Probability Of Rain Research Articles

The complexity of forecast testing

Consider a weather forecaster predicting the probability of rain for the next day. We consider tests that given a finite sequence of forecast predictions and outcomes will either pass or fail the forecaster. It is known that any test which passes a forecaster who knows the distribution of nature can also be probabilistically passed by a forecaster with no knowledge of future events. This note summarizes and examines the computational complexity of such forecasters.

EFEKTIFITAS EMBUNG UNTUK IRIGASI TANAMAN HORTIKULTURA DI CIKAKAK SUKABUMI

Dryland farming provides a promising opportunity in increasing agricultural production in rural areas. But, the lack of available water during dry season poses a problem in developing dryland farming. An effective water conservation technique should be developed to alleviate this problem. The use of a small farm reservoir (embung) can be considered as one viable option for such conservation techniques. The purpose of this research was to study the effectivity of small farm reservoirs to supply irrigation water for horticulture commodities. Two different types of small farm reservoir (SFR) were constructed in the micro catchment for the research, i.e. a) SFR built with concrete, b) SFR built without concrete. SFR built with concrete had higher water available for irrigation, which is 34% higher compared to SFR without concrete. In addition, the empirical equation that was used in this research was quite reliable in predicting colected water in the SFRs. Using 80% monthly rain probability, on average one small farm reservoir with dimension 8 m x 2m x 2 m was able to supply irrigation water for 100 m2 horticulture plants for the whole growing period.
 Keywords: Small farm reservoir, dry season, irrigation, dryland farming.

Differences in rain rate intensities between TRMM observations and community atmosphere model simulations

Precipitation related latent heating is important in driving the atmospheric general circulation and in generating intraseasonal to decadal atmospheric variability. Our ability to project future climate change, especially trends in costly precipitation extremes, hinges upon whether coupled GCMs capture processes that affect precipitation characteristics. Our study compares the tropical‐subtropical precipitation characteristics of simulations by the NCAR CAM3.1 atmospheric GCM and observations derived from the NASA Tropical Rainfall Measuring Mission (TRMM) satellite. Despite a fairly good simulation of the annual mean rain rate, CAM rains about 10–50% more often than the real world and fails to capture heavy rainfall associated with deep convective systems over subtropical South America and U.S. Southern Plains. When it rains, there is a likelihood of 0.96–1.0 that it rains lightly in the model, compared to values of 0.84–1.0 in TRMM data. On the other hand, the likelihood of the occurrence of moderate to heavy rainfall is an order of magnitude higher in observations (0.12–0.2) than that in the model (<0.02). Comparison of regionally aggregated PDFs of the rain rate shows that CAM underestimates the probability of NOT raining, overestimates the probability of light rain and almost completely misses the tails of the PDFs. The model compensates for the lack of heavy precipitation through raining more frequently within the light rain category, which leads to an annual rainfall amount close to what is observed. CAM captures the qualitative change of rain rate PDF from a “dry” oceanic to a “wet” oceanic region, but it fails to simulate the change of precipitation characteristics from an oceanic region to a land region where thunderstorm rainfall dominates.

Cloud cover analysis associated to cut-off low-pressure systems over Europe using Meteosat Imagery

This paper reports a cloud cover analysis of cut-off low pressure systems (COL) using a pattern recognition method applied to IR and VIS bispectral histograms. 35 COL occurrences were studied over five years (1994-1998). Five cloud types were identified in COLs, of which high clouds (HCC) and deep convective clouds (DCC) were found to be the most relevant to characterize COL systems, though not the most numerous. Cloud cover in a COL is highly dependent on its stage of development, but a higher percentage of cloud cover is always present in the frontal zone, attributable due to higher amounts of high and deep convective clouds. These general characteristics are most marked during the first stage (when the amplitude of the geopotencial wave increases) and second stage (characterized by the development of a cold upper level low), closed cyclonic circulation minimizing differences between rearward and frontal zones during the third stage. The probability of heavy rains during this stage decreases considerably. The centres of mass of high and deep convective clouds move towards the COL-axis centre during COL evolution.

“A 30% Chance of Rain Tomorrow”: How Does the Public Understand Probabilistic Weather Forecasts?

