A Prototype Algorithm for Gauge – Satellite Merged Analysis of Daily Precipitation over Land

Background [1] Sources of Precipitation Information Gauge measurements Accurate point measurements Insufficient station networks Radar observations reasonable temporal / spatial coverage around radar sites Relatively accurate estimations Blocked by mountains / inavailability over some remote regions Satellite estimates –Infrared (IR) observations –Indirect and less accurate estimates –Frequent sampling (every 30-min) –Fine spatial resolution (4kmx4km) –Passive Microwave (PMW) observations –Physically-based / more accurate estimates of instantaneous rain rates –Poor sampling (up to twice a day from a single satellite) Precipitation generated by numerical models Less-than desirable performance for convective precipitation and precipitation ocean Good performance for large-scale stratiform precipitation over extra-tropics during cold season

Background [2] Strategy and Status Basic Strategy –Two-step merging approach to combined gauge & sate First, to merge observations from multiple satellites to form an all-satellite merged precipitation estimates (CMORPH) Over land, to combine the all-satellite estimates with in situ observations (gauge); Over ocean, to adjust the CMORPH against a long-term data with coarser resolution (pentad GPCP) to facilitate the definition of anomaly Status Land :finished development of the prototype algorithm (to introduced here) in process of implementation over the globe Ocean :finished development of a test algorithm

Objective To develop a prototype algorithm to define high-resolution analysis of daily precipitation over land by combining gauge observations and satellite estimates 0.25 o lat/lon over China Tested for May – September, 2007

Input Data Gauge data Gridded analysis of daily precipitation defined by interpolating gauge observations from over 2,400 stations over China Daily reports are available from only 198 Chinese stations through GTS High-resolution satellite precipitation estimates Generated by CPC Morphing Technique (CMORPH, Joyce et al. 2004) Precip estimstes of 8km/30-min resolution regridded into 0.25 o lat/lon/daily

Gauge Data  Daily precipitation  0.25 o lat/lon over China  May 1 – Sep.30, 2007  Daily precip analysis defined by interpolating station data over ~2400 gauges and used as the truth in the development

Characteristics of Input Data Sources Gauge data Accurate point measurement of precipitation (unbiased) Gauge network of insufficient density over most of the global land areas Random error in gauge-based analysis representing areal mean due to spatial variations in precip and inappropriate gauge network to catch them Satellite estimates Ability to catch spatial pattern and temporal variations of precipitation with reasonable accuracy Regionally, seasonally, and range-dependent BIAS Random error

Basic Strategy to Merge Gauge and Satellite Data First Step --- Removing Satellite Bias Assuming gauge-analysis is unbiased Removing bias in the satellite estimates through comparison against the gauge analysis Second Step --- Combining Gauge and Bias-corrected Satellite Estimates Combination through OI Bias-corrected satellite estimates as first guess Gauge analysis used to improve the first guess over regions with gauge stations

Part I : Bias Correction

Bias Correction Through PDF Matching Principal –Match the PDF of the CMORPH against that of daily gauge to define and remove the bias, assuming PDF of the gauge analysis represents that of the truth Implementation –Collect co-located pairs of gauge and CMORPH over grid boxes within a spatial window centering at the target grid box and a time period ending at the target date; –Define PDF for the CMORPH and gauge analysis

Sample Results Precipitation for August 2, 2007

Cross-Validation Tests How are they carried out Each time, gauge analysis at 10% randomly selected grid boxes is withdrawn PDF bias correction is performed using gauge data over the remaining 90% grid boxes The above processes are repeated 10 times so that analysis at each grid box is withdrawn once Compare the original and bias-corrected CMORPH with the gauge analysis at the withdrawn grid boxes to ensure independence Only data over grid boxes with at least one gauge are included in the calculation to ensure reliable quality of the ground truth

Cross-Validation Tests Combined space / time domain CMORPHBias (%)Correlation Original-9.7%0.706 Adjusted-0.0%0.785  Successful correction of the bias;  Substantial improvements in correlation

Cross-Validation Tests Time Series

Cross-Validation Tests PDF of Daily Precip over 0.25 o lat/lon Grid Boxes  Adjusted CMORPH presents PDF very close to that of the gauge analysis  Frequencies of no-rain and light rain in the adjusted CMORPH is slightly larger / smaller than those in the gauge analysis

