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  • Lee, T. H., J. E. Janowiak, and P. A. Arkin, 1991: Atlas of products from the algorithm intercomparison project 1: Japan and surrounding oceanic regions June–August 1989. University Corporation for Atmospheric Research, Boulder, Colorado, 139 pp. [Available from the Climate Analysis Center, NOAA, Washington, DC 20233.].

  • Lovejoy, S., and G. L. Austin, 1979: The delineation of rain areas from visible and IR satellite data for GATE and mid-latitudes. Atmos.–Ocean,17, 77–92.

  • Murao, H., I. Nishikawa, S. Kitamura, M. Yamada, and P. Xie, 1993: A hybrid neural network system for the rainfall estimation using satellite imagery. Proceedings of International Joint Conference on Neural Networks, IEEE Press, 1211–1214.

  • Negri, A. J., and R. F. Adler, 1993: An intercomparison of three satellite infrared rainfall techniques over Japan and surrounding waters. J. Appl. Meteor.,32, 357–373.

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  • Simpson, J., R. F. Adler, and G. R. North, 1988: A proposed Tropical Rainfall Measuring Mission (TRMM) satellite. Bull. Amer. Meteor. Soc.,69, 278–295.

  • Wu, R., J. A. Weinman, and R. T. Chin, 1985: Determination of rainfall rates from GOES satellite images by pattern recognition techniques. J. Atmos. Oceanic Technol.,2, 314–330.

  • Xie, P., and P. A. Arkin, 1996: Analyses of global monthly precipitation using gauge observations, satellite estimates, and model predictions. J. Climate,9, 840–858.

  • View in gallery

    Study areas: (a) Japanese islands and (b) Florida peninsula.

  • View in gallery

    Statistics for the relationships between surface rainfall rate and cloud-top IR brightness temperature Tb for (a) the Japanese islands mean rainfall rate (R: solid line) and associated standard deviation (σR: bar plot) for eight IR brightness temperature ranges and (b) the average R–Tb relationships identified for three different seasonal/regional cases. These plots were prepared using GMS satellite IR imagery and AMeDAS ground-based rain-rate estimates for Japan, and the GOES-8 satellite IR imagery and NEXRAD radar-based rain-rate estimates for Florida.

  • View in gallery

    The structure of a three-layer feedforward artificial neural network and the detail of each internal processing element.

  • View in gallery

    The structure of the ModifiedCounter Propogation Network ANN model and its input–output variables.

  • View in gallery

    Estimates of the observed and computed monthly rainfall distributions for three test cases: (subplots Ia–Id) case I—Japan, June 1989, frontal rainfall; (subplots IIa–IId) case II—Japan, 15 July to 15 August 1989, tropical convective rainfall; (subplots IIIa–IIId) case III—Florida peninsula, January 1996. In all cases, a is the ground-based estimate, b is the GPI method estimate, c is the ANN fixed parameter model estimates, and d is the ANN adaptive parameter model estimates.

  • View in gallery

    Scatterplots comparing observed monthly rainfall distributions for three test cases with model estimates: (subplots Ia–Ic) case I—Japan, June 1989, frontal rainfall; (subplots IIa–IIc) case II—Japan, 15 July to 15 August 1989, tropical convective rainfall; (subplots IIIa–IIIc) case III—Florida peninsula, January 1996. In all cases a is the comparison with GPI method estimates, b is the comparison with ANN fixed parameter model estimates, and c is the comparison with ANN adaptive parameter model estimates.

  • View in gallery

    Comparison of ground-based and ANN model estimates of hourly rainfall time series at five representative Japanese island locations (see Fig. 1) for the period 14–20 June 1989.

  • View in gallery

    Same as Fig. 7 for January 1996 in the Florida peninsula.

  • View in gallery

    The “maps” (value distribution) of average rainfall and model input features associated with the 15 × 15 nodes of the SOFM classification matrix after adaptive training using the January 1996 Florida peninsula data: (a) output map of mean ground-based rainfall estimate (mm), (b) input map of feature T1b (K) (c) input map of feature SURF (dimensionless, 0 is the ocean, 0.5 is the coast, 1 is the land), and (d) input map of feature SDT5b (K).

  • View in gallery

    Comparison showing improvement in the Florida peninsula “output map” of model-estimated average rainfall associated with the (15 × 15) nodes of the SOFM classification matrix: (a) estimates obtained using initial parameter estimates (based on training using the Japanese island 1–15 June 1989 data), and (b) estimates obtained after subsequent adaptive updating of the parameter estimates using Florida peninsula January 1996 data. The comparable ground-based estimates appear in Fig. 9a.

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Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks

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  • 1 Department of Hydrology and Water Resources, The University of Arizona, Tucson, Arizona
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Abstract

A system for Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) is under development at The University of Arizona. The current core of this system is an adaptive Artificial Neural Network (ANN) model that estimates rainfall rates using infrared satellite imagery and ground-surface information. The model was initially calibrated over the Japanese Islands using remotely sensed infrared data collected by the Geostationary Meteorological Satellite (GMS) and ground-based data collected by the Automated Meteorological Data Acquisition System (AMeDAS). The model was then validated for both the Japanese Islands (using GMS and AMeDAS data) and the Florida peninsula (using GOES-8 and NEXRAD data). An adaptive procedure is used to recursively update the network parameters when ground-based data are available. This feature dramatically improves the estimation performance in response to the diverse precipitation characteristics of different geographical regions and time of year. The model can also be successfully updated using only spatially and/or temporally limited observation data such as ground-based rainfall measurements. Another important feature is a procedure that provides insights into the functional relationships between the input variables and output rainfall rate.

