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Planning for robust reserve networks using uncertainty analysis

Planning land-use for biodiversity conservation frequently involves computer-assisted reserve selection algorithms. Typically such algorithms operate on matrices of species presence?absence in sites, or on species-specific distributions of model predicted probabilities of occurrence in grid cells. There are practically always errors in input data?erroneous species presence?absence data, structural and parametric uncertainty in predictive habitat models, and lack of correspondence between temporal presence and long-run persistence. Despite these uncertainties, typical reserve selection methods proceed as if there is no uncertainty in the data or models. Having two conservation options of apparently equal biological value, one would prefer the option whose value is relatively insensitive to errors in planning inputs. In this work we show how uncertainty analysis for reserve planning can be implemented within a framework of information-gap decision theory, generating reserve designs that are robust to uncertainty. Consideration of uncertainty involves modifications to the typical objective functions used in reserve selection. Search for robust-optimal reserve structures can still be implemented via typical reserve selection optimization techniques, including stepwise heuristics, integer-programming and stochastic global search.

Ecological Modelling↗

Earthquake classification, location, and error analysis in a volcanic environment: implications for the magmatic system of the 1989-1990 eruptions at redoubt volcano, Alaska

Determination of the precise locations of seismic events associated with the 1989-1990 eruptions of Redoubt Volcano posed a number of problems, including poorly known crustal velocities, a sparse station distribution, and an abundance of events with emergent phase onsets. In addition, the high relief of the volcano could not be incorporated into the hypoellipse earthquake location algorithm. This algorithm was modified to allow hypocenters to be located above the elevation of the seismic stations. The velocity model was calibrated on the basis of a posteruptive seismic survey, in which four chemical explosions were recorded by eight stations of the permanent network supplemented with 20 temporary seismographs deployed on and around the volcanic edifice. The model consists of a stack of homogeneous horizontal layers; setting the top of the model at the summit allows events to be located anywhere within the volcanic edifice. Detailed analysis of hypocentral errors shows that the long-period (LP) events constituting the vigorous 23-hour swarm that preceded the initial eruption on December 14 could have originated from a point 1.4 km below the crater floor. A similar analysis of LP events in the swarm preceding the major eruption on January 2 shows they also could have originated from a point, the location of which is shifted 0.8 km northwest and 0.7 km deeper than the source of the initial swarm. We suggest this shift in LP activity reflects a northward jump in the pathway for magmatic gases caused by the sealing of the initial pathway by magma extrusion during the last half of December. Volcano-tectonic (VT) earthquakes did not occur until after the initial 23-hour-long swarm. They began slowly just below the LP source and their rate of occurrence increased after the eruption of 01:52 AST on December 15, when they shifted to depths of 6 to 10 km. After January 2 the VT activity migrated gradually northward; this migration suggests northward propagating withdrawal of magma from a plexus of dikes and/or sills located in the 6 to 10 km depth range. Precise relocations of selected events prior to January 2 clearly resolve a narrow, steeply dipping, pencil-shaped concentration of activity in the depth range of 1-7 km, which illuminates the conduit along which magma was transported to the surface. A third event type, named hybrid, which blends the characteristics of both VT and LP events, originates just below the LP source, and may reflect brittle failure along a zone intersecting a fluid-filled crack. The distribution of hybrid events is elongated 0.2-0.4 km in an east-west direction. This distribution may offer constraints on the orientation and size of the fluid-filled crack inferred to be the source of the LP events. ?? 1994.

Journal of Volcanology and Geothermal Research↗

Wildlife tradeoffs based on landscape models of habitat

It is becoming increasingly clear that the spatial structure of landscapes affects the habitat choices and abundance of wildlife. In contrast to wildlife management based on preservation of critical habitat features such as nest sites on a beach or mast trees, it has not been obvious how to incorporate spatial structure into management plans. We present techniques to accomplish this goal. We used multiscale logistic regression models developed previously for neotropical migrant bird species habitat use in South Carolina (USA) as a basis for these techniques. Based on these models we used a spatial optimization technique to generate optimal maps (probability of occurrence, P = 1.0) for each of seven species. To emulate management of a forest for maximum species diversity, we defined the objective function of the algorithm as the sum of probabilities over the seven species, resulting in a complex map that allowed all seven species to coexist. The map that allowed for coexistence is not obvious, must be computed algorithmically, and would be difficult to realize using rules of thumb for habitat management. To assess how management of a forest for a single species of interest might affect other species, we analyzed tradeoffs by gradually increasing the weighting on a single species in the objective function over a series of simulations. We found that as habitat was increasingly modified to favor that species, the probability of presence for two of the other species was driven to zero. This shows that whereas it is not possible to simultaneously maximize the likelihood of presence for multiple species with divergent habitat preferences, compromise solutions are possible at less than maximal likelihood in many cases. Our approach suggests that efficiency of habitat management for species diversity can by maximized for even small landscapes by incorporating spatial context. The methods we present are suitable for wildlife management, endangered species conservation, and nature reserve design.

