UC Irvine
UC Irvine Previously Published Works
Title
Improving Precipitation Estimation Using Convolutional Neural Network
Permalink
https://escholarship.org/uc/item/8nb145xd
Journal
Water Resources Research, 55(3)
ISSN
0043-1397
Authors
Pan, B
Hsu, K
AghaKouchak, A
et al.
Publication Date
2019-03-01
DOI
10.1029/2018WR024090
Copyright Information
This work is made available under the terms of a Creative Commons Attribution License,
availalbe at https://creativecommons.org/licenses/by/4.0/
Peer reviewed
eScholarship.org Powered by the California Digital Library
University of California
Improving Precipitation Estimation Using Convolutional
Neural Network
Baoxiang Pan
1
, Kuolin Hsu
1
, Amir AghaKouchak
1,2
, and Soroosh Sorooshian
1,2
1
Center for Hydrometeorology and Remote Sensing, University of California, Irvine, CA, USA,
2
Department of Earth
System Science, University of California, Irvine, CA, USA
Abstract Precipitation process is generally considered to be poorly represented in numerical
weather/climate models. Statistical downscaling (SD) methods, which relate precipitation with model
resolved dynamics, often provide more accurate precipitation estimates compared to model's raw
precipitation products. We introduce the convolutional neural network model to foster this aspect of SD
for daily precipitation prediction. Specifically, we restrict the predictors to the variables that are directly
resolved by discretizing the atmospheric dynamics equations. In this sense, our model works as an
alternative to the existing precipitation-related parameterization schemes for numerical precipitation
estimation. We train the model to learn precipitation-related dynamical features from the surrounding
dynamical fields by optimizing a hierarchical set of spatial convolution kernels. We test the model at
14 geogrid points across the contiguous United States. Results show that provided with enough data,
precipitation estimates from the convolutional neural network model outperform the reanalysis
precipitation products, as well as SD products using linear regression, nearest neighbor, random forest, or
fully connected deep neural network. Evaluation for the test set suggests that the improvements can be
seamlessly transferred to numerical weather modeling for improving precipitation prediction. Based on
the default network, we examine the impact of the network architectures on model performance. Also,
we offer simple visualization and analyzing approaches to interpret the models and their results. Our
study contributes to the following two aspects: First, we offer a novel approach to enhance numerical
precipitation estimation; second, the proposed model provides important implications for improving
precipitation-related parameterization schemes using a data-driven approach.
Plain Language Summary The precipitation process is not well simulated in numerical
weather models, since it takes place at the scales beyond the resolution of current models. We develop a
statistical model using deep learning technique to improve the estimation of precipitation in numerical
weather models.
1. Introduction
The modeling of the atmosphere is typically based on a particular set of partial differential equations, which
is derived by applying the conservation laws and thermodynamic laws on the continuous “control volume”
of the atmosphere (Bjerknes, 1906; Holton & Hakim, 2012). With the rapid growth of computing power, we
can discretize and resolve these equations on increasingly finer computing grids. However, there remains
many critical subgrid scale processes that are not explicitly resolved.
A well-concerned example is the precipitation process. Precipitation estimation involves explicit and implicit
representations of the cloud physics, such as the water vapor convection, phase change, and particle coa-
lescence. These processes take place at millimeter to molecule scales, which far surpass the resolution of
current numerical models (O(1 km)∕O(10 km)−O(100 km) for weather/climate models). Also, the assump-
tions of thermodynamic equilibrium and continuity lose their validity in describing some of the microscopic
processes (Stensrud, 2009), making it necessary to adopt supplementary equations for physically solid
simulations.
