .
Figure 11.High-resolution mean monthly air temperature maps generated by the MLR model.

Figure 14 .
Figure 14.High-resolution maps of mean annual humidity by hybrid RBF networks with Gaussian/RS/ IM function, MLR model and Kriging interpolation.

Figure 13 .
Figure 13.Probability distribution function of observed and simulated monthly humidity by hybrid RBF networks, pure RBF networks, MLR model and Kriging interpolation.
Figure 16.High-resolution mean monthly humidity maps generated by the MLR model.

Figure 15 .
Figure 15.High-resolution mean monthly humidity maps generated by the hybrid RBF network with a Gaussian function.

Figure 17 .
Figure 17.High-resolution mean monthly humidity maps generated by the Kriging interpolation.

M
. James C. Crabbe is a Professor and Fellow at Oxford University and the University of Reading, UK.His research focuses on climate change and ecosystems.Prof. Crabbe has served as a member of the Executive Committee of the UK Deans of Science, a member of the Council of University Deans of Arts, Social Sciences and Humanities, and a member of the Boards of the EU.Prof. Crabbe has won the 6th Aviva/Earthwatch International Award for Climate Change Research.

Table 1 .
Geographical locations of 34 meteorological stations.

Table 2 .
The average accuracy of downscaled monthly precipitation for the four models.

Table 3 .
The average accuracy of downscaled weekly precipitation map generated by the four models.

Table 4 .
The K-S test on downscaled monthly precipitation maps.

Table 5 .
The average accuracy of downscaled monthly air temperature downscaled by the four models

Table 7 .
The K-S test on downscaled monthly air temperature.

Table 8 .
The average accuracy of downscaled monthly humidity by the four models

Table 10 .
The K-S test on downscaled monthly humidity maps by four models.