Corresponding author address: Dr. Soroosh Sorooshian, Department of Hydrology and Water Resources, The University of Arizona, College of Engineering and Mines, Building 11, Tucson, AZ 85721.

soroosh@hwr.arizona.edu

Abstract

A system for Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) is under development at The University of Arizona. The current core of this system is an adaptive Artificial Neural Network (ANN) model that estimates rainfall rates using infrared satellite imagery and ground-surface information. The model was initially calibrated over the Japanese Islands using remotely sensed infrared data collected by the Geostationary Meteorological Satellite (GMS) and ground-based data collected by the Automated Meteorological Data Acquisition System (AMeDAS). The model was then validated for both the Japanese Islands (using GMS and AMeDAS data) and the Florida peninsula (using GOES-8 and NEXRAD data). An adaptive procedure is used to recursively update the network parameters when ground-based data are available. This feature dramatically improves the estimation performance in response to the diverse precipitation characteristics of different geographical regions and time of year. The model can also be successfully updated using only spatially and/or temporally limited observation data such as ground-based rainfall measurements. Another important feature is a procedure that provides insights into the functional relationships between the input variables and output rainfall rate.

Corresponding author address: Dr. Soroosh Sorooshian, Department of Hydrology and Water Resources, The University of Arizona, College of Engineering and Mines, Building 11, Tucson, AZ 85721.

soroosh@hwr.arizona.edu

Introduction

Accurate observations of the global distribution of precipitation are necessary for monitoring the variability of weather and climate and are crucial to the development of a proper understanding of the hydrologic cycle as it passes through the ocean, land, and atmosphere. For hundreds of years, rainfall has been measured by the conventional method of rain gauges, but this method facilitates only a relatively sparse sampling of rainfall, primarily over the land. The use of ground-based radar now enables the measurement of rainfall over relatively large areas, but the coverage is still essentially limited to land surfaces and coastal regions. With the current rapid growth in satellite remote-sensing technology, we will soon be able to routinely monitor the global distribution of rainfall, even over the oceans, which cover approximately 71% of the earth’s surface.

Since the 1960s, techniques for the estimation of surface rainfall from multichannel visible (VIS) and infrared (IR) imagery collected by the Geostationary Operational Environmental Satellites (GOES) have been under development. These approaches attempt to correlate the surface rain rate with cloud-top brightness temperatures provided by the satellite. One approach is based on the analysis of individual cloud pixel information (Arkin and Meisner 1987; Barrett et al. 1986; Lovejoy and Austin 1979; Bellon et al. 1992). For example, the GOES precipitation index (GPI) method(Arkin and Meisner 1987) assigns an estimated instantaneous rainfall value of 3 mm h−1 to any pixel location for which the satellite image indicates a cloud-top temperature lower than 235 K and averages the results over an area of approximately 2.5° latitude by 2.5° longitude. The result is then accumulated over a longer period, usually several days to a month, to increase the accuracy. Another approach is based on the analysis of cloud image types and their variations in time (Griffith et al. 1978; Scofield 1987; Negri et al. 1984; Adler and Negri 1988; Wu et al. 1985). For example, the Automatic Satellite-Derived Precipitation Estimates method of NOAA/NESDIS (Scofield 1987) is currently being used to estimate and publish instantaneous and accumulated rainfall distributions for the continental United States.

While the methods mentioned above provide much needed information about the spatial distribution and temporal variability of regional and global rainfall, they suffer from inadequate reliability, accuracy, and resolution in space and time (Arkin and Ardanuy 1989; Lee et al. 1991; Petty 1995). In the next section, these limitations are discussed with particular reference to the use of satellite IR imagery. A newly developed approach that is based on the computational strength and flexibility of adaptive Artificial Neural Networks (ANNs) is then presented. The new approach, entitled Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN), is designed to be capable of extracting and combining information from data of various types including, for example, IR and microwave satellite imagery, rain gauge and ground-based radar data, and ground-surface topographic information.

We present a model that was developed using data from the Japanese Islands, including surface-type information, remotely sensed IR data collected by the Geostationary Meteorological Satellite (GMS), and ground-based data collected by the Automated Meteorological Data Acquisition System (AMeDAS). The model was validated for both the Japanese Islands (using GMS and AMeDAS data) and the Florida peninsula (using GOES-8 and NEXRAD data). The adaptive feature of the method enables recursive updating of the ANN parameters when ground-based data are available, thereby dramatically improving the estimation performance in response to varying spatial and temporal rainfall properties. This feature also enables the model to effectively adjust to the differing precipitation characteristics of diverse geographical regions. Tests show that the model can be successfully updated using only spatially and/or temporally limited observation data, such as ground-based rainfall measurements. An important feature of this model is the use of a strategy that provides interesting insights into the functional relationships between input variables and output rainfall rates.

Background

The statistical relationship between GMS cloud pixel brightness temperature and AMeDAS hourly surface rainfall measurements over the Japanese Islands and the surrounding oceanic regions (Fig. 1a) for the month of June 1989 is presented in Fig. 2a (details are given in Table 1). Note that the mean rainfall rate R varies as a function of brightness temperature Tb. Further, the uncertainty σR in rainfall rate is quite large and also varies with Tb. The GPI method uses a simple two-piece threshold function approximation ofthis relationship (R = 3 mm h−1 when Tb ≤ 235 K and R = 0 otherwise). Although crude, the GPI method works quite well for the estimation of monthly rainfall over large areas, partly because the over- and underestimation of spatial and temporal errors cancel each other in the aggregation procedure. While, as Arkin and Xie (1994) suggested, the method could be improved to produce better aggregate estimates by tuning the threshold values for different geographical locations, that will not help as we seek to produce finer-scale estimates of precipitation.