Conference Paper↗

Recognition of fiducial surfaces in lidar surveys of coastal topography

A new method for the recognition and mapping of surfaces in coastal landscapes that provide accurate and low variability topographic measurements with respect to airborne lidar surveys is described and demonstrated in this paper. Such surfaces are herein termed "fiducial" because they can represent reference baseline morphology in Studies of coastal change due to natural or anthropogenic causes. Non-fiducial surfaces may also be identified in each separate lidar survey to be used in a given geomorphic change analysis. Sites that are non-fiducial in either or both lidar surveys that bracket the time period under investigation may be excluded from consideration in subsequent calculations of survey-to-survey elevation differences to eliminate spurious indications of landscape change. This new analysis method, or lidar fiducial surface recognition (LFSR) algorithm, is intended to more fully enable the non-ambiguous Use of topographic lidar in a range of coastal investigations. The LFSR algorithm may be widely applied, because it is based solely on the information inherent in the USGS/NASA/NOAA airborne topographic lidar coverage that exists for most of the contiguous U.S. coastline.

Photogrammetric Engineering and Remote Sensing↗

Hydroacoustic Current Meters for the Measurement of Discharge in Shallow Rivers and Streams

The U.S. Geological Survey (USGS) is evaluating the use of hydroacoustic current meters for making discharge measurements in shallow rivers and streams. The USGS historically has made discharge measurements in shallow rivers using mechanical, impellor-type current meters attached to a wading rod. The evaluation project has focused on three categories of hydroacoustic meters: an acoustic Doppler velocimeter (ADV) called a Flowtracker3, an acoustic Doppler velocity profiler (BoogieDopp), and bottom-tracking acoustic Doppler current profilers (ADCPs). The USGS role in this project includes providing USGS discharge-computation methods and algorithms to instrument manufacturers and evaluating instruments in the laboratory and field. An ADV (Flowtracker) designed for making discharge measurements in shallow rivers, has been tested in a USGS tow tank and was found to meet USGS calibration standards for mechanical, impellor-type current meters. The Flowtracker was field tested by USGS offices in five states; the tests were conducted by comparing discharge measurements made with the ADV to discharge measurements made with mechanical, impellor-type current meters. In general, the comparisons of Flowtracker performance to mechanical-meter results were favorable. An acoustic Doppler velocity profiler (BoogieDopp) is being evaluated for making discharge measurements in shallow rivers. The Boogiedopp will measure vertical velocity profiles at stationary positions across a channel, and the velocity profiles will be used to compute discharge. Discharge-computation software based on USGS methods and algorithms is under development for the acoustic Doppler velocity profiler. The USGS will evaluate bottom-tracking ADCPs from two manufacturers for making discharge measurements in shallow water. The bottom-tracking feature allows ADCPs to compute discharge from a moving platform as the platform moves across the channel.

Conference Paper↗

Extracting transient Rayleigh wave and its application in detecting quality of highway roadbed

This paper first explains the tau-p mapping method of extracting Rayleigh waves (LR waves) from field shot gathers. It also explains a mathematical model of physical character parameters of quality of high-grade roads. This paper then discusses an algorithm of computing dispersion curves using adjacent channels. Shear velocity and physical character parameters are obtained by inversion of dispersion curves. The algorithm using adjacent channels to calculating dispersion curves eliminates average effects that exist by using multi-channels to obtain dispersion curves so that it improves longitudinal and transverse resolution of LR waves and precision of non-invasive detection, and also broadens its application fields. By analysis of modeling results of detached computation of the ground roll and real examples of detecting density and pressure strength of a high-grade roadbed, and by comparison of shallow seismic image method with borehole cores, we concluded that: 1 the abnormal scale and configuration obtained by LR waves are mostly the same as the result of shallow seismic image method; 2 an average relative error of density obtained from LR waves inversion is 1.6% comparing with borehole coring; 3 transient LR waves in detecting density and pressure strength of a high-grade roadbed is feasible and effective.

