Analysis of daily variability of precipitation in a nested regional climate model: comparison with observations and doubled CO2 results

Analysis of daily variability of precipitation in a nested regional climate model: comparison with observations and doubled CO2 results

GLOBALANNGtNETARY ELSEVIER Global and Planetary Change 10 (199.5) 55-78 Analysis of daily variability of precipitation in a nested regional climate...

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GLOBALANNGtNETARY ELSEVIER

Global and Planetary

Change 10 (199.5) 55-78

Analysis of daily variability of precipitation in a nested regional climate model: comparison with observations and doubled CO, results L.O. Mearns, F. Giorgi, L. McDaniel, C. Shields National Center Received

for Atmospheric Research ‘, Boulder, Colorado,

USA

19 April 1993; accepted after revision 17 March 1994

Abstract We analyze daily mean, variability, and frequency of precipitation in two continuous 3 l/2 year long climate simulations over the continental U.S., one for present conditions and one for conditions under doubled carbon dioxide concentration, conducted with a regional climate model (RegCM) nested in a general circulation model (GCM). The purpose of the work is to analyze model errors and limitations in greater detail than previously done and to calculate quantities that eventually will be used to form climate change scenarios that account for changes in daily variability of precipitation. The models used are a version of the NCAR Community Climate Model (CCM) and the climate version (RegCM) of the NCAR/Penn State mesoscale model (MM4) at 60 km horizontal grid point spacing. Model output is compared with a 30-year daily observational data set for mainly two regions of the U.S.: the Northwest, and the central Great Plains. Statistics compared include mean daily precipitation, mean daily intensity, frequency, transition probabilities, quantiles of precipitation intensity, and interquartile ranges. We discuss how different measures of daily precipitation lead to different conclusions about the quality of the control run. For example, good agreement between model and observed data regarding mean daily precipitation usually results from compensating errors in the intensity and frequency fields (too high frequency and too low intensity). We analyze how detailed topographic features of the RegCM enhance the simulation of daily precipitation compared to the CCM simulation. In general, errors in all measures are smallest at the Northwest grid points, and the damping of the seasonal cycle of mean daily precipitation from the coast to inland Oregon is basically well reproduced. However, some errors in the frequency and intensity fields can be traced to inadequate representation of topography, even with a horizontal resolution of 60 km. Differences in the control and doubled CO, runs (for both RegCM and CCM) for these regions are also presented. The most significant changes for the RegCM grid points is increased variability of daily precipitation under doubled CO, conditions. Areas with significant changes (both increases and decreases) of precipitation frequency and intensity are found. There are some areas where frequency decreases, but precipitation mean daily amounts increase. Such changes, which would be masked by more traditional analyses of precipitation change, are important from a climate impacts point of view. The limitations on the analyses posed by small sample sizes are discussed.

’ The National Center for Atmospheric

Research

is sponsored

by the National Science Foundation.

0921-8181/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0921.8181(94)00020-4

1. Introduction In this paper we provide a detailed analysis of the daily precipitation climatology produced by the nested climate model experiments of Giorgi et al. (1994). The fine spatial resolution that can be attained with the nested regional climate model provides the opportunity to perform a detailed statistical analysis in order to: (1) more thoroughly diagnose model errors and limitations, including higher order moments of precipitation; (2) eventually include changes in daily climate variability in climate change scenarios; and (3) to examine changes in statistical properties over space. To these ends, the use of statistics suitable to evaluate daily variability of precipitation are necessary. We present and apply a suite of statistics and statistical tests, which forms a methodology for analyzing mean and variability of daily precipitation in climate models and observations. We also address several ancillary issues associated with the comparisons of observations and model output that affect the statistical results. These include: the effect of spatial aggregation of observations, the effect of changing the threshold of precipitation amount for defining rainfall occurrence, and the effect of sample size on the power of statistical tests applied. As introduction we first briefly review the general results for both temperature and precipitation of the climate experiments of Giorgi et al. (19941, provide background on other investigations of daily precipitation in climate models, and elaborate on the goals of our investigation. In section 2 we present the statistical methodology applied, and in section 3 the regions investigated and the comparisons made. The results for comparisons of observations with control run model output are presented in section 4, and in section 5 the results for comparisons of doubled CO, and control run outputs. Finally, we provide concluding remarks in section 6. 1.1. Ol,erc,iew

of the model experiment anulyzed

In recent years a regional climate modeling technique has been developed at the National Center for Atmospheric Research (NCAR) to produce high resolution regional climate simulations. This consists of increasing the model resolution locally by nesting a high resolution regional climate model (RegCM) in a

GCM over given areas of interest. In the (one way) nesting technique the lateral meteorological boundary conditions needed to run the RegCM are provided by the output of a GCM global climate run. The strategy is that the GCM can simulate the response of the global circulation to large scale forcings and the nested RegCM can account in a physically-based way for local, sub-GCM grid scale forcings (Giorgi and Mearns, 19911. Preliminary tests of the nesting technique have been carried out by Dickinson et al. (1989) and Giorgi (19901 for the U.S. using the NCAR Community Climate Model (CCM) and a version of the NCAR/Penn State mesoscale model (MM41 suitably modified for climate application (hereafter referred to as RegCM, Dickinson et al. 1989; Giorgi, 1990). These studies have clearly shown that the use of nested models leads to a much improved simulation of regional climatic detail than the USC of GCMs alone. Recently (Giorgi et al., 19941, RegCM was used to generate two continuous 3 l/2 year-long high resolution climate simulations over the continental United States, one for present-day conditions and one for conditions under doubled carbon dioxide concentration. The simulations were produced with RegCM nested in the GENESIS version of the CCM (Pollard and Thompson, 1995a,Thompson and Pollard, 1995). RegCM was run with a 60 km horizontal resolution over a domain encompassing the whole continental U.S. and adjacent ocean waters. The analysis of results was accomplished by computing a number of relevant spatial statistics (i.e. averages, spatial standard deviations and correlations) and seasonal patterns for the driving CCM and nested RegCM present day and 2 X CO, surface climatology. These statistics were then compared with each other and with climatic observations. For the present day conditions experiment, the nested regional model mean seasonal temperatures were within 1-2” C of observations (Legates and Willmott, 199Oa) except over the Great Lakes region, where temperature was overpredicted by 460 C. The CCM overpredicted precipitation throughout the continental U.S. (overall by about 60%) and especially over the West (by up to 300%). The nested RegCM overpredicted precipitation over the

L.O. Mearns et al. /Global and Planetary Change IO (1995) 55-78

West but underpredicted it over the Eastern U.S. It produced a considerable amount of topographicallyand lake-induced sub-GCM grid scale detail which, especially during the cold season, compared well (on a mean seasonal basis) with available high resolution climate data. Overall, based on a number of objective measures of climate simulation skill, the nested RegCM reproduced better than the driving CCM observed spatial and seasonal precipitation and temperature patterns. 2 X CO,-induced temperature change scenarios produced by the two models generally differed by less than several tenths of a degree except over the Great Lakes region where, because of the presence of the lakes in the nested model, the two model scenarios differed by more than one degree. Conversely, precipitation change scenarios from the two model simulations differed locally, in magnitude, sign, spatial and seasonal detail. These differences were often statistically significant and clearly associated with topographical features in RegCM, such as the presence of steep coastal ranges in the western U.S. 1.2. Reciew of analysis performed ated daily precipitation

on GCM-gener-

Studies that concern daily analysis of precipitation in climate models are relatively few. The studies by Reed (1986), and Wilson and Mitchell (1987) examine daily precipitation variability in the U. K. Meteorological Office climate model. In both studies, which focussed on the European section of the global domain, mean precipitation was overestimated, as was the frequency of precipitation, but extreme daily maximum values were underpredicted. Rind et al. (1989) found that in the control run of the Goddard Institute for Space Studies Model, over selected regions of North America, the model distributions of daily precipitation differed significantly from observations. In addition, too few light rain days were produced, and extreme daily values were overpredieted in the winter. Mearns et al. (1990) examined several versions of the CCM and found errors of too high and too low daily variability of precipitation depending on the version investigated. Most of these studies also include analysis of perturbed climate runs. For example, Gordon et al. (1992) present an analysis of the statistical changes

