A Neural Network Approach To Estimate Snowfall Parameters From Passive

A Neural Network Approach to Estimate Snowfall Parameters from Passive Microwave Radiometer Wei Huang∗ December 19, 2008

Abstract Using space-borne passive microwave sensors to estimate snowfall for decades. Thermal emission from the precipitating systems provides the basis to infer both spatial and temporal intensity of snowfall. Both physical and statistical methods have been applied to map the observed microwave radiance (brightness temperature) into snowfall. Physical inversion methods are based on forward modeling of microwave radiative transfer through a model parameter space, the retrieval can be achieved by finding the parameters that can provide smallest radiance difference with the real observations; while statistical methods are based on direct relation of microwave radiance and parameters observed from on-site snowfall gauge. In this paper, a physically-based neural network approach is proposed. A 3-D precipitation model are applied to generate the training set, a neural network is developed to estimate the snowfall parameters from the real data. Comparisons with different data set and methods are performed.

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Introduction

The comprehensive measurement of precipitation is valuable for a wide range of research area and related applications with practical benefits for human society. Due to the ability of microwave radiation to penetrate clouds, space-borne, air-borne and ground based passive and active observations in the microwave band have been used for estimation of precipitation parameters over the last few decades ([1];[2]). Unlike air-borne and ground based observation, space-borne microwave sensors are unique in being able to provide maps of precipitation on global scales. Quantitative retrieval methods of precipitation parameters through decoupling the observed microwave signals are conveniently lumped into two basic categories: statistical and physical. Statistical algorithms are those which are based primarily on empirically determined relationships between satellite brightness temperatures and the parameters to retrieved. Physical algorithms, on the other hand, depend on an accurate theoretical Depart. of Atmospheric and Oceanic Science, Univ. of Wisc at Madison. Contact email: [email protected] ∗

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solution of the forward problem, that is, the prediction of brightness temperature from a known state of the environment, coupled with some means for inverting the functional relationship in order to estimate the precipitation parameters from the satellite observation. Generally, different thermal sources contribute to the total signal of passive microwave observation. The problem of microwave observation inversion to obtain the snowfall rate is ill-posed, additional constrains has to be applied. Passive microwave sensors have channels located at window frequencies, in which the atmosphere is relatively transparent. As a result, the radiant energy observed by the passive microwave sensors normally consists of some combination of surface emission/reflection and the integrated emission and attenuation occurring in the atmosphere. In the process of retrieval of precipitation parameters, the surface spectral characteristics need to be carefully treated in order to extract the signal that is exclusively related to precipitation. Over land, surface emissivity is typically about 0.9, and generally shows a large variability according to different surface type. Over the ocean, the situation is quite different. Water surface have microwave emissivities which are both relatively low (0.3 <  < 0.7) and highly polarized. When precipitation presents, additional microwave radiances from precipitation hydrometeors contribute to the total radiances observed by passive microwave sensors. At the window channels, rain attenuates and emits radiation more effectively than any other atmospheric constituents. The emissivity of an optically thick rain cloud is more closer to unity than that of the ocean surface; rain may normally be observed against the cold ocean surface as a drastic increase in brightness temperature. Unlike the liquid precipitation, the solid particles have a large single scattering albedo and can depress the observed brightness temperature severely at higher frequencies. Estimations of snowfall were thus focus on frequencies in 37 GHz and above. The empirical retrieval method, which resort to the use of measurement of parameters to be estimated and the observables(e.g. in the snowfall retrieval, surface snowfall rate is the quantity to be estimated and brightness temperature is the observable), is limited due to the lack of physical understanding of the problem. The physical retrieval methods are typically based on the parameterization of precipitation microphysics and a set of radiative transfer method. Furthermore, the retrieval of precipitation is generally based on mapping the observed brightness temperature to the predefined model output brightness temperature. It is apparent that, the quality of the physical retrieval generally depend of the representness of the forward model and the optimal method that will applied to find the solution of ill posed problem. However, the optimization process which is to find a solution through a possible solution space is time consuming and can be formidable for operational real-time snowfall retrieval ([4]). Neural network (NN) provides an alternative to this kind of problem, although in the training stage computational time may be big for NN method, once the NN is set up, the NN can work as a robust and efficient method for estimation of snowfall rate. The structure of the project is as follows: Sec.2 describes the major methodology, Sec.3 gives the major result, Sec.4 presents the major conclusion.