Conference Paper↗

Striping artifact reduction in lunar orbiter mosaic images

Photographic images of the moon from the 1960s Lunar Orbiter missions are being processed into maps for visual use. The analog nature of the images has produced numerous artifacts, the chief of which causes a vertical striping pattern in mosaic images formed from a series of filmstrips. Previous methods of stripe removal tended to introduce ringing and aliasing problems in the image data. This paper describes a recently developed alternative approach that succeeds at greatly reducing the striping artifacts while avoiding the creation of ringing and aliasing artifacts. The algorithm uses a one dimensional frequency domain step to deal with the periodic component of the striping artifact and a spatial domain step to handle the aperiodic residue. Several variations of the algorithm have been explored. Results, strengths, and remaining challenges are presented. ?? 2006 IEEE.

Conference Paper↗

A semi-implicit finite difference model for three-dimensional tidal circulation,

A semi-implicit finite difference formulation for the numerical solution of three-dimensional tidal circulation is presented. The governing equations are the three-dimensional Reynolds equations in which the pressure is assumed to be hydrostatic. A minimal degree of implicitness has been introduced in the finite difference formula so that in the absence of horizontal viscosity the resulting algorithm is unconditionally stable at a minimal computational cost. When only one vertical layer is specified this method reduces, as a particular case, to a semi-implicit scheme for the solutions of the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm is fast, accurate and mass conservative. This formulation includes the simulation of flooding and drying of tidal flats, and is fully vectorizable for an efficient implementation on modern vector computers.

Conference Paper↗

Consistent and efficient processing of ADCP streamflow measurements

The use of Acoustic Doppler Current Profilers (ADCPs) from a moving boat is a commonly used method for measuring streamflow. Currently, the algorithms used to compute the average depth, compute edge discharge, identify invalid data, and estimate velocity and discharge for invalid data vary among manufacturers. These differences could result in different discharges being computed from identical data. Consistent computational algorithm, automated filtering, and quality assessment of ADCP streamflow measurements that are independent of the ADCP manufacturer are being developed in a software program that can process ADCP moving-boat discharge measurements independent of the ADCP used to collect the data.

Conference Paper↗

Preparing for THEMIS controlled global Mars mosaics

We have begun work to prepare for producing controlled 2001 Mars Odyssey THEMIS infrared (IR) and visible (VIS) global mosaics of Mars. This effort is being coordinated with colleagues from Arizona State University and on the THEMIS team who plan to address radiometric issues in making such mosaics. We are concentrating on geometric issues. Several areas of investigation are now in progress, including: a) characterizing the absolute pointing accuracy of THEMIS images; b) investigating whether automatic tie point matching algorithms could be used to provide connections between overlapping THEMIS images; c) developing algorithms to allow for the photogrammetric (bundle) adjustment of the THEMIS IR (line scanner) camera images. Our primary goal in this pilot study effort will be to make several test control THEMIS mosaics and better determine which methods could be used, which require development, and what level of effort is required, in order to make large regional or global controlled THEMIS mosaics.

Conference Paper↗

Model structural uncertainty quantification and hydrogeophysical data integration using airborne electromagnetic data

A irborne electromagnetic (AEM) data are used to estimate large - scale model structural geometry, i.e. the spatial distribution of different lit hological units based on assumed or estimated resistivity - lithology relationships, and the uncertainty in those structures given imperfect measurements. Geophysically derived estimates of model structural uncertainty are then combined with hydrologic obse rvations to assess the impact of model structural error on hydrologic calibration and prediction errors. Using a synthetic numerical model, we describe a sequential hydrogeophysical approach that: (1) uses Bayesian Markov chain Monte Carlo (McMC) methods to produce a robust estimate of uncertainty in electrical resistivity parameter s , (2) combines geophysical parameter uncertainty estimates with borehole observations of lithology to produce probabilistic estimates of model structural uncertainty over the e ntire AEM survey area using geostatistical sequential indicator simulation algorithms, and (3) uses model structural estimates along with hydrologic observations to quantify both hydrologic parameter and prediction uncertainty using a second McMC sampling algorithm. Results of simulations will be presented that illustrate the complete workflow from geophysical parameter uncertainty analysis to the impact of model structural uncertainty on hydrologic parameter estimates.