57

in rainfall under greenhouse conditions in the Commonwealth Scientific and Industrial Research Organization (CSIRO) GCM. The model indicates that in the middle latitudes of both the Northern and Southern hemispheres, the number of rain days declines and rainfall intensities increase. Houghton et al. (1990,, 1992) summarize 2 X CO, model results, and conclude that there is some indication that daily variability of precipitation could increase in selected regions, as could the frequency of heavy rainfall events. These statements, however, remain speculative. Some suggest (e.g., W. Washington, pers. comm.) that the analysis of daily rainfall in general circulation models probably is of limited value, given the crude horizontal resolution (i.e., the models cannot resolve important topographic influences on rainfall, nor synoptic scale precipitation processes) and the crude parameterizations of precipitation. Models, however, steadily improve, and the nested modeling technique described above mitigates some of the limitations of GCMs such that examination of daily precipitation may prove more fruitful. In addition, investigation of daily variability of, for example, precipitation, serves as a further model diagnostic. Finally, this analysis serves as a necessary precursor to developing daily climate data sets from the model output that can serve as inputs for impacts models (e.g., crop yield models), to analyze possible impacts of climate perturbations on various resource systems such as agriculture. The high resolution runs from the nested modeling approach provide the opportunity to investigate more sophisticated means of producing scenarios and quantifying uncertainties based on climate model errors in the control run. A complete description of the research steps involved in this process is provided by Mearns (1995). The lack of sufficiently detailed spatial and temporal scenarios, which include consideration of changes in daily climate variability have placed serious limitations on analysis of possible climate change impacts on various resource systems (Mearns, 1989).

2. Statistical methods employed Precipitation two processes:

can be viewed as a combination of an occurrence process and an inten-

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and Planetury

sity process. In general, the analysis of precipitation in climate models has ignored the two process nature of precipitation. Traditionally, validation of control runs, and analysis of changes from control run to some perturbed climate state proceed on the basis of comparing mean monthly or seasonal precipitation (e.g., Giorgi et al., 19941, very often without the use of statistical tests (e.g., Boer et al., 1992). Another important aspect of precipitation is the well known non-Gaussian nature of its distribution on various time scales, but particularly for time scales of one day or less, and for small sample sizes. Hence, many statistical tests that take as one of their assumptions a normal distribution of data, are not applicable to daily precipitation time series. Also, the treatment of day-to-day persistence of a mixed continuous/discrete process is more difficult than that of a continuous process, such as temperature. Because the present model runs are relatively short, rigorous statistical analysis of mean annual or monthly fields is limited, since the power of relevant statistical tests (with a sample size of three) would be relatively low. This limitation particularly affects the interpretation of the doubled CO? results and limits to a certain degree the entire enterprise of statistical evaluation. This is less so with regard to daily data, which in our case have, for example, a sample size of approximately 90 for investigating daily variability on a monthly basis. In this paper we emphasize the analysis of precipitation as a combination of processes and the use of statistical tests appropriate to the distribution characteristics of this variable. We present both overview graphical representations of comparisons between model output and observations as well as detailed statistical measures. Where possible, we eschew specific significance levels which result in making arbitrary, absolute distinctions between the model and observations, and instead rely on confidence intervals for the most part, so that the relatiL~e agreement between model and observed data can be discerned (Katz, 1992). Some of the statistics used have been chosen on the basis of future plans to formulate detailed quantitative scenarios of climate change. Regarding precipitation, this entails simulating precipitation as a stochastic process, the occurrence modeled as, for example, a first order Markov chain and the intensity

Change

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modeled according to some distribution, such as the gamma distribution. To construct such a model certain parameters must be estimated such as transition probabilities and the two parameters of the gamma distribution. Recent discussions of the use of such models in the analysis of observed daily precipitation and in the formulation of climate change scenarios may be found in Wilks (1992) and Gregory et al. t 1993). Katz (1985) provides a good review of daily precipitation occurrence models using Markov chains. The statistics presented here include: mean daily precipitation (on a monthly basis, average rainfall per day), mean daily intensity (i.e., rainfall per rain day), and frequency. These are presented as overview plots that display the seasonal cycle of these quantities. The first factor represents the traditional means of presenting climate model results. The latter two present the more detailed disaggregation of precipitation into intensity and frequency processes. First order transition probabilities are also calculated and one of them is presented, the likelihood of rain tomorrow given that it rained today (P,,). Alternatively, the persistence parameter, d, representing the over all first order autocorrelation of the occurrence process, defined as P,,:P,,,, could have been presented. We chose the former because this is one of the parameters actually used in a first order Markov chain model. The nature of the precipitation distributions is explored via monthly representations of certain quantiles of the distributions: 25th, 50th, 75th, and 90th. More detailed presentations are made via box plots of these quantiles including the absolute maximum value of the distribution. We also considered lengths of runs of wet and dry periods on a seasonal basis. Statistical tests include a test of the ratio of medians, which is a better measure of location than the mean for variables with asymmetric distributions. Specifically 95% confidence intervals of the ratios of medians are calculated. For this test the lognormal transform of the daily values is used to eliminate the skewness and minimize the distance between median and mean (Katz, 1983). The data are then retransformed for display of results. Comparisons of daily variability are analyzed via the interquartile range test, which is a good means of comparing daily precipitation variability, because of the asymmetric

L.O. Mearns et al. /Global and Planetary Change 10 (1995) 55-78

59

b: 1. :’ . .._ ,‘._ ‘._.

Fig. 1. Difference between model control run and observed precipitation and Willmott (1990b). Contour interval is 2 mm/day.

(mm/day)

for (a) January and (b) July. Observations

from Legates

60

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and Planetary Change 10 (19951 55-78

nature of the distribution (Mearns et al., 1990). Given that medians are compared to measure location, it is also then appropriate to use the interquartile ranges as a measure of scale of the precipitation distributions. The occurrence process is statistically analyzed by calculating confidence (95%) intervals of differences between precipitation frequency. The calculation of the two confidence intervals are described in Katz (1983), and details of the interquartile range test are provided in Mearns et al. (1989). The latter test is constructed to determine if the interquartile ranges of two different distributions of precipitation intensity are equal, using the difference between the ranges. Many more tests could have been performed (e.g., on the transition probabilities, which order Markov chain best fits the data), but what we selected is a good representation of tests related to the mean and variability of daily precipitation.