The weather forecast says that there is a "30% chance of rain," and we think we understand what it means. This quantitative statement is assumed to be unambiguous and to convey more information than does a qualitative statement like "It might rain tomorrow." Because the forecast is expressed as a single-event probability, however, it does not specify the class of events it refers to. Therefore, even numerical probabilities can be interpreted by members of the public in multiple, mutually contradictory ways. To find out whether the same statement about rain probability evokes various interpretations, we randomly surveyed pedestrians in five metropolises located in countries that have had different degrees of exposure to probabilistic forecasts--Amsterdam, Athens, Berlin, Milan, and New York. They were asked what a "30% chance of rain tomorrow" means both in a multiple-choice and a free-response format. Only in New York did a majority of them supply the standard meteorological interpretation, namely, that when the weather conditions are like today, in 3 out of 10 cases there will be (at least a trace of) rain the next day. In each of the European cities, this alternative was judged as the least appropriate. The preferred interpretation in Europe was that it will rain tomorrow "30% of the time," followed by "in 30% of the area." To improve risk communication with the public, experts need to specify the reference class, that is, the class of events to which a single-event probability refers.

Gonadal steroids vary with reproductive stage in a tropically breeding female anuran

Tropically breeding anurans that require heavy rainfall in order to reproduce are subject to favorable breeding conditions that are sporadic. Although there is an increased probability of rain during the rainy season, the probability of local rainfall is unpredictable and this may influence female anuran reproductive strategies. The female túngara frog, a neotropical frog that requires standing water to breed, maintains readiness to breed at any time via asynchronous oogenesis. Although females constantly produce and maintain oocytes during the breeding season, this study shows that they have cyclic fluctuations in gonadal hormone levels. Plasma levels of estrogen significantly change during three reproductive stages within a single reproductive cycle ( P = 0.03), as do plasma levels of progesterone and androgen ( P < 0.001 and P = 0.001, respectively). Furthermore, elevation in plasma estrogen and progesterone concentrations occurs during the same reproductive stage in which it has been reported that females display the maximum frequency of reproductive behaviors, the amplexed stage. Androgen levels, however, are elevated prior to the reproductive stage in which females display maximal reproductive behavior, that is, the unamplexed stage. Our study suggests that the pattern of gonadal hormone fluctuation in a tropically breeding female anuran is similar to the classic paradigm in which there is a temporal relationship between the appearance of reproductive hormones and reproductive behaviors.

Impacts of the North Atlantic Oscillation on the probability of dry and wet winters in Spain

In many regions of the world, agricultural and water management is usually based on prob- abilities of seasonal or monthly rainfall, commonly grouped into 3 categories: drought, normal rainfall, and abundant rainfall. Changes in the probabilities of the occurrence of rainfall amounts within these climatic rainfall categories will influence decision-making by farmers and water managers. This study explores the changes induced by the North Atlantic Oscillation (NAO) on the probability of winter rain- fall in Spain. The evolution of the NAO was divided into 3 phases: negative NAO (NAO-), neutral NAO (NAOn), and positive NAO (NAO+), and rainfall series were divided into 3 groups corresponding to each NAO phase. Resulting empirical distribution functions allow an estimate of the changes in the proba- bilities of wet and dry winters due to changes in the NAO phase. Changes in the probability of the occurrence of the rainfall categories are more complex than mere increases in rainfall amount during NAO- and decreases during NAO+ phase. The spatial distribution of impacts is asymmetric, with higher probability of extremes linked to NAO- in the western area of the Iberian Peninsula.

Global Oceanic Precipitation Derived from TOPEX and TMR: Climatology and Variability

Abstract A detailed study on global oceanic precipitation is carried out using the simultaneous TOPEX and TMR (TOPEX Microwave Radiometer) data. It is motivated by the success of a series of feasibility studies based on a few years of TOPEX–TMR data, and the availability of a decade-long new dataset that spans 1992–2002. In this context, a previously proposed rain probability index is improved by taking into account the difference of the dynamic range of the TOPEX-measured backscatter coefficients at the Ku and C bands and the latitudinally complementary sensitivities of the TOPEX and TMR rain detections, leading to a refined joint precipitation index, which is generally consistent and quantitatively comparable with existing precipitation climatologies from the Global Precipitation Climatology Project (GPCP) and the Comprehensive Ocean–Atmosphere Data Set (COADS). The new TOPEX–TMR precipitation climatology, on the one hand, confirms the fundamental features of global oceanic rainfall with additional deta...