If we are to produce precipitation estimates at finer temporal and spatial resolutions, it is necessary to develop an improved method. We first notice that the mean relationship depicted in Fig. 2a suggests a classification of the mean curve into finer ranges. However, the large uncertainty in each temperature range would still preclude accurate estimation of the rainfall rate. Further, the significant variation in the RTb curves illustrated in Fig. 2b indicates that the relationship is likely to be seasonally and regionally dependent; a relationship derived from one special case will not accurately fit another. Therefore, to improve discrimination, we must successfully model a relationship that is characterized by significant transience, heterogeneity, and variability. Such a model must necessarily be able to

  1. extract information from multiple input features (variables) that are related to the precipitation process,

  2. perform sophisticated classification and mapping in a multidimensional input–output space,

  3. rapidly process the large amounts of data that make up satellite images while in an operational mode, and

  4. be able to automatically update itself whenever ground-based or other sources of data are available.

Various attempts to improve the estimation of precipitation from satellite IR imagery have been reported in the literature. Adler et al. (1993) and others proposed methods that incorporate both IR and microwave information. Xie and Arkin (1996) developed an algorithm that merges the rainfall estimates obtained from GPI, microwave, and rain gauge measurements. Negri and Adler (1993) combined the IR technique with a numerical cloud model. Scofield (1987), Grassotti and Garand (1994), and others included sounding measurements and physical fields calculated by numerical weather forecast models into the IR algorithms. From the viewpoint of information systems, all of these methods, whether based on the analysis of cloud physics or instrument/sensor characteristics, are primarily attempts to enhance the effectiveness of the input system to reduce the rainfall mapping uncertainty for certain types of clouds. Our objective is to take advantage of all these developments and build a comprehensive tool that achieves the four requirements listed above, through the use of methods that synthesize computer-based artificial intelligence techniques with the theory of precipitation processes and practical experience.

In this paper, we demonstrate the applicability of an ANN technique in the development of such a tool. The only relevant publication in this area is by Murao et al. (1993), who used the textural features extracted from IR satellite imagery as inputs to a nonadaptive ANN model to estimate areal average rainfall intensity for a specific 1.25° latitude by 1.25° longitude region over the ocean just east of Japan. In our approach, we develop an adaptive ANN approach to estimate rainfall intensity at a finer(0.25° latitude by 0.25° longitude) spatial scale over the entire land mass and surrounding coastal regions of the Japanese Islands. We also show the ability of the model to adaptively retrain itself to the different physiographic and seasonal precipitation characteristics of the Florida peninsula. In addition to providing improved estimation performance, the ANN method is able to provide valuable insights into the physical factors that influence the relationships between precipitation and remotely sensed satellite imagery.

The Artificial Neural Network (ANN) model

ANN models have been widely applied in various fields of science and technology involving time series forecasting, pattern recognition, and process control. The ANN structure has been mathematically proven to be a universal function approximator that is capable of mapping any complicated nonlinear function to an arbitrary degree of accuracy. Since the late 1980s, ANNs have been successfully used to model a variety of different functions. The network is able to intelligently “learn” these functions through an automatic “training process.” However, because many issues related to network architecture are still not well understood, many researchers seem to view the ANN as a “black box” approach that is unable to provide important and useful insights into the underlying nature of the physical process. In this paper, we demonstrate that this view is incorrect.

The basic form of an ANN is called a multilayer feedforward network (MFN). The most popular type of MFN, the three-layer feedforward neural network (TLFNN), is shown in Fig. 3; it consists of three layers of processing nodes (neurons) with connections linking the nodes in successive layers. The first layer consists of n0 input nodes, one for each normalized input variable xi, (i = 1, . . . , n0). The intermediate layer consists of n1 “hidden” nodes, one for each intermediate variable yj, (j = 1, . . . , n1). Both layers have an additional “bias” node (indicated with input equals 1.0), which enables the mapping to represent the output levels associated with zero inputs. The final layer consists of n2 output nodes, one for each output variable zk, (k = 1, . . . , n2). The input-hidden layer transformation performs a continuous nonlinear mapping of the n0 input values xi to the intermediate variables yj; the parameters of this transformation are the weights wji. In a similar fashion, the hidden-output layer transformation performs a (linear or nonlinear) mapping of the n1 intermediate variables yj to the output values zk; the parameters of this transformation are the weights υkj. Although it has been shown that the TLFNN is theoretically capable of implementing any continuous, bounded input–output function mapping to an arbitrary degree of accuracy (see, e.g., Hecht-Nielsen 1990), many researchers have reported difficulties in training the network parameters (e.g., Hecht-Nielsen 1989, 1990; Haykin 1994; Gupta et al. 1997) caused by parameter interdependence, parameter insensitivity, and multilocal optima.

An alternative kind of MFN that does not suffer from the training problems associated with the TLFNN, and which is particularlysuited to our research objectives, is the Modified Counter Propagation Network (MCPN) under development at The University of Arizona (Hsu 1996). For a discussion of the original Counter-Propagation Network, see Hecht-Nielsen (1987). The MCPN is a hybrid three-layer network (Fig. 4) consisting of two components. The input-hidden layer transformation xiyj forms a self-organizing feature map (SOFM) (Kohonen 1982) that performs automatic clustering (discretization) of the input space. The hidden-output layer transformation yjzk consists of an improved version of the Grossberg linear layer (Grossberg 1969), which maps the discrete SOFM clusters to the continuous output space. A powerful feature of the MCPN is that, unlike the TLFNN, the input-hidden and hidden-output transformations can be trained separately. First, the parameters wji of the SOFM are trained, as the name suggests, through an “unsupervised” self-organizing clustering procedure. Subsequently, the parameters υkj of the modified Grossberg linear layer (MGLL) are trained using a “supervised” process based on a simple recursive gradient search. Because the training of the input-hidden and hidden-output transformations is decoupled, the MCPN network typically requires orders of magnitude fewer training trials than networks such as the TLFNN. This makes the network amenable to rapid processing of large volumes of data. These components and their training strategies are described briefly below; for more detail, please refer to Hsu (1996).