3. Regions

investigated

and comparisons

We initially examined four regions for possible detailed investigation: the Northwest, the central Great Plains, the Great Lakes region, and the Southeast. In the first three regions errors in mean seasonal precipitation in the general analysis (Giorgi et al., 1994) were at a relative minimum. Fig. 1 presents a comparison of differences between observed (Legates and Willmott, 1990b) and model mean monthly precipitation for January and July for the entire model domain. The positive bias in the west and negative

Table 1 Observation Station

stations and corresponding

bias in the east are clearly evident. In regions where the mean fields were seriously biased (e.g., the Southeast, Fig. l), it seemed unlikely that a detailed analysis of more subtle characteristics of the precipitation field would be very fruitful. We also determined from preliminary analysis that the results for the Great Lakes region illustrated no additional research conclusions made from the Northwest and central Great Plains portions of the domain. Hence, those results are not presented. Within each region six grid points of the high resolution RegCM were chosen for analysis. These points were selected on the basis of their co-location with stations used for the development of long term daily temperature and precipitation data sets used for an earlier study (Mearns et al., 1990). Table 1 presents station locations, altitude, and other metrics. Of the six stations chosen in the central Great Plains, only three are discussed. The greatest attention is given to the Northwest region, since results there were the most interesting, and most clearly illustrated conclusions common to all areas. We chose to represent each RegCM grid point with one observation station. The observations consist of thirty years of daily data (1951-1980). However, we tested the sensitivity of the statistics of interest to averaging increasing numbers of stations within a grid area. It is particularly important to determine this effect when dealing with frequency and variability statistics, which can change markedly on different spatial scales (Reed, 1986; Mearns et al., 1990). A further comparison is made between the RegCM

model grid points

State

Latitude

Oregon Oregon Oregon California California Nevada

44.1 44.0 44.0 40.8 41.7 40.9 3Y.7 39.8 39.7

(N)

Longitude

(W)

State elevation (m)

Grid elevation (m)

Northwest Eugene Bend Malheur Eureka Yreka Winnemucca

Central Great Plains Goodland Kansas Phillipsburg Kansas Centralia Kansas

1OY

117.8

1126 695 206 809 1322

566 1175 1286 319 1240 1571

101.7 99.3 Y6.1

1111 S81 402

1105 686 343

123.1 121.3 117.0 124.3 122.6

L.O. Mearns et al. /Global and Planetary Change 10 (1995) 55-7U

grids points, the observations at the corresponding stations, and the coarse resolution (4.5” latitude by 7.5” longitude) driving CCM results (see Giorgi et al., 1994 for a description of the CCM used). An observational data set made up from averaging the 6 observation stations represents the larger CCM grid area. This comparison is somewhat problematic, because when the original CCM model runs were made, the precipitation field was saved on the 2” X 2” grid scale, the scale at which surface processes are modeled. The 2” X 2” grid closest to the relevant R1.5 (rhomboidal 15 spectral resolution) grid point was chosen to represent the CCM large scale precipitation. It must be noted, however, that the 2” X 2” precipitation is bilinearly interpolated from the R1.5 grid points, which effectively destroys the precipitation frequency field. Precipitation frequencies are very high for any given 2” X 2” grid, since precipitation will occur at the 2” X 2” grid whenever there is precipitation in any one of the four R15 grids surrounding each 2” X 2” grid. Most versions of the CCM produce too many rain days, which is a feature common to many GCMs (Wilson and Mitchell, 1987; Mearns et al., 1990, Houghton et al., 1990). However, in this instance it would be impossible to separate the positive frequency bias of the model itself from the frequency “inflation effect” of the interpolation. Finally, a comparison is made of the doubled CO, results for both the selected nested RegCM grid points and the relevant CCM grids.

4. Results tions

for model

control

61

Fig. 2. Eugene, Oregon observed and model monthly plots of (a) daily mean precipitation, (b) intensity of daily mean precipitation and Cc) frequency of precipitation.

intensity processes (Fig. 2b,c). Frequency is greatly overestimated whereas intensity is generally underestimated. The correct seasonal cycle (strong winter

runs and observa-

4.1. Northwest Figs. 2-5 present overview comparisons of three RegCM grid points and observations that form a west to east transect from the northern Oregon coast to its eastern border with Idaho. The grid points are represented by the observation stations Eugene, Bend, and Malheur. Fig. 6 presents station and grid locations for the Northwest. At Eugene the reproduction by the model of mean daily precipitation is very good (Fig. 2a). However, this success is actually a result of compensating errors in the frequency and

1

2

3

4

5

6

7

8

9

1”

Months Fig. 3. Same as 2 for Eugene, Oregon, but including calculated from 3 different representative non-overlapping segments of observations (long dash lines).

1,

12

values 3-year

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maxima) is reproduced for all three quantities. Table 2 provides quantitative frequency results for four representative months. Given the large difference in the sample size of observations and model control run, we investigated how representative the three year model control output is compared to 3-year nonoverlapping segments of the 30-year observation time series. This may help determine to what degree the comparative differences in observations and model are because of random noise resulting from small sample size. Fig. 3 presents the same results as in Fig. 2, but portrays in addition three of the 10 different possible 3 year samples of observations. Although there is much more noise in the 3 year observation sets, the overall comparisons discussed for Fig. 2 still hold: a fairly good representation of mean daily precipitation, underprediction of mean intensity, and overprediction of frequency. Moving inland from the coast (to Bend and Malheur, Figs. 4 and 5) the seasonal cycle of mean daily precipitation and frequency is damped in the observations. Also in the model, the seasonal cycle of mean daily precipitation is less pronounced at the inland locations. However, mean daily precipitation is overpredicted at Bend and the observed decrease in frequency is not captured (Fig. 4). Instead, com-

B :i i_-_.--...

5

.........

Fig. 4. Same as (2) for Bend, Oregon.

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IO (1995)

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3

55-78

4

5

6

7

R

9

1”

11

12

Months Fig. 5. Same as (2) for Malhcur, Oregon.

pared to the coastal location the frequencies increase, especially in winter and spring. This tendency continues at Malheur (Fig. 5), although the errors are slightly less striking. Roughly the same pattern exists in the southern transect (Eureka, Yreka, and Winnemuccal. Why the frequencies unrealistically increase at Bend is at least partially related to the model topography. Although the nested regional model greatly improves the representation of topography compared to the CCM, for such a topographically varied region as the Northwest, it is likely that at some grid points the corresponding observation station would be in a different topographic environment. Such is the case with the grid point represented by Bend. In the model (Fig. 6) no distinction is made between the coastal and Cascade ranges, but rather one slope rises until a plateau area is resolved in western Oregon. Hence, the grid point is located on a relatively steep windward slope, whereas in reality, Bend is located in the lee of the Cascade range. This likely contributes to the greater frequency of precipitation compared to the observed site. On the other hand, precipitation intensities (Fig. 4b) are well reproduced for most of the months, and the reduction in the seasonal cycle of intensity seen in the observations is clearly evident in the model.

L.O. Mearns et al./Global

and Planetary Change 10 (1995) 55-78

At Malheur (Fig. 5), conditions resemble those at Eugene. There is still a positive frequency bias, but a negative intensity bias, for half of the year, centered on the summer. What is encouraging regarding the transect as a whole, is the realistic representation of the changing shape and amplitude of the seasonal cycle of precipitation mean daily and intensity values along the transect. Obviously, this degree of detail is not possible from the larger scale driving CCM. Figs. 7 and 8 present the precipitation from the 2” x 2” surface process grids of the CCM (GENESIS) model, which bracket the location of the CCM R15 grid associated with this area. The observations in this case are composed of the average of the six observation stations used in the RegCM grid point analysis. It can be seen that the coastal 2” X 2” grid

63

represents quite well the seasonal cycle, although it does not resemble any of the individual observation stations. In addition, the inland grid (Fig. 8) does not exhibit the degree of diminution of the seasonal cycle shown by the interior individual station observations or RegCM grid points. The very high frequency values for all months are, as noted earlier, a result of both the interpolation scheme and the tendency of the CCM to overestimate precipitation occurrence. It is interesting to note, however, that, apart from an overestimation of mean daily precipitation, the CCM produces reasonably well the seasonal cycles of mean and intensity of the six-station average precipitation. This result has been observed in other versions of the CCM (Mearns et al., 1990). We thus see an example of how a coarse scale GCM

Mal heur

Winnehucca Fig. 6. Topography of northwest segment of model domain showing location of grid points and corresponding observation stations. Small x represents location of observation stations and small o represents location of corresponding grid point. Contour interval is 100 m.