Responses of gas exchange and growth in Merkus pine seedlings to expected climatic changes in Thailand

AbstractResponses of gas exchange and growth in Merkus pine (Pinus merkusii Jungh. et de Vriese) seedlings to changing climate were analysed for high‐ and low‐altitude sites in Thailand. A gas exchange model, based on the optimality approach, derived the effect of drought from the probability of rains. A carbon‐and nitrogen‐balance growth model applied structural regularities of a tree and a modification of functional balance between foliage and fine roots as growth‐ guiding rules. Adaptation to local climates was incorporated in the models. The simulations yielded physiologically reasonable behaviour for annual photosynthesis (A) and transpiration (E) in relation to the distributions of precipitation over the course of a year. An annual temperature increase of 2 °C and a prolonged dry season (scenario 2) reduced A by 5–11% and E by 5–8% as compared to present climate (scenario 1). Doubled CO2 concentration and the increased temperature (scenario 3) enhanced A by 56–59% and E by 14%. Simultaneously these changes (scenario 4) increased A by 41–53% and E by 1–5%. Simulated growth in scenario 1 fitted reasonably well to field data. By the age of five years, simulated total biomass (TB) and height (h) were reduced by 31–67% and 12–42%, respectively, in scenario 2 compared to scenario 1. In scenario 3, TB and h increased by 279–330% and 94–191%, and in scenario 4, by 83–241% and 55–69%, respectively. Large increases in TB and h are explained by the exponential growth phase of the young seedlings. These results suggest that climatic changes enhance growth and thus shorten the duration of the grass stage in these seedlings. However, the effects of climatic changes on growth depend strongly on how rainfall seasonality is altered in SE Asia because prolonged drought episodes may retard the fertilizing effects of the increasing CO2 concentration.

Annual Ryegrass Stored as Balage, Haylage, or Hay for Lactating Dairy Cows

Frequent rainfall in south Louisiana often limits the successful harvest of annual ryegrass (Lolium multiflorum L.) as high quality hay. A 2-yr study was conducted to determine the effect of conserving ryegrass as balage on ensiling efficiency, storage losses, and feeding value. Ryegrass conservation treatments were balage (BLG), haylage (HLG, positive control), and hay (HAY, negative control). Ryegrass was cut at the boot stage and, following a 48-h wilt, was baled and wrapped with stretch film (BLG) or was chopped and stored in a bag silo (HLG), HAY (bloom stage) was harvested approximately 3 wk later when weather permitted and was stored indoors. At the conclusion of the 6-mo storage period, the nutritional value of stored forages was assessed with lactating Holstein cows (n = 21). Ryegrass pH values were lower, and lactate concentrations were slightly higher for HLG than BLG. Storage losses averaged 8.9% of dry matter (DM) for BLG compared with 3.7% for barn-stored HAY. Forage nutritive value was similar between ensiled forages; however, HAY was lower in protein and energy than other treatments. Cows fed HLG consumed 17.3% more forage DM and tended to produce more fat-corrected milk (FCM) than cows fed BLG. Feed efficiency (Ib FCM/Ib dry matter intake [DMI]) was higher for the BLG treatment than HAY. No treatment differences were observed for milk composition or cow weight/condition changes, Balage is an acceptable means of storing high quality ryegrass forage.

Regional climate change in Portugal: precipitation variability associated with large-scale atmospheric circulation

Four major circulation patterns, associated with daily precipitation in Portugal, are classified from daily sea level pressure fields over the northeastern Atlantic and western Europe, based on the K-means clustering algorithm coupled with principal component analysis. A rainy pattern is clearly identified with a probability of rain of 74.6%, as well as two distinct dry patterns, one prevailing in summer and the other occurring frequently in winter; a blocking-like pattern with a probability of rain of 36.8% has also been identified. These patterns are quasi-stationary, normally persisting for 1 week and sometimes even for 1 month, especially the dry ones; they represent the principal weather regimes associated with precipitation in Portugal. Interannual variations in monthly precipitation associated with the circulation patterns are also investigated; results show that these variations match fluctuations in the frequencies of occurrence of both the rainy and the dry patterns. The decreasing trend of March monthly rainfall in southern Portugal is closely related to corresponding trends in the frequencies of both the rainy pattern and the summer dry pattern. Long term trends are not significant either in other monthly rainfall sequences or in the frequencies of different circulation patterns. Interannual variations seem, in most months, to be quasi-periodic. Singular spectrum analysis (SSA) is performed on these sequences to detect quasi-periodic oscillations. Relationships between oscillations in rainfall and in frequencies of occurrence of circulation patterns are studied. Results show that four weather circulation patterns or weather regimes are important for investigating regional climate change in Portugal and its relationship with variability of large-scale atmospheric circulation. © 1998 Royal Meteorological Society

