Uncertainty in rainfall forecasts affects the level of quality and assurance for decisions made to manage water resource-based systems. However, eliminating uncertainty in a complete manner could be difficult, decision-makers thus are challenged to make decisions in the light of uncertainty. This study provides statistical models as an approach to cope with uncertainty, including: a) a statistical method relying on a Gaussian mixture (GM) model to assist in better characterize uncertainty in climate model projections and evaluate their performance in matching observations; b) a stochastic model that incorporates the El Niño–Southern Oscillation (ENSO) cycle to narrow uncertainty in seasonal rainfall forecasts; and c) a statistical approach to determine to what extent drought events forecasted using ENSO information could be utilized in the water resources decision-making process. This study also investigates the relationship between calibration and lead time on the ability to narrow the interannual uncertainty of forecasts and the associated usefulness for decision making. These objectives are demonstrated for the northwest region of Costa Rica as a case study of a developing country in Central America. This region of Costa Rica is under an increasing risk of future water shortages due to climate change, increased demand, and high variability in the bimodal cycle of seasonal rainfall. First, the GM model is shown to be a suitable approach to compare and characterize long-term projections of climate models. The GM representation of seasonal cycles is then employed to construct detailed comparison tests for climate models with respect to observed rainfall data. Three verification metrics demonstrate that an acceptable degree of predictability can be obtained by incorporating ENSO information in reducing error and interannual variability in the forecast of seasonal rainfall. The predictability of multicategory rainfall forecasts in the late portion of the wet season surpasses that in the early portion of the wet season. Later, the value of drought forecast information for coping with uncertainty in making decisions on water management is determined by quantifying the reduction in expected losses relative to a perfect forecast. Both the discrimination ability and the relative economic value of drought-event forecasts are improved by the proposed forecast method, especially after calibration. Positive relative economic value is found only for a range of scenarios of the cost-loss ratio, which indicates that the proposed forecast could be used for specific cases. Otherwise, taking actions (no-actions) is preferred as the cost-loss ratio approaches zero (one). Overall, the approach of incorporating ENSO information into seasonal rainfall forecasts would provide useful value to the decision-making process - in particular at lead times of one year ahead.

The work presented in the thesis focuses on systematically documenting the multi scale nature of the temporal persistence and spatial coherence of tropical rainfall. There are three parts to the thesis: The first two parts utilize satellite-retrieved rainfall at multiple observational resolutions to characterize the space-time organization of rain; the third part assesses the ability of state-of-the-art coupled models to reproduce some of the observed features. In the first part of the study, which focuses on the temporal persistence of rain, we analyze the Tropical Rainfall Measurement Mission (TRMM) satellite-based observations to compare and contrast wet and dry spell characteristics over the tropics (30 S-30 N). Defining a wet (dry) spell as the number of consecutive rainy (nonrainy) days, we find that the distributions of wet spells (independent of spatial resolution) exhibit universality in the following sense. While both ocean and land regions with high seasonal rainfall accumulation (humid regions) show a predominance of 2-4 day wet spells, those regions with low seasonal rainfall accumulation (arid regions) exhibit a wet spell duration distribution that is essentially exponential in nature, with a peak at 1 day. The behaviour that we observed for wet spells is reversed for dry spell distributions. The total rainfall accumulated in each wet spell has also been analyzed, and we find that the major contribution to seasonal rainfall for arid regions comes from very short length wet spells; however, for humid regions, this contribution comes from wet spells of duration as long as 30 days. An exhaustive sensitivity study of factors that can potentially affect the wet and dry spell characteristics (e.g., resolution) shows that our findings are robust. We also explore the role of chance in determining the 2-4 day mode, as well as the inuence of organized convection in separating reality from chance. The second part deals with the spatial coherence of tropical rain. We take two different approaches, namely, a global and local view. The global view attempts to quantify the con-ventional view of rain, i.e., the dominance of the intertropical convergence zone (ITCZ), while the local view tries to answer the question: if it rains, how far is the influence felt in zonal and meridional directions? In both approaches, the classical e-folding length for spatial decorrelation is used as a measure of spatial coherence. The major finding in the global view approach is that, at short timescales of accumulation (daily to pentad to even monthly), rain over the Equator shows the most dominant zonal scale. It is only at larger timescales of accumulation (seasonal or annual) that the dominance of ITCZ around 7 N is evident. In addition, we also find a semi-log linearity between the spatial scales, seen from afar, and timescale of accumulation, with a break in linearity around typical synoptic timescales of 5-10 days. The local view quantifies the dominance of the zonal scale in the tropical ocean convergence zones, with an anisotropy value (ratio of zonal to meridional scales) of 3-4. Over land, on the other hand, the zonal and meridional scales are comparable in magnitude, suggesting that rain tends to be mostly isotropic over continental regions. This latter finding holds true, irrespective of the spatial and temporal resolutions at which rain is observed. Interestingly, the anisotropy over ocean, while invariant with spatial resolution, is found to be a function of temporal resolution: from a value of 3-4 at daily timescale, it decreases to around 1.5 at 3-hourly resolution, suggesting that perhaps rain fundamentally might be isotropic in nature at an event scale. The final part analyses a few models from the suite of Coupled Model Intercomparison Project (CMIP5) models, to evaluate their ability to reproduce some of these aforementioned features. For all the strong biases that models are known to have, some of the observed features are captured well by the models. Specifically, on the temporal persistence front, the observed 2-4 day mode of wet (dry) spells of rain over humid (arid) regions is also seen in models. The overestimation of longer duration wet spells appears to be the primary cause of a positive bias in the number of rainy days from the models. In general, the tendency of models to not stop raining results in lower and higher number of shorter and longer duration wet spells, respectively, and consequently an overall reduction in dry spells of all durations. On the spatial coherence front, the main finding from the global view approach is that the observed semi-log linearity of the zonal spatial scale of rainfall as a function of timescale of accumulation is strikingly well-reproduced by the models. Even more remarkable is that the models are able to mimic the break in this linearity around 5 days (typical synoptic scale). What the models fail to do prominently is the transition of the dominance of equatorial rain at smaller timescales of accumulation to the dominance of ITCZ at around 7 N at higher timescales of accumulation. Based on the local view approach, we find that, in general, even though the zonal and meridional scales are overestimated, the observed isotropy of continental rain is captured very well by the models. Over the oceans, the success is less prominent, especially with the core of the ITCZ showing much larger ratios than those observed. Thus, the models seem to be able to reproduce the anisotropy for the wrong reasons, and the proposed anisotropy ratio could be a useful metric in further diagnosis of climate models.

