The PRISM Approach to Mapping Climate in Complex Regions

The PRISM Approach to Mapping Climate in Complex Regions
Christopher Daly Director, PRISM Group Northwest Alliance for Computational Science and Engineering Department of Geosciences Oregon State University Corvallis, Oregon, USA GROUP PRISM PRISM Overview

PRISM Group Facts PRISM GROUP
5-FTE applied research team at Oregon State University, 100% externally funded The PRISM Group is the only center in the world dedicated solely to the spatial analysis of climate PRISM climate mapping technology has been continuously developed, and repeatedly peer-reviewed, since 1991 The PRISM Group is the de facto climate mapping center for the US The PRISM Group is advancing “Geospatial Climatology” as an emerging discipline GROUP PRISM PRISM Overview

It the landscape typically looked like the wheat fields of South Dakota, there probably wouldn’t be much call for climate mapping system such as PRISM… PRISM Overview

Oregon Annual Precipitation
But complex terrain must be considered in many places. PRISM Overview

Elevation has a profound impact on climate…moving from the bottom of this mountain in Colorado is like moving northward hundreds of kilometers for temperature, and precipitation also changes dramatically. PRISM Overview

Unfortunately, most climate observations are taken in places where people live, because they are accessible and convenient. PRISM Overview

A good climate mapping scheme needs to be able to extrapolate below the lowest stations… PRISM Overview

…and above the highest stations. The summit of Mt. McKinley is more than 18,000 feet above the highest routine climate station; not taking into account elevation in mapping here would be a big mistake. PRISM Overview

Rationale Observations are rarely sufficient to directly represent the spatial patterns of climate Human-expert mapping methods often produce the best products, but are slow, inconsistent, and non-repeatable Purely statistical mapping methods are fast and repeatable, but rarely provide the best accuracy, detail, and realism Therefore… The best method may be a statistical approach that is automated, but developed, guided and evaluated with expert knowledge GROUP PRISM PRISM Overview

Knowledge-Based System KBS
Knowledge acquisition capability – Elicit expert information Knowledge base – Store of knowledge Inference Engine – Infer solutions from stored knowledge User interface – Interaction and explanation Independent verification – Knowledge refinement The knowledge-based system (KBS), used in computer science, is a good conceptual model for how to inject knowledge into a climate mapping system. The KBS has a knowledge acquisition capability, a place to store the acquired knowledge, an inference engine which makes decisions based upon this knowledge, and a user interface that allows interaction between the user and program. An additional component we have added is independent verification. Independent evaluation of results is often overlooked, but is critical to the ongoing process of knowledge acquisition and refinement. GROUP PRISM PRISM Overview

Parameter-elevation Regressions on Independent Slopes Model
PRISM Parameter-elevation Regressions on Independent Slopes Model Generates gridded estimates of climatic parameters Moving-window regression of climate vs. elevation for each grid cell Uses nearby station observations Spatial climate knowledge base weights stations in the regression function by their physiographic similarity to the target grid cell PRISM (Parameter-elevation Regressions on Independent Slopes Model) is an example of a KBS for climate mapping. It generates gridded estimates of climate parameters through a moving-window regression of climate vs. elevation for each grid cell, using nearby stations to populate the regression. The unique part of PRISM is its spatial climate knowledge base that weights stations entering the regression function by their physiographic, and hence climatic, similarity to the target grid cell (cell being modeled). GROUP PRISM PRISM Overview

Interface This figure outlines the conceptual structure of a spatial climate KBS, using PRISM as the central computer model. Our KBS is not a mature one, and the problem domain is very large. Therefore, knowledge must be accumulated, generalized, and refined through an ongoing process of model application; development of algorithm prototypes, parameters, and parameter settings; and verification of results. Over time, there is a slow but steady transfer of knowledge from the user to the model (thick arrow marked KA). PRISM Overview

PRISM Knowledge Base PRISM Elevation Influence on Climate GROUP
Let’s take a look at the major components of the PRISM knowledge base. The first, and most important, is the influence of elevation on climate. GROUP PRISM PRISM Overview

1961-90 Mean January Precipitation, Sierra Nevada, CA, USA
Oregon Annual Precipitation In these examples from around the world, we see that precipitation generally increases with elevation and temperature decreases; the form of these variations is often linear. PRISM Overview

1961-90 Mean August Max Temperature, Sierra Nevada, CA, USA
Oregon Annual Precipitation PRISM Overview