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Fig. 7. Comparison of observations (six station average) and CCM GENESIS 2” X 2” grid corresponding - to western portion of northwest segment of RegCM model domain. Panels as in Fig. 2.

Month

intervals for diffcrcnces

P

1

2 3 4 5 6 7 x 9 10 11 12 = P = Cl = 0 = M=

in probability

Eugene (‘I

0

M

0.60 0.54 0.5 1 0.4 1 0.33 II.20 0.06 0.13 0.20 0.35 0.53 0.62

0.67 0.85 0.71 0.79 0.66 0.57 0.34 0.42 0.32 0.59 0.56 0.62

* * * * * . * I *

~ 0.04 0.22 < 0.10 < 0.29 < 0.23 < 0.26 < 0.

I8 <

0.18 < 0.02 i 0.13 < ~ 0.08 - 0.10

< O.Oh < 0.16 0.30 < 0.3’) 0.19 < 0.30 0.38 < 0.47 0.32 < 0.43 0.36 < 0.47 0.28 < 0.38 0.28 < 0.39 0.12 < 0.22 0.23 < 0.34 < 0.02 < 0.13 < 0.00 < 0. I I

Model and observed significantly Probability of precipitation. Confidence interval. Observed. Model.

10 (1995) 55-78

Fig. 8. Comparison of observations (six station average) and CCM GENESIS 2” X 2” grid corresponding to eastern portion of northwest segment of RegCM model domain. Panels as in Fig. 2.

reproduces large scale patterns of precipitation, but not regional detail. Such detail is improved by the use of the nested model. We did look at the CCM grid precipitation for the

Table 2 95%) Confidence

Change

appropriate R15 grid from a more recent control run of the GENESIS model (Pollard and Thompson, 1995a; Thompson and Pollard, 1995). The main

of precipitation Bend

Malheur

P

P

CI

0

M

0.37 0.24 0.24 0.17 0.19 0.1 Y

0.76 0.87 0.88 0.91 0.85 0.71

* * *

0.08

0.48

1

0.13

0.71 * 0.37 / 0.70 * 0.74 * 0.71 .

0. I 1 0.18 0.25 0.32

different at 0.05 level

*

0.30 0.55 0.57 0.68 0.58 0.43

< < < < < <

0.38 O.62 0.64 0.74 0.65 0.52

< < < < < <

0.48 0.71 0.71 0.81 0.74 0.62

0.30 < 0.40 < 05

0.4Y 0.I6 0.42 0.40 0.29

< < < < <

0.58 0.25 0.51 0.43 0.38

< < < < <

i

0.6X 0.36 0.61 O.SY 0.48

CI

0

M

0.32 0.28 0.24 0.20 0.18 0.18

0.72 0.79 0.73 0.71 0.72 0.56

* * 1 * * *

0.0s

0.33

*

0. 10 0.11 0.18 0.28 0.32

0.23 * 0.18 0.53 * 0.59 . 0.73 *

0.30 0.41 0.39 0.42 0.44 0.27

< < < < < < 0.19< 0.04 < ~ 0.01 0.25 < 0.20 < 0.32 <

0.39 < 0.50 < 0.48 < 0.51 < 0.53 < 0.3X < 0.28 < 0.12 < < 0.06 0.34 < (3.30 < 0.41 <

0.4’) 0.60 0.58 0.61 0.63 0.49 0.38 0.22 < 0.15 0.4.5 0.41 0.5 I

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65

a) 1

“OX

40

40

July

42

I October

30 6 -o \

20

E E 10

0Ic)

Fig. 9. Box plots for four cardinal months of precipitation intensity, observed versus RegCM for Eugene, Oregon. Dot represents percentile, and numbers associated with arrow indicates off graph maximum values: (a) December, (b) April, (c) July, (d) October.

difference between the two GENESIS versions is how convection is parameterized. In the earlier version (used to drive the nested model runs) a standard

Table 3 NW Transects

comoarisons

95% confidence

Month

Eugene

1 2 3 4 5 6 7 8 9 10 11 12

* 0.43 0.55 < * 0.38 * 0.34 * 0.45 0.58 < 0.49 < * 0.16 * 0.16 * 0.23 * 0.35 0.54 <

* = model and observed

convective adjustment scheme is used, whereas the newer version uses a penetrative sub-grid scale convective plume scheme (Pollard and Thompson,

intervals of ratio of median intensities Bend

< 0.64 0.79 < < 0.55 < 0.46 < 0.63 0.86 < 0.83 < < 0.23 < 0.26 < 0.37 < 0.57 0.81 <

< 0.95 10.15 < 0.79 < 0.64 < 0.87 1.27 1.43 < 0.34 < 0.43 < 0.60 < 0.92 1.21

are significantly

different

0.88 < * 1.14 1.00 < * 1.30 * 1.04 * 1.52 0.48 < 0.46 < 0.68 < 0.54 < 0.57 < 0.69 < at the 0.05 level.

90th

model/observations Malheur

1.26 < < 1.63 1.39 < < 1.83 < 1.49 < 2.11 0.75 < 0.68 < 1.14 < 0.82 < 0.85 < 1.00 <

1.80 < 2.34 1.93 < 2.59 < 2.12 < 2.93 1.16 1.00 1.90 1.25 1.26 1.45

0.65 < 0.72 < 0.82 < * 0.36 * 0.31 * 0.25 * 0.26 * 0.21 * 0.28 * 0.41 0.73 < 0.64 <

0.91 < 1.00 < 1.12 < < 0.52 < 0.44 < 0.37 < 0.43 < 0.33 < 0.33 < 0.61 1.09 < 0.92 <

1.29 1.39 1.53 < 0.73 < 0.61 < 0.55 < 0.73 < 0.54 < 0.54 < 0.91 1.64 1.32

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0.8 ._: g

0.6

2 P a

0.4

0.0

0

1

'2

3

4

5 6 7 Months

8

9

10

11 12

Fig. 10. Transition probability P,, (monthly) for Eugene, observed and RegCM grid point. One sample of values calculated from a 3 year observation segment (long dash) (1960-1962) is also shown. The vertical bars on the 3Wyear observation line rcpresent+the standard deviation composed of P,, valuescalculated from the 10 non-overlapping 3-year segments making up the 30.year observation set.