Conference Paper↗

New operational national satellite burned area product

Introduction Lack of consistent spatial and temporal fire information with relevant spatial resolution hinders land management and broad-scale assessments of fire activity, especially in the eastern United States and the Great Plains where fi re is important ecologically and culturally. Remote sensing can be used to monitor fi re activity, augment existing fi re data, and fill information gaps. In particular, Landsat offers one of the most complete time series of remote sensing data sets as the Landsat satellites with spectral bands useful for mapping fi res and burn severity have been operational since 1984. Furthermore, Landsat satellite imagery collect data at a resolution useful for on-the-ground comparisons and management decisions. Methods A gradient-boosting regression model algorithm was used to predict burn probabilities (BP), indicating the likelihood that a pixel had burned in a fire. Then the algorithm translated the burn probability images to burn classification (BC) images using thresholding and region growing. Burned areas smaller than 5 acres were removed to reduce noise. The BP and BC products were generated for Landsat scenes collected from 1984 to present with <= 80% cloud cover and are available for download from USGSs EarthExplorer website (www.earthexplorer. usgs.gov). Annual summaries were also produced from the scene-level BC and BP products. These include: 1) the maximum burn probability value from all scenes in a year, (2) the burn classification count, or the number of times a pixel was classified as burned in a year, (3) the burn date, or the day of year of the first Landsat scene a pixel was classified as burned, and (4) a burn classification which removes burned areas still visible from previous years with a filter. Results The Landsat Burned Area Products identified 183% more burned area than the Monitoring Trends in Burn Severity and 56% more burned area than the MODIS MCD64A1.006 products2. From 1984 through 2018, annual burned area mapped by the Landsat Burned Area Products averaged 30,000 km2, ranged between 14,000 km2 in 1991 and 46,500 km2 in 2012, and increased over time at a rate of 356 km2/year. The Landsat Burned Area products consistently map burned areas 5 acres or larger over time while capturing unburned islands within fi res. Such characteristics are critical for understanding long-term impacts of fi res on human and natural systems. The products are being routinely produced as new Landsat data are collected and demonstrate the utility remote sensing offers for monitoring landscape change.

Report↗

Camera trap distance sampling survey design, Andersen Airforce Base, Guam

Reliable population estimates of animal density is one of the most elementary needs for the control and management of wildlife, particularly for introduced ungulates on oceanic islands. On Guam, Philippine deer (Rusa marianna) and wild pigs (Sus scrofa; wild boar and descendants of domestic pigs) cause agricultural and ecological damage and are hunted for recreational, nutritional, and cultural uses. Most common population estimation methods are based on capture-recapture and related methods that require marking or uniquely identifying individuals. Capturing, marking, and either recapturing or resighting individuals repeatedly is labor intensive and expensive. In many situations marking or individually distinguishing animals is not feasible, necessitating estimating densities and abundance from unmarked animal populations. Motion-triggered camera traps are a relatively low-cost approach that can be used to generate presence/pseudo-absence and indices of relative abundance on multiple species simultaneously. We used distance sampling with camera traps to estimate deer and pig densities from non-independent observations of unmarked animals while accounting for imperfect detection where some present individuals are not detected. We present methods to (1) process the digital imagery data automatically for species detection and species categorization using a machine learning algorithm, (2) automatically estimate distance to detected species using a separate machine learning algorithm, and (3) estimate densities using distance sampling with camera trap methods. We compare accuracy statistics and results of ungulate densities estimated from automated methods to those estimated from manual assessment. We collected 7,695 videos: 381 videos contained deer and 377 contained pigs. The object detection and identification model performed well with overall accuracy above 80% and F1 scores above 0.9. The hazard-rate key detection function was chosen for deer and pigs based on Akaike’s information criterion accounting for overdispersion. Deer density estimates were 0.53 ± 0.20 deer/ha with higher density in the Plateau area than the Tarague area of Guam. Pig density estimates were 0.53 ± 0.32 pigs/ha, also with higher densities in the Plateau area than the Tarague area. Coefficients of variation ranged from 0.38 to 1.15, and greater numbers of camera traps would be required for pigs than deer to achieve desired coefficients of variation. On average, 101.9 ± 82.3 deer and 131.6 ± 118.8 pigs were detected per day. Microsite heterogeneity affected densities where orientation-specific estimates were less precise than estimates made with the full dataset. We developed a camera trap survey design based on standard camera trapping sampling protocols using motion-activated, digital cameras and determined that distance sampling methods using camera traps produce reliable densities of unmarked deer and pigs on Guam. Our camera trap survey design is based on a regularly sized trapping grid that is generalizable and can be expanded to survey other areas of Guam.

