A Neural Network Approach to EstimateSnowfall Parameters from PassiveMicrowave RadiometerWei Huang∗December 19, 2008AbstractUsing space-borne passive microwave sensors to estimate snowfall for decades.Thermal emission from the precipitating systems provides the basis to infer bothspatial and temporal intensity of snowfall. Both physical and statistical methodshave been applied to map the observed microwave radiance (brightness tempera-ture) into snowfall. Physical inversion methods are based on forward modeling ofmicrowave radiative transfer through a model parameter space, the retrieval canbe achieved by finding the parameters that can provide smallest radiance differencewith the real observations; while statistical methods are based on direct relation ofmicrowave radiance and parameters observed from on-site snowfall gauge. In thispaper, a physically-based neural network approach is proposed. A 3-D precipita-tion model are applied to generate the training set, a neural network is developedto estimate the snowfall parameters from the real data. Comparisons with differentdata set and methods are performed.1 IntroductionThe comprehensive measurement of precipitation is valuable for a wide range of researcharea and related applications with practical benefits for human society. Due to the abilityof microwave radiation to penetrate clouds, space-borne, air-borne and ground basedpassive and active observations in the microwave band have been used for estimation ofprecipitation parameters over the last few decades ([1];[2]). Unlike air-borne and groundbased observation, space-borne microwave sensors are unique in being able to providemaps of precipitation on global scales.Quantitative retrieval methods of precipitation parameters through decoupling theobserved microwave signals are conveniently lumped into two basic categories: statisticaland physical. Statistical algorithms are those which are based primarily on empiricallydetermined relationships between satellite brightness temperatures and the parametersto 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] of the forward problem, that is, the prediction of brightness temperature from aknown state of the environment, coupled with some means for inverting the functional re-lationship in order to estimate the precipitation parameters from the satellite observation.Generally, different thermal sources contribute to the total signal of passive microwaveobservation. The problem of microwave observation inversion to obtain the snowfall rateis ill-posed, additional constrains has to be applied.Passive microwave sensors have channels located at window frequencies, in whichthe atmosphere is relatively transparent. As a result, the radiant energy observed bythe passive microwave sensors normally consists of some combination of surface emis-sion/reflection and the integrated emission and attenuation occurring in the atmosphere.In the process of retrieval of precipitation parameters, the surface spectral characteristicsneed to be carefully treated in order to extract the signal that is exclusively related toprecipitation. Over land, surface emissivity is typically about 0.9, and generally showsa large variability according to different surface type. Over the ocean, the situation isquite 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 hy-drometeors contribute to the total radiances observed by passive microwave sensors. Atthe window channels, rain attenuates and emits radiation more effectively than any otheratmospheric constituents. The emissivity of an optically thick rain cloud is more closerto unity than that of the ocean surface; rain may normally be observed against the coldocean surface as a drastic increase in brightness temperature. Unlike the liquid precipita-tion, the solid particles have a large single scattering albedo and can depress the observedbrightness temperature severely at higher frequencies. Estimations of snowfall were thusfocus on frequencies in 37 GHz and above.The empirical retrieval method, which resort to the use of measurement of parametersto be estimated and the observables(e.g. in the snowfall retrieval, surface snowfall rateis the quantity to be estimated and brightness temperature is the observable), is limiteddue to the lack of physical understanding of the problem. The physical retrieval methodsare typically based on the parameterization of precipitation microphysics and a set ofradiative transfer method. Furthermore, the retrieval of precipitation is generally based onmapping the observed brightness temperature to the predefined model output brightnesstemperature. It is apparent that, the quality of the physical retrieval generally depend ofthe representness of the forward model and the optimal method that will applied to findthe solution of ill posed problem. However, the optimization process which is to find asolution through a possible solution space is time consuming and can be formidable foroperational real-time snowfall retrieval ([4]). Neural network (NN) provides an alternativeto this kind of problem, although in the training stage computational time may be bigfor NN method, once the NN is set up, the NN can work as a robust and efficient methodfor 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.22 MethodologyAs aforementioned, ice particles have relatively low emissivity and high single scatteringalbedo, which makes snowfalls are only retrievable at higher frequencies. Also, in mostcases, the variability on surface type, water vapor, cloud vapor, makes the inversion ofsnowfall rate from microwave brightness temperature a ill posed problem. The accuracyof real case physical retrieval are particularly depend on the quality to represent the realworld snowfall of the pre-defined model space. The quality of the forward simulation isquite another issue, which is out of the scope of this project. To overcome the modelingproblem, snowfall on ocean surface was selected for this study. The ocean surface isrelatively well known and can be modeled with relatively high accuracy in
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