1995b). These differences would most likely affect precipitation in the warmer months, when most precipitation is convective as opposed to large scale. Hence, we feel more comfortable suggesting that the results for winter are more similar to those of the older version than the results in summer. For the more recent control run, the probability of precipitation in January (3 year average) is 0.88 and 0.56 for July. This compares with observed values (six station

Table 4 Diffcrenccs Month

in interquartile

2 3 4 5 6 7 x Y 10 11 12

0.41 0.52 ~ 3.22 - 3.73 ~ 2.61 0.01 ~ 1.47 -5.70 ~ 6.41 -2.18 -2.81 ~ 1.81

4.2. Quantitatil.e comparison terquartile runges

and Z values for IQR Test

IQRDIFF

Z 0.21 0.32 -2.50 * -4.97 * -2.89 / 0.01 - 1.43 -6.59 1 ~7.26 ’ ~ 1.19 ~ 0.83 ~ 0.67

of’ medians

1.69 2.39 3.25 3.Y3 0.87 0.7 1 ~ 0.22 ~ 1.16 0.36 0.99 0.44 1.25

* = model and observed are significantly different at the 0.05 level Critical Z value i 1.96. IQRDIFF = model-observed interquartile ranges (mm).

and in-

Figs. 9a-d provide samples of box plots for four cardinal season months (December, April, July, and October) for Eugene. Table 3 provides the results of the median intensity test, and Table 4 same for the interquartile range tests, for the three pairs of RegCM grid points and observing stations. The box plots of Fig. 9 graphically present the medians and interquartile ranges, as well as the 90th percentiles and maximum values. In the winter on the coast, the daily

Malheur

Bend

Eugene IQRDIFF

1

ranges (model-observed)

average) of 0.72 and 0.20 respectively and values from the most relevant 2” X 2” grid of the driving GENESIS version of 1.0 and 0.97. This only serves to verify that some portion of the uniformly high frequencies from the 2” X 2” grid is due to the interpolation. Comparing these values to the results of Eugene, for example, it is clear that the RegCM frequency values are more in line with the single observation station than GENESIS frequency values are with the six station average observations. The issue of observational correspondence with a grid point or area is more problematic regarding precipitation frequency than mean amounts. Given the differences in the GENESIS model versions this is as detailed a comment as can be made regarding the frequency comparisons of the two models.

Z 1.61 1.88 3.20 3.34 0.62 0.44 - 0.31 PO.99 0.19 0.‘) I 0.56 1.0s

IQRDIFF

* ~ ~ ~

1.28 2.03 0.67 2.43 3.94 3.40 2.34 3.78 3.42 0.79 3.20 I .34

Z 1.16 2.41 ” 1.06 -3.79 / ~ 4.02 ^ -5.27 _ -5.34 * ~4.25 ’ - 3.55 ~().‘)I 3.18 + I .23

L.O. Mearns et al./Global and PlanetaryChange 10 (1995) 55-78

variability of precipitation is well duplicated, with no significant difference between observed and RegCM grid points for the months of November through February (Table 4, Eugene). For most other months (March-May, August-September) the model underestimates the interquartile range, even when the median daily values are not significantly different (but are lower than observed) (Table 3). The 90th percentile (Fig. 9) is also well reproduced in the winter, but tends to be too low in the other seasons. At Eureka (statistics not shown) there is more underprediction of variability in the winter and spring but none in the fall. Thus, for the coastal grids, the seasonal cycle of variability is somewhat overestimated. At Bend, the observed variability is accurately reproduced in fall and winter, but is overpredicted in spring, and underpredicted in summer. These errors follow to a degree the errors in the median intensity (Table 31, which is overpredicted in April, May and June, but is well reproduced in other months. At the Winnemucca grid (statistics not shown), the model accurately reproduces the median and variability November through May, but variability is underpredieted June through October. The model generally underpredicts variability in warm months and occasionally overpredicts it in cool months (November and February) at Malheur (Table 4). Thus, overall the model does a fairly good job of reproducing variability in this region, and most errors tend to be underpredictions in the summer. The tendency for underpredictions most likely follows from some adjustments made in the model to reduce the occurrence of excessively high point storm events associated with explosive convection (Giorgi, 1991). This correction, which involved the attenuation of release of latent heat under convective conditions, likely results in the upper quartiles being underpredieted. 4.3. Transition probabilities Related to the issue of frequency of precipitation are the probabilities of going from one rain day state to another, i.e., the sequencing of wet and dry days in a precipitation time series. We calculated P, and P,,, from which the other two transition probabilities can be deduced, as well as (assuming a first order

Markov chain) the unconditional day (7~) according to: n=

67

probability

of a wet

(I -~,,)/(2-P0,-~,,)

Results for transition probabilities will thus obviously be related to the frequency values displayed in the earlier figures, and to a degree, errors will also be correlated. The small sample size is particularly problematic in the case of transitions, such that in the model results there are extreme fluctuations in the transition probabilities from month to month, which do not appear in the observations. Fig. 10 presents the P,, transition probabilities for Eugene. The fluctuations make it difficult to determine if the probabilities follow the seasonal cycle of the observations, but a rough agreement is found. The “error” bars on the 30-year observation curve represent + the standard deviation formed from calculating P,, values from the 10 possible non-overlapping three-year segments of the 30-year observations. This provides some indication of the noise present in observed three year samples. Note that the standard deviations increase dramatically in the summer months when frequency is low and few transitions from rain day to rain day occur. In addition, a sample for 1960--1962 of the P,, values (long dash) on Fig. 10, provides a sense of the actual month to month fluctuations in a three year sample. The noise from the 3-year observations sample is not dissimilar from the noise in the three year model values. As expected, the model tends to overpredict, P,,, particularly in the summer, but there are slight underpredictions in the winter months. At Bend (Fig. 11) the model roughly reproduces the seasonal cycle of Pi,, but contains a relatively constant positive bias. Interestingly, in the observations, the Bend P,, pattern is very similar to that of Eugene, but at a generally reduced level. It is particularly interesting that the model ostensibly more successfully reproduces the seasonal cycle of P,, than of the unconditional probability of precipitation (Fig. 5~). 4.4. Pilot study of spatial aggregation One of the concerns in performing validation of precipitation is how to compare a grid point from the model, which presumably represents a grid area mean, with observational data, which are taken at

L.O. Mearns eial./GlobalandPlanrtar~~Change I0 (1995)55-78

68

discrete points. Given the relatively small area of each grid in this instance, and the density of observational stations, we chose to use one station to represent each grid point. However, certain statistics, especially higher order statistics, are sensitive to spatial aggregation. We conducted two aggregation experiments to see how statistics change as the number of points averaged increases. We chose the grid box containing Malheur, and located three other observation stations that fall within the 60 km grid box. The maximum distance between stations is about 40 km. We aggregated the stations one by one and compared averages over 2, 3, and 4 stations with Malheur for a 25 year period. The 4-station average results compared to the single station results are presented in Fig. 12. Performing the four stations average did not affect mean daily precipitation, whereas frequency values increased, and intensity values decreased. The direction of change for frequency and intensity corresponds with the direction of error of the RegCM generated precipitation on the 60 km grid scale, when mean daily precipitation is relatively accurately reproduced. However, differences between 4-station averages and single station data are much smaller than the model errors in Figs. 2-5. For example, differences in frequency (i.e., the probability of precipitation), are about 0.12 in winter months, whereas typical differences between the Malheur observation station and the corresponding grid point are 0.4 in winter. This indicates that, not all of the model “error” can be attributed to a

1.0

0.9

-

I

I

9

10

/

__.~. . . . ..- -.----.-

fii 0.8 E

0.7 -

2

0.6 -

0 _n g

0.4

a

0.5 -

0.3 0.2

lXCO2 -

30

YRS

3

4

OBS

0.1 0.0

0

1

2

5

6

7

8

11 12

Months Fig. 11. Transition probability RegCM grid point.