The function of the SOFM portion of the network is to detect and classify patterns in the input data, without reference to the output data. As depicted in Fig. 4, the n1 nodes of the hidden layer are typically arranged in the form of a square matrix. We begin by randomly assigning a vector of parameters (wji; i = 1, . . . , n0) to each of the hidden nodes (indicated by the subscript j) and conducting a training process based on the principle of competition as follows. For each normalized input vector (xoi; i = 1, . . . , n0), a measure of the distance dj between the input pattern vector xoi and the hidden node parameter vector wji is computed for each hidden node as
i1520-0450-36-9-1176-e1
The hidden node c with the smallest distance dj to the sample input vector [i.e., dc = min (dj)] is selected, and the parameter vectors associated with a neighborhood Λc of surrounding hidden nodes are updated, moving their component values in the direction of the input vector as follows.
i1520-0450-36-9-1176-e2
A recursive process of competitive node selection and parameter adjustment is continued by repetitive sequential processing of the input dataset, and the size of the neighborhood Λc and training rate parameter η are gradually reduced as the training proceeds (for details, see Hsu 1996). This brings about a reorganization of the hidden nodes so that their parameter vectorsmimic the distribution of the input data. Training is terminated when the locations of the cluster centers become stable. Because there are a limited number of hidden nodes, the hidden layer becomes a filter that associates each input vector with one of the n1 classes. In addition, because of the training strategy employed, the hidden nodes “self-organize” in such a manner so that neighboring nodes (i.e., structurally close to each other) are also functionally “similar.” Once the SOFM has been trained, its response to an arbitrary input vector xi is determined as follows. The “winning” hidden node c for which the distance measure dj is smallest [dc = min(dj)] is determined, and the intermediate variables yj are computed according to
i1520-0450-36-9-1176-e3
where Ω defines a surrounding neighborhood of hidden nodes centered on node c. Note that each input pattern will only activate nonzero yj responses for the small portion of the hidden layer defined by the neighborhood Ω. In this research, the surrounding neighborhood was selected to consist only of the 3 × 3 matrix of nodes immediately adjacent to the center node.
The function of the MGLL portion of the network is to compute a specific rainfall rate for each input pattern classified by the SOFM. The MGLL output layer has the same number and arrangement of nodes as the hidden layer; each node has a one-to-one correspondence with its counterpart in the hidden layer and is connected to the counterpart hidden node and its Ω neighborhood by a vector (υkj; j ∈ Ω) of parameters. Based on this arrangement, the output rainfall rate is calculated as z = zk, where
i1520-0450-36-9-1176-e4
In section 10, we will discuss how this network layout enables us to visually investigate the functional relationships identified by the model by plotting the distribution of input features against the structural layout of the hidden layer and the corresponding distribution of rainfall rates against the structural layout of the output layer.
Once the SOFM component has been trained, the parameters υkj of the MGLL component can be estimated using a straightforward “supervised learning” strategy. This is conducted in two stages. First, a “batch” training procedure based on linear least squares estimation is applied, using a selected portion of the input–output dataset, to obtain preliminary estimates for the parameters. Subsequently, the parameters are recursively updated through a sequential training mechanism that makes small adjustments to the parameters in the neighborhood Ω of an active node according to
υnewkjυoldkjβzokzkyjυkj
where β is a learning rate parameter (0 ≤ β ≤ 1; here, we used β = 0.1) and zok is the target value of zk. This process of recursive updating enables the MCPN to track and adjust to seasonal and regional variations in the rainfall rate relationship.

Current model structure and inputvariables

To implement the MCPN model described above, the input–output data and the number of nodes in each layer must be specified. The specific structure used to generate the results reported in this paper is displayed in Fig. 4. In this paper, we present the results for a network structure consisting of six normalized input variables (n0 = 6) in the hidden layer and 225 nodes each (n1 = n2 = 225) arranged in a 15 × 15 matrix in the hidden and output layers.

The most important requirement for successful estimation of rainfall using this model is the selection of input variables that provide sufficient information to enable proper rainfall rate discrimination. As discussed in section 2, the basic GPI approach uses only the satellite IR image brightness temperature Tb. In contrast, the MCPN is able to construct a model that uses as many input variables as might be considered to be informative about the rainfall process. We have only just begun to explore the issue of selection of model inputs; in this paper, we report on the results of a preliminary investigation involving the use of the six input variables listed in Table 2. The first variable (T1b) is the pixel brightness temperature. The second variable SURF is an initial attempt to account for the effect of underlying surface features on the cloud precipitation process, and the remaining four variables (T3b, SDT3b, T5b and SDT5b) are a simple initial attempt to account for cloud structural features.

Model calibration

Two regions, the Japanese Islands and the Florida peninsula, were selected for the model development and testing studies reported here. These regions were selected because 1) the availability of “ground-based” surface rainfall data of high spatial and temporal resolution, 2) the variety of geographical and climatological conditions influencing the meteorology of precipitation, and 3) the extensive prior investigation of the Japan data by the Algorithm Intercomparison Project 1 (AIP-1) (Lee et al. 1991) and its follow-up studies. The Japanese data were collected for two months during the summer of 1989 (1–30 June and 15 July–15 August). The precipitation data are based on a composite of data from 1300 rain gauges and 15 precipitation radars of the Japanese Automated Meteorological Data Acquisition System (AMeDAS) networks supported by the Japanese Meteorological Agency (JMA). The IR brightness temperature images were collected by the GMS geostationary satellite. These data are quite familiar to researchers working in the field of rainfall estimation using satellite imagery. The Florida data were collected for the month of January 1996. The rainfall data were collected by the network of NEXRAD radars operated by the U.S. National Weather Service, and the IR brightness temperature images were collected by GOES-8.

