# Precipitation Machine ## --Estimating Precipitation from Atmospheric Dynamics using Machine Learning Overview Today, when we are making weather forecast, we are actually integrating forward a particular set of partial differential equations that characterizes the atmospheric dynamics. Generally, precipitation forecast contains more uncertainty compared to other atmospheric variables, for instance, pressure. This is because we can explicitly resolve pressure evolution at computing grids when integrating forward the atmospheric fluid dynamical equations; while we can not resolve precipitation, since it involves complicated cloud processes taking place at unresolved spatial scale. The unresolved precipitation process should be inferred from the resolved atmospheric dynamics. This inference process is critical for both precipitation forecast and many other precipitation-related aspects in earth system modeling. Conventionally, in atmospheric modeling, we adopt a mix of intuition, empiricism, and phenomenological laws to establish the relation between the unresolved physical process and resolved dynamics. This strategy is known as "parameterization". Here we provide a dataset that contains precipitation time series and its associated atmospheric dynamics. The primary objective is to leverage more accurate precipitation forecast by "learning" the connection between precipitation and atmospheric dynamics. Below we provide a brief description of the data and a simple example using convolutional neural networks. Data Description **_Precipitation Data_** The precipitation data are obtained from the *Climate Prediction Center (CPC) Unified Gauge-Based Analysis of Daily Precipitation* database. The database merges various information sources and is taken as the “realistic” precipitation records. The data cover 1948 to 2017 with resolution of 0.25°× 0.25°. To match the grid size of the dynamical field, the precipitation data are resampled to 32km× 32km using nearest neighbor method. **_Atmospheric Dynamics Data_** The predictors used for precipitation estimation are the geopotential height (GPH) and precipitable water (PW) field data. The data are obtained from the National Centers for Environmental Prediction (NCEP) North American Regional Reanalysis (NARR) dataset. The dataset is generated by regional downscaling of the NCEP Global Reanalysis for the North America region, using the NCEP Eta Model and the 3D Variational Data Assimilation System. Also, the updated Noah Land-surface model and numerous datasets additional to the global reanalysis were applied to improve the data quality. The dataset covers 1979 to near present and is provided every three hours, with spatial resolution of 32km/45 vertical layers. The every-3h total column PW, GPH at 500hPa, 850hPa and 1000hPa from 1979 to 2017 are provided here. Consider a characteristic wind speed of 10m/s. For a single day time, the dynamics within the coverage of 10m/s × 3600s/h × 24h ≈ 800km may exert direct impact on the precipitation process of a target geogrid. Thus, the dynamical field covers 800km×800km (25×25 grids). **_Baseline_** The precipitation product from the NARR is used as baseline here. It should be noted that the NARR precipitation product is not raw output from the numerical models, but is achieved by assimilating precipitation observations as latent heating profiles. Thus, the data quality is superior to the raw numerical precipitation estimates or conventional reanalysis precipitation products that do not assimilate precipitation. Thus, to beat baseline here constitutes a challenging task for the proposed model. An Example using Convolutional Neural Network To better illustrate the problem, we provide an example using convolutional neural network: Each 3h snapshot of the dynamical field is represented by a 4×25×25 tensor. 4 indicates that there are 4 variables types, namely GPH at 1000hPa, 850hPa, and 500hPa, as well as PW; 25×25 indicates that there are 25×25 grids surrounding the target geogrid. We process the dynamical field using a hierarchy of convolutional neural layers and max pooling layers for useful feature extraction. The extracted features are flattened and processes by two consecutive dense layers for precipitation estimation. A same CNN is mapped to several snapshots of the dynamical field in a single day time, and their outputs are summed up as the final estimate of the daily precipitation. We train the model to learn the precipitation-related dynamical features from the surrounding dynamical fields through optimizing the hierarchical set of spatial convolution kernels. Our results show significant advantage over baseline in frontal precipitation cases. Acknowledgements The CPC US Unified Precipitation data data are provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA. Data are available from their Web site at https://www.esrl.noaa.gov/psd/. The NARR data are provided by the the National Centers for Environmental Prediction (NCEP). Data are available from https://www.ncdc.noaa.gov/data-access/model-data/model-datasets/north-american-regional-reanalysis-narr. References Bukovsky, M. S., and D. J. Karoly (2007), A brief evaluation of precipitation from the North American Regional Reanalysis, Journal of Hydrometeorology, 8(4), 837–846. Lin, Y., K. Mitchell, E. Rogers, M. Baldwin, and G. DiMego (1999), Test assimilations of the real-time, multi-sensor hourly precipitation analysis into the NCEP Eta model, in Preprints, 8th Conf. on Mesoscale Meteorology, Boulder, CO, Amer. Meteor. Soc, pp. 341–344. Xie, P., M. Chen, and W. Shi (2010), CPC unified gauge-based analysis of global daily precipitation, in Preprints, 24th Conf. on Hydrology, Atlanta, GA, Amer. Meteor. Soc, vol. 2.