P,, for Bend 30.year

observed

and

/ -

MALHEUR --

W/VALE

Spatial aggregation comparison, Malheur observed MALHECIR) versus four observation station average (labeled W/ VALE). Plots as in Fig. 2

between observations and grid spatial “mismatch” boxes. Moreover, there are exceptions to the general tendency for station aggregation to improve the agreement with the grid box average. For example, the aggregation in observing stations resulted in smaller interquartile ranges for every month, whereas there is variability across the months as to direction of difference between the observations and the model grid point output. To compare these results with those of a region with very different topography and climate, we performed a second aggregation of three stations in northwestern Kansas over an area between Goodland and Phillipsburg. The stations, Norton Dam, Norton, and Lenora, had good data (i.e., few missing values) for a 10 year period, 1971-1980. The stations are all within 37 km of one another, and thus would fit into a single 60 km grid square. Differences of all measured statistics were very slight, although frequency did increase as more stations are added, and intensity generally decrease. We found no differentiating seasonal effects, such as larger frequency differences in summer. The smaller effect of aggregation found in Kansas compared to Malheur likely concerns the much more varied terrain in Eastern Oregon com-

69

L.O. Mearns et al. / Global and Planetary Change 10 (1995) 55-78

pared to the Central Plains as well as greater precipitation amounts in general at Malheur. Although these are limited tests, the results are consistent with some preliminary work performed for an earlier study (Mearns et al., 1990) wherein 15 stations were aggregated over a 4.5” X 7.5” grid box centered over Kansas. Frequency increased in all seasons, but while it reached an asymptote after around six stations in the winter, it continued to increase in the summer. These results reflect the contrasting nature of summer and winter precipitation in this region whereby synoptic scale processes dominate in the winter, and local convective processes in the summer. The lack of this seasonal effect in the Kansas 60 km aggregation discussed here reflects the fact that this grid scale is much closer to that of convective processes (compared to the 500 km grid scale of the CCM). These empirical studies do not resolve the problem of how to represent grid points with single point observations; but they do provide some guidance as to how certain statistics change over space, and hence have the potential for providing insights regarding how spatial averaging of observations can aid in distinguishing between model errors due to inadequacies in the physics representations and error due to lack of agreement in the spatial nature of observations and model grid points. 4.5. Changing

thresholds

of precipitation

We noted above that in general the frequency of precipitation is overestimated in the nested model. This is at least partially because of the way in which precipitation processes are modeled. For large scale precipitation an explicit moisture scheme is used such that rain occurs every time step that relative humidity exceeds 100%. No build-up of condensed moisture is allowed for, nor is re-evaporation of precipitation before reaching the surface. Hence, more rain days are likely to occur in the model than in observations. Given these limitations, it is useful to determine the relative degree of error when different thresholds are used to define a rain day. In the general case, in the observations, trace amounts (defined as 0.1 mm) are considered the lower limit, i.e., only amounts greater than trace amounts are considered, and only days when greater than trace amounts

c

-

OBS

Fig. 13. One millimeter threshold case. Eugene, Oregon observed and RegCM monthly plots of (a) daily mean precipitation, (b) intensity of daily mean precipitation and (c) frequency of precipitation.

occur are considered rain days. We tested two thresholds above the trace amount to compare the effect of excluding different levels of small amounts, which make up a disproportionately large number of rain days in the model. We selected thresholds of 1.0 and 2.5 mm and calculated the same statistics as for the trace amount threshold case. This procedure necessarily increases mean intensities and decreases frequencies, but the important consideration is the relative change in the observations compared to the model precipitation. When the threshold is 1.0 mm (Fig. 13) a clear improvement in the reproduction of frequency is seen at Eugene, while the intensities are less affected. There are still months (February, April through July) when model frequencies are too high (according to the 95% confidence interval for frequency) and months (April, August, September) when the intensities and daily variability are too low. Fig. 14 presents the overview graph for Eugene for the 2.5 mm threshold case. Using this higher threshold results in a much better agreement between observations and the model grid point both in frequencies and intensities. The positive bias of precipitation frequency has disappeared as well as the nega-

70

LO. Mearns et al./ Global and Planetmy

Change 10 (1995) 55-7X

4.6. Central Great Plains

Fig. 14. 2.5 mm threshold case. Eugene, Oregon observed and RegCM monthly plots of (a) daily mean precipitation, (b) intensity of daily mean precipitation and (c) frequency of precipitation.

tive bias in precipitation intensity. For all months except June, July, and September, there are no significant differences based on the 95% confidence interval for frequencies of precipitation. There is still some tendency for intensities to be underpredicted, but there were no significant differences in medians as indicated by the median ratio test. March, August, and April still exhibit model variabilities that are too low. The model distributions are more skewed than those of observations. This would partly be a result of differences in sample size, especially since fewer days are included with the higher thresholds defining a rain day. At Bend and Malheur, the same types of corrections are obtained when increasing the thresholds, but since the errors in frequency are greater at these locations, there are still significant errors in late winter and spring even in the 2.5 mm threshold case. In summary, as anticipated, increasing the threshold results in a better match between observations and model precipitation, further confirming the tendency of the model to produce many rain days with small amounts. Results are still better for winter than for summer, regardless of the threshold used.

Fig. 15 presents the overview results for Goodland, where the errors in mean precipitation are relatively small. Goodland, as well as the other stations in the Central Plains, exhibits quite a different seasonal precipitation characteristic from the Northwest stations analyzed above. While in the Northwest the rainy season occurs in winter and the precipitation minimum in summer, in the Great Plains a well defined summer maximum is found. As shown in Fig. 1.5 the model produced this change in seasonal cycle but shows errors similar to those described for Eugene. Mean daily precipitation is well reproduced in all months (except August) but frequencies are too high and intensities too low. Compared to Eugene, however, the errors in intensity and frequency are greater, such that there are statistically significant differences in frequencies, medians, and quartile ranges for all months. This is illustrated by Fig. 16, which presents box plots for comparison with the Eugene plots of Fig. 9. This points out that the compensating errors at Goodland, which results in very good mean daily precipitation results are more pronounced than those at grids in the North-

Fig. 15. Goodland, Kansas observed and RegCM model grid point monthly plots of (a) daily mean precipitation, (b) intensity of daily mean precipitation and (cl frequency of precipitation.

L.O. Mearns et al./Clobal

71

and Planetary Change 10 (1995) 55-78

west. The relatively large frequency and intensity errors at Goodland (compared to Eugene) may be associated with the prevalence of summer precipitation there. It should be noted that analysis of only the mean daily precipitation not only disguises errors in the intensity and frequency fields, but also potentially the varying magnitudes of such errors. At the two stations and grids to the east of Goodland (Phillipsburg and Centralia), the underpredictions are more severe, and are evident in the daily mean fields (not shown). Still high overpredictions of frequency are found (58%) even when the mean daily precipitation is underpredicted as much as 84% in the summer. These high frequency errors further confirm fundamental problems in the parameterization of precipitation in the model discussed above. The longitudinal gradient of precipitation is not at all reproduced by the model, since the model becomes drier moving eastward, whereas in reality there is a very steep increase of precipitation from

40

western to eastern Kansas. This failure is clearly a function of the increasingly negative bias in the model in the eastern part of the domain, which is discussed in Giorgi et al. (1994). 4.7. Goodland changing

threshold study

We examined changing the threshold that defines a wet day at Goodland as we had done in the Northwest. As in the Northwest, increasing the threshold greatly improves the model frequency of precipitation compared to observations, more so than the intensity, which remains underpredicted for both the 1.0 and 2.5 thresholds. Transition probability PO0 compares very well with observations in the 2.5 mm case. Due to small sample sizes, for P,, , there is too much noise in the model results to compare with observations. It appears that it is more feasible to correctly reproduce frequency fields at higher thresholds of precipitation than intensity. This would be

40 GOODLAND April

GOODLAND December 30

u

,l, Cl) ma*

OBS

1xcoz

43

52

b)

OBS

lXCO2

July 30. ZF n \ 20. E E lo-

OL L cl

A L ,

I OBS

r

lXCO2

Fig. 16. BOX plots for four months of precipitation intensity, observed versus RegCM for Goodland, Kansas. Dot represents and numbers associated with arrow indicates off graph maximum values. (a) December, (b) April, (c) July, (d) October.