The MCPN model was initially trained in “batch mode” using 15 days of data (1–15 June 1989) from the Japanese Islands. In each of the studies reported below, the model was tested in two modes: 1) nonadaptive estimation mode, in which the parameters wji and υkj were not updated, and 2) adaptive estimation mode, in which the MGLL parameters υkj are recursively updated with each new piece of information (1-h time step) before computing theprecipitation estimates for the next time step. In all cases, the adaptive MCPN model was initialized from the parameters obtained by the 15-day batch training.

Application to monthly rainfall estimation

We first explore the performance of the model when applied to the problem of estimating accumulated monthly rainfall. Three case studies were run to test various features of the model. In case I, the MCPN model is applied to the Japanese Islands for the month of June 1989, during which the “Baiu” frontal type of rainfall events occur (Lee et al. 1991). In case II, the performance of the model is examined for the same region for the period 15 July to 15 August 1989, when the meteorological regime switches to subtropical convective rainfall. Case III illustrates the transferability of the model from the Japanese Islands to the Florida peninsula, using data for January 1996. The details of the remotely sensed and ground-based data used in these cases are presented in Table 1.

Case I: (Japan, June 1989, frontal rainfall)

The MCPN model was used to estimate the hourly rainfall rate distribution (at 0.25° latitude by 0.25° longitude pixel size) over the Japanese Islands using the GMS IR images for June 1989. Note that this period includes the 15 days used to calibrate the MCPN model. The results were aggregated up to 1.25° latitude by 1.25° longitude pixel scale and accumulated for the entire month. The observed mean precipitation over the study area for this period was 157 mm. Figures 5-Ia–Id show the observed data (AMeDAS ground-based measurements), the GPI estimate, the nonadaptive MCPN estimate, and the adaptive MCPN estimate, respectively. Figures 6-Ia–Id show the scatterplots comparing observed and estimated results. Consistent with our expectations, we find that

  1. At this temporal and spatial aggregation scale, all three methods provide generally good estimates of the actual spatial pattern of rainfall (Figs. 5-Ia–Id).

  2. The nonadaptive MCPN estimates are superior to the traditional GPI estimates (not surprising, given that the GPI model was not calibrated to the Japanese data); the correlation statistic (CORR) improves from 0.61 to 0.81, the bias statistic (BIAS) improves from 61.47 mm to 1.48 mm, and the root-mean-square error (RMSE) statistic improves from 101.4 mm to 63.9 mm. There is, however, a tendency to underestimate at high rainfall values and overestimate at low rainfall values (Figs. 6-Ia and Ib).

  3. The adaptive strategy provides much better estimates at high rainfall values than the nonadaptive strategy, but the improvement at low values is marginal (Figs. 6-Ib and 6-Ic). The CORR statistic improves from 0.81 to 0.88, and the RMSE statistic improves from 63.90 to 55.36 mm. However, because the adaptive scheme resulted only in improvements to estimation of high monthly rainfall, the bias has become worse (23.12 mm).

Case II: (Japan, 15 July to 15 August 1989, tropical convective rainfall)

Figures 5-IIa–IId and Figs. 6-IIa–IIc show the results of applying the model to the quite different meteorological conditions characterized by convective rainfall. The observed mean precipitation over the study area for this period was 143 mm. The results indicate that

  1. The GPI method performs well for monthly precipitation below 100 mm per month but seriously underestimates the rainfall at high values (Figs. 5-IIb and 6-IIa).

  2. The nonadaptive MCPN estimates reproduce the observations quite well in the southern part of the Japanese Islands but are poor in the central region, which is characterized by high mountains and possible orographic effects (Figs. 5-IIc and 6-IIb). This agrees with Arkin and Xie (1994), who identified the existence of different rainfall-cloud regimes in the southern and central regions of the islands.

  3. The adaptive MCPN estimates are, again, superior both in the representation of spatial distribution and in accuracy of rainfall values (Figs. 6-IIb and -IIc). The CORR statistic improves from 0.73 to 0.88, the BIAS improves from −33.12 to 22.15 mm, and the RMSE statistic improves from 86.85 to 63.41 mm. Note, in particular, that the improved representation of rainfall in the central part of the islands is significant.

As we might expect, because the MCPN model was calibrated using a very limited amount of data, the model is currently unable to recognize and account for seasonal shifts in meteorological regimes. Further, the model does not account for orographic effects. Although the adaptive scheme is able to somewhat correct for these weaknesses of the model, we should expect that further improvements in the basic (nonadaptive) model performance over the land could be achieved by using more extensive and varied datasets for calibration and by incorporating topographic information (elevation) as one of the input variables.

Case III: (Florida peninsula, January 1996)

We next examine the results of transferring the calibrated MCPN model to the different meteorological and geographical conditions of the Florida peninsula (Fig. 1b). The MCPN model was used to estimate the hourly rainfall rate distribution (at 0.25° latitude by 0.25° longitude pixel size) over the Florida peninsula using the GOES-8 IR images for January 1996. The results were aggregated up to 1° × 1° pixel scale and accumulated for the entire month. NEXRAD radar data were used as the ground-based information. The observed mean precipitation over the study area for this period was 156 mm. As illustrated in Fig. 2b, the same brightness temperatures give rise to much higher average rainfall intensities over Florida than over Japan. Figures 5-IIIa–IIId and Figs. 6-IIIa–IIIc indicate that

  1. The GPI method performs well for monthly precipitation below 100 mm per month. However, both the GPI and nonadaptive MCPN estimates seriously underestimate the higher rainfall values (Figs. 5-IIIb, 5-IIIc, 6-IIIa, and 6-IIIb). This result is consistent with the R–Tb relationship shown in Fig. 2b.