Part II : Combining Gauge with Bias Corrected CMORPH

The OI-based Combining Algorithm Analyzed fields of precipitation are defined by combining bias-corrected satellite estimates and the gauge data (gauge-based analysis, in this test) The satellite estimates are used as the first guess The gauge data are used as the observations to correct the first guess where gauge data are available The combined analysis will be the same as the first guess over regions with no gauges nearby Weighting coefficients used in the combining are computed from error structures for the first guess and observation fields following the OI formula

Error Structures See backup slides for details Both gauge data and bias-corrected satellite estimates are bias free Random error in gauge analysis is a function of gauge network density and intensity of precipitation No spatial correlation in gauge random error CMORPH random error is a function of sampling size (number of original satellite data used) and the intensity of precipitation determined empirically through comparison with gauge data Spatial correlation in CMORPH error declines with distance

OI Combined Analysis [1]  Sample for August 2, 2007  Both the precipitation analysis and the error estimation seem reasonable

OI Combined Analysis [2]  Precipitation distribution looks better than the gauge-based analysis and the CMORPH estimates

OI Combined Analysis [3]  Comparison between the combined analysis and the CMORPH, for August 2, 2007  Differences over regions with gauge data  Grid boxes with negative/positive differences distributed randomly, implying the bias correction for CMORPH works well

OI Combined Analysis [4]  Comparison between the combined analysis and the gauge data, for August 2, 2007  Differences over regions with less gauge data  Grid boxes with negative/positive differences distributed randomly

OI Combined Analysis [5]  Mean precipitation (mm/day) for May 1 – Sep.30, 2007, from gauge analysis (top), bias corrected CMORPH (middle), and combined analysis (bottom)  Combined analysis presents better distribution than gauge and CMORPH

OI Combined Analysis [6]  Comparison between the combined analysis - the gauge data, and combined analysis – CMORPH for May 1 – Sep.30, 2007  RMS differences are computed for grid boxes with different numbers of gauges  Differences between the combined analysis and the gauge / CMORPH are smaller / larger over grid boxes with more gauges  This confirms that our algorithm works as we designed

Part III : Real-Time Operation System

Objective To construct a LINUX-based real-time operational system to create analyses of daily precipitation over East Asia by combining gauge observations and satellite estimates 60 o E – 160 o E; 0 o – 60 o N 0.25 o lat/lon grid Daily precipitation ending at 00Z

Structure of the Analysis System Gauge Data CMORPH 8km/30min InterpolationRegridding Gauge Analysis (0.25 o lat/lon) CMORPH (0.25 o lat/lon) Binary DataGIF Pictures Merging

Merging Procedures Gauge Analysis (0.25 o lat/lon) CMORPH (0.25 o lat/lon) PDF Matching Bias Correction Bias-Corrected CMORPH OI Combining Merged Analysis

Sample Merged Analysis Over China, June 4, 2008

Sample Merged Analysis Over East Asia, June 4, 2008

Sample Merged Analysis Over China, Animation

Sample Merged Analysis Over East Asia, Animation

Summary A prototype algorithm is developed to define daily precipitation analysis on a 0.25 o lat/lon over land by merging gauge observations and CMORPH satellite estimates More work needs to be done to refine the system and to implement the system for global applications Fine tuning of data pair collecting scheme for the PDF matching procedures Accurate definition of error structure for the gauge analysis and satellite estimates Comprehensive examinations of system performance Modifications of the system structure to better fit the input data availability, quality, and stability

CMORPH Error [1]  Assuming CMORPH error variance is proportional to the estimated precipitation amount  Proportional constant is determined through comparison with gauge analysis over grid boxes with at least one gauge using data over China for summer 2007  CMORPH error is defined for each grid box of 0.25 o lat/lon using the curve in the bottom panel of the figure  Further work is required to set the error also as a function of region, season and sampling

CMORPH Error [2]  Sample CMORPH error estimation for August 2, 2007

CMORPH Error [3]  In performing OI, we also need to set the correlation between errors occurred over two separate points  For observations (gauge), we assume that the correlation between errors at two different locations is zero  For CMORPH, we assume the error correlation is a function of the distance between the two points, expressed as an exponential function of the negative distance  In this test, we arbitrarily set the e- folding distance as 30km  Further work is required to accurately define the error function

Gauge Error [1]  Assuming gauge error variance is proportional to the observed precipitation amount and inversely proportional to the number of gauges  Proportional constant is set arbitrarily in this test, to make sure the gauge error is smaller than the CMORPH error when there is at least one gauge  Further work is needed to accurately define the error function, through comparison with gauge data over a region with dense network (e.g. OKALAHOMA MESONET)

Gauge Error [2]  Sample gauge error estimation for August 2, 2007

Cross-Validation Tests Spatial Distribution