90th percentile,

expected, since frequency is a simpler process (i.e., only two possible values) than the continually varying intensity process (infinite possible values).

5. Doubled

CO, results

As expected, and as has usually been the case with GCM analyses, the differences between the control and doubled CO, runs are smaller than the differences between the observations and control run. In evaluating the climate changes discussed here one should keep in mind the sample size problem. Given that only three years of control and doubled CO, runs were analyzed, the power of the statistical tests reported here are low, that is to say, confidence intervals tend to be rather wide. It is likely that, with a larger sample size (say II = 3O), more of the differences discussed in this section would be statistically significant.

Eugene, Oregon I xCO, vs. 2 xCO, RegCM model monthly plots of (a) daily mean precipitation, (b) intensity of daily mean precipitation and (c) frequency of precipitation.

5. I. Northwest At the coastal stations, annual precipitation increases, and is dominated by increases in the winter months. These mean increases are mainly due to intensity increases, as opposed to increases in frequency (Fig. 17 for Eugene). Most of the changes in

median intensity are not significant at the 0.05 level (only June and August at Eugene), but there are mainly increases in the winter months. There are very few frequency changes (Fig. 17~).

Table 5 Northwest

ranges and Z Values of IQR Test

Month

2 3 4 5 6 7 8 Y 10 11 12

comparisons,

2 X CO: ~ 1 X CO, Diffcrcnces

Eugene

in interquartile

Genesis 2 X 2

Genesis 2 X 2

Malheur

IQRDIFF

Z

IQRDIFF

Z

IQRDIFF

Z

IQRDIFF

- 1.6

-0.68

1.5 5.2 15 0.3 0.3 0.7 0.8 1.4 0.4 1.1 1.3 2.3

1.04 3.37 I.57 0.5 1 0.48 0.98 2.45 0.72

0.2 3.S 1.4 1.6 ~ O.6 1.7 2.3 0.3 ~ 0.3 0.3 ~ 2.6 2.0

0. 14 2.17 I .29 2.11 ~ 0.94 2.Yl S.66 2.63

1.4 3.4 2.0 0.3 0.2 0.0 1.2 0.2 0.1 1.5 _ 1.3 3.0

5.7 2.5 0.8 0.8 ~ 2.x - 0.9 1.8 2.3 1.7 - 1.8 14.8

2.12

.

1.40 0.64 0.x4 - 1.6’) - O.Y3 4.43 I 2.57 * 0.55 ~ o.so 2.79 _

f 1.96 = critical Z value at 0.05 significance level. * = Z value > 1.96 or < - l.Yh. QRDIFF = 2 x CO, - 1 X CO, interquartile range (mm).

1.22 I.00 0.74 1.48

*

. I L ’ *

~ 0.38 0.27 ~ I.‘)6

I.55

*

Z 0.98

2.12 2.10

0.3I ~ 0.3I 0.02 3.23 0.45 - 0. IS l.S2 - 0.88 2.07

.

L.O. Mearns et al. /Global and Planetary Change 10 (1995) 55-78

At both coastal locations there are larger and more significant changes in variability than there are in medians, although changes are correlated, i.e., if there is a significant change in medians, there tends to be a change (and in the same direction) in interquartile ranges. At Eugene (Table 5) December, February, March, September and August show variability increases, whereas only June shows a striking variability decrease, which corresponds with a decrease in the median value. At the midland locations, Bend and Yreka, changes in frequencies are more common (3 at each location) and occur in the spring and summer. There are some significant increases in medians (3 at each location) in the winter and significant increases in variability occur throughout the year at both stations. There are no clear patterns of changes in transition probabilities. At the two farthest inland stations (Malheur, Table 5 and Winnemucca), variability significantly increases. The clearest seasonal pattern is variability increase in the summer at Malheur (Table 5). Seven months (total for both stations) show significant changes in precipitation frequency (in both directions); half of the months at Malheur and two at Winnemucca exhibit significant changes in medians (mixed increases and decreases). Comparing changes in the variability of intensity at the the RegCM and the corresponding GENESIS 2” X 2” grid points, at Eugene and Malheur the RegCM run exhibits greater numbers of, and larger increases than, the GENESIS run (Table 5). These variability contrasts indicate an intensification of the mesoscale precipitation signal over topography in the regional climate model. There is even an occasional case (e.g., July at Eugene) where the direction of change of variability at the RegCM and corresponding GENESIS grid point is opposite. The clearest 2 X CO, signal in these representative grids is a dominance of increased precipitation variability. We initially suspected that this condition was most likely connected to the increased percentage of convective events compared to large scale precipitation, which is a common result of perturbed climate model experiments (Mitchell et al., 1990; Gordon et al., 1992; Houghton et al., 1992), and to topographic interactions with increased convective precipitation. However, when we investigated the

73

changes in percentage of convective events for the particular grid points and months when there were large increases in precipitation variability, we found mixed results, with both increases and decreases in convective precipitation fraction. However, most months that exhibited large variability increases did experience increases in the absolute amount of convective precipitation. This may be a more salient consideration than the change in fraction of convective precipitation. Longer runs will have to be produced and analyzed before this issue can be resolved. Regarding frequency changes, increases in the summer and decreases in the spring are seen at the inland grids. There is a lack of change at the coastal locations, which is likely related to their proximity to an upwind constant moisture source. 5.2. Power of statistical tests The relative paucity of significant changes in the metrics discussed here is at least partially due to the sample size problem, and this factor of course affects all climate change results. We present an example of a calculation of the power of the frequency test to quantitatively demonstrate this difficulty. Such a consideration is rarely discussed in climate modeling papers, although its importance to what conclusions can be made about change detection is well known (Laurmann and Gates, 1977; Katz, 1992). Detection of a change of 0.1 in the unconditional probability of precipitation, say a change from 0.5 to 0.6, assuming (Y (significance level) of 0.05 (two sided test), a power (1 - p) of 0.9, and a variance representative of the results presented here, would require a sample size of each group of 518, which, assuming the tests were performed in monthly units, would require a climate model run of at least 17 years. Given the current sample size of 276 for 30-day months and three years of model output, detection of a change of 0.1 would be extremely unlikely since such a test would have a power of only about 0.68. At a power level of 0.9 (still assuming a representative variance) the finest distinction that could be made would be a difference in proportions of about 0.17 (Dixon and Massey, 1983). Because of the correlations in the frequency data, the actual finest distinction is even lower than 0.17, since the power calculation used here assumes no autocorrelation in the data.

L.O. Mearn.s et ul./Globnl

and Planetary

Change IO (1995) 55-78

Fig. 18. RegCM change (2 X COz-I X COz) in: (a) probability of precipitation (0.1 contour interval for posit& values) and (h) mean daily precipitation amount (2 mm/day contour interval) for the month of August. Negative values are lightly stippled on both a and h, values 2 0.2 are heavily stippled on a, and 2 I on h.