1963-1993 Mean November Precipitation, Puerto Rico
PRISM Overview

1963-93 Mean June Maximum Temperature, Puerto Rico
PRISM Overview

1971-90 Mean February Precipitation, European Alps
PRISM Overview

1961-90 Mean September Max Temperature, Qin Ling Mountains, China
Oregon Annual Precipitation PRISM Overview

PRISM Moving-Window Regression Function Oregon Annual Precipitation
Mean April Precipitation, Qin Ling Mountains, China Here is output from the PRISM Graphical User Interface (GUI), showing a precipitation-elevation regression function for the north slope of the Qin Ling Mountains in central China. The red square is the target pixel, and the black dots are the surrounding station locations. On the scatterplot, the blue dots represent the stations, plotted by elevation on the x-axis and precipitation on the y-axis. The size of each dot represents the relative weight of the station in the regression function. Weighted linear regression PRISM Overview

Governing Equation PRISM
Moving-window regression of climate vs elevation y = β1x + β0 Y = predicted climate element x = DEM elevation at the target cell β0 = y-intercept β1 = slope x,y pairs - elevation and climate observations from nearby climate stations Because of the controlling influence of elevation on climate patterns, the basic assumption in PRISM is that, given a homogenous hillslope, climate can be predicted through a moving-window regression function with elevation in a linear fashion. GROUP PRISM PRISM Overview

W = f {Wd Wz Wc Wf Wp Wl Wt We}
Station Weighting Combined weight of a station is: W = f {Wd Wz Wc Wf Wp Wl Wt We} Distance Elevation Clustering Topographic Facet (orientation) Coastal Proximity Vertical Layer (inversion) Topographic Index (cold air pooling) Effective Terrain Height (orographic profile) The influence of each nearby station in the regression function is dictated by a series of weighting functions, each designed to minimize the effects of factors other than elevation on the regression prediction. The farther away a station is, both horizontally and vertically, the less weight is given. Stations clustered with each other are down-weighted so as to not over-sample a given location. Stations on the same side of a terrain feature as the target grid cell are weighted more highly than others. Depending if the target cell is within the boundary layer or the free atmosphere, stations in the same atmospheric layer are weighted more highly than those in a different layer. Stations with similar proximity to coastal influences are weighted more highly than those that are not. Stations on terrain features that present a profile of similar steepness and prominence that is similar to that of the target cell are weighted highly. GROUP PRISM PRISM Overview

PRISM Knowledge Base PRISM Elevation Influence on Climate
Terrain-Induced Climate Transitions (topographic facets, moisture index) Let’s look at some of the meteorological concepts behind these weighting functions. The first is topographic facet weighting, which accounts for terrain-induce climatic transitions, such as rain shadows. GROUP PRISM PRISM Overview

This is a PRISM map of mean annual precipitation in Oregon
This is a PRISM map of mean annual precipitation in Oregon. A well-defined rain shadow is evident in the middle of the state, produced by the blocking effects of the Cascade Mountains. PRISM Overview

Rain Shadow: 1961-90 Mean Annual Precipitation
Oregon Cascades Portland Mt. Hood Eugene Dominant PRISM KBS Components Elevation Terrain orientation Terrain steepness Moisture Regime Mt. Jefferson 2500 mm/yr 2200 mm/yr Sisters Three Sisters 350 mm/yr Here is a 3D view of the Oregon Cascades rain shadow. Mean annual precipitation drops from 2200 mm/yr at the crest of the Cascades, to only 350 mm/yr just down the hill to the east. Redmond N Bend PRISM Overview

Let’s take a closed look at how PRISM works in these areas, and visit Santiam Pass, and area with one of the steepest rain shadows in the country. PRISM Overview

1961-90 Mean Annual Precipitation, Cascade Mtns, OR, USA
Here is a graphic output of the PRISM GUI, showing mean annual precipitation vs elevation for a grid cell just west of the pass, on the windward side (white vertical line represents the Cascade crest). Here, the predicted precipitation is about 2000 per year. PRISM Overview

1961-90 Mean Annual Precipitation, Cascade Mtns, OR, USA
When we move PRISM to just east of the crest, the regression function “jumps” down to a new position that is much drier than the windward position, weighting stations on the east side more highly than those on the west side, despite the large number and proximity of west-slope stations. PRISM Overview

Olympic Peninsula, Washington, USA
Another useful case study is the Olympic Mountains, Washington. Here, winter storms bring moisture in from the southwest, and are uplifted by the terrain, creating a precipitation maximum on the windward side and a minimum on the leeward side. The large black dots represent available station data. Note the lack of stations in the interior mountains. Flow Direction PRISM Overview