Global oceanic precipitation: A joint view by TOPEX and the TOPEX microwave radiometer

The TOPEX/POSEIDON mission offers the first opportunity to observe rain cells over the ocean by a dual‐frequency radar altimeter (TOPEX) and simultaneously observe their natural radiative properties by a three‐frequency radiometer (TOPEX microwave radiometer (TMR)). This work is a feasibility study aimed at understanding the capability and potential of the active/passive TOPEX/TMR system for oceanic rainfall detection. On the basis of past experiences in rain flagging, a joint TOPEX/TMR rain probability index is proposed. This index integrates several advantages of the two sensors and provides a more reliable rain estimate than the radiometer alone. One year's TOPEX/TMR data are used to test the performance of the index. The resulting rain frequency statistics show quantitative agreement with those obtained from the Comprehensive Ocean‐Atmosphere Data Set (COADS) in the Intertropical Convergence Zone (ITCZ), while qualitative agreement is found for other regions of the world ocean. A recent finding that the latitudinal frequency of precipitation over the Southern Ocean increases steadily toward the Antarctic continent is confirmed by our result. Annual and seasonal precipitation maps are derived from the index. Notable features revealed include an overall similarity in rainfall pattern from the Pacific, the Atlantic, and the Indian Oceans and a general phase reversal between the two hemispheres, as well as a number of regional anomalies in terms of rain intensity. Comparisons with simultaneous Global Precipitation Climatology Project (GPCP) multisatellite precipitation rate and COADS rain climatology suggest that systematic differences also exist. One example is that the maximum rainfall in the ITCZ of the Indian Ocean appears to be more intensive and concentrated in our result compared to that of the GPCP. Another example is that the annual precipitation produced by TOPEX/TMR is constantly higher than those from GPCP and COADS in the extratropical regions of the northern hemisphere, especially in the northwest Pacific Ocean. Analyses of the seasonal variations of prominent rainy and dry zones in the tropics and subtropics show various behaviors such as systematic migration, expansion and contraction, merging and breakup, and pure intensity variations. The seasonality of regional features is largely influenced by local atmospheric events such as monsoon, storm, or snow activities. The results of this study suggest that TOPEX and its follow‐on may serve as a complementary sensor to the special sensor microwave/imager in observing global oceanic precipitation.

A satellite infrared technique for estimating “deep/shallow” precipitation

This paper describes the statistical characteristics of the Japanese geosynchronous satellite, Geostationary Meteorological Satellite-5 (GMS-5), infrared (IR) data for estimating both “deep/shallow” precipitation. For this study, geographically matched data sets of GMS-5 IR data and composite digital radar data were prepared. By using those data sets, three-dimensional (3-D) matrices of Probability of Rain (PoR) and Mean Rain Rate (mRR) were calculated, where the input variables consisted of three parameters: IR 11 μm brightness temperature (TB 11); IR TB difference between 11 μm and 12 μm (TB 11–12); and IR TB difference between 11 μm and 6.7 μm (TB 11-6.7). The resulting statistical characteristics from those matrices are as follows: • • TB 11–12 is an useful parameter for the removal of thin cirrus with no precipitation • • TB 11-6.7 is an useful parameter for the extraction of deep convective cloud with heavy precipitation By using those matrices for looking up PoR and mRR, an empirical algorithm for estimating precipitation was developed. The potential of this technique (denoted as 3-D looking-up table (LUT)) as a now casting tool for severe weather was tested in the case of typhoon “RYAN (T9514)”. The error and scatter of the 3-D LUT estimations were relatively large, but they captured peak rainfalls and accumulative rainfall in good agreement.