  2. The adaptive scheme is successfully able to adjust the model parameters to better represent the new conditions encountered by the model (Figs. 5-IIId and 6-IIIc). The CORR statistic improves from 0.75 to 0.78, the BIAS statistic improves from −78.63 to 22.50 mm, and the RMSE statistic improves from 110.60 to 65.48 mm.

Application to hourly rainfall estimation

The cases discussed above compared the accuracies of the methods with regard to producing estimates of monthly accumulated rainfall. Our goal, however, is to provide accurate estimates of rainfall at the spatial and temporal resolution of the available satellite imagery.Clearly, it is much more difficult to produce accurate estimates of hourly rainfall than of monthly accumulated rainfall because, in the latter, the accumulation process tends to cancel the random estimation errors.

Japanese Islands

To illustrate the accuracy of the hourly rainfall estimates generated by the MCPN, we show the results generated for five representative sites within the Japan study area (Fig. 1a; sites A–E). These five sites are the locations studied by the AIP-1 project. Note that two of the sites are over land and three are over the ocean. Sites A–D are at 1.25° × 1.25° resolution, while site E is at 2.5° × 2.5° resolution. The nonadaptive and adaptive MCPN models were run for the months of June, July, and August 1989. Figure 7 shows some typical results consisting of estimated rainfall time series for a 7-day period during June, which was selected for the occurrence of heavy rainfall. Results for July and August were quite similar. We observed the following.

  1. In general, the nonadaptive model is able to correctly indicate the occurrence of the rainfall event, but there is a strong tendency to underestimate, particularly for land site C. The performance of the model is better over the ocean and coastal regions (sites B, D, E) than over the land (sites A, C).

  2. The adaptive model shows the ability to correct for the tendency of the nonadaptive model to underestimate peak rainfall events. The most significant correction is for site C, which is thought to be strongly influenced by orographic effects (not accounted for by the model).

  3. The adaptive model shows an additional peak at midnight on 18 June 1989 that leads the peaks in the observed precipitation for sites D and E. The reason for this is not known. On the one hand, there may be errors in the model; however, it should be mentioned that the quality of the data at these sites located at the edge of the study region might also be suspect.

Florida peninsula

We show the results for two representative sites within the Florida peninsula study area (Fig. 1b, sites I and II). The resolution for both sites is 2° × 2°. The nonadaptive and adaptive MCPN models were run for January 1996. Figure 8a shows the estimated rainfall time series at site I for a 4-day period at the start of the month, and Fig. 8b shows the estimates at site II for a different 4-day period near the end of the month. We observe that

  1. In both cases, the nonadaptive model results are very poor. Although the correlation statistic is quite good—indicating that the pattern of variation of rainfall intensity has been captured—the magnitude is too low. In light of the difference in R–Tb relationships for Japan and Florida (Fig. 2b), this result is not surprising.

  2. The adaptive model results show improved performance. However, note that the results for site II appear to be better than the results for site I. This is because the site I time period is at the beginning of the estimation time period, and the adaptive scheme (beginning with parameters calibrated for Japan) has not yet had enough time to completely adjust the model to properly represent the different conditions encountered for Florida. By the end of the month, the adaptive scheme has successfully corrected the model, as illustrated by the site II results.

Ability of the model to use spatially limited ground-based information

Sections 6 and 7 have shown the benefit of theadaptive scheme for improving model performance in the presence of seasonal and geographical variations in the R–Tb relationships. This scheme requires that we have available spatially distributed ground-based data by which to train the model. In some parts of the “developed” world (e.g., United States, Japan, and Europe), it is now possible to obtain radar estimates of precipitation for this purpose. However, most countries of the world still rely on point-based rain gauge information. Therefore, we examine the performance of the adaptive MCPN under the conditions of spatially limited ground-based data.

To simulate the availability of limited ground-based data, we randomly selected a number of pixels over the land region of the Florida peninsula and assumed that the NEXRAD radar data for these pixels represent “rain gauge” data. The validity of this assumption is, of course, dependent on the accuracy with which the pixel scale radar-based estimate has been calibrated to match the point scale gauge-based estimate (Sauvageot 1992). The adaptive MCPN model was run for January 1996 using only these limited ground-based data to update the model parameters. As with all the adaptive model runs, we initialized the model at the parameters obtained by batch processing the 15-day data from the Japanese Islands.

The results, in terms of the accumulated monthly rainfall for each 1° × 1° grid cell for the entire study area, are presented in Table 3 for increasing numbers of rain gauges. The model performance improves steadily until about 50 rain gauges and stabilizes thereafter. In fact, the 50 rain gauge result is statistically similar to the result obtained using the entire spatial data. Surprisingly good performance is obtained with as few as 10 rain gauges, considering the fact that the entire study area is represented by about 1350 pixels covering approximately 840 000 km2.

This gauge density represents, on average, approximately one gauge per 2.9° latitude by 2.9° longitude grid box. Because, as indicated by Xie and Arkin (1996), only about half of the 2.5° latitude by 2.5° longitude grid boxes over land will have one or more gauges in them, the use of rain gauges for model calibration will inevitably result in a certain amount of bias over nongauged regions. Meanwhile, we can still reap the benefits provided by the adaptive scheme over the considerable portions of the land mass for which more than one gauge per 2.5° latitude by 2.5° longitude grid are available.

Ability of the model to use temporally limited ground-based information

We now explore the performance of the model when the data available for updating are spatially extensive but temporally limited. For example, polar-orbiting satellite microwave images are currently available at the same location only two times a day. To simulate the availability of temporally limited precipitation estimates from alternative data sources, we use the radar data for the entire study area, but assume different temporal intervals of availability (e.g., 1-, 2-, 4-, etc., and 12-h spacing). The adaptive MCPN model was run for all three of the cases (I, II, and III), as discussed in section 6. As with all the adaptive model runs, we initialized the model at the parameters obtained by batch processing the 15-day data from the Japanese Islands.