Topographic Facets  = 4 km  = 60 km PRISM Overview 5-8-08
PRISM topographic facets are depicted at up to 6 spatial scales. On the left, facets for a DEM at 4-km effective wavelength are shown. There are many small facets that are not represented by station data. On the rights, facets at a 60-km effective wavelength are shown. At this scale, the mountain range becomes oval in shape, and has a relatively simple facet pattern. In operation, PRISM starts with the smallest wavelength facet grid, and works up to the larger wavelength grids, accumulating similarly-oriented stations along the way. Once enough have been accumulated (specified by the user), the process stops. Thus , PRISM chooses the smallest scale facet representation allowable given the data density.  = 4 km  = 60 km PRISM Overview

Mean Annual Precipitation, 1961-90
Oregon Annual Precipitation Max ~ 7900 mm Full Model 3452 mm 3442 mm 4042 mm Max ~ 6800 mm This is a mean annual precipitation map produced by the full PRISM model. The numbers above the black arrows show the mean annual streamflow for three rivers on the windward side of the mountains. PRISM Overview

Max ~ 4800 mm 3452 mm 3442 mm 4042 mm Facet Weighting Disabled We now produce the same map, but with topographic facet weighting turned off. Note how the 7900-mm precipitation maximum has “collapsed” under the weight of the more numerous and nearby dry-side stations. Now, the predicted precipitation falls far short of the amount needed to account for streamflow, let alone evapotranspiration. PRISM Overview

Oregon Annual Precipitation Max ~ 3300 mm 3452 mm 3442 mm 4042 mm Elevation = 0 Now, we add insult to injury and turn off vertical extrapolation above the highest stations, leaving us with a map that is similar to that produced by an inverse-distance weighting interpolation algorithm. Precipitation amounts now are clearly very low, and do not reflect the orographic (terrain-driven) patterns in the region. PRISM Overview

Oregon Annual Precipitation Max ~ 7900 mm Full Model 3452 mm 3442 mm 4042 mm Max ~ 6800 mm …and back to the original map for comparison purposes. PRISM Overview

The rain shadows just shown operate all along the Pacific coast and into Canada and Alaska.
PRISM Overview

North of the conterminous US, data are often too sparse to use just topographic facet weighting to delineate the position and magnitude of the rain shadow. In these areas, a straight-line trajectory model is run over the coastal terrain to define relative moisture regimes, from wet to dry. Stations are then weighted by moisture regime, rather than topographic, facet when station data are sparse. The basic concept is the same, however: terrain should define the position of the rain shadow, not the density and placement of station data. PRISM Overview

Terrain-Induced Climate Transitions (topographic facets, moisture index) Coastal Effects The next component of the PRISM spatial climate knowledge base is coastal influence. GROUP PRISM PRISM Overview

Coastal Effects: 1971-00 July Maximum Temperature
Central California Coast – 1 km Sacramento Stockton San Francisco 34° Dominant PRISM KBS Components Elevation Coastal Proximity Inversion Layer Oakland Fremont San Jose Preferred Trajectories Santa Cruz 27° Pacific Ocean 20° Hollister The central California coast is well-known for its extreme gradients in maximum temperature in summer, caused by the interaction of the warm land mass and the adjacent cool Pacific Ocean. Coastal proximity is estimated with the PRISM coastal influence trajectory model, which performs a cost-benefit path analysis to find the optimum path marine air might take, given prevailing winds and terrain. Penalties are assessed for moving uphill, and for the length of the path, requiring the optimal path to be a compromise between the shortest path, and path of least terrain resistance. Monterey Salinas N PRISM Overview

1961-90 Mean July Maximum Temperature, Central California, USA
Here is a comparison of mean July maximum temperature for central California with and without coastal proximity weighting. With the weighting function enabled, the integrity of the cool coastal strip is maintained to a much greater degree. PRISM Overview Coastal Proximity Weighting OFF Coastal Proximity Weighting ON

Terrain-Induced Climate Transitions (topographic facets, moisture index) Coastal Effects The next component of the PRISM knowledge base is the two-later atmosphere. Two-Layer Atmosphere and Topographic Index GROUP PRISM PRISM Overview