Guam↗

State-parameter estimation of ecosystem models using a smoothed ensemble Kalman filter

Much of the effort in data assimilation methods for carbon dynamics analysis has focused on estimating optimal values for either model parameters or state variables. The main weakness of estimating parameter values alone (i.e., without considering state variables) is that all errors from input, output, and model structure are attributed to model parameter uncertainties. On the other hand, the accuracy of estimating state variables may be reduced if the temporal evolution of parameter values is not incorporated. This research develops a smoothed ensemble Kalman filter (SEnKF) to estimate simultaneously the system states and model parameters of an eddy flux partition model. The approach is used to assimilate observed fluxes of carbon and major driving forces at an AmeriFlux forest station: Howland, Maine, USA. The aim of applying a kernel-smoothing algorithm to an ensemble Kalman filter is to overcome the dramatic, sudden change of parameter values in time and the loss of continuity between two consecutive points in time. Our analysis demonstrates that model parameters, such as light use efficiency, respiration coefficients, minimum and optimum temperatures for photosynthetic activity, and so on, are highly constrained by eddy flux data at daily-to-seasonal time scales. The SEnKF stabilizes parameter values quickly regardless of the initial values of the parameters. Potential ecosystem light use efficiency demonstrates a strong seasonality. Results show that the simultaneous parameter estimation procedure significantly improves model predictions. Results also show that the SEnKF can dramatically reduce variance in state variables stemming from the uncertainty of parameters and driving variables. The SEnKF is a robust and effective algorithm in evaluating and developing ecosystem models and in improving understanding and quantification of carbon cycle parameters and processes.

Conference Paper↗

Pattern recognition analysis and classification modeling of selenium-producing areas

Established chemometric and geochemical techniques were applied to water quality data from 23 National Irrigation Water Quality Program (NIWQP) study areas in the Western United States. These techniques were applied to the NIWQP data set to identify common geochemical processes responsible for mobilization of selenium and to develop a classification model that uses major-ion concentrations to identify areas that contain elevated selenium concentrations in water that could pose a hazard to water fowl. Pattern recognition modeling of the simple-salt data computed with the SNORM geochemical program indicate three principal components that explain 95% of the total variance. A three-dimensional plot of PC 1, 2 and 3 scores shows three distinct clusters that correspond to distinct hydrochemical facies denoted as facies 1, 2 and 3. Facies 1 samples are distinguished by water samples without the CaCO 3 simple salt and elevated concentrations of NaCl, CaSO 4 , MgSO 4 and Na 2 SO 4 simple salts relative to water samples in facies 2 and 3. Water samples in facies 2 are distinguished from facies 1 by the absence of the MgSO 4 simple salt and the presence of the CaCO 3 simple salt. Water samples in facies 3 are similar to samples in facies 2, with the absence of both MgSO 4 and CaSO 4 simple salts. Water samples in facies 1 have the largest selenium concentration (10 μg l −1 ), compared to a median concentration of 2·0 μg l −1 and less than 1·0 μg l −1 for samples in facies 2 and 3. A classification model using the soft independent modeling by class analogy (SIMCA) algorithm was constructed with data from the NIWQP study areas. The classification model was successful in identifying water samples with a selenium concentration that is hazardous to some species of water-fowl from a test data set comprised of 2,060 water samples from throughout Utah and Wyoming. Application of chemometric and geochemical techniques during data synthesis analysis of multivariate environmental databases from other national-scale environmental programs such as the NIWQP could also provide useful insights for addressing ‘real world’ environmental problems.