Diese Dissertation beschäftigt sich mit regionaler Klimamodellierung über Südamerika, der Analyse von Modellsensitivitäten bezüglich Wolkenparametrisierungen und der Entwicklung neuer Methoden zur Modellevaluierung mithilfe von Klimanetzwerken. Im ersten Teil untersuchen wir Simulationen mit dem COnsortium for Small scale MOdeling model in CLimate Mode (COSMO-CLM) und stellen die erste umfassende Evaluierung dieses dynamischen regionalen Klimamodells über Südamerika vor. Dabei untersuchen wir insbesondere die Abhängigkeit simulierter tropischer Niederschläge von Parametrisierungen subgitterskaliger cumuliformer und stratiformer Wolken und finden starke Sensitivitäten bezüglich beider Wolkenparametrisierungen über Land. Durch einen simultanen Austausch der entsprechenden Schemata gelingt uns eine beträchtliche Reduzierung von Fehlern in klimatologischen Niederschlags- und Strahlungsmitteln, die das COSMO-CLM über tropischen Regionen für lange Zeit charakterisierten. Im zweiten Teil führen wir neue Metriken für die Evaluierung von Klimamodellen bezüglich räumlicher Kovariabilitäten ein. Im Kern bestehen diese Metriken aus Unähnlichkeitsmaßen für den Vergleich von simulierten mit beobachteten Klimanetzwerken. Wir entwickeln lokale und globale Unähnlichkeitsmaße zum Zwecke der Darstellung lokaler Unähnlichkeiten in Form von Fehlerkarten sowie der Rangordnung von Modellen durch Zusammenfassung lokaler zu globalen Unähnlichkeiten. Die neuen Maße werden dann für eine vergleichende Evaluierung regionaler Klimasimulationen mit COSMO-CLM und dem Statistical Analogue Resampling Scheme über Südamerika verwendet. Dabei vergleichen wir die sich ergebenden Modellrangfolgen mit solchen basierend auf mittleren quadratischen Abweichungen klimatologischer Mittelwerte und Varianzen und untersuchen die Abhängigkeit dieser Rangfolgen von der betrachteten Jahreszeit, Variable, dem verwendeten Referenzdatensatz und Klimanetzwerktyp. / This dissertation is about regional climate modeling over South America, the analysis of model sensitivities to cloud parameterizations, and the development of novel model evaluation techniques based on climate networks. In the first part we examine simulations with the COnsortium for Small scale MOdeling weather prediction model in CLimate Mode (COSMO-CLM) and provide the first thorough evaluation of this dynamical regional climate model over South America. We focus our analysis on the sensitivity of simulated tropical precipitation to the parameterizations of subgrid-scale cumuliform and stratiform clouds. It is shown that COSMO-CLM is strongly sensitive to both cloud parameterizations over tropical land. Using nondefault cumulus and stratus parameterization schemes we are able to considerably reduce long-standing precipitation and radiation biases that have plagued COSMO-CLM across tropical domains. In the second part we introduce new performance metrics for climate model evaluation with respect to spatial covariabilities. In essence, these metrics consist of dissimilarity measures for climate networks constructed from simulations and observations. We develop both local and global dissimilarity measures to facilitate the depiction of local dissimilarities in the form of bias maps as well as the aggregation of those local to global dissimilarities for the purposes of climate model intercomparison and ranking. The new measures are then applied for a comparative evaluation of regional climate simulations with COSMO-CLM and the STatistical Analogue Resampling Scheme (STARS) over South America. We compare model rankings obtained with our new performance metrics to those obtained with conventional root-mean-square errors of climatological mean values and variances, and analyze how these rankings depend on season, variable, reference data set, and climate network type.