In numerical models, such unresolved processes are inferred from the resolved dynamics on the computa-
tional grid (Kalnay, 2003). This process is known as parameterization. Specific to precipitation, the directly
related parameterization schemes are cloud microphysics and subgrid convection. Given the intrinsic
RESEARCH ARTICLE
10.1029/2018WR024090
Special Section:
Big Data & Machine Learning in
Wa ter Sciences: Recent Progress
and Their Use in Advancing
Science
Key Points:
• We offer a novel approach to enhance
numerical precipitation estimation
using deep convolutional neural
network (CNN)
• The model provides important
implications for improving
precipitation-related
parameterization schemes
using a data-driven approach
• The CNN model outperforms
existing precipitation statistical
downscaling approaches by learning
dominant spatial dynamics features
Supporting Information:
• Supporting Information S1
Correspondence to:
B. Pan,
baoxianp@uci.edu
Citation:
Pan, B., Hsu, K., AghaKouchak, A.,
& Sorooshian, S. (2019). Improving
precipitation estimation using
convolutional neural network. Water
Resources Research, 55, 2301–2321.
https://doi.org/10.1029/2018WR024090
Received 19 SEP 2018
Accepted 9 JAN 2019
Accepted article online 15 JAN 2019
Published online 22 MAR 2019
©2019. American Geophysical Union.
All Rights Reserved.
PANETAL. 2301
Water Resources Research 10.1029/2018WR024090
complexity of the cloud and precipitation process, the equations and their associated parameters in these
parameterization schemes are generally of high structural and parametric uncertainties (Draper, 1995). As a
result, models' precipitation products are usually considered less reliable compared to the directly resolved
variables, such as pressure and temperature (Betts et al., 1998; Bukovsky & Karoly, 2007; Higgins et al., 1996;
Tian et al., 2017; Vitart, 2004).
Statistical downscaling (SD) methods are also used for the purpose of inferring the poorly represented pro-
cesses from the resolved dynamics and other data sources. However, SD has distinct objectives compared
to the parameterization schemes. The main purpose of parameterization is to depict the subgrid scale pro-
cesses for realistic atmosphere modeling. The primary concern for SD, as indicated by the name, is to resolve
the scale discrepancy between the existing model simulations and application requirements (Maraun et al.,
2010). Accordingly, the model input/output, resolution, usage, and complexity of parameterization schemes
and SD are different.
Besides the scaling issue, another aspect of SD is noted in practices: Compared to raw outputs or the
dynamically downscaled outputs from numerical models, SD occasionally provides more accurate estimates
of the unresolved processes. This is because SD is customized for specific objective, region, and climate
condition. The data-driven model with carefully designed model architecture and calibrated parameters
may outperform the default parameterization schemes in relating the unresolved processes to resolved
circulation. This phenomenon offers valuable implications for improving the relevant parameterization
schemes and opportunities for enhancing the prediction of the parameterized processes (Rasp et al., 2018;
Schneider et al., 2017).
Here we focus on fostering this aspect of SD for weather-scale precipitation forecast. Specifically, we propose
to improve the accuracy of daily precipitation estimates through relating the precipitation process with the
circulation data that are explicitly resolved in the atmospheric primitive equations. Compared to conven-
tional SD applications, the task here poses much higher requirements on model resolution and accuracy.
Recent developments in machine learning (ML) techniques, especially the branch of deep neural networks
(DNNs), offer an opportunity for describing and predicting such complicated physical processes using a
compose of big data and advanced model architectures. Here we illustrate how a particular form of DNN,
named convolutional neural network (CNN; LeCun et al., 1998), can be adapted to address the precipitation
estimation problem.
The rest of the paper is organized as follows: We start with a brief review of relevant works. Then, we
formulate the problem and illustrate the model requirements for this application.
The model is described and tested thereafter. We show the model results and provide methods for analyz-
ing and interpreting the models. We compare the model performance with some of the widely adopted SD
approaches. Conclusions are drawn at last.
2. Related Works
Many studies have been conducted on improving precipitation prediction accuracy with statistical
approaches. We review the relevant SD methods, for which the objective and methodology are closely related
to our work here. Also, we briefly review the basic concepts of DNNs, with a special emphasis on their
applications in physical processes.
2.1. Statistical Downscaling
Following the survey in Maraun et al. (2010), SD approaches are classified into perfect prognosis (PP),
model output statistics (MOS), and weather generators. Since the objective for our study is deterministic
precipitation prediction, we focus on SD approaches that make deterministic estimates of precipitation or
its estimation biases. This includes PP and MOS. The weather generator models are not reviewed here.