L.O. Means

et al/Global

and Planetary Change 10 (1995) 55-78

75

only changes in mean monthly precipitation amounts were considered from the modeling experiments. 5.3. Central Great Plains 0

0 15

30

1

,

,

,

,

,

/

(

/

/

(

Fig. 19. Goodland, Kansas 1 XCOz vs. 2 XCO, RegCM model monthly plots of (a) daily mean precipitation, (b);ntensity of daily mean precipitation and (c) frequency of precipitation.

There are perhaps some physical reasons why large changes in frequency are not as likely as changes in medians or variability in some areas. The formulation of precipitation processes in the model results in conservation of frequency, since in either control or 2” X CO, cases there will tend to be many days with very small precipitation amounts. Therefore, to significantly change frequencies would most likely require a fairly large shift in the large scale circulation patterns and/or rather large changes in precipitation amounts. This is born out by comparing changes in precipitation amounts and frequency. Fig. 18 provides an example for the entire domain for August. By inspection it is seen that regions of frequency decreases (Fig. 18a) generally correspond with regions of decreases in mean amount (Fig. 18b). The opposite occurs in southern California and parts of the Southeast where amount increases while frequency decreases, Such occurrences could be of particular importance from an impacts point of view, since increased intensity and decreased frequency could actually be a negative condition from the point of view of certain resource systems, such as agriculture. This negative effect would not be apparent if

For all grids considered here, most changes are in frequency as opposed to median intensity or variability. We find that frequencies tend to decrease in summer and increase in spring. For all measures, July experiences the most striking change, with increased variability and intensity, and decreased frequency (although all changes at all grids are not statistically significant). Results from Goodland, which are similar to those for the other locations, illustrate these changes. On an annual basis there is very little difference in the climate perturbed and control mean daily precipitation (1.35 mm/day vs. 1.41 mm/day). This lack of difference continues on a seasonal basis as shown by the top panel of Fig. 19, except for a peaked increase of mean precipitation in July and decrease in August. As shown in the middle panel, the July increase is due solely to increased intensity, since precipitation frequency actually declines in July (Fig. 20). Most changes aside for July are seen in the frequency fields, where there is a clear decrease from July through October (significant in May, July, and October). Frequency increases are seen in late winter and early spring (only March is significant). The clearest tendency in the transition probabilities is the series of decreases from May through October in P,,, which corresponds with the period of general reduction in frequency. The greater number of significant changes in frequency compared to intensity at Goodland contrasts with results from the Northwest, particularly the coastal stations. This difference is at least partially a result of the smaller precipitation increases at Goodland compared to Eugene (Fig. 17a versus Fig. 19a). Very few of the interquartile range changes are significant, and the increased variability in July is the largest (Fig. 201. The interquartile range decreases considerably in August and follows the direction of median change. At all grid points investigated there is never a case of significant median decrease associated with variability increase, although there are cases of frequency decline with intensity increase. Examining the GENESIS 2” X 2” grid nearest to the location of Goodland we see a very different set

L.0.

Meurns

et al./

max

Global

and

Planetq

C‘hangc~

IO

52

(1995)

4

55-7X

July lXCO2

2xco2

Mean 1.94

Daily Precip 5.05

%

Roindays 60

Prob.

of

40 Wet

Confidence -0.34

Dcy interval

< -0.21

<-0.06

Intensity Mean 3.2

12.7

7.4

33.3

230.

263.

SD cv Confidence for / \

lXCO2

/

/

0.84

Interval

ratio

of

<

1.74

medians <

3.61

2xco2

Fig. 20. Goodland, Kansas I X CO2 vs. 2 X CO? RegCM box plots of July precipitation and some associated statistics. Solid dot on vertical lines extending from the boxes represent the 90th percentile. Numbers associated with arrows arc maximum values. Prob. of wet day confidcncc interval (CI) means the 95% CI for the diffcrcncc bctwcen 2 X CO? and 1 X CO: unconditional probability of a wet day. The Cl for the ratio of medians is the 95% CI for the ratio of 2 X COz/l X CO, median precipitation intensity. Z ih the Z value for the intcrquartilc range test. The critical Z value for significant difference at the 0.05 level is + 1.96. SD = standard deviation; CV = coefficient variation.

of changes in the summer. At the 2” X 2” grid corresponding to Goodland there is no major shift in the peak summer precipitation to July. The most significant changes are decreases in the median intensity in May and June, and reduced variability in June. These changes are completely absent at the RegCM grid.

6. Summary

and conclusions

We have presented a methodology for analyzing model errors and changes in daily precipitation that includes measures of location (median) and scale (interquartile range) and also considers the two-component nature of the precipitation process (intensity and frequency). In terms of model validation, successful reproduction of mean daily precipitation may mask errors in intensity (overestimation) and frequency (underestimation). Given the variable success in mean field

evaluation (Fig. 1 and Giorgi et al., 1994), there is also variable success in reproducing higher order statistical moments, such as variability. In general, validation of higher order statistics reveals both more errors, and some very good agreements with observations. For example, in the Northwest, even with large errors in frequency, the reproduction of variability was quite good. Some statistics such as transition probabilities, and runs of wet and dry days, were very difficult to analyze because of small sample sizes. Although, compared to the CCM, increased spatial resolution in the nested model results in much better resolution of topography, some errors, such as at Bend, Oregon, can be traced to a still excessive smoothing at 60 km grid point spacing. Some of these model errors may have implications for climate assessments. For example, if the control run precipitation data were used directly in crop models, the unrealistically high frequencies could lead to unrealistically high control run yields, since the high frequencies would most likely create

L.O. Mearns et al. /Global and Planetary Change 10 (1995) 55-78

an overly benign environment for the crop. Such a project is currently under way. Regarding the evaluation of the perturbed climate, again the problem of sample size imposed serious limitations on the conclusions that can be drawn. The power of the statistical tests, i.e., their ability to detect changes, is relatively low, with only three years of data. Future model runs should be substantially longer. The major feature of climate change in the areas investigated are significant increases of variability in daily precipitation intensity (with or without changes in median intensity). In this regard our study lends support to the tentative conclusions presented by Houghton et al. (1992). In certain areas (mainly the Northwest coast) there were relatively conservative changes in frequency, regardless of the direction and magnitude of change in mean precipitation. However, in the Central Plains, frequency decrease was the major change, sometimes accompanied by intensity increases. These last changes are particularly interesting, since they are completely obscured when examining only mean daily precipitation change. More detailed contrasts between driving CCM scenario and nested model grids are elucidated by more detailed statistical analysis, and evidence for mesoscale magnification of changes (e.g., magnified increases in variability) in RegCM were found. Many of the statistics discussed here, such as transition probabilities, are currently being used to formulate climate change scenarios that include daily variability changes of precipitation (Mearns and Rosenzweig, 1994). The greater detail of changes in precipitation provided by these results may alter conclusions regarding climate change effects on crop yields presented earlier based on consideration of only mean monthly changes (Smith and Tirpak, 1989, Rosenzweig, 1990). It is hoped that as climate modeling techniques continue to improve, more detailed investigations of climate variables will become more common, as will the application of the methodology presented here.

Acknowledgements We thank the reviewers of this paper for useful comments. This work was funded in part by the

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National Oceanic and Atmospheric Administration, Global Climate Change Program, under contract number NRAZ0000200124. The National Center for Atmospheric Research is sponsored by the National Science Foundation.

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