Satellite retrieval of tropical precipitation using combined International Satellite Cloud Climatology Project DX and SSM/I Data

A new precipitation retrieval scheme for use in the tropics is developed using a combination of visible (VIS)/IR and microwave satellite observations. The new scheme combines the advantages of both the ample coverage of VIS/IR sampling and the physical directness between precipitation and microwave radiances. A VIS/IR algorithm is “trained” using Special Sensor Microwave/Imager (SSM/I) derived values of precipitation. Cloud top temperatures and visible optical depths provided by the International Satellite Cloud Climatology Project (ISCCP) level DX analyses are “binned” by every 10 K and every 10 unit optical depth, respectively. Lookup tables for the probability of rain and mean rainfall rate are constructed for each cloud top temperature/optical depth cell whenever the optical depth is available (daytime). For the nighttime, the tables are based only on cloud top temperature. The instantaneous rainfall rates are obtained by multiplying the mean rainfall rate by the probability of rain, both characterized by the cloud top temperature and/or visible optical depth associated with the satellite pixel. The satellite retrieval always retains results from optimal parameters, which means SSM/I results are used whenever SSM/I samplings are available; otherwise, VIS/IR results are used during daytime, while IR‐only results are used during nighttime. The final precipitation product can have resolution as high as 3 hours in time and about 0.3° in space. However, averaging in space and/or time improves the statistics of the derived rainfall rates, since the statistics of the algorithm are more fully utilized. The satellite‐derived rainfall product compares well with ship rain gauge data in terms of rain/no rain determination, and agrees well with daily rainfall accumulation derived from a large‐scale moisture budget. The satellite retrieved rainfall rates are biased high relative to radar observations. In the absence of satisfactory data with which to validate the satellite‐derived rainfall rates, it can be concluded that there is useful information in the ISCCP data set that relates to precipitation and that the inclusion of visible optical depth information improves the daytime retrieval of precipitation relative to IR‐only methods.

Infection period forecasting for improved apple black spot management in Hawke's Bay

Two methods for timing pre-infection protective sprays for apple black spot management, infection period forecasts (IPFs) and rain probability forecasts (RPFs), were compared for their ability to predict infection periods (IPs) identified by an apple black spot infection model from September-December. For RPFs, 88% (1993) and 81% (1994) of recorded IPs were correctly forecast, but 58% and 81% of the forecasts falsely predicted that IPs would occur when they did not. For IPFs, 81%, 29% and 100% of recorded IPs were correctly forecast in 1993, 1994 and 1995 and only 28%, 20% and 29% falsely predicted IPs when none occurred. IPFs were considered more useful than RPFs because of less overprediction, although the ability of IPFs to correctly predict IPs varied between years. In a field trial in 1993-94, a pre-infection protective fungicide programme, where sprays were timed using IPFs, gave as good control of black spot, with three fewer sprays, as an ‘industry-standard’ programme. In 1994-95, an IP-based programme which combined pre-infection spraying using IPFs, with post-infection curative fungicides after monitored IPs, gave equivalent disease control, using up to six fewer sprays, to a standard programme.

Optimal Control of Gas Exchange during Drought: Theoretical Analysis

An optimal strategy of stomatal control during a drought period, in plants adapted to a humid climate, is derived by maximizing the photosynthetic production during the expected duration of drought. The expected duration of drought is calculated from the probability that rain occurs during a certain period, which is assumed constant. The underlying plant model describes photosynthetic production and the consumption of water from the soil, with a given initial soil water content. Water is consumed through transpiration at a rate dependent on water vapour deficit, temperature and stomatal conductance and carbon is assimilated at a rate dependent on light intensity and stomatal conductance. The optimization problem is solved with driving variables and the probability of rain corresponding to a Fenno-Scandian climate. The resulting optimal stomatal control consists of two processes with different time constants: (1) daily variation depending on the driving variables, and (2) a declining trend as a function of the initial soil water content and the probability of rain. The result allows for a physical interpretation of the so-called ‘cost of water’ used in similar optimization studies. An approximate model is derived from the optimal solution, such that the ‘cost of water’ is a function of the soil water content.

Estimating the Probability of Rain in an SSM/I FOV Using Logistic Regression

The SSM/I has been used successfully to estimate precipitation and to determine the fields of view (FOV) that contain precipitating clouds. The use of multivariate logistic regression with the SSM/I brightness temperatures to estimate the probability that it is raining in an FOV is examined. The predictors used in this study are those that have been evaluated by other investigators to estimate rain events using other procedures. The logistic regression technique is applied to a matched set of SSM/I and radar data for a limited area from June to August 1989. For this limited dataset the results are quite good. In one example, if the predicted probability is less than 0.1, the radar data shows only 2 of 340 FOVs have precipitation. If the predicted probability is greater than 0.9, the radar data shows precipitation in 748 of 774 FOVS. These probabilities can be used for both instantaneous and climate timescale retrievals.