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Methodology

As aforementioned, ice particles have relatively low emissivity and high single scattering albedo, which makes snowfalls are only retrievable at higher frequencies. Also, in most cases, the variability on surface type, water vapor, cloud vapor, makes the inversion of snowfall rate from microwave brightness temperature a ill posed problem. The accuracy of real case physical retrieval are particularly depend on the quality to represent the real world snowfall of the pre-defined model space. The quality of the forward simulation is quite another issue, which is out of the scope of this project. To overcome the modeling problem, snowfall on ocean surface was selected for this study. The ocean surface is relatively well known and can be modeled with relatively high accuracy in comparison to that of land. There are large amount of snowfalls near Wakasabay near Japan in the winter time. The primary mechanism of the intensive, large scale snow fall is the heating of cold air from the continent by the relatively warm ocean surface. Large sets of historical data are available for both validation and research purpose. A numerical weather prediction model WRF was applied to generate 3D distribution of snowfall near Wakasabay in 12/19/2003. A Monte-Carlo method by Petty [3] was adopted to generate the 2D brightness temperature at 18.7, 36.5 and 89.0 GHz, which is comparable to that of Adanced Microwave Scanning Radiometer (AMSR). Real data set for AMSR in 12/25/2005 near Wakasabay, as well as the radar retrieved snowfall rate which were supposed to be the ground truth for researcher in meteorology field, were used as testing case. The overall pattern of the two precipitation process do not differ too much, which facilitate the retrieval process by training NN to the model. For this radiometric application, a feed forward neural network are chosen , which has a layer of No observables and a hidden layer of neurons with tan-sigmoid transfer functions and Nh hidden layer with a linear transfer functions and 1 output neuron for the snowfall rate estimation. The neural network was setup by the standard Matlab package. Instead of the standard back-propagation, for a faster training, the Levenberg-Marquardt method algorithm was selected for training stage. Results and discussion are shown in following sections.

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Results and Discussion

Different neural network configurations are selected to tested the validity of the NN method used in these study. The first experiment is the selection of feature vectors. Since the brightness temperatures are the combination of different thermal sources, the frequencies that are most related to the snowfall need to be determined so as to gain a better result. Once the proper feature space is decided, the configuation of the NN, such as the number of the hidden layer, has to be tested. The simulated brightness temperature field are shown in Fig. 1, and snowfall rate through NN are shown in Fig. 2. The result of the numerical experiment is presented in Tab.1. Following features can be grasped from these experiments. Generally, larger number of hidden layer can have a better prediction of the snowfall rate, e.g with the same feature vectors , the NN with larger number of hidden layer neurons perform better than small number of hidden layer neurons. From the experiments, it is apparent that, the snowfall rate is most correlated to high frequencies, adding higher frequency can generate

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Frequency(GH) 18.7 18.7 36.5 36.5 89.0 89.0 18.7,36.5 18.7,36.5 36.5,89.0 36.5,89.0 18.7,89.0 18.7,89.0 18.7,36.5,89.0 18.7,36.5,89.0

NN config 1-4-1 1-15-1 1-4-1 1-15-1 1-4-1 1-15-1 1-4-1 1-15-1 1-4-1 1-15-1 1-4-1 1-15-1 1-4-1 1-15-1

Training Corr. 0.6917 0.7832 0.9399 0.9410 0.8848 0.9443 0.9322 0.9538 0.9401 0.9801 0.9210 0.9411 0.9712 0.9799

Testing Corr. 0.6036 0.7151 0.8898 0.9203 0.7626 0.8485 0.9210 0.9320 0.8917 0.9533 0.8736 0.8910 0.9328 0.9412

Table 1: Different NN configuration and correlation with the real snowfall rate

better results. However, single frequency such as the 36.5, 89.0GHz can not provide a global view of the response of snow to that of microwave. Only combined multichannel retrieval can reach an acceptable result. Low frequencies, which are supposed to react more to that of liquid cloud water, can sometime even lower the accuracy of the retrieval, this might be the reason that, the structure of cloud layer can deviate from that of snowfall area, thus make a noise term in the snowfall retrieval. It is also interesting that, adding all the channels does not justify a increase of performance of the NN, which suggests that selecting a good feature space may be a top issue.

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Conclusion

From the study above, it can be conclude that, the NN provide a fast and statistical basis that the accuracy of which can be comparable to conventional optimization process. The NN method has the advantage that, once NN is set up, no exhaustive computational time has to be consumed in order to achieve acceptable results. However, the NN in nature provide a more accurate optimization problem, the quality of the forward model is the key part in the snowfall retrieval.

References [1] R. F. Adler, C. Kidd, G. Petty, M. Morrissey, and H. M. Goodman. Intercomparison of global precipitation products: The Third Precipitation Intercomparison Project (PIP-3). Bull. Amer. Meteor. Soc., 82(7):1377–1396, 2001. [2] C. Kidd. Satellite rainfall climatology: A review. Int. J. Clim., 21(9):1041–1066, July 2001.

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Figure 1: Brightness temperature at 36.5 and 89 GHz on vertical and horizontal polarization

[3] G. W. Petty. Physical retrievals of over-ocean rain rate from multichannel microwave imagery. Part I: Theoretical characteristics of normalized polarization and scattering indices. Meteorol. Atmos. Phys., 54(1-4):79–100, 1994. [4] G. W. Petty. Physical and microwave radiative properties of precipitating clouds. Part II: A parametric 1d rain-cloud model for use in microwave radiative transfer simulations. J. Appl. Meteor., 40(12):2115–2129, 2001.

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Figure 2: (A.) NN on the training set. (B.) True mapping of snowfall rate in the training stage (C.) NN on the real set (D.) True mapping of snowfall rate in the testing stage

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