The results for different temporal updating intervals are presented in Table 4. Note that 1-h updating is equivalent here to “complete” temporal availability (24 updates per day), while 12-h updating represents only two updates each day. For comparison, the model performance without adaptive updating is included in the final column. The results indicatethat

  1. For case I (Japan, June 1989), the adaptive scheme is ineffective for updating intervals longer than 6 h, and

  2. For both case II (Japan, July and August 1989) and case III (Florida, January 1996), the adaptive scheme is effective even when the update interval is as long as 12 h.

These results seem reasonable. In case I, because the model was originally calibrated to the first 15 days of the same data period, the additional information gained by updating is not as significant as in cases II and III. In the latter two cases, the R–Tb relationships are quite different from that of the calibration data and, hence, the adaptive scheme is able to successfully extract information and improve the model even from data spaced 12 h apart.

Insights provided by the SOFM

The key to successful use of the neural network modeling approach is to identify a broad and informative set of input features (variables) that, taken together, provide fine discrimination in the mapping of precipitation. When including a new input variable, it would be useful to be able to evaluate its importance in explaining precipitation variability. The self-organizing feature map (SOFM) component of the MCPN model provides a simple way to do this.

Figure 9a shows the “output map” of monthly average rainfall (Florida, January 1996) associated with each of the 15 × 15 nodes of the SOFM. Figures 9b–d show the corresponding “input maps” of the brightness temperature Tb, the surface feature variable SURF, and the temperature variability index SDT5b; the input variables have been transformed into their original scale for simplicity of interpretation. First, notice that the unsupervised learning process has organized Tb (Fig. 9b) so that high temperatures (270–280 K) appear in the left central location of the map and the lower temperatures appear toward the edges, particularly on the right side of the map. Comparing with Fig. 9a, it is easy to see that the high temperature nodes correspond to low rainfall, and the low temperature nodes correspond to higher rainfall, as we expect. Notice, however, that different node locations having similar low temperature values have quite different rainfall amounts (consistent with our discussion in section 2). By referring to the input maps associated with the other explanatory variables, we can obtain some insights into this variability.

For example, Fig. 9c shows that the input variable SURF has been mapped into three topological regions corresponding to its three index values (land, coast, and ocean). Comparing the SURF map and the Tb map to the rainfall map, it is clear that similar temperatures give rise to different amounts of rainfall over the three different surface types. Further, the two output map locations P1 and P3 with high rainfall (see Fig. 9a) are associated with moderate temperatures (Tb = 240–250 K) and high temperature variability index (SDTb > 14 K), while the location P2 with high rainfall is associated with very low temperatures (Tb < 230 K) and low temperature variability (SDTb < 8 K).

The SOFM also provides a useful way to view the improvements in model performance provided by on-line updating. Figure 10a shows the “outputmap” of monthly average rainfall (Florida, January 1996) computed by the model before applying the adaptive procedure—that is, using the parameters obtained by batch processing the 15-day Japanese Island data. When compared to the observed data (Fig. 9a), we see that estimation performance appears to be fairly well over the coastal region but poorly (underestimation) over the land and ocean. Figure 10b shows that the updating procedure is able to successfully reconstruct the rainfall distribution associated with the actual data.

Summary and discussion

There is a critical need for global estimates of precipitation at relatively fine temporal and spatial scales (Simpson et al. 1988). Various research teams are working to develop methods that will provide such estimates using the information contained in remotely sensed images collected by geostationary and polar-orbiting satellites. At The University of Arizona, a system entitled PERSIANN (Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks) has been under development to extract and combine information from data of various types including, for example, infrared and microwave satellite imagery, rain gauge and ground-based radar data, and ground-surface topographic information. This system is based on the synthesis of computer-based artificial intelligence techniques with the theory of precipitation processes and practical experience.

The current core of our system, which utilizes the computational strength and flexibility of an adaptive Artificial Neural Network model to estimate rainfall rates using infrared satellite imagery and ground-surface information, has been discussed in this paper. The performance and capabilities of this model (at both monthly and hourly timescales) have been demonstrated using data from the Japanese Islands and the Florida peninsula. Key features of the model include the abilities to

  1. use multiple sources of information,

  2. rapidly process large amounts of satellite data,

  3. adaptively adjust to the diverse precipitation characteristics of different geographical regions and time of year,

  4. perform successful updating using spatially and temporally limited observations, and

  5. provide insights into the manner in which the explanatory variables interact to give rise to variability in rainfall.

A great deal of work is still required to develop and strengthen the methods introduced in this paper. Research is ongoing to identify which input variables will be most informative with regard to the estimation of rainfall from remotely sensed imagery and other readily available sources, including sounding data, meteorological model outputs, etc. Similarly, the use of additional output observations (e.g., rain gauge data, Special Sensor Microwave/Imager estimated ocean precipitation fields, etc.) for improving the model-updating procedure is also being studied. However, the need for a more long-term investigation involving a much larger study region is critical. Hence, we have recently broadened our study to include the Pan American region. Future extensions will include the tropical oceans using data soon to become available through the Tropical Rainfall Measuring Mission (Simpson et al. 1988).