Journal of Chemometrics↗

Parameter optimization, sensitivity, and uncertainty analysis of an ecosystem model at a forest flux tower site in the United States

Ecosystem models are useful tools for understanding ecological processes and for sustainable management of resources. In biogeochemical field, numerical models have been widely used for investigating carbon dynamics under global changes from site to regional and global scales. However, it is still challenging to optimize parameters and estimate parameterization uncertainty for complex process-based models such as the Erosion Deposition Carbon Model (EDCM), a modified version of CENTURY, that consider carbon, water, and nutrient cycles of ecosystems. This study was designed to conduct the parameter identifiability, optimization, sensitivity, and uncertainty analysis of EDCM using our developed EDCM-Auto, which incorporated a comprehensive R package—Flexible Modeling Framework (FME) and the Shuffled Complex Evolution (SCE) algorithm. Using a forest flux tower site as a case study, we implemented a comprehensive modeling analysis involving nine parameters and four target variables (carbon and water fluxes) with their corresponding measurements based on the eddy covariance technique. The local sensitivity analysis shows that the plant production-related parameters (e.g., PPDF1 and PRDX) are most sensitive to the model cost function. Both SCE and FME are comparable and performed well in deriving the optimal parameter set with satisfactory simulations of target variables. Global sensitivity and uncertainty analysis indicate that the parameter uncertainty and the resulting output uncertainty can be quantified, and that the magnitude of parameter-uncertainty effects depends on variables and seasons. This study also demonstrates that using the cutting-edge R functions such as FME can be feasible and attractive for conducting comprehensive parameter analysis for ecosystem modeling.

Massachusetts↗

Assessment of parametric uncertainty for groundwater reactive transport modeling,

The validity of using Gaussian assumptions for model residuals in uncertainty quantification of a groundwater reactive transport model was evaluated in this study. Least squares regression methods explicitly assume Gaussian residuals, and the assumption leads to Gaussian likelihood functions, model parameters, and model predictions. While the Bayesian methods do not explicitly require the Gaussian assumption, Gaussian residuals are widely used. This paper shows that the residuals of the reactive transport model are non-Gaussian, heteroscedastic, and correlated in time; characterizing them requires using a generalized likelihood function such as the formal generalized likelihood function developed by Schoups and Vrugt (2010). For the surface complexation model considered in this study for simulating uranium reactive transport in groundwater, parametric uncertainty is quantified using the least squares regression methods and Bayesian methods with both Gaussian and formal generalized likelihood functions. While the least squares methods and Bayesian methods with Gaussian likelihood function produce similar Gaussian parameter distributions, the parameter distributions of Bayesian uncertainty quantification using the formal generalized likelihood function are non-Gaussian. In addition, predictive performance of formal generalized likelihood function is superior to that of least squares regression and Bayesian methods with Gaussian likelihood function. The Bayesian uncertainty quantification is conducted using the differential evolution adaptive metropolis (DREAM (zs) ) algorithm; as a Markov chain Monte Carlo (MCMC) method, it is a robust tool for quantifying uncertainty in groundwater reactive transport models. For the surface complexation model, the regression-based local sensitivity analysis and Morris- and DREAM (ZS) -based global sensitivity analysis yield almost identical ranking of parameter importance. The uncertainty analysis may help select appropriate likelihood functions, improve model calibration, and reduce predictive uncertainty in other groundwater reactive transport and environmental modeling.

Water Resources Research↗

A Bayesian kriging approach for blending satellite and ground precipitation observations

Drought and flood management practices require accurate estimates of precipitation. Gauge observations, however, are often sparse in regions with complicated terrain, clustered in valleys, and of poor quality. Consequently, the spatial extent of wet events is poorly represented. Satellite-derived precipitation data are an attractive alternative, though they tend to underestimate the magnitude of wet events due to their dependency on retrieval algorithms and the indirect relationship between satellite infrared observations and precipitation intensities. Here we offer a Bayesian kriging approach for blending precipitation gauge data and the Climate Hazards Group Infrared Precipitation satellite-derived precipitation estimates for Central America, Colombia, and Venezuela. First, the gauge observations are modeled as a linear function of satellite-derived estimates and any number of other variables&mdash;for this research we include elevation. Prior distributions are defined for all model parameters and the posterior distributions are obtained simultaneously via Markov chain Monte Carlo sampling. The posterior distributions of these parameters are required for spatial estimation, and thus are obtained prior to implementing the spatial kriging model. This functional framework is applied to model parameters obtained by sampling from the posterior distributions, and the residuals of the linear model are subject to a spatial kriging model. Consequently, the posterior distributions and uncertainties of the blended precipitation estimates are obtained. We demonstrate this method by applying it to pentadal and monthly total precipitation fields during 2009. The model's performance and its inherent ability to capture wet events are investigated. We show that this blending method significantly improves upon the satellite-derived estimates and is also competitive in its ability to represent wet events. This procedure also provides a means to estimate a full conditional distribution of the &ldquo;true&rdquo; observed precipitation value at each grid cell.

Water Resources Research↗