TMAX-Elevation Plot for January TMIN-Elevation Plot for January
January Temperature, HJ Andrews Forest, Oregon, USA TMAX-Elevation Plot for January Layer Layer 2 TMIN-Elevation Plot for January In many parts of the world, especially at mid and high latitudes in winter, temperatures in the boundary layer are partly or totally decoupled from the free atmosphere. Temperature inversions are common, and can be powerful and persistent. Above are temperature maps and vertical profiles for the HJ Andrews Experimental Forest, some 80 km east of Eugene, Oregon, in the Oregon Cascades. Terrain here is steep, and solar radiation in winter in limited. The fitted lines show how PRISM would estimate minimum and maximum temperature in this situation. Based on an a priori estimation of the inversion top, PRISM divides the atmosphere into two layers, and performs the elevation regressions on each layer separately, allowing for a certain amount of crosstalk between layers near the inversion top. This allows temperature profiles with sharp changes in slope due to atmospheric layering to be simulated. Layer Layer 2 PRISM Overview

Mean Annual Precipitation, Hawaii
The two-layer model is also used to simulate mid-slope precipitation maxima that occur within moist layers on limited vertical extent. This 3D map of precipitation over the island of Hawaii shows the precipitation maximum at about 1000 m, with strong drying above the trade-wind inversion. Also note the rain shadow on the northwestern side of the island. PRISM Overview

United States Potential Winter Inversion
For mapping the country, the height of a potential wintertime inversion has been estimated and input to PRISM. Colored terrain is thought to be predominantly in the free atmosphere. PRISM Overview

Western US Topographic Index
Another factor that influence’s a site’s temperature regime is its susceptibility to cold air pooling. A useful way to assess this is to determine a site’s vertical position relative to local topographic features, such as valley bottom, mid slope, or ridge top. A “topographic index” grid was created, which describes the height of a pixel relative to the surrounding terrain height. PRISM uses this information to further weight stations during temperature interpolation. PRISM Overview

Central Colorado Terrain and Topographic Index
Gunnison Gunnison Here is a close-up of the terrain and topographic index in the Gunnison Valley and vicinity in central Colorado. The topographic index grid looks like the terrain grid, except that the average elevation within a ~20 km area is subtracted out, leaving the local elevation only. Sites in the Gunnison Valley have similar topographic index values than surrounding valleys, even though the surrounding valleys are not at the same elevation. Terrain Topographic Index PRISM Overview

January Minimum Temperature Central Colorado
Gunnison Gunnison Here are some snapshots of the PRISM GUI in operation for January minimum temperature in the same area. This first shot shows PRISM running for a pixel deep in the Gunnison Valley. PRISM down-weights stations that are not also in valley bottoms and within the climatological inversion layer. As can be seen in the scatterplot, these stations are colder than the others, and a low temperature is predicted. Valley Bottom Elev = 2316 m Below Inversion Lapse = 5.3°C/km T = -16.2°C PRISM Overview

Gunnison Mid-Slope Elev = 2921 m Above Inversion Lapse = 6.9°C/km T = -12.7°C We now move up the mountain to a mid-slope position. The group of highly-weighted stations has changed dramatically, and have temperatures that are significantly warmer than those in the valley bottoms. These stations are located on locally higher terrain, and are above the climatological inversion, and therefore should be less susceptible to cold air pooling. The predicted temperature is more than 3.5C warmer than the valley bottom, despite a 600-m increase in elevation. [The “station” at 5800m is a 500-mb upper-air estimate from the Global Upper Air Statistics reanalysis data base.] PRISM Overview

Gunnison Ridge Top Elev = 3779 m Above Inversion Lapse = 6.0°C/km T = -17.9°C On the ridge top, the regression line does not change much from its mid-slope position. But an additional 800-m elevation increase brings the predicted temperature down near or below that on the valley floor. PRISM Overview

Inversions – 1971-00 January Minimum Temperature
Central Colorado N Dominant PRISM KBS Components Elevation Topographic Index Inversion Layer Taylor Park Res. Crested Butte -18° -13° Gunnison -18°C This 3D view of the Gunnison Valley and vicinity in central Colorado show a temperature increase of 5C from the valley bottom to a midslope location at the inversion top, then a 5-C drop in temperature in the free atmosphere above that. Note the extensive “banana belts” along many mid-slope locations. Lake City PRISM Overview

Snake Plain PRISM 1971-2000 Mean January Minimum Temperature, 800-m
“Banana Belt” Here is a detail of just one of the many areas of the western US where cold air pooling and drainage are prevalent. In the mountains of eastern Idaho, cold air flows down from high-elevation ridges into the valleys each night, and out into the Snake Plain. The result are pockets of extremely cold air in local valleys, “banana belts” on hillslopes at middle elevations, with cold temperatures returning at the highest elevations. Note that not all the valleys are cold; many that are not susceptible to cold air pooling are much warmer than the surrounding mountainsides. Cold air drainage Snake Plain PRISM Overview