Acknowledgments

This research was supported by the NOAA PACS Research Program (NA56GPO185) and the NASA-EOS Interdisciplinary Research Program (NASA IDP-88-086). Dr. P. A. Arkin and Dr. P. Xie of the National Meteorological Center, NOAA, made many constructive suggestions and shared with us the benefits of their extensive experience and profound knowledge. Dan Braithwaite performed the programming required to access the data and to develop the internet web site. The carefulreading and editing of the manuscript by Ms. Corrie Thies and the constructive criticism provided by the anonymous reviewers resulted in significant improvements to the manuscript. The satellite and ground-based data for Japan were kindly made available to us by Dr. Arkin; the original source of the data is the Global Precipitation Climatology Project (GPCP) First Algorithm Intercomparison Project (AIP-1), which was supported by the World Climate Research Programme (WCRP). NASA Ames Research Center provided the GOES satellite data, and NASA Marshall Space Flight Center DAAC provided the NEXRAD WSR-88D radar composite data for Florida. To all of these people and organization, we are profoundly grateful.

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Fig. 1.
Fig. 1.

Study areas: (a) Japanese islands and (b) Florida peninsula.

Citation: Journal of Applied Meteorology 36, 9; 10.1175/1520-0450(1997)036<1176:PEFRSI>2.0.CO;2

Fig. 2.
Fig. 2.

Statistics for the relationships between surface rainfall rate and cloud-top IR brightness temperature Tb for (a) the Japanese islands mean rainfall rate (R: solid line) and associated standard deviation (σR: bar plot) for eight IR brightness temperature ranges and (b) the average R–Tb relationships identified for three different seasonal/regional cases. These plots were prepared using GMS satellite IR imagery and AMeDAS ground-based rain-rate estimates for Japan, and the GOES-8 satellite IR imagery and NEXRAD radar-based rain-rate estimates for Florida.

Citation: Journal of Applied Meteorology 36, 9; 10.1175/1520-0450(1997)036<1176:PEFRSI>2.0.CO;2

Fig. 3.
Fig. 3.

The structure of a three-layer feedforward artificial neural network and the detail of each internal processing element.

Citation: Journal of Applied Meteorology 36, 9; 10.1175/1520-0450(1997)036<1176:PEFRSI>2.0.CO;2

Fig. 4.
Fig. 4.

The structure of the ModifiedCounter Propogation Network ANN model and its input–output variables.

Citation: Journal of Applied Meteorology 36, 9; 10.1175/1520-0450(1997)036<1176:PEFRSI>2.0.CO;2

Fig. 5.
Fig. 5.

Estimates of the observed and computed monthly rainfall distributions for three test cases: (subplots Ia–Id) case I—Japan, June 1989, frontal rainfall; (subplots IIa–IId) case II—Japan, 15 July to 15 August 1989, tropical convective rainfall; (subplots IIIa–IIId) case III—Florida peninsula, January 1996. In all cases, a is the ground-based estimate, b is the GPI method estimate, c is the ANN fixed parameter model estimates, and d is the ANN adaptive parameter model estimates.

Citation: Journal of Applied Meteorology 36, 9; 10.1175/1520-0450(1997)036<1176:PEFRSI>2.0.CO;2

Fig. 6.
Fig. 6.

Scatterplots comparing observed monthly rainfall distributions for three test cases with model estimates: (subplots Ia–Ic) case I—Japan, June 1989, frontal rainfall; (subplots IIa–IIc) case II—Japan, 15 July to 15 August 1989, tropical convective rainfall; (subplots IIIa–IIIc) case III—Florida peninsula, January 1996. In all cases a is the comparison with GPI method estimates, b is the comparison with ANN fixed parameter model estimates, and c is the comparison with ANN adaptive parameter model estimates.

Citation: Journal of Applied Meteorology 36, 9; 10.1175/1520-0450(1997)036<1176:PEFRSI>2.0.CO;2

Fig. 7.
Fig. 7.

Comparison of ground-based and ANN model estimates of hourly rainfall time series at five representative Japanese island locations (see Fig. 1) for the period 14–20 June 1989.

Citation: Journal of Applied Meteorology 36, 9; 10.1175/1520-0450(1997)036<1176:PEFRSI>2.0.CO;2

Fig. 8.
Fig. 8.

Same as Fig. 7 for January 1996 in the Florida peninsula.

Citation: Journal of Applied Meteorology 36, 9; 10.1175/1520-0450(1997)036<1176:PEFRSI>2.0.CO;2

Fig. 9.
Fig. 9.

The “maps” (value distribution) of average rainfall and model input features associated with the 15 × 15 nodes of the SOFM classification matrix after adaptive training using the January 1996 Florida peninsula data: (a) output map of mean ground-based rainfall estimate (mm), (b) input map of feature T1b (K) (c) input map of feature SURF (dimensionless, 0 is the ocean, 0.5 is the coast, 1 is the land), and (d) input map of feature SDT5b (K).

Citation: Journal of Applied Meteorology 36, 9; 10.1175/1520-0450(1997)036<1176:PEFRSI>2.0.CO;2

Fig. 10.
Fig. 10.

Comparison showing improvement in the Florida peninsula “output map” of model-estimated average rainfall associated with the (15 × 15) nodes of the SOFM classification matrix: (a) estimates obtained using initial parameter estimates (based on training using the Japanese island 1–15 June 1989 data), and (b) estimates obtained after subsequent adaptive updating of the parameter estimates using Florida peninsula January 1996 data. The comparable ground-based estimates appear in Fig. 9a.

Citation: Journal of Applied Meteorology 36, 9; 10.1175/1520-0450(1997)036<1176:PEFRSI>2.0.CO;2

Table 1. Information about the three study cases.

i1520-0450-36-9-1176-t01

Table 2. The currently used input variables for the ANN model.

i1520-0450-36-9-1176-t02

Table 3. The statistics of model performance (estimated monthly rainfall via observation) using increasing number of radar imagepixels for model parameter updating in the case of January 1996 in the Florida peninsula.

i1520-0450-36-9-1176-t03

Table 4. The statistics of model performance (estimated monthly rainfall via observation) using increasingly spaced “snapshot” observation data for model parameter updating.

i1520-0450-36-9-1176-t04
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