Support theory: A nonextensional representation of subjective probability.

This article presents a new theory of subjective probability according to which different descriptions of the same event can give rise to different judgments. The experimental evidence confirms the major predictions of the theory. First, judged probability increases by unpacking the focal hypothesis and decreases by unpacking the alternative hypothesis. Second, judged probabilities are complementary in the binary case and subadditive in the general case, contrary to both classical and revisionist models of belief. Third, subadditivity is more pronounced for probability judgments than for frequency judgments and is enhanced by compatible evidence. The theory provides a unified treatment of a wide range of empirical findings. It is extended to ordinal judgments and to the assessment of upper and lower probabilities. Both laypeople and experts are often called upon to evaluate the probability of uncertain events such as the outcome of a trial, the result of a medical operation, the success of a business venture, or the winner of a football game. Such assessments play an important role in deciding, respectively, whether to go to court, undergo surgery, invest in the venture, or bet on the home team. Uncertainty is usually expressed in verbal terms (e.g., unlikely or probable), but numerical estimates are also common. Weather forecasters, for example, often report the probability of rain (Murphy, 1985), and economists are sometimes required to estimate the chances of recession (Zarnowitz, 1985). The theoretical and practical significance of subjective probability has inspired psychologists, philosophers, and statisticians to investigate this notion from both descriptive and prescriptive standpoints.

Model for the prediction of the differential rain attenuation between a terrestrial line‐of‐sight radio relay system and a low‐angle satellite path based on the two‐dimensional lognormal distribution

The main propagation effect on interference of a terrestrial line‐of‐sight radio relay system from a low‐angle satellite path is the differential rain attenuation. In the present paper, a predictive method for the differential rain attenuation statistics is proposed which is based on a modified model convective raincell structure by taking into account the conventional limits of the raincell size. The assumption that the point rainfall statistics follows a lognormal form is also adopted. The results of the predictive procedure are applied to a particular problem of terrestrial line‐of‐sight system interference from a low‐angle broadcasting satellite service in the 22.5–23 GHz band. The sensitivity of the various parameters affecting the differential attenuation is also examined. As a general remark, the conditional differential rain probability is found to be significantly dependent upon the rainfall characteristics of the climatic zone and the parameters of the spatial rainfall structure. Finally, a comparison of the present predictive procedure with a semiempirical developed model is treated and gives a quite reasonable agreement.

On the evaluation of probability judgments: Calibration, resolution, and monotonicity.

Judgments of probability are commonly evaluated by two criteria: calibration, namely, the correspondence between stated confidence and rate of occurrence, and resolution, namely, the ability to distinguish between events that do and do not occur. Two representations of probability judgments are contrasted: the designated form that presupposes a particular coding of outcomes (e.g., rain vs. no rain) and the inclusive form that incorporates all events and their complements. It is shown that the indices of calibration and resolution derived from these representations measure different characteristics of judgment. Calibration is distinguished from two types of overconfidence: specific and generic. An ordinal measure of performance is proposed and compared to the standard measures in forecasts of recession and in both numerical and verbal assessments of general knowledge. Much research on judgment under uncertainty has focused on the comparison of probability judgments with the corresponding relative frequency of occurrence. In a typical study, judges are presented with a series of prediction or knowledge problems and asked to assess the probability of the events in question. Judgments of probability or confidence are used both in research (Lichtenstein, Fischhoff, & Phillips, 1982; Wallsten & Budescu, 1983) and in practice. For example, weather forecasters often report the probability of rain (Murphy & Daan, 1985), and economists are sometimes called upon to estimate the chances of recession (Zarnowitz & Lambros, 1987). The two main criteria used to evaluate such judgments are calibration and resolution. A judge is said to be calibrated if his or her probability judgments match the corresponding relative frequency of occurrence. More specifically, consider all events to which the judge assigns a probability p; the judge is calibrated if the proportion of events in that class that actually occur equals p. Calibration is a desirable property, especially for communication, but it does not ensure informativeness. A judge can be properly calibrated and entirely noninformative if, for example, he or she predicts the sex of each newborn with