Inversions – 1971-00 July Minimum Temperature Northwestern California
Pacific Ocean Willits 9° Dominant PRISM KBS Components Elevation Inversion Layer Topographic Index Coastal Proximity Ukiah Lake Pilsbury. 10° 17° 16° Cloverdale Lakeport 12° Clear Lake 17° Inversions occur frequently on clear, calm, summer mornings. In northwestern California, summer minimum temperatures are highly inverted. Low temperature in the valleys are five or more degrees Celsius lower than those on the surrounding highlands. PRISM Overview

Terrain-Induced Climate Transitions (topographic facets, moisture index) Coastal Effects The next component of the PRISM knowledge base is the orographic effectiveness of terrain. Not all mountains have the same effect on precipitation patterns as others. Those presenting a steep profile to moisture-bearing winds will probably have a greater impact on precipitation patterns than those that are gently sloping or rolling. Two-Layer Atmosphere and Topographic Index Orographic Effectiveness of Terrain (Profile) GROUP PRISM PRISM Overview

United States Effective Terrain
United States Orographically Effective Terrain United States Effective Terrain Here is a map of mountains in the US that have an impact on precipitation patterns that is noticeable in the observed data. In these green (3D) areas, PRISM operates as it normally does. In the white (2D) areas, the interpolation method shifts away from a vertical, 3D approach, to a more horizontal, 2D approach. This is because terrain effects no longer dominate the observed patterns. PRISM Overview

The eastern slope of Colorado is an example of 2D-3D transition area. In the mountains, a 3D approach is needed. As one moves from the mountains to the plains, however, the terrain affect fades. When a strictly 3D approach is used everywhere, small, intricate features appear, even in relatively flat areas. These small features may not be real. In the 2D-3D transition mode, these small features fade and a simpler pattern emerges. PRISM Overview

Terrain-Induced Climate Transitions (topographic facets, moisture index) Coastal Effects Two-Layer Atmosphere and Topographic Index Once a high-quality climate is developed, it can be used as the basis for other maps, because basic spatial patterns of climate are relatively stable. This is the basis for “climatologcially-aided interpolation,” in which a climate map is used as the explanatory variable in the PRISM regression function, rather than a DEM. Orographic Effectiveness of Terrain (Profile) Persistence of climatic patterns (climatologically-aided interpolation) GROUP PRISM PRISM Overview

Leveraging Information Content of High-Quality Climatologies to Create New Maps with Fewer Data and Less Effort This method is being used operationally at the PRISM Group to create near real time climate maps for each month, 7-14 days after the end of that month. In the above example, July 2003 (right) was one of the warmest on record in the West. Even so, the local patterns of temperature bear a striking resemblance to the long-term climatological average for July (left). Climatology used in place of DEM as PRISM predictor grid PRISM Overview

PRISM Regression of “Climate vs Climate” or “Weather vs Climate”
This is a scatterplot showing how this method can be used for daily interpolation, as well. On the x-axis is the mean July temperature, and it is being regressed with the daily maximum temperature for July 20, This plot, for a location new Mount Hood in Oregon, shows that even though the temperature is nearly 5C above the mean, the spatial patterns are remarkably similar. 20 July 2000 Tmax vs Mean July Tmax PRISM Overview

Recent Projects Updated mean monthly P, Tmax, Tmin maps for the US at 800-m resolution (USDA-NRCS, NPS, USFS) Spatial-Probabilistic QC system for SNOTEL observations (NRCS) monthly precipitation climatologies for NW Oregon conditional on 700-mb flow direction (NWS Western Region) Extended monthly time series maps of P, Tmax, Tmin, Tdew for climate monitoring (USFS) GROUP PRISM PRISM Overview

Future Directions PRISM
Engage in collaborative projects to develop the use of PRISM and PRISM climatologies for downscaling numerical weather prediction models Continue to develop technology to move to smaller time steps and towards real time operation Explore using remotely-sensed data to improve PRISM accuracy in under-sampled areas (and vice-versa) Continue to develop PRISM’s Spatial Climate Knowledge Base GROUP PRISM PRISM Overview

The PRISM Approach to Mapping Climate in Complex Regions

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The PRISM Approach to Mapping Climate in Complex Regions

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