PP models construct statistical relations between the large-scale predictors and local scale predictands
(Fowler et al., 2007; Maraun et al., 2010). Both the predictors and predictands are considered to be realisti-
cally simulated or observed, hence the name of “perfect.” Along with the advancement of general circulation
models (GCMs), many precipitation PP methods have been developed. The simplest form is linear regres-
sion, which estimates precipitation using an optimized linear combination of the local circulation features
(Hannachi et al., 2007; Jeong et al., 2012; Li & Smith, 2009; Murphy, 2000). The predictors usually consist of
PANETAL. 2302
Water Resources Research 10.1029/2018WR024090
the raw variables or the leading principal components (PCs) of the moisture, pressure, and wind field (Wilby
& Wigley, 2000). Besides the linear models, there are also approaches that utilize the nonlinear features
of relevant circulation field, such as self-organizing map (Hope, 2006), support vector machine (Tripathi
et al., 2006), nearest neighbor (Gangopadhyay et al., 2005), random forest (Hutengs & Vohland, 2016), and
artificial neural network (ANN; Schoof & Pryor, 2001).
MOS stands for the practice of using statistical approaches to enhance the model's prediction accuracy
(Glahn & Lowry, 1972). Compared to PP, MOS is more frequently used in regional circulation models (RCMs)
than in GCMs (Maraun et al., 2010). Also, the predictors of MOS are numerical models' raw outputs, which
are not assumed to be perfectly estimated. For instance, a typical application of MOS is to correct the biases
of the numerical model's raw precipitation estimates (Jakob Themeßl et al., 2011). It should be noted that
the validity and universality of precipitation MOS rely on the consistency of precipitation estimation biases,
which is usually not guaranteed, given the continuous improvements of numerical models.
The performances of the above-mentioned SD approaches have been compared with dynamical downscaling
results (Ayar et al., 2016; Gutmann et al., 2012; Haylock et al., 2006; Murphy, 1999; Schmidli et al., 2007;
Tang et al., 2016). For instance, an intercomparison of six SD models and five RCMs for Europe indicated
that PP and MOS models achieved higher skill scores in estimating certain aspects of precipitation, such
as the occurrence and intensity (Ayar et al., 2016). On the other hand, another comparison study showed
clear advantage of RCMs for estimating precipitation over complex terrain (Schmidli et al., 2007). Overall,
the performance of SD depends on many factors, including the selection of predictors, the model and its
implementation, the available data, and the climate condition.
2.2. DNNs and Their Applications for Physical Processes
DNNs belong to the domain of ML, which covers a general scope of computer-aided statistical modeling.
DNNs differ from traditional ML approaches in their modeling workflow. In a canonical ML modeling pro-
cess, the raw form data, which quantify certain attributes of the study object, should be transformed into a
suitable feature vector before being effectively processed for the learning objective (Goodfellow et al., 2016;
LeCun et al., 2015). The feature extraction process is typically performed in separation with the modeling
process. Despite the expert knowledge and engineering works required for the feature extraction process,
a predefined feature extractor captures little useful information beyond our prior knowledge. This issue is
particularly severe for high-dimensional problems, where it is difficult to have foresight in the intricate but
important data structures.
On the other hand, DNNs, together with a broader family of representation learning approaches (Bengio
et al., 2013), offer an “end-to-end” modeling workflow: The feature extraction process is integrated into
the modeling process, which allows the model to learn customized features rather than subject to the
pre-engineered features.
DNNs learn to customize features through building multiple levels of representation of the data, which are
achieved by composing simple but nonlinear modules (named as neurons) that each transform the repre-
sentation at one level into a representation at a higher, slightly more abstract level (LeCun et al., 2015).
The differentiability of the hierarchical model allows applying the gradient descent algorithm to tune the
neurons' parameters in order to make the model exhibit desired behavior. This process is widely known as
backpropagation training (Rumelhart et al., 1985; Werbos, 1982). In addition to these basic concepts, mod-
ern DNNs involve numerous network architecture variations, training algorithms and tricks, regularization
methods, among others. A comprehensive review is beyond the scope of this work and can be found in
LeCun et al. (2015), Schmidhuber (2015), and Goodfellow et al. (2016). A transdisciplinary review of DNN
relevant to water resources-related research can be found in Shen (2018) and Shen et al. (2018).
DNNs have dramatically improved the state of the art in applications that cannot be adequately solved with
a deterministic rule-based solution, such as visual recognition (Krizhevsky et al., 2012), speech recognition
(Amodei et al., 2016), video prediction (Lotter et al., 2016), and natural language processing (Socher et al.,
2011). For the modeling of the natural physical processes, where we have established principled solutions
through analytic descriptions of the scientist's prior knowledge of the underlying processes (de Bezenac
et al., 2017), dynamical simulations are preferred to ML-based approaches. However, recent developments
showed that provided with (1) big amount of data and (2) well-designed network architectures that encode
PANETAL. 2303
Water Resources Research 10.1029/2018WR024090
Figure 1. (a) The case study area of a 32 km × 32 km geogrid centered at 46
◦
N, 122
◦
W. Its surrounding circulation field is delineated with the 800 km × 800 km
red polygon. (b) The geogrid's daily precipitation time series from 1979 to 2017. The red thick line represents the gage-based precipitation records from the
National Oceanic and Atmospheric Administration Climate Prediction Center (CPC); the blue slim line represents the model reanalysis records from the
National Centers for Environmental Prediction North American Regional Reanalysis Project (NARR). Data details are given in the section 5.1. (c) The every 3-hr
snapshots of the circulation profile for the storm event that happened on 7 November 2006. The g eopotential height (GPH) at 1,000, 850, and 500 hPa and the
total column precipitable water are obtained form NARR. Data are normalized by subtracting the field mean (
𝜇) and dividing by the field standard deviation (𝜎).
the physical background knowledge, DNNs are competitive with numerical methods in simulating complex
natural processes.
Generally, two motivations are found for adopting a data-driven model besides the classical dynamical
simulation. The first is computing efficiency. The computational demanding components in numerical sim-
ulations can be replaced by data-driven model counterparts to accelerate the simulation without significant
loss of accuracy. Examples include using DNNs to simulate the Eulerian fluid (Tompson et al., 2016) and
to predict the pressure field evolution in fluid flow (Wiewel et al., 2018). The other concern is to repre-
sent the unresolved processes beyond the original numerical simulation. For instance, Gentine et al. (2018)
trained a neural network to represent the subgrid scale convection process in atmospheric modeling. The
trained model was coupled in GCMs and skillfully predicted many of the convective heating, moistening,
and radiative features. Xie et al. (2018) applied a a conditional generative adversarial network to generate
spatiotemporal coherent high-resolution fluid flow based on its low-resolution estimates.
For the applications mentioned above, a particular DNN architecture named CNN acts as a core building
block. Compared to conventional neural networks, CNNs have significantly enhanced our capacity in pro-
cessing structured high-dimensional data. This is achieved by utilizing the inner structure of the data to
reduce the model structural redundancy and foster effective information extraction. Geophysical data are
intrinsically structured in space and time. The huge geophysical data sets from remote sensing observations,
numerical simulations, and their composite offer precious deposits for the application of DNNs (Tao et al.,
2016). CNNs have found applications in detecting extreme weather from the climate data sets (Liu et al.,
2016) and precipitation nowcasting (Shi et al., 2017; Xingjian et al., 2015). More related to our objective,
Vandal et al. (2017) developed a super-resolution convolutional neural network for precipitation SD. The
low-resolution precipitation field (
1
◦
) and elevation field data were fed into the super-resolution convolu-
tional neural network to produce the high-resolution precipitation field (
1
8
◦
). We noted that many of these
geophysical CNN applications took little use of the atmospheric dynamical modeling products, which offer
physically solid and comprehensive information of the atmosphere. While many recent research works have
started to explore the applicability of DNN for parameterizing the unresolved processes in fluid and geofluid
modeling (Ling et al., 2016; Rasp et al., 2018), it remains a question how DNN can translate the big data of
observations and numerical simulations into precipitation estimation improvements (Pan et al., 2017).